delay independence of mutual information rate of two symbolic sequences introduced by shannon as a rate of actual transmission mutual information rate mir is an extension of mutual information to a pair of dynamical processes we show a delay independence theorem according to which mir is not sensitive to a time shift between the two processes numerical studies of several benchmark situations confirm that this theoretical asymptotic property remains valid for realistic finite sequences estimations based on block entropies and a causal state machine algorithm perform better than an estimation based on a lempel ziv compression algorithm provided that block length and maximum history length respectively can be chosen larger than the delay mir is thus a relevant index for measuring nonlinear correlations between two experimental or simulated sequences when the transmission delay in input output devices or dephasing in coupled systems is variable or unknown

hidden sl n symmetry in conformal field theories we prove that an irreducible representation of the virasoro algebra can be extracted from an irreducible representation space of thesl 2 current algebra by putting a constraint on the latter using the becchi rouet stora tyutin formalism thus there is asl 2 symmetry in the virasoro algebra but it is gauged and hidden this construction of the virasoro algebra is the quantum analogue of the hamiltonian reduction we then are naturally lead to consider a constrainedsl 2 wess zumino witten model this system is also related to quantum field theory of coadjoint orbit of the virasoro group based on this result we present a canonical derivation of thesl 2 current algebra in polyakov s theory of two dimensional gravity it is a manifestation of thesl 2 symmetry in conformal field theory hidden by the quantum hamiltonian reduction we also discuss the quantum hamiltonian reduction of thesl 2 current algebra and its relation to thew n algebra of zamolodchikov this makes it possible to define a natural generalization of the geometric action for thew n algebra despite its non lie algebraic nature

sdiff s2 and the orbit method the group of area preserving diffeomorphisms of the two sphere sdiff s2 is one of the simplest examples of an infinite dimensional lie group it plays a key role in incompressible hydrodynamics and it recently appeared in general relativity as a subgroup of two closely related newly defined symmetry groups we investigate its representation theory using the method of coadjoint orbits we describe the casimir functions and the cartan algebra then we evaluate the trace of a simple sdiff s2 operator using the atiyah bott fixed point formula the trace is divergent but we show that it has well defined truncations related to the structure of sdiff s2 finally we relate our results back to the recent appearances of sdiff s2 in black hole physics the group of area preserving diffeomorphisms of the two sphere sdiff s2 is one of the simplest examples of an infinite dimensional lie group it plays a key role in incompressible hydrodynamics and it recently appeared in general relativity as a subgroup of two closely related newly defined symmetry groups we investigate its representation theory using the method of coadjoint orbits we describe the casimir functions and the cartan algebra then we evaluate the trace of a simple sdiff s2 operator using the atiyah bott fixed point formula the trace is divergent but we show that it has well defined truncations related to the structure of sdiff s2 finally we relate our results back to the recent appearances of sdiff s2 in black hole physics

on b function spectrum and rational singularity by duality 18 because r tr ccy 0 for i 0 by 6 31 this follows also from 13 21 23 where rc is assumed projective here coy denotes the dualizing sheaf i e the dualizing complex 18 shifted by the dimension to the right the trace morphism 0 2 is injective and its image is independent of the choice of resolution because 0 2 is an isomorphism if y is smooth we will denote by csy the image of 0 2 see 2 4 8 below now assume y is a reduced divisor d on a complex manifold x of dimension n let f be a reduced defining equation of d on a neighborhood of a c d the b function i e bernstein polynomial of f is a monic polynomial bf s in s with rational coefficients and is a generator of the ideal whose element b s satisfies the relation

the geometry of the universal teichmuller space and the euler weil petersson equation on the identity component of the universal teichmuller space endowed with the takhtajan teo topology the geodesics of the weil petersson metric are shown to exist for all time this component is naturally a subgroup of the quasisymmetric homeomorphisms of the circle viewed this way the regularity of its elements is shown to be h3 2 epsilon for all epsilon 0 the evolutionary pde associated to the spatial representation of the geodesics of the weil petersson metric is derived using multiplication and composition below the critical sobolev index 3 2 geodesic completeness is used to introduce special classes of solutions of this pde analogous to peakons our setting is used to prove that there exists a unique geodesic between each two shapes in the plane in the context of the application of the weil petersson metric in imaging c 2015 elsevier inc all rights reserved

