Sign Patterns That Allow the Given Matrix

Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M matrix, an inverse M matrix and a P 0 matrix are considered. The complete characterizations are obtained.

Inertia Set of a Nonnegative Symmetric Sign Pattern

For a symmetric sign pattern S1 the inertia set of S is defined to be the set of all ordered triples si（S） = {i（A） ： A = A^T ∈ Q（S）} Consider the n × n sign pattern Sn, where Sn is the pattern with zero entry （i,j） for 1 ≤ i = j ≤ n or｜i -j｜=n- 1 and positive entry otherwise. In this paper, it is proved that si（Sn） = {（n1, n2, n - n1 - n2）｜n1≥ 1 and n2 ≥ 2} for n ≥ 4.

TWO CLASSES OF SYMMETRIC SIGN PATTERNS THAT REQUIRE UNIQUE INERTIA

A sign pattern is a matrix whose entries are from the set {+,-,0}. Associated with each sign pattern A of order n is a qualitative class of A,defined by Q(A). For a symmetric sign pattern A of order n,the inertia of A is a set i(A)={i(B)=(i +(B),i -(B),i 0(B))|B=B T∈ Q(A)},where i +(B) (respectively,i -(B),i 0(B)) denotes the number of positive (respectively,negative,zero) eigenvalues. That the symmetric sign pattern A requires unique intertia means i(B 1)=i(B 2) for all real symmetric matrices B 1,B 2∈Q(A).The purpose of this paper is to characterize double star and cycle sign patterns that require unique inertia. Further,their unique inertia is also obtained.

SIGN PATTERNS REQUIRING ALL DISTINCT EIGENVALUES

A sign pattern(matrix)is a matrix whose entries are the symbols+,-and 0.Foran n×n sign pattern matrix A,the sign pattern class of A,denoted by Q(A),is the set ofall n×n real matrices whose entries have signs indicated by the corresponding entries of A.We say that a sign pattern matrix A requires a matrix property P if every real matrix in Q(A)has the property P.A matrix with all distinct eigenvalues has many nice

SYMMETRIC SIGN PATTERN MATRICES THAT REQUIRE UNIQUE INERTIA

In qualitative and combinatorial matrix theory,we study properties of a matrix basedon qualitative information,such as the signs of entries in the matrix.A matrix whose en-tries are from the set{+,-,0}is called a sign pattern matrix (or sign pattern).For a re-al matrix B,by sgn (B) we mean the sign pattern matrix in which each positive (respec-tively,negative,zero) entry of B is replaced by+(respectively,-,0).If A is an

THE STRUCTURE OF TRIPOTENT SIGN PATTERN MATRICES

A matrix whose entries are +,-, and 0 is called a sign pattern matrix. For a sign pattern matrix A , if A 3=A , then A is said to be sign tripotent. In this paper, the characterization of the n by n(n≥2) sign pattern matrices A which are sign tripotent has been given out. Furthermore, the necessary and sufficient condition of A 3=A but A 2≠A is obtained, too.

Minimal Critical Sets of Refined Inertias for Irreducible Sign Patterns of Order 2

Let S be a nonempty, proper subset of all refined inertias. Then, S is called a critical set of refined inertias for ireducible sign patterns of order n if is sufficient for any sign pattern A to be refined inertially arbitrary. If no proper subset of Sis a critical set of refined inertias, then S is a minimal critical set of refined inertias for sign patterns of order n . In this paper, all minimal critical sets of refined inertias for irreducible sign patterns of order 2 are identified. As a by-product, a new approach is presented to identify all minimal critical sets of inertias for irreducible sign patterns of order 2.

INERTIA SETS OF SYMMETRIC SIGN PATTERN MATRICES

A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. The symmetric sign pattern matrices that require unique inertia have recently been characterized. The purpose of this paper is to more generally investigate the inertia sets of symmetric sign pattern matrices. In particular, nonnegative tri-diagonal sign patterns and the square sign pattern with all + entries are examined. An algorithm is given for generating nonnegative real symmetric Toeplitz matrices with zero diagonal of orders n≥3 which have exactly two negative eigenvalues. The inertia set of the square pattern with all + off-diagonal entries and zero diagonal entries is then analyzed. The types of inertias which can be in the inertia set of any sign pattern are also obtained in the paper. Specifically, certain compatibility and consecutiveness properties are established.

