Sharif Digital Repository

The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all noncentral elements of R, and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this article we investigate some graph-theoretic properties of Γ(Mn(F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GLn(F) and SLn(F). We show that Γ(Mn(F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GLn(F)) and Γ(SL n(F)). Also we show... 

With the advent of cloud-based parallel processing techniques, services such as MapReduce have been considered by many businesses and researchers for different applications of big data computation including matrix multiplication, which has drawn much attention in recent years. However, securing the computation result integrity in such systems is an important challenge, since public clouds can be vulnerable against the misbehavior of their owners (especially for economic purposes) and external attackers. In this paper, we propose an efficient approach using Merkle tree structure to verify the computation results of matrix multiplication in MapReduce systems while enduring an acceptable... 

We have studied the phase diagram of the one-dimensional S= 1 2 XXZ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We have applied the quantum renormalization group (QRG) approach to obtain stable fixed points and the scaling of coupling constants. The QRG prescription has to be implemented to the second order of interblock interactions to obtain a self-similar Hamiltonian after each step of the QRG. This model shows a rich phase diagram which includes quantum spin-fluid and dimer phases in addition to the classical Néel and ferromagnetic ones. We have found the border between different phases by tracing the scaling of coupling constants.... 

Embedding metrics into constant-dimensional geometric spaces, such as the Euclidean plane, is relatively poorly understood. Motivated by applications in visualization, ad-hoc networks, and molecular reconstruction, we consider the natural problem of embedding shortest-path metrics of unweighted planar graphs (planar graph metrics) into the Euclidean plane. It is known that, in the special case of shortest-path metrics of trees, embedding into the plane requires Θ(√n) distortion in the worst case [M1], [BMMV], and surprisingly, this worst-case upper bound provides the best known approximation algorithm for minimizing distortion. We answer an open question posed in this work and highlighted by... 

ABSTRACT Compressed sensing is a new theory that samples a signal below the Nyquist rate. While Gaussian and Bernoulli random measurements perform quite well on the average, structured matrices such as Toeplitz are mostly used in practice due to their simplicity. However, the signal compression performance may not be acceptable. In this paper, we propose to optimize the Toeplitz matrices to improve its compression performance to recover sparse signals. We establish the optimization on minimizing the coherence of the measurement matrix by an intelligent optimization method called Particle Swarm Optimization. Our simulation results show that the optimized Toeplitz matrix outperforms the... 

In this study two-dimensional finite element models of Al/SiC metal matrix composites (MMC) by using of ABAQUS Explicit software are investigated. Chip formations and machining forces for three types of MMC with 5, 15 and 20% of SiC reinforcement particles were studied and compared with experimental data. The resulted chips in simulation and the generated chips in experiments have both continuous and saw tooth in appearance. On the other hand, the variation of the cutting forces with the cutting time in simulation and experiment have fluctuating diagram. This is due to the interaction between cutting tool and SiC particles during chip formation. ABAQUS explicit software was used for... 

Let (Formula presented.) be a signed graph, where G is the underlying simple graph and (Formula presented.) is the sign function on the edges of G. The adjacency matrix of a signed graph has (Formula presented.) or (Formula presented.) for adjacent vertices, depending on the sign of the connecting edges. In this paper, the eigenvalues of signed complete graphs are investigated. We prove that (Formula presented.) and 1 are the eigenvalues of the signed complete graph with the multiplicity at least t if there are (Formula presented.) vertices whose all incident edges are positive or negative, respectively. We study the spectrum of a signed complete graph whose negative edges induce an... 

Let G be a simple connected graph of order n. Let (Formula presented.) be the Laplacian eigenvalues of G. In this paper, we show that if X and Y are two subsets of vertices of G such that (Formula presented.) and the set of all edges between X and Y decomposed into r disjoint perfect matchings, then, (Formula presented.) where (Formula presented.). Also, we determine a relation between the Laplacian eigenvalues and matchings in a bipartite graph by showing that if (Formula presented.) is a bipartite graph, (Formula presented.) and (Formula presented.), then G has a matching that saturates U. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group  

We introduce a simple representation for irreducible spherical tensor operators of the rotation group of arbitrary integer or half integer rank and use these tensor operators to construct matrix product states corresponding to all the variety of valence bond states proposed in the Affleck-Kennedy-Lieb- Tasaki (AKLT) construction. These include the fully dimerized states of arbitrary spins, with uniform or alternating patterns of spins, which are ground states of Hamiltonians with nearest and next-nearest-neighbor interactions, and the partially dimerized or AKLT/valence bond solid states, which are constructed from them by projection. The latter states are translation-invariant ground states... 

