percolation processes in monomer polyatomic mixtures in this paper the percolation of mixtures of monomers and polyatomic species kk mers on a square lattice is studied by means of a finite size scaling analysis the critical exponents and the scaling collapsing of the fraction of percolating lattices are found a phase diagram separating a percolating from a non percolating region is determined the main features of the phase diagram are discussed in order to predict its evolution for larger kk mer sizes

on the relationship between robust minimum variance beamformers with probabilistic and worst case distortionless response constraints an interesting relationship between the probability constrained and worst case optimization based robust minimum variance mv beamformers has been discovered it is shown that both in the cases of circularly symmetric gaussian and worst case distributions of the steering vector mismatch the probability constrained robust mv beamforming problem can be tightly approximated as a convex second order cone programming socp problem the latter problem is mathematically equivalent to that resulting from the deterministic worst case approach and therefore probability constrained beamformers can be interpreted and implemented using their deterministic worst case counterparts however an important advantage of the developed probability constrained mv beamformers with respect to their standard worst case counterparts is that the former approaches enable to explicitly quantify the parameters of the uncertainty region in terms of the beamformer outage probability

random sequential addition a distribution function approach random sequential addition rsa of hard objects is an irreversible process defined by three rules objects are introduced on a surface or ad dimensional volume randomly and sequentially two objects cannot overlap and once inserted an object is clamped in its position the configurations generated by an rsa can be characterized in the macroscopic limit by a unique set of distribution functions and a density we show that these nonequilibrium rsa configurations can be described in a manner which in many respects parallels the usual statistical mechanical treatment of equilibrium configurations kirkwood salsburg like hierarchies for the distribution functions zero separation theorems diagrammatic expansions and approximate equations for the pair distribution function approximate descriptions valid for low to intermediate densities can be combined with exact results already derived for higher densities close to the jamming limit of the process similarities and differences between the equilibrium and the rsaconfigurations are emphasized finally the potential application of rsa processes to the study of glassy phases is discussed

long range geometrical correlations in two dimensional foams the statistical properties of two dimensional space filling random cellular structures foams or their dual random triangulations in statistical equilibrium are obtained by maximum entropy inference and topological simulations we show by maximum entropy inference that for a broad class of foams shell structured including three sided cell inclusions all two cell topological correlators aj k n average number of pairs of k cell and n cell at a topological distance j are linear in n and k the numbers of neighbours of the cells this generalizes a correlation known for neighbouring cells j d 1 which implies the linearity of aboav s relation between the total number of neighbours of the cells adjacent to a n neighboured cell andn our results verified by simulations also build up gauss s theorem for cellular structures any additional restriction in exploring local cell configurations besides the constraints of filling space at random will manifest itself through a deviation from linearity of the correlators aj k n and the aboav relation notably foams made of feynman diagrams have additional context dependent restrictions and their aboav relation is slightly curved it is essential that the local random variablen denotes the number of neighbours of the cell and not that of its sides whenever the two are different

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

the bandwidth performance of a two element adaptive array with tapped delay line processing the bandwidth performance of a two element adaptive array with a tapped delay line behind each element is examined it is shown how the number of taps and the delay between taps affect the bandwidth performance of the array an array with two weights and one delay behind each element is found to yield optimal performance equal to that obtained with continuous wave interference for any value of intertap delay between zero and t sub 90 b where t sub 90 is a quarter wavelength delay time and b is the fractional signal bandwidth delays less that t sub 90 yield optimal performance but result in large array weights delays larger than t sub 90 b yield suboptimal signal to interference plus noise ratio when each element has only two weights for delays between t sub 90 b and 4t sub 90 b the performance is suboptimal with only two taps but approaches the optimal if more taps are added to each element delays larger than t sub 90 b result in suboptimal performance regardless of the number of taps used

universal properties of voronoi tessellations of hard discs the authors describe a 2d mosaic obtained by the voronoi tessellation of a monosize assembly of discs at different packing fractions the experimental device hard discs moving on an air table produces for every packing fraction a succession of mosaics in statistical equilibrium which constitutes a statistical ensemble this ensemble is large enough for fluctuations from the most probable distributions to be negligible they use the maximum entropy principle to get the distribution of the polygons in 2d mosaics generated from an assembly of hard discs steric exclusion yields an extra conservation law which is sufficient to give a good agreement with the experimental data a similar behaviour in the six fold parameter seems to hold for other mosaics

shrinkage of covariance matrices for linear signal estimation using cross validation linear estimation of signals is often based on covariance matrices estimated from training which can perform poorly if the training data are limited and the estimated covariance matrices are ill conditioned shrinking the covariance matrix toward a scaled identity matrix can improve the robustness against the model uncertainty provided the shrinkage factor is appropriately chosen this paper introduces several cross validation schemes for choosing the shrinkage factors in applications where the covariance matrices are replaced with sample covariance matrices or constructed from least squares estimates of the linear model parameters for cases where the training and out of training data are identically distributed we derive leave one out cross validation loocv schemes that repeatedly split the training data with respect to time to determine the optimal shrinkage factors for either model fitting or signal estimation for cases where they are distributed differently we develop alternative loocv schemes that repeatedly split the out of training observations with respect to space we derive computationally efficient implementations of those schemes and provide examples to demonstrate their performance

