testing for the cointegrating rank of a var process with a time trend standard tests for the cointegrating rank of a vector autoregressive var process have nonstandard limiting distributions which depend on the characteristics of intercept terms and time trends in the system in practice these characteristics are often unknown therefore modified tests are considered which allow for deterministic linear trends in the data generation process dgp the tests are based on the lagrange multiplier lm principle and in contrast to likelihood ratio lr tests proposed for this situation our tests take into account the cointegrating rank specified under the null hypothesis in estimating the trend parameters the tests are shown to have nonstandard limiting distributions which do not depend on deterministic terms and have better local power and small sample properties than the competing lr tests in many situations

some further results on the eccentric distance sum abstract let g v g e g be a simple connected graph then the eccentric distance sum of g which is a novel graph invariant by offering a great potential for structure activity property relationships is defined as d g v v e g v d g v where e g v is the eccentricity of the vertex v and d g v is the sum of all distance from the vertex v as a continuation to the parts of 22 li et al j math anal appl 43 1149 1162 2015 and 17 hua et al discrete appl math 160 170 180 2012 this paper answers one of some remaining problems in 22 is how to determine the bipartite graphs of even diameter with the minimum eds and gives a nordhaus gaddum bound for eccentric distance sum which is the generalization of the corresponding results in 17 moreover some sharp lower bounds on the eds of halin graphs and of triangle free and quadrangle free graphs are respectively presented

on spacelike hypersurfaces with constant mean curvature in the de sitter space soit n n n 1 c g une variete de lorentz a n 1 dimensions de courbure constante positive c soit m une hypersurface du genre espace complete a courbure moyenne constante h dans n on suppose que 1 h c 1 2 quand n 2 2 h 2 n 1 c 1 2 n quand n 3 alors m est totalement ombilicale

on the minimum eccentric distance sum of bipartite graphs with some given parameters the eccentric distance sum is a novel graph invariant with vast potential in structure activity property relationships this graph invariant displays high discriminating power with respect to both biological activity and physical properties if g vg eg is a simple connected graph then the eccentric distance sum eds of g is defined as d g v vgeg v dg v where eg v is the eccentricity of the vertex v and dg v u vgdg u v is the sum of all distances from the vertex v much extremal work has been done on trees with some given parameters by yu et al 2011 25 li et al 2012 19 and geng et al 2013 6 it is natural to consider this extremal problem on bipartite graphs with some given parameters in this paper sharp lower bound on the eds in the class of all connected bipartite graphs with a given matching number q is determined the minimum eds is realized only by the graph kq n q the extremal graph with the minimum eds in the class of all the n vertex connected bipartite graphs of odd diameter is characterized all the extremal graphs having the minimum eds in the class of all connected n vertex bipartite graphs with a given vertex connectivity are identified as well

predicting global temperature anomaly a definitive investigation using an ensemble of twelve competing forecasting models in this paper we analyze whether anthropometric co 2 can forecast global temperature anomaly gt over an annual out of sample period of 1907 2012 which corresponds to an initial in sample of 1880 1906 for our purpose we use 12 parametric and nonparametric univariate of gt only and multivariate including both gt and co 2 models our results show that the horizontal multivariate singular spectral analysis hmssa techniques both recurrent r and vector v consistently outperform the other competing models more importantly from the performance of the hmssa v model we find conclusive evidence that co 2 can forecast gt and also predict its direction of change our results highlight the superiority of the nonparametric approach of ssa which in turn allows us to handle any statistical process linear or nonlinear stationary or non stationary gaussian or non gaussian

inference in linear time series models with some unit roots this paper considers estimation and hypothesis testing in linear time series models when some or all of the variables have unit roots our motivating example is a vector autoregression with some unit roots in the companion matrix which might include polynomials in time as regressors in the general formulation the variable might be integrated or cointegrated of arbitrary orders and might have drifts as well we show that parameters that can be written as coefficients on mean zero nonintegrated regressors have jointly normal asymptotic distributions converging at the rate t 2 in general the other coefficients including the coefficients on polynomials in time will have nonnormal asymptotic distributions the results provide a formal characterization of which t or f tests such as granger causality tests will be asymptotically valid and which will have nonstandard limiting distributions

testing the constancy of regression parameters against continuous structural change abstract a standard explicit or implicit assumption underlying many parameter constancy tests in linear models is that there is a single structural break in the sample in this paper that assumption is replaced by a more general one stating that the parameters of the model may change continuously over time the pattern of change is parameterized giving rise to a set of parameter constancy tests against a parameterized alternative the power properties of the lm type tests in small samples are compared to those of other tests like the cusum and fluctuation test by simulation and found very satisfactory an application is considered

