the m matrix inverse problem for singular and symmetric jacobi matrices abstract we aim here at characterizing when the moore penrose inverse of a singular and symmetric jacobi m matrix is also an m matrix this characterization involves a highly non linear system of inequalities in the off diagonal entries of the matrix we obtain all the solutions of this system for n 3 but when n 4 the system becomes much more complicated our main result establishes that for any n there exist singular symmetric and tridiagonal m matrices of order n whose moore penrose inverse is also an m matrix

an affine invariant bivariate version of the sign test abstract the generalized median of h oja yields a notion of bivariate quantile and in turn an affine invariant bivariate analogue of the sign test its properties include a simple null covariance formula facilitating a permutation or sign change test in the case of bivariate symmetry normal efficiency coinciding with that of the oja median and bounded influence hence strong robustness author

on certain bivariate sign tests and medians abstract brown and hettmansperger proposed an affine invariant bivariate analogue of the sign test the os test based on the generalized median of oja on the other hand oja and nyblom introduced a family of locally most powerful affine invariant sign tests in the case of elliptic distributions the locally most powerful blumen s test and the os test are shown to be asymptotically equivalent formulas for calculating asymptotic relative efficiencies of the os test and the oja bivariate median are given it is shown that if the contours of a distribution are of a similar shape the relative efficiencies of the os test and blumen s test depend on the distribution only through the shape of the contours for the power family of contours x 1 p x 2 p c p 0 numerical calculations show that the efficiency of the os test relative to blumen s test attains its minimum 1 as p 2 spherical elliptic case and increases to infinity as p 0 in the bivariate laplace case with independent marginals p

the dynamics of an impulsive delay predator prey model with variable coefficients abstract in this paper we formulate a new robust two species nonautonomous predator prey model with multi delays and impulsive effects and perform a systematic mathematical and ecological study our results in this paper indicate that under the appropriate linear periodic impulsive perturbations the system is permanent and has a unique positive globally attractive semi trivial periodic solution by using the brouwer fixed point theorem we prove that if the periodic system is permanent then there is at least one positive periodic solution of the system we show that the conditions for global attractivity of the positive semi trivial periodic solution and permanence of the population of the model depend on time delay so we call it profitless in this paper the main feature is that we introduce multi delays and impulses into the predator prey model exhibit a new modeling method which is applied to investigate multi species impulsive multi delays differential equations

dynamic complexities of a predator prey model with generalized holling type iii functional response and impulsive effects based on the predator prey natural enemy pest system with generalized holling type iii functional response an impulsive differential system to model the processes of periodically releasing natural enemies and spraying pesticides at different fixed times for pest control is proposed and investigated it is shown that if the impulsive period is less than a threshold then the pest eradication periodic solution is globally asymptotically stable otherwise the system is permanent when the system is permanent further influences of the impulsive perturbations are studied by numerical simulation numerical simulation indicates that the system may have complex dynamics

global attractivity of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion by employing the continuation theorem of coincidence degree theory the existence of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion is established further by constructing a lyapunov functional and using the result of the existence of positive periodic solution the attractivity of a positive periodic solution for above system is obtained

on an adaptive transformation retransformation estimate of multivariate location an affine equivariant estimate of multivariate location based on an adaptive transformation and retransformation approach is studied the work is primarily motivated by earlier work on different versions of the multivariate median and their properties we explore an issue related to efficiency and equivariance that was originally raised by bickel and subsequently investigated by brown and hettmansperger our estimate has better asymptotic performance than the vector of co ordinatewise medians when the variables are substantially correlated the finite sample performance of the estimate is investigated by using monte carlo simulations some examples are presented to demonstrate the effect of the adaptive transformation retransformation strategy in the construction of multivariate location estimates for real data

multivariate functional halfspace depth this article defines and studies a depth for multivariate functional data by the multivariate nature and by including a weight function it acknowledges important characteristics of functional data namely differences in the amount of local amplitude shape and phase variation we study both population and finite sample versions the multivariate sample of curves may include warping functions derivatives and integrals of the original curves for a better overall representation of the functional data via the depth we present a simulation study and data examples that confirm the good performance of this depth function supplementary materials for this article are available online