the hamiltonian formalism of the dnls equation with a nonvanished boundary value the hamiltonian formalism of the derivative nonlinear schrodinger equation with a nonvanishing boundary value is developed by the standard procedure the action angle variables are given explicitly at the end of this work a galileo transformation is introduced to ensure that the conservative quantities obtained satisfy the hamiltonian equation

on the derivative nonlinear schro dinger equation abstract in this paper we discuss the cauchy problem for the derivative nonlinear schrodinger equation i t 2i x 2 0 0 x x where 0 under an explicit smallness condition of the initial data we prove the unique global existence of solutions to this problem in the usual sobolev spaces in the weighted sobolev spaces and in the schwartz class we describe the smoothing effect in detail furthermore for the data decaying exponentially at infinity we prove that the above equation has unique local solutions which are analytic in the space direction

a bayesian approach to robust adaptive beamforming an adaptive beamformer that is robust to uncertainty in source direction of arrival doa is derived using a bayesian approach the doa is assumed to be a discrete random variable with a known a priori probability density function pdf that reflects the level of uncertainty in the source doa the resulting beamformer is a weighted sum of minimum variance distortionless response mvdr beamformers pointed at a set of candidate doas where the relative contribution of each mvdr beamformer is determined from the a posteriori pdf of the doa conditioned on previously observed data a simple approximation to the a posteriori pdf results in a straightforward implementation performance of the approximate bayesian beamformer is compared with linearly constrained minimum variance lcmv beamformers and data driven approaches that attempt to estimate signal characteristics or the steering vector from the data

random cuts in binary mixtures of spheres three dimensional 3d disordered media may be studied by performing random planar cuts through the material and trying to go back to 3d geometry from two dimensional information we have studied from this point of view numerical packings of spheres of two sizes for which the radii of the spheres and the composition of the mixtures have been obtained from the cuts we have also studied the froths generated by the related laguerre voronoi tessellation of the packings and their cuts stereological relations in this specific frame are derived in both cases

towards statistical mechanics of a 2d random cellular structure using the methods of statistical mechanics the authors construct the partition function of a system of a large number of 2d cells that covers without pores or overlaps a flat surface each cell is defined by its position area perimeter and number of sides besides topological and space filling constraints they impose new ones regarding the energy and maximum area of the cells the entropy and free energy of the system are calculated and the mean values of the macroscopic parameters are determined in the equilibrium configuration the results are compared with experimental ones for soap froths and metallurgical aggregates

the voronoi tessellation generated from eigenvalues of complex random matrices the voronoi froth generated from eigenvalues of asymmetric complex random matrices is studied by numerical simulation it is more regular than the random voronoi froth irvf generated from a poisson process the existence of a unique tessellation called here random matrix voronoi froth rmvf follows from the universality of the distribution of eigenvalues which is also briefly commented on the geometrical and topological properties of the rmvf have been characterised an empirical and accurate distribution function is also proposed for the cell side length of a rvf deviations from the aboav weaire law are discussed their magnitude may be interpreted as a measure ofthe departure from an equilibrium structure in the frame of the statistical crystallography theory of rivier

a comment on rivier s maximum entropy method of statistical crystallography in the literature rivier s maximum entropy method was used to prove lewis law and a linear aboav s law in this paper we show that the functional forms of these two laws for a statistically equilibrated cellular network even if such a network really exists cannot be derived or proved by this method for example within the maximum entropy method we demonstrate that a quadratic aboav s or lewis s law is as probable as a linear one

global well posedness of the derivative nonlinear schrodinger equation with periodic boundary condition in h12 abstract we establish the global well posedness of the derivative nonlinear schrodinger equation with periodic boundary condition in the sobolev space h 1 2 provided that the mass of initial data is less than 4 this result matches the one by miao wu and xu and its recent mass threshold improvement by guo and wu in the non periodic setting below h 1 2 we show that the uniform continuity of the solution map on bounded subsets of h s does not hold for any gauge equivalent equation

random sequential adsorption of spheres of different sizes the random sequential adsorption of spheres selected from monodisperse binary and polydisperse distributions on a three dimensional substrate has been studied by computer simulations in the monodisperse case the adsorbed particle density algebraically approaches an asymptotic value of 0 384 0 001 according to feder s law feder j theor biol 87 1980 237 for the case of spheres of two different sizes the large sphere density approaches its asymptotic value exponentially while the small sphere density increases according to feder s law if the sphere radii ri are uniformly distributed over the range ra ri rb before testing for overlaps then the approach to the asymptotic density is algebraic but the effective exponent depends on the model parameter r rb ra

random sequential adsorption relationship to dead leaves and characterization of variability a new construction for the planar unbounded random sequential adsorption rsa model is presented which allows for a direct comparison with matheron s dead leaves model furthermore for the case of disks with random radii the problem of statistical determination of the proposal radius distribution is discussed finally second order characteristics related to the pair correlation function are suggested for describing the variability of the rsa disk systems

linear minimax regret estimation of deterministic parameters with bounded data uncertainties we develop a new linear estimator for estimating an unknown parameter vector x in a linear model in the presence of bounded data uncertainties the estimator is designed to minimize the worst case regret over all bounded data vectors namely the worst case difference between the mean squared error mse attainable using a linear estimator that does not know the true parameters x and the optimal mse attained using a linear estimator that knows x we demonstrate through several examples that the minimax regret estimator can significantly increase the performance over the conventional least squares estimator as well as several other least squares alternatives

