a homographic best approximation problem with application to optimized schwarz waveform relaxation we present and study a homographic best approximation problem which arises in the analysis of waveform relaxation algorithms with optimized transmission conditions its solution characterizes in each class of transmission conditions the one with the best performance of the associated waveform relaxation algorithm we present the particular class of first order transmission conditions in detail and show that the new waveform relaxation algorithms are well posed and converge much faster than the classical one the number of iterations to reach a certain accuracy can be orders of magnitudes smaller we illustrate our analysis with numerical experiments

adaptive ofdm synchronization algorithms based on discrete stochastic approximation this paper presents discrete stochastic approximation algorithms dsa for time synchronization in orthogonal frequency division multiplexing ofdm systems it is shown that the discrete stochastic approximation algorithms can be effectively used to achieve a significant reduction in computational complexity compared to brute force maximum likelihood ml methods for ofdm synchronization the most important property of the proposed algorithms is their recursive self learning capability most of the computational effort is spent at the global or a local optimizer of the objective function the convergence of the algorithms is analyzed an adaptive version of the discrete stochastic approximation algorithm is also presented for tracking time varying time delays and frequency offsets in time selective fading channels detailed numerical examples illustrate the performance gains of these dsa based synchronization algorithms

optimized domain decomposition methods for the spherical laplacian the schwarz iteration decomposes a boundary value problem over a large domain omega into smaller subproblems by iteratively solving dirichlet problems on a cover omega 1 dots omega p of omega in this paper we discuss alternate transmission conditions that lead to faster convergence for the laplacian on the sphere omega we look at robin conditions second order tangential conditions and a discretized version of an optimal but nonlocal operator

system identification regime switching unmodeled dynamics and binary sensors abstract this paper is concerned with persistent system identification for plants that are equipped with binary sensors whose unknown parameter is a random process represented by a markov chain we treat two classes of problems in the first class the parameter is a stochastic process modeled by an irreducible and aperiodic markov chain with transition rates sufficiently faster than adaptation rates of identification algorithms in this case an averaged behavior of the parameter process can be derived from the stationary measure of the markov chain and can be estimated with empirical measures upper and lower error bounds are established that explicitly show impact of unmodeled dynamics in the second class of problems the state switches values infrequently a moving window maximum a posterior map algorithm is introduced for tracking the time varying parameters numerical results are presented to illustrate the tracking performance of the map algorithm and compare it with the widely used viterbi algorithm

performance of blind and group blind multiuser detectors in blind or group blind linear multiuser detection the detector is estimated from the received signals with the prior knowledge of only the signature waveform of the desired user or the signature waveforms of some but not all users the performance of a number of such estimated linear detectors including the direct matrix inversion dmi blind linear minimum mean square error mmse detector the subspace blind linear mmse detector and the form i and form ii group blind linear hybrid detectors are analyzed asymptotic limit theorems for each of the estimates of these detectors when the signal sample size is large are established based on which approximate expressions for the average output signal to interference plus noise ratios sinrs and bit error rates bers are given to gain insights on these analytical results the performance of these detectors in an equicorrelated code division multiple acces cdma system is compared examples are provided to demonstrate the excellent match between the theory developed here and the simulation results

new bounds on the total squared correlation and optimum design of ds cdma binary signature sets the welch lower bound see welch r l ieee trans inform theory vol it 20 p 397 9 1974 on the total squared correlation tsc of signature sets is known to be tight for real valued signatures and loose for binary signatures whose number is not a multiple of four we derive new bounds on the tsc of binary signature sets for any number of signatures k and any signature length l then for almost all k l in 1 2 256 we design optimum binary signature sets that achieve the new bounds the design procedure is based on simple transformations of hadamard matrices

iterative construction of optimum signature sequence sets in synchronous cdma systems optimum signature sequence sets that maximize the capacity of single cell synchronous code division multiple access cdma systems have been identified optimum signature sequences minimize the total squared correlation tsc they form a set of orthogonal sequences if the number of users is less than or equal to the processing gain and a set of welch 1994 bound equality wbe sequences otherwise we present an algorithm where users update their transmitter signature sequences sequentially in a distributed fashion by using available receiver measurements we show that each update decreases the tsc of the set and produces better signature sequence sets progressively we prove that the algorithm converges to a set of orthogonal signature sequences when the number of users is less than or equal to the processing gain we observe and conjecture that the algorithm converges to a wbe set when the number of users is greater than the processing gain at each step the algorithm replaces one signature sequence from the set with the normalized minimum mean squared error mmse receiver corresponding to that signature sequence since the mmse filter can be obtained by a distributed algorithm for each user the proposed algorithm is amenable to distributed implementation

