a deterministic equivalent for the analysis of correlated mimo multiple access channels in this article novel deterministic equivalents for the stieltjes transform and the shannon transform of a class of large dimensional random matrices are provided these results are used to characterize the ergodic rate region of multiple antenna multiple access channels when each point to point propagation channel is modelled according to the kronecker model specifically an approximation of all rates achieved within the ergodic rate region is derived and an approximation of the linear precoders that achieve the boundary of the rate region as well as an iterative water filling algorithm to obtain these precoders are provided an original feature of this work is that the proposed deterministic equivalents are proved valid even for strong correlation patterns at both communication sides the above results are validated by monte carlo simulations

convergence of accelerated modulus based matrix splitting iteration methods for linear complementarity problem with an h matrix the theoretical analysis of the accelerated modulus based matrix splitting iteration methods for the solution of the large sparse linear complementarity problem is further studied the convergence conditions are presented by fully utilizing the h matrix property of the system matrix and the optimal iteration parameters in accelerated modulus based accelerated overrelaxation method are determined by minimizing the spectral radius of the iteration matrix numerical experiments further confirm the theoretical discussion and show that the proposed methods accelerate the convergence of the modulus based matrix splitting methods with less iteration steps and cpu time

robust estimates of covariance matrices in the large dimensional regime this paper studies the limiting behavior of a class of robust population covariance matrix estimators originally due to maronna in 1976 in the regime where both the number of available samples and the population size grow large using tools from random matrix theory we prove that for sample vectors made of independent entries having some moment conditions the difference between the sample covariance matrix and a scaled version of such robust estimator tends to zero in spectral norm almost surely this result can be applied to various statistical methods arising from random matrix theory that can be made robust without altering their first order behavior

on the capacity of block multiantenna channels in this paper we consider point to point multiantenna channels with certain block distributional symmetries that do not require the entries of the channel matrix to be either gaussian or independent or identically distributed a main contribution is a capacity theorem for these channels which might be regarded as a generalization of telatar s theorem 1999 which reduces the numerical optimization domain in the capacity computation with this information theoretic result and some free probability arguments we prove an asymptotic capacity theorem that in addition to reducing the optimization domain does not depend on the dimension of the channel matrix this theorem allows us to apply free probability techniques to numerically compute the asymptotic capacity of the channels under consideration these theorems provide a very efficient method for numerically approximating both the capacity and a capacity achieving input covariance matrix of certain channels

stability of travelling wave solutions for coupled surface and grain boundary motion we investigate the spectral stability of the travelling wave solution for the coupled motion of a free surface and grain boundary that arises in materials science in this problem a grain boundary which separates two materials that are identical except for their crystalline orientation evolves according to mean curvature at a triple junction this boundary meets the free surfaces of the two crystals which move according to surface diffusion the model is known to possess a unique travelling wave solution we study the linearization about the wave which necessarily includes a free boundary at the location of the triple junction this makes the analysis more complex than that of standard travelling waves and we discuss how existing theory applies in this context furthermore we compute numerically the associated point spectrum by restricting the problem to a finite computational domain with appropriate physical boundary conditions numerical results strongly suggest that the two dimensional wave is stable with respect to both two and three dimensional perturbations

an adaptive moving mesh method for forced curve shortening flow we propose a novel adaptive moving mesh method for the numerical solution of a forced curve shortening geometric evolution equation control of the mesh quality is obtained using a tangential mesh velocity derived from a mesh equidistribution principle where a positive adaptivity measure or monitor function is approximately equidistributed along the evolving curve central finite differences are used to discretize in space the governing evolution equation for the position vector and a second order implicit scheme is used for the temporal integration simulations are presented indicating the generation of meshes which resolve areas of high curvature and are of second order accuracy furthermore the new method delivers improved solution accuracy compared to the use of uniform arc length meshes

the inverse mean curvature flow and the riemannian penrose inequality let m be an asymptotically flat 3 manifold of nonnegative scalar curvature the riemannian penrose inequality states that the area of an outermost minimal surface n in m is bounded by the adm mass m according to the formula n 16 m 2 we develop a theory of weak solutions of the inverse mean curvature flow and employ it to prove this inequality for each connected component of n using geroch s monotonicity formula for the adm mass our method also proves positivity of bartnik s gravitational capacity by computing a positive lower bound for the mass purely in terms of local geometry

on the variational approximation of combined second and fourth order geometric evolution equations we present a variational formulation of combined motion by minus the laplacian of curvature and mean curvature flow as well as related flows the proposed scheme covers both the closed curve case and the case of curves that are connected via triple or quadruple junction points or intersect the external boundary on introducing a parametric finite element approximation we prove stability bounds and compare our scheme with existing approaches the presented scheme has very good properties with respect to the equidistribution of mesh points and if applicable area conservation

sum rate optimal precoding for multi cell large scale mimo uplink based on statistical csi we investigate the sum rate optimal precoding for the uplink of the multi cell large scale mimo systems specifically we focus on transmitter precoder design based only on the statistical channel state information csi we first consider the partial cooperation system where only the csi is shared among cells and its base station bs decodes its in cell users by treating out cell signals as colored gaussian noise we derive the ergodic sum rate and its deterministic approximation for the regime where both the number of total user antennas and the number of bs antennas are large we obtain the necessary conditions to maximize the deterministic approximation of the sum rate under the transmit power constraint based on which a gradient search algorithm is proposed to find the local optimal precoders furthermore a super cell system is also considered where users from all cells are jointly decoded the deterministic approximation to the sum rate and optimal precoder design for such systems are given numerical experiments show that the proposed precoders achieve significant performance gains over systems with no precoding compared with the existing precoding methods that require perfect csi the proposed precoders achieve similar sum rates and require only the statistical csi

