state estimation in stochastic hybrid systems with sparse observations in this note we study the problem of state estimation for a class of sampled measurement stochastic hybrid systems where the continuous state x satisfies a linear stochastic differential equation and noisy measurements y are taken at assigned discrete time instants the parameters of both the state and measurement equation depend on the discrete state q of a continuous time finite markov chain even in the fault detection setting we consider at most one transition for q is admissible the switch may occur between two observations whence it turns out that the optimal estimates cannot be expressed in parametric form and time integrations are unavoidable so that the known estimation techniques cannot be applied we derive and implement an algorithm for the estimation of the states x q and of the discrete state switching time that is convenient for both recursive update and the eventual numerical quadrature numerical simulations are illustrated

moment ratios for absorbing state phase transitions we determine the first through fourth moments of the order parameter and various ratios for several one and two dimensional models with absorbing state phase transitions we perform a detailed analysis of the system size dependence of these ratios and confirm that they are indeed universal for three models the contact process the a model and the pair contact process belonging to the directed percolation universality class our studies also yield a refined estimate for the critical point of the pair contact process

low density series expansions for directed percolation i a new efficient algorithm with applications to the square lattice a new algorithm for the derivation of low density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems numerical evidence shows that the computational complexity grows exponentially but with a growth factor which is much smaller than the growth factor of the previous best algorithm for bond site percolation on the directed square lattice the series has been extended to order 171 158 analysis of the series yields sharper estimates of the critical points and exponents

identification of time varying systems in reproducing kernel hilbert spaces we consider a class of linear systems in state space form whose parameters evolve in time according to a continuous time gauss markov process our problem is to identify the system from a finite set of noisy output measurements we derive a connection between this problem and tikhonov regularization in reproducing kernel hilbert spaces relying upon this result conditions that ensure the existence of the maximum a posteriori estimate of the parameter trajectory are provided and an identification algorithm is worked out simulated data are used to test the goodness of the proposed approach

broue s abelian defect group conjecture holds for the harada norton sporadic simple group hn abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block b of the normaliser n g p of p in g are derived equivalent rickard equivalent this conjecture is called broue s abelian defect group conjecture we prove in this paper that broue s abelian defect group conjecture is true for a non principal 3 block a with an elementary abelian defect group p of order 9 of the harada norton simple group hn it then turns out that broue s abelian defect group conjecture holds for all primes p and for all p blocks of the harada norton simple group hn

stationary filter for linear minimum mean square error estimator of discrete time markovian jump systems we derive in this paper a stationary filter for the linear minimum mean square error estimator lmmse of discrete time markovian jump linear systems mjlss we obtain the convergence of the error covariance matrix of the lmmse to a stationary value under the assumption of mean square stability of the mjls and ergodicity of the associated markov chain it is shown that there exists a unique solution for the stationary riccati filter equation and moreover this solution is the limit of the error covariance matrix of the lmmse the advantage of this scheme is that it is very easy to implement and all calculations can be performed off line leading to a linear time invariant filter

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

hybrid filtering for linear systems with non gaussian disturbances this paper is concerned with hybrid filtering of a non gaussian system coupled by a hidden switching process an optimal control approach is used to derive a finite dimensional recursive filter that is optimal in the sense of the most probable trajectory mpt estimate an approximate scheme is obtained when the probability distribution of the switching process converges to a limiting distribution which is often easier to obtain numerical examples are considered and computational experiments are reported in these examples our schemes outperform popular filtering schemes available in the literature

iterative algorithms for state estimation of jump markov linear systems jump markov linear systems jmlss are linear systems whose parameters evolve with time according to a finite state markov chain given a set of observations our aim is to estimate the states of the finite state markov chain and the continuous in space states of the linear system in this paper we present original deterministic and stochastic iterative algorithms for optimal state estimation of jmlss the first stochastic algorithm yields minimum mean square error mmse estimates of the finite state space markov chain and of the continuous state of the jmls a deterministic and a stochastic algorithm are given to obtain the marginal maximum a posteriori mmap sequence estimate of the finite state markov chain finally a deterministic and a stochastic algorithm are derived to obtain the mmap sequence estimate of the continuous state of the jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problem of deconvolution of bernoulli gaussian bg processes and the problem of tracking a maneuvering target are addressed

