optimal designs for space time linear precoders and decoders we introduce a new paradigm for the design of transmitter space time coding that we refer to as linear precoding it leads to simple closed form solutions for transmission over frequency selective multiple input multiple output mimo channels which are scalable with respect to the number of antennas size of the coding block and transmit average peak power the scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension the specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses under average and peak power constraints the solutions are shown to convert the mimo channel with memory into a set of parallel flat fading subchannels regardless of the design criterion while appropriate power bits loading on the subchannels is the specific signature of the different designs the proposed designs are compared in terms of various performance measures such as information rate ber and symbol mean square error

efficient construction of reversible jump markov chain monte carlo proposal distributions the major implementational problem for reversible jump markov chain monte carlo methods is that there is commonly no natural way to choose jump proposals since there is no euclidean structure in the parameter space to guide our choice we consider mechanisms for guiding the choice of proposal the first group of methods is based on an analysis of acceptance probabilities for jumps essentially these methods involve a taylor series expansion of the acceptance probability around certain canonical jumps and turn out to have close connections to langevin algorithms the second group of methods generalizes the reversible jump algorithm by using the so called saturated space approach these allow the chain to retain some degree of memory so that when proposing to move from a smaller to a larger model information is borrowed from the last time that the reverse move was performed the main motivation for this paper is that in complex problems the probability that the markov chain moves between such spaces may be prohibitively small as the probability mass can be very thinly spread across the space therefore finding reasonable jump proposals becomes extremely important we illustrate the procedure by using several examples of reversible jump markov chain monte carlo applications including the analysis of autoregressive time series graphical gaussian modelling and mixture modelling

a fast method for robot location determination abstract a fast single view method for determining the location of mobile robot in 3 d space is proposed in the method a tetragon mark is used as the reference target and no prerequisite condition is imposed in grabbing the image the method utilizes the 3 d vector analysis technique and simple algebraic computation to achieve the fast location determination error analysis on the effects of sensor resolution in different distances and elevation angles is included experimental results show that the location determination time is about 0 22 s in a 12 mhz ibm compatible pc at computer system and the location error is less than 2 in average

fdma capacity of gaussian multiple access channels with isi this paper proposes a numerical method for characterizing the rate region achievable with frequency division multiple access fdma for a gaussian multiple access channel with intersymbol interference the frequency spectrum is divided into discrete frequency bins and the discrete bin assignment problem is shown to have a convex relaxation making it tractable to numerical optimization algorithms a practical low complexity algorithm for the two user case is also proposed the algorithm is based on the observation that the optimal frequency partition has a two band structure when the two channels are identical or when the signal to noise ratio is high the simulation result shows that the algorithm performs well in other cases as well the fdma capacity algorithm is used to devise the optimal frequency division duplex plan for very high speed digital subscriber lines

the k user vector gaussian multiple access channel with general messages sets capacity polymatroidal structure and efficient computation the capacity region of the k user vector gaussian multiple access channel with general message sets is established furthermore due to the presence of convexity both in the discrete and continuous senses it is shown that this capacity region is efficiently computable the capacity result is obtained by specializing recent results by the authors for the discrete memoryless multiple access channel and demonstrating that it suffices to only consider jointly gaussian input and auxiliary random variables for this second conclusion it is shown that jointly gaussian random variables maximize entropy subject to lattice conditional independence and covariance constraints a result that is of interest in its own right discrete convexity arises since the capacity region is a union of polymatroids over each polymatroid computing the maximal weighted sum rates is simple due to submodularity a discrete analog of concavity of the set function associated with the linear inequalities that define the polymatroid continuous convexity arises as the set of admissible covariance matrices is convex and the polymatroidal bounds are concave in these covariances

seismic sparse layer reflectivity inversion using basis pursuit decomposition a basis pursuit inversion of seismic reflection data for reflection coefficients is introduced as an alternative method of incorporating a priori information in the seismic inversion process the inversion is accomplished by building a dictionary of functions representing reflectivity patterns and constituting the seismic trace as a superposition of these patterns basis pursuit decomposition finds a sparse number of reflection responses that sum to form the seismic trace when the dictionary of functions is chosen to be a wedge model of reflection coefficient pairs convolved with the seismic wavelet the resulting reflectivity inversion is a sparse layer inversion rather than a sparse spike inversion synthetic tests suggest that a sparse layer inversion using basis pursuit can better resolve thin beds than a comparable sparse spike inversion application to field data indicates that sparse layer inversion results in the potentially improved detectability and resolution of some thin layers and reveals a

