dual h _ infty algorithms for signal processing application to speech enhancement this paper deals with the joint signal and parameter estimation for linear state space models an efficient solution to this problem can be obtained by using a recursive instrumental variable technique based on two dual kalman filters in that case the driving process and the observation noise in the state space representation for each filter must be white with known variances these conditions however are too strong to be always satisfied in real cases to relax them we propose a new approach based on two dual hinfin filters once a new observation of the disturbed signal is available the first hinfin algorithm uses the latest estimated parameters to estimate the signal while the second hinfin algorithm uses the estimated signal to update the parameters in addition as the hinfin filter behavior depends on the choice of various weights we present a way to recursively tune them this approach is then studied in the following cases 1 consistent estimation of the ar parameters from noisy observations and 2 speech enhancement where no a priori model of the additive noise is required for the proposed approach in each case a comparative study with existing methods is carried out to analyze the relevance of our solution

an efficient robust adaptive filtering algorithm based on parallel subgradient projection techniques this paper presents a novel robust adaptive filtering scheme based on the interactive use of statistical noise information and the ideas developed originally for efficient algorithmic solutions to the convex feasibility problems the statistical noise information is quantitatively formulated as stochastic property closed convex sets by the simple design formulae developed in this paper a simple set theoretic inspection also leads to an important statistical reason for the sensitivity to noise of the affine projection algorithm apa the proposed adaptive algorithm is computationally efficient and robust to noise because it requires only an iterative parallel projection onto a series of closed half spaces that are highly expected to contain the unknown system to be identified and is free from the computational load of solving a system of linear equations the numerical examples show that the proposed adaptive filtering scheme realizes dramatically fast and stable convergence for highly colored excited speech like input signals in severe noise situations

entropic nonsignaling correlations we introduce the concept of entropic nonsignaling correlations i e entropies arising from probabilistic theories that are compatible with the fact that we cannot transmit information instantaneously we characterize and show the relevance of these entropic correlations in a variety of different scenarios ranging from typical bell experiments to more refined descriptions such as bilocality and information causality in particular we apply the framework to derive the first entropic inequality testing genuine tripartite nonlocality in quantum systems of arbitrary dimension and also prove the first known monogamy relation for entropic bell inequalities further within the context of complex bell networks we show that entropic nonlocal correlations can be activated

supervised learning of perceptron and output feedback dynamic networks a feedback analysis via the small gain theorem this paper provides a time domain feedback analysis of the perceptron learning algorithm and of training schemes for dynamic networks with output feedback it studies the robustness performance of the algorithms in the presence of uncertainties that might be due to noisy perturbations in the reference signals or due to modeling mismatch in particular bounds are established on the step size parameters in order to guarantee that the resulting algorithms will behave as robust filters the paper also establishes that an intrinsic feedback structure can be associated with the training schemes the feedback configuration is motivated via energy arguments and is shown to consist of two major blocks a time variant lossless i e energy preserving feedforward path and a time variant feedback path the stability of the feedback structure is then analyzed via the small gain theorem and choices for the step size parameter in order to guarantee faster convergence are deduced by using the mean value theorem simulation results are included to demonstrate the findings

cyclical interactions with alliance specific heterogeneous invasion rates we study a six species lotka volterra type system on different two dimensional lattices when each species has two superior and two inferior partners the invasion rates from predator sites to a randomly chosen neighboring prey site depend on the predator prey pair whereby cyclic symmetries within the two three species defensive alliances are conserved monte carlo simulations reveal an unexpected nonmonotonous dependence of alliance survival on the difference of alliance specific invasion rates this behavior is qualitatively reproduced by a four point mean field approximation the study addresses fundamental problems of stability for the competition of two defensive alliances and thus has important implications in natural and social sciences

optimum performance levels for minimax filters predictors and smoothers abstract for both discrete and continuous time linear time varying systems we obtain the achievable performance levels for minimax filters predictors and smoothers in terms of the finite escape times of some related discrete and continuous time riccati equations our game theoretic approach also yields an alternative derivation for the corresponding minimax estimators which were first obtained in 1 they are all bayes estimators with respect to particular gaussian distributions and admit recursive structures