quasistationary analysis of the contact process on annealed scale free networks we present an analysis of the quasistationary qs state of the contact process cp on annealed scale free networks using a mapping of the cp dynamics in a one step process and analyzing numerically and analytically the corresponding master equation the relevant qs quantities determined via the master equation exhibit an excellent agreement with direct qs stochastic simulations of the cp the high accuracy of the resulting data allows a probe of the strong corrections to scaling present in both the critical and supercritical regions corrections that mask the correct finite size scaling obtained analytically by applying an exact heterogeneous mean field approach our results represent a promising starting point for a deeper understanding of the contact process and absorbing phase transitions on real quenched complex networks

blocks with cyclic defect groups and clifford extensions abstract we prove that the residual clifford extension of any non exceptional character belonging to a p block with cyclic defect groups of a twisted group algebra is naturally isomorphic to the clifford extension of any simple module belonging to that block we also show that dade s inductive conjecture holds for blocks with cyclic defect groups

particle filters for state estimation of jump markov linear systems jump markov linear systems jmls are linear systems whose parameters evolve with time according to a finite state markov chain in this paper our aim is to recursively compute optimal state estimates for this class of systems we present efficient simulation based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed lag smoothing problem our algorithms combine sequential importance sampling a selection scheme and markov chain monte carlo methods they use several variance reduction methods to make the most of the statistical structure of jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problems of on line deconvolution of impulsive processes and of tracking a maneuvering target are considered it is shown that our algorithms outperform the current methods

broueʼs abelian defect group conjecture holds for the double cover of the higman sims sporadic simple group abstract in the representation theory of finite groups there is a well known and important conjecture due to broue saying that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block b of the normaliser n g p of p in g are derived equivalent we prove in this paper that broue s abelian defect group conjecture and even rickard s splendid equivalence conjecture are true for the faithful 3 block a with an elementary abelian defect group p of order 9 of the double cover 2 hs of the higman sims sporadic simple group it then turns out that both conjectures hold for all primes p and for all p blocks of 2 hs

a superposition principle for the kalman filter abstract in this paper decomposition formulas for the discrete time kalman filter are presented both the state estimate and the error covariance matrix are expressed as the sum of two terms the first being the estimate corresponding to zero initial conditions and the second being an explicit function of the initial values x 0 and p 0 the representation is updated in time by well behaved finite complexity matrix recursions and allows for a direct evaluation of the estimates for variable initial conditions applications to stochastic hybrid filtering are discussed

broueʼs abelian defect group conjecture holds for the sporadic simple conway group co3 in the representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding block an of the normaliser ng p of p in g are derived equivalent rickard equivalent this conjecture is called strong version of broue s abelian defect group conjecture in this paper we prove that the strong version of broue s abelian defect group conjecture is true for the non principal 2 block a with an elementary abelian defect group p of order 8 of the sporadic simple conway group co3 this result completes the verification of the strong version of broue s abelian defect group conjecture for all primes p and for all p blocks of co3

trivial source modules in blocks with cyclic defect groups we shall present a method to get trivial source modules easily just by looking at values of ordinary characters at non identity p elements in finite groups instead of doing huge calculation the method is only for a case where defect groups are cyclic nevertheless it works well at least when we want to prove broue s abelian defect group conjecture for blocks which have elementary abelian defect groups of order p2

linear minimum mean square error estimation for discrete time markovian jump linear systems the linear minimum mean square error estimator lmmse for discrete time linear systems subject to abrupt changes in the parameters modeled by a markov chain spl theta k spl epsiv 1 n is considered the filter equations are derived from geometric arguments in a recursive form resulting in an on line algorithm suitable for computer implementation the author s approach is based on estimating x k 1 sub spl theta k i instead of estimating directly x k the uncertainty introduced by the markovian jumps increases the dimension of the filter to n n 1 where n is the dimension of the state variable an example where the dimension of the filter can be reduced to n is presented as well as a numerical comparison with the imm filter

stochastic sampling algorithms for state estimation of jump markov linear systems jump markov linear systems are linear systems whose parameters evolve with time according to a finite state markov chain given a set of observations our aim is to estimate the states of the finite state markov chain and the continuous in space states of the linear system the computational cost in computing conditional mean or maximum a posteriori map state estimates of the markov chain or the state of the jump markov linear system grows exponentially in the number of observations we present three globally convergent algorithms based on stochastic sampling methods for state estimation of jump markov linear systems the cost per iteration is linear in the data length the first proposed algorithm is a data augmentation da scheme that yields conditional mean state estimates the second proposed scheme is a stochastic annealing sa version of da that computes the joint map sequence estimate of the finite and continuous states finally a metropolis hastings da scheme based on sa is designed to yield the map estimate of the finite state markov chain convergence results of the three above mentioned stochastic algorithms are obtained computer simulations are carried out to evaluate the performances of the proposed algorithms the problem of estimating a sparse signal developing from a neutron sensor based on a set of noisy data from a neutron sensor and the problem of narrow band interference suppression in spread spectrum code division multiple access cdma systems are considered

