on the structural stability of the euler voigt and navier stokes voigt models abstract we consider the euler voigt equations and the navier stokes voigt equations which are obtained by an inviscid regularization from the corresponding equations the main result we show is the structural stability of the system in terms of the variations of both viscosity and regularization parameters

viscosity versus vorticity stretching global well posedness for a family of navier stokes alpha like models abstract we study global well posedness and regularity of solutions for a family of incompressible three dimensional navier stokes alpha like models that employ fractional laplacian operators this family of equations depends on two parameters 1 and 2 which affect the strength of non linearity vorticity stretching and the degree of viscous smoothing varying 1 and 2 interpolates between the incompressible navier stokes equations and the incompressible lagrangian averaged navier stokes model our main result which contains previously established results of j l lions and others provides a relationship between 1 and 2 that is sufficient to guarantee global existence uniqueness and regularity of solutions

on tracking control of a class of complementary slackness hybrid mechanical systems abstract in this note we consider the problem of feedback control of n dof degree of freedom rigid manipulators subject to a scalar frictionless unilateral constraint f x 0 x r n is the vector of generalized coordinates the stability analysis relies on a stability concept that incorporates the hybrid and nonsmooth dynamical feature of the overall system it is shown that stability of the closed loop system can be obtained this work generalizes the results in brogliato et al ieee trans automat control 42 2 1997 200 215 which were mainly restricted to the 1 dof case it also clarifies some concepts related to the hybrid nature of closed loop complementary slackness mechanical systems

on the controllability of linear juggling mechanical systems this paper deals with the controllability of a class of nonsmooth complementarity mechanical systems due to their particular structure they can be decomposed into an object and a robot consequently they are named juggling systems it is shown that the accessibility of the object can be characterized by nonlinear constrained equations or generalized equations examples are presented including a simple model of backlash the main focus of the work is about linear jugglers 2005 elsevier b v all rights reserved

on the global regularity of generalized leray alpha type models abstract we generalize leray alpha type models studied in cheskidov et al 2005 1 and linshiz and titi 2007 4 via fractional laplacians and employ besov space techniques to obtain global regularity results with the logarithmically supercritical dissipation

stopping time resampling for sequential monte carlo methods summary motivated by the statistical inference problem in population genetics we present a new sequential importance sampling with resampling strategy the idea of resampling is key to the recent surge of popularity of sequential monte carlo methods in the statistics and engineering communities but existing resampling techniques do not work well for coalescent based inference problems in population genetics we develop a new method called stopping time resampling which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on to illustrate the idea we first apply the new method to approximate the solution of a dirichlet problem and the likelihood function of a non markovian process then we focus on its application in population genetics all our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods

the regularized 3d boussinesq equations with fractional laplacian and no diffusion abstract in this paper we study the 3d regularized boussinesq equations the velocity equation is regularized a la leray through a smoothing kernel of order in the nonlinear term and a fractional laplacian we consider the critical case 5 4 and we assume 1 2 5 4 the temperature equation is a pure transport equation where the transport velocity is regularized through the same smoothing kernel of order we prove global well posedness when the initial velocity is in h r and the initial temperature is in h r for r max 2 1 this regularity is enough to prove uniqueness of solutions we also prove a continuous dependence of solutions on the initial conditions

large eddy simulation for turbulent flows with critical regularization abstract in this paper we establish the existence of a unique regular weak solution to the large eddy simulation les models of turbulence with critical regularization we first consider the critical les for the navier stokes equations and we show that its solution converges to a solution of the navier stokes equations as the averaging radii converge to zero then we extend the study to the critical les for magnetohydrodynamic equations

on some modification navier stokes equations abstract this article investigates some modification of the navier stokes equations of type as the modification that was suggested by lions quelques methodes de resolution des problemes aux limites non lineares dunod gauthier villaris paris 1969 in the form u j t i 1 n d i u j p i 2 d i u j i 1 n u i d i u j p x j h j t x t x q r n 1 div u 0 t x q 0 t t 0 0 u j 0 x 0 x u 0 0 t under p i p i 1 i n n 2 in this we prove the existence theorem for the different pi max 2 3 2 n and on some additional conditions i e of the pi p 4 in the isotropic nonlinearity case we prove the uniqueness theorem for the considered problem

a class of fast exact bayesian filters in dynamical models with jumps we address the statistical filtering problem in dynamical models with jumps when a particular application is adequately modeled by linear and gaussian probability density functions with jumps a usual method consists in approximating the optimal bayesian estimate in the sense of the minimum mean square error mmse in a linear and gaussian jump markov state space system jmss practical solutions include algorithms based on numerical approximations or on sequential monte carlo smc methods in this paper we propose a class of alternative methods which consists in building statistical models which locally similarly model the problem of interest but in which the computation of the mmse estimate can be be computed exactly without numerical nor smc approximations and at a computational cost which is linear in the number of observations