a multivariate signed rank test for the one sample location problem abstract an affine invariant signed rank test is proposed for the one sample multivariate location problem the test suggested is a modification of randles s multivariate sign test based on interdirections which extends blumen s bivariate procedure to the multidimensional setting comparisons are made between the proposed statistic and several competitors via pitman asymptotic relative efficiencies and monte carlo results the signed rank statistic appears to be robust it performs better than its competitors when the distribution is light tailed and virtually as well as hotelling s t 2 under multivariate normality for heavy tailed distributions the signed rank statistic performs better than hotelling s t 2 but not as well as randles s statistic

existence of positive periodic solutions of a neutral delay lotka volterra system with impulses sufficient conditions are obtained for the existence of periodic positive solutions of a class of neutral impulsive delay lotka volterra systems n i t n i t a i t j 1n b i j t n j t t i j t j 1nc i j t n j t c i j t n i t k n i t k b i kn i t k i 1 2 n k 1 2 by using some techniques of mawhin coincidence degree theory my results generalize some known results it is shown that under the appropriate linear periodic impulsive perturbations the neutral impulsive delay lotka volterra system preserves the original periodicity of the neutral nonimpulsive delay lotka volterra system

affine invariant rank methods in the bivariate location model abstract the generalized multivariate median of h oja is used to define a multivariate notion of quantile or rank and to define a measure of scatter of multivariate linear models the latter when applied to the one and two sample bivariate location models yields affine invariant analogs of the wilcoxon rank sum and signed rank tests and of the corresponding estimates additional keywords dispersion measures rank statics author

analysis of a predator prey model with holling ii functional response concerning impulsive control strategy according to biological and chemical control strategy for pest control we investigate the dynamic behavior of a holling ii functional response predator prey system concerning impulsive control strategy periodic releasing natural enemies and spraying pesticide at different fixed times by using floquet theorem and small amplitude perturbation method we prove that there exists a stable pest eradication periodic solution when the impulsive period is less than some critical value further the condition for the permanence of the system is also given numerical results show that the system we consider can take on various kinds of periodic fluctuations and several types of attractor coexistence and is dominated by periodic quasiperiodic and chaotic solutions which implies that the presence of pulses makes the dynamic behavior more complex finally we conclude that our impulsive control strategy is more effective than the classical one if we take chemical control efficiently

periodic solution of a delayed ratio dependent predator prey model with monotonic functional response and impulse abstract in this paper a delayed ratio dependent predator prey model with monotonic functional response and impulse is investigated by using the continuation theorem of coincidence degree theory an easily verifiable sufficient condition for the existence of at least one positive periodic solution is established in particular our results generalize some known criteria

a stage structured holling mass defence predator prey model with impulsive perturbations on predators abstract in this work we consider a stage structured holling mass defence predator prey model with time delay and impulsive transmitting on predators sufficient conditions which guarantee the global attractivity of pest extinction periodic solution and permanence of the system are obtained we also prove that all solutions of the system are uniformly ultimately bounded our results provide reliable tactic basis for the practical pest management

on the first and second order derivatives of the perron vector abstract in a previous work 5 the authors developed formulas for the second order partial derivatives of the perron root as a function of the matrix entries at an essentially nonnegative and irreducible matrix these formulas which involve the group generalized inverse of an associated m matrix were used to investigate the concavity and convexity of the perron root as a function of the entries the authors now combine the above results together with an approach taken in an earlier joint paper 6 of the second author with l elsner and c johnson and they develop formulas for the second order derivatives of an appropriately normalized perron vector with respect to the matrix entries which again are given in terms the group generalized inverse of an associated m matrix convexity properties of the perron vector as a function of the entries of the matrix are then examined in addition formulas for the first derivative of the perron vector resulting from different normalizations of this eigenvector are also given a by product of one of these formulas yields that the group generalized inverse of a singular and irreducible m matrix can be diagonally scaled to a matrix which is entrywise column diagonally dominant

classifier selection using the predicate depth typically one approaches a supervised machine learning problem by writing down an objective function and finding a hypothesis that minimizes it this is equivalent to finding the maximum a posteriori map hypothesis for a boltzmann distribution however map is not a robust statistic we present an alternative approach by defining a median of the distribution which we show is both more robust and has good generalization guarantees we present algorithms to approximate this median one contribution of this work is an efficient method for approximating the tukey median the tukey median which is often used for data visualization and outlier detection is a special case of the family of medians we define however computing it exactly is exponentially slow in the dimension our algorithm approximates such medians in polynomial time while making weaker assumptions than those required by previous work