capacity of the discrete time gaussian channel with intersymbol interference the discrete time gaussian channel with intersymbol interference isi where the inputs are subject to a per symbol average energy constraint is considered the capacity of this channel is derived by means of a hypothetical channel model called the n circular gaussian channel ncgc whose capacity is readily derived using the theory of the discrete fourier transform the results obtained for the ncgc are used further to prove that in the limit of increasing block length n the capacity of the discrete time gaussian channel dtgc with isi using a per block average energy input constraint n block dtgc is indeed also the capacity when using the per symbol average energy constraint

ofdma capacity analysis in mimo channels in this paper the performance of orthogonal frequency division multiple access orthogonal frequency division multiple access ofdma is studied in the context of the general multiuser multicarrier multiple input multiple output mimo m3 system for both uplink up and downlink dl channels the relationship between ofdma and the optimal m3 solution is investigated from an information theoretical point of view specifically the necessary and sufficient conditions of ofdma being the capacity maximizing m3 transmission scheme is derived in addition ofdma optimality is explicitly analyzed in some special cases

parameter estimation for differential equations a generalized smoothing approach summary we propose a new method for estimating parameters in models that are defined by a system of non linear differential equations such equations represent changes in system outputs by linking the behaviour of derivatives of a process to the behaviour of the process itself current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to the realization of statistical objectives such as inference and interval estimation the paper describes a new method that uses noisy measurements on a subset of variables to estimate the parameters defining a system of non linear differential equations the approach is based on a modification of data smoothing methods along with a generalization of profiled estimation we derive estimates and confidence intervals and show that these have low bias and good coverage properties respectively for data that are simulated from models in chemical engineering and neurobiology the performance of the method is demonstrated by using real world data from chemistry and from the progress of the autoimmune disease lupus

multiuser transmit optimization for multicarrier broadcast channels asymptotic fdma capacity region and algorithms we derive optimal and suboptimal multiuser transmit optimization methods for a multicarrier broadcast channel with intersymbol interference under the frequency division multiple access fdma restriction the general fdma based multicarrier broadcast problem is formulated as a maximum weighted rate sum problem given each user s subchannel assignment the optimal transmit strategy is achieved by multilevel waterfilling unfortunately the problem of finding the optimal subchannel assignments is combinatorial however by relaxing the fdma restriction we obtain a convex reformulation that allows for efficient computation of the optimal solution and therefore a characterization of the fdma capacity region for a broadcast channel if all users share the same transmission medium we prove that the optimal frequency partitioning among the users has an ordered structure that can be exploited to significantly reduce the computational complexity to make multiuser transmit optimization schemes practical for applications with relatively fast time varying user data rate requirements or priorities further reduction in computational complexity is necessary this is achieved by restricting the energy distribution to be constant across the used subchannels simulations indicate the low complexity constant energy methods presented are very robust and suffer from negligible performance loss

capacity achieving distributions in gaussian multiple access channel with peak power constraints this paper addresses a two user gaussian multiple access channel mac under peak power constraints at the transmitters it is shown that generating the code books of both users according to discrete distributions with a finite number of mass points achieves the largest weighted sum rate in the network this verifies that any point on the boundary of the capacity region of a two user mac under peak power constraints at both transmitters is achieved by discrete distributions with a finite number of mass points although the capacity achieving distributions are not necessarily unique it is verified that only discrete distributions with a finite number of mass points can achieve a point on the boundary of the capacity region it is shown that there exist an infinite number of sum rate optimal points on the boundary of the capacity region in contrast to the gaussian mac with average power constraints we verify that time division td cannot achieve any of the sum rate optimal points in the gaussian mac with peak power constraints using the so called i mmse identity of guo et al the largest achievable sum rate by orthogonal code division ocd is characterized where it is shown that walsh hadamard spreading codes of length 2 are optimal in the symmetric case where the peak power constraints at both transmitters are identical we verify that ocd can achieve a sum rate that is strictly larger than the highest sum rate achieved by td finally it is demonstrated that there are values for the maximum peak power at the transmitters such that ocd can not achieve any of the sum rate optimal points on the boundary of the capacity region

