inverse numerical range and determinantal representation abstract the numerical range w a of an n n matrix a is the collection of quadratic forms z a over unit sphere 1 the inverse numerical range problem aims to find a unit vector which corresponds to a given point z of the numerical range w a given a matrix a the helton vinnikov theorem produces a symmetric matrix s so that a and s have the same numerical range w a w s in this paper we investigate the inverse numerical range problem for the boundary points and points on the boundary generating curve of the numerical range in place of the construction of unit vectors satisfying z a we express the kernel vector function of the linear pencil x s y s z i n as a function on the abel jacobi variety of the associated elliptic curve of a the kernel function plays a key role for the inverse numerical problem we perform this process when s is a generic 3 3 symmetric matrix

generalized structured component analysis with latent interactions generalized structured component analysis gsca is a component based approach to structural equation modeling in practice researchers may often be interested in examining the interaction effects of latent variables however gsca has been geared only for the specification and testing of the main effects of variables thus an extension of gsca is proposed to effectively deal with various types of interactions among latent variables in the proposed method a latent interaction is defined as a product of interacting latent variables as a result this method does not require the construction of additional indicators for latent interactions moreover it can easily accommodate both exogenous and endogenous latent interactions an alternating least squares algorithm is developed to minimize a single optimization criterion for parameter estimation a monte carlo simulation study is conducted to investigate the parameter recovery capability of the proposed method an application is also presented to demonstrate the empirical usefulness of the proposed method

laplacian graph eigenvectors abstract if g is a graph its laplacian is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix the main thrust of the present article is to prove several laplacian eigenvector principles which in certain cases can be used to deduce the effect on the spectrum of contracting adding or deleting edges and or of coalescing vertices one application is the construction of two isospectral graphs on 11 vertices having different degree sequences only one of which is bipartite and only one of which is decomposable

the decomposable numerical radius and numerical radius of a compound matrix let a be an n n complex matrix with singular values 1 2 n and eigenvalues 1 2 n where 1 2 n denote by cm a 1 m n the mth compound of a and by mcn the mth grassmann space over cn in which the elements are regarded as complex row vectors with nm coordinates we have the relation i 1m i rd cm a r cm a i 1m i where rd cm a max xcm a x x is decomposable in mcn xx 1 and rd cm a max xcm a x x mcn xx 1 are the decomposable numerical radius and numerical radius of cm a respectively in this note we classify those matrices for which mi 1 i rd cm a m i 1 i r cm a rd cm a r cm a etc some of these results answer the questions raised by marcus and andresen concerning the decomposable numerical radius of a complex matrix

the fitness evaluation strategy in particle swarm optimization abstract the particle swarm optimization pso computational method has recently become popular however it has limitations it may trap into local optima and cause the premature convergence phenomenon especially for multimodal and high dimensional problems in this paper we focus on investigating the fitness evaluation in terms of a particle s position particularly we find that the fitness evaluation strategy in the standard pso has two drawbacks i e two steps forward and one step back and two steps back and one step forward in addition we propose a general fitness evaluation strategy gfes by which a particle is evaluated in multiple subspaces and different contexts in order to take diverse paces towards the destination position as demonstrations of gfes a series of psos with gfes are presented experiments are conducted on several benchmark optimization problems the results show that gfes is effective at handling multimodal and high dimensional problems

on the c numerical range of a matrix abstract given two n n complex matrices c and t we prove that if the differentiable mapping q u n c r 2 defined by q u tr cu tu is of rank at most 1 on a nonempty open set then the c numerical range w c t of t is a line segment the same conclusion holds whenever the interior of w c t is empty

estimation for polynomial structural equation models abstract structural equation analysis is one of the most widely used statistical methods in social and behavioral science research and has become a popular tool in marketing subject matter needs for considering nonlinear structural models have been well documented but current fitting procedures are available only for a limited class of models in this article a systematic statistical approach is developed for the general polynomial structural equation model the new procedure applies a method of moments procedure similar to the one used in errors in variables regression to the factor score estimates from the measurement model fit the asymptotic properties of the estimator are derived and a modified estimator with better small sample properties is introduced simulation studies are reported to show the usefulness of the procedure and to compare its performance to other methods an example from a substance abuse prevention study is also discussed

