negative holomorphic curvature and positive canonical bundle in this note we show that if a projective manifold admits a kahler metric with negative holomorphic sectional curvature then the canonical bundle of the manifold is ample this confirms a conjecture of the second author

traveling wave solutions in a diffusive system with two preys and one predator abstract this paper is concerned with the traveling wave solutions in a diffusive system with two preys and one predator by constructing upper and lower solutions the existence of nontrivial traveling wave solutions is established the asymptotic behavior of traveling wave solutions is also confirmed by combining the asymptotic spreading with the contracting rectangles applying the theory of asymptotic spreading the nonexistence of traveling wave solutions is proved

gromov witten invariants in algebraic geometry gromov witten invariants for arbitrary non singular projective vari eties and arbitrary genus are constructed using the techniques from k behrend b fantechi the intrinsic normal cone

an empirical bayes formulation of cohort models in cancer epidemiology this paper concerns the incidence rates of malignant skin melanoma for several age sex groups and time periods in three geographic regions uses a method of cohort analysis and employs a two stage random effects model the first stage entails the assumption that the within region variation in the frequency of disease incidence for a fixed age sex cohort group has a poisson distribution with mean proportional to the population at risk the second stage after adjusting for age and sex entails the assumption that the between region geographic variation in the logarithm of the true incidence rate has a prior distribution with parameters estimated by the method of maximum likelihood after adjusting for age effects we estimate random geographic specific cohort effects for each sex with use of an empirical bayes method and compare the results with the usual multiplicative poisson model that assumes fixed geographic specific cohort effects for each sex this comparison shows that the method presented here provides more stable estimates of geographic specific cohort effects and in addition the random effects model describes these data more adequately

pull back morphisms for reflexive differential forms abstract let f x y be a morphism between normal complex varieties where y is kawamata log terminal given any differential form defined on the smooth locus of y we construct a pull back form on x the pull back map obtained by this construction is y linear uniquely determined by natural universal properties and exists even in cases where the image of f is entirely contained in the singular locus of y one relevant setting covered by the construction is that where f is the inclusion or normalisation of the singular locus y sing as an immediate corollary we show that differential forms defined on the smooth locus of y induce forms on every stratum of the singularity stratification the same result also holds for many whitney stratifications

reduction of manifolds with semi negative holomorphic sectional curvature in this note we continue the investigation of a projective kahler manifold m of semi negative holomorphic sectional curvature h we introduce a new differential geometric numerical rank invariant which measures the number of linearly independent truly flat directions of h in the tangent spaces we prove that this invariant is bounded above by the nef dimension and bounded below by the numerical kodaira dimension of m we also prove a splitting theorem for m in terms of the nef dimension and under some additional hypotheses in terms of the new rank invariant

weak approximation for isotrivial families we study weak approximation for isotrivial families of rationally connected varieties over a smooth projective curve in the case where the family is formed by taking a quotient of a cyclic group action we find a necessary and sufficient condition for weak approximation to hold in most other cases there is also a sufficient condition we also check that this condition is satisfied for all smooth fano hypersurfaces in projective spaces

spreading speeds of a lotka volterra predator prey system the role of the predator abstract this paper is concerned with the spreading speeds of a modified lotka volterra predator prey system the intention is to describe the propagation mode whereby the two species coinvade a new habitat under some assumptions it is proved that the spreading speed of the prey is slower than in the case where the predator vanishes and the density of the prey on the coexistence domain is also smaller compared with the case where interspecies actions disappear therefore the predator has a negative effect on the evolution of the prey by slowing the spreading speed and decreasing the population density of the prey

singular foliations with trivial canonical class this paper describes the structure of singular codimension one foliations with numerically trivial canonical bundle on complex projective manifolds

estimation of cancer mortality rates a bayesian analysis of small frequencies a bayesian method is presented for estimating mortality rates of specific diseases when the frequency of deaths over a specified time period is assumed to have a poisson distribution with mean proportional to the population size the estimators use information from related populations each having its own rate which is assumed distributed according to a common prior distribution about which some information is available the method is illustrated using data from an epidemiological study on the geographic variation of cancer mortality in missouri comparisons are also made with a simpler empirical bayes method excerpt

