susy vertex algebras and supercurves given a strongly conformal susy vertex algebra v and a supercurve x we construct a vector bundle fancyscript v r x on x the fiber of which is isomorphic to v moreover the state field correspondence of v canonically gives rise to local sections of these vector bundles we also define chiral algebras on any supercurve x and show that the vector bundle fancyscript v r x corresponding to a susy vertex algebra carries the structure of a chiral algebra

vanishing of principal value integrals on surfaces principal value integrals are associated to multi valued rational differential forms with normal crossings support on a non singular algebraic variety we prove their vanishing on rational surfaces in the context of a conjecture of denef jacobs as an appli cation we obtain a strong vanishing result for candidate poles of p adic and motivic igusa zeta functions

an overview of wavelet based multiresolution analyses in this paper an overview of wavelet based multiresolution analyses is presented first the continuous wavelet transform in its simplest form is discussed then the definition of a multiresolution analysis is given and how wavelets fit into it is shown the authors take a closer look at orthogonal biorthogonal and semiorthogonal wavelets the fast wavelet transform wavelets on an interval multidimensional wavelets and wavelet packets are discussed several examples of wavelet families are introduced and compared finally the essentials of two major applications are outlined data compression and compression of linear operators

towards the singular locus of the space of arcs we give a theory on the space of arcs x infty of a singular variety x based on the finiteness property of the stable points of x infty we also show how computations can be made in this theory as a consequence we obtain a process of determining invariants of x from its space of arcs x infty and from its spaces of wedges arcs in the space of arcs more precisely we give two concepts of regularity for the stable points of x infty and we show that we have regularity in codimension 1 and for all stable points of the space of arcs of a curve as another application we show concrete examples obtained from the spaces of arcs of noetherian 1 dimensional local rings which are analytically ramified

some concepts of negative dependence abstract the theory of positive dependence notions cannot yield useful results for some widely used distributions such as the multinomial dirichlet and the multivariate hypergeometric some conditions of negative dependence that are satisfied by these distributions and which have practical meaning are introduced preservation results for some of these concepts are derived useful inequalities for some widely used distributions are obtained results of mallows 1969 that apply to the multinomial distributions are extended to more distributions examples are listed author

tail behavior of random sums of negatively associated increments abstract let x x k k 1 be a sequence of negatively associated random variables with a common distribution function and finite expectation and let be a nonnegative integer valued random variable independent of x k k 1 in this paper we give unified form for the asymptotic behavior of the random sums s k 1 x k in the case of lim x p x x p x c 0 the results extend the earlier results of aleskeviciene et al 2008 2

directionlets anisotropic multidirectional representation with separable filtering in spite of the success of the standard wavelet transform wt in image processing in recent years the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions one dimensional 1 d discontinuities in images edges and contours that are very important elements in visual perception intersect too many wavelet basis functions and lead to a nonsparse representation to efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions a more complex multidirectional m dir and anisotropic transform is required we present a new lattice based perfect reconstruction and critically sampled anisotropic m dir wt the transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two dimensional wt unlike in the case of some other directional transform constructions e g curvelets contourlets or edgelets the corresponding anisotropic basis functions directionlets have directional vanishing moments along any two directions with rational slopes furthermore we show that this novel transform provides an efficient tool for nonlinear approximation of images achieving the approximation power o n sup 1 55 which while slower than the optimal rate o n sup 2 is much better than o n sup 1 achieved with wavelets but at similar complexity

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

a discrete transform and triebel lizorkin spaces on the bidisc we use a discrete transform to study the triebel lizorkin spaces on bidisc fpaq jq and establishes the boundedness of transform sek p jq and tt jq q fp we also define the almost diagonal operator and prove its boundedness with the use of discrete transform and journe lemma we get the atomic decomposition of jq for 0 1 a e r is established too the case for p q is similar 0 introduction in this paper we use a discrete transform to study the triebel lizorkin spaces on the bidisc in 1 we define the sequence space fp and the distribution space fp 7 our fundamental formula is f eq f qq yiq where q runs over all dyadic rectangles and qq yq are translates and dilates of x y associated with q respectively fourier transforms of x y have compact support and suppqq q c l 2 2v11 1 4 in 2 we define almost diagonal operators and prove the boundedness of such operators on fp by duality we also define 3 m rectangle molecules received by the editors july 8 1993 and in revised form december 28 1993 originally communicated to the proceedings of the ams by andrew bruckner 1991 mathematics subject classification primary 42b20 supported by nnsf zpnsf and the doctoral foundation in china 1995 american mathematical society 0002 9947 95 1 00 25 per page

