cramer rao lower bounds for subcarrier snr estimates over multicarrier channels considering orthogonal frequency division multiplexing transmissions analytical expressions for the cramer rao lower bounds for the subcarrier signal to noise ratio snr estimates are derived the transmitted signal is assumed to be corrupted by additive white gaussian noise on the different subcarriers the channel is assumed to be slowly time varying over the observation interval so that it can be assumed constant it will be shown that the achievable performance on subcarrier snr estimation can be significantly improved by exploiting the mutual information the same experienced noise power between the different tones

a comparison of snr estimation techniques for the awgn channel the performances of several signal to noise ratio snr estimation techniques reported in the literature are compared to identify the best estimator the snr estimators are investigated by the computer simulation of baseband binary phase shift keying psk signals in real additive white gaussian noise awgn and baseband 8 psk signals in complex awgn the mean square error is used as a measure of performance in addition to comparing the relative performances the absolute levels of performance are also established the simulated performances are compared to a published cramer rao bound crb for real awgn and a crb for complex awgn that is derived here some known estimator structures are modified to perform better on the channel of interest estimator structures for both real and complex channels are examined

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

higher genus wall crossing in the gauged linear sigma model we introduce a technique for proving all genus wall crossing formulas in the gauged linear sigma model as the stability parameter varies without assuming factorization properties of the virtual class implementing this technique to the gauged linear sigma model associated to a complete intersection in weighted projective space we obtain a uniform proof of the wall crossing formula in both the geometric and the landau ginzburg phase

cramer rao lower bounds for nda snr estimates of square qam modulated transmissions in this paper we derive for the first time analytical expressions for the exact cramer rao lower bounds on the variance of unbiased non data aided nda signal to noise ratio snr estimators of square qam modulated signals the channel is assumed to be constant over the observation interval and the received signal is supposed to be corrupted by additive white gaussian noise awgn the derived expressions corroborate previous attempts to numerically compute the considered crlbs it will be shown that the nda crlbs differ widely from one modulation order to another especially at moderate snr levels

family gromov witten invariants for kahler surfaces we use analytic methods to define family gromov witten invariants for kahler surfaces we prove that these are well defined invariants of the deformation class of the kahler structure gromov witten invariants are counts of holomorphic curves in a symplectic manifold x to define them using the analytic approach one chooses an almost complex structure j compatible with the symplectic structure and considers the set of maps f x from riemann surfaces which satisfy the nonlinear elliptic j holomorphic map equation

semi infinite cohomology and string theory abstract we develop the theory of semi infinite cohomology of graded lie algebras first introduced by feigin we show that the relative semi infinite cohomology has a structure analogous to that of the de rham cohomology in kahler geometry we prove a vanishing theorem for a special class of modules and we apply our results to the case of the virasoro algebra and the fock module in this case the zero cohomology is identified as the physical subspace of the fock module and the no ghost theorem follows we reveal the profound relation of semi infinite cohomology theory to the gauge invariant free string theory constructed by banks and peskin we then indicate the connection between gauge invariant interacting string theories and the geometric realizations of the infinite dimensional lie algebras

the construction of the sh lie algebra of closed bosonic strings we present a construction of the closed string algebra in terms of gaussian processes and crossed products also we give a purely functional analytical prove of the sh lie structure

the operator quantization of the open bosonic string field algebra our aim in this paper is to make explicit the operator theory of the heuristic open bosonic string and to abstract a suitable field algebra for the string this is done on a fock krein space and we examine integrability and j unitary implementability of all the defining transformations of the string i e time translations gauge transformations and poincare transformations the results obtained agree partially with those of bowick and rajeev i e the gauge transformations do not leave the fock krein complex structure invariant once we obtained integrated transformation groups on a suitable symplectic space for the infinitesimal transformations of the string and proved implementability of these for the fock krein representation we are then free to define an abstract c algebra carrying all the algebraic information of the string and to examine different representations

characters of the infinite symplectic group a riesz ring approach we classify both the finite and infinite characters of the inductive limit symplectic group g an important feature of our technique is the systematic use of a multiplicative structure on an ordered completion of the k0 group for the group c algebra a of g we also give explicit examples of the k theory for certain primitive quotients of a

