2024-03-29T01:51:01Zhttps://edoc.hu-berlin.de/oai/request/oai:edoc.hu-berlin.de:18452/142712020-03-07T04:31:54Zcom_18452_25col_18452_26doc-type:reportddc:004textPublicationprimusddc:150open_accessddc:600ddc:510ddc:100ddc:500ddc:620
Fortschritte der Künstlichen Intelligenz
Wolfgang
Weller
Künstliche Intelligenz
intelligente Systeme
maschinelle Intelligenz
004
620
510
500
100
150
600
Die Fachdisziplin Künstliche Intelligenz erfreut sich derzeit einer beschleunigten Weiterentwicklung, der hier nachgegangen wird. Als Hauptursachen dafür gelten einerseits der beträchtliche Ausbau der Möglichkeiten der Wissensverarbeitung unter Nutzung des gigantischen Informationspotenzials des Internets. Der andere Grund wird in der vertieften und stufenweise erfolgenden Informationsverarbeitung unter Einbeziehung von Lerneffekten gesehen. Der wesentliche Effekt besteht in der zunehmenden Fähigkeit künstlicher intelligenter Systeme, die Bedeutung der Ergebnisse von Informationsverarbeitungsprozessen zu erkennen. Demgegenüber unterliegt die Implementierung von Denkprozessen noch erheblichen Beschränkungen. Auch ein echtes Gefühlsleben intelligenter technischer Systeme ist nicht in Sicht. Im Ausblick wird auf derzeitige Entwicklungsschwerpunkte der Künstlichen Intelligenz verwiesen und ein weiter in die Zukunft gerichteter Blick auf mögliche Konstellationen des Zusammenwirkens von Menschen und intelligenten künstlichen Wesen sowie solche in Gemeinschaften geboten.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-17
report
Text
publishedVersion
urn:nbn:de:kobv:11-100227932
ger
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/14271/1/21ICtfhWBaQA.pdf
10.18452/13619
http://edoc.hu-berlin.de/18452/14271
oai:edoc.hu-berlin.de:18452/147732020-03-07T04:33:56Zcom_18452_1col_18452_4textPublicationprimusopen_accessdoc-type:masterThesisddc:510
Isospectral orbifolds with different isotropy orders
Martin
Weilandt
Laplace-Operator
Orbifolds
Isospektralität
Spektralgeometrie
kristallographische Gruppen
orbifolds
Laplacian
isospectrality
spectral geometry
crystallographic groups
510
Die Spektralgeometrie befasst sich mit der Frage, welche geometrischen Eigenschaften eines Raums durch das Spektrum seines Laplace-Operators bestimmt werden. Die vorliegende Arbeit führt in die Spektralgeometrie guter Orbifolds (als Verallgemeinerung Riemannscher Mannigfaltigkeiten) ein und enthält eine ausführliche Abhandlung über ein Paar isospektraler flacher Orbifolds mit verschiedenen maximalen Isotropieordnungen. Außerdem werden weitere Beispiele isospektraler nicht-isometrischer flacher Orbifolds angegeben.
Spectral geometry deals with the question which geometric properties of a space are determined by the spectrum of its Laplace operator. The work at hand is an introduction to the spectral geometry of good orbifolds (as a generalization of Riemannian manifolds) and contains an extensive study of a pair of isospectral flat orbifolds with different maximal isotropy orders. Moreorever, other examples of isospectral non-isometric flat orbifolds are given.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Dorothee
Schüth
2017-06-18
masterThesis
Text
publishedVersion
urn:nbn:de:kobv:11-100175649
eng
master
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/14773/1/weilandt.pdf
10.18452/14121
http://edoc.hu-berlin.de/18452/14773
oai:edoc.hu-berlin.de:18452/33382020-03-07T04:03:05Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Primal and Dual Methods for Unit Commitment in a Hydro-Thermal Power System
R.
Gollmer
Andris
Möller
Matthias Peter
Nowak
Werner
Römisch
Rüdiger
Schultz
Unit commitment
Lagrangian relaxation
bundle methods
mixed-integer linear programming
polyhedral cominatorics
510
The unit commitment problem in a power generation system comprising thermal and pumped-storage hydro units is adressed. A large-scale mixed-integer optimization model for unit commitment in a real power system is developed and solved by primal and dual approaches. Both solution methods employ state-of-the-art algorithms and software. Results of test runs are reported.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10053605
eng
Preprints aus dem Institut für Mathematik, Band 1998,20, 1998
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3338/1/20.pdf
10.18452/2686
http://edoc.hu-berlin.de/18452/3338
oai:edoc.hu-berlin.de:18452/247572023-10-31T04:00:07Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
EDP-convergence for nonlinear fast–slow reaction systems with detailed balance
Alexander
Mielke
Mark
Peletier
Artur
Stephan
reaction system
mass-action kinetics
gradient structure
evolutionary gamma convergence
510
We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with Lagrange multipliers and a set of nonlinear constraints that ask the fast reactions to be in equilibrium. Our aim is to study the limiting gradient structure which is available if the reaction system satisfies the detailed-balance condition. The gradient structure on the set of concentration vectors is given in terms of the relative Boltzmann entropy and a cosh-type dissipation potential. We show that a limiting or effective gradient structure can be rigorously derived via EDP-convergence, i.e. convergence in the sense of the energy-dissipation principle for gradient flows. In general, the effective entropy will no longer be of Boltzmann type and the reactions will no longer satisfy mass-action kinetics.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2022-02-04
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/24757-1
Nonlinearity, Band 34, Ausgabe 8, Seite 5762-5798, 2021
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/24757/4/non_34_8_5762.pdf
10.1088/1361-6544/ac0a8a
10.18452/24116
http://edoc.hu-berlin.de/18452/24757
oai:edoc.hu-berlin.de:18452/171532020-03-07T04:44:40Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
The exponent of Hölder calmness for polynomial systems
Jan
Heerda
Stabilität
Hölder Calmness
Fehlerabschätzung
Polynomiale Ungleichungssysteme
Hörmander-Lojasiewicz-Ungleichung
stability
Hölder calmness
error bounds
polynomial inequality systems
Hörmander-Lojasiewicz inequality
510
SK 910
Diese Arbeit befasst sich mit Untersuchung der Hölder Calmness, eines Stabilitätskonzeptes das man als Verallgemeinerung des Begriffs der Calmness erhält. Ausgehend von Charakterisierungen dieser Eigenschaft für Niveaumengen von Funktionen, werden, unter der Voraussetzung der Hölder Calmness, Prozeduren zur Bestimmung von Elementen dieser Mengen analysiert. Ebenso werden hinreichende Bedingungen für Hölder Calmness studiert. Da Hölder Calmness (nichtleerer) Lösungsmengen endlicher Ungleichungssysteme mittels (lokaler) Fehlerabschätzungen beschrieben werden kann, werden auch Erweiterungen der lokalen zu globalen Ergebnissen diskutiert. Als Anwendung betrachten wir speziell den Fall von Niveaumengen von Polynomen bzw. allgemeine Lösungsmengen polynomialer Gleichungen und Ungleichungen. Eine konkrete Frage, die wir beantworten wollen, ist die nach dem Zusammenhang zwischen dem größten Grad der beteiligten Polynome sowie dem Typ, d.h. dem auftretenden Exponenten, der Hölder Calmness des entsprechenden Systems.
This thesis is concerned with an analysis of Hölder calmness, a stability property derived from the concept of calmness. On the basis of its characterization for (sub)level sets, we will cogitate about procedures to determine points in such sets under a Hölder calmness assumption. Also sufficient conditions for Hölder calmness of (sub)level sets and of inequality systems will be given and examined. Further, since Hölder calmness of (nonempty) solution sets of finite inequality systems may be described in terms of (local) error bounds, we will as well amplify the local propositions to global ones. As an application we investigate the case of (sub)level sets of polynomials and of general solution sets of polynomial equations and inequalities. A concrete question we want to answer here is, in which way the maximal degree of the involved polynomials is connected to the exponent of Hölder calmness or of the error bound for the system in question.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Bernd
Kummer
Michael
Hintermüller
Diethard
Klatte
2012-01-24
2017-06-18
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-100201565
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/17153/1/heerda.pdf
10.18452/16501
http://edoc.hu-berlin.de/18452/17153
oai:edoc.hu-berlin.de:18452/273002023-10-31T04:00:10Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
Students’ Understanding of the Economic Interpretation of the Derivative in the Context of Marginal Cost
Frank
Feudel
Rolf
Biehler
Derivative
Mathematics for economics students
Conceptual understanding
Connection between mathematics and economics
Marginal cost
510
Many disciplines make use of mathematical concepts. However, there are often discrepancies between the way mathematical concepts are understood and taught in mathematics and the way they are used in other disciplines. The literature suggests that such discrepancies might make it hard for students in mathematics service courses to make a connection between the mathematical concepts taught and the way they are used in the students’ major disciplines. We investigated this hypothesis for one specific example in mathematics for economics students – the derivative and its interpretation commonly used in economics as the amount of change when increasing the production by one unit. We conducted an interview study investigating to what extent economics students can make a connection between the mathematical concept of the derivative and this common economic interpretation of the derivative. This study provides empirical evidence that it is actually difficult for economics students to make this connection, even though it was covered in their calculus course. In particular, the study reveals difficulties students have when trying to make this connection, which could be addressed in teaching.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2023-05-25
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/27300-5
International journal of research in undergraduate mathematics education, Band 8, Ausgabe 3, Seite 437-468, 2021
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/27300/4/s40753-021-00144-x.pdf
10.1007/s40753-021-00144-x
10.18452/26600
http://edoc.hu-berlin.de/18452/27300
oai:edoc.hu-berlin.de:18452/180372020-03-07T04:48:50Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
Two-scale homogenization of systems of nonlinear parabolic equations
Sina
Reichelt
periodische Homogenisierung
Zwei-Skalen Konvergenz
Fehlerabschätzungen
Reaktions-Diffusions Systeme
Cahn-Hilliard Gleichungen
two-scale convergence
periodic homogenization
error estimates
reaction-diffusion systems
Cahn-Hilliard equations
510
SK 560
Ziel dieser Arbeit ist es zwei verschiedene Klassen von Systemen nichtlinearer parabolischer Gleichungen zu homogenisieren, und zwar Reaktions-Diffusions-Systeme mit verschiedenen Diffusionslängenskalen und Gleichungen vom Typ Cahn-Hilliard. Wir betrachten parabolische Gleichungen mit periodischen Koeffizienten, wobei die Periode dem Verhältnis der charakteristischen mikroskopischen zu der makroskopische Längenskala entspricht. Unser Ziel ist es, effektive Gleichungen rigoros herzuleiten, um die betrachteten Systeme besser zu verstehen und den Simulationsaufwand zu minimieren. Wir suchen also einen Konvergenzbegriff, mit dem die Lösung des Ausgangsmodells im Limes der Periode gegen Null gegen die Lösung des effektiven Modells konvergiert. Um die periodische Mikrostruktur und die verschiedenen Diffusivitäten zu erfassen, verwenden wir die Zwei-Skalen Konvergenz mittels periodischer Auffaltung. Der erste Teil der Arbeit handelt von Reaktions-Diffusions-Systemen, in denen einige Spezies mit der charakteristischen Diffusionslänge der makroskopischen Skala und andere mit der mikroskopischen diffundieren. Die verschiedenen Diffusivitäten führen zu einem Verlust der Kompaktheit, sodass wir nicht direkt den Grenzwert der nichtlinearen Terme bestimmen können. Wir beweisen mittels starker Zwei-Skalen Konvergenz, dass das effektive Modell ein zwei-skaliges Modell ist, welches von der makroskopischen und der mikroskopischen Skale abhängt. Unsere Methode erlaubt es uns, explizite Raten für die Konvergenz der Lösungen zu bestimmen. Im zweiten Teil betrachten wir Gleichungen vom Typ Cahn-Hilliard, welche ortsabhängige Mobilitätskoeffizienten und allgemeine Potentiale beinhalten. Wir beweisen evolutionäre Gamma-Konvergenz der zugehörigen Gradientensysteme basierend auf der Gamma-Konvergenz der Energien und der Dissipationspotentiale.
The aim of this thesis is to derive homogenization results for two different types of systems of nonlinear parabolic equations, namely reaction-diffusion systems involving different diffusion length scales and Cahn-Hilliard-type equations. The coefficient functions of the considered parabolic equations are periodically oscillating with a period which is proportional to the ratio between the charactersitic microscopic and macroscopic length scales. In view of greater structural insight and less computational effort, it is our aim to rigorously derive effective equations as the period tends to zero such that solutions of the original model converge to solutions of the effective model. To account for the periodic microstructure as well as for the different diffusion length scales, we employ the method of two-scale convergence via periodic unfolding. In the first part of the thesis, we consider reaction-diffusion systems, where for some species the diffusion length scale is of order of the macroscopic length scale and for other species it is of order of the microscopic one. Based on the notion of strong two-scale convergence, we prove that the effective model is a two-scale reaction-diffusion system depending on the macroscopic and the microscopic scale. Our approach supplies explicit rates for the convergence of the solution. In the second part, we consider Cahn-Hilliard-type equations with position-dependent mobilities and general potentials. It is well-known that the classical Cahn-Hilliard equation admits a gradient structure. Based on the Gamma-convergence of the energies and the dissipation potentials, we prove evolutionary Gamma-convergence, for the associated gradient system such that we obtain in the limit of vanishing periods a Cahn-Hilliard equation with homogenized coefficients.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Alexander
Mielke
Dorothee
Knees
Adrian
Muntean
2015-11-27
2017-06-18
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-100234195
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/18037/1/reichelt.pdf
10.18452/17385
http://edoc.hu-berlin.de/18452/18037
oai:edoc.hu-berlin.de:18452/163482020-03-07T04:40:50Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
Large deviations and exit time asymptotics for diffusions and stochastic resonance
Dierk
Peithmann
grosse Abweichungen
stochastische Resonanz
Austrittszeiten
selbststabilisierende Diffusionen
large deviations
stochastic resonance
exit times
self-stabilizing diffusions
510
Diese Arbeit behandelt die Asymptotik von Austritts- und Übergangszeiten für gewisse schwach zeitinhomogene Diffusionsprozesse. Darauf basierend wird ein probabilistischer Begriff der stochastischen Resonanz (SR) studiert. Techniken der großen Abweichungen spielen eine zentrale Rolle. Im ersten Teil der Arbeit (Kapitel 1-3) werden Resultate aus der Theorie der großen Abweichungen für zeithomogene Diffusionen rekapituliert. Es werden die klassischen Resultate von Freidlin und Wentzell und Erweiterungen dieser Theorie präsentiert, und es wird an das Kramers''sche Austrittszeitengesetz erinnert. Teil II befasst sich mit dem Phänomen der SR, d.h. mit Periodizitätseigenschaften von Diffusionen. In Kapitel 4 werden physikalische Maße zur Messung der Periodizität diskutiert. Deren Nachteile legen es nahe, einem alternativen, probabilistischen Ansatz zu folgen, der hier behandelt wird. Das 5. Kapitel dient der Herleitung eines gleichmäßigen Prinzips der großen Abweichungen für Diffusionen mit schwach zeitabhängigem, periodischem Drift. Die Gleichmäßigkeit des Prinzips ermöglicht die exakte Bestimmung exponentieller Übergangsraten in Kapitel 6, das die zentralen Ergebnisse des 2. Teils beinhaltet. Hierdurch wird die Maximierung gewisser Übergangswahrscheinlichkeiten ermöglicht, was zum in Kapitel 7 studierten Resonanzbegriff führt. Teil III der Arbeit setzt sich mit der Asymptotik von Austrittszeiten sogenannter selbststabilisierender Diffusionen auseinander. In Kapitel 8 wird der Zusammenhang zwischen interagierenden Teilchensystemen und selbststabilisierenden Diffusionen erläutert und die Existenz- und Eindeutigkeitsfrage behandelt. Das 9. Kapitel dient dem Studium der großen Abweichungen dieser Klasse von Diffusionen. In Kapitel 10 wird das Kramers''sche Austrittszeitengesetz auf selbststabilisierende Diffusionen übertragen, und in Kapitel 11 wird der Einfluß der selbststabilisierenden Komponente auf das Austrittszeitengesetz illustriert.
In this thesis, we study the asymptotic behavior of exit and transition times of certain weakly time inhomogeneous diffusion processes. Based on these asymptotics, a probabilistic notion of stochastic resonance (SR) is investigated. Large deviations techniques play the key role throughout this work. In the first part (Chapters 1-3) we recall the large deviations theory for time homogeneous diffusions. We present the classical results due to Freidlin and Wentzell and extensions thereof, and we remind of Kramers'' exit time law. Part II deals with the phenomenon of stochastic resonance. That is, we study periodicity properties of diffusion processes. In Chapter 4 we explain the paradigm of stochastic resonance and discuss physical notions of measuring periodicity of diffusions. Their drawbacks suggest to follow an alternative probabilistic approach, which is treated in this work. In Chapter 5 we derive a large deviations principle for diffusions subject to a weakly time dependent periodic drift term. The uniformity of the obtained large deviations bounds w.r.t. the system''s parameters plays a key role for the treatment of transition time asymptotics in Chapter 6, which contains the main result of the second part. The exact exponential transition rates obtained here allow for maximizing transition probabilities, which finally leads to the announced probabilistic notion of resonance studied in Chapter 7. In the third part we investigate the exit time asymptotics of a certain class of so-called self-stabilizing diffusions. In Chapter 8 we explain the connection between interacting particle systems and self-stabilizing diffusions, and we address the question of existence. The following Chapter 9 is devoted to the study of the large deviations behavior of these diffusions. In Chapter 10 Kramers'' exit law is carried over to our class of self-stabilizing diffusions. Finally, the influence of self-stabilization is illustrated in Chapter 11.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Peter
Imkeller
Ludwig
Arnold
Michael
Scheutzow
2007-08-13
2017-06-18
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-10083968
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/16348/1/peithmann.pdf
10.18452/15696
http://edoc.hu-berlin.de/18452/16348
oai:edoc.hu-berlin.de:18452/34292020-03-07T04:03:11Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Boundary Layer Solutions to Singularly Perturbed Problems via the Implicit Function Theorem
Oleh
Omel'chenko
Lutz
Recke
singular perturbation
asymptotic approximation
boundary layer
implicit function theorem
510
We prove existence, local uniqueness and asymptotic estimates for boundary layer solutions to singularly perturbed problems of the type $\varepsilon^2 u''=f(x,u,\varepsilon u',\varepsilon), 0< x
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-100190645
eng
Preprints aus dem Institut für Mathematik, Band 2007,20, 2007
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3429/1/20.pdf
10.18452/2777
http://edoc.hu-berlin.de/18452/3429
oai:edoc.hu-berlin.de:18452/32422020-03-07T04:02:58Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Topological analysis of qualitative features in electrical circuit theory
Ricardo
Riaza
Caren
Tischendorf
modified nodal analysis
asymptotic stability
hyperbolicity
differential-algebraic equation
circuit model
graph topology
matrix pencil
510
Several qualitative properties of equilibria in electrical circuits are analyzed in this paper. Specifically, non-singularity, hyperbolicity, and asymptotic stability are addressed in terms of the circuit topology, which is captured through the use of Modified Nodal Analysis (MNA) models. The differential-algebraic or semistate nature of these models drives the analysis of the spectrum to a matrix pencil setting, and puts the results beyond the ones already known for state-space models, unfeasible in many actual problems. The topological conditions arising in this qualitative study are proved independent of those supporting the index, and therefore they apply to both index-1 and index-2 configurations. The analysis combines results coming from graph theory, matrix analysis, matrix pencil theory, and Lyapunov theory for DAEs. The study is restricted to problems with independent sources; qualitative properties of circuits including controlled sources are the focus of future research.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10052243
eng
Preprints aus dem Institut für Mathematik, Band 2004,18, 2004
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3242/1/18.pdf
10.18452/2590
http://edoc.hu-berlin.de/18452/3242
oai:edoc.hu-berlin.de:18452/142602020-03-07T04:31:52Zcom_18452_25col_18452_26doc-type:reportddc:004textPublicationprimusopen_accessddc:600ddc:590ddc:510ddc:500ddc:620
Schwarmintelligenz am Beispiel der Ameisen
Wolfgang
Weller
Künstliche Intelligenz
Optimierungsverfahren
Schwarmverhalten
Ameisen
004
620
510
500
600
590
Der Begriff Schwarmintelligenz bezeichnet eine Sonderform der Künstlichen Intelligenz, dadurch gekennzeichnet, dass Gemeinschaften natürlicher Wesen durchaus komplexe Aufgaben bewältigen können, obwohl ihre Mitglieder nur über begrenzte kognitive Ressourcen verfügen. Das Verhalten solcher Systeme wird u. a. in sog. Ameisenalgorithmen nachgebildet. Diese ermöglichen eine neue von der Natur abgeschaute Art der Optimierung. Im Beitrag werden das Wesen, die algorithmische Umsetzung und bekannt gewordene Anwendungen dieses Optimierungsverfahrens dargelegt.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-17
report
Text
publishedVersion
urn:nbn:de:kobv:11-100225604
ger
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/14260/1/25ltx2EU2MLA.pdf
10.18452/13608
http://edoc.hu-berlin.de/18452/14260
oai:edoc.hu-berlin.de:18452/149182020-03-07T04:34:25Zcom_18452_1col_18452_4textPublicationprimusopen_accessdoc-type:masterThesisddc:510
Parallel reversal schedules using more checkpoints than processors
Volker
Diels-Grabsch
Mathematik
Simulation
Diplomarbeit
automatisches Differenzieren
algorithmisches Differenzieren
Scheduling
Rückwärts-Ablaufpläne
Diskrete Optimierung
Parallelrechner
mathematics
simulation
automatic differentiation
scheduling
diploma thesis
algorithmic differentiation
reversal schedules
discrete optimization
parallel computing
510
Parallele Umkehr-Ablaufpläne (Parallel reversal schedules) beschreiben, wie die Zustände eines evolutionären Systems, etwa einer atmosphärischen oder ozeanographischen Simulation, in umgekehrter Reihenfolge berechnet werden können, ohne dass alle Zustände im Speicher gehalten werden müssen. Auf einem Mehrprozessorsystem ist das ohne Anstieg der benötigten Rechenzeit möglich, indem Zwischenergebnisse zwar mehrfach berechnet werden, aber gleichzeitig auf mehreren Prozessoren. Diese Ablaufpläne werden nicht nur verwendet, um Simulationen rückwärts abzuspielen, sondern auch in der algorithmischen Differenzierung, die wiederum in der nichtlinearen Optimierung sowie beim Lösen von partiellen Differentialgleichungen eingesetzt wird. Die bisherige Forschung ermittelte optimale Pläne für den Fall, dass folgende zentrale Annahme erfüllt ist: Können k Zustände gleichzeitig im Speicher gehalten werden, so sind stets etwa k/2 Prozessoren verfügbar, die die Berechnung von k/2 Zuständen fortsetzen. Die übrigen k/2 Zustände werden in reinen Speicherpunkten (Checkpoints) vorgehalten. In dieser Diplomarbeit wird die zentrale Annahme gelockert und so die Forschung fortgesetzt. Es ist nun möglich, dass deutlich weniger als k/2 Prozessoren verfügbar sind, oder gleichbedeutend, dass viel mehr Speicherpunkte genutzt werden können. Für diese neue Aufgabenstellung wird eine symbolische Herangehensweise an parallele Umkehr-Ablaufpläne vorgestellt. Es wird eine umfassende Algebra entwickelt, die einen direkten Zugang zu den Profilen der Pläne bietet und so deren Analyse erleichtert. Diese Algebra ist sehr generisch und könnte weitere Anwendungen haben. Es werden neue Pläne entwickelt, die in Situationen anwendbar sind, in denen die bisher bekannten Pläne ungeeignet waren. In einigen Fällen sind sie optimal, für alle übrigen Fälle werden suboptimale Pläne vorgestellt, die ebenfalls eine deutliche Verbesserung zu den bisherigen Plänen darstellen.