parallel and sequential block kalman filtering and their implementations using systolic arrays two sets of block kalman filtering equations that differ in the manner of generating the initial and updated estimates are derived parallel and sequential schemes for generating these estimates are adopted it is shown that the parallel implementation inherently leads to a block kalman estimator which provides filtered estimates at the vector block level and fixed lag smoother estimates at the sample level the sequential implementation scheme on the other hand generates the estimates of each sample recursively leading naturally to a scalar filter estimator these scalar estimates are arranged in a vector form resulting in a block estimator which solely generates filtered estimates both at the vector and sample levels simulation results on a speech signal are presented which indicate the advantages of the sequential block kalman filter an algorithm for iterative calculation of kalman gain and error covariance matrices is given which does not require any matrix inversion operation the implementation of this algorithm using available systolic array processors is presented a ring systolic array which can be used to implement the state update part of the block kalman filter is suggested

polynomial matrix solution of the h infinity filtering problem and the relationship to riccati equation state space results a solution to the standard suboptimal h filtering problem is presented using a new polynomial systems ap proach the polynomial matrix solution is closely related to the recent h state space based riccati equation results and the links between the polynomial and state equation methodologies are demonstrated the h filter is derived by solving a special type of minimum variance filtering problem using a technique based on game theory the solution of this game problem in a stochastic setting by polynomial methods is novel the cal culation of the h filter involves a j spectral factorization and the solution of two coupled diophantine equations there are several computational advantages over previous polynomial methods for calculating h filters

existence and uniqueness of risk sensitive estimates risk sensitive criteria have been used to derive robust filters identifiers and controllers the fundamental issues of existence and uniqueness of an estimate of a random variable given a random vector with respect to an order spl lambda p risk sensitive criterion are studied in this note more precisely we prove the existence of a unique risk sensitive estimate provided spl lambda 0 and p 1 for the remaining cases a general existence result is not available at this time we do however prove the existence in certain special cases moreover we present examples with uncountably many optimal risk sensitive estimates i e exhibiting an extremely high level of nonuniqueness

mean escape time in a system with stochastic volatility we study the mean escape time in a market model with stochastic volatility the process followed by the volatility is the cox ingersoll and ross process which is widely used to model stock price fluctuations the market model can be considered as a generalization of the heston model where the geometric brownian motion is replaced by a random walk in the presence of a cubic nonlinearity we investigate the statistical properties of the escape time of the returns from a given interval as a function of the three parameters of the model we find that the noise can have a stabilizing effect on the system as long as the global noise is not too high with respect to the effective potential barrier experienced by a fictitious brownian particle we compare the probability density function of the return escape times of the model with those obtained from real market data we find that they fit very well

nonuniform filter bank design with noises this work solves the signal reconstruction problem involving nonuniform filter bank systems with rational decimation factors and noise three main nonuniform filter bank systems i e filter block decimator fbd structure upsampler filter downsampler ufd structure and tree structure are included in this study according to different operating conditions two different signal reconstruction problems for nonuniform filter bank systems with noise under the unknown but identifiable input signal model and the unknown input signal model are discussed respectively at the first stage a unified block state space model for different nonuniform filter bank systems with noise is developed then by incorporating the identified input signal model with this unified state space model and appropriate choice of the augmented state vector the signal reconstruction problem is reduced to an equivalent state estimation problem for resulting augmented systems if the input signal is identifiable if the input signal is lacking in modeling the signal reconstruction is discussed from the minimax estimation point of view two state estimation techniques involving robust kalman filtering and h sub spl infin filtering are employed respectively to treat the signal reconstruction problem of nonuniform filter bank systems according to different a priori knowledge of the input signal finally several numerical examples are presented to illustrate the proposed algorithms and exhibit the performances

on upsampling downsampling and rational sampling rate filter banks solutions to the problem of design of rational sampling rate filter banks in one dimension has previosly been proposed the ability to interchange the operations of upsampling downsampling and filtering plays an important role in these solutions the present paper develops a complete theory for the analysis of arbitrary combinations of upsamplers downsamplers and filters in multiple dimensions although some of the simpler results are well known the more difficult results concerning swapping upsamplers and downsamplers and variations thereof are new as an application of this theory the authors obtain algebraic reductions of the general multidimensional rational sampling rate problem to a multidimensional uniform filter bank problem however issues concerning the design of the filters themselves are not addressed in multiple dimensions upsampling and downsampling operators are determined by integer matrices as opposed to scalars in one dimension and the noncommutativity of matrices makes the problem considerably more difficult cascades of upsamplers and downsamplers in one dimension are easy to analyze the new results for the analysis of multidimensional upsampling and downsampling operators are derived using the aryabhatta bezout identity over integer matrices as a fundamental tool a number of new results in the theory of integer matrices that a relevant to the filter bank problem are also developed special cases of some of the results pertaining to the commutativity of upsamplers downsamplers have been obtained in parallel by several authors

