on optimal multilayer cyclotomic space time code designs high rate and large diversity product or coding advantage or coding gain or determinant distance or minimum product distance are two of the most important criteria often used for good space time code designs in recent linear lattice based space time code designs more attention is paid to the high rate criterion but less to the large diversity product criterion in this paper we consider these two criteria together for multilayer cyclotomic space time code designs in a previous paper we recently proposed a systematic cyclotomic diagonal space time code design over a general cyclotomic number ring that has infinitely many designs for a fixed number of transmit antennas where diagonal codes correspond to single layer codes in this paper in this paper we first propose a general multilayer cyclotomic space time codes we present a general optimality theorem for these infinitely many cyclotomic diagonal or single layer space time codes over general cyclotomic number rings for a general number of transmit antennas we then present optimal multilayer full rate cyclotomic space time code designs for two and three transmit antennas we also present an optimal two layer cyclotomic space time code design for three and four transmit antennas the optimality here is in the sense that for a fixed mean transmission signal power its diversity product is maximized or equivalently for a fixed diversity product its mean transmission signal power is minimized it should be emphasized that all the optimal multilayer cyclotomic space time codes presented in this paper have the nonvanishing determinant property

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

accelerating ordered subsets image reconstruction for x ray ct using spatially nonuniform optimization transfer statistical image reconstruction algorithms in x ray computed tomography ct provide improved image quality for reduced dose levels but require substantial computation time iterative algorithms that converge in few iterations and that are amenable to massive parallelization are favorable in multiprocessor implementations the separable quadratic surrogate sqs algorithm is desirable as it is simple and updates all voxels simultaneously however the standard sqs algorithm requires many iterations to converge this paper proposes an extension of the sqs algorithm that leads to spatially nonuniform updates the nonuniform nu sqs encourages larger step sizes for the voxels that are expected to change more between the current and the final image accelerating convergence while the derivation of nu sqs guarantees monotonic descent ordered subsets os algorithms can also accelerate sqs provided suitable subset balance conditions hold these conditions can fail in 3 d helical cone beam ct due to incomplete sampling outside the axial region of interest roi this paper proposes a modified os algorithm that is more stable outside the roi in helical ct we use ct scans to demonstrate that the proposed nu os sqs algorithm handles the helical geometry better than the conventional os methods and converges in less than half the time of ordinary os sqs

adaptive penalty based distributed stochastic convex optimization in this work we study the task of distributed optimization over a network of learners in which each learner possesses a convex cost function a set of affine equality constraints and a set of convex inequality constraints we propose a fully distributed adaptive diffusion algorithm based on penalty methods that allows the network to cooperatively optimize the global cost function which is defined as the sum of the individual costs over the network subject to all constraints we show that when small constant step sizes are employed the expected distance between the optimal solution vector and that obtained at each node in the network can be made arbitrarily small two distinguishing features of the proposed solution relative to other approaches is that the developed strategy does not require the use of projections and is able to track drifts in the location of the minimizer due to changes in the constraints or in the aggregate cost itself the proposed strategy is able to cope with changing network topology is robust to network disruptions and does not require global information or rely on central processors

an energetic variational approach for the cahn hilliard equation with dynamic boundary condition model derivation and mathematical analysis the cahn hilliard equation is a fundamental model that describes phase separation processes of binary mixtures in recent years several types of dynamic boundary conditions have been proposed in order to account for possible short range interactions of the material with the solid wall our first aim in this paper is to propose a new class of dynamic boundary conditions for the cahn hilliard equation in a rather general setting the derivation is based on an energetic variational approach that combines the least action principle and onsager s principle of maximum energy dissipation one feature of our model is that it naturally fulfills three important physical constraints conservation of mass dissipation of energy and force balance relations next we provide a comprehensive analysis of the resulting system of partial differential equations under suitable assumptions we prove the existence and uniqueness of global weak strong solutions to the initial boundary value problem with or without surface diffusion furthermore we establish the uniqueness of the asymptotic limit as t to infty and characterize the stability of local energy minimizers for the system