Parallel reversal schedules describe how to calculate the states of an evolutionary system, such as atmospheric and oceanographic simulations, in reverse order without having to keep all states in memory. This is possible without any increase in computation time, by recalculating intermediate results using multiple processors on a parallel computer system. These schedules are not only applied physical simulations that need to run in reverse, but also in algorithmic differentiation, which in turn is used, among others, in nonlinear optimization and to solve partial differential equations. Earlier research led to optimal schedules under the central assumption that if k states can be kept in memory, there are enough processors to run computations on roughly half of them in parallel, while the other half can only be used for holding checkpoints. This diploma thesis is an attempt to continue the research by relaxing the central assumption, such that memory for a large number of plain checkpoints can be used with a comparatively small number of processors. To cope with this challenge, a symbolic approach to reversal schedules is proposed, and a comprehensive algebra is developed to analyze schedules via their profiles. This algebra is very generic and could have applications outside parallel reversal schedules. Using that instrument, new optimal schedules are developed, to be applied in situations where the earlier schedules are not applicable. Moreover, suboptimal schedules are provided where optimal schedules could not be found in a systematic way.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Andreas
Griewank
Andrea
Walther
2017-06-18
masterThesis
Text
publishedVersion
urn:nbn:de:kobv:11-100236764
eng
master
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/14918/1/diels-grabsch.pdf
10.18452/14266
http://edoc.hu-berlin.de/18452/14918
oai:edoc.hu-berlin.de:18452/227012020-10-08T01:05:30Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
Groundwater−Surface Water Interactions: Recent Advances and Interdisciplinary Challenges
Jörg
Lewandowski
Karin
Meinikmann
Stefan
Krause
aquifer–stream interface
hyporheic zone
benthic zone
lacustrine groundwater discharge
submarine groundwater discharge
riparian corridors
510
The interactions of groundwater with surface waters such as streams, lakes, wetlands, or oceans are relevant for a wide range of reasons—for example, drinking water resources may rely on hydrologic fluxes between groundwater and surface water. However, nutrients and pollutants can also be transported across the interface and experience transformation, enrichment, or retention along the flow paths and cause impacts on the interconnected receptor systems. To maintain drinking water resources and ecosystem health, a mechanistic understanding of the underlying processes controlling the spatial patterns and temporal dynamics of groundwater–surface water interactions is crucial. This Special Issue provides an overview of current research advances and innovative approaches in the broad field of groundwater–surface water interactions. The 20 research articles and 1 communication of this Special Issue cover a wide range of thematic scopes, scales, and experimental and modelling methods across different disciplines (hydrology, aquatic ecology, biogeochemistry, environmental pollution) collaborating in research on groundwater–surface water interactions. The collection of research papers in this Special Issue also allows the identification of current knowledge gaps and reveals the challenges in establishing standardized measurement, observation, and assessment approaches. With regards to its relevance for environmental and water management and protection, the impact of groundwater–surface water interactions is still not fully understood and is often underestimated, which is not only due to a lack of awareness but also a lack of knowledge and experience regarding appropriate measurement and analysis approaches. This lack of knowledge exchange from research into management practice suggests that more efforts are needed to disseminate scientific results and methods to practitioners and policy makers.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2020-10-07
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/22701-6
Water, Band 22, Ausgabe 1, 2020
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/22701/5/water-12-00296-v2.pdf
10.3390/w12010296
10.18452/22020
http://edoc.hu-berlin.de/18452/22701
oai:edoc.hu-berlin.de:18452/290732024-03-27T02:00:09Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
Convergent adaptive hybrid higher-order schemes for convex minimization
Carsten
Carstensen
Ngoc-Tien
Tran
Convex minimization
Degenerate convex
Convexity control
Hybrid high-order
p-Laplacian
Optimal design problem
Double-well problem
A posteriori
Adaptive mesh-refining
Convergence
Lavrentiev gap
510
This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p-growth. Examples include the p-Laplacian, an optimal design problem in topology optimization, and the convexified double-well problem. The hybrid high-order method utilizes a gradient reconstruction in the space of piecewise Raviart–Thomas finite element functions without stabilization on triangulations into simplices or in the space of piecewise polynomials with stabilization on polytopal meshes. The main results imply the convergence of the energy and, under further convexity properties, of the approximations of the primal resp. dual variable. Numerical experiments illustrate an efficient approximation of singular minimizers and improved convergence rates for higher polynomial degrees. Computer simulations provide striking numerical evidence that an adopted adaptive HHO algorithm can overcome the Lavrentiev gap phenomenon even with empirical higher convergence rates.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2024-03-26
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/29073-3
Numerische Mathematik, Band 151, Ausgabe 2, Seite 329-367, 2022
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/29073/1/s00211-022-01284-1.pdf
10.18452/28442
10.1007/s00211-022-01284-1
http://edoc.hu-berlin.de/18452/29073
oai:edoc.hu-berlin.de:18452/91002020-03-07T04:14:47Zcom_18452_152com_18452_44col_18452_372textPublicationprimusopen_accessdoc-type:bookddc:510
Convergence of the Smoothed Empirical Process in Nested Distance
Georg Ch.
Pflug
Alois
Pichler
stochastic optimization
decision trees
optimal transportation
510
The nested distance, also process distance, provides a quantitative measure of distance for stochastic processes. It is the crucial and determining distance for stochastic optimization problems.In this paper we demonstrate first that the empirical measure, which is built from observed sample paths, does not converge in nested distance to its underlying distribution. We show that smoothing convolutions, which are appropriately adapted from classical density estimation using kernels, can be employed to modify the empirical measure in order to obtain stochastic processes, which converge in nested distance to the underlying process. We employ the results to estimate transition probabilities at each time moment. Finally we construct processes with discrete sample space from observed empirical paths, which approximate well the original stochastic process as they converge in nested distance.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-100232119
eng
Stochastic Programming E-Print Series, Band 2015,4, 2015
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/9100/1/4.pdf
10.18452/8448
http://edoc.hu-berlin.de/18452/9100
oai:edoc.hu-berlin.de:18452/88752020-03-07T04:13:59Zcom_18452_152com_18452_44col_18452_356textPublicationprimusopen_accessdoc-type:bookddc:510
Intertemporal Surplus Management
Markus
Rudolf
William T.
Ziemba
Asset
Beta
Funding Ratio
HARA utility function
Hedge Portfolio
Intertemporal Capital Asset Pricing Model
Itô process
J-function
Liabilities
Log utility function
Safety First
Shortfall risk
State variable
Surplus management
510
This paper presents an intertemporal portfolio selection model for pension funds that maximize the intertemporal expected utility of the surplus of assets net of liabilities. Following Merton (1973) it is assumed that both the asset and the liability return follow Ito processes as functions of a state variable. The optimum occurs for investors holding four funds: the market portfolio, the hedge portfolio for the state variable, the hedge portfolio for the liabilities, and the riskless asset. It is shown that pension funds should purchase hedging for liabilities. In contrast to Merton's result in the assets only case, this hedge depends exclusively on the funding ratio of a specific pension fund and not on preferences. With HARA utility the investments in the state variable hedge portfolios are also preference independent. With log utility the market portfolio investment depends only on the current funding ratio.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-10057396
eng
Stochastic Programming E-Print Series, Band 1999,7, 2000
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/8875/1/7.pdf
10.18452/8223
http://edoc.hu-berlin.de/18452/8875
oai:edoc.hu-berlin.de:18452/90102020-03-07T04:14:28Zcom_18452_152com_18452_44col_18452_363textPublicationprimusopen_accessdoc-type:bookddc:510
Convexity of chance constraints with independent random variables
René
Henrion
Cyrille
Strugarek
510
We investigate the convexity of chance constraints with independent random variables. It will be shown, how concavity properties of the mapping related to the decision vector have to be combined with a suitable property of decrease for the marginal densities in order to arrive at convexity of the feasible set for large enough probability levels. It turns out that the required decrease can be verified for most prominent density functions. The results are applied then, to derive convexity of linear chance constraints with normally distributed stochastic coefficients when assuming independence of the rows of the coefficient matrix.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-10066261
eng
Stochastic Programming E-Print Series, Band 2006,9, 2006
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/9010/1/9.ps
10.18452/8358
http://edoc.hu-berlin.de/18452/9010
oai:edoc.hu-berlin.de:18452/34822020-03-07T04:03:16Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Oscillator Construction of su(n|m) Q-Operators
Rouven
Frassek
Tomasz
Lukowski
Carlo
Meneghelli
Matthias
Staudacher
510
We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded Yang-Baxter equation, leading to an amalgam of bosonic and fermionic oscillator algebras. Our approach is fully algebraic, and leads to the exact solution of the associated compact spin chains while avoiding Bethe ansatz techniques. It furthermore elucidates the algebraic and combinatorial structures underlying the system of nested Bethe equations. Finally, our construction naturally reproduces the representation, due to Z. Tsuboi, of the hierarchy of Baxter Q-operators in terms of hypercubic Hasse diagrams.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-100193461
eng
Preprints aus dem Institut für Mathematik, Band 2010,13, 2010
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3482/1/13.pdf
10.18452/2830
http://edoc.hu-berlin.de/18452/3482
oai:edoc.hu-berlin.de:18452/286832024-01-13T02:00:12Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
Lorentzian Gromov–Hausdorff theory and finiteness results
Olaf
Müller
Metrization
Space-time
Functorial
510
Cheeger–Gromov finiteness results, asserting that there are only finitely many diffeomorphism types of manifolds satisfying certain geometric bounds, feature among the most prominent results in Riemannian geometry. To transplant those into Lorentzian geometry, one could use a functor between a Lorentzian and a Riemannian category, which, however, can be shown not to exist if the former contains Minkowski space and its isometries. Here, we construct a functor from a restricted category of Lorentzian manifolds-with-boundary (regions between two Cauchy surfaces) to a category of Riemannian manifolds-with-boundary that preserves geometric bounds and obtain, as a corollary, the first known Lorentzian Cheeger–Gromov type finiteness result.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2024-01-12
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/28683-2
General relativity and gravitation, Band 54, Ausgabe 10, 2022
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/28683/3/s10714-022-03000-8.pdf
10.18452/27896
10.1007/s10714-022-03000-8
http://edoc.hu-berlin.de/18452/28683
oai:edoc.hu-berlin.de:18452/195452020-03-07T04:54:13Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
Essays on Market Microstructure and Pathwise Directional Derivatives
Jana
Bielagk
Prinzipal-Agenten-Modell
Gleichgewichtspreis
stochastische Rückwärtsgleichung
repräsentativer Agent
Malliavin-Kalkül
principal-agent model
equilibrium pricing
feedback
performance concerns
BSDE
Malliavin calculus
representative agent
510
SK 980
Wir befassen uns mit Gleichgewichtsproblemen, die bei dem Zusammentreffen von Märkten und Marktteilnehmern entstehen, zuerst in einem Modell mit konkurrierenden Märkten mit Feedback und asymmetrischer Information und dann mit strategisch interagierenden Händlern. Zudem untersuchen wir spezielle Richtungsableitung im Kontext des pfadweisen Malliavinkalküls.
Im ersten Kapitel analysieren wir ein Prinzipal-Agenten-Problem mit einem monopolistischen Dealer, der mit einem Crossing-Netzwerk (CN) um den Handel mit Agenten mit privater Information konkurriert. Wir untersuchen die gewinnmaximierenden Angebote des Dealers für unterschiedliche Outside-Optionen und formulieren hinreichende Bedingungen für die Existenz und Eindeutigkeit einer optimalen Lösung. In unserem Modell ist die Einführung des CN für die Agenten vorteilhaft und ein Gleichgewichtspreis existiert.
Im zweiten Kapitel analysieren wir den Einfluss vergleichender Leistungsbewertung von Händlern auf die Preisfindung im Marktgleichgewicht. Ein Derivat soll einen markträumenden Preis bekommen unter Beachtung der strategisch handelnden Agenten. Das Risiko eines Händlers setzt sich aus dem eigenen Risikoprofil und dem Erfolg des Handelns relativ zum durchschnittlichen Handelserfolg aller zusammen und er wird durch eine BSDE gemessen. Wir bestimmen einen repräsentativen Agenten und zeigen so die Existenz und Eindeutigkeit eines Gleichgewichtspreises. Weiterhin können wir diesen charakterisieren und im Spezialfall von entropischen Risikomaßen konkret berechnen. In diesem Spezialfall führen wir auch eine Parameteranalyse durch.
Das dritte Kapitel verknüpft klassischen und pfadweisen Malliavinkalkül. Wir definieren und analysieren pfadweise Richtungsableitungen mit Hilfe von Perturbationen mit Cameron-Martin-Funktionen, mit (Hölder-)stetigen Funktionen, mit unstetigen Funktionen und mit Maßen. Somit sind sowohl die klassische Malliavin-Ableitung als auch Dupires vertikale Ableitung als Spezialfälle enthalten.
We analyze equilibrium problems arising from interacting markets and market participants, first competing markets with feedback and asymmetric information, then strategically interacting traders; moreover we analyze a new notion of a pathwise directional derivative in the context of pathwise Malliavin calculus.
The first chapter analyzes a principal-agent game in which a monopolistic profit-maximizing dealer competes with a crossing network (CN) for trading with privately informed agents. We analyze the structure of the dealer’s offered pricing schedules for different outside options. We give sufficient conditions for the existence and uniqueness of a solution to the dealer’s problem and show that in our setting the introduction of the CN is beneficial for the agents. Additionally, we discuss existence and uniqueness of an equilibrium price for the feedback between dealer and CN.
In the second chapter we analyze the impact of performance concerns on a problem of equilibrium pricing. A derivative is priced such that the market clears, given strategically behaving agents. Their risk stems from a risky position in the future and the relative trading gains compared to all other agents. The risk measure of each agent is specified by a BSDE. In spite of the strategic interaction, we are able to apply a representative agent approach to obtain existence and uniqueness of the equilibrium market price of external risk. In the special case of entropic risk measures, we perform a parameter analysis.
The third chapter provides a link between classical and pathwise Malliavin calculus. We define and analyze pathwise directional derivatives via perturbations with Cameron-Martin functions, (Hölder-)continuous functions, discontinuous functions and measures, thereby including both the traditional Malliavin derivative and the vertical derivative from Dupire’s work.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Ulrich
Horst
Peter
Imkeller
Traian
Pirvu
2017-11-20
2018-02-23
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/19545-0
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/19545/3/dissertation_bielagk_jana.pdf
10.18452/18817
http://edoc.hu-berlin.de/18452/19545
oai:edoc.hu-berlin.de:18452/34072020-03-07T04:03:10Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
How fast is fast fictitious play?
Bernd
Kummer
510
We present a modification of the fictitious play algorithm for matrix games by aggregating trivial original steps. The resulting new algorithm consists of comparable simple steps but has a much better rate of convergence. Modifications for solving large scale LP-programs, numerical results and some conjecture concerning the total effort of elementary steps for esuring an error $ < \varepsilon$ will be discussed.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10086822
eng
Preprints aus dem Institut für Mathematik, Band 2006,25, 2006
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3407/1/25.pdf
10.18452/2755
http://edoc.hu-berlin.de/18452/3407
oai:edoc.hu-berlin.de:18452/34552020-03-07T04:03:13Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Iterative Operator Splitting Methods
Jürgen
Geiser
Iterative operator-splitting method
Pade approximations
510
In this paper we describe a technique for closed formulation of an iterative operator-splitting method and embed the method in the classical exponential splitting methods. Since iterative operator splitting have been developed, an abstract framework to relate the method to other classical splitting methods is needed. Here an abstract framework considering the iterative splitting method as waveform-relaxation or ex- ponential splitting method is devised. This is achieved by basing the analysis on semi-groups and fixed-point schemes. Abstract results illustrate differential equations with constant and time- dependent coefficients.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-100192986
eng
Preprints aus dem Institut für Mathematik, Band 2009,8, 2009
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3455/1/8.pdf
10.18452/2803
http://edoc.hu-berlin.de/18452/3455
oai:edoc.hu-berlin.de:18452/32142020-03-07T04:02:56Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Feedback solutions of optimal control problems with DAE constraints
Galina A.
Kurina
Roswitha
März
linear-quadratic optimal control problems
feedback control
differentialalgebraic equations
descriptor systems
Riccati equations
Hamiltonian systems
510
An optimal feedback control has been obtained for linear-quadratic optimal control problems with constraints described by differential-algebraic equations. For that purpose, a new implicit Riccati equation (Riccati differential algebraic system) is provided, and its solvability is investigated. It is shown that one can do without those strong consistency conditions as used in several previous papers. Also the solvability of the resulting closed loop system is considered and the relations between Riccati equations and Hamiltonian systems are elucidated.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10051824
eng
Preprints aus dem Institut für Mathematik, Band 2005,9, 2005
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3214/1/9.pdf
10.18452/2562
http://edoc.hu-berlin.de/18452/3214
oai:edoc.hu-berlin.de:18452/272322023-10-31T04:00:22Zcom_18452_25col_18452_26ddc:530doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
Renormalization in Combinatorially Non-Local Field Theories: The Hopf Algebra of 2-Graphs
Johannes
Thürigen
Hopf algebra
Non-local field theory
Renormalization
Random geometry
510
530
Renormalization in perturbative quantum field theory is based on a Hopf algebra of Feynman diagrams. A precondition for this is locality. Therefore one might suspect that non-local field theories such as matrix or tensor field theories cannot benefit from a similar algebraic understanding. Here I show that, on the contrary, perturbative renormalization of a broad class of such field theories is based in the same way on a Hopf algebra. Their interaction vertices have the structure of graphs. This gives the necessary concept of locality and leads to Feynman diagrams defined as “2-graphs” which generate the Hopf algebra. These results set the stage for a systematic study of perturbative renormalization as well as non-perturbative aspects, e.g. Dyson-Schwinger equations, for a number of combinatorially non-local field theories with possible applications to random geometry and quantum gravity.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2023-05-12
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/27232-9
Mathematical physics, analysis and geometry, Band 24, Ausgabe 2, 2021
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/27232/4/s11040-021-09390-6.pdf
10.1007/s11040-021-09390-6
10.18452/26536
http://edoc.hu-berlin.de/18452/27232
oai:edoc.hu-berlin.de:18452/196562020-03-07T04:54:14Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
The height of compact nonsingular Heisenberg-like Nilmanifolds
Sebastian
Boldt
Höhe
Funktionaldeterminante
Laplace-Beltrami Operator
Heisenbergartig
Heisenberg-typ
Nilmannigfaltigkeit
height
functional determinant
Laplace-Beltrami operator
Heisenberg-like
Heisenberg-type
nilmanifold
510
516
515
SK 620
Die vorliegende Arbeit beschäftigt sich mit der Höhe (-log Determinante) kompakter nicht-singulärer heisenbergartiger Nilmannigfaltigkeiten. Heisenbergartige Nilmannigfaltigkeiten sind Verallgemeinerungen von Heisenbergmannigfaltigkeiten, d.h., kompakter Quotienten der Heisenberg-Gruppe, ausgestattet mit einer linksinvarianten Metrik.