non universality of the absorbing state phase transition in a linear chain with power law diluted long range connections abstract in this work we study the critical behavior of the absorbing state phase transition exhibited by the contact process in a linear chain with power law diluted long range connections each pair of sites is connected with a probability p r that decays with the distance between the sites r as 1 r the model allows for a continuous tuning between a standard one dimensional chain with only nearest neighbor couplings to a fully connected network 0 we develop a finite size scaling analysis to obtain the critical point and a set of dynamical and stationary critical exponents for distinct values of the decay exponent 2 corresponding to finite average bond lengths and low average site connectivity data for the order parameter collapse over a universal curve when plotted after a proper rescaling of parameters we show further that the critical exponents depend on in the regime of diverging bond length fluctuations 3

morita equivalences related to the glauberman correspondence abstract starting with p interior algebras where p is a finite p group we prove two theorems establishing certain group graded morita equivalences these apply in particular to the case of blocks with normal defect groups and defect zero blocks of normal subgroups respectively

irreversible phase transitions in contact processes with levy exchanges and long range interactions the contact process cp is generalized allowing the exchange of particles via l evy flights where the flying length l is a random variable with a probability distribution given by p l ensuremath propto mathit l mathrm ensuremath mathit d mathrm ensuremath mathrm ensuremath sigma where d is the spacial dimension and ensuremath sigma is the dimension of the random walk the contact process with l evy flights cplf exhibits irreversible phase transitions between an active state and a vacuum state it is show that within the superdiffusive regime of the walkers i e ensuremath sigma 1 the l evy mechanism effectively build up additional long range correlations therefore the critical exponents of the cplf model depart from those of the standard cp and they are tunable functions of ensuremath sigma comparison of the critical exponents characteristic of branching annihilating l evy walkers e albano europhys lett 34 97 1996 and those of the cplf gives strong evidences on a universality class which comprises second order irreversible phase transitions in systems involving l evy exchanges and or flights it is suggested that the cplf is equivalent to the standard cp with long range interactions generated by a potential decaying with distance r as a power law of the form v r ensuremath propto mathit r mathrm ensuremath mathit d mathrm ensuremath mathrm ensuremath sigma textcopyright 1996 the american physical society

exact hybrid filters in discrete time using the reference probability method and the change of measure in discrete time the state estimator problem is considered for linear systems observed in gaussian noise when the coefficients are functions of a noisily observed finite state markov chain the methods are new and finite dimensional filters are obtained however the number of statistics increases in time a numerical comparison of this filter with the interactive multiple model algorithm introduced by blom and bar shalom 1988 is given

state estimation for markovian jump linear systems with bounded disturbances in this paper we investigate the state estimation problem for a class of markovian jump linear systems mjlss in the presence of bounded polyhedral disturbances a set membership estimation algorithm is first proposed to find the smallest consistent set of all possible states which is shown to be expressed by a union of multiple polytopes the posterior probabilities of the system jumping modes are then estimated by introducing the lebesgue measure based on which the optimal point estimate is further provided moreover a similarity relationship for polytopes is defined and an approximate method is presented to calculate the minkowski sum of polytopes which can help reduce the computational complexity of the overall estimation algorithm

conditional densities for continuous time nonlinear hybrid systems with applications to fault detection continuous time nonlinear stochastic differential state and measurement equations all of which have coefficients capable of abrupt changes at a random time are considered finite state jump markov chains are used to model the changes conditional probability densities which are essential in obtaining filtered estimates for these hybrid systems are then derived they are governed by a coupled system of stochastic partial differential equations when the q matrix of the markov chain is either lower or upper diagonal it is shown that the system of conditional density equations is finite dimensional computable these findings are then applied to a fault detection problem to compute state estimates that include the failure time

the indecomposability of a certain bimodule given by the brauer construction broue s abelian defect conjecture 3 6 2 predicts for a p block of a finite group g with an abelian defect group p a derived equivalence between the block algebra and its brauer correspondent by a result of rickard 11 such a derived equivalence would in particular imply a stable equivalence induced by tensoring with a suitable bimodule and it appears that these stable equivalences in turn tend to be obtained by gluing together morita equivalences at the local levels of the considered blocks see e g 4 6 3 8 3 1 12 4 1 and 13 5 6 a 4 1 this note provides a technical indecomposability result which is intended to verify in suitable circumstances the hypotheses that are necessary to apply gluing results as mentioned above this is used in 7 to show that broue s abelian defect group conjecture holds for nonprincipal blocks of the simple held group and the sporadic suzuki group

