Das Forschungskolloquium betrachtet mathematische Themen tiefergreifend und differenziert. So soll ein Austausch über die mathematischen Spezialisierungen der verschiedenen Arbeitsgruppen am Institut und darüber hinaus gefördert werden. Außerdem sollen auch Studierende (hauptsächlich Master-Studierende) durch das Kolloquium die Gelegenheit erhalten, sich über spezifische Aspekte mathematischer Themen zu informieren.

Forschungskolloquium mit Herrn Prof. Dr. Johannes Moritz Jirak (Universität Wien)

"Cram\'{e}r-type moderate deviation principles, optimal transport and weak dependence"

Consider a stationary, weakly dependent sequence of random variables. Given only mild conditions, allowing for polynomial decay in correlation, we show Cram\'{e}r-type moderate deviation bounds with optimal rate $n^{-1/2}$. As an application, we derive non-uniform Berry-Esseen bounds with an optimal moment to weight-function relation $p \mapsto (1 + |x|)^{p}$ and rate $n^{-1/2}$. In addition, we also obtain rate-optimal bounds for the central limit theorem with respect to optimal transport distances $\mathrm{W}_q$, $q \geq 1$, where we bypass arguments based on higher order moment-matching like Edgeworth expansions or Stein's method in connection with Rio's inequality. The setup is quite general, and contains many prominent dynamical systems and time series models, including random walks on the general linear group and other slowly or quickly mixing dynamical systems arising from intermittent, logistic or nonuniformly hyperbolic maps, functionals of (augmented) Garch models of any order, functionals of dynamical systems arising from SDEs like the Langevin diffusion, iterated random functions and many more.
 
Mittwoch, 18.06.2025, 15:15 Uhr, Ulmenstr. 69, Haus 3, HS 125   
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Forschungskolloquium mit Herrn Dr. Paul-Albert Schneide (University of Copenhagen)

"Multi-linear tensor decomposition and constrained non-negative matrix factorization for data mining from instrumental analytical data"

Variants of multi-linear tensor decomposition and non-negative matrix factorization (NNMF) play an important role for extracting chemically meaningful information from instrumental data such as data acquired from chromatography hyphenated to mass spectrometry detectors. Multi-linear decomposition with the CP model can provide unique solutions to help overcome the factor ambiguity inherent to non-negative matrix factorization. However, the signals to be unmixed do not, in many cases, obey to the strict assumptions of multi-linearity which limits the chemical interpretability of the extracted factors. Therefore, new models are required that accommodate deviations from multi-linear behavior while ideally maintaining uniqueness. This talk will discuss challenges in modelling instrumental data with different matrix and tensor decomposition methods (such as CP, PARAFAC 2 and NNMF) and will introduce a novel approach for shift-invariant multi-linear decompositions.
 
Montag, 17.03.2025, 15:00 Uhr, Ulmenstr. 69, Haus 3, SR 228   
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Institutskolloquium mit Herrn Prof Dr. Konstantinos Spiliotis (Demokritus University of Thrace, Greece)

"Mathematical Modelling and Analysis of Neuronal Network Activity for Movement Disorders and Deep Brain Stimulation (DBS)"

Studying and exploring mechanisms in neuroscience, mathematical models and methods are powerful tools being complementary to medical experiments. In this work, recent developments of mathematical models and methods are presented which were done at the University of Rostock (under SFB 1270/2 -Elaine) to better understand movement disorders, i.e., Parkinson’s disease (PD) and Dystonia. The model contains parts of the cortex-thalamus-basal ganglia (CTBG) and striatum, forming a large-scale biophysical network. Using the mathematical model, we explore the network dynamics and the transition from healthy to Parkinsonian behaviour. 

Additionally, we studied the dynamics of the striatum area, which is central to motor and cognitive functions. The striatum model uses modified Hodgkin-Huxley dynamics for neurons and connectivity informed by a detailed human atlas. In this slow-fast complex system, different spatiotemporal activity patterns emerge during healthy and pathological states (neurological disorder), depending on the intensity of the cortical inputs. The equation-free approach enables a numerical analysis of the macroscopic dynamics of the striatum network,  including numerical bifurcation and stability analysis. Finally, the effect of deep brain stimulation on the spatiotemporal pattern formation in the network is discussed, and strategies for an efficient treatment are proposed.
 
Mittwoch, 15.01.2025, 15:15 Uhr, Ulmenstr. 69, Haus 3, HS 326/327   
→ Auch interessierte Studierende sind herzlich eingeladen.