the discontinuous enrichment method for medium frequency helmholtz problems with a spatially variable wavenumber numerical dispersion or what is often referred to as the pollution effect presents a challenge to an efficient finite element discretization of the helmholtz equation in the medium frequency regime to alleviate this effect and improve the unsatisfactory pre asymptotic convergence of the classical galerkin finite element method based on piecewise polynomial basis functions several discretization methods based on plane wave bases have been proposed among them is the discontinuous enrichment method that has been shown to offer superior performance to the classical galerkin finite element method for a number of constant wavenumber helmholtz problems and has also outperformed two representative methods that use plane waves the partition of unity and the ultra weak variation formulation methods in this paper the discontinuous enrichment method is extended to the variable wavenumber helmholtz equation to this effect the concept of enrichment functions based on free space solutions of the homogeneous form of the governing differential equation is enlarged to include free space solutions of approximations of this equation obtained in this case by successive taylor series expansions of the wavenumber around a reference point this leads to plane wave enrichment functions based on the piece wise constant approximation of the wavenumber and to airy wave enrichment functions several elements based on these enrichment functions are constructed and evaluated on benchmark problems modeling sound hard scattering by a disk submerged in an acoustic fluid where the speed of sound varies in space all these elements are shown to outperform by a substantial margin their continuous polynomial counterparts

scale free patterns at a saddle node bifurcation in a stochastic system we demonstrate that scale free patterns are observed in a spatially extended stochastic system whose deterministic part undergoes a saddle node bifurcation remarkably the scale free patterns appear only at a particular time in relaxation processes from a spatially homogeneous initial condition we characterize the scale free nature in terms of the spatial configuration of the exiting time from a marginal saddle where the pair annihilation of a saddle and a node occurs at the bifurcation point critical exponents associated with the scale free patterns are determined by numerical experiments

jamming at zero temperature and zero applied stress the epitome of disorder we have studied how two and three dimensional systems made up of particles interacting with finite range repulsive potentials jam i e develop a yield stress in a disordered state at zero temperature and zero applied stress at low packing fractions phi the system is not jammed and each particle can move without impediment from its neighbors for each configuration there is a unique jamming threshold phi c at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become nonzero the distribution of phi c values becomes narrower as the system size increases so that essentially all configurations jam at the same packing fraction in the thermodynamic limit this packing fraction corresponds to the previously measured value for random close packing in fact our results provide a well defined meaning for random close packing in terms of the fraction of all phase space with inherent structures that jam the jamming threshold point j occurring at zero temperature and applied stress and at the random close packing density has properties reminiscent of an ordinary critical point as point j is approached from higher packing fractions power law scaling is found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure shear modulus and excess number of overlapping neighbors moreover near point j certain quantities no longer self average suggesting the existence of a length scale that diverges at j however point j also differs from an ordinary critical point the scaling exponents do not depend on dimension but do depend on the interparticle potential finally as point j is approached from high packing fractions the density of vibrational states develops a large excess of low frequency modes indeed at point j the density of states is a constant all the way down to zero frequency all of these results suggest that point j is a point of maximal disorder and may control behavior in its vicinity perhaps even at the glass transition

the fourier version of the variational theory of complex rays for medium frequency acoustics the variational theory of complex rays vtcr is a wave based computational approach dedicated to the resolution of medium frequency problems it uses a variational formulation of the problem which enables one to use any type of shape function within the substructures provided that it satisfies the governing equation thus the solution can be approximated using plane waves which is very interesting in the medium frequency vibration domain and also leads to a strong convergence of the method in the previous works this was shown in the case of acoustic problems in which the amplitudes of the plane waves were calculated as wavebands in this paper we propose a new approximation of these amplitudes based on fourier series we show that this approach increases the robustness of the method makes it more efficient numerically and extends its applicability to somewhat higher frequencies

it formulae for gamma target mutual information and relative entropy in this paper we introduce new stein identities for gamma target distribution as well as a new non linear channel specifically designed for gamma inputs from these two ingredients we derive an explicit and simple formula for the derivative of the input output mutual information of this non linear channel with respect to the channel quality parameter this relation is reminiscent of the well known link between the derivative of the input output mutual information of additive gaussian noise channel with respect to the signal to noise ratio and the minimum mean square error the proof relies on a rescaled version of de bruijn identity for gamma target distribution together with a stochastic representation for the gamma specific fisher information finally we are able to derive precise bounds and asymptotics for the input output mutual information of the non linear channel with gamma inputs