stochastic learning under random reshuffling with constant step sizes in empirical risk optimization it has been observed that stochastic gradient implementations that rely on random reshuffling of the data achieve better performance than implementations that rely on sampling the data uniformly recent works have pursued justifications for this behavior by examining the convergence rate of the learning process under diminishing step sizes this work focuses on the constant step size case and strongly convex loss functions in this case convergence is guaranteed to a small neighborhood of the optimizer albeit at a linear rate the analysis establishes analytically that random reshuffling outperforms uniform sampling by showing explicitly that iterates approach a smaller neighborhood of size o mu 2 around the minimizer rather than o mu furthermore we derive an analytical expression for the steady state mean square error performance of the algorithm which helps clarify in greater detail the differences between sampling with and without replacement we also explain the periodic behavior that is observed in random reshuffling implementations

linear dispersion codes for mimo systems based on frame theory multiple input multiple output mimo wireless communication systems provide high capacity due to the plurality of modes available in the channel existing signaling techniques for mimo systems have focused primarily on multiplexing for high data rate or diversity for high link reliability in this paper we present a new linear dispersion code design for mimo rayleigh fading channels the proposed design bridges the gap between multiplexing and diversity and yields codes that typically perform well both in terms of ergodic capacity as well as error probability this is important because as we show designs performing well from an ergodic capacity point of view do not necessarily perform well from an error probability point of view various techniques are presented for finding codes with good error probability performance monte carlo simulations illustrate performance of some example code designs in terms of ergodic capacity codeword error probability and bit error probability

globally convergent image reconstruction for emission tomography using relaxed ordered subsets algorithms we present two types of globally convergent relaxed ordered subsets os algorithms for penalized likelihood image reconstruction in emission tomography modified block sequential regularized expectation maximization bsrem and relaxed os separable paraboloidal surrogates os sps the global convergence proof of the existing bsrem de pierro and yamagishi 2001 required a few a posteriori assumptions by modifying the scaling functions of bsrem we are able to prove the convergence of the modified bsrem under realistic assumptions our modification also makes stepsize selection more convenient in addition we introduce relaxation into the os sps algorithm erdogan and fessler 1999 that otherwise would converge to a limit cycle we prove the global convergence of diagonally scaled incremental gradient methods of which the relaxed os sps is a special case main results of the proofs are from nedic and bertsekas 2001 and correa and lemarechal 1993 simulation results showed that both new algorithms achieve global convergence yet retain the fast initial convergence speed of conventional unrelaxed ordered subsets algorithms

convergence of approximate and incremental subgradient methods for convex optimization we present a unified convergence framework for approximate subgradient methods that covers various stepsize rules including both diminishing and nonvanishing stepsizes convergence in objective values and convergence to a neighborhood of the optimal set we discuss ways of ensuring the boundedness of the iterates and give efficiency estimates our results are extended to incremental subgradient methods for minimizing a sum of convex functions which have recently been shown to be promising for various large scale problems including those arising from lagrangian relaxation

a new class of incremental gradient methods for least squares problems the least mean squares lms method for linear least squares problems differs from the steepest descent method in that it processes data blocks one by one with intermediate adjustment of the parameter vector under optimization this mode of operation often leads to faster convergence when far from the eventual limit and to slower sublinear convergence when close to the optimal solution we embed both lms and steepest descent as well as other intermediate methods within a one parameter class of algorithms and we propose a hybrid class of methods that combine the faster early convergence rate of lms with the faster ultimate linear convergence rate of steepest descent these methods are well suited for neural network training problems with large data sets furthermore these methods allow the effective use of scaling based for example on diagonal or other approximations of the hessian matrix

