on simultaneous linearization of diffeomorphisms of the sphere let r1 r2 rm be rotations generating sod 1 d 2 and f1 f2 fm be their small smooth perturbations we show that f can be simultaneously linearized if and only if the associated random walk has zero lyapunov exponents as a consequence we obtain stable ergodicity of actions of random rotations in even dimensions 1 main results let f1 f2 fm be diffeomorphisms of s d 2 let i i n be a sequence of independent random variables uniformly distributed on 1 m consider the markov process on s 1 xn f nxn 1 if is an invariant measure for this process let 1 2 d be the lyapunov exponents of denote

optimal mock jacobi theta functions abstract we classify the optimal mock jacobi forms of weight one with rational coefficients the space they span is thirty four dimensional and admits a distinguished basis parameterized by genus zero groups of isometries of the hyperbolic plane we show that their fourier coefficients can be expressed explicitly in terms of singular moduli and obtain positivity conditions which distinguish the optimal mock jacobi forms that appear in umbral moonshine we find that many of ramanujan s mock theta functions can be expressed simply in terms of the optimal mock jacobi forms with rational coefficients

coupling control variates for markov chain monte carlo we show that markov couplings can be used to improve the accuracy of markov chain monte carlo calculations in some situations where the steady state probability distribution is not explicitly known the technique generalizes the notion of control variates from classical monte carlo integration we illustrate it using two models of nonequilibrium transport

graded lie superalgebras and super replicable functions abstract in this paper we investigate the properties of super replicable functions and their connections with graded lie superalgebras the euler poincare principle for the homology of graded lie superalgebras yields a certain product identity called the generalized denominator identity applying the formal directional derivatives and the laplacian we derive a recursive supertrace formula for the graded lie superalgebras with gradation preserving endomorphisms on the other hand the super replicable functions are characterized by certain product identities that have the same form as the generalized denominator identities for some graded lie superalgebras we derive many interesting relations among the fourier coefficients of super replicable functions and their super replicates and compute the supertraces of monstrous lie superalgebras associated with super replicable functions finally we study the properties of the hauptmoduln j 1 n of 1 n for n 5 8 10 12 which are super replicable functions and determine the fourier coefficients of their super replicates j 1 n m m 1

conformal field theory and elliptic cohomology abstract in this paper we use conformal field theory to construct a generalized cohomology theory which has some properties of elliptic cohomology theory which was some properties of elliptic cohomology a part of our presentation is a rigorous definition of conformal field theory following segal s axioms and some examples such as lattice theories associated with a unimodular even lattice we also include certain examples and formulate conjectures on modular forms and monstrous moonshine related to the present work

on the estimation of transfer functions this paper treats the close conceptual relationships between basic approaches to the estimation of transfer functions of linear systems the classical methods of frequency and spectral analysis are shown to be related to the well known time domain methods of prediction error type via a common empirical transfer function estimate asymptotic properties of the estimates obtained by the respective methods are also described and discussed an important feature that is displayed by this treatment is a frequency domain weighting function that determines the distribution of bias in case the true system cannot be exactly described within the chosen model set the choice of this weighting function is made in terms of noise models for time domain methods the noise model thus has a dual character from the system approximation point of view

on the relationship between monstrous moonshine and the uniqueness of the moonshine module we consider the relationship between the conjectured uniqueness of the moonshine module open image in new window and monstrous moonshine the genus zero property of the modular invariance group for each monster group thompson series we first discuss a family of possiblezn meromorphic orbifold constructions of open image in new window based on automorphisms of the leech lattice compactified bosonic string we reproduce the thompson series for all 51 non fricke classes of the monster groupm together with a new relationship between the centralisers of these classes and 51 corresponding conway group centralisers generalising a well known relationship for 5 such classes assuming that open image in new window is unique we consider meromorphic orbifoldings of open image in new window and show that monstrous moonshine holds if and onlyzr if the only meromorphic orbifoldings of open image in new window are open image in new window itself or the leech theory this constraint on the meromorphic orbifoldings of open image in new window therefore relates monstrous moonshine to the uniqueness of open image in new window in a new way

