The seminar takes place on Fridays, at 14:15 in SR 2.040.

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In order to receive e-mails about the Group seminar, please subscribe to the mailing list or send a short e-mail to cristian(at)iam.uni-bonn(dot)de (Iulia Cristian).
To be decided:

Seminar will take place at a different time on: April 26, June 07
We will choose a different day of the week for: May 31

Friday July 19

Speaker: Irina Alexandrova

Title: Stability tests for time delay systems: A delay Lyapunov matrix approach

In this talk, finite-dimensional necessary and sufficient Lyapunov stability tests developed recently for linear time delay systems of retarded and neutral types are discussed. The tests are expressed in terms of the delay Lyapunov matrix which naturally extends Lyapunov stability theory to the case of delay equations and determines the so-called Lyapunov—Krasovskii functionals with prescribed derivatives. The key factor ensuring the finite dimension of the criteria for a class of infinite-dimensional systems is the use of a special Razumikhin-type set of functions in the context of bounding the functionals. Stability tests based on various discretization schemes for either argument or kernels of the Lyapunov—Krasovskii functionals are presented, and finding a balance between the structure and the dimension of the stability criteria is discussed.

Title: Periodicities hidden in a random noise and response functions

Motivated by the discussions of the information hidden in response functions for
linear dynamical systems, we consider a parametric joint detection-estimation problem
for discrete signals with periodicities and an additive random noise. The number
of periodicities, their frequencies and amplitudes, as well as the distribution of the
i.i.d. random noise are assumed to be unknown. We show that under rather mild
assumptions the deterministic part of the signal can be recovered by a sequence of
strongly consistent estimators. The results are applicable to certain cases where the
random noise has a heavy-tailed distribution. The proof of consistency of estimators
relies on the convergence theory for random Fourier series. The talk is based primarily
on the joint paper with Jürgen Prestin.

Title: Criticality of the Sedimentation problem: Mean-field limits for randomly distributed particles with singular interaction

Recent years have seen tremendous progress regarding the derivation of effective models for sedimentation, in particular the transport-Stokes equation, from microscopic models. The strategy is usually to approximate the interaction of the microscopic particles through the fluid, which is very implicit and non-binary, by an explicit binary, albeit singular, interaction. In a second step one can use mean-field results for such explicit systems to conclude. However, this strategy requires good control of the minimal distance between the particles whence all known results require some unphysical condition on the scaling of the minimal distance of the particles. After reviewing some of the results, I will show how to overcome this limitation in the case of binary interacting systems with a non-attracting kernel and singularity just below the one of sedimentation. This is based on joint work with Richard Höfer (Regensburg).

Friday June 21

Speaker: Konstantinos Zemas

Title: Homogenization of Nonlinear Dirichlet Problems in randomly perforated domains via Γ-convergence

In this talk I would like to discuss the convergence of integral functionals with $q$-growth in a
randomly perforated domain of $R^n$, with $1 < q < n$. Assuming that the perforations
are small balls whose centres and radii are generated by a stationary short-range marked point
process, we obtain in the critical-scaling limit an averaged analogue of the nonlinear capacitary
term obtained by Ansini and Braides in the deterministic periodic case.

The geometry of the admissible randomly perforated sets is in direct analogy to the setting introduced by Giunti, Höfer, and Velázquez to study the linear Poisson equation, i.e., we essentially only require that the random radii have finite $(n − q)$-moment. Although this does not exclude the presence
of balls with large radii that can cluster up, we show that the critical rescaling of the perforations is sufficient to ensure that no percolating-like structures appear in the limit.

This is joint work with L. Scardia, C. I. Zeppieri.

