optimum sequence multisets for synchronous code division multiple access channels it is shown that the sum capacity of the symbol synchronous code division multiple access channel with equal average input energy constraints is maximized precisely by those spreading sequence multisets that meet welch s lower bound on total squared correlation it is further shown that the symmetric capacity of the channel determined by these same sequence multisets is equal to the sum capacity

signals on graphs uncertainty principle and sampling in many applications the observations can be represented as a signal defined over the vertices of a graph the analysis of such signals requires the extension of standard signal processing tools in this paper first we provide a class of graph signals that are maximally concentrated on the graph domain and on its dual then building on this framework we derive an uncertainty principle for graph signals and illustrate the conditions for the recovery of band limited signals from a subset of samples we show an interesting link between uncertainty principle and sampling and propose alternative signal recovery algorithms including a generalization to frame based reconstruction methods after showing that the performance of signal recovery algorithms is significantly affected by the location of samples we suggest and compare a few alternative sampling strategies finally we provide the conditions for perfect recovery of a useful signal corrupted by sparse noise showing that this problem is also intrinsically related to vertex frequency localization properties

stability theorem and truncation error analysis for the glimm scheme and for a front tracking method for flows with strong discontinuities typical nonlinear wave interaction problems involve strong waves moving through a background of weak disturbance previous existence theorems and error analysis for computations are usually restricted to more idealized situations such as small data or single equations we consider here the problem of a single strong discontinuity interacting with a weak background for general hyperbolic systems of conservation laws we obtain the stability consistency theorems and upper bounds of the truncation errors for the glimm scheme and for a front tracking method the major error in the glimm scheme is the error generated by the strong discontinuity this error is reduced when a front tracking method is applied to follow the location of the strong discontinuity this demonstrates an advantage of front tracking methods in one space dimension

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

kinetic relations and the propagation of phase boundaries in solids this paper treats the dynamics of phase transformations in elastic bars the specific issue studied is the compatibility of the field equations and jump conditions of the one dimensional theory of such bars with two additional constitutive requirements a kinetic relation controlling the rate at which the phase transition takes place and a nucleation criterion for the initiation of the phase transition a special elastic material with a piecewise linear non monotonic stress strain relation is considered and the riemann problem for this material is analyzed for a large class of initial data it is found that the kinetic relation and the nucleation criterion together single out a unique solution to this problem from among the infinitely many solutions that satisfy the entropy jump condition at all strain discontinuities

information based objective functions for active data selection learning can be made more efficient if we can actively select particularly salient data points within a bayesian learning framework objective functions are discussed that measure the expected informativeness of candidate measurements three alternative specifications of what we want to gain information about lead to three different criteria for data selection all these criteria depend on the assumption that the hypothesis space is correct which may prove to be their main weakness

tangent bundle maps on the grassmann manifold application to empirical arithmetic averaging the present paper elaborates on tangent bundle maps on the grassmann manifold with application to subspace arithmetic averaging in particular the present contribution elaborates on the work about retraction lifting maps devised for the stiefel manifold in the recently published paper t kaneko s fiori and t tanaka empirical arithmetic averaging over the compact stiefel manifold ieee trans signal process vol 61 no 4 pp 883 894 february 2013 and discusses the extension of such maps to the grassmann manifold tangent bundle maps are devised on the basis of the thin qr matrix decomposition the polar matrix decomposition and the exponential map also tangent bundle pseudo maps based on the matrix cayley transform are devised theoretical and numerical comparisons about the devised tangent bundle maps are performed in order to get an insight into their relative merits and demerits with special emphasis to their computational burden the averaging algorithm based on the thin qr decomposition maps stands out as it exhibits the best trade off between numerical precision and computational burden such algorithm is further compared with two grassmann averaging algorithms drawn from the scientific literature on an handwritten digits recognition data set the thin qr tangent bundle maps based algorithm exhibits again numerical features that make it preferable over such algorithms

instabilities in glimm s scheme for two systems of mixed type the behavior of glimm s scheme is examined when applied to two systems from nonlinear elasticity which change type from hyperbolic to elliptic or mixed type i e a pair of wave speeds coalesce and turn complex the hyperbolic regime is invariant for glimm s scheme but not for smooth solutions so strong convergence is not possible in general some simple exact solutions for these systems are considered which illustrate how the approximate solutions are affected by the oscillatory instabilities in these systems the approximations exhibit macroscopically random transitions to new states and nonconvergence in one example however convergence in expectation is observed and weak convergence can be observed if the courant friedrichs levy cfl number is fixed

