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We propose Radiation Exposure Theory (RET), a mathematical framework to estimate biological damage caused by irradiation. This is an extension of LDM model which was proposed in the paper [Y. Manabe et al.: J. Phys. Soc. Jpn. 81,…
We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the…
The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices (n points). In this paper, we generalize many aspects of this situation. We introduce random shifts of…
Transactional data may be represented as a bipartite graph $G:=(L \cup R, E)$, where $L$ denotes agents, $R$ denotes objects visible to many agents, and an edge in $E$ denotes an interaction between an agent and an object. Unsupervised…
The subject of this thesis is the rigorous construction of QFT models with nontrivial interaction. Two different approaches in the framework of AQFT are discussed. On the one hand, an inverse scattering problem is considered. A given…
This article characterizes the exact asymptotics of random Fourier feature (RFF) regression, in the realistic setting where the number of data samples $n$, their dimension $p$, and the dimension of feature space $N$ are all large and…
We consider a model for a directed polymer in a random environment defined on a hierarchical diamond lattice in which i.i.d. random variables are attached to the lattice bonds. Our focus is on scaling schemes in which a size parameter $n$,…
The Generalized Elastic Model is a linear stochastic model which accounts for the behaviour of many physical systems in nature, ranging from polymeric chains to single-file systems. If an external perturbation is exerted \emph{only} on a…
Motivated by interpretability and reliability, we investigate whether large language models (LLMs) deploy universal geometric structures to encode discrete, graph-structured knowledge. To this end, we present two complementary experimental…
We consider the class of simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). For this class of graphs we determine the asymptotic behavior of the number of Eulerian orientations. In…
We review the effects of macromolecular crowding on the folding of RNA by considering the simplest scenario when excluded volume interactions between crowding particles and RNA dominate. Using human telomerase enzyme as an example, we…
Given $n,m\in \mathbb{N}$, we study two classes of large random matrices of the form $$ \mathcal{L}_n =\sum_{\alpha=1}^m\xi_\alpha \mathbf{y}_\alpha \mathbf{y}_\alpha ^T\quad\text{and}\quad \mathcal{A}_n =\sum_{\alpha =1}^m\xi_\alpha…
We construct representations of the Heisenberg algebra by pushing the perturbation expansion to high orders. If the multiplication operators $B_{1,2}$ tend to differential operators of order $l_{2,1}$, respectively, the singularity is…
We present a molecular modeling study analyzing nanometer-scale strain variations in graphene as a function of externally applied tensile strain. We consider two different mechanisms that could underlie nanometer-scale strain variations:…
We provide a perturbative expansion for the empirical spectral distribution of a Hermitian matrix with large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent…
We present some results on the proportion of permutations of length $n$ containing certain mesh patterns as $n$ grows large, and give exact enumeration results in some cases. In particular, we focus on mesh patterns where entire rows and…
Our aim is to predict how often genic and non-genic promoters fire within a cell. We first review a parsimonious pan-genomic model for genome organization and gene regulation, where transcription rate is determined by proximity in 3D space…
We consider the ensemble of N-dimensional random symmetric matrices A that have, in average, p non-zero elements per row. We study the asymptotic behavior of the norm of A in the limit of infinitely increasing N and p. We prove that the…
We investigate the renormalisation group effects induced on neutrino mass and mixing parameters in a triplet-extended minimal supersymmetric standard model where a vector-like pair of hypercharge $\pm 1$ triplet superfields is added. We…
A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in $d$ dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when…