hodge integrals and degenerate contributions hodge integral techniques are used to compute the degree 1 degenerate contributions of curves of arbitrary genus in the gromov witten theory of 3 folds in the calabi yau case the contributions are compared to related m theoretic calculations in the fano case the contributions suggest new integrality conditions

givental formula in terms of virasoro operators we present a conjecture that the universal enveloping algebra of differential operators tk over c coincides in the origin with the universal enveloping algebra of the borel subalgebra of virasoro generators from the kontsevich model thus we can decompose any pseudo differential operator to a combination of the virasoro operators using this decomposition we present the right hand side of the givental formula math ag 0008067 as a constant part of the differential operator we introduce in the case of cp1 studied in the paper by song and song hep th 0103254 the left hand side of the givental formula is a unit which imposes certain constraints on this differential operator we explicitly check that these constraints are correct up to o q4 we also propose a conjecture of factorization modulo hirota equation of the differential operator introduced and check this conjecture with the same accuracy

compactified picard stacks over the moduli stack of stable curves with marked points abstract in this paper we give a construction of algebraic artin stacks endowed with a modular map onto the moduli stack of stable curves of genus g with n marked points the stacks we construct are smooth irreducible and have dimension 4 g 3 n yielding a geometrically meaningful compactification of the universal picard stack parametrizing n pointed smooth curves together with a line bundle

a new regularization method for mathematical programs with complementarity constraints with strong convergence properties mathematical programs with equilibrium or complementarity constraints mpecs form a difficult class of optimization problems the feasible set has a very special structure and violates most of the standard constraint qualifications therefore one typically applies specialized algorithms in order to solve mpecs one very prominent class of specialized algorithms are the regularization or relaxation methods the first regularization method for mpecs is due to scholtes siam j optim 11 2001 pp 918 936 but in the meantime there exist a number of different regularization schemes which try to relax the difficult constraints in different ways however almost all regularization methods converge to c stationary points only which is a very weak stationarity concept an exception is a recent method by kadrani dussault and benchakroun siam j optim 20 2009 pp 78 103 whose limit points are shown to be m stationary here we provide a new regularization method which also converges to m sta

tau functions as widom constants we define a tau function for a generic riemann hilbert problem posed on a union of non intersecting smooth closed curves with jump matrices analytic in their neighborhood the tau function depends on parameters of the jumps and is expressed as the fredholm determinant of an integral operator with block integrable kernel constructed in terms of elementary parametrices its logarithmic derivatives with respect to parameters are given by contour integrals involving these parametrices and the solution of the riemann hilbert problem in the case of one circle the tau function coincides with widom s determinant arising in the asymptotics of block toeplitz matrices our construction gives the jimbo miwa ueno tau function for riemann hilbert problems of isomonodromic origin painleve vi v iii garnier system etc and the sato segal wilson tau function for integrable hierarchies such as gelfand dickey and drinfeld sokolov

a new particle swarm optimization algorithm with an application abstract in this paper for dealing with the portfolio model from stocks market a new particle swarm optimization algorithm npso is presented in which the optimal and sub optimal positions of each particle are considered in the iteration process and the crossover operation is used to avoid premature it is demonstrated from optimization tests that npso outperforms existed pso then npso is used to solve a discontinuous programming model and four different optimal portfolio selections are displayed which are denoted by s 1 s 2 s 3 and s 4 respectively finally actual return rates of these portfolios are obtained and it is analyzed from related graphs that s 2 and s 3 gain better results

the decorated teichmuller space of punctured surfaces a principal 5 bundle over the usual teichmuller space of ans times punctured surface is introduced the bundle is mapping class group equivariant and admits an invariant foliation several coordinatizations of the total space of the bundle are developed there is furthermore a natural cell decomposition of the bundle finally we compute the coordinate action of the mapping class group on the total space the total space is found to have a rich equivariant geometric structure we sketch some connections with arithmetic groups diophantine approximations and certain problems in plane euclidean geometry furthermore these investigations lead to an explicit scheme of integration over the moduli spaces and to the construction of a universal teichmuller space which we hope will provide a formalism for understanding some connections between the teichmuller theory the kp hierarchy and the virasoro algebra these latter applications are pursued elsewhere

