second order boltzmann gibbs principle for polynomial functions and applications in this paper we give a new proof of the second order boltzmann gibbs principle introduced in goncalves and jara arch ration mech anal 212 2 597 644 2014 the proof does not impose the knowledge on the spectral gap inequality for the underlying model and it relies on a proper decomposition of the antisymmetric part of the current of the system in terms of polynomial functions in addition we fully derive the convergence of the equilibrium fluctuations towards 1 a trivial process in case of super diffusive systems 2 an ornstein uhlenbeck process or the unique energy solution of the stochastic burgers equation as defined in gubinelli and jara spdes anal comput 1 325 350 2013 and gubinelli and perkowski arxiv 1508 07764 2015 in case of weakly asymmetric diffusive systems examples and applications are presented for weakly and partial asymmetric exclusion processes weakly asymmetric speed change exclusion processes and hamiltonian systems with exponential interactions

solving the kpz equation we introduce a new concept of solution to the kpz equation which is shown to extend the classical cole hopf solution this notion provides a factorisation of the cole hopf solution map into a universal measurable map from the probability space into an explicitly described auxiliary metric space composed with a new solution map that has very good continuity properties the advantage of such a formulation is that it essentially provides a pathwise notion of a solution together with a very detailed approximation theory in particular our construction completely bypasses the cole hopf transform thus laying the groundwork for proving that the kpz equation describes the uctuations of systems in the kpz universality class as a corollary of our construction we obtain very detailed new regularity results about the solution as well as its derivative with respect to the initial condition other byproducts of the proof include an explicit approximation to the stationary solution of the kpz equation a well posedness result for the fokker planck equation associated to a particle diusing in a rough space time dependent potential and a new periodic homogenisation result for the heat equation with a space time periodic potential one ingredient in our construction is an example of a non gaussian rough path such that the area process of its natural approximations needs to be renormalised by a diverging term for the approximations to converge

speech coding decoding method having an excitation signal a speech coding method in which spectrum parameter representing a spectrum envelope and a pitch parameter representing a pitch are obtained from an input discrete speech signal a frame interval is divided into subintervals in accordance with the pitch parameter a sound source signal in one of the subintervals is obtained by obtaining a multipulse with respect to a difference signal obtained by performing prediction on the basis of a past sound source signal correction information for correcting at least one of the amplitude and the phase of the sound source signal are obtained and output in other pitch intervals in the frame

multi pulse excitation linear predictive speech coder a multi pulse excitation linear predictive speech coder operates in accordance with an analysis by synthesis method for determining the excitation the coder 10 comprises an lpc analyzer 11 a multi phase excitation generator 13 means 12 14 for forming an error signal representative of the difference between an original speech signal s n and a synthetic speech signal s n a filter 15 for perceptually weighting the error signal and means 16 responsive to the weighted error signal e n for generating pulse parameters controlling the excitation generator 13 so as to minimize a predetermined measure of the weighted error signal the lpc parameters and the pulse parameters of the excitation signal x n are encoded for efficient storage or transmission the bit capacity required for pulse position encoding of the excitation signal x n is considerably reduced by arranging the excitation generator 16 for an excitation signal x n which in each excitation interval l consists of a pulse pattern having a grid of a predetermined number q of equidstant pulses and by arranging the control means 16 for generating pulse parameters characterizing the grid position k relative to the beginning of the excitation interval l and the variable amplitudes bk j 1 j q of the pulses of the grid

method of transmitting at low throughput a speech signal by celp coding and corresponding system a method is provided for transmitting a digital speech signal at low throughput coding is performed by code excited linear prediction in order to generate a code signal a waveform being represented by an initial vector o of dimension l from a filter for synthesizing by a reference waveform selected from a dictionary of reference vectors v relating to a criterion of minimum deviation min h v 2 representing a target vector through perceptual weighting of the initial vector o a dictionary y factorized as a product of basis vectors yi of n ary form which are corrected by a scale factor i of distribution of the excitation energy and a dictionary g y of gains gk are established to represent the dictionary of the reference vectors v vk i gk yi the criterion is established by calculating c gk i yi 2gk gk 2 formed of the scalar products and perceptual energies to the initial vector o is assigned the optimal reference vector vk i gk i yi represented by just the index values k i

convergence condition for convex combinations of two polynomials a necessary and sufficient condition is derived for a convex combination of two given polynomials to be a convergent polynomial i e a polynomial having roots all within the unit circle in the complex plane this can be regarded as a discrete counterpart to the existing result for the continuous case a simple numerical example is provided to demonstrate the theorem obtained