on the eccentric distance sum of trees and unicyclic graphs abstract let g be a simple connected graph with the vertex set v g the eccentric distance sum of g is defined as d g v v g e v d g v where e v is the eccentricity of the vertex v and d g v u v g d u v is the sum of all distances from the vertex v in this paper we characterize the extremal unicyclic graphs among n vertex unicyclic graphs with given girth having the minimal and second minimal eccentric distance sum in addition we characterize the extremal trees with given diameter and minimal eccentric distance sum

joint independent subspace analysis using second order statistics this paper deals with a novel generalization of classical blind source separation bss in two directions first relaxing the constraint that the latent sources must be statistically independent this generalization is well known and sometimes termed independent subspace analysis isa second jointly analyzing several isa problems where the link is due to statistical dependence among corresponding sources in different mixtures when the data are one dimensional i e multiple classical bss problems this model known as independent vector analysis iva has already been studied in this paper we combine iva with isa and term this new model joint independent subspace analysis jisa we provide full performance analysis of jisa including closed form expressions for minimal mean square error mse fisher information and cramer rao lower bound in the separation of gaussian data the derived mse applies also for non gaussian data when only second order statistics are used we generalize previously known results on iva including its ability to uniquely resolve instantaneous mixtures of real gaussian stationary data and having the same arbitrary permutation at all mixtures numerical experiments validate our theoretical results and show the gain with respect to two competing approaches that either use a finer block partition or a different norm

the spurious effect of unit roots on vector autoregressions an analytical study abstract this paper analyzes whether inclusion of a statistically independent random walk in a vector autoregression can result in spurious inference the problem was raised originally by ohanian 1988 in a monte carlo simulation based on the var s estimated by sims 1980 1982 ohanian found that block exogeneity of the genuine variables with respect to an artificially generated random walk variable was rejected too often in the present paper we attempt a full analytical study of this problem it can be shown that if the genuine variables are nonstationary the wald statistic for testing the block exogeneity hypothesis does not have the usual asymptotic chi square distribution the derived asymptotic distribution is free of nuisance parameters so that we can unambiguously determine the effect of including the random walk some simulated critical values for the asymptotic distribution are reported interestingly it can also be shown that if the genuine variables of the model are stationary the asymptotic distribution is still chi square in spite of the inclusion of the random walk

partial orderings preorderings and the polar decomposition of matrices abstract when a unique decomposition of a complex rectangular matrix into two components is given then a partial ordering on the domain of one of the components induces a preordering on the whole set of matrices and partial orderings on the domains of both components induce a partial ordering on the whole set in this not we consider the three main partial orderings lo wner star and rank subtractivity on the respective domains of the two components of matrices subjected to polar decomposition a ben israel t n e greville generalized inverses theory and applications wiley new york 1974 p 255 and investigate the resulting pre and partial orderings

spectrum and trace invariance criterion and its statistical applications abstract necessary and sufficient conditions are established for the set of nonzero eigenvalues of the product b a to be invariant with respect to the choice of a generalized inverse b it turns out that the same conditions constitute a criterion for the invariance of trace b a the algebraic result derived is then applied to investigate some properties of canonical correlations in the context of the general gauss markov model m y x 2 v in particular the results of watson 1967 and puntanen 1987 are generalized and a new characterization of the best linear unbiased estimator of x under the model m is established

robust inference in nonlinear models with mixed identification strength abstract the paper studies inference in regression models composed of nonlinear functions with unknown transformation parameters and loading coefficients that measure the importance of each component in these models non identification and weak identification present in multiple parts of the parameter space resulting in mixed identification strength for different unknown parameters this paper proposes robust tests and confidence intervals for sub vectors and linear functions of the unknown parameters in particular the results cover applications where some nuisance parameters are non identified under the null davies 1977 1987 and some nuisance parameters are subject to a full range of identification strength to construct this robust inference procedure we develop a local limit theory that models mixed identification strength the asymptotic results involve both inconsistent estimators that depend on a localization parameter and consistent estimators with different rates of convergence a sequential argument is used to peel the criterion function based on identification strength of the parameters

delta method inference for a class of set identified svars abstract we study vector autoregressions that impose equality and or inequality restrictions to set identify the dynamic responses to a single structural shock we make three contributions first we present an algorithm to compute the largest and smallest value that an impulse response coefficient can attain over its identified set second we provide conditions under which these largest and smallest values are directionally differentiable functions of the model s reduced form parameters third we propose a delta method approach to conduct inference about the structural impulse response coefficients we use our results to assess the effects of the announcement of the quantitative easing program in august 2010