geometry of w algebras from the affine lie algebra point of view to classify the classical field theories with w symmetry one has to classify the symplectic leaves of the corresponding w algebra which are the intersection of the defining constraint and the coadjoint orbit of the affine lie algebra if the w algebra in question is obtained by reducing a wess zumino novikov witten wznw model the fields that survive the reduction will obey nonlinear poisson bracket or commutator relations in general for example the toda models are well known theories which possess such a nonlinear w symmetry and many features of these models can only be understood if one investigates the reduction procedure in this paper we analyse the sl n case from which the so called wn algebras can be obtained one advantage of the reduction viewpoint is that it gives a constructive way to classify the symplectic leaves of the w algebra for the n 2 case corresponding to the coadjoint orbits of the virasoro algebra and for the n 3 case which gives rise to the zamolodchikov algebra our method in principle is capable of constructing explicit representatives on each leaf another attractive feature of this approach is the fact that the global nature of the w transformations can be explicitly described the reduction method also enables one to determine the classical highest weight hw states which are the stable minima of the energy on a w leaf these are important as only to those leaves can a hw representation space of the w algebra be associated which contains a classical hw state

non abelian harmonic oscillators and chiral theories we show that a large class of physical theories which has been under intensive investigation recently share the same geometric features in their hamiltonian formulation these dynamical systems range from harmonic oscillations to wzw like models and to the kdv dynamics on diff0s1 to the same class belong also the hamiltonian systems on groups of maps the common feature of these models are the chiral equations of motion for so called chiral decomposition of the phase space

jumping coefficients and spectrum of a hyperplane arrangement in an earlier version of this paper written by the second named author we showed that the jumping coefficients of a hyperplane arrangement depend only on the combinatorial data of the arrangement as conjectured by musta for this we proved a similar assertion on the spectrum after this first proof was written the first named author found a more conceptual proof using the hirzebruch riemann roch theorem where the assertion on the jumping numbers was proved without reducing to that for the spectrum in this paper we improve these methods and show that the jumping numbers and the spectrum are calculable in low dimensions without using a computer in the reduced case we show that these depend only on fewer combinatorial data and give completely explicit combinatorial formulas for the jumping coefficients and part of the spectrum in the case the ambient dimension is 3 or 4 we also give an analogue of musta s formula for the spectrum

iterated vanishing cycles convolution and a motivic analogue of a conjecture of steenbrink we prove a motivic analogue of steenbrink s conjecture 25 conjecture 2 2 on the hodge spectrum proved by m saito in 21 to achieve this we construct and compute motivic iterated vanishing cycles associated with two functions we are also led to introduce a more general version of the convolution operator appearing in the motivic thom sebastiani formula throughout the article we use the framework of relative equivariant grothendieck rings of varieties endowed with an algebraic torus action

universal teichmuller space and diff s 1 s 1 we point out that the coset space diffs1 s1 is a dense complex submanifold of the universal teichmuller spaces of compact riemann spaces of genus g 1 a holomorphic map ofs into the inifinite dimensional segal diskd1 is constructed this is the universal analogue of the map of teichmuller spaces into the siegel disk provided by the period matrix the kahler potential for the general homogenous metric on diffs1 s1 is computed explicitly using the map intod1 some applications to string theory are discussed

estimating entropy rates with bayesian confidence intervals the entropy rate quantifies the amount of uncertainty or disorder produced by any dynamical system in a spiking neuron this uncertainty translates into the amount of information potentially encoded and thus the subject of intense theoretical and experimental investigation estimating this quantity in observed experimental data is difficult and requires a judicious selection of probabilistic models balancing between two opposing biases we use a model weighting principle originally developed for lossless data compression following the minimum description length principle this weighting yields a direct estimator of the entropy rate which compared to existing methods exhibits significantly less bias and converges faster in simulation with monte carlo techinques we estimate a bayesian confidence interval for the entropy rate in related work we apply these ideas to estimate the information rates between sensory stimuli and neural responses in experimental data shlens kennel abarbanel chichilnisky in preparation

zygmund vector fields hilbert transform and fourier coefficients in shear coordinates we parametrize the space cal z of zygmund vector fields on the unit circle in terms of infinitesimal shear functions on the farey tesselation then we express the hilbert transform and the fourier coefficients of the zygmund vector fields in terms of the above parametrization by infinitesimal shear functions finally we compute the weil petersson metric on the teichm uller space of a punctured surface in terms of shears

variable length markov chains we study estimation in the class of stationary variable length markov chains vlmc on a finite space the processes in this class are still markovian of high order but with memory of variable length yielding a much bigger and structurally richer class of models than ordinary high order markov chains from an algorithmic view the vlmc model class has attracted interest in information theory and machine learning but statistical properties have not yet been explored provided that good estimation is available the additional structural richness of the model class enhances predictive power by finding a better tradeoff between model bias and variance and allowing better structural description which can be of specific interest the latter is exemplified with some dna data a version of the tree structured context algorithm proposed by rissanen in an information theoretical setup is shown to have new good asymptotic properties for estimation in the class of vlmcs this remains true even when the underlying model increases in dimensionality fur thermore consistent estimation of minimal state spaces and mixing properties of fitted models are given we also propose a new bootstrap scheme based on fitted vlmcs we show its validity for quite general stationary categorical time series and for a broad range of statistical procedures

