tensors of nonnegative rank two abstract a nonnegative tensor has nonnegative rank at most 2 if and only if it is supermodular and has flattening rank at most 2 we prove this result then explore the semialgebraic geometry of the general markov model on phylogenetic trees with binary states and comment on possible extensions to tensors of higher rank

total positivity in markov structures we discuss properties of distributions that are multivariate totally positive of order two mtp2 related to conditional independence in particular we show that any independence model generated by an mtp2 distribution is a compositional semi graphoid which is upward stable and singletontransitive in addition we prove that any mtp2 distribution satisfying an appropriate support condition is faithful to its concentration graph finally we analyze factorization properties of mtp2 distributions and discuss ways of constructing mtp2 distributions in particular we give conditions on the log linear parameters of a discrete distribution which ensure mtp2 and characterize conditional gaussian distributions which satisfy mtp2

the foundations of factor analysis summary a new approach to factor analysis and related latent variable methods is proposed which is based on data reduction using the idea of bayesian sufficiency considerations of symmetry invariance and independence are used to determine an appropriate family of models the results are expressed in terms of linear functions of the manifest variables after the manner of principal components analysis the approach justifies some of the practices based on the normal theory factor model and lays a foundation for the treatment of nonnormal including categorical variables 1 background factor analysis is a widely used statistical technique but its theoretical foundations are somewhat obscure and subject to dispute it is one of a family of multivariate methods which also includes latent structure and latent trait analysis the common feature of the models underlying these methods is that the observed random variables are assumed to depend on latent that is unobserved random variables there is sometimes debate about whether these latent variables are real in any sense but they can be viewed simply as constructs designed to simplify and summarize the complex web of interrelated variables with which nature confronts us by expressing these relationships in terms of a small number of latent variables or factors the models effect a reduction in dimensionality which aids comprehension an early theoretical account of the subject is by anderson rubin 1956 and more recent and comprehensive treatments are provided by lawley maxwell 1971 and harman 1968 the present paper is an attempt to provide a coherent framework within which existing methodology can be evaluated and a base from which new methods can be developed our approach is to start from a very general statement of the problem in terms of the distributions of the random variables involved and then to invoke ideas of symmetry invariance and conditional independence to determine the class of models that it is reasonable to consider this not only exhibits the unity of the various models already in existence but resolves many of the ambiguities and obscurities with which the subject has been bedevilled an early approach on these lines is given by anderson 1959 and was recognized by birnbaum in his contribution to lord novick 1968 the same line was followed by bartholomew 1980 in spite of this the practical implications do not seem to have been made fully explicit or generally recognized

characterizing the manifest probabilities of latent trait models the problem of characterizing the manifest probabilities of a latent trait model is considered the item characteristic curve is transformed to the item passing odds curve and a corresponding transformation is made on the distribution of ability this results in a useful expression for the manifest probabilities of any latent trait model the result is then applied to give a characterization of the rasch model as a log linear model for a 2 j contingency table partial results are also obtained for other models the question of the identifiability of guessing parameters is also discussed

nonlinear lie derivations of triangular algebras in this paper we prove that every nonlinear lie derivation of triangular algebras is the sum of an additive derivation and a map into its center sending commutators to zero

multiplicative lie n derivations of generalized matrix algebras abstract the aim of the paper is to give a description of multiplicative lie n derivations for a certain class of generalized matrix algebras as a consequence multiplicative lie n derivations of full matrix algebras are determined this solves a conjecture due to benkovic and eremita in 2012

nonlinear mappings on upper triangular matrices derivable at zero point abstract let t n f be the set of all n n upper triangular matrices over a field f recently by using a technique from graph theory l wang in 8 proved that a bijective mapping on t n f with f a finite field preserves zero product i e x y 0 whenever x y 0 if and only if can be decomposed into the product of an inner automorphism an automorphism of t n f induced by an automorphism of f and a regular automorphism of the zero divisor graph of t n f algebraic group theory shows that derivations of an algebra often go parallel with automorphisms of the algebra this viewpoint encourages us to determine nonlinear mappings on t n f which are derivable at zero point i e x y x y 0 whenever x y 0 it is proved that a mapping on t n f is derivable at zero point if and only if is the sum of an inner derivation an additive derivation of t n f induced by an additive derivation of f and a regular mapping on t n f