lambert w solves the noncommutative varphi 4 φ 4 model the closed dyson schwinger equation for the 2 point function of the noncommutative lambda phi 4 2 model is rearranged into the boundary value problem for a sectionally holomorphic function in two variables we prove an exact formula for a solution in terms of lambert s w function this solution is holomorphic in lambda inside a domain which contains 1 log 4 infty our methods include the hilbert transform perturbation series and lagrange burmann resummation

isomonodromic deformations of a rational differential system and reconstruction with the topological recursion the sl2 case in this paper we show that it is always possible to deform a differential equation x x l x x with l x sl2 c x by introducing a small formal parameter in such a way that it satisfies the topological type properties of bergere borot and eynard annales henri poincare 16 12 2713 2782 2015 this is obtained by including the former differential equation in an isomonodromic system and using some homogeneity conditions to introduce the topological recursion is then proved to provide a formal series expansion of the corresponding tau function whose coefficients can thus be expressed in terms of intersections of tautological classes in the deligne mumford compactification of the moduli space of surfaces we present a few examples including any fuchsian system of sl2 c x as well as some elements of painleve hierarchies

hodge integrals and tau symmetric integrable hierarchies of hamiltonian evolutionary pdes for an arbitrary semisimple frobenius manifold we construct hodge integrable hierarchy of hamiltonian partial differential equations in the particular case of quantum cohomology the tau function of a solution to the hierarchy generates the intersection numbers of the gromov witten classes and their descendents along with the characteristic classes of hodge bundles on the moduli spaces of stable maps for the one dimensional frobenius manifold the hodge hierarchy is a deformation of the korteweg de vries hierarchy depending on an infinite number of parameters conjecturally this hierarchy is a universal object in the class of scalar hamiltonian integrable hierarchies possessing tau functions mathematics subject classication 2010 primary 53d45 secondary 37k10

on certain vanishing identities for gromov witten invariants in this paper we study certain vanishing identities for gromov witten invariants conjectured by k liu and h xu we will prove their conjectures when the summation range is big compared to the genus in such cases we actually obtained vanishing identities which are stronger than their conjectures we also prove these conjectures in low genus cases

computation of open gromov witten invariants for toric calabi yau 3 folds by topological recursion a proof of the bkmp conjecture the bkmp conjecture 2006 2008 proposed a new method to compute closed and open gromov witten invariants for every toric calabi yau 3 folds through a topological recursion based on mirror symmetry so far this conjecture has been verified to low genus for several toric cy3folds and proved to all genus only for mathbb c 3 in this article we prove the general case our proof is based on the fact that both sides of the conjecture can be naturally written in terms of combinatorial sums of weighted graphs on the a model side this is the localization formula and on the b model side the graphs encode the recursive algorithm of the topological recursion

all loop topological string amplitudes from chern simons theory we demonstrate the equivalence of all loop closed topological string amplitudes on toric local calabi yau threefolds with computations of certain knot invariants for chern simons theory we use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera in particular we explicitly compute the topological string amplitudes for open image in new window 2 up to degree 12 and open image in new window 1 open image in new window 1 up to total degree 10 to all genera this also leads to certain novel large n dualities in the context of ordinary superstrings involving duals of type ii superstrings on local calabi yau three folds without any fluxes

topological recursion in enumerative geometry and random matrices we review the method of symplectic invariants recently introduced to solve matrix models loop equations in the so called topological expansion and further extended beyond the context of matrix models for any given spectral curve one defines a sequence of differential forms and a sequence of complex numbers fg called symplectic invariants we recall the definition of fg s and we explain their main properties in particular symplectic invariance integrability modularity as well as their limits and their deformations then we give several examples of applications in particular matrix models enumeration of discrete surfaces maps algebraic geometry and topological strings and non intersecting brownian motions

the structure of 2d semi simple field theories i classify the cohomological 2d field theories based on a semi simple complex frobenius algebra a they are controlled by a linear combination of classes and by an extension datum to the deligne mumford boundary their effect on the gromov witten potential is described by givental s fock space formulae this leads to the reconstruction of gromov witten ancestor invariants from the quantum cup product at a single semi simple point and the first chern class of the manifold confirming givental s higher genus reconstruction conjecture this in turn implies the virasoro conjecture for manifolds with semi simple quantum cohomology the classification uses the mumford conjecture proved by madsen and weiss european congress of mathematics pp 283 303 2005