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

bounds on the information rate of intertransition time restricted binary signaling over an awgn channel upper and lower bounds on the capacity of a continuous time additive white gaussian noise awgn channel with bilevel spl plusmn spl radic p input signals subjected to a minimum inter transition time t sub min constraint are derived the channel model and input constraints reflect basic features of certain magnetic recording systems the upper bounds are based on duncan s relation between the average mutual information in an awgn regime and the mean square error mse of an optimal causal estimator evaluation or upper bounding the mse of suboptimal causal estimators yields the desired upper bounds the lower bound is found by invoking the extended mrs gerber s lemma and asymptotic properties of the entropy of max entropic bipolar d k codes asymptotic results indicate that at low snr pt sub min n sub 0 with n sub 0 designating the noise one sided power spectral density the capacity tends to p n sub 0 nats per second nats s i e it equals the capacity in the simplest average power limited case at high snr the capacity in the simplest average power limited case at high snr the capacity behaves asymptotically as t sub min sup 1 ln snr ln snr nats s demonstrating the degradation relatively to t sub avg sup 1 lnsnr which is the asymptotic known behavior of the capacity with a bilevel average intertransition time t sub avg restricted channel input additional lower bounds are obtained by considering specific signaling formats such as pulsewidth modulation the effect of mild channel filtering on the lower bounds on capacity is also addressed and novel techniques to lower bound the capacity in this case are introduced

on trefftz and weak trefftz discontinuous galerkin approaches for medium frequency acoustics in this paper the wave approach called the variational theory of complex rays vtcr which was developed for medium frequency acoustics and vibrations is revisited as a discontinuous galerkin method extensions leading to a weak trefftz constraint are introduced this weak trefftz discontinuous galerkin approach enables hybrid fem vtcr strategies to be developed easily and paves the way for new computational techniques for the resolution of engineering problems this paper presents some of the fundamental properties of the approach which is illustrated by several numerical examples

mismatched estimation and relative entropy a random variable with distribution p is observed in gaussian noise and is estimated by a mismatched minimum mean square estimator that assumes that the distribution is q instead of p this paper shows that the integral over all signal to noise ratios snrs of the excess mean square estimation error incurred by the mismatched estimator is twice the relative entropy d p q in nats this representation of relative entropy can be generalized to nonreal valued random variables and can be particularized to give new general representations of mutual information in terms of conditional means inspired by the new representation we also propose a definition of free relative entropy which fills a gap in and is consistent with the literature on free probability

numerical integration of stochastic differential equations several numerical methods for treating stochastic differential equations are considered both the convergence in the mean square limit and the convergence of the moments is discussed and the generation of appropriate random numbers is treated the necessity of simulations at various time steps with an extrapolation to time step zero is emphasized and demonstrated by a simple example

relations between information and estimation in discrete time levy channels fundamental relations between information and estimation have been established in the literature for the discrete time gaussian and poisson channels in this paper we demonstrate that such relations hold for a much larger class of observation models we introduce the natural family of discrete time levy channels where the distribution of the output conditioned on the input is infinitely divisible for levy channels we establish new representations relating the mutual information between the channel input and output to an optimal expected estimation loss thereby unifying and considerably extending results from the gaussian and poisson settings we demonstrate the richness of our results by working out two examples of levy channels namely the gamma channel and the negative binomial channel with corresponding relations between information and estimation extensions to the setting of mismatched estimation are also presented