on line inference for multiple changepoint problems we propose an on line algorithm for exact filtering of multiple changepoint problems this algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models the computational cost of this exact algorithm is quadratic in the number of observations we further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations at the expense of introducing small errors and propose two new optimum resampling algorithms for this problem one a version of rejection control allows the particle filter to automatically choose the number of particles required at each time step the new resampling algorithms substantially out perform standard resampling algorithms on examples we consider and we demonstrate how the resulting particle filter is practicable for segmentation of human gc content

on approximate maximum likelihood methods for blind identification how to cope with the curse of dimensionality we discuss approximate maximum likelihood methods for blind identification and deconvolution these algorithms are based on particle approximation versions of the expectation maximization em algorithm we consider three different methods which differ in the way the posterior distribution of the symbols is computed the first algorithm is a particle approximation method of the fixed interval smoothing the two filter smoothing and the novel joined two filter smoothing involve an additional backward information filter because the state space is finite it is furthermore possible at each step to consider all the offsprings of any given particle it is then required to construct a novel particle swarm by selecting among all these offsprings particle positions and computing appropriate weights we propose here a novel unbiased selection scheme which minimizes the expected loss with respect to general distance functions we compare these smoothing algorithms and selection schemes in a monte carlo experiment we show a significant performance increase compared to the expectation maximization viterbi algorithm emva a fixed lag smoothing algorithm and the block constant modulus algorithm cma

a gaussian mixture filter for range only tracking range only tracking problems arise in extended data collection for inverse synthetic radar applications robotics navigation and other areas for such problems the conditional density of the state variable given the measurement history is multi modal or exhibits curvature even in seemingly benign scenarios for this reason the use of extended kalman filter ekf and other nonlinear filtering techniques based on gaussian approximations can result in inaccurate estimates we introduce a new filter for such tracking problems in two dimensions called the gaussian mixture range only filter gmrof which generates gaussian mixture approximations to the conditional densities the filter equations are derived by analytic techniques based on the specific nonlinearities of range only tracking a slight modification of the standard measurement process model noise before nonlinearity is used to simplify the moment calculations implementation requires at each step the fitting of a low order gaussian mixture to a simple exponentiated trigonometric function of a scalar variable simulations involving scenarios from earlier comparative studies indicate that the gmrof consistently outperformed the ekf and achieved the accuracy of particle filters while significantly reducing the computational cost

α regularization of the pod galerkin dynamical systems of the kuramoto sivashinsky equation abstract in order to improve the dynamics and stability of the pod galerkin models of strongly stiff systems an like regularization is suggested and assessed in the present article in this method the pod eigenmodes of the non linear terms are replaced by their helmholtz filtered counterparts while the other terms are remained unchanged as an example the method is applied to the pod galerkin models of the one dimensional kuramoto sivashinsky ks equation in a full chaotic regime and the fidelity of the original and regularized models to the direct numerical simulations dns are investigated moreover the effects of regularization on the dynamics of various terms and whole of the systems are analyzed via eigenvalue analysis of each term separately and the total dynamical system as a whole the numerical experiments show definite effectiveness of the method and excellent improvements in the predicted dynamics and stability by minimum number of free parameters

particle markov chain monte carlo methods summary markov chain monte carlo and sequential monte carlo methods have emerged as the two main tools to sample from high dimensional probability distributions although asymptotic convergence of markov chain monte carlo algorithms is ensured under weak assumptions the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and or if highly correlated variables are updated independently we show here how it is possible to build efficient high dimensional proposal distributions by using sequential monte carlo methods this allows us not only to improve over standard markov chain monte carlo schemes but also to make bayesian inference feasible for a large class of statistical models where this was not previously so we demonstrate these algorithms on a non linear state space model and a levy driven stochastic volatility model

on a leray α model of turbulence in this paper we introduce and study a new model for three dimensional turbulence the leray model this model is inspired by the lagrangian averaged navier stokes model of turbulence also known navier stokes model or the viscous camassa holm equations as in the case of the lagrangian averaged navier stokes model the leray model compares successfully with empirical data from turbulent channel and pipe flows for a wide range of reynolds numbers we establish here an upper bound for the dimension of the global attractor the number of degrees of freedom of the leray model of the order of l l d 12 7 where l is the size of the domain and l d is the dissipation length scale this upper bound is much smaller than what one would expect for three dimensional models i e l l d 3 this remarkable result suggests that the leray model has a great potential to become a good sub grid scale large eddy simulation model of turbulence we support this observation by studying analytically and computationally the energy spectrum and show that in addition to the usual k 5 3 kolmogorov power law the inertial range has a steeper power law spectrum for wavenumbers larger than 1 finally we propose a prandtl like boundary layer model induced by the leray model and show a very good agreement of this model with empirical data for turbulent boundary layers