Zunächst werden explizite Formeln für die spektrale Zeta-Funktion und die Höhe bewiesen. Mithilfe dieser Formeln werden im Weiteren mehrere Resultate zur Existenz unterer Schranken/Minima der Höhe auf verschiedenen Moduli bewiesen. Zum Beispiel ist die Höhe stets von unten beschränkt, wenn man nur Metriken vom Heisenberg-Typ und mit Volumen 1 auf einer gegebenen Nilmannigfaltigkeit betrachtet. Im Gegensatz dazu hängt die Existenz unterer Schranken für die Höhe auf dem Modulraum der heisenbergartigen Metriken mit Volumen 1 von der Dimension Modulo 4 der zugrundeliegenden Mannigfaltigkeit ab.
Im letzten Abschnitt werden konkrete Minima der Höhe behandelt. Wir zeigen, dass gewisse 3-, 5-, 9- und 25-dimensionale Nilmannigfaltigkeiten vom Heisenberg-Typ lokale Minima sind. Diese stehen in Zusammenhang mit den Minima der Höhe flacher Tori in der jeweiligen Dimension minus 1.
Zum Abschluss werden diejenigen linksinvarianten Metriken charakterisiert, an denen die Höhe ein globales Minimum auf einer gegebenen dreidimensionalen Nilmannigfaltigkeit annimmt, indem sie zur Höhe flacher 2-dimensionaler Tori in Bezug gesetzt werden.
This thesis deals with the height (-log determinant) of compact nonsingular Heisenberg-like nilmanifolds. Heisenberg-like nilmanifolds are generalisations of Heisenberg manifolds, i.e., compact quotients of the Heisenberg group endowed with a left invariant metric.
First, an explicit formula for the spectral zeta-function and the height is proved. By means of these formulas, several results concerning the existence of lower bounds/minima for the height on different moduli are proved. For example, while the height is always bounded from below when one considers only volume normalised Heisenberg-type metrics on a fixed nilmanifold, the existence of lower bounds for the height on the moduli space of volume normalised Heisenberg-like metrics depends on the dimension modulo 4 of the underlying nilmanifold. In the last part, we consider concrete minima of the height on Heisenberg manifolds. We show that certain 3-, 5-, 9- and 25-dimensional Heisenberg-type nilmanifolds are (local) minima for the height. These nilmanifolds are related to the minima of the height of flat tori in dimensions one less.
Finally, the left invariant metrics at which the height attains a global minimum on any three-dimensional nilmanifold are characterised by relating them to the height of flat 2-dimensional tori.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Dorothee
Schüth
Carolyn
Gordon
Werner
Ballmann
2017-10-27
2018-03-13
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/19656-8
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/19656/1/dissertation_boldt_sebastian.pdf
10.18452/18924
http://edoc.hu-berlin.de/18452/19656
oai:edoc.hu-berlin.de:18452/89302020-03-07T04:14:11Zcom_18452_152com_18452_44col_18452_359textPublicationprimusopen_accessdoc-type:bookddc:510
Integrated chance constraints
Willem K. Klein
Haneveld
Maarten H. van der
Vlerk
chance constraints
simple recourse
algorithm
510
We consider integrated chance constraints (ICC), which provide quantitative alternatives for traditional chance constraints. We derive explicit polyhedral descriptions for the convex feasible sets induced by ICCs, for the case that the underlying distribution is discrete. Based on these reduced forms, we propose an efficient algorithm for this problem class.The relation to conditional value-at-risk models and (simple) recourse models is discussed, leading to a special purpose algorithm for simple recourse models with discretely distributed technology matrix. For both algorithms, numerical results are presented.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/8930-6
eng
Stochastic Programming E-Print Series, Band 2002,14, 2002
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/8930/1/14.pdf
10.18452/8278
http://edoc.hu-berlin.de/18452/8930
oai:edoc.hu-berlin.de:18452/32752020-03-07T04:03:00Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Resolution of degree ≤ 6 algebraic equations by genus two theta constants
Angel
Zhivkov
roots of polynomials
theta constants
510
We adjoin complete first kind Abelian integrals of genus two to solve the general degree six algebraic equation a 0 z 6 + a 1 z 5 + ... + a 6 = 0 by genus two theta constants. Using the same formulas, later we resolve degree five, four and three algebraic equations. We study the monodromy group, which permutes the roots of degree six polynomials.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10052574
eng
Preprints aus dem Institut für Mathematik, Band 2002,11, 2002
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3275/1/11.pdf
10.18452/2623
http://edoc.hu-berlin.de/18452/3275
oai:edoc.hu-berlin.de:18452/33652020-03-07T04:03:07Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Criteria for the trivial solution of differential algebraic equations with small nonlinearities to be asymptotically stable
Roswitha
März
differential algebraic equations
initial value problems
asymptotical stability
implicit differential equations
510
Differential algebraic equations consisting of a constant coefficient linear part and a small nonlinearity are considered. Conditions that enable linearizations to work well are discussed. In particular, for index-2 differential algebraic equations there results a kind of Perron-Theorem that sounds as clear as its classical model except for the expensive proofs.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10053875
eng
Preprints aus dem Institut für Mathematik, Band 1997,13, 1997
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3365/1/13.pdf
10.18452/2713
http://edoc.hu-berlin.de/18452/3365
oai:edoc.hu-berlin.de:18452/268052023-10-31T04:00:25Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510ddc:500
Splitting Methods for Partial Differential-Algebraic Systems with Application on Coupled Field-Circuit DAEs
Malak
Diab
Differential-algebraische Gleichungen
Operator-Splitting-Methoden
Schaltungssimulation
gekoppelten Feld-Schaltungssystems
Port-Hamiltonsche DAE
Differential-Algebraic Equations
Operator Splitting Method
Circuit Simulations
Coupled Field-Circuit Systems
Port-Hamiltonian Systems
510
500
SK 810
SK 540
Die Anwenung von Operator-Splitting-Methoden auf gewöhnliche Differentialgleichungen ist gut etabliert. Für Differential-algebraische Gleichungen und partielle Differential-algebraische Gleichungen unterliegt sie jedoch vielen Einschränkungen aufgrund des Vorhandenseins von Nebenbedingungen. Die räumliche Diskretisierung reduziert PDAEs und lenkt unseren Fokus auf das Konzept der DAEs. Um eine reibungslose Übertragung des Operator-Splittings von ODEs auf DAEs durchzuführen, ist es wichtig, eine geeignete entkoppelte Struktur für das gewünschte Differential-algebraische System zu haben.
In dieser Arbeit betrachten wir ein Modell, das partielle Differentialgleichungen für elektromagnetische Bauelemente - modelliert durch die Maxwell-Gleichungen - mit Differential-algebraischen Gleichungen koppelt, die die elementaren Schaltungselemente beschreiben. Nach der räumlichen Diskretisierung der klassischen Formulierung der Maxwell-Gleichungen mit Hilfe der finiten Integrationstechnik formulieren wir das resultierende gekoppelte System als Differential-algebraische Gleichung. Um eine geeignete Entkopplung zu bekommen, verwenden wir den zweigorientierten Loop-Cutset-Ansatz für die Schaltungsmodellierung. Daraus folgt, dass wir in der Lage sind, eine geeignete Operatorzerlegung so zu konstruieren, dass wir eine natürliche topologisch entkoppelte Port-Hamiltonsche DAE-Struktur erhalten.
Wir schlagen einen Operator-Splitting-Ansatz für die Schaltungs-DAEs und gekoppelten Feld-Schaltungs-DAEs in entkoppelter Form vor und analysieren seine numerischen Eigenschaften. Darüber hinaus nutzen wir das Hamiltonsche Verhalten der inhärenten gewöhnlichen Differentialgleichung durch die Verwendung expliziter und energieerhaltender Zeitintegrations-methoden. Schließlich führen wir numerische Tests, um das mathematische Modell zu illustrieren und die Konvergenzergebnisse für das vorgeschlagene DAE-Operator-Splitting zu demonstrieren.
Le equazioni algebriche differenziali e algebriche alle derivate parziali hanno avuto un
enorme successo come modelli di sistemi dinamici vincolati. Nella modellazione matem-
atica, spesso si desidera catturare diversi aspetti di una situazione come le leggi di conservazione della fisica, il trasporto convettivo o la diffusione. Queste aspetti si riflettono nel sistema di equazioni del modello come operatori diversi. La tecnica dell’Operator Splitting si è rivelata una strategia di successo per affrontare problemi così complicati.
L’applicazione dei metodi di Operator Splitting alle equazioni differenziali ordinarie (ODE) è ormai una tecnologia ben consolidata. Tuttavia, per equazioni algebriche differenziali (DAE) e algebriche differenziali parziali (PDAE), l’approccio è soggetto a molte restrizioni dovute alla presenza di vincoli e alla proprietà di indice. La discretizzazione spaziale riduce le PDAE e indirizza la nostra attenzione al concetto di DAE. Le DAE emergono in problemi dinamici vincolati come circuiti elettrici o reti di trasporto di energia. Al fine di generalizzare agevolmente la tecnica dell’Operator Splitting dalle ODE alle DAE, è importante avere una struttura disaccoppiata adeguata per il sistema algebrico differenziale desiderato.
In questa tesi, consideriamo un modello che accoppia equazioni differenziali alle derivate parziali per dispositivi elettromagnetici -modellati dalle equazioni di Maxwell- con equazioni algebriche differenziali che descrivono gli elementi base del circuito. Dopo aver discretizzato spazialmente la formulazione classica delle equazioni di Maxwell usando la tecnica di integrazione finita, formuliamo il sistema accoppiato risultante come una equazione algebrica differenziale. Interpretando il dispositivo elettromagnetico come un elemento capacitivo, l’indice dell’intero sistema di circuito e campo accoppiato può essere specificato utilizzando le proprietà topologiche del circuito e non supera il valore di due. Per eseguire un disaccoppiamento appropriato, utilizziamo l’approccio loop-cutset per la modellazione dei circuiti. In tal modo siamo in grado di costruire una opportuna decomposizione dell’operatore tale da ottenere una naturale struttura disaccoppiata port-Hamiltonian DAE.
Proponiamo un approccio di suddivisione dell’operatore per i DAE a circuito disaccoppiato e a circuito di campo accoppiato utilizzando gli algoritmi di divisione Lie-Trotter e Strang e per analizzare le proprietà numeriche di questi sistemi. Inoltre, sfruttiamo il comportamento hamiltoniano del sistema di equazioni differenziali ordinarie mediante l’utilizzo di metodi di integrazione temporale con esatta conservazione dell’energia. Poggiando sull’analisi di convergenza del metodo di suddivisione dell’operatore ODE, deriviamo i risultati di convergenza per l’approccio proposto che dipendono dall’indice delsistema e quindi dalla sua struttura topologica. Infine, eseguiamo prove numeriche di sistemi circuitali, nonchè sistemi accoppiati a circuito di campo, per testare il modello matematico e dimostrare i risultati di convergenza per la proposta Operator Splitting DAE.
The application of operator splitting methods to ordinary differential equations (ODEs)
is well established. However, for differential-algebraic equations (DAEs) and partial
differential-algebraic equations (PDAEs), it is subjected to many restrictions due to the
presence of constraints. In constrained dynamical problems as electrical circuits or energy transport networks, DAEs arise. In order to perform a smooth
transfer of the operator splitting from ODEs to DAEs, it is important to have a suitable
decoupled structure for the desired differential-algebraic system.
In this thesis, we consider a model which couples partial differential equations for electro-
magnetic devices -modeled by Maxwell’s equations- with differential-algebraic equations
describing the basic circuit elements. After spatially discretizing the classical formulation
of Maxwell’s equations using the finite integration technique, we formulate the resulting
coupled system as a differential-algebraic equation. To perform an appropriate decoupling, we use the branch oriented loop-cutset approach for circuit modeling. It follows that we are able to construct a suitable operator decomposition such that we obtain a natural topologically decoupled
port-Hamiltonian DAE structure.
We propose an operator splitting approach for the decoupled circuit and coupled field-
circuit DAEs using the Lie-Trotter and Strang splitting algorithms and analyze its numerical properties. Furthermore, we exploit the Hamiltonian behavior of the system’s
inherent ordinary differential equation by the utilization of explicit and energy-preserving
time integration methods. Based on the convergence analysis of the ODE operator splitting method, we derive convergence results for the proposed approach that depends on
the index of the system and thus on its topological structure. Finally, we perform numerical tests, to underline the mathematical model and to demonstrate the convergence results for the proposed DAE operator splitting.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Caren
Tischendorf
Volker
Mehrmann
Michael
Günther
2022-11-21
2023-02-28
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/26805-7
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/26805/5/dissertation_diab_malak.pdf
10.18452/25731
http://edoc.hu-berlin.de/18452/26805
oai:edoc.hu-berlin.de:18452/34162020-03-07T04:03:11Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Operator-splitting methods for wave equations
Jürgen
Geiser
Volker
Schlosshauer
partial differential equations
consistency analysis
seismic sources and waves
operator-splitting methods
iterative methods
510
The motivation for our studies is coming from the simulation of earthquakes, that are modeled by elastic wave equations. In our paper we focus on stiff phanomenons for the wave equations. In the course of this article we discuss iterative operator-splitting methods for wave equations motivated by realistic problems dealing with seismic sources and waves. The operator-splitting methods are well-known to solve this kind of multi-dimensional and multi-physical problems. We present the consistency analysis for iterative methods as theoretical background with respect to the underlying boundary conditions. From an algorithmic point of view we discuss the decoupling and non-decoupling method with respect to the eigenvalues. We verify our methods with test examples, for which analytical solutions can be derived. Multi-dimensional examples are presented for realistic applications for the wave equation. Finally we discuss the results.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-100189256
eng
Preprints aus dem Institut für Mathematik, Band 2007,6, 2007
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3416/1/6.pdf
10.18452/2764
http://edoc.hu-berlin.de/18452/3416
oai:edoc.hu-berlin.de:18452/286932024-01-16T02:00:26Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
Relating Siegel cusp forms to Siegel–Maaß forms
Jürg
Kramer
Antareep
Mandal
Siegel upper half-space
Siegelmodular forms
Maaß forms
Maaß operators
510
In this paper we generalize a well-known isomorphism between the space of cusp forms of weight k for a Fuchsian subgroup of the first kind $$\Gamma \subset \mathrm {SL}_{2}({\mathbb {R}})$$ and the space of certain Maaß forms of weight k for $$\Gamma $$ to an isomorphism between the space of Siegel cusp forms of weight k for a subgroup $$\Gamma \subset \mathrm {Sp}_{n}({\mathbb {R}})$$, which is commensurable with the Siegel modular group $$\mathrm {Sp}_{n}({\mathbb {Z}})$$, and a suitable space of Siegel–Maaß forms of weight k for $$\Gamma $$.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2024-01-15
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/28693-0
Research in number theory, Band 8, Ausgabe 3, 2022
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/28693/3/s40993-022-00351-8.pdf
10.18452/27882
10.1007/s40993-022-00351-8
http://edoc.hu-berlin.de/18452/28693
oai:edoc.hu-berlin.de:18452/199802020-03-07T04:57:53Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
A regularized arithmetic Riemann-Roch theorem via metric degeneration
Gaetano, Giovanni
arithmetische Riemann-Roch
automorphe Formen
regularisierte Determinante
Wärmeleitungskern auf Tensoren
Whittaker Gleichung
arithmetic Riemann-Roch
automorphic forms
regularized determinant
heat kernel on tensors
Whittaker equation
510
SK 370
Das Hauptresultat dieser Arbeit ist ein regularisierter arithmetischer Satz von Riemann-Roch für ein hermitesches Geradenbündel, die isometrisch zum Geradenbündel den Spitzenformen vom geraden Gewicht ist, auf eine arithmetische Fläche, deren komplexe Faser isometrisch zu einer hyperbolischen Riemannschen Fläche ohne elliptische Punkte ist.
Der Beweis des Resultats erfolgt durch metrische Degeneration: Wir regularisieren die betreffenden Metriken in einer Umgebung der Singularitäten, wenden dann den arithmetischen Riemann-Roch-Satz von Gillet und Soulé an und lassen schließlich den Parameter gegen Null gehen. Durch die metrische Degeneration entsteht auf beiden Seiten der Formel ein divergenter Term. Die asymptotische Entwicklung der Divergenz berechnet sich auf der einen Seite direkt aus der Definition der glatten arithmetischen Selbstschnittzahlen.
Der divergente Term auf der anderen Seite ist die zeta-regularisierte Determinante des zu den regularisierten Metriken assoziierten Laplace-Operators, der auf den 1-Formen mit Werten in dem betrachteten hermitischen Geradenbündel operiert. Wir definieren und berechnen zuerst eine Regularisiereung des entsprechenden zu den singulären Metriken assoziierten Laplace-Operators; diese wird später im regularisierten Riemann-Roch-Satz auftauchen. Zu diesem Zweck passen wir Ideen von Jorgenson-Lundelius, D'Hoker-Phong und Sarnak auf die vorliegende Situation an und verallgemeinern diese.
Schließlich beweisen wir eine Formel für den zum betrachteten hermitischen Geradenbündel assoziierten Wärmeleitungskern auf der Diagonalen bei einer Modellspitze. Diese Darstellung steht im Zusammenhang mit einer Entwicklung nach zur Whittaker-Gleichung assoziierten Eigenfunktionen, die im Anhang bewiesen wird. Weitere Abschätzungen des zum betrachteten hermitischen Geradenbündel gehörigen Wärmeleitungskern auf der komplexe Faser der arithmetischen Fläche schließen den Beweis des Hauptresultats ab.
The main result of the dissertation is an arithmetic Riemann-Roch theorem for the hermitian line bundle of cusp form of given even integer weights on an arithmetic surface whose complex fiber is isometric to an hyperbolic Riemann surface without elliptic points.
The proof proceeds by metric degeneration: We regularize the metric under consideration in a neighborhood of the singularities, then we apply the arithmetic Riemann-Roch theorem of Gillet and Soulé, and finally we let the parameter go to zero. Both sides of the formula blow up through metric degeneration. On one side the exact asymptotic expansion is computed from the definition of the smooth arithmetic intersection numbers.
The divergent term on the other side is the zeta-regularized determinant of the Laplacian acting on 1-forms with values in the chosen hermitian line bundle associated to the regularized metrics. We first define and compute a regularization of the determinant of the corresponding Laplacian associated to the singular metrics, which will later occur int he regularized arithmetic Riemann-Roch theorem. To do so we adapt and generalize ideas od Jorgenson-Lundelius, D'Hoker-Phong, and Sarnak.
Then, we prove a formula for the on-diagonal heat kernel associated to the chosen hermitian line bundle on a model cusp, from which its behavior close to a cusp is transparent. This expression is related to an expansion in terms of eigenfunctions associated to the Whittaker equation, which we prove in an appendix. Further estimates on the heat kernel associated to the chosen hermitian line bundle on the complex fiber of the arithmetic surface prove the main theorem.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Jürg
Kramer
Gerard
Freixas
Pippich, Anna
2017-07-20
2018-06-14
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/19980-1
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/19980/5/dissertation_degaetano_giovanni.pdf
10.18452/19227
http://edoc.hu-berlin.de/18452/19980
oai:edoc.hu-berlin.de:18452/221982021-08-31T08:18:55Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
On the derivation of effective gradient systems via EDP-convergence
Thomas
Frenzel
EDP-Konvergenz
Gadientenflüsse
Evolutionsgleichungen
Gamma-Konvergenz
EDP-convergence
gradient flows
evolution equations
Gamma convergence
515
SK 540
Diese Dissertation beschäftigt sich mit EDP-Konvergenz. Dabei handelt es sich um einen Konvergenzbegriff auf dem Gebiet der verallgemeinerten Gradientensysteme und metrischen Gradientensysteme, der geeignet ist für Gradientenflüsse, die von einem kleinen Parameter abhängen. EDP-Konvergenz liefert einen Algorithmus, der es erlaubt in der Energie und dem Dissipationspotenzial zum Grenzwert überzugehen. Es ist die fundamentale Frage evolutionärer Γ-Konvergenz, wie das Limes-Dissipationspotenzial berechnet werden kann.