higher weil petersson volumes of moduli spaces of stable n pointed curves moduli spaces of compact stablen pointed curves carry a hierarchy of cohomology classes of top dimension which generalize the weil petersson volume forms and constitute a version of mumford classes we give various new formulas for the integrals of these forms and their generating functions

connecting the kontsevich witten and hodge tau functions by the widehat gl infty operators in this paper we present an explicit formula that connects the kontsevich witten tau function and the hodge tau function by differential operators belonging to the widehat gl infty group indeed we show that the two tau functions can be connected using virasoro operators this proves a conjecture posted by alexandrov in from hurwitz numbers to kontsevich witten tau function a connection by virasoro operators letters in mathematical physics doi 10 1007 s11005 013 0655 0 2014

triangulated riemann surfaces with boundary and the weil petersson poisson structure given a hyperbolic surface with geodesic boundary s the lengths of a maximal system of disjoint simple geodesic arcs on s that start and end at s perpendicularly are coordinates on the teichmuller space t s we express the weil petersson poisson structure of t s in this system of coordinates and we prove that it limits pointwise to the piecewise linear poisson structure defined by kontsevich on the arc complex of s at the same time we obtain a formula for the first order variation of the distance between two closed geodesics under fenchel nielsen deformation

a new regularization scheme for mathematical programs with complementarity constraints we propose a new regularization scheme for mathematical programs with complementarity constraints mpcc by relaxing all the constraints of the complementarity system we show that under the mpcc linear independence constraint qualifications mpcc licq the lagrange multipliers exist for this regularization our method has strong convergence properties under mpcc linear independence constraint qualifications and some weak conditions of the strict complementarity in particular under mpcc licq it is shown that any accumulation point of the regularized stationary points is m stationary for the mpcc problem and if the asymptotically weak nondegeneracy condition holds at a stationary point of the regularized problem then it is strongly stationary an algorithm for solving the proposed regularization is presented and numerical experiments are reported some comparisons with other methods are discussed with illustrative examples

from stochastic dominance to mean risk models semideviations as risk measures abstract two methods are frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches the former is based on an axiomatic model of risk averse preferences but does not provide a convenient computational recipe the latter quantifies the problem in a lucid form of two criteria with possible trade off analysis but cannot model all risk averse preferences in particular if variance is used as a measure of risk the resulting mean variance markowitz model is in general not consistent with stochastic dominance rules this paper shows that the standard semideviation square root of the semivariance as the risk measure makes the mean risk model consistent with the second degree stochastic dominance provided that the trade off coefficient is bounded by a certain constant similar results are obtained for the absolute semideviation and for the absolute and standard deviations in the case of symmetric or bounded distributions in the analysis we use a new tool the outcome risk o r diagram which appears to be particularly useful for comparing uncertain outcomes

calmness modulus of fully perturbed linear programs this paper provides operative point based formulas only involving the nominal data and not data in a neighborhood for computing or estimating the calmness modulus of the optimal set argmin mapping in linear optimization under uniqueness of nominal optimal solutions our analysis is developed in two different parametric settings first in the framework of canonical perturbations i e perturbations of the objective function and the right hand side of the constraints the paper provides a computationally tractable formula for the calmness modulus which goes beyond some preliminary results of the literature second in the framework of full perturbations perturbations of all coefficients after characterizing the calmness property for the optimal set mapping the paper provides an operative upper bound for the corresponding calmness modulus as well as some illustrative examples we provide two applications related to algorithms traced out from the literature the first one to a descent method in lp and the second to a regularization method for linear programs with complementarity constraints

intersection theory on the moduli space of curves and the matrix airy function we show that two natural approaches to quantum gravity coincide this identity is nontrivial and relies on the equivalence of each approach to kdv equations we also investigate related mathematical problems

on quantum cohomology rings for hypersurfaces in cp n 1 using the torus action method we construct a one variable polynomial representation of quantum cohomology ring for degree k hypersurface in cpn 1 the results interpolate the well known result of cpn 2 model and the one of calabi yau hypersuface in cpn 1 we find in the k n 2 case the principal relation of this ring has a very simple form compatible with toric compactification of moduli space of holomorphic maps from cp1 to cpn 1