correlation polytopes their geometry and complexity a family of polytopes correlation polytopes which arise naturally in the theory of probability and propositional logic is defined these polytopes are tightly connected to combinatorial problems in the foundations of quantum mechanics and to the ising spin model correlation polytopes exhibit a great deal of symmetry exponential size symmetry groups which leave the polytope invariant and act transitively on its vertices are defined using the symmetries a large family of facets is determined a conjecture concerning the full facet structure of correlation polytopes is formulated the conjecture however implies that np co np various complexity results are proved it is shown that deciding membership in a correlation polytope is an np complete problem and deciding facets is probably not even in np the relations between the polytope symmetries and its complexity are indicated

subband coding systems incorporating quantizer models a new method for dealing with the effects of quantization in a subband system is proposed it uses the gain plus additive noise linear model for the lloyd max quantizer based on this it is demonstrated how by an appropriate choice of synthesis filters one can cancel all signal dependent errors at the output of the system the only remaining error is random in nature and not correlated with the input signal we therefore have a tradeoff between the error being only random or having signal dependent components as well since the error variances in both cases are comparable as a result of having only a random error it is possible to reduce this error using for example a noise removal technique the result is then extended to the case where the input is a multidimensional signal and arbitrary sampling lattices are used as well as to the qmf alias cancellation case to demonstrate the validity of the proposed approach two types of experiments on images are carried out in a toy example it is shown that using noise removal could be beneficial for a more realistic coding scheme however it is demonstrated that even in the case when the model is no longer valid when some of the subbands are discarded the output error is still much less correlated with the input signal as opposed to the commonly used subband system while visually the reconstructed images look very similar

theoretical analysis and simulations of the generalized lotka volterra model the dynamics of generalized lotka volterra systems is studied by theoretical techniques and computer simulations these systems describe the time evolution of the wealth distribution of individuals in a society as well as of the market values of firms in the stock market the individual wealths or market values are given by a set of time dependent variables w i i 1 dots n the equations include a stochastic autocatalytic term representing investments a drift term representing social security payments and a time dependent saturation term due to the finite size of the economy the w i mathrm mathrm s turn out to exhibit a power law distribution of the form p w ensuremath sim w ensuremath 1 ensuremath ensuremath alpha it is shown analytically that the exponent ensuremath alpha can be expressed as a function of one parameter which is the ratio between the constant drift component social security and the fluctuating component investments this result provides a link between the lower and upper cutoffs of this distribution namely between the resources available to the poorest and those available to the richest in a given society the value of ensuremath alpha is found to be insensitive to variations in the saturation term which represent the expansion or contraction of the economy the results are of much relevance to empirical studies that show that the distribution of the individual wealth in different countries during different periods in the 20th century has followed a power law distribution with 1l ensuremath alpha l2

the origin of power law distributions in self organized criticality the origin of power law distributions in self organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process an avalanche is then regarded as a first return random walk process in a one dimensional lattice power law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions this shows that power law distributions in self organized criticality may be caused by the balance of competitive interactions at the mean time the mean spatial size for avalanches with the same lifetime is found to increase in a power law with the lifetime

learning the structure of linear latent variable models we describe anytime search procedures that 1 find disjoint subsets of recorded variables for which the members of each subset are d separated by a single common unrecorded cause if such exists 2 return information about the causal relations among the latent factors so identified we prove the procedure is point wise consistent assuming a the causal relations can be represented by a directed acyclic graph dag satisfying the markov assumption and the faithfulness assumption b unrecorded variables are not caused by recorded variables and c dependencies are linear we compare the procedure with standard approaches over a variety of simulated structures and sample sizes and illustrate its practical value with brief studies of social science data sets finally we consider generalizations for non linear systems

information theoretic bell inequalities we formulate information theoretic bell inequalities which apply to any pair of widely separated physical systems if local realism holds the two systems must carry information consistent with the inequalities two spin s particles in a state of zero total spin violate these information bell inequalities