modularity in orbifold theory for vertex operator superalgebras this paper is about the orbifold theory for vertex operator superalgebras given a vertex operator superalgebra v and a finite automorphism group g of v we show that the trace functions associated to the twisted sectors are holomorphic in the upper half plane for any commuting pairs in g under the c2 cofinite condition we also establish that these functions afford a representation of the full modular group if v is c2 cofinite and g rational for any g g

polymer transport in random flow the dynamics of polymers in a random smooth flow is investigated in the framework of the hookean dumbbell model the analytical expression of the time dependent probability density function of polymer elongation is derived explicitly for a gaussian rapidly changing flow when polymers are in the coiled state the pdf reaches a stationary state characterized by power law tails both for small and large arguments compared to the equilibrium length the characteristic relaxation time is computed as a function of the weissenberg number in the stretched state the pdf is unstationary and exhibits multiscaling umerical simulations for the two dimensional navier stokes flow confirm the relevance of theoretical results obtained for the correlated model

entropy formula for random transformations we exhibit random strange attractors with random sinai bowen ruelle measures for the composition of independent random diffeomorphisms

superprocesses of stochastic flows we construct a continuous superprocess x on m r d which is the unique weak feller extension of the empirical process of consistent k point motions generated by a family of differential operators the process x differs from known dawson watanabe type fleming viot type and ornstein uhlenbeck type superprocesses this new type of superprocess provides a connection between stochastic flows and measure valued processes and determines a stochastic coalescence which is similar to those of smoluchowski moreover the support of x describes how an initial measure on r d is transported under the flow as an example the process realizes a viewpoint of darling about the isotropic stochastic flows under certain conditions

integration of brownian vector fields summary using the wiener chaos decomposition we show that strong solutions of non lipschitzian s d e s are given by random markovian kernels the example of sobolev flows is studied in some detail exhibiting interesting phase transitions

bps algebras genus zero and the heterotic monster in this note we expand on some technical issues raised in paquette et al 2016 commun number theory phys 10 433 526 by the authors as well as providing a friendly introduction to and summary of our previous work we construct a set of heterotic string compactifications to 0 1 dimensions intimately related to the monstrous moonshine module of frenkel lepowsky and meurman and orbifolds thereof using this model we review our physical interpretation of the genus zero property of monstrous moonshine furthermore we show that the space of second quantized bps states forms a module over the monstrous lie algebras m g some of the first and most prominent examples of generalized kac moody algebras constructed by borcherds and carnahan in particular we clarify the structure of the module present in the second quantized string theory we also sketch a proof of our methods in the language of vertex operator algebras for the interested mathematician

paper unprejudiced optimal open loop input design for identification of transfer functions the problem to estimate transfer functions of linear systems is considered the quality of the resulting estimate depends among other things on the input used during the identification experiment we measure the quality using a quadratic norm in the frequency domain the problem to determine optimal inputs i e inputs that minimize the chosen norm subject to constrained input variance has long been studied we point out that such procedures may involve a prejudice that the system is to be found in a certain model set that may have some surprising effects we discuss how such a prejudice can be reduced by allowing the possibility that the true system cannot be exactly described in the chosen model set we also calculate explicit expressions for the resulting unprejudiced optimal inputs these expressions relate the signal to noise ratio as a function of frequency to the chosen weighting function in the quadratic norm we also point out the role of the employed noise model for the design

stochastic flows on the boundaries of sl n r we study the asymptotic stability of the stochastic flows on a class of compact spaces induced by a diffusion process in sl n r or gl n r these compact spaces are called boundaries of sl n r which include so n the flag manifold the spheresn 1 and the grassmannians the one point motions of these flows are brownian motions for almost every we determine the set of stable points this is a random open set whose complement has zero lebesgue measure the distance between any two points in the same component of this set tends to zero exponentially fast under the flow the lyapunov exponents at stable points are computed explicitly we apply our results to a stochastic flow onsn 2 generated by a stochastic differential equation which exhibits some nice symmetry

