adaptive filtering in subbands with critical sampling analysis experiments and application to acoustic echo cancellation an exact analysis of the critically subsampled two band modelization scheme is given and it is demonstrated that adaptive cross filters between the subbands are necessary for modelization with small output errors it is shown that perfect reconstruction filter banks can yield exact modelization these results are extended to the critically subsampled multiband schemes and important computational savings are seen to be achieved by using good quality filter banks the problem of adaptive identification in critically subsampled subbands is considered and an appropriate adaptation algorithm is derived the authors give a detailed analysis of the computational complexity of all the discussed schemes and experimentally verify the theoretical results that are obtained the adaptive behavior of the subband schemes that were tested is discussed

taming correlations through entropy efficient measure decompositions with applications to mean field approximation the analysis of various models in statistical physics relies on the existence of decompositions of measures into mixtures of product like components where the goal is to attain a decomposition into measures whose entropy is close to that of the original measure yet with small correlations between coordinates we prove a related general result for every measure mu on mathbb r n and every varepsilon 0 there exists a decomposition mu int mu theta d m theta such that h mu mathbb e theta sim m h mu theta le mathrm tr mathrm cov mu varepsilon and mathbb e theta sim m mathrm cov mu theta preceq mathrm id varepsilon as an application we derive a general bound for the mean field approximation of ising and potts models which is in a sense dimension free in both continuous and discrete settings in particular for an ising model on pm 1 n or on 1 1 n we show that the deficit between the mean field approximation and the free energy is at most c frac 1 p p left n vert j vert s p right frac p 1 p for all p 0 where vert j vert s p denotes the schatten p norm of the interaction matrix for the case p 2 this recovers the result of jain et al mean field approximation convex hierarchies and the optimality of correlation rounding a unified perspective arxiv 1808 07226 2018 but for an optimal choice of p it often allows to get almost dimension free bounds

a unified approach to time and frequency domain realization of fir adaptive digital filters specific implementations of the finite impulse response fir block adaptive filter in the frequency domain are presented and some of their important properties are discussed the time domain block adaptive filter implemented in the frequency domain is shown to be equivalent to the frequency domain adaptive filter derived in the frequency domain provided data sectioning is done properly all of the known time and frequency domain adaptive filters 1 12 16 18 are contained in the set of possible block adaptive filter structures thus the block adaptive filter is generic and its formulation unifies the current theory of time and frequency domain fir adaptive filter structures a detailed analysis of overlap save and overlap add implementations shows that the former is to be preferred for adaptive applications because it requires less computation a fact that is not true for fixed coefficient filters

the transonic shock in a nozzle 2 d and 3 d complete euler systems abstract in this paper we study a transonic shock problem for the euler flows through a class of 2 d or 3 d nozzles the nozzle is assumed to be symmetric in the diverging or converging part if the supersonic incoming flow is symmetric near the divergent or convergent part of the nozzle then as indicated in section 147 of r courant k o friedrichs supersonic flow and shock waves interscience publ new york 1948 there exist two constant pressures p 1 and p 2 with p 1 p 2 such that for given constant exit pressure p e p 1 p 2 a symmetric transonic shock exists uniquely in the nozzle and the position and the strength of the shock are completely determined by p e moreover it is shown in this paper that such a transonic shock solution is unique under the restriction that the shock goes through the fixed point at the wall in the multidimensional setting furthermore we establish the global existence stability and the long time asymptotic behavior of an unsteady symmetric transonic shock under the exit pressure p e when the initial unsteady shock lies in the symmetric diverging part of the 2 d or 3 d nozzle on the other hand it is shown that an unsteady symmetric transonic shock is structurally unstable in a global in time sense if it lies in the symmetric converging part of the nozzle

block realization of multirate adaptive digital filters in this paper we study multirate transversal adaptive digital filters adf s based on the block least mean square blms algorithms these include an adf with decimation adfd and an adf with interpolation adfi we first formulate these filters based on the block mean squared error bmse criterion and derive blms multi rate weight adjustment algorithms and then study efficient realization of those filters it is shown that the blms adfd can be realized efficiently in the direct form or in the filter bank structure both using the fast fourier transform fft and an appropriate sectioning procedure according to our analysis of computational complexity the fft realization of the blms adfd in the filter bank structure is more efficient than in the direct form and the two structures using the fft become more efficient in comparison to the lms adfd as the number of weights increases unlike the direct form realization the filter bank realization of the blms adfd using the fft becomes more efficient as the decimation ratio increases similar results have been obtained for the blms adfi finally we investigate by computer simulation the effects of different weight adjustment algorithms and several system parameters on the performances of adfd s the results of simulation indicate that as expected the convergence speed of the blms adfd can be significantly improved by self orthogonalization of weight adjustment in the frequency domain furthermore the convergence factor of the self orthogonalizing blms adfd can be chosen such that the steady state performance of the new adfd is the same as that of the existing lms adfd