several inequalities involving khatri rao products of positive semidefinite matrices abstract the khatri rao and tracy singh products for partitioned matrices are viewed as generalized hadamard and generalized kronecker products respectively based on the connection between the khatri rao and tracy singh products we establish new inequalities involving khatri rao products of positive semidefinite matrices the results lead to inequalities involving hadamard products as a special case

vector gaussian two terminal source coding we derive a lower bound on each supporting line of the rate region of the vector gaussian two terminal ceo problem which is a special case of the indirect vector gaussian two terminal source coding problem the key technical ingredient is a new extremal inequality it is shown that the lower bound coincides with the berger tung upper bound in the high resolution regime similar results are derived for the direct vector gaussian two terminal source coding problem

space like submanifolds in de sitter spaces let m n be a space like submanifold in a de sitter space mpn p c with flat normal bundle this paper gives some intrinsic conditions for m n to be totally umbilical

the positive semidefiniteness of partitioned matrices abstract the positive semidefiniteness of a partitioned matrix is characterized in terms of its submatrices the result is applied to a variety of problems concerning lowner ordered matrices which need not be partitioned themselves

containment problems for polytopes and spectrahedra we study the computational question of whether a given polytope or spectrahedron s a as given by the positive semidefiniteness region of a linear matrix pencil a x is contained in another s b first we classify the computational complexity extending results on the polytope polytope case by gritzmann and klee to the polytope spectrahedron case for various restricted containment problems np hardness is shown we then study in detail semidefinite conditions to certify containment building upon work by ben tal and nemirovski and helton klep and mccullough in particular we discuss variations of a sufficient semidefinite condition to certify containment of a spectrahedron in a spectrahedron it is shown that these sufficient conditions even provide exact semidefinite characterizations for containment in several important cases including containment of a spectrahedron in a polyhedron moreover in the case of bounded s a the criteria will always succeed in certifying containment of some scale

on the lowner minus and star partial orderings of nonnegative definite matrices and their squares abstract we investigate how the ordering of two hermitian nonnegative definite matrices a and b relates to the ordering of their squares a 2 and b 2 in the sense of the lowner partial ordering the minus partial ordering and the star partial ordering the condition that a and b commute appears essential in these investigations we also give some comments on possible extensions of our results by replacing the squares a 2 and b 2 with the k th powers a k and b k

asymptotic normality when regressors have a unit root under fairly general conditions ordinary least squares and linear instrumental variables estimators are asymptotically normal when a regression equation has nonstationary right hand side variables standard formulas may be used to calculate a consistent estimate of the asymptotic variance covariance matrix of the estimated parameter vector even if the disturbances are conditionally heteroskedastic and autocorrelated so inference may proceed in the usual way the key requirements are that the nonstationary variables share a common unit root and that the unconditional mean of their first differences is nonzero copyright 1988 by the econometric society

on the extremal values of the eccentric distance sum of trees abstract let g v g e g be a simple connected graph the eccentric distance sum of g is defined as d g v v g e g v d g v where e g v is the eccentricity of the vertex v and d g v u v g d u v is the sum of all distances from the vertex v in this paper we first characterize the extremal trees among n vertex conjugated trees trees with a perfect matching having the minimal and second minimal eccentric distance sums then we identify the trees with the minimal and second minimal eccentric distance sums among the n vertex trees with matching number m finally we characterize the extremal tree with the second minimal eccentric distance sum among the n vertex trees of a given diameter consequently we determine the trees with the third and fourth minimal eccentric distance sums among the n vertex trees which is a continuance study as the results in g h yu l h feng a ilic on the eccentric distance sum of trees and unicyclic graphs j math anal appl 375 2011 99 107

some further results on hermitian matrix inequalities abstract some new results on the lowner partial ordering between certain sums products and direct products of matrices are derived proofs of these results are based on a necessary and sufficient condition for the nonnegative definiteness of the difference of two hermitian matrices which follows from the criterion for the nonnegative definiteness of a partitioned hermitian matrix due to albert 1969

rotation hypersurfaces in spaces of constant curvature rotation hypersurfaces in spaces of constant curvature are defined and their principal curvatures are computed a local characterization of such hypersurfaces with dimensions greater than two is given in terms of principal curvatures some special cases of rotation hypersurfaces with constant mean curvature in hyperbolic space are studied in particular it is shown that the well known conjugation between the helicoid and the catenoid in euclidean three space extends naturally to hyperbolic three space h3 in the latter case catenoids are of three different types and the explicit correspondence is given it is also shown that there exists a family of simply connected complete embedded nontotally geodesic stable minimal surfaces in h3

