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Mathematisches Kolloquium

  • 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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