eigenvalue distributions of sums and products of large random matrices via incremental matrix expansions this paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions a e d s of sums and products of large random matrices we show that the result can be derived directly as a consequence of two common assumptions and matches the results obtained from using and transforms in free probability theory we also give a direct derivation of the a e d of the sum of certain random matrices which are not free this is used to determine the asymptotic signal to interference ratio of a multiuser code division multiple access cdma system with a minimum mean square error linear receiver

a variational formulation of anisotropic geometric evolution equations in higher dimensions we present a novel variational formulation of fully anisotropic motion by surface diffusion and mean curvature flow in mathbb r d d 2 this new formulation leads to an unconditionally stable fully discrete parametric finite element approximation in the case d 2 or 3 the resulting scheme has very good properties with respect to the distribution of mesh points and if applicable volume conservation this is demonstrated by several numerical experiments for d 3 including regularized crystalline mean curvature flow and regularized crystalline surface diffusion

on slow fading mimo systems with nonseparable correlation in a frequency selective slow fading channel in a multiple input multiple output mimo system the channel matrix is of the form of a block matrix a method is proposed to calculate the limit of the eigenvalue distribution of block matrices if the size of the blocks tends to infinity asymptotic eigenvalue distribution of is also calculated where the entries of are jointly gaussian with a correlation of the form where is fixed and does not increase with the size of the matrix an operator valued free probability approach is used to achieve this goal using this method a system of equations is derived which can be solved numerically to compute the desired eigenvalue distribution

the capacity region of the gaussian multiple input multiple output broadcast channel the gaussian multiple input multiple output mimo broadcast channel bc is considered the dirty paper coding dpc rate region is shown to coincide with the capacity region to that end a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality to show that a superposition of gaussian codes is optimal for the degraded vector broadcast channel and that dpc is optimal for the nondegraded case furthermore the capacity region is characterized under a wide range of input constraints accounting as special cases for the total power and the per antenna power constraints

evolution equations for phase separation and ordering in binary alloys we explore two phenomenological approaches leading to systems of coupled cahn hilliard and cahn allen equations for describing the dynamics of systems which can undergo first order phase separation and order disorder transitions simultaneously starting from the same discrete lattice free energy function in the first approach a quasicontinuum limit is taken for this discrete energy and the evolution of the system is then assumed to be given by gradient flow in the second approach a discrete set of gradient flow evolution equations is derived for the lattice dynamics and a quasicontinuum limit is then taken we demonstrate in the context of bcc fe al binary alloys that it is important that variables be chosen that accommodate the variations in the average concentration as well as the underlying ordered structure of the possible coexistent phases only then will the two approaches lead to roughly the same continuum descriptions we conjecture that in general the number of variables necessary to describe the dynamics of such systems is equal ton 1 n 2 1 wheren 1 is given by the dimension of the span of the bases of the irreducible representations needed to describe the symmetry groups of the possible equilibrium phases andn 2 is the number of chemical components n 1 of these variables are nonconserved and the remaining are conserved and represent the average concentrations for the fe al alloys this implies a description of one conserved order parameter and one nonconserved order parameter the resultant description is given by a cahn hilliard equation coupled to a cahn allen equation via the lower order nonlinear terms the rough equivalence of the two phenomenological methods adds credibility to the validity of the resulting evolution equations a similar description should also be valid for alloy systems in which the structure of the competing phases is more complicated

limit of the smallest eigenvalue of a large dimensional sample covariance matrix in this paper the authors show that the smallest if p leq n or the p n 1 th smallest if p n eigenvalue of a sample covariance matrix of the form 1 n xx tends almost surely to the limit 1 sqrt y 2 as n rightarrow infty and p n rightarrow y in 0 infty where x is a p times n matrix with iid entries with mean zero variance 1 and fourth moment finite also as a by product it is shown that the almost sure limit of the largest eigenvalue is 1 sqrt y 2 a known result obtained by yin bai and krishnaiah the present approach gives a unified treatment for both the extreme eigenvalues of large sample covariance matrices

approximation of large bending isometries with discrete kirchhoff triangles we devise and analyze a simple numerical method for the approximation of large bending isometries the discretization employs a discrete kirchhoff triangle to deal with second order derivatives and convergence of discrete solutions to minimizers of the continuous formulation is proved unconditional stability and convergence of an iterative scheme for the computation of discrete minimizers that is based on a linearization of the isometry constraint is verified numerical experiments illustrate the performance of the proposed method

capacity scaling in mimo wireless systems under correlated fading previous studies have shown that single user systems employing n element antenna arrays at both the transmitter and the receiver can achieve a capacity proportional to n assuming independent rayleigh fading between antenna pairs we explore the capacity of dual antenna array systems under correlated fading via theoretical analysis and ray tracing simulations we derive and compare expressions for the asymptotic growth rate of capacity with n antennas for both independent and correlated fading cases the latter is derived under some assumptions about the scaling of the fading correlation structure in both cases the theoretic capacity growth is linear in n but the growth rate is 10 20 smaller in the presence of correlated fading we analyze our assumption of separable transmit receive correlations via simulations based on a ray tracing propagation model results show that empirical capacities converge to the limit capacity predicted from our asymptotic theory even at moderate n 16 we present results for both the cases when the transmitter does and does not know the channel realization

sinr statistics of correlated mimo linear receivers linear receivers offer a low complexity option for multiantenna communication systems therefore understanding the outage behavior of the corresponding sinr is important in a fading mobile environment in this paper we introduce a large deviation method valid nominally for a large number m of antennas which provides the probability density of the sinr of gaussian channel mimo minimum mean square error mmse and zero forcing zf receivers with arbitrary transmission power profiles and in the presence of receiver antenna correlations this approach extends the gaussian approximation of the sinr valid for large m asymptotically close to the center of the distribution to obtain the non gaussian tails of the distribution our methodology allows us to calculate the sinr distribution to next to leading order o 1 m and showcase the deviations from approximations that have appeared in the literature e g the gaussian or the generalized gamma distribution we also analytically evaluate the outage probability as well as the uncoded bit error rate we find that our approximation is quite accurate even for the smallest antenna arrays 2 2

