​​Guessing the size of nano particles​.

​Nanoparticles, particles of sizes ranging from 1nm to 100nm, have a​ ​number of beneficial as well as possibly harmful properties. These​ ​properties not only depend on the material and on the concentration but​ ​also on the geometry, most notably on the size of the particles. Atomic​ ​absorption spectroscopy can detect all three characteristics, the​ ​elemental composition, the concentration and the size. The method works​ ​by vaporising the particles and shining a laser through the vapor. The​ ​resulting signal directly gives material and concentration, and if​ ​recorded as a time series even information on the particle size.​
I​f the sample consists of a mixture of different particle sizes, the​ ​signal less easy to read and recovering the particles sizes becomes a​ ​challenge. In a project with colleagues from the Institute of Analytical​ ​Chemistry we try to disentangle the signals in order to estimate the​ ​particle sizes.​

Data quality engineering: Main challenges and ways to solve them.

This presentation will provide an overview of practical experience in applying machine learning methods to address pressing contemporary scientific and engineering challenges. Particular attention will be devoted to the implementation of computer vision techniques aimed at fostering inclusivity and improving the quality of life for individuals with visual impairments. The proposed approaches demonstrate how intelligent image processing and real-time object recognition systems can enhance environmental awareness, navigation, and accessibility.
In addition, the presentation will examine the application of reinforcement learning algorithms to improve the efficiency and operational optimization of freight transportation within the railway sector. By leveraging adaptive decision-making models, it is possible to optimize routing strategies, resource allocation, and dynamic scheduling under uncertainty. The discussed solutions highlight the potential of data-driven and AI-based approaches to increase system performance, reduce operational costs, and support sustainable development in large-scale transportation networks.

Two lunch options are available on campus: the University Cafeteria and the Red Cross Cafeteria.

Utility maximization under endogenous pricing.

We study the expected utility maximization problem of a large investor who is allowed to make transactions on a tradable asset in an incomplete financial market with endogenous permanent market impacts. The asset price is assumed to follow a nonlinear price curve quoted in the market as the utility indifference curve of a representative liquidity supplier. We show that optimality can be fully characterized via a system of coupled forward-backward stochastic differential equations (FBSDEs) which is equivalent to a highly non-linear backward stochastic partial differential equation (BSPDE). We show existence and uniqueness solutions for FBSDEs in the case where the driver function of the representative market maker grows at least quadratic or the utility function of the large investor falls faster than quadratic or is exponential. Explicit examples are provided when the market is complete or the driver function is positively homogeneous.

A Statistical Method for Crack Pre-Detection in Large-Scale 3D Concrete CT Images.

This talk presents a statistical framework for crack pre-detection in large-scale 3D computed tomography images of concrete. The method combines a lightweight Maximal Hessian Entry filter, geometric descriptors computed on a regular spatial partition, and a spatial multiple testing procedure with explicit false discovery rate control, enabling reliable identification of crack regions in high-dimensional volumetric data while maintaining linear computational complexity and minimal dependence on annotated training data.

During the coffee break, water, coffee, tea, and light snacks will be available. 

Extinction of solutions for nonlinear parabolic equations.

My short talk will be focused to the study of some questions from qualitative theory of solutions to PDEs. Investigations are devoted to the study of the extinction–property of solutions in a finite time to initial-boundary value problems for a wide classes of nonlinear parabolic equations of the second and higher orders with a degenerate absorption potential a(x), whose presence plays a significant role for the mentioned nonlinear phenomena.

Generalized periodic solution of the linear implicit difference equation.

Consider a linear non-homogeneous difference equation of n-th order over an arbitrary ring. Often, it has no more than one solution in this ring, but this solution is difficult to find. In the case of rings with non-Archimedean topology, there is a rather narrow class of equations for which the uniqueness and existence of a solution can be proven and this solution can be written in the form of a series convergent under the topology under consideration. But there are also many equations for which nothing can be said for arbitrary inhomogeneity. We will consider the case of inhomogeneity given by some linear recurrent relation (let us call it generalized periodic). In this case, it can be proved that the solution, if it exists and is unique, is also generalized periodic. This makes it easy to find. If we consider an equation over the ring of integers, then we can use the Polya and Piso theorems on integer-valued functions to prove uniqueness, and then obtain the solution in explicit form.