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

the symplectic sum formula for gromov witten invariants in the symplectic category there is a connect sum operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds this paper establishes a formula for the gromov witten invariants of a symplectic sum z x y in terms of the relative gw invariants of x and y several applications to enumerative geometry are given gromov witten invariants are counts of holomorphic maps into symplectic manifolds to define them on a symplectic manifold x w one introduces an almost complex structure j compatible with the symplectic form w and

two point extremal gromov witten invariants of hilbert schemes of points on surfaces given an algebraic surface x the hilbert scheme x n of n points on x admits a contraction morphism to the n fold symmetric product x n with the extremal ray generated by a class n of a rational curve we determine the two point extremal gw invariants of x n with respect to the class d n for a simply connected projective surface x and the extremal quantum first chern class operator of the tautological bundle on x n the methods used are vertex algebraic description of h x n the localization technique applied to x mathbb p 2 and the results on quantum cohomology of x n when x mathbb c 2 in okounkov and pandharipande invent math 179 3 523 557 2010 and a generalization of the reduction theorem of kiem j li to the case of meromorphic 2 forms

measures on infinite dimensional grassmann manifolds abstract a 1 parameter family of quasi invariant measures is presented these measures are cylinder measures in graph coordinates their characteristic functions are represented as integrals relative to an infinite product measure this is applied to the problem of determining the support properties of the measures one of the measures can be used to define the unitary structure for the basic representation of the affine extension of the restricted unitary group

landau ginzburg calabi yau correspondence for the complete intersections x3 3 and x2 2 2 2 abstract we define a generalization of fan jarvis ruan witten theory a hybrid model associated to a collection of quasihomogeneous polynomials of the same weights and degree which is expected to match the gromov witten theory of the calabi yau complete intersection cut out by the polynomials in genus zero we prove that the correspondence holds for any such complete intersection of dimension three in ordinary rather than weighted projective space these results generalize those of chiodo ruan for the quintic threefold and as in that setting givental s quantization can be used to yield a conjectural relation between the full higher genus theories

a structure theorem for the gromov witten invariants of kahler surfaces we prove a structure theorem for the gromov witten invariants of compact kahler surfaces with geometric genus pg 0 under the technical assumption that there is a canonical divisor that is a disjoint union of smooth components the theorem shows that the gw invariants are universal functions determined by the genus of this canonical divisor components and the holomorphic euler characteristic of the surface we compute special cases of these universal functions much of the work on the gromov witten invariants of kahler surfaces has focused on rational and ruled surfaces which have geometric genus pg 0 this paper focuses on surfaces with pg 0 a class that includes most elliptic surfaces and most surfaces of general type in this context we prove a general structure theorem that shows with one technical assumption how the gw invariants are completely determined by the local geometry of a generic canonical divisor the structure theorem is a consequence of a simple fact the image localization lemma of section 3 given a kahler surface x and a canonical divisor d kx this lemma shows that the complex structure j on x can be perturbed to a non integrable almost complex structure jd with the property the image of all jd holomorphic maps lies in the support of d this immediately gives some striking vanishing theorems for the gw invariants of kahler surfaces see section 3 more importantly it implies that the gromov witten invariant of x for genus g and n marked points is a sum gwg n x a gw loc g n dk ak over the connected components dk of d of local invariants that count the contribution of maps whose image lies in or after perturbing to a generic moduli space near dk these local invariants have not been previously defined the proof of their existence relies on using non integrable structures and geometric analysis techniques our structure theorem characterizes the local invariants by expressing them in terms of usual gw invariants of certain standard surfaces for this we make the mild assumption that one can deform the kahler structure on x and choose a canonical divisor d so that all components of d are smooth with this assumption the restriction of kx to each component dk of multiplicity mk is the normal bundle nk to dk and nk k kdk partially supported by the n s f

snr estimation for nonconstant modulus constellations we propose a new technique to estimate the signal to noise ratio snr over the flat fading channel this is a nondata aided envelope based estimator that can be applied to nonconstant modulus constellations which is a feature not found in existing approaches we also analyze the performance of our estimators for both phase shift keying psk and non psk constellations by deriving their asymptotic variances and comparing with the crame spl acute r rao bounds crbs moreover we discuss how the snr estimates can be used to approximate the bit error rate ber and how the accuracy of the snr estimate is related to that of the ber estimate which justifies the necessity for the accurate estimation of snr the analytical performance is shown for both psk and non psk constellations such as 8 quadrature amplitude modulation qam and 16 qam monte carlo simulation results corroborate our analysis