inversion of seismic reflection data in the acoustic approximation the nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation the method is based on the generalized least squares criterion and it can handle errors in the data set and a priori information on the model multiply reflected energy is naturally taken into account as well as refracted energy or surface waves the inverse problem can be solved using an iterative algorithm which gives at each iteration updated values of bulk modulus density and time source function each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation backward in time of the data residuals the correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models this shows in particular that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data and commerc

bayesian closed skew gaussian inversion of seismic avo data for elastic material properties bayesian closed skew gaussian inversion is defined as a generalization of traditional bayesian gaussian inversion which is used frequently in seismic amplitude versus offset avo inversion the new model captures skewness in the variables of interest hence the posterior model for log transformed elastic material properties given seismic avo data might be a skew probability density function the model is analytically tractable and this makes it applicable in high dimensional 3d inversion problems assessment of the posterior models in high dimensions requires numerical approximations however the bayesian closed skew gaussian inversion approach has been applied on real elastic material properties from a well in the sleipner field in the north sea a comparison with results from traditional bayesian gaussian inversion shows that the mean square error of predictions of p wave and s wave velocities are reduced by a factor of two although somewhat less for density predictions

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

particle markov chain monte carlo methods summary markov chain monte carlo and sequential monte carlo methods have emerged as the two main tools to sample from high dimensional probability distributions although asymptotic convergence of markov chain monte carlo algorithms is ensured under weak assumptions the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and or if highly correlated variables are updated independently we show here how it is possible to build efficient high dimensional proposal distributions by using sequential monte carlo methods this allows us not only to improve over standard markov chain monte carlo schemes but also to make bayesian inference feasible for a large class of statistical models where this was not previously so we demonstrate these algorithms on a non linear state space model and a levy driven stochastic volatility model

approximate riemannian conjugate gradient learning for fixed form variational bayes variational bayesian vb methods are typically only applied to models in the conjugate exponential family using the variational bayesian expectation maximisation vb em algorithm or one of its variants in this paper we present an efficient algorithm for applying vb to more general models the method is based on specifying the functional form of the approximation such as multivariate gaussian the parameters of the approximation are optimised using a conjugate gradient algorithm that utilises the riemannian geometry of the space of the approximations this leads to a very efficient algorithm for suitably structured approximations it is shown empirically that the proposed method is comparable or superior in efficiency to the vb em in a case where both are applicable we also apply the algorithm to learning a nonlinear state space model and a nonlinear factor analysis model for which the vb em is not applicable for these models the proposed algorithm outperforms alternative gradient based methods by a significant margin

precoding for the multiantenna downlink multiuser snr gap and optimal user ordering this paper develops a practical design method for implementing tomlinson harashima precoding thp in a downlink channel with multiple antennas at the transmitter and a single antenna at each receiver a two step design process is proposed for minimizing the total transmit power while satisfying every user s minimum data rate and maximum bit error rate ber requirements first the ber and rate requirements are converted to virtual rate requirements which account for the gap to capacity introduced by practical quadrature amplitude modulation qam and thp the second step is to determine the transmit covariance matrices which specify the entire thp system that will provide these virtual rates at the minimum total transmit power as one of the main features in the proposed scheme an algorithm for finding the optimal user encoding or presubtraction order in polynomial time is proposed in addition we also propose an algorithm that finds a near optimal order but which is much less complex the proposed method outperforms existing zero forcing based thp systems in term of power efficiency

minorization conditions and convergence rates for markov chain monte carlo abstract general methods are provided for analyzing the convergence of discrete time general state space markov chains such as those used in stochastic simulation algorithms including the gibbs sampler the methods provide rigorous a priori bounds on how long these simulations should be run to give satisfactory results results are applied to two models of the gibbs sampler a bivariate normal model and a hierarchical poisson model with gamma conditionals the methods use the notion of minorization conditions for markov chains