linearized oscillation theory for a nonlinear delay impulsive equation for a scalar nonlinear impulsive delay differential equation y t k 1m rk t fk y hk t 0 t j y j ij y j with rk t 0 hk t t limj j such an auxiliary linear impulsive delay differential equation x t k 1m rk t ak t x hk t 0 x j bjx j is constructed that oscillation nonoscillation of the nonlinear equation can be deduced from the corresponding properties of the linear equation coefficients rk t and delays are not assumed to be continuous explicit oscillation and nonoscillation conditions are established for some nonlinear impulsive models of population dynamics such as the impulsive logistic equation and the impulsive generalized lasota wazewska equation which describes the survival of red blood cells it is noted that unlike nonimpulsive delay logistic equations a solution of a delay impulsive logistic equation may become negative

sign tests in multidimension inference based on the geometry of the data cloud abstract multivariate sign tests attracted several statisticians in the past and it is evident from recent nonparametric literature that they still continue to draw attention one of the most important features of the univariate sign test is that it does not involve much technical assumptions or complicacy and this makes it quite popular among statistics users in this article we have come up with a new method for constructing multivariate sign tests that have reasonable statistical properties and can be used conveniently to solve one sample location problems our principal strategy here is to make a wise utilization of certain geometric structures in the constellation of data points for making inference about the location of their distribution as we proceed with the development of a fairly broad and general methodology we indicate its relationship with previous work done by others and sometimes attempt to unify some of the earlier ideas in particular we pick up some well known tests for uniform dis

on a geometric notion of quantiles for multivariate data abstract an extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered the approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles both of which have been extensively studied in the literature these geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many other l estimates of multivariate location and they lead to a directional notion of central and extreme points in a multidimensional setup such quantiles can be defined as meaningful and natural objects even in infinite dimensional hilbert and banach spaces and they yield an effective generalization of quantile regression in multiresponse linear model problems desirable equivariance properties are shown to hold for these multivariate quantiles and issues related to their computation for data in finite dimensional spaces are discussed n 1 2 consistenc

derivatives and perturbations of eigenvectors for a matrix bf a z whose entries are complex valued functions of a complex variable z results are presented concerning derivatives of an eigenvector bf x z of bf a z associated with a simple eigenvalue lambda z when bf x z is restricted to satisfy a constraint of the form sigma bf x z 1 where sigma is a rather arbitrary scaling function the differentiation formulas lead to a new approach for analyzing the sensitivity of an eigenvector under small perturbations in the underlying matrix finally an application is given which concerns the analysis of a finite markov chain subject to perturbations in the transition probabilities

a delayed lotka volterra model with birth pulse and impulsive effect at different moment on the prey in this paper we consider a lotka volterra model with birth pulse and impulsive catching or poisoning for the prey at different moment and stage structure on the predator we prove that all solutions of the system are uniformly ultimately bounded sufficient conditions of the global attractivity of predator extinction periodic solution and the permanence of the system are obtained these results show that impulsive effects on the prey play an important role for the permanence of the system in this paper the main feature is to introduce birth pulse and impulse catching into lotka volterra model and to give pest management strategies

a delayed stage structured predator prey model with impulsive stocking on prey and continuous harvesting on predator abstract in this work we investigate a delayed stage structured holling ii predator prey model with impulsive stocking on prey and continuous harvesting on predator sufficient conditions of the global attractivity of predator extinction periodic solution and the permanence of the system are obtained these results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system we also prove that all solutions of the system are uniformly ultimately bounded our results provide reliable tactical basis for the biological resource management

permanence of a stage structured predator prey system with impulsive stocking prey and harvesting predator abstract in this paper we propose a stage structured predator prey system with impulsive stocking immature prey and harvesting predator at different moment we analyze the global attractivity of the mature prey extinction periodic solution and obtain sufficient conditions for the permanence of the system numerical simulations are also inserted to verify the feasibility of the theoretical results moreover the obtained results show that impulsive stocking immature prey or harvesting predator may play a key role on the permanence of the system and provide tactical basis for the biological resources management

