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Mathematisches Kolloquium

  • Prof. Dr. Natalie Neumeyer (Universität Hamburg)

"Regressionsmodelle mit Transformation der Beobachtung"
Abstract: Vor der Anpassung eines Regressionsmodells an Daten wird in Anwendungen häufig die Beobachtungsvariable transformiert. Der Zweck der Transformation ist z.B. Schiefe oder Heteroskedastizität zu reduzieren. Oft wird dazu eine parametrische Klasse von Transformationen betrachtet, z.B. die Box-Cox-Transformationen. Datenbasiert soll die für die Daten am besten geeignete Transformation ausgewählt werden. Wir betrachten Profile-Likelihood-Schätzer des Transformationsparameters und passen ein nichtparametrisches Lokations-Skalen-Regressionsmodell an die transformierten Daten an. Wir stellen einen Test auf Gültigkeit des  semiparametrischen Transformations-Regressionsmodells vor. Dieser basiert auf einem geschätzten empirischen Prozess, für den wir schwache Konvergenz zeigen. Wir diskutieren weitere Anpassungstests unter Gültigkeit des Modells.
11.07.2016, 11:15 Uhr, HS 228 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. A. Meister

  • Prof. Dr. Hajo Holzmann (Philipps-Universität Marburg)

"Nonparametric identification and maximum likelihood estimation for hidden Markov models"
Abstract: Finite-state hidden Markov models (HMMs), also called Markov-dependent finite mixtures,  form a popular, frequently used model class for serially dependent observations with unobserved heterogeneity.
In this talk nonparametric identification and maximum likelihood estimation for finite-state HMMs are investigated. We obtain identification of the parameters as  well as the order of the Markov chain if the transition probability matrices have full-rank and are ergodic, and if the state-dependent distributions are all distinct, but not necessarily linearly independent. Based on this identification result, we develop nonparametric maximum likelihood estimation theory. First, we show that the asymptotic contrast, the Kullback-Leibler divergence of the hidden Markov model, identifies the true parameter vector nonparametrically as well. Second, for classes of state-dependent densities which are arbitrary mixtures of a parametric family, we show consistency of the nonparametric maximum likelihood estimator. Here, identification of the mixing distributions need not be assumed.
Consequences for a-posteriori clustering when using HMMs with state-dependent finite mixtures are also briefly discussed.
References
(1)Alexandrovich, G., Holzmann, H. and Leister, A. (2015) Nonparametric identification and maximum likelihood estimation for hidden Markov models. to appear: BIOMETRIKA
(2)Holzmann, H. and Schwaiger, F. (2015) Hidden Markov Models with state-dependent mixtures: Minimal representation, model testing and applications to clustering. Statistics and Computing 25, 1185-1200.
06.07.2016, 15:00 Uhr, Seminarraum 221 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. A. Meister

  • Doz. Dr. Arne Winterhof (Johann Radon Institut Linz)

"Über die Vorhersagbarkeit automatischer Folgen"
Abstract
24.06.2016, 15:00 Uhr, HS 125 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Konrad Engel

  • Prof. Dr. Anna Mercaldo (Universität Neapel (Italien))

"Sharp a priori estimates and uniqueness results for a class of nonlinear elliptic equations"
Abstract
15.06.2016, 15:00 Uhr, HS 326 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. F. Brock

  • Prof. Dr. Michael Neumann (Friedrich-Schiller-Universität Jena)

"Nichtparametrische Schätzung isotoner Funktionen"
Abstract: Wir betrachten das Problem des Schätzens einer isotonen Regressionsfunktion. Im univariaten Fall erreicht der isotone Kleinste-Quadrate-Schätzer die optimale Konvergenzrate, ohne dass ein Glättungsparameter (Bandbreite) adäquat eingestellt werden muss. In höheren Dimensionen ist jedoch nur die Konsistenz dieser naheliegenden Methode bekannt. Wir konzentrieren uns auf den multivariaten Fall und zeigen, dass eine Modifikation des isotonen Kleinste-Quadrate-Schätzers optimale Konvergenzraten erreicht.
09.06.2016, 17:00 Uhr, Hörsaal 125 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. A. Meister

  • Prof. Dr. Heiko Harborth (TU Braunschweig)

"Zum Pascalschen Dreieck"
Abstract: Im Zusammenhang mit dem klassischen Pascaldreieck werden offene Probleme mit Teillösungen vorgestellt: Häufigkeit von Binomialkoeffizienten - Teilbarkeit - Ungerade Zahlen in den ersten Zeilen - Primzahlkriterien - Anzahl von Einsen in einem verallgemeinerten Pascaldreieck - Fermat ähnliche Gleichungen - Steinhaus Dreiecke - Lineare Kombinationen in den Zeilen.        
01.06.2016, 15:00 Uhr, HS 228 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. H.-D. Gronau

  • Dr. Roman Glebov (Hebrew University of Jerusalem)

"Finitely forcible graphons and permutons"
Abstract: In extremal graph theory, we often consider large graphs that are in the limit uniquely determined by finitely many densities of their subgraphs. The corresponding limits (so-called graphons) are called finitely forcible. Motivated by classical results in extremal combinatorics as well as by recent developments in the study of finitely forcible graphons, Lovasz and Szegedy made some conjectures about the structure of such graphons. In particular, they conjectured that the topological space of typical points of every finitely forcible graphon is compact and finitely dimensional.
In this talk we give a brief overview about the corresponding results, and in particular show that these two conjectures are false. We will go into more details on one particular example, where a permuton (limit of permutations) is finitely forcible, but the corresponding graphon is not.           
25.05.2016, 15:00 Uhr, HS 228 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Konrad Engel