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

optimized schwarz methods without overlap for the helmholtz equation the classical schwarz method is a domain decomposition method to solve elliptic partial differential equations in parallel convergence is achieved through overlap of the subdomains we study in this paper a variant of the schwarz method which converges without overlap for the helmholtz equation we show that the key ingredients for such an algorithm are the transmission conditions we derive optimal transmission conditions which lead to convergence of the algorithm in a finite number of steps these conditions are however nonlocal in nature and we introduce local approximations which we optimize for performance of the schwarz method this leads to an algorithm in the class of optimized schwarz methods we present an asymptotic analysis of the optimized schwarz method for two types of transmission conditions robin conditions and transmission conditions with second order tangential derivatives numerical results illustrate the effectiveness of the optimized schwarz method on a model problem and on a problem from industry

the multiscale robin coupled method for flows in porous media abstract a multiscale mixed method aiming at the accurate approximation of velocity and pressure fields in heterogeneous porous media is proposed the procedure is based on a new domain decomposition method in which the local problems are subject to robin boundary conditions the domain decomposition procedure is defined in terms of two independent spaces on the skeleton of the decomposition corresponding to interface pressures and fluxes that can be chosen with great flexibility to accommodate local features of the underlying permeability fields the well posedness of the new domain decomposition procedure is established and its connection with the method of douglas et al 1993 12 is identified also allowing us to reinterpret the known procedure as an optimized schwarz or two lagrange multiplier method the multiscale property of the new domain decomposition method is indicated and its relation with the multiscale mortar mixed finite element method mmmfem and the multiscale hybrid mixed mhm finite element method is discussed numerical simulations are presented aiming at illustrating several features of the new method initially we illustrate the possibility of switching from mmmfem to mhm by suitably varying the robin condition parameter in the new multiscale method then we turn our attention to realistic flows in high contrast channelized porous formations we show that for a range of values of the robin condition parameter our method provides better approximations for pressure and velocity than those computed with either the mmmfem and the mhm this is an indication that our method has the potential to produce more accurate velocity fields in the presence of rough realistic permeability fields of petroleum reservoirs

irreducible modules over finite simple lie conformal superalgebras of type k we construct all finite irreducible modules over lie conformal superalgebras of type k we construct all finite irreducible modules over lie conformal superalgebras of type k

on the stability of jump diffusions with markovian switching in this paper we consider the stability for a class of jump diffusions with markovian switching we first construct them successively and show that they can be associated with some appropriate generators and they are non explosive we then prove their feller continuity by the coupling methods furthermore we also prove their strong feller continuity by making use of the relation between the transition probabilities of jump diffusions and the corresponding diffusions finally we also investigate their exponential ergodicity

stability analysis of stochastic differential equations with markovian switching abstract this paper discusses the asymptotic stability of the nonlinear stochastic differential equations with markovian switching sdewmss the equations under consideration are more general whose transition jump rates matrix q is not precisely known by using the switching process jump times to subdivide the time and then investigate the related sequence we provide sufficient conditions for asymptotic stability of sdewmss when each subsystem is stable and a certain slow switching condition holds for the general multi dimensional linear sdewmss sufficient conditions via bi linear matrix inequalities are also proposed for the design of robust stabilization some examples are given to illustrate the effectiveness of our results

cdma codeword optimization interference avoidance and convergence via class warfare interference avoidance has been shown to reduce total square correlation tsc for given ensembles of user signature waveforms codewords in a synchronous code division multiple access cdma system in all experiments we have conducted sequential application of interference avoidance produces an optimal codeword set when starting from randomly chosen initial codewords here we provide the first formal proof of convergence to optimal codeword ensembles for greedy interference avoidance algorithms augmented by a technique called class warfare whereby users which reside in more heavily loaded areas of the signal space purposely interfere with attack the reception of users in less crowded areas coordination of deliberate interference by a complete class of aggrieved user is also sometimes necessary such attacks and subsequent codeword adjustment by attacked users are shown to strictly decrease tsc along the way we also show using linear algebra and a variant of stochastic ordering equivalence between minimization of tsc and maximization of sum capacity

a convergence theory for an overlapping schwarz algorithm using discontinuous iterates a new type of overlapping schwarz methods using discontinuous iterates is constructed by modifying the classical overlapping schwarz algorithm this new algorithm allows for discontinuous iterates across the artificial interface for poisson s equation this algorithm can be considered as an overlapping version of lions robin iteration method for which little is known concerning the rate of convergence since overlap improves the performance of the classical algorithms considerably the existence of a uniform convergence factor is the fundamental question for our algorithm a new theory using lagrange multipliers is developed and conditions are found for the existence of an almost uniform convergence factor for the dual variables which implies rapid convergence of the primal variables in the two overlapping subdomain case our result also shows a relation between the boundary conditions of the given problem and the artificial interface condition numerical results for the general case with cross points are also presented they indicate possible extensions of our results to this more general case

