reconstructing state spaces from multivariate data using variable delays we study two methods for constructing a nonuniform embedding for multivariate data a nonuniform embedding is a state space reconstruction which is more flexible than the common delay coordinates with fixed delays since it contains variable delays using these methods we can extract causal relationships among many variables in a more suitable way we demonstrate that the proposed methods can give more precise predictions and simpler models than some previous methods

comparison of systems with complex behavior abstract we present a formalism for comparing the asymptotic dynamics of dynamical systems with physical systems that they model based on the spectral properties of the koopman operator we first compare invariant measures and discuss this in terms of a statistical takens theorem proved here we also identify the need to go beyond comparing only invariant ergodic measures of systems and introduce an ergodic theoretic treatment of a class of spectral functionals that allow for this the formalism is extended for a class of stochastic systems discrete random dynamical systems the ideas introduced in this paper can be used for parameter identification and model validation of driven nonlinear models with complicated behavior as an illustration we provide an example in which we compare the asymptotic behavior of a combustion system measured experimentally with the asymptotic behavior of a class of models that have the form of a random dynamical system

identification of composite local linear state space models using a projected gradient search an identification method is described to determine a weighted combination of local linear state space models from input and output data normalized radial basis functions are used for the weights

a review of geometric transformations for nonrigid body registration this paper provides a comprehensive and quantitative review of spatial transformations models for nonrigid image registration it explains the theoretical foundation of the models and classifies them according to this basis this results in two categories physically based models described by partial differential equations of continuum mechanics e g linear elasticity and fluid flow and basis function expansions derived from interpolation and approximation theory e g radial basis functions b splines and wavelets recent work on constraining the transformation so that it preserves the topology or is diffeomorphic is also described the final section reviews some recent evaluation studies the paper concludes by explaining under what conditions a particular transformation model is appropriate

cooling schedules for optimal annealing a monte carlo optimization technique called simulated annealing is a descent algorithm modified by random ascent moves in order to escape local minima which are not global minima the level of randomization is determined by a control parameter t called temperature which tends to zero according to a deterministic cooling schedule we give a simple necessary and sufficient condition on the cooling schedule for the algorithm state to converge in probability to the set of globally minimum cost states in the special case that the cooling schedule has parametric form tt c log1 t the condition for convergence is that c be greater than or equal to the depth suitably defined of the deepest local minimum which is not a global minimum state

size and shape analysis of landmark data summary the paper deals with statistical analysis of landmark data using the exact joint distribution theory for the size and shape of planar gaussian configurations this is an extension of earlier work which considered marginal shape analysis special cases of the size and shape distribution are examined and the isotropic gaussian model is investigated in particular detail various properties are studied including conditional distributions and a curve of regression finally we consider some possible approaches to inference including exact maximum likelihood estimation of size and shape a practical biological application is given which investigates the size and shape of mouse vertebrae

diffusions for global optimizations we seek a global minimum of u 0 1 n to r the solution to d dt x t nabla u x t will find local minima the solution to dx t nabla u x t dt sqrt 2t dw t where w is standard n dimensional brownian motion and the boundaries are reflecting will concentrate near the global minima of u at least when temperature t is small the equilibrium distribution for x t is gibbs with density pi t x alpha exp u x t this suggests setting t t t downarrow 0 to find the global minima of u we give conditions on u x and t t such that the solution to dx t nabla u x t dt sqrt 2t dw t converges weakly to a distribution concentrated on the global minima of u

structural image restoration through deformable templates abstract prior knowledge on the space of possible images is given in the form of a function or template in some domain the set of all possible true images is assumed to be formed by a composition of that function with continuous mappings of the domain into itself a prior gaussian distribution is given on the set of continuous mappings the observed image is assumed to be a degradation of the true image with additive noise given the observed image a posterior distribution is then obtained and has the form of a nonlinear perturbation of the gaussian measure on the space of mappings we present simulations of the posterior distribution that lead to structural reconstructions of the true image in the sense that it enables us to determine landmarks and other characteristic features of the image as well as to spot pathologies in it moreover we show that the reconstruction algorithm is relatively robust when the images are degraded by noise that is not necessarily additive