motivic height zeta functions we consider a motivic analogue of the height zeta function for integral points of equivariant partial compactifications of affine spaces we establish its rationality and determine its largest pole a major problem of diophantine geometry is to understand the distribution of rational or integral points of algebraic varieties defined over number fields for example a well studied question put forward by manin in 1 is that of an asymptotic expansion for the number of rational integral points of bounded height a basic tool is the height zeta function which is a dirichlet series around 2000 e peyre suggested to consider the analogous problem over function fields which has then an even more geometric flavor since it translates as a problem of enumerative geometry namely counting algebraic curves of given degree and establishing properties of the corresponding generating series in view of the developments of motivic integration by kontsevich denef loeser 11 etc it is natural to look at a more general generating series which not only counts the number of such algebraic curves but takes into account the space they constitute in a suitable hilbert scheme a natural coefficient ring for the generating series is the grothendieck ring of varieties kvark if k is a field this ring is generated as a group by the isomorphism classes of k schemes of finite type the addition being subject to obvious cut and paste relations and the product is induced by the product of k varieties one interest of this generalization is that it also makes sense in a purely geometric context where no counting is available such a situation has been first studied in a paper by kapranov in 15 where the analogy with the mentioned diophantine problem is not pointed out later bourqui made some progress on the motivic analogue of manin s problem see 4 as well as his survey report 5 manuscript received april 14 2014 revised march 3 2015 research of the first author supported by the institut universitaire de france by the national science foundation under agreement no dms 0635607 as well as by the positive project of agence nationale de la recherche under agreement anr 2010 blan 0119 01 research of the second author supported in part by the european research council under the european community s seventh framework programme fp7 2007 2013 erc grant agreement nr 246903 nmnag also partially supported by valcomo anr 13 bs01 0006 american journal of mathematics 138 2016 1 59 c 2016 by johns hopkins university press

poincare series of a toric variety abstract for an affine toric variety x we compute the poincare series of the multi index filtration defined by a finite number of monomial divisorial valuations on the ring o x 0 we give an alternative description of the poincare series as an integral with respect to the euler characteristic over the projectivization of the space of germs o x 0 in particular we study divisorial valuations on the ring o c d 0 that arise by considering toric constellations we give an explicit formula for the poincare series and a nice geometric description this generalizes an expression of the poincare series for curves and rational surface singularities

elliptic genera of singular varieties the notions of orbifold elliptic genus and elliptic genus of singular varieties are introduced and the relation between them is studied the elliptic genus of singular varieties is given in terms of a resolution of singularities and extends the elliptic genus of calabi yau hypersurfaces in fano gorenstein toric varieties introduced earlier the orbifold elliptic genus is given in terms of the fixed point sets of the action we show that the generating function for the orbifold elliptic genus ellorb x 6n p for symmetric groups 6n acting on n fold products coincides with the one proposed by r dijkgraaf g moore e verlinde and h verlinde the two notions of elliptic genera are conjectured to coincide

the arc space of the grassmannian abstract we study the arc space of the grassmannian from the point of view of the singularities of schubert varieties our main tool is a decomposition of the arc space of the grassmannian that resembles the schubert cell decomposition of the grassmannian itself just as the combinatorics of schubert cells is controlled by partitions the combinatorics in the arc space is controlled by plane partitions sometimes also called 3d partitions a combination of a geometric analysis of the pieces in the decomposition and a combinatorial analysis of plane partitions leads to invariants of the singularities as an application we reduce the computation of log canonical thresholds of pairs involving schubert varieties to an easy linear programming problem we also study the nash problem for schubert varieties showing that the nash map is always bijective in this case

perfect sampling for the wavelet reconstruction of signals the coupling from the past cftp procedure is a protocol for finite state markov chain monte carlo mcmc methods whereby the algorithm itself can determine the necessary runtime to convergence in this paper we demonstrate how this protocol can be applied to the problem of signal reconstruction using bayesian wavelet analysis where the dimensionality of the wavelet basis set is unknown and the observations are distorted by gaussian white noise of unknown variance mcmc simulation is used to account for model uncertainty by drawing samples of wavelet bases for approximating integrals or summations on the model space that are either too complex or too computationally demanding to perform analytically we extend the cftp protocol by making use of the central limit theorem to show how the algorithm can also monitor its own approximation error induced by mcmc in this way we can assess the number of mcmc samples needed to approximate the integral to within a user specified tolerance level hence the method automatically ensures convergence and determines the necessary number of iterations needed to meet the error criteria