monstrous moonshine from orbifolds we consider the monster module of frenkel lepowsky and meurman as az2 orbifold of a bosonic string compactified by the leech lattice we show that the main conway and norton monstrous moonshine properties stating that the thompson series for each monster group conjugacy class has a modular invariance group of genus zero follow from an orbifold construction based on an orbifold group composed of monster group elements it is shown that a conjectured vacuum structure for the orbifold twisted sectors is sufficient to specify the modular group and the genus zero property for each thompson series it is also shown that the power map formula of conway and norton follows from the same vacuum structure finally we demonstrate the validity of the vacuum conjectures for sectors twisted by leech lattice automorphisms in many cases

variance analysis of identified linear miso models having spatially correlated inputs with application to parallel hammerstein models this contribution concerns variance analysis of linear multi input single output models when the inputs are temporally white but where different inputs may be correlated an expression is provided for the variance of a linearly parametrized estimate of the frequency response function from one block i e from one input to the output in particular this expression reveals that the variance increases in one block when the number of estimated parameters in another block is increased but levels off when the number of parameters in the other block reaches the number of parameters in the block in question it also quantifies exactly how correlation between inputs affects the resulting accuracy and a graphical representation is provided for this purpose the results are applicable to parallel miso hammerstein models when the nonlinearities are known and generalize an existing variance expression for this type of model

dimension formula for random transformations we consider compositions of random diffeomorphisms and show that the dimension of sample measures equals lyapunov dimension as conjectured in the nonrandom case by yorke et al

modular equations and the genus zero property of moonshine functions and let n be the normalizer of 0 n in sl 2 r we shall call a discrete subgroup of sl 2 r a congruence group if it contains n for some n necessarily the index of n in is finite and acts on the extended upper half plane h h q i by fractional linear transformations the quotient h has the structure of a compact riemann surface and will be denoted by x conway and norton cn conjectured relationships between certain congruence groups and m known as the moonshine conjectures these have been proved by borcherds

global anomalies on orbifolds we consider global anomalies for heterotic string theory formulated on orbifolds the vanishing of certain characteristic classes in group cohomology provides sufficient conditions for the absence of global anomalies for abelian orbifolds level matching implies these cohomology conditions so suffices for the absence of anomalies for nonabelian orbifolds level matching does not suffice and there are additional constraints we give some examples to illustrate these new constraints

ergodicity of a measure valued markov chain induced by random transformations let z1 z2 be a sequence of i i d random transformations possibly discontinuous of a compact metric space m and let e denote the space of normalized mass distributions on m given in e let n denote the random measure z n z1 1 when well defined we construct the transition probability p of the e valued markov chain n and give a necessary and sufficient condition for p to have a unique invariant measure concentrated on the degenerate mass distributions convergence to statistical equilibrium of the associated discrete time stochastic flow is investigated

modulus of continuity of the canonic brownian motion on the group of diffeomorphisms of the circle abstract an explicit modulus of holder continuity is given for the flow associated to the canonic brownian motion on the diffeomorphism group of the circle

black box identification of multivariable transfer functions asymptotic properties and optimal input design abstract the problem of estimating the transfer function of a multivariable linear stochastic system is considered the transfer function is parametrized as a black box and no order is chosen a priori this means that the model order may increase to infinity as the number of observed data tends to infinity the asymptotic covariance of the transfer function estimate is calculated and is found to be independent of the noise model when the model order increases to infinity the derived expressions are also used to determine optimal unprejudiced input signals for the identification experiment

paper on the estimation of transfer functions this paper treats the close conceptual relationships between basic approaches to the estimation of transfer functions of linear systems the classical methods of frequency and spectral analysis are shown to be related to the well known time domain methods of prediction error type via a common empirical transfer function estimate asymptotic properties of the estimates obtained by the respective methods are also described and discussed an important feature that is displayed by this treatment is a frequency domain weighting function that determines the distribution of bias in case the true system cannot be exactly described within the chosen model set the choice of this weighting function is made in terms of noise models for time domain methods the noise model thus has a dual character from the system approximation point of view

