on centers of blocks with one simple module abstract let g be a finite group and let b be a non nilpotent block of g with respect to an algebraically closed field of characteristic 2 suppose that b has an elementary abelian defect group of order 16 and only one simple module the main result of this paper describes the algebra structure of the center of b this is motivated by a similar analysis of a certain 3 block of defect 2 in kessar 2012 15

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

existence of dynamical hull functions with two variables for the ac driven frenkel kontorova model abstract in this paper we are concerned with the dynamics of incommensurate structures in the overdamped limit case of the frenkel kontorova model with periodic driving force we show in the infinite dimensional phase space there exists an ordered circle on which both the poincare map and the space shift map induce orientation preserving circle homeomorphisms with rotation numbers and respectively the latter characterizing the mean spacing of particles furthermore we prove that the average velocity for the particle chain with irrational exists and t where t denotes the period of the driving force and it is continuous and nondecreasing with respect to f the average of the external driving force if the shift map on the invariant ordered circle is ergodic we demonstrate the existence of two variable dynamical hull functions and that there are no mode locking behaviors

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

character tables and defect groups abstract let b be a block of a finite group g with defect group d we prove that the exponent of the center of d is determined by the character table of g in particular we show that d is cyclic if and only if b contains a large family of irreducible p conjugate characters more generally for abelian d we obtain an explicit formula for the exponent of d in terms of character values in small cases even the isomorphism type of d is determined in this situation moreover it can read off from the character table whether d d 4 where d denotes the commutator subgroup of d we also propose a new characterization of nilpotent blocks in terms of the character table

the discrete frenkel kontorova model and its extensions i exact results for the ground states abstract we present a rigorous study of the classical ground states under boundary conditions of a class of one dimensional models generalizing the discrete frenkel kontorova model the extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic quasi periodic and chaotic orbits for all boundary conditions we select among all the extremum solutions of the energy of the model those which correspond to the ground states of the infinite system we prove that these ground states are either periodic commensurate or quasi periodic incommensurate but are never chaotic we also prove the existence of elementary discommensurations which are minimum energy configuration of the model for certain special boundary conditions the topological structure of the whole set of ground states is described in details in addition to physical applications consequences for twist map homeomorphisms are mentioned part ii s aubry p y ledaeron and g andre will be mostly devoted to exact results on the transition by breaking of analyticity which occurs on the incommensurate ground states when the model parameters vary and on its connection with the stochasticity threshold in the corresponding twist map

efficient particle filtering for jump markov systems application to time varying autoregressions we present an efficient particle filtering method to perform optimal estimation in jump markov nonlinear systems jmss such processes consist of a mixture of heterogeneous models and possess a natural hierarchical structure we take advantage of these specificities in order to develop a generic filtering methodology for these models the method relies on an original and nontrivial combination of techniques that have been presented recently in the filtering literature namely the auxiliary particle filter and the unscented transform this algorithm is applied to the complex problem of time varying autoregressive estimation with an unknown time varying model order more precisely we develop an attractive and original probabilistic model that relies on a flexible pole representation that easily lends itself to interpretations we show that this problem can be formulated as a jms and that the associated filtering problem can be efficiently addressed using the generic methodology developed in this paper simulations demonstrate the performance of our method compared to standard particle filtering techniques

nilpotent blocks of quasisimple groups for odd primes we investigate the nilpotent blocks of positive defect of the quasisimple groups for odd primes in particular it is shown that every nilpotent block of a quasisimple group has abelian defect groups a conjecture of puig concerning the recognition of nilpotent blocks is also shown for these groups

bounds on achievable performance in the identification and adaptive control of time varying systems treats the identification and adaptive control of time varying linear systems for linear systems with a gauss markov parameter process a global lower bound on the mean square error is obtained which is valid for any causal parameter estimator a similar lower bound is obtained for any causal one step ahead predictor these bounds are applied to the adaptive control of time varying systems to obtain a lower bound on closed loop mean square performance for any causal control law for a specific control law mean square stability is established and through simulations it is seen that the performance nearly meets the theoretical lower bound

