consistent estimation of non bandlimited spectral density from uniformly spaced samples in the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process irregular sampling schemes such as poisson sampling are often preferred over regular uniform sampling a major reason for this preference is the well known problem of inconsistency of estimators based on regular sampling when the underlying power spectral density is not bandlimited it is argued in this paper that in consideration of a large sample property like consistency it is natural to allow the sampling rate to go to infinity as the sample size goes to infinity through appropriate asymptotic calculations under this scenario it is shown that the smoothed periodogram based on regularly spaced data is a consistent estimator of the spectral density even when the latter is not band limited it transpires that under similar assumptions the estimators based on uniformly sampled and poisson sampled data have about the same rate of convergence apart from providing this reassuring message the paper also gives a guideline for practitioners regarding appropriate choice of the sampling rate theoretical calculations for large samples and monte carlo simulations for small samples indicate that the smoothed periodogram based on uniformly sampled data have less variance and more bias than its counterpart based on poisson sampled data

global existence of large solutions to initial boundary value problems for a viscous heat conducting one dimensional real gas abstract the existence of global classical solutions to initial boundary value problems in the dynamics of a one dimensional viscous heat conducting gas is established the nonlinear dissipative effects turn out to be sufficiently strong to prevent the development of singularities

global existence and large time behavior of solutions to the cauchy problem of one dimensional viscous radiative and reactive gas abstract in this paper we consider the global existence and large time behavior of solutions of one dimensional viscous radiative and reactive gas with large initial data in precedent studies the case for the initial boundary value problem in bounded domain has been investigated and our main purpose focuses on the corresponding problem in unbounded domain if the initial data is a large perturbation of a non vacuum constant equilibrium state and is assumed to be without vacuum mass concentrations or vanishing temperatures then we can show that its cauchy problem admits a unique global smooth non vacuum solution which tends time asymptotically to such an equilibrium state the key point in the analysis is to deduce the uniform positive lower and upper bounds on the specific volume and the absolute temperature

near optimal sensor placement for linear inverse problems a classic problem is the estimation of a set of parameters from measurements collected by only a few sensors the number of sensors is often limited by physical or economical constraints and their placement is of fundamental importance to obtain accurate estimates unfortunately the selection of the optimal sensor locations is intrinsically combinatorial and the available approximation algorithms are not guaranteed to generate good solutions in all cases of interest we propose framesense a greedy algorithm for the selection of optimal sensor locations the core cost function of the algorithm is the frame potential a scalar property of matrices that measures the orthogonality of its rows notably framesense is the first algorithm that is near optimal in terms of mean square error meaning that its solution is always guaranteed to be close to the optimal one moreover we show with an extensive set of numerical experiments that framesense achieves state of the art performance while having the lowest computational cost when compared to other greedy methods

mlps mono layer polynomials and multi layer perceptrons for nonlinear modeling this paper presents a model selection procedure which stresses the importance of the classic polynomial models as tools for evaluating the complexity of a given modeling problem and for removing non significant input variables if the complexity of the problem makes a neural network necessary the selection among neural candidates can be performed in two phases in an additive phase the most important one candidate neural networks with an increasing number of hidden neurons are trained the addition of hidden neurons is stopped when the effect of the round off errors becomes significant so that for instance confidence intervals cannot be accurately estimated this phase leads to a set of approved candidate networks in a subsequent subtractive phase a selection among approved networks is performed using statistical fisher tests the series of tests starts from a possibly too large unbiased network the full network and ends with the smallest unbiased network whose input variables and hidden neurons all have a significant contribution to the regression estimate this method was successfully tested against the real world regression problems proposed at the nips2000 unlabeled data supervised learning competition two of them are included here as illustrative examples

symmetric nonbarotropic flows with large data and forces we prove the global existence of weak solutions of the navier stokes equations of compressible nonbarotropic flow in three space dimensions with initial data and external forces which are large discontinuous and spherically or cylindrically symmetric the analysis allows for the possibility that a vacuum state emerges at the origin or axis of symmetry and the equations hold in the sense of distributions in the set where the density is positive in addition the mass and momentum equations hold weakly in the entire space time domain but with a nonstandard interpretation of the viscosity terms as distributions solutions are obtained as limits of solutions in annular regions between two balls or cylinders and the analysis allows for the possibility that energy is absorbed into the origin or axis and is lost in the limit as the inner radius goes to zero