duality achievable rates and sum rate capacity of gaussian mimo broadcast channels we consider a multiuser multiple input multiple output mimo gaussian broadcast channel bc where the transmitter and receivers have multiple antennas since the mimo bc is in general a nondegraded bc its capacity region remains an unsolved problem we establish a duality between what is termed the dirty paper achievable region the caire shamai see proc ieee int symp information theory washington dc june 2001 p 322 achievable region for the mimo bc and the capacity region of the mimo multiple access channel mac which is easy to compute using this duality we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the mimo bc we also show that the dirty paper achievable region achieves the sum rate capacity of the mimo bc by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the mimo bc

on affine plane curve evolution abstract an affine invariant curve evolution process is presented in this work the evolution studied is the affine analogue of the euclidean curve shortening flow evolution equations for both affine and euclidean invariants are developed an affine version of the classical euclidean isoperimetric inequality is proved this inequality is used to show that in the case of affine evolution of convex plane curves the affine isoperimetric ratio is a non decreasing function of time convergence of this affine isoperimetric ratio to the ellipse s value 8 2 as well as convergence in the hausdorff metric of the evolving curve to an ellipse is also proved

two step modulus based matrix splitting iteration method for a class of nonlinear complementarity problems abstract in this paper we reformulate the nonlinear complementarity problem as an implicit fixed point equation we establish a modulus based matrix splitting iteration method based on the implicit fixed point equation and prove its convergence theorem under suitable conditions furthermore we propose a two step modulus based matrix splitting iteration method which may achieve higher computing efficiency we can obtain many matrix splitting iteration methods by suitably choosing the matrix splittings and the parameters the proposed methods can be regarded as extensions of the methods for linear complementarity problem numerical experiments are presented to show the effectiveness of the proposed methods

variational discretization of axisymmetric curvature flows we present natural axisymmetric variants of schemes for curvature flows introduced earlier by the present authors and analyze them in detail although numerical methods for geometric flows have been used frequently in axisymmetric settings numerical analysis results so far are rare in this paper we present stability equidistribution existence and uniqueness results for the introduced approximations numerical computations show that these schemes are very efficient in computing numerical solutions of geometric flows as only a spatially one dimensional problem has to be solved the good mesh properties of the schemes also allow them to compute in very complex axisymmetric geometries

mmse analysis of certain large isometric random precoded systems linear precoding consists in multiplying by an n spl times k matrix a k dimensional vector obtained by serial to parallel conversion of a symbol sequence to be transmitted in this paper new tools borrowed from the so called free probability theory are introduced for the purpose of analyzing the performance of minimum mean square error mmse receivers for certain large random isometric precoded systems on fading channels the isometric condition represents the case of precoding matrices with orthonormal columns it is shown in this contribution that the signal to interference plus noise ratio sinr at the equalizer output converges almost surely to a deterministic value depending on the probability distribution of the channel coefficients when n spl rarr spl infin and k n spl rarr spl alpha spl les 1 these asymptotic results are used to analyze the impact of orthogonal spreading as well as to optimally balance the redundancy introduced between linear precoding versus classical convolutional coding while preserving a simple mmse equalization scheme at the receiver

no eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices let b n 1 n t n 1 2 x n x n t n 1 2 where x n is n times n with i i d complex standardized entries having finite fourth moment and t n 1 2 is a hermitian square root of the nonnegative definite hermitian matrix t n it is known that as n to infty if n n converges to a positive number and the empirical distribution of the eigenvalues of t n converges to a proper probability distribution then the empirical distribution of the eigenvalues of b n converges a s to a nonrandom limit in this paper we prove that under certain conditions on the eigenvalues of t n for any closed interval outside the support of the limit with probability 1 there will be no eigenvalues in this interval for all n sufficiently large

motion of multiple junctions a level set approach abstract a coupled level set method for the motion of multiple junctions is proposed the new method extends the hamilton jacobi level set formulation of osher and sethian it retains the feature of tracking fronts by following level sets and allows the specification of arbitrary velocities on each front the diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature dependent speed systems of reaction diffusion equations are shown to possess inherent properties which prohibit efficient numerical solutions when applied to curvature dependent motion

numerical simulation and linear well posedness analysis for a class of three phase boundary motion problems we investigate the linear well posedness for a class of three phase boundary motion problems and perform some numerical simulations in a typical model three phase boundaries evolve under certain evolution laws with specified normal velocities the boundaries meet at a triple junction with appropriate conditions applied a system of partial differential equations and algebraic equations pdae is proposed to describe the problems with reasonable assumptions all problems are shown to be well posed if all three boundaries evolve under the same evolution law for problems involving two or more evolution laws we show the well posedness case by case for some examples numerical simulations are performed for some examples

a deterministic equivalent for the analysis of non gaussian correlated mimo multiple access channels using large dimensional random matrix theory rmt we conduct mutual information analysis of a multiple input multiple output mimo multiple access channel mac our channel model reflects the characteristics in small cell networks where antenna correlations line of sight components and general type of fading distributions have to be included the mutual information expression can be expressed as functionals of the stieltjes transform through the so called shannon transform ideally if the stieltjes transform is known in the context of the large dimensional rmt then the problem is solved however it is difficult to derive the stieltjes transform of the considered channel models directly especially when the transmit correlation matrices are generally nonnegative definite and the channel entries are non gaussian to overcome this we use the generalized lindeberg principle to show that the stieltjes transforms of this class of random matrices with gaussian or non gaussian independent entries coincide in the large dimensional regime this result permits to derive the deterministic equivalents e g the stieltjes transform and the ergodic mutual information for non gaussian mimo channels from the known results developed for gaussian mimo channels as an application we determine the capacity achieving input covariance matrices for the mimo macs and prove that the capacity achieving input covariance matrices are asymptotically independent of the fading distribution

