Mathematics Research Center

Stability of (sub)critical nonlocal spatial branching processes with and without immigration

We consider the setting of either a general nonlocal branching particle process or a general nonlocal superprocess, in both cases, with and without immigration. Under the assumption that the mean semigroup has a Perron–Frobenious-type behaviour, as well as the existence of second...

Free probability via entropic optimal transport

Abstract Let $\mu $ μ and $\nu $ ν be compactly supported probability measures on ℝ, and let $\mu \boxplus \nu $ μ ⊞ ν denote their additive free convolution. We show that for all sufficiently large real $z$ z , $$ \int _{-\infty }^{\infty }\log (z - x) \, (\mu \boxplus \nu )( \m...

A multimedia encryption scheme based on a lightweight predator-prey simulation and chaotic dynamics

Current encryption systems face increasing challenges from ever more sophisticated attacks, motivating the exploration of alternative schemes that offer stronger security and higher performance. In this work, we propose a dynamic multimedia encryption system based on a lightweigh...

Back to the Future of qEEG: Lifespan Normative Modeling of Spectral Ratios and Functional Indices with Potential Applications to Therapeutic Monitoring

Quantitative EEG (qEEG) provides objective, millisecond-resolution measures of brain dynamics. Despite decades of methodological advances, clinically relevant derived indices-spectral power ratios, cognitive-emotional state markers, and physiological parameters-are typically repo...