an initial boundary value problem for screw pinches in plasma physics with temperature dependent viscosity coefficients abstract this paper is concerned with an initial boundary value problem for screw pinches arisen from plasma physics a global in time classical solution to this physically very important problem is shown to exist uniquely and converge exponentially to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent the main difficulties in the proof lie in the temperature dependent magnetic resistive coefficients induced by the magnetic field the initial data can be large if is sufficiently close to 1

sampling moments and reconstructing signals of finite rate of innovation shannon meets strang fix consider the problem of sampling signals which are not bandlimited but still have a finite number of degrees of freedom per unit of time such as for example nonuniform splines or piecewise polynomials and call the number of degrees of freedom per unit of time the rate of innovation classical sampling theory does not enable a perfect reconstruction of such signals since they are not bandlimited recently it was shown that by using an adequate sampling kernel and a sampling rate greater or equal to the rate of innovation it is possible to reconstruct such signals uniquely these sampling schemes however use kernels with infinite support and this leads to complex and potentially unstable reconstruction algorithms in this paper we show that many signals with a finite rate of innovation can be sampled and perfectly reconstructed using physically realizable kernels of compact support and a local reconstruction algorithm the class of kernels that we can use is very rich and includes functions satisfying strang fix conditions exponential splines and functions with rational fourier transform this last class of kernels is quite general and includes for instance any linear electric circuit we thus show with an example how to estimate a signal of finite rate of innovation at the output of an rc circuit the case of noisy measurements is also analyzed and we present a novel algorithm that reduces the effect of noise by oversampling

random sampling of deterministic signals statistical analysis of fourier transform estimates this paper considers the estimation of the fourier transform of continuous time deterministic signals from a finite number n of discrete time nonuniform observations we first extend the recent results mean and variance of tarczynski and allay by providing both distributional properties as well as rates of almost sure convergence for the simple random sampling scheme of tarczynski and allay the primary focus is to consider and investigate the properties of a class of stratified random sampling estimates we establish the statistical properties of the estimates including precise expressions and rate of convergence of the mean square errors we also establish the asymptotic normality of the estimates useful for confidence interval calculations further we optimize over the class of the estimates in order to obtain the best performance in particular we show that for functions with a first order continuous derivative the mean square estimation error decays precisely at the fast rate of 1 n sup 3 this rate is significantly higher than the rate of 1 n for simple random sampling estimates the analytical results are illustrated by numerical examples the effect of observation errors on the performance is also investigated

sampling signals with a finite rate of innovation on the sphere the state of the art in sampling theory now contains several theorems for signals that are non bandlimited for signals on the sphere however most theorems still require the assumptions of bandlimitedness in this work we show that a particular class of non bandlimited signals which have a finite rate of innovation can be exactly recovered using a finite number of samples we consider a sampling scheme where k weighted diracs are convolved with a kernel on the rotation group we prove that if the sampling kernel has a bandlimit l 2k then 2k 1 4k 1 1 equiangular samples are sufficient for exact reconstruction if the samples are uniformly distributed on the sphere we argue that the signal can be accurately reconstructed using 4k2 samples and validate our claim through numerical simulations to further reduce the number of samples required we design an optimal sampling kernel that achieves accurate reconstruction of the signal using only 3k samples the number of parameters of the weighted diracs in addition to weighted diracs we show that our results can be extended to sample diracs integrated along the azimuth finally we consider kernels with antipodal symmetry which are common in applications such as diffusion magnetic resonance imaging