bootstrap algorithms for testing and determining the cointegration rank in var models in this paper a bootstrap algorithm for a reduced rank vector autoregressive model with a restricted linear trend and independent identically distributed errors is analyzed for testing the cointegration rank the asymptotic distribution under the hypothesis is the same as for the usual likelihood ratio test so that the bootstrap is consistent it is furthermore shown that a bootstrap procedure for determining the rank is asymptotically consistent in the sense that the probability of choosing the rank smaller than the true one converges to zero

some further matrix extensions of the cauchy schwarz and kantorovich inequalities with some statistical applications abstract the well known cauchy schwarz and kantorovich inequalities may be expressed in terms of vectors and a positive definite matrix we consider what happens to these inequalities when the vectors are replaced by matrices the positive definite matrix is allowed to be positive semidefinite singular and the usual inequalities are replaced by lowner partial orderings some examples in the context of linear statistical models are presented

lowner partial ordering and space preordering of hermitian non negative definite matrices abstract if a matrix a is below a matrix b with respect to the lowner partial ordering within the set of hermitian non negative definite matrices then the columns of a are linear combinations of the columns of b in this note the class of all such combinations providing a complete characterization of the lowner partial ordering is presented in addition new results on partial ordering of squares of hermitian non negative definite matrices are given

on the maximal connective eccentricity index of bipartite graphs with some given parameters abstract the connective eccentricity index is a novel graph invariant with vast potential in structure activity property relationships this graph invariant displays high discriminating power with respect to both biological activity and physical properties given a simple connected graph g the connective eccentricity index cei of g is defined as e e g u v e g 1 e g u 1 e g v where e g denotes the eccentricity of the corresponding vertex in this paper we first determine the sharp upper bound on the cei of graphs in the class of all n vertex connected bipartite graphs with matching number q the maximum cei is realized only by the graph k q n q second we characterize the graph with the maximum cei in the class of all the n vertex connected bipartite graphs of given diameter finally all the extremal graphs having the maximum cei in the class of all the connected n vertex bipartite graphs with a given connectivity s are identified as well

connective steiner 3 eccentricity index and network similarity measure abstract for a set s v g in a network g the steiner distance dg s of s is the minimum size among all connected subnetworks whose vertex sets contain s the steiner k eccentricity k v of a vertex v of g is the maximum steiner distance among all k vertex set s which contains the vertex v i e e k v max d s s v g s k v s based on steiner k eccentricity the connective steiner k eccentricity index is introduced as a newly structural invariant some properties of the connective steiner 3 eccentricity index are investigated firstly we present an o n2 polynomial time algorithm to calculate the connective steiner 3 eccentricity index of trees secondly some optimal problems among some network classes are discussed as its application finally we consider the network similarity measure based on the connective steiner 3 eccentricity index by two different methods we study its advantages numerical results show that the measure based on the connective steiner 3 eccentricity index has more advantages than the ones based on other topological indices graph energy randic index the largest adjacent eigenvalue the largest laplacian eigenvalue

on the eccentric distance sum of graphs the eccentric distance sum is a novel topological index that offers a vast potential for structure activity property relationships for a graph g it is defined as d g v ve v d v where e v is the eccentricity of the vertex v and d v u v g d u v is the sum of all distances from the vertex v motivated by g yu l feng a ilic on the eccentric distance sum of trees and unicyclic graphs j math anal appl 375 2011 934 944 in this paper we characterize the extremal trees and graphs with maximal eccentric distance sum various lower and upper bounds for the eccentric distance sum in terms of other graph invariants including the wiener index the degree distance eccentric connectivity index independence number connectivity matching number chromatic number and clique number are established in addition we present explicit formulae for the values of eccentric distance sum for the cartesian product applied to some graphs of chemical interest like nanotubes and nanotori

uncertain exit time multi period mean variance portfolio selection with endogenous liabilities and markov jumps this paper considers an uncertain exit time multi period mean variance portfolio selection problem with endogenous liabilities in a markov jump market where assets and liabilities of the balance sheet are simultaneously optimized the random returns of assets and liabilities depend on the states of the financial market by applying the lagrange duality method the khatri rao matrix product technique and the dynamic programming approach the explicit expressions for the mean variance efficient strategy and efficient frontier are derived in addition the optimal balance sheet structures in both cases with and without boundary constraints are studied moreover some degenerate cases are discussed and some results in the literature are recovered as degenerate cases under our setting furthermore a numerical example based on real data from the chinese stock market is provided to illustrate the results obtained in this paper and some interesting findings are presented