a new computational method for transient dynamics including the low and the medium frequency ranges this paper deals with a new computational method for transient dynamic analysis which enables one to cover both the low and medium frequency ranges this is a frequency approach in which the low frequency part is obtained through a classical technique while the medium frequency part is handled through the variational theory of complex rays vtcr initially introduced for vibrations preliminary examples are shown

the variational theory of complex rays an answer to the resolution of mid frequency 3d engineering problems the variational theory of complex rays vtrc is an approach to the simulation of mid frequency phenomena whose wavelengths are relatively small compared to the dimensions of the domain this is a wave based computational technique which involves a nonclassical variational formulation this paper focuses on the development of the approach for 3d engineering problems and shows that it is a mature technique illustrations are given to show the capabilities of this method

a class of discontinuous petrov galerkin methods part iv the optimal test norm and time harmonic wave propagation in 1d the phase error or the pollution effect in the finite element solution of wave propagation problems is a well known phenomenon that must be confronted when solving problems in the high frequency range this paper presents a new method with no phase errors for one dimensional 1d time harmonic wave propagation problems using new ideas that hold promise for the multidimensional case the method is constructed within the framework of the discontinuous petrov galerkin dpg method with optimal test functions we have previously shown that such methods select solutions that are the best possible approximations in an energy norm dual to any selected test space norm in this paper we advance by asking what is the optimal test space norm that achieves error reduction in a given energy norm this is answered in the specific case of the helmholtz equation with l 2 norm as the energy norm we obtain uniform stability with respect to the wave number we illustrate the method with a number of 1d numerical experiments using discontinuous piecewise polynomial hp spaces for the trial space and its corresponding optimal test functions computed approximately and locally a 1d theoretical stability analysis is also developed

a symmetric trefftz dg formulation based on a local boundary element method for the solution of the helmholtz equation a general symmetric trefftz discontinuous galerkin method is built for solving the helmholtz equation with piecewise constant coefficients the construction of the corresponding local solutions to the helmholtz equation is based on a boundary element method a series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters and more importantly its outstanding ability to reduce the instabilities known as the pollution effect in the literature on numerical simulations of long range wave propagation

a comparison of techniques for overcoming non uniqueness of boundary integral equations for the collocation partition of unity method in two dimensional acoustic scattering the partition of unity method has become an attractive approach for extending the allowable frequency range for wave simulations beyond that available using piecewise polynomial elements the non uniqueness of solution obtained from the conventional boundary integral equation cbie is well known the cbie derived through green s identities suffers from a problem of non uniqueness at certain characteristic frequencies two of the standard methods of overcoming this problem are the so called combined helmholtz integral equation formulation chief method and that of burton and miller the latter method introduces a hypersingular integral which may be treated in various ways in this paper we present the collocation partition of unity boundary element method pubem for the helmholtz problem and compare the performance of chief against a burton miller formulation regularised using the approach of li and huang

on mutual information likelihood ratios and estimation error for the additive gaussian channel this paper considers the model of an arbitrarily distributed signal x observed through an added independent white gaussian noise w y x w new relations between the minimal mean square error of the noncausal estimator and the likelihood ratio between y and w are derived this is followed by an extended version of a recently derived relation between the mutual information i x y and the minimal mean square error these results are applied to derive infinite dimensional versions of the fisher information and the de bruijn identity a comparison between the causal and noncausal estimation errors yields a restricted form of the logarithmic sobolev inequality the derivation of the results is based on the malliavin calculus

second order asymptotics of mutual information a formula for the second order expansion of the input output mutual information of multidimensional channels as the signal to noise ratio snr goes to zero is obtained while the additive noise is assumed to be gaussian we deal with very general classes of input and channel distributions as special cases these channel models include fading channels channels with random parameters and channels with almost gaussian noise when the channel is unknown at the receiver the second term in the asymptotic expansion depends not only on the covariance matrix of the input signal but also on the fourth mixed moments of its components the study of the second order asymptotics of mutual information finds application in the analysis of the bandwidth power tradeoff achieved by various signaling strategies in the wideband regime

