simultaneous parameter tracking and state estimation in a linear system abstract the task of simultaneous tracking of time varying parameters and estimation of the state is treated for a linear system described by a time varying input output armax or delta model with known c noise parameters first a bayesian approach based conceptual solution is presented then it is shown that utilizing the properties of the observer canonical state model algebraic recursion operating on the joint parameter and state mean and covariance matrix can be obtained with no approximation involved several illustrative examples are included

some q analogues of the carter payne theorem we prove a q analogue of the carter payne theorem for the two special cases cor responding to moving an arbitrary number of nodes between adjacent rows or moving one node between an arbitrary number of rows as a consequence we show that these homomorphism spaces are one dimensional when q 6 1 we apply these results to complete the classification of the reducible specht modules for the hecke algebras of the symmetric groups when q 6 1 our methods can also be used to determine certain other pairs of specht modules between which there is a homomorphism in particular we describe the homomorphism space homh s n s for an arbitrary partition s although widely conjectured no q analogue of the full carter payne theorem is known in this paper we prove such an analogue in two important special cases namely when b a 1 or when 1 combinatorially this corresponds to moving an arbitrary number of nodes between adjacent rows or moving one node between an arbitrary number of rows it turns out that our proof has interesting implications we will turn our attention to the classification of the reducible specht modules for the algebras hf q sn when q 6 1 recent work see section 5 3 has resulted in the completion of this classification when q 1 combining our main result theorem 4 5 4 with previously published work we prove that a specht module is reducible if and only if it is e p reducible as defined in definition 5 1 we will also use our discussion of semistandard homomorphisms to obtain a description of the specht modules which contain a submodule isomorphic to the trivial module s n see

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

dynamic quantizer design for hidden markov state estimation via multiple sensors with fusion center feedback this paper considers the state estimation of hidden markov models by sensor networks the objective is to minimize the long term average of the mean square estimation error for the underlying finite state markov chain by employing feedback from the fusion center a dynamic quantization scheme for the sensor nodes is proposed and analyzed by a stochastic control approach dynamic rate allocation is also considered when the sensor nodes generate mode dependent measurements

multiple model estimation with variable structure existing multiple model mm estimation algorithms have a fixed structure i e they use a fixed set of models an important fact that has been overlooked for a long time is how the performance of these algorithms depends on the set of models used limitations of the fixed structure algorithms are addressed first in particular it is shown theoretically that the use of too many models is performance wise as bad as that of too few models apart from the increase in computation this paper then presents theoretical results pertaining to the two ways of overcoming these limitations select construct a better set of models and or use a variable set of models this is in contrast to the existing efforts of developing better implementable fixed structure estimators both the optimal mm estimator and practical suboptimal algorithms with variable structure are presented a graph theoretic formulation of multiple model estimation is also given which leads to a systematic treatment of model set adaptation and opens up new avenues for the study and design of the mm estimation algorithms the new approach is illustrated in an example of a nonstationary noise identification problem

irreducible projective representations of the alternating group which remain irreducible in characteristic 2 abstract for any finite group g it is an interesting question to ask which ordinary irreducible representations of g remain irreducible in a given characteristic p we answer this question for p 2 when g is the proper double cover of the alternating group as a key ingredient in the proof we prove a formula for the decomposition numbers in rouquier blocks of double covers of symmetric groups in terms of schur p functions

brief paper structure detection and parameter estimation for narx models in a unified em framework in this paper we consider structure detection and parameter estimation of the nonlinear auto regressive with exogenous inputs narx model using the em expectation maximisation algorithm the parameter estimation step uses particle smoothing to obtain the necessary expectations in the e step and the parameters are then estimated in closed form in the m step the model structure detection is performed using an f test which makes use of the parameter information matrix inverse of the covariance matrix obtained from an augmentation of the em algorithm the steps for obtaining the information matrix are robust guaranteeing a positive semi definite information matrix to use in the structure detection step for the case of unknown model orders a method is proposed using the stochastic complexity sc information criterion for selecting between candidate models the sc is composed of the information matrix representing model complexity and a likelihood estimate representing model accuracy which are both generated as byproducts of the augmented em algorithm numerical results demonstrate that the em approach performs well in comparison to a standard alternative based on orthogonal least squares and also avoids the need to estimate a noise model for the case of measurement noise corrupted output signals