gaussian multiaccess channels with isi capacity region and multiuser water filling the capacity region of a two user gaussian multiaccess channel with intersymbol interference isi in which the inputs pass through respective linear systems and are superimposed before being corrupted by an additive gaussian noise process is discussed a geometrical method for obtaining the optimal input power spectral densities and the capacity region is presented this method can be viewed as a nontrivial generalization of the single user water filling argument it is shown that as in the traditional memoryless multiaccess channel frequency division multiaccess fdma with optimally selected frequency bands for each user achieves the total capacity of the multiuser gaussian multiaccess channel with isi however the capacity region of the two user channel with memory is in general not a pentagon unless the channel transfer functions for both users are identical

geometry of stochastic state vector reduction the state space of a quantum mechanical system is a complex projective space the space of rays in the associated hilbert space the state space comes equipped with a natural riemannian metric the fubini study metric and a compatible symplectic structure the operations of ordinary quantum mechanics can thus be reinterpreted in the language of differential geometry it is interesting in this spirit to scrutinize the probabilistic assumptions that are brought in at various stages in the analy sis of quantum dynamics particularly in connection with state vector reduction a promising approach to understanding reduction studied recently by a number of authors involves the use of nonlinear stochastic dynamics to modify the ordinary linear schrodinger evolution here we use stochastic differential geometry to give a systematic geometric formulation for such stochastic models of state vector collapse in this picture the conventional schrodinger evolution which corresponds to the unitary flow associated with a killing vector of the fubini study metric is replaced by a more general stochastic flow on the state manifold in the simplest example of such a flow the volatility term in the stochastic differential equation for the state trajectory is proportional to the gradient of the expectation of the hamiltonian the conservation of energy is represented by the requirement that the actual process followed by the expectation of the hamiltonian as the state evolves should be a martingale this requirement implies the existence of a nonlinear term in the drift vector of the state process which is always oriented opposite to the direction of in creasing energy uncertainty as a consequence the state vector necessarily collapses to an energy eigenstate and a martingale argument can be used to show that the probability of collapse to a given eigenstate from any particular initial state is in fact given by precisely the usual quantum mechanical probability

spatio temporal coding for wireless communication multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels this paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed a compact model is developed for the multiple input multiple output mimo dispersive spatially selective wireless communication channel the multivariate information capacity is analyzed for high signal to noise ratio snr conditions the mimo channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components the number of input antennas or the number of output antennas this desirable result is contrasted with the lower capacity slope of the well studied case with multiple antennas at only one side of the radio link a spatio temporal vector coding stvc communication structure is suggested as a means for achieving mimo channel capacity the complexity of stvc motivates a more practical reduced complexity discrete matrix multitone dmmt space frequency coding approach both of these structures are shown to be asymptotically optimum an adaptive lattice trellis coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the dmmt channel experimental examples that support the theoretical results are presented

asymptotic capacity of multicarrier transmission with frequency selective fading and limited feedback we study the capacity of multicarrier transmission through a slow frequency selective fading channel with limited feedback which specifies channel state information our results are asymptotic in the number of subchannels we first assume independent and identically distributed i i d subchannel gains and show that for a large class of fading distributions a uniform power distribution over an optimized subset of subchannels or on off power allocation gives the same asymptotic growth in capacity as optimal water filling e g with rayleigh fading furthermore the growth in data rate can be achieved with a feedback rate as if the number of active subchannels is bounded the capacity grows only as with the feedback rate of we then consider correlated subchannels modeled as a markov process and study the savings in feedback assuming a fixed ratio of coherence bandwidth to the total bandwidth the ratio between minimum feedback rates with correlated and i i d subchannels converges to zero with e g as for rayleigh fading subchannels satisfying a first order autoregressive process we also show that adaptive modulation or rate control schemes in which the rate on each subchannel is selected from a quantized set achieves the same asymptotic growth rates in capacity and required feedback finally our results are extended to cellular uplink and downlink channel models

power allocation over parallel gaussian multiple access and broadcast channels in this correspondence we determine the optimal power allocation that achieves any specified point on the boundary of the capacity region for sets of parallel gaussian multiple access channels macs and sets of parallel gaussian broadcast channels bcs the power allocation is across the parallel channels and within each channel across the users in both cases there is a single constraint on the total power used first the allocation for the parallel macs is determined in a simple form using the karush kuhn tucker kkt conditions and a simple lagrangian argument using this result the allocation for the parallel bcs is derived using recent findings on the duality of the mac and bc