optimal signal reconstruction in noisy filter bank systems multirate kalman synthesis filtering approach a multirate kalman synthesis filter is proposed in this paper to replace the conventional synthesis filters in a noisy filter bank system to achieve optimal reconstruction of the input signal based on an equivalent block representation of subband signals a state space model is introduced for an m band filter bank system with subband noises the composite effect of the input signal analysis filter bank decimators and interpolators is represented by a multirate state space model the input signal is embedded in the state vector and the corrupting noises in subband paths are generally considered as additive noises hence the signal reconstruction problem in the m band filter bank systems with subband noises becomes a state estimation procedure in the resultant multirate state space model the multirate kalman filtering algorithm is then derived according to the multirate state space model to achieve optimal signal reconstruction in noisy filter bank systems based on the optimal state estimation theory the proposed multirate kalman synthesis filter provides the minimum variance reconstruction of the input signal two numerical examples are also included the simulation results indicate that the performance improvement of signal reconstruction in noisy filter bank systems is remarkable

dynamics of money and income distributions we formulate a model of personal income distributions within society our aim is to understand the origin of the natural law first proposed by pareto who suggested that the high end part of the income distribution follows a power law where f 1 w w 1 we generalise a model proposed the so called cc ccm model introducing the possibility of exchanges of money at random times unlike the cc ccm model this generalisation predicts tail exponents greater than unity in line with pareto s prediction and empirical observation

h sup spl infin optimality of the lms algorithm we show that the celebrated least mean squares lms adaptive algorithm is h sup spl infin optimal the lms algorithm has been long regarded as an approximate solution to either a stochastic or a deterministic least squares problem and it essentially amounts to updating the weight vector estimates along the direction of the instantaneous gradient of a quadratic cost function we show that the lms can be regarded as the exact solution to a minimization problem in its own right namely we establish that it is a minimax filter it minimizes the maximum energy gain from the disturbances to the predicted errors whereas the closely related so called normalized lms algorithm minimizes the maximum energy gain from the disturbances to the filtered errors moreover since these algorithms are central h sup spl infin filters they minimize a certain exponential cost function and are thus also risk sensitive optimal we discuss the various implications of these results and show how they provide theoretical justification for the widely observed excellent robustness properties of the lms filter

linear estimation in krein spaces i theory the authors develop a self contained theory for linear estimation in krein spaces the derivation is based on simple concepts such as projections and matrix factorizations and leads to an interesting connection between krein space projection and the recursive computation of the stationary points of certain second order or quadratic forms the authors use the innovations process to obtain a general recursive linear estimation algorithm when specialized to a state space structure the algorithm yields a krein space generalization of the celebrated kalman filter with applications in several areas such as h sup spl infin filtering and control game problems risk sensitive control and adaptive filtering

self similarity and power like tails in nonconservative kinetic models in this paper we discuss the large time behavior of solution of a simple kinetic model of boltzmann maxwell type such that the temperature is time decreasing and or time increasing we show that under the combined effects of the nonlinearity and of the time monotonicity of the temperature the kinetic model has non trivial quasi stationary states with power law tails in order to do this we consider a suitable asymptotic limit of the model yielding a fokker planck equation for the distribution the same idea is applied to investigate the large time behavior of an elementary kinetic model of economy involving both exchanges between agents and increasing and or decreasing of the mean wealth in this last case the large time behavior of the solution shows a pareto power law tail numerical results confirm the previous analysis

h optimality and a posteriori output estimate of the forgetting factor nlms algorithm the normalized least mean squares nlms algorithm is widely used for adaptive filtering the nlms algorithm may be extended using a variety of weight parameters that improve its performance one such extension involves appropriately introducing a forgetting factor into the nlms algorithm using the h framework the resultant forgetting factor nlms ffnlms algorithm may be regarded as a special case of the improved proportionate nlms ipnlms algorithm this work reveals that the ffnlms algorithm is h optimal and the a posteriori output estimate is identical to the observation signal for sufficiently large times

on a kinetic model for a simple market economy in this paper we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading we show that the kinetic model admits non trivial quasi stationary states with power law tails of pareto type in order to do this we consider a suitable asymptotic limit of the model yielding a fokker planck equation for the distribution of wealth among individuals for this equation the stationary state can be easily derived and shows a pareto power law tail numerical results confirm the previous analysis