a neurodynamic optimization approach to bilevel quadratic programming this paper presents a neurodynamic optimization approach to bilevel quadratic programming bqp based on the karush kuhn tucker kkt theorem the bqp problem is reduced to a one level mathematical program subject to complementarity constraints mpcc it is proved that the global solution of the mpcc is the minimal one of the optimal solutions to multiple convex optimization subproblems a recurrent neural network is developed for solving these convex optimization subproblems from any initial state the state of the proposed neural network is convergent to an equilibrium point of the neural network which is just the optimal solution of the convex optimization subproblem compared with existing recurrent neural networks for bqp the proposed neural network is guaranteed for delivering the exact optimal solutions to any convex bqp problems moreover it is proved that the proposed neural network for bilevel linear programming is convergent to an equilibrium point in finite time finally three numerical examples are elaborated to substantiate the efficacy of the proposed approach

theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints mathematical programs with equilibrium constraints mpecs are difficult optimization problems whose feasible sets do not satisfy most of the standard constraint qualifications hence mpecs cause difficulties both from a theoretical and a numerical point of view as a consequence a number of mpec tailored solution methods have been suggested during the last decade which are known to converge under suitable assumptions among these mpec tailored solution schemes the relaxation methods are certainly one of the most prominent class of solution methods several different relaxation schemes are available in the meantime and the aim of this paper is to provide a theoretical and numerical comparison of these schemes more precisely in the theoretical part we improve the convergence theorems of several existing relaxation methods there we also take a closer look at the properties of the feasible sets of the relaxed problems and show which standard constraint qualifications are satisfied for these relaxed problems finally the numerical comparison is based on the macmpec test problem collection

how covariant closed string theory solves a minimal area problem for a given genusg riemann surface withn 0 punctures n 3 forg 0 we consider the problem of finding the metric of minimal area under the condition that the length of any nontrivial closed curve be greater or equal to 2 the minimal area metrics are found for the case of all punctured genus zero surfaces and for many of the higher genus surfaces both with and without punctures these metrics are induced by jenkins strebel quadratic differentials they arise from the string diagrams corresponding to restricted feynman graphs of a closed string field theory action containing classical and quantum restricted polyhedra

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

towards the geometry of double hurwitz numbers abstract double hurwitz numbers count branched covers of cp 1 with fixed branch points with simple branching required over all but two points 0 and and the branching over 0 and specified by partitions of the degree with m and n parts respectively single hurwitz numbers or more usually hurwitz numbers have a rich structure explored by many authors in fields as diverse as algebraic geometry symplectic geometry combinatorics representation theory and mathematical physics the remarkable elsv formula relates single hurwitz numbers to intersection theory on the moduli space of curves this connection has led to many consequences including okounkov and pandharipande s proof of witten s conjecture in this paper we determine the structure of double hurwitz numbers using techniques from geometry algebra and representation theory our motivation is geometric we give evidence that double hurwitz numbers are top intersections on a moduli space of curves with a line bundle a universal picard variety in particular we prove a piecewise polynomiality result analogous to that implied by the elsv formula in the case m 1 complete branching over one point and n is arbitrary we conjecture an elsv type formula and show it to be true in genus 0 and 1 the corresponding witten type correlation function has a richer structure than that for single hurwitz numbers and we show that it satisfies many geometric properties such as the string and dilaton equations and an itzykson zuber style genus expansion ansatz we give a symmetric function description of the double hurwitz generating series which leads to explicit formulae for double hurwitz numbers with given m and n as a function of genus in the case where m is fixed but not necessarily 1 we prove a topological recursion on the corresponding generating series which leads to closed form expressions for double hurwitz numbers and an analogue of the goulden jackson polynomiality conjecture an early conjectural variant of the elsv formula in a later paper faber s intersection number conjecture and genus 0 double hurwitz numbers 2005 in preparation the formulae in genus 0 will be shown to be equivalent to the formulae for top intersections on the moduli space of smooth curves m g for example three formulae we give there will imply faber s intersection number conjecture in moduli of curves and abelian varieties aspects of mathematics vol e33 vieweg braunschweig 1999 pp 109 129 in arbitrary genus with up to three points