stochastic discrete optimization in this paper a stochastic search method is proposed for finding a global solution to the stochastic discrete optimization problem in which the objective function must be estimated by monte carlo simulation although there are many practical problems of this type in the fields of manufacturing engineering operations research and management science there have not been any nonheuristic methods proposed for such discrete problems with stochastic infrastructure the proposed method is very simple yet it finds a global optimum solution the method exploits the randomness of monte carlo simulation and generates a sequence of solution estimates this generated sequence turns out to be a nonstationary markov chain and it is shown under mild conditions that the markov chain is strongly ergodic and that the probability that the current solution estimate is global optimum converges to one furthermore the speed of convergence is also analyzed

a method for discrete stochastic optimization this paper addresses the problem of optimizing a function over a finite or countably infinite set of alternatives in situations where this objective function cannot be evaluated exactly but has to be estimated or measured a special focus is on situations where simulation is used to evaluate the objective function we present two versions of a new iterative method for solving such discrete stochastic optimization problems in each iteration of the proposed method a neighbor of the current alternative is selected and estimates of the objective function evaluated at the current and neighboring alternatives are compared the alternative that has a better observed function value becomes the next current alternative we show how one version of the proposed method can be used to solve discrete optimization problems where the objective function is evaluated using transient or steady state simulation and we show how the other version can be applied to solve a special class of discrete stochastic optimizati

adaptive step size algorithms for blind interference suppression in ds cdma systems this paper develops adaptive step size blind lms algorithms and adaptive forgetting factor blind rls algorithms for code aided suppression of multiple access interference mai and narrowband interference nbi in ds cdma systems these algorithms optimally adapt both the step size forgetting factor and the weight vector of the blind linear multiuser detector using the received measurements simulations are provided to compare the proposed algorithms with previously studied blind rls and blind lms algorithms they show that the adaptive step size blind lms algorithm and adaptive forgetting factor blind rls algorithm field significant improvements over the standard blind lms algorithm and blind rls algorithm in dynamic environments where the number of interferers are time varying

a robin type domain decomposition method with red black partition in this paper we present a new robin type nonoverlapping domain decomposition dd preconditioner the unknown variables to be solved in this preconditioned algebraic system are the robin transmission data on the interface which are different from the well known dd methods like substructuring nonoverlapping dd method and feti method through choosing suitable parameter on each subdomain boundary and using the tool of energy estimate for the second order elliptic problem we prove that the condition number of the preconditioned system is c 1 log frac h h 2 where h is the coarse mesh size and h is the fine mesh size moreover in this paper we always assume that there is a red black partition for the whole domain omega numerical results are given to illustrate the efficiency of our dd preconditioner

convergence rate of some domain decomposition methods for overlapping and nonoverlapping subdomains three iterative domain decomposition methods are considered simultaneous updates on all subdomains additive schwarz method flow directed sweeps and double sweeps by using some techniques of formal language theory we obtain a unique criterion of convergence for the three methods the convergence rate is a function of the criterion and depends on the algorithm

optimal schwarz waveform relaxation for the one dimensional wave equation we introduce a nonoverlapping variant of the schwarz waveform relaxation algorithm for wave propagation problems with variable coefficients in one spatial dimension we derive transmission conditions which lead to convergence of the algorithm in a number of iterations equal to the number of subdomains independently of the length of the time interval these optimal transmission conditions are in general nonlocal but we show that the nonlocality depends on the time interval under consideration and we introduce time windows to obtain optimal performance of the algorithm with local transmission conditions in the case of piecewise constant wave speed we show that convergence in two iterations can be achieved independently of the number of subdomains in that case the algorithm thus scales optimally with the number of subdomains provided the time windows are chosen appropriately for continuously varying coefficients we prove convergence of the algorithm with local transmission conditions using energy estimates we then introduce a finite volume discretization which permits computations on nonmatching grids and we prove convergence of the fully discrete schwarz waveform relaxation algorithm we finally illustrate our analysis with numerical experiments

finite conformal modules over n 2 3 4 superconformal algebras in this paper we continue the study of representation theory of formal distribution lie superalgebras initiated by cheng and kac asian j math 1 181 193 1997 2 153 156 1998 erratum we study finite verma type conformal modules over the n 2 n 3 and the two n 4 superconformal algebras and also find explicitly all singular vectors in these modules from our analysis of these modules we obtain a complete list of finite irreducible conformal modules over the n 2 n 3 and the two n 4 superconformal algebras

structured threshold policies for dynamic sensor scheduling a partially observed markov decision process approach we consider the optimal sensor scheduling problem formulated as a partially observed markov decision process pomdp due to operational constraints at each time instant the scheduler can dynamically select one out of a finite number of sensors and record a noisy measurement of an underlying markov chain the aim is to compute the optimal measurement scheduling policy so as to minimize a cost function comprising of estimation errors and measurement costs the formulation results in a nonstandard pomdp that is nonlinear in the information state we give sufficient conditions on the cost function dynamics of the markov chain and observation probabilities so that the optimal scheduling policy has a threshold structure with respect to a monotone likelihood ratio mlr ordering as a result the computational complexity of implementing the optimal scheduling policy is inexpensive we then present stochastic approximation algorithms for estimating the best linear mlr order threshold policy