trace orthonormal full diversity cyclotomic space time codes in this paper we consider the design of full diversity space time codes for a coherent multiple input multiple output mimo communication system starting from both the information theoretic and detection error viewpoints we first establish that a desirable property for general linear dispersion ld codes is to have an interunitary as well as an intraunitary structure a structure we call trace orthonormality by imposing the trace orthonormal structure on an ld code and applying cyclotomic number theory we establish for an arbitrary number of transmitter and receiver antennas a systematic and simple method to jointly design a unitary cyclotomic matrix the diophantine number and the corresponding constellation for an ld code as a result this enables us to construct full diversity rectangular cyclotomic ld codes with any symbol transmission rate less than or equal to the number of transmitter antennas in addition for the case when the number of transmitter antennas is greater than the number of receiver antennas by taking advantage of the delay we also arrive at the design of a special trace orthonormal full diversity cyclotomic space time block code which for the number of transmitter antenna being equal to 2m can be proved to minimize the worst case pairwise error probability of a maximum likelihood ml detector for a q ary quadrature amplitude modulation qam signal constellation and therefore achieves optimal coding gain computer simulations show that these codes have bit error performance advantages over currently available codes

full diversity high rate space time block codes from division algebras we present some general techniques for constructing full rank minimal delay rate at least one space time block codes stbcs over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras field extensions as well as using noncommutative division algebras of the rational field spl qopf embedded in matrix rings the first half of the paper deals with constructions using field extensions of spl qopf working with cyclotomic field extensions we construct several families of stbcs over a wide range of signal sets that are of full rank minimal delay and rate at least one appropriate for any number of transmit antennas we study the coding gain and capacity of these codes using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas we also present a method of constructing stbcs using noncyclotomic field extensions in the later half of the paper we discuss two ways of embedding noncommutative division algebras into matrices left regular representation and representation over maximal cyclic subfields the 4 spl times 4 real orthogonal design is obtained by the left regular representation of quaternions alamouti s 1998 code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it also we discuss a general principle for constructing cyclic division algebras using the nth root of a transcendental element and study the capacity of the stbcs obtained from this construction another family of cyclic division algebras discovered by brauer 1933 is discussed and several examples of stbcs derived from each of these constructions are presented

descent methods with linesearch in the presence of perturbations we consider the class of descent algorithms for unconstrained optimization with an armijo type stepsize rule in the case when the gradient of the objective function is computed inexactly an important novel feature in our theoretical analysis is that perturbations associated with the gradient are not assumed to be relatively small or to tend to zero in the limit as a practical matter we expect them to be reasonably small so that a meaningful approximate solution can be obtained this feature makes our analysis applicable to various difficult problems encounted in practice we propose a modified armijo type rule for computing the stepsize which guarantees that the algorithm obtains a reasonable approximate solution furthermore if perturbations are small relative to the size of the gradient then our algorithm retains all the standard convergence properties of descent methods

error estimates for approximate optimization by the extended ritz method an alternative to the classical ritz method for approximate optimization is investigated in the extended ritz method sets of admissible solutions are approximated by their intersections with sets of linear combinations of all n tuples of functions from a given basis this alternative scheme called variable basis approximation includes functions computable by trigonometric polynomials with free frequencies free node splines neural networks and other nonlinear approximating families estimates of rates of approximate optimization by the extended ritz method are derived upper bounds on rates of convergence of suboptimal solutions to the optimal one are expressed in terms of the degree n of variable basis functions the modulus of continuity of the functional to be minimized the modulus of tikhonov well posedness of the problem and certain norms tailored to the type of basis the results are applied to convex best approximation and to kernel methods in machine learning

unitary space time modulation for multiple antenna communications in rayleigh flat fading motivated by information theoretic considerations we propose a signaling scheme unitary space time modulation for multiple antenna communication links this modulation is ideally suited for rayleigh fast fading environments since it does not require the receiver to know or learn the propagation coefficients unitary space time modulation uses constellations of t spl times m space time signals spl phi sub i l 1 l where t represents the coherence interval during which the fading is approximately constant and m t is the number of transmitter antennas the columns of each spl phi sub i are orthonormal when the receiver does not know the propagation coefficients which between pairs of transmitter and receiver antennas are modeled as statistically independent this modulation performs very well either when the signal to noise ratio snr is high or when t spl gt m we design some multiple antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding we demonstrate that two antennas have a 6 db diversity gain over one antenna at 15 db snr

