Mathematical Institute of the Slovak Academy of Sciences

A Likelihood-Based Framework for Simultaneously Learning Both Noise and Growth Dynamics Using Biologically-Informed Neural Networks

In recent years, neural ordinary differential equation frameworks such as Biologically-Informed Neural Networks (BINNs) have shown promise for learning mechanistic laws from sparse data. However, most existing approaches implicitly assume homoscedastic Gaussian noise, and therefo...

The magneto-elastic instability of Kirchhoff rings

Abstract Understanding the interplay between electromagnetic forces and elasticity is a fundamental problem in the mechanics of deformable structures, particularly when electrical currents interact with magnetic fields to generate distributed body forces. A paradigm for this prob...

Lorentzian Gromov–Hausdorff convergence and pre-compactness

Abstract The goal of this paper is to introduce a notion of convergence à la Gromov–Hausdorff for Lorentzian spaces, based on 𝜀-nets formed by causal diamonds and depending solely on the time-separation function. This provides a geometric framework for convergence that applies bo...

The Fyodorov–Hiary–Keating conjecture on mesoscopic intervals

We derive precise upper bounds for the maximum of the Riemann zeta function on a typical short interval of the critical line. We show that for fixed θ∈(−1,0], large T, and y≥2 satisfying y=O(loglogT/logloglogT), the proportion of points t∈[T,2T] for which max|h|≤logθT|ζ(12+it+ih)...

How well does quantifying ‘capillary supply’ assess oxygen transport capacity in skeletal muscle?

Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

Tunable asymmetric swimming in biflagellate microswimmers

Many biological microswimmers can modulate their swimming gait to achieve directional control of motility, especially when performing steering towards specific directional cues. This can be achieved without the need for obvious morphological or structural asymmetries in the form...

Tame Symmetric Algebras of Period Four with Small Gabriel Quivers

The tame symmetric algebras of period four, TSP4 algebras for short, form an important class of algebras, with interesting connections to various branches of modern algebra. The study of this class has been recently developed in two major directions. The first embraces new classe...

Joint economic and epidemiological modelling of alternative pandemic response strategies

Abstract In an emerging pandemic, policymakers need to make decisions with limited information and require trade-offs between the health impact of the pandemic and the economic costs of the response. Most mathematical models have focused on direct health impacts, neglecting the e...

Orthogonality related to Steiner and Pappus chains

The focus of this paper is on the study of specific circle formations known as orthogonal Pappus chains and the related incidence results that involve points of tangency between the circles in the construction. Using circle inversion as a key tool, it is shown that these chains g...

The case for using flexible healthcare capacity constraints to optimize pandemic control strategies

Abstract During the COVID-19 pandemic, a key challenge was designing control strategies that balance the benefits and costs of public health measures while preventing healthcare systems from becoming overwhelmed. This was often addressed by epidemiological modellers by implementi...