finite element solution of the helmholtz equation with high wave number part ii the h p version of the fem in this paper which is part ii in a series of two the investigation of the galerkin finite element solution to the helmholtz equation is continued while part i contained results on the h version with piecewise linear approximation the present part deals with approximation spaces of order p ge 1 as in part i the results are presented on a one dimensional model problem with dirichlet robin boundary conditions in particular there are proven stability estimates both with respect to data of higher regularity and data that is bounded in lower norms the estimates are shown both for the continuous and the discrete spaces under consideration further there is proven a result on the phase difference between the exact and the galerkin finite element solutions for arbitrary p that had been previously conjectured from numerical experiments these results and further preparatory statements are then employed to show error estimates for the galerkin finite element method fem it becomes evident that the error estimate for higher approximation can with certain assumptions on the data be written in the same form as the piecewise linear case namely as the sum of the error of best approximation plus a pollution term that is of the order of the phase difference the paper is concluded with a numerical evaluation

a new entropy power inequality a strengthened version of shannon s entropy power inequality for the case where one of the random vectors involved is gaussian is proved in particular it is shown that if independent gaussian noise is added to an arbitrary multivariate random variable the entropy power of the resulting random variable is a concave function of the variance power of the added noise the strengthened inequality is shown to hold for the class of stable distributions

fading channels how perfect need perfect side information be the analysis of flat fading channels is often performed under the assumption that the additive noise is white and gaussian and that the receiver has precise knowledge of the realization of the fading process these assumptions imply the optimality of gaussian codebooks and of scaled nearest neighbor decoding here we study the robustness of this communication scheme with respect to errors in the estimation of the fading process we quantify the degradation in performance that results from such estimation errors and demonstrate the lack of robustness of this scheme for some situations we suggest the rule of thumb that in order to avoid degradation the estimation error should be negligible compared to the reciprocal of the signal to noise ratio snr

a least squares method for the helmholtz equation abstract we investigate the use of least squares methods to approximate the helmholtz equation the basis used in the discrete method consists of solutions of the helmholtz equation either consisting of plane waves or bessel functions on each element of a finite element grid unlike previous methods of this type we do not use polynomial based finite elements the use of small elements and relatively few basis functions per element allows us to prove convergence theorems for the method and to some extent control the conditioning of the resulting linear sy stem numerical results show the efficiency of the new method and suggest that it may be possible to obtain accurate results with a coarser grid than is usual for standard finite element methods

a galerkin least squares finite element method for the two dimensional helmholtz equation in this paper a galerkin least squares gls finite element method in which residuals in least squares form are added to the standard galerkin variational equation is developed to solve the helmholtz equation in two dimensions an important feature of gls methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes previous work has accomplished this for the one dimensional helmholtz equation using dispersion analysis in this paper the selection of the gls mesh parameter for two dimensions is considered and leads to elements that exhibit improved phase accuracy for any given direction of wave propagation an optimal gls mesh parameter is determined using two dimensional fourier analysis in general problems the direction of wave propagation will not be known a priori in this case an optimal gls parameter is found which reduces phase error for all possible wave vector orientations over elements the optimal gls parameters are derived for both consistent and lumped mass approximations several numerical examples are given and the results compared with those obtained from the galerkin method the extension of gls to higher order quadratic interpolations is also presented

critical phenomena in globally coupled excitable elements critical phenomena in globally coupled excitable elements are studied by focusing on a saddle node bifurcation at the collective level critical exponents that characterize divergent fluctuations of interspike intervals near the bifurcation are calculated theoretically the calculated values appear to be in good agreement with those determined by numerical experiments the relevance of our results to jamming transitions is also mentioned

