In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in relation to...
We describe a proof-of-concept development and application of a phase averaging technique to the nonlinear rotating shallow water equations on the sphere, discretised using compatible finite element methods. Phase averaging consists of averaging the...
Transient segregated finite-volume solver of the Biot equations for linear-elastic, small-strain deformation of a solid skeleton coupled with pore water flow and pressure governed by Darcy's law. (⭐ 2)
We investigate the problem of minimizing the excess generalization error with respect to the best expert prediction in a finite family in the stochastic setting, under limited access to information. We assume that the learner only has access to a lim...
We compute the low degree $\ell$-adic intersection cohomology of symplectic local systems on the Satake compactification of the moduli space $A_g$ of principally polarized abelian varieties. We prove that only a small finite list of irreducible Galoi...
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption of finite...
Future wireless networks are expected to adopt many different network technologies and architectures that promise to greatly enhance data rate and provide ubiquitous coverage for end users, all while enabling higher spectral efficiency. These benefit...
A new accurate analysis is presented for an OFDM-based multicast-broadcast single-frequency network (MBSFN). The topology of the network is modeled by a constrained random spatial model involving a fixed number of base stations placed over a finite a...
Over any partially ordered abelian group whose positive cone is closed in an appropriate sense and has finitely many faces, modules that satisfy a weak finiteness condition admit finite primary decompositions. This conclusion rests on the introductio...
ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but not quite the same
$\mathit{C}$-clones are polymorphism sets of so-called clausal relations, a special type of relations on a finite domain, which first appeared in connection with constraint satisfaction problems in [Creignou et al. 2008]. We completely describe the r...
Given a number field $k$, a finitely generated subgroup $\mathcal{A}\subseteq k^\times$, and an integer $n\geq 3$, we study the distribution of $S_n$-extensions of $k$ such that the elements of $\mathcal{A}$ are norms. For $n\leq 5$, and conjecturall...
We prove a structural result concerning the exit path category associated to a manifold $M$ equipped with a smooth action of a finite group $G$. Specifically, the functor $Π: \mathsf{Exit}(M) \rightarrow \mathsf{Exit}(M/G)$ is a right fibration and...
The theory of tournament limits and tournament kernels (often called graphons) is developed by extending common notions for finite tournaments to this setting; in particular we study transitivity and irreducibility of limits and kernels. We prove tha...
The theory of flows was used as a crucial tool in the recent proof by Margolis, Rhodes and Schilling that Krohn-Rhodes complexity is decidable. In this paper we begin a systematic study of aperiodic flows. We give the foundations of the theory of flo...
Inspired by the work of Izakhian and Rhodes, a theory of representation of hereditary collections by boolean matrices is developed. This corresponds to representation by finite $\vee$-generated lattices. The lattice of flats, defined for hereditary c...
We introduce homing vector automata, which are finite automata augmented by a vector that is multiplied at each step by a matrix determined by the current transition, and have to return the vector to its original setting in order to accept the input....
Dowling and Rhodes defined different lattices on the set of triples (Subset, Partition, Cross Section) over a fixed finite group G. Although the Rhodes lattice is not a geometric lattice, it defines a matroid in the sense of the theory of Boolean rep...
An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an infinite approx...
We study isometric actions of finitely presented groups on $\mathbb{R}$-trees. In this paper, we develop a relative version of the Rips machine to study $\textit{pairs}$ of such actions. An important example of a $\textit{pair}$ is a group action on...
Fix a finite set of points in Euclidean $n$-space $\euc^n$, thought of as a point-cloud sampling of a certain domain $D\subset\euc^n$. The Rips complex is a combinatorial simplicial complex based on proximity of neighbors that serves as an easily-c...
The Rips complex at scale r of a set of points X in a metric space is the abstract simplicial complex whose faces are determined by finite subsets of X of diameter less than r. We prove that for X in the Euclidean 3-space R^3 the natural projection m...
