Productivity issues such as lengthy compilation and limited code reuse have restricted usage of field-programmable gate arrays (FPGAs), despite significant technical advantages. Recent work into overlays -- virtual coarse-grained architectures implem...
Diffusion in complex heterogeneous media such as biological tissues or porous materials typically involves constrained displacements in tortuous structures and {\em sticky} environments. Therefore, diffusing particles experience both entropic (exclud...
Heavenly abelian varieties are abelian varieties defined over number fields that exhibit constrained $\ell$-adic Galois representations for some rational prime $\ell$. At the ICMS Workshop held in November 2024, we presented evidence for two finitene...
We present the scalar moduli stabilization from the perspective of the real intrinsic geometry. In this paper, we describe the physical nature of the vacuum moduli fluctuations of an arbitrary Fayet configuration. For finitely many abelian scalar fie...
In the {\em Musical Chairs} game $MC(n,m)$ a team of $n$ players plays against an adversarial {\em scheduler}. The scheduler wins if the game proceeds indefinitely, while termination after a finite number of rounds is declared a win of the team. At e...
We discuss the early evolution of ultrarelativistic heavy-ion collisions within a multi-fluid dynamical model. In particular, we show that due to the finite mean-free path of the particles compression shock waves are smeared out considerably as com...
We propose distributed link reversal algorithms to circumvent communication voids in geographic routing. We also solve the attendant problem of integer overflow in these algorithms. These are achieved in two steps. First, we derive partial and full l...
This document contains lecture notes from the Ph.D. course given at Scuola Superiore Meridionale by Daniele Di Pietro in February 2025. The goal of the course is to provide an overview of polytopal methods, focusing on the Hybrid High-Order (HHO) met...
Let $G$ be a finite group. To every smooth $G$-action on a compact, connected and oriented Riemann surface we can associate its data of singular orbits. The set of such data becomes an Abelian group $B_G$ under the $G$-equivariant connected sum. Th...
Let G be a finite group. To every smooth G-action on a compact, connected and oriented surface we can associate its data of singular orbits. The set of such data becomes an Abelian group B_G under the G-equivariant connected sum. We will show that...
We investigate Bethe Ansatz equations for the one-dimensional spin-$\frac{1}{2}$ Heisenberg XXX chain with a special interest in a finite system. Solutions for the two-particle sector are obtained. The ground state in antiferromagnetic case has bee...
In the window mean-payoff objective, given an infinite path, instead of considering a long run average, we consider the minimum payoff that can be ensured at every position of the path over a finite window that slides over the entire path. Chatterjee...
We show that there is a rational vector space $V$ such that, whenever $V$ is finitely coloured, there is an infinite set $X$ whose sumset $X+X$ is monochromatic. Our example is the rational vector space of dimension $\sup\{\aleph_0,2^{\aleph_0},2^{2^...
In this paper, we establish a condition on weighted graphs with finite measure that guarantees the validity of a global Poincaré inequality. This condition can be viewed as a discrete analogue of the criterion introduced by J. Boman in 1982 for Whit...
We analyze combined Quasi-Monte Carlo quadrature and Finite Element approximations in Bayesian estimation of solutions to countably-parametric operator equations with holomorphic dependence on the parameters as considered in [Cl.~Schillings and Ch.~S...
Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we identify the...
Few-nucleon correlations in nuclear matter at finite densities and temperatures are explored. Using the Dyson equation approach leads to effective few-body equations that include self energy corrections and Pauli blocking factors in a systematic wa...
The point at absolute zero where matter becomes unstable to new forms of order is called a quantum critical point (QCP). The quantum fluctuations between order and disorder that develop at this point induce profound transformations in the finite te...
Constant dimension codes are subsets of the finite Grassmann variety. The study of these codes is a central topic in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are defined as orbits of a su...
We give formulas, in terms of graph theoretical invariants, for the minimum distance and the generalized Hamming weights of the linear code generated by the rows of the incidence matrix of a signed graph over a finite field, and for those of its dual...