universal attractor for some singular phase transition systems a singular parabolic system describing the thermal diffusion in a substance possibly subject to a phase transition is introduced the physical process is described by the variables absolute temperature and order parameter the latter may have or not conserved total mass with respect to time in both cases after recalling and sometimes improving some known well posedness results the long time behavior of the system is studied it is shown that the process is dissipative and the compact universal attractor is constructed it turns out to attract the trajectories of the system in a rather strong metric which is strictly linked to the constraints imposed to both variables the techniques used in the proofs seem likely to be applied to other types of evolution systems containing maximal monotone nonlinearities

incremental subgradient methods for nondifferentiable optimization we consider a class of subgradient methods for minimizing a convex function that consists of the sum of a large number of component functions this type of minimization arises in a dual context from lagrangian relaxation of the coupling constraints of large scale separable problems the idea is to perform the subgradient iteration incrementally by sequentially taking steps along the subgradients of the component functions with intermediate adjustment of the variables after processing each component function this incremental approach has been very successful in solving large differentiable least squares problems such as those arising in the training of neural networks and it has resulted in a much better practical rate of convergence than the steepest descent method in this paper we establish the convergence properties of a number of variants of incremental subgradient methods including some that are stochastic based on the analysis and computational experiments the methods appear very promising and effective for important classes of large problems a particularly interesting discovery is that by randomizing the order of selection of component functions for iteration the convergence rate is substantially improved

random algorithms for convex minimization problems this paper deals with iterative gradient and subgradient methods with random feasibility steps for solving constrained convex minimization problems where the constraint set is specified as the intersection of possibly infinitely many constraint sets each constraint set is assumed to be given as a level set of a convex but not necessarily differentiable function the proposed algorithms are applicable to the situation where the whole constraint set of the problem is not known in advance but it is rather learned in time through observations also the algorithms are of interest for constrained optimization problems where the constraints are known but the number of constraints is either large or not finite we analyze the proposed algorithm for the case when the objective function is differentiable with lipschitz gradients and the case when the objective function is not necessarily differentiable the behavior of the algorithm is investigated both for diminishing and non diminishing stepsize values the almost sure convergence to an optimal solution is established for diminishing stepsize for non diminishing stepsize the error bounds are established for the expected distances of the weighted averages of the iterates from the constraint set as well as for the expected sub optimality of the function values along the weighted averages

hybrid deterministic stochastic methods for data fitting many structured data fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements incremental gradient algorithms offer inexpensive iterations by sampling a subset of the terms in the sum these methods can make great progress initially but often slow as they approach a solution in contrast full gradient methods achieve steady convergence at the expense of evaluating the full objective and gradient on each iteration we explore hybrid methods that exhibit the benefits of both approaches rate of convergence analysis shows that by controlling the sample size in an incremental gradient algorithm it is possible to maintain the steady convergence rates of full gradient methods we detail a practical quasi newton implementation based on this approach numerical experiments illustrate its potential benefits

gradient convergence in gradient methods with errors we consider the gradient method x t 1 x t g t s t w t where s t is a descent direction of a function f rn to re and w t is a deterministic or stochastic error we assume that gr f is lipschitz continuous that the stepsize g t diminishes to 0 and that s t and w t satisfy standard conditions we show that either f x t to infty or f x t converges to a finite value and gr f x t to0 with probability 1 in the stochastic case and in doing so we remove various boundedness conditions that are assumed in existing results such as boundedness from below of f boundedness of gr f x t or boundedness of xt