estimation of fourier transform using alias free hybrid stratified sampling this paper proposes a novel method of estimating the fourier transform ft of deterministic continuous time signals from a finite number n of their samples taken from a fixed length observation window it uses alias free hybrid stratified sampling to probe the processed signal at a mixture of deterministic and random time instants the ft estimator specifically designed to work with this sampling scheme is unbiased consistent and fast converging it is shown that if the processed signal has continuous third derivative then the estimator s rate of uniform convergence in mean square is n 5 therefore in terms of frequency independent upper bounds on the ft estimation error the proposed approach significantly outperforms existing estimators that utilize alias free sampling such as total random stratified sampling and antithetical stratified whose rate of uniform convergence is n 1 it is proven here that n 1 is a guaranteed minimum rate for all stratified sampling based estimators satisfying four weak conditions formulated in this paper owing to the alias free nature of the sampling scheme no constraints are imposed on the spectral support of the processed signal or the frequency ranges for which the fourier transform is estimated

incomplete sampling series and the recovery of missing samples from oversampled band limited signals it is well known that a band limited oversampled signal is completely determined even if an arbitrary finite number of samples is lost it is shown that an alternative simple proof of this fact carries over to generalized sampling expansions more precisely it is shown that any finite number of missing samples can be recovered from the remaining ones in the case of generalized kramer sampling expansions if an appropriate oversampling constraint is satisfied the recovery can be accomplished either iteratively or noniteratively

field estimation from randomly located binary noisy sensors the estimation of bounded multivariate fields from 1 bit quantized and dithered noisy observations is considered we consider two models for random sensor deployment based on regular monte carlo simple random sampling and stratified sampling we propose linear estimators and for both sensors deployment methods we establish exact expressions for the bias and variance of the estimates including integrated mean square errors we show in particular that estimates of the field on the basis of stratified sensor locations always outperform estimates based on regular monte carlo sensor locations for both estimation schemes we also establish central limit theorems which can be used to compute the probability of events involving the estimates including confidence intervals

a practical bayesian framework for backpropagation networks a quantitative and practical bayesian framework is described for learning of mappings in feedforward networks the framework makes possible 1 objective comparisons between solutions using alternative network architectures 2 objective stopping rules for network pruning or growing procedures 3 objective choice of magnitude and type of weight decay terms or additive regularizers for penalizing large weights etc 4 a measure of the effective number of well determined parameters in a model 5 quantified estimates of the error bars on network parameters and on network output and 6 objective comparisons with alternative learning and interpolation models such as splines and radial basis functions the bayesian evidence automatically embodies occam s razor penalizing overflexible and overcomplex models the bayesian approach helps detect poor underlying assumptions in learning models for learning models well matched to a problem a good correlation between generalization ability and the bayesian evidence is obtained

global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain we consider the equations of a viscous polytropic ideal gas in the domain exterior to a ball in n n 2 or 3 and prove the global existence of spherically symmetric smooth solutions for large initial data with spherical symmetry the large time behavior of the solutions is also discussed to prove the existence we first study an approximate problem in a bounded annular domain and then obtain a priori estimates independent of the boundedness of the annular domain letting the diameter of the annular domain tend to infinity we get a global spherically symmetric solution as the limit

asymptotic behavior of compressible p th power newtonian fluid with large initial data abstract in this paper we study a large time behavior of the global spherically or cylindrically symmetric solutions in h 1 for the p th power compressible newtonian fluid in multi dimension with large initial data precisely if the initial data is spherically symmetric the space dimension can be taken not less than two on the other hand if the initial data is cylindrically symmetric the smallness of initial data is not needed the main concern of the present paper is to investigate the exponential decay rate of a solution toward the stationary solution as time goes to infinity we get the uniform positive lower and upper bounds of the density by using different methods

neural network uncertainty assessment using bayesian statistics a remote sensing application neural network nn techniques have proved successful for many regression problems in particular for remote sensing however uncertainty estimates are rarely provided in this article a bayesian technique to evaluate uncertainties of the nn parameters i e synaptic weights is first presented in contrast to more traditional approaches based on point estimation of the nn weights we assess uncertainties on such estimates to monitor the robustness of the nn model these theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature microwave surface emissivities and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land the weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs i e error bars and correlation structure of these errors such quantities are very important for evaluating any application of an nn model the uncertainties on the nn jacobians are then considered in the third part of this article used for regression fitting nn models can be used effectively to represent highly nonlinear multivariate functions in this situation most emphasis is put on estimating the output errors but almost no attention has been given to errors associated with the internal structure of the regression model the complex structure of dependency inside the nn is the essence of the model and assessing its quality coherency and physical character makes all the difference between a blackbox model with small output errors and a reliable robust and physically coherent model such dependency structures are described to the first order by the nn jacobians they indicate the sensitivity of one output with respect to the inputs of the model for given input data we use a monte carlo integration procedure to estimate the robustness of the nn jacobians a regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these jacobians robust and physically meaningful