weil petersson volumes and intersection theory on the moduli space of curves in this paper we establish a relationship between the weil petersson volume vgin b of the moduli space mg n b of hyperbolic riemann surfaces with geodesic boundary components of lengths b bn and the intersection numbers of tauto logical classes on the moduli space mg n of stable curves as a result by using the recursive formula for vg n b obtained in 22 we derive a new proof of the virasoro constraints for a point this result is equivalent to the witten kontsevich formula 14

on the tautological ring of mg we prove that any product of tautological classes of g of degreed in the chow ring of g with rational coefficients vanishes ford g 2 and is proportional to the class of the hyperelliptic locus in degreeg 2

a new proof of faber s intersection number conjecture we give a new proof of faber s intersection number conjecture concerning the top intersections in the tautological ring of the moduli space of curves mg the proof is based on a very straightforward geometric and combinatorial computation with double ramification cycles

an improved particle swarm optimization algorithm an improved particle swarm optimization ipso is proposed in this paper in the new algorithm a population of points sampled randomly from the feasible space then the population is partitioned into several sub swarms each of which is made to evolve based on particle swarm optimization pso algorithm at periodic stages in the evolution the entire population is shuffled and then points are reassigned to sub swarms to ensure information sharing this method greatly elevates the ability of exploration and exploitation simulations for three benchmark test functions show that ipso possesses better ability to find the global optimum than that of the standard pso algorithm compared with pso ipso is also applied to identify the hydrologic model the results show that ipso remarkably improves the calculation accuracy and is an effective global optimization to calibrate hydrologic model

topological recursive relations in h2g ℳg n we show that any degree at least g monomial in descendant or tautological classes vanishes on g n when g 2 this generalizes a result of looijenga and proves a version of getzler s conjecture the method we use is the study of the relative gromov witten invariants of 1 relative to two points combined with the degeneration formulas of ip1

correlation functions of the kdv hierarchy and applications to intersection numbers over m g n we derive an explicit generating function of correlations functions of an arbitrary tau function of the kdv hierarchy in particular applications our formulation gives closed formulae of a new type for the generating series of intersection numbers of classes as well as of mixed and classes in full genera

perturbative series and the moduli space of riemann surfaces on utilise des techniques de la theorie quantique des champs pour calculer des quantites reliees aux groupes de symetrie de paires f g ou f est une surface et g une epine de f

volume optimization normal surfaces and thurston s equation on triangulated 3 manifolds we propose a finite dimensional variational principle on triangulated 3 manifolds so that its critical points are related to solutions to thurston s gluing equation and haken s normal surface equation the action functional is the volume

a modified particle swarm optimization algorithm with applications abstract in this paper firstly a modified particle swarm optimization algorithm mpso is developed in which the mean value of past optimal positions for each particle and the mutation operation are considered for avoiding premature in the optimization test mpso performs better than particle swarm optimization algorithm pso then mpso is applied to solve four portfolio optimization models with the real data from the hong kong stock market and optimal values are obtained when the number of swarm n 80 160 respectively finally actual return rates of these models are calculated in numerical experiments and it is illustrated from these graphs of actual return rates that when considering higher return cai s model performs better in short term investment

matrix integration and combinatorics of modular groups integration over gaussian matrix ensembles was used to obtain the virtual euler characteristics of mapping class groups we present some simplifications in the combinatorial part of the calculation

analyticity of the total ancestor potential in singularity theory abstract k saito s theory of primitive forms gives a natural semi simple frobenius manifold structure on the space of miniversal deformations of an isolated singularity on the other hand givental introduced the notion of a total ancestor potential for every semi simple point of a frobenius manifold and conjectured that in the settings of singularity theory his definition extends analytically to non semisimple points as well in this paper we prove givental s conjecture by using the eynard orantin recursion

a proof of the faber intersection number conjecture we prove the famous faber intersection number conjecture and other more general results by using a recursion formula of n point functions for intersection numbers on moduli spaces of curves we also present some vanishing properties of gromov witten invariants

the stable moduli space of riemann surfaces mumford s conjecture d mumford conjectured in 30 that the rational cohomology of the stable moduli space of riemann surfaces is a polynomial algebra generated by certain classes i of di mension 2i for the purpose of calculating rational cohomology one may replace the stable moduli space of riemann surfaces by b 1 where 1 is the group of isotopy classes of automorphisms of a smooth oriented connected surface of large genus tillmann s insight 41 that the plus construction makes b 1 into an infinite loop space led to a stable homo topy version of mumford s conjecture stronger than the original 22 we prove the stronger version relying on harer s stability theorem 15 vassiliev s theorem concerning spaces of functions with moderate singularities 43 42 and methods from homotopy theory