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

a peak preserving algorithm for the removal of colored noise from signals we employ the simulated annealing method in order to restore signals that may contain peaks we wish to preserve but otherwise are smooth and buried in colored noise the problem is formulated as a global optimization one we propose a piecewise linear model for the noise free signal that is appropriate for preserving peaks that are often encountered in biomedical or industrial signals an iterative algorithm is proposed the restored signal is used to estimate the model parameters that are subsequently used to improve the signal estimation the algorithm stops when self consistency has been achieved i e the estimated values of the noise model parameters agree to within the accuracy of their estimation with the parameters used to restore the signal application of the method to simulated data with various levels of noise showed that the underlying signal can be restored sufficiently well the algorithm is also applied to some evoked response magneto encephalographic data as well as to some signals from an automatic industrial inspection problem our results are compared with those obtained by using the iterative conditional modes algorithm and shown to be better in terms of preserving the peaks in the signals

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

chain graph models and their causal interpretations chain graphs are a natural generalization of directed acyclic graphs and undirected graphs however the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent there are many simple and apparently plausible but ultimately fallacious interpretations of chain graphs that are often invoked implicitly or explicitly these interpretations also lead to flawed methods for applying background knowledge to model selection we present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated from the equilibrium distributions of dynamic models with feed back these dynamic interpretations lead to a simple theory of intervention extending the theory developed for directed acyclic graphs finally we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feed back in econometrics

markov chain monte carlo 10 years and still running although markov chain monte carlo mcmc techniques can be traced back to the early 1950s and are almost contemporary with independent monte carlo methods the use of these techniques has only really taken off in the past 10 years at least in mainstream statistics with the work of gelfand and smith 1990 and the rediscovery of metropolis s and hastings s papers the impact on the discipline is deep and durable because these methods have opened new horizons in the scale of the problems that one can deal with thus enhancing the position of statistics in most applied fields the mcmc revolution has in particular boosted bayesian statistics to new heights by providing a virtually universal tool for dealing with integration and optimization problems this can be seen in for instance the explosion of papers dealing with complex models hierarchical modelings nonparametric bayesian estimation and spatial statistics this trend has also created new synergies with mathematicians and probabilists as well as econometricians engineers ecologists astronomers and others for theoretical requests and practical implications of mcmc techniques it is impossible to provide here a complete perspective on mcmc methods and applications for this as well as for other references we refer the reader to the books by gilks richardson and spiegelhalter 1995 and robert and casella 1999 here we focus on four particular aspects of mcmc algorithms theoretical foundations practical implementation bayesian inference and prospects the web provides many relevant sites including the mcmc preprint server http www statslab cam ac uk r mcmc which offers a most useful window to the current research on mcmc wilson s site on perfect simulation http dimacs rutgers edu dbwilson exact h which keeps track of papers and applets on this topic and a site on convergence control techniques http www ensae fr crest statistique robert mcdiag even more recent developments allow for on line computations through applets like breyer s http www maths lancs ac uk breyer java html which impressively illustrates the behavior of different samplers for simple problems note also that the bugs and coda software are freely available at http www mrc bsu cam ac uk bu