generalized lie derivations on skew elements of prime algebras with involution we characterize generalized lie derivations on skew elements of prime algebras a with involution provided that a does not satisfy polynomial identities of low degree the analogous result for matrix algebras is also described

a singular reaction diffusion system modelling prey predator interactions invasion and co extinction waves abstract we consider a singular reaction diffusion system arising in modelling prey predator interactions in a fragile environment since the underlying odes system exhibits a complex dynamics including possible finite time quenching one first provides a suitable notion of global travelling wave weak solution then our study focusses on the existence of travelling waves solutions for predator invasion in such environments we devise a regularized problem to prove the existence of travelling wave solutions for predator invasion followed by a possible co extinction tail for both species under suitable assumptions on the diffusion coefficients and on species growth rates we show that travelling wave solutions are actually positive on a half line and identically zero elsewhere such a property arising for every admissible wave speeds

sharp profiles in degenerate and doubly degenerate fisher kpp equations this paper investigates the effects of a degenerate diffusion term in reaction diffusion models ut d u ux x g u with fisher kpp type g both in the case when d 0 0 and when d 0 d 1 0 with d u 0 elsewhere we obtain a continuum of travelling wave solutions having wave speed c greater than a threshold value c and we show the appearance of a sharp type profile when c c these results solve recent conjectures formulated by sanchez garduno and maini j differential equations 117 1995 281 and satnoianu et al discrete continuous dyn systems series b 1 2000 339

a bayesian information criterion for singular models summary we consider approximate bayesian model choice for model selection problems that involve models whose fisher information matrices may fail to be invertible along other competing submodels such singular models do not obey the regularity conditions underlying the derivation of schwarz s bayesian information criterion bic and the penalty structure in bic generally does not reflect the frequentist large sample behaviour of the marginal likelihood although large sample theory for the marginal likelihood of singular models has been developed recently the resulting approximations depend on the true parameter value and lead to a paradox of circular reasoning guided by examples such as determining the number of components in mixture models the number of factors in latent factor models or the rank in reduced rank regression we propose a resolution to this paradox and give a practical extension of bic for singular model selection problems

a rasch model for partial credit scoring a unidimensional latent trait model for responses scored in two or more ordered categories is developed this partial credit model is a member of the family of latent trait models which share the property of parameter separability and so permit specifically objective comparisons of persons and items the model can be viewed as an extension of andrich s rating scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item the difference between the parameters in this model and the category boundaries in samejima s graded response model is demonstrated an unconditional maximum likelihood procedure for estimating the model parameters is developed

commuting traces and commutativity preserving maps on triangular algebras abstract let a be a triangular algebra the problem of describing the form of a bilinear map b a a a satisfying b x x x x b x x for all x a is considered as an application commutativity preserving maps and lie isomorphisms of certain triangular algebras e g upper triangular matrix algebras and nest algebras are determined

generalized lie derivations on triangular algebras let a be a unital algebra and let m be a unitary a bimodule we consider generalized lie derivations mapping from a to m our results are applied to triangular algebras in particular to nest algebras and block upper triangular matrix algebras we prove that under certain conditions each generalized lie derivation of a triangular algebra a is the sum of a generalized derivation and a central map which vanishes on all commutators of a

derivations of upper triangular matrix rings we give a description of the derivations in tn r the ringof upper triangular matrices over a ring r assuming only the existence of an identity element we show that every derivation is the sum of an inner derivation and another one induced from r