quantitative description and numerical simulation of random microstructures of composites and their effective elastic moduli abstract a digital image processing technique is used for measurement of centroid coordinates of fibers with forthcoming estimation of statistical parameters and functions describing the stochastic structure of a real fiber composite comparative statistical analysis of the real and numerically simulated structure are performed accompanying of known methods of the generation of random configurations by the random shaking procedure allows creating of the most homogenized and mixed structures that do not depend on the initial protocol of particle generation we consider a linearly elastic composite medium which consists of a homogeneous matrix containing a statistically homogeneous set of ellipsoidal inclusions the multiparticle effective field method see for references buryachenko appl mech rev 2001a 54 1 47 based on the theory of functions of random variables and green s functions is used for demonstration of the dependence of effective elastic moduli of fiber composites on the radial distribution functions estimated from the real experimental data as well as from the ensembles generated by the method proposed

geometry of random sequential adsorption by sequentially adding line segments to a line or disks to a surface at random positions without overlaps we obtain configurations of the one and two dimensional random sequential adsorption rsa problem we have simulated the one and two dimensional problem with periodic boundary condition the one dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation in two dimensions the geometrical properties of the rsa configuration are discussed and in addition known results of the rsa process are reproduced various statistical distributions of the voronoi dirichlet vd network corresponding to the rsa disk configuration are analyzed in order to characterize pores in the rsa configuration we introduce circular holes there is a direct correspondence between vertices of the vd network and these holes and also between direct indirect geometrical neighbors and these holes the hole size distribution is found to be a parabola we also find general relations that connect the asymptotic behavior of the surface coverage the correlation function and the hole size distribution

a competitive mean squared error approach to beamforming we treat the problem of beamforming for signal estimation where the goal is to estimate a signal amplitude from a set of array observations conventional beamforming methods typically aim at maximizing the signal to interference plus noise ratio sinr however this does not guarantee a small mean squared error mse so that on average the resulting signal estimate can be far from the true signal here we consider strategies that attempt to minimize the mse between the estimated and unknown signal waveforms the methods we suggest all maximize the sinr but at the same time are designed to have good mse performance since the mse depends on the signal power which is unknown we develop competitive beamforming approaches that minimize a robust mse measure two design strategies are proposed minimax mse and minimax regret we demonstrate through numerical examples that the suggested minimax beamformers can outperform several existing standard and robust methods over a wide range of signal to noise ratio snr values finally we apply our techniques to subband beamforming and illustrate their advantage in estimating a wideband signal

random sequential adsorption with restructuring in two dimensions a modified version of the random sequential adsorption model for the deposition of spherical particles onto a plane is presented successive particles are added via randomly positioned vertical trajectories and if they do not stick to the plane at first contact follow the path of steepest descent on the previously deposited particles before being adsorbed all particles reaching a stable position in contact with three previously adsorbed particles are removed the limiting coverage is found to be 0 610 56 or 0 000 05 larger than that of the standard rsa model and is shown to be reached exponentially with the number of trials the size distribution of connected clusters of spheres is analysed and is found to exhibit an exponential decay for large cluster sizes

random sequential adsorption of polydisperse mixtures asymptotic kinetics and structure the authors study the asymptotic kinetics of the random sequential adsorption rsa of a mixture of particles with a continuous distribution of sizes their results provide further support for the idea that the power law exponent for the approach to the jamming limit is simply related to the number of degrees of freedom of the adsorbing species they also predict the behaviour of the mean radial distribution function in the asymptotic regime

minimax estimation of deterministic parameters in linear models with a random model matrix we consider the problem of estimating an unknown deterministic parameter vector in a linear model with a random model matrix with known second order statistics we first seek the linear estimator that minimizes the worst case mean squared error mse across all parameter vectors whose possibly weighted norm is bounded above we show that the minimax mse estimator can be found by solving a semidefinite programming problem and develop necessary and sufficient optimality conditions on the minimax mse estimator using these conditions we derive closed form expressions for the minimax mse estimator in some special cases we then demonstrate through examples that the minimax mse estimator can improve the performance over both a baysian approach and a least squares method we then consider the case in which the norm of the parameter vector is also bounded below since the minimax mse approach cannot account for a nonzero lower bound we consider in this case a minimax regret method in which we seek the estimator that minimizes the worst case difference between the mse attainable using a linear estimator that does not know the parameter vector and the optimal mse attained using a linear estimator that knows the parameter vector for analytical tractability we restrict our attention to the scalar case and develop a closed form expression for the minimax regret estimator

a competitive minimax approach to robust estimation of random parameters we consider the problem of estimating in the presence of model uncertainties a random vector x that is observed through a linear transformation h and corrupted by additive noise we first assume that both the covariance matrix of x and the transformation h are not completely specified and develop the linear estimator that minimizes the worst case mean squared error mse across all possible covariance matrices and transformations h in the region of uncertainty although the minimax approach has enjoyed widespread use in the design of robust methods we show that its performance is often unsatisfactory to improve the performance over the minimax mse estimator we develop a competitive minimax approach for the case where h is known but the covariance of x is subject to uncertainties and seek the linear estimator that minimizes the worst case regret namely the worst case difference between the mse attainable using a linear estimator ignorant of the signal covariance and the optimal mse attained using a linear estimator that knows the signal covariance the linear minimax regret estimator is shown to be equal to a minimum mse mmse estimator corresponding to a certain choice of signal covariance that depends explicitly on the uncertainty region we demonstrate through examples that the minimax regret approach can improve the performance over both the minimax mse approach and a plug in approach in which the estimator is chosen to be equal to the mmse estimator with an estimated covariance matrix replacing the true unknown covariance we then show that although the optimal minimax regret estimator in the case in which the signal and noise are jointly gaussian is nonlinear we often do not lose much by restricting attention to linear estimators