semidefinite tests for latent causal structures testing whether a probability distribution is compatible with a given bayesian network is a fundamental task in the field of causal inference where bayesian networks model causal relations here we consider the class of causal structures where all correlations between observed quantities are solely due to the influence from latent variables we show that each model of this type imposes a certain signature on the observable covariance matrix in terms of a particular decomposition into positive semidefinite components this signature and thus the underlying hypothetical latent structure can be tested in a computationally efficient manner via semidefinite programming this stands in stark contrast with the algebraic geometric tools required if the full observable probability distribution is taken into account the semidefinite test is compared with tests based on entropic inequalities

control of ecological outcomes through deliberate parameter changes in a model of the gut microbiome the generalized lotka volterra glv equations are a mathematical proxy for ecological dynamics we focus on a glv model of the gut microbiome in which the evolution of the gut microbial state is determined in part by pairwise interspecies interaction parameters that encode environmentally mediated resource competition between microbes we develop an in silico method that controls the steady state outcome of the system by adjusting these interaction parameters this approach is confined to a bistable region of the glv model in this method a dimensionality reduction technique called steady state reduction ssr is first used to generate a two dimensional 2d glv model that approximates the high dimensional dynamics on the 2d subspace spanned by the two steady states then a bifurcation analysis of the 2d model analytically determines parameter modifications that drive an initial condition to a target steady state this parameter modification of the reduced 2d model guides parameter modifications of the original high dimensional model resulting in a change of steady state outcome in the high dimensional model this control method called ssr guided parameter change sparc bypasses the computational challenge of directly determining parameter modifications in the original high dimensional system sparc could guide the development of indirect bacteriotherapies which seek to change microbial compositions by deliberately modifying gut environmental variables such as gut acidity or macronutrient availability

robust discrete time minimum variance filtering the bounded variance filtered estimation of the state of an uncertain linear discrete time system with an unknown norm bounded parameter matrix is considered an upper bound on the variance of the estimation error is found for all admissible systems and estimators are derived that minimize the latter bound we treat the finite horizon time varying case and the infinite time case where the nominal system model is time invariant in the special stationary case where it is known that the uncertain system is time invariant we provide a robust filter for all uncertainties that still keep the system asymptotically stable

on steady distributions of kinetic models of conservative economies we analyze the large time behavior of various kinetic models for the redistribution of wealth in simple market economies introduced in the pertinent literature in recent years as specific examples we study models with fixed saving propensity introduced by chakraborti and chakrabarti eur phys j b 17 167 170 2000 as well as models involving both exchange between agents and speculative trading as considered by cordier et al j stat phys 120 253 277 2005 we derive a sufficient criterion under which a unique non trivial stationary state exists and provide criteria under which these steady states do or do not possess a pareto tail in particular we prove the absence of pareto tails in pointwise conservative models like the one in eur phys j b 17 167 170 2000 while models with speculative trades introduced in j stat phys 120 253 277 2005 develop fat tails if the market is risky enough the results are derived by a fourier based technique first developed for the maxwell boltzmann equation gabetta et al in j stat phys 81 901 934 1995 bisi et al in j stat phys 118 1 2 301 331 2005 pareschi and toscani in j stat phys 124 2 4 747 779 2006 and from a recursive relation which allows to calculate arbitrary moments of the stationary state

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

trek separation for gaussian graphical models gaussian graphical models are semi algebraic subsets of the cone of positive definite covariance matrices submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables we give a precise graph theoretic characterization of when submatrices of the covariance matrix have small rank for a general class of mixed graphs that includes directed acyclic and undirected graphs as special cases our new trek separation criterion generalizes the familiar d separation criterion proofs are based on the trek rule the resulting matrix factorizations and classical theorems of algebraic combinatorics on the expansions of determinants of path polynomials

perfect reconstruction filter banks with rational sampling factors an open problem namely how to construct perfect reconstruction filter banks with rational sampling factors is solved such filter banks have n branches each one having a sampling factor of p i qi and their sum equals one in this way the well known theory of filter banks with uniform band splitting is extended to allow for nonuniform divisions of the spectrum this can be very useful in the analysis of speech and music the theory relies on two transforms the first transform leads to uniform filter banks having polyphase components as individual filters the other results in a uniform filter bank containing shifted versions of same filters this in turn introduces dependencies in design and is left for future work as an illustration several design examples for the 2 3 1 3 case are given filter banks are then classified according to the possible ways in which they can be built it is shown that some cases cannot be solved even with ideal filters with real coefficients