a global search method for discrete stochastic optimization this paper is concerned with the problem of optimizing the performance of a stochastic system over a finite set of alternatives in situations where the performance of the system cannot be evaluated analytically but must be estimated or measured for instance through simulation we present two variants of a new method for solving such discrete stochastic optimization problems this new method uses global search to look for the optimal solution it generates a sequence taking values in the set of feasible alternatives where each new element of the sequence is generated by comparing the current element with another candidate alternative and letting the next element of the sequence be the one of the current and candidate alternatives that appears to yield better performance for both versions of the proposed method the element of the set of feasible alternatives that the generated sequence visits most often is shown to converge almost surely to a globally optimal solution of the underlying optimization pr

iterate averaging sign algorithms for adaptive filtering with applications to blind multiuser detection motivated by the developments on iterate averaging of recursive stochastic approximation algorithms and asymptotic analysis of sign error algorithms for adaptive filtering this work develops two stage sign algorithms for adaptive filtering the proposed algorithms are based on constructions of a sequence of estimates using large step sizes followed by iterate averaging our main effort is devoted to improving the performance of the algorithms by establishing asymptotic normality of a suitably scaled sequence of the estimation errors the asymptotic covariance is calculated and shown to be the smallest possible hence the asymptotic efficiency or asymptotic optimality is obtained then variants of the algorithm including sign regressor procedures and constant step algorithms are studied the minimal window width of averaging is also dealt with finally iterate averaging algorithms for blind multiuser detection in direct sequence code division multiple access ds cdma systems are proposed and developed and numerical examples are examined

a modification of the stochastic ruler method for discrete stochastic optimization abstract we propose a modified stochastic ruler method for finding a global optimal solution to a discrete optimization problem in which the objective function cannot be evaluated analytically but has to be estimated or measured our method generates a markov chain sequence taking values in the feasible set of the underlying discrete optimization problem it uses the number of visits this sequence makes to the different states to estimate the optimal solution we show that our method is guaranteed to converge almost surely a s to the set of global optimal solutions then we show how our method can be used for solving discrete optimization problems where the objective function values are estimated using either transient or steady state simulation finally we provide some numerical results to check the validity of our method and compare its performance with that of the original stochastic ruler method

condition number estimates and weak scaling for 2 level 2 lagrange multiplier methods for general domains and cross points the 2 lagrange multiplier method is a domain decomposition method which can be used to parallelize the solution of linear problems arising from partial differential equations in order to scale to large numbers of subdomains and processors domain decomposition methods require a coarse grid correction to transport low frequency information more rapidly between subdomains that are far apart we introduce two new 2 level methods by adding a coarse grid correction to 2 lagrange multiplier methods we prove that if we shrink h the grid parameter while maintaining bounded the ratio frac h h where h is the size of the subdomains the condition number of the method remains bounded we confirm our analysis with experiments on the hector high end computing terascale resource supercomputer this proves that the new methods scale weakly opening the door to massively parallel implementations

how does a stochastic optimization approximation algorithm adapt to a randomly evolving optimum root with jump markov sample paths stochastic optimization approximation algorithms are widely used to recursively estimate the optimum of a suitable function or its root under noisy observations when this optimum or root is a constant or evolves randomly according to slowly time varying continuous sample paths in comparison this paper analyzes the asymptotic properties of stochastic optimization approximation algorithms for recursively estimating the optimum or root when it evolves rapidly with nonsmooth jump changing sample paths the resulting problem falls into the category of regime switching stochastic approximation algorithms with two time scales motivated by emerging applications in wireless communications and system identification we analyze asymptotic behavior of such algorithms our analysis assumes that the noisy observations contain a nonsmooth jump process modeled by a discrete time markov chain whose transition frequency varies much faster than the adaptation rate of the stochastic optimization algorithm using stochastic averaging we prove convergence of the algorithm rate of convergence of the algorithm is obtained via bounds on the estimation errors and diffusion approximations remarks on improving the convergence rates through iterate averaging and limit mean dynamics represented by differential inclusions are also presented

adaptive search algorithms for discrete stochastic optimization a smooth best response approach this paper considers simulation based optimization of the performance of a regime switching stochastic system over a finite set of feasible configurations inspired by the stochastic fictitious play learning rules in game theory we propose an adaptive random search algorithm that uses a smooth best response sampling strategy and tracks the set of global optima yet distributes the search so that most of the effort is spent on simulating the system performance at the global optima the algorithm responds properly to the random unpredictable jumps of the global optimum even when the observations data are temporally correlated as long as a weak law of large numbers holds numerical examples show that the proposed scheme yields faster convergence and superior efficiency for finite sample lengths compared with several existing random search and pure exploration methods in the literature