robust competitive estimation with signal and noise covariance uncertainties robust estimation of a random vector in a linear model in the presence of model uncertainties has been studied in several recent works while previous methods considered the case in which the uncertainty is in the signal covariance and possibly the model matrix but the noise covariance is assumed to be completely specified here we extend the results to the case where the noise statistics may also be subjected to uncertainties we propose several different approaches to robust estimation which differ in their assumptions on the given statistics in the first method we assume that the model matrix and both the signal and the noise covariance matrices are uncertain and develop a minimax mean squared error mse estimator that minimizes the worst case mse in the region of uncertainty the second strategy assumes that the model matrix is given and tries to uniformly approach the performance of the linear minimum mse estimator that knows the signal and noise covariances by minimizing a worst case regret measure the regret is defined as the difference or ratio between the mse attainable using a linear estimator ignorant of the signal and noise covariances and the minimum mse possible when the statistics are known as we show earlier solutions follow directly from our more general results however the approach taken here in developing the robust estimators is considerably simpler than previous methods

random sequential adsorption of lines and ellipses infinitely many lines of zero thickness may be adsorbed onto a plane without overlap and it is shown that the number of lines adsorbed should scale as 13 where is the number of adsorption trials per unit area of surface this is confirmed by numerical simulation the adsorption of ellipses with major and minor axes 2a 2b respectively is also studied the area coverage theta approaches its maximum value theta max as alpha as to infinity where alpha is typically 1 3 as b a decreases from unity theta max first increases to a maximum value 0 58 or 0 01 when b approximately 0 5 and then decreases a feature not noted in previous work

well posedness for a generalized derivative nonlinear schrodinger equation abstract we study the cauchy problem for a generalized derivative nonlinear schrodinger equation with the dirichlet boundary condition we establish the local well posedness results in the sobolev spaces h 1 and h 2 solutions are constructed as a limit of approximate solutions by a method independent of a compactness argument we also discuss the global existence of solutions in the energy space h 1

robustness of adaptive narrowband beamforming with respect to bandwidth this paper addresses the robustness of adaptive narrowband beamforming with respect to bandwidth based on the loss of performance in terms of signal to interference plus noise ratio sinr the criterion used by zatman to define a narrowband environment i e the ratio between the jammer plus noise covariance matrix and the noise eigenvalue is studied from the point of view of a loss of sinr after narrowband beamforming under non narrowband conditions using theoretical results about the eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency by lee it is shown that zatman s criterion can be interpreted as an upper bound on the sinr loss which is nearly reached under certain conditions that are specified

applicability of the lewis and aboav weaire laws to 2d and 3d cellular structures based on poisson partitions two and three dimensional networks of a columnar type are described which result from partitions based on poisson point distributions the metric and topological properties of such laminated poisson networks are derived and the applicability of the lewis and aboav weaire laws to them is tested the 2d poisson network contains cells with i or 4 i is the number of sides and both laws are obeyed the 3d poisson networks are of various types and have f or 6 f is the number of faces in a cell and f 14 in one particular type of 3d poisson network the two laws are again exactly obeyed in another type the laws show large deviations at low f but are asymptotically obeyed when f tends to infinite

global well posedness for schrodinger equation with derivative in h 1 2 r abstract in this paper we consider the cauchy problem of the cubic nonlinear schrodinger equation with derivative in h s r this equation was known to be the local well posedness for s 1 2 takaoka 1999 27 ill posedness for s 1 2 biagioni and linares 2001 1 etc and global well posedness for s 1 2 i team 2002 10 in this paper we show that it is global well posedness in the endpoint space h 1 2 r which remained open previously the main approach is the third generation i method combined with a new resonant decomposition technique the resonant decomposition is applied to control the singularity coming from the resonant interaction

on the correlation between sizes and shapes of cells in epithelial mosaics it is shown that lewis s empirical linear relationship between the average area of a cell and the number of its sides in two dimensional mosaics corresponds to maximal arbitrariness in the cellular distribution an expression for the distribution is given in the general case

scaling properties of three dimensional foams we obtain the scaling states of three dimensional soap foams by using equilibrium statistical mechanics techniques we consider a phase space where each bubble is characterized by its center of mass position volume surface and number of faces a gibbs entropy function is then defined and as done in standard statistical mechanics we obtain the probability density function defined in the phase space by maximizing the entropy subject to convenient constraints the froth is supposed to completely fill the available volume and we consider energy terms accounting for surface tension and the thermal energy of the gas inside the bubbles we find that the volume distribution presents an exponential decay with cell size and the correlation between cell volume and number of faces fits very well the available numerical data additional distribution functions and average values are also in good agreement with numerical simulations

pair correlation function in random sequential adsorption processes an analytical expression of the pair distribution function is derived for the car parking problem and for the random sequential adsorption of k mers onto a one dimensional lattice both on a lattice and in the continuum limit super exponential decay of the distribution function is observed a comparison of the spatial correlations with those at equilibrium demonstrates the influence of the irreversibility of the rsa process