beauty and the beast superconformal symmetry in a monster module frenkel lepowsky and meurman have constructed a representation of the largest sporadic simple finite group the fischer griess monster as the automorphism group of the operator product algebra of a conformal field theory with central chargec 24 in string terminology their construction corresponds to compactification on az2 asymmetric orbifold constructed from the torusr24 where is the leech lattice in this note we point out that their construction naturally embodies as well a larger algebraic structure namely a super virasoro algebra with central charge 16 with the supersymmetry generator constructed in terms of bosonic twist fields

sample path properties of the stochastic flows we consider a stochastic flow driven by a finite dimensional brownian motion we show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the equilibrium state and the central limit theorem the proof uses new estimates of the mixing rates of the multi point motion

kraichnan flow in a square an example of integrable chaos the kraichnan flow provides an example of a random dynamical system accessible to an exact analysis we study the evolution of the infinitesimal separation between two lagrangian trajectories of the flow its long time asymptotics is reflected in the large deviation regime of the statistics of stretching exponents whereas in the flow that is isotropic at small scales the distribution of such multiplicative large deviations is gaussian this does not have to be the case in the presence of an anisotropy we analyze in detail the flow in a two dimensional periodic square where the anisotropy generally persists at small scales the calculation of the large deviation rate function of the stretching exponents reduces in this case to the study of the ground state energy of an integrable periodic schrodinger operator of the lame type the underlying integrability permits to explicitly exhibit the non gaussianity of the multiplicative large deviations and to analyze the time scales at which the large deviation regime sets in in particular we indicate how the divergence of some of those time scales when the two lyapunov exponents become close allows a discontinuity of the large deviation rate function in the parameters of the flow the analysis of the two dimensional anisotropic flow permits to identify the general scenario for the appearance of multiplicative large deviations together with the restrictions on its applicability

isotropic stochastic flows on considere les flots stochastiques isotropes dans un espace euclidien de d dimensions d 2 on relie la tendance des distances entre deux points et des vecteurs tangents a se borner ou s etendre a la dimension et a la proportion du flot solenoidal ou potentiel

t e harris s contributions to recurrent markov processes and stochastic flows this is a brief survey of t e harris s work on recurrent markov processes and on stochastic flows and of some more recent work in these fields

asymptotic behaviour of stochastic flows of diffeomorphisms two case studies the two stochastic flows studied are i the canonical stochastic flow on the orthonormal frame bundle of hyperbolic space which gives stochastic parallel translation along brownian paths in hyperbolic space and ii a stochastic flow on the spheres n 1 arising from its embedding as the unit sphere in n both flows are controlled by the same stochastic differential equation in a finite dimensional lie group in each case the lyapunov exponents are computed and a complete description is given of the local and global stability of the flow

lyapunov exponents for a stochastic analogue of the geodesic flow new invariants for a riemannian manifold are defined as lya punov exponents of a stochastic analogue of the geodesic flow a lower bound is given reminiscent of corresponding results for the geodesic flow and an upper bound is given for surfaces of positive curvature for surfaces of con stant negative curvature a direct method via the doob rt transform is used to determine the full lyapunov structure relating the stable manifolds to the horocycles

the distribution of lyapunov exponents exact results for random matrices simple exact expressions are derived for all the lyapunov exponents of certainn dimensional stochastic linear dynamical systems in the case of the product of independent random matrices each of which has independent gaussian entries with mean zero and variance 1 n the exponents have an exponential distribution asn in the case of the time ordered product integral of exp n 1 2dw where the entries of then n matrixw t are independent standard wiener processes the exponents are equally spaced for fixedn and thus have a uniform distribution as n

graded lie superalgebras and the superdimension formula in this paper we investigate the structure of graded lie superalgebras l a a l a where is a countable abelian semigroup and a is a countable abelian group with a coloring map satisfying a certain finiteness condition given a denominator identity for the graded lie superalgebra l we derive a superdimension formula for the homogeneous subspaces l a a a which enables us to study the structure of graded lie superalgebras in a unified way we discuss the applications of our superdimension formula to free lie superalgebras generalized kac moody superalgebras and monstrous lie superalgebras in particular the product identities for normalized formal power series are interpreted as the denominator identities for free lie superalgebras we also give a characterization of replicable functions in terms of product identities and determine the root multiplicities of monstrous lie superalgebras