automorphisms and derivations of upper triangular matrix rings abstract kezlan proved that for a commutative ring c every c automorphism of the ring of upper triangular matrices over c is inner we generalize this result to rings in which all idempotents are central moreover we show that for a semiprime ring a and central subring c every c automorphism of the ring of upper triangular matrices over c is the composite of an inner automorphism and an automorphism induced from a c automorphism of a by the method of proof we re prove results of s p coelho and c p milies and of mathis stating that a derivation of a ring of upper triangular matrices of a c algebra n n matrices over a is a sum of an inner derivation and a derivation induced from a c derivation of a by an example we show that an extra assumption is needed for proving the above result of automorphisms of upper triangular matrices finally we consider automorphisms of subrings of n n matrices over a commutative ring c where entries over the diagonal are from c and below the diagonal are taken from a nil ideal we prove that all such automorphisms are inner

qualitative behavior and traveling waves for flux saturated porous media equations arising in optimal mass transportation abstract this paper is devoted to the analysis of qualitative properties of porous media flux saturated type operators which combine the effects of reaction terms of fkpp type in dimension one specifically we study the existence of traveling wave profiles sub and super solutions waiting time and dynamical properties of the support the paper also deals with the connection between these minimal traveling waves with those of other related models porous media flux saturated mechanism and the heat equation

commuting traces of biadditive mappings commutativity preserving mappings and lie mappings biadditive mappings b r r r where r is a prime ring with certain additional properties satisfying b x x x xb x x for all x r are characterized as an application we determine the structures of commutativity preserving mappings lie isomorphisms and lie derivations of certain prime rings

independence via uncorrelatedness under certain dependence structures a characterization of independence via uncorrelatedness is shown to hold for the families satisfying positive and negative dependence conditions for the associated random variables the bounds on covariance functions obtained by lebowitz comm math phys 28 1972 313 321 readily yield such a characterization an elementary proof for the same characterization is also given for a condition weaker than association labeled as strong positive negative orthant dependence this condition is compared with the linear positive dependence under which newman and wright ann probab 9 1981 671 675 obtained the characterization

additive lie ξ lie derivations and generalized lie ξ lie derivations on nest algebras abstract for a scalar a notion of generalized lie derivations is introduced which coincides with the notion of generalized lie derivations if 1 some characterizations of additive generalized lie derivations on the triangular algebras and the standard operator subalgebras of banach space nest algebras are given it is shown under some suitable assumption that an additive map l is an additive generalized lie derivation if and only if it is the sum of an additive generalized derivation and an additive map from the algebra into its center vanishing all commutators is an additive generalized lie derivation with 1 if and only if it is an additive generalized derivation satisfying l a l a for all a

on the ideals of equivariant tree models we introduce equivariant tree models in algebraic statistics which unify and generalise existing tree models such as the general markov model the strand symmetric model and group based models such as the jukes cantor and kimura models we focus on the ideals of such models we show how the ideals for general trees can be determined from the ideals for stars a corollary of theoretical importance is that the ideal for a general tree is generated by the ideals of its flattenings at vertices the main novelty is that our results yield generators of the full ideal rather than an ideal which only defines the model set theoretically

convergence to travelling waves for quasilinear fisher kpp type equations we consider the cauchy problem ut u xx u t x r r u 0 x u0 x x r when the increasing function satisfies that 0 0 and the equation may degenerate at u 0 in the case of 0 0 we consider the case of u0 l r 0 u0 x 1 a e x r and the special case of u u u we prove that the solution approaches the travelling wave solution with speed c 1 spreading either to the right or to the left or to the two travelling waves moving in opposite directions

the structure of lie derivations on c algebras we prove that every lie derivation on a c algebra is in standard form that is it can be

pattern formation in a flux limited reaction diffusion equation of porous media type a non linear pde featuring flux limitation effects together with those of the porous media equation non linear fokker planck is presented in this paper we analyze the balance of such diverse effects through the study of the existence and qualitative behavior of some admissible patterns namely traveling wave solutions to this singular reaction diffusion equation we show the existence and qualitative behavior of different types of traveling waves classical profiles for wave speeds high enough and discontinuous waves that are reminiscent of hyperbolic shock waves when the wave speed lowers below a certain threshold some of these solutions are of particular relevance as they provide models by which the whole solution and not just the bulk of it as it is the case with classical traveling waves spreads through the medium with finite speed