gromov witten theory of orbicurves the space of tri polynomials and symplectic field theory of seifert fibrations we compute with symplectic field theory sft techniques the gromov witten theory of mathbb p 1 alpha 1 ldots alpha a i e the complex projective line with a orbifold points a natural subclass of these orbifolds the ones with polynomial quantum cohomology gives rise to a family of polynomial frobenius manifolds and integrable systems of hamiltonian pdes which extend the dispersionless bigraded toda hierarchy carlet the extended bigraded toda hierarchy arxiv preprint arxiv math ph 0604024 we then define a frobenius structure on the spaces of polynomials in three complex variables of the form f x y z xyz p1 x p2 y p3 z which contains as special cases the ones constructed on the space of laurent polynomials dubrovin geometry of 2d topologica field theories integrable systems and quantum groups springer lecture notes in mathematics 1620 120 348 1996 milanov and tseng the space of laurent polynomials mathbb p 1 orbifolds and integrable hierarchies preprint arxiv math 0607012v3 math ag we prove a mirror theorem stating that these frobenius structures are isomorphic to the ones found before for polynomial mathbb p 1 orbifolds finally we link rational sft of seifert fibrations over mathbb p 1 a b c with orbifold gromov witten invariants of the base extending a known result bourgeois a morse bott approach to contact homology ph d dissertation stanford university 2002 valid in the smooth case

the partition function of the two matrix model as an isomonodromic τ function we consider the itzykson zuber eynard mehta two matrix model and prove that the partition function is an isomonodromic function in a sense that generalizes that of jimbo et al monodromy preserving deformation of linear ordinary differential equations with rational coefficients physica d 2 306 1981 in order to achieve the generalization we need to define a notion of function for isomonodromic systems where the adregularity of the leading coefficient is not a necessary requirement

a minimax portfolio selection rule with linear programming solution a new principle for choosing portfolios based on historical returns data is introduced the optimal portfolio based on this principle is the solution to a simple linear programming problem this principle uses minimum return rather than variance as a measure of risk in particular the portfolio is chosen that minimizes the maximum loss over all past observation periods for a given level of return this objective function avoids the logical problems of a quadratic nonmonotone utility function implied by mean variance portfolio selection rules the resulting minimax portfolios are diversified for normal returns data the portfolios are nearly equivalent to those chosen by a mean variance rule framing the portfolio selection process as a linear optimization problem also makes it feasible to constrain certain decision variables to be integer or 0 1 valued this feature facilitates the use of more complex decision making models including models with fixed transaction charges and models with boolean type constraints on allocations

the unstable integral homology of the mapping class groups of a surface with boundary we construct a graph complex calculating the integral homology of the bordered mapping class groups we compute the homology of the bordered mapping class groups of the surfaces s 1 1 s 1 2 and s 2 1 using the circle action on this graph complex we build a double complex and a spectral sequence converging to the homology of the unbordered mapping class groups we compute the homology of the punctured mapping class groups associated to the surfaces s 1 1 and s 2 1 finally we use miller s operad to get the first kudo araki and browder operations on our graph complex we also consider an unstable version of the higher kudo araki dyer lashoff operations

the euler characteristic of the moduli space of curves let fg 1 g 1 be the mapping class group consisting of all isotopy classes of base point and orientation preserving homeomorphisms of a closed oriented surface f of genus g let 1 be its euler characteristic in the sense of wall that is z f i fgl f l z e f where f is any torsion free subgroup of finite index in f 1 and e is a contractible space on which f acts freely and properly discontinuously an example of such a space is the teichmiiller space 1 and g f can be interpreted as the orbifold euler characteristic of f i join the moduli space of curves of genus g with base point the purpose of this paper is to prove the following formula for f i