estimating information rates with confidence intervals in neural spike trains information theory provides a natural set of statistics to quantify the amount of knowledge a neuron conveys about a stimulus a related work kennel shlens abarbanel chichilnisky 2005 demonstrated how to reliably estimate with a bayesian confidence interval the entropy rate from a discrete observed time series we extend this method to measure the rate of novel information that a neural spike train encodes about a stimulus the average and specific mutual information rates our estimator makes few assumptions about the underlying neural dynamics shows excellent performance in experimentally relevant regimes and uniquely provides confidence intervals bounding the range of information rates compatible with the observed spike train we validate this estimator with simulations of spike trains and highlight how stimulus parameters affect its convergence in bias and variance finally we apply these ideas to a recording from a guinea pig retinal ganglion cell and compare results to a simple linear decoder

a period mapping in universal teichmuller space in previous work it had been shown that the remarkable homogeneous space m diff s 1 psl 2 r sits as a complex analytic and kahler submanifold of the universal teichmuller space there is a natural immersion of m into the infinite dimensional version due to segal of the siegel space of period matrices that map is proved to be injective equivariant holomorphic and kahler isometric with respect to the canonical metrics regarding a period mapping as a map describing the variation of complex structure we explain why is an infinite dimensional period mapping

characters of the bms group in three dimensions using the frobenius formula we evaluate characters associated with certain induced representations of the centrally extended bms3 group this computation involves a functional integral over a coadjoint orbit of the virasoro group a delta function localizes the integral to a single point allowing us to obtain an exact result the latter is independent of the specific form of the functional measure and holds for all values of the bms3 central charges and all values of the chosen mass and spin it can also be recovered as a flat limit of virasoro characters

entropy and the consistent estimation of joint distributions the k th order joint distribution for an ergodic finite alphabet process can be estimated from a sample path of length n by sliding a window of length k along the sample path and counting frequencies of k blocks in this paper the problem of consistent estimation when k k n grows as a function of n is addressed it is shown that the variational distance between the true k n block distribution and the empirical k n block distribution goes to 0 almost surely for the class of weak bernoulli processes provided k n leq log n h epsilon where h is the entropy of the process the weak bernoulli class includes the i i d processes the aperiodic markov chains and functions thereof and the aperiodic renewal processes a similar result is also shown to hold for functions of irreducible markov chains this work sharpens prior results obtained for more general classes of processes by ornstein and weiss and by ornstein and shields which used the bar d distance rather than the variational distance

asymptotic bias in information estimates and the exponential bell polynomials we present a new derivation of the asymptotic correction for bias in the estimate of information from a finite sample the new derivation reveals a relationship between information estimates and a sequence of polynomials with combinatorial significance the exponential bell polynomials and helps to provide an understanding of the form and behavior of the asymptotic correction for bias

bits and brains information flow in the nervous system abstract until recently there have been no convincing quantitative measurements on the rates of information transmission in real neurons here we review the theoretical basis for making such measurements together with the data which demonstrate remarkably high information rates in a variety of systems in fact these rates are within a factor of two of the absolute physical limits set by the entropy of neural spike trains theses observations lead to sharp theoretical questions about the structure of the code and the strategy for adapting the code to different ensembles of input signals

algebraic quantization on a group and nonabelian constraints a generalization of a previous group manifold quantization formalism is proposed in the new version the differential structure is circumvented so that discrete transformations in the group are allowed and a nonabelian group replaces the ordinary central u 1 subgroup of the heisenberg weyl like quantum group as an example of the former we obtain the wave functions associated with the system of two identical particles and the latter modification is used to account for the virasoro constraints in string theory

bounding bar d distance by informational divergence a method to prove measure concentration there is a simple inequality by pinsker between variational distance and informational divergence of probability measures defined on arbitrary probability spaces we shall consider probability measures on sequences taken from countable alphabets and derive from pinsker s inequality bounds on the bar d distance by informational divergence such bounds can be used to prove the concentration of measure phenomenon for some nonproduct distributions

directionality of coupling from bivariate time series how to avoid false causalities and missed connections we discuss some problems encountered in inference of directionality of coupling or in the case of two interacting systems in inference of causality from bivariate time series we identify factors and influences that can lead to either decreased test sensitivity or false detections and propose ways to cope with them in order to perform tests with high sensitivity and a low rate of false positive results

virasoro model space the representations of a compact lie groupg can be studied via the construction of an associated model space this space has the property that when geometrically quantized its hilbert space contains every irreducible representation ofg just once we construct an analogous space for the group diffs1 it is naturally a complex manifold with a holomorphic free action of diffs1 preserving a family of pseudo kahler structures all of the good coadjoint orbits are obtained from our space by hamiltonian constraint reduction we briefly discuss the connection to the work of alekseev and shatashvili