robust stability and stabilization of linear stochastic systems with markovian switching and uncertain transition rates abstract this paper is concerned with the robust stabilization problem for a class of linear uncertain stochastic systems with markovian switching the uncertain stochastic system with markovian switching under consideration involves parameter uncertainties both in the system matrices and in the mode transition rates matrix new criteria for testing the robust stability of such systems are established in terms of bi linear matrix inequalities blmis and sufficient conditions are proposed for the design of robust state feedback controllers a numerical example is given to illustrate the effectiveness of our results

identification of systems with regime switching and unmodeled dynamics this paper is concerned with persistent identification of systems that involve deterministic unmodeled dynamics and stochastic observation disturbances and whose unknown parameters switch values possibly large jumps that can be represented by a markov chain two classes of problems are considered in the first class the switching parameters are stochastic processes modeled by irreducible and aperiodic markov chains with transition rates sufficiently faster than adaptation rates of the identification algorithms in this case tracking real time parameters by output observations becomes impossible and we show that an averaged behavior of the parameter process can be derived from the stationary measure of the markov chain and can be estimated with periodic inputs and least squares type algorithms upper and lower error bounds are established that explicitly show impact of unmodeled dynamics in contrast the second class of problems represents systems whose state transitions occur infrequently an adaptive algorithm with variable step sizes is introduced for tracking the time varying parameters convergence and error bounds are derived numerical results are presented to illustrate the performance of the algorithm

regime switching stochastic approximation algorithms with application to adaptive discrete stochastic optimization this work is devoted to a class of stochastic approximation problems with regime switching modulated by a discrete time markov chain our motivation stems from using stochastic recursive algorithms for tracking markovian parameters such as those in spreading code optimization in cdma code division multiple access wireless communication the algorithm uses constant step size to update the increments of a sequence of occupation measures it is proved that least squares estimates of the tracking errors can be developed assume that the adaptation rate is of the same order of magnitude as that of the time varying parameter which is more difficult to deal with than that of slower parameter variations due to the time varying characteristics and markovian jumps the usual stochastic approximation sa techniques cannot be carried over in the analysis by a combined use of the sa method and two time scale markov chains asymptotic properties of the algorithm are obtained which are distinct from the usual sa

singularly perturbed discrete time markov chains originating from a wide range of applications in optimization and control of large scale systems such as telecommunications queueing networks and manufacturing systems this work is devoted to a class of singularly perturbed discrete time markov chains the states of the markov chain are naturally decomposable into recurrent and transient classes such that within each class the interactions are strong and among different classes the interactions are weak our study focuses on the difference equations representing the probabilityvector and aims at deriving matched asymptotic expansions of the solutions justification and error analysis are also provided both time homogeneous and time inhomogeneous models are examined

schwarz solvers and preconditioners for the closest point method the discretization of surface intrinsic elliptic partial differential equations pdes poses interesting challenges not seen in flat spaces the discretization of these pdes typically proceeds by e

optimized schwarz methods for maxwell s equations over the last two decades classical schwarz methods have been extended to systems of hyperbolic partial differential equations using characteristic transmission conditions and it has been observed that the classical schwarz method can be convergent even without overlap in certain cases this is in strong contrast to the behavior of classical schwarz methods applied to elliptic problems for which overlap is essential for convergence more recently optimized schwarz methods have been developed for elliptic partial differential equations these methods use more effective transmission conditions between subdomains than the classical dirichlet conditions and optimized schwarz methods can be used both with and without overlap for elliptic problems we show here why the classical schwarz method applied to both the time harmonic and time discretized maxwell s equations converges without overlap the method has the same convergence factor as a simple optimized schwarz method for a scalar elliptic equation based on this insight we develop an entire new hierarchy of optimized overlapping and nonoverlapping schwarz methods for maxwell s equations with greatly enhanced performance compared to the classical schwarz method we also derive for each algorithm asymptotic formulas for the optimized transmission conditions which can easily be used in implementations of the algorithms for problems with variable coefficients we illustrate our findings with numerical experiments

adaptive mimo antenna selection via discrete stochastic optimization recently it has been shown that it is possible to improve the performance of multiple input multiple output mimo systems by employing a larger number of antennas than actually used and selecting the optimal subset based on the channel state information existing antenna selection algorithms assume perfect channel knowledge and optimize criteria such as shannon capacity or various bounds on error rate this paper examines mimo antenna selection algorithms where the set of possible solutions is large and only a noisy estimate of the channel is available in the same spirit as traditional adaptive filtering algorithms we propose simulation based discrete stochastic optimization algorithms to adaptively select a better antenna subset using criteria such as maximum mutual information bounds on error rate etc these discrete stochastic approximation algorithms are ideally suited to minimize the error rate since computing a closed form expression for the error rate is intractable we also consider scenarios of time varying channels for which the antenna selection algorithms can track the time varying optimal antenna configuration we present several numerical examples to show the fast convergence of these algorithms under various performance criteria and also demonstrate their tracking capabilities

