Related papers: Discrete Morse functions for graph configuration s…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
One of approaches to quantum gravity is different models of a discrete pregeometry. An example of a discrete pregeometry on a microscopic scale is introduced. This is the particular case of a causal set. The causal set is a locally finite…
In this thesis, we study connections between metric and combinatorial graphs from a Dirichlet space point of view.
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
Conformal field theories have been extremely useful in our quest to understand physical phenomena in many different branches of physics, starting from condensed matter all the way up to high energy. Here we discuss applications of…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
Differential equations on metric graphs can describe many phenomena in the physical world but also the spread of information on social media. To efficiently compute the solution is a hard task in numerical analysis. Solving a design…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
How can sparse graph theory be extended to large networks, where algorithms whose running time is estimated using the number of vertices are not good enough? I address this question by introducing 'Local Separators' of graphs. Applications…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
In this paper, we study the massive Dirac equation with the presence of the Morse potential in polar coordinate. The Dirac Hamiltonian is written as two second-order differential equations in terms of two spinor wavefunctions. Since the…
We define a notion of Morse function and establish Morse theory-like theorems over offsets of any compact set in a Euclidean space at regular values of their distance function. Using non-smooth analysis and tools from geometric measure…
The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in ${\mathbb Z}^d$. We illustrate the use of the method for sums of independent integer valued random vectors, and…
We introduce a variational approach for extracting curves between a list of possible endpoints, based on the discretization of an energy and Smirnov's decomposition theorem for vector fields. It is used to design a bi-level minimization…
We construct one Yang-Mills measure on a compact surface for each isomorphism class of principal bundles over this surface. For this, we define a new discrete gauge theory which is essentially a covering of the usual one. We prove that the…
In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…
We use discrete Morse theory to give a new proof of the Degree Theorem in Auter space A_n. There is a filtration of A_n into subspaces A_{n,k} using the degree of a graph, and the Degree Theorem says that each A_{n,k} is (k-1)-connected.…
A careful treatment of closed string BRST cohomology shows that there are more discrete states and associated symmetries in $D=2$ string theory than has been recognized hitherto. The full structure, at the $SU(2)$ radius, has a natural…
A particular case of a causal set is considered that is a directed dyadic acyclic graph. This is a model of a discrete pregeometry on a microscopic scale. The dynamics is a stochastic sequential growth of the graph. New vertexes of the…
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…