on the convergence of the lms algorithm with adaptive learning rate for linear feedforward networks we consider the problem of training a linear feedforward neural network by using a gradient descent like lms learning algorithm the objective is to find a weight matrix for the network by repeatedly presenting to it a finite set of examples so that the sum of the squares of the errors is minimized kohonen showed that with a small but fixed learning rate or stepsize some subsequences of the weight matrices generated by the algorithm will converge to certain matrices close to the optimal weight matrix in this paper we show that by dynamically decreasing the learning rate during each training cycle the sequence of matrices generated by the algorithm will converge to the optimal weight matrix we also show that for any given 0 the lms algorithm with decreasing learning rates will generate an optimal weight matrix i e a matrix of distance at most away from the optimal matrix after o 1 training cycles this is in contrast to 1 log 1 training cycles needed to generate an optima

a stochastic successive minimization method for nonsmooth nonconvex optimization with applications to transceiver design in wireless communication networks consider the problem of minimizing the expected value of a cost function parameterized by a random variable the classical sample average approximation method for solving this problem requires minimization of an ensemble average of the objective at each step which can be expensive in this paper we propose a stochastic successive upper bound minimization method ssum which minimizes an approximate ensemble average at each iteration to ensure convergence and to facilitate computation we require the approximate ensemble average to be a locally tight upper bound of the expected cost function and be easily optimized the main contributions of this work include the development and analysis of the ssum method as well as its applications in linear transceiver design for wireless communication networks and online dictionary learning moreover using the ssum framework we extend the classical stochastic sub gradient method to the case of minimizing a nonsmooth nonconvex objective function and establish its convergence

systematic construction of full diversity algebraic constellations a simple and systematic approach for constructing full diversity m dimensional constellations carved from lattices over a number ring r is proposed for an arbitrary dimension m when r z wn the nth cyclotomic number ring all the possible dimensions that allow for achieving the optimal minimum product distances using the proposed approach are determined it turns out that one can construct optimal unitary transformations using our construction if and only if m factors into a power of 2 and powers of the primes dividing n for m not satisfying these conditions a method based on diophantine approximation theory is proposed to optimize the minimum product distance a lower bound on the product distance is given in this case thus ensuring full diversity with good minimum product distances furthermore the proposed approach subsumes the optimal unitary transformations proposed by giraud et al over r z w4 and r z w3 while giving optimal unitary transformations for infinitely many new values of n and m

on the design of minimum ber linear space time block codes for mimo systems equipped with mmse receivers in this paper we consider the design of a full rate linear space time block code for coherent multiple input multiple output mimo communication systems under a quasi static rayleigh flat fading environment our design targets specifically at the use of a linear minimum mean square error mmse receiver that minimizes the asymptotic average bit error rate ber when the transmitted signal is selected from a 4 qam constellation this optimization problem is solved in two main stages 1 a lower bound on the ber is first minimized and 2 how this minimized lower bound can be achieved is then shown by exploiting a rigorous convex optimization technique without any assumption on the code we prove that individual unitary and trace orthogonal structures are the necessary and sufficient conditions to assure the minimum asymptotic average ber with an mmse detector an algorithm is provided for an efficient generation of our codes and simulation results confirm that our optimally designed codes are indeed superior in performance compared to some other commonly used codes

a class of quasi linear allen cahn type equations with dynamic boundary conditions abstract in this paper we consider a class of coupled systems of pdes denoted by ace e for e 0 for each e 0 the system ace e consists of an allen cahn type equation in a bounded spacial domain and another allen cahn type equation on the smooth boundary and besides these coupled equations are transmitted via the dynamic boundary conditions in particular the equation in is derived from the non smooth energy proposed by visintin in his monography models of phase transitions hence the diffusion in is provided by a quasilinear form with singularity the objective of this paper is to build a mathematical method to obtain meaningful l 2 based solutions to our systems and to see some robustness of ace e with respect to e 0 on this basis we will prove two main theorems 1 and 2 which will be concerned with the well posedness of ace e for each e 0 and the continuous dependence of solutions to ace e for the variations of e 0 respectively

