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 1

 A simple arithmetic criterion for graphs being determined by their generalized spectra
 [期刊] , 2017, 122(): 438451 SCIE SCOPUS
 被引用 2 (Web of Science℠)

摘要A graph G is said to be determined by its generalized spectrum (DGS for short) if, whenever H is a graph such that H and G are cospectral with cospectral complements, then H must be isomorphic to G. It turns out that whether a graph G is DGS is closely related to the arithmetic properties of its walkmatrix. More precisely, let A be the adjacency matrix of a graph G on n vertices, and let W = [e, Ae, A(2)e, ... , A(n1)e] (e is the allones vector) be its walk matrix. In Wang (2013) [16], the author defined a large family of graphs Fn = {G vertical bar det(W)/2left parpendicular(n/2)wright perpendicular is an odd square free integer} (which may have positive density among all graphs, as suggested by some numerical experiments) and conjectured every graph in Fn, is DGS. In this paper, we show that the conjecture is actually true, thereby giving a simple arithmetic condition for determining whether a graph is DGS. (C) 2016 Elsevier Inc. All rights reserved.关键词Cospectral graphs , Determined by spectrum , Spectra of graphs
 2

 A uniqueness theorem on matrices and reconstruction
 [期刊] , 2009, 99(1): 261265 SCIE SCOPUS 1.155
 被引用 0 (Web of Science℠)

摘要We prove the following simple uniqueness theorem: Let A and B be two integral symmetric matrices with the same irreducible characteristic polynomial, If there exist rational orthogonal matrices Q Such that B = Q(T)AQ, then Q is unique up to a sign. An application of the theorem to the reconstruction conjecture is provided. (C) 2008 Elsevier Inc. All rights reserved关键词Reconstruction , Hypomorphic , Hadamard matrix
 3

 Generalized Spectral Characterization of Graphs Revisited

[期刊]
,
2013, 20(4):
SCIE
SCOPUS
0.568
 被引用 5 (Web of Science℠)

摘要A graph G is said to be determined by its generalized spectrum (DGS for short) if for any graph H , H and G are cospectral with cospectral complements implies that H is isomorphic to G . Wang and Xu (2006) gave some methods for determining whether a family of graphs are DGS. In this paper, we shall review some of the old results and present some new ones along this line of research. More precisely, let A be the adjacency matrix of a graph G , and let W=[e,Ae,...,A(n1) e] (e is the allone vector) be its walkmatrix. Denote by G n the set of all graphs on n vertices with det(W)not equal 0 . We define a large family of graphs F n ={G?G n det(W) 2 ?n/2? is squarefree and 2 ?n/2?+1 / det(W)} (which may have positive density among all graphs, as suggested by some numerical experiments). The main result of the paper shows that for any graph G? F n , if there is a rational orthogonal matrix Q with Qe=e such that Q T AQ is a (0,1)matrix, then 2Q must be an integral matrix (and hence, Q has wellknown structures). As a consequence, we get the conclusion that almost all graphs in F n are DGS.关键词Spectra of graphs , Cospectral graphs , Determined by spectrum
 4

 A counterexample to a conjecture of Friedland
 [期刊] , 2009, 430(89): 20262029 EI SCIE SCOPUS 1.073
 被引用 0 (Web of Science℠)

摘要This paper is concerned with a conjecture of Friedland [S. Friedland, Rational orthogonal similarity of rational symmetric matrices, Linear Algebra Appl. 192 (1993) 109114]. A method for constructing counterexamples to the above conjecture is provided. (C) 2008 Elsevier Inc. All rights reserved.关键词Rational orthogonal similarity , pAdic numbers
 5

 Generalized Spectral Characterization of Graphs Revisited

[期刊]
,
2013, 20(4):
SCIE
SCOPUS
0.568
 被引用 5 (Web of Science℠)

摘要A graph G is said to be determined by its generalized spectrum (DGS for short) if for any graph H , H and G are cospectral with cospectral complements implies that H is isomorphic to G . Wang and Xu (2006) gave some methods for determining whether a family of graphs are DGS. In this paper, we shall review some of the old results and present some new ones along this line of research. More precisely, let A be the adjacency matrix of a graph G , and let W=[e,Ae,...,A(n1) e] (e is the allone vector) be its walkmatrix. Denote by G n the set of all graphs on n vertices with det(W)not equal 0 . We define a large family of graphs F n ={G?G n det(W) 2 ?n/2? is squarefree and 2 ?n/2?+1 / det(W)} (which may have positive density among all graphs, as suggested by some numerical experiments). The main result of the paper shows that for any graph G? F n , if there is a rational orthogonal matrix Q with Qe=e such that Q T AQ is a (0,1)matrix, then 2Q must be an integral matrix (and hence, Q has wellknown structures). As a consequence, we get the conclusion that almost all graphs in F n are DGS.关键词Cospectral graphs , Determined by spectrum , Spectra of graphs
 6