a coupled kpz equation its two types of approximations and existence of global solutions abstract this paper concerns the multi component coupled kardar parisi zhang kpz equation and its two types of approximations one approximation is obtained as a simple replacement of the noise term by a smeared noise with a proper renormalization while the other one introduced in 6 is suitable for studying the invariant measures by applying the paracontrolled calculus introduced by gubinelli et al 8 9 we show that two approximations have the common limit under the properly adjusted choice of renormalization factors for each of these approximations in particular if the coupling constants of the nonlinear term of the coupled kpz equation satisfy the so called trilinear condition the renormalization factors can be taken the same in two approximations and the difference of the limits of two approximations are explicitly computed moreover under the trilinear condition the wiener measure twisted by the diffusion matrix becomes stationary for the limit and we show that the solution of the limit equation exists globally in time when the initial value is sampled from the stationary measure this is shown for the associated tilt process combined with the strong feller property shown by hairer and mattingly 12 this result can be extended for all initial values

controlling rough paths abstract we formulate indefinite integration with respect to an irregular function as an algebraic problem which has a unique solution under some analytic constraints this allows us to define a good notion of integral with respect to irregular paths with holder exponent greater than 1 3 e g samples of brownian motion and study the problem of the existence uniqueness and continuity of solution of differential equations driven by such paths we recover young s theory of integration and the main results of lyons theory of rough paths in holder topology

multi pulse speech coder speech is coded such that it can be generated by a pulse excitation sequence filtered by an lpc linear preductive coding filter the sequence contains in each of successive frame periods pulses whose positions and amplitudes may be varied these variables are selected at the coding end to reduce the error between the input and regenerated speech signals the selection process involves derivation of an initial estimate followed by an iterative adjustment process in which pulses having a low energy contribution are tested in alternative positions and transferred to them if a reduced error results

space time discrete kpz equation we study a general family of space time discretizations of the kpz equation and show that they converge to its solution the approach we follow makes use of basic elements of the theory of regularity structures hairer in invent math 198 2 269 504 2014 as well as its discrete counterpart hairer and matetski in discretizations of rough stochastic pdes 2015 arxiv 1511 06937 since the discretization is in both space and time and we allow non standard discretization for the product the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study

speech analysis synthesis method and apparatus therefor an impulse sequence of a pitch frequency is detected from a phase equalized prediction residual of an input speech signal s t and a quasi periodic impulse sequence is obtained by processing the impulse sequence so that a fluctuation in its pitch frequency is within an allowed limit range the magnitudes of the quasi periodic impulse sequence are so determined as to minimize an error between the waveform of a synthesized speech obtainable by exciting an all pole filter 18 with the quasi periodic impulse sequence and the waveform of a phase equalized speech obtainable by applying the input speech signal to a phase equalizing filter 5 preferably the quasi periodic impulse sequence is supplied to the all pole filter after being applied to a zero filter 10 in which it is given features of the prediction residual of the speech coefficients of the zero filter are also determined so that the error of the waveforms of the synthesized speech and the phase equalized speech is minimum

a theory of regularity structures we introduce a new notion of regularity structure that provides an algebraic framework allowing to describe functions and or distributions via a kind of jet or local taylor expansion around each point the main novel idea is to replace the classical polynomial model which is suitable for describing smooth functions by arbitrary models that are purpose built for the problem at hand in particular this allows to describe the local behaviour not only of functions but also of large classes of distributions we then build a calculus allowing to perform the various operations multiplication composition with smooth functions integration against singular kernels necessary to formulate fixed point equations for a very large class of semilinear pdes driven by some very singular typically random input this allows for the first time to give a mathematically rigorous meaning to many interesting stochastic pdes arising in physics the theory comes with convergence results that allow to interpret the solutions obtained in this way as limits of classical solutions to regularised problems possibly modified by the addition of diverging counterterms these counterterms arise naturally through the action of a renormalisation group which is defined canonically in terms of the regularity structure associated to the given class of pdes our theory also allows to easily recover many existing results on singular stochastic pdes kpz equation stochastic quantisation equations burgers type equations and to understand them as particular instances of a unified framework one surprising insight is that in all of these instances local solutions are actually smooth in the sense that they can be approximated locally to arbitrarily high degree as linear combinations of a fixed family of random functions distributions that play the role of polynomials in the theory as an example of a novel application we solve the long standing problem of building a natural markov process that is symmetric with respect to the finite volume measure describing the phi 4 3 euclidean quantum field theory it is natural to conjecture that the markov process built in this way describes the glauber dynamic of 3 dimensional ferromagnets near their critical temperature

energy solutions of kpz are unique the kardar parisi zhang kpz equation is conjectured to universally describe the fluctuations of weakly asymmetric interface growth here we provide the first intrinsic well posedness result for the kpz equation on the real line by showing that its energy solutions as introduced by goncalves and jara in gj14 and refined in gj13 are unique together with the convergence results of gj14 and many follow up papers this establishes the weak kpz universality conjecture for a wide class of models our proof builds on an observation of funaki and quastel fq15 a remarkable consequence is that the energy solution to the kpz equation is not equal to the cole hopf solution but it involves an additional drift t 12