a numerical analysis of the cahn hilliard equation with non permeable walls in this article we consider the numerical analysis of the cahn hilliard equation in a bounded domain with non permeable walls endowed with dynamic type boundary conditions the dynamic type boundary conditions that we consider here have been recently proposed in ruiz goldstein et al phys d 240 8 754 766 2011 in order to describe the interactions of a binary material with the wall the equation is semi discretized using a finite element method for the space variables and error estimates between the exact and the approximate solution are obtained we also prove the stability of a fully discrete scheme based on the backward euler scheme for the time discretization numerical simulations sustaining the theoretical results are presented

steered sequential projections for the inconsistent convex feasibility problem we study a steered sequential gradient algorithm which minimizes the sum of convex functions by proceeding cyclically in the directions of the negative gradients of the functions and using steered step sizes this algorithm is applied to the convex feasibility problem by minimizing a proximity function which measures the sum of the bregman distances to the members of the family of convex sets the resulting algorithm is a new steered sequential bregman projection method

abstract approach to evolution equations of phase field type and applications a general system of abstract nonlinear parabolic equations deriving from phase field models of heat transfer in anisotropic fluids with phase transitions is studied through a backward finite differences approximation scheme and existence and uniqueness theorems are proved then applications are presented to two physical situations first a standard heat diffusion problem is briefly discussed mainly as a justification of the choices of the abstract setting second a more interesting transmission problem between two different adjoining fluids is studied under very general compatibility hypotheses and the abstract results are adapted to provide an existence and uniqueness theorem also in this case moreover through convex analysis techniques it is performed a mathematical study of the subdifferential type relations linking the phase fields and the temperatures to the internal energies of the fluids email schimper dragon ian pv cnr it keywords phase field models subdifferential operators abstract evolution equations

a convergent incremental gradient method with a constant step size an incremental aggregated gradient method for minimizing a sum of continuously differentiable functions is presented the method requires a single gradient evaluation per iteration and uses a constant step size for the case that the gradient is bounded and lipschitz continuous we show that the method visits infinitely often regions in which the gradient is small under certain unimodality assumptions global convergence is established in the quadratic case a global linear rate of convergence is shown the method is applied to distributed optimization problems arising in wireless sensor networks and numerical experiments compare the new method with other incremental gradient methods

on boundary detachment phenomena for the total variation flow with dynamic boundary conditions abstract we combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions we analyze the behavior of facets at the parts of the boundary where these conditions are imposed we devote particular attention to the radially symmetric data we observe that the boundary layer detachment actually can happen at concave parts of the boundary

convergent incremental optimization transfer algorithms application to tomography no convergent ordered subsets os type image reconstruction algorithms for transmission tomography have been proposed to date in contrast in emission tomography there are two known families of convergent os algorithms methods that use relaxation parameters and methods based on the incremental expectation maximization em approach this paper generalizes the incremental em approach by introducing a general framework incremental optimization transfer the proposed algorithms accelerate convergence speeds and ensure global convergence without requiring relaxation parameters the general optimization transfer framework allows the use of a very broad family of surrogate functions enabling the development of new algorithms this paper provides the first convergent os type algorithm for nonconcave penalized likelihood pl transmission image reconstruction by using separable paraboloidal surrogates sps which yield closed form maximization steps we found it is very effective to achieve fast convergence rates by starting with an os algorithm with a large number of subsets and switching to the new transmission incremental optimization transfer triot algorithm results show that triot is faster in increasing the pl objective than nonincremental ordinary sps and even os sps yet is convergent

normalized incremental subgradient algorithm and its application the problem of minimizing the sum of a number of component functions is of great importance in the real world in this paper a new incremental optimization algorithm named normalized incremental subgradient nis algorithm is proposed for a class of such problems where the component functions have common local minima the nis algorithm is performed incrementally just as the general incremental subgradient is algorithm and thus can be implemented in a distributed way in the nis algorithm the update of each subiteration is based on a search direction obtained by individually normalizing each component of subgradients of component functions resulting in much better convergence performance as compared to the is algorithm and other traditional optimization methods e g gauss newton method the convergence of the nis algorithm with both diminishing stepsizes and constant stepsizes is proved and analyzed theoretically two important applications are presented one is to solve a class of convex feasibility problems in a distributed way and the other is distributed maximum likelihood estimation numerical examples arising from two important topics in the area of wireless sensor networks source localization and node localization demonstrate the effectiveness and efficiency of the nis algorithm