extended conformal symmetries and u 1 currents the authors investigate the structure of extended conformal algebras generated by local chiral fields of spin 1 2 n using the gelfand dickey algebra of formal pseudodifferential operators for the gl n algebra the commutation relations of zamolodchikov s spin 3 operator algebra 1985 are derived in the presence of an additional u 1 conserved current

a quantum group structure in integrable conformal field theories we discuss a quantization prescription of the conformal algebras of a class ofd 2 conformal field theories which are integrable we first give a geometrical construction of certain extensions of the classical virasoro algebra known as classicalw algebras in which these algebras arise as the lie algebra of the second hamiltonian structure of a generalized korteweg de vries hierarchy this fact implies that thew algebras obtained as a reduction with respect to the nilpotent subalgebras of the kac moody algebra describe the integrability of a toda field theory subsequently we determine the coadjoint operators of thew algebras and relate these to classical yang baxter matrices the quantization of these algebras can be carried out using the concept of a so called quantum group we derive the condition under which the representations of these quantum groups admit a hilbert space completion by exploring the relation with the braid group then we consider a modification of the miura transformation which we use to define a quantumw algebra this leads to an alternative interpretation of the coset construction for kac moody algebras in terms of nonlinear integrable hierarchies subsequently we use the connection between the induced braid group representations and the representations of the mapping class group of riemann surfaces to identify an action of thew algebras on the moduli space of stable curves and we give the invariants of this action this provides a generalization of the situation for the virasoro algebra where such as invariant is given by the so called mumford form which describes the partition function of the bosonic string

the ricci curvature of diff s1 sl 2 r previous calculations of the ricci curvature for the manifold diff diff s1 s1 are extended to diff s1 sl 2r these manifolds are distinguished by being coadjoint orbits of diff s1 which admit compatible symphectic and complex structures making them kahler manifolds

mutual information functions versus correlation functions this paper studies one application of mutual information to symbolic sequences the mutual information functionm d this function is compared with the more frequently used correlation function d an exact relation betweenm d and d is derived for binary sequences for sequences with more than two symbols no such general relation exists in particular d 0 may or may not lead tom d 0 this linear but not general independence between symbols separated by a distance is studied for ternary sequences also included is the estimation of the finite size effect on calculating mutual information finally the concept of symbolic noise is discussed

characteristic classes of complex hypersurfaces abstract the milnor hirzebruch class of a locally complete intersection x in an algebraic manifold m measures the difference between the poincare dual of the hirzebruch class of the virtual tangent bundle of x and respectively the brasselet schurmann yokura homology hirzebruch class of x in this note we calculate the milnor hirzebruch class of a globally defined algebraic hypersurface x in terms of the corresponding hirzebruch invariants of vanishing cycles and singular strata in a whitney stratification of x our approach is based on schurmann s specialization property for the motivic hirzebruch class transformation of brasselet schurmann yokura the present results also yield calculations of todd chern and l type characteristic classes of hypersurfaces

on steenbrink s conjecture let f x c be a holomorphic function on a complex manifold using the monodromy and mixed hodge structure on the cohomology of milnor fiber we can associate the spectrum sp f x of f at x e xo f 1 0 it is a fractional laurent polynomial n t with n z this notion is first introduced by steenbrink 15 cteq in the isolated singularity case cf also 19 and 16 in general if f has isolated singularity n are nonnegative and 0 n 0 counted with multiplicity are called the exponents or spectra 19 of f assume f has one dimensional singular locus and consider a deformation of the form f g where g is a linear form i e a function such that g x 0 and dg 0 at x then f g has isolated singularity if g is generic let zk be a local irreducible component of singf at x and mk its multiplicity along z zk x f is viewed as constant deformation of isolated singularity let k j be its exponents which are constant on z 20 we can also define ilk j e 0 1 in a compatible way with k j so that exp 2ni 3k j are the eigenvalues of the monodromy along z then steenbrink conjectured

symplectic manifolds coherent states and semiclassical approximation the symplectic structure and hamiltonian dynamics for a class of grassmannian manifolds are described here using the two dimensional sphere s2 and disc d2 as illustrative cases we write their path integral representations using coherent state techniques these path integrals can be evaluated exactly by semiclassical methods thus providing examples of the localization formula along the way we also give a local coordinate description for a class of grassmannians

multiplier ideals v filtrations and transversal sections we show that the restriction to a smooth transversal section commutes to the computation of multiplier ideals and v filtrations as an application we prove the constancy of the jumping numbers and the spectrum along any stratum of a whitney regular stratification