mutual information relative entropy and estimation in the poisson channel let be a nonnegative random variable and let the conditional distribution of a random variable given be poisson for a parameter we identify a natural loss function such that 1 the derivative of the mutual information between and with respect to is equal to the minimum mean loss in estimating based on regardless of the distribution of 2 when is estimated based on by a mismatched estimator that would have minimized the expected loss had the integral over all values of of the excess mean loss is equal to the relative entropy between and for a continuous time setting where is a nonnegative stochastic process and the conditional law of given is that of a non homogeneous poisson process with intensity function under the same loss function 1 the minimum mean loss in causal filtering when is equal to the expected value of the minimum mean loss in noncausal filtering smoothing achieved with a channel whose parameter is uniformly distributed between 0 and bridging the two quantities is the mutual information between and 2 this relationship between the mean losses in causal and noncausal filtering holds also in the case where the filters employed are mismatched i e optimized assuming a law on which is not the true one bridging the two quantities in this case is the sum of the mutual information and the relative entropy between the true and the mismatched distribution of thus relative entropy quantifies the excess estimation loss due to mismatch in this setting these results are parallel to those recently found for the gaussian channel the i mmse relationship of guo the relative entropy and mismatched estimation relationship of verdu and the relationship between causal and noncasual mismatched estimation of weissman

a generalized finite element method for solving the helmholtz equation in two dimensions with minimal pollution when using the galerkin fem for solving the helmholtz equation in two dimensions the error of the corresponding solution differs substantially from the error of the best approximation and this effect increases with higher wave number k in this paper we will design a generalized finite element method gfem for the helmholtz equation such that the pollution effect is minimal

information estimation relationships over binomial and negative binomial models in recent years a number of new connections between information measures and estimation have been found under various models including predominantly gaussian and poisson models this paper develops similar results for the binomial and negative binomial models in particular it is shown that the derivative of the relative entropy and the derivative of the mutual information for the binomial and negative binomial models can be expressed through the expectation of closed form expressions that have conditional estimates as the main argument under mild conditions those derivatives take the form of an expected bregman divergence

functional properties of minimum mean square error and mutual information in addition to exploring its various regularity properties we show that the minimum mean square error mmse is a concave functional of the input output joint distribution in the case of additive gaussian noise the mmse is shown to be weakly continuous in the input distribution and lipschitz continuous with respect to the quadratic wasserstein distance for peak limited inputs regularity properties of mutual information are also obtained several applications to information theory and the central limit theorem are discussed

application of an ultra weak variational formulation of elliptic pdes to the two dimensional helmholtz problem a new technique to solve elliptic linear pdes called ultra weak variational formulation uwvf in this paper is introduced in b despres c r acad sci paris 318 1994 pp 939 944 this paper is devoted to an evaluation of the potentialities of this technique it is applied to a model wave problem the two dimensional helmholtz problem the new method is presented in three parts following the same style of presentation as the classical one of the finite elements method even though they are definitely conceptually different methods the first part is committed to the variational formulation and to the continuous problem the second part defines the discretization process using a galerkin procedure the third part actually studies the efficiency of the technique from the order of convergence point of view this is achieved using theoretical proofs and a series of numerical experiments in particular it is proven and shown the order of convergence is lower bounded by a linear function of the number of degrees of freedom an application to scattering problems is presented in a fourth part

residual free bubbles for the helmholtz equation the galerkin method enriched with residual free bubbles is considered for approximating the solution of the helmholtz equation two dimensional tests demonstrate the improvement over the standard galerkin method and the galerkin least squares method using piecewise bilinear interpolations