weakly asymmetric non simple exclusion process and the kardar parisi zhang equation we analyze a class of non simple exclusion processes and the corresponding growth models by generalizing the discrete cole hopf transformation of gartner stoch process appl 27 233 260 1987 we identify the main non linearity and eliminate it by imposing a gradient type condition for hopping range at most 3 using the generalized transformation we prove the convergence of the exclusion process toward the kardar parisi zhang kpz equation this is the first universality result under the weak asymmetry concerning interacting particle systems while this class of exclusion processes are not explicitly solvable under the weak asymmetry we obtain the exact one point limiting distribution for the step initial condition by using the previous result of amir et al commun pure appl math 64 4 466 537 2011 and our convergence result

a method to determine the excitation pulse positions within a speech frame a method of determining the positions within a speech frame for a given number n j n1 n2 of excitation pulses in a linear predictive speech encoder the method is a combination of two known methods in accordance with the invention the positions of the excitation pulses are calculated in a number of calculation stages j in accordance with the first method and the positions of the excitation pulses are calculated in a number of calculation stages n1 n2 nl in accordance with the second method each with a starting point from one of a number of positions mi mk mr calculated in accordance with the first method therewith to obtain one of a number l of pulse placements and the proportion between the number of calculation stages j and max n1 n2 respectively according to the first and the second method respectively is chosen so as to obtain the least calculation complexity for a certain given speech quality two different embodiments of the second method are described

a central limit theorem for the kpz equation we consider the kpz equation in one space dimension driven by a stationary centred space time random field which is sufficiently integrable and mixing but not necessarily gaussian we show that in the weakly asymmetric regime the solution to this equation considered at a suitable large scale and in a suitable reference frame converges to the hopf cole solution to the kpz equation driven by space time gaussian white noise while the limiting process depends only on the integrated variance of the driving field the diverging constants appearing in the definition of the reference frame also depend on higher order moments

kpz equation limit of higher spin exclusion processes we prove that under a particular weak scaling the 4 parameter interacting particle system introduced by corwin and petrov comm math phys 343 2016 651 700 converges to the kardar parisi zhang kpz equation this expands the relatively small number of systems for which weak universality of the kpz equation has been demonstrated

stochastic burgers and kpz equations from particle systems we consider two strictly related models a solid on solid interface growth model and the weakly asymmetric exclusion process both on the one dimensional lattice it has been proven that in the diffusive scaling limit the density field of the weakly asymmetric exclusion process evolves according to the burgers equation and the fluctuation field converges to a generalized ornstein uhlenbeck process we analyze instead the density fluctuations beyond the hydrodynamical scale and prove that their limiting distribution solves the non linear burgers equation with a random noise on the density current for the solid on solid model we prove that the fluctuation field of the interface profile if suitably rescaled converges to the kardar parisi zhang equation this provides a microscopic justification of the so called kinetic roughening i e the non gaussian fluctuations in some non equilibrium processes our main tool is the cole hopf transformation and its microscopic version we also develop a mathematical theory for the macroscopic equations

nonlinear fluctuations of weakly asymmetric interacting particle systems we introduce what we call the second order boltzmann gibbs principle which allows one to replace local functionals of a conservative one dimensional stochastic process by a possibly nonlinear function of the conserved quantity this replacement opens the way to obtain nonlinear stochastic evolutions as the limit of the fluctuations of the conserved quantity around stationary states as an application of this second order boltzmann gibbs principle we introduce the notion of energy solutions of the kpz and stochastic burgers equations under minimal assumptions we prove that the density fluctuations of one dimensional stationary weakly asymmetric conservative particle systems are sequentially compact and that any limit point is given by energy solutions of the stochastic burgers equation we also show that the fluctuations of the height function associated to these models are given by energy solutions of the kpz equation in this sense unfortunately we lack a uniqueness result for these energy solutions we conjecture these solutions to be unique and we show some regularity results for energy solutions of the kpz burgers equation supporting this conjecture

field theoretic thermodynamic uncertainty relation general formulation exemplified with the kardar parisi zhang equation we propose a field theoretic thermodynamic uncertainty relation as an extension of the one derived so far for a markovian dynamics on a discrete set of states and for overdamped langevin equations we first formulate a framework which describes quantities like current entropy production and diffusivity in the case of a generic field theory we will then apply this general setting to the one dimensional kardar parisi zhang equation a paradigmatic example of a non linear field theoretic langevin equation in particular we will treat the dimensionless kardar parisi zhang equation with an effective coupling parameter measuring the strength of the non linearity it will be shown that a field theoretic thermodynamic uncertainty relation holds up to second order in a perturbation expansion with respect to a small effective coupling constant the calculations show that the field theoretic variant of the thermodynamic uncertainty relation is not saturated for the case of the kardar parisi zhang equation due to an excess term stemming from its non linearity