on the mixed hodge structure on the cohomology of the milnor fibre in 18 the second author introduced a mixed hodge structure on the cohomology of the milnor fibre of an isolated hypersurface singularity for the definition of a mixed hodge structure el 17 sect 3 4 the weight filtration is essentially the monodromy weight filtration 18 sect 4 and thus simplifies the jordan normal form of the unipotent part of the monodromy the significance of the hodge filtration however is not so dear and its description seems difficult to use this paper gives another description of the hodge filtration which we hope is easier to understand and apply its definition does not use resolution of singularities instead it relies on the theory of holonomic modules in one variable with regular singularities this paper arose from conversations at the 1980 arbeitstagung in bonn where varchenko s conjectured hodge filtration 22 had been discussed in brieskorn s seminar we have since learned that varchenko obtained similar results to those in this paper in the summer and autumn of 1980 23 25 in sect 1 the milnor fibration is embedded in a family of smooth projective hypersurfaces the hodge theory of a smooth projective hypersurface is explained in the fashion of brylinski 2 in sect 2 in sect 3 we recall the description of the gauss manin system from 8 our new formula for the hodge filtration is explained in sects 4 5 in sect 6 we prove that it gives the same result as 18 we prove a thom sebastiani formula for the hodge filtration in sect 7 which leads to a proof of conjecture 5 4 of 18 in sect 8 we show how to prove varchenko s result about the jordan normal forms of multiplication by f in the jacobian ring of f and the logarithm of the unipotent monodormy of f with our method in the last chapter the mixed hodge structure is calculated for two examples

field models from two cocycles on infinite dimensional lie groups and symplectic structures 2d gravity and chern simons theory in this paper the connection between field models and infinite dimensional lie groups is widely analysed on the bases of a new group quantization approach we also relate the poincare cartan form of variational calculus to the symplectic current structure of the covariant phase space formulation of higher derivative field theory the virasoro and kac moody groups are considered in the first case the action functional of the 2d induced gravity in the light cone formulation is derived the hidden sl 2 r simply appears as generated by the kernel of the lie algebra two cocycle and plays the role of a gauge type symmetry nevertheless it is shown that a proper space like formulation is out of reach of the virasoro group the corresponding symplectic structure of the nonlocal action functional is determined showing that it is related to the symplectic structure associated with the sl 2 r kac moody group this unravels the proper geometrical meaning of the hidden symmetry and differs from the analysis in related works based on the coadjoint orbit approach the relation between the kac moody groups and the chern simons gauge theory on a disc in the presence of a source is considered using the new approach

leibniz chern simons theory and phases of exceptional field theory we discuss a generalization of chern simons theory in three dimensions based on leibniz or loday algebras which are generalizations of lie algebras special cases of such theories appear in gauged supergravity where the leibniz algebra is defined in terms of the global lie symmetry algebra of the ungauged limit and an embedding tensor we show that the leibniz algebra of generalized diffeomorphisms in exceptional field theory can similarly be obtained from a lie algebra that describes the enhanced symmetry of an ungauged phase of the theory moreover we show that a topological phase of e8 8 exceptional field theory can be interpreted as a chern simons theory for an algebra unifying the three dimensional poincare algebra and the leibniz algebra of e8 8 generalized diffeomorphisms

higher spins from nambu chern simons theory we propose a new theory of higher spin gravity in three spacetime dimensions this is defined by what we will call a nambu chern simons ncs action this is to a nambu 3 algebra as an ordinary chern simons cs action is to a lie 2 algebra the novelty is that the gauge group of this theory is simple this stands in contrast to previously understood interacting 3d higher spin theories in the frame like formalism we also consider the n 8 supersymmetric ncs matter model blg theory where the ncs action originated its fully supersymmetric m2 brane configurations are interpreted as hopf fibrations the homotopy type of the infinite gauge group is calculated and its instantons are classified

spectral hirzebruch milnor classes of singular hypersurfaces we introduce spectral hirzebruch milnor classes for singular hypersurfaces these can be identified with steenbrink spectra in the isolated singularity case and may be viewed as their global analogues in general their definition uses vanishing cycles of mixed hodge modules and the todd class transformation these are compatible with the pushforward by proper morphisms and the classes can be calculated by using resolutions of singularities formulas for hirzebruch milnor classes of projective hypersurfaces in terms of these classes are given in the case where the multiplicity of a generic hyperplane section is not 1 these formulas using hyperplane sections instead of hypersurface ones are easier to calculate in certain cases here we use the thom sebastiani theorem for the underlying filtered d modules of vanishing cycles from which we can deduce the thom sebastiani type theorem for spectral hirzebruch milnor classes for the chern classes after specializing to y 1 we can give a relatively simple formula for the localized milnor classes which implies a new formula for the euler numbers of projective hypersurfaces using iterated hyperplane sections applications to log canonical thresholds and du bois singularities are also explained for instance the latter can be detected by using hirzebruch milnor classes in the projective hypersurface case