global subsonic and subsonic sonic flows through infinitely long axially symmetric nozzles abstract in this paper we establish existence of global subsonic and subsonic sonic flows through infinitely long axially symmetric nozzles by combining variational method various elliptic estimates and a compensated compactness method more precisely it is shown that there exist global subsonic flows in nozzles for incoming mass flux less than a critical value moreover uniformly subsonic flows always approach to uniform flows at far fields when nozzle boundaries tend to be flat at far fields and flow angles for axially symmetric flows are uniformly bounded away from 2 finally when the incoming mass flux tends to the critical value subsonic sonic flows exist globally in nozzles in the weak sense by using angle estimate in conjunction with a compensated compactness framework

transonic shock in a nozzle i 2d case in this paper we establish the existence and uniqueness of a transonic shock for the steady flow through a general two dimensional nozzle with variable sections the flow is governed by the inviscid potential equation and is supersonic upstream has no flow boundary conditions on the nozzle walls and an appropriate boundary condition at the exit of the exhaust section the transonic shock is a free boundary dividing two regions of c 1 1 0 flow in the nozzle the potential equation is hyperbolic upstream where the flow is supersonic and elliptic in the downstream subsonic region in particular our results show that there exists a solution to the corresponding free boundary problem such that the equation is always subsonic in the downstream region of the nozzle when the pressure in the exit of the exhaustion section is appropriately larger than that in the entry this problem is motivated by the conjecture of courant and friedrichs on the transonic phenomena in a nozzle 10 furthermore the stability of the transonic shock is also proven when the upstream supersonic flow is a small steady perturbation for the uniform supersonic flow and the corresponding pressure at the exit has a small perturbation the main ingredients of our analysis are a generalized hodograph transformation and multiplier methods for elliptic equation with mixed boundary conditions and comer singularities

performance of transform domain lms adaptive digital filters in this paper we analyze the performance particularly the convergence behavior of the transform domain least mean square lms adaptive digital filter adf using the discrete fourier transform and discrete orthogonal transforms such as discrete cosine and sine transforms we first obtain the optimum wiener solution and the minimum mean squared error mse in the transform domain it is shown that the two minimum mse s in the time and transform domains are identical independently of the transforms used we then study the convergence conditions and the steady state excess mse s of the transform domain lms trlms algorithms both for the cases of having a constant and a time varying convergence factors when a constant convergence factor is used the convergence behaviors of the lms and trlms adf s appear to be almost identical provided that each has an appropriate value of the convergence factor depending on the transform used also based on the concept of a self orthogonalizing algorithm in the transform domain it is shown that the convergence speed of the trlms adf can be improved significantly for the same excess mse as that of the lms adf in addition we compare the computational complexities of the lms and trlms adf s finally we investigate by computer simulation the effects of system parameter values and different transforms on the convergence behavior of the trlms adf

the conormal derivative problem for elliptic equations of variational type on considere des solutions du probleme qu 0 dans nu 0 sur ou est un domaine borne dans r n et q et n sont definis par qu x div a x u x du x b x u x du x x nu x a x u x du x x x x

two dimensional subsonic euler flows past a wall or a symmetric body the existence and uniqueness of two dimensional steady compressible euler flows past a wall or a symmetric body are established more precisely given positive convex horizontal velocity in the upstream there exists a critical value rho rm cr such that if the incoming density in the upstream is larger than rho rm cr then there exists a subsonic flow past a wall furthermore rho rm cr is critical in the sense that there is no such subsonic flow if the density of the incoming flow is less than rho rm cr the subsonic flows possess large vorticity and positive horizontal velocity above the wall except at the corner points on the boundary moreover the existence and uniqueness of a two dimensional subsonic euler flow past a symmetric body are also obtained when the incoming velocity field is a general small perturbation of a constant velocity field and the density of the incoming flow is larger than a critical value the asymptotic behavior of the flows is obtained with the aid of some integral estimates for the difference between the velocity field and its far field states