monstrous moonshine and monstrous lie superalgebras we prove conway and norton s moonshine conjectures for the infinite dimensional representation of the monster simple group constructed by frenkel lepowsky and meurman to do this we use the no ghost theorem from string theory to construct a family of generalized kac moody superalgebras of rank 2 which are closely related to the monster and several of the other sporadic simple groups the denominator formulas of these superalgebras imply relations between the thompson functions of elements of the monster i e the traces of elements of the monster on frenkel lepowsky and meurman s representation which are the replication formulas conjectured by conway and norton these replication formulas are strong enough to verify that the thompson functions have most of the moonshine properties conjectured by conway and norton and in particular they are modular functions of genus 0 we also construct a second family of kac moody superalgebras related to elements of conway s sporadic simple group col these superalgebras have even rank between 2 and 26 for example two of the lie algebras we get have ranks 26 and 18 and one of the superalgebras has rank 10 the denominator formulas of these algebras give some new infinite product identities in the same way that the denominator formulas of the a n n e kac moody algebras give the macdonald identities

intermittency of the tracer gradient the problem of stirring a passive scalar tracer by a random velocity field is considered for gaussian velocity fields with infinitely small time and space scales it is shown that the tracer gradient is concentrated in a discrete set of points the points that form a random point process independent of the initial tracer distribution a complete description of this point process is given if the initial tracer field is a random function with homogeneous increments a full statistics of the jumps is also given

the asymptotic crlb for the spectrum of arma processes this paper addresses the issue of quantifying the frequency domain accuracy of autoregressive moving average arma spectral estimates as dictated by the cramer rao lower bound crlb classical work in this area has led to expressions that are asymptotically exact as both data length and model order tend to infinity although they are commonly used in finite model order and finite data length settings as approximations more recent work has established quantifications that for ar models are exact for finite model order by employing new analysis methods based on rational orthonormal parameterizations together with the ideas of reproducing kernel hilbert spaces this paper develops quantifications that extend this previous work by being exact for finite model order in all of the ar ma and arma system cases these quantifications via their explicit dependence on poles and zeros of the underlying spectral factor reveal certain fundamental aspects of the accuracy achievable by spectral estimates of arma processes

asymptotic support theorem for planar isotropic brownian flows it has been shown by various authors that the diameter of a given nontrivial bounded connected set x grows linearly in time under the action of an isotropic brownian flow ibf which has a nonnegative top lyapunov exponent in case of a planar ibf with a positive top lyapunov exponent the precise deterministic linear growth rate k of the diameter is known to exist in this paper we will extend this result to an asymptotic support theorem for the time scaled trajectories of a planar ibf which has a positive top lyapunov exponent starting in a nontrivial compact connected set x r2 that is we will show convergence in probability of the set of time scaled trajectories in the hausdorff distance to the set of lipschitz continuous functions on 0 1 starting in 0 with lipschitz constant k

modular functions arising from some finite groups to each element m of the fischer griess monster group m and conjectured that these functions are hauptmoduls for certain genus zero modular groups we have found for a large number of values of n all the genus zero groups between r0 n and psl 2 r that have hauptmoduls of the above form and this provides the necessary verification that the series assigned in 21 to particular elements of m really are such hauptmoduls atkin and fong 11 have recently verified that h m really is a character of m for all n we compute thompson series for various finite groups and discuss the differences between these groups and m we find that the resulting thompson series are all hauptmoduls for suitable genus zero subgroups of psl 2 r

isotropic brownian motions over complex fields as a solvable model for may wigner stability analysis we consider matrix valued stochastic processes known as isotropic brownian motions and show that these can be solved exactly over complex fields while these processes appear in a variety of questions in mathematical physics our main motivation is their relation to a may wigner like stability analysis for which we obtain a stability phase diagram the exact results establish the full joint probability distribution of the finite time lyapunov exponents and may be used as a starting point for a more detailed analysis of the stability instability phase transition our derivations rest on an explicit formulation of a fokker planck equation for the lyapunov exponents this formulation happens to coincide with an exactly solvable class of models of the calgero sutherland type originally encountered for a model of phase coherent transport the exact solution over complex fields describes a determinantal point process of biorthogonal type similar to recent results for products of random matrices and is also closely related to hermitian matrix models with an external source