oversampled a d conversion and error rate dependence of nonbandlimited signals with finite rate of innovation we study the problem of a d conversion and error rate dependence of a class of nonbandlimited signals with finite rate of innovation in particular we analyze a continuous periodic stream of diracs characterized by a finite set of time positions and weights previous research has only considered sampling of this type of signals ignoring the presence of quantization necessary for any practical implementation to this end we first define the concept of consistent reconstruction and introduce corresponding oversampling in both time and frequency high accuracy in a consistent reconstruction is achieved by enforcing the reconstructed signal to satisfy three sets of constraints related to low pass filtering quantization and the space of continuous periodic streams of diracs we provide two schemes to reconstruct the signal for the first one we prove that the estimation mean squared error of the time positions is o 1 r sub t sup 2 r sub f sup 3 where r sub t and r sub f are the oversampling ratios in time and frequency respectively for the second scheme it is experimentally observed that at the cost of higher complexity the estimation accuracy lowers to o 1 r sub t sup 2 r sub f sup 5 our experimental results show a clear advantage of consistent over nonconsistent reconstruction regarding the rate we consider a threshold crossing based scheme where as opposed to previous research both oversampling in time and in frequency influence the coding rate we compare the error rate behavior resulting on the one hand from increasing the oversampling in time and or frequency and on the other hand from decreasing the quantization stepsize

exact phase retrieval for a class of 2 d parametric signals we address the problem of two dimensional 2 d phase retrieval from magnitude of the fourier spectrum we consider 2 d signals that are characterized by first order difference equations which have a parametric representation in the fourier domain we show that under appropriate stability conditions such signals can be reconstructed uniquely from the fourier transform magnitude we formulate the phase retrieval problem as one of computing the parameters that uniquely determine the signal we show that the problem can be solved by employing the annihilating filter method particularly for the case when the parameters are distinct for the more general case of the repeating parameters the annihilating filter method is not applicable we circumvent the problem by employing the algebraically coupled matrix pencil acmp method in the noiseless measurement setup exact phase retrieval is possible we also establish a link between the proposed analysis and 2 d cepstrum in the noisy case we derive cramer rao lower bounds crlbs on the estimates of the parameters and present monte carlo performance analysis as a function of the noise level comparisons with state of the art techniques in terms of signal reconstruction accuracy show that the proposed technique outperforms the fienup and relaxed averaged alternating reflections raar algorithms in the presence of noise

perfect reconstruction formulas and bounds on aliasing error in sub nyquist nonuniform sampling of multiband signals we examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples this sampling scheme which has been studied previously has an interesting optimality property that uniform sampling lacks one can sample and reconstruct the class spl bscr spl fscr of multiband signals with spectral support spl fscr at rates arbitrarily close to the landau 1969 minimum rate equal to the lebesgue measure of spl fscr even when spl fscr does not tile r under translation using the conditions for exact reconstruction we derive an explicit reconstruction formula we compute bounds on the peak value and the energy of the aliasing error in the event that the input signal is band limited to the span of spl fscr the smallest interval containing spl fscr which is a bigger class than the valid signals spl bscr spl fscr band limited to spl fscr we also examine the performance of the reconstruction system when the input contains additive sample noise

sampling signals with finite rate of innovation the authors consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation examples of signals with a finite rate of innovation include streams of diracs e g the poisson process nonuniform splines and piecewise polynomials even though these signals are not bandlimited we show that they can be sampled uniformly at or above the rate of innovation using an appropriate kernel and then be perfectly reconstructed thus we prove sampling theorems for classes of signals and kernels that generalize the classic bandlimited and sinc kernel case in particular we show how to sample and reconstruct periodic and finite length streams of diracs nonuniform splines and piecewise polynomials using sinc and gaussian kernels for infinite length signals with finite local rate of innovation we show local sampling and reconstruction based on spline kernels the key in all constructions is to identify the innovative part of a signal e g time instants and weights of diracs using an annihilating or locator filter a device well known in spectral analysis and error correction coding this leads to standard computational procedures for solving the sampling problem which we show through experimental results applications of these new sampling results can be found in signal processing communications systems and biological systems