bending of layers weakened by cuts abstract in the present paper a method proposed by one of the authors is extended to a class of skew symmetric elastic problems for the stress analysis of a layer supported by sliding fixed supports and weakened by several stress raisers the corresponding boundary value problem is reduced to an infinite system of one dimensional singular integral equations of the second kind the expressions for the stress components in an elastic layer weakened by stress raisers are presented based on the developed analytical algorithm extensive numerical investigations have been conducted the results of these investigations are illustrated graphically exposing some novel qualitative and quantitative knowledge about stress concentration in the layer depending on some geometric parameters of stress raisers and poisson s ratio of a layer material

reducible specht modules abstract james and mathas conjecture a criterion for the specht module s for the symmetric group to be irreducible over a field of prime characteristic we extend a result of lyle to prove this conjecture in one direction our techniques are elementary

equilibrium of layers weakened by loaded cuts abstract in this paper a symmetric boundary value problem of the stress analysis for an equilibrium of layer with end supports covered by diaphragms and weakened by several loaded stress raisers is investigated the given boundary value problem is reduced to an infinite system of singular integral equations of the second kind the expressions for stress components in an elastic layer weakened by stress raisers are presented based on the developed analytical procedure extensive numerical investigations have been conducted the results of these investigations are illustrated graphically exposing some novel qualitative and quantitative knowledge about stress concentration in the layer depending on some geometric parameters of stress raisers and poisson s ratio of a layer material

signed young modules and simple specht modules abstract by a result of hemmer every simple specht module of a finite symmetric group over a field of odd characteristic is a signed young module while specht modules are parametrized by partitions indecomposable signed young modules are parametrized by certain pairs of partitions the main result of this article establishes the signed young module labels of simple specht modules along the way we prove a number of results concerning indecomposable signed young modules that are of independent interest in particular we determine the label of the indecomposable signed young module obtained by tensoring a given indecomposable signed young module with the sign representation as consequences we obtain the green vertices green correspondents cohomological varieties and complexities of all simple specht modules and a class of simple modules of symmetric groups and extend the results of gill on periodic young modules to periodic indecomposable signed young modules

an em algorithm for nonlinear state estimation with model uncertainties in most solutions to state estimation problems e g target tracking it is generally assumed that the state transition and measurement models are known a priori however there are situations where the model parameters or the model structure itself are not known a priori or are known only partially in these scenarios standard estimation algorithms like the kalman filter and the extended kalman filter ekf which assume perfect knowledge of the model parameters are not accurate in this paper the nonlinear state estimation problem with possibly non gaussian process noise in the presence of a certain class of measurement model uncertainty is considered it is shown that the problem can be considered as a special case of maximum likelihood estimation with incomplete data thus in this paper we propose an em type algorithm that casts the problem in a joint state estimation and model parameter identification framework the expectation e step is implemented by a particle filter that is initialized by a monte carlo markov chain algorithm within this step the posterior distribution of the states given the measurements as well as the state vector itself are estimated consequently in the maximization m step we approximate the nonlinear observation equation as a mixture of gaussians mog model during the m step the mog model is fit to the observed data by estimating a set of mog parameters the proposed procedure called em pf expectation maximization particle filter algorithm is used to solve a highly nonlinear bearing only tracking problem where the model structure is assumed unknown a priori it is shown that the algorithm is capable of modeling the observations and accurately tracking the state vector in addition the algorithm is also applied to the sensor registration problem in a multi sensor fusion scenario it is again shown that the algorithm is successful in accommodating an unknown nonlinear model for a target tracking scenario

some reducible specht modules for iwahori hecke algebras of type a with q 1 abstract let p be a prime and f a field of characteristic p and let h n denote the iwahori hecke algebra of the symmetric group s n over f at q 1 we prove that there are only finitely many partitions such that both and are 2 singular and the specht module s for h is irreducible

solution of the elastic boundary value problems for a layer with tunnel stress raisers abstract a novel procedure for solving three dimensional problems for elastic layer weakened by through thickness tunnel cracks has been developed and is presented in this paper this procedure reduces the given boundary value problem to an infinite system of one dimensional singular integral equations and is based on a system of homogeneous solutions for a layer integral representations of single and double layer potentials are used for metaharmonic and harmonic functions entering in the singular integral equations these representations provide a continuous extendibility of the stress vector while allowing a jump in the displacement vector in the transition through the cut expanding the potential and biharmonic solutions in the fourier series over the thickness coordinate yields the integral representations of the displacement vector and stress tensor the problem of reducing a denumerable set of the integral equations of the given boundary value problem to one to one correspondence with the set of unknown densities appearing in the fourier s coefficient representations has been settled efficiently numerical investigations show a rapid convergence of the proposed reduction procedure as applied to the solution of the infinite system of one dimensional integral equations numerical examples illustrate the proposed method and demonstrate its advantages