leibniz gauge theories and infinity structures we formulate gauge theories based on leibniz loday algebras and uncover their underlying mathematical structure various special cases have been developed in the context of gauged supergravity and exceptional field theory these are based on tensor hierarchies which describe towers of p form gauge fields transforming under non abelian gauge symmetries and which have been constructed up to low levels here we define infinity enhanced leibniz algebras that guarantee the existence of consistent tensor hierarchies to arbitrary level we contrast these algebras with strongly homotopy lie algebras l infty algebras which can be used to define topological field theories for which all curvatures vanish any infinity enhanced leibniz algebra carries an associated l infty algebra which we discuss

coarse grained entropy rates for characterization of complex time series abstract a method for classification of complex time series using coarse grained entropy rates cer s is presented the cer s which are computed from information theoretic funcionals redundancies are relative measures of regularity and predictability and for data generated by dynamical systems they are related to kolmogorov sinai entropy a deterministic dynamical origin of the data under study however is not a necessary condition for the use of the cer s since the entropy rates can be defined for stochastic processes as well sensitivity of the cer s to changes in data dynamics and their robustness with respect to noise are tested by using numerically generated time series resulted from both deterministic chaotic and stochastic processes potential application of the cer s in analysis of physiological signals or other complex time series is demonstrated by using examples from pharmaco eeg and tremor classification

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

coadjoint orbits of the virasoro group the coadjoint orbits of the virasoro group which have been investigated by lazutkin and pankratova and by segal should according to the kirillov kostant theory be related to the unitary representations of the virasoro group in this paper the classification of orbits is reconsidered with an explicit description of the possible centralizers of coadjoint orbits the possible orbits are diff s1 itself diff s1 s1 and diff s1 sl n 2 r withsl n 2 r a certain discrete series of embeddings ofsl 2 r in diff s1 and diffs1 t wheret may be any of certain rather special one parameter subgroups of diffs1 an attempt is made to clarify the relation between orbits and representations it appears that quantization of diffs1 s1 is related to unitary representations with nondegenerate kac determinant unitary verma modules while quantization of diffs1 sl n 2 r is seemingly related to unitary representations with null vectors in leveln a better understanding of how to quantize the relevant orbits might lead to a better geometrical understanding of virasoro representation theory in the process of investigating virasoro coadjoint orbits we observe the existence of left invariant symplectic structures on the virasoro group manifold as is described in an appendix these give rise to lie bialgebra structures with the virasoro algebra as the underlying lie algebra

short distance expansion from the dual representation of infinite dimensional lie algebras we develop a method for computing the short distance expansion of fields or operators that live in the coadjoint representation of an infinite dimensional lie algebra by using only properties of the adjoint representation and its dual we explicitly implement this method by computing the short distance expansion for the duals of the virasoro algebra affine lie algebras and the geometrically realized n extended supersymmetric virasoro algebra this method can also be used to compute short distance expansions between fields that transform in the adjoint and those that transform in the coadjoint representations

on the classification of the coadjoint orbits of the sobolev bott virasoro group the purpose of this paper is to give the classification of the bott virasoro coadjoint orbits with nonzero central charge in the functional analytic setting of smooth hilbert manifolds the central object of the paper is thus the completion of the bott virasoro group with respect to a sobolev topology giving rise to a smooth hilbert manifold and topological group called the sobolev bott virasoro group as a consequence of this approach analytic and geometric properties of the coadjoint orbits are studied c 2008 elsevier inc all rights reserved

aspects of infinite dimensional l super galilean conformal algebra in this work we construct an infinite dimensional l super galilean conformal algebra which is a generalization of the l 1 algebra found in the literature we give a classification of central extensions the vector field representation the coadjoint representation and the operator product expansion of the infinite dimensional l super galilean conformal algebra keeping possible applications in physics and mathematics in mind

application of entropy measures derived from the ergodic theory of dynamical systems to rat locomotor behavior abstract measures of complexity derived from ergodic theory of dynamical systems were developed and applied to an exemplary data set describing locomotor movements of rats in a bounded space a symbolic dynamical system was obtained by partitioning the event space into equally probable partition elements using a k dimensional tree the measures calculated from the symbolic sequences included the topological entropy ht i e the rate of increase of all possible sequences with increasing sequence length and the metric entropy hm i e the rate of increase of all likely sequences with increasing sequence length these measures were used to assess changes in rat locomotor behavior as recorded in the behavioral pattern monitor bpm that were induced by amphetamine 0 25 0 50 1 0 or 2 0 mg kg and 3 4 methylenedioxymethamphetamine mdma 1 25 2 5 5 0 or 10 0 mg kg amphetamine increased the mean activity ht and hm mdma resulted in a monotonic dose response curve for activity but exhibited a biphasic dose response in ht and hm in particular some animals in the higher dose groups showed a ht in the range of the saline controls whereas other animals exhibited a significantly reduced ht and a greater decrease in hm suggesting that two different behavioral reactions coexist within the same higher dose range of mdma an important implication of our method is that in applied ergodic measure theoretic approaches the partition that determines the elements of the symbolic dynamical system should not be specified a priori on abstract mathematical grounds but should be chosen relative to its significance with respect to the data set in question here the animal constructs its own spatiotemporal partition in behavioral phase space

