on the relationship between continuous and discrete time quantum walk quantum walk is one of the main tools for quantum algorithms defined by analogy to classical random walk a quantum walk is a time homogeneous quantum process on a graph both random and quantum walks can be defined either in continuous or discrete time but whereas a continuous time random walk can be obtained as the limit of a sequence of discrete time random walks the two types of quantum walk appear fundamentally different owing to the need for extra degrees of freedom in the discrete time case

generic predation in age structure predator prey models in this paper we use analytical tools based in the painleve analysis and bifurcation theory to offer stable predator prey models with age structure such models account for within species and the approach is based at the level of individual organisms we analyze the type of theoretical predation that a system requires to have real solutions where only poles as singularities are allowed and also to have periodic solutions the main feature sought is the coexistence of the interacting populations

recent improvements in the complexity of the effective nullstellensatz we bring up to date the estimates on the complexity of the effective nullstellensatz and the membership problem

right veering diffeomorphisms of compact surfaces with boundary we initiate the study of the monoid of right veering diffeomorphisms on a compact oriented surface with nonempty boundary the monoid strictly contains the monoid of products of positive dehn twists we explain the relationship to tight contact structures and open book decompositions

taut foliations in punctured surface bundles i this model a given fibration can be perturbed to give nearby fibrations in this paper we describe an alternative way of perturbing fibrations with non empty boundary instead of fibrations this construction yields taut foliations very closely related to the original fibration but with different boundary behaviour given m with torus boundary component t and assigned coordinate system for t we say that a fibration or taut foliation f realizes slope r on t iff intersects t in simple curves of slope r when f is a fibration r is necessarily rational in general however we assume only that r is real when a compact orientable fibred manifold m has a single boundary component exactly one slope is realized by fibrations however the closely related taut foliations realize a non empty interval of slopes in 4 we prove the following theorem theorem 4 1 given an orientable fibred compact 3 manifold with single boundary component a fibration with fibre surface of negative euler charac teristic can be perturbed to yield taut foliations realizing an open interval of boundary slopes about the boundary slope of the fibration remark when m is fibred with fibre a once punctured torus the taut foliations realized are those of 11 in different guise as corollary we have information about manifolds obtained by performing dehn surgery along slopes sufficiently close to the slope of a fibre such manifolds necessarily contain taut foliations hence by novikov 16 they are irreducible with infinite fundamental group by palmeira 20 they have universal cover r 3 in certain cases it is possible to say precisely what sufficiently close means that is to identify the interval realized in 11 hatcher does this for the once punctured torus bundles over s 1 i n 23 we describe the intervals for once punctured surface bundles in terms of their gabai degeneracy in 5 we begin an investigation of generalizations of the construction we give an analogous result for manifolds containing a taut foliation with compact leaf a punctured surface of positive genus and possessing a non separating comple mentary product disc see 5 then for those readers familiar with essential laminations we show that if m contains an essential spanning surface s with non separating complementary product disc then s can be perturbed to yield

tight contact structures with no symplectic fillings we exhibit tight contact structures on 3 manifolds that do not admit any symplectic fillings

a subdivision based algorithm for the sparse resultant multivariate resultants generalize the sylvester resultant of two polynomials and characterize the solvability of a polynomial system they also reduce the computation of all common roots to a problem in linear algebra we propose a determinantal formula for the sparse resultant of an arbitrary system of n 1 polynomials in n variables this resultant generalizes the classical one and has significantly lower degree for polynomials that are sparse in the sense that their mixed volume is lower than their bezout number our algorithm uses a mixed polyhedral subdivision of the minkowski sum of the newton polytopes in order to construct a newton matrix its determinant is a nonzero multiple of the sparse resultant and the latter equals the gcd of at most n 1 such determinants this construction implies a restricted version of an effective sparse nullstellensatz for an arbitrary specialization of the coefficients there are two methods that use one extra variable and yield the sparse resultant this is the first algorithm to handle the general case with complexity polynomial in the resultant degree and simply exponential in n we conjecture its extension to producing an exact rational expression for the sparse resultant

