pareto optimal strategy for stochastic weakly coupled large scale systems with state dependent system noise this note is concerned with the decentralized infinite horizon stochastic pareto optimal static output feedback strategy for a class of weakly coupled systems with state dependent noise first pareto optimal control problems are formulated using a static output feedback strategy the necessary conditions are given by the cross coupled stochastic algebraic riccati type equations csares for proving the existence of the static output feedback strategy that minimizes the quadratic cost function after determining the asymptotic structure of the solutions of the csares a new sequential numerical algorithm and newton s method for solving the csares are described the resulting numerical solution is used to develop the pareto optimal strategy finally the efficiency of the proposed algorithm is demonstrated by solving a numerical example for a practical megawatt frequency control problem

transitional regression models with application to environmental time series abstract environmental epidemiologists often encounter time series data in the form of discrete or other nonnormal outcomes for example in modeling the relationship between air pollution and hospital admissions or mortality rates we present a case study examining the association between pollen counts and meteorologic covariates although such time series data are inadequately described by standard methods for gaussian time series they are often autocorrelated and warrant an analysis beyond those provided by ordinary generalized linear models glms transitional regression models trms signifying nonlinear regression models expressed in terms of conditional means and variances given past observations provide a unifying framework for two mainstream approaches to extending the glm for autocorrelated data the first approach models current outcomes with a glm that incorporates past outcomes as covariates whereas the second models individual outcomes with marginal glms and then couples the error term

pareto optimality in infinite horizon linear quadratic differential games in this article we derive conditions for the existence of pareto optimal solutions for linear quadratic infinite horizon cooperative differential games first we present a necessary and sufficient characterization for pareto optimality which translates to solving a set of constrained optimal control problems with a special structure next we show that if the dynamical system is controllable certain transversality conditions hold true and as a result all the pareto candidates can be obtained by solving a weighted sum optimal control problem further exploiting the linear structure we investigate the relationship between pareto optimality and weighted sum minimization finally for the scalar case we present an algorithm to find all the pareto optimal solutions assuming mild conditions on the control space

necessary and sufficient conditions for pareto optimal solutions of cooperative differential games in this paper we present necessary as well as sufficient conditions for the existence of a pareto optimum for cooperative differential games the obtained results are used to analyze the regular indefinite linear quadratic differential game for the scalar case an algorithm is devised to find all pareto efficient solutions

generalized autoregressive moving average models a class of generalized autoregressive moving average garma models is developed that extends the univariate gaussian arma time series model to a flexible observation driven model for non gaussian time series data the dependent variable is assumed to have a conditional exponential family distribution given the past history of the process the model estimation is carried out using an iteratively reweighted least squares algorithm properties of the model including stationarity and marginal moments are either derived explicitly or investigated using monte carlo simulation the relationship of the garma model to other models is shown including the autoregressive models of zeger and qaqish the moving average models of li and the reparameterized generalized autoregressive conditional heteroscedastic garch model providing the formula for its fourth marginal moment not previously derived the model is demonstrated by the application of the garma model with a negative binomial conditional distribution to

on hyperelliptic involutions of hyperbolic 3 manifolds by classical results a compact riemann surface or equivalently an orientable closed hyperbolic 2 manifold has at most one hyperelliptic involution i e the quotient by the involution is the 2 sphere a hyperelliptic involution is central in the automorphism or isometry group of such a hyperelliptic surface its fixed points are exactly the weierstrass points of the surface see e g fk in the present paper we consider hyperelliptic involutions of hyperbolic 3manifolds by definition these are isometric involutions whose quotient is the 3 sphere the situation is more complicated in dimension three in particular a hyperbolic 3 manifold can have more than one hyperelliptic involution our main result states that there is a universal bound on the number of non conjugate hyperelliptic involutions of closed hyperbolic 3 manifolds this bound is quite small and we compute it for various situations our methods also determine how different hyperelliptic involutions are related there remains a small gap between these upper bounds and the number of different involutionswhichwe can actually construct see r1 rz we remark that the question on the number of different hyperelliptic involutions of hyperbolic 3 manifolds has explicitly been asked in mv we obtain also results for hyperelliptic isometries of orders greater than two in particular for prime numbers p 2 we give a complete solution to the problem on the number of different hyperelliptic isometries of order p i e the upper bound we obtain is sharp let isom m denote the orientation preserving isometry group of a hyperbolic 3 manifoldm