existence and modulation of uniform sliding states in driven and overdamped particle chains in this paper we are mainly concerned with existence and modulation of uniform sliding states for particle chains with damping and external driving force f if the on site potential vanishes then for each f 0 there exist trivial uniform sliding states x n t n t for which the particles are uniformly spaced with spacing 0 the sliding velocity of each particle is f and the phase is arbitrary if the particle chain with convex interaction potential is placed in a periodic on site potential we show under some conditions the existence of modulated uniform sliding states of the form x n t n omega nu t alpha u n omega nu t alpha where the modulation function u is periodic and unique up to phase the conditions are that the system is overdamped and the driving force f exceeds some critical value f d 0 depending on mean spacing if f in 0 f d omega the system possesses a set of rotationally ordered equilibrium states for irrational which can be described by a non decreasing hull function just as the case f 0 where aubry mather theory applies to ground states meanwhile we prove that f d 0 which was argued physically much earlier if the hull function of ground states with irrational rotation number for f 0 is continuous

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

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

exponentially weighted least squares identification of time varying systems with white disturbances the paper is devoted to the stochastic analysis of recursive least squares rls identification algorithms with an exponential forgetting factor a persistent excitation assumption of a conditional type is made that does not prevent the regressors from being a dependent sequence moreover the system parameter is modeled as the output of a random walk type equation without extra constraints on its variance it is shown that the estimation error can be split into two terms depending on the parameter drift and the disturbance noise respectively the first term turns out to be proportional to the memory length of the algorithm whereas the second is proportional to the inverse of the same quantity even though these dependence laws are well known in very special mathematical frameworks deterministic excitation and or independent observations this is believed to be the first contribution where they are proven in a general dependent context some idealized examples are introduced in the paper to clarify the link between generality of assumptions and applicability of results in the developed analysis

hyperbolic cantori have dimension zero it is proved that cantori for area preserving twist maps have dimension zero only finitely many orbits of gaps and gap widths go to zero exponentially in each orbit if they are hyperbolic

cantori for multiharmonic maps abstract we compute all the cantori and their gap and turnstile structures for area preserving twist maps near non degenerate anti integrable limits with arbitrarily many wells per period the results imply a rich bifurcation diagram for cantori of families of maps containing degenerate anti integrable limits we conjecture the structure of this bifurcation diagram in the case of the two harmonic family

brief paper solutions of nonlinear control and estimation problems in reproducing kernel hilbert spaces existence and numerical determination many nonlinear optimal control and estimation problems can be formulated as tikhonov variational problems in an infinite dimensional reproducing kernel hilbert space this paper shows that any closed ball contained in such spaces is compact in the sup norm topology this result is exploited to obtain conditions which guarantee existence of solutions for the aforementioned problems as well as numerical algorithms whose convergence is guaranteed in the space of continuous functions

nonparametric identification of population models via gaussian processes population models are used to describe the dynamics of different subjects belonging to a population and play an important role in drug pharmacokinetics a nonparametric identification scheme is proposed in which both the average impulse response of the population and the individual ones are modelled as gaussian stochastic processes assuming that the average curve is an integrated wiener process it is shown that its estimate is a cubic spline an empirical bayes algorithm for estimating both the average and the individual curves is worked out the model is tested on simulated data sets as well as on xenobiotics pharmacokinetic data

optical hamiltonians and symplectic twist maps abstract this paper concentrates on optical hamiltonian systems of t t n i e those for which hpp is a positive definite matrix and their relationship with symplectic twist maps we present theorems of decomposition by symplectic twist maps and existence of periodic orbits for these systems the novelty of these results resides in the fact that no explicit asymptotic condition is imposed on the system

exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant ori abstract an approximate renormalisation scheme is derived for the breakup of invariant tori of arbitrary winding ratio in hamiltonian systems of one and a half degrees of freedom similar to that of escande and doveil it is a free semi group with two generators this scheme is solved exactly for its orbits stable manifolds unstable manifolds and critical set various results are found including a cantor set of universal fractal diagrams the robustness of noble tori and a scaling law for areas near critical circles

smooth approximation of mather sets of monotone twist mappings in the theory of monotone twist mappings of a cylinder one constructs for every rotation number invariant minimal sets m in this paper an approximation of these mather sets by smooth invariant curves mv is devised which for v 0 converge to m almost everywhere the main point of the construction is that the approximating curves mv form for v 0 a smooth foliation the approximation is achieved with the help of a regularized version of the percival variational problem 1994 john wiley sons inc