A new class of spectrally arbitrary complex sign pattern

Assume that S is an nth-order complex sign pattern.If for every nth degree complex coefficient polynomial f(λ)with a leading coefficient of 1,there exists a complex matrix C∈Q(S)such that the characteristic polynomial of C is f(λ),then S is called a spectrally arbitrary complex sign pattern.That is,if the spectrum of nth-order complex sign pattern S is a set comprised of all spectra of nth-order complex matrices,then S is called a spectrally arbitrary complex sign pattern.This paper presents a class of spectrally arbitrary complex sign pattern with only 3n nonzero elements by adopting the method of Schur complement and row reduction.

Pattern Matrix Design of PDMA for 5G UL Applications

Pattern division multiple access(PDMA),which is a novel non-orthogonal multiple access(NOMA),has been proposed to address the challenges of massive connectivity and higher spectral efficiency for fifth generation(5G) mobile network.The performance of PDMA mainly depends on the design of PDMA pattern matrix.In this paper,pattern matrix design of PDMA for 5G uplink(UL) applications in massive machine type communication(mMTC) and enhanced mobile broadband(eMBB) deployment scenarios are studied.The design criteria and examples for application in UL mMTC and UL eMBB are investigated.The performance of the PDMA pattern matrix is analyzed with the discrete constellation constrained capacity(CC-Capacity),and verified by Monte Carlo simulation.The simulation results show that the preferred PDMA pattern matrix can achieve good performance with different overloading factors(OF).

Ranks of Generalized Star Sign Patterns

A sign pattern is a matrix whose entries axe from the set {＋,-,0}. A sign pattern is a generalized star sign pattern if it is combinatorial symmetric and its graph is a generalized star graph. The purpose of this paper is to obtain the bound of minimal rank of any generalized star sign pattern （possibly with nonzero diagonal entries）.

Sign Patterns of Orders up to 4 that Allow Diagonalizability

Finding the necessary and sufficient conditions for a sign pattern to allow diagonalizability is an open problem. In this paper,we identify sign patterns of up to four orders that allow diagonalizability.

SIGN MATRIX, REGULAR SPLITTINGS AND MONOTONIC ENCLOSURE OF SOLUTIONS FOR NONLINEAR SYSTEM OF EQUATIONS, PARTI

In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.

On the Sign Pattern Matrices with Nonpositive κ-power

A matrix whose entries are +,-, and 0 is called a sign pattern matrix. Let k be arbitrary positive integer. We first characterize sign patterns A such that .Ak≤0. Further, we determine the maximum number of negative entries that can occur in A whenever Ak≤0. Finally, we give a necessity and sufficiency condition for A2≤0.

A New Class of Minimally Spectrally Arbitrary Sign Patterns

If every monic real polynomial of degree n can be achieved as the characteristic polynomial of some matrix B∈Q(A),then sign pattern A of order n is a spectrally arbitrary pattern.A sign pattern A is minimally spectrally arbitrary if it is spectrally arbitrary but is not spectrally arbitrary if any nonzero entry(or entries)of A is replaced by zero.In this article,we give some new sign patterns which are minimally spectrally arbitrary for order n≥9.

A Pattern Classification Model for Vowel Data Using Fuzzy Nearest Neighbor

Classification of the patterns is a crucial structure of research and applications. Using fuzzy set theory, classifying the patterns has become of great interest because of its ability to understand the parameters. One of the problemsobserved in the fuzzification of an unknown pattern is that importance is givenonly to the known patterns but not to their features. In contrast, features of thepatterns play an essential role when their respective patterns overlap. In this paper,an optimal fuzzy nearest neighbor model has been introduced in which a fuzzifi-cation process has been carried out for the unknown pattern using k nearest neighbor. With the help of the fuzzification process, the membership matrix has beenformed. In this membership matrix, fuzzification has been carried out of the features of the unknown pattern. Classification results are verified on a completelyllabelled Telugu vowel data set, and the accuracy is compared with the differentmodels and the fuzzy k nearest neighbor algorithm. The proposed model gives84.86% accuracy on 50% training data set and 89.35% accuracy on 80% trainingdata set. The proposed classifier learns well enough with a small amount of training data, resulting in an efficient and faster approach.