  • Prof. Dr. Volker Kühn (Uni Rostock, Institut für Nachrichtentechnik)

"Sampling and Reconstruction of Sparse Signals -- Compressed Sensing"          
18.05.2016, 15:00 Uhr, HS 228 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Achill Schürmann

  • Dr. Maryna Viazovska (HU Berlin)

"Solution of the sphere packing problem in 8 and 24 dimensions"
20.04.2016, 15:00 Uhr, HS 125 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Achill Schürmann

  • Prof.Dr. Gerd Christoph (Otto-von-Guericke Universität Magdeburg)

"Unterschiede im Zentralen Grenzwertsatz mit normaler und nicht-normaler stabiler Grenzverteilung"
Abstract
31.03.2016, 13:00 Uhr, HS 125 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. W.-D.Richter

  • JP Dr. Erik von Harbou (Laboratory of Engineering Thermodynamics, University of Kaiserslautern)

"Interaction of Reaction and Separation:
Mathematical Challenges in Experiments, Modelling, and Simulation"

Abstract: Reactive separation processes such as reactive absorption and reactive distillation are widely used in the chemical industries. Examples are scrubbing of CO2 from synthesis gas using aqueous solutions of amines as solvents or the synthesis of esters in reactive distillation columns. To develop energy and resource efficient processes, a careful design, scale-up, and optimisation of the processes is necessary. The key for that are process models that can describe the process and can predict its behaviour reliably.
Several examples will be presented in the talk that demonstrate the mathematical challenges that arise when reactive separation processes are investigated, modelled, and simulated. The examples range from the development of fast magnetic resonance imaging methods using compressed sensing to the description of a chromatographic fixed-bed reactor with a system of strongly coupled partial differential equations. A special focus of the talk will be the robust analysis of large numbers of NMR signals that are acquired for reaction and process monitoring.
24.02.2016, 16:00 Uhr, HS 228 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Klaus Neymeyr

  • Prof. Dr. Klaus Obermayer (TU-Berlin)

"Reward-based Learning and Decision Making"
Abstract:Reinforcement learning provides a framework for making agents learn policies by feedback (reward) about whether their actions or action sequences were successful or not. Reinforcement learning also provides a framework for understanding, how humans learn and decide given reward information only. Standard reinforcement learning assumes that good decisions / actions / policies are the ones which maximize expected reward as a proxy of success. Humans and animals, on the other hand, often do not behave this way, and there is ample evidence for multiple reward-based learning systems as well as for multiple factors influencing learning and decision making.

In my talk I will first address the interaction between stimulus-response and response-outcome learning in two tasks, where subjects are presented with both visual stimuli and rewards. One task involves implicit (shifts of covert visual attention) the other task explicit (button presses) decisions and actions. Using a model-based analysis I will show, how "bottom-up" stimulus and "top-down" reward information interact, and I will present signatures of these interactions in neural signals measured with EEG and fMRI.

Second I will address the interaction between risk and reward. I will present a new mathematical framework for including risk into reinforcement learning on Markov decision processes, and I will derive a risk-sensitive variant of the (model free) Q-learning scheme. The new framework is then applied to quantify the risk-sensitivity of human subjects playing a stock-market investment game.
20.01.2016, 15:00 Uhr, HS 125 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Konrad Engel

  • Dr. Francesco Chiacchio (Universität Neapel)

"An inverse spectral problem for the Hermite operator"
Abstract: We prove, generalizing already existing results for the bounded case, that, for any convex planar set Ω the first non-trivial Neumann  eigenvalue μ1(Ω) of the Hermite operator is greater than or equal to 1. Conversely, under some further assumptions on Ω, we show that if μ1(Ω)=1 then Ω is a strip. The study of the equality case requires, among other things, an asymptotic analysis of the eigenvalues of the Hermite operator in thin domains.
(Joint works with B. Brandolini, A. Henrot, D. Krejcirik and C. Trombetti)           
12.01.2016, 17:00 Uhr, HS 125 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Friedemann Brock

  • Prof. Dr.  Arnold Janssen (Heinrich-Heine-Universität Düsseldorf)

"Statistische Likelihoodverfahren in der Finanzmathematik"
Abstract: In dem Vortrag wird eine Brücke zwischen der Le Cam Theorie der Statistik und einigen Modellen der Finanzmathematik geschlagen. Damit erfahren Optionspreisformeln vom Black und Scholes Typ eine Interpretation als statistische Größen der Testtheorie. Weitere Anwendungen beziehen sich auf asymptotische Preisformeln und auf die Herleitung von Hedgingstrategien für spezielle Modelle.  
Literatur:
1) Janssen, A., Tietje, M. (2013). Applications of the Likelihood Theory in Finance: Modelling and Pricing. International Statistical Review 81, 107-133.
2) Janssen, A., Tietje, M. (2014). Statistical likelihood methods in finance. arXiv: 1310.4400.  
07.01.2016, 13:00 Uhr, HS 228 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. A. Meister

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