a precise algorithm to detect voids in polydisperse circle packings computer simulations are the primary tool for studying polydisperse particle packings quanti tatively for the problem of packing n unequal circles in a larger container circle nothing is known a priori about the optimal packing i e the packing with the highest packing fraction simulations usually start from a random initial configuration with the aim to finish with a dense final packing unfortunately smaller circles often get stuck in trapped positions and prevent the rest of the packing from growing larger hence the knowledge of the structure of unoccupied areas or holes inside a packing is important to be able to move trapped circles into free circular places or voids a novel algorithm is proposed for detecting such voids in two dimensional arbitrary circle packings by a decomposition of the contact graph combined with a clever object jumping strategy and together with other heuristic methods like swaps and shifts this approach increases the packing fraction significantly its effectiveness for jumping across the maximally random jammed barrier mrj 0 8575 in the large n limit for small benchmark instances as well as for large problem sizes up to n 103 is demonstrated

simulations of aggregation in 2d a study of kinetics structure and topological properties abstract colloidal aggregation in 2d has been studied using off lattice simulations structural kinetic and topological properties these last using the voronoi construction have been analysed in diffusion limited cluster aggregation dlca and reaction limited cluster aggregation rlca the simulations show dynamic scaling of the cluster size distribution for large sizes and times it has been observed that when the system reaches dynamic scaling some topological properties become stationary furthermore kinetic and topological aspects are related among them

instability of solitary wave solutions for the nonlinear schrodinger equation of derivative type in degenerate case abstract we study the stability theory of solitary wave solutions for a type of derivative nonlinear schrodinger equation i t u x 2 u i u 2 x u b u 4 u 0 b 0 the equation has a two parameter family of solitary wave solutions of the form u c x t exp i t i c 2 x c t i 4 x c t c 2 d c x c t here c is some suitable function and 2 c 2 the stability in the frequency region of 2 c 2 for some 0 1 and the instability in the frequency region of 2 c 2 were proved by ohta 2014 recently in the endpoint case c 2 the instability of u c was proved by ning et al 2017 then the stability and instability region has been established except the degenerate case c 2 in this paper we address the problem and prove its instability in the degenerate case

purely nonlinear instability of standing waves with minimal energy we consider hamiltonian systems with u 1 symmetry we prove that in the generic situation the standing wave that has the minimal energy among all other standing waves is unstable in spite of the absence of linear instability essentially the instability is caused by higher algebraic degeneracy of the zero eigenvalue in the spectrum of the linearized system we apply our theory to the non

asymptotically optimal linear shrinkage of sample lmmse and mvdr filters conventional implementations of the linear minimum mean square lmmse and minimum variance distortionless response mvdr estimators rely on the sample matrix inversion smi technique i e on the sample covariance matrix scm this approach is optimal in the large sample size regime nonetheless in small sample size situations those sample estimators suffer a large performance degradation thus the aim of this paper is to propose corrections of these sample methods that counteract their performance degradation in the small sample size regime and keep their optimality in large sample size situations to this aim a twofold approach is proposed first shrinkage estimators are considered as they are known to be robust to the small sample size regime namely the proposed methods are based on shrinking the sample lmmse or sample mvdr filters towards a variously called matched filter or conventional bartlett beamformer in array processing second random matrix theory is used to obtain the optimal shrinkage factors for large filters the simulation results highlight that the proposed methods outperform the sample lmmse and mvdr also provided that the sample size is higher than the observation dimension they improve classical diagonal loading dl and ledoit wolf lw techniques which counteract the small sample size degradation by regularizing the scm finally compared to state of the art dl the proposed methods reduce the computational cost and the proposed shrinkage of the lmmse obtains performance gains

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

broadband beamforming using tdl form iir filters conventional broadband beamforming structures make use of finite impulse response fir filters in each channel large numbers of coefficients are required to retain the desired signal to interference plus noise ratio sinr performance as the operating bandwidth increases it has been proven that the optimal frequency dependent array weighting of broadband beamformers could be better approximated by infinite impulse response iir filters however some potential problems such as stability monitoring and sensitivity to quantization errors of the iir filters make the implementation of the iir beamformers difficult in this paper new broadband iir beamformers are proposed to solve these problems the main contributions of this paper include 1 the frost based and generalized sidelobe canceller gsc based broadband beamformers utilizing a kind of tapped delay line form tdl form iir filters are proposed 2 the combined recursive gauss newton rgn algorithm is designed to compute the feedforward and feedback weights in the frost based implementation and 3 in the gsc based structure the unconstrained rgn algorithm is customized for the tdl form iir filters in the adaptive beamforming part compared with the beamformer using direct form iir filters the new iir beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization while comparable sinr improvement over the conventional fir beamformer is achieved