the expectation maximization algorithm for symbol unsynchronized sequence detection the expectation maximization em algorithm for maximizing likelihood functions combined with the viterbi algorithm is applied to the problem of sequence detection when symbol timing information is not present although the em algorithm is noncausal results obtained using the algorithm on the problem of nonsynchronized sequence detection indicate that it converges most of the time in three iterations making it both of theoretical and of practical interest a practical algorithm based on the em algorithm is introduced it reduces the computational burden and improves performance by making use of timing estimates in previous observation windows

data driven zero sum neuro optimal control for a class of continuous time unknown nonlinear systems with disturbance using adp this paper is concerned with a new data driven zero sum neuro optimal control problem for continuous time unknown nonlinear systems with disturbance according to the input output data of the nonlinear system an effective recurrent neural network is introduced to reconstruct the dynamics of the nonlinear system considering the system disturbance as a control input a two player zero sum optimal control problem is established adaptive dynamic programming adp is developed to obtain the optimal control under the worst case of the disturbance three single layer neural networks including one critic and two action networks are employed to approximate the performance index function the optimal control law and the disturbance respectively for facilitating the implementation of the adp method convergence properties of the adp method are developed to show that the system state will converge to a finite neighborhood of the equilibrium the weight matrices of the critic and the two action networks are also convergent to finite neighborhoods of their optimal ones finally the simulation results will show the effectiveness of the developed data driven adp methods

counting characters above invariant characters in solvable groups abstract this paper discusses two related questions first given a g invariant character of a normal subgroup n of a solvable group what can we say if the number of characters of g above is in some sense as small as possible isaacs and navarro 5 have shown that under certain assumptions about primes dividing the order of the group one can show that g n must have a very particular structure here we show that these assumptions can be weakened to obtain results about all solvable groups we also discuss a related question about blocks for a prime p and a p block b of g we let k b denote the number of ordinary characters in b it is relatively easy to show that k b is bounded below by k g d which is the number of conjugacy classes of g that intersect the defect group d of b in this paper we ask what can be said if equality is achieved we show that for p solvable groups if k b k g d then b is nilpotent and thus k b irr d in addition we show that this result holds for many blocks of arbitrary finite groups including all blocks of the symmetric groups we also extend a result on fully ramified coprime actions in 5

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

expansiveness hyperbolicity and hausdorff dimension we show that there exists a simple upper bound on the dimension of a hyperbolic compact set of a dynamical system in terms of topological entropy and a uniform contraction rate on the stable and unstable manifolds this allows us to give proofs of several apparently unrelated theorems

aubry mather sets and birkhoff s theorem for geodesic flows on the two dimensional torus in this paper we state the graph property for incompressible continuouse tori invariant under goedesic flows of riemannian metrics on the two dimensional torus also our method gives a new proof of birkhoff s theorem for twist maps of the cylinder we prove that if there exist an invariant incompressible torus of geodesic flow with irrational rotation number then it necessarily contains the aubry mather set with this rotation number

estimating time varying parameters by the kalman filter based algorithm stability and convergence convergence and stability properties of the kalman filter based parameter estimator are established for linear stochastic time varying regression models the main features are both the variances and sample path averages of the parameter tracking error are shown to be bounded the regression vector includes both stochastic and deterministic signals and no assumptions of stationarity or independence are requires and the unknown parameters are only assumed to have bounded variations in an average sense

slide window bounded error time varying systems identification this technical note presents a new identification method for discrete linear systems with time varying parameters based on bounded error approach it is assumed a bounded additive error on measurements and a bound on parameter variation each time instant the identification method uses a slide window along historical data and an explicit expression to provide an outer bound of the set of model parameters that is consistent with measurements model structure and bounds on error and variations considered furthermore the center estimation of the obtained outer solution set is a suitable nominal estimation of the parameters this center is the optimal solution of a least squares problem that penalizes the prediction error of the model and the parameter variations the explicit expression that provides the outer bound of the parameters and the optimal property of the center estimation are the main contributions of the technical note in order to clarify the proposed method an application example and a comparison with a previous recursive bounded error method are included