solutions in the large for the nonlinear hyperbolic conservation laws of gas dynamics the constraints under which a gas at a certain state will evolve can be given by three partial differential equations which express the conservation of momentum mass and energy in these equations a particular gas is defined by specifying the constitutive relation e e u s where e specific internal energy v specific volume and s specific entropy the energy function e in u s r describes a polytropic gas for the exponent y 1 and for this choice of e v s global weak solutions for bounded measurable data having finite total variation were given by nishida in lo here the following general existence theorem is obtained let e v s be any smooth one parameter family of energy functions such that at e 0 the energy is given by e v s in v s r it is proven that there exists a constant c independent of e such that if e total variation of the initial data c then there exists a global weak solution to the equations since any energy function can be connected to e v s by a smooth parameterization our results give an existence theorem for all the conservation laws of gas dynamics as a corollary we obtain an existence theorem of liu indiana univ math j 26 no 1 1977 for polytropic gases the main point in this argument is that the nonlinear functional used to make the glimm scheme converge depends only on properties of the equations at e 0 for general n x n systems of conservation laws this technique provides an alternate proof for the interaction estimates in glimm s 1965 paper the new result here is that certain interaction differences are bounded by e as well as by the approaching waves

effect of inter sample spacing constraint on spectrum estimation with irregular sampling a practical constraint that comes in the way of spectrum estimation of a continuous time stationary stochastic process is the minimum separation between successively observed samples of the process when the underlying process is not band limited sampling at any uniform rate leads to aliasing while certain stochastic sampling schemes including poisson process sampling are rendered infeasible by the constraint of minimum separation it is shown in this paper that subject to this constraint no point process sampling scheme is alias free for the class of all spectra it turns out that point process sampling under this constraint can be alias free for band limited spectra however the usual construction of a consistent spectrum estimator does not work in such a case simulations indicate that a commonly used estimator which is consistent in the absence of this constraint performs poorly when the constraint is present these results should help practitioners in rationalizing their expectations from point process sampling as far as spectrum estimation is concerned and motivate researchers to look for appropriate estimators of bandlimited spectra

fractional spectrum analysis for nonuniform sampling in the presence of clock jitter and timing offset this paper focuses on analyzing the fractional spectrum of nonuniform sampling which is affected by clock jitter and timing offset both cases of single channel and recurrent samplings with limited bandwidth in the fractional fourier domain are considered for which we study two types of discrete time fractional fourier transforms dtfrfts for the first type dtfrfts we perform their statistical analyses and meanwhile establish relationships between the fractional spectra of the input and output signals of non ideal single multi channel analog to digital converter such relationships indicate that the statistical mean of each fractional spectrum contains periodic replicas of the spectrum for the input signal and these replicas are particularly modulated by the characteristic function of the perturbations introduced by the clock jitter moreover we interpret the first type dtfrfts from the perspective of linear frequency modulation signal decomposition for nonuniform sampling the second type dtfrfts serve as approximate dtfrfts and they especially deal with the general situation when the nonuniform sampling instants are unknown to this end we study modified forms of the first type dtfrfts with known inputs in kernels based on which the statistical mean of the approximate fractional spectra for both cases are derived then we compensate the fractional spectrum bias with high accuracy by developing optimal filters that minimize the mean square error between the original and the compensated fractional spectra for both cases different from single channel sampling the compensation for recurrent sampling involves an additional step before optimal filtering which gives better accuracy simulation results show that the proposed methods outperform existing methods

the reconstruction of a band limited function and its fourier transform from a finite number of samples at arbitrary locations by singular value decomposition a method for the stable interpolation of a bandlimited function known at sample instants with arbitrary locations in the presence of noise is given singular value decomposition is used to provide a series expansion that in contrast to the method of sampling functions permits simple identification of vectors in the minimum norm space poorly represented in the sample values three methods miller regularization least squares estimation and maximum a posteriori estimation are given for obtaining regularized reconstructions when noise is present the singular value decomposition svd method is used to interrelate these methods examples illustrating the technique are given

