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A consistent approach to the description of integral coordinate invariant functionals of the metric on manifolds ${\cal M}_{\alpha}$ with conical defects (or singularities) of the topology $C_{\alpha}\times\Sigma$ is developed. According to…
This paper studies the properties of convergence of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semi-cyclic impulsive self-mappings on the union of a number of nonempty…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
The critical loci of a map $f:X\to Y$ between smooth schemes over a field $k$ are the locally closed subschemes $\Sigma^i(f)\subseteq X$ where the differential of $f$ has constant rank. We prove that if $f : X\to \mathbb A^r$ is the general…
We present theory and practice for robust implementations of bivariate Jacobi set and Reeb space algorithms. Robustness is a fundamental topic in computational geometry that deals with the issues of numerical errors and degenerate cases in…
This paper introduces a framework designed to accurately predict piecewise linear mappings of arbitrary meshes via a neural network, enabling training and evaluating over heterogeneous collections of meshes that do not share a…
Orbit-finite models of computation generalise the standard models of computation, to allow computation over infinite objects that are finite up to symmetries on atoms, denoted by $\mathbb{A}$. Set theory with atoms is used to reason about…
We study the numerical simulation of supersymmetric models having a local Nicolai map. The mapping can be regarded as a stochastic equation and its numerical integration provides an algorithm for the simulation of the original model. In…
Machine learning (ML) enables the development of interatomic potentials that promise the accuracy of first principles methods while retaining the low cost and parallel efficiency of empirical potentials. While ML potentials traditionally…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
Owing to the advances in computational techniques and the increase in computational power, atomistic simulations of materials can simulate large systems with higher accuracy. Complex phenomena can be observed in such state-of-the-art…
We present a physically motivated strategy for the construction of training sets for transferable machine learning interatomic potentials. It is based on a systematic exploration of all possible space groups in random crystal structures,…
We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…
Can high energy physics be simulated by low-energy, non-relativistic, many-body systems, such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in…
A number of physical systems exhibit a particular form of asymptotic conformal invariance: within a particular range of distances, they are characterized by a long-range conformal interaction (inverse square potential), the absence of…
Motivated by the definition of the smooth manifold structure on a suitable mapping space, we consider the general problem of how to transfer local properties from a smooth space to an associated mapping space. This leads to the notion of…
Spectral differentiations are basic ingredients of spectral methods. In this work, we analyze the pointwise rate of convergence of spectral differentiations for functions containing singularities and show that the deteriorations of the…
The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…
It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…