c 4 exploring multiple solutions in graphical models by cluster sampling this paper presents a novel markov chain monte carlo mcmc inference algorithm called c4 clustering with cooperative and competitive constraints for computing multiple solutions from posterior probabilities defined on graphical models including markov random fields mrf conditional random fields crf and hierarchical models the graphs may have both positive and negative edges for cooperative and competitive constraints c4 is a probabilistic clustering algorithm in the spirit of swendsen wang 34 by turning the positive edges on off probabilistically c4 partitions the graph into a number of connected components ccps and each ccp is a coupled subsolution with nodes connected by positive edges then by turning the negative edges on off probabilistically c4 obtains composite ccps called cccps with competing ccps connected by negative edges at each step c4 flips the labels of all nodes in a cccp so that nodes in each ccp keep the same label while different ccps are assigned different labels to observe both positive and negative constraints thus the algorithm can jump between multiple competing solutions or modes of the posterior probability in a single or a few steps it computes multiple distinct solutions to preserve the intrinsic ambiguities and avoids premature commitments to a single solution that may not be valid given later context c4 achieves a mixing rate faster than existing mcmc methods such as various gibbs samplers 15 26 and swendsen wang cuts 2 34 it is also more dynamic than common optimization methods such as icm 3 lbp 21 37 and graph cuts 4 20 we demonstrate the c4 algorithm in line drawing interpretation scene labeling and object recognition

learning the dynamical system behind sensory data this letter looks at the physics behind sensory data by identifying the parameters that govern the physical system and estimating them from sensory observations we extend takens s delay embedding theorem to the dynamical systems controlled by parameters an embedding of the product space of the phase and the parameter spaces of the dynamical system can be obtained by the delay embedding map provided that the parameter of the dynamical system changes slowly the reconstruction error is bounded for slowly varying parameters a manifold learning technique is applied to the embedding obtained to extract a low dimensional global coordinate system representing the product space the phase space of the deterministic dynamics can be contracted by using the adjacency relationship in time which enables recovery of only the parameter space as examples the manifolds of synthetic and real world vowels with time varying fundamental frequency f0 are analyzed and the f0 contours are extracted by an unsupervised algorithm experimental results show that the proposed method leads to robust performance under various noise conditions and rapid changes of f0 compared with the current state of the art f0 estimation algorithms

phase space embedding of electrocardiograms we study properties of the human electrocardiogram under the working hypothesis that fluctuations beyond the regular structure of single cardiac cycles are unpredictable against this background we discuss the possibility of using the phase space embedding method for this kind of signal in particular the specific nature of the stochastic or high dimensional component allows us to use phase space embeddings for certain signal processing tasks as practical applications we discuss noise filtering fetal ecg extraction and the automatic detection of clinically relevant features the main purpose of the paper is to connect results of embedding theory that have not been previously applied in practice and practical applications that have not yet been justified theoretically

inertial manifolds the non self adjoint case abstract in contrast with the existing theories of inertial manifolds which are based on the self adjoint assumption of the principal differential operator in this paper we show that for general dissipative evolutionary systems described by semilinear parabolic equations with principal differential operator being sectorial and having compact resolvent there exists an inertial manifold provided that certain gap conditions hold we also show that by using an elliptic regularization this theory can be extended to a class of kdv equations where the principal differential operator is not sectorial

relaxation algorithms for map estimation of gray level images with multiplicative noise the authors present a comparison between stochastic and deterministic relaxation algorithms for maximum a posteriori estimation of gray level images modeled by noncausal gauss markov random fields gmrf and corrupted by film grain noise the degradation involves nonlinear transformation and multiplicative noise parameters for the gmrf model were estimated from the original image using maximum likelihood techniques to overcome modeling errors a constraint minimization approach is suggested for estimating the parameters to ensure the positivity of the power spectral density function real image experiments with various noise variances and magnitudes of the nonlinear transformation are presented

an algorithm of uniform ultimate boundedness for a class of switched linear systems uniform ultimate boundedness of a class of switched linear systems is studied a switched linear system in this class consists of m subsystems and none of the individual subsystems need to be stabilizable the switched linear system is shown to be uniformly ultimately bounded for any pre given bound if the union of individual controllable subspaces covers the entire state space an algorithm for guaranteeing uniform ultimate boundedness is given to provide the design of continuous controllers and the switching strategy