the riemann problem for thermoelastic materials with phase change abstract we consider the riemann problem for a system of conservation laws related to a phase transition problem the system is nonisentropic and we treat the case where the latent heat is not zero we study the cases where the initial data are given in the same phase and in the different phases the role of the entropy condition is studied as well as the kinetic relation and the entropy rate admissibility criterion we confine our attention to the case where the speeds of phase boundaries are close to zero this is one interesting case in physics we discuss the number of phase boundaries consistent with the above criteria and the uniqueness and nonuniqueness issue of the solution to the riemann problem

reconstructing gaussian sources by spatial sampling consider a gaussian memoryless multiple source gmms with m components with joint probability distribution known only to lie in a given class of distributions a subset of k leq m components is sampled and compressed with the objective of reconstructing all the m components within a specified level of distortion under a mean squared error criterion in bayesian and nonbayesian settings the notion of universal sampling rate distortion function for gaussian sources is introduced to capture the optimal tradeoffs among sampling compression rate and distortion level single letter characterizations are provided for the universal sampling rate distortion function our achievability proofs highlight the following structural property it is optimal to compress and reconstruct first the sampled components of the gmms alone and then form estimates for the unsampled components based on the former

admissible riemann solvers for genuinely nonlinear p systems of mixed type abstract we consider in this paper the riemann problem for p systems of mixed type that define two hyperbolic phases with a stress function satisfying general genuinely nonlinear hypotheses we describe here all the global riemann solvers that are continuous for the l 1 distance with respect to initial data while conserving the natural symmetry properties of the p system and coinciding with the lax solution when defined these riemann solvers can be described entirely by a kinetic function used to select a manifold of subsonic phase transitions and a corresponding set of supersonic phase transitions

sensor placement by maximal projection on minimum eigenspace for linear inverse problems this paper presents two new greedy sensor placement algorithms named minimum nonzero eigenvalue pursuit mnep and maximal projection on minimum eigenspace mpme for linear inverse problems with greater emphasis on the mpme algorithm for performance comparison with existing approaches in both mnep and mpme we select the sensing locations one by one in this way the least number of required sensor nodes can be determined by checking whether the estimation accuracy is satisfied after each sensing location is determined for the mpme algorithm the minimum eigenspace is defined as the eigenspace associated with the minimum eigenvalue of the dual observation matrix for each sensing location the projection of its observation vector onto the minimum eigenspace is shown to be monotonically decreasing w r t the worst case error variance wcev of the estimated parameters we select the sensing location whose observation vector has the maximum projection onto the minimum eigenspace of the current dual observation matrix the proposed mpme is shown to be one of the most computationally efficient algorithms our monte carlo simulations showed that mpme outperforms the convex relaxation method the sparsense method and the framesense method in terms of wcev and the mean square error mse of the estimated parameters especially when the number of available sensor nodes is very limited

propagating phase boundaries formulation of the problem and existence via the glimm method this paper treats the hyperbolic elliptic system of two conservation laws which describes the dynamics of an elastic material having a non monotone strain stress function followingabeyaratne knowles we propose a notion of admissible weak solution for this system in the class of functions of bounded variation the formulation includes an entropy inequality a kinetic relation imposed along any subsonic phase boundary and an initiation criterion for the appearance of new phase boundaries we prove thel1 continuous dependence of the solution to the riemann problem our main result yields the existence and the stability of propagating phase boundaries the proofs are based onglimm s scheme and in particular on the techniques ofglimm andlax in order to deal with the kinetic relation we prove a result of pointwise convergence of the phase boundary