DC-SIGN与免疫调节

树突状细胞(DC)是目前所知体内功能最强大的专职抗原递呈细胞,它既能启动初始免疫应答,也能负向调控免疫反应,具有独特的免疫调节功能。DC-SIGN属于DC表面C型凝集素受体超家族成员,它既是DC病原体模式识别和黏附受体,又作为DC特征性多功能免疫分子,参与DC免疫调节作用。DC-SIGN在调节DC黏附迁移及炎症反应,激活初始T细胞及启动免疫应答,以及病原体与肿瘤的免疫逃逸等诸多方面发挥重要作用,已日益受到人们的关注。而对DC-SIGN在天然免疫和获得性免疫中调节作用及其相关机制的更深入研究,可为临床相关疾病机制探讨与防治进一步提供新的有力依据和干预途径。

Even Signed Permutations Avoiding 2-Letter Signed Patterns

Let Dn be the set of all signed permutations on n = {1,...,n} with even signs,and let Dn(T) be the set of all signed permutations in Dn which avoids a set T of signed patterns.In this paper,we find all the cardinalities of the sets Dn(T) where T■B2.Some of the cardinalities encountered involve inverse binomial coefficients,binomial coefficients,Catalan numbers,and Fibonacci numbers.

Effect of perforation on flow past a conic cylinder at Re =100: wavy vortex and sign laws

In order to find the intrinsic physical mechanism of the original Kármán vortex wavily distorted across the span due to the introduction of three-dimensional (3-D) geometric disturbances,a flow past a peak-perforated conic shroud is numerically simulated at a Reynolds number of 100.Based on previous work by Meiburg and Lasheras (1988),the streamwise and vertical interactions with spanwise vortices are introduced and analyzed.Then vortex-shedding patterns in the near wake for different flow regimes are reinspected and illustrated from the view of these two interactions.Generally,in regime Ⅰ,spanwise vortices are a little distorted due to the weak interaction.Then in regime Ⅱ,spanwise vortices,even though curved obviously,are still shed synchronously with moderate streamwise and vertical interactions.But in regime Ⅲ,violently wavy spanwise vortices in some vortex-shedding patterns,typically an Ω-type vortex,are mainly attributed to the strong vertical interactions,while other cases,such as multiple vortex-shedding patterns in sub-regime Ⅲ-D,are resulted from complex streamwise and vertical interactions.A special phenomenon,spacial distribution of streamwise and vertical components of vorticity with specific signs in the near wake,is analyzed based on two models of streamwise and vertical vortices in explaining physical reasons of top and bottom shear layers wavily varied across the span.Then these two models and above two interactions are unified.Finally two sign laws are summarized:the first sign law for streamwise and vertical components of vorticity is positive in the upper shear layer,but negative in the lower shear layer,while the second sign law for three vorticity components is always negative in the wake.

Fabrication of micro-nano patterned materials mimicking the topological structure of extracellular matrix for biomedical applications

With the advent of tissue engineering and biomedicine,the creation of extracellular matrix(ECM)biomaterials for in vitro applications has become a prominent and promising strategy.These ECM materials provide physical,biochemical,and mechanical properties that guide cellular behaviors,such as proliferation,differentiation,migration,and apoptosis.Because micro-and nano-patterned materials have a unique surface topology and low energy replication process that directly affect cellular biological behaviors at the interface,the fabrication of micro-nano pattern biomaterials and the regulation of surface physical and chemical properties are of great significance in the fields of cell regulation,tissue engineering,and regenerative medicine.Herein,we provide a comprehensive review of the progress in the fabrication and application of patterned materials based on the coupling of mechanical action at the micro-and nano-meter scale,including photolithography,micro-contact printing,electron beam lithography,electrospinning,and 3D printing technology.Furthermore,a summary of the fabrication process,underlying principles,as well as the advantages and disadvantages of various technologies are reviewed.We also discuss the influence of material properties on the fabrication of micro-and nano-patterns.