conditional association and unidimensionality in monotone latent variable models latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables usually assuming the conditional independence of the observable variables given the latent variables these models play an important role in educational measurement and psychometrics in sociology and in population genetics and are implicit in some work on systems reliability we study a broad class of latent variable models namely the monotone unidimensional models in which the latent variable is a scalar the observable variables are conditionally independent given the latent variable and the conditional distribution of the observables given the latent variable is stochastically increasing in the latent variable all models in this class imply a new strong form of positive dependence among the observable variables namely conditional positive association this positive dependence condition may be used to test whether any model in this class can provide an adequate fit to observed data various applications generalizations and a numerical example are discussed

stochastic factorizations sandwiched simplices and the topology of the space of explanations we study the space of stochastic factorizations of a stochastic matrix v motivated by the statistical problem of hidden random variables we show that this space is homeomorphic to the space of simplices sandwiched between two nested convex polyhedra and use this geometrical model to gain some insight into its structure and topology we prove theorems describing its homotopy type and in the case where the rank of v is 2 we give a complete description including bounds on the number of connected components and examples in which these bounds are attained we attempt to make the notions of topology accessible and relevant to statisticians

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

lie derivations of the skew elements of prime rings with involution abstract letrbe a prime ring with involution of the first kind and characteristic 2 3 letkdenote the skew elements ofr and letcdenote the extended centroid ofr assume that rc c 1 4 16 it is shown that any lie derivation ofkinto itself can be extended to an ordinary derivation of k counterexamples are given for the low dimension cases

m matrices as covariance matrices of multinormal distributions abstract the class of multivariate normal densities n 0 whose inverse covariance matrix 1 is an m matrix is equivalent to this normal density being multivariate totally positive of order 2 mtp 2 equivalent characterizations are given in terms of certain partial correlation coefficients being positive it is further shown that related partial and multiple regression coefficients and canonical correlation are positive when is an m matrix the corresponding normal random vector components are negatively associated this concept and some extensions are discussed

the correlation space of gaussian latent tree models and model selection without fitting we provide a complete description of possible distributions consistent with any gaussian latent tree model this description consists of polynomial equations and inequalities involving covariances between the observed variables testing inequality constraints can be done using the inverse wishart distribution and this leads to simple preliminary assessment of tree compatibility to test equality constraints we employ general techniques of tetrad analyses this approach is effective even for small sample sizes and can be easily adjusted to test either entire models or just particular macrostructures of a tree our methods are simple to implement and do not require fitting of the model the versatility of the techniques is illustrated by performing exploratory and confirmatory tetrad analyses in linguistic and biological settings respectively

the structure of nonlinear lie derivation on von neumann algebras national natural science foundation of china 11071201 youth national natural science foundation of china 11001230 youth talented natural science foundation of fujian 2008f3103 fundamental research funds for the central universities 2010121001

biderivations of triangular algebras abstract let a be a triangular algebra a bilinear map a a a is called a biderivation if it is a derivation with respect to both arguments in this paper we define the concept of an extremal biderivation and prove that under certain conditions a biderivation of a triangular algebra a is a sum of an extremal and an inner biderivation the main result is then applied to block upper triangular matrix algebras and nest algebras we also consider the question when a derivation of a triangular algebra is an inner derivation

real rank two geometry abstract the real rank two locus of an algebraic variety is the closure of the union of all secant lines spanned by real points we seek a semi algebraic description of this set its algebraic boundary consists of the tangential variety and the edge variety our study of segre and veronese varieties yields a characterization of tensors of real rank two

