Conveners
Poster session + káva: prezentácie vedeckých výsledkov FMFI UK Zamestnanci Matematika
- Zuzana Chladna
Advances in experimental biology increasingly provide time-resolved data that capture essential aspects of complex biological dynamics. Yet, uncovering how the underlying components interact remains a challenging inverse problem, requiring the separation of systematic behavior from stochastic fluctuations and measurement noise.
Among existing approaches, the method of Brückner et al. (2020)...
A system of two doubly nonlinear diffusion equations acting on two different rectangles in $\mathbb{R}^2$, connected by nonlinear boundary conditions on the contact line, is studied. The goal is to present numerical simulations of this coupled problem. We use a conservative finite-volume discretization in space and fully implicit time stepping with adaptive step sizes and adaptive damping. The...
The study of three-dimensional objects in school mathematics is frequently mediated through planar projections. For many students, however, these two-dimensional representations do not sufficiently support the development of accurate spatial imagery, making it difficult to mentally reconstruct the intended 3D structure. Recent advances in low-cost 3D printing technologies provide new...
We present selected results from the work in the topology group at KAG FMFI UK supported by the grant VEGA 1/0425/25. The main focus is on the results of the PhD student Ajay Raj, who defended his thesis in August 2025. His work is located in surgery theory which is a specific way of approaching classification problems of topological and smooth manifolds. His aim was to calculate the...
We introduce a stochastic model of cancer–immune coevolution, where mutations trigger effector responses. Simulations show that interactions impact outcomes (e.g. suppression), with implications for immunotherapy. We find signatures of selection in sequencing statistics such as the single-cell mutational burden distribution. (based on the paper: https://doi.org/10.7554/eLife.103970.3)
This presentation provides a statistical analysis of personality data based on the Diagnostic and Statistical Manual of Mental Disorders (DSM-5). Across three independent studies, we examine the psychometric and statistical properties of the instruments used to evaluate personality psychopathology. The first study tests the reliability and validity of the Structured Interview of Personality...
We introduce a birth–death model of neutral tumour evolution uniting summary statistics via dynamical matrices. We derive and solve recurrence relations to find analytical expressions for expected mutational distributions. We compare to known results and simulated data, validating our predictions. (based on the paper: https://doi.org/10.1371/journal.pcbi.1013241)
We prove the existence and uniqueness of periodic solutions of a first order differential equation
$$x'(t)=f(x(t))+x(\lfloor t \rfloor)g(t-\lfloor t \rfloor),\quad t\geq 0$$
that contains a piecewise constant term. Such equations admit periodic solutions and hence they can be used for numerical modelling of temperature changes in a space surrounded by environment with different...
Iterated function systems (IFSs) with probabilities have been investigated in various settings. In the simplest case, they can be interpreted as Markov chains. In this context, it was proved that for every continuous probability distribution $\mu$ with support in $\mathbb{R}$, there exists an IFS for which $\mu$ is the unique stationary distribution of the associated Markov chain. Moreover,...
Tento konferenčný príspevok je venovaný predstaveniu a zhodnoteniu spolupráce dvoch matematických pracovísk na Fakulte matematiky, fyziky a informatiky Univerzity Komenského v Bratislave (FMFI UK) s praktickou sférou. Katedra matematickej analýzy a numerickej matematiky a Katedra aplikovanej matematiky a štatistiky sú v priamom kontakte s desiatkami spoločností, ktoré pôsobia v rôznych...