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

turbo space time processing to improve wireless channel capacity by deriving a generalized shannon capacity formula for multiple input multiple output rayleigh fading channels and by suggesting a layered space time architecture concept that attains a tight lower bound on the capacity achievable foschini see wireless pers commun vol 6 no 3 p 311 35 1998 has shown a potential enormous increase in the information capacity of a wireless system employing multiple element antenna arrays at both the transmitter and receiver the layered space time architecture allows signal processing complexity to grow linearly rather than exponentially with the promised capacity increase this paper includes two important contributions first we show that foschini s lower bound is in fact the shannon bound when the output signal to noise ratio snr of the space time processing in each layer is represented by the corresponding matched filter bound this proves the optimality of the layered space time concept second we present an embodiment of this concept for a coded system operating at a low average snr and in the presence of possible intersymbol interference this embodiment utilizes the already advanced space time filtering coding and turbo processing techniques to provide yet a practical solution to the processing needed performance results are provided for quasi static rayleigh fading channels with no channel estimation errors we see for the first time that the shannon capacity for wireless communications can be both increased by n times where n is the number of the antenna elements at the transmitter and receiver and achieved within about 3 db in average snr about 2 db of which is a loss due to the practical coding scheme we assume the layered space time processing itself is nearly information lossless

on information transfer by envelope constrained signals over the awgn channel using t e duncan s theorem 1970 on the relation between mutual information and the mean square error of the optimum causal estimator of a random signal in additive white gaussian noise awgn the maximum achievable information transfer over the awgn channel is derived with the random telegraph wave input the information transfer is bounded and symptotically determined for the wiener phase modulated process input at large signal to noise ratio snr both results are compared to the information transfer for the capacity achieving gauss markov input process for both the wiener phase modulated and the gauss markov processes the information transfer increases asymptotically as the square root of snr but for the random telegraph wave it increases only as its logarithm

equation of motion for interacting pulses we develop a systematic method of deriving the equation of motion for interacting fronts or pulses in one dimension the theory is applicable to both dissipative and dispersive systems in the case of the time dependent ginzburg landau equation which is a typical example of a dissipative system the front equation obtained is the same as has been obtained previously the pulse interaction is also derived for the korteweg char21 de vries equation emphasizing the difference between the cases with and without dissipative terms

the variational theory of complex rays a predictive tool for medium frequency vibrations abstract today the main numerical modeling techniques for the analysis of medium frequency vibrations are all based on finite element or boundary element approaches in order to represent small wavelength phenomena in complex structures such as car chassis satellites or ships these techniques require a huge number of degrees of freedom at least seven elements per wavelength are required to represent oscillating solutions in addition the solution obtained is highly sensitive to material properties and boundary conditions the use of high frequency approaches such as the statistical energy analysis sea or any of its improvements does not appear to be suitable for medium frequency vibrations the vibrational behavior becomes too smooth and in general the coupling loss factor cannot be calculated in a predictive way in this paper a new and multiscale approach to the calculation of the vibrations of elastic structures in the medium frequency range called the variational theory of complex rays is presented the feasibility and effectiveness of the method are demonstrated for structures made of plate assemblies several 3d examples are analyzed and compared to the results from a classical finite element approach and from a sea code this comparison shows that our method is able to predict the effective quantities at a very low numerical cost

theoretical analysis for critical fluctuations of relaxation trajectory near a saddle node bifurcation a langevin equation whose deterministic part undergoes a saddle node bifurcation is investigated theoretically it is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle node bifurcation point in the weak noise limit while the final value of the deterministic solution changes discontinuously at the point a systematic formulation for analyzing a path probability measure is constructed on the basis of a singular perturbation method in this formulation the critical nature turns out to originate from the neutrality of exiting time from a saddle point the theoretical calculation explains results of numerical simulations