the bayesian evidence scheme for regularizing probability density estimating neural networks training probability density estimating neural networks with the expectation maximization em algorithm aims to maximize the likelihood of the training set and therefore leads to overfitting for sparse data in this article a regularization method for mixture models with generalized linear kernel centers is proposed which adopts the bayesian evidence approach and optimizes the hyperparameters of the prior by type ii maximum likelihood this includes a marginalization over the parameters which is done by laplace approximation and requires the derivation of the hessian of the log likelihood function the incorporation of this approach into the standard training scheme leads to a modified form of the em algorithm which includes a regularization term and adapts the hyperparameters on line after each em cycle the article presents applications of this scheme to classification problems the prediction of stochastic time series and latent space models

ergodic fading interference channels sum capacity and separability the sum capacity for specific sub classes of ergodic fading gaussian two user interference channels ifcs is developed under the assumption of perfect channel state information at all transmitters and receivers for the sub classes of uniformly strong every fading state is strong and ergodic very strong two sided ifcs a mix of strong and weak fading states satisfying specific fading averaged conditions the optimality of completely decoding the interference i e converting the ifc to a compound multiple access channel c mac is proved it is also shown that this capacity achieving scheme requires encoding and decoding jointly across all fading states as an achievable scheme and also as a topic of independent interest the capacity region and the corresponding optimal power policies for an ergodic fading c mac are developed for the sub class of uniformly weak ifcs every fading state is weak genie aided outer bounds are developed the bounds are shown to be achieved by treating interference as noise and by separable coding for one sided fading ifcs finally for the sub class of one sided hybrid ifcs a mix of weak and strong states that do not satisfy ergodic very strong conditions an achievable scheme involving rate splitting and joint coding across all fading states is developed and is shown to perform at least as well as a separable coding scheme

transdimensional seismic inversion using the reversible jump hamiltonian monte carlo algorithm abstractprestack or angle stack gathers are inverted to estimate pseudologs at every surface location for building reservoir models recently several methods have been proposed to increase the resolution of the inverted models all of these methods however require that the total number of model parameters be fixed a priori we have investigated an alternate approach in which we allow the data themselves to choose model parameterization in other words in addition to the layer properties the number of layers is also treated as a variable in our formulation such transdimensional inverse problems are generally solved by using the reversible jump markov chain monte carlo rjmcmc approach which is a tool for model exploration and uncertainty quantification this method however has very low acceptance we have developed a two step method by combining rjmcmc with a fixed dimensional mcmc called hamiltonian monte carlo which makes use of gradient information to take large steps acceptance probability

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

constant gap to capacity and generalized degrees of freedom regions of the mimo mac ic mac the mac ic mac is a class of multiple access interference channels consisting of two multiple access channels macs that are mutually interfering but in which there is interference only from one transmitter of each mac to the receiver of the other mac two achievable rate regions that are within a quantifiable gap of the capacity region for the discrete memoryless semi deterministic mac ic mac were obtained in a previous companion work by the authors using inner and outer bounds that are unions of polytopes over admissible random coding distributions in this paper we obtain single distribution and hence explicit inner and outer bounds that characterize the capacity region of the mimo gaussian mac ic mac to within a constant gap we also evaluate and study the generalized degrees of freedom gdof region via multidimensional signal level partitioning for mimo networks through its lens the achievability of the key vertices of the gdof region are examined this analysis as well as the symmetric gdof curve reveal that at high snr when the ratio of the interference to noise to the signal to noise ratios both taken in db is within a certain range non interfering transmitters in that cell can fully occupy the receivers signal partitions in one or more dimensions that cannot otherwise be utilized by the interfering transmitter alone this extends the same finding in the companion paper which established the results of this work for the scalar gaussian mac ic mac