percival variational principle for invariant measures and commensurate incommensurate phase transitions in one dimensional chains we prove for a one dimensional system of classical particles with potential energy u alpha gamma sum limits n left alpha v x n f x n 1 x n gamma right the existence of such a smooth function 0 0 that the system with potential energyu has the equilibrium state at the temperaturet 0 this is the incommensurate phase with the ratio of periods equal to the prescribed irrational number badly approximated by rational ones a simple geometric condition for the invariant curve of the corresponding dynamical system is established under which it is the support of the invariant measure minimizing percival s energy functional

the link between the shape of the irrational aubry mather sets and their lyapunov exponents we consider the irrational aubry mather sets of an exact symplectic monotone c 1 twist map of the two dimensional annulus introduce for them a notion of c 1 regularity related to the notion of bouligand paratingent cone and prove that a mather measure has zero lyapunov exponents if and only if its support is c 1 regular almost everywhere a mather measure has nonzero lyapunov exponents if and only if its support is c 1 irregular almost everywhere an aubry mather set is uniformly hyperbolic if and only if it is irregular everywhere the aubry mather sets which are close to the kam invariant curves even if they may be c 1 irregular are not too irregular i e have small paratingent cones the main tools that we use in the proofs are the so called green bundles

persistent identification of time varying systems identification of time varying systems especially slowly time varying systems is of importance in the development of a comprehensive theory of adaptation the persistent identification measures employed in this paper capture a main characterization in such identification problems namely one input signal must be used for identification of all possible observation windows this paper establishes several essential features in persistent identification problems which highlight their potential utility in adaptation 1 they have computable upper and lower bounds for typical classes of prior uncertainty sets 2 any full rank n periodic signals are optimal and the simple least squares estimates are optimal identification algorithms 3 optimal probing inputs can be approximately generated in a closed loop configuration when the plant and the controller are slowly time varying and 4 n periodic signals are asymptotically optimal for slowly time varying systems the main results of this paper have been successfully combined with a certain slow h sup spl infin design to derive an adaptive stabilization scheme

amount of rotation about a point and the morse index for the case of exact area preserving monotone twist diffeomorphisms we give formulas relating the amount of rotation about an orbit and certain morse indices

brief regularization networks for inverse problems a state space approach linear inverse problems with discrete data are equivalent to the estimation of the continuous time input of a linear dynamical system from samples of its output the solution obtained by means of regularization theory has the structure of a neural network similar to classical rbf networks however the basis functions depend in a nontrivial way on the specific linear operator to be inverted and the adopted regularization strategy by resorting to the bayesian interpretation of regularization we show that such networks can be implemented rigorously and efficiently whenever the linear operator admits a state space representation an analytic expression is provided for the basis functions as well as for the entries of the matrix of the linear system used to compute the weights the results are illustrated through a deconvolution problem where the spontaneous secretory rate of luteinizing hormone lh of the hypophisis is reconstructed from measurements of plasma lh concentrations

brief optimal filtering of doubly stochastic auto regressive processes in this paper exact finite dimensional filters are derived for a class of doubly stochastic auto regressive models the parameters of the doubly stochastic auto regressive process vary according to a nonlinear function of a gauss markov process we develop a difference equation for the evolution of an unnormalized conditional density related to the state of the doubly stochastic auto regressive process we then give a characterization of the general solution followed by examples for which the state of the filter is determined by a finite number of sufficient statistics these new finite dimensional filters build upon the discrete time kalman filter

denjoy minimal sets and birkhoff periodic orbits for non exact monotone twist maps abstract a non exact monotone twist map f is a composition of an exact monotone twist map with a generating function h and a vertical translation v f with v f x y x y f we show in this paper that for each r there exists a critical value f d 0 depending on h and such that for 0 f f d the non exact twist map f has an invariant denjoy minimal set with irrational rotation number lying on a lipschitz graph or birkhoff p q periodic orbits for rational p q like the aubry mather theory we also construct heteroclinic orbits connecting birkhoff periodic orbits and show that quasi periodic orbits in these denjoy minimal sets can be approximated by periodic orbits in particular we demonstrate that at the critical value f f d the denjoy minimal set is not uniformly hyperbolic and can be approximated by smooth curves