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

the grothendieck ring of varieties and piecewise isomorphisms let k0 var k be the grothendieck ring of algebraic varieties over a field k l et x y be two algebraic varieties over k which are piecewise isomorphic i e x and y admit finite partitions x1 xn y1 yn into locally closed subvarieties such that xi is iso morphic to yi for all i n then x y in k0 var k larsen and lunts ask whether the converse is true for characteristic zero and algebraically closedfield k we answer positively this question when dim x 1o rx is a smooth connected projective surface or if x contains only finitely many rational curves

hermitian metrics of positive holomorphic sectional curvature on fibrations the main result of this note essentially is that if the base and fibers of a compact fibration carry hermitian metrics of positive holomorphic sectional curvature then so does the total space of the fibration the proof is based on the use of a warped product metric as in the work by cheung in case of negative holomorphic sectional curvature but differs in certain key aspects e g in that it does not use the subadditivity property for holomorphic sectional curvature due to grauert reckziegel and wu

on fano foliations abstract in this paper we address fano foliations on complex projective varieties these are foliations whose anti canonical class k is ample we focus our attention on a special class of fano foliations namely del pezzo foliations on complex projective manifolds we show that these foliations are algebraically integrable with one exceptional case when the ambient space is p n we also provide a classification of del pezzo foliations with mild singularities

traveling waves in diffusive predator prey equations periodic orbits and point to periodic heteroclinic orbits we demonstrate the existence of periodic traveling wave train and traveling front solutions for a diffusive predator prey system the analysis is in the three dimensional phase space of the nonlinear ordinary differential equation system given by the diffusive predator prey system in the traveling wave variable the analysis shows the existence of periodic orbits heteroclinic orbits and a heteroclinic connection of a point and a periodic orbit the proof uses shooting techniques invariant manifold theory and the qualitative theory of ordinary differential equations

invasion traveling wave solutions of a predator prey system abstract this paper is concerned with the traveling wave solutions of a predator prey system in which intra specific conflictions are involved by using the comparison principle and the asymptotic speed of spreading the existence nonexistence and minimal wave speed of non negative traveling wave solutions are established such a traveling wave solution can model the spatial temporal process where the predator invades the territory of the prey and they eventually coexist

asymptotic spreading in a lotka volterra predator prey system abstract this paper is concerned with the asymptotic spreading of a lotka volterra predator prey system with self limit effect in which the intrinsic growth rates of both species are positive the spreading speeds of both species are estimated which implies the role of nonlinearities in asymptotic spreading biologically our results confirm that the prey may contribute to the asymptotic spreading of the predator

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

mathbb a 1 connected varieties of rank one over nonclosed fields in this paper we prove two results regarding the arithmetics of separably mathbb a 1 connected varieties of rank one first we prove that over a large field there is an mathbb a 1 curve through any rational point of the boundary if the boundary divisor is smooth and separably rationally connected secondly we generalize a theorem of hassett tschinkel for the zariski density of integral points over function fields of curves

traveling wave solutions for a continuous and discrete diffusive predator prey model abstract we study a diffusive predator prey model of lotka volterra type functional response in which both species obey the logistic growth such that the carrying capacity of the predator is proportional to the prey population and the one for prey is a constant both continuous and discrete diffusion are addressed our aim is to see whether both species can survive eventually if an alien invading predator is introduced to the habitat of an existing prey the answer to this question is positive under certain restriction on the parameter applying schauder s fixed point theory with the help of suitable upper and lower solutions the existence of traveling wave solutions for this model is proven furthermore by deriving the non existence of traveling wave solutions we also determine the minimal speed of traveling waves for this model this provides an estimation of the invasion speed

traveling wave solutions of diffusive lotka volterra equations a heteroclinic connection in we establish the existence of traveling wave solutions for a reaction dif fusion system based on the lotka volterra differential equation model of a predator and prey interaction the waves are of transition front type analogous to the solutions discussed by fisher and kolmogorov et al for a scalar reaction diffusion equation the waves discussed here are not necessarily monotone there is a speed c 0 such that for c c there is a traveling wave moving with speed c the proof uses a shooting argument based on the nonequivalence of a simply connected region and a nonsimply connected region together with a liapunov function to guarantee the existence of the traveling wave solution the traveling wave solution is equivalent to a heteroclinic orbit in 4 dimensional phase space

degenerations of rationally connected varieties we prove that a degeneration of rationally connected varieties over a field of characteristic zero always contains a geometrically irreducible subvariety which is rationally connected

rational curves in holomorphic symplectic varieties and gromov witten invariants abstract we use gromov witten theory to study rational curves in holomorphic symplectic varieties we present a numerical criterion for the existence of uniruled divisors swept out by rational curves in the primitive curve class of a very general holomorphic symplectic variety of k 3 n type we also classify all rational curves in the primitive curve class of the fano variety of lines in a very general cubic 4 fold and prove the irreducibility of the corresponding moduli space our proofs rely on gromov witten calculations by the first author and in the fano case on a geometric construction of voisin in the fano case a second proof via classical geometry is sketched