particle swarm optimization using dimension selection methods particle swarm optimization pso has undergone many changes since its introduction in 1995 being a stochastic algorithm pso and its randomness present formidable challenge for the theoretical analysis of it and few of the existing pso improvements have make an effort to eliminate the random coefficients in the pso updating formula this paper analyzes the importance of the randomness in the pso and then gives a pso variant without randomness to show that traditional pso cannot work without randomness based on our analysis of the randomness another way of using randomness is proposed in pso with random dimension selection psords algorithm which utilizes random dimension selection instead of stochastic coefficients finally deterministic methods to do the dimension selection are proposed and the resultant pso with distance based dimension selection psodds algorithm is greatly superior to the traditional pso and pso with heuristic dimension selection psohds algorithm is comparable to traditional pso algorithm in addition using our dimension selection method to a newly proposed modified particle swarm optimization mpso algorithm also gets improved results the experiment results demonstrate that our analysis about the randomness is correct and the usage of deterministic dimension selection method is very helpful

the witten equation mirror symmetry and quantum singularity theory for any nondegenerate quasi homogeneous hypersurface singularity we describe a family of moduli spaces a virtual cycle and a corresponding cohomological eld theory associated to the singularity this theory is analogous to gromov witten theory and generalizes the theory of r spin curves which corresponds to the simple singularity ar 1 we also resolve two outstanding conjectures of witten the rst conjecture is that ade singularities are self dual and the second conjecture is that the total potential functions of ade singularities satisfy corresponding ade integrable hierarchies other cases of integrable hierarchies are also discussed

a formula of two partition hodge integrals jmg n where tpi ci l is the first chern class of l and xj cj e is the j th chern class of the hodge bundle the study of hodge integrals is an important part of intersection theory on mg n hodge integrals also naturally arise when one computes gromov witten invariants by localization techniques for example the following generating series of hodge integrals arises when one computes local invariants of a toric fano surface in a calabi yau 3 fold by virtual localization 33

computing top intersections in the tautological ring of mg we derive effective recursion formulae of top intersections in the tautological ring r mathcal m g of the moduli space of curves of genus g 2 as an application we prove a convolution type tautological relation in r g 2 mathcal m g and some interesting bernoulli number identities

tau functions and virasoro symmetries for drinfeld sokolov hierarchies abstract for each drinfeld sokolov integrable hierarchy associated to affine kac moody algebra we obtain a uniform construction of tau function by using tau symmetric hamiltonian densities moreover we represent its virasoro symmetries as linear nonlinear actions on the tau function the relations between the tau function constructed in this paper and those defined for particular cases of drinfeld sokolov hierarchies in the literature are clarified we also show that whenever the affine kac moody algebra is simply laced or twisted the tau function of the drinfeld sokolov hierarchy coincides with the solution of the corresponding kac wakimoto hierarchy constructed from the principal vertex operator realization of the affine algebra

advances in random matrix theory zeta functions and sphere packing over four hundred years ago sir walter raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles these investigations aroused the curiosity of the astronomer johannes kepler and led to a problem that has gone centuries without a solution why is the familiar cannonball stack the most efficient arrangement possible here we discuss the solution that hales found in 1998 almost every part of the 282 page proof relies on long computer verifications random matrix theory was developed by physicists to describe the spectra of complex nuclei in particular the statistical fluctuations of the eigenvalues the energy levels follow certain universal laws based on symmetry types we describe these and then discuss the remarkable appearance of these laws for zeros of the riemann zeta function which is the generating function for prime numbers and is the last special function from the last century that is not understood today explaining this phenomenon is a central problem these topics are distinct so we present them separately with their own introductory remarks

equations of the moduli of pointed curves in the infinite grassmannian the main result of this paper is the explicit computa tion of the equations defining the moduli space of triples c p where c is an integral and complete algebraic curve p a smooth rational point anda certain isomorphism this is achieved by introducing algebraically infinite grassmannians tau and baker ahkiezer functions and by proving an addition formula for tau functions

on certain infinite dimensional aspects of arakelov intersection theory letk y x be an embedding of compact complex manifolds bismut and lebeau have calculated the quillen norm of the canonical isomorphism identifying the determinant of the cohomology of a holomorphic vector bundle overy and the determinant of the cohomology of a resolution by a complex of holomorhic vector bundles overx the purpose of this paper is to show that the formula of bismut lebeau can be viewed as an equivariant intersection formula over the loop space of the considered manifolds in the presence of an infinite dimensional excess normal bundle this excess normal bundle is responsible for the appearance of the additive genusr of gillet and soule in the formula of bismut and lebeau