Related papers: Binary self-similar one-dimensional quasilattices:…
It is shown that every scalar linear quadrilateral lattice equation lies within a family of similar equations, members of which are compatible between one another on a higher dimensional lattice. There turn out to be two such families, a…
Modulated symmetries are internal symmetries that are not invariant under spacetime symmetry actions. We propose a general way to describe the lattice translation modulated symmetries in 1+1D, including the non-invertible ones, via the…
We develop a relational duality for semilattices with adjunctions (SLatas) based on binary meet-relations. First, we introduce the category of MoS-spaces and establish a dual equivalence with modal semilattices. Then, by means of…
The paper is concerned with the unsteady solutions to the model of mutually penetrating continua and quasilinear hyperbolic modification of the Burgers equation (QHMB). The studies were focused on the peculiar solutions of models in…
Machine-Learned Likelihoods (MLL) combines machine-learning classification techniques with likelihood-based inference tests to estimate the experimental sensitivity of high-dimensional data sets. We extend the MLL method by including Kernel…
Lattice QCD is notorious for its computational expense. Modern lattice simulations require large-scale computational resources to handle the large number of Dirac operator inversions used to construct correlation functions. Machine learning…
In this paper we consider a class of semihamiltonian systems characterized by the existence of a special conservation law. The density and the current of this conservation law satisfy a second order system of PDEs which has a natural…
Multi-task learning (MTL) has emerged as a pivotal paradigm in machine learning by leveraging shared structures across multiple related tasks. Despite its empirical success, the development of likelihood-based efficiently solvable…
This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…
Comparison principles are developed for discrete quasilinear elliptic partial differential equations. We consider the analysis of a class of nonmonotone Leray-Lions problems featuring both nonlinear solution and gradient dependence in the…
We study the promising idea of using dipolar molecular systems as analog quantum simulators for quantum link models, which are discrete versions of lattice gauge theories. In a quantum link model the link variables have a finite number of…
A novel technique using machine learning (ML) to reduce the computational cost of evaluating lattice quantum chromodynamics (QCD) observables is presented. The ML is trained on a subset of background gauge field configurations, called the…
We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…
We calculate the fusion rules among $\mathbb{Z}_2$-twisted modules $L_{\mathfrak{sl}_2}(\ell,0)$ at admissible levels. We derive a series MLDEs for normalized characters of ordinary twisted modules of quasi-lisse vertex algebras. Examples…
Curriculum learning can improve neural network training by guiding the optimization to desirable optima. We propose a novel curriculum learning approach for image classification that adapts the loss function by changing the label…
In this paper, we study the unimodular equivalence of sublattices in an $n$-dimensional lattice. A recursive procedure is given to compute the cardinalities of the unimodular equivalent classes with the indices which are powers of a prime…
We consider codes over the two semi-local non-unital rings of order six, \[ H_{23} = \langle a,b \mid 2a=0, 3b = 0, a^2=a, b^2 = 0, ab = 0 = ba \rangle,\] and \[H_{32} = \langle a,b \mid 2a=0, 3b = 0, a^2=0, b^2 = b, ab = 0 = ba \rangle. \]…
Quantum link models (QLMs) are generalizations of Wilson's lattice gauge theory formulated with finite-dimensional link Hilbert spaces. In certain cases, the non-Abelian Gauss Law constraint can be exactly solved, and the gauge invariant…
Using quasiparticle models and imposing thermodynamic consistency, lattice data for the equation of state of deconfined QCD can be mapped to finite chemical potential. We consider a refinement of existing simple massive quasiparticle models…
We consider the Quasilocal Quark Model of NJL type (QNJLM) as an effective theory of non-perturbative QCD including scalar (S), pseudoscalar (P), vector (V) and axial-vector (A) four-fermion interaction with derivatives. In the presence of…