incremental least squares methods and the extended kalman filter in this paper we propose and analyze nonlinear least squares methods which process the data incrementally one data block at a time such methods are well suited for large data sets and real time operation and have received much attention in the context of neural network training problems we focus on the extended kalman filter which may be viewed as an incremental version of the gauss newton method we provide a nonstochastic analysis of its convergence properties and we discuss variants aimed at accelerating its convergence

a cahn hilliard model in a domain with non permeable walls abstract we consider in this article a cahn hilliard model in a bounded domain with non permeable walls characterized by dynamic type boundary conditions dynamic boundary conditions for the cahn hilliard system have recently been proposed by physicists in order to account for the interactions with the walls in confined systems and are obtained by writing that the total bulk mass is conserved and that there is a relaxation dynamics on the boundary however in the case of non permeable walls one should also expect some mass on the boundary it thus seems more realistic to assume that the total mass in the bulk and on the boundary is conserved which leads to boundary conditions of a different type for the resulting mathematical model we prove the existence and uniqueness of weak solutions and study their asymptotic behavior as time goes to infinity

corrigendum to existence of global solutions to the caginalp phase field system with dynamic boundary conditions and singular potentials j math anal appl 343 2008 557 566

convergence and applications of a gossip based gauss newton algorithm the gauss newton algorithm is a popular and efficient centralized method for solving non linear least squares nlls problems in this paper a multi agent distributed version of this algorithm is proposed to solve general nlls problems in a network named gossip based gauss newton ggn algorithm furthermore we analyze and present sufficient conditions for its convergence and show numerically that the ggn algorithm achieves performance comparable to the centralized algorithm with graceful degradation in case of network failures more importantly the ggn algorithm provides significant performance gains compared to other distributed first order methods

the iterated kalman smoother as a gauss newton method the kalman smoother is known to be the maximum likelihood estimator when the measurement and transition functions are affine i e a linear function plus a constant a new proof of this result is presented that shows that the kalman smoother decomposes a large least squares problem into a sequence of much smaller problems the iterated kalman smoother is then presented and shown to be a gauss newton method for maximizing the likelihood function in the nonaffine case this method takes advantage of the decomposition obtained with the kalman smoother

the ordered subsets mirror descent optimization method with applications to tomography we describe an optimization problem arising in reconstructing three dimensional medical images from positron emission tomography pet a mathematical model of the problem based on the maximum likelihood principle is posed as a problem of minimizing a convex function of several million variables over the standard simplex to solve a problem of these characteristics we develop and implement a new algorithm ordered subsets mirror descent and demonstrate theoretically and computationally that it is well suited for solving the pet reconstruction problem

constellations matched to the rayleigh fading channel we introduce a new technique for designing signal sets matched to the rayleigh fading channel in particular we look for n dimensional n spl ges 2 lattices whose structure provides nth order diversity our approach is based on a geometric formulation of the design problem which in turn can be solved by using a number geometric approach specifically a suitable upper bound on the pairwise error probability makes the design problem tantamount to the determination of what is called a critical lattice of the body s x x sub 1 spl middot spl middot spl middot x sub n spl isin r sup n spl pi sub i 1 sup n x sub i spl les 1 the lattices among which we search for an optimal solution are the standard embeddings in r sup n of the number ring of some totally real number field of degree n over q simulation results confirm that this approach yields lattices with considerable coding gains

an incremental gradient projection method with momentum term and adaptive stepsize rule we consider an incremental gradient method with momentum term for minimizing the sum of continuously differentiable functions this method uses a new adaptive stepsize rule that decreases the stepsize whenever sufficient progress is not made we show that if the gradients of the functions are bounded and lipschitz continuous over a certain level set then every cluster point of the iterates generated by the method is a stationary point in addition if the gradient of the functions have a certain growth property then the method is either linearly convergent in some sense or the stepsizes are bounded away from zero the new stepsize rule is much in the spirit of heuristic learning rules used in practice for training neural networks via backpropagation as such the new stepsize rule may suggest improvements on existing learning rules finally extension of the method and the convergence results to constrained minimization is discussed as are some implementation issues and numerical experience