new characterizations for hyperbolic cylinders in anti de sitter spaces abstract in this paper we study complete maximal spacelike hypersurfaces in anti de sitter space h 1 n 1 with either constant scalar curvature or constant non zero gauss kronecker curvature we characterize the hyperbolic cylinders h m c 1 h n m c 2 1 m n 1 as the only such hypersurfaces with n 1 principal curvatures with the same sign everywhere in particular we prove that a complete maximal spacelike hypersurface in h 1 5 with negative constant gauss kronecker curvature is isometric to h 1 c 1 h 3 c 2

new examples of maximal space like surfaces in the anti de sitter space abstract let h 1 3 be the three dimensional anti de sitter space in this paper we will construct new examples of complete maximal space like surfaces in h 1 3 moreover we will prove that any complete maximal space like surface in h 1 3 with principal curvatures bounded away from zero must be isometric to the hyperbolic cylinder since the new examples that we have constructed have exactly two principal curvatures everywhere we conclude that the condition on the principal curvatures on the previous result i e the condition m c 0 cannot be replaced by the condition m 0

a geometrical correspondence between maximal surfaces in anti de sitter space time and minimal surfaces in h2 r abstract a geometrical correspondence between maximal surfaces in anti de sitter space time and minimal surfaces in the riemannian product of the hyperbolic plane and the real line is established new examples of maximal surfaces in anti de sitter space time are obtained in order to illustrate this correspondence

interpreting the evidence on money income causality abstract previous researchers have reached strikingly different conclusions about the usefulness of money for forecasting real output based on closely related regression based tests an examination of this and additional new evidence reveals that innovations in m1 have statistically significant marginal predictive value for industrial production both in a bivariate model and in a multivariate setting including a price index and an interest rate this conclusion follows from focusing on the trend properties of the data both stochastic and deterministic and from drawing inferences using asymptotic theory that explicitly addresses the implications of these trends for the distributions of the various test statistics

eccentric distance sum a novel graph invariant for predicting biological and physical properties abstract eccentric distance sum a novel graph invariant with vast potential in structure activity property relationships has been conceptualized in the present study this graph invariant displayed high discriminating power with respect to both biological activity and physical properties the structure activity relationship of eccentric distance sum was investigated with regard to anti hiv activity of dihydroseselins the values of eccentric distance sum of each analogue in the data set were computed and active range identified subsequently biological activity was assigned to each analogue in the data set which was then compared with the reported anti hiv activity of dihydroseselin analogues surprisingly the accuracy of prediction was found to be more than 88 with regard to anti hiv activity on the other hand investigations pertaining to quantitative structure property relationship of the novel graph invariant with regard to various physical properties of diverse nature for data sets consisting of primary amines secondary amines and alcohols revealed correlation percentages ranging from 93 to 99 the over all results with regard to structure activity and quantitative structure property studies using eccentric distance sum were better than the corresponding values obtained using wiener s index

a new characterization of hyperbolic cylinder in anti de sitter space h1n 1 1 abstract by investigating n dimensional complete maximal spacelike hypersurfaces with two distinct principal curvatures in an n 1 dimensional anti de sitter space h 1 n 1 1 we give a new characterization of hyperbolic cylinder h m n m h n m n n m in h 1 n 1 1

new characterizations of hyperbolic cylinders in semi riemannian space forms abstract through the study of the so called linear weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector in a semi riemannian space form q p n p c of index p and constant sectional curvature c 1 0 1 our aim in this paper is establish new characterizations for the hyperbolic cylinders of q p n p c our approach is based on the use of a simons type formula related to an appropriated cheng yau modified operator jointly with the application of suitable generalized maximum principles

matrix results on the khatri rao and tracy singh products abstract we establish a connection between the khatri rao and tracy singh products introduced by khatri and rao c g khatri c r rao sankhya 30 1968 167 180 and tracy and singh d s tracy r p singh statistica neerlandica 26 1972 143 157 respectively and present further results including matrix equalities and inequalities involving the two products also we give two statistical applications

general transmission lemma and wiener complexity of triangular grids abstract the transmission lemma from rajasingh et al 2016 is extended to the general transmission lemma it gives a formula for the transmission of a vertex u as a function of a collection of edge cuts and a u routing that uniformly intersects the edge cuts the applicability of the general transmission lemma is demonstrated by computing the wiener complexity of triangular grid networks