a geometric effective nullstellensatz the purpose of this paper is to present a geometric theorem which clarifies and extends in several directions work of brownawell kollar and others on the effective nullstellensatz specifically we work on an arbitrary smooth complex projective variety x with the previous classical results corresponding to the case when x is projective space in this setting we prove a local effective nullstellensatz for ideal sheaves and a corresponding global division theorem for adjoint type bundles we also make explicit the connection with the intersection theory of fulton and macpherson finally constructions involving products of prime ideals that appear in earlier work are replaced by geometrically more natural conditions involving orders of vanishing along subvarieties much of the previous activity in this area has been algebraic in nature and seems perhaps not well known in detail among geometers therefore we have felt it worthwhile to include here a rather extended introduction we start with an overview of the questions and earlier work on them then we present the set up and statement of our main theorem we conclude with a series of examples which can be read before the general result of what it yields in special cases

global asymptotic behavior of a chemostat model with discrete delays this paper studies the global asymptotic behavior of an exploitative competition model between n species in a chemostat the model incorporates discrete time delays to describe the delay in the conversion of nutrient consumed to viable biomass and hence includes delays simultaneously in variables of nutrient and species concentrations in the case where only two species are engaged in competition it is shown that competitive exclusion holds for any monotone growth response functions sufficient conditions are also obtained for the model to exhibit competitive exclusion in the n species case in regard to the delay effects on the qualitative outcome of competition it is demonstrated that when the delays are relatively small the predictions of the model are identical with the predictions given by corresponding models without time delays however including large delays in the model may alter the predicted outcome of competition the techniques used also work when different removal rates are permitted an

a construction of pseudo anosov homeomorphisms we describe a generalization of thurston s original construction of pseudo anosov maps on a surface f of negative euler characteristic in fact we construct whole semigroups of pseudo anosov maps by taking appropriate compositions of dehn twists along certain families of curves our arguments furthermore apply to give examples of pseudo anosov maps on nonorientable surfaces for each self map f f f arising from our recipe we construct an invariant bigon track a slight generalization of train track whose incidence matrix is perron frobenius standard arguments produce a projective measured foliation invariant by f to finally prove that f is pseudo anosov we directly produce a transverse invariant projective measured foliation using tangential measures on bigon tracks as a consequence of our argument we derive a simple criterion for a surface automorphism to be pseudo anosov introduction a homeomorphism p of a surface f is said to be pseudo anoosov if no iterate of p fixes any essential nonboundaryor puncture parallel free homotopy class of simple curves in f examples of these homeomorphisms date back to the work of nielsen see n and gi but a systematic study of these maps was not undertaken until the work of thurston t1 anosov a studied maps of the torus which preserve two foliations of the torus by lines of irrational slope and pseudo anosov maps on f similarly preserve a pair of foliations with singularities pseudo anosov maps are by no means special indeed the monodromy of any nontorus fibred knot which is not a satellite is pseudo anosov t4 note that being pseudo anosov is a conjugacy invariant moreover these maps play an important role in the geometrization of three manifolds indeed a mapping torus has hyperbolic structure if and only if the monodromy is pseudo anosov t4 in the original preprint t1 there is described a construction of pseudo anosov maps which we will recall later in this paper we generalize thurston s construction and give a recipe for constructing whole semigroups of pseudo anosov maps many of which do not arise from thurston s construction our recipe is also applicable to nonorientable surfaces and we give examples of pseudo anosov maps in this setting in t3 thurston proved the existence of such and ay gave the first explicit examples this paper is organized as follows in 1 we review the basic terminology and results on train tracks in surfaces and indicate the connection between measured train tracks and measured foliations 2 is devoted to tangential measure on bigon received by the editors march 7 1986 and in revised form june 17 1987 1980 mathematics subject cassification 1985 revision primary 57n06 57n50

