SPMS 2025

Session

Stochastic Monitoring Systems

Jun 20, 2025, 9:00 AM

Conveners

Stochastic Monitoring Systems

• Tomáš Hobza (FJFI CVUT)

Stochastic Monitoring Systems

• Václav Kůs (KM FJFI CVUT)

2. Dispersion of a point set

Matěj Trödler

6/20/25, 9:00 AM

This presentation addresses the mathematical concept of dispersion of a point set, defined as the volume of the largest axis-aligned empty box within the unit cube that avoids a given set of points. Dispersion, closely related to discrepancy, serves as a measure of uniformity in point distributions and has applications in numerical integration, optimization, machine learning, and computer...

11. Gamma linear mixed models for estimation of small area additive parameters

Vendula Rusá

6/20/25, 9:25 AM

This study presents an approach to predicting population means and poverty proportions in small area estimation using gamma mixed linear models. Extending the framework of (Hobza et al.,2020), which utilizes an inverse link function, we introduce a model based on a logarithmic link. Parameter estimation is carried out via maximum likelihood, employing the Laplace approximation. To estimate...

12. Implementation of a Monitoring Dashboard for the AMBER Experiment at CERN

Jan Chrastina

6/20/25, 9:50 AM

This presentation introduces the design and implementation of a monitoring dashboard for the AMBER experiment conducted at CERN. The goal of the project was to evaluate existing software solutions for IT infrastructure monitoring, analyze the requirements for a new monitoring system, and most importantly, develop and implement an optimal solution. The resulting system enables aggregation and...

14. Constrained Convolution Schema: A Deterministic Framework for Random Walks on Fractal Sets

František Gašpar (FJFI)

6/22/25, 11:20 AM

Random walks on fractal sets are central to modelling diffusion in complex systems, but traditional Monte Carlo simulations introduce stochastic noise and rely on averaging, often obscuring fine structural effects. We present a deterministic method, the constrained convolution schema for modelling random walks on sparse grids. Grounded in a standard Markovian framework, this approach yields an...

19. Dirichlet Forms and Soft Boundary Conditions in Discrete Potential Theory

Daniel Khol (Department of Mathematics)

6/22/25, 11:40 AM

This presentation introduces a novel framework of soft boundary conditions for discrete potential theory, where energetic preferences replace rigid constraints. We will show a "Quadratic Orbit Theorem" to calculate minimal energy under these conditions using sums over specifically defined soft orbits. This framework is then applied to a continuous double-well potential model. The Main theorem...

16. Explainable AI Models for Knowledge Assessment

Barbora Bumbálková

6/22/25, 12:00 PM

This presentation focuses on the use of explainable artificial intelligence methods in the context of knowledge testing, with a particular emphasis on Bayesian networks. Building on a research project originally conducted as part of a master's thesis, the aim was to demonstrate how these models can not only accurately assess students’ skills based on their responses but also provide clear and...

13. Numerical implementation of Singular Value Decomposition.

Ruslan Guliev

6/22/25, 12:15 PM

While SVD has been a cornerstone of numerical linear algebra for over a century, its efficient computation remains an active domain: Golub–Kahan bidiagonalisation, Jacobi and QR iterations, divide-and-conquer schemes, and modern randomized or block-Krylov variants now coexist with GPU-accelerated implementations. Each algorithm offers distinct trade-offs among accuracy, stability, memory...