on the complete linear weingarten spacelike hypersurfaces with two distinct principal curvatures in lorentzian space forms abstract we deal with complete linear weingarten spacelike hypersurfaces immersed in a lorentzian space form having two distinct principal curvatures in this setting we show that such a spacelike hypersurface must be isometric to a certain isoparametric hypersurface of the ambient space under suitable restrictions on the values of the mean curvature and of the norm of the traceless part of its second fundamental form our approach is based on the use of a simons type formula related to an appropriated cheng yau modified operator jointly with some generalized maximum principles

the riemannian product structures of spacelike hypersurfaces with constant k th mean curvature in the de sitter spaces abstract in this paper we investigate complete spacelike hypersurfaces in the de sitter space s 1 n 1 c with constant k th mean curvature and two distinct principal curvatures one of which is simple we obtain some characterizations of the riemannian product h 1 c 1 s n 1 c 2 or h n 1 c 1 s 1 c 2 in the de sitter space s 1 n 1 c

on semi orthogonality and a special class of matrices abstract the concept of semi orthogonality of two complex vectors is introduced as a consequence a generalization of the class of orthogonal projectors is investigated

some extremal results on the connective eccentricity index of graphs abstract the connective eccentricity index cei of a graph g is defined as ce g v i v g d v i e v i where e v i and d v i are the eccentricity and the degree of vertex v i respectively in g in this paper we obtain some lower and upper bounds on the connective eccentricity index for all trees of order n and with matching number and characterize the corresponding extremal trees and the maximal graphs of order n and with matching number and n edges have been determined which maximize the connective eccentricity index also the extremal graphs with maximal connective eccentricity index are completely characterized among all connected graphs of order n and with matching number moreover we establish some relations between connective eccentricity index and eccentric connectivity index as another eccentricity based invariant of graphs

inference on one way effect and evidence in japanese macroeconomic data this paper provides an approach to testing a variety of causal characteristics expressed in terms of the measures of one way effect for cointegrated vector time series for this purpose we propose wald tests and their computational algorithm by means of the measures of one way effect incorporating johansen s algorithm for the maximum likelihood estimates and the likelihood ratio tests using the wald test statistics the paper also provides a method of confidence set construction for the causal measures the approach proposed in the paper includes testing granger s non causality as an instance of its multiple applications as an illustration the paper presents a characterization of the causal structure of the recent japanese macroeconomy on the basis of the proposed method and the derived evidence

uniqueness of entire graphs in warped products abstract under suitable restrictions on the higher order mean curvatures we establish uniqueness results for entire graphs in a warped product space satisfying a standard convergence condition consequences are given for such graphs to be slices by using comparison inequalities of their higher order mean curvatures applications to the study of the rigidity of minimal and radial graphs in the euclidean space are also given

application of graph theory relationship of eccentric connectivity index and wiener s index with anti inflammatory activity abstract graph theory was successfully applied in developing a relationship between chemical structure and biological activity the relationship of two graph invariants the eccentric connectivity index and the wiener s index was investigated with regard to anti inflammatory activity for a data set consisting of 76 pyrazole carboxylic acid hydrazide analogues the values of the eccentric connectivity index and the wiener s index of each analogue in the data set were computed and active ranges were identified subsequently each analogue was assigned a biological activity that was compared with the anti inflammatory activity reported as percent reduction in paw swelling prediction with an accuracy of 90 was obtained using the eccentric connectivity index as compared to 84 in the case of wiener s index

vector gaussian multiterminal source coding we derive an outer bound of the rate region of the vector gaussian l terminal ceo problem by establishing a lower bound on each supporting hyperplane of the rate region to this end we prove a new extremal inequality by exploiting the connection between differential entropy and fisher information as well as some fundamental estimation theoretic inequalities it is shown that the outer bound matches the berger tung inner bound in the high resolution regime we then derive a lower bound on each supporting hyperplane of the rate region of the direct vector gaussian l terminal source coding problem by coupling it with the ceo problem through a limiting argument the tightness of this lower bound in the high resolution regime and the weak dependence regime is also proved

spatially varying coefficient model for neuroimaging data with jump discontinuities motivated by recent work on studying massive imaging data in various neuroimaging studies we propose a novel spatially varying coefficient model svcm to capture the varying association between imaging measures in a three dimensional volume or two dimensional surface with a set of covariates two stylized features of neuorimaging data are the presence of multiple piecewise smooth regions with unknown edges and jumps and substantial spatial correlations to specifically account for these two features svcm includes a measurement model with multiple varying coefficient functions a jumping surface model for each varying coefficient function and a functional principal component model we develop a three stage estimation procedure to simultaneously estimate the varying coefficient functions and the spatial correlations the estimation procedure includes a fast multiscale adaptive estimation and testing procedure to independently estimate each varying coefficient function while preserving its edges among