Quasi-infinitely divisible distributions.

A quasi-infinitely divisible distribution is a probability distribution whose characteristic function can be written as the quotient of the characteristic functions of two infinitely divisible distributions. Equivalently, a probability distribution is quasi-infinitely divisible if and only if its characteristic function admits a Lévy-Khintchine representation with a "signed Lévy measure". In this talk we give some examples of quasi-infinitely divisible distributions and study some of their properties. The talk is based on joint works with Berger, Kutlu, Pan and Sato.

Model reduction for PDEs – Benefits, chances, limitations and challenges.

In many cases of practical interest, partial differential equations (PDEs) depend on parameters – one may think of coefficients, boundary conditions, material parameters or the geometry. Moreover, the PDE needs to be solved very often or in extremely short time for different parameter values. Such situations occur in optimization, uncertainty quantification (multi-query) or in situations where an approximate solution is needed extremely fast (realtime) or on devices with very limited capacity (embedded systems with low storage, CPU or energy demands).
In such situations, the reduced basis method (RBM) offers the chance to determine a reduced system in an offline training phase and then to solve the reduced system online extremely fast. Both training phase and online certification rely on a posteriori analysis, which provide (1) a reduced system with guaranteed accuracy and (2) a reduced online solution with a certified upper bound for the error.
In this talk, we will give an introduction into the RBM and show some applications where the RBM gives enormous speedup. We will also address the theoretical foundation leading to an understanding of chances and limitations of the RBM.

Two lunch options are available on campus: the University Cafeteria and the Red Cross Cafeteria.

Singular Limit Analysis of Training with Noise Injection.

Many training algorithms inject some form of noise during the training process. A classic example is mini-batch noise in stochastic gradient descent, but other examples include dropout, data augmentation, "noise nodes", "label noise", and input-data noise.
The additional noise is believed to improve generalization performance. However, there is little mathematical understanding of how this is achieved. In this talk, I will present a recent work (arXiv:2404.12293) with Mark Peletier (TU/e) and Anna Shalova (UvA) in which we analyze a fairly general class of iterative training schemes with noise injection. In the limit of small noise, we prove that the training process, appropriately rescaled in time, converges to solutions of an auxiliary evolution equation. The limit equation is a gradient flow driven by a functional for which we obtain an explicit expression, thus opening the door to understanding the different types of regularization generated by different types of noise injection.

Elastic Brownian Motions with Jumps and Delays.

We study an elastic Brownian motion on smooth domains, where the particle, instead of being killed at the boundary, restarts from a random position inside the domain. We characterize the process through its SDE and generator, and describe its invariant measure.
We then discuss possible applications in biophysics, in particular for modeling systems that escape from trapping mechanisms.
Moreover, we introduce another generalization of elastic Brownian motion, where the particle spends a non-exponential random time at the boundary before re-entering the domain with a reflection. This feature makes the dynamics non-Markovian.

During the coffee break, water, coffee, tea, and light snacks will be available.

Topological Tools in PAC Learning.

We are going to talk about a connection between PAC learning and topological combinatorics. In particular, we are going to discuss how the topological Radon theorem can be used to prove that some classes require at least exponential blowup in their VC dimension to be embedded into extremal ones. We will further discuss how it relates to the sample compression conjecture and how it fits into a broader topological perspective on PAC learning.
We assume no prior knowledge of neither learning theory nor topological combinatorics. In paricular, we will explain the PAC learning setup and the contents of the topological Radon theorem.

Introduction to artificial neural networks and their applications in structural analysis and modeling of polycrystalline materials.

Abstract

Participants are cordially invited to a conference dinner, where we can continue our discussions and enjoy a warm, friendly atmosphere.