capacity region of the finite state multiple access channel with and without feedback the capacity region of the finite state multiple access channel fs mac with feedback that may be an arbitrary time invariant function of the channel output samples is considered we characterize both an inner and an outer bound for this region using massey s directed information these bounds are shown to coincide and hence yield the capacity region of indecomposable fs macs without feedback and of stationary and indecomposable fs macs with feedback where the state process is not affected by the inputs though multiletter in general our results yield explicit conclusions when applied to specific scenarios of interest for example our results allow us to do the following 1 identify a large class of fs macs that includes the additive mod2 noise mac where the noise may have memory for which feedback does not enlarge the capacity region 2 deduce that for a general fs mac with states that are not affected by the input if the capacity region without feedback is zero then so is the capacity region with feedback 3 deduce that the capacity region of a mac that can be decomposed into a multiplexer concatenated by a point to point channel with without or with partial feedback the capacity region is given by sigmam rm les c where c is the capacity of the point to point channel and m indexes the encoders moreover we show that for this family of channels source channel coding separation holds

bayesian linearized avo inversion a new linearized avo inversion technique is developed in a bayesian framework the objective is to obtain posterior distributions for p wave velocity s wave velocity and density distributions for other elastic parameters can also be assessed for example acoustic impedance shear impedance and p wave to s wave velocity ratio the inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the zoeppritz equation the solution is represented by a gaussian posterior distribution with explicit expressions for the posterior expectation and covariance hence exact prediction intervals for the inverted parameters can be computed under the specified model the explicit analytical form of the posterior distribution provides a computationally fast inversion method tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero with realistic noise levels acoustic impedance was the best determined parameter

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

optimal linear precoding strategies for wideband noncooperative systems based on game theory part i nash equilibria in this two part paper we propose a decentralized strategy based on a game theoretic formulation to find out the optimal precoding multiplexing matrices for a multipoint to multipoint communication system composed of a set of wideband links sharing the same physical resources i e time and bandwidth we assume as optimality criterion the achievement of a nash equilibrium and consider two alternative optimization problems 1 the competitive maximization of mutual information on each link given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies and 2 the competitive maximization of the transmission rate using finite order constellations under the same constraints as above plus a constraint on the average error probability in this first part of the paper we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies then we prove that the optimal precoding multiplexing scheme for both games leads to a channel diagonalizing structure so that both matrix valued problems can be recast in a simpler unified vector power control game with no performance penalty thus we study this simpler game and derive sufficient conditions ensuring the uniqueness of the nash equilibrium interestingly although derived under stronger constraints incorporating for example spectral mask constraints our uniqueness conditions have broader validity than previously known conditions finally we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a pareto optimal centralized scheme to reach the nash equilibria of the game in part ii we propose alternative distributed algorithms along with their convergence conditions

transceiver optimization for block based multiple access through isi channels in this paper we describe a formulation of the minimum mean square error mmse joint transmitter receiver design problem for block based multiple access communication over intersymbol interference isi channels since the direct formulation of this problem turns out to be nonconvex we develop various alternative convex formulations using techniques of linear matrix inequalities lmis and second order cone programming socp in particular we show that the optimal mmse transceiver design problem can be reformulated as a semidefinite program sdp which can be solved using highly efficient interior point methods when the channel matrices are diagonal as in cyclic prefixed multicarrier systems we show that the optimal mmse transceivers can be obtained by subcarrier allocation and optimal power loading to each subcarrier for all the users moreover the optimal subcarrier allocation and power loading can be computed fairly simply in polynomial time by the relative ratios of the magnitudes of the subchannel gains corresponding to all subcarriers we also prove that any two users can share no more than one subcarrier in the optimal mmse transceivers by exploiting this property we design an efficient strongly polynomial time algorithm for the determination of optimal powerloading and subcarrier allocation in the two user case

riemann manifold langevin and hamiltonian monte carlo methods the paper proposes metropolis adjusted langevin and hamiltonian monte carlo sampling methods defined on the riemann manifold to resolve the shortcomings of existing monte carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations the methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for metropolis hastings or indeed hamiltonian monte carlo and metropolis adjusted langevin algorithms this allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the markov chain the methodology proposed exploits the riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold providing highly efficient convergence and exploration of the target density the performance of these riemann manifold monte carlo methods is rigorously assessed by performing inference on logistic regression models log gaussian cox point processes stochastic volatility models and bayesian estimation of dynamic systems described by non linear differential equations substantial improvements in the time normalized effective sample size are reported when compared with alternative sampling approaches matlab code that is available from http www ucl ac uk statistics research rmhmc allows replication of all the results reported