posterior cramer rao bounds for discrete time nonlinear filtering a mean square error lower bound for the discrete time nonlinear filtering problem is derived based on the van trees 1968 posterior version of the cramer rao inequality this lower bound is applicable to multidimensional nonlinear possibly non gaussian dynamical systems and is more general than the previous bounds in the literature the case of singular conditional distribution of the one step ahead state vector given the present state is considered the bound is evaluated for three important examples the recursive estimation of slowly varying parameters of an autoregressive process tracking a slowly varying frequency of a single cisoid in noise and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation

optimal estimation of sensor biases for asynchronous multi sensor data fusion an important step in a multi sensor surveillance system is to estimate sensor biases from their noisy asynchronous measurements this estimation problem is computationally challenging due to the highly nonlinear transformation between the global and local coordinate systems as well as the measurement asynchrony from different sensors in this paper we propose a novel nonlinear least squares formulation for the problem by assuming the existence of a reference target moving with an unknown constant velocity we also propose an efficient block coordinate decent bcd optimization algorithm with a judicious initialization to solve the problem the proposed bcd algorithm alternately updates the range and azimuth bias estimates by solving linear least squares problems and semidefinite programs in the absence of measurement noise the proposed algorithm is guaranteed to find the global solution of the problem and the true biases simulation results show that the proposed algorithm significantly outperforms the existing approaches in terms of the root mean square error

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

on one skew symmetric problem of electroelasticity for inhomogeneous cylinder of finite length abstract in the present paper static bending problem of the electroelasticity for an inhomogeneous cylinder of finite length with sliding fixed end supports is investigated the given boundary value problem is reduced to a system of 12 k k 1 2 integro differential equations expressions for the components characterizing the state of stress for the inhomogeneous cylinder are presented based on the developed analytical algorithm extensive numerical investigations associated with the stress analysis of an inhomogeneous piezoceramic cylinder have been conducted the results of these investigations are illustrated graphically demonstrating the stress distributions in piezoceramic circular and elliptical cylinders with inclusions of various geometries

the irreducible representations of the alternating group which remain irreducible in characteristic p let p be an odd prime and an the alternating group of degree n we determine which ordinary irreducible representations of u n remain irreducible in characteristic p verifying the author s conjecture from 2010 given the preparatory work done in 2010 our task is to determine which self conjugate partitions label specht modules for the symmetric group in characteristic p having exactly two composition factors this is accomplished through the use of the robinson brundan kleshchev i restriction functors together with known results on decomposition numbers for the symmetric group and additional results on the mullineux map and homomorphisms between specht modules

some reducible specht modules we wish to consider which ordinary irreducible representations of the symmetric group sn remain irreducible modulo a prime p this is the same as asking which partitions of n have the property that the corresponding specht module s is reducible over a field of characteristic p if or its conjugate partition is p regular then the answer is known 6 8 it is also known in the case p 2 7 this paper discusses some of the reducible specht modules in the case that p 3 throughout p will be an odd prime and a partition of some integer n we will prove some cases of a conjecture by james and mathas 9 given below we begin with some definitions

an optimizing design strategy for multiple model adaptive estimation and control a method is proposed for designing multiple model adaptive estimators to provide combined state and parameter estimation in the presence of an uncertain parameter vector it is assumed that the parameter varies over a continuous region and a finite number of constant gain filters are available for the estimation the estimator elemental filters are shown by minimizing a cost functional representing the average state prediction error autocorrelation with the average taken as the true parameter ranges over the admissible parameter set an analogous method is proposed for designing multiple model adaptive regulators to provide stabilizing control in the presence of an uncertain parameter vector by minimizing a cost functional representing the average regulation error autocorrelation with the average taken as the true parameter ranges over the admissible parameter set an example is used to demonstrate the improvement in performance over previously accepted design methods

irreducible specht modules for hecke algebras of type a abstract let f be a field n a non negative integer a partition of n and s the corresponding specht module for the iwahori hecke algebra h f q s n james and mathas conjecture a necessary and sufficient condition on for s to be irreducible we prove the sufficiency of this condition in the case where f has infinite characteristic and also in the case where q 1