global travelling waves in reaction convection diffusion equations we study the existence and properties of solutions in travelling wave form u x t x st defined for every z x st r for the reaction convection diffusion equationut a um xx b un x kupforx r t 0 with a m n 0 b k p r in the reaction case k 0 we prove that there exist travelling waves vanishing for z if and only if b 0 and min 1 n m p2 max 1 n p max 1 n moreover if m p 2n there exists a minimal velocity s a b k m n p 0 for which there are travelling waves only with s s while in the case m p 2n there are travelling waves only when 4amk b2n and for every velocity s 0 some properties of the function s are established all the waves are decreasing in their support and waves having bounded support from the right exist if and only if m min 1 n also the absorption case k 0 is treated where we find that for different values of the parameters there exists a unique travelling wave for every velocity s r but for some case where only negative velocities exist the cases b 0 or k 0 are well known in the literature

nonlinear lie derivations on factor von neumann algebras abstract in this paper we prove that every nonlinear lie derivation from a factor von neumann algebra into itself is an additive derivation

reductions and symmetries for a generalized fisher equation with a diffusion term dependent on density and space abstract in this work a generalized fisher equation with a space density diffusion term is analyzed by applying the theory of symmetry reductions for partial differential equations the study of this equation is relevant in terms of its applicability in cell dynamics and tumor invasion therefore classical lie symmetries admitted by the equation are determined in addition by using the multipliers method we derive some nontrivial conservation laws for this equation finally we obtain a direct reduction of order of the ordinary differential equations associated and a particular solution

multiplicative lie n derivations of triangular rings abstract we introduce the notion of a multiplicative lie n derivation of a ring generalizing the notion of a lie triple derivation the main goal of the paper is to consider the question of when do all multiplicative lie n derivations of a triangular ring t have the so called standard form the main result is applied to the classical examples of triangular rings nest algebras and block upper triangular matrix rings

models of collective cell spreading with variable cell aspect ratio a motivation for degenerate diffusion models continuum diffusion models are often used to represent the collective motion of cell populations most previous studies have simply used linear diffusion to represent collective cell spreading while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles in the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations furthermore there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate here we provide a link between individual based and continuum models using a multi scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice based exclusion process for round agents that occupy a single lattice site we find that the relevant continuum description of the system is a linear diffusion equation whereas for elongated rod shaped agents that occupy l adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation pme the exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles results suggest that when using continuum models to represent cell population spreading we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models

lie triple derivations of triangular algebras abstract let r be a commutative ring with identity a b be unital algebras over r and m be a unital a b bimodule which is faithful as a left a module and also as a right b module let t a m 0 b be the triangular algebra consisting of a b and m this work is motivated by some intensive works of bresar 4 cheung 9 and zhang et al 30 here we study lie triple derivations of t it is shown that under mild assumptions every lie triple derivation on t is of standard form that is l can be expressed through an additive derivation and a linear functional vanishing on all second commutators of t examples of lie triple derivations on some classical triangular algebras are supplied

traveling wave phenomena in some degenerate reaction diffusion equations abstract in this paper we study the existence of travelling wave solutions t w s u x t x ct for the equation formula g u where the reactive part g u is as in the fisher kpp equation and different assumptions are made on the non linear diffusion term d u both functions d and g are defined on the interval 0 1 the existence problem is analysed in the following two cases case 1 d 0 0 d u 0 u 0 1 d and g c 2 0 1 d 0 0 and d 0 0 we prove that if there exists a value of c c for which the equation possesses a travelling wave solution of sharp type it must be unique by using some continuity arguments we show that for 0 c c there are no t w s while for c c the equation has a continuum of t w s of front type the proof of uniqueness uses a monotonicity property of the solutions of a system of ordinary differential equations which is also proved case 2 d 0 d 0 0 d and g c 2 0 1 d 0 0 if in addition we impose d 0 0 with d u 0 u 0 1 we give sufficient conditions on c for the existence of t w s of front type meanwhile if d 0 d u u 0 1 we analyse just one example d u u 2 and g u u 1 u which has oscillatory t w s for 0 c 2 and t w s of front type for c 2 in both the above cases we use higher order terms in the taylor series and the centre manifold theorem in order to get the local behaviour around a non hyperbolic point of codimension one in the phase plane