residue calculus and effective nullstellensatz multivariate residue calculus in the spirit of j lipman is developed from the computational point of view for example with several variants of the classical transformation law and used in order to make totally explicit the bezout identity and therefore the algebraic nullstellensatz in k x 1 x n where k is an infinite field of arbitrary characteristic such identities provide sharp size estimates for the denominator and the divisors in the bezout identity when k is the quotient field of a factorial regular ring a equipped with a size such as z or f p 1 q the estimates obtained by the authors in a previous work in the case a z are sharpened here while analytic techniques are replaced with an algebraic approach

new effective differential nullstellensatz abstract we show new upper and lower bounds for the effective differential nullstellensatz for differential fields of characteristic zero with several commuting derivations seidenberg was the first to address this problem in 1956 without giving a complete solution in the case of one derivation the first bound is due to grigoriev in 1989 the first bounds in the general case appeared in 2009 in a paper by golubitsky kondratieva szanto and ovchinnikov with the upper bound expressed in terms of the ackermann function d alfonso jeronimo and solerno using novel ideas obtained in 2014 a new bound if restricted to the case of one derivation and constant coefficients to obtain the bound in the present paper without this restriction we extend this approach and use the new methods of freitag and leon sanchez and of pierce which represent a model theoretic approach to differential algebraic geometry

the height of the mixed sparse resultant we present an upper bound for the height of the mixed sparse resultant defined as the logarithm of the maximum modulus of its coefficients we obtain a similar estimate for its mahler measure

sharp effective nullstellensatz the usual proofs of this result however give no information about the g1 s for instance they give no bound on their degrees this question was first considered by g hermann h she used elimination theory to get a bound on the degree of the gi s which was doubly exponential in the number of variables her results were later improved in mw and in th all these produce bounds that are doubly exponential in the number of variables a major breakthrough was achieved by brownawell b1 who proved the following result

on a question of davenport and lewis and new character sum bounds in finite fields let be a nontrivial multiplicative character of fpn we obtain the following results 1 let e 0 be given if b nj 1 xj j xj nj 1 nj hj z j 1 n is a box satisfying n j 1 hj p 5 e n then for p p e and some absolute constant c 0 we have denoting a nontrivial multiplicative character x b x p e b 2 assume a b fp such that a p 9 e b p 9 e b b 1 4 4 1 then for a non principal multiplicative character x i y d x y p 2 4 i d we also improve a result of karacuba typeset by ams tex

integrability and singularity structure of predator prey system the extended ars ablowitz ramani and segur algorithm is introduced to characterize a dynamical system as painleve or otherwise to that end it is required that the formal series the laurent series logarithmic algebraic psi series about a movable singularity are shown to converge in the deleted neighborhood of the singularity the determinations thus obtained are compared with those following from the method of painleve an attempt is made to relate the structure of solutions about a movable singularity with that of first integrals when they exist all these ideas are illustrated by a comprehensive analysis of the general two dimensional predator prey system

quantum algorithms for some hidden shift problems almost all of the most successful quantum algorithms discovered to date exploit the ability of the fourier transform to recover subgroup structures of functions especially periodicity the fact that fourier transforms can also be used to capture shift structure has received far less attention in the context of quantum computation in this paper we present three examples of unknown shift problems that can be solved efficiently on a quantum computer using the quantum fourier transform for one of these problems the shifted legendre symbol problem we give evidence that the problem is hard to solve classically by showing a reduction from breaking algebraically homomorphic cryptosystems we also define the hidden coset problem which generalizes the hidden shift problem and the hidden subgroup problem this framework provides a unified way of viewing the ability of the fourier transform to capture subgroup and shift structure