algebraic factor analysis tetrads pentads and beyond factor analysis refers to a statistical model in which observed variables are conditionally independent given fewer hidden variables known as factors and all the random variables follow a multivariate normal distribution the parameter space of a factor analysis model is a subset of the cone of positive definite matrices this parameter space is studied from the perspective of computational algebraic geometry grobner bases and resultants are applied to compute the ideal of all polynomial functions that vanish on the parameter space these polynomials known as model invariants arise from rank conditions on a symmetric matrix under elimination of the diagonal entries of the matrix besides revealing the geometry of the factor analysis model the model invariants also furnish useful statistics for testing goodness of fit

sea ice floe size distribution in the context of spontaneous scaling emergence in stochastic systems sea ice floe size distribution fsd in ice pack covered seas influences many aspects of ocean atmosphere interactions however data concerning fsd in the polar oceans are still sparse and processes shaping the observed fsd properties are poorly understood typically power law fsds are assumed although no feasible explanation has been provided neither for this one nor for other properties of the observed distributions consequently no model exists capable of predicting fsd parameters in any particular situation here i show that the observed fsds can be well represented by a truncated pareto distribution p x x 1 exp 1 x which is an emergent property of a certain group of multiplicative stochastic systems described by the generalized lotka volterra glv equation building upon this recognition a possibility of developing a simple agent based glv type sea ice model is considered contrary to simple power law fsds glv gives consistent estimates of the total floe perimeter as well as floe area distribution in agreement with observations

derivation of the maximum entropy h controller and a state space formula for its entropy the problem of maximizing the entropy of a stabilized closed loop system is solved the solution exploits the parametrization of all closed loop systems that meet an h norm bound the central solution of this set is shown to maximize the entropy at infinity and for this case a particularly simple formula is derived for the maximum value of the entropy

the p norm generalization of the lms algorithm for adaptive filtering recently much work has been done analyzing online machine learning algorithms in a worst case setting where no probabilistic assumptions are made about the data this is analogous to the h sup spl infin setting used in adaptive linear filtering bregman divergences have become a standard tool for analyzing online machine learning algorithms using these divergences we motivate a generalization of the least mean squared lms algorithm the loss bounds for these so called p norm algorithms involve other norms than the standard 2 norm the bounds can be significantly better if a large proportion of the input variables are irrelevant i e if the weight vector we are trying to learn is sparse we also prove results for nonstationary targets we only know how to apply kernel methods to the standard lms algorithm i e p 2 however even in the general p norm case we can handle generalized linear models where the output of the system is a linear function combined with a nonlinear transfer function e g the logistic sigmoid

linear estimation in krein spaces ii applications we have shown that several interesting problems in h sup spl infin filtering quadratic game theory and risk sensitive control and estimation follow as special cases of the krein space linear estimation theory developed in part i we show that all these problems can be cast into the problem of calculating the stationary point of certain second order forms and that by considering the appropriate state space models and error gramians we can use the krein space estimation theory to calculate the stationary points and study their properties the approach discussed here allows for interesting generalizations such as finite memory adaptive filtering with varying sliding patterns

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

entropic inequalities and marginal problems a marginal problem asks whether a given family of marginal distributions for some set of random variables arises from some joint distribution of these variables here we point out that the existence of such a joint distribution imposes nontrivial conditions already on the level of shannon entropies of the given marginals these entropic inequalities are necessary but not sufficient criteria for the existence of a joint distribution for every marginal problem a list of such shannon type entropic inequalities can be calculated by fourier motzkin elimination and we offer a software interface to a fourier motzkin solver for doing so for the case that the hypergraph of given marginals is a cycle graph we provide a complete analytic solution to the problem of classifying all relevant entropic inequalities and use this result to bound the decay of correlations in stochastic processes furthermore we show that shannon type inequalities for differential entropies are not relevant for continuous variable marginal problems non shannon type inequalities are both in the discrete and in the continuous case in contrast to other approaches our general framework easily adapts to situations where one has additional conditional independence requirements on the joint distribution as in the case of graphical models we end with a list of open problems a complementary article discusses applications to quantum nonlocality and contextuality