brownian motions on the homeomorphisms of the plane let z denote a point of r 2 we study random flows z st z in r 2 0 leq s leq t infty z in r 2 z tu z st z z su z for s leq t leq u such flows are called brownian if z is continuous in s t z and has appropriate spatial and temporal homogeneity properties and if z st z uv cdots are independent homeomorphisms of r 2 onto r 2 when s leq t leq u leq v leq cdots for a brownian flow the coordinates of any k points are a 2k dimensional continuous markov process k 1 2 cdots if these processes are diffusions whose diffusion matrices have bounded continuous derivatives of order leq 2 i e are c 2 bounded then the diffusion matrices are necessarily obtained in a certain way from the covariance tensor of the field of infinitesimal displacements a converse is given in the incompressible isotropic case given a c 2 bounded covariance tensor of an isotropic solenoidal r 2 valued field in r 2 there exists a corresponding incompressible isotropic brownian flow

infinite products of random isotropically distributed matrices statistical properties of infinite products of random isotropically distributed matrices are investigated both for continuous processes with finite correlation time and discrete sequences of independent matrices a formalism that allows to calculate easily the lyapunov spectrum and generalized lyapunov exponents is developed this problem is of interest to probability theory statistical characteristics of matrix t exponentials are also needed for turbulent transport problems dynamical chaos and other parts of statistical physics

on isotropic brownian motions this paper includes a detailed study of isotropic brownian motion on matrices and brownian flows associated with isotropic gaussian fields characteristic exponents stability asymptotic behaviour statistical equilibrium are the topics on which the main results are obtained

polymer stretching in the inertial range of turbulence we study the deformation of flexible polymers whose contour length lies in the inertial range of a homogeneous and isotropic turbulent flow by using the elastic dumbbell model and a stochastic velocity field with nonsmooth spatial correlations we obtain the probability density function of the extension as a function of the weissenberg number and of the scaling exponent of the velocity structure functions in a spatially rough flow as in the inertial range of turbulence the statistics of polymer stretching differs from that observed in laminar flows or in smooth chaotic flows in particular the probability distribution of polymer extensions decays as a stretched exponential and the most probable extension grows as a power law of the weissenberg number furthermore the ability of the flow to stretch polymers weakens as the flow becomes rougher in space

on geometric properties of stochastic flows related to the lyapunov spectrum we study the geometric properties of two stochastic flows on spheres in euclidean space the underlying one point motion in both cases is brownian both flows arise from the action of a lie group valued brownian motion on a quotient for both flows the curvature of a curve moving under the flow is shown to be a diffusion null recurrent in one case and transient in the other

lyapunov exponents and relative entropy for a stochastic flow of diffeomorphisms the lyapunov exponents 1 2 d for a stochastic flow of diffeomorphisms of a d dimensional manifold m with a strongly recurrent one point motion describe the almost sure limiting exponential growth rates of tangent vectors under the flow this paper shows how the lyapunov exponents are related to measure preserving properties of the stochastic flow on m and of the induced stochastic flow on the projective bundle pm relative entropy is used to quantify the extent to which a measure fails to be invariant under the flow the results include the following if m is compact and if the one point motion on m is a non degenerate diffusion with stationary probability measure then 1 d 0 with equality if and only if the flow preserves almost surely if in addition the induced one point motion on pm satisfies a weak non degeneracy condition then 1 d if and only if there is a smooth riemannian structure on m with respect to which the flow is conformal almost surely

brief paper accuracy of linear multiple input multiple output mimo models obtained by maximum likelihood estimation in this paper we study the accuracy of linear multiple input multiple output mimo models obtained by maximum likelihood estimation we present a frequency domain representation for the information matrix for general linear mimo models we show that the variance of estimated parametric models for linear mimo systems satisfies a fundamental integral trade off this trade off is expressed as a multivariable water bed effect an extension to spectral estimation is also discussed