geodesic flow on super bott virasoro group and harry dym family we show various harry dym type equations and super harry dym equations introduced by brunelli das and popowicz 2003 supersymmetric extensions of the harry dym hierarchy j math phys 44 4756 4767 2003 follow from the geodesic flows on the bott virasoro group and its supersymmetric generalization superconformal group in fact their bi hamiltonian structures can be derived from the lie poisson structures on the super bott virasoro orbit we also show that that m2kdv or calogero degasperis equation is also connected to the bott virasoro group

nonparametric entropy estimation for stationary processes and random fields with applications to english text we discuss a family of estimators for the entropy rate of a stationary ergodic process and prove their pointwise and mean consistency under a doeblin type mixing condition the estimators are cesaro averages of longest match lengths and their consistency follows from a generalized ergodic theorem due to maker 1940 we provide examples of their performance on english text and we generalize our results to countable alphabet processes and to random fields

construction of local one parameter subgroups generated by the virasoro operators via feynman path integrals abstract it is well known that the virasoro algebra acts on the representations of an infinite dimensional heisenberg algebra called the fock models we calculate feynman path integrals on an coadjoint orbit of the infinite dimensional heisenberg group to give explicit formulae of actions of local one parameters subgroups generated by the virasoro operators

dynamics on sl 2 r tilde x u 1 a complete analysis of the quantum dynamical system defined by the quantum group sl 2 r tilde x u 1 is made this quantum group which is primarily related to the relativistic harmonic oscillator is also shown to provide the quantum dynamics of a free particle moving in 1 1 dimensional anti de sitter spacetime the latter interpretation illustrates the capabilities of the present group approach to quantisation in dealing with dynamical systems in more general spacetimes

on lempel ziv complexity for multidimensional data analysis abstract in this paper a natural extension of the lempel ziv complexity for several finite time sequences defined on finite size alphabets is proposed some results on the defined joint lempel ziv complexity are given as well as properties in connection with the lempel ziv complexity of the individual sequences also some links with shannon entropies are exhibited and by analogy some derived quantities are proposed lastly the potential use of the extended complexities for data analysis is illustrated on random boolean networks and on a proposed multidimensional extension of the minority game

invariant measures on polarized submanifolds in group quantization we provide an explicit construction of quasi invariant measures on polarized coadjoint orbits of a lie group g the use of specific trivial central extensions of g by the multiplicative group r allows us to restore the strict invariance of the measures and accordingly the unitarity of the quantization of coadjoint orbits as an example the representations of sl 2 r are recovered

entropy estimation of very short symbolic sequences while entropy per unit time is a meaningful index to quantify the dynamic features of experimental time series its estimation is often hampered in practice by the finite length of the data we here investigate the performance of entropy estimation procedures relying either on block entropies or lempel ziv complexity when only very short symbolic sequences are available heuristic analytical arguments point at the influence of temporal correlations on the bias and statistical fluctuations and put forward a reduced effective sequence length suitable for error estimation numerical studies are conducted using as benchmarks the wealth of different dynamic regimes generated by the family of logistic maps and stochastic evolutions generated by a markov chain of tunable correlation time practical guidelines and validity criteria are proposed for instance block entropy leads to a dramatic overestimation for sequences of low entropy whereas it outperforms lempel ziv complexity at high entropy as a general result the quality of entropy estimation is sensitive to the sequence temporal correlation hence self consistently depends on the entropy value itself thus promoting a two step procedure lempel ziv complexity is to be preferred in the first step and remains the best estimator for highly correlated sequences

the upward bias in measures of information derived from limited data samples extracting information measures from limited experimental samples such as those normally available when using data recorded in vivo from mammalian cortical neurons is known to be plagued by a systematic error which tends to bias the estimate upward we calculate here the average of the bias under certain conditions as an asymptotic expansion in the inverse of the size of the data sample the result agrees with numerical simulations and is applicable as an additive correction term to measurements obtained under such conditions moreover we discuss the implications for measurements obtained through other usual procedures