permutation tests for equality of distributions in high dimensional settings motivated by applications in high dimensional settings we suggest a test of the hypothesis h 0 that two sampled distributions are identical it is assumed that two independent datasets are drawn from the respective populations which may be very general in particular the distributions may be multivariate or infinite dimensional in the latter case representing for example the distributions of random functions from one euclidean space to another our test uses a measure of distance between data this measure should be symmetric but need not satisfy the triangle inequality so it is not essential that it be a metric the test is based on ranking the pooled dataset with respect to the distance and relative to any fixed data value and repeating this operation for each fixed datum a permutation argument enables a critical point to be chosen such that the test has concisely known significance level conditional on the set of all pairwise distances

an approach to multivariate rank tests in multivariate analysis of variance abstract a class of multivariate rank like quantities is defined and used to develop multivariate tests to mimic popular one dimensional rank tests such as the mann whitney wilcoxon two sample test the jonckheere terpstra test for trend and the kruskal wallis one way analysis of variance test tests in one way analysis of variance are developed based on qualitative orthogonal contrasts allowing decomposition of an overall statistic into asymptotically independent components based on the contrasts the class of tests includes the usual normal theory tests and the componentwise rank tests but the main focus is on the tests based on a particular definition of multivariate rank a study of the pitman efficiency of the latter tests to those based on multivariate medians shows them to be superior at the normal slightly heavy tailed and light tailed distributions whereas the median based tests are superior for heavy tails these results are analogous to the univariate case

on the influence functions of certain bivariate medians the asymptotic efficiency influence function and breakdown properties of the multivariate median proposed by oja are investigated and comparisons are made with two other generalizations of the median the spatial median and the vector of marginal medians it is shown that for distributions with finite expectations the oja median has a bounded influence function although this median has 0 breakdown for circular distributions the influence functions of the oja median and the spatial median coincide the oja median is then as efficient as the spatial median in the circular case but strictly better for any other elliptical case it is noteworthy that the spatial median however has the best possible 50 breakdown this phenomenon is analysed in the paper it is shown that the finite sample breakdown point of the oja median depends on the dispersion of the corrupted observations

pest regulation by means of impulsive controls in this paper we consider an integrated pest management model which is impulsively controlled by means of biological and chemical controls these controls are assumed to act in a periodic fashion a nonlinear incidence rate being used to account for the dynamics of the disease caused by the application of the biological control the floquet theory for impulsive ordinary differential equations is employed to obtain a condition in terms of an inequality involving the total action of the nonlinear force of infection in a period under which the susceptible pest eradication solution is globally asymptotically stable if the opposite inequality is satisfied then it is shown that the system under consideration becomes uniformly persistent a biological interpretation of the persistence condition is also provided

a distribution free multivariate sign test based on interdirections abstract distribution free tests are investigated for the one sample multivariate location problem counts called interdirections which measure the angular distance between two observation vectors relative to the positions of the other observations are introduced these counts are invariant under nonsingular linear transformations and have a small sample distribution free property over a broad class of population models called distributions with elliptical directions which includes all elliptically symmetric populations and many skewed populations a sign test based on interdirections is described including as special cases the two sided univariate sign test and blumen s bivariate sign test the statistic is shown to have a limiting 2 p null distribution and because it is based on interdirections it is also seen to be invariant and to have a small sample distribution free property pitman asymptotic relative efficiencies and a monte carlo study show the test to perform well compared with hotell

dynamical analysis of a stage structured predator prey system with impulsive diffusion and generic functional response based on the predator prey system with stage structure and generalized functional response an impulsive differential system to model the process of periodical diffusion at different fixed time is proposed and investigated by using comparison theorem of impulsive differential equation and some analysis techniques sufficient conditions ensuring the existence of a predator extinction positive periodic solution and the permanence of the system are established numerical simulation shows that impulses and functional response affect the dynamics of the system which may be very complex

group inverses of m matrices associated with nonnegative matrices having few eigenvalues abstract we continue here earlier investigations of the structure of group generalized inverses a of singular and irreducible m matrices a ri m where m is an n n nonnegative and irreducible matrix whose spectral radius is r and where m is assumed to belong to one of several special classes of nonnegative matrices we now focus on cases where m has only a few distinct eigenvalues we are particularly interested in instances of such matrices m which cause all or almost all of the off diagonal entries of the corresponding a to be nonpositive we then apply our results to the study of the sign pattern of the off diagonal entries of the group generalized inverse of a ri m where m comes from one of the following families of nonnegative matrices 1 the magic square of order n 4k generated by matlab 2 the doubly regular tournament matrices the latter type is an example of a special type of a nonnegative matrix m for which the group inverse of the associated m matrix satisfies a a t for some 0

