on the tropical torelli map abstract we construct the moduli spaces of tropical curves and tropical principally polarized abelian varieties working in the category of what we call stacky fans we define the tropical torelli map between these two moduli spaces and we study the fibers tropical torelli theorem and the image of this map tropical schottky problem finally we determine the image of the planar tropical curves via the tropical torelli map and we use it to give a positive answer to a question raised by namikawa on the compactified classical torelli map

joint cycle frequencies and lags utilization in cyclostationary feature spectrum sensing cognitive radio cr systems require awareness of spectrum occupancy in order to operate without causing harmful interference to primary users pus cyclostationary feature detection cfd is a preferred method for spectrum sensing under low signal to noise ratio snr or and noise uncertainty scenarios to determine the presence or otherwise of pu signals conventional cfd schemes tend to use test statistics over either multiple cycle frequencies for a fixed lag set or multiple lags for a fixed cycle frequency this paper proposes a new method that jointly utilizes cycle frequencies and lags to produce more reliable test statistics as the optimal way to apply this joint utilization requires prior knowledge of the 4th order cyclic cumulant which can be challenging to obtain an alternative sub optimal scheme independent of this cumulant knowledge will also be provided it will be shown that in the low snr region where it is most critical for cr applications the proposed sub optimal scheme can lead to similar detection performances as the optimal maximum likelihood technique it will also be demonstrated that compared to multi cycle frequency detection with selection combining equal gain combining or maximum ratio combining the proposed provide superior performance

generalized calabi yau manifolds and the chiral de rham complex abstract we show that the chiral de rham complex of a generalized calabi yau manifold carries n 2 supersymmetry we discuss the corresponding topological twist for this n 2 algebra we interpret this as an algebroid version of the super sugawara or kac todorov construction

extending the torelli map to toroidal compactifications of siegel space it has been known since the 1970s that the torelli map m g a g associating to a smooth curve its jacobian extends to a regular map from the deligne mumford compactification overline operatorname m g to the 2nd voronoi compactification overline operatorname a g mathrm vor we prove that the extended torelli map to the perfect cone 1st voronoi compactification overline operatorname a g mathrm perf is also regular and moreover overline operatorname a g mathrm vor and overline operatorname a g mathrm perf share a common zariski open neighborhood of the image of overline operatorname m g we also show that the map to the igusa monoidal transform central cone compactification is not regular for g 9 this disproves a 1973 conjecture of namikawa

on cy lg correspondence for 0 2 toric models abstract we conjecture a description of the vertex chiral algebras of the 0 2 nonlinear sigma models on smooth quintic threefolds we provide evidence in favor of the conjecture by connecting our algebras to the cohomology of a twisted chiral de rham sheaf we discuss cy lg correspondence in this setting

comparing perfect and 2nd voronoi decompositions the matroidal locus we compare two rational polyhedral admissible decompositions of the cone of positive definite quadratic forms the perfect cone decomposition and the 2nd voronoi decomposition we determine which cones belong to both the decompositions thus providing a positive answer to a conjecture of alexeev and brunyate invent math doi 10 1007 s00222 011 0347 2 2011 as an application we compare the two associated toroidal compactifications of the moduli space of principal polarized abelian varieties the perfect cone compactification and the 2nd voronoi compactification

robust nonparametric cyclic correlation based spectrum sensing for cognitive radio cognitive radios sense the radio spectrum in order to find underutilized spectrum and then exploit it in an agile manner spectrum sensing has to be performed reliably in challenging propagation environments characterized by shadowing and fading effects as well as heavy tailed noise distributions in this paper a robust computationally efficient nonparametric cyclic correlation estimator based on the multivariate spatial sign function is proposed nonparametric statistics provide additional robustness against heavy tailed noise and when the noise statistics are not fully known asymptotic distribution of the spatial sign cyclic correlation estimator under the null hypothesis is established tests using constraint on false alarm rate are derived based on the estimated spatial sign cyclic correlation for single user and collaborative spectrum sensing by multiple secondary users theoretical justification for detecting cyclostationary signals using the spatial sign cyclic correlation is provided a sequential detection scheme for reducing the average detection time is proposed simulation experiments and theoretical results comparing the proposed method with cyclostationary spectrum sensing methods employing the conventional cyclic correlation estimator are presented simulations demonstrate the reliable and highly robust performance of the proposed nonparametric spectrum sensing method in both gaussian and non gaussian noise environments

