the orbifold chow ring of toric deligne mumford stacks the orbifold chow ring of a deligne mumford stack defined by abramovich graber and vistoli 2 is the algebraic version of the orbifold cohomology ring in troduced by w chen and ruan 7 8 by design this ring incorporates numerical invariants such as the orbifold euler characteristic and the orbifold hodge num bers of the underlying variety the product structure is induced by the degree zero part of the quantum product in particular it involves gromov witten invariants inspired by string theory and results in batyrev 3 and yasuda 28 one expects that in nice situations the orbifold chow ring coincides with the chow ring of a resolution of singularities fantechi and g ttsche 14 and uribe 25 verify this conjecture when the orbifold is symn 5 where 5 is a smooth projective surface with ks 0 and the resolution is hilbn the initial motivation for this project was to compare the orbifold chow ring of a simplicial toric variety with the chow ring of a cr pant resolution to achieve this goal we first develop the theory of toric deligne mumford stacks modeled on simplicial toric varieties a toric deligne mumford stack corresponds to a combinatorial object called a stacky fan as a first approximation this object is a simplicial fan with a distinguished lattice point on each ray in the fan more precisely a stacky fan s is a triple consisting of a finitely generated abelian group n a simplicial fan e in q z n with n rays and a map zn n where the image of the standard basis in zn generates the rays in e a rational simplicial fan e produces a canonical stacky fan s n e where n is the distinguished lattice and is the map defined by the minimal lattice points on the rays hence there is a natural toric deligne mumford stack associated to every simplicial toric variety a stacky fan encodes a group action on a quasi affine variety and the toric deligne mumford stack is the quotient if e corresponds to a smooth toric variety x e and s is the canonical stacky fan associated to e then we simply have x z we show that many of the basic concepts such as open and closed toric substacks line bundles and maps between toric deligne mumford stacks correspond to combinatorial notions we expect that many more results about toric varieties lift to the realm of stacks and hope that toric deligne mumford stacks will serve as a useful testing ground for general theories

aggregation vs global diffusive behavior in the higher dimensional keller segel model abstract we consider the classical parabolic parabolic keller segel system u t u u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n it is proved that in space dimension n 3 for each q n 2 and p n one can find e 0 0 such that if the initial data u 0 v 0 satisfy u 0 l q e and v 0 l p e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic equations in particular u v approaches the steady state m m as t where m is the total mass m u 0 of the population moreover we shall show that if is a ball then for arbitrary prescribed m 0 there exist unbounded solutions emanating from initial data u 0 v 0 having total mass u 0 m

mellin barnes integrals as fourier mukai transforms we study the generalized hypergeometric system introduced by gelfand kapranov and zelevinsky and its relationship with the toric deligne mumford dm stacks recently studied by borisov chen and smith we construct series solutions with values in a combinatorial version of the chen ruan orbifold cohomology and in the k theory of the associated dm stacks in the spirit of the homological mirror symmetry conjecture of kontsevich we show that the k theory action of the fourier mukai functors associated to basic toric birational maps of dm stacks are mirrored by analytic continuation transformations of mellin barnes type

asymptotic behavior of global solutions of aerotaxis equations abstract we study asymptotic behavior of global solutions of one dimensional aerotaxis model proposed in knosalla and nadzieja 2015 9

the simes method for multiple hypothesis testing with positively dependent test statistics abstract the simes method for testing intersection of more than two hypotheses is known to control the probability of type i error only when the underlying test statistics are independent although this method is more powerful than the classical bonferroni method it is not known whether it is conservative when the test statistics are dependent this article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple hypothesis testing situations the simes method indeed controls the probability of type i error this extends some results established very recently in the special case of two hypotheses