incremental proximal methods for large scale convex optimization we consider the minimization of a sum sum i 1 mf i x consisting of a large number of convex component functions f i for this problem incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective we propose new incremental methods consisting of proximal iterations applied to single components as well as combinations of gradient subgradient and proximal iterations we provide a convergence and rate of convergence analysis of a variety of such methods including some that involve randomization in the selection of components we also discuss applications in a few contexts including signal processing and inference machine learning

diffusion strategies outperform consensus strategies for distributed estimation over adaptive networks adaptive networks consist of a collection of nodes with adaptation and learning abilities the nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a distributed manner in this work we compare the mean square performance of two main strategies for distributed estimation over networks consensus strategies and diffusion strategies the analysis in the paper confirms that under constant step sizes diffusion strategies allow information to diffuse more thoroughly through the network and this property has a favorable effect on the evolution of the network diffusion networks are shown to converge faster and reach lower mean square deviation than consensus networks and their mean square stability is insensitive to the choice of the combination weights in contrast and surprisingly it is shown that consensus networks can become unstable even if all the individual nodes are stable and able to solve the estimation task on their own when this occurs cooperation over the network leads to a catastrophic failure of the estimation task this phenomenon does not occur for diffusion networks we show that stability of the individual nodes always ensures stability of the diffusion network irrespective of the combination topology simulation results support the theoretical findings

equation and dynamic boundary condition of cahn hilliard type with singular potentials abstract the well posedness of a system of partial differential equations and dynamic boundary conditions both of cahn hilliard type is discussed the existence of a weak solution and its continuous dependence on the data are proved using a suitable setting for the conservation of a total mass in the bulk plus the boundary a very general class of double well like potentials is allowed moreover some further regularity is obtained to guarantee the strong solution

higher order cahn hilliard equations with dynamic boundary conditions abstract our aim in this paper is to study the well posedness and the dissipativity of higher order cahn hilliard equations with dynamic boundary conditions more precisely we prove the existence and uniqueness of solutions and the existence of the global attractor

diagonal algebraic space time block codes we construct a new family of linear space time st block codes by the combination of rotated constellations and the hadamard transform and we prove them to achieve the full transmit diversity over a quasi static or fast fading channels the proposed codes transmit at a normalized rate of 1 symbol s when the number of transmit antennas n 1 2 or n is a multiple of four we spread a rotated version of the information symbol vector by the hadamard transform and send it over n transmit antennas and n time periods for other values of n we construct the codes by sending the components of a rotated version of the information symbol vector over the diagonal of an n spl times n st code matrix the codes maintain their rate diversity and coding gains for all real and complex constellations carved from the complex integers ring z i and they outperform the codes from orthogonal design when using complex constellations for n 2 the maximum likelihood ml decoding of the proposed codes can be implemented by the sphere decoder at a moderate complexity it is shown that using the proposed codes in a multiantenna system yields good performances with high spectral efficiency and moderate decoding complexity

some asymptotic results for learning in single hidden layer feedforward network models abstract we investigate the properties of a recursive estimation procedure the method of back propagation for a class of nonlinear regression models single hidden layer feedforward network models recently developed by cognitive scientists the results follow from more general results for a class of recursive m estimators obtained using theorems of ljung 1977 and walk 1977 for the method of stochastic approximation conditions are given ensuring that the back propagation estimator converges almost surely to a parameter value that locally minimizes expected squared error loss provided the estimator does not diverge and that the back propagation estimator is asymptotically normal when centered at this minimizer this estimator is shown to be statistically inefficient and a two step procedure that has efficiency equivalent to that of nonlinear least squares is proposed practical issues are illustrated by a numerical example involving approximation of the henon map