analytic expressions for rate and cv of a type i neuron driven by white gaussian noise we study the one dimensional normal form of a saddle node system under the influence of additive gaussian white noise and a static bias current input parameter a model that can be looked upon as the simplest version of a type i neuron with stochastic input this is in contrast with the numerous studies devoted to the noise driven leaky integrate and fire neuron we focus on the firing rate and coefficient of variation cv of the interspike interval density for which scaling relations with respect to the input parameter and noise intensity are derived quadrature formulas for rate and cv are numerically evaluated and compared to numerical simulations of the system and to various approximation formulas obtained in different limiting cases of the model we also show that caution must be used to extend these results to the neuron model with multiplicative gaussian white noise the correspondence between the first passage time statistics for the saddle node model and the neuron model is obtained only in the stratonovich interpretation of the stochastic neuron model while previous results have focused only on the ito interpretation the correct stratonovich interpretation yields cvs that are still relatively high although smaller than in the ito interpretation it also produces certain qualitative differences especially at larger noise intensities our analysis provides useful relations for assessing the distance to threshold and the level of synaptic noise in real type i neurons from their firing statistics we also briefly discuss the effect of finite boundaries finite values of threshold and reset on the firing statistics

proper generalized decomposition applied to linear acoustic a new tool for broad band calculation the calculation of the acoustic response of systems in frequency bands is becoming increasingly important in simulation based engineering design this is particularly true in medium frequency bands where the response is very sensitive to the frequency some standard techniques for addressing these problems present a frequency dependent formulation and may involve fixed frequency calculations at many different frequencies in this paper we propose a new technique which combines the variational theory of complex rays vtcr with proper generalized decomposition pgd and does not require the resolution of acoustic problems at many frequencies in this approach the vtcr is used to find an approximate solution of a medium frequency acoustic problem using only a few degrees of freedom dofs then pgd is used to find a representation of the approximate solution which is separated between two variables the wave propagation direction and the frequency a relevant numerical example is used to present the strategy and illustrate its applicability for frequency band calculations

an mse based transfer chart for analyzing iterative decoding schemes using a gaussian approximation an alternative to extrinsic information transfer exit charts called mean square error mse charts that use a measure related to the mse instead of mutual information is proposed using the relationship between mutual information and minimum mean square error mmse for the additive white gaussian noise awgn channel a relationship between the rate of any code and the area under a plot of mmse versus signal to noise ratio snr is obtained when the a priori log likelihood ratio llr is from a binary input gaussian channel using this result a justification is provided for designing concatenated codes by matching the exit curves of the inner and outer decoder when the llrs are assumed to be gaussian which is also the typical assumption used for code design using exit charts even though the gaussian assumption is almost never true the results presented in this paper represent a step toward the analysis of iterative decoding schemes using a single parameter finally for the special case of awgn channel it is shown that any capacity achieving code has an exit curve that is a step function

a quasi optimal petrov galerkin method for helmholtz problem a petrov galerkin finite element formulation is introduced for helmholtz problem in two dimensions using polynomial weighting functions at each node of the mesh a global basis function for the weighting space is obtained adding to the bilinear c 0 lagrangian weighting function linear combinations of polynomial bubbles defined on a macroelement containing this node quasi optimal weighting functions with the same support of the corresponding global test functions are obtained after computing the coefficients of these linear combinations attending to optimality criteria this is done numerically through a simple preprocessing technique naturally applied to non uniform and unstructured meshes in particular for uniform mesh a quasi optimal interior stencil of the same order of the quasi stabilized finite element method stencil derived by babuska et al comput methods appl mech engrg 1995 128 325 359 is obtained numerical results are presented illustrating the great stability and accuracy of this formulation with uniform and non uniform meshes

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

element free galerkin solutions for helmholtz problems fomulation and numerical assessment of the pollution effect abstract the element free galerkin method efgm a particular case of the meshless methods is examined in its application to acoustic wave propagation addressed by the helmholtz equation dispersion and pollution effects two problems encountered by the classical numerical methods are reviewed numerical tests on two dimensional problems focus on the parameters governing the formulation of the efgm they also demonstrate that the efgm is affected by dispersion and pollution effects as well as fem but these effects are rather low showing that the efgm is a promising method