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

empirical bayes estimates of cancer mortality rates using spatial models we give results of empirical bayes eb estimation of mortality rates designed to smooth observed smr when random fluctuation of the observed deaths is important we have specially studied the case where the prior distributions of the eb method have a spatial structure the need for spatial modelling of cancer mortality rates in france is first shown with testing autocorrelation and fitting autoregressive spatial models conditional car or simultaneous sar a positive autocorrelation of the rates is shown for most cancer sites studied as expected eb estimates of mortality rates for common tumours are similar to smrs for rare tumours the eb method identifies the extreme rates more clearly than smrs by smoothing the smrs with large variances car or sar models are adequate prior distributions for autocorrelated rates and produce quite similar rate estimates

cohomologie non ramifiee et conjecture de hodge entiere en nous appuyant sur la conjecture de bloch kato en k theorie de milnor nous etablissons un lien general entre le defaut de la conjecture de hodge entiere pour la cohomologie de degre 4 et le troisieme groupe de cohomologie non ramifiee a coefficients q z ceci permet de montrer que sur un solide en anglais threefold uniregle le troisieme groupe de cohomologie non ramifiee a coefficients q z s annule ce que la k theorie algebrique ne permet d obtenir que dans certains cas ceci permet a l inverse de deduire d exemples ayant leur source en k theorie que la conjecture de hodge entiere pour la cohomologie de degre 4 peut etre en defaut pour les varietes rationnellement connexes pour certaines familles a un parametre de surfaces on etablit un lien entre la conjecture de hodge entiere et l indice de la fibre generique

some remarks concerning voevodsky s nilpotence conjecture in this article we extend voevodsky s nilpotence conjecture from smooth projective schemes to the broader setting of smooth proper dg categories making use of this noncommutative generalization we then address voevodsky s original conjecture in the following cases quadric fibrations intersection of quadrics linear sections of grassmannians linear sections of determinantal varieties homological projective duals and moishezon manifolds

a variance components approach to categorical data models with heterogeneous cell populations analysis of spatial gradients in lung cancer mortality rates in north carolina counties a mixed categorical continuous variable model is proposed for the analysis of mortality rates this model differs from other available models such as weighted least squares and loglinear models in that the within cell populations are assumed to be heterogeneous in their levels of mortality risk heterogeneity implies that in addition to the sampling variance considered in other available models there will be a second component of variance due solely to within cell heterogeneity maximum likelihood procedures are presented for the estimation of the model parameters these procedures are based on the assumption that the distribution function for each cell death count is the negative binomial probability function this assumption is shown to be equivalent to assuming a mixture of poisson processes with the differential risk levels among individuals within each cell being governed by a two parameter gamma distribution the model is applied to data on lung cancer mortality for 1970 1975 for the 100 counties of north carolina the analysis shows that though a gradient in lung cancer mortality rates exist in space the gradient is restricted to specific demographic categories identified by race age and sex

traveling wavefronts for delayed reaction diffusion systems via a fixed point theorem abstract by using schauder s fixed point theorem we prove some existence results for traveling wavefronts of reaction diffusion systems with quasimonotonicity reactions more precisely we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice finally to illustrate our main results we study the existence of traveling wavefronts for a delayed predator prey model with diffusion as well as the reaction diffusion system with the well known belousov zhabotinskii reaction and the obtained results improve the existing ones