efficient implementations of quadratic digital filters efficient implementation structures of quadratic filters are introduced in this paper using systolic arrays distributed arithmetic and linear convolutions with multipliers the implementations are based on matrix decompositions and consist of a set of parallel 1 d fir filters in cascade with a set of sequential square in add out type of operations the structures are compared using various realistic figures of merit such as data throughput delay cost that is proportional to chip area and variance of roundoff errors in the filter output assuming fixed point arithmetic for comparison purposes the direct and biglieri quadratic structures are included in this study evaluating the comparative results the conclusion drawn is that the matrix decomposition realization of a quadratic filter implemented with systolic arrays seems to be offering the best compromise among the various conflicting figures of merit

enhanced frequency analysis using wavelets an enhanced frequency analysis method is introduced using a phase shift wavelet representation to analyse individual frequency components and to reveal features of a given signal the frequency representation provides details at each time location without the loss caused by local orthogonality between the wavelet basis functions and the given signal which occurs when a normal wavelet decomposition is employed movement of the local orthogonality locations corresponding to the phase shift of the wavelet basis functions are studied and it is shown that these movements are important and can be used to reveal features of the signal in the frequency domain such as continuities smoothness and trends several examples are presented to illustrate the method and an application to a permanent magnet synchronous drive system is provided to demonstrate the approach

terminal valuations and the nash problem let x be an algebraic variety of characteristic zero terminal valuations are defined in the sense of the minimal model program as those valuations given by the exceptional divisors on a minimal model over x we prove that every terminal valuation over x is in the image of the nash map and thus it corresponds to a maximal family of arcs through the singular locus of x in dimension two this result gives a new proof of the theorem of fernandez de bobadilla and pe pereira stating that for surfaces the nash map is a bijection

chiral de rham complex we define natural sheaves of vertex algebras over smooth manifolds which may be regarded as semi infinite de rham complexes of certain d modules over the loop spaces for calabi yau manifolds they admit n 2 supersymmetry connection with wakimoto modules is discussed

differential arcs and regular types in differential fields we introduce differential arc spaces in analogy to the algebraic arc spaces and show that a differential variety is determined by its arcs at a point using differential arcs we show that if k 1 n is a differentially closed field of characteristic zero with n commuting derivations and p s k is a regular type over k then either p is locally modular or there is a definable subgroup g k of the additive group having a regular generic type that is nonorthogonal to p

dimensions of jet schemes of log singularities we characterize kawamata log terminal singularities and log canonical singularities by dimensions of jet schemes our main result is theorem 2 4

characters of topological n 2 vertex algebras are jacobi forms on the moduli space of elliptic supercurves abstract we show that trace functions on modules of topological n 2 super vertex algebras give rise to conformal blocks on elliptic supercurves we show that they satisfy a system of linear partial differential equations with respect to the modular parameters of the supercurves under some finiteness condition on the vertex algebra these differential equations can be interpreted as a connection on the vector bundle of conformal blocks we show that this connection is equivariant with respect to a natural action of the jacobi modular group on the modular parameters and the trace functions in the appendix we prove the convergence of the trace functions

germs of arcs on singular algebraic varieties and motivic integration we study the scheme of formal arcs on a singular algebraic variety and its images under truncations we prove a rationality result for the poincare series of these images which is an analogue of the rationality of the poincare series associated to p adic points on a p adic variety the main tools which are used are semi algebraic geometry in spaces of power series and motivic integration a notion introduced by m kontsevich in particular we develop the theory of motivic integration for semi algebraic sets of formal arcs on singular algebraic varieties we prove a change of variable formula for birational morphisms and we prove a geometric analogue of a result of oesterle

tensor product basis approximations for volterra filters the paper studies approximations for a class of nonlinear filters known as volterra filters although the volterra filter provides a relatively simple and general representation for nonlinear filtering it is often highly overparameterized due to the large number of parameters the utility of the volterra filter is limited the overparameterization problem is addressed in the paper using a tensor product basis approximation tpba in many cases a volterra filter may be well approximated using the tpba with far fewer parameters hence the tpba offers considerable advantages over the original volterra filter in terms of both implementation and estimation complexity furthermore the tpba provides useful insight into the filter response the paper studies the crucial issue of choosing the approximation basis several methods for designing an appropriate approximation basis and error bounds on the resulting mean square output approximation error are derived certain methods are known to be nearly optimal