a convergent evolving finite element algorithm for mean curvature flow of closed surfaces a proof of convergence is given for semi and full discretizations of mean curvature flow of closed two dimensional surfaces the numerical method proposed and studied here combines evolving finite elements whose nodes determine the discrete surface like in dziuk s method and linearly implicit backward difference formulae for time integration the proposed method differs from dziuk s approach in that it discretizes huisken s evolution equations for the normal vector and mean curvature and uses these evolving geometric quantities in the velocity law projected to the finite element space this numerical method admits a convergence analysis in the case of finite elements of polynomial degree at least two and backward difference formulae of orders two to five the error analysis combines stability estimates and consistency estimates to yield optimal order h 1 norm error bounds for the computed surface position velocity normal vector and mean curvature the stability analysis is based on the matrix vector formulation of the finite element method and does not use geometric arguments the geometry enters only into the consistency estimates numerical experiments illustrate and complement the theoretical results

optimality of beamforming in fading mimo multiple access channels we consider the sum capacity of a multi input multi output mimo multiple access channel mac where the receiver has the perfect channel state information csi while the transmitters have either no or partial csi when the transmitters have partial csi it is in the form of either the covariance matrix of the channel or the mean matrix of the channel for the covariance feedback case we mainly consider physical models that result in single sided correlation structures for the mean feedback case we consider physical models that result in in phase received signals under these assumptions we analyze the mimo mac from three different viewpoints first we consider a finite sized system we show that the optimum transmit directions of each user are the eigenvectors of its own channel covariance and mean feedback matrices in the covariance and mean feedback models respectively also we find the conditions under which beamforming is optimal for all users second in the covariance feedback case we prove that the region where beamforming is optimal for all users gets larger with the addition of new users into the system in the mean feedback case we show through simulations that this is not necessarily true third we consider the asymptotic case where the number of users is large we show that in both no and partial csi cases beamforming is asymptotically optimal in particular in the case of no csi we show that a simple form of beamforming which may be characterized as an arbitrary antenna selection scheme achieves the sum capacity in the case of partial csi we show that beamforming in the direction of the strongest eigenvector of the channel feedback matrix achieves the sum capacity finally we generalize our covariance feedback results to double sided correlation structures in the appendix

on the affine heat equation for non convex curves 1998 american mathematical society first published in journal of the american mathematical society vol 11 no 3 july 1998 published by the american mathematical society

error analysis of finite element approximations of the inverse mean curvature flow arising from the general relativity this paper proposes and analyzes a finite element method for a nonlinear singular elliptic equation arising from the black hole theory in the general relativity the nonlinear equation which was derived and analyzed by huisken and ilmanen in j diff geom 59 353 437 represents a level set formulation for the inverse mean curvature flow describing the evolution of a hypersurface whose normal velocity equals the reciprocal of its mean curvature we first propose a finite element method for a regularized flow which involves a small parameter a rigorous analysis is presented to study well posedness and convergence of the scheme under certain mesh constraints and optimal rates of convergence are verified we then prove uniform convergence of the finite element solution to the unique weak solution of the nonlinear singular elliptic equation as the mesh size h and the regularization parameter both tend to zero computational results are provided to show the efficiency of the proposed finite element method and to numerically validate the jumping out phenomenon of the weak solution of the inverse mean curvature flow numerical studies are presented to evidence the existence of a polynomial scaling law between the mesh size h and the regularization parameter for optimal convergence of the proposed scheme finally a numerical convergence study for another approach recently proposed by r moser the inverse mean curvature flow and p harmonic functions preprint u bath 2005 for approximating the inverse mean curvature flow via p harmonic functions is also included

a multiphase field concept numerical simulations of moving phase boundaries and multiple junctions we present numerical simulations which support the formal asymptotic analysis relating a multiorder parameter allen cahn system to a multiphase interface problem with curvature dependent evolution of the interfaces and angle conditions at triple junctions within the gradient energy of the allen cahn system the normal to an interface between phases i and j is modeled by the irreducible representations u i nabla u j u j nabla u i u i nabla u j u j nabla u i where ui and uj are the ith and jth components of the vectorial order parameter bu in rz n in the vectorial case the dependence of the limiting surface tensions and mobilities on the bulk potentials of the allen cahn system is not given explicitly but in terms of all the n components of the planar stationary wave solutions one of the issues of this paper is to find bulk potentials which allow a rather easy access to the resulting surface tensions and mobilities we compare numerical computations for planar and circular phase bound

a parametric finite element method for fourth order geometric evolution equations we present a finite element approximation of motion by minus the laplacian of curvature and related flows the proposed scheme covers both the closed curve case and the case of curves that are connected via triple junctions on introducing a parametric finite element approximation we prove stability bounds and compare our scheme with existing approaches it turns out that the new scheme has very good properties with respect to area conservation and the equidistribution of mesh points we state also an extension of our scheme to willmore flow of curves and discuss possible further generalizations

a modified general modulus based matrix splitting method for linear complementarity problems of h matrices abstract in this paper we establish a modified general modulus based matrix splitting iteration method for solving the large sparse linear complementarity problems and present the convergence analysis when the system matrix is an h matrix our result always improves some existing ones in addition numerical examples are given to show the effectiveness of the new method

modeling cell movement and chemotaxis using pseudopod based feedback a computational framework is presented for the simulation of eukaryotic cell migration and chemotaxis an empirical pattern formation model based on a system of nonlinear reaction diffusion equations is approximated on an evolving cell boundary using an arbitrary lagrangian eulerian surface finite element method ale sfem the solution state is used to drive a mechanical model of the protrusive and retractive forces exerted on the cell boundary movement of the cell is achieved using a level set method results are presented for cell migration with and without chemotaxis the simulated behavior is compared with experimental results of migrating dictyostelium discoideum cells