the existence of periodic travelling waves for singularly perturbed predator prey equations via the conley index this paper is concerned with the existence of periodic travelling wave solutions of reactiondiffusion equations which arise as models of predator prey interactions in mathematical ecology the relevant equations are somewhat similar to the fitz hugh nagumo equations and our results apply to this latter system as well in studying the fitz hugh nagumo equations conley 3 i initiated a new topological approach to this problem his method depends on the construction of an isolating neighborhood cf section 2a about a singular periodic solution associated with such a neighborhood is a topological invariant the conley index which when nontrivial implies the existence of a smooth solution near the singular one the new aspects of the present discussion are in the method used to construct the isolating neighborhood in ifi4 and in the computation of the index with regard to the isolating neighborhood our construction is global in that a parameter taken to be small in conley s equations is now allowed to assume large values in order to compute the index we continue our equations to those studied by conley actually we go one step further and continue conley s equations to the van der pol equations crossed with a pair of linear equations admitting a repelling critical point the index for this latter system is easily computed and turns out to be non trivial it follows from the invariance of the index under continuation 21 that the desired

the natural variability of vital rates and associated statistics the first concern of this work is the development of approximations to the distributions of crude mortality rates age specific mortality rates age standardized rates standardized mortality ratios and the like for the case of a closed population or period study it is found that assuming poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate poisson distribution it is suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic poisson distribution for the number of deaths with mean proportional to the population size and an exponential function of a linear combination of the explanatories such a model is fit to mortality data for canadian females classified by age and year a dynamic variant of the model is further fit to the time series of total female deaths alone by year the models with extra poisson variation are found to lead to substantially improved fits excerpt

asymptotic spreading fastened by inter specific coupled nonlinearities a cooperative system abstract this paper is concerned with the asymptotic spreading of a lotka volterra cooperative system by using the theory of asymptotic spreading of nonautonomous equations the asymptotic speeds of spreading of unknown functions formulated by a coupled system are estimated our results imply that the asymptotic spreading of one species can be significantly fastened by introducing a mutual species which indicates the role of cooperation described by the coupled nonlinearities

weak approximation over function fields of curves over large or finite fields let k k c be the function field of a curve over a field k and let x be a smooth projective separably rationally connected k variety with x k neq emptyset under the assumption that x admits a smooth projective model pi mathcal x to c we prove the following weak approximation results 1 if k is a large field then x k is zariski dense 2 if k is an infinite algebraic extension of a finite field then x satisfies weak approximation at places of good reduction 3 if k is a nonarchimedean local field and r equivalence is trivial on one of the fibers mathcal x p over points of good reduction then there is a zariski dense subset w subseteq c k such that x satisfies weak approximation at places in w as applications of the methods we also obtain the following results over a finite field k 4 if k 10 then for a smooth cubic hypersurface x k the specialization map x k longrightarrow prod p in p mathcal x p kappa p at finitely many points of good reduction is surjective 5 if mathrm char k neq 2 3 and k 47 then a smooth cubic surface x over k satisfies weak approximation at any given place of good reduction

polarized minimal families of rational curves and higher fano manifolds in this paper we investigate fano manifolds x whose chern characters rm ch k x satisfy some positivity conditions our approach is via the study of it polarized minimal families of rational curves h x l x through a general point x in x first we translate positivity properties of the chern characters of x into properties of the pair h x l x this allows us to classify polarized minimal families of rational curves associated to fano manifolds x satisfying rm ch 2 x geq 0 and rm ch 3 x geq 0 this classification enables us to find new examples of higher fano manifolds we also provide sufficient conditions for these manifolds to be covered by subvarieties isomorphic to bbb p 2 and bbb p 3

potentially non klt locus and its applications we introduce the notion of potentially klt pairs for normal projective varieties with pseudoeffective anticanonical divisor the potentially non klt locus is a subset of x which is birationally transformed precisely into the non klt locus on a k x minimal model of x we prove basic properties of potentially non klt locus in comparison with those of classical non klt locus as applications we give a new characterization of varieties of fano type and we also improve results on the rational connectedness of uniruled varieties with pseudoeffective anticanonical divisor

traveling waves for a generalized holling tanner predator prey model abstract we study traveling wave solutions for holling tanner type predator prey models where the predator equation has a singularity at zero prey population the traveling wave solutions here connect the prey only equilibrium 1 0 with the unique constant coexistence equilibrium u v first we give a sharp existence result on weak traveling wave solutions for a rather general class of predator prey systems with minimal speed explicitly determined such a weak traveling wave u v connects 1 0 at but needs not connect u v at next we modify the holling tanner model to remove its singularity and apply the general result to obtain a weak traveling wave solution for the modified model and show that the prey component in this weak traveling wave solution has a positive lower bound and thus is a weak traveling wave solution of the original model these results for weak traveling wave solutions hold under rather general conditions then we use two methods a squeeze method and a lyapunov function method to prove that under additional conditions the weak traveling wave solutions are actually traveling wave solutions namely they converge to the coexistence equilibrium as