Das Ziel dieser Arbeit ist es aufzuzeigen, dass EDP-Konvergenz das mikro- und das makroskopische Dissipationspotenzial in einer sinnvollen und eindeutigen Art und Weise in Beziehung setzt. Anhand von drei Beispielen wird der Konvergenzbegriff untersucht: die Diffusionsgleichung auf einem dünnen, dreischichtigen Gebiet, die Poröse-Medien-Gleichung mit einer dünnen Membran und ein Modell mit oszillierender Energie.
Es wird die Definition von relaxierter EDP-Konvergenz und EDP-Konvergenz mit Kippung motiviert. EDP-Konvergenz basiert auf dem Prinzip, dass es ein Gleichgewicht zwischen Energie und Dissipation gibt – das Energie-Dissipations-Prinzip (EDP). Mittels Γ-Konvergenz wird sowohl in der Energie, als auch dem totalen Dissipationsfunktional zum Grenzwert übergegangen. Durch die zusätzliche Entkopplung von Zustand und Triebkraft wird die Dissipationslandschaft erkundet und die kinetische Beziehung des Limessystems ermittelt.
Das Modell mit oszillierender Energie zeigt die Bedeutung der kinetischen Beziehung – und damit der Kippung – für die Herleitung des Limes-Dissipationspotenzials auf. Die Modelle mit Wasserstein-Dissipation zeigen, dass das Limes-Dissipationspotenzial nicht der naive Grenzwert ist. Insbesondere können klassische Gradientensysteme mit quadratischer Dissipation zu verallgemeinerten Gradientensysteme konvergieren.
In the realm of generalized gradient systems and metric gradient systems we study a notion of convergence suited for gradient flows which depend on a small parameter. This notion is called EDP-convergence. In order to understand the convergence of gradient systems we need an algorithm to derive the limiting energy as well as the limiting dissipation potential. The fundamental question of evolutionary Γ-convergence is how to compute the limit dissipation potential.
The aim of this thesis is to show that EDP-convergence connects the microscopic dissipation potential with the macroscopic, i.e. limiting, dissipation potential in a meaningful and unique way. As a proof of concept 3 different examples are presented: (i) the diffusion equation on a thin sandwich-like domain, (ii) the porous medium equation with a thin interface and (iii) a wiggly energy model.
We show how the gradient flow concept that is used in this thesis can be used to obtain also gradient flows with respect to the Wasserstein metric. We motivate the definition of relaxed EDP-convergence and EDP-
convergence with tilting. EDP-convergence is based upon the principle that there is an energy-dissipation-balance involving the total dissipation functional and the energy difference – the energy-dissipation-principle (EDP). The limit passage, in both the energy and the total dissipation functional, is performed in terms of Γ-convergence. By perturbing the flow as well as the driving force, the dissipation-landscape is explored and a kinetic relation for the limit system can be established.
The wiggly energy model demonstrates the importance of the kinetic relation for the construction of the limiting dissipation potential and thus the introduction of tilts. The models with a Wasserstein dissipation show that the limiting dissipation potential is not the naive limit. In particular, classical gradient systems with a quadratic dissipation potential converge to a generalized gradient systems.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Alexander
Mielke
Barbara
Zwicknagl
Stefan
Neukamm
2019-06-26
2020-06-10
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/22198-9
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/22198/5/dissertation_frenzel_thomas.pdf
10.18452/21391
http://edoc.hu-berlin.de/18452/22198
oai:edoc.hu-berlin.de:18452/32292020-03-07T04:02:57Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Fine decouplings of regular differential algebraic equations
Roswitha
März
regularity
tractability index
differential algebraic equations
decoupling
projectors
510
In this paper, the previously formulated conjecture concerning the existence of fine and complete decouplings of regular DAEs with tractability index $\mu$ is verified.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10052113
eng
Preprints aus dem Institut für Mathematik, Band 2004,4, 2004
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3229/1/4.pdf
10.18452/2577
http://edoc.hu-berlin.de/18452/3229
oai:edoc.hu-berlin.de:18452/284552023-11-29T02:00:14Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:330ddc:510
A note on testing restrictions for the cointegration parameters of a VAR with I(2) variables
Søren
Johansen
Helmut
Lütkepohl
330
510
We give a brief introduction to the vector autoregressive model for cointegrated I(2) variables and show how some plausible economic relations can be formulated in the I(2) framework in such a way that likelihood ratio tests for their validity are asymptotically χ2 distributed.The authors thank Paolo Paruolo for helpful comments and the ESF for financial support in the framework of the EMM network.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2023-11-28
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/28455-5
Econometric theory, Band 21, Ausgabe 3, Seite 653-658, 2005
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/28455/1/10.1017_S0266466605050280.pdf
10.18452/27802
10.1017/S0266466605050280
http://edoc.hu-berlin.de/18452/28455
oai:edoc.hu-berlin.de:18452/33952020-03-07T04:03:09Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Convergence of adaptive FEM for a class of degenerate convex minimization problems
Carsten
Carstensen
convergence
a posteriori error estimates
adaptive finite element methods
error reduction
convex minimization
degenerate convex problems
energy reduction
adaptive mesh-refining
discrete local efficiency
discrete residual control
510
A class of degenerate convex minimization problems allows for some adaptive finite element method (AFEM) to compute strongly converging stress approximations. The algorithm AFEM consists of successive loops of the form \begin{equation*} \texttt{SOLVE} \rightarrow \texttt{ESTIMATE} \rightarrow \texttt{MARK} \rightarrow \texttt{REFINE} \end{equation*} and employs the bulk criterion. The convergence in $L^{p'}(\Omega; \R^{m \times n})$ relies on new sharp strict convexity estimates of degenerate convex minimization problems with \[ \J(v):=\int_{\Omega}W(Dv)\,dx-\int_{\Omega}fv\,dx\quad\mbox{for } v\in V:=W^{1,p}_0(\Omega;\R^m). \] The class of minimization problems includes strong convex problems and allows applications in an optimal design task, Hencky elastoplasticity, or relaxation of 2-well problems allowing for microstructures.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10068021
eng
Preprints aus dem Institut für Mathematik, Band 2006,15, 2006
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3395/1/15.pdf
10.18452/2743
http://edoc.hu-berlin.de/18452/3395
oai:edoc.hu-berlin.de:18452/33792020-03-07T04:03:08Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Internal Layer Solutions in Quasilinear Integro-Differential Equations
N.N.
Nefedov
O.E.
Omelchenko
Lutz
Recke
510
The Dirichlet boundary value problem for a class of singularly perturbed quasilinear integro-differential equations is considered. The asymptotic expansion for a new class of solutions, which have internal layers, is constructed. Theorems on existence, local uniqueness and asymptotic stability of such internal layer solutions are proved.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10066770
eng
Preprints aus dem Institut für Mathematik, Band 2005,16, 2005
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3379/1/16.pdf
10.18452/2727
http://edoc.hu-berlin.de/18452/3379
oai:edoc.hu-berlin.de:18452/32202020-03-07T04:02:56Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
A Convergent Adaptive Finite Element Method For The Primal Problem Of Elastoplasticity
Carsten
Carstensen
Antonio
Orlando
Jan
Valdman
Variational inequality of second kind
elastoplasticity
conforming finite element method
a posteriori error estimates
adaptive finite element methods
error reduction
510
The boundary value problem representing one time step of the primal formulation of elastoplasticity with positive hardening leads to a variational inequality of the second kind with some non-differentiable functional. This paper establishes an adaptive finite element algorithm for the solution of this variational inequality that yields the energy reduction and, up to higher order terms, the $R$-linear convergence of the stresses with respect to the number of loops. Applications include several plasticity models: linear isotropic-kinematic hardening, linear kinematic hardening, and multisurface plasticity as model for nonlinear hardening laws. For perfect plasticity the adaptive algorithm yields strong convergence of the stresses. Numerical examples confirm an improved linear convergence of the stresses. Numerical examples confirm an improved linear convergence rate and study the performance of the algorithm in comparison with the more frequently applied maximum refinement rule.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10051880
eng
Preprints aus dem Institut für Mathematik, Band 2005,12, 2005
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3220/1/12.pdf
10.18452/2568
http://edoc.hu-berlin.de/18452/3220
oai:edoc.hu-berlin.de:18452/163282020-03-07T04:40:44Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
A kinetic model for grain growth
Reiner
Henseler
Kornwachstum
kinetisches Modell
unendlich--dimensional
hyperbolisch
grain growth
kinetic model
infinite--dimensional
hyperbolic
510
In dieser Arbeit wird eine detaillierte Analysis des konsistenten kinetischen Modells zum Kornwachstum von Fradkov durchgeführt. Dieses Modell beschreibt - basierend auf dem von Neumann--Mullins Gesetz - die Flächenänderung eines Korns abhängig von seiner Topologieklasse, d.h. der Anzahl der Kanten. Topologieänderungen werden durch Kopplungsterme zwischen den Gleichungen für die Anzahldichten der verschiedenen Topologieklassen beschrieben. Daraus resultiert ein unendlich-dimensionales System von Transportgleichungen mit tridiagonaler Kopplungsstruktur. Durch eine spezielle Wahl des Kopplungsgewichts, welche die Gleichungen nichtlinear und räumlich nichtlokal macht, wird das Modell konsistent. Nach einer Einführung wird das Modell von Fradkov im zweiten Kapitel hergeleitet; formale Rechnungen zeigen die Konsistenz des Modells auf. Im dritten Kapitel wird das Kopplungsgewicht a priori beschränkt. Dadurch kann im ersten Teil des vierten Kapitels Existenz und Eindeutigkeit von Lösungen für endlich-dimensionale Systeme gezeigt werden. Weitere Schranken an die Anzahldichten im fünften Kapitel ermöglichen den Grenzübergang hinsichtlich der Anzahl der Gleichungen im zweiten Teil des vierten Kapitels. Die Existenz von Lösungen des unendlich-dimensionalen Systems wird somit über eine geeignete Approximation gezeigt. Energiemethoden liefern Eindeutigkeit und stetige Abhängigkeit von den Daten. Im sechsten Kapitel wird das Langzeitverhalten untersucht. Besonderes Augenmerk liegt dabei auf stationären Lösungen eines reskalierten Systems als Kandidaten für selbstähnliche Lösungen. Abschließend wird das Lewis''sche Gesetz asymptotisch verifiziert.
The subject matter of this thesis is a detailed analysis of the self--consistent kinetic model for grain growth introduced by Fradkov. The model is based on the von Neumann--Mullins law describing the change of area of grains according to their topological class, i.e. the number of edges they have. Topological events are performed by coupling terms between equations for the number densities of different topological classes. The resulting system of transport equations is infinite-dimensional with a tridiagonal coupling structure. Self-consistency of this kinetic model is achieved by introducing a coupling''s weight making the equations nonlinear and nonlocal in space. We start with an introduction in the first chapter. Afterwards in the second chapter we derive Fradkov''s model and carry out formal calculations to illustrate self-consistency. In the third chapter we present a priori calculations mainly allowing us to bound the nonlinearity. This enables us to prove existence and uniqueness of solutions to finite-dimensional systems in the first part of the fourth chapter. Further bounds on the number densities established in the fifth chapter allow for passing to the limit concerning the number of equations in the second part of the fourth chapter. Therefore we prove existence of solutions to the infinite-dimensional system by a suitable approximation procedure. Uniqueness and continuous dependence on the data is then provided by energy methods. The sixth chapter focusses on long-time behaviour and mainly on stationary solutions of a rescaled system as candidates for self-similar solutions. Finally we prove Lewis'' law asymptotically.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Barbara
Niethammer
Juan J. L.
Velazquez
Lutz
Recke
2007-09-17
2017-06-18
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-10080926
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/16328/1/henseler.pdf
10.18452/15676
http://edoc.hu-berlin.de/18452/16328
oai:edoc.hu-berlin.de:18452/33532020-03-07T04:03:06Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
On Maxwell's equations in exterior domains
Frank
Jochmann
asymptotic behaviour
Maxwell's equations
exterior boundary-value-problem
510
In this paper the long time asymptotic behavior of solutions of Maxwell's equations with electric conductivity in an exterior domain with mixed boundary conditions is investigated. It is shown that the solution behaves asymptotically like a free space solution provided it obeys a suitable local decay-property. As a consequence the completeness of the wave-operators is obtained under very general assumptions on the coefficients. (This paper will appear in the Journal Asymptotic Analysis.)
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10053755
eng
Preprints aus dem Institut für Mathematik, Band 1999,17, 1999
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3353/1/17.pdf
10.18452/2701
http://edoc.hu-berlin.de/18452/3353
oai:edoc.hu-berlin.de:18452/34632020-03-07T04:03:14Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Mixed Finite Element Methods of Higher-Order for Model Contact Problems
Andreas
Schröder
contact problems
higher-order FEM
mixed methods
510
This paper presents mixed finite element methods of higher-order for a simplified Signorini problem and an idealized frictional problem. The discretization is based on a mixed variational formulation proposed by Haslinger et al. which is extended to higher-order finite elements. To guarantee the unique existence of the solution of the mixed method, a discrete inf-sup condition is proven. Approximation results of the p-method of finite elements and some inverse estimates for higher-order polynomials are applied. Numerical results confirm the theoretical findings.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-100193065
eng
Preprints aus dem Institut für Mathematik, Band 2009,16, 2009
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3463/1/16.pdf
10.18452/2811
http://edoc.hu-berlin.de/18452/3463
oai:edoc.hu-berlin.de:18452/33272020-03-07T04:03:04Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Qantitative stability for scenario-based stochastic programs
Jitka
Dupacová
Werner
Römisch
probability metrics
stochastic programs
stability wrt. probability measure
random recourse
discrete distributions
application
510
General quantitative stability results for stochastic programs are formulated in terms of probability metrics, specified to scenario-based stochastic programs and applied to a bond portfolio managemant problem.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10053474
eng
Preprints aus dem Institut für Mathematik, Band 1998,7, 1998
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3327/1/7.pdf
10.18452/2675
http://edoc.hu-berlin.de/18452/3327
oai:edoc.hu-berlin.de:18452/89982020-03-07T04:14:26Zcom_18452_152com_18452_44col_18452_362textPublicationprimusopen_accessdoc-type:bookddc:510
Ambiguous chance constrained problems and robust optimization
E.
Erdogan
G.
Iyengar
510
In this paper we study ambiguous chance constrained problems where the distributions of the random parameters in the problem are themselves uncertain. We focus primarily on the special case where the uncertainty set Q of the distributions is of the form $Q = {Q : \rho_p(Q;Q_0) \le \beta}$, where $\rho_p$ denotes the Prohorov metric. The ambiguous chance constrained problem is approximated by a robust sampled problem where each constraint is a robust constraint centered at a sample drawn according to the central measure $Q_0$. The main contribution of this paper is to show that the robust sampled problem is a good approximation for the ambiguous chance constrained problem with a high probability. This result is established using the Strassen-Dudley Representation Theorem that states that when the distributions of two random variables are close in the Prohorov metric one can construct a coupling of the random variables such that the samples are close with a high probability. We also show that the robust sampled problem can be solved efficiently both in theory and in practice.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-10059939
eng
Stochastic Programming E-Print Series, Band 2005,17, 2005
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/8998/1/17.pdf
10.18452/8346
http://edoc.hu-berlin.de/18452/8998
oai:edoc.hu-berlin.de:18452/33692020-03-07T04:03:07Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Topological index calculation of DAEs in circuit simulation
Caren
Tischendorf
DAE
circuit simulation
modified nodal analysis
index
differential-algebraic equation
MNA
integrated circuit
510
Electric circuits are present in a number of applications, e.g. in home computers, television, credit cards, electric power networks, etc. The development of integrated circuit requires numerical simulation. Modern modeling techniques like the Modified Nodal Analysis (MNA) lead to differential algebraic equations (DAEs). Properties like the stability of solutions of such systems depend strongly on the DAE index. The paper deals with lumped circuits containing voltage sources, current sources as well as general nonlinear but time-invariant capacitances, inductances and resistances. We present network-topological criteria for the index of the DAEs obtained by the classical and the charge oriented MNA. Furthermore, the index is shown to be limited to 2 for our model-class.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10053918
eng
Preprints aus dem Institut für Mathematik, Band 1997,17, 1997
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3369/1/17.pdf
10.18452/2717
http://edoc.hu-berlin.de/18452/3369
oai:edoc.hu-berlin.de:18452/230162021-02-09T11:51:45Zcom_18452_19149col_18452_19156researchDataprimusopen_accessddc:510dissertationRelatedResearchData
octAFEM3D software package for PhD thesis „Adaptive least-squares finite element method with optimal convergence rates“
Philipp
Bringmann
Least-Squares Finite-Elemente-Methode
adaptive Netzverfeinerung
Poisson-Modellproblem
Stokes-Gleichungen
lineare Elastizität
Dirichlet-Randbedingungen
Neumann-Randbedingungen
Matlab
Octave
least-squares finite element method
adaptive mesh-refinement
Poisson model problem
Stokes equations
linear elasticity
Dirichlet boundary conditions
Neumann boundary conditions
Matlab
Octave
518
Das octAFEM3D Softwarepaket dient der numerischen Lösung von partiellen Differentialgleichungen. Drei lineare Modellprobleme in drei Raumdimensionen können mit einer Least-Squares Finiten-Elemente-Methode niedrigsten Polynomgrades gelöst werden. Die Approximation von inhomogenen Randdaten ist möglich. Die adaptive Netzverfeinerung wird mit einer kollektiven Markierungsstrategie umgesetzt. Die Implementierung basiert auf dem AFEM Softwarepaket der Arbeitsgruppe der Numerischen Mathematik von Prof. Carsten Carstensen an der Humboldt-Universität zu Berlin. Die Programme wurden implementiert und getestet für die Matlab Version 9.6.0.1072779 (R2019a) und Octave Version 5.1.0. Dieses Softwarepaket ist Teil der Dissertation „Adaptive least-squares finite element method with optimal convergence rates“ von Philipp Bringmann an der Humboldt-Universität zu Berlin unter der Betreuung von Prof. Carsten Carstensen.
This is the octAFEM3D package for the numerical solution of partial differential equations. Three linear model problems in three spatial dimensions can be solved by a lowest-order least-squares finite element method. The approximation of inhomogeneous boundary conditions is included. Adaptive mesh-refinement is realised with a collective marking strategy. The software is derived from the AFEM package of the numerical analysis working group of Prof. Carsten Carstensen at Humboldt-Universität zu Berlin. The code is implemented and tested for Matlab 9.6.0.1072779 (R2019a) and Octave 5.1.0. This software package is part of the PhD thesis „Adaptive least-squares finite element method with optimal convergence rates“ by Philipp Bringmann at Humboldt-Universität zu Berlin under the supervision of Prof. Carsten Carstensen.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2021-01-27
ResearchData
Software
publishedVersion
urn:nbn:de:kobv:11-110-18452/23016-7
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/23016/1/octafem3d.zip
10.18452/22346
http://edoc.hu-berlin.de/18452/23016
oai:edoc.hu-berlin.de:18452/32132020-03-07T04:02:56Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Transformation of Lebesgue Measure and Integral by Lipschitz Mappings
Joachim
Naumann
Implicit function theorems
Jacobians
transformations with several variables
None of the above
but in this section
510
We first show that {\sc Lipschitz} mappings transform measurable sets into measurable sets. Then we prove the following theorem:\par {\it Let $E\subseteq \mathbb{R}^n$ be open, and let $\phi: E\to\mathbb{R}^n$ be continuous. If $\phi$ is differentiable at $x_0\in E$, then} \[ \lim\limits_{r\to 0} \dfrac{\lambda_n(\phi(B_r(x_0)))}{\lambda_n(B_r)} = \Big| \det\phi'(x_0)\Big|. \] From this result the change of variables formula for injective and locally {\sc Lipschitz} mappings is easily derived by using the {\sc Radon-Nikodym} theorem. We finally discuss the transformation of $L^p$ functions by {\sc Lipschitz} mappings.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10051810
eng
Preprints aus dem Institut für Mathematik, Band 2005,8, 2005
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3213/1/8.pdf
10.18452/2561
http://edoc.hu-berlin.de/18452/3213
oai:edoc.hu-berlin.de:18452/205132020-03-07T05:00:48Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
Generic pro-p Hecke algebras, the Hecke algebra of PGL(2, Z), and the cohomology of root data
Nicolas Alexander
Schmidt
Hecke-Algebren
Coxetergruppen
Wurzeldaten
Erweiterte modulare Gruppe
hecke algebras
coxeter groups
root data
extended modular group
510
SK 230
Es wird die Theorie der generischen pro-$p$ Hecke-Algebren und ihrer Bernstein-Abbildungen entwickelt. Für eine Unterklasse diese Algebren, der \textit{affinen} pro-$p$ Hecke-Algebren wird ein Struktursatz bewiesen, nachdem diese Algebren unter anderem stets noethersch sind, wenn es der Koeffizientenring ist. Hilfsmittel ist dabei der Nachweis der Bernsteinrelationen, der in abstrakter Weise geführt wird und so die bestehende Theorie verallgemeinert.
Ferner wird der top. Raum der Orientierungen einer Coxetergruppe eingeführt und im Falle der erweiterten modularen Gruppe $\operatorname{PGL}_2(\mathds{Z})$ untersucht, und ausgenutzt um Kenntnisse über die Struktur der zugehörigen Hecke-Algebra als Modul über einer gewissen Unteralgebra, welche zur Spitze im Unendlichen zugeordnet ist, zu erlangen.