dispersion and pollution of the fem solution for the helmholtz equation in one two and three dimensions for high wave numbers the helmholtz equation suffers the so called pollution effect this effect is directly related to the dispersion a method to measure the dispersion on any numerical method related to the classical galerkin fem is presented this method does not require to compute the numerical solution of the problem and is extremely fast numerical results on the classical galerkin fem p method is compared to modified methods presented in the literature a study of the influence of the topology triangles is also carried out the efficiency of the different methods is compared the numerical results in two of the mesh and for square elements show that the high order elements control the dispersion well the most effective modified method is the qsfem 1 2 but it is also very complicated in the general setting the residual free bubble 3 4 is effective in one dimension but not in higher dimensions the least square method 1 5 approach lowers the dispersion but relatively little the results for triangular meshes show that the best topology is the criss cross pattern copyright 1999 john wiley sons ltd

extension of the variational theory of complex rays to shells for medium frequency vibrations a new approach to the calculation of vibrations of weakly damped elastic structures in the medium frequency range called the variational theory of complex rays vtcr is being developed here the extension of this theory to shells of relatively small curvature is considered numerical examples of structures made of plates and shells demonstrate the capabilities of the vtcr

the generalized finite element method an example of its implementation and illustration of its performance the generalized finite element method gfem was introduced in reference 1 as a combination of the standard fem and the partition of unity method the standard mapped polynomial finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data the geometry of the domain the loads and the boundary conditions the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and are pasted to the existing finite element basis to construct a conforming approximation the essential boundary conditions can be imposed exactly as in the standard fem adaptive numerical quadrature is used to ensure that the errors in integration do not affect the accuracy of the approximation this paper gives an example of how the gfem can be developed for the laplacian in domains with multiple elliptical voids and illustrates implementation issues and the superior accuracy of the gfem versus the standard fem copyright 2000 john wiley sons ltd

novel basis functions for the partition of unity boundary element method for helmholtz problems the bem is a popular technique for wave scattering problems given its inherent ability to deal with infinite domains in the last decade the partition of unity bem in which the approximation space is enriched with a linear combination of plane waves has been developed this significantly reduces the number of dofs required per wavelength it has been shown that the element ends are more susceptible to errors in the approximation than the mid element regions in this paper the authors propose that this is due to the use of a collocation approach in combination with a reduced order of continuity in the lagrangian shape function component of the basis functions it is demonstrated using numerical examples that choosing trigonometric shape functions rather than classical polynomial shape functions quadratic in this case provides accuracy benefits collocation schemes are investigated it is found that the somewhat arbitrary choice of collocating at equally spaced points about the surface of a scatterer is better than schemes based on the roots of polynomials or consideration of the fock domain

a multiscale finite element method for the helmholtz equation it is well known that when the standard galerkin method is applied to the helmholtz equation it exhibits an error in the wavenumber and the solution does not therefore preserve the phase characteristics of the exact solution improvements on the galerkin method including galerkin least squares gls methods have been proposed however these approaches rely on a dispersion analysis of the underlying difference stencils in order to reduce error in the solution in this paper we propose a multiscale finite element for the helmholtz equation the method employs a multiscale variational formulation which leads to a subgrid model in which subgrid scales are incorporated analytically through appropriate green s functions it is shown that entirely new and accurate methods emerge and that gls methods can be obtained as special cases of the more general subgrid model

fixed point smoothing of scalar diffusions ii the error of the optimal smoother the problem of fixed point smoothing of a scalar diffusion process consists of estimating the initial value of the process given its noisy measurements as a function of time an asymptotic expansion of the joint filtering smoothing conditional density function is constructed in the limit of small measurements noise the approximate optimal nonlinear fixed point smoother of part i siam j appl math 54 1994 pp 833 853 is rederived from the expansion a detailed analysis of the conditional mean square estimation error cmsee of the optimal fixed point smoother and of its leading order approximation is presented it is shown that if the initial error is small e g if asymptotically optimal filtering is used first the leading order approximation to the optimal smoother is three dimensional and thus simpler than the four dimensional extended kalman smoother furthermore nonlinear fixed point smoothing can reduce the cmsee relative to that of filtering by a factor of frac 1 2 within smoothin