Related papers: Method for searching higher symmetries for quad gr…
It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…
In this paper we discuss the integrability properties of a nonlinear partial difference equation on the square obtained by the multiple scale integrability test from a class of multilinear dispersive equations defined on a four points…
We carry out the generalized symmetry classification of polylinear autonomous discrete equations defined on the square, which belong to a twelve-parametric class. The direct result of this classification is a list of equations containing no…
This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that…
A complete classification of isotropic vector equations of the geometric type that possess higher symmetries is proposed. New examples of integrable multi-component systems of the geometric type and their auto-Backlund transformations are…
A quantum algorithm for combinatorial search is presented that provides a simple framework for utilizing search heuristics. The algorithm is evaluated in a new case that is an unstructured version of the graph coloring problem. It performs…
The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
The discrete heat equation is worked out in order to illustrate the search of symmetries of difference equations. It is paid an special attention to the Lie structure of these symmetries, as well as to their dependence on the derivative…
We study 2D discrete integrable equations of order 1 with respect to one independent variable and $m$ with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The…
A new layers method is presented for multipartite separability of density matrices from simple graphs. Full separability of tripartite states is studied for graphs on degree symmetric premise. The models are generalized to multipartite…
A method of classification of integrable equations on quad-graphs is discussed based on algebraic ideas. We assign a Lie ring to the equation and study the function describing the dimensions of linear spaces spanned by multiple commutators…
In the context of integrable systems on quad-graphs, the boundary consistency around a half of a rhombic dodecahedron, as a companion notion to the three-dimensional consistency around a cube, was introduced as a criterion for defining…
A set of fundamental matrices relating pairs of cameras in some configuration can be represented as edges of a "viewing graph". Whether or not these fundamental matrices are generically sufficient to recover the global camera configuration…
It is investigated how two (standard or generalized) $\lambda-$symmetries of a given second-order ordinary differential equation can be used to solve the equation by quadratures. The method is based on the construction of two commuting…
Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the…
We give a rational form of a generic two-dimensional "quad" map, containing the so-called $Q_4$ case, but whose coefficients are free. Its integrability is proved using the calculation of algebraic entropy.
We define an analytic version of the graph property testing problem, which can be formulated as studying an unknown 2-variable symmetric function through sampling from its domain and studying the random graph obtained when using the…
We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…