Schließlich wird die Frage des Zerfallens des Normalisators eines maximalen zerfallenden Torus innerhalb einer zerfallenden reduktiven Gruppe als Erweiterung der Weylgruppe durch die Gruppe der rationalen Punkte des Torus untersucht, und mittels zuvor erreichter Ergebnisse auf eine kohomologische Frage zurückgeführt. Zur Teilbeantwortung dieser werden dann die Kohomologiegruppen bis zur Dimension drei der Kocharaktergitter der fasteinfachen halbeinfachen Wurzeldaten einschließlich des Rangs 8 berechnet. Mittels der Theorie der $\mathbf{FI}$-Moduln wird daraus die Berechnung der Kohomologie der mod-2-Reduktion der Kowurzelgitter für den Typ $A$ in allen Rängen bewiesen.
The theory of generic pro-$p$ Hecke algebras and their Bernstein maps is developed. For a certain subclass, the \textit{affine} pro-$p$ Hecke algebras, we are able to prove a structure theorem that in particular shows that the latter algebras are always noetherian if the ring of coefficients is. The crucial technical tool are the Bernstein relations, which are proven in an abstract way that generalizes the known cases.
Moreover, the topological space of orientations is introduced and studied in the case of the extended modular group $\operatorname{PGL}_2(\mathds{Z})$, and used to determine the structure of its Hecke algebra as a module over a certain subalgebra, attached to the cusp at infinity.
Finally, the question of the splitness of the normalizer of a maximal split torus inside a split reductive groups as an extension of the Weyl group by the group of rational points is studied. Using results obtained previously, this questioned is then reduced to a cohomological one. A partial answer to this question is obtained via computer calculations of the cohomology groups of the cocharacter lattices of all almost-simple semisimple root data of rank up to $8$. Using the theory of $\mathbf{FI}$-modules, these computations are used to determine the cohomology of the mod 2 reduction of the coroot lattices for type $A$ and all ranks.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Elmar
Große-Klönne
Yuval Zvi
Flicker
Ulrich
Görtz
2018-10-11
2019-02-08
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/20513-1
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/20513/5/dissertation_schmidt_nicolas%20alexander.pdf
10.18452/19724
http://edoc.hu-berlin.de/18452/20513
oai:edoc.hu-berlin.de:18452/195162023-10-31T04:00:36Zcom_18452_1col_18452_4textPublicationprimusopen_accessdoc-type:masterThesisddc:510
Hierarchical Multiclass Topic Modelling with Prior Knowledge
Ken
Schröder
Bayes
Gibbs-Sampling
Latent Dirichlet Allocation
maschinelles Lernen
Variationsinferenz
Themenmodellierung
natural language processing
variational inference
Topicmodeling
Bayes
Gibbs sampling
graphical models
machine learning
natural language processing
Latent Dirichlet Allocation
variational inference
519
Eine neue Multi-Label-Dokument-Klassifizierungstechnik namens CascadeLDA wird in dieser Arbeit eingeführt. Statt sich auf diskriminierende Modellierungstechniken zu konzentrieren, erweitert CascadeLDA ein generatives Basismodell durch die Einbeziehung von zwei Arten von Vorinformationen.
Erstens wird das Wissen aus einem gekennzeichneten Trainingsdatensatz verwendet, um das generative Modell zu steuern. Zweitens wird die implizite Baumstruktur der Labels ausgenutzt, um diskriminierende Eigenschaften zwischen eng verwandten Labels hervorzuheben. Durch die Transformation des Klassifizierungsproblems in einem
Ensemble von kleineren Problemen, werden vergleichbare out-of-sample Resultate circa 25 mal schneller erreicht als im Basismodell. In diesem Paper wird CascadeLDA auf Datensätzen mit akademischen Abstracts und vollständige wissenschaftliche angewendet. Das Modell wird eingesetzt, um Autoren beim Klassifizieren ihrer Publikationen automatisch zu unterstützen.
A new multi-label document classification technique called CascadeLDA is introduced
in this thesis. Rather than focusing on discriminative modelling techniques, CascadeLDA
extends a baseline generative model by incorporating two types of prior information.
Firstly, knowledge from a labeled training dataset is used to direct the generative model.
Secondly, the implicit tree structure of the labels is exploited to emphasise discriminative
features between closely related labels. By segregating the classification problem in an
ensemble of smaller problems, out-of-sample results are achieved at about 25 times the
speed of the baseline model. In this thesis, CascadeLDA is performed on datasets with
academic abstracts and full academic papers. The model is employed to assist authors in
tagging their newly published articles.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Cathy
Chen
Wolfgang Karl
Härdle
2018-01-29
2018-02-12
masterThesis
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/19516-9
eng
master
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/19516/3/thesis_schroeder_ken.pdf
10.18452/18795
http://edoc.hu-berlin.de/18452/19516
oai:edoc.hu-berlin.de:18452/31642020-03-07T04:02:53Zcom_18452_66com_18452_45com_18452_5col_18452_67textPublicationprimusopen_accessdoc-type:bookddc:510
Preface
Eberhard
Griepentrog
Michael
Hanke
Roswitha
März
510
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10045837
ger
Berliner Seminar on Differential-Algebraic Equations. Seminar Notes, Band 1992,1, 1992
other
Humboldt-Universität zu Berlin
Berlin
2
http://edoc.hu-berlin.de/download/18452/3164-flat-files.zip
10.18452/2512
http://edoc.hu-berlin.de/18452/3164
urn:nbn:de:kobv:11-10045840
oai:edoc.hu-berlin.de:18452/31692020-03-07T04:02:54Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Transfer of boundary conditions for DAEs ofindex 1
Katalin
Balla
Roswitha
März
differential-algebraic equations
boundary value problems
transfer method
510
In this paper, the concept of Abramov’s method for transferring boundary conditions posed for regular ordinary differential equations is applied to index 1 DAEs. Having discussed the reduction of inhomogeneous problems to homogeneous ones and analyzed the underlying ideas of Abramov’s method, we consider boundary value problems for index 1 linear DAEs both with constant and varying leading matrix. We describe the relations defining the subspaces of solutions satisfying the prescribed boundary conditions at one end of the interval. The index 1 DAEs that realize the transfer are given and their properties are studied. The results are reformulated for inhomogeneous index 1 DAEs, as well.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10050695
eng
Preprints aus dem Institut für Mathematik, Band 1995,3, 1995
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3169/1/3.pdf
10.18452/2517
http://edoc.hu-berlin.de/18452/3169
oai:edoc.hu-berlin.de:18452/7322020-03-07T04:00:21Zcom_18452_390col_18452_433textPublicationopen_accessdoc-type:doctoralThesisddc:510
Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse
Carl Friedrich
Gauß
Funktionale Algebra
Rationale Integrale
510
SK 220
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-100246246
lat
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
2
http://edoc.hu-berlin.de/download/18452/732-flat-files.zip
10.18452/80
http://edoc.hu-berlin.de/18452/732
urn:nbn:de:kobv:11-1009000
oai:edoc.hu-berlin.de:18452/89592020-03-07T04:14:17Zcom_18452_152com_18452_44col_18452_360textPublicationprimusopen_accessdoc-type:bookddc:510
Efficient point methods for probabilistic optimization problems
Darinka
Dentcheva
Bogumila
Lai
Andrzej
Ruszczynski
Stochastic Programming
Convex Programming
Probabilistic Constraints
Dual Methods
510
We consider nonlinear stochastic programming problems with probabilistic constraints. The concept of a p-efficient point of a probability distribution is used to derive equivalent problem formulations, and necessary and sufficient optimality conditions. We analyze the dual functional and its subdifferential. Two numerical methods are developed based on approximations of the p-efficient frontier. The algorithms yield an optimal solution for problems involving r-concave probability distributions. For arbitrary distributions, the algorithms provide upper and lower bounds for the optimal value and nearly optimal solutions. The operation of the methods is illustrated on a cash matching problem with a probabilistic liquidity constraint.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/8959-3
eng
Stochastic Programming E-Print Series, Band 2003,25, 2004
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/8959/1/25.pdf
10.18452/8307
http://edoc.hu-berlin.de/18452/8959
oai:edoc.hu-berlin.de:18452/271742023-05-06T01:01:04Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
On the Kodaira dimension of Hurwitz spaces
Gavril
Farkas
Scott
Mullane
Mathematics, general
510
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2023-05-05
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/27174-8
Mathematische Zeitschrift, Band 300, Ausgabe 4, Seite 3417-3432, 2021
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/27174/1/s00209-021-02882-9.pdf
10.1007/s00209-021-02882-9
10.18452/26492
http://edoc.hu-berlin.de/18452/27174
oai:edoc.hu-berlin.de:18452/33302020-03-07T04:03:04Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Evaluation of the epi-convergence
Petr
Lachout
510
The paper presents an equivalent characterization of the epi-convergence of lower semicontinuous functions. The proposed ‘measures’ naturally estimate the distance between optimal values of two optimization programs. A comparison of optimal solutions is more complex. We propose an estimation for a given function which can be taken as the excess of a set over another, being in metric space. Hence, we receive an estimate of the distance between optimal solutions.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10053503
eng
Preprints aus dem Institut für Mathematik, Band 1998,10, 1998
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3330/1/10.pdf
10.18452/2678
http://edoc.hu-berlin.de/18452/3330
oai:edoc.hu-berlin.de:18452/91072020-03-07T04:14:48Zcom_18452_152com_18452_44col_18452_632textPublicationprimusopen_accessdoc-type:bookddc:510
Quantitative Stability Analysis for Minimax Distributionally Robust RiskOptimization
Alois
Pichler
Huifu
Xu
distortion risk measure
&zeta-ball
Wasserstein ball
quantitative stability analysis
510
This paper considers distributionally robust formulations of a two stage stochastic programmingproblem with the objective of minimizing a distortion risk of the minimal cost incurred at the secondstage.We carry out stability analysis by looking into variations of the ambiguity set under theWassersteinmetric, decision spaces at both stages and the support set of the random variables. In the case when itis risk neutral, the stability result is presented with the variation of the ambiguity set being measuredby generic metrics of ζ-structure, which provides a unified framework for quantitative stability analysisunder various metrics including total variation metric and Kantorovich metric. When the ambiguity set isstructured by a ζ-ball, we find that the Hausdorff distance between two ζ-balls is bounded by the distanceof their centres and difference of their radius. The findings allow us to strengthen some recent convergenceresults on distributionally robust optimization where the centre of the Wasserstein ball is constructed bythe empirical probability distribution.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-100246239
eng
Stochastic Programming E-Print Series, Band 2017,3, 2017
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/9107/1/3.pdf
10.18452/8455
http://edoc.hu-berlin.de/18452/9107
oai:edoc.hu-berlin.de:18452/32842020-03-07T04:03:01Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
The index of linear differential algebraic equations with properly stated leading terms
Roswitha
März
regularity
differential algebraic equations
index
510
In a linear differential algebraic equation with properly stated leading term, the involved derivatives of the unknown function are figured out by an additional matrix coefficient being in some sense well matched with the leading coefficient matrix. Supposed all matrix coefficients are continuous, for these equations, the notion of regularity with index $\mu$ is introduced via a certain matrix sequence built up from the coefficient matrices and then proved to be invariant under regular transformations. The Kronecker index, the global index, and the tractability index for standard form differential algebraic equations are covered as well. Moreover, inherent regular ordinary differential equations that govern the dynamics are described in detail and it is shown that transformations applied to them are closely related to refactorizations of the leading term in the original equation.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10052666
eng
Preprints aus dem Institut für Mathematik, Band 2001,7, 2001
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3284/1/7.pdf
10.18452/2632
http://edoc.hu-berlin.de/18452/3284
oai:edoc.hu-berlin.de:18452/262352023-10-31T04:00:42Zcom_18452_25col_18452_26ddc:530doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
Duality Hierarchies and Differential Graded Lie Algebras
Roberto
Bonezzi
Olaf
Hohm
530
510
The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require higher-form gauge fields. Recently, we proposed that the algebraic structure allowing for consistent tensor hierarchies is axiomatized by ‘infinity-enhanced Leibniz algebras’ defined on graded vector spaces generalizing Leibniz algebras. It was subsequently shown that, upon appending additional vector spaces, this structure can be reinterpreted as a differential graded Lie algebra. We use this observation to streamline the construction of general tensor hierarchies, and we formulate dynamics in terms of a hierarchy of first-order duality relations, including scalar fields with a potential.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2022-11-28
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/26235-1
Communications in mathematical physics, Band 382, Ausgabe 1, Seite 277-315, 2021
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/26235/1/s00220-021-03973-8.pdf
10.18452/25506
10.1007/s00220-021-03973-8
http://edoc.hu-berlin.de/18452/26235
oai:edoc.hu-berlin.de:18452/33542020-03-07T04:03:06Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Locally Exact Lower Bounds and Optimality Cuts for All-Quadratic Programs with Convex Constraints
Ivo
Nowak
Lagrangian relaxation
global optimization
nonconvex quadratic programming
locally exact lower bounds
optimality cuts
510
A central problem of branch-and-bound methods for global optimization is that lower bounds are often not exact even if the diameter of the subdivided regions shrinks to zero. This can lead to a large number of subdivisions preventing the method from terminating in reasonable time. For the all-quadratic optimization problem with convex constraints we present locally exact lower bounds and optimality cuts based on Lagrangian relaxation. If all global minimizers fulfill a certain second order optimality condition it can be shown that locally exact lower bounds or optimality cuts lead to finite termination of a branch-and-bound algorithm. Since there exist efficient methods for computing Lagrangian relaxation bounds of all-quadratic optimization problems exploiting problem structure our approach should be applicable to large scale structured optimization problems.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10053767
eng
Preprints aus dem Institut für Mathematik, Band 1999,18, 1999
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3354/1/18.pdf
10.18452/2702
http://edoc.hu-berlin.de/18452/3354
oai:edoc.hu-berlin.de:18452/31982020-03-07T04:02:55Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Equilibrium in abstract economies without the lower semi-continuity of the constraint maps
Adib
Bagh
abstract economy
equilibrium
set convergence
set valued maps
L-majorized maps
Walrasian equilibrium
510
We use graph convergence of set valued maps to show the existence of an equilibrium for an abstract economy without assuming the lower semi continuity of the constraint maps.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10051245
eng
Preprints aus dem Institut für Mathematik, Band 1996,18, 1996
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3198/1/18.pdf
10.18452/2546
http://edoc.hu-berlin.de/18452/3198
oai:edoc.hu-berlin.de:18452/222092020-06-12T01:09:02Zcom_18452_1col_18452_4textPublicationprimusopen_accessdoc-type:masterThesisddc:510
Deep Generalized Additive Regression Models for Location, Scale and Shape using TensorFlow
Kang
Yang
GAMLSS
DFNN
Variationsinferenz
Tiefes Lernen
Tensorflow-Wahrscheinlichkeit
GAMLSS
DFNN
Variational Inference
Deep learning
Tensorflow probability
519
Das Deep Distributional Learning-Modell oder Deep Generalized Additive Regression Models für Locations, Scale and Shape (DGAMLSS) ist ein flexibles Framework, das von Rügamer et al. [1] entwickelt wurde und in das sowohl strukturierte additive als auch Deep Neural Network-Teile einbezogen sind der additive Prädiktor für die Verteilungsregression. In diesem Artikel verwenden wir eine Reihe von Datensätzen, die separat durch verschiedene Verteilungen simuliert wurden, untersuchen die Leistung von Deep GAMLSS und vergleichen sie mit anderen drei hochmodernen Designs für GAMLSS, nämlich GAMLSS mit maximaler Wahrscheinlichkeit [2]. BAMLSS [3] und GamboostLSS [4]. Ein solcher Vergleich wird unter verschiedenen Gesichtspunkten demonstriert. Schätzungen sowohl zu linearen als auch zu nichtlinearen Begriffen werden untersucht und anhand verschiedener Modelle verglichen, um ihre Stärken und Schwächen zu ermitteln. DGAMLSS übertrifft im Allgemeinen andere Modelle in Bezug auf Vorhersagegenauigkeit, Konvergenzgeschwindigkeit und Robustheit unter Rauschen, insbesondere bei der Annahme einer komplexen Verteilung, unterscheidet jedoch nicht zwischen linearen, nichtlinearen und unstrukturierten Schätzern.
Deep Distributional Learning model, or Deep Generalized Additive Regression Models for Locations, Scale and Shape (DGAMLSS), is a flexible framework de- signed by Rügamer et al[1], where both structured additive and deep neural net- work parts are included into the additive predictor for distributional regression. In this paper, we employ a series of datasets separately simulated by different dis- tributions, examine performance of deep GAMLSS, and compare it with other three state-of-the-art designs for GAMLSS, namely GAMLSS with maximum likelihood[2], BAMLSS[3] and gamboostLSS[4]. Such comparison is demon- strated from different aspects. Estimations on both linear and non-linear terms are studied and compared through different models to address their strength and weakness. DGAMLSS generally outperforms other models in respect of predic- tion accuracy, convergence speed and robustness under noises especially for com- plex distributional assumption, but fails to distinguish structure linear, non-linear estimator, and unstructured estimator.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Nadja
Klein
David
Rügamer
2020-03-02
2020-06-11
masterThesis
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/22209-7
eng
master
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/22209/3/master_yang_kang.pdf
10.18452/21366
http://edoc.hu-berlin.de/18452/22209
oai:edoc.hu-berlin.de:18452/90222020-03-07T04:14:31Zcom_18452_152com_18452_44col_18452_363textPublicationprimusopen_accessdoc-type:bookddc:510
Airline Network Revenue Management by Multistage Stochastic Programming
Andris
Möller
Werner
Römisch
Klaus
Weber
510
A multistage stochastic programming approach to airline network revenue management is presented. The objective is to determine seatprotection levels for all itineraries, fare classes, point of sales of the airlinenetwork and all data collection points of the booking horizon such that theexpected revenue is maximized. While the passenger demand and cance-lation rate processes are the stochastic inputs of the model, the stochasticprotection level process represents its output and allows to control the booking process. The stochastic passenger demand and cancelation rate processesare approximated by a finite number of tree structured scenarios. The scenario tree is generated from historical data using a stability-based recursivescenario reduction scheme. Numerical results for a small hub-and-spoke network are reported.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-10072315
eng
Stochastic Programming E-Print Series, Band 2006,21, 2006
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/9022/1/21.pdf
10.18452/8370
http://edoc.hu-berlin.de/18452/9022
oai:edoc.hu-berlin.de:18452/289812024-02-23T10:54:06Zcom_18452_19149col_18452_19156researchDataprimusopen_accessddc:510dissertationRelatedResearchData
Software for PhD Thesis "Direct guaranteed lower eigenvalue bounds with quasi-optimal adaptive mesh-refinement"
Sophie Louise
Puttkammer
Eigenwertproblem
garantierte untere Schranken
Laplace
bi-Laplace
AFEM
Crouzeix-Raviart
Morley
MATLAB
Adaptivität
Finite-Elemente-Methode
hybrid-high-order Methode (HHO)
extra-stabilisiert
eigenvalue problem
guaranteed lower bounds
Laplace
bi-Laplace
AFEM
Crouzeix-Raviart
Morley
MATLAB
adaptivity
finite element method
hybrid high-order method (HHO)
extra-stabilized
518
Diese Software ist Teil der Dissertation »Direct guaranteed lower eigenvalue bounds with quasi-optimal adaptive mesh-refinement« von Sophie Puttkammer, Humboldt-Universität zu Berlin, Arbeitsgruppe Numerische Analysis von Prof. C. Carstensen.
Sie enthält ein Framework zum Lösen des Laplace und bi-Laplace Eigenwertproblems mit verschiedenen Finite-Element-Methoden. Zur Berechnung garantierter unterer Eigenwertschranken für das Laplace Eigenwertproblem stehen eine modifizierte HHO Methode niedrigster Ordnung und eine extra-stabilisierte Crouzeix-Raviart Methode zur Verfügung. Für die Berechnung garantierter unterer Eigenwertschranken für das bi-Laplace Eigenwertproblem ist eine extra-stabilisierte Morley Methode enthalten. Vergleichswerte können mittels Postprocessing einer klassischen Crouzeix-Raviart bzw. Morley Methode berechnet werden. Für alle Methoden sind Löser und Funktionen zur Berechnung von Fehlerschätzern für die adaptive Netzverfeinerung enthalten.
Details zu den Methoden, mit dieser Software durchgeführte Experimente inklusive Auswertung und eine Kurzdokumentation finden sich in der oben genannten Dissertation.
Die Software wurde geschrieben für und getestet mit der MATLAB-Version 9.9.0.1495850 (MATLAB R2020b).
This code is part of the PhD thesis »Direct guaranteed lower eigenvalue bounds with quasi-optimal adaptive mesh-refinement« by Sophie Puttkammer, Humboldt-Universität zu Berlin, Numerical Analysis Group of Prof. C. Carstensen.