admissible transverse surgery does not preserve tightness we produce the first examples of closed tight contact 3 manifolds which become overtwisted after performing admissible transverse surgeries along the way we clarify the relationship between admissible transverse surgery and legendrian surgery we use this clarification to study a new invariant of transverse knots namely the range of slopes on which admissible transverse surgery preserves tightness and to provide some new examples of knot types which are not uniformly thick our examples also illuminate several interesting new phenomena including the existence of hyperbolic universally tight contact 3 manifolds whose heegaard floer contact invariants vanish and which are not weakly fillable and the existence of open books with arbitrarily high fractional dehn twist coefficients whose compatible contact structures are not deformations of co orientable taut foliations

a global lojasiewicz inequality for algebraic varieties let x be the locus of common zeros of polynomials f 1 f in n complex variables a global upper bound for the distance to x is given in the form of a lojasiewicz inequality the exponent in this inequality is bounded by d min n k where d max 3 deg f i the estimates are also valid over an algebraically closed field of any characteristic

floer homology and fractional dehn twists abstract we establish a relationship between heegaard floer homology and the fractional dehn twist coefficient of surface automorphisms specifically we show that the rank of the heegaard floer homology of a 3 manifold bounds the absolute value of the fractional dehn twist coefficient of the monodromy of any of its open book decompositions with connected binding we prove this by showing that the rank of floer homology gives bounds for the number of boundary parallel right or left dehn twists necessary to add to a surface automorphism to guarantee that the associated contact manifold is tight or overtwisted respectively by examining branched double covers we also show that the rank of the khovanov homology of a link bounds the fractional dehn twist coefficient of its odd stranded braid representatives

sharp estimates for the arithmetic nullstellensatz we present sharp estimates for the degree and the height of the polynomials in the nullstellensatz over the integer ring zz the result improves previous work of philippon berenstein yger and krick pardo we also present degree and height estimates of intrinsic type which depend mainly on the degree and the height of the input polynomial system as an application we derive an effective arithmetic nullstellensatz for sparse polynomial systems the proof of these results relies heavily on the notion of local height of an affine variety defined over a number field we introduce this notion and study its basic properties

travelling wave solutions in multigroup age structured epidemic models age structured epidemic models have been used to describe either the age of individuals or the age of infection of certain diseases and to determine how these characteristics affect the outcomes and consequences of epidemiological processes most results on age structured epidemic models focus on the existence uniqueness and convergence to disease equilibria of solutions in this paper we investigate the existence of travelling wave solutions in a deterministic age structured model describing the circulation of a disease within a population of multigroups individuals of each group are able to move with a random walk which is modelled by the classical fickian diffusion and are classified into two subclasses susceptible and infective a susceptible individual in a given group can be crisscross infected by direct contact with infective individuals of possibly any group this process of transmission can depend upon the age of the disease of infected individuals the goal of this paper is to provide sufficient conditions that ensure the existence of travelling wave solutions for the age structured epidemic model the case of two population groups is numerically investigated which applies to the crisscross transmission of feline immunodeficiency virus fiv and some sexual transmission diseases

the structure of rational and ruled symplectic 4 manifolds this paper investigates the structure of compact symplectic 4 manifolds v w which contain a symplectically embedded copy c of s2 with nonnegative self intersection number such a pair v c w is called minimal if in addition the open manifold v c contains no exceptional curves i e symplectically embedded 2 spheres with self intersection 1 we show that every such pair v c w covers a minimal pair v c c which may be obtained from v by blowing down a finite number of disjoint exceptional curves in v c further the family of manifold pairs v c w under consideration is closed under blowing up and down we next give a complete list of the possible minimal pairs we show that v is symplectomorphic either to p2 with its standard form or to an s2 bundle over a compact surface with a symplectic structure which is uniquely determined by its cohomology class moreover this symplectomorphism may be chosen so that it takes c either to 2 a complex line or quadric in cp2 or in the case when v is a bundle to a fiber or section of the bundle department of mathematics state university of new york at stony brook stony brook new york 11794 3651 e mail address dusa math sunysb edu this content downloaded from 207 46 13 145 on wed 27 apr 2016 05 10 07 utc all use subject to http about jstor org terms