a novel color detection method based on hsl color space for robotic soccer competition in a robotic soccer competition the locations of the ball and the robot are recognized through the vision system in a strong dynamic environment therefore the robot and the computer need to identify the object in real time and accurately through the vision system due to the influence of the game ball under different brightnesses the color clusters of glossy materials will produce a nonlinear behavior and will cause difficulty of recognition thus we propose a novel color detection method based on hue saturation and lightness hsl color space in this paper firstly by utilizing the hue histogram the hue and saturation hs plane and the hue and lightness hl plane can be obtained respectively in addition based on the obtained information from two planes the databases can be built for decreasing the running time and increasing the recognition success rate of identifying object moreover a novel algorithm is presented for the game ball in the robotic soccer competition finally some examples under different brightnesses are illustrated to demonstrate the preciseness and the accuracy of the proposed method are better than the traditional method

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

learning in an uncertain world mimo covariance matrix optimization with imperfect feedback in this paper we present a distributed learning algorithm for the optimization of signal covariance matrices in gaussian multiple input and multiple output mimo multiple access channel with imperfect and possibly delayed feedback the algorithm is based on the method of matrix exponential learning mxl and it has the same information and computation requirements as distributed water filling however unlike water filling the proposed algorithm converges to the system s optimum signal covariance profile even under stochastic uncertainty and imperfect feedback moreover the algorithm also retains its convergence properties in the presence of user update asynchronicities random delays and or ergodically changing channel conditions our theoretical analysis is complemented by extensive numerical simulations which illustrate the robustness and scalability of mxl in realistic network conditions in particular the algorithm retains its convergence speed even for large numbers of users and or antennas per user

variable rate coding for slowly fading gaussian multiple access channels we consider a nonergodic multiple access gaussian block fading channel where a fixed number of independent and identically distributed i i d fading coefficients affect each codeword variable rate coding with input power constraint enforced on a per codeword basis is examined a centralized power and rate allocation policy is determined as a function of the previous and present fading coefficients the power control policy that optimizes the expected rates is obtained through dynamic programming and the average capacity region and the average capacity region per unit energy are characterized moreover we study the slope of spectral efficiency curve versus e sub b n sub 0 db and we quantify the penalty incurred by time division multiple access tdma over superposition coding in the low power regime

delayed rejection in reversible jump metropolis hastings summary in a metropolis hastings algorithm rejection of proposed moves is an intrinsic part of ensuring that the chain converges to the intended target distribution however persistent rejection perhaps in particular parts of the state space may indicate that locally the proposal distribution is badly calibrated to the target as an alternative to careful off line tuning of state dependent proposals the basic algorithm can be modified so that on rejection a second attempt to move is made a different proposal can be generated from a new distribution that is allowed to depend on the previously rejected proposal we generalise this idea of delaying the rejection and adapting the proposal distribution due to tierney mira 1999 to generate a more flexible class of methods that applies in particular to a variable dimension setting the approach is illustrated by two pedagogical examples and a more realistic application to a changepoints analysis for point processes some key wor ds adaptive changepoint efficiency of markov chain monte carlo estimation integrated autocorrelation time peskun ordering

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

balanced capacity of wireline multiple access channels with individual power constraints this paper applies the concept of balanced capacity a fair trade off between individual and global performance to the uplink of a gaussian frequency selective multiuser channel with k users where k can be much larger than 2 individual power constraints are applied to each transmitter which makes the computation of the balanced capacity very complex the concept of equivalent channel is used to derive an explicit expression of the optimal power allocation that remains compatible with the individual power constraints the computation of the balanced capacity is then formulated as a set of 2k nonlinear equations an iterative algorithm providing the exact solution is firstly introduced a suboptimal solution based on the iterative multiuser water filling imwf algorithm is then proposed and shown to be very close to the optimal solution the idea of this alternative method called balanced water filling is to modify the power allocation obtained with the imwf algorithm in order to get balanced data rates results are provided for a wireline access network with 20 users