brief paper detection and estimation for abruptly changing systems the problem of state estimation and system structure detection for discrete stochastic dynamical systems with parameters which may switch among a finite set of values is considered the switchings are modelled by a markov chain with known transition probabilities a brief survey and a unified treatment of the existing suboptimal algorithms are provided the optimal algorithms require exponentially increasing memory and computations with time simulation results comparing the various suboptimal algorithms are presented

follow the bouncing ball global results on tracking and state estimation with impacts in this paper we formulate tracking and state estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set due to the discontinuous trajectories arising from the impacts we use hybrid systems stability analysis tools to establish the results using a novel concept of mirrored images of the target mass we prove that 1 a tracking control algorithm and 2 an observer algorithm guarantee global exponential stability results for specific classes of polyhedral billiards including rectangles moreover we combine these two algorithms within dynamic controllers that guarantee global output feedback tracking the results are illustrated via simulations

dynamical systems with active singularities of elastic type a modeling and controller synthesis framework a new class of systems characterized by admitting impulsive control action within their singular motion phases such as dimension changes state discontinuities and other irregularities is introduced this class termed dynamical systems with active or controlled singularities encompasses various applications with sensing and or actuation ultra fast in comparison with the natural system time scale including mechanisms with impact induced motion power and sensor networks under faults fast positioning devices smart skins and switching electronic circuits the present work focuses on systems with impact type singularities induced through system interaction with controlled or active state constraints the latter are assumed to be characterized by parameter dependent elastic type constraint violation that vanishes in the limit as the parameter value tends to infinity a physically well justified representation of this class of systems is proposed but found to be not well suited for controller synthesis in the singular phase to address this problem two equations are derived one describing controlled rigid impacts in auxiliary stretched time and compatible with the regular control design techniques termed controlled infinitesimal dynamics equation and another incorporating controlled impact dynamics in the infinitesimal form in terms of the shift operator along the trajectories of the first equation termed the limit model the latter is demonstrated to generate a unique isolated discontinuous system motion i e to provide a tight and well behaved description of the collision with rigid constraint it is then shown that the corresponding paths generated by the original physically based and the limit representations can be made arbitrarily close to each other uniformly except possibly in the vicinities of the jump points by the appropriate choice of the value of the constraint violation parameter this is shown to permit enforcing for sufficiently large values of the parameter the desired limit system behavior onto the original system by simply taking the control signals found through the limit representation time rescaling them and inserting the resulting signals directly into the original system these features show that the procedure developed in fact provides a well posed controller synthesis framework for the class of systems considered using this framework a ball racket rotationally controlled impact representation is developed and on its basis a singular phase control signal in the form of racket rotation velocity is designed demonstrating that the soft racket provides the specified bounce off angle increment under a noticeably lower racket rotation velocity and a longer rotation phase than the hard racket

the camassa holm equations and turbulence abstract in this paper we will survey our results on the camassa holm equations and their relation to turbulence as discussed in s chen c foias d d holm e olson e s titi s wynne the camassa holm equations as a closure model for turbulent channel and pipe flow phys rev lett 81 1998 5338 s chen c foias d d holm e olson e s titi s wynne a connection between the camassa holm equations and turbulent flows in channels and pipes phys fluids in press in particular we will provide a more detailed mathematical treatment of those equations for pipe flows which yield accurate predictions of turbulent flow profiles for very large reynolds numbers there are many facts connecting the camassa holm equations to turbulent fluid flows the dimension of the attractor agrees with the heuristic argument based on the kolmogorov statistical theory of turbulence the statistical properties of the energy spectrum agree in numerical simulation with the kolmogorov power law furthermore comparison of mean flow profiles for turbulent flow in channels and pipes given by experimental and numerical data show acceptable agreement with the profile of the corresponding solution of the camassa holm equations

discrete data assimilation in the lorenz and 2d navier stokes equations consider a continuous dynamical system for which partial information about its current state is observed at a sequence of discrete times discrete data assimilation inserts these observational measurements of the reference dynamical system into an approximate solution by means of an impulsive forcing in this way the approximating solution is coupled to the reference solution at a discrete sequence of points in time this paper studies discrete data assimilation for the lorenz equations and the incompressible two dimensional navier stokes equations in both cases we obtain bounds on the time interval h between subsequent observations which guarantee the convergence of the approximating solution obtained by discrete data assimilation to the reference solution