Friday June 7, time: 11:30

Speaker: Eugenia Franco

Title: A stochastic version of the Hopfield-Ninio kinetic proofreading model

In this talk, I will describe a stochastic version of the Hopfield-Ninio kinetic proofreading model, introduced in the 1970s to explain the extremely low number of errors in some biological processes, like
DNA transcription and mRNA translation. The model was then adapted by McKeithan in order to explain the capability of T-cells to discriminate between self-antigens and foreign antigens. The stochastic version of the model that I will present is characterized by means of two parameters, the unbinding time, which depends on the binding energy between a ligand and a receptor, and the number of times M that a ligand attaches to a receptor. I will show that, under suitable assumptions on the parameters, our model has an extreme specificity, i.e., it is capable to discriminate between different ligands, and a high sensitivity, i.e., the response of the system does not change in a significant manner for ranges of ligands varying within several orders of magnitude. Additional quantities, like the amount of energy used by the network or the time required to yield a response will also be
computed.

This work has been done in collaboration with Professor J. J. L. Velázquez.

Title: Dynamics of Extended Fermi Gases at High Density

In my talk, I will discuss the quantum evolution of many-body Fermi gases confined in arbitrarily large domains, focusing on a high-density/semiclassical scaling regime. I will show that, as the density approaches infinity, the many-body evolution of the reduced one-particle density matrix converges to the solution of the Hartree equation, with convergence rate depending on the density only. The result holds for short macroscopic times for non-relativistic particles, but extends to arbitrary times in the case of pseudo-relativistic dispersion.

Joint work with Marcello Porta and Benjamin Schlein.

Friday May 17

Speaker: Eugenia Franco

Title: Characterizing the detailed balance property by means of measurements in chemical networks

Many biological systems must spend energy in order to function.
Therefore, one of the most important features of a biochemical network is whether it satisfies the detailed balance property or not (i.e., whether it spends energy or not).
In this talk, we assume that the detailed knowledge of all the reactions taking place in biochemical networks is not available. As a consequence, it is not possible to determine if a network satisfies the detailed balance property or not by analyzing the chemical rates.
On the other hand, we assume that it is possible to measure the concentration R_{ij}(t) of a substance j at time t>0, after the injection of a substance i \neq j at time t=0. Similarly we assume that also the concentration R_{ji}(t) is available.
We will formulate a condition, involving Rij(t) and Rji(t), that is necessary, but not sufficient, for the detailed balance property to hold in the network.
Moreover, we will show that this necessary condition is also sufficient if a topological condition is satisfied, as well as a stability property that guarantees that the chemical rates are not fine-tuned.

The talk is based on a joint work with B. Kepka and J. J. L. Velázquez

Friday April 26 at 10:00

Speaker: Théophile Dolmaire

Title: Inelastic collapse of three particles in dimension $d\geq 2$

Title: Existence theory for a general class of stationary radiative transfer equations

The distribution of the temperature in a body where the heat is transmitted only by radiation can be studied using the radiative transfer equation (RTE). In this talk we consider the stationary RTE for absorption and scattering coefficients which can depend on both frequency and local temperature. The problem can be reformulated as an equivalent fixed-point equation for the temperature T. The main difficulty arises when we want to obtain compactness for the resulting non-linear problem involving exponentials of some integrals along straight lines. This requires a new compactness result for such operators. Moreover, when dealing with the full equation with both absorption/emission and scattering terms we have to combine the compactness result with the definition of suitable Green functions. This is joint work with Jin Woo Jang and Juan J.L. Velázquez.

News

Prof. Dr. Lisa Sauermann has been honored with the von Kaven Award 2023 for her outstanding scientific achievements. (16.11.2023)

Prof. Dr. Angkana Rüland has been awarded the Calderon Prize that is awarded every two years by the Inverse Problems International Association. (06.09.2023)

Prof. Dr. Karl-Theodor Sturm has been elected into the Academia Europaea. (28.06.2022)

Florian Schweiger erhielt den Hausdorff-Gedächtnispreis 2021 der Fachgruppe Mathematik für die beste Dissertation. Er fertigte die Dissertation unter der Betreuung von Prof. Stefan Müller an. Unter anderen wurde Vanessa Ryborz mit einem Preis der Bonner Mathematischen Gesellschaft für ihre von Prof. Sergio Conti betreute Bachelorarbeit ausgezeichnet. (18.01.2022)