two level schwarz method for solving variational inequality with nonlinear source terms in this paper we extend the two level schwarz method to solve the variational inequality problems with nonlinear source terms and establish a convergence theorem the method converges within finite steps with an appropriate initial point the numerical results show that the methods are efficient

preconditioning a class of fourth order problems by operator splitting we develop preconditioners for systems arising from finite element discretizations of parabolic problems which are fourth order in space we consider boundary conditions which yield a natural splitting of the discretized fourth order operator into two discrete linear second order elliptic operators and exploit this property in designing the preconditioners the underlying idea is that efficient methods and software to solve second order problems with optimal computational effort are widely available we propose symmetric and non symmetric preconditioners along with theory and numerical experiments they both document crucial properties of the preconditioners as well as their practical performance it is important to note that we neither need h s regularity s 1 of the continuous problem nor quasi uniform grids

fast reaction slow diffusion and curve shortening the reaction diffusion problem u 1 varepsilon delta u varepsilon 1 v n u quad u x 0 varepsilon g x quad partial n u 0 text on partial omega for a vector u x t varepsilon is considered in a domain omega in r m an asymptotic solution is constructed for varepsilon small it shows that at each x u tends quickly to a minimum of v u when v has several minima when u tends to a piecewise constant function boundary layer expansions are constructed around the resulting surfaces of discontinuity or fronts each front is found to move along its normal with a constant velocity determined by the discontinuity v in v across it when v 0 the front s normal velocity is varepsilon kappa where kappa is its mean curvature the motion of fronts in this manner is studied for arcs in the plane which are normal to partial omega at their endpoints and for fronts that are closed curves it is shown a front can shrink to a point in

eigen inference for energy estimation of multiple sources in this paper a new method is introduced to blindly estimate the transmit power of multiple signal sources in multiantenna fading channels when the number of sensing devices and the number of available samples are sufficiently large compared to the number of sources recent advances in the field of large dimensional random matrix theory are used that result in a simple and computationally efficient consistent estimator of the power of each source a criterion to determine the minimum number of sensors and the minimum number of samples required to achieve source separation is then introduced simulations are performed that corroborate the theoretical claims and show that the proposed power estimator largely outperforms alternative power inference techniques

a finite element method for surface diffusion the parametric case surface diffusion is a fourth order highly nonlinear geometric driven motion of a surface with normal velocity proportional to the surface laplacian of mean curvature we present a novel variational formulation for parametric surfaces with or without boundaries the method is semi implicit requires no explicit parametrization and yields a linear system of elliptic pde to solve at each time step we next develop a finite element method propose a schur complement approach to solve the resulting linear systems and show several significant simulations some with pinch off in finite time we introduce a mesh regularization algorithm which helps prevent mesh distortion and discuss the use of time and space adaptivity to increase accuracy while reducing complexity

finite element approximation of level set motion by powers of the mean curvature in this paper we study the level set formulations of certain geometric evolution equations from a numerical point of view specifically we consider the flow by powers greater than one of the mean curvature and the inverse mean curvature flow since the corresponding equations in level set form are quasilinear degenerate and especially possibly singular a regularization method is used in the literature to approximate these equations to overcome the singularities of the equations motivated by the paper 29 which studies the finite element approximation of inverse mean curvature flow we prove error estimates for the finite element approximation of the regularized equations for the flow by powers of the mean curvature we validate the rates with numerical examples additionally the regularization error in the rotational symmetric case for both flows is analyzed numerically all calculations are performed in the 2d case

a computational method for the coupled solution of reaction diffusion equations on evolving domains and manifolds in this paper we devise a moving mesh finite element method for the approximate solution of coupled bulk surface reaction diffusion equations on an evolving two dimensional domain fundamental to the success of the method is the robust generation of bulk and surface meshes for this purpose we use a novel moving mesh partial differential equation mmpde approach the developed method is applied to model problems with known analytical solutions these experiments indicate second order spatial and temporal accuracy coupled bulk surface problems occur frequently in many areas in particular in the modelling of eukaryotic cell migration and chemotaxis we apply the method to a model of the two way interaction of a migrating cell in a chemotactic field where the bulk region corresponds to the extracellular region and the surface to the cell membrane

cauchy noise loss for stochastic optimization of random matrix models via free deterministic equivalents abstract for random matrix models the parameter estimation based on the traditional likelihood functions is not straightforward in particular when we have only one sample matrix we introduce a new parameter optimization method for random matrix models which works even in such a case the method is based on the spectral distribution instead of the traditional likelihood in the method the cauchy noise has an essential role because the free deterministic equivalent which is a tool in free probability theory allows us to approximate the spectral distribution perturbed by cauchy noises by a smooth and accessible density function moreover we study an asymptotic property of determination gap which has a similar role as generalization gap besides we propose a new dimensionality recovery method for the signal plus noise model and experimentally demonstrate that it recovers the rank of the signal part even if the true rank is not small it is a simultaneous rank selection and parameter estimation procedure

linking anisotropic sharp and diffuse surface motion laws via gradient flows we compare four surface motion laws for sharp surfaces with their diffuse interface counterparts by means of gradient flows on corresponding energy functionals the energy functionals can be defined to give the same dependence on normal direction for the energy of sharp plane surfaces as for their diffuse counterparts the anisotropy of the kinetics can be incorporated into the inner product without affecting the energy functional

asymptotic and non asymptotic analysis of uplink sum rate for relay assisted mimo cellular systems we consider uplink relay assisted mimo cellular systems with multiple relays deployed in each cell that perform the amplify and forward operations we are interested in obtaining deterministic expressions for the ergodic sum rate of such systems we first consider the large mimo dimension scenario and obtain two asymptotic sum rate expressions corresponding to the cases of fixed number of users and large number of users respectively we then consider the case of arbitrary mimo dimension and large number of users and obtain an upper and lower bound that the sum rate lies in between with high probability the bounds are tight when the number of users is large both single cell and multi cell systems are considered where the latter assumes full base station cooperation numerical experiments show that these deterministic sum rate expressions match well with the monte carlo simulation results therefore they can be useful tools for the design and analysis of relay assisted mimo cellular systems