the fibration method over real function fields let mathbb r c be the function field of a smooth irreducible projective curve over mathbb r let x be a smooth projective geometrically irreducible variety equipped with a dominant morphism f onto a smooth projective rational variety with a smooth generic fibre over mathbb r c assume that the cohomological obstruction introduced by colliot thelene is the only one to the local global principle for rational points for the smooth fibres of f over mathbb r c valued points then we show that the same holds for x too by adopting the fibration method similarly to harpaz wittenberg

fully nonlinear elliptic equations for conformal deformations of chern ricci forms abstract we study a general class of fully nonlinear elliptic equations of second order on hermitian manifolds we derive a priori estimates and prove some existence results for these equations in particular we prove interior estimates for the complex hessian which in general do not hold for other types of equations we apply our results to draw geometric conclusions on conformal deformations of the mixed chern ricci forms a notion we introduced in the article our work is motivated by the close connections of these equations to problems in non kahler geometry and the fact that there have been increasing interests in fully nonlinear pde s beyond the complex monge ampere equation from complex geometry

local global principle for 0 cycles on fibrations over rationally connected bases abstract we study the brauer manin obstruction to the hasse principle and to weak approximation for 0 cycles on algebraic varieties that possess a fibration structure the issue is to establish the exactness of a local to global sequence e of chow groups of 0 cycles recently harpaz and wittenberg proved the exactness of e for rationally connected fibrations whose smooth fibres verify the exactness of e and whose base is either the projective space or a curve verifying the exactness of e in the present paper we prove the exactness of e for fibrations whose bases are ch telet surfaces or smooth proper models of homogeneous spaces of connected linear algebraic groups with connected stabilizers we require that either the fibration is valuatively split in codimension 1 and most closed fibres satisfy weak approximation for 0 cycles or the generic fibre has a 0 cycle of degree 1 and e is exact for most fibres

stability of travelling wave solutions of diffusive predator prey systems the stability of travelling wave solutions of singularly perturbed diffusive predator prey systems is proved by showing that the linearized operator about such a solution has no unstable spectrum and that the translation eigenvalue at a 0 is simple the proof illustrates the application of some recently developed geometric and topological methods for counting eigenvalues

on the fibration method for zero cycles and rational points conjectures on the existence of zero cycles on arbitrary smooth projective varieties over number elds were proposed by colliot th el ene sansuc kato and saito in the 1980 s we prove that these conjectures are compatible with brations for brations into rationally connected varieties over a curve in particular they hold for the total space of families of homogeneous spaces of linear groups with connected geometric stabilisers we prove the analogous result for rational points conditionally on a conjecture on locally split values of polynomials which a recent work of matthiesen establishes in the case of linear polynomials over the rationals

a bivariate bayes method for improving the estimates of mortality rates with a twofold conditional autoregressive model a bivariate bayes method is proposed for estimating the mortality rates of a single disease for a given population using additional information from a second disease the information on the two diseases is assumed to be from the same population groups or areas the joint frequencies of deaths for the two diseases for given populations are assumed to have a bivariate poisson distribution with joint means proportional to the population sizes the relationship between the mortality rates of the two different diseases if formulated through the twofold conditional autoregressive car model where spatial effects as well as indexes of spatial dependence are introduced to capture the structured clusterings among areas this procedure is compared to a univariate hierarchical bayes procedure that uses information from one disease only comparisons of two procedures are made by the optimal property a monte carlo study real data and the bayes factor all of the methods that we consider demonstrate a substantial

families of rationally connected varieties recall that a proper variety x is said to be rationally connected if two general points p q x are contained in the image of a map g p x this is clearly a birationally invariant property when x is smooth this turns out to be equivalent to the a priori weaker condition that two general points can be joined by a chain of rational curves and also to the a priori stronger condition that for any finite subset x there is a map g p x whose image contains and such that gtx is an ample bundle

holomorphic sectional curvature nefness and miyaoka yau type inequality on a compact kahler manifold we introduce a notion of almost nonpositivity for the holomorphic sectional curvature which by definition is weaker than the existence of a kahler metric with semi negative holomorphic sectional curvature we prove that a compact kahler manifold of almost nonpositive holomorphic sectional curvature has a nef canonical line bundle contains no rational curves and satisfies some miyaoka yau type inequalities in the course of the discussions we attach a real value to any fixed kahler class which up to a constant factor depending only on the dimension of manifold turns out to be an upper bound for the nef threshold