mmse interference suppression for direct sequence spread spectrum cdma we consider interference suppression for direct sequence spread spectrum code division multiple access cdma systems using the minimum mean squared error mmse performance criterion the conventional matched filter receiver suffers from the near far problem and requires strict power control typically involving feedback from receiver to transmitter for acceptable performance multiuser detection schemes previously proposed mitigate the near far problem but are complex and require explicit knowledge or estimates of the interference parameters in this paper we present and analyze several new mmse interference suppression schemes which have the advantage of being near far resistant to varying degrees depending on their complexity and can be implemented adaptively when interference parameters are unknown and or time varying numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver we conclude that mmse detectors can alleviate the need for stringent power control in cdma systems and may be a practical alternative to the matched filter receiver

an optimal parallel nonoverlapping domain decomposition iterative procedure a nonoverlapping domain decomposition iterative procedure is developed and analyzed for second order elliptic problems in mathbb r n its convergence is proved the method is based on a robin type consistency condition with two parameters called a transmission coefficient and a penalty coefficient as a transmission condition together with a derivative free transmission data updating technique on the artificial interfaces then the method is applied to the nonconforming finite element problems a nonoverlapping domain decomposition iterative procedure for solving the nonconforming finite element problems of second order partial differential equations is developed and analyzed which is directly presented to the nonconforming finite element problems without introducing any lagrange multipliers its convergence is demonstrated and the convergence rate is derived the convergence analyses imply that the convergence rate is independent of the finite element meshes size while choosing the right parameters furthermore the conclusions are extended to the unstructured finite element meshes for both continuous problems and discrete problems the method of this paper can be applied to general multisubdomain decompositions and implemented on parallel machines with local communications naturally the method also allows choosing subdomains very flexibly even as small as an individual element for finite element problems

classification of quasifinite representations of a lie algebra related to block type abstract a well known theorem of mathieu s states that a harish chandra module over the virasoro algebra is either a highest weight module a lowest weight module or a module of the intermediate series it is proved in this paper that an analogous result also holds for the lie algebra b related to block type with basis l i c i z i 0 and relations l i l j i 1 j 1 l i j 0 i j 0 3 12 c namely an irreducible quasifinite b module is either a highest weight module a lowest weight module or a module of the intermediate series

absorbing boundary conditions for the wave equation and parallel computing absorbing boundary conditions have been developed for truncating unbounded computational domains to bounded ones the authors investigate the use of absorbing boundary conditions in domain decomposition algorithms for the wave equation moreover they optimize the absorbing boundary conditions in order to obtain a good performance of the schwarz waveform relaxation algorithm the analysis given is confirmed by numerical experiments

the 2 lagrange multiplier method applied to nonlinear transmission problems for the richards equation in heterogeneous soil with cross points we formulate the 2 lagrange multiplier method for the richards equation in heterogeneous soil this allows a rigorous formulation of a discrete version of the richards equation on subdomain decompositions involving cross points using kirchhoff transformation the individual subdomain problems can be transformed into convex minimization problems and solved efficiently using a monotone multigrid method we discuss and compare weak formulations of the time discrete and fully discretized multidomain problem it is shown that in the case of two subdomains when solving the resulting discrete system with a richardson iteration the new method is equivalent to a parallel version of the nonlinear robin method for the richards equation proposed in h berninger and o sander comput vis sci 13 2010 pp 187 205 we give numerical results for a problem with realistic soil parameters

balancing exploitation and exploration in discrete optimization via simulation through a gaussian process based search random search algorithms are often used to solve discrete optimization via simulation dovs problems the most critical component of a random search algorithm is the sampling distribution that is used to guide the allocation of the search effort a good sampling distribution can balance the trade off between the effort used in searching around the current best solution which is called exploitation and the effort used in searching largely unknown regions which is called exploration however most of the random search algorithms for dovs problems have difficulties in balancing this trade off in a seamless way in this paper we propose a new scheme that derives a sampling distribution from a fast fitted gaussian process based on previously evaluated solutions we show that the sampling distribution has the desired properties and can automatically balance the exploitation and exploration trade off furthermore we integrate this sampling distribution into a random research algorithm called a gaussian process based search gps and show that the gps algorithm has the desired global convergence as the simulation effort goes to infinity we illustrate the properties of the algorithm through a number of numerical experiments

classification of finite irreducible conformal modules over a class of lie conformal algebras of block type abstract we classify finite irreducible conformal modules over a class of infinite lie conformal algebras b p of block type where p is a nonzero complex number in particular we obtain that a finite irreducible conformal module over b p may be a nontrivial extension of a finite conformal module over vir if p 1 where vir is a virasoro conformal subalgebra of b p as a byproduct we also obtain the classification of finite irreducible conformal modules over a series of finite lie conformal algebras b n for n 1