large system analysis of linear precoding in correlated miso broadcast channels under limited feedback in this paper we study the sum rate performance of zero forcing zf and regularized zf rzf precoding in large miso broadcast systems under the assumptions of imperfect channel state information at the transmitter and per user channel transmit correlation our analysis assumes that the number of transmit antennas m and the number of single antenna users k are large while their ratio remains bounded we derive deterministic approximations of the empirical signal to interference plus noise ratio sinr at the receivers which are tight as m k in the course of this derivation the per user channel correlation model requires the development of a novel deterministic equivalent of the empirical stieltjes transform of large dimensional random matrices with generalized variance profile the deterministic sinr approximations enable us to solve various practical optimization problems under sum rate maximization we derive 1 for rzf the optimal regularization parameter 2 for zf the optimal number of users 3 for zf and rzf the optimal power allocation scheme and 4 the optimal amount of feedback in large fdd tdd multiuser systems numerical simulations suggest that the deterministic approximations are accurate even for small m k

on the convergence of modulus based matrix splitting iteration methods for a class of nonlinear complementarity problems with h matrices abstract a class of modulus based iteration methods for the nonlinear complementarity problem are presented by reformulating the complementarity problem to an implicit fixed point equation in order to efficiently implement these methods practical iteration schemes based on matrix splitting and the choices of the parameters are presented and well studied moreover we extend the convergence theory from the h compatible splitting to h splitting when the matrix is an h matrix which results in more choices for the parameters numerical experiments are given to verify the theoretical results and illustrate the efficiency of the proposed methods

on the parametric finite element approximation of evolving hypersurfaces in r 3 we present a variational formulation of motion by minus the laplacian of curvature and mean curvature flow as well as related second and fourth order flows of a closed hypersurface in r 3 on introducing a parametric finite element approximation we prove stability bounds and compare our scheme with existing approaches the presented scheme has very good properties with respect to the distribution of mesh points and if applicable volume conservation

eliminating spurious velocities with a stable approximation of viscous incompressible two phase stokes flow abstract we present a parametric finite element approximation of two phase flow this free boundary problem is given by the stokes equations in the two phases which are coupled via jump conditions across the interface using a novel variational formulation for the interface evolution gives rise to a natural discretization of the mean curvature of the interface in addition the mesh quality of the parametric approximation of the interface does not deteriorate in general over time and an equidistribution property can be shown for a semidiscrete continuous in time variant of our scheme in two space dimensions moreover on using a simple xfem pressure space enrichment we obtain exact volume conservation for the two phase regions furthermore our fully discrete finite element approximation can be shown to be unconditionally stable we demonstrate the applicability of our method with some numerical results which in particular demonstrate that spurious velocities can be avoided in the classical test cases

on the capacity achieving covariance matrix for frequency selective mimo channels using the asymptotic approach in this contribution an algorithm for evaluating the capacity achieving input covariance matrices for frequency selective rayleigh mimo channels is proposed in contrast with the flat fading rayleigh case no closed form expressions for the eigenvectors of the optimum input covariance matrix are available classically both the eigenvectors and eigenvalues are computed numerically and the corresponding optimization algorithms remain computationally very demanding in this paper it is proposed to optimize w r t the input covariance matrix a large system approximation of the average mutual information derived by moustakas and simon the validity of this asymptotic approximation is clarified thanks to gaussian large random matrices methods it is shown that the approximation is a strictly concave function of the input covariance matrix and that the average mutual information evaluated at the argmax of the approximation is equal to the capacity of the channel up to a o 1 t term where t is the number of transmit antennas an algorithm based on an iterative waterfilling scheme is proposed to maximize the average mutual information approximation and its convergence studied numerical simulation results show that even for a moderate number of transmit and receive antennas the new approach provides the same results as direct maximization approaches of the average mutual information

finite element approximation of large bending isometries a finite element scheme for the approximation of large isometric deformations with minimal bending energy is devised and analyzed the convergence to a stationary point and energy decreasing property of an iterative algorithm for the numerical solution of the scheme is proved numerical experiments illustrate the performance of the iteration and show that the discretization leads to accurate approximations for large vertical loads and compressive boundary conditions

parametric approximation of isotropic and anisotropic elastic flow for closed and open curves deckelnick and dziuk math comput 78 266 645 671 2009 proved a stability bound for a continuous in time semidiscrete parametric finite element approximation of the elastic flow of closed curves in mathbb r d d geq2 we extend these ideas in considering an alternative finite element approximation of the same flow that retains some of the features of the formulations in barrett et al j comput phys 222 1 441 462 2007 siam j sci comput 31 1 225 253 2008 ima j numer anal 30 1 4 60 2010 in particular an equidistribution mesh property for this new approximation we obtain also a stability bound for a continuous in time semidiscrete scheme apart from the isotropic situation we also consider the case of an anisotropic elastic energy in addition to the evolution of closed curves we also consider the isotropic and anisotropic elastic flow of a single open curve in the plane and in higher codimension that satisfies various boundary conditions