spectral analysis of randomly sampled signals suppression of aliasing and sampler jitter nonuniform sampling can facilitate digital alias free signal processing dasp i e digital signal processing that is not affected by aliasing this paper presents two dasp approaches for spectrum estimation of continuous time signals the proposed algorithms named the weighted sample ws and weighted probability wp density functions respectively utilize random sampling to suppress aliasing both methods produce unbiased estimators of the signal spectrum to achieve this effect the computational procedure for each method has been suitably matched with the probability density function characterising the pseudorandom generators of the sampling instants both proposed methods are analyzed and the qualities of the estimators they produce have been compared with each other although none of the proposed spectrum estimators is universally better than the other one it has been shown that in practical cases the wp estimator produces generally smaller errors than those obtained from ws estimation a practical limitation of the approaches caused by the sampling instant jitter is also studied it has been proven that in the presence of jitter the theoretically infinite bandwidths of ws and wp signal analyses are limited the maximum frequency up to which these analyses can be performed is inversely proportional to the size of the jitter

symmetric flows for compressible heat conducting fluids with temperature dependent viscosity coefficients abstract we consider the navier stokes equations for compressible heat conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature a global in time spherically or cylindrically symmetric classical solution to the initial boundary value problem is shown to exist uniquely and converge exponentially to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent the initial data can be large if is sufficiently close to 1 these results are of nishida smoller type and extend the work liu et al 2014 16 restricted to the one dimensional flows

sampling designs for the detection of signals in noise sampling designs for the detection of sure signals in gaussian noise are considered both deterministic and random sampling schemes using optimal and nonoptimal detectors are presented and their performance is studied the analytical results are supplemented by comparison of performance for small and large sample size for some representative processes including the gauss markov and wiener processes

k space deep learning for accelerated mri the annihilating filter based low rank hankel matrix approach aloha is one of the state of the art compressed sensing approaches that directly interpolates the missing k space data using low rank hankel matrix completion the success of aloha is due to the concise signal representation in the k space domain thanks to the duality between structured low rankness in the k space domain and the image domain sparsity inspired by the recent mathematical discovery that links convolutional neural networks to hankel matrix decomposition using data driven framelet basis here we propose a fully data driven deep learning algorithm for k space interpolation our network can be also easily applied to non cartesian k space trajectories by simply adding an additional regridding layer extensive numerical experiments show that the proposed deep learning method consistently outperforms the existing image domain deep learning approaches

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

global spherically symmetric flows for a viscous radiative and reactive gas in an exterior domain abstract we consider the equations for a viscous compressible radiative and reactive gas pressure p r a 4 3 internal energy e c v a 4 over an unbounded exterior domain in r n where n 2 is the space dimension the existence uniqueness and large time behavior of global spherically symmetric solutions are established for large initial data the key point in the analysis is to deduce certain uniform a priori estimates on the solutions especially on lower and upper bounds of the specific volume and temperature

shapes from pixels continuous domain visual signals are usually captured as discrete digital images this operation is not invertible in general in the sense that the continuous domain signal cannot be exactly reconstructed based on the discrete image unless it satisfies certain constraints e g bandlimitedness in this paper we study the problem of recovering shape images with smooth boundaries from a set of samples thus the reconstructed image is constrained to regenerate the same samples consistency as well as forming a shape bilevel image we initially formulate the reconstruction technique by minimizing the shape perimeter over the set of consistent binary shapes next we relax the non convex shape constraint to transform the problem into minimizing the total variation over consistent non negative valued images we also introduce a requirement called reducibility that guarantees equivalence between the two problems we illustrate that the reducibility property effectively sets a requirement on the minimum sampling density we also evaluate the performance of the relaxed alternative in various numerical experiments