It contains a finite element framework to solve the Laplace and bi-Laplace eigenvalue problem. For the computation of guaranteed lower eigenvalue bounds for the Laplace problem a lowest-order modified HHO method and an extra-stabilized Crouzeix-Raviart method are available. For the computation of guaranteed lower eigenvalue bounds for the bi-Laplace problem the package contains an extra-stabilized Morley method. A comparison with the post-processing of the classic Crouzeix-Raviart and Morley method is possible. All methods come with solvers and functions to calculate error estimators to drive adaptive mesh refinement. The thesis mentioned above contains details regarding these methods, numerical experiments executed with this software and a short documentation.
The software was written for and tested under MATLAB version 9.9.0.1495850 (MATLAB R2020b).
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2024-02-23
ResearchData
Software
publishedVersion
urn:nbn:de:kobv:11-110-18452/28981-1
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/28981/1/code_dissertation_puttkammer_sophie.zip
10.18452/28039
http://edoc.hu-berlin.de/18452/28981
oai:edoc.hu-berlin.de:18452/231932021-03-17T12:40:11Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
How Secure Are Two-Way Ping-Pong and LM05 QKD Protocols under a Man-in-the-Middle Attack?
Mladen
Pavičić
quantum cryptography
quantum key distribution
two-way communication
510
We consider a man-in-the-middle attack on two-way quantum key distribution ping-pong and LM05 protocols in which an eavesdropper copies all messages in the message mode, while being undetectable in the mode. Under the attack there is therefore no disturbance in the message mode and the mutual information between the sender and the receiver is always constant and equal to one and messages copied by the eavesdropper are always genuine. An attack can only be detected in the control mode but the level of detection at which the protocol should be aborted is not defined. We examine steps of the protocol to evaluate its security and find that the protocol should be redesigned. We also compare it with the security of a one-way asymmetric BB84-like protocol in which one basis serves as the message mode and the other as the control mode but which does have the level of detection at which the protocol should be aborted defined.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2021-03-11
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/23193-4
Entropy, Band 23, Ausgabe 2, 2021
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/23193/1/entropy-23-00163.pdf
10.3390/e23020163
10.18452/22570
http://edoc.hu-berlin.de/18452/23193
oai:edoc.hu-berlin.de:18452/31792020-03-07T04:02:54Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Integrating Logical Functions with ILF
Bernd I.
Dahn
Jürgen
Gehne
Thomas
Honigmann
Lutz
Walther
Andreas
Wolf
510
This is a description of the system ILF developed at the Humboldt-University at Berlin. ILF is a system that integrates automated theorem provers, proof tactics for interactive deductive systems and models within a graphical user interface. The structure and commands of ILF are presented. A special part is devoted to the TreeViewer _ a part of ILF used for visualising directed acyclic graphs, which can be used as a separate programme. We describe the possibilities to extend ILF by integrating more interactive and automated deductive systems. The last part describes the ProofPad - a sample configuration for editing proofs in the field of lattice ordered groups.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10050917
eng
Preprints aus dem Institut für Mathematik, Band 1994,10, 1994
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3179/1/10.pdf
10.18452/2527
http://edoc.hu-berlin.de/18452/3179
oai:edoc.hu-berlin.de:18452/33152020-03-07T04:03:03Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Analyzing the stability behaviour of DAE solutions and their approximations
Roswitha
März
Antonio R. Rodríguez
Santiesteban
Differential algebraic equations
numerical stability
logarithmic norms
contractivity
510
New stability results are proved for linear index-2 differential algebraic equations (DAE). They are obtained by means of an improved projector decoupling. On the background of logarithmic norms related to invariant subspaces, contractivity is considered. The asymptotical behaviour of approximations generated by the BDF as well as by IRK and PIRK methods is analyzed in some detail. In particular, under weaker invariance conditions than used by Hanke, Macana and Maerz (1998), it is shown that standard properties known from the case of regular ODEs like A-stability, B-stability etc. apply also to index-2 DAEs. Moreover, the same invariance condition permits index reduction by differentiating constraints and discretization to commute.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10053207
eng
Preprints aus dem Institut für Mathematik, Band 1999,2, 1999
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3315/1/2.pdf
10.18452/2663
http://edoc.hu-berlin.de/18452/3315
oai:edoc.hu-berlin.de:18452/90372020-03-07T04:14:34Zcom_18452_152com_18452_44col_18452_365textPublicationprimusopen_accessdoc-type:bookddc:510
Disjunctive decomposition for two-stage stochastic mixed-binary programs with random recourse
Lewis
Ntaimo
stochastic programming
random recourse
disjunctive decomposition
set convexification
cutting plane
510
This paper introduces disjunctive decomposition for two-stage mixed 0-1 stochastic integer programs (SIPs) with random recourse. Disjunctive decomposition allows for cutting planes based on disjunctive programming to be generated for each scenario subproblem under a temporal decomposition setting of the SIP problem.A new class of valid inequalities for mixed 0-1 SIP with random recourse is presented. In particular, valid inequalities that allow for sharing cut coefficients among scenario subproblems for SIP with random recourse but deterministic technology matrix and righthand side vector are obtained. The valid inequalities are used to derive a disjunctive decomposition method whose derivation has been motivatedby real-life stochastic server location problems with random recourse, which find many applications in operations research. Computational results with large-scaleinstances to demonstrate the potential of the method are reported.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-10086928
eng
Stochastic Programming E-Print Series, Band 2008,1, 2008
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/9037/1/1.pdf
10.18452/8385
http://edoc.hu-berlin.de/18452/9037
oai:edoc.hu-berlin.de:18452/152772020-03-07T04:36:06Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
Identifizierung und Charakterisierung evolutionär konservierter Komponenten des Protein-Translokationsapparates im Endoplasmatischen Retikulum
Hellmuth-Alexander
Meyer
Sec61
Signalpeptidase
ER-Transport
Sec63
Sec61
signalpeptidase
Translocation
Sec63
510
WE 3150
Im Gegensatz zur den monomeren Leaderpeptidasen der bakteriellen Plasmamembran bestehen die eukaryotischen Signalpeptidasen der ER-Membran aus einem heteromeren Protein-Komplex. In der Hefe S. cerevisiae setzt sich die Signalpeptidase aus den vier Membranproteinen Sec11p, Spc1p, Spc2p und Spc3p zusammen. Neben der zur prokaryontischen Leaderpeptidase homologen Untereinheit Sec11p wird auch Spc3p benötigt um die Spaltungsfunktion in der Zelle auszuüben. Die Deletion von SPC3 führt zu einer lethalen Akkumulation von sekretorischen Vorstufenproteinen in vivo, sowie zum Verlust der Spaltungsaktivität in vitro. Spc1p und Spc2p sind nicht essentiell für die Hefe. Für Spc2p konnte jedoch gezeigt werden, daß die Signalpeptidase über die Spc2p Untereinheit mit den b-Untereinheiten des Sec61-Komplexes und des Ssh1-Komplexes interagiert. Vermutlich wird es so dem Komplex ermöglicht, während des Translokationsprozesses engen Kontakt zu der im Translokationskanal befindlichen Signalsequenz aufzunehmen. Im zweiten Teil der Arbeit wurden neue Komponenten aus der ER Membran von Säugern aufgereinigt. Dabei wurde ein ribosomenfreier Sec61-Komplex entdeckt, der mit zwei weiteren Membranproteinen assoziiert ist. Die beiden neuen Membranproteine weisen Homologien zu essentiellen Untereinheiten des postranslational aktiven Sec-Komplexes der Hefe S. cerevisiae auf. Die Rolle des neu entdeckten Säugerkomplexes während der Proteintranslokation ist noch unbekannt, in der Arbeit werden mögliche Funktionen des Komplexes diskutiert.
In contrast to the monomer leaderpeptidase of the prokaryotic plasmamembrane, the eukaryotic signalpeptidase of the ER-membrane is a heteromer protein complex. In yeast the signalpeptidase consist of the four subunits Sec11p, Spc1p, Spc2p and Spc3p. Additional to Sec11p also Spc3p is essential for cell growth and cell life. The depletion of Spc3p cause lethal accumulation of precursor proteins in vivo and lost of cleavage activity in vitro. Spc1p and Spc2p are not essential for the cell. We show here, that the Spc2p subunit interacts with the ß-subunits of the Sec61- and the Ssh1-complex. These data implicate that Spc2p facilitates the interactions between different components of the translocation site. In yeast, efficient protein transport across the endoplasmic reticulum (ER) membrane may occurco-translationally or post-translationally. The latter process is mediated by a membrane protein complex that consists of the Sec61p complex and the Sec62p-Sec63p subcomplex. In contrast, in mammalian cells protein translocation is almost exclusively co-translational. This transport depends on the Sec61 complex, which is homologous to the yeast Sec61p complex and has been identified in mammals as a ribosome-bound pore-forming membrane protein complex. We report here the existence of ribosome-free mammalian Sec61 complexes that associate with two ubiquitous proteins of the ER membrane. According to primary sequence analysis both proteins display homology to the yeast proteins Sec62p and Sec63p and are therefore named Sec62 and Sec63, respectively. The probable function of the mammalian Sec61-Sec62-Sec63 complex is discussed with respect to its abundance in ER membranes, which, in contrast to yeast ER membranes, apparently lack efficient post-translational translocation activity.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Enno
Hartmann
Ralf
Erdmann
Wolfgang
Lockau
2001-05-18
2017-06-18
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-10015266
ger
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
3
http://edoc.hu-berlin.de/download/18452/15277-flat-files.zip
10.18452/14625
http://edoc.hu-berlin.de/18452/15277
urn:nbn:de:kobv:11-10015257
urn:nbn:de:kobv:11-10015273
oai:edoc.hu-berlin.de:18452/90312020-03-07T04:14:33Zcom_18452_152com_18452_44col_18452_364textPublicationprimusopen_accessdoc-type:bookddc:510
Computations with Disjunctive Cuts for Two-Stage Stochastic Mixed 0-1 Integer Programs
Lewis
Ntaimo
Matthew W.
Tanner
stochastic programming
integer programming
disjunctive programming
lift-and-project cuts
510
Two-stage stochastic mixed-integer programming (SMIP) problems with recourse are generally difficult to solve. This paper presents a first computationalstudy of a disjunctive cutting plane method for stochastic mixed 0-1 programsthat uses lift-and-project cuts based on the extensive form of the two-stage SMIPproblem. An extension of the method based on where the data uncertainty appearsin the problem is made, and it is shown how a valid inequality derived for onescenario can be made valid for other scenarios, potentially reducing solution time.Computational results amply demonstrate the effectiveness of disjunctive cuts insolving several large-scale problem instances from the literature. The results arecompared to the computational results of disjunctive cuts based on the subproblemspace of the formulation and it is shown that the two methods are equivalentlyeffective on the test instances.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-10078813
eng
Stochastic Programming E-Print Series, Band 2007,7, 2007
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/9031/1/7.pdf
10.18452/8379
http://edoc.hu-berlin.de/18452/9031
oai:edoc.hu-berlin.de:18452/283532023-11-14T02:00:22Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersionddc:004textPublicationprimusopen_accessddc:510
The Lovász Number of Random Graphs
Amin
Coja-Oghlan
510
004
We study the Lovász number $\vartheta$ along with two related SDP relaxations $\vartheta_{1/2}$, $\vartheta_2$ of the independence number and the corresponding relaxations $\bar\vartheta$, $\bar\vartheta_{1/2}$, $\bar\vartheta_2$ of the chromatic number on random graphs $G_{n,p}$. We prove that $\vartheta,\vartheta_{1/2},\vartheta_2(G_{n,p})$ are concentrated about their means, and that $\bar\vartheta,\bar\vartheta_{1/2},\bar\vartheta_2(G_{n,p})$ in the case $p<n^{-1/2-\varepsilon}$ are concentrated in intervals of constant length. Moreover, extending a result of Juhász [28], we estimate the probable value of $\vartheta,\vartheta_{1/2},\vartheta_2(G_{n,p})$ for edge probabilities $c_0/n\leq p\leq 1-c_0/n$, where $c_0>0$ is a constant. As an application, we give improved algorithms for approximating the independence number of $G_{n,p}$ and for deciding $k$-colourability in polynomial expected time.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2023-11-13
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/28353-7
Combinatorics, Probability and Computing, Band 14, Ausgabe 4, Seite 439-465, 2005
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/28353/1/the-lovasz-number-of-random-graphs.pdf
10.18452/27695
10.1017/S0963548305006826
http://edoc.hu-berlin.de/18452/28353
oai:edoc.hu-berlin.de:18452/31742020-03-07T04:02:54Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Solvability Properties of Linear Elliptic Boundary Value Problems with Non-smooth Data
Lutz
Recke
510
In this paper linear elliptic boundary value problems of second order with non-smooth data (L∞-coefficients, Lipschitz domain, mixed boundary conditions) are considered. It is shown that the weak solutions are Hölder continuous and that they depend smoothly - in the sense of Hölder spaces - on the coefficients of the equation.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10050749
eng
Preprints aus dem Institut für Mathematik, Band 1994,3, 1994
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3174/1/3.pdf
10.18452/2522
http://edoc.hu-berlin.de/18452/3174
oai:edoc.hu-berlin.de:18452/163522020-03-07T04:40:51Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
Neurodynamische Module zur Bewegungssteuerung autonomer mobiler Roboter
Manfred
Hild
Robotik
Rekurrente Neuronale Netze
Neurodynamik
Neuromodul
Dynamische Systeme
Lernregel
Homöostase
Autonome Mobile Roboter
Humanoide Roboter
Bewegungssteuerung
Oszillator
Ringoszillator
Sensomotorische Schleife
Recurrent Neural Networks
Neurodynamics
Neuromodule
Dynamical Systems
Learning Rule
Homeostasis
Autonomous Mobile Robots
Humanoid Robots
Robotics
Motion Control
Oscillator
Ring Oscillator
Sensorimotor Loop
510
In der vorliegenden Arbeit werden rekurrente neuronale Netze im Hinblick auf ihre Eignung zur Bewegungssteuerung autonomer Roboter untersucht. Nacheinander werden Oszillatoren für Vierbeiner, homöostatische Ringmodule für segmentierte Roboter und monostabile Neuromodule für Roboter mit vielen Freiheitsgraden und komplexen Bewegungsabläufen besprochen. Neben dem mathematisch-theoretischen Hintergrund der Neuromodule steht in gleichberechtigter Weise deren praktische Implementierung auf realen Robotersystemen. Hierzu wird die funktionale Einbettung ins Gesamtsystem ebenso betrachtet, wie die konkreten Aspekte der zugrundeliegenden Hardware: Rechengenauigkeit, zeitliche Auflösung, Einfluss verwendeter Materialien und dergleichen mehr. Interessante elektronische Schaltungsprinzipien werden detailliert besprochen. Insgesamt enthält die vorliegende Arbeit alle notwendigen theoretischen und praktischen Informationen, um individuelle Robotersysteme mit einer angemessenen Bewegungssteuerung zu versehen. Ein weiteres Anliegen der Arbeit ist es, aus der Richtung der klassischen Ingenieurswissenschaften kommend, einen neuen Zugang zur Theorie rekurrenter neuronaler Netze zu schaffen. Gezielte Vergleiche der Neuromodule mit analogen elektronischen Schaltungen, physikalischen Modellen und Algorithmen aus der digitalen Signalverarbeitung können das Verständnis von Neurodynamiken erleichtern.
How recurrent neural networks can help to make autonomous robots move, will be investigated within this thesis. First, oscillators which are able to control four-legged robots will be dealt with, then homeostatic ring modules which control segmented robots, and finally monostable neural modules, which are able to drive complex motion sequences on robots with many degrees of freedom will be focused upon. The mathematical theory of neural modules will be addressed as well as their practical implementation on real robot platforms. This includes their embedding into a major framework and concrete aspects, like computational accuracy, timing and dependance on materials. Details on electronics will be given, so that individual robot systems can be built and equipped with an appropriate motion controller. It is another concern of this thesis, to shed a new light on the theory of recurrent neural networks, from the perspective of classical engineering science. Selective comparisons to analog electronic schematics, physical models, and digital signal processing algorithms can ease the understanding of neural dynamics.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Hans-Dieter
Burkhard
Frank
Pasemann
Ralf
Der
2007-09-21
2017-06-18
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-10084033
ger
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/16352/1/hild.pdf
10.18452/15700
http://edoc.hu-berlin.de/18452/16352
oai:edoc.hu-berlin.de:18452/34592020-03-07T04:03:14Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
On the intrinsic complexity of point finding in real singular hypersurfaces
Bernd
Bank
Marc
Giusti
Joos
Heintz
Luis-Miguel
Pardo
real polynomial equation solving
Computational complexity
singular hypersurface
510
In previous work we designed an efficient procedure that finds an algebraic sample point for each connected component of a smooth real complete intersection variety. This procedure exploits geometric properties of generic polar varieties and its complexity is intrinsic with respect to the problem. In the present paper we introduce a natural construction that allows to tackle the case of a non–smooth real hypersurface by means of a reduction to a smooth complete intersection.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-100193020
eng
Preprints aus dem Institut für Mathematik, Band 2009,12, 2009
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3459/1/12.pdf
10.18452/2807
http://edoc.hu-berlin.de/18452/3459
oai:edoc.hu-berlin.de:18452/89272020-03-07T04:14:11Zcom_18452_152com_18452_44col_18452_359textPublicationprimusopen_accessdoc-type:bookddc:510
Integration quadratures in discretization of stochastic programs
Teemu
Pennanen
Matti
Koivu
510
Because of its simplicity, conditional sampling is the most popular method for generating scenario trees in stochastic programming. It is based on approximating probability measures by empirical ones generated by random samples. Because of computational restrictions, these samples cannot be very large, so the empirical measures can be poor approximations of the original ones. This paper shows that modern integration quadratures provide a simple and an attractive alternative to random sampling. These quadratures are designed to give good approximations of given (probability) measures by a small number of quadrature points. The performance of the resulting scenario generation methods is demonstrated by numerical examples.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-10058449
eng
Stochastic Programming E-Print Series, Band 2002,11, 2002
other
Humboldt-Universität zu Berlin
Berlin
2
http://edoc.hu-berlin.de/download/18452/8927-flat-files.zip
10.18452/8275
http://edoc.hu-berlin.de/18452/8927
urn:nbn:de:kobv:11-10058458
oai:edoc.hu-berlin.de:18452/252342023-10-31T04:00:52Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
Brauer groups of moduli of hyperelliptic curves via cohomological invariants
Lorenzo, Andrea
Roberto
Pirisi
510
Using the theory of cohomological invariants for algebraic stacks, we compute the Brauer group of the moduli stack of hyperelliptic curves Hg over any field of characteristic 0. In positive characteristic, we compute the part of the Brauer group whose order is prime to the characteristic of the base field.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2022-04-27
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/25234-9
Forum of mathematics. Sigma, Band 9, 2021
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/25234/1/brauer-groups-of-moduli-of-hyperelliptic-curves-via-cohomological-invariants.pdf
10.18452/24562
10.1017/fms.2021.55
http://edoc.hu-berlin.de/18452/25234
oai:edoc.hu-berlin.de:18452/89322020-03-07T04:14:11Zcom_18452_152com_18452_44col_18452_359textPublicationprimusopen_accessdoc-type:bookddc:510
Frontiers of stochastically nondominated portfolios
Andrzej
Ruszczynski
Robert J.