bayesian calibration of computer models we consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models such models implemented as computer codes are often generic in the sense that by a suitable choice of some of the model s input parameters the code can be used to predict the behaviour of the system in a variety of specific applications however in any specific application the values of necessary parameters may be unknown in this case physical observations of the system in the specific context are used to learn about the unknown parameters the process of fitting the model to the observed data by adjusting the parameters is known as calibration calibration is typically effected by ad hoc fitting and after calibration the model is used with the fitted input values to predict the future behaviour of the system we present a bayesian calibration technique which improves on this traditional approach in two respects first the predictions allow for all sources of uncertainty including the remaining uncertainty over the fitted parameters second they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best fitting parameter values the method is illustrated by using data from a nuclear radiation release at tomsk and from a more complex simulated nuclear accident exercise

ricci curvature for metric measure spaces via optimal transport we dene a notion of a measured length space x having nonnegative n ricci curvature for n 2 1 1 or having1 ricci curvature bounded below byk fork2 r the denitions are in terms of the displacement convexity of certain functions on the associated wasserstein metric space p2 x of probability measures we show that these properties are preserved under measured gromov hausdor limits we give geometric and analytic consequences this paper has dual goals one goal is to extend results about optimal transport from the setting of smooth riemannian manifolds to the setting of length spaces a second goal is to use optimal transport to give a notion for a measured length space to have ricci curvature bounded below we refer to 11 and 44 for background material on length spaces and optimal transport respectively further bibliographic notes on optimal transport are in appendix f in the present introduction we motivate the questions that we address and we state the main results to start on the geometric side there are various reasons to try to extend notions of curvature from smooth riemannian manifolds to more general spaces a fairly general setting is that of length spaces meaning metric spaces x d in which the distance between two points equals the inmum of the lengths of curves joining the points in the rest of this introduction we assume that x is a compact length space alexandrov gave a good notion of a length space having curvature bounded below by k with k a real number in terms of the geodesic triangles in x in the case of a riemannian manifold m with the induced length structure one recovers the riemannian notion of having sectional curvature bounded below by k length spaces with alexandrov curvature bounded below by k behave nicely with respect to the gromovhausdor topology on compact metric spaces modulo isometries they form

polyhedron recognition using three view analysis abstract using three view analysis this paper proposes a new approach for single polyhedron recognition both the 3d surface data and 2d image projection patterns are used to find the exact corresponding model of an unknown input object the recognition process first applies a hypothesis generation verification process to match the 3d partial object of the unknown input which is reconstructed by applying the three view matching strategy chiou et al proc ics 88 pp 1516 1521 1988 and the polyhedron reconstruction process hung et al pattern recognition 22 231 246 1989 against the data based models for selecting the possible corresponding models candidates it then backprojects each candidate onto the three image planes and matches the outer boundaries of the three backprojections by a simple method for judging the exact corresponding model measurement error is also analyzed theoretically to give a bound of the threshold value so that it can be automatically chosen in each decision making process the approach is implemented on a pc level vision system experimental results show that the system is feasible and reliable even in a noisy environment

capacity region of the asynchronous gaussian vector multiple access channel in this paper we derive explicit expressions for the capacity region of the two user symbol asynchronous gaussian vector multiple access channel verdu considered the case where each user linearly modulates a fixed waveform in each symbol period where the symbol periods for the users are not perfectly aligned at the receiver he derived explicit capacity region expressions for the case where the transmitters have knowledge of the mutual offset and also for the case where the transmitters have no knowledge of the mutual offset in this paper we extend verdu s results to allow each user to linearly modulate a set of orthonormal waveforms instead of a single waveform in each symbol period and with no restrictions imposed on the waveforms we consider group power constraints which include individual sum power constraints as orthonormal waveforms assigned to each user may come from different frequency bands with different power constraints similar to the case where each user is allowed to linearly modulate only a single waveform our results hold regardless of whether or not the transmitters are frame synchronous in addition we present some results that are necessary to numerically compute the capacity region expressions with general purpose convex optimization algorithms next we simplify the capacity region expression when there are only individual sum power constraints and when the transmitters know the mutual offset we also prove a sufficient condition for a similar simplification to hold when the transmitters have no knowledge of the mutual offset finally we consider a specialized algorithm to numerically compute the simplified capacity region expression when the transmitters know the mutual offset