Related papers: Method for searching higher symmetries for quad gr…
We use two variational techniques to prove upper bounds for sums of the lowest several eigenvalues of matrices associated with finite, simple, combinatorial graphs. These include estimates for the adjacency matrix of a graph and for both…
This research focuses on analyzing the depth of generalized binomial edge ideals. We extend the notion of $d$-compatible map for the pairs of a complete graph and an arbitrary graph, and using it, we give a combinatorial lower bound for the…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
Query answering routinely employs knowledge graphs to assist the user in the search process. Given a knowledge graph that represents entities and relationships among them, one aims at complementing the search with intuitive but effective…
A general discussion is presented of the possible symmetries responsible for confinement of color and of their evidence in lattice simulations. The consequences on the phase diagram of $QCD$ are also analyzed.
We study quantum automorphism group of vertex-transitive graphs using intertwinner spaces of the magic unitary matrix associated to this quantum subgroups of $S_n^+$. We also give some applications to quantum symmetries of circulant graphs…
The Conjugate Gradient method (CGM) is known to be the fastest generic iterative method for solving linear systems with symmetric sign definite matrices. In this paper, we modify this method so that it could find fundamental solitary waves…
In this work, we propose an efficient method for solving box constrained derivative free optimization problems involving high dimensions. The proposed method relies on exploring the feasible region using a direct search approach based on…
In this paper, we consider a matroid generalization of the stable matching problem. In particular, we consider the setting where preferences may contain ties. For this generalization, we propose a polynomial-time algorithm for the problem…
We study graph-directed conjugate functional equations on the unit interval indexed by the complete digraph with self-loops on two vertices. We focus on the singularity and regularity of the solutions for compatible systems of weak…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
In lattice field theory, the interactions of elementary particles can be computed via high-dimensional integrals. Markov-chain Monte Carlo (MCMC) methods based on importance sampling are normally efficient to solve most of these integrals.…
We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border)…
We introduce a new method for deriving Feynman integral symmetry relations. By solving the ansatz of momentum transformation in the field of rational functions rather than constants, this method can sometimes find more symmetry relations,…
These lectures provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1 (Ch. 2): Basic techniques for QCD and results for hadron spectroscopy using the simplest discretizations; lecture 2…
Methods for obtaining additional sensitivities to Lorentz violation in the fermion sector of the Standard-Model Extension using gravitational couplings are discussed.
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
We study the connectedness and the diameter of orthogonality graphs of upper triangular matrix algebras over arbitrary fields.
This paper proposes novel methods to test for simultaneous diagonalization of possibly asymmetric matrices. Motivated by various applications, a two-sample test as well as a generalization for multiple matrices are proposed. A partial…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…