collaborative cyclostationary spectrum sensing for cognitive radio systems this paper proposes an energy efficient collaborative cyclostationary spectrum sensing approach for cognitive radio systems an existing statistical hypothesis test for the presence of cyclostationarity is extended to multiple cyclic frequencies and its asymptotic distributions are established collaborative test statistics are proposed for the fusion of local test statistics of the secondary users and a censoring technique in which only informative test statistics are transmitted to the fusion center fc during the collaborative detection is further proposed for improving energy efficiency in mobile applications moreover a technique for numerical approximation of the asymptotic distribution of the censored fc test statistic is proposed the proposed tests are nonparametric in the sense that no assumptions on data or noise distributions are required in addition the tests allow dichotomizing between the desired signal and interference simulation experiments are provided that show the benefits of the proposed cyclostationary approach compared to energy detection the importance of collaboration among spatially displaced secondary users for overcoming shadowing and fading effects as well as the reliable performance of the proposed algorithms even in very low signal to noise ratio snr regimes and under strict communication rate constraints for collaboration overhead

statistical tests for presence of cyclostationarity the presence of kth order cyclostationarity is defined in terms of nonvanishing cyclic cumulants or polyspectra relying upon the asymptotic normality and consistency of kth order cyclic statistics asymptotically optimal spl chi sup 2 tests are developed to detect the presence of cycles in the kth order cyclic cumulants or polyspectra without assuming any specific distribution on the data constant false alarm rate tests are derived in both time and frequency domain and yield consistent estimates of possible cycles present in the kth order cyclic statistics explicit algorithms for k spl les 4 are discussed existing approaches are rather empirical and deal only with k spl les 2 case simulation results are presented to confirm the performance of the given tests

detection of multivariate cyclostationarity this paper derives an asymptotic generalized likelihood ratio test glrt and an asymptotic locally most powerful invariant test lmpit for two hypothesis testing problems 1 is a vector valued random process cyclostationary cs or is it wide sense stationary wss 2 is a vector valued random process cs or is it nonstationary our approach uses the relationship between a scalar valued cs time series and a vector valued wss time series for which the knowledge of the cycle period is required this relationship allows us to formulate the problem as a test for the covariance structure of the observations the covariance matrix of the observations has a block toeplitz structure for cs and wss processes by considering the asymptotic case where the covariance matrix becomes block circulant we are able to derive its maximum likelihood ml estimate and thus an asymptotic glrt moreover using wijsman s theorem we also obtain an asymptotic lmpit these detectors may be expressed in terms of the loeve spectrum the cyclic spectrum and the power spectral density establishing how to fuse the information in these spectra for an asymptotic glrt and lmpit this goes beyond the state of the art where it is common practice to build detectors of cyclostationarity from ad hoc functions of these spectra

determinant bundles and virasoro algebras we consider the interplay of infinite dimensional lie algebras of virasoro type and moduli spaces of curves suggested by string theory we will see that the infinitesimal geometry of determinant bundles is governed by virasoro symmetries the mumford forms are just invariants of these symmetries the representations of virasoro algebra define twisted d modules on moduli spaces thesed modules are equations on correlators in conformal field theory