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

robust stability analysis of kalman bucy filter under parametric and noise uncertainties the linear kalman bucy filter with both uncertain second order statistical noise properties and uncertain system model parameters is considered we investigate the conditions for robust stability based on the upper norm bound of noise and parametrical uncertainties saddlepoint theory and the gronwall lemma are employed to solve this problem

a polynomial approach to minimax frequency domain optimization of multivariable feedback systems the properties of a feedback system where the plant has rational transfer matrix h and the compensator has transfer matrix g can be characterized through the system functions s i hg and t g i hg 1 good disturbance attenuation robustness limited bandwidth and compensator roll off may be obtained by minimizing a criterion of the form z where z v s t w1 wls t w2 w2t v with respect to the compensator transfer matrix g here v w1 and w2 are suitable rational weighting matrices the solution of the problem can be reduced to a pair of matrix polynomial equations since the optimal solution is highly non unique special solutions with additional optimality properties are considered as well the paper includes a discussion of the numerical solution of the polynomial equations and of the question how to choose the weighting matrices to ensure required feedback system properties an example illustrates the results

can a quantum state over time resemble a quantum state at a single time the standard formalism of quantum theory treats space and time in fundamentally different ways in particular a composite system at a given time is represented by a joint state but the formalism does not prescribe a joint state for a composite of systems at different times if there were a way of defining such a joint state this would potentially permit a more even handed treatment of space and time and would strengthen the existing analogy between quantum states and classical probability distributions under the assumption that the joint state over time is an operator on the tensor product of single time hilbert spaces we analyse various proposals for such a joint state including one due to leifer and spekkens one due to fitzsimons jones and vedral and another based on discrete wigner functions finding various problems with each we identify five criteria for a quantum joint state over time to satisfy if it is to play a role similar to the standard joint state for a composite system that it is a hermitian operator on the tensor product of the single time hilbert spaces that it represents probabilistic mixing appropriately that it has the appropriate classical limit that it has the appropriate single time marginals that composing over multiple time steps is associative we show that no construction satisfies all these requirements if hermiticity is dropped then there is an essentially unique construction that satisfies the remaining four criteria

investments in random environments we present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment the dynamics of the investor s budget x t depends on the stochasticity of the return on investment r t for which different model assumptions are discussed the fat tail distribution of the budget is investigated and compared with theoretical predictions we are mainly interested in the most probable value xmp of the budget that reaches a constant value over time based on an analytical investigation of the dynamics we are able to predict x stat we find a scaling law that relates the most probable value to the characteristic parameters describing the stochastic process our analytical results are confirmed by stochastic computer simulations that show a very good agreement with the predictions

krylov proportionate adaptive filtering techniques not limited to sparse systems this paper proposes a novel adaptive filtering scheme named the krylov proportionate normalized least mean square kpnlms algorithm kpnlms exploits the benefits i e fast convergence for sparse unknown systems of the proportionate nlms algorithm but its applications are not limited to sparse unknown systems a set of orthonormal basis vectors is generated from a certain krylov sequence it is proven that the unknown system is sparse with respect to the basis vectors in case of fairly uncorrelated input data different adaptation gain is allocated to a coefficient of each basis vector and the gain is roughly proportional to the absolute value of the corresponding coefficient of the current estimate kpnlms enjoys i fast convergence ii linear complexity per iteration and iii no use of any a priori information numerical examples demonstrate significant advantages of the proposed scheme over the reduced rank method based on the multistage wiener filter mwf and the transform domain adaptive filter tdaf both in noisy and silent situations

the design of uniformly and nonuniformly spaced pseudoquadrature mirror filters in the past quadrature mirror filters qmf s have been used to derive both uniformly and nonuniformly spaced filterbanks a pair of qmf s divides a signal into two equal bands which can be decimated at 2 1 and subsequently combined to reconstruct the original signal in order to derive filterbanks with more than two bands qmf s are combined in a binary tree structure pseudoquadrature mirror filters are similar to qmf s but can be designed to split a signal directly into any number of equally spaced bands thus generalizing the qmf concept in this paper the theory of pseudoquadrature mirror filters is reviewed these filters retain the desirable property that the channel signals from a uniformly spaced bank of m filters can be decimated by m 1 then interpolated and reassembled to reproduce the original signal an extension is made to the theory to allow a set of nonuniformly spaced filters to be derived from a uniformly spaced set and still retain all the desirable characteristics another extension to the theory is the derivation of a family of different sized filterbanks all derived from the same original prototype potential applications for the new filterbanks include improvements in subband coding of speech and music and analog scrambling of speech