jet closures and the local isomorphism problem abstract if a morphism of germs of schemes induces isomorphisms of all local jet schemes does it follow that the morphism is an isomorphism this problem is called the local isomorphism problem in this paper we use jet schemes to introduce various closure operations among ideals and relate them to the local isomorphism problem this approach leads to a partial solution of the local isomorphism problem which is shown to have a negative answer in general and a positive one in several situations of geometric interest

tail probability of a random sum with a heavy tailed random number and dependent summands abstract let k k 1 be a sequence of widely orthant dependent random variables with common distribution f satisfying e 0 let be a nonnegative integer valued random variable in this paper we discuss the tail probabilities of random sums s n 1 n when the random number has a heavier tail than the summands i e p x p x 0 as x under some additional technical conditions we prove that if has a consistently varying tail then s has a consistently varying tail and p s x p x e on the other hand the converse problem is also equally interesting we prove that if s has a consistently varying tail then has a consistently varying tail and that p s x p x e still holds in particular the random number is not necessarily assumed to be independent of the summands k k 1 in theorem 3 1 and theorem 3 3 finally some applications to the asymptotic behavior of the finite time ruin probabilities in some insurance risk models are given

invertibility of higher order moment matrices signal processing algorithms based on volterra filter structures often require that a matrix composed of higher order moments of the underlying process be invertible previously this problem has been studied for uncorrelated random variables the paper establishes conditions under which a wide class of correlated processes have invertible higher order moment matrices

gerbes of chiral differential operators ii vertex algebroids introduction 605 0 recollections and notation 612 1 vertex algebroids 615 2 from vertex algebras to vertex algebroids 622 3 category of vertex algebroids 628 4 cofibered structure 633 5 computation of a cocycle 637 6 characteristic classes of vector bundles 643 7 torseurs and gerbes 647 8 gerbes of vertex algebroids 653 9 chiral differential operators on curves and sheaves of virasoro algebras 657 10 enveloping algebra of a vertex algebroid 664 11 calabi yau structures 668 12 virasoro and calabi yau structures 671 references 680

wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra we derive minimax rates for estimation in anisotropic smoothness classes this rate is attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis with separate scale parameter for every dimension it is shown that this basis is superior to its one scale multiresolution analog if different degrees of smoothness in different directions are present as an important application we introduce a new adaptive wavelet estimator of the time dependent spectrum of a locally stationary time series using this model which was resently developed by dahlhaus we show that the resulting estimator attains nearly the rate which is optimal in gaussian white noise simultaneously over a wide range of smoothness classes moreover by our new approach we overcome the difficulty of how to choose the right amount of smoothing i e how to adapt to the appropriate resolution for reconstructing the local structure of the evolutionary spectrum in the time frequency plane

constructible motivic functions and motivic integration 1 1 in this paper intended to be the first in a series we lay new general foundations for motivic integration and give answers to some important issues in the subject since its creation by maxim kontsevich 23 motivic integration developed quickly and has spread out in many directions in a nutshell in motivic integration numbers are replaced by geometric objects like virtual varieties or motives but classicaly not only numbers are defined using integrals but also interesting classes of functions the previous constructions of motivic integration were all quite geometric and it was quite unclear how they could be generalized to handle integrals depending on parameters the new approach we present here based on cell decomposition allows us to develop a very general theory of motivic integration taking parameters into account more precisely we define a natural class of functions constructible motivic functions which is stable under integration the basic idea underlying our approach is to construct more generally push forward morphisms f which are functorial they satisfy f g f g so that performing motivic integration corresponds to taking the push forward to the point this strategy has many technical advantages in essence it allows to reduce the construction of f to the case of closed immersions and projections and in the latter case we can perform induction on the relative dimension the basic case being that of relative dimension 1

definable sets motives and p adic integrals 0 1 let x be a scheme reduced and separated of finite type over z for p a prime number one may consider the set x zp of its zp rational points for every n in n there is a natural map n x zp x z p assigning to a zp rational point its class modulo p the image yn p of x zp by n is exactly the set of z p rational points which can be lifted to zp rational points denote by nn p the cardinality of the finite set yn p by a result of the first author 7 the poincare series

indecomposable representations of special linear lie superalgebras abstract the main result of this paper is a classification of finite dimensional representations of the lie superalgebras sl m 1 of supertraceless endomorphisms of the vector superspace of dimension m 1 the classification extends to the so called singly atypical blocks of the lie superalgebras sl m n but there exist wild representation type blocks as soon as bothmandnare 2

on grothendieck rings and algebraically constructible functions we investigate grothendieck rings appearing in real geometry notably for arc symmetric sets and focus on the relative case in analogy with the properties of the ring of algebraically constructible functions defined by mccrory and parusinski we study in particular the duality and link operators including their behaviour with respect to motivic milnor fibres with signs