on the limiting distributions of multivariate depth based rank sum statistics and related tests a depth based rank sum statistic for multivariate data introduced by liu and singh j amer statist assoc 88 1993 252 260 as an extension of the wilcoxon rank sum statistic for univariate data has been used in multivariate rank tests in quality control and in experimental studies those applications however are based on a conjectured limiting distribution provided by liu and singh j amer statist assoc 88 1993 252 260 the present paper proves the conjecture under general regularity conditions and therefore validates various applications of the rank sum statistic in the literature the paper also shows that the corresponding rank sum tests can be more powerful than hotelling s t 2 test and some commonly used multivariate rank tests in detecting location scale changes in multivariate distributions

on the concept of depth for functional data the statistical analysis of functional data is a growing need in many research areas in particular a robust methodology is important to study curves which are the output of many experiments in applied statistics as a starting point for this robust analysis we propose analyze and apply a new definition of depth for functional observations based on the graphic representation of the curves given a collection of functions it establishes the centrality of an observation and provides a natural center outward ordering of the sample curves robust statistics such as the median function or a trimmed mean function can be defined from this depth definition its finite dimensional version provides a new depth for multivariate data that is computationally feasible and useful for studying high dimensional observations thus this new depth is also suitable for complex observations such as microarray data images and those arising in some recent marketing and financial studies natural properties of these

estimates of regression coefficients based on the sign covariance matrix the influence function and asymptotic theory are developed to consider robustness and limiting efficiencies of the scm regression estimate the estimate is shown to be consistent with a limiting multinormal distribution the influence function as a function of the length of the contamination vector is shown to be linear in elliptic cases for the least squares ls estimate it is quadratic the asymptotic relative efficiencies with respect to the ls estimate are given in the multivariate normal as well as the t distribution cases the scm regression estimate is highly efficient in the multivariate normal case and for heavy tailed distributions it performs better than the ls estimate simulations are used to consider finite sample efficiencies with similar results the theory is illustrated with an example

derivatives of the perron root at an essentially nonnegative matrix and the group inverse of an m matrix abstract the results of the work in this paper can be divided into two major parts in the first part we develop formulae using group inverses of irreducible m matrices for the second order partial derivatives with respect to the entries of the perron root r at an essentially nonnegative and irreducible matrix a we use these formulae to obtain explicit expressions for the matrices 2 r a ij 2 and 2 r a ii jj and examine these expressions at some special cases when for example in addition to a being essentially nonnegative and irreducible a is row stochastic or a is of rank 1 and so on in the second major part of this paper we investigate for a singular and irreducible m matrix q a certain matrix g which is a positive diagonal scaling of the group inverse q of q we show for instance that z gz 0 for all real vectors z and use this result and some of the formulae obtained in the first part of the paper to provide a matrix theoretic proof of a theorem due to j e cohen math proc cambridge philos soc 86 1979 343 350 which states that for an essentially nonnegative and irreducible matrix a the perron root is a convex function of the main diagonal of a

existence and global attractivity of positive periodic solution for an impulsive lasota wazewska model abstract sufficient conditions are obtained for the existence and global attractivity of periodic positive solution of an impulsive lasota wazewska model for the survival of red blood cells

on a notion of data depth based on random simplices for a distribution f on mathbb r p and a point x in mathbb r p the simplical depth d x is introduced which is the probability that the point x is contained inside a random simplex whose vertices are p 1 independent observations from f mathematically and heuristically it is argued that d x indeed can be viewed as a measure of depth of the point x with respect to f an empirical version of d cdot gives rise to a natural ordering of the data points from the center outward the ordering thus obtained leads to the introduction of multivariate generalizations of the univariate sample median and l statistics this generalized sample median and l statistics are affine equivariant

statistical uses of the spatial median the spatial median called the mediancentre in an earlier paper by j c gower is defined as the bivariate location measure to minimize the sum of absolute distances to observations its asymptotic efficiency relative to the sample mean vector with normal data is shown to exceed the usual univariate 2 ir 0 637 its estimating equations have an angular aspect and are used to develop angle tests which are analogues of sign tests in one dimension