a short and unified proof of yu et al ʼs two results on the eccentric distance sum abstract the eccentric distance sum eds is a novel topological index that offers a vast potential for structure activity property relationships for a connected graph g the eccentric distance sum is defined as d g v v g ec g v d g v where ec g v is the eccentricity of a vertex v in g and d g v is the sum of distances of all vertices in g from v more recently yu et al g yu l feng a ilic on the eccentric distance sum of trees and unicyclic graphs j math anal appl 375 2011 99 107 proved that for an n vertex tree t d t 4 n 2 9 n 5 with equality holding if and only if t is the n vertex star s n and for an n vertex unicyclic graph g d g 4 n 2 9 n 1 with equality holding if and only if g is the graph obtained by adding an edge between two pendent vertices of n vertex star in this note we give a short and unified proof of the above two results

a proof via operator means of an order preserving inequality abstract we give an alternative and simplified proof via operator means of an order preserving inequality on a and b in the case a b 0 where an operator is a bounded linear operator on a hilbert space

index of hadamard multiplication by positive matrices ii for each n n positive semidefinite matrix a we define the minimal index i a max 0 a b b for all b 0 and for each norm n the n index in a min n a b b 0 and n b 1 where a b aijbij is the hadamard or schur product of a aij and b bij and b 0 means that b is a positive semidefinite matrix a comparison between these indexes is done for different choices of the norm n as an application we find for each bounded invertible selfadjoint operator s on a hilbert space the best constant m s such that sts s 1ts 1 m s t for all t 0

on the umbilicity of complete constant mean curvature spacelike hypersurfaces in this paper we show that a complete spacelike hypersurface immersed with constant mean curvature either in the de sitter space or in the anti de sitter space must be totally umbilical provided that its gauss mapping has some suitable behavior in particular we use an extension of hopf s maximum principle due to yau in order to give new positive answers to goddard s conjecture

on the connective eccentricity index of trees and unicyclic graphs with given diameter abstract the connective eccentricity index cei of a graph g is defined as ce g v v g d v e v where e v d v denote the eccentricity and the degree of v respectively in this paper we investigate the connective eccentricity index of trees and unicyclic graphs on n vertices with diameter d we also characterize the extremal graphs

some new connections between matrix products for partitioned and non partitioned matrices this paper is concerned with a long list of matrix products for partitioned and non partitioned matrices including kronecker khatri rao of first kind hadamard tracy singh khatri rao block kronecker block hadamard and box products sums our contribution is to gather the most useful connections of the matrix products from various sources and present them in one place several new attractive connections are also added to this collection we give as an example two applications in order to show that these connections play a central role in many applications these applications are a block diagonal least squares problem and a generalization of matrix inequalities involving khatri rao products of positive definite matrices

fully modified ols estimation and inference for seemingly unrelated cointegrating polynomial regressions and the environmental kuznets curve for carbon dioxide emissions abstract this paper develops two fully modified ols fm ols estimators for systems of seemingly unrelated cointegrating polynomial regressions i e systems of regressions that include deterministic variables integrated processes and integer powers of integrated processes as explanatory variables the stationary errors are allowed to be serially correlated and the regressors to be endogenous furthermore the errors and regressors are allowed to be dynamically cross sectionally correlated the developed estimators have zero mean gaussian mixture limiting distributions that allow for asymptotic chi squared inference the wald type hypothesis test results are the basis for considering detailed tests for general forms of group wise poolability we provide the corresponding group wise pooled variants of our estimators in case the poolability restrictions are not rejected our simulations indicate that appropriate pooling leads as expected to improved performance of the estimators and tests data driven group wise pooling turns out to be crucial in our illustrative application that analyzes the environmental kuznets curve for co 2 emissions for six early industrialized countries

on semi star related matrices abstract in this note we introduce semi star related matrices investigate some of their properties and demonstrate how the usual definition of drazin s 1978 star partial ordering can be relaxed

new calabi bernstein type results in lorentzian product spaces with density abstract we investigate the rigidity of complete spacelike hypersurfaces immersed in a weighted lorentzian product space of the type r 1 p f n endowed with a weight function f which does not depend on the parameter t r and whose riemannian fiber p n has nonnegative bakry emery ricci tensor in this direction supposing that the f mean curvature is constant and assuming appropriate constraints on the norm of the gradient of f we prove that such a spacelike hypersurface must be a slice of the ambient space as application of our investigation we obtain new calabi bernstein type results concerning entire spacelike graphs constructed over p n our approach is based on an extension for the drift laplacian of a generalized maximum principle of akutagawa 1987 and a liouville type result due to pigola et al 2005

