Related papers: On dummy variables of structure-preserving transfo…
The paper studies numerical methods that preserve a Lyapunov function of a dynamical system, i.e. numerical approximations whose energy decreases, just like in the original differential equation. With this aim, a discrete gradient method is…
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
We consider the tomography problem of recovering a covector field on a simple Riemannian manifold based on its weighted Doppler transformation over a family of curves $\Gamma$. This is a generalization of the attenuated Doppler transform.…
For a polynomial ring over a commutative ring of positive characteristic, we define on the associated de Rham-Witt complex a set of functions, and show that they are pseudovaluations in the sense of Davis, Langer and Zink. To achieve it, we…
In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several…
Certain criteria are demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms of that algebra. These are then used to establish a converse to recent results of Borchers and of…
Mimicry is a resemblance between species that benefits at least one of the species. It is a ubiquitous evolutionary phenomenon particularly common among prey species, in which case the advantage involves better protection from predation. We…
This paper mainly studies nonnegativity decision of forms based on variable substitutions. Unlike existing research, the paper regards simplex subdivisions as new perspectives to study variable substitutions, gives some subdivisions of the…
Representation learning seeks meaningful sensory representations without supervision and can model aspects of human development. Although many neural networks empirically learn useful features, a principled account of what makes a…
Calculating free energy differences is a topic of substantial interest and has many applications including molecular docking and hydration, solvation, and binding free energies which is used in computational drug discovery. However, in…
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the…
A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation, by means of its differential representation. The package provides functions which enable us to solve the determining…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
This paper presents the notion of a variation entropy. This concept is an entropy framework for the gradient of the solution of a conservation law instead of on the solution itself. It appears that all semi-norms are admissible variation…
To classify is to put things in meaningful groups, but the criteria for doing so can be problematic. Study of evolution of classification includes ontogenetic analysis of change in classification over time. We present an empirical analysis…
The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. As biological systems are generally not…
A brief review of the construction and classifiaction of the bicovariant differential calculi on quantum groups is given.
We formulate and prove relative versions of several classical decompositions known in the theory of Chevalley groups over commutative rings. As an application we obtain upper estimates for the width of principal congruence subgroups in…
This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use…
We consider the problem of extracting entropy by sparse transformations, namely functions with a small number of overall input-output dependencies. In contrast to previous works, we seek extractors for essentially all the entropy without…