multiobjective tracking control design of t s fuzzy systems in this study a multiobjective fuzzy control design method is introduced for nonlinear dynamic systems to guarantee the optimal h 2 and h reference tracking performance simultaneously first the takagi and sugeno t s fuzzy model is used to represent the nonlinear dynamic system then based on the t s fuzzy model multiobjective h 2 h tracking control design problem is formulated as a multiobjective problem mop to minimize the h 2 tracking error and h disturbance attenuation level for the fuzzy system at the same time since it is not easy to solve this mop directly an indirect method is proposed for the multiobjective h 2 h tracking control design finally in order to achieve the simultaneous optimization of the mop linear matrix inequality lmi based multiobjective evolution algorithm lmi based moea is developed based on non dominating sorting scheme to efficiently search the set of pareto optimal solutions for the mop from which designer can select one design according to his own preference further the multiobjective h 2 h fuzzy control design problem based on the weighted sum method is also solved as an alternative choice finally a simulation example of a robotic system is given to illustrate the design procedure and to confirm the robust and optimal tracking performance of the proposed method

negative binomial additive models summary the generalized additive model is extended to handle negative binomial responses the extension is complicated by the fact that the negative binomial distribution has two parameters and is not in the exponential family the methodology is applied to data involving dna adduct counts and smoking variables among ex smokers with lung cancer a more detailed investigation is made of the parametric relationship between the number of adducts and years since quitting while retaining a smooth relationship between adducts and the other covariates

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

a nonstationary negative binomial time series with time dependent covariates enterococcus counts in boston harbor boston harbor has a history of poor water quality including contamination by enteric pathogens we conduct a statistical analysis of data collected by the massachusetts water resources authority mwra between 1996 and 2002 to evaluate the effects of court mandated improvements in sewage treatment motivated by the ineffectiveness of standard poisson mixture models and their zero inflated counterparts we propose a new negative binomial model for time series of enterococcus counts in boston harbor where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor without further restrictions this function is not identifiable in the presence of time dependent covariates consequently we use a basis orthogonal to the space spanned by the covariates and use penalized quasi likelihood pql for estimation we conclude that enterococcus counts were greatly reduced near the nut island treatment plant nitp outfalls following the transfer of wastewaters fro

pareto optimal strategy for linear stochastic systems with h constraint in finite horizon abstract in this paper we derive conditions for the existence of pareto efficient strategy and pareto solution under h constraint for the linear quadratic lq finite horizon cooperative differential game of stochastic systems with state control and disturbance multiplicative noise firstly we present a stochastic bounded real lemma sbrl with any initial condition for the considered stochastic system next a necessary and sufficient condition for pareto optimal strategy under the h constraint is researched by two cross coupled generalized differential riccati equations gdres which is the key contribution of this paper another contribution is that the pareto solution for every controller is given under the pareto efficient strategy and worst case external disturbance finally a practical example is given to illustrate the effectiveness of our results

necessary sufficient conditions for pareto optimality in finite horizon mean field type stochastic differential game abstract this paper is concerned with necessary and sufficient conditions for the existence of pareto solutions in finite horizon mean field type stochastic cooperative differential game based on the equivalent characterization of pareto optimality the problem is transformed into a set of constrained mean field type stochastic optimal control problems with a special structure utilizing the mean field type stochastic minimum principle the necessary conditions are put forward under certain convex assumptions it is shown that the necessary conditions are also sufficient ones next the indefinite linear quadratic lq case is studied it is pointed out that the solvability of two related generalized differential riccati equations gdres provides a sufficient condition under which pareto efficient strategies are equivalent to weighted sum optimal controls in addition all pareto solutions are obtained based on the solutions of two generalized differential lyapunov equations gdles at last an example sheds light on the effectiveness of the theoretical results

non standard components of the character variety for a family of montesinos knots we show that there are montesinos knots with n 1 geq 4 tangles whose character varieties contain arbitrarily many irreducible components of dimension d for any 1 le d le n 2 moreover these irreducible components can be chosen so that the trace of the meridian is non constant

on character varieties sets of discrete characters and nonzero degree maps a it knot manifold is a compact connected irreducible orientable 3 manifold whose boundary is an incompressible torus we first investigate virtual epimorphisms between the fundamental groups of small knot manifolds and prove minimality results for small knot manifolds with respect to nonzero degree maps these results are applied later in the paper where we fix a small knot manifold m and investigate various sets of characters of representations rho pi 1 m to rm psl 2 bbb c whose images are discrete we show that the topology of these sets is intimately related to the algebraic structure of the rm psl 2 bbb c character variety of m as well as dominations of manifolds by m and its dehn fillings we apply our results to the following question of shicheng wang it are nonzero degree maps between infinitely many distinct dehn fillings of two hyperbolic knot manifolds m and n induced by a nonzero degree map m to n we show that the answer is yes generically using this we show that if a small mathcal h minimal hyperbolic knot manifold admits non homeomorphic mathcal h minimal dehn fillings it admits infinitely many such fillings we also construct the first infinite families of small closed connected orientable manifolds which are minimal in the sense that they do not admit nonzero degree maps other than homotopy equivalences to any aspherical manifold