condition number estimates for the nonoverlapping optimized schwarz method and the 2 lagrange multiplier method for general domains and cross points the optimized schwarz method and the closely related 2 lagrange multiplier method are domain decomposition methods which can be used to parallelize the solution of partial differential equations although these methods are known to work well in special cases e g when the domain is a square and the two subdomains are rectangles the problem has never been systematically stated nor analyzed for general domains with general subdomains the problem of cross points when three or more subdomains meet at a single vertex has been particularly vexing we introduce a 2 lagrange multiplier method for domain decompositions with cross points we estimate the condition number of the iteration and provide an optimized robin parameter for general domains we hope that this new systematic theory will allow broader utilization of optimized schwarz and 2 lagrange multiplier preconditioners

stochastic comparison algorithm for discrete optimization with estimation in this paper we study a class of discrete optimization problems where the objective function for a given configuration can be expressed as the expectation of a random variable in such problems only samples of the random variables are available for the optimization process an iterative algorithm called the stochastic comparison sc algorithm is developed the convergence of the sc algorithm is established based on an examination of the quasi stationary probabilities of a time inhomogeneous markov chain we also present some numerical experiments

schwarz waveform relaxation algorithms for the linear viscous equatorial shallow water equations we are interested in numerically solving the viscous shallow water equations with a small coriolis force on a large domain specifically we develop and analyze schwarz waveform relaxation algorithms we split the domain of computation into two subdomains and with appropriate transmission conditions an iterative procedure leads to the global solution we first analyze the dirichlet type transmission conditions computing the convergence rate in fourier laplace variables and proving it is less than 1 yields the convergence of the algorithm the algorithm requires an overlap between subdomains and the convergence is slow we propose a better algorithm for which the overlap is unnecessary the transmission conditions are now an approximation of the absorbing boundary conditions we also prove convergence if the domains overlap the arguments are similar to the dirichlet type problem if not we use variational arguments a numerical scheme is then proposed and numerical results are shown which highlight the

optimized schwarz methods for circular domain decompositions with overlap optimized schwarz methods are based on transmission conditions between subdo mains which are optimized for the problem class that is being solved such optimizations have been performed for many different types of partial differential equations but were almost exclusively based on the assumption of straight interfaces we study in this paper the influence of curvature on the optimization and we obtain four interesting new results first we show that the curvature does indeed enter the optimized parameters and the contraction factor estimates second we develop an asymptotically accurate approximation technique based on turan type inequalities in our case to solve the much harder optimization problem on the curved interface and this approximation tech nique will also be applicable to currently too complex best approximation problems in the area of optimized schwarz methods third we show that one can obtain transmission conditions from a simple circular model decomposition which have also been found using microlocal analysis but that these are not the best choices for the performance of the optimized schwarz method finally we find that in the case of curved interfaces optimized schwarz methods are not necessarily convergent for all admissible parameters our optimization leads however to parameter choices that give the same good performance for a circular decomposition as for a straight interface decomposition we illustrate our analysis with numerical experiments

multi objective ordinal optimization for simulation optimization problems ordinal optimization oo has been successfully applied to accelerate the simulation optimization process with single objective by quickly narrowing down the search space in this paper we extend the oo techniques to address multi objective simulation optimization problems by using the concept of pareto optimality we call this technique the multi objective oo moo to define the good enough set and the selected set we introduce two performance indices based on the non dominance relationship among the designs then we derive several lower bounds for the alignment probability under various scenarios by using a bayesian approach numerical experiments show that the lower bounds of the alignment probability are valid when they are used to estimate the size of the selected set as well as the expected alignment level though the lower bounds are conservative they have great practical value in terms of narrowing down the search space

on the geometric convergence of optimized schwarz methods with applications to elliptic problems the schwarz method can be used for the iterative solution of elliptic boundary value problems on a large domain one subdivides into smaller more manageable subdomains and solves the differential equation in these subdomains using appropriate boundary conditions optimized schwarz methods use robin conditions on the artificial interfaces for information exchange at each iteration and for which one can optimize the robin parameters while the convergence theory of classical schwarz methods with dirichlet conditions on the artificial interface is well understood the overlapping optimized schwarz methods still lack a complete theory in this paper an abstract hilbert space version of the optimized schwarz method osm is presented together with an analysis of conditions for its geometric convergence it is also shown that if the overlap is relatively uniform these convergence conditions are met for optimized schwarz methods for two dimensional elliptic problems for any positive robin parameter in the discrete setting we obtain that the convergence factor h varies like a polylogarithm of h numerical experiments show that the methods work well and that the convergence factor does not appear to depend on h

optimized schwarz methods optimized schwarz methods are a new class of schwarz methods with greatly enhanced convergence properties they converge uniformly faster than classical schwarz methods and their convergence rates dare asymptotically much better than the convergence rates of classical schwarz methods if the overlap is of the order of the mesh parameter which is often the case in practical applications they achieve this performance by using new transmission conditions between subdomains which greatly enhance the information exchange between subdomains and are motivated by the physics of the underlying problem we analyze in this paper these new methods for symmetric positive definite problems and show their relation to other modern domain decomposition methods like the new finite element tearing and interconnect feti variants