higher genus wall crossing in landau ginzburg theory abstract for a fermat quasi homogeneous polynomial we study the associated weighted fan jarvis ruan witten theory with narrow insertions we prove a wall crossing formula in all genera via localization on a master space which is constructed by introducing an additional tangent vector to the moduli problem this is a landau ginzburg theory analogue of the higher genus quasi map wall crossing formula proved by ciocan fontanine and kim it generalizes the genus 0 result by ross ruan and the genus 1 result by guo ross

cycle groups for artin stacks we construct an algebraic homology functor for artin stacks of finite type over a field and we develop intersection theoretic properties

a new method toward the landau ginzburg calabi yau correspondence via quasi maps the landau ginzburg calabi yau correspondence claims that the gromov witten invariant of the quintic calabi yau 3 fold should be related to the fan jarvis ruan witten invariant of the associated landau ginzburg model via wall crossings in this paper we consider the stack of quasi maps with a cosection and introduce sequences of stability conditions which enable us to interpolate between the moduli stack for gromov witten invariants and the moduli stack for fan jarvis ruan witten invariants

the c algebra of bosonic strings we give a rigorous definition of witten sc string algebra to this end we present a new construction ofc algebras associated to special geometric situations kahler foliations and generalize this later construction to the string case through this we get a natural geometrical interpretation of the string of semi infinite forms as well as the fermionic algebra structure using the non commutative geometric concepts for investigating the string algebra we get a natural fredholm module representation of dimension 26

string quantization on group manifolds and the holomorphic geometry of diffs1 s1 the recent results by bowick and rajeev on the relation of the geometry of diffs1 s1 and string quantization in d are extended to a string moving on a group manifold a new derivation of the curvature formula 26 12m3 1 6m n m for the canonical holomorphic line bundle over diffs1 s1 is given which clarifies the relation of that bundle with the complex line bundles over infinite dimensional grassmannians studied by pressley and segal

witten s top chern class via cosection localization for a landau ginzburg space mathbb c n g w we construct witten s top chern class as an algebraic cycle using cosection localized virtual cycles in the case where all sectors are narrow verify all axioms of this class and derive an explicit formula for it in the free case we prove that this construction is equivalent to the constructions of polishchuk vaintrob chiodo and fan jarvis ruan

quantum cohomology of the hilbert scheme of points in the plane we determine the ring structure of the equivariant quantum cohomology of the hilbert scheme of points of 2 the operator of quantum multiplication by the divisor class is a nonstationary deformation of the quantum calogero sutherland many body system a relationship between the quantum cohomology of the hilbert scheme and the gromov witten donaldson thomas correspondence for local curves is proven

genus zero gopakumar vafa type invariants for calabi yau 4 folds abstract in analogy with the gopakumar vafa conjecture on cy 3 folds klemm and pandharipande defined gv type invariants on calabi yau 4 folds using gromov witten theory and conjectured their integrality in this paper we propose a sheaf theoretic interpretation of their genus zero invariants using donaldson thomas theory on cy 4 folds more specifically we conjecture genus zero gv type invariants are d t 4 invariants for one dimensional stable sheaves on cy 4 folds some examples are computed for both compact and non compact cy 4 folds to support our conjectures we also propose an equivariant version of the conjectures for local curves and verify them in certain cases

symbolic method in invariant theory abstract a symbolic method based on an extension of the straightening algorithm is developed for the representation of joint invariants of symmetric and skew symmetric tensors for skew symmetric tensors the method holds over infinite fields of arbitrary characteristic

cramer rao lower bound for non data aided snr estimation of linear modulation schemes powerful parameter estimators exhibit a jitter variance which is fairly close to the cramer rao lower bound crlb as the theoretical limit in contrast to symbol timing and carrier frequency phase not very much information is available from the open literature with respect to the signal to noise ratio snr i e the crlb has been reported only for the data aided case and some simple m psk examples for non data aided estimation of the snr motivated by this background an efficient algorithm is presented which applies to any m ary one two dimensional modulation scheme with axis halfplane symmetry and a channel distorted by additive white gaussian noise finally the performance of different snr estimators is compared to the derived bound