partial update lms algorithms partial updating of lms filter coefficients is an effective method for reducing computational load and power consumption in adaptive filter implementations this paper presents an analysis of convergence of the class of sequential partial update lms algorithms s lms under various assumptions and shows that divergence can be prevented by scheduling coefficient updates at random which we call the stochastic partial update lms algorithm spu lms specifically under the standard independence assumptions for wide sense stationary signals the s lms algorithm converges in the mean if the step size parameter spl mu is in the convergent range of ordinary lms relaxing the independence assumption it is shown that s lms and lms algorithms have the same sufficient conditions for exponential stability however there exist nonstationary signals for which the existing algorithms s lms included are unstable and do not converge for any value of spl mu on the other hand under broad conditions the spu lms algorithm remains stable for nonstationary signals expressions for convergence rate and steady state mean square error of spu lms are derived the theoretical results of this paper are validated and compared by simulation through numerical examples

a fast exact least mean square adaptive algorithm a general block formulation of the least mean square lms algorithm for adaptive filtering is presented this formulation has an exact equivalence with the original lms algorithm hence it retains its convergence properties while allowing a reduction in arithmetic complexity even for very small block lengths working with small block lengths is interesting from an implementation point of view large blocks result in large memory and large system delay and allows a significant reduction in the number of operations tradeoffs between a number of operations and a convergence rate are obtainable by applying certain approximations to a matrix involved in the algorithm hence the usual block lms appears as a special case which explains its convergence behavior according to the type of input signal correlated or uncorrelated

on two dimensional sonic subsonic flow a compensated compactness framework is established for sonic subsonic approximate solutions to the two dimensional euler equations for steady irrotational flows that may contain stagnation points only crude estimates are required for establishing compactness it follows that the set of subsonic irrotational solutions to the euler equations is compact thus flows with sonic points over an obstacle such as an airfoil may be realized as limits of sequences of strictly subsonic flows furthermore sonic subsonic flows may be constructed from approximate solutions the compactness framework is then extended to self similar solutions of the euler equations for unsteady irrotational flows

subsonic sonic limit of approximate solutions to multidimensional steady euler equations a compactness framework is established for approximate solutions to subsonic sonic flows governed by the steady full euler equations for compressible fluids in arbitrary dimension the existing compactness frameworks for the two dimensional irrotational case do not directly apply for the steady full euler equations in higher dimensions the new compactness framework we develop applies for both non homentropic and rotational flows one of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass balance and the vorticity along with the bernoulli law and the entropy relation through a more delicate analysis on the phase space as direct applications we establish two existence theorems for multidimensional subsonic sonic full euler flows through infinitely long nozzles

universality of the mean field for the potts model we consider the potts model with q colors on a sequence of weighted graphs with adjacency matrices a n allowing for both positive and negative weights under a mild regularity condition on a n we show that the mean field prediction for the log partition function is asymptotically correct whenever mathrm tr a n 2 o n in particular our results are applicable for the ising and the potts models on any sequence of graphs with average degree going to infty using this we establish the universality of the limiting log partition function of the ferromagnetic potts model for a sequence of asymptotically regular graphs and that of the ising model for bi regular bipartite graphs in both ferromagnetic and anti ferromagnetic domain we also derive a large deviation principle for the empirical measure of the colors for the potts model on asymptotically regular graphs

a roundoff error analysis of the lms adaptive algorithm the steady state output error of the least mean square lms adaptive algorithm due to the finite precision arithmetic of a digital processor is analyzed it is found to consist of three terms 1 the error due to the input data quantization 2 the error due to the rounding of the arithmetic operations in calculating the filter s output and 3 the error due to the deviation of the filter s coefficients from the values they take when infinite precision arithmetic is used the last term is of paricular interest because its mean squared value is inversely proportional to the adaptation step size both fixed and floating point arithmetics are examined and the expressions for the final mean square error are found to be similar the relation between the quantization error and the error that occurs when adaptation possibly ceases due to quantization is also investigated

nonlinear large deviations abstract we present a general technique for computing large deviations of nonlinear functions of independent bernoulli random variables the method is applied to compute the large deviation rate functions for subgraph counts in sparse random graphs previous technology based on szemeredi s regularity lemma works only for dense graphs applications are also made to exponential random graphs and three term arithmetic progressions in random sets of integers

on a weak solution for a transonic flow problem on essaie d etablir l existence de solutions faibles pour un ecoulement stationnaire bidimensionnel irrotationnel compressible non visqueux dans un canal de longueur infinie ou autour d un profil aerodynamique la vitesse de l ecoulement etant donnee a l infini

multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type we are concerned with the existence and stability of multidimensional transonic shocks for the euler equations for steady potential compressible fluids the euler equations consisting of the conservation law of mass and the bernoulli law for the velocity can be written as the following second order nonlinear equation of mixed elliptic hyperbolic type for the velocity potential r r 1 1 div d d 0 where the density function q is