finite element approximation of a phase field model for surface diffusion of voids in a stressed solid we consider a fully practical finite element approximation of the degenerate cahn hilliard equation with elasticity find the conserved order parameter theta x t in 1 1 and the displacement field underline u x t in bbb r 2 such that gamma frac partial theta partial t nabla cdot b theta nabla gamma delta theta gamma 1 psi theta tfrac 12 c theta cal c underline underline cal e underline u underline underline cal e underline u quad nabla cdot c theta cal c underline underline cal e underline u underline 0 subject to an initial condition theta 0 cdot in 1 1 on theta and boundary conditions on both equations here gamma in bbb r 0 is the interfacial parameter psi is a nonsmooth double well potential underline underline cal e is the symmetric strain tensor cal c is the possibly anisotropic elasticity tensor c s c 0 frac 12 1 c 0 1 s with c 0 gamma in bbb r 0 and b s 1 s 2 is the degenerate diffusion mobility in addition to showing stability bounds for our approximation we prove convergence and hence existence of a solution to this nonlinear degenerate parabolic system in two space dimensions finally some numerical experiments are presented

an algorithm for evolutionary surfaces an algorithm is presented which allows to split the calculation of the mean curvature flow of surfaces with or without boundary into a series of poisson problems on a series of surfaces this gives a new method to solve plateau s problem forh surfaces

on the capacity achieving covariance matrix for rician mimo channels an asymptotic approach in this paper the capacity achieving input covariance matrices for coherent block fading correlated multiple input multiple output mimo rician channels are determined in contrast with the rayleigh and uncorrelated rician cases no closed form expressions for the eigenvectors of the optimum input covariance matrix are available classically both the eigenvectors and eigenvalues are computed numerically and the corresponding optimization algorithms remain computationally very demanding in the asymptotic regime where the number of transmit and receive antennas converge to infinity at the same rate new results related to the accuracy of the approximation of the average mutual information are provided based on the accuracy of this approximation an attractive optimization algorithm is proposed and analyzed this algorithm is shown to yield an effective way to compute the capacity achieving matrix for the average mutual information and numerical simulation results show that even for a moderate number of transmit and receive antennas the new approach provides the same results as direct maximization approaches of the average mutual information

mimo channel modeling and the principle of maximum entropy we devise theoretical grounds for constructing channel models for multiple input multiple output mimo systems based on information theoretic tools the paper provides a general method to derive a channel model which is consistent with one s state of knowledge the framework we give here has already been fruitfully explored with success in the context of bayesian spectrum analysis and parameter estimation for each channel model we conduct an asymptotic analysis in the number of antennas of the achievable transmission rate using tools from random matrix theory a central limit theorem is provided on the asymptotic behavior of the mutual information and validated in the finite case by simulations the results are useful both in terms of designing a system based on criteria such as quality of service and in optimizing transmissions in multiuser networks

on the convergence analysis of two step modulus based matrix splitting iteration method for linear complementarity problems in this paper we analyze the convergence of the two step modulus based matrix splitting iteration method for the large sparse linear complementarity problems which is proposed by zhang 2011 7 the convergence conditions are presented when the system matrix is a positive definite matrix and an h matrix respectively in particular we establish new convergence conditions when the system matrix is an h matrix

on the sum rate of multiuser mimo uplink channels with jointly correlated rician fading in this paper we study the capacity achieving input covariance matrices for the multiuser multiple input multiple output mimo uplink channel under jointly correlated rician fading when perfect channel state information csi is known at the receiver or csir while only statistical csi at the transmitter or csit is available the jointly correlated mimo channel or the weichselberger model accounts for the correlation at two link ends and is shown to be highly accurate to model real channels classically numerical techniques together with monte carlo methods named stochastic programming are used to resolve the problem concerned but at a high computational cost to tackle this we derive the asymptotic sum rate of the multiuser mu mimo uplink channel in the large system regime where the numbers of antennas at the transmitters and the receiver go to infinity with constant ratios several insights are gained from the analytic asymptotic sum rate expression based on which an efficient optimization algorithm is further proposed to obtain the capacity achieving input covariance matrices simulation results demonstrate that even for a moderate number of antennas at each link the new approach provides indistinguishable results as those obtained by the complex stochastic programming approach

capturing the behavior of bubbles and drops using the variational level set approach we reproduce the general behavior of complicated bubble and droplet motions using the variational level set formulation introduced by the authors earlier our approach here ignores inertial effects thus the motion is only correct as an approximation for very viscous problems however the steady states are true equilibrium solutions inertial forces will be added in future work the problems include soap bubbles colliding and merging drops falling or remaining attached to a generally irregular ceiling and liquid penetrating through a funnel in both two and three dimensions each phase is identified with a particular level set function the zero level set of this function is that particular phase boundary the level set functions all evolve in time through a constrained gradient descent procedure so as to minimize an energy functional the functions are coupled through physical constraints and through the requirements that different phases do not overlap and vacuum regions do not develop both boundary conditions and inequality constraints are cast in terms of either local or global equality constraints the gradient projection method leads to a system of perturbed by curvature if surface tension is involved hamilton jacobi equations coupled through a constraint the coupling is enforced using the lagrange multiplier associated with this constraint the numerical implementation requires much of the modern level set technology in particular we achieve a significant speed up by using the fast localization algorithm of h k zhao m kang b merriman d peng and s osher

a numerical method for tracking curve networks moving with curvature motion abstract a finite difference method is proposed to track curves whose normal velocity is given by their curvature and which meet at different types of junctions the prototypical example is that of phase interfaces that meet at prescribed angles although eutectic junctions and interactions through nonlocal effects are also considered the method is based on a direct discretization of the underlying parabolic problem and boundary conditions a linear stability analysis is presented for our scheme as well as computational studies that confirm the second order convergence to smooth solutions after a singularity in the curve network where the solution is no longer smooth we demonstrate almost second order convergence a numerical study of singularity types is done for the case of networks that meet at prescribed angles at triple junctions finally different discretizations and methods for implicit time stepping are presented and compared

nonstationary extrapolated modulus algorithms for the solution of the linear complementarity problem abstract the linear complementarity problem lcp has many applications as e g in the solution of linear and convex quadratic programming in free boundary value problems of fluid mechanics etc in the present work we assume that the matrix coefficient m r n n ccccc cof the lcp is symmetric positive definite and we introduce the optimal nonstationary extrapolation to improve the convergence rates of the well known modulus algorithm and block modulus algorithm for its solution two illustrative numerical examples show that the optimal nonstationary extrapolated block modulus algorithm is far better than all the previous similar algorithms