a trade investment model for distribution of wealth econophysics provides a strategy for understanding the potential mechanisms underlying the anomalous distribution of wealth found in real societies we present a computational nonlinear stochastic model for the distribution of wealth that depends upon three parameters and two mechanisms trade and investment to avoid economic paradoxes the trade mechanism is assumed to be related to the poorer trader s wealth and to statistically advantage the poorer of the two traders the two mechanisms together are shown to generate a distribution that reproduces the full range of the empirical wealth distribution and not only the inverse power law tail that pareto found in western societies at the end of the 19th century

langevin processes agent models and socio economic systems abstract we review some approaches to the understanding of fluctuations of financial asset prices our approach builds on the development of a simple langevin equation that characterises stochastic processes this provides a unifying approach that allows first a straightforward description of the early approaches of bachelier we generalize the approach to stochastic equations that model interacting agents the agent models recently advocated by marsilli and solomon are motivated using a simple change of variable we show that the peer pressure model of marsilli and the wealth dynamics model of solomon are essentially equivalent the methods are further shown to be consistent with a global free energy functional that invokes an entropy term based on the boltzmann formula there follows a brief digression on the heston model that extends the simple model to one that in the language of physics exhibits a temperature this is subject to stochastic fluctuations mathematically the model corresponds to a feller process dragulescu and yakovenko have shown how the model yields some of the stylised features of asset prices a more recent approach by michael and johnson maximised a tsallis entropy function subject to simple constraints they obtain a distribution function for financial returns that exhibits power law tails and which can describe the distribution of returns not only over low but also high frequencies minute by minute data for the dow jones index we show how this approach can be developed from an agent model where the simple langevin process is now conditioned by local rather than global noise such local noise may of course be the origin of speculative frenzy or herding in the market place the approach yields a bbgky type hierarchy of equations for the system correlation functions of especial interest is that the results can be obtained from a new free energy functional similar to that mentioned above except that a tsallis like entropy term replaces the boltzmann entropy term a mean field approximation yields the results of michael and johnson we show how personal income data for brazil the us germany and the uk analyzed recently by borgas can be qualitatively understood by this approach

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

an h sub spl infin optimization and its fast algorithm for time variant system identification in some estimation or identification techniques a forgetting factor spl rho has been used to improve the tracking performance for time varying systems however the value of spl rho has been typically determined empirically without any evidence of optimality in our previous work this open problem is solved using the framework of h sub spl infin optimization the resultant h sub spl infin filter enables the forgetting factor spl rho to be optimized through a process noise that is determined by the filter riccati equation this paper seeks to further explain the previously derived h sub spl infin filter giving an h sub spl infin interpretation of its tracking capability additionally a fast algorithm of the h sub spl infin filter called the fast h sub spl infin filter is presented when the observation matrix has a shifting property finally the effectiveness of the derived fast algorithm is illustrated for time variant system identification using several computer simulations here the fast h sub spl infin filter is shown to outperform the well known least mean square algorithm and the fast kalman filter in convergence rate

phase diagrams for three strategy evolutionary prisoner s dilemma games on regular graphs evolutionary prisoner s dilemma games are studied with players located on square lattice and random regular graph defining four neighbors for each one the players follow one of the three strategies tit for tat unconditional cooperation and defection the simplified payoff matrix is characterized by two parameters the temptation b to choose defection and the cost c of inspection reducing the income of tit for tat the strategy imitation from one of the neighbors is controlled by pairwise comparison at a fixed level of noise using monte carlo simulations and the extended versions of pair approximation we have evaluated the b c phase diagrams indicating a rich plethora of phase transitions between stationary coexistence absorbing and oscillatory states including continuous and discontinuous phase transitions by reasonable costs the tit for tat strategy prevents extinction of cooperators across the whole span of b determining the prisoner s dilemma game irrespective of the connectivity structure we also demonstrate that the system can exhibit a repetitive succession of oscillatory and stationary states upon changing a single payoff value which highlights the remarkable sensitivity of cyclical interactions on the parameters that define the strength of dominance

the statistical distribution of money and the rate of money transference abstract the distribution of money is analysed in connection with the boltzmann distribution of energy in the degenerate states of molecules plots of the population density of income distribution for various countries are well reproduced by a gamma function confirming the validity of the statistical distribution at equilibrium the equilibrium state is reached through pair wise money transference processes independently of the shape of the initial distribution and also of the detailed nature of the money transactions between the economic agents