This paper presents an open-source software library that provides a set of finite-state transducer (FST) components and corresponding utilities for manipulating the writing systems of languages that use the Perso-Arabic script. The operations include...
We consider partitions of n-dimensional boxes in R^n, n>1, into a finite number of boxes with pairwise disjoint interiors. We study sets X \subseteq (0,\infty) with the Property (W_n): for every n-dimensional box P and every partition of P, if each...
Most of the approaches published in the literature to construct S-boxes via Cellular Automata (CA) work by either iterating a finite CA for several time steps, or by a one-shot application of the global rule. The main characteristic that brings toget...
Let G be a reductive complex Lie group with Lie algebra g. We call a subgroup H of G {\bf cramped} if there is an integer b(G,H) such that each finite dimensional representation of G has a non-trivial invariant subspace of dimension less than b(G,H...
Goldreich-Weber solutions constitute a finite-parameter of expanding and collapsing solutions to the mass-critical Euler-Poisson system. Two subclasses of this family correspond to compactly supported density profiles suitably modulated by the dynami...
Precise asymptotics for moderate deviation probabilities are established for open convex sets in both the finite- and infinite-dimensional settings. Our results are based on the existence of dominating points for these sets, a related representati...
Motivated by the results of Scott and Patel about "untangling" closed geodesics in finite covers of hyperbolic surfaces, we introduce and study primitivity, simplicity and non-filling index functions for finitely generated free groups. We obtain lowe...
Stable infiniteness, strong finite witnessability, and smoothness are model-theoretic properties relevant to theory combination in satisfiability modulo theories. Theories that are strongly finitely witnessable and smooth are called strongly polite a...
This paper is an MGM version of arXiv.org:1703.04266 and arXiv:1907.03364, and a follow-up to Section 5 of arXiv:1503.05523. In the setting of a commutative ring $S$ with a weakly proregular finitely generated ideal $J\subset S$, we consider the maxi...
We summarize the usual implementations of the large $N$ limit of $O(N)$ models and show in detail why and how they can miss some physically important fixed points when they become singular in the limit $N\to\infty$. Using Wilson's renormalization gro...
We perform a global renormalization group study of O(N) symmetric Wess-Zumino theories and their phases in three euclidean dimensions. At infinite N the theory is solved exactly. The phases and phase transitions are worked out for finite and infinite...
Let $ x\geq 1 $ be a large number, let $ [x]=x-\{x\} $ be the largest integer function, and let $ \varphi(n)$ be the Euler totient function. The asymptotic formula for the new finite sum over the primes $ \sum_{p\leq x}\varphi([x/p])=(6/π^2)x\log \l...
We have performed a direct numerical simulation of dilute turbulent particulate flow in a vertical plane channel, fully resolving the phase interfaces. The flow conditions are the same as those in the main case of "Uhlmann, M., Phys. Fluids, vol. 20,...
Let $G$ be a finite group and let $h$ be a positive integer. A $\text{BH}(G,h)$ matrix is a $G$-invariant $|G|\times |G|$ matrix $H$ whose entries are complex $h$th roots of unity such that $HH^*=|G|I_{|G|}$, where $H^*$ denotes the complex conjugate...
We present mathematical techniques for exhaustive studies of long-term dynamics of asynchronous biological system models. Specifically, we extend the notion of $κ$-equivalence developed for graph dynamical systems to support systematic analysis of a...
In this work we investigate the dynamics of inertial particles using finite-time Lyapunov exponents (FTLE). In particular, we characterize the attractor and repeller structures underlying preferential concentration of inertial particles in terms of F...
We investigate the finite dimensional dynamical system derived by Braden and Hone in 1996 from the solitons of $A_{n-1}$ affine Toda field theory. This system of evolution equations for an $n\times n$ Hermitian matrix $L$ and a real diagonal matrix $...
We present a formalism for Petri nets based on polynomial-style finite-set configurations and etale maps. The formalism supports both a geometric semantics in the style of Goltz and Reisig (processes are etale maps from graphs) and an algebraic seman...
If a rectangular diagram represents the trivial knot, then it can be deformed into the trivial rectangular diagram with only four edges by a finite sequence of merge operations and exchange operations, without increasing the number of edges, which wa...