sampling rate distortion consider a discrete memoryless multiple source with m components of which k leq m possibly different sources are sampled at each time instant and jointly compressed in order to reconstruct all the m sources under a given distortion criterion a new notion of sampling rate distortion function is introduced and is characterized first for the case of fixed set sampling next for independent random sampling performed without knowledge of the source outputs it is shown that the sampling rate distortion function is the same regardless of whether or not the decoder is informed of the sequence of sampled sets furthermore memoryless random sampling is considered with the sampler depending on the source outputs and with an informed decoder it is shown that deterministic sampling characterized by a conditional point mass is optimal and suffices to achieve the sampling rate distortion function for memoryless random sampling with an uninformed decoder an upper bound for the sampling rate distortion function is seen to possess a similar property of conditional point mass optimality it is shown by example that memoryless sampling with an informed decoder can outperform strictly any independent random sampler and that memoryless sampling can do strictly better with an informed decoder than without

analysis and design of optimum sparse array configurations for adaptive beamforming in this paper we analyze the effect of nonuniform array configurations on adaptive beamforming for enhanced signal to interference plus noise ratio sinr the array is configured using a given number of antennas or through a selection of subset of antennas from a larger available set leading to a sparse array in both cases the bounds on the highest achievable sinr for a given number of antennas are formulated and used to offer new insights into open loop adaptive beamforming the upper and lower bounds underscore the role of array configurations in optimizing performance for interference free and interference active environments respectively this paper considers the general case of multiple sources and interferences in the field of view we formulate three angles namely eigenspace angle conventional angle and minimum canonical angle for characterizing spatial separation between the source and interference subspaces which represent performance loss incurred by interference nulling three sparse array design methods incorporating these angles are proposed simulation examples confirm the role of subspace angles in optimum beamforming and validate the utility of antenna selection algorithms for sparse array design

the uniqueness and stability of the solution of the riemann problem of a system of conservation laws of mixed type we establish the uniqueness and stability of the similarity solution of the riemann problem for a 2 2 system of conservation laws of mixed type with initial data separated by the elliptic region which satisfies the viscosity capillarity travelling wave admissibility criterion

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

the riemann problem for a van der waals fluid with entropy rate admissibility criterion nonisothermal case where a and b are the characteristic constants of the fluid thus when the temperature is sufficiently low p v is positive and thus the system i 1 is elliptic on a certain interval c fl while p v is negative on b liquid phase as well as on oo vapor phase on which 1 1 is hyperbolic the riemann problem for i 1 is a special initial value problem in which the initial data are of the form

a vanishing viscosity approach on the dynamics of phase transitions in van der waals fluids abstract the existence of solutions for the riemann problem of a mixed type system is established by a vanishing similarity viscosity approach the solutions that we construct are also admissible by the travelling wave criterion derived from the most common form of viscosity the assumption needed includes the constitutive function of van der waals fluids

near optimal sensor placements in gaussian processes theory efficient algorithms and empirical studies when monitoring spatial phenomena which can often be modeled as gaussian processes gps choosing sensor locations is a fundamental task there are several common strategies to address this task for example geometry or disk models placing sensors at the points of highest entropy variance in the gp model and a d or e optimal design in this paper we tackle the combinatorial optimization problem of maximizing the mutual information between the chosen locations and the locations which are not selected we prove that the problem of finding the configuration that maximizes mutual information is np complete to address this issue we describe a polynomial time approximation that is within 1 1 e of the optimum by exploiting the submodularity of mutual information we also show how submodularity can be used to obtain online bounds and design branch and bound search procedures we then extend our algorithm to exploit lazy evaluations and local structure in the gp yielding significant speedups we also extend our approach to find placements which are robust against node failures and uncertainties in the model these extensions are again associated with rigorous theoretical approximation guarantees exploiting the submodularity of the objective function we demonstrate the advantages of our approach towards optimizing mutual information in a very extensive empirical study on two real world data sets

the riemann problem and the existence of weak solutions to a system of mixed type in dynamic phase transition abstract we discuss the riemann problem and the existence of weak solutions to a dynamic phase transition problem to estimate the wave strength of outgoing waves containing the phase boundary we obtain the reflection and transmission coefficients for phase boundary then employing the entropy rate admissibility criterion and the initiation criterion we prove the existence of global weak solutions via glimm scheme

a limiting viscosity approach to the riemann problem for materials exhibiting a change of phase ii describes the one dimensional isothermal motion of a compressible elastic fluid or solid in lagrangian coordinates considerable study has been made for the case p w 0 in which the system 1 i a b is hyperbolic however in some material models for instance in the van der waals fluid p w may be positive for some values of w in this paper we consider a function p w with graph shown in fig 1 more precisely we assume that p e c1 and