multivariate sign based high dimensional tests for the two sample location problem abstractthis article concerns tests for the two sample location problem when data dimension is larger than the sample size existing multivariate sign based procedures are not robust against high dimensionality producing tests with type i error rates far away from nominal levels this is mainly due to the biases from estimating location parameters we propose a novel test to overcome this issue by using the leave one out idea the proposed test statistic is scalar invariant and thus is particularly useful when different components have different scales in high dimensional data asymptotic properties of the test statistic are studied compared with other existing approaches simulation studies show that the proposed method behaves well in terms of sizes and power supplementary materials for this article are available online

generalized inverses of symmetric m matrices abstract in this work we carry out an exhaustive analysis of the generalized inverses of singular irreducible symmetric m matrices the key idea in our approach is to identify any symmetric m matrix with a positive semi definite schrodinger operator on a connected network whose conductances are given by the off diagonal elements of the m matrix moreover the potential of the operator is determined by the positive eigenvector of the m matrix we prove that any generalized inverse can be obtained throughout a green kernel plus some projection operators related to the positive eigenfunction moreover we use the discrete potential theory associated with any positive semi definite schrodinger operator to get an explicit expression for any generalized inverse in terms of equilibrium measures finally we particularize the obtained result to the cases of tridiagonal matrices and circulant matrices

multidimensional trimming based on projection depth as estimators of location parameters univariate trimmed means are well known for their robustness and efficiency they can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy tailed models this paper introduces multidimensional trimmed means based on projection depth induced regions robustness of these depth trimmed means is investigated in terms of the influence function and finite sample breakdown point the influence function captures the local robustness whereas the breakdown point measures the global robustness of estimators it is found that the projection depth trimmed means are highly robust locally as well as globally asymptotics of the depth trimmed means are investigated via those of the directional radius of the depth induced regions the strong consistency asymptotic representation and limiting distribution of the depth trimmed means are obtained relative to the mean and other leading competitors the depth trimmed means are highly efficient at normal or symmetric models and overwhelmingly more efficient when these models are contaminated simulation studies confirm the validity of the asymptotic efficiency results at finite samples

dynamical analysis and optimal control in a hybrid stochastic double delayed bioeconomic system with impulsive contaminants emission and levy jumps abstract in this paper a hybrid stochastic double delayed prey predator bioeconomic system with impulses and levy jumps is established where commercial harvesting on each population and impulsive contaminants emission from surrounding environment on each population growth are taken into account sufficient conditions for persistence in the mean and extinction of interacting population are investigated the asymptotical stability in distribution of the proposed system is studied furthermore optimal price control strategy and maximum of expectation of sustainable yield are discussed numerical simulations are carried out to illustrate theoretical analysis

m matrix generalized inverses of m matrices abstract let p be an n n nonnegative irreducible and stochastic matrix and consider the associated singular and irreducible m matrix q i p we show that without further restrictive spectral or combinatorial assumptions on p it is reasonable to expect that the group inverse q of q will be an m matrix only when p lies in a small wedge about a rank 1 nonnegative matrix a wedge whose existence is itself dependent on p we go on to consider the question of when q has a nonzero generalized inverse not necessarily the group inverse which is an m matrix we give examples of all sorts of classes of p for which such is the case but point out that the general problem remains unsolved

on convexity properties of the spectral radius of nonnegative matrices abstract elementary matrix theoretic proofs are given for the following well known results r d max re an eigenvalue of a d and s d ln e d a are convex here d is diagonal a a nonnegative n n matrix and the spectral radius

dynamics behaviors of a delayed stage structured predator prey model with impulsive effect in this paper we analyzed a delayed stage structured predator prey model with impulsive stocking on prey and continuous harvesting on predator sufficient conditions for the global attractivity of predator eradication periodic solution and permanence of the system are obtained the results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system

projection correlation between two random vectors we propose the use of projection correlation to characterize dependence between two random vectors projection correlation has several appealing properties it equals zero if and only if the two random vectors are independent it is not sensitive to the dimensions of the two random vectors it is invariant with respect to the group of orthogonal transformations and its estimation is free of tuning parameters and does not require moment conditions on the random vectors we show that the sample estimate of the projection correction is formula see text consistent if the two random vectors are independent and root formula see text consistent otherwise monte carlo simulation studies indicate that the projection correlation has higher power than the distance correlation and the ranks of distances in tests of independence especially when the dimensions are relatively large or the moment conditions required by the distance correlation are violated