fixed points of the em algorithm and nonnegative rank boundaries matrices of nonnegative rank r represent mixtures of r independent distributions likelihood inference for this model leads to problems in real algebraic geometry that are addressed here for the first time we characterize the fixed point locus of expectation maximization and we study the boundary of the space of matrices with nonnegative rank at most 3 both of these are algebraic varieties with many irreducible components

comparing latent structures of the grade of membership rasch and latent class models this paper focuses on model interpretation issues and employs a geometric approach to compare the potential value of using the grade of membership gom model in representing population heterogeneity we consider population heterogeneity manifolds generated by letting subject specific parameters vary over their natural range while keeping other population parameters fixed in the marginal space based on marginal probabilities and in the full parameter space based on cell probabilities the case of a 2 2 contingency table is discussed in detail and a generalization to 2j tables with j 3 is sketched our approach highlights the main distinction between the gom model and the probabilistic mixture of classes by demonstrating geometrically the difference between the concepts of partial and probabilistic memberships by using the geometric approach we show that in special cases the gom model can be thought of as being similar to an item response theory irt model in representing population heterogeneity finally we show that the gom item parameters can provide quantities analogous to more general logistic irt item parameters as a latent structure model the gom model might be considered a useful alternative for a data analysis when both classes of extreme responses and additional heterogeneity that cannot be captured by those latent classes are expected in the population

generalized biderivations of nest algebras let n be a nest on a complex separable hilbert space h and n be the associated nest algebra in this paper we prove that every biderivation of n is an inner biderivation if and only if dim 0 1 or dimh 1 and that every generalized biderivation of n is an inner generalized biderivation if dim 0 1 and dimh 1

self scaled bounds for atomic cone ranks applications to nonnegative rank and cp rank the nonnegative rank of a matrix a is the smallest integer r such that a can be written as the sum of r rank one nonnegative matrices the nonnegative rank has received a lot of attention recently due to its application in optimization probability and communication complexity in this paper we study a class of atomic rank functions defined on a convex cone which generalize several notions of positive ranks such as nonnegative rank or cp rank for completely positive matrices the main contribution of the paper is a new method to obtain lower bounds for such ranks additionally the bounds we propose can be computed by semidefinite programming using sum of squares relaxations the idea of the lower bound relies on an atomic norm approach where the atoms are self scaled according to the vector or matrix in the case of nonnegative rank of interest this results in a lower bound that is invariant under scaling and that enjoys other interesting structural properties for the case of the nonnegative rank we show that our bound has an appealing connection with existing combinatorial bounds and other norm based bounds for example we show that our lower bound is a non combinatorial version of the fractional rectangle cover number while the sum of squares relaxation is closely related to the lovasz bar vartheta number of the rectangle graph of the matrix we also prove that the lower bound is always greater than or equal to the hyperplane separation bound and other similar norm based bounds we also discuss the case of the tensor nonnegative rank as well as the cp rank and compare our bound with existing results

semi centralizing maps of generalized matrix algebras abstract the present article is a continuation of our former work xiao and wei 2010 35 to some extent motivated by bresar s and cheung s wonderful ideas we will study semi centralizing maps of generalized matrix algebras and describe its general form by routine and complicated computations skew commuting maps and semi centralizing maps of generalized matrix algebras are specially considered we prove that any skew commuting map on a class of generalized matrix algebras is zero and that any semi centralizing derivation on a generalized matrix algebra is zero these results not only give new perspectives to the work of bresar 2004 6 but also extend the main results of cheung 2001 13 a number of applications related to semi centralizing maps are given

when are item response models consistent with observed data the problem of deciding whether a set of mental test data is consistent with any one of a large class of item response models is considered the classical assumption of locla independence is weakened to a new condition local nonnegative dependence lnd necessary and sufficient conditions are derived for a lnd item response model to fit a set of data this leads to a condition that a set of data must satisfy if it is to be representable by any item response model that assumes both local independence and monotone item characteristic curves an example is given to show that lnd is strictly weaker than local independence thus rejection of lnd models implies rejection of all item response models that assume local independence for a given set of data