اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAn algebraic Monte-Carlo algorithm for the Partition Adjacency Matrix realization problem
75
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The graphical realization of a given degree sequence and given partition adjacency matrix simultaneously is a relevant problem in data driven modeling of networks. Here we formulate common generalizations of this problem and the Exact Matching Problem, and solve them with an algebraic Monte-Carlo algorithm that runs in polynomial time if the number of partition classes is bounded.
قيم البحث
اقرأ أيضاً
During routine state space circuit analysis of an arbitrarily connected set of nodes representing a lossless LC network, a matrix was formed that was observed to implicitly capture connectivity of the nodes in a graph similar to the conventional inci
dence matrix, but in a slightly different manner. This matrix has only 0, 1 or -1 as its elements. A sense of direction (of the graph formed by the nodes) is inherently encoded in the matrix because of the presence of -1. It differs from the incidence matrix because of leaving out the datum node from the matrix. Calling this matrix as forward adjacency matrix, it was found that its inverse also displays useful and interesting physical properties when a specific style of node-indexing is adopted for the nodes in the graph. The graph considered is connected but does not have any closed loop/cycle (corresponding to closed loop of inductors in a circuit) as with its presence the matrix is not invertible. Incidentally, by definition the graph being considered is a tree. The properties of the forward adjacency matrix and its inverse, along with rigorous proof, are presented.
This contribution gives an extensive study on spectra of mixed graphs via its Hermitian adjacency matrix of the second kind introduced by Mohar [21]. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc fro
m $u$ to $v$ is equal to the sixth root of unity $omega=frac{1+{bf i}sqrt{3}}{2}$ (and its symmetric entry is $overline{omega}=frac{1-{bf i}sqrt{3}}{2}$); the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. The main results of this paper include the following: Some interesting properties are discovered about the characteristic polynomial of this novel matrix. Cospectral problems among mixed graphs, including mixed graphs and their underlying graphs, are studied. We give equivalent conditions for a mixed graph that shares the same spectrum of its Hermitian adjacency matrix of the second kind ($H_S$-spectrum for short) with its underlying graph. A sharp upper bound on the $H_S$-spectral radius is established and the corresponding extremal mixed graphs are identified. Operations which are called three-way switchings are discussed--they give rise to a large number of $H_S$-cospectral mixed graphs. We extract all the mixed graphs whose rank of its Hermitian adjacency matrix of the second kind ($H_S$-rank for short) is $2$ (resp. 3). Furthermore, we show that all connected mixed graphs with $H_S$-rank $2$ can be determined by their $H_S$-spectrum. However, this does not hold for all connected mixed graphs with $H_S$-rank $3$. We identify all mixed graphs whose eigenvalues of its Hermitian adjacency matrix of the second kind ($H_S$-eigenvalues for short) lie in the range $(-alpha,, alpha)$ for $alphainleft{sqrt{2},,sqrt{3},,2right}$.
An oriented hypergraph is an oriented incidence structure that generalizes and unifies graph and hypergraph theoretic results by examining its locally signed graphic substructure. In this paper we obtain a combinatorial characterization of the coeffi
cients of the characteristic polynomials of oriented hypergraphic Laplacian and adjacency matrices via a signed hypergraphic generalization of basic figures of graphs. Additionally, we provide bounds on the determinant and permanent of the Laplacian matrix, characterize the oriented hypergraphs in which the upper bound is sharp, and demonstrate that the lower bound is never achieved.
UKQCDs dynamical fermion project uses the Generalised Hybrid Monte-Carlo (GHMC) algorithm to generate QCD gauge configurations for a non-perturbatively O(a) improved Wilson action with two degenerate sea-quark flavours. We describe our implementation
of the algorithm on the Cray-T3E, concentrating on issues arising from code verification and performance optimisation, such as parameter tuning, reversibility, the effect of precision, the choice of matrix inverter and the behaviour of different molecular dynamics integration schemes.
We present a polynomial Hybrid Monte Carlo (PHMC) algorithm as an exact simulation algorithm with dynamical Kogut-Susskind fermions. The algorithm uses a Hermitian polynomial approximation for the fractional power of the KS fermion matrix. The system
atic error from the polynomial approximation is removed by the Kennedy-Kuti noisy Metropolis test so that the algorithm becomes exact at a finite molecular dynamics step size. We performed numerical tests with $N_f$$=$2 case on several lattice sizes. We found that the PHMC algorithm works on a moderately large lattice of $16^4$ at $beta$$=$5.7, $m$$=$0.02 ($m_{mathrm{PS}}/m_{mathrm{V}}$$sim$0.69) with a reasonable computational time.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