perturbation of the q numerical radius of a weighted shift operator abstract we formulate the taylor series expansion for the q numerical radius of a weighted shift operator with periodic weights near q 0 coefficients up to the fourth order in the expansion are found via the perturbation theory of hermitian matrices

davis wielandt shell and q numerical range abstract we describe the boundary of the q numerical range of a square matrix using its davis wielandt shell the result is used to generate an algorithm for plotting the q numerical range of the square matrix computations of the q numerical ranges of a special class of matrices are explicitly given

the distribution of low variability periods in human heartbeat dynamics abstract we study the long term dynamics of the short time variability level of human heart rate an aspect which is not addressed by the traditional methods of non linear time series analysis the length distribution of low variability periods in human heartbeat dynamics typically follows a multi scaling power law the values of the scaling exponents are personal characteristics and depend on the daily habits of the subjects though the distribution function of the low variability periods as a whole discriminates efficiently between several heart pathologies

the constrained bilinear form and the c numerical range abstract let v be an n dimentional unitary space with inner product and s the set x v x x 1 for any a hom v v and q c with q 1 we define w a q ax y x y s x y q if q 1 then w a q is just the classical numerical range ax x x s the convexity of which is well known another generalization of the numerical range is the c numerical range which is defined to be the set w c a tr cu au u unitary where c hom v v in this note we prove that w a q is always convex and that wc a is convex for all a if rank c 1 or n 2

commute times for a directed graph using an asymmetric laplacian the expected commute times for a strongly connected directed graph are related to an asymmetric laplacian matrix as a direct extension to similar well known formulas for undirected graphs we show the close relationships between the asymmetric laplacian and the so called fundamental matrix we give bounds for the commute times in terms of the stationary probabilities for a random walk over the graph together with the asymmetric laplacian and show how this can be approximated by a symmetrized laplacian derived from a related weighted undirected graph

the moore penrose inverse of the normalized graph laplacian abstract we prove a formula that relates the moore penrose inverses of two matrices a b such that a n 1 b m 1 and discuss some applications in particular to the representation of the moore penrose inverse of the normalized laplacian of a graph the laplacian matrix of an undirected graph is symmetric and is strictly related to its connectivity properties however our formula applies to asymmetric matrices so that we can generalize our results for asymmetric laplacians whose importance for the study of directed graphs is increasing

fuzzy preorder and fuzzy topology this paper presents by means of alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces a systematic investigation of the interrelationship between fuzzy preordered sets topological spaces and fuzzy topological spaces

conditions for the generalized numerical range to be real abstract necessary and sufficient conditions are given for the c numerical range of a matrix a to be a subset of the real axis in particular it is shown that both a and c must be translates of hermitian matrices

laplacian matrices and alexandrov topologies of digraphs abstract we explore the spectral properties of digraph laplacians and how they relate to topological properties of digraphs such as openness closure and strong connectedness under the alexandrov topology

tracial bounds for multilinear schur multipliers abstract we derive new types of two sided bounds for traces of multilinear schur multipliers that sharpen existing bounds in a number of situations we also characterize the tracial positivity of the n linear multipliers on symmetric tuples assuming their symbols are mildly sparse when n 5

isometries of a generalized numerical radius abstract for 0 q 1 the q numerical range is defined on the algebra m n of all n n complex matrices by w q a x ay x y c n x y 1 y x q the q numerical radius is defined by r q a max w q a we characterize isometries of the metric space m n r q i e the maps m n m n that satisfy r q a b r q a b we also characterize maps on m n that preserves the q numerical range the maps are not assumed to be linear

the q numerical radius of weighted shift operators with periodic weights we deal with the q numerical radius of weighted unilateral and bilateral shift operators in particular the q numerical radius of weighted shift operators with periodic weights is discussed and computed