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

some probability inequalities for ordered rm mtp sb 2 random variables a proof of the simes conjecture some new probability inequalities involving the ordered components of an mtp 2 random vector are derived which provide an analytical proof of an important conjecture in the field of multiple hypothesis testing this conjecture has been mostly validated so far using simulation

tilting sheaves on toric varieties in 19 a king states the following conjecture any smooth complete toric variety has a tilting bundle whose summands are line bundles the goal of this paper is to prove king s conjecture for the following types of smooth complete toric varieties i any d dimensional smooth complete toric variety with splitting fan ii any d dimensional smooth complete toric variety with picard number 2 iii the blow up of any smooth complete minimal toric surface at t invariants points

frobenius morphisms and derived categories on two dimensional toric deligne mumford stacks abstract for a toric deligne mumford dm stack x we can consider a certain generalization of the frobenius endomorphism for such an endomorphism f x x on a 2 dimensional toric dm stack x we show that the push forward f o x of the structure sheaf generates the bounded derived category of coherent sheaves on x we also choose a full strong exceptional collection from the set of direct summands of f o x in several examples of two dimensional toric dm orbifolds x

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

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

beyond aztec castles toric cascades in the dp 3 quiver given one of an infinite class of supersymmetric quiver gauge theories string theorists can associate a corresponding toric variety which is a calabi yau 3 fold as well as an associated combinatorial model known as a brane tiling in combinatorial language a brane tiling is a bipartite graph on a torus and its perfect matchings are of interest to both combinatorialists and physicists alike a cluster algebra may also be associated to such quivers and in this paper we study the generators of this algebra known as cluster variables for the quiver associated to the cone over the del pezzo surface d p 3 in particular mutation sequences involving mutations exclusively at vertices with two in coming arrows and two out going arrows are referred to as toric cascades in the string theory literature such toric cascades give rise to interesting discrete integrable systems on the level of cluster variable dynamics we provide an explicit algebraic formula for all cluster variables that are reachable by toric cascades as well as a combinatorial interpretation involving perfect matchings of subgraphs of the d p 3 brane tiling for these formulas in most cases

monodromy of monomially admissible fukaya seidel categories mirror to toric varieties abstract mirror symmetry for a toric variety involves laurent polynomials whose symplectic topology is related to the algebraic geometry of the toric variety we show that there is a monodromy action on the monomially admissible fukaya seidel categories of these laurent polynomials as the arguments of their coefficients vary that corresponds under homological mirror symmetry to tensoring by a line bundle naturally associated to the monomials whose coefficients are rotated in the process we introduce the monomially admissible fukaya seidel category as a new interpretation of the fukaya seidel category of a laurent polynomial on c n which has other potential applications and give evidence of homological mirror symmetry for non compact toric varieties

chip chip data model and analysis summary chip chip or chip on chip is a technology for isolation and identification of genomic sites occupied by specific dna binding proteins in living cells the chip chip signals can be obtained over the whole genome by tiling arrays where a peak shape is generally observed around a protein binding site in this article we describe the chip chip process and present a probability model for chip chip data we then propose a model based method for recognizing the peak shapes for the purpose of detecting protein binding sites we also investigate the issue of bandwidth in nonparametric kernel smoothing method

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

on the conjecture of king for smooth toric deligne mumford stacks abstract we construct full strong exceptional collections of line bundles on smooth toric fano deligne mumford stacks of picard number at most two and of any picard number in dimension two it is hoped that the approach of this paper will eventually lead to the proof of the existence of such collections on all smooth toric nef fano deligne mumford stacks

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

projective toric varieties as fine moduli spaces of quiver representations this paper proves that every projective toric variety is the fine moduli space for stable representations of an appropriate bound quiver to accomplish this we study the quiver q with relations r corresponding to the finite dimensional algebra mathop rm end nolimits textstyle bigoplus nolimits i 0 r l i where cal l scr o x l 1 ldots l r is a list of line bundles on a projective toric variety x the quiver q defines a smooth projective toric variety called the multilinear series cal l and a map x longrightarrow cal l we provide necessary and sufficient conditions for the induced map to be a closed embedding as a consequence we obtain a new geometric quotient construction of projective toric varieties under slightly stronger hypotheses on cal l the closed embedding identifies x with the fine moduli space of stable representations for the bound quiver q r

eventual smoothness and stabilization of large data solutions in a three dimensional chemotaxis system with consumption of chemoattractant abstract this paper deals with positive solutions of u t u u v x t 0 v t v u v x t 0 under homogeneous neumann boundary conditions in bounded convex domains r 3 with smooth boundary it is shown that for arbitrarily large initial data this problem admits at least one global weak solution for which there exists t 0 such that u v is bounded and smooth in t moreover it is asserted that such solutions approach spatially constant equilibria in the large time limit