the shifted rayleigh mixture filter for bearings only tracking of maneuvering targets this paper introduces the shifted rayleigh mixture filter srmf which is based on jump markov linear systems the formulation permits the presence of clutter for bearings only tracking problems involving maneuvering targets the conditional density of the target state given the available measurements evolves as a growing mixture of probability density functions associated with a history of manoeuvre modes similar to other mixture algorithms the srmf approximates this conditional density by a gaussian mixture of fixed order unlike the extended or unscented kalman filters the shifted rayleigh filter incorporates an exact calculation of the posterior density when the prior is assumed to be gaussian given the latest bearings measurement computer simulations are provided to demonstrate the performance of the algorithm

multidimensional advection and fractional dispersion extension of the fractional diffusion equation to two or three dimensions is not as simple as extension of the second order equation this is revealed by the solutions of the equations unlike the gaussian the most general stable vector cannot be generated with an atomistic measure on the coordinate axes a random combination of maximally skewed stable variables on the unit sphere generates a stable vector that is a general model of a diffusing particle subsets are symmetric stable vectors that have previously appeared in the literature and the well known multidimensional brownian motion a multidimensional fractional differential operator is defined in the process

velocity observers for linear mechanical systems subject to single non smooth impacts abstract in this paper we consider the problem of the velocity estimation from position measurement for linear mechanical systems with multiple degrees of freedom subject to single non smooth impacts both elastic and inelastic i e with coefficient of restitution e 1 and e 0 1 respectively through a simple example it is shown that a classical luenberger observer is not able to reproduce instantaneously the jumps in the mass velocities since it recovers the error induced by such jumps only asymptotically an infinite sequence of impacts can prevent the estimation error to asymptotically go to zero a new observer structure is proposed for linear mechanical systems subject to single unilateral constraints that guarantees that the corresponding error dynamics are exponentially stable also in presence of an infinite sequence of non smooth impacts the observer that we propose switches at the impact times that can be recognized by position measurements only to validate the proposed observer both simulation and experimental tests have been carried out and are briefly reported pointing out the drawbacks and advantages of the observer

state estimation of otherwise unobservable linear mechanical systems through the use of non smooth impacts in this paper we consider a particular mechanism constituted by a pair of infinitely rigid mating gears subject to backlash where only the position of the actuated gear is measured so that the system is unobservable if the impacts between the teeth of the gears are ignored under the assumption that there is an infinite sequence of non smooth impacts which assumption is generally satisfied during a usual task e g when the mechanism is actuated by a constant torque it is possible to design an observer that asymptotically estimates also the position and the velocity of the non actuated gear simulation results are included to verify the effectiveness of the proposed observer

global regularity of logarithmically supercritical 3 d lamhd alpha system with zero diffusion abstract we study the three dimensional lagrangian averaged magnetohydrodynamics alpha system with zero diffusion despite the dissipation strength at the logarithmically supercritical level using dyadic decomposition techniques we show that given initial data sufficiently smooth the solution pair remains smooth for all time this settles the global regularity case suggested by the authors in 27

on line inference for hidden markov models via particle filters we consider the on line bayesian analysis of data by using a hidden markov model where inference is tractable conditional on the history of the state of the hidden component a new particle filter algorithm is introduced and shown to produce promising results when analysing data of this type the algorithm is similar to the mixture kalman filter but uses a different resampling algorithm we prove that this resampling algorithm is computationally efficient and optimal among unbiased resampling algorithms in terms of minimizing a squared error loss function in a practical example that of estimating break points from well log data our new particle filter outperforms two other particle filters one of which is the mixture kalman filter by between one and two orders of magnitude

operator levy motion and multiscaling anomalous diffusion the long term limit motions of individual heavy tailed power law particle jumps that characterize anomalous diffusion may have different scaling rates in different directions operator stable motions y t tg 0 are limits of d dimensional random jumps that are scale invariant according to c h y t y mathrm ct where h is a d ifmmode times else texttimes fi d matrix the eigenvalues of the matrix have real parts 1 ensuremath alpha j with each positive ensuremath alpha j l 2 in each of the j principle directions the random motion has a different fickian or super fickian diffusion dispersion rate proportional to t 1 ensuremath alpha j these motions have a governing equation with a spatial dispersion operator that is a mixture of fractional derivatives of different order in different directions subsets of the generalized fractional operator include i a fractional laplacian with a single order ensuremath alpha and a general directional mixing measure m ensuremath theta and ii a fractional laplacian with uniform mixing measure the riesz potential the motivation for the generalized dispersion is the observation that tracers in natural aquifers scale at different super fickian rates in the directions parallel and perpendicular to mean flow