 On Regional Public Security Threshold EffectExploration Based on VulnerabilityAbility Analysis Framework

[其他]
International Conference on Public Management (ICPM)  Crisis Management in the Time of Changing World,
2012 : 204209
CPCISSH
 被引用 0 (Web of Science℠)

摘要By the "vulnerabilityability" framework, the paper carries a systematic analysis of the threshold value of regional public security through the collection of 20032010 provincial data calculated. Based on the objective data evaluation and fuzzy comprehensive evaluation algorithm, the research makes the results more true and effective. Following the analysis of threshold value, this paper furthermore takes an analysis on the mechanism principle, points out the differences and relations for vulnerability and ability in the system to achieve threshold before and after. It also verifies the reliability of the threshold and expounds the position and function of threshold value in regional complex system of public security.关键词vulnerabilityability , public security , threshold value
 7

 Feature selection for text categorization using filtering and wrapping

[期刊]
,
2006, 2(4): 13331342
EI
SCOPUS

摘要After analyzing the advantages and disadvantages of filtering and wrapping approaches for feature selection, a hybrid approach named filteringwrapping feature selection (FWFS) is proposed. This approach addresses feature selection as a sequential forward selections procedure. It uses information gain to evaluate feature's relevance to the target class and mutual information to evaluate redundancies among features. In search, a candidate set of individually discriminating and weakly dependent features added into Selecting Set. Then the actual classifier is used as a 'black box' to evaluate the fitness of the Selecting Set. F1 Microaveraged measure is employed to evaluate classification performance. When F1 Microaveraged measure is no improvement, search stop. Experiments over two different corpora show that the proposed approach performs better than traditional feature selection approaches.
 8

 On a conjecture of He concerning the spectral reconstruction of matrices
 [期刊] , 2009, 30(3): 311321 EI SCIE SCOPUS 1.137
 被引用 0 (Web of Science℠)

摘要This paper is concerned with a recent conjecture of He (Electron. J. Comb. 14(1), 2007) on the spectral reconstruction of matrices. A counterexample is provided by using Hadamard matrices. We also give some results to the above mentioned conjecture (with slight modifications) in the positive direction.关键词Reconstruction , Hadamard matrix
 9

 A note on nonℝcospectral graphs

[期刊]
,
2017, 24(1):
SCOPUS

摘要© 2017, Australian National University. All rights reserved. Two graphs G and H are called ℝcospectral if A(G)+ y J and A(H)+ y J (where A(G), A(H) are the adjacency matrices of G and H, respectively, J is the allone matrix) have the same spectrum for all y ∈ ℝ. In this note, we give a necessary condition for having ℝcospectral graphs. Further, we provide a sufficient condition ensuring only irrational orthogonal similarity between certain cospectral graphs. Some concrete examples are also supplied to exemplify the main results.关键词Irrational orthogonal matrix  Walk generating function  ℝcospectral graphs
 10

 Improving Multicontrast Imaging with Reference Guided Location and Orientation Priors on Edges
 [期刊] , 2018, (): SCOPUS

摘要© 2018, SpringerVerlag GmbH Austria, part of Springer Nature. The multicontrast magnetic resonance imaging can provide rich clinical and diagnostic information, but it requires long scanning time in data acquisition. In this paper, we propose a reference guided joint reconstruction method to address this problem. The proposed method both incorporates the location and orientation priors on edge regions from a highresolution reference image into joint sparsity constraints, enabling to effectively reconstruct highquality multicontrast images from the undersampled kspace data. The alternating direction method of multipliers is used to solve the joint sparsitypromoting optimization problem. In addition, a generalized frame with multiple reference images is developed to further improve the reconstruction performance, and the proposed method in combination with parallel imaging is also demonstrated to analyze the feasibility in the practical multichannel acquisition of multicontrast images. The experiments have demonstrated the superiority of our proposed method compared to those existing reconstruction technologies in multicontrast imaging.
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