limited information likelihood analysis of survey data analysts of survey data are often interested in modelling the population process or superpopulation that gave rise to a target set of survey variables an important tool for this is maximum likelihood estimation a survey is said to provide limited information for such inference if data used in the design of the survey are unavailable to the analyst in this circumstance sample inclusion probabilities which are typically available provide information which needs to be incorporated into the analysis we consider the case where these inclusion probabilities can be modelled in terms of a linear combination of the design and target variables and only sample values of these are available strict maximum likelihood estimation of the underlying superpopulation means of these variables appears to be analytically impossible in this case but an analysis based on approximations to the inclusion probabilities leads to a simple estimator which is a close approximation to the maximum likelihood estimator in a simulation study this estimator outperformed several other estimators that are based on approaches suggested in the sampling literature

some properties of matrix partial orderings abstract the matrix partial orderings considered are 1 the star ordering and 2 the minus ordering or rank subtractivity both in the set of m n complex matrices and 3 the lowner ordering in the set of m m matrices the problems discussed are 1 inheriting certain properties under a given ordering 2 preserving an ordering under some matrix multiplications 3 relationships between an ordering among direct or kronecker and hadamard products and the corresponding orderings between the factors involved 4 orderings between generalized inverses of a given matrix and 5 preserving or reversing a given ordering under generalized inversions several generalizations of results known in the literature and a number of new results are derived

asymptotic properties of multivariate nonstationary processes with applications to autoregressions asymptotic properties of multivariate time series with characteristic roots on the unit circle are considered for a vector autoregressive moving average process we derive the limiting distributions of certain statistics which are useful in understanding nonstationary processes these distributions are derived in a unified manner for all types of characteristic roots and are expressed in terms of stochastic integrals of brownian motions we use the limiting distributions to establish the consistency properties of the ordinary least squares estimates of various autoregressions of a vector process

some remarks on partial orderings of nonnegative definite matrices abstract baksalary and pukelsheim 1990 investigated partial orderings of nonnegative definite matrices some additional remarks are given in this note

on the extremal total reciprocal edge eccentricity of trees abstract the total reciprocal edge eccentricity is a novel graph invariant with vast potential in structure activity property relationships this graph invariant displays high discriminating power with respect to both biological activity and physical properties if g v g e g is a simple connected graph then the total reciprocal edge eccentricity ree of g is defined as e e g u v e g 1 e g u 1 e g v where e g v is the eccentricity of the vertex v in this paper we first introduced four edge grafting transformations to study the mathematical properties of the reciprocal edge eccentricity of g using these elegant mathematical properties we characterize the extremal graphs among n vertex trees with given graphic parameters such as pendants matching number domination number diameter vertex bipartition et al some sharp bounds on the reciprocal edge eccentricity of trees are determined

the eccentric connectivity index of nanotubes and nanotori let g be a molecular graph the eccentric connectivity index x c g is defined as x c g email protected u v g deg g u e g u where deg g u denotes the degree of vertex u and e g u is the largest distance between u and any other vertex v of g in this paper exact formulas for the eccentric connectivity index of tuc 4c 8 s nanotube and tc 4c 8 s nanotorus are given

on spacelike hypersurfaces with constant scalar curvature in locally symmetric lorentz spaces the purpose of this paper is to study compact or complete spacelike hypersurfaces with constant normalized scalar curvature in a locally symmetric lorentz space satisfying some curvature conditions we give an optimal estimate of the squared norm of the second fundamental form of such hypersurfaces furthermore the totally umbilical hypersurfaces are characterized

iterative generalized likelihood ratio test for mimo radar we consider a multiple input multiple output mimo radar system where both the transmitter and receiver have multiple well separated subarrays with each subarray containing closely spaced antennas because of this general antenna configuration both the coherent processing gain and the spatial diversity gain can be simultaneously achieved we compare several spatial spectral estimators including capon and apes for target detection and parameter estimation we introduce a generalized likelihood ratio test glrt and a conditional generalized likelihood ratio test cglrt for the general antenna configuration based on glrt and cglrt we then propose an iterative glrt iglrt procedure for target detection and parameter estimation via several numerical examples we show that iglrt can provide excellent detection and estimation performance at a low computational cost

the matrix inequality m b mb abstract the loewner partial ordering between nonnegative definite matrices m and b mb is considered the main result obtained generalizes a number of results known in the literature the rank subtractivity partial ordering and the drazin partial ordering between m and b mb are also discussed

weighted average geodesic distance of vicsek network abstract this paper concerns weighted average distances of vicsek fractal and vicsek networks by using the integral of geodesic distance in terms of self similar measure with respect to the weight vector