an ell _ 1 laplace robust kalman smoother robustness is a major problem in kalman filtering and smoothing that can be solved using heavy tailed distributions e g l1 laplace this paper describes an algorithm for finding the maximum a posteriori map estimate of the kalman smoother for a nonlinear model with gaussian process noise and l1 laplace observation noise the algorithm uses the convex composite extension of the gauss newton method this yields convex programming subproblems to which an interior point path following method is applied the number of arithmetic operations required by the algorithm grows linearly with the number of time points because the algorithm preserves the underlying block tridiagonal structure of the kalman smoother problem excellent fits are obtained with and without outliers even though the outliers are simulated from distributions that are not l1 laplace it is also tested on actual data with a nonlinear measurement model for an underwater tracking experiment the l1 laplace smoother is able to construct a smoothed fit without data removal from data with very large outliers

spectral scaling of the leray α model for two dimensional turbulence we present data from high resolution numerical simulations of the navier stokes and the leray models for two dimensional turbulence it was shown previously lunasin et al 2007 j turbul 8 30 that for wavenumbers k such that k 1 the energy spectrum of the smoothed velocity field for the two dimensional navier stokes ns model scales as k 7 t his result is in agreement with the scaling deduced by dimensional analysis of the flux of the conserved enstrophy using its characteristic time scale we therefore hypothesize that the spectral scaling of any model in the sub spatial scales must depend only on the characteristic time scale and dynamics of the dominant cascading quantity in that regime of scales the data presented here from simulations of the two dimensional leray model confirm our hypothesis we show that for k 1 the energy spectrum for the twodimensional leray scales as k 5 as expected by the characteristic time scale for the flux of the conserved enstrophy of the leray model these results lead to our conclusion that the dominant directly cascading quantity of the model equations must determine the scaling of the energy spectrum

sequential monte carlo samplers summary we propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space each distribution being known up to a normalizing constant these probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential monte carlo methods this methodology allows us to derive simple algorithms to make parallel markov chain monte carlo algorithms interact to perform global optimization and sequential bayesian estimation and to compute ratios of normalizing constants we illustrate these algorithms for various integration tasks arising in the context of bayesian inference

control of contact problem in constrained euler lagrange systems stabilization of an euler lagrange system onto a constraint surface when the system makes contact with a nonzero impact velocity is an important problem in systems interacting with external environments potential applications include robotic surface following and surface finishing operations in manufacturing industry in the paper the constrained dynamic equations are modeled as a set of nonsmooth differential equations depending on whether the system lies on the constraint surface or the system repeatedly makes and loses contact with the constraint surface the focus is on the initial condition problem i e the system hits the constraint with a nonzero impact velocity a new discontinuous control scheme is proposed that ensures stable regulation of the system onto the constraint surface

modeling and control of systems with active singularities under energy constraints single and multi impact sequences a controller synthesis setting for systems with controlled singularities under incomplete information is extended to the cases characterized by a constraint on the total physical impulse as well as on the time interval between the adjacent engagement phases the use of this setting for the optimal control law calculation is illustrated on the ball racket system representative of a large class of controlled impact problems where there are two separate bodies interacting through controlled viscoelastic force

trajectory tracking for a particle in elliptical billiards an infinitely rigid unitary mass particle is considered moving on a planar region delimited by a rigid elliptical barrier elliptical billiards under the action of proper control forces a class of periodic trajectories involving an infinite sequence of non smooth impacts between the mass and the barrier at fixed times is found by using an lmis based procedure the jumps in the velocities at the impact times render difficult if not impossible to obtain the classical stability and attractivity properties for the dynamic system describing the tracking error behaviour hence the tracking control problem is properly stated using notions similar to the quasi stability concept in v lakshmikantham d d bainov and p s simeonov theory of impulsive differential equations 6 world scientific 1989 a controller whose state is subject to discontinuities based on the internal model principle is shown to solve the proposed tracking problem giving rise to control forces that are piecewise continuous fun

non uniqueness of weak solutions to 2d hypoviscous navier stokes equations abstract through an adaption of the convex integration scheme in the two dimensional case a result of the h principle type is presented for the two dimensional hypoviscous incompressible navier stokes equations it is shown that the c t 0 l x 2 weak solutions can possess compact temporal supports and thus are not unique in general