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

pareto optimal filter design for nonlinear stochastic fuzzy systems via multiobjective h_ bf 2 h_ bm infty optimization this paper is concerned with the multiobjective h 2 h infty filtering design problem in nonlinear signal processing which can be approximated by a takagi sugerno t s fuzzy signal system we propose a multiobjective filter design to estimate state variables from noisy measurements for nonlinear signal systems and we focus our effort on achieving optimal concurrent performance for h 2 and h infty filtering in general it is difficult to solve the multiobjective mo h 2 h infty fuzzy filter problem directly and we therefore propose an indirect approach to minimize the upper bounds and transform the mo h 2 h infty filtering problem in to a linear matrix inequality lmi constrained multiobjective problem mop in addition we propose an lmi based multiobjective evolution algorithm to efficiently find pareto optimal solutions for the mop of multiobjective fuzzy filter design for nonlinear stochastic signal processing furthermore for comparison we also suggest the mo h 2 h infty filter design problem based on the weighted sum method our proposed indirect method can be widely employed to practically address the mo filter design problem in nonlinear signal processing finally a trajectory estimation of reentry vehicle by radar is provided to illustrate the design procedure of the pareto mo optimal filter

indefinite stochastic linear quadratic control and generalized differential riccati equation a stochastic linear quadratic lq control problem is indefinite when the cost weighting matrices for the state and the control are allowed to be indefinite indefinite stochastic lq theory has been extensively developed and has found interesting applications in finance however there remains an outstanding open problem which is to identify an appropriate riccati type equation whose solvability is it equivalent to the solvability of the indefinite stochastic lq problem this paper solves this open problem for lq control in a finite time horizon a new type of differential riccati equation called the generalized differential riccati equation is introduced which involves algebraic equality inequality constraints and a matrix pseudoinverse it is then shown that the solvability of the generalized riccati equation is not only sufficient but also necessary for the well posedness of the indefinite lq problem and the existence of optimal feedback open loop controls moreover all of the optimal controls can be identified via the solution to the riccati equation an example is presented to illustrate the theory developed

the π orbifold group of a link on associe a un enlacement l dans s 3 un groupe o l appele le groupe de variete d orbite de l on etudie certaines proprietes du groupe o l reliees a la geometrie de l enlacement l

on the complexity of the heegaard structure of hyperbolic 3 manifolds a well known result of waldhausen 22 states that all heegaard splittings of s 3 and of s 2 s 1 of a given genus g are homeomorphic and even isotopic recent work of various authors see 20 19 2 shows that there are more simple 3 manifolds where such a uniqueness holds however this is not true for most 3 manifolds see 12 15 pitts rubinstein 18 have announced a proof of the waldhausen conjecture 23 that for any 3 manifold m the maximal number hm g of non homeomorphic heegaard splittings is finite for any given genus g n this was shown by hass 10 for genus 2 manifolds and g 2 and by johannson 11 for haken manifolds it is expected that the number hm g grows for generic m i e not the above mentioned simple ones with the complexity of m in this note we consider heegaard splittings of minimal genus gmin m and show that for a large class of hyperbolic 3 manifolds hm gmin m grows exponentially theorem a let k s 3 be the montesinos knot m e 1 1 g g such that all i are mutually distinct odd primes and let g c d 1 g 22g 1 1 g let m be the closed 3 manifold obtained from k by m n surgery where m is even then for each m tupel e1 eg 1 1 g 1 1 there exists a minimal genus heegaard splitting y e1 eg and these are pairwise non homeomorphic

technical communique the regular convex cooperative linear quadratic control problem in this note we consider the cooperative linear quadratic control problem that is the problem where a number of players all facing a different linear quadratic control problem decide to cooperate in order to optimize their performance it is well known when the performance criteria are positive definite how one can determine the set of pareto efficient equilibria for these games in this note we generalize this result for indefinite criteria

necessary and sufficient conditions for pareto optimality of the stochastic systems in finite horizon abstract this paper is concerned with the necessary and sufficient conditions for the pareto optimality in the finite horizon stochastic cooperative differential game based on the necessary and sufficient characterization of the pareto optimality the problem is transformed into a set of constrained stochastic optimal control problems with a special structure utilizing the stochastic pontryagin minimum principle the necessary conditions for the existence of the pareto solutions are put forward under certain convex assumptions it is shown that the necessary conditions are also sufficient ones next we study the indefinite linear quadratic lq case it is pointed out that the solvability of the related generalized differential riccati equation gdre provides the sufficient condition under which all pareto efficient strategies can be obtained by the weighted sum optimality method two examples shed light on the effectiveness of theoretical results

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

bias correction in generalized linear mixed models with multiple components of dispersion abstract general formulas are derived for the asymptotic bias in regression coefficients and variance components estimated by penalized quasi likelihood pql in generalized linear mixed models with canonical link function and multiple sets of independent random effects easily computed correction matrices result in variance component estimates that have satisfactory asymptotic behavior for small values of the variance components and significantly reduce bias for larger values both first order and second order correction procedures are developed for regression coefficients estimated by pql the methods are illustrated through an analysis of an experiment on salamander matings involving crossed male and female random effects and their properties are evaluated in a simulation study