steady subsonic ideal flows through an infinitely long nozzle with large vorticity in this paper the existence uniqueness and far field behavior of a class of subsonic flows with large vorticity for the steady euler equations in infinitely long nozzles are established more precisely for any given convex horizontal velocity of incoming flow in the upstream there exists a critical value mcr if the mass flux is larger than mcr then there exists a unique smooth subsonic euler flow through the infinitely long nozzle this well posedness result is proved by a new observation for the method developed in xie and xin siam j math anal 42 751 784 2010 to deal with the euler system furthermore the optimal convergence rates of the subsonic flows at far fields are obtained via the maximum principle and an elaborate choice of the comparison functions

existence of steady subsonic euler flows through infinitely long periodic nozzles abstract in this paper we study the global existence of steady subsonic euler flows through infinitely long nozzles which are periodic in x 1 direction with the period l it is shown that when the variation of bernoulli function at some given section is small and mass flux is in a suitable regime there exists a unique global subsonic flow in the nozzle furthermore the flow is also periodic in x 1 direction with the period l if in particular the bernoulli function is a constant we also get the existence of subsonic sonic flows when the mass flux takes the critical value

on a degenerate free boundary problem and continuous subsonic sonic flows in a convergent nozzle this paper concerns the well posedness of a boundary value problem for a quasilinear second order elliptic equation which is degenerate on a free boundary such problems arise when studying continuous subsonic sonic flows in a convergent nozzle with straight solid walls it is shown that for a given inlet being a perturbation of an arc centered at the vertex of the nozzle and a given incoming mass flux belonging to an open interval depending only on the adiabatic exponent and the length of the arc there is a unique continuous subsonic sonic flow from the given inlet with the angle of the velocity orthogonal to the inlet and the given incoming mass flux furthermore the sonic curve of this continuous subsonic sonic flow is a free boundary where the flow is singular in the sense that while the speed is c1 2 holder continuous at the sonic state the acceleration blows up at the sonic state

transonic shocks for the full compressible euler system in a general two dimensional de laval nozzle in this paper we study the transonic shock problem for the full compressible euler system in a general two dimensional de laval nozzle as proposed in courant and friedrichs supersonic flow and shock waves interscience new york 1948 given the appropriately large exit pressure pe x if the upstream flow is still supersonic behind the throat of the nozzle then at a certain place in the diverging part of the nozzle a shock front intervenes and the gas is compressed and slowed down to subsonic speed so that the position and the strength of the shock front are automatically adjusted such that the end pressure at the exit becomes pe x we solve this problem completely for a general class of de laval nozzles whose divergent parts are small and arbitrary perturbations of divergent angular domains for the full steady compressible euler system the problem can be reduced to solve a nonlinear free boundary value problem for a mixed hyperbolic elliptic system one of the key ingredients in the analysis is to solve a nonlinear free boundary value problem in a weighted holder space with low regularities for a second order quasilinear elliptic equation with a free parameter the position of the shock curve at one wall of the nozzle and non local terms involving the trace on the shock of the first order derivatives of the unknown function

running fir and iir filtering using multirate filter banks the computational complexity of running fir finite impulse response and iir infinite impulse response filtering using multirate filter banks is considered no restrictions are put on signal filter or block lengths it is shown how to map long running convolutions into smaller ones by using filter banks based on aperiodic convolution algorithms and short time fourier transforms with the proposed approach good tradeoffs among computational complexity system architecture and input output delay are achieved

three dimensional steady subsonic euler flows in bounded nozzles abstract the existence and uniqueness of three dimensional steady subsonic euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit if in addition the normal component of the voriticity and the variation of bernoulli s function at the entrance are both zero then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number as the magnitude of the normal component of the momentum approaches the critical number the associated flows converge to a subsonic sonic flow furthermore when the normal component of vorticity and the variation of bernoulli function are both small the existence and uniqueness of subsonic euler flows with non zero vorticity are established the proof of these results is based on a new formulation for the euler system a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions detailed study for a linear div curl system and delicate estimate for the transport equations

steady euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles abstract we establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets entropy waves for the steady euler equations for both compressible and incompressible fluids in arbitrary infinitely long nozzles we first develop a new approach to establish the existence of smooth solutions without assumptions on the sign of the second derivatives of the horizontal velocity or the bernoulli and entropy functions at the inlet for the smooth case then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheets entropy waves by nonlinear arguments this is the first result on the global existence of solutions of the multidimensional steady compressible full euler equations with free boundaries which are not necessarily small perturbations of piecewise constant background solutions the subsonic sonic limit of the solutions is also shown finally through the incompressible limit we establish the existence and uniqueness of incompressible euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheets the methods and techniques developed here will be useful for solving other problems involving similar difficulties