on the control of finite dimensional mechanical systems with unilateral constraints this paper focuses on the problem of the control of a class of mechanical systems with a finite number of degrees of freedom subject to unilateral constraints on the position roughly speaking those systems are described by a set of ordinary differential equations that represent smooth dynamics together with an algebraic inequality condition f q spl ges 0 where q is the vector of generalized coordinates and an impact rule relating the interaction impulse and the velocity nonsmooth dynamics is at the core of the study of such systems this implies that one can suitably define solutions and stability concepts that fit with the considered model we then discuss the closed loop control problem and analyze various switching control strategies

remark on the rate of decay of higher order derivatives for solutions to the navier stokes equations in rn we present a new derivation of upper bounds for the decay of higher order derivatives of solutions to the unforced navier stokes equations in rn the method based on so called gevrey estimates also yields explicit bounds on the growth of the radius of analyticity of the solution in time moreover under the assumption that the navier stokes solution stays sufficiently close to a solution of the heat equation in the l2 norm a result known to be true for a large class of initial data lower bounds on the decay of higher order derivatives can be obtained

association pattern discovery via theme dictionary models summary discovering patterns from a set of text or more generally categorical data is an important problem in many disciplines such as biomedical research linguistics artificial intelligence and sociology we consider here the well known market basket problem that is often discussed in the data mining community and is also quite ubiquitous in biomedical research the data under consideration are a set of baskets where each basket contains a list of items our goal is to discover themes which are defined as subsets of items that tend to co occur in a basket we describe a generative model i e the theme dictionary model for such data structures and describe two likelihood based methods to infer themes that are hidden in a collection of baskets we also propose a novel sequential monte carlo method to overcome computational challenges using both simulation studies and real applications we demonstrate that the new approach proposed is significantly more powerful than existing methods such as association rule mining and topic modelling in detecting weak and subtle interactions in the data

a particle filtering scheme for processing time series corrupted by outliers the literature in engineering and statistics is abounding in techniques for detecting and properly processing anomalous observations in the data most of these techniques have been developed in the framework of static models and it is only in recent years that we have seen attempts that address the presence of outliers in nonlinear time series for a target tracking problem described by a nonlinear state space model we propose the online detection of outliers by including an outlier detection step within the standard particle filtering algorithm the outlier detection step is implemented by a test involving a statistic of the predictive distribution of the observations such as a concentration measure or an extreme upper quantile we also provide asymptotic results about the convergence of the particle approximations of the predictive distribution and its statistics and assess the performance of the resulting algorithms by computer simulations of target tracking problems with signal power observations

logarithmically extended global regularity result of lans alpha mhd system in two dimensional space abstract we study the two dimensional generalized lans alpha magnetohydrodynamics system we show that the solution pairs of velocity and magnetic fields to this system preserve their initial regularity in two cases dissipation logarithmically weaker than a full laplacian and zero diffusion zero dissipation and diffusion logarithmically weaker than a full laplacian

modeling and control of impact in mechanical systems theory and experimental results considers the equations of motion of mechanical systems subject to inequality constraints which can be obtained by looking for the stationary value of the action integral two different methods are used to take into account the inequality constraints in the computation of the stationary value of the action integral the valentine variables method and the penalty functions method the equations of motion resulting from the application of the valentine variables method which introduces the concept of nonsmooth impacts constitute the exact model of the constrained mechanical system such a model is suitable to be employed when the impacting parts of the actual mechanical system are very stiff the equations of motion resulting from the application of the penalty functions method which introduces the concept of smooth impacts constitute an approximate model of the constrained mechanical system such a model is suitable to be employed when the impacting parts of the actual mechanical system show some flexibility various feedback control laws from the natural outputs and from their time derivatives are studied with reference to both models of impact the closed loop systems resulting from the application of the same control law to both models show pretty much the same global asymptotic stability properties the proposed control laws are only concerned with regulation problems in the presence of possible contacts and impacts among parts of the mechanical system or with the external environment the effectiveness of the proposed control structure has been tested experimentally with reference to a single link robot arm showing a valuable behavior

inertial manifolds for the 3d modified leray α model abstract in this paper we investigate the critical modified leray model in t 3 and prove the existence of an n dimensional inertial manifold for this problem

uniqueness in the elastic bounce problem ii in a recent paper uniqueness for the elastic bounce problem has been studied in a very general framework the aim of this paper is to show that if u is assumed to be real analytic and u equiv 0 then these phenomena disappear and the solution to the elastic bounce problem is unique for every choice of the cauchy data