galois coverings and endomorphisms of projective varieties we prove that the vector bundle associated to a galois covering of projective manifolds is ample resp nef under very mild conditions this results is applied to the study of ramified endomorphisms of fano manifolds with b2 1 it is conjectured that mathbb p n is the only fano manifold admitting an endomorphism of degree d 2 and we verify this conjecture in several cases an important ingredient is a generalization of a theorem of andreatta wisniewski characterizing projective space via the existence of an ample subsheaf in the tangent bundle

constructing rational curves on k3 surfaces we develop a mixed characteristic version of the morimukai technique for producing rational curves on k3 surfaces we reduce modulo p produce rational curves on the resulting k3 surface over a finite field and lift to characteristic zero as an application we prove that all complex k3 surfaces with picard group generated by a class of degree two have an infinite number of rational curves

ample subvarieties and rationally connected fibrations under some positivity assumptions extension properties of rationally connected fibrations from a submanifold to its ambient variety are studied given a family of rational curves on a complex projective manifold x inducing a covering family on a submanifold y with ample normal bundle in x the main results relate under suitable conditions the associated rational connected fiber structures on x and on y applications of these results include an extension theorem for mori contractions of fiber type and a classification theorem in the case y has a structure of projective bundle or quadric fibration

the intrinsic normal cone let x be an algebraic stack in the sense of deligne mumford we construct a purely 0 dimensional algebraic stack over x in the sense of artin the intrinsic normal cone frak c x the notion of perfect obstruction theory for x is introduced and it is shown how to construct given a perfect obstruction theory for x a pure dimensional virtual fundamental class in the chow group of x we then prove some properties of such classes both in the absolute and in the relative context via a deformation theory interpretation of obstruction theories we prove that several kinds of moduli spaces carry a natural obstruction theory and sometimes a perfect one

symplectic geometry of rationally connected threefolds we study the symplectic geometry of rationally connected 3 folds the first result shows that rational connectedness is a symplectic deformation invariant in dimension 3 if a rationally connected 3 fold x is fano or has picard number 2 we prove that there is a nonzero gromov witten invariant with two insertions being the class of a point that is x is symplectic rationally connected finally we prove that many rationally connected 3 folds are birational to a symplectic rationally connected variety

local curvature estimates of long time solutions to the kahler ricci flow abstract we study the local curvature estimates of long time solutions to the normalized kahler ricci flow on compact kahler manifolds with semi ample canonical line bundle using these estimates we prove that on such a manifold the set of singular fibers of the semi ample fibration on which the riemann curvature blows up at time infinity is independent of the choice of the initial kahler metric moreover when a regular fiber of the semi ample fibration is not a finite quotient of a torus we determine the exact curvature blow up rate of the kahler ricci flow near the regular fiber

empirical bayes confidence intervals based on bootstrap samples abstract consider the model with data generated by the following two stage process first a parameter is sampled from a prior distribution g and then an observation is sampled from the conditional distribution f y if the prior distribution is known then the bayes estimate under squared error loss is the posterior expectation of conditional on the data y for example if g is gaussian with mean and variance 2 and f y is gaussian with mean and variance 2 then the posterior distribution is gaussian with mean b 1 b y and variance 2 1 b where b 2 2 2 inferences about are based on this distribution we study the application of the bootstrap to situations where the prior must be estimated from the data empirical bayes methods for this model we observe data y t y 1 y k t each independent y k following the compound model described previously as first shown by james and stein 1961 setting each k equal to its estimated posterior mean where and pr

an extension of a theorem of wu yau we show that a compact kahler manifold with nonpositive holomorphic sectional curvature has nef canonical bundle if the holomorphic sectional curvature is negative then it follows that the canonical bundle is ample confirming a conjecture of yau the key ingredient is the recent solution of this conjecture in the projective case by wu yau

fano 4 folds flips and blow ups of points abstract we study smooth complex fano 4 folds x with large picard number x with techniques from birational geometry our main result is that if x is isomorphic in codimension one to the blow up of a smooth projective 4 fold y at a point then x 12 we give examples of such x with picard number up to 9 the main theme and tool is the study of fixed prime divisors in fano 4 folds especially in the case x 6 in which we give some general results of independent interest