tracking and identification of regime switching systems using binary sensors this work is concerned with tracking and system identification for time varying parameters the parameters are markov chains and the observations are binary valued with noise corruption to overcome the difficulties due to the limited measurement information wonham type filters are developed first then based on the filters two popular estimators namely mean squares estimator msq and maximum posterior map estimator are constructed for the mean squares estimator we derive asymptotic normality in the sense of weak convergence and in the sense of strong approximation the asymptotic normality is then used to derive error bounds when the markov chain is infrequently switching we derive error bounds for map estimators when the markovian parameters are fast varying we show that the averaged behavior of the parameter process can be derived from the stationary measure of the markov chain and that can be estimated using empirical measures upper and lower error bounds on estimation errors are also established

stability of markov modulated discrete time dynamic systems motivated by various control applications this paper develops stability analysis of discrete time systems with regime switching in which the dynamics are modulated by markov chains with two time scales using the high contrast of the different transition rates among the markovian states singularly perturbed markov chains are used in the formulations taking into consideration of the regime changes and time scale separation makes the stability analysis a difficult task in this work asymptotic stability analysis is carried out using perturbed liapunov function techniques it is demonstrated that if the limit system is stable then the original system is also stable in addition we examine path excursion derive bounds on mean recurrence time and obtain the associated probability bounds

analysis of adaptive step size sa algorithms for parameter tracking we present proofs and data for adaptive step size algorithms for tracking time varying parameters when recursive stochastic approximation type algorithms are used a classical problem in adaptive control and communication theory concerns the tracking of the best fit of a given form when the statistics or the parameters change slowly a major and yet unresolved problem has been the choice of the step sizes in the tracking algorithm an algorithm for adapting the step size using the same system measurements which are used for the tracking was suggested by benveniste and various examples worked out by brossier the numerical results were very encouraging but proofs were lacking these proofs are supplied here together with supporting numerical data the proofs are based on recent results in stochastic approximation the adaptive step size technique works very well indeed much supporting analysis is presented particularly concerning the interpretation of certain stationary processes as stationary pathwise derivatives finite difference forms are also treated these are mathematically simpler and can be applied to a wide variety of systems even when the system is not well modeled the data shows that they work well

classification of finite irreducible conformal modules over lie conformal superalgebras of block type abstract we introduce a class of infinite lie conformal superalgebras s p of block type and classify their finite irreducible conformal modules for any nonzero parameter p in particular we show that such a conformal module admits a nontrivial extension of a finite conformal module over ns if p 1 where ns is a neveu schwarz conformal subalgebra of s p as a byproduct we also obtain the classification of finite irreducible conformal modules over a series of finite lie conformal superalgebras s n for n 1

computing efforts allocation for ordinal optimization and discrete event simulation ordinal optimization has emerged as an efficient technique for simulation and optimization exponential convergence rates can be achieved in many cases in this paper we present a new approach that can further enhance the efficiency of ordinal optimization our approach intelligently determines the optimal number of simulation replications or samples and significantly reduces the total simulation cost numerical illustrations are included the results indicate that our approach can obtain an additional 74 computation time reduction above and beyond the reduction obtained through the use of ordinal optimization for a 10 design example

stabilization and destabilization of hybrid systems of stochastic differential equations this paper aims to determine whether or not a stochastic feedback control can stabilize or destabilize a given nonlinear hybrid system new methods are developed and sufficient conditions on the stability and instability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization and destabilization

a singular perturbation approach to modeling and control of markov chains finite state continuous time markov processes with weak interactions are modeled as singularly perturbed systems aggregate states are obtained using a grouping algorithm two time scale expansions simplify cost equations and lead to decentralized optimization algorithms

representations of simple finite lie conformal superalgebras of type w and s we construct all finite irreducible modules over lie conformal superalgebras of type w and s

infinite rank schrodinger virasoro type lie conformal algebras motivated by the structure of certain modules over the loop virasoro lie conformal algebra and the lie structures of schrodinger virasoro algebras we construct a class of infinite rank lie conformal algebras csv a b where a b are complex numbers the conformal derivations of csv a b are uniformly determined the rank one conformal modules and graded free intermediate series modules over csv a b are classified corresponding results of the conformal subalgebra chv a b of csv a b are also presented

spreading code optimization and adaptation in cdma via discrete stochastic approximation the aim of this paper is to develop discrete stochastic approximation algorithms that adaptively optimize the spreading codes of users in a code division multiple access cdma system employing linear minimum mean square error mmse receivers the proposed algorithms are able to adapt to slowly time varying channel conditions one of the most important properties of the algorithms is their self learning capability they spend most of the computational effort at the global optimizer of the objective function tracking analysis of the adaptive algorithms is presented together with mean square convergence an adaptive step size algorithm is also presented for optimally adjusting the step size based on the observations numerical examples illustrating the performance of the algorithms in multipath fading channels show substantial improvement over heuristic algorithms