on directional regression for dimension reduction we introduce directional regression dr as a method for dimension reduction like contour regression dr is derived from empirical directions but achieves higher accuracy and requires substantially less computation dr naturally synthesizes the dimension reduction estimators based on conditional moments such as sliced inverse regression and sliced average variance estimation and in doing so combines the advantages of these methods under mild conditions it provides exhaustive and consistent estimate of the dimension reduction space we develop the asymptotic distribution of the dr estimator and from that a sequential test procedure to determine the dimension of the central space we compare the performance of dr with that of existing methods by simulation and find strong evidence of its advantage over a wide range of models finally we apply dr to analyze a data set concerning the identification of hand written digits

affine invariant multivariate multisample sign tests summary invariant sign type tests for the multivariate multisample location models are developed the definition of sign is based on the oja criterion function emphasis is on the twosample location model and the associated equivariant estimate of shift asymptotic theory is developed to provide large sample approximations for the null distribution of the test and to provide a framework for a discussion of efficiency tests are then developed for the one way and two way lay outs

affine invariant multivariate one sample signed rank tests abstract brown and hettmansperger introduced affine invariant bivariate analogs of the sign rank and signed rank tests based on the oja median in this article affine invariant k variate extensions of the one sample signed rank test and the hodges lehmann estimate are considered the necessary distribution theory is developed and asymptotic pitman efficiencies with respect to hotelling s t 2 test under multivariate t distributions are tabulated an application of the signed rank tests to a repeated measurement setting is presented

penalty based aggregation of multidimensional data abstract research in aggregation theory is nowadays still mostly focused on algorithms to summarize tuples consisting of observations in some real interval or of diverse general ordered structures of course in practice of information processing many other data types between these two extreme cases are worth inspecting this contribution deals with the aggregation of lists of data points in r d for arbitrary d 1 even though particular functions aiming to summarize multidimensional data have been discussed by researchers in data analysis computational statistics and geometry there is clearly a need to provide a comprehensive and unified model in which their properties like equivariances to geometric transformations internality and monotonicity may be studied at an appropriate level of generality the proposed penalty based approach serves as a common framework for all idempotent information aggregation methods including componentwise functions pairwise distance minimizers and data depth based medians it also allows for deriving many new practically useful tools

effects of toxin delay on the dynamics of a phytoplankton zooplankton model abstract this paper is concerned with a phytoplankton zooplankton model with toxin delay it is shown that the positive equilibrium of the system is stable when the toxin delay is not included however we find that the incorporation of a discrete toxin delay not only can destabilize the positive equilibrium of the system but also can cause a hopf bifurcation at the positive equilibrium as it crosses some critical values in particular the normal form of the hopf bifurcation arising in the system is determined to investigate the direction and the stability of periodic solutions bifurcating from these hopf bifurcations to verify the obtained conditions a special numerical example is also included these results in this work demonstrate that the toxin delay plays an important role on deriving the complex dynamics

the stationary distribution and ergodicity of a stochastic phytoplankton zooplankton model with toxin producing phytoplankton under regime switching abstract this paper addresses a stochastic phytoplankton zooplankton model with toxin producing phytoplankton under regime switching the stochastic model in this paper includes white and colored noises for the model we first prove the existence of the global positive solution of the model and then by using khasminskii s method and lyapunov function we derive sufficient conditions for the existence of a unique ergodic stationary distribution finally numerical simulations are carried out to support our results

stability for impulsive delay differential equations abstract in this paper the stability for the scalar impulsive delay differential equation y t a t y t f t y 0 t 0 t k y k y k i k y k k 1 2 lim k k where delay arguments may be bounded or unbounded is investigated some new stability theorems are established which improve and extend several known results in the literature

practical stabilization of control systems with impulse effects abstract in this paper we investigate practical stabilization of control systems with impulse effects utilizing piecewise continuous lyapunov functions and impulsive differential inequalities we prove some general comparison results through which we establish some sufficient conditions for practical stabilization of control systems with impulse effects we also use two different measures which gives a unified approach and include many interesting special cases