on cyclostationarity based spectrum sensing under uncertain gaussian noise detection of cyclostationary primary user pu signals in colored gaussian noise for cognitive radio systems is considered based on looking for single or multiple cycle frequencies at single or multiple time lags in the cyclic autocorrelation function caf of the noisy pu signal we explicitly exploit the knowledge that under the null hypothesis of pu signal absent the measurements originate from possible colored gaussian noise with unknown correlation function our formulation allows us to simplify the spectrum sensing detector and obviates the need for estimating an unwieldy covariance matrix needed in some prior works we consider both single and multiple antenna receivers and both nonconjugate and conjugate cafs a performance analysis of the proposed detector is carried out supporting simulation examples are provided to demonstrate the efficacy of the proposed approaches and to compare them with some existing approaches our proposed approaches are computationally cheaper than the dandawate giannakis and related approaches while having quite similar detection performance for a given false alarm rate

lagrangian approach to sheaves of vertex algebras we explain how sheaves of vertex algebras are related to mathematical structures encoded by a class of lagrangians the exposition is focused on two examples the wzw model and the 1 1 supersymmetric model we conclude by showing how to construct a family of vertex algebras with base the barannikov kontsevich moduli space thus furnishing the b model moduli for witten s half twisted model

cyclic statistic estimators with uncertain cycle frequencies for almost cyclostationary processes sufficient conditions are derived such that estimates of the second order cyclic probabilistic functions with estimated cycle frequencies are mean square consistent and asymptotically complex normal cyclic conjugate autocorrelation functions and cyclic conjugate spectra are considered under the derived conditions asymptotically as the data record length approaches infinity the estimates of cyclic statistics with estimated cycle frequencies have the same complex normal distribution as the case of exactly known cycle frequencies the results are applied to the detection of a moving cyclostationary source in the presence of strong doppler effect and for low values of snr

the zero section of the universal semiabelian variety and the double ramification cycle we study the chow ring of the boundary of the partial compactification of the universal family of principally polarized abelian varieties ppav we describe the subring generated by divisor classes and we compute the class of the partial compactification of the universal zero section which turns out to lie in this subring our formula extends the results for the zero section of the universal uncompactified family the partial compactification of the universal family of ppav can be thought of as the first two boundary strata in any toroidal compactification of ag our formula provides a first step in a program to understand the chow groups of a g especially of the perfect cone compactification by induction on genus by restricting to the image of mg under the torelli map our results extend the results of hain on the double ramification cycle answering eliashberg s question

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

a chiral borel weil bott theorem abstract we compute the cohomology of modules over the algebra of twisted chiral differential operators over the flag manifold this is applied to 1 finding the character of g integrable irreducible highest weight modules over the affine lie algebra at the critical level and 2 computing a certain elliptic genus of the flag manifold the main tool is a result that interprets the drinfeld sokolov reduction as a derived functor

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

freely generated vertex algebras and non linear lie conformal algebras we introduce the notion of a non linear lie conformal superalgebra and prove a pbw theorem for its universal enveloping vertex algebra we also show that conversely any graded freely generated vertex algebra is the universal enveloping algebra of a unique up to isomorphism non linear lie conformal superalgebra this correspondence will be applied in the subsequent work to the problem of classification of finitely generated simple graded vertex algebras

complete moduli in the presence of semiabelian group action i prove the existence and describe the structure of moduli space of pairs p consisting of a projective variety p with semiabelian group action and an ample cartier divisor on it satisfying a few simple conditions every connected component of this moduli space is proper a component containing a projective toric variety is described by a configuration of several polytopes the main one of which is the secondary polytope on the other hand the component containing a principally polarized abelian variety provides a moduli compactification of a g the main irreducible component of this compactification is described by an infinite periodic analog of the secondary polytope and coincides with the toroidal compactification of a g for the second voronoi decomposition

signal interception a unifying theoretical framework for feature detection the unifying framework of the spectral correlation theory of cyclostationary signals is used to present a broad treatment of weak random signal detection for interception purposes the relationships among a variety of previously proposed ad hoc detectors optimum detectors and newly proposed detectors are established the spectral correlation plane approach to the interception problem is put forth as especially promising for detection classification and estimation in particularly difficult environments involving unknown and changing noise levels and interference activity a fundamental drawback of the popular radiometric methods in such environments is explained

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

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