u invariant sampling and reconstruction in atomic spaces with multiple generators given a u invariant sampling scheme on a hilbert space h this paper characterizes atomic subspaces a of h such that every signal x a can be reconstructed from its generalized samples acquired with the u invariant sampling scheme if signal recovery is possible a linear filter is derived which reconstructs the signal from the samples moreover the paper gives necessary and sufficient conditions on a sequence of sampling functions such that it forms a pseudoframe or pseudo riesz basis for a given atomic subspace a

frequency domain analysis of signals with stochastic sampling times in nonuniform sampling nus signal amplitudes and time stamps are delivered in pairs several methods to compute an approximate fourier transform aft have appeared in literature and their posterior properties in terms of alias suppression and leakage have been addressed in this paper the sampling times are assumed to be generated by a stochastic process the main result gives the prior distribution of several afts expressed in terms of the true fourier transform and variants of the characteristic function of the sampling time distribution the result extends leakage and alias suppression with bias and variance terms due to nus specific sampling processes as described in literature are analyzed in detail the results are illustrated on simulated signals with particular focus to the implications for spectral estimation

cardinal interpolation a bayesian probability density for an interpolating function is developed and its desirable properties and practical potential are demonstrated this density has an often needed but previously unachieved property here called cardinal interpolation which ensures extrapolation to the density of the least squares linear model in particular the mean of the cardinal interpolation density is a smooth function that intersects given x y points and which extrapolates to their least squares line and the variance of this density is a smooth function that is zero at the point x values that increases with distance from the nearest point x value and that extrapolates to the well known quadratic variance function for the least squares line the new cardinal interpolation density is developed for gaussian radial basis interpolators using fully bayesian methods that optimize interpolator smoothness this optimization determines the basis function widths and yields an interpolating density that is non gaussian except for large magnitude x and which is therefore not the outcome of a gaussian process further new development shows that the salient property of extrapolation to the density of the least squares linear model can be achieved for more general approximating not just interpolating functions

the weight smoothing regularization of mlp for jacobian stabilization in an approximation problem with a neural network a low output root mean square error is not always a universal criterion we investigate problems where the jacobians first derivative of an output value with respect to an input value of the approximation model are needed and propose to add a quality criterion on these jacobians during the learning step more specifically we focus on the approximation of functionals spl ascr from a space of continuous functions discretized in practice to a scalar space in this case the approximation is confronted with the compensation phenomenon a lower contribution of one input can be compensated by a larger one of its neighboring inputs in this case profiles with respect to the input index of neural jacobians are very irregular instead of smooth then the approximation of spl ascr becomes an ill posed problem because many solutions can be chosen by the learning process we propose to introduce the smoothness of jacobian profiles as an a priori information via a regularization technique and develop a new and efficient learning algorithm called weight smoothing we assess the robustness of the weight smoothing algorithm by testing it on a real and complex problem stemming from meteorology the neural approximation of the forward model of radiative transfer equation in the atmosphere the stabilized jacobians of this model are then used in an inversion process to illustrate the improvement of the jacobians after weight smoothing

on a simplified compressible navier stokes equations with temperature dependent viscosity abstract we consider a simplified compressible navier stokes equations with cylindrical symmetry when viscosity coefficient and heat conductivity coefficient depend on temperature we obtain global existence of strong solution and vanishing shear viscosity limit to the initial boundary value problem in eulerian coordinates the analysis for the global existence is based on the assumption that const 0 1 c m c 1 m q for m 0 1 q m for the part of vanishing shear viscosity limit we require in addition that 1 c 1 m c 1 m in the paper the acceleration effect in one direction is neglected however we do not need any smallness assumption for the initial data

random sampling estimates of fourier transforms antithetical stratified monte carlo we estimate the fourier transform of continuous time signals on the basis of n discrete time nonuniform observations we introduce a class of antithetical stratified random sampling schemes and we obtain the performance of the corresponding estimates we show that when the underlying function f t has a continuous second order derivative the rate of mean square convergence is 1 n 5 which is considerably faster that the rate of 1 n 3 for stratified sampling and the rate of 1 n for standard monte carlo integration in addition we establish joint asymptotic normality for the real and imaginary parts of the estimate and give an explicit expression for the asymptotic covariance matrix the theoretical results are illustrated by examples for low pass and high pass signals