Vanderbei
stochastic dominance
linear programming
Fenchel duality
mean-risk analysis
Portfolio optimization
least absolute deviations
parametric simplex method
robust statistics
510
We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose mean-risk models which are solvable by linear programming and generate portfolios whose returns are nondominated in the sense of second-order stochastic dominance. Next, we develop a specialized parametric method for recovering the entire mean-risk efficient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and realizations.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/8932-8
eng
Stochastic Programming E-Print Series, Band 2002,16, 2003
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/8932/1/16.pdf
10.18452/8280
http://edoc.hu-berlin.de/18452/8932
oai:edoc.hu-berlin.de:18452/101242020-03-07T04:17:40Zcom_18452_25col_18452_26doc-type:articletextPublicationprimusopen_accessddc:510
Adaptive Step-Size Control in Simulation of Diffusive CVD Processes
Jürgen
Geiser
Christian
Fleck
510
We present control strategies of a diffusion process for chemical vapor deposition for metallic bipolar plates. In the models, we discuss the application of different models to simulate the plasma-transport of chemical reactants in the gas-chamber. The contribution are an optimal control problem based on a PID control to obtain a homogeneous layering. We have taken into account one- and two-dimensional problems that are given with constraints and control functions. A finite-element formulation with adaptive feedback control for time-step selection has been developed for the diffusion process. The optimization is presented with efficient algorithms. Numerical experiments are discussed with respect to the diffusion processes of the macroscopic model.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-17
article
Text
publishedVersion
urn:nbn:de:kobv:11-100100541
Mathematical Problems in Engineering, Band Volume 2009, Seite 1-34, 2009
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/10124/1/23gWDe3c9t46o.pdf
doi:10.1155/2009/728105
10.18452/9472
http://edoc.hu-berlin.de/18452/10124
oai:edoc.hu-berlin.de:18452/89992020-03-07T04:14:26Zcom_18452_152com_18452_44col_18452_362textPublicationprimusopen_accessdoc-type:bookddc:510
Aggregation and Discretization in Multistage Stochastic Programming
Daniel
Kuhn
aggregation
stochastic programming
approximation
discretization
bounds
510
Multistage stochastic programs have applications in many areas and support policy makers in finding rational decisions that hedge against unforeseen neg- ative events. In order to ensure computational tractability, continuous-state stochastic programs are usually discretized; and frequently, the curse of dimensionality dictates that decision stages must be aggregated. In this article we construct two discrete, stage-aggregated stochastic programs which provide upper and lower bounds on the optimal value of the original problem. The approximate problems involve finitely many decisions and constraints, thus principally allowing for numerical solution.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-10059940
eng
Stochastic Programming E-Print Series, Band 2005,18, 2005
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/8999/1/18.pdf
10.18452/8347
http://edoc.hu-berlin.de/18452/8999
oai:edoc.hu-berlin.de:18452/183512020-03-07T04:50:20Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
Arithmetic intersections on modular curves
Miguel Daygoro Grados
Fukuda
Arakelovtheorie
Modulkurven
automorphe Formen
kanonische Greensche Funktion
Zetafunktionen
Arakelov theory
moduli problems
modular curves
automorphic forms
canonical Green’s function
zeta functions
510
SK 240
Eine wichtige Invariante von Modulkurven ist die arithmetische Selbstschnittzahl der relativ dualisierenden Garbe. Auf dem minimalen regulären Modell von X(N) ist diese Selbstschnittzahl durch den gewöhnlichen Schnitt einiger ausgezeichneter vertikaler Divisoren (dem geometrischen Beitrag) und durch die Auswertung der kanonischen Greenschen Funktion an einigen Spitzen (dem analytischen Beitrag) vollständig festgelegt. Das Ziel dieser Arbeit ist es, jeden dieser Beiträge in Abhängigkeit von der Stufe N zu bestimmen und das asymptotische Verhalten der Selbstschnittzahl zu studieren, wenn die Stufe N gegen unendlich geht.
An important invariant of modular curves is the arithmetic self-intersection of the relative dualizing sheaf. On the minimal regular model of X(N) this self-intersection is completely described by the usual intersection of some distinguished vertical divisors (geometric contribution) and the evaluation of the canonical Green’s function at certain cusps (analytic contribution). The aim of this thesis is to determine each of these contributions in terms of the level N and study the asymptotic behaviour of the self-intersection as N tends to infinity.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Jürg
Kramer
Anna-Maria von
Pippich
Bas
Edixhoven
2017-02-07
2017-06-18
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-100244093
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/18351/1/grados-fukuda.pdf
10.18452/17699
http://edoc.hu-berlin.de/18452/18351
oai:edoc.hu-berlin.de:18452/33462020-03-07T04:03:05Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
The characters of the generalized Steinberg representations of finite general linear groups on the regular elliptic set
Allan J.
Silberger
Ernst-Wilhelm
Zink
reductive group
general linear group
finite field
character
unitary representation
Steinberg representation
Whittaker vector
generic representation
510
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10053689
eng
Preprints aus dem Institut für Mathematik, Band 1999,10, 1999
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3346/1/10.pdf
10.18452/2694
http://edoc.hu-berlin.de/18452/3346
oai:edoc.hu-berlin.de:18452/287452024-01-18T02:00:32Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
Exploring the Unfolding of Dynamic Effects with Continuous-Time Models: Recommendations Concerning Statistical Power to Detect Peak Cross-Lagged Effects
Martin
Hecht
Steffen
Zitzmann
continuous-time modeling
cross-lagged effects
statistical power
time series
519
Cross-lagged panel models have been commonly applied to investigate the dynamic interplay of variables. In such discrete-time models, the size of the cross-lagged effects depends on the length of the time interval between the measurement occasions. Continuous-time modeling allows to explore this interval dependence of cross-lagged effects and thus to identify the maximal “peak” cross-lagged effects. To detect these peak effects, sufficient statistical power is needed. Based on results from a simulation study, we employed machine learning algorithms to identify a highly accurate prediction model. Results are incorporated into a Shiny App (available at https://psychtools.shinyapps.io/ContinuousTimePowerCalculation) for easy power calculations. Although limitations apply, our results might be helpful for study planning.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2024-01-17
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/28745-6
Structural equation modeling, Band 28, Ausgabe 6, Seite 894-902, 2021
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/28745/1/10.1080_10705511.2021.1914627.pdf
10.18452/28106
10.1080/10705511.2021.1914627
http://edoc.hu-berlin.de/18452/28745
oai:edoc.hu-berlin.de:18452/183492020-03-07T04:50:20Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
K-theoretic methods in the representation theory of p-adic analytic groups
Tamás
Csige
Reflexives Ideal
volltreu
Iwasawaalgebra
Grothendieckgruppe
Distributionalgebra
Reflexive ideal
completely faithful
Iwasawa algebra
Grothendieck group
Distribution algebra
510
SK 300
Sei G eine p-adische analytische gruppe, welche die direkte Summe einer torsionfreien p-adische analytische gruppe H mit zerfallender halbeinfacher Liealgebra und einer n-dimensionalen abelschen p-adische analytische gruppe Z ist. In Kapitel 3 zeigen wir folgenden Satz: Sei M ein endlich erzeugter Torsionmodul über der Iwasawaalgebra von G, welcher keine nichtrivialen pseudo-null-Untermoduln besitzt. Dann ist q(M), das Bild von M in der Quotientenkategorie Q, genau dann volltreu, wenn M als Modul über der Iwasawaalgebra von Z torsionsfrei ist. Hierbei bezeichne Q den Serre-Quotienten der Kategorie der Moduln über der Iwasawaalgebra von G nach der Serre-Unterkategorie der pseudo-null-Moduln. In Kapitel 4 zeigen wir folgenden Satz: Es bezeichne T die Kategorie, deren Objekte die endlich erzeugten Modulen über der Iwasawaalgebra von G sind, welche auch als Moduln über der Iwasawaalgebra von H endlich erzeugt sind. Seien M, N zwei Objekte von T. Wir nehmen an, dass M, N keine nichttrivialen pseudo-null-Untermoduln besitzen und q(M) in Q volltreu ist. Dann gilt: Ist [M]=[N] in der Grothendieckgruppe von Q, so ist das Bild von N ebenfalls volltreu. In Kapitel 5 zeugen wir folgenden Satz: Sei G eine beliebige p-adische analytische Gruppe, welche keine Element der Ordung p besitzt. Dann sind die Grothendieckgruppen der Algebra stetiger Distributionen und der Algebra beschränkter Distributionen isomorph zu c Kopien des Rings der ganzen Zahlen, wobei c die Anzahl der p-regulären Konjugationsklassen des Quotienten von G nach einer offenen uniformen pro-p-Untergruppe H bezeichnet.
Let G be a compact p-adic analytic group with no element of order p such that it is the direct sum of a torsion free compact p-adic analytic group H whose Lie algebra is split semisimple and an abelian p-adic analytic group Z of dimension n. In chapter 3, we show that if M is a finitely generated torsion module over the Iwasawa algebra of G with no non-zero pseudo-null submodule, then the image q(M) of M via the quotient functor q is completely faithful if and only if M is torsion free over the Iwasawa algebra of Z. Here the quotient functor q is the unique functor from the category of modules over the Iwasawa algebra of G to the quotient category with respect to the Serre subcategory of pseudo-null modules. In chapter 4, we show the following: Let M, N be two finitely generated modules over the Iwasawa algebra of G such that they are objects of the category Q of those finitely generated modules over the Iwasaw algebra of G which are also finitely generated as modules over the Iwasawa algebra of H. Assume that q(M) is completely faithful and [M] =[N] in the Grothendieck group of Q. Then q(N) is also completely faithful. In chapter 6, we show that if G is any compact p-adic analytic group with no element of order p, then the Grothendieck groups of the algebras of continuous distributions and bounded distributions are isomorphic to c copies of the ring of integers where c denotes the number of p-regular conjugacy classes in the quotient group of G with an open normal uniform pro-p subgroup H of G.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Elmar
Groÿe-Klönne
Peter
Schneider
Gergely
Zábrádi
2017-01-11
2017-06-18
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-100244059
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/18349/1/csige.pdf
10.18452/17697
http://edoc.hu-berlin.de/18452/18349
oai:edoc.hu-berlin.de:18452/252002022-08-15T07:42:09Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
Uniform sup-norm bounds for Siegel cusp forms
Antareep
Mandal
Siegelsche Modulformen
Kugelfunktionen
Wärmeleitungskern
Schranken für Supremumsnormen
Siegel modular forms
Spherical function
Heat kernel
Sup-norm bound
510
SK 340
Es sei Γ eine torsionsfreie arithmetische Untergruppe der symplektischen Gruppe Sp(n,R), die auf dem Siegelschen oberen Halbraum H_n vom Grad n wirkt. Wir betrachten den d-dimensionalen Raum der Siegelschen Spitzenformen vom Gewicht k zur Gruppe Γ, mit einer Orthonormalbasis {f_1,…,f_d}. In der vorliegenden Dissertation zeigen wir mit Hilfe des Wärmeleitungskerns, dass die Supremumsnorm von S_k(Z):=det(Y)^k (|f_1(Z)|^2+…+|f_d(Z)|^2) (Z∈H_n) für n=2 ohne zusätzliche Bedingungen und für n>2 unter Annahme einer vermuteten Determinanten-Ungleichung nach oben beschränkt ist. Wenn M:=Γ\H_n kompakt ist, dann ist die obere Schranke durch c_(n,Γ) k^{n(n+1)/2} gegeben. Wenn M nicht kompakt und von endlichem Volumen ist, dann ist die obere Schranke durch c_(n,Γ) k^{3n(n+1)/4} gegeben. In beiden Fällen ist c_(n,Γ) eine positive reelle Konstante, die nur vom Grad n und der Gruppe Γ abhängt. Wir zeigen weiter, dass die obere Schranke in dem Sinne gleichmäßig ist, dass bei fixierter Gruppe Γ_0 die Konstante c_(n,Γ) für Untergruppen Γ von endlichem Index nur vom Grad n und der Gruppe Γ_0 abhängt.
Let Γ be a torsion-free arithmetic subgroup of the symplectic group Sp(n,R) acting on the Siegel upper half-space H_n of degree n. Consider the d-dimensional space of Siegel cusp forms of weight k for Γ with an orthonormal basis {f_1,…,f_d}. In this thesis we show using the heat kernel method that for n=2 unconditionally and for n>2 subject to a conjectural determinant-inequality, the sup-norm of the quantity S_k(Z):=det(Y)^k (|f1(Z)|^2+…+|f_d(Z)|^2) (Z∈H_n) is bounded above by c_(n,Γ) k^{n(n+1)/2} when M:=Γ\H_n is compact and by c_(n,Γ) k^{3n(n+1)/4} when M is non-compact of finite volume, where c_(n,Γ) denotes a positive real constant depending only on the degree n and the group Γ. Furthermore, we show that this bound is uniform in the sense that if we fix a group Γ_0 and take Γ to be a subgroup of Γ_0 of finite index, then the constant c_(n,Γ) in these bounds depends only on the degree n and the fixed group Γ_0.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Jürg
Kramer
Anilatmaja
Aryasomayajula
Valentin
Blomer
2022-03-07
2022-04-25
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/25200-8
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/25200/5/dissertation_mandal_antareep.pdf
10.18452/24464
http://edoc.hu-berlin.de/18452/25200
oai:edoc.hu-berlin.de:18452/272332023-10-31T04:00:59Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
Non-tautological Hurwitz cycles
Carl
Lian
Mathematics, general
510
We show that various loci of stable curves of sufficiently large genus admitting degree d covers of positive genus curves define non-tautological algebraic cycles on Mg,N, assuming the non-vanishing of the d-th Fourier coefficient of a certain modular form. Our results build on those of Graber-Pandharipande and van Zelm for degree 2 covers of elliptic curves; the main new ingredient is a method to intersect the cycles in question with boundary strata, as developed recently by Schmitt-van Zelm and the author.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2023-05-12
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/27233-5
Mathematische Zeitschrift, Band 301, Ausgabe 1, Seite 173-198, 2021
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/27233/1/s00209-021-02903-7.pdf
10.1007/s00209-021-02903-7
10.18452/26537
http://edoc.hu-berlin.de/18452/27233
oai:edoc.hu-berlin.de:18452/89412020-03-07T04:14:13Zcom_18452_152com_18452_44col_18452_360textPublicationprimusopen_accessdoc-type:bookddc:510
Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints
Darinka
Dentcheva
Andrzej
Ruszczynski
Stochastic Programming
Duality
Stochastic Dominance
Optimality
Decomposition
510
We consider a new class of optimization problems involving stochastic dominance constraints of second order. We develop a new splitting approach to these models, optimality conditions and duality theory. These results are used to construct special decomposition methods.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/8941-8
eng
Stochastic Programming E-Print Series, Band 2003,7, 2004
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/8941/1/7.pdf
10.18452/8289
http://edoc.hu-berlin.de/18452/8941
oai:edoc.hu-berlin.de:18452/33522020-03-07T04:03:06Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Picard-Einstein Metrics and Class Fields Connected with Apollonius Cycle
Rolf-Peter
Holzapfel
A.
Piñeiro
N.
Vladov
unit ball
Kähler-Einstein metric
arithmetic group
Picard modular group
negative constant curvature
algebraic curves
moduli space
Shimura surface
Gauß lattice
510
We define Picard-Einstein metrics on complex algebraic surfaces as Kähler-Einstein metrics with negative constant sectional curvature pushed down from the unit ball via Picard modular groups allowing degenerations along cycles. We demonstrate how the tool of orbital heights, especially the Proportionality Theorem presented in [H98], works for detecting such orbital cycles on the projective plane. The simplest cycle we found on this way is supported by a quadric and three tangent lines (Apollonius configuration). We give a complete proof for the fact that it belongs to the congruence subgroup of level 1+i of the full Picard modular group of Gauß numbers together with precise octahedral- symmetric interpretation as moduli space of an explicit Shimura family of curves of genus 3. Proofs are based only on the Proportionality Theorem and classification results for hermitian lattices and algebraic surfaces.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10053743
eng
Preprints aus dem Institut für Mathematik, Band 1999,16, 1999
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3352/1/16.pdf
10.18452/2700
http://edoc.hu-berlin.de/18452/3352
oai:edoc.hu-berlin.de:18452/32442020-03-07T04:02:58Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
General Linear Methods for nonlinear DAEs in Circuit Simulation
Steffen
Voigtmann
differential-algebraic equations
Methods for differential-algebraic equations
Implicit equations
510
The Modified Nodal Analysis leads to differential algebraic equations with properly stated leading terms. In this article a special structure of the DAEs modelling electrical circuits is exploited in order to derive a new decoupling for nonlinear index-2 DAEs. This decoupling procedure leads to a solvability result and is also used to study general linear methods, a class of numerical schemes that covers both Runge-Kutta and linear multistep methods. Convergence for index-2 DAEs is proved.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10052262
eng
Preprints aus dem Institut für Mathematik, Band 2004,20, 2004
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3244/1/20.pdf
10.18452/2592
http://edoc.hu-berlin.de/18452/3244
oai:edoc.hu-berlin.de:18452/173372020-03-07T04:45:32Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
Variational methods for evolution
Matthias
Liero
Gradientenstrukturen
Gradientenflüsse
Wasserstein-Distanz
Reaktions-Diffusionssysteme
Gamma-convergence
Weighted-Energy-Dissipation-Funktionale
Dynamische Randbedingungen
Gamma-convergence
Gradient structures
Gradient flows
Wasserstein distance
Reaction-diffusion systems
Weighted-Energy-Dissipation functional
dynamic boundary conditions
510
SK 560
Das Thema dieser Dissertation ist die Anwendung von Variationsmethoden auf Evolutionsgleichungen parabolischen und hyperbolischen Typs. Im ersten Teil der Arbeit beschäftigen wir uns mit Reaktions-Diffusions-Systemen, die sich als Gradientensysteme schreiben lassen. Hierbei verstehen wir unter einem Gradientensystem ein Tripel bestehend aus einem Zustandsraum, einem Entropiefunktional und einer Dissipationsmetrik. Wir geben Bedingungen an, die die geodätische Konvexität des Entropiefunktionals sichern. Geodätische Konvexität ist eine wertvolle aber auch starke strukturelle Eigenschaft und schwer zu zeigen. Wir zeigen anhand zahlreicher Beispiele, darunter ein Drift-Diffusions-System, dass dennoch interessante Systeme existieren, die diese Eigenschaft besitzen. Einen weiteren Punkt dieser Arbeit stellt die Anwendung von Gamma-Konvergenz auf Gradientensysteme dar. Wir betrachten hierbei zwei Modellsysteme aus dem Bereich der Mehrskalenprobleme: Erstens, die rigorose Herleitung einer Allen-Cahn-Gleichung mit dynamischen Randbedingungen und zweitens, einer Interface-Bedingung für eine eindimensionale Diffusionsgleichung jeweils aus einem reinen Bulk-System. Im zweiten Teil der Arbeit beschäftigen wir uns mit dem sog. Weighted-Inertia-Dissipation-Energy-Prinzip für Evolutionsgleichungen. Hierbei werden Trajektorien eines Systems als (Grenzwerte von) Minimierer(n) einer parametrisierten Familie von Funktionalen charakterisiert. Dies erlaubt es, Werkzeuge aus der Theorie der Variationsrechung auf Evolutionsprobleme anzuwenden. Wir zeigen, dass Minimierer der WIDE-Funktionale gegen Lösungen des Ausgangsproblems konvergieren. Hierbei betrachten wir getrennt voneinander den Fall des beschränkten und des unbeschränkten Zeitintervalls, die jeweils mit verschiedenen Methoden behandelt werden.
This thesis deals with the application of variational methods to evolution problems governed by partial differential equations. The first part of this work is devoted to systems of reaction-diffusion equations that can be formulated as gradient systems with respect to an entropy functional and a dissipation metric. We provide methods for establishing geodesic convexity of the entropy functional by purely differential methods. Geodesic convexity is beneficial, however, it is a strong structural property of a gradient system that is rather difficult to achieve. Several examples, including a drift-diffusion system, provide a survey on the applicability of the theory. Next, we demonstrate the application of Gamma-convergence, to derive effective limit models for multiscale problems. The crucial point in this investigation is that we rely only on the gradient structure of the systems. We consider two model problems: The rigorous derivation of an Allen-Cahn system with bulk/surface coupling and of an interface condition for a one-dimensional diffusion equation. The second part of this thesis is devoted to the so-called Weighted-Inertia-Dissipation-Energy principle. The WIDE principle is a global-in-time variational principle for evolution equations either of conservative or dissipative type. It relies on the minimization of a specific parameter-dependent family of functionals (WIDE functionals) with minimizers characterizing entire trajectories of the system. We prove that minimizers of the WIDE functional converge, up to subsequences, to weak solutions of the limiting PDE when the parameter tends to zero. The interest for this perspective is that of moving the successful machinery of the Calculus of Variations.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Alexander
Mielke
Ulisse
Stefanelli
Annegret
Glitzky
2012-12-07
2017-06-18
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-100207628
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/17337/1/liero.pdf
10.18452/16685
http://edoc.hu-berlin.de/18452/17337
oai:edoc.hu-berlin.de:18452/245462022-01-11T02:17:00Zcom_18452_25col_18452_26doc-type:articlestatus-type:publishedVersiontextPublicationprimusopen_accessddc:510
Strong pure infiniteness of crossed products
Eberhard
Kirchberg
Adam
Sierakowski
510
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2022-01-10
article
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/24546-8
Ergodic Theory and Dynamical Systems, Band 38, Ausgabe 1, Seite 220-243, 2018
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/24546/1/strong-pure-infiniteness-of-crossed-products.pdf
10.18452/23888
10.1017/etds.2016.25
http://edoc.hu-berlin.de/18452/24546
oai:edoc.hu-berlin.de:18452/205972023-10-31T04:01:00Zcom_18452_1col_18452_4textPublicationopen_accessdoc-type:bachelorThesisddc:510
The Influence of Terrorist Hotbeds on the Global Transformation of Terrorist Tactics
Anna Franziska
Bothe
Terrorismus
Clusteranalyse
gewichteter Jaccard-Koeffizient
Heatmaps
Hotbeds
kategorielle Datenanalyse
Ausbreitung terroristischer Taktiken
terrorism
cluster analysis
weighted Jaccard coefficient
heatmaps
hotbeds
categorial data analysis
global transformation of terrorist tactics
diffusion of terrorist tactics
Global Terrorism Database (GTD)
519
Das Interesse an wissenschaftlichen Arbeiten bezüglich der Ausbreitung von transnationalem Terrorismus wächst ständig. Dennoch gilt es wenig zur Verfügung stehende Literatur. Das Ziel dieser Arbeit ist die Untersuchung des Einflusses von Hotbeds auf die weltweite Veränderung terroristischer Taktiken. Die Veränderung und Ausbreitung dieser Taktiken wird anhand von Daten im Zeitraum 1977-2017 analysiert. Zwei verschiedene Clusteranalysen werden mit dem Ziel angewendet, ähnliche Beobachtungen zu identifizieren. Zusätzlich werden Heatmaps zur Visualisierung generiert, um die Ausbreitungen von Taktiken zu untersuchen. Die Kausalität von den beobachtbaren Mustern wird anschließend detailliert diskutiert. Darüber hinaus werden die Begriffe Hotbeds und Taktiken definiert und ein gewichteter Jaccard-Koeffizient vorgestellt. Außerdem werden Herausforderungen bei der Analyse von kategoriellen Daten beschrieben und mögliche Lösungsansätze diskutiert.