nonnegative alternating circulants leading to m matrix group inverses abstract let c be the set of all an n n nonnegative irreducible alternating circulant matrices we characterize a subset c of c such that if b c and the perron root of b is r then the group inverse ri b of the singular and irreducible m matrixri b is also an m matrix this is equivalent to the fact that for each such b the perron root at b is a concave function in each of the off diagonal entries the characterization for the case when n is odd presents more difficulties than for the case when n is even so the two cases are treated separately

new comparison results for impulsive integro differential equations and applications we prove some new maximum principles for ordinary integro differential equations this allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first order impulsive integro differential equation

a quality index based on data depth and multivariate rank tests let f and g be the distribution functions of two given populations on rp p 1 we introduce and study a parameter q q f g which measures the overall outlyingness of population g relative to population f the parameter q can be defined using any concept of data depth its value ranges from 0 to 1 and is 5 when f and g are identical we show that within the dass of elliptical distributions when g departs from f in location or g has a larger spread or both the value of q dwindles down from 5 hence q can be used to detect the loss of accuracy or precision of a manufacturing process and thus it should serve as an important measure in quality assurance this in fact is the reason why we refer to q as a quality index in this article in addition to studying the properties of q we provide an exact rank test for testing q 5 vs q 5 this can be viewed as a multivariate analog of wilcoxon s rank sum test the tests proposed here have power against location change and scale increase simultaneo

taylor expansions of eigenvalues of perturbed matrices with applications to spectral radii of nonnegative matrices let a and b be two n n complex matrices and let be an eigenvalue of a the purpose of this paper is to derive under certain conditions taylor power series expansions of the form k 1 kek and k 0 kek respectively for eigenvalues and corresponding eigenvectors of the perturbed matrices a eb for e that has sufficiently small absolute value our results apply to the case where is a simple eigenvalue of a e g when a is nonnegative and irreducible and is the spectral radius of a in particular if a eb is nonnegative for sufficiently small nonnegative e and a is irreducible we obtain power series expansions for the spectral radii of the perturbed matrices a eb and for corresponding eigenvectors the coefficients of the expansions yield explicit expressions for the regular and mixed derivatives of the spectral radius and of a corresponding eigenvector of a nonnegative irreducible matrix when viewed as a function of the elements of the matrix our approach is constructive and we present a recursive algorithm that will compute the coefficients of the above series

boundedness for impulsive delay differential equations and applications to population growth models abstract in this paper criteria on uniform ultimate boundedness are derived for impulsive delay differential equations using lyapunov functions and razumikhin techniques it should be noted that the boundedness criteria establish global existence of solutions as well as boundedness without assuming a priori that solutions can necessarily be continued to infinity those criteria are then used to obtain permanence results for population growth models some examples are discussed to illustrate the theorems

the dynamics of an impulsive one prey multi predators system with delay and holling type ii functional response considering the effects of changing environments delays impulses and functional response a one prey multi predators system is established in this paper using comparison theorem and some analysis techniques sufficient conditions ensuring the global attractivity of the prey extinction positive periodic solution and the permanence of the system are obtained finally examples and numerical simulations are given to show the effectiveness of the main results

bivariate sign tests abstract in this article the bivariate location problem is treated new appealing bivariate analogs of the univariate sign tests are proposed for testing the null hypothesis concerning the unknown symmetry center these tests remain unaltered under any nonsingular linear transformation from these promising findings a whole family of locally most powerful invariant sign tests is introduced the tests proposed earlier blumen 1958 hodges 1955 are specific members of this family for example blumen s test appears to be optimal against bivariate normal or any other elliptic alternatives the limiting distributions are derived both under the null hypothesis and under the contiguous alternatives these limiting distributions are then used to derive asymptotic relative efficiencies it is found that blumen s test has the efficiency 785 relative to hotelling s test against bivariate normal alternatives for other locally most powerful sign tests the corresponding efficiency depends on the significance leve

a simpler affine invariant multivariate distribution free sign test abstract a simpler multivariate sign test is proposed that uses the transformation retransformation approach of chakraborty chaudhuri and oja together with a directional transformation due to tyler this produces a multivariate sign test that is practical to apply to data of any dimension makes minimal assumptions about the underlying distribution and has a small sample distribution free property over a broad class of population models it is shown to perform very well in comparison to hotelling s t 2 and other multivariate sign tests for heavy tailed and skewed distributions