unconstrained frequency domain adaptive filter an unconstrained frequency domain least mean squares uflms algorithm is presented the algorithm is based on the overlap save technique used in frequency domain filtering the proposed algorithm converges to the wiener solution without the time domain constraint on the impulse response as proposed by ferrara for a large number of taps geq32 the uflms algorithm offers a significant reduction in computation another advantage is its fast convergence for highly correlated input signals the performance of the algorithm is illustrated by a simulation

subsonic flows in a multi dimensional nozzle in this paper we study the global subsonic irrotational flows in a multi dimensional n 2 infinitely long nozzle with variable cross sections the flow is described by the inviscid potential equation which is a second order quasilinear elliptic equation when the flow is subsonic first we prove the existence of the global uniformly subsonic flow in a general infinitely long nozzle for arbitrary dimension with sufficiently small incoming mass flux and obtain the uniqueness of the global uniformly subsonic flow then we show that there exists a critical value of the incoming mass flux such that a global uniformly subsonic flow exists uniquely provided that the incoming mass flux is less than the critical value this gives a positive answer to the problem of bers on global subsonic irrotational flows in infinitely long nozzles for arbitrary dimension bers in surveys in applied mathematics vol 3 wiley new york 1958 finally under suitable asymptotic assumptions of the nozzle we obtain the asymptotic behavior of the subsonic flow in far fields by means of a blow up argument the main ingredients of our analysis are methods of calculus of variations the moser iteration techniques for the potential equation and a blow up argument for infinitely long nozzles

a set of algorithms linking nlms and block rls algorithms this paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares nlms and the block recursive least squares brls algorithms all these algorithms use small block lengths thus allowing easy implementation and small input output delay it is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares lms algorithm while converging much faster a precise evaluation of the arithmetic complexity is provided and the adaptive behavior of the algorithm is analyzed simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the nlms algorithm the conclusions of the theoretical analysis are checked by simulations illustrating that even in the case where noise is added to the reference signal the proposed algorithm allows altogether a faster convergence and a lower residual error than the nlms algorithm finally a sample by sample version of this algorithm is outlined which is the link between the nlms and recursive least squares rls algorithms

factor models on locally tree like graphs we consider homogeneous factor models on uniformly sparse graph sequences converging locally to a unimodular random tree t and study the existence of the free energy density the limit of the log partition function divided by the number of vertices n as n tends to infinity we provide a new interpolation scheme and use it to prove existence of and to explicitly compute the quantity subject to uniqueness of a relevant gibbs measure for the factor model on t by way of example we compute for the independent set or hard core model at low fugacity for the ferromagnetic ising model at all parameter values and for the ferromagnetic potts model with both weak enough and strong enough interactions even beyond uniqueness regimes our interpolation provides useful explicit bounds on in the regimes in which we establish existence of the limit we show that it coincides with the bethe free energy functional evaluated at a suitable fixed point of the belief propagation bethe recursions on t in the special case that t has a galton watson law this formula coincides with the nonrigorous bethe prediction obtained by statistical physicists using the replica or cavity methods thus our work is a rigorous generalization of these heuristic calculations to the broader class of sparse graph sequences converging locally to trees we also provide a variational characterization for the bethe prediction in this general setting which is of independent interest

existence and optimal convergence rates of multi dimensional subsonic potential flows through an infinitely long nozzle with an obstacle inside in this paper the well posedness and optimal convergence rates of subsonic irrotational flows through a three dimensional infinitely long nozzle with a smooth obstacle inside are established more precisely the global existence and uniqueness of the uniformly subsonic flow are obtained via variational formulation as long as the incoming mass flux is less than a critical value furthermore with the aid of delicate choice of weight functions we prove the optimal convergence rates of the flow at far fields via weighted energy estimates and nash moser iteration

information theoretic thresholds from the cavity method abstract vindicating a sophisticated but non rigorous physics approach called the cavity method we establish a formula for the mutual information in statistical inference problems induced by random graphs and we show that the mutual information holds the key to understanding certain important phase transitions in random graph models we work out several concrete applications of these general results for instance we pinpoint the exact condensation phase transition in the potts antiferromagnet on the random graph thereby improving prior approximate results contucci et al 2013 34 further we prove the conjecture from krzakala et al 2007 55 about the condensation phase transition in the random graph coloring problem for any number q 3 of colors moreover we prove the conjecture on the information theoretic threshold in the disassortative stochastic block model decelle et al 2011 35 additionally our general result implies the conjectured formula for the mutual information in low density generator matrix codes montanari 2005 73