Selective Rips complexes corresponding to a sequence of parameters are a generalization of Vietoris-Rips complexes utilizing the idea of thin simplices. We prove that if a metric space $Y$ is close (in Gromov-Hausdorff distance) to a closed Riemannia...
Let $\mathscr{F}=(F_n)$ be a sequence of nonempty finite subsets of $ω$ such that $\lim_n |F_n|=\infty$ and define the ideal $$\mathcal{I}(\mathscr{F}):=\left\{A\subseteq ω: |A\cap F_n|/|F_n|\to 0~\mbox{as}~n\to \infty \right\}.$$ The case $F_n=\{1...
This paper presents predictions of the consequences of tongue surgery on speech production. For this purpose, a 3D finite element model of the tongue is used that represents this articulator as a deformable structure in which tongue muscles anatomy...
This report is mostly written for educational purposes. It is meant as a self contained introduction to regular languages, regular expressions, and regular expression matching by using Brzozowski derivatives. As such it is mostly based on the work by...
Rotationally coherent Lagrangian vortices (RCLVs) are identified from satellite-derived surface geostrophic velocities in the Eastern Pacific (180$^\circ$-130$^\circ$ W) using the objective (frame-invariant) finite-time Lagrangian-coherent-structure...
We find closed-form solutions to the stochastic game between a broker and a mean-field of informed traders. In the finite player game, the informed traders observe a common signal and a private signal. The broker, on the other hand, observes the trad...
We describe a significant update to the existing InvariantRing package for Macaulay2. In addition to expanding and improving the methods of the existing package for actions of finite groups, the updated package adds functionality for computing invari...
Recent experiments with Feshbach-resonant cesium Bose-Einstein condensates have led to unexplained molecule formation: a sudden switch of the magnetic field to its resonance value, followed by a finite hold time and another sudden switch to magneti...
We prove here that the Poincaré exponent of a geometrically finite group od isometries of the 3-dimensionnal hyperbolic space coincides with the Hausdorff dimension of its limit set. We also compare the natural measures supported by this set: the Pa...
We propose a combinatorial game on finite graphs, called Salmagundy, that is played by two protagonists, Dido and Mephisto. The game captures the logical structure of a proof of the resolution of singularities. In each round, the graph of the game is...
Stanley (1986) showed how a finite partially ordered set gives rise to two polytopes, called the order polytope and chain polytope, which have the same Ehrhart polynomial despite being quite different combinatorially. We generalize his result to a wi...
The existence of bistability in quantum optical systems remains a intensely debated open question beyond the mean-field approximation. Quantum fluctuations are finite-size corrections to the mean-field approximation used because the full exact soluti...
We give a finite presentation of the cobordism symmetric monoidal bicategory of (smooth, oriented) closed manifolds, cobordisms and cobordisms with corners as an extension of the bicategory of closed manifolds, cobordisms and diffeomorphisms. The gen...
For a finite group G, we introduce the complete suboperad $Q_G$ of the categorical G-Barratt-Eccles operad $P_G$. We prove that $P_G$ is not finitely generated, but $Q_G$ is finitely generated and is a genuine $E_\infty$ G-operad (i.e., it is $N_\inf...
We introduce a new five-parameter family of size distributions on the semi-finite interval $[x_0, \infty), x_0 \geqslant 0$, with two attractive features. First, it interpolates between power laws, such as the Pareto distribution, and power laws with...
We study the DC conductivity of a weakly disordered 2D electron gas with two bands and spectral nodes, employing the field theoretical version of the Kubo--Greenwood conductivity formula. Disorder scattering is treated within the standard perturbatio...
We investigate the finite-size scaling behavior of the conductivity in a two-dimensional Dirac electron gas within a chiral sigma model. Based on the fact that the conductivity is a function of system size times scattering rate, we obtain a two-param...
This work is devoted to the study of uncertainty principles for finite combinations of Hermite functions. We establish some spectral inequalities for control subsets that are thick with respect to some unbounded densities growing almost linearly at i...