generalized fourier and toeplitz results for rational orthonormal bases this paper provides a generalization of certain classical fourier convergence and asymptotic toeplitz matrix properties to the case where the underlying orthonormal basis is not the conventional trigonometric one but rather a rational generalization which encompasses the trigonometric one as a special case these generalized fourier and toeplitz results have particular application in dynamic system estimation theory specifically the results allow a unified treatment of the accuracy of least squares system estimation using a range of model structures including those that allow the inclusion of prior knowledge of system dynamics via the specification of fixed pole or zero locations

frequency domain accuracy of identified 2 d causal ar models the author studies parametric estimation of 2 d autoregressive models using the least squares method the analysis is concentrated on the frequency domain accuracy of the estimated models first results for the accuracy of the parameter estimates are discussed the estimates are asymptotically gaussian distributed the variance of the estimated model evaluated in the frequency domain can be expressed using these results for the parameters this however gives no insight of the dependence on the true transfer function an illuminating result is obtained if one lets the model order tend to infinity the limiting results show good correspondence with monte carlo simulations even for small data sets using low model orders

calculus of twisted vertex operators starting from an arbitrary isometry of an arbitrary even lattice twisted and shifted vertex operators are introduced under commutators these operators provide realizations of twisted affine lie algebras this construction generalizing a number of known ones is based on a self contained calculus

fricke lie algebras and the genus zero property in moonshine we give a new simpler proof that the canonical actions of finite groups on fricke type monstrous lie algebras yield genus zero functions in generalized monstrous moonshine using a borcherds kac moody lie algebra decomposition due to jurisich we describe a compatibility condition arising from the no ghost theorem in bosonic string theory that yields the genus zero property we give evidence for and against the conjecture that such a compatibility for symmetries of the monster lie algebra gives a characterization of the monster group

analysis of identified 2 d noncausal models there are two approaches to the identification of noncausal autoregressive systems in two dimensions differing in the assumed noise model for both approaches the maximum likelihood estimator formulated in the frequency domain is presented the fisher information matrix is evaluated and found to be the sum of a block toeplitz and a block hankel matrix the variance of the parameters however cannot be used for comparison of the two approaches so the variance in the frequency domain is evaluated assuming that the true system in each case can be described by a model of that type possibly high order in particular the variance of the spectrum estimate is derived if the number of parameters tends to infinity it is shown that the two approaches give the same spectrum estimate variance the question of which set of true spectra can be described by the respective approaches is discussed

estimation of transfer functions asymptotic theory and a bound of model uncertainty abstract the problem of transfer function estimation is considered we will discuss the problem in two related aspects firstly how to obtain a good black box transfer function model secondly how to derive a suitable description of the model uncertainty modelling errors we will emphasize the second point we shall discuss the asymptotic theory on the properties of transfer function estimates developed recently by ljung and yuan this new theory shows that the transfer function estimate is consistent the error of the estimate is asymptotically normal with a very simple expression for its variance their results will be extended here to cases where spectral analysis is used based on this theory we will propose the method for obtaining a low order nominal model of linear processes and define and estimate an upper bound of the model uncertainty an upper bound of the model uncertainty is a suitable description of the modelling errors for the robust controller design

liapounov exponents of stochastic flows we obtain a formula for liapounov exponents of stochastic flows generated by stochastic differential equations on compact manifolds as an application the exponents of a class of stochastic flows on spheres are determined explicitly

the fundamental role of general orthonormal bases in system identification the purpose of this paper is threefold firstly it is to establish that contrary to what might be expected the accuracy of well known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure secondly it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any fixed poles or zeros this is achieved by employing certain new results on generalized fourier series and the asymptotic properties of toeplitz like matrices in such a way that the new variance expressions presented here encompass pre existing ones as special cases via this latter analysis a new perspective emerges on recent work pertaining to the use of orthonormal basis structures in system identification namely that orthonormal bases are much more than an implementational option offering improved numerical properties in fact they are an intrinsic part of estimation since as shown here orthonormal bases quantify the asymptotic variability of the estimates whether or not they are actually employed in calculating them