interface interactions in modulated phases and upsilon points certain features in frenkel kontorova and other models of phases with a one dimensional modulation can be analyzed by assuming parallel interfaces separating sets of lattice planes belonging to two different phases and treating the free energy to create interfaces as well as the interaction of two three or more interfaces as phenomenological parameters a strategy employed by fisher and szpilka for interacting defects can be extended to the case of interfaces allowing a systematic study of the phase diagram by ignoring all interface interactions and then successively taking into account pair triple and higher order terms the possible phase diagrams which can occur near the point where 0 include various sorts of endpoints analogous to critical endpoints an accumulation point of first order transitions and triple points and a self similar structure which we call an upsilon point which turns out to be an accumulation point of an infinite number of segments of first order transition lines each of which terminates in two upsilon points

bounded error identification of time varying parameters by rls techniques the performance of the recursive least squares algorithm with constant forgetting factor in the identification of time varying parameters is studied in a stochastic framework it is shown that the mean square tracking error keeps bounded if and only if the so called covariance matrix of the algorithm is l sup 1 bounded then a feasibility range for the forgetting factor is worked out in correspondence of which the covariance matrix and therefore the tracking error keeps bounded

on aubry maher sets abstract let f be a two dimensional area preserving twist map for each irrational rotation number in a certain nontrivial interval there is an f invariant minimal set which preserves order with respect to that rotation number for large nonlinearity these sets are typically cantor sets and they are referred to as aubry mather sets we prove that under some assumptions these sets are ordered vertically according to ascending rotation number monotonicity furthermore if f satisfies certain conditions the right hand points of the gaps in an irrational cantor set lie on a single orbit single gap and diffusion through these aubry mather sets can be understood as a limit of resonance overlaps convergence of turnstiles these conditions essentially establish the existence of a hyperbolic structure and limit the number of homoclinic minimizing orbits some other results along similar lines are given such as the continuity at irrational rotation numbers of the lyapunov exponent on aubry mather sets

lyapunov exponents of minimizing measures for globally positive diffeomorphisms in all dimensions the globally positive diffeomorphisms of the 2n dimensional annulus are important because they represent what happens close to a completely elliptic periodic point of a symplectic diffeomorphism where the torsion is positive definite for these globally positive diffeomorphisms an aubry mather theory was developed by garibaldi and thieullen that provides the existence of some minimizing measures using the two green bundles g and g that can be defined along the support of these minimizing measures we will prove that there is a deep link between the angle between g and g along the support of the considered measure mu the size of the smallest positive lyapunov exponent of mu the tangent cone to the support of mu

recent developments in the theory of hamiltonian systems area preserving mappings of an annulus occur as poincare mappings of hamiltonian systems they were studied extensively by g d birkhoff recently aubry and mather investigated the subclass of so called monotone twist mappings for which they constructed independently closed invariant cantor sets their work led to important new results their theory is discussed and related to hamiltonian systems satisfying a legendre condition the connection of this theory with the stability problem kam theory and in particular the disintegration of invariant tori is discussed various constructions of mather sets are explained in which minimal solutions of variational problems play a central role this theory has a close relation to the differential geometric investigations by morse and hedlund on geodesics on two dimensional surfaces

finite dimensional smoothers for map state estimation of bilinear systems in this paper we present two finite dimensional iterative algorithms for maximum a posteriori map state sequence estimation of bilinear systems bilinear models are appealing in their ability to represent or approximate a broad class of nonlinear systems our iterative algorithms for state estimation are based on the expectation maximization em algorithm and outperform the widely used extended kalman smoother eks unlike the eks these em algorithms are optimal in the map sense finite dimensional solutions to the state sequence estimation problem for bilinear models we also present recursive on line versions of the two algorithms and show that they outperform the extended kalman filter ekf our main conclusion is that the em based algorithms presented in this paper are novel nonlinear filtering methods that perform better than traditional methods such as the ekf

on blocks with one simple module in any brauer correspondent abstract we prove that a block of a finite group such that the defect groups are abelian and all the brauer correspondents the block itself included have a unique isomorphism class of simple modules is nilpotent