evolution of plane curves driven by a nonlinear function of curvature and anisotropy in this paper we study evolution of plane curves satisfying a geometric equation v beta k nu where v is the normal velocity and k and nu are the curvature and tangential angle of a plane curve gamma we follow the direct approach and we analyze the so called intrinsic heat equation governing the motion of plane curves obeying such a geometric equation the intrinsic heat equation is modified to include an appropriate nontrivial tangential velocity functional alpha we show how the presence of a nontrivial tangential velocity can prevent numerical solutions from forming various instabilities from an analytical point of view we present some new results on short time existence of a regular family of evolving curves in the degenerate case when beta k nu gamma nu k m 0 m le 2 and the governing system of equations includes a nontrivial tangential velocity functional

modulus based matrix splitting iteration methods for a class of nonlinear complementarity problem some modulus based matrix splitting iteration methods for a class of nonlinear complementarity problem are presented and convergence analyses of the methods are given numerical experiments confirm the theoretical analysis and show that the proposed methods are efficient

asymptotic performance analysis of blind minimum output energy receivers for large ds cdma systems the random matrix theory is used to analyze the asymptotic performance of the blind minimum output energy moe receiver in direct sequence code division multiple access ds cdma systems in the presence of unknown multipath channel under the condition that the spreading factor and the number of users go to infinity with the same rate as a special case the asymptotic properties of the blind capon receiver are also studied and the conditions of convergence of the signal to interference plus noise ratio sinr of this receiver to that of the optimal minimum mean square error mmse receiver are discussed in particular it is shown that the sinr performances of the capon and mmse receivers are nearly identical in the uplink scenario while the performance of the capon receiver may be considerably inferior to that of the mmse receiver in the downlink transmission case as the performance of the capon receiver is closely related to the performance of the capon channel estimator the asymptotic properties of the latter estimator are also studied and the conditions of convergence of the capon channel estimate to a scaled version of the channel vector of the user of interest are obtained

on three phase boundary motion and the singular limit of a vector valued ginzburg landau equation we present a formal asymptotic analysis which suggests a model for three phase boundary motion as a singular limit of a vector valued ginzburg landau equation we prove short time existence and uniqueness of solutions for this model that is for a system of three phase boundaries undergoing curvature motion with assigned angle conditions at the meeting point such models pertain to grain boundary motion in alloys the method we use based on linearization about the initial conditions applies to a wide class of parabolic systems we illustrate this further by its application to an eutectic solidification problem

multiple access channels with memory with and without frame synchronism the capacity region of frame synchronous and frame asynchronous discrete two user multiple access channels with finite memory is obtained frame synchronism refers to the ability of the transmitters to send their code words in unison the absence of frame synchronism in memoryless multiple access channels is known to result in the removal of the convex hull operation from the expression of the capacity region it is shown that when the channel has memory frame asynchronism rules out nonstationary inputs to achieve any point in the capacity region thereby allowing only coding strategies that involve cooperation in the frequency domain but not in the time domain this restriction drastically reduces the capacity region of some multiple access channels with memory and in particular the total capacity of the channel which is invariant to frame asynchronism for memoryless channels

asymptotic spectral efficiency of the uplink in spatially distributed wireless networks with multi antenna base stations the spectral efficiency of a representative uplink of a given length in interference limited spatially distributed wireless networks with hexagonal cells simple power control and multiantenna linear minimum mean square error receivers is found to approach an asymptote as the numbers of base station antennas n and wireless nodes go to infinity an approximation for the area averaged spectral efficiency of a representative link averaged over the spatial base station and mobile distributions for poisson distributed base stations is also provided for large n in the interference limited regime the area averaged spectral efficiency is primarily a function of the ratio of the product of n and the ratio of base station to wireless node densities indicating that it is possible to scale such networks by linearly increasing the product of the number of base station antennas and the relative density of base stations to wireless nodes with wireless node density the results are useful for designers of wireless systems with high inter cell interference because it provides simple expressions for spectral efficiency as a function of tangible system parameters like base station and wireless node densities and number of antennas these results were derived combining infinite random matrix theory and stochastic geometry

optimization of linear iterative interference cancellation receivers for cdma communications iterative methods to solve a linear equation system can be used to derive multistage interference cancellers ics that converge to the decorrelating or the minimum mean square error linear detectors the link between linear multistage ic and iterative solution methods is well known however the parameters needed for fastest convergence are functions of the eigenvalues of the channel matrix in this letter we propose new methods for finding optimal parameters without eigendecomposition

impact of antenna correlation on the capacity of multiantenna channels this paper applies random matrix theory to obtain analytical characterizations of the capacity of correlated multiantenna channels the analysis is not restricted to the popular separable correlation model but rather it embraces a more general representation that subsumes most of the channel models that have been treated in the literature for arbitrary signal to noise ratios snr the characterization is conducted in the regime of large numbers of antennas for the low and high snr regions in turn we uncover compact capacity expansions that are valid for arbitrary numbers of antennas and that shed insight on how antenna correlation impacts the tradeoffs among power bandwidth and rate

a diffuse interface model for alloys with multiple components and phases a nonisothermal phase field model for alloys with multiple phases and components is derived the model allows for arbitrary phase diagrams we relate the model to classical sharp interface models by formally matched asymptotic expansions in addition we discuss several examples and relate our model to the ones already existing

parallel nonlinear aor method and its convergence abstract we set up a class of parallel nonlinear aor method in the sense of matrix multi splitting for solving the large scale system of nonlinear equations ax x b with a l rn nonsingular b rn and rn rn being continuously diagonal the global as well as the monotone convergence of this method is proved