approximate bayesian inference in conditionally independent hierarchical models parametric empirical bayes models abstract we consider two stage models of the kind used in parametric empirical bayes peb methodology calling them conditionally independent hierarchical models we suppose that there are k units which may be experimental subjects cities study centers etcetera at the first stage the observation vectors yi for units i 1 k are independently distributed with densities p yi i or more generally p yi i at the second stage the unit specific parameter vectors i are iid with densities p i the peb approach proceeds by regarding the second stage distribution as a prior and noting that if were known inference about could be based on its posterior since is not known the simplest peb methods estimate the parameter by maximum likelihood or some variant and then treat as if it were known to be equal to this estimate although this procedure is sometimes satisfactory a well known defect is that it neglects the uncertainty due to the estimation of in this article w

bloch s conjecture for catanese and barlow surfaces catanese surfaces are regular surfaces of general type with pg 0 they specialize to double covers of barlow surfaces we prove that the ch0 group of a catanese surface is equal to z which implies the same result for the barlow surfaces

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

existence of travelling wave solutions of predator prey systems via the connection index we consider a reaction diffusion system which arises as a model of predator prey interactions in mathematical ecology the system admits four constant equilibria two of which are stable the main result is an existence theorem for travelling wave solutions which connect the two stable equilibria most previous efforts with regard to travelling waves for systems employ singular perturbations to locate the connecting orbit the new aspect of the present discussion lies in devising some novel methods for locating the connecting solution in phase space which do not require that the equations be singularly perturbed in certain cases the main result holds for an arbitrary choice of diffusion coefficients

hermitian metrics of negative holomorphic sectional curvature on some hyperbolic manifolds on montre que pour certains types de varietes hyperboliques compactes on peut construire une metrique hermitienne dessus avec partout une courbure sectionnelle holomorphe negative

jordan property for cremona groups assuming the borisov alexeev borisov conjecture we prove that there is a constant j j n such that for any rationally connected variety x of dimension n and any finite subgroup g subset rm bir x there exists a normal abelian subgroup a subset g of index at most j in particular we obtain that the cremona group rm cr 3 rm bir bbb p 3 enjoys the jordan property

an approximate bivariate bayesian method for analyzing small frequencies an approximate bayesian method is developed to study the joint mortality rates of two cancer sites over several geographic areas a conditionally independent two stage hierarchical model is used to model the sources of variability in these data at the first stage conditional on area specific parameters the within area variation in the joint frequencies of death from two sites is modeled by a bivariate poisson distribution with means proportional to the populations at risk at the second stage conditional on parameters for the prior the between area variation in the joint logits of true mortality rates is modeled by a bivariate normal distribution the prior distribution in estimating area mortality rates of one site it is shown that the simultaneous use of data on both sites is superior to that based on a single site only the relation between two sites is studied using the correlation between the logits of true mortality rates a monte carlo simulation is conducted to investigate the performance of this method as a function of the prior correlation the method is applied to two data sets

existence of traveling wave solutions for diffusive predator prey type systems abstract in this work we investigate the existence of traveling wave solutions for a class of diffusive predator prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions the profile equations for the above system can be reduced as a four dimensional ode system and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system applying the methods of wazewski theorem lasalle s invariance principle and hopf bifurcation theory we obtain the existence results our results can apply to various kinds of ecological models

every rationally connected variety over the function field of a curve has a rational point in a paper from 1992 kollar miyaoka and mori posed the following question given a proper flat morphism f p x with target a nonsingular curve and whose geometric generic fiber is rationally connected does it follow that f admits a regular section in the case that the ground field is an algebraically closed field of characteristic zero this was answered affirmatively by graber harris and starr using a topological argument we prove that f admits a regular section when the ground field is an algebraically closed field of arbitrary characteristic the key ingredients in the proof are the following a proposition 2 1 which shows that after taking the reduced fiber product of f with a generically etale morphism y x we may assume that the smooth locus of f intersects every geometric fiber and b proposition 1 1 which is a purely algebraic analogue of the moving branch points argument in graber harris starr the reader is cautioned that our definition of separably rationally connected differs slightly from the original definition

log fano varieties over function fields of curves consider a smooth log fano variety over the function field of a curve suppose that the boundary has positive normal bundle choose an integral model over the curve then integral points are zariski dense after removing an explicit finite set of points on the base curve