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

detecting change points for shifts in mean and variance using fuzzy classification maximum likelihood change point algorithms knowing the time of changes called change point cp in a process is crucial for engineers to recognize the root cause fast and accurately since special causes may induce simultaneous changes in mean and variance detecting changes in both at once is required many methodologies in quality control were developed for detecting changes in either mean or variance only and process parameters were assumed known often however they are rarely known exactly and a small estimation error may lead to unfavorable cp estimates fuzzy partitioning is better suited to cases of vague boundaries between two segments which appear very often in reality a new mechanism called fuzzy classification maximum likelihood change point fcml cp algorithm is proposed to detect shifts in mean and variance simultaneously a cp framework is transferred into a mixture model and then a fcml cp algorithm is created through fuzzy classification maximum likelihood procedures the proposed fcml cp can be applied to phase i and ii processes without knowledge of in control process parameters it can estimate multiple cps of process mean or and variance simultaneously the effectiveness and superiority of fcml cp are shown by extensive experiments with numerical and real data sets specifically the proposed fcml cp is superior to the commonly used statistical mixture likelihood approach using expectation maximization em algorithm it is much more time saving especially the remarkable performance of fcml cp in detecting cps for small changes is particularly important and helpful for engineers to recognize the special cause fast and correctly since an out of control signal resulted from small changes is usually delayed long we propose a new algorithm fcml cp to detect change points in a statistical process the mixture likelihood embedded fuzzy c partition is utilized to estimate the change points the method outperforms statistical likelihood approaches various experiments show the effectiveness and practicability of the proposed method excellent performance in detecting small changes is helpful for root cause analyses

following a moving target monte carlo inference for dynamic bayesian models markov chain monte carlo mcmc sampling is a numerically intensive simulation technique which has greatly improved the practicality of bayesian inference and prediction however mcmc sampling is too slow to be of practical use in problems involving a large number of posterior target distributions as in dynamic modelling and predictive model selection alternative simulation techniques for tracking moving target distributions known as particle filters which combine importance sampling importance resampling and mcmc sampling tend to suffer from a progressive degeneration as the target sequence evolves we propose a new technique based on these same simulation methodologies which does not suffer from this progressive degeneration

global well posedness of the velocity vorticity voigt model of the 3d navier stokes equations abstract the velocity vorticity formulation of the 3d navier stokes equations was recently found to give excellent numerical results for flows with strong rotation in this work we propose a new regularization of the 3d navier stokes equations which we call the 3d velocity vorticity voigt vvv model with a voigt regularization term added to momentum equation in velocity vorticity form but with no regularizing term in the vorticity equation we prove global well posedness and regularity of this model under periodic boundary conditions we prove convergence of the model s velocity and vorticity to their counterparts in the 3d navier stokes equations as the voigt modeling parameter tends to zero we prove that the curl of the model s velocity converges to the model vorticity which is solved for directly as the voigt modeling parameter tends to zero finally we provide a criterion for finite time blow up of the 3d navier stokes equations based on this inviscid regularization

a new gaussian mixture algorithm for gmti tracking under a minimum detectable velocity constraint this paper introduces a new methodology to account for doppler blind zone constraints arising for example in ground moving target indicator gmti tracking applications in such problems target measurements are suppressed when the range rate doppler of the target drops below a specified threshold in magnitude the minimum detectable velocity the proposed method employing gaussian mixture approximations to the filtering density differs from earlier gaussian mixture approaches in the way missed measurements are modelled the distinctive feature of the algorithm as compared with other gaussian mixture filters is that it is based on an exact calculation of the filtering density when a measurement is not recorded algorithms that result from applying this methodology are simple to implement and computationally undemanding simulation results indicate a uniform improvement in estimation accuracy over that of earlier proposed analytic techniques and a tracking performance comparable to that of state of the art particle filters

approximate deconvolution model in a bounded domain with vertical regularization abstract we study the global existence issue for a three dimensional approximate deconvolution model with a vertical filter we consider this model in a bounded cylindrical domain where we construct a unique global weak solution the proof is based on a refinement of the energy method given by berselli 2012 in 4

asymptotic tracking of periodic trajectories for a simple mechanical system subject to nonsmooth impacts an infinitely rigid mass is considered which moves on a plane under the action of proper control forces within a closed region delimited by an infinitely massive and rigid circular barrier a suitably amended tracking problem for a class of periodic trajectories involving an infinite number of nonsmooth impacts between the mass and the barrier is formally stated and solved

