Mathematisches Kolloquium 2016
- Prof. Poul Hjorth (Technische Universität Dänemark)
"European Study Group with Industry"
30.11.2016, 13:15 Uhr, Raum 427 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Jens Starke - Prof. Dr. Danijel Krizmanic (University of Rijeka)
"Functional convergence of partial maxima processes"
Abstract: Let $(X_n)$ be a sequence of independent and identically distributed nonnegative random variables, and let $M_{n}= \max\{X_{1}, \ldots, X_{n}\}$ be its accompanying sequence of partial maxima. We present selected topics of the classical theory on functional convergence of the partial maxima stochastic processes $$M_{n}(t) = a_{n}^{-1} M_{\lfloor nt \rfloor}, \qquad t \in [0,1],$$ where $(a_{n})$ is a sequence of positive real numbers such that $n \mathrm{P} ( X_{1} > a_{n}) \to 1$ as $n \to \infty$. The convergence takes place in the space $D[0,1]$ endowed with the Skorohod $J_{1}$ topology, with the limit process being an extremal process. Here, $D[0, 1]$ denotes the space of real-valued right continuous functions on $[0,1]$ with left limits. We also present briefly some results on functional convergence under some weak dependence conditions on the sequence $(X_{n})$.
22.11.2016, 13:15 Uhr, SR 221 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof.Dr.W.-D.Richter - Assoc. Prof. Stefan Hoderlein (Boston College, USA)
"Triangular model with Random Coefficients"
Abstract: The triangular model is a very popular way to allow for causal inference in the presence of endogeneity. In this model, an outcome is determined by an endogenous regressor, which in turn is first caused by an instrument. In this paper, we study the triangular model with random coefficients and exogenous regressors in both equations. We establish non-identification of the joint distribution of the random coefficients, implying that counterfactual outcomes are also not identified. This result continues to hold, if we confine ourselves to the joint distribution of coefficients in the outcome equation or any marginal, except the one on the endogenous regressor. Identification continues to fail, even if we focus on means of random coefficients (implying that IV is generally biased), or let the instrument enter the first stage in a monotonic fashion. Based on this insight, we derive bounds on the joint distribution of random parameters, and suggest an additional restriction that allows to point identify the distribution of random coefficients in the outcome equation. We extend this framework to cover the case where the regressors and instruments have limited support, and analyze semi- and nonparametric sample counterpart estimators in finite! and large samples. Finally, we provide an application of the framework to consumer demand.
17.11.2016, 15:15 Uhr, SR 022 (Ulmenstraße 69, Haus 1)
Kolloquiumsleiter: Prof. Dr. A. Meister - Prof. Dr. Andrzej Zuk (Université Paris 7)
"Random walks on random symmetric groups"
Abstract: Finite simple groups are generated by two elements. Asymptotically almost surely a random choice of elements provides generators. We are interested in efficiency of generating symmetric and alternating groups in terms of mixing times. The results are based on expansion properties of certain random graphs.
26.10.2016, 15:15 Uhr, HS 228 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. J.-C. Schlage-Puchta - PD Dr. Gohar Kyureghyan (Otto-von-Guericke Universität Magdeburg)
"Special Monomial Maps: Examples, Classification, Open Problems"
Abstract: Numerous objects in coding theory, combinatorics or cryptology can be described as (or constructed from) special types of maps on finite fields. The first step in understanding maps with particular properties is the study of such monomial maps, which surprisingly often yield even optimal solutions.In this talk we describe monomial maps which were used to construct Kakeya sets in finite vector spaces. Further we survey progress on classification and constructions of monomial maps satisfying certain non-linearity criteria like being APN, crooked or planar.
15.09.2016, 15:00 Uhr, HS 125 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. K. Engel - Patrick Doetsch (RWTH Aachen)
"Sequence discriminative training in neural networks"
Abstract: Qualität von Sprach- und Handschrifterkennungssystemen wird üblicherweise durch die Wortfehlerrate gemessen. Dieses Fehlermaß wird allerdings während des Trainings nicht direkt optimiert, sondern durch lokale Optimalitätskriteria ersetzt. "Sequence discriminative training" erlaubt es, die Satzebene in die Optimierung einfließen zu lassen und ermöglicht direkt die Satzfehlerrate zu minimieren. In meinem Vortrag werde ich Vorteile und Probleme beim Umgang mit den am häufigsten verwendeten diskriminativen Trainingskriteria erläutern und aktuelle Ergebnisse aus der Handschrifterkennung präsentieren.
08.09.2016, 15:00 Uhr, HS 228 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. R. Labahn - Prof. Dr. Bahram Hemmateenejad (Shiraz University, Shiraz, Iran)
"On the dependency between principal components in spectroscopic monitoring of the evolutionary chemical processes"
Abstract: Principal component analysis (PCA) or factor analysis (FA) plays a central role in the most of chemometrics methods and it regards as the heart of chemometrics. There are many benefits in PCA for chemometricians; it reduces the data dimension dramatically and hence it lowers down the computation cost, it produces orthogonal variables, which are simpler to interpret and to work with them, it reduces the noise and last but not the least it can be used in describing the chemical process under study. Linear independency is one of the main feature of the PCs extracted by PCA. However, in some situations, they are not really independent.I will present the results of our recent investigation on the mutual association of PCs in PCA. We used two novel non-parametric measure of dependency, named maximal information coefficient (MIC) and distance correlation (DIC), to investigate the dependency between PCs. A lot of simulations were done to investigate different chemical evolutionary process including acid-base titration, complex formation, kinetics and chromatography. Some experimental data sets were also investigated. It was found that in the case of random design, there is not any dependency between PCs. However, in the evolutionary chemical process, in which correlated signals are created (i.e., the signal obtained at (i+1)th step is dependent on the signal obtained at ith step), they are dependent although they are not correlated. We meant that the Pearson correlation coefficients between PCs is always very low (close to zero). However, they are nonlinearly dependent. Interestingly, only PCs that carry systematic information are dependent and no significant association could be detected between a pair of noisy PCs or a pair of systematic and noisy PCs. Thus, the level of dependency could be used as an indication of the number of significant PCs. Finally, based on the combination of the measure of dependency using MIC and DIC and Eigen-value we suggested an indicator function for determination of the number of significant PCS.
23.08.2016, 11:00 Uhr, HS 327 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Klaus Neymeyr - 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