effective bezout identities in q z1 zn abstract if p sub 1 p sub m are n variate polynomials with integral coefficients and no common zeros in c exp n brownawell has shown in 1986 that there exist q sub 1 q sub m polynomials with integral coefficients and nu is an element of z such that p sub 1 q sub 1 p sub m q sub m nu and max deg q sub j max deg p sub j exp n on the other hand if h logarithm of the largest coefficient of all the p sub j and h sub 1 is the corresponding quantity for the q sub j then there is no sharp estimate of h sub 1 in terms of h and max deg p sub j in this paper we show that when the variety of common zeros at infinity of the p sub j is discrete then essentially we have h sub 1 d exp cn h for an absolute constant c if there were an algorithm to compute the q sub j in d exp cn time one would obtain exactly the above estimate current algorithms require about d exp n squared operations

definability and fast quantifier elimination in algebraically closed fields abstract the bezout inequality an affine version not including multiplicities of the classical bezout theorem is derived for applications in algebraic complexity theory upper bounds for the cardinality and number of sets definable by first order formulas over algebraically closed fields are given this is used for fast quantifier elimination in algebraically closed fields

on the hidden shifted power problem we consider the problem of recovering a hidden element s of a finite field mathbb f q of q elements from queries to an oracle that for a given x in mathbb f q returns x s e for a given divisor e mid q 1 we use some techniques from additive combinatorics and analytic number theory that lead to more efficient algorithms than the naive interpolation algorithm for example they use substantially fewer queries to the oracle

on degree bounds for the sparse nullstellensatz abstract we prove new upper bounds for the degrees in hilbert s nullstellensatz and for the noether exponent of polynomial ideals in terms of the monomial structure of the polynomials involved our bounds improve the previously known bounds in the sparse setting and are the first to take into account the different supports of the polynomials

equivalence of heegaard floer homology and embedded contact homology via open book decompositions we sketch the proof of the equivalence between the hat versions of heegaard floer homology and embedded contact homology ech the key point is to express these two floer homology theories in terms of an open book decomposition of the ambient manifold

cabling and transverse simplicity we study legendrian knots in a cabled knot type specifically given a topological knot type c we analyze the legendrian knots in knot types ob tained from k by cabling in terms of legendrian knots in the knot type k as a corollary of this analysis we show that the 2 3 cable of the 2 3 torus knot is not transversely simple and moreover classify the transverse knots in this knot type this is the first classification of transverse knots in a non transversely simple knot type we also classify legendrian knots in this knot type and exhibit the first example of a legendrian knot that does not destabi lize yet its thurston bennequin invariant is not maximal among legendrian representatives in its knot type in this paper we continue the investigation of legendrian knots in tight contact 3 manifolds using 3 dimensional contact topological methods in eh1 the authors introduced a general framework for analyzing legendrian knots in tight contact 3 manifolds there we streamlined the proof of the classification of legendrian unknots originally proved by eliashberg eraser in ef and gave a complete classification of legendrian torus knots and figure eight knots in eh2 we gave the first structure theorem for legendrian knots namely the reduction of the analysis of connected sums of legendrian knots to that of the prime summands this yielded a plethora of non legendrian simple knot types a topological knot type is legendrian simple if legendrian knots in this knot type are determined by their thurston bennequin invariant and rotation number moreover we exhibited pairs of legendrian knots in the same topological knot type with the same thurston bennequin and rotation numbers which required arbitrarily many stabilizations before they became legendrian isotopic see eh2

ozsvath szabo invariants and fillability of contact structures recently ozsvath and szabo defined an invariant of contact structures with values in the heegaard floer homology groups they also proved that a version of the invariant with twisted coefficients is non trivial for weakly symplectically fillable contact structures in this article we show that their non vanishing result does not hold in general for the contact invariant with untwisted coefficients as a consequence of this fact heegaard floer theory can distinguish between weakly and strongly symplectically fillable contact structures