Related papers: Lattice induced threshold functions and Boolean fu…
We propose to consider lattice monopoles in gluodynamics as continuum monopoles blocked to the lattice. In this approach the lattice is associated with a measuring device consisting of finite-sized detectors of monopoles (lattice cells).…
Within the path integral formalism, we derive exact expressions for correlation functions measuring the lattice charge induced by an electron and associated polarization in Frohlich polaron problem. We prove that a sum rule for the total…
We study functional clones, which are sets of non-negative pseudo-Boolean functions (functions $\{0,1\}^k\to\mathbb{R}_{\geq 0}$) closed under (essentially) multiplication, summation and limits. Functional clones naturally form a lattice…
We present a unified framework to study threshold functions for the existence of solutions to linear systems of equations in random sets which includes arithmetic progressions, sum-free sets, $B_{h}[g]$-sets and Hilbert cubes. In…
This article intends to characterize triangular norms on a finite lattice. We first give a method for generating a triangular norm on an atomistic lattice by the values of atoms. Then we prove that every triangular norm on a non-Boolean…
Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for vanishing flow velocity and at a singular value of the temperature. To that end, we…
We introduce and study finite lattice kinetic equations for bosons, fermions, and discrete NLS. For each model this closed evolution equation provides an approximate description for the evolution of the appropriate covariance function in…
We study systematically cross sections of probability preserving actions of unimodular groups and their associated transverse measures, and introduce the invariant \emph{intersection covolume} to quantify their periodicity. Our main…
We prove that functionality of compositions of top-down tree transducers is decidable by reducing the problem to the functionality of one top-down tree transducer with look-ahead.
Boolean-type algebra (BTA) is investigated. A BTA is decomposed into Boolean-type lattice (BTL) and a complementation algebra (CA). When the object set is finite, the matrix expressions of BTL and CA (and then BTA) are presented. The…
Occupation probabilities for primary-secondary-primary cell strings and correlation functions for primary sites of a decorated lattice model are expressed through the well-studied partition function and correlation functions of the Ising…
We consider complete lattices equipped with preorderings indexed by the ordinals less than a given (limit) ordinal subject to certain axioms. These structures, called stratified complete lattices, and weakly monotone functions over them,…
Application of a strong electric field to insulators induces a finite current. This phenomenon is called dielectric breakdown and is known as a fundamental nonequilibrium and nonlinear transport phenomenon in solids. Here, we study the…
A numerical simulation shows that the osmotic pressure of compressed lattice knots is a function of knot type, and so of entanglements. The osmotic pressure for the unknot goes through a negative minimum at low concentrations, but in the…
The breakdown of Hooke's law marks the onset of nonlinear behaviour: when displacements become large, restoring forces weaken and conventional proportionality fails. In quantum materials, intense optical excitation can drive the crystal…
Chang's lemma (Duke Mathematical Journal, 2002) is a classical result with applications across several areas in mathematics and computer science. For a Boolean function $f$ that takes values in {-1,1} let $r(f)$ denote its Fourier rank. For…
Using Ohkawa's theorem that the collection of Bousfield classes is a set, we perform a number of constructions with Bousfield classes. In particular, we describe a greatest lower bound operator; we also note that a certain subset DL of the…
Real-world machine learning applications may require functions that are fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for…
Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be…
Lattice Boltzmann methods are numerical schemes derived as a kinetic approximation of an underlying lattice gas. A numerical convergence theory for nonlinear convective-diffusive lattice Boltzmann methods is established. Convergence,…