hirzebruch milnor classes of complete intersections abstract we prove a new formula for the hirzebruch milnor classes of global complete intersections with arbitrary singularities describing the difference between the hirzebruch classes and the virtual ones this generalizes a formula for the chern milnor classes in the hypersurface case that was conjectured by s yokura and was proved by a parusinski and p pragacz it also generalizes a formula of j seade and t suwa for the chern milnor classes of complete intersections with isolated singularities

higher order polarizations on the virasoro group and anomalies in a previous paper the authors showed that the space of first order polarized functions on the virasoro group is not in general irreducible the full reduction was explicitly achieved by taking the orbit of the enveloping algebra through the vacuum this additional step provided the proper quantization in the strong coupling domain 0 c 1 in this paper we introduce the concept of higher order polarization as a generalization of that of polarization we prove that the imposing of the additional higher order polarization conditions is equivalent to the taking of the above mentioned orbit this demonstrates that the generalized higher order polarization conditions suffice to obtain the irreducible hilbert spaces we also discuss the need for higher order polarizations in terms of anomalies

quantum computation as gravity we formulate nielsen s geometric approach to circuit complexity in the context of two dimensional conformal field theories where series of conformal transformations are interpreted as unitary circuits built from energy momentum tensor gates we show that the complexity functional in this setup can be written as the polyakov action of two dimensional gravity or equivalently as the geometric action on the coadjoint orbits of the virasoro group this way we argue that gravity sets the rules for optimal quantum computation in conformal field theories

the embedding tensor leibniz loday algebras and their higher gauge theories we show that the data needed for the method of the embedding tensor employed in gauging supergravity theories are precisely those of a leibniz algebra with one of its induced quotient lie algebras embedded into a rigid symmetry lie algebra that provides an additional representation constraint every leibniz algebra gives rise to a lie n algebra in a canonical way for every n in mathbb n cup infty it is the gauging of this l infty algebra that explains the tensor hierarchy of the bosonic sector of gauged supergravity theories the tower of p from gauge fields corresponds to lyndon words of the universal enveloping algebra of the free lie algebra of an odd vector space in this construction truncation to some n yields the reduced field content needed in a concrete spacetime dimension

group quantization on configuration space gauge symmetries and linear fields a new configuration space picture of a formalism of group quantization the gaq formalism is presented in the context of a previous algebraic generalization this presentation serves to make a comprehensive discussion in which other extensions of the formalism principally to incorporate gauge symmetries are developed as well both images are combined in order to analyze in a systematic manner and with complete generality the case of linear fields abelian current groups to illustrate these developments we particularize them for several fields and in particular we carry out the quantization of the abelian chern simons models over an arbitrary closed surface in detail

quantization on the virasoro group the quantization of the virasoro group is carried out by means of a previously established group approach to quantization we explicitly work out the two cocycles on the virasoro group as a preliminary step in our scheme the carrier space for all the virasoro representations is made out of polarized functions on the group manifold it is proved that this space does not contain null vector states even forc 1 although it is not irreducible the full reduction is achieved in a striaghtforward way by just taking a well defined invariant subspace c h the orbit of the enveloping algebra through the vacuum which is irreducible for any value ofc andh c h is a proper subspace of the space of polarized functions for those values ofc andh for which the kac determinant is zero we give the local version of these group representations as well as the associated classical phase space structures i e symplectic form and noether invariants

on hodge spectrum and multiplier ideals we describe a relation between two invariants which measure the complexity of a hypersurface singularity one is the hodge spectrum which is related to the monodromy and the hodge filtration on the cohomology of the milnor fiber the other is the multiplier ideal having to do with log resolutions

estimation of entropy and mutual information we present some new results on the nonparametric estimation of entropy and mutual information first we use an exact local expansion of the entropy function to prove almost sure consistency and central limit theorems for three of the most commonly used discretized information estimators the setup is related to grenander s method of sieves and places no assumptions on the underlying probability measure generating the data second we prove a converse to these consistency theorems demonstrating that a misapplication of the most common estimation techniques leads to an arbitrarily poor estimate of the true information even given unlimited data this inconsistency theorem leads to an analytical approximation of the bias valid in surprisingly small sample regimes and more accurate than the usual 1 n formula of miller and madow over a large region of parameter space the two most practical implications of these results are negative 1 information estimates in a certain data regime are likely contaminated by bias even if bias corrected estimators are used and 2 confidence intervals calculated by standard techniques drastically underestimate the error of the most common estimation methods finally we note a very useful connection between the bias of entropy estimators and a certain polynomial approximation problem by casting bias calculation problems in this approximation theory framework we obtain the best possible generalization of known asymptotic bias results more interesting this framework leads to an estimator with some nice properties the estimator comes equipped with rigorous bounds on the maximum error over all possible underlying probability distributions and this maximum error turns out to be surprisingly small we demonstrate the application of this new estimator on both real and simulated data