levy flights and random searches in this work we discuss some recent contributions to the random search problem our analysis includes superdiffusive levy processes and correlated random walks in several regimes of target site density mobility and revisitability we present results in the context of mean field like and closed form average calculations as well as numerical simulations we then consider random searches performed in regular lattices and lattices with defects and we discuss a necessary criterion for distinguishing true superdiffusion from correlated random walk processes we invoke energy considerations in relation to critical survival states on the edge of extinction and we analyze the emergence of levy behavior in deterministic search walks finally we comment on the random search problem in the context of biological foraging

source algebras and source modules the aim of this article is to give a self contained approach in module theoretic terms to two fundamental results in block theory due to puig 6 14 6 first there is an embedding of the source algebra of the brauer correspondent of a block of some finite group into a source algebra of that block and second the source algebras of the brauer correspondence can be described explicitly our proof of the first result theorem 5 and its corollary 6 below is essentially the translation to our terminology of the proof in 1 4 10 the second result describing the source algebras of the brauer correspondent follows also from 3 but the proofs in 3 use both the main result on the structure of nilpotent blocks in 5 as well as techniques from 6 sects 4 6 while our approach from proposition 9 onwards requires only some classical results on the structure of blocks with a central defect group an account of the results in 6 on source algebras of blocks with a normal defect group can also be found in 7 sect 45 except for the explicit description of the central extension e see section 10 below as being defined in terms of the multiplicity algebra of the block which is quoted in 7 45 10 b without proof referring back to 6 at the end of 7 sect 45

kalman filtering for linear systems with coefficients driven by a hidden markov jump process abstract we present an explicit algorithm for the solution of the nonlinear filtering problem concerning a linear partially observed diffusion type model where the coefficients are driven by a hidden markov jump process of which one can observe the occurrence of a jump the recursive filter is of a branching type with its finite dimension growing for each jump of the hidden markov process

broue s abelian defect group conjecture for the held group and the sporadic suzuki group abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a p block a of a finite group g has an abelian defect group p then a and its brauer corresponding p block b of ng p are derived equivalent we demonstrate in this paper that broue s conjecture holds for non principal 3 blocks a with elementary abelian defect group p of order 9 of the simple held group and the sporadic simple suzuki group

critical behaviour of a long range non equilibrium system the critical behaviour of a long range one dimensional non equilibrium system where the desorption rate decreases with distance as some power approximately r alpha d is studied by means of the coherent anomaly method the alpha dependence of the critical parameter lambda c and the critical exponent beta is determined

mixture kalman filters in treating dynamic systems sequential monte carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling importance sampling and weighted resampling to complete the on line filtering task we propose a special sequential monte carlo method the mixture kalman filter which uses a random mixture of the gaussian distributions to approximate a target distribution it is designed for on line estimation and prediction of conditional and partial conditional dynamic linear models which are themselves a class of widely used non linear systems and also serve to approximate many others compared with a few available filtering methods including monte carlo methods the gain in efficiency that is provided by the mixture kalman filter can be very substantial another contribution of the paper is the formulation of many non linear systems into conditional or partial conditional linear form to which the mixture kalman filter can be applied examples in target tracking and digital communications are given to demonstrate the procedures proposed

expectation maximization algorithms for map estimation of jump markov linear systems in a jump markov linear system the state matrix observation matrix and the noise covariance matrices evolve according to the realization of a finite state markov chain given a realization of the observation process the aim is to estimate the state of the markov chain assuming known model parameters computing conditional mean estimates is infeasible as it involves a cost that grows exponentially with the number of observations we present three expectation maximization em algorithms for state estimation to compute maximum a posteriori map state sequence estimates which are also known as bayesian maximum likelihood state sequence estimates mlses the first em algorithm yields the map estimate for the entire sequence of the finite state markov chain the second em algorithm yields the map estimate of the continuous state of the jump linear system the third em algorithm computes the joint map estimate of the finite and continuous states the three em algorithms optimally combine a hidden markov model hmm estimator and a kalman smoother ks in three different ways to compute the desired map state sequence estimates unlike the conditional mean state estimates which require computational cost exponential in the data length the proposed iterative schemes are linear in the data length