consistent reduced rank lmmse estimation with a limited number of samples per observation dimension an improved construction of the optimal reduced rank linear minimum mean square error mmse estimator of a signal waveform of interest is derived that is consistent under a limited number of samples per filtering degree of freedom the new filter design generalizes traditional filter realizations based on directly replacing the theoretical covariance matrix by its sample estimate and being consistent when all dimensions in the model but the number of samples remain bounded our solution not only generalizes the conventional estimator but also turns out to appropriately characterize model mismatch constraints due to finite sample size limitations of fundamental importance in practical situations the proposed implementation results from a generalized consistent estimation of the set of mmse filter subspace coefficients on the reduced dimensional subspace results are based on the theory of the spectral analysis of large dimensional random matrices in particular we build on the analytical description of the asymptotic spectrum of sample covariance type matrices in the limiting regime defined as both the number of samples and the observation dimension grow without bound at the same rate as a result the proposed mmse signal waveform estimator is shown to present a superior mean square error performance under a finite sample size by avoiding the breakdown experienced as the selected rank increases

scaling properties of the number of random sequential adsorption iterations needed to generate saturated random packing the properties of the number of iterations in random sequential adsorption protocol needed to generate finite saturated random packing of spherically symmetric shapes were studied numerical results obtained for one two and three dimensional packings were supported by analytical calculations valid for any dimension d it has been shown that the number of iterations needed to generate finite saturated packing is subject to pareto distribution with exponent 1 1 d and the median of this distribution scales with packing size according to the power law characterized by exponent d obtained results can be used in designing effective random sequential adsorption simulations

packing of spheroids in three dimensional space by random sequential addition packings of spheroidal particles with semi axes of length a b b were generated by random sequential addition rsa simulations as the jamming limit is approached the volume fraction occupied by particles tends towards an asymptote which was determined as a function of aspect ratio this asymptote has a local minimum at spheres with local maxima at prolate spheroids and oblate values of agree with results from rsa simulations of sphere packings but lie below volume fractions obtained in simulations of near spheres packed under gravity volume fractions reported for simulations of spheroids packed under gravity vary widely when the aspect ratio is very large or small differences between these results and the predictions of rsa are discussed

monte carlo simulation of the percolation process caused by the random sequential adsorption of k mers on heterogeneous triangular lattices abstract mixed site bond percolation is studied for a random sequential adsorption process of k mers on heterogeneous lattices with variable connectivity by means of monte carlo simulation the percolation phase diagrams are built to render evidence about complex structures critical exponents are also calculated to show that the universality class corresponding to ordinary percolation in two dimensions is preserved

probability distribution function for the random sequential adsorption of hard disks abstract the distribution of the number of hard core objects deposited in a finite region through a random sequential adsorption process is analyzed three idealized model probability distributions for this problem are tested by comparing them with computer simulation distributions for the random sequential adsorption of hard disks on a flat surface a hypergeometric distribution where the effects of mutual exclusion between particles are incorporated by a coverage dependent effective volume per particle is shown to give best agreement with simulation results this effective volume is derived in terms of the fluctuations in the particle number finite size effects in the fluctuations are taken into account

robust adaptive beamforming for general rank signal models the performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment sources or sensor array this is especially true when the desired signal components are present in the beamformer training data snapshots because in this case the adaptive array performance is very sensitive to array and model imperfections the similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly but the training sample size is small we propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary type mismatches of the desired signal array response our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank one point source and higher rank scattered source fluctuating wavefront desired signal models the proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst case performance optimization simple closed form solutions to the considered robust adaptive beamforming problems are derived our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms while at the same time offer a significantly improved robustness and faster convergence rates

eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency the eigenstructures of common covariance matrices are identified for the general case of m closely spaced signals it is shown that the largest signal space eigenvalue is relatively insensitive to signal separation by contrast the ith largest eigenvalue is proportional to delta omega sup 2 i 1 or delta omega sup 4 i 1 where delta omega is a measure of signal separation therefore matrix conditioning degrades rapidly as signal separation is reduced it is also shown that the limiting eigenvectors have remarkably simple structures the results are very general and apply to planar far field direction finding problems involving almost arbitrary scenarios and also to time series analysis of sinusoids exponentials and other signals

a class of constrained adaptive beamforming algorithms based on uniform linear arrays a new class of adaptive beamforming algorithms is proposed based on a uniformly spaced linear array by constraining its weight vector to a specific conjugate symmetric form the method is applied to the well known reference signal based rsb beamformer and the linearly constrained minimum variance lcmv beamformer as two implementation examples the effect of the additional constraint is equivalent to adding a second step in the derived adaptive algorithm however a difference arises for the rsb case since no direction of arrival doa information of the desired signal is available which leads to a two stage structure for incorporating the imposed constraint compared to the traditional algorithms the proposed ones can achieve a faster convergence speed and a higher steady state output signal to interference plus noise ratio given the same stepsize

stable manifolds for all monic supercritical focusing nonlinear schrodinger equations in one dimension keywords critical schrodinger equation stable manifolds modulation theory spectral theory klein gordon equations non linear schrodinger blow up rate standing waves nonintegrable equations invariant manifolds stability theory solitary waves ground states instability reference epfl article 155183doi 10 1090 s0894 0347 06 00524 8 record created on 2010 11 19 modified on 2017 05 12

lattice free models of directed cell motility directed cell migration often occurs when individual cells move in response to an external chemical stimulus cells can respond by moving in either the direction of increasing chemoattraction or decreasing chemorepulsion concentration many previous models of directed cell migration use a lattice based framework where agents undergo a lattice based random walk and the direction of nearest neighbour motility events is biased in a preferred direction such lattice based models can lead to unrealistic configurations of agents since the agents always move on an artificial lattice structure which is never observed experimentally we present a lattice free model of directed cell migration that incorporates two key features first agents move on a continuous domain with the possibility that there is some preferred direction of motion second to be consistent with experimental observations we enforce a crowding mechanism so that motility events that would lead to agent overlap are not permitted we compare simulation data from the new lattice free model with a more traditional lattice based model to provide additional insight into the lattice free model we construct an approximate conservation statement which corresponds to a nonlinear advection diffusion equation in the continuum limit the solution of this mean field model compares well with averaged data from the individual based model