aggregation of inertial particles in random flows we consider the trajectories of particles suspended in a randomly moving fluid if the lyapunov exponent of these trajectories is negative the paths of these particles coalesce so that particles aggregate here we give a detailed account of a method b mehlig and m wilkinson phys rev lett 92 250602 2004 for calculating this exponent it is expressed as the expectation value of a random variable evolving under a stochastic differential equation we analyze this equation in detail in the limit where the correlation time of the velocity field of the fluid is very short such that the stochastic differential equation is a langevin equation we derive an asymptotic perturbation expansion of the lyapunov exponent for particles suspended in three dimensional flows in terms of a dimensionless measure of the inertia of the particles epsilon and a measure of the relative intensities of potential and solenoidal components of the velocity field gamma we determine the phase diagram in the epsilon gamma plane

the brownian motion and the canonical stochastic flow on a symmetric space we study the limiting behavior of brownian motion xt on a symmetric space v g k of noncompact type and the asymptotic stability of the canonical stochastic flow ft on o v we show that almost surely xt has a limiting direction as it goes to infinity the study of the asymptotic stability of ft is reduced to the study of the limiting behavior of the adjoint action on the lie algebra of g by the horizontal diffusion in g we determine the lyapunov exponents and the associated filtration of ft in terms of root space structure of

asymptotic variance expressions for identified black box transfer function models identification of black box transfer function models is considered it is assumed that the transfer function models possess a certain shift property which is satisfied for example by all polynomial type models expressions for the variances of the transfer function estimates are derived that are asymptotic both in the number of observed data and in the model orders the result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance respectively is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise the factor of proportionality is the ratio of model order to number of data this result is independent of the particular model structure used the result is applied to evaluate the performance degradation due to variance for a number of typical model uses some consequences for input design are also drawn

generalized kac moody algebras on etudie une classe d algebres de lie qui ont une forme bilineaire contravariante qui est presque definie positive ces algebres generalisent celles de kac moody et peuvent etre considerees comme des algebres de kac moody avec des racines simples imaginaires

variance analysis of linear simo models with spatially correlated noise in this paper we address the identification of linear time invariant single input multi output simo systems in particular we assess the performance of the prediction error method by quantifying

generators of function fields of the modular curves x_1 5 and x_1 6 we show that the modular functions j 1 5 and j 1 6 generate function fields of the modular curves x 1 n n 5 6 respectively and find some number theoretic properties of these modular functions

generalized moonshine ii borcherds products the goal of this paper is to construct infinite dimensional lie algebras by using infinite product identities and to use these lie algebras to reduce the generalized moonshine conjecture to a pair of hypotheses about group actions on vertex algebras and lie algebras we expect the lie algebras that we construct to manifest as algebras of physical states in an orbifold conformal field theory yet to be fully constructed with symmetries given by the monster simple group we introduce vector valued modular functions attached to families of modular functions of different levels and we prove infinite product identities for a distinguished class of automorphic functions on a product of two half planes we recast this result using the borcherds harvey moore singular theta lift and show that the vector valued functions attached to completely replicable modular functions with integer coefficients lift to automorphic functions with infinite product expansions at all cusps for each element of the monster simple group we construct an infinite dimensional lie algebra such that its denominator formula is an infinite product expansion of the automorphic function arising from that element s mckay thompson series these lie algebras have the unusual property that their simple roots and all root multiplicities are known we show that under certain hypotheses characters of groups acting on these lie algebras form functions on the upper half plane that are either constant or invariant under a genus zero congruence group

asymptotic properties of black box identification of transfer functions the problem of estimating the transfer function of a linear stochastic system is considered the transfer function is parametrized as a black box and no given order is chosen a priori this means that the model orders may increase to infinity when the number of observed data tends to infinity the consistency and convergence properties of the resulting transfer function estimates are investigated asymptotic expressions for the variances and distributions of these estimates are also derived for the case that the model orders increase it is shown that the variance of the transfer function estimate at a certain frequency is asymptotically given by the noise to signal ratio at that frequency mulliplied by the model order to number of data points ratio