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

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

donaldson thomas type invariants via microlocal geometry we prove that donaldson thomas type invariants are equal to weighted euler characteristics of their moduli spaces in particular such invariants depend only on the scheme structure of the moduli space not the symmetric obstruction theory used to define them we also introduce new invariants generalizing donaldson thomas type invariants to moduli problems with open moduli space these are useful for computing donaldson thomas type invariants over stratifications

cramer rao bounds of doa estimates for bpsk and qpsk modulated signals this paper focuses on the stochastic cramer rao bound crb of direction of arrival doa estimates for binary phase shift keying bpsk and quaternary phase shift keying qpsk modulated signals corrupted by additive circular complex gaussian noise explicit expressions of the crb for the doa parameter alone in the case of a single signal waveform are given these crbs are compared on the one hand with those obtained with different a priori knowledge and on the other hand with crbs under the noncircular and circular complex gaussian distribution and with different deterministic crbs it is shown in particular that the crbs under the noncircular respectively circular complex gaussian distribution are tight upper bounds on the crbs under the bpsk respectively qpsk distribution at very low and very high signal to noise ratios snrs only finally these results and comparisons are extended to the case of two independent bpsk or qpsk distributed sources where an explicit expression of the crb for the doa parameters alone is given for large snr

nested hilbert schemes on surfaces virtual fundamental class abstract we construct virtual fundamental classes on nested hilbert schemes of points and curves in complex nonsingular projective surfaces these classes recover the virtual classes of seiberg witten theory as well as the reduced stable theory and play a crucial role in the reduced donaldson thomas theory of local surface threefolds that we study in 15 we show that certain integrals against the virtual fundamental classes of punctual nested hilbert schemes are expressed as integrals over the products of the hilbert scheme of points we are able to find explicit formulas for some of these integrals by relating them to carlsson okounkov s vertex operator formulas

some remarks on brs transformations anomalies and the cohomology of the lie algebra of the group of gauge transformations we show that ghosts in gauge theories can be interpreted as maurer cartan forms in the infinite dimensional group of gauge transformations we examine the cohomology of the lie algebra of and identify the coboundary operator with the brs operator we describe the anomalous terms encountered in the renormalization of gauge theories triangle anomalies as elements of these cohomology groups

a note on the construction of the c algebra of bosonic strings this work continues investigations on the c algebra of bosonic strings started in comm math phys 136 369 1991 there a canonical section of a bundle was used implicitly in order to pass to an algebra of functions in this article an algebra of sections is worked with directly this clarifies the discussion on associativity of the algebra

counting rational curves on text k3 surfaces the aim of these notes is to explain the remarkable formula found by yau and zaslow y z to express the number of rational curves on a k3 surface projective k3 surfaces fall into countably many families fg g 1 a surface in fg admits a gdimensional linear system of curves of genus g a naive count of constants suggests that such a system will contain a positive number say n g of rational highly singular curves the formula is

torus localization and wall crossing for cosection localized virtual cycles abstract the theory of virtual fundamental class defines important invariants such as the gromov witten and the donaldson thomas invariants it has been generalized to the cosection localized virtual cycle which has applications in seiberg witten fan jarvis ruan witten and other invariants in this paper we prove the formulas of virtual pullback torus localization and wall crossing for cosection localized virtual cycles

a conjectural generating function for numbers of curves on surfaces i give a conjectural generating function for the numbers of nodal curves in a linear system of dimension on an algebraic surface it reproduces the results of vainsencher v for the case le 6 and kleiman piene k p for the case le 8 the numbers of curves are expressed in terms of five universal power series three of which i give explicitly as quasimodular forms this gives in particular the numbers of curves of arbitrary genus on a k3 surface and an abelian surface in terms of quasimodular forms generalizing the formula of yau zaslow for rational curves on k3 surfaces the coefficients of the other two power series can be determined by comparing with the recursive formulas of caporaso harris for the severi degrees in 2 we verify the conjecture for genus 2 curves on an abelian surface we also discuss a link of this problem with hilbert schemes of points