stability of bound states of hamiltonian pdes in the degenerate cases abstract we consider a hamiltonian systems which is invariant under a one parameter unitary group and give a criterion for the stability and instability of bound states for the degenerate case we apply our theorem to the single power nonlinear klein gordon equation and the double power nonlinear schrodinger equation

a priori estimates and weak solutions for the derivative nonlinear schrodinger equation on torus below h 1 2 abstract we propose a priori estimates for a weak solution to the derivative nonlinear schrodinger equation dnls on torus with small l 2 norm datum in low regularity sobolev spaces these estimates allow us to show the existence of solutions in h s t with some s 1 2 in a relatively weak sense furthermore we make some remarks on the error estimates arising from the finite dimensional approximation solutions of dnls using the fourier lesbesgue type as auxiliary spaces despite the fact that nahmod oh rey bellet and staffilani 12 have already seen them

equilibrium versus random sequential addition of dimers on a lattice the statistical mechanical properties of particles forming dimers are compared with the results obtained on a two dimensional lattice through a random sequential addition rsa experiment the relation between the most likely fraction of dimers filling the lattice at equilibrium in the disordered phase and the corresponding non equilibrium jamming limit attained through rsa is explored some implications relevant for the physics of the liquid state are also discussed

infinitely many solutions for a class of sublinear schrodinger equations with indefinite potentials in this paper we are concerned with qualitative properties of entire solutions to a schrodinger equation with sublinear nonlinearity and sign changing potentials our analysis considers three distinct cases and we establish sufficient conditions for the existence of infinitely many solutions

blind minimax estimation we consider the linear regression problem of estimating an unknown deterministic parameter vector based on measurements corrupted by colored gaussian noise we present and analyze blind minimax estimators bmes which consist of a bounded parameter set minimax estimator whose parameter set is itself estimated from measurements thus our approach does not require any prior assumption or knowledge and the proposed estimator can be applied to any linear regression problem we demonstrate analytically that the bmes strictly dominate the least squares ls estimator i e they achieve lower mean squared error mse for any value of the parameter vector both stein s estimator and its positive part correction can be derived within the blind minimax framework furthermore our approach can be readily extended to a wider class of estimation problems than stein s estimator which is defined only for white noise and nontransformed measurements we show through simulations that the bmes generally outperform previous extensions of stein s technique

robust mean squared error estimation in the presence of model uncertainties we consider the problem of estimating an unknown parameter vector x in a linear model that may be subject to uncertainties where the vector x is known to satisfy a weighted norm constraint we first assume that the model is known exactly and seek the linear estimator that minimizes the worst case mean squared error mse across all possible values of x we show that for an arbitrary choice of weighting the optimal minimax mse estimator can be formulated as a solution to a semidefinite programming problem sdp which can be solved very efficiently we then develop a closed form expression for the minimax mse estimator for a broad class of weighting matrices and show that it coincides with the shrunken estimator of mayer and willke with a specific choice of shrinkage factor that explicitly takes the prior information into account next we consider the case in which the model matrix is subject to uncertainties and seek the robust linear estimator that minimizes the worst case mse across all possible values of x and all possible values of the model matrix as we show the robust minimax mse estimator can also be formulated as a solution to an sdp finally we demonstrate through several examples that the minimax mse estimator can significantly increase the performance over the conventional least squares estimator and when the model matrix is subject to uncertainties the robust minimax mse estimator can lead to a considerable improvement in performance over the minimax mse estimator

a projection approach for robust adaptive beamforming it is well known that calibration errors can seriously degrade performance in adaptive arrays particularly when the input signal to noise ratio is large the effect is caused by the perturbation of the presumed steering vector from its optimal value although it is not as widely known similar degradation occurs in sampled matrix inversion processing when the covariance matrix is estimated while the desired signal is present in the snapshot data under these conditions performance loss is due to errors in the estimated covariance matrix and occurs even when the steering vector is known exactly in the paper a new method based of modification of the steering vector is proposed to overcome both the problems of perturbation and of sample covariance errors the method involves projection of the presumed steering vector onto the observed signal plus interference subspace an analysis is also presented illustrating that the sample covariance errors can be viewed as a particular type of perturbation error and a simple approximation is derived for the expected beamformer performance as a function of the number of data snapshots both analytical and experimental results are presented that illustrate the advantages of the proposed method

response vector constrained robust lcmv beamforming based on semidefinite programming although linearly constrained minimum variance lcmv beamforming is robust against imprecise target information it usually leads to relatively high sidelobe and distorted mainlobe which would induce a high false alarm probability to circumvent this problem this work devises a novel robust lcmv beamforming approach by utilizing response vector optimization it intends to find the optimal response vector in lieu of the all one response vector in traditional lcmv beamformer the proposed robust beamformer is first formulated as a nonconvex quadratically constrained quadratic programming problem and then transformed into a semidefinite programming problem which can be efficiently and exactly solved the proposed beamformer not only improves the performance in terms of signal to interference plus noise ratio substantially but also possesses low sidelobe and well maintained mainlobe moreover since the response vector is quite small in size the complexity of calculating the optimal response vector is negligible additionally the proposed beamformer is also extended to two dimensional space time adaptive processing simulation results are presented to demonstrate the superiority of the proposed approach