A new description of uniformly spread discrete sets and its​ ​continuous analogue.

Let E be a discrete set in Euclidean space. Suppose that for each x, every shift E + x​ ​is boundedly close to E in some sense (we call this property "E is roughly​ ​shift-invariant"). Then E is a bounded perturbation of a cubic lattice.​
This result is a discrete analog of the following continuous result: if M is a positive​ ​measure such that every shift M + x is boundedly close to M in sense of the​ ​transportation distance, then M is boundedly close in the same sence to the​ ​Lebesgue measure, up to a constant.​

Distributed Computations Unified Mathematical Model For Dynamic and Static Analysis.

The migration of software from on-premises environments to cloud platforms has become a global trend in modern information technology. This shift poses new challenges for both software engineering and computer science, as distributed systems exhibit increased complexity, concurrency, and uncertainty compared to traditional on-premises applications. Ensuring correctness and efficiency in such systems is complicated by the difficulties of monitoring and analyzing distributed computing without disrupting its behavior. In the talk we will discuss a general approach that combines formal methods with simulation modeling to address these issues.

Two lunch options are available on campus: the University Cafeteria and the Red Cross Cafeteria.

Graph Neural Networks for Estimating Permeability in Models of Porous Media.

We study the problem of predicting the effective permeability of a porous medium from its binary microstructure. The reference permeability values are obtained by solving the discrete steady flow problem on the pore geometry. Each microstructure is represented by a graph that reflects pore connectivity, and a graph neural network is used to approximate the mapping from this graph representation to the effective permeability. In addition, for each geometry we compute a graph-based measure of tortuosity. These quantities are used to partition the dataset into different connectivity regimes and to examine the prediction error of the surrogate model, in particular near the percolation threshold. The numerical results show that the surrogate provides accurate predictions on the calibration domain, whereas under extrapolation the error increases, with the largest deviations observed in the vicinity of the transition region.

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On expand-contract plasticity of metric spaces.

A metric space (M, d) is called expand-contract plastic if every bijective non-expansive map F : M → M is an isometry. For now there is no simple characterization of plastic metric spaces. The talk is devoted to known partial results and open questions regarding the plasticity problem.

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During the coffee break, water, coffee, tea, and light snacks will be available. 

Filter theory applications in classical analysis.

Filter theory is a relatively young branch of mathematical science. It was proposed by a great french mathematician Henry Cartan in 1937 for studying non-metrizable spaces, where we cannot use classical analytical tools as convergence, limits etc. Using methods of filters we can obtain many fruitful results on non-metrizable spaces. Moreover, we can revise our knowledge on classical mathematical concepts, for example, derivative and defined integral. Using filters we can rewrite definitions of that concepts more generally. It allows us to obtain much more general results on derivative and defined integral theories.

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Constant mean curvature surfaces with harmonic Gauss maps in three-dimensional Lie groups.

A well-known result of E.A. Ruh and J. Vilms states that the Gauss map of a submanifold in the Euclidean space is harmonic if and only if its mean curvature vector field is parallel. The notion of the Gauss map can be naturally generalized to submanifolds in any Lie group G. It is known that a Gauss map of a hypersurface M in a Lie group with a bi-invariant metric is harmonic if and only if M has constant mean curvature (CMC). However, for general left-invariant metrics, this equivalence does not hold. For example, the class of CMC hypersurfaces in the (2m+1)-dimensional Heisenberg group with the harmonic Gauss map is rather narrow: such complete hypersurfaces are precisely cylinders over CMC hypersurfaces in the 2m-dimensional Euclidean space. We prove similar results for surfaces in different classes of threedimensional Lie groups. Namely, we give complete descriptions of connected CMC surfaces with harmonic left-invariant Gauss maps in unimodular groups endowed with left-invariant metrics that are also right-invariant with respect to one-dimensional Lie subgroups, as well as in the hyperbolic space. (Based on a joint work with Iryna Savchuk).

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