The interest in studies regarding the diffusion of transnational terrorism increases constantly. Nevertheless, the existing literature is scarce. The objective of the underlying thesis is to examine the influence of hotbeds on the global transformation of tactics. The transformation and diffusion of terrorist tactics is analyzed from 1977-2017. Two cluster analysis are applied with the objective to group similar observations. Afterwards, heatmaps are generated to visualize and demonstrate the diffusion of tactics. The causality of observed patterns is discussed in detail. Moreover, definitions for the terms hotbeds and tactics are given and a weighted Jaccard coefficient is introduced. Also challenges regarding the analysis of categorical data are presented and possible approaches to solve those difficulties are given.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Wolfgang Karl
Härdle
Weining
Wang
2019-02-18
2019-03-19
bachelorThesis
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/20597-4
eng
bachelor
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/20597/3/Bachelorthesis_Bothe_Anna.pdf
10.18452/19800
http://edoc.hu-berlin.de/18452/20597
oai:edoc.hu-berlin.de:18452/34852020-03-07T04:03:16Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Superspace calculation of the four-loop spectrum in N=6 supersymmetricChern-Simons theory
Matias
Leoni
Andrea
Mauri
Joseph A.
Minahan
Olof Ohlsson
Sax
Alberto
Santambrogio
Christoph
Sieg
Gabriele
Tartaglino-Mazzucchelli
510
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-100193498
eng
Preprints aus dem Institut für Mathematik, Band 2010,16, 2010
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3485/1/16.pdf
10.18452/2833
http://edoc.hu-berlin.de/18452/3485
oai:edoc.hu-berlin.de:18452/90732024-02-28T10:21:11Zcom_18452_152com_18452_44col_18452_369textPublicationprimusopen_accessdoc-type:bookddc:510
Gradient estimates for Gaussian distribution functions: Application to probabilistically constrained optimization problems
René
Henrion
probabilistic constraints
chance constraints
stochastic optimization
Gaussian distribution function
sensitivity of optimal values
510
We provide lower estimates for the norm of gradients of Gaussian distribution functions and apply the results obtained to a special class ofprobabilistically constrained optimization problems. In particular, it is shown how the precision of computing gradients in such problems can be controlled by the precision of function values for Gaussian distribution functions. Moreover, a sensitivity result for optimal values with respect to perturbations of theunderlying random vector is derived. It is shown that the so-called maximal increasing slope of the optimal value with respect to the Kolmogorov distance between original and perturbed distribution can be estimated explicitly fromthe input data of the problem.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-100199486
eng
Stochastic Programming E-Print Series, Band 2012,1, 2012
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/9073/1/1.pdf
10.18452/8421
http://edoc.hu-berlin.de/18452/9073
oai:edoc.hu-berlin.de:18452/162472020-03-07T04:40:22Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
Numerical treatment of the Black-Scholes variational inequality in computational finance
Karin
Mautner
Amerikanische Optionen
Variationsungleichung
Finite Element Diskretisierung
Fehleranalysis
American options
variational inequality
finite element discretisation
error analysis
510
In der Finanzmathematik hat der Besitzer einer amerikanische Option das Recht aber nicht die Pflicht, eine Aktie innerhalb eines bestimmten Zeitraums, für einen bestimmten Preis zu kaufen oder zu verkaufen. Die Bewertung einer amerikanische Option wird als so genanntes optimale stopping Problem formuliert. Erfolgt die Modellierung des Aktienkurses durch eine geometrische Brownsche Bewegung, wird der Wert einer amerikanischen Option durch ein deterministisches freies Randwertproblem (FRWP), oder einer äquivalenten Variationsungleichung (VU) auf ganz R in gewichteten Sobolev Räumen gegeben. Um Standardmethoden der Numerischen Mathematik anzuwenden, wird das unbeschränkte Gebiet zu einem beschränkten Gebiet abgeschnitten. Mit Hilfe der Fourier-Transformation wird eine Integraldarstellung der Lösung die den freien Rand explizit beinhaltet, hergeleitet. Mittels dieser Integraldarstellung werden Abschneidefehlerschranken bewiesen. Danach werden gewichtete Poincare Ungleichungen mit expliziten Konstanten bewiesen. Der Abschneidefehler und die gewichtete Poincare Ungleichung ermöglichen, einen zuverlässigen a posteriori Fehlerschätzer zwischen der exakten Lösung der VU und der semidiskreten Lösung des penalisierten Problems auf R herzuleiten. Eine hinreichend glatte Lösung der VU garantiert die Konvergenz der Lösung des penaltisierten Problems zur Lösung der VU. Ein a priori Fehlerschätzer für den Fehler zwischen der exakten Lösung der VU und der semidiskreten Lösung des penaltisierten Problems beendet die numerische Analysis. Die eingeführten aposteriori Fehlerschätzer motivieren einen Algorithmus für adaptive Netzverfeinerung. Numerische Experimente zeigen die verbesserte Konvergenz des adaptiven Verfahrens gegenüber der uniformen Verfeinerung. Der zuverlässige a posteriori Fehlerschätzer ermöglicht es, den Abschneidepunkt so zu wählen, dass der Gesamtfehler (Diskretisierungsfehler plus Abschneidefehler) kleiner als eine gegebenen Toleranz ist.
Among the central concerns in mathematical finance is the evaluation of American options. An American option gives the holder the right but not the obligation to buy or sell a certain financial asset within a certain time-frame, for a certain strike price. The valuation of American options is formulated as an optimal stopping problem. If the stock price is modelled by a geometric Brownian motion, the value of an American option is given by a deterministic parabolic free boundary value problem (FBVP) or equivalently a non-symmetric variational inequality (VI) on weighted Sobolev spaces on R. To apply standard numerical methods, the unbounded domain R is truncated to a bounded one. Applying the Fourier transform to the FBVP yields an integral representation of the solution including the free boundary explicitely. This integral representation allows to prove explicit truncation errors. Since the VI is formulated within the framework of weighted Sobolev spaces, we establish a weighted Poincare inequality with explicit determined constants. The truncation error estimate and the weighted Poncare inequality enable a reliable a posteriori error estimate between the exact solution of the VI and the semi-discrete solution of the penalised problem on R. A sufficient regular solution provides the convergence of the solution of the penalised problem to the solution of the VI. An a priori error estimate for the error between the exact solution of the VI and the semi-discrete solution of the penalised problem concludes the numerical analysis. The established a posteriori error estimates motivates an algorithm for adaptive mesh refinement. Numerical experiments show the improved convergence of the adaptive algorithm compared to uniform mesh refinement. The reliable a posteriori error estimate including explicit truncation errors allows to determine a truncation point such that the total error (discretisation and truncation error) is below a given error tolerance.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Carsten
Carstensen
Martin
Brokate
Ralf
Kornhuber
2006-12-15
2017-06-18
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-10075837
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/16247/1/mautner.pdf
10.18452/15595
http://edoc.hu-berlin.de/18452/16247
oai:edoc.hu-berlin.de:18452/32432020-03-07T04:02:58Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
On Artin's L-funcions. II: Dirichlet Coefficients
Florin
Nicolae
Zeta functions and $L$-functions of number fields
510
Let $K/\Q$ be a finite Galois extension, let $\chi$ be a character of the Galois group $G=\Gal(K/\Q)$ which does not contain the principal character, let $L_{ur}(s,\chi,K/\Q)$ be the unramified part of the corresponding Artin $L$-function, and let $$L_{ur}(s,\chi,K/\Q)^\frac{1}{\chi(1)}=\sum_{n=1}^\infty\frac{a_n}{n^s}$$ for $\Re(s)>1$. Then:\\ (i) The coefficients $a_n$ are algebraic numbers of the field $\Q(e^\frac{2\pi i}{|G|})$ and $|a_n|\leq 1$ for every $n\geq 1$ ;\\ (ii) The summatory function $\sum_{n\leq x}a_n$ is ${\bf o}(x)$ as $x\rightarrow\infty$.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10052253
eng
Preprints aus dem Institut für Mathematik, Band 2004,19, 2004
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3243/1/19.pdf
10.18452/2591
http://edoc.hu-berlin.de/18452/3243
oai:edoc.hu-berlin.de:18452/230272021-08-31T08:28:07Zcom_18452_1col_18452_2textPublicationopen_accessdoc-type:doctoralThesisddc:510
Adaptive least-squares finite element method with optimal convergence rates
Philipp
Bringmann
adaptive Netzverfeinerung
Adaptivität
AFEM
alternativer a posteriori Fehlerschätzer
inhomogene Dirichlet-Randbedingungen
diskrete Zuverlässigkeit
elliptische partielle Differentialgleichungen
expliziter residuenbasierter Fehlerschätzer
FEM
Finite Elemente Methoden
Least-Squares Finite Elemente Methode
lineare Elastizität
LSFEM
inhomogene Neumann-Randbedingungen
Poisson-Modellproblem
Quasi-Interpolation
Randdatenapproximation
separiertes Markieren
Stokes-Gleichungen
Randdatenapproximation
adaptive mesh-refinement
adaptivity
AFEM
alternative a posteriori error estimator
inhomogeneous Dirichlet boundary conditions
discrete reliability
elliptic partial differential equations
explicit residual-based error estimator
FEM
finite element method
least-squares finite element method
linear elasticity
LSFEM
inhomogeneous Neumann boundary conditions
Poisson model problem
quasi-interpolation
separate marking
Stokes equations
boundary data approximation
518
SK 910
Die Least-Squares Finite-Elemente-Methoden (LSFEMn) basieren auf der Minimierung des Least-Squares-Funktionals, das aus quadrierten Normen der Residuen eines Systems von partiellen Differentialgleichungen erster Ordnung besteht. Dieses Funktional liefert einen a posteriori Fehlerschätzer und ermöglicht die adaptive Verfeinerung des zugrundeliegenden Netzes. Aus zwei Gründen versagen die gängigen Methoden zum Beweis optimaler Konvergenzraten, wie sie in Carstensen, Feischl, Page und Praetorius (Comp. Math. Appl., 67(6), 2014) zusammengefasst werden. Erstens scheinen fehlende Vorfaktoren proportional zur Netzweite den Beweis einer schrittweisen Reduktion der Least-Squares-Schätzerterme zu verhindern. Zweitens kontrolliert das Least-Squares-Funktional den Fehler der Fluss- beziehungsweise Spannungsvariablen in der H(div)-Norm, wodurch ein Datenapproximationsfehler der rechten Seite f auftritt. Diese Schwierigkeiten führten zu einem zweifachen Paradigmenwechsel in der Konvergenzanalyse adaptiver LSFEMn in Carstensen und Park (SIAM J. Numer. Anal., 53(1), 2015) für das 2D-Poisson-Modellproblem mit Diskretisierung niedrigster Ordnung und homogenen Dirichlet-Randdaten. Ein neuartiger expliziter residuenbasierter Fehlerschätzer ermöglicht den Beweis der Reduktionseigenschaft. Durch separiertes Markieren im adaptiven Algorithmus wird zudem der Datenapproximationsfehler reduziert.
Die vorliegende Arbeit verallgemeinert diese Techniken auf die drei linearen Modellprobleme das Poisson-Problem, die Stokes-Gleichungen und das lineare Elastizitätsproblem. Die Axiome der Adaptivität mit separiertem Markieren nach Carstensen und Rabus (SIAM J. Numer. Anal., 55(6), 2017) werden in drei Raumdimensionen nachgewiesen. Die Analysis umfasst Diskretisierungen mit beliebigem Polynomgrad sowie inhomogene Dirichlet- und Neumann-Randbedingungen. Abschließend bestätigen numerische Experimente mit dem h-adaptiven Algorithmus die theoretisch bewiesenen optimalen Konvergenzraten.
The least-squares finite element methods (LSFEMs) base on the minimisation of the least-squares functional consisting of the squared norms of the residuals of first-order systems of partial differential equations. This functional provides a reliable and efficient built-in a posteriori error estimator and allows for adaptive mesh-refinement. The established convergence analysis with rates for adaptive algorithms, as summarised in the axiomatic framework by Carstensen, Feischl, Page, and Praetorius (Comp. Math. Appl., 67(6), 2014), fails for two reasons. First, the least-squares estimator lacks prefactors in terms of the mesh-size, what seemingly prevents a reduction under mesh-refinement. Second, the first-order divergence LSFEMs measure the flux or stress errors in the H(div) norm and, thus, involve a data resolution error of the right-hand side f. These difficulties led to a twofold paradigm shift in the convergence analysis with rates for adaptive LSFEMs in Carstensen and Park (SIAM J. Numer. Anal., 53(1), 2015) for the lowest-order discretisation of the 2D Poisson model problem with homogeneous Dirichlet boundary conditions. Accordingly, some novel explicit residual-based a posteriori error estimator accomplishes the reduction property. Furthermore, a separate marking strategy in the adaptive algorithm ensures the sufficient data resolution.
This thesis presents the generalisation of these techniques to three linear model problems, namely, the Poisson problem, the Stokes equations, and the linear elasticity problem. It verifies the axioms of adaptivity with separate marking by Carstensen and Rabus (SIAM J. Numer. Anal., 55(6), 2017) in three spatial dimensions. The analysis covers discretisations with arbitrary polynomial degree and inhomogeneous Dirichlet and Neumann boundary conditions. Numerical experiments confirm the theoretically proven optimal convergence rates of the h-adaptive algorithm.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
Carsten
Carstensen
Eun-Jae
Park
Gerhard
Starke
2020-01-31
2021-01-29
doctoralThesis
Text
publishedVersion
urn:nbn:de:kobv:11-110-18452/23027-9
eng
thesis.doctoral
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/23027/1/dissertation_bringmann_philipp.pdf
10.18452/22350
http://edoc.hu-berlin.de/18452/23027
oai:edoc.hu-berlin.de:18452/89082020-03-07T04:14:07Zcom_18452_152com_18452_44col_18452_358textPublicationprimusopen_accessdoc-type:bookddc:510
A multi-stage stochastic integer programming approach for capacity expansion under uncertainty
Shabbir
Ahmed
Alan J.
King
Gyana
Parija
510
This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost functions to model the economies of scale in expansion costs, we develop a multi-stage stochastic integer programming formulation for the problem. A reformulation of the problem is proposed using variable disaggregation to exploit the lot-sizing substructure of the problem. The reformulation significantly reduces the LP relaxation gap of this large scale integer program. A heuristic scheme is presented to perturb the LP relaxation solutions to produce good quality integer solutions. Finally, we outline a branch and bound algorithm that makes use of the reformulation strategy as a lower bounding scheme, and the heuristic as an upper bounding scheme, to solve the problem to global optimality. Our preliminary computational results indicate that the proposed strategy has significant advantages over straightforward use of commercial solvers.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-10058161
eng
Stochastic Programming E-Print Series, Band 2001,5, 2001
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/8908/1/5.pdf
10.18452/8256
http://edoc.hu-berlin.de/18452/8908
oai:edoc.hu-berlin.de:18452/90942020-03-07T04:14:46Zcom_18452_152com_18452_44col_18452_371textPublicationprimusopen_accessdoc-type:bookddc:510
Dynamic Generation of Scenario Trees
Georg Ch.
Pflug
Alois
Pichler
stochastic optimization
decision trees
optimal transportation
510
We present new algorithms for the dynamic generation of scenario trees for multistagestochastic optimization. The different methods described are based on random vectors, whichare drawn from conditional distributions given the past and on sample trajectories.The structure of the tree is not determined beforehand, but dynamically adapted to meeta distance criterion, which insures the quality of the approximation. The criterion is built ontransportation theory, which is extended to stochastic processes.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-100220742
eng
Stochastic Programming E-Print Series, Band 2014,4, 2014
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/9094/1/4.pdf
10.18452/8442
http://edoc.hu-berlin.de/18452/9094
oai:edoc.hu-berlin.de:18452/31922020-03-07T04:02:55Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
Parametric Linear Complementarity Problems
Klaus
Tammer
510
We study linear complementarity problems depending on parameters in the right-hand side and (or) in the matrix. For the case that all elements of the right-hand side are independent parameters we give a new proof for the equivalence of three different important local properties of the corresponding solution set map in a neighbourhood of an element of its graph. For one- and multiparametric problems this equivalence does not hold and the corresponding graph may have a rather complicate structure. But we are able to show that for a generic class of linear complementarity problems depending linearly on only one real parameter the situation is much more easier.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10051048
eng
Preprints aus dem Institut für Mathematik, Band 1996,12, 1996
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3192/1/12.pdf
10.18452/2540
http://edoc.hu-berlin.de/18452/3192
oai:edoc.hu-berlin.de:18452/101002020-03-07T04:17:36Zcom_18452_25col_18452_26doc-type:articletextPublicationprimusopen_accessddc:510
Error estimates for finite volume element methodsfor convection–diffusion–reaction equations
Rajen K.
Sinha
Jürgen
Geiser
Convection–diffusion–reaction equation
Finite volume element method
Spatially discrete scheme
Discrete-in-time scheme
Error estimates
510
In this paper, we study finite volume element (FVE) method for convection–diffusion–reaction equations in a two-dimensional convex polygonal domain. These types of equations arise in the modeling of a waste scenario of a radioactive contaminant transport and reaction in flowing groundwater. Both spatially discrete scheme and discrete-in-time scheme are analyzed in this paper. For the spatially discrete scheme, optimal order error estimates in L2 and H1 norms are obtained for the homogeneous equation using energy method. Further, a quasi-optimal order error estimate in L∞ norm is shown to hold in an interior subdomain away from the corners. Based on backward Euler method, a time discretization scheme is discussed and related error estimates are derived.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-17
article
Text
publishedVersion
urn:nbn:de:kobv:11-10099085
Applied Numerical Mathematics, Band Volume 57, Ausgabe Issue 1, Seite 59-72, 2007
eng
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/10100/1/21tOrJGcEomGc.pdf
10.1016/j.apnum.2005.12.002
10.18452/9448
http://edoc.hu-berlin.de/18452/10100
oai:edoc.hu-berlin.de:18452/33962020-03-07T04:03:09Zcom_18452_66com_18452_45com_18452_5col_18452_68textPublicationprimusopen_accessdoc-type:bookddc:510
A Geometric Interpretation of Reduction in the Jacobians of C ab Curves
Régis
Blache
Jorge Estrada
Sarlabous
Maria
Petkova
Jacobian Varieties
Addition Law
Reduction Algorithm
C ab Curves
Projective Model
510
In this paper, we show that the reduction of divisors in the Jacobian of a curve $C$ can be performed by considering the intersections of a suitable projective model of $C$ with quadrics in projective space. We apply this idea to certain projective model of elliptic and hyperelliptic curves on one hand, and to the canonical model of $C_{ab}$ curves on the other hand, and we generalize (and recover) some well known algorithms.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-15
book
Text
publishedVersion
urn:nbn:de:kobv:11-10068034
eng
Preprints aus dem Institut für Mathematik, Band 2006,16, 2006
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/3396/1/16.pdf
10.18452/2744
http://edoc.hu-berlin.de/18452/3396
oai:edoc.hu-berlin.de:18452/90882020-03-07T04:14:45Zcom_18452_152com_18452_44col_18452_370textPublicationprimusopen_accessdoc-type:bookddc:510
Bidding in sequential electricity markets: The Nordic case
Trine Krogh
Boomsma
Nina
Juul
Stein-Erik
Fleten
stochastic programming
scenario generation
bidding
electricity markets
510
For electricity market participants trading in sequential markets with differences in price levels and riskexposure, coordinated bidding is highly relevant. We consider a Nordic power producer who engages inthe day-ahead spot market and the near real-time balancing market. In both markets, clearing prices anddispatched volumes are unknown at the time of bidding. However, in the balancing market, the agent facesan additional risk of not being dispatched. Taking into account the sequential clearing of these marketsand the gradual realization of market prices, we formulate the bidding problem as a multi-stage stochasticprogram. We investigate whether higher risk exposure can explain the hesitation, often observed in practice,to bid into the balancing market, even in cases of higher expected price levels. Furthermore, we quantify thegain from coordinated bidding, and by deriving bounds on this gain, assess the performance of alternativebidding strategies used in practice.
Humboldt-Universität zu Berlin
Berlin
Unter den Linden 6, 10099 Berlin
2017-06-16
book
Text
publishedVersion
urn:nbn:de:kobv:11-100211184
eng
Stochastic Programming E-Print Series, Band 2013,6, 2013
other
Humboldt-Universität zu Berlin
Berlin
1
https://edoc.hu-berlin.de/bitstream/18452/9088/1/6.pdf
10.18452/8436
http://edoc.hu-berlin.de/18452/9088
xMetaDissPlus///ddc:510/100