global solutions of the derivative schrodinger equation in a class of functions analytic in a strip lower bounds on the rate of decrease in time of a uniform radius of spatial analyticity for solutions of the derivative schrodinger equation are derived the bounds depend algebraically on time they are valid as long as the initial datum is of order one in l2 norm and satisfies suitable spatial decay requirements on the real axis

existence and uniqueness of solution for a generalized nonlinear derivative schrodinger equation in this work we study the well posedness for the initial value problem associated to a generalized derivative schrodinger equation for small size initial data in weighted sobolev space the techniques used include parabolic regularization method combined with sharp linear estimates an important point in our work is that the contraction principle is likely to fail but gives us inspiration to obtain certain uniform estimates that are crucial to obtain the main result to prove such uniform estimates we assume smallness on the initial data in weighted sobolev spaces

effect of packing method on the randomness of disc packings the randomness of disc packings generated by random sequential adsorption rsa random packing under gravity rpg and mason packing mp which gives a packing density close to that of the rsa packing has been analysed based on the delaunay tessellation and is evaluated at two levels i e the randomness at individual subunit level which relates to the construction of a triangle from a given edge length distribution and the randomness at network level which relates to the connection between triangles from a given triangle frequency distribution the delaunay tessellation itself is also analysed and its almost perfect randomness at the two levels is demonstrated which verifies the proposed approach and provides a random reference system for the present analysis it is found that i the construction of a triangle subunit is not random for the rsa mp and rpg packings with the degree of randomness decreasing from the rsa to mp and then to rpg packing ii the connection of triangular subunits in the network is almost perfectly random for the rsa packing acceptable for the mp packing and not good for the rpg packing packing method is an important factor governing the randomness of disc packings

random sequential adsorption series expansion and monte carlo simulation abstract random sequential adsorption is an irreversible surface deposition of extended objects in systems with continuous degrees of freedom coverage follows a power law t j ct where the exponent depends on the geometric shape symmetry of the objects lattice models give typically exponential saturation to jamming coverage we discuss how such function t can be computed by series expansions and analyzed with pade approximations we consider the applications of efficient monte carlo computer simulation method event driven method to random sequential adsorptions with high precision and at very long time scale

kinetics of random sequential parking on a line we study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line for the simplest fixed length parking distribution the model reduces to the known car parking problem and we present an alternate solution to this problem we also consider the general homogeneous case when the parking distribution varies asx 1 atx 1 with the lengthx of the filling interval we develop a scaling theory describing such mixture deposition processes and show that the scaled hole size distribution with xtz a scaling variable decays with the scaled mass as exp const 1 as we determine scaling exponentsz and and find that at large times the coverage t has a power law form 1 t t v with nonuniversal exponent 2 1 depending on the homogeneity index

instability of bound states for abstract nonlinear schrodinger equations abstract we study the instability of bound states for abstract nonlinear schrodinger equations we prove a new instability result for a borderline case between stability and instability we also reprove some known results in a unified way

random sequential addition of hard spheres in high euclidean dimensions sphere packings in high dimensions have been the subject of recent theoretical interest employing numerical and theoretical methods we investigate the structural characteristics of random sequential addition rsa of congruent spheres in d dimensional euclidean space mathbb r d in the infinite time or saturation limit for the first six space dimensions 1 ensuremath le d ensuremath le 6 specifically we determine the saturation density pair correlation function cumulative coordination number and the structure factor in each of these dimensions we find that for 2 ensuremath le d ensuremath le 6 the saturation density ensuremath phi s scales with dimension as ensuremath phi s c 1 2 d c 2 d 2 d where c 1 0 202 phantom rule 0 2em 0ex 048 and c 2 0 973 phantom rule 0 2em 0ex 872 we also show analytically that the same density scaling is expected to persist in the high dimensional limit albeit with different coefficients a byproduct of this high dimensional analysis is a relatively sharp lower bound on the saturation density for any d given by ensuremath phi s ensuremath ge d 2 1 ensuremath s 0 2 d 1 where s 0 0 1 is the structure factor at k 0 i e infinite wavelength number variance in the high dimensional limit we demonstrate that a pal asti type conjecture the saturation density in mathbb r d is equal to that of the one dimensional problem raised to the d th power cannot be true for rsa hyperspheres we show that the structure factor s k must be analytic at k 0 and that rsa packings for 1 ensuremath le d ensuremath le 6 are nearly hyperuniform consistent with the recent decorrelation principle we find that pair correlations markedly diminish as the space dimension increases up to six we also obtain kissing contact number statistics for saturated rsa configurations on the surface of a d dimensional sphere for dimensions 2 ensuremath le d ensuremath le 5 and compare to the maximal kissing numbers in these dimensions we determine the structure factor exactly for the related ghost rsa packing in mathbb r d and demonstrate that its distance from hyperuniformity increases as the space dimension increases approaching a constant asymptotic value of 1 2 our work has implications for the possible existence of disordered classical ground states for some continuous potentials in sufficiently high dimensions