This article studies the fundamental problem of separating two adhesive elastic fibers based on numerical simulation employing a recently developed finite element model for molecular interactions between curved slender fibers. Specifically, it covers...
A dicut in a directed graph is a cut for which all of its edges are directed to a common side of the cut. A famous theorem of Lucchesi and Younger states that in every finite digraph the least size of an edge set meeting every dicut equals the maximu...
Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set.
Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. The traditional way of
In this paper, we study the combinatorics of a certain minimal factorization of the elements in a finite lattice $L$ called the canonical join representation. The join $\bigvee A =w$ is the canonical join representation of $w$ if $A$ is the unique lo...
Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of propagation o...
Adding superconducting (SC) electron pairing via the proximity effect to pristinely non-superconducting materials can lead to a variety of interesting physical phenomena. Particular interest has recently focused on inducing SC into two-dimensional su...
Let $G = (V, E)$ be a finite simple graph. In this paper, we characterize the degree of the $h$-polynomial of the edge ideal of $G$ in terms of the independence number of $G$. The key tools are the value of the independence polynomial of $G$ at $-1$...
We offer a rationalization of the weak generalized axiom of revealed preference (WGARP) for both finite and infinite data sets of consumer choice. We call it maximin rationalization, in which each pairwise choice is associated with a "local" utility...
Suppose X is any finite complex with vanishing L^2 Betti number. We prove upper bounds on the Betti numbers for regular coverings of X, sublinear in the order of covering. The bounds are sensitive to the Novikov-Shubin invariants of X, and are impr...
The $g$-fan $Σ(A)$ of a finite dimensional algebra $A$ is a non-singular fan in its real Grothendieck group, defined by tilting theory. If the union ${\rm P}(A)$ of the simplices associated with the cones of $Σ(A)$ is convex, we call $A$ $g$-convex...
The family $\mathcal{OG}(4)$ consisting of graph-group pairs $(Γ, G)$, where $Γ$ is a finite, connected, 4-valent graph admitting a $G$-vertex-, and $G$-edge-transitive, but not $G$-arc-transitive action, has recently been examined using a normal q...
We prove several forms of renewal theorem tailored to renewal processes with marks and clusters. In particular, for an i.i.d. sequence $(ξ_i,X_i)_{i \geq 0}$, where $ξ_0$ denotes a finite point process on $\mathbb{R}$ and $X_0$ denotes a nonnegativ...
Let F be a set of relational trees and let Forbh(F) be the class of all structures that admit no homomorphism from any tree in F; all this happens over a fixed finite relational signature $σ$. There is a natural way to expand Forbh(F) by unary rel...
For a finite word $w$ we define and study the Kolmogorov structure function $h_w$ for nondeterministic automatic complexity. We prove upper bounds on $h_w$ that appear to be quite sharp, based on numerical evidence....
A quasi-automatic semigroup is a finitely generated semigroup with a rational set of representatives such that the graph of right multiplication by any generator is a rational relation. A asynchronously automatic semigroup is a quasi-automatic semigr...
A MAD (maximal almost disjoint) family is an infinite subset A of the infinite subsets of {0,1,2,..} such that any two elements of A intersect in a finite set and every infinite subset of {0.1.2...} meets some element of $å$ in an infinite set. A...
Quantum detailed balance is formulated in terms of elementary transitions, in close analogy to detailed balance in a classical Markov chain on a finite set of points. An elementary transition is taken to be a pure state of two copies of the quantum s...
Given a finite honest time, we first show that the associated Azéma optional supermartingale can be expressed as the drawdown and the relative drawdown of some local optional supermartingales with continuous running supremum. The relative drawdown r...
We studied pairing mechanism of the heavily electron doped FeSe (HEDIS) systems, which commonly have one incipient hole band -- a band top below the Fermi level by a finite energy distance $ε_b$ -- at $Γ$ point and ordinary electron bands at $M$ po...
A special spine of a three-manifold is said to be poor if it does not contain proper simple subpolyhedra. Using the Turaev-Viro invariants, we establish that every compact three-dimensional manifold M with connected nonempty boundary has a finite num...