We investigate quantum phase transitions in ladders of spin- 1 2 particles by engineering suitable matrix product states for these ladders. We take into account both discrete and continuous symmetries and provide general classes of such models. We also study the behavior of entanglement between different neighboring sites near the transition point and show that quantum phase transitions in these systems are accompanied by divergences in derivatives of entanglement. © 2007 The American Physical Society  

An analytic expression for energy and angular dependence of a secondary charged lepton in the decay of a polarized top quark with anomalous tWb couplings in the presence of all anomalous couplings are derived. The angular distribution of the b-quark is derived as well. It is presented that the charged lepton spin correlation coefficient is not very sensitive to the anomalous couplings. However, the b-quark spin correlation coefficient is sensitive to anomalous couplings and could be used as a powerful tool in the search for non-SM coupling. © 2007 IOP Publishing Ltd  

Let G be a graph and M be a matrix associated with G whose characteristic polynomial is M(G,x)=∑i=0nαi(G)xn-i. We say that the spectrum of G is determined by non-constant coefficients (simply M-SDNC), if for any graph H with ai(H)=ai(G), 0≤i≤n-1, then Spec(G)=Spec(H) (if M is the adjacency matrix or the Laplacian matrix of G, then G is called an A-SDNC graph or L-SDNC graph). In this paper, we study some properties of graphs which are A-SDNC or L-SDNC. Among other results, we prove that the path of order at least five is L-SDNC and moreover stars of order at least five are both A-SDNC and L-SDNC. Furthermore, we construct infinitely many trees which are not A-SDNC graphs. More precisely, we... 

In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming a low-rank structure for the matrix, one natural solution would be to first apply a matrix completion to the data, and then to solve the resulting compressed sensing problem. In big data applications such as massive MIMO and medical data, the matrix completion step imposes a huge computational burden. Here, we propose to reduce the computational cost of the completion task by ignoring the columns corresponding to zero elements in the sparse vector. To... 

A weighted graph Gω consists of a simple graph G with a weight ω, which is a mapping, ω: E(G)→Z∖{0}. A signed graph is a graph whose edges are labelled with −1 or 1. In this paper, we characterize graphs which have a sign such that their signed adjacency matrix has full rank, and graphs which have a weight such that their weighted adjacency matrix does not have full rank. We show that for any arbitrary simple graph G, there is a sign σ so that Gσ has full rank if and only if G has a {1,2}-factor. We also show that for a graph G, there is a weight ω so that Gω does not have full rank if and only if G has at least two {1,2}-factors. © 2020 Elsevier B.V  

Let G be a graph of order n and rank(G) denotes the rank of its adjacency matrix. Clearly, n ≤ rank (G) + rank (over(G, -)) ≤ 2 n. In this paper we characterize all graphs G such that rank (G) + rank (over(G, -)) = n, n + 1 or n + 2. Also for every integer n ≥ 5 and any k, 0 ≤ k ≤ n, we construct a graph G of order n, such that rank (G) + rank (over(G, -)) = n + k. © 2006 Elsevier Inc. All rights reserved  

The existence of periodic solutions for a forced Hill's equation is proved. The proof is then extended to the case of a non-homogeneous matrix valued Hill's equation. Under the stated conditions, using Lyapunov's criteria [Proc. AMS 13 (1962) 601; Hill's Equation, Interscience Publishers, New York, 1966] some results on the stability oh Hill's equation are obtained. © 2004 Elsevier Inc. All rights reserved  

In this paper, the problem of convolutive source separation via multimodal soft Nonnegative Matrix Co-Factorization (NMCF) is addressed. Different aspects of a phenomenon may be recorded by sensors of different types (e.g., audio and video of human speech), and each of these recorded signals is called a modality. Since the underlying phenomenon of the modalities is the same, they have some similarities. Especially, they usually have similar time changes. It means that changes in one of them usually correspond to changes in the other one. So their active or inactive periods are usually similar. Assuming this similarity, it is expected that the activation coefficient matrices of their... 

In this article, we investigate the limiting spectral distribution of the sample covariance matrix (SCM) of weighted/windowed complex data. We use recent advances in random matrix theory and describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We obtain an approximation for the spectral distribution of the SCM obtained from windowed data. We also determine a condition on the coefficients of the window, under which the fragmentation of the support of noise eigenvalues can be avoided, in the noise-only data case. For the commonly used exponential window, we derive an explicit expression for the l.s.d of the noise-only data. In addition, we present a method to... 

In this paper, we investigate the effect of applying an exponential window on the limiting spectral distribution (l.s.d.) of the exponentially windowed sample covariance matrix (SCM) of complex array data. We use recent advances in random matrix theory which describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We derive an explicit expression for the l.s.d. of the noise-only data. Simulations are performed to support our theoretical claims  

In this paper, we investigate PN-sequences with ideal autocorrelation property and the consequences of this property on the number of +1s and -1s and run structure of sequences. We begin by discussing and surveying about the length of PN-sequences with ideal autocorrelation property. From our discussion and survey we introduce circulant matrix representation of PN-sequence. Through circulant matrix representation we obtain system of non-linear equations that lead to ideal autocorrelation property. Rewriting PN-sequence and its autocorrelation property in {0,1} leads to a definition based on Hamming weight and Hamming distance and hence we can easily prove some results on the PN-sequences...