on a regularization of a scalar conservation law with discontinuous coefficients this paper is devoted to a scalar conservation law with a linear flux function involving discontinuous coefficients it is clear that the delta standing wave should be introduced into the riemann solution in some nonclassical situation in order to study the formation of delta standing wave we consider a regularization of the discontinuous coefficient with the helmholtz mollifier and then obtain a regularized system which depends on a regularization parameter 0 the regularization mechanism is a nonlinear bending of characteristic curves that prevents their finite time intersection it is proved rigorously that the solutions of regularized system converge to the delta standing wave solution in the 0 limit compared with the classical method of vanishing viscosity here it is clear to see how the delta standing wave forms naturally along the characteristics

velocity observers for non linear mechanical systems subject to non smooth impacts this paper is concerned with the estimation of the velocity variables when the position variables are the measured outputs for non linear mechanical systems subject to non smooth impacts both elastic and inelastic i e with coefficient of restitution e 1 and e 0 1 respectively a reduced order observer is proposed which guarantees that the corresponding error system despite the possible presence of an infinite sequence of non smooth impacts is locally exponentially stable an estimate of the basin of attraction is also given

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

blind deconvolution via sequential imputations abstract the sequential imputation procedure is applied to adaptively and sequentially reconstruct discrete input signals that are blurred by an unknown linear moving average channel and contaminated by additive gaussian noises a problem known as blind deconvolution in digital communication a rejuvenation procedure for improving the efficiency of sequential imputation is introduced and theoretically justified the proposed method does not require the channel to be nonminimum phase and can be used in real time signal restoration two simulated systems are studied to illustrate the proposed method our result shows that the ideas of multiple imputations and flexible simulation techniques are as powerful in engineering as in survey sampling

optimal control problems in hybrid systems with active singularities abstract the optimal control problem for systems with controlled unilateral phase constraints is considered the definition of the generalized solutions is introduced the transformation method for the original optimal control problem within the class of generalized solution to a standard optimal control problem is proposed and the necessary optimality conditions are found

boundary effects on exact solutions of the lagrangian averaged navier stokes α equations in order to clarify the behavior of solutions of the lagrangian averaged navier stokes lans equations in the presence of solid walls we identify a variety of exact solutions of the full equations and their boundary layer approximations the solutions demonstrate that boundary conditions suggested for the lans equations in the literature 1 for a bounded domain do not apply in a semi infinite domain the convergence to solutions of the navier stokes equations as 0 is elucidated for infinite energy solutions in a semi infinite domain and non uniqueness of these solutions is discussed we also study the boundary layer approximation of lans equations denoted the prandtl equations and report solutions for turbulent jets and wakes our version of the prandtl equations includes an extra term necessary to conserve linear momentum and corrects an earlier result of cheskidov 2

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

a finite dimensional attractor for three dimensional flow of incompressible fluids abstract the asymptotic behavior of the flow for a system of the navier stokes type is investigated in the considered model the viscous part of the stress tensor is generally a nonlinear function of the symmetric part of the velocity gradient provided that the function describing this dependence satisfies the polynomial p 1 growth condition a unique weak solution exists if either p 2 n 2 and u 0 h or p 1 2 n n 2 and u 0 w 1 2 c n h in the first case the existence of a global attractor in h is proved in order to indicate the finite dimensional behavior of the flow at infinity the fractal dimension of the new invariant set composed from all short trajectories with initial value in the attractor is estimated in the l 2 0 h topology having uniqueness only for more regular data in the second case many trajectories can start from the initial value u 0 h this does not allow one to define a semigroup on the space h therefore the set of short trajectories x s closed in l 2 0 h is introduced along with a semigroup working on this set the existence of a global attractor with a finite fractal dimension is then demonstrated

fuzzy change point algorithms for regression models change point cp regression models have been widely applied in various fields where detecting cps is an important problem detecting the location of cps in regression models could be equivalent to partitioning data points into clusters of similar individuals in the literature fuzzy clustering has been widely applied in various fields but it is less used in locating cps in cp regression models in this paper a new method called fuzzy cp fcp algorithm is proposed to detect the cps and simultaneously estimate the parameters of regression models the fuzzy c partitions concept is first embedded into the cp regression models any possible collection of all cps is considered as a partitioning of data with a fuzzy membership we then transfer these memberships into the pseudomemberships of data points belonging to each individual cluster and therefore we can obtain the estimates for model parameters by the fuzzy c regressions method subsequently we use the fuzzy c means clustering to obtain the new iterates of the cp collection memberships by minimizing an objective function concerning the deviations between the predicted response values and data values we illustrate the new approach with several numerical examples and real datasets experimental results actually show that the proposed fcp is an effective and useful cp detection algorithm for cp regression models and can be applied to various fields such as econometrics medicine quality control and signal processing