vertex algebras and mirror symmetry mirror symmetry for calabi yau hypersurfaces in toric varieties is by now well established however previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror we are able to calculate explicitly vertex algebras that correspond to holomorphic parts of a and b models of calabi yau hypersurfaces and complete intersections in toric varieties we establish the relation between these vertex algebras for mirror calabi yau manifolds this should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra as well as some basic results of the theory of vertex algebras ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties

formal loops iii additive functions and the radon transform to any algebraic variety x and closed 2 form on x we associate the symplectic action functional t which is a function on the formal loop space lx introduced by the authors earlier the correspondence t can be seen as a version of the radon transform we give a characterization of the functions of the form t in terms of factorizability infinitesimal analog of additivity in holomorphic pairs of pants as well as in terms of vertex operator algebras these results will be used in the subsequent paper which will relate the gerbe of chiral differential operators on x whose lien is the sheaf of closed 2 forms and the determinantal gerbe of the tangent bundle of lx whose lien is the sheaf of invertible functions on lx on the level of liens this relation associates to a closed 2 form the invertible function expt

measure of nonlinearity for estimation nonlinearity among other factors is often the root cause of difficulties in nonlinear problems it is important to quantify a problem s degree of nonlinearity to decide a proper solution for example a full blown nonlinear filter is needed in general if the estimation problem is highly nonlinear but a quasi linear filter e g an extended kalman filter is sufficient for a weakly nonlinear case this paper first surveys various measures of nonlinearity mons for different applications for nonlinear estimation we conclude that these mons are not suitable and a better measure is needed in view of this we propose a general mon for estimation it measures the mean square closeness between a point and a subspace in a functional space properties and computation of this measure are studied numerical examples of static models for parameter estimation and dynamic models for process estimation are given to illustrate our measure

on the generalized nash problem for smooth germs and adjacencies of curve singularities abstract in this paper we explore the generalized nash problem for arcs on a germ of smooth surface given two prime divisors above its special point to determine whether the arc space of one of them is included in the arc space of the other one we prove that this problem is combinatorial and we explore its relation with several notions of adjacency of plane curve singularities

supersymmetry and the formal loop space abstract for any algebraic super manifold m we define the super ind scheme lm of formal loops and study the transgression map radon transform on differential forms in this context applying this to the super manifold m s x the spectrum of the de rham complex of a manifold x we obtain in particular that the transgression map for x is a quasi isomorphism between the 2 3 truncated de rham complex of x and the additive part of the 1 2 truncated de rham complex of l x the proof uses the super manifold ss x and the action of the lie super algebra sl 1 2 on this manifold this quasi isomorphism result provides a crucial step in the classification of sheaves of chiral differential operators in terms of geometry of the formal loop space

non commutative periods and mirror symmetry in higher dimensions we study an analog for higher dimensional calabi yau manifolds of the standard predictions of mirror symmetry we introduce periods associated with non commutative deformations of calabi yau manifolds these periods define a map on the moduli space of such deformations which is a local isomorphism using these non commutative periods we introduce invariants of variations of semi infinite generalized hodge structures living over the moduli space it is shown that the generating function of such invariants satisfies the system of wdvv equations exactly as in the case of gromov witten invariants we prove that the total collection of rational gromov witten invariants of complete intersection calabi yau manifold can be identified with the collection of invariants of variations of generalized semi infinite hodge structures attached to the mirror variety the basic technical tool utilized is the deformation theory

wavelet based transformations for nonlinear signal processing nonlinearities are often encountered in the analysis and processing of real world signals we introduce two new structures for nonlinear signal processing the new structures simplify the analysis design and implementation of nonlinear filters and can be applied to obtain more reliable estimates of higher order statistics both structures are based on a two step decomposition consisting of a linear orthogonal signal expansion followed by scalar polynomial transformations of the resulting signal coefficients most existing approaches to nonlinear signal processing characterize the nonlinearity in the time domain or frequency domain in our framework any orthogonal signal expansion can be employed in fact there are good reasons for characterizing nonlinearity using more general signal representations like the wavelet expansion wavelet expansions often provide very concise signal representations and thereby can simplify subsequent nonlinear analysis and processing wavelets also enable local nonlinear analysis and processing in both time and frequency which can be advantageous in nonstationary problems moreover we show that the wavelet domain offers significant theoretical advantages over classical time or frequency domain approaches to nonlinear signal analysis and processing