inertial manifolds for nonlinear evolutionary equations abstract in this paper we introduce the concept of an inertial manifold for nonlinear evolutionary equations in particular for ordinary and partial differential equations these manifolds which are finite dimensional invariant lipschitz manifolds seem to be an appropriate tool for the study of questions related to the long time behavior of solutions of the evolutionary equations the inertial manifolds contain the global attractor they attract exponentially all solutions and they are stable with respect to perturbations furthermore in the infinite dimensional case they allow for the reduction of the dynamics to a finite dimensional ordinary differential equation

stochastic analysis of recurrence plots with applications to the detection of deterministic signals recurrence plots have been widely used for a variety of purposes such as analyzing dynamical systems denoising as well as detection of deterministic signals embedded in noise though it has been postulated previously that recurrence plots contain time correlation information here we make the relationship between unthresholded recurrence plots and the covariance of a random process more precise computations using examples from harmonic processes autoregressive models and outputs from nonlinear systems are shown to illustrate this relationship finally the use of recurrence plots for detection of deterministic signals in the presence of noise is investigated and compared to traditional signal detection methods based on the likelihood ratio test results using simulated data show that detectors based on certain statistics derived from recurrence plots are sub optimal when compared to well known detectors based on the likelihood ratio

statistical principles in image modeling images of natural scenes contain a rich variety of visual patterns to learn and recognize these patterns from natural images it is necessary to construct statistical models for these patterns in this review article we describe three statistical principles for modeling image patterns the sparse coding principle the minimax entropy principle and the meaningful alignment principle we explain these three principles and their relationships in the context of modeling images as compositions of gabor wavelets these three principles correspond to three regimes of composition patterns of gabor wavelets and these three regimes are connected by changes in scale or resolution

updating schemes correlation structure blocking and parameterization for the gibbs sampler in this paper many convergence issues concerning the implementation of the gibbs sampler are investigated exact computable rates of convergence for gaussian target distributions are obtained different random and non random updating strategies and blocking combinations are compared using the rates the effect of dimensionality and correlation structure on the convergence rates are studied some examples are considered to demonstrate the results for a gaussian image analysis problem several updating strategies are described and compared for problems in bayesian linear models several possible parameterizations are analysed in terms of their convergence rates characterizing the optimal choice

a generalized least absolute deviation method for parameter estimation of autoregressive signals this paper proposes a generalized least absolute deviation glad method for parameter estimation of autoregressive ar signals under non gaussian noise environments the proposed glad method can improve the accuracy of the estimation of the conventional least absolute deviation lad method by minimizing a new cost function with parameter variables and noise error variables compared with second and high order statistical methods the proposed glad method can obtain robustly an optimal ar parameter estimation without requiring the measurement noise to be gaussian moreover the proposed glad method can be implemented by a cooperative neural network nn which is shown to converge globally to the optimal ar parameter estimation within a finite time simulation results show that the proposed glad method can obtain more accurate estimates than several well known estimation methods in the presence of different noise distributions

finding metastable states in real world time series with recurrence networks in the framework of time series analysis with recurrence networks we introduce a self adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real world time series as initial step we introduce a way to set the embedding parameters used to reconstruct the state space from the time series we set them as the ones giving the maximum shannon entropy of the diagonal line length distribution for the first simultaneous minima of recurrence rate and shannon entropy to identify metastable states as well as the transitions between them we use a soft partitioning algorithm for module finding which is specifically developed for the case in which a system shows metastability we illustrate our method with a complex time series example finally we show the robustness of our method for identifying metastable states our results suggest that our method is robust for identifying metastable states in complex time series even when introducing considerable levels of noise and missing data points

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

phase relationships between two or more interacting processes from one dimensional time series i basic theory a general approach is developed for the detection of phase relationships between two or more different oscillatory processes interacting within a single system using one dimensional time series only it is based on the introduction of angles and radii of return times maps and on studying the dynamics of the angles an explicit unique relationship is derived between angles and the conventional phase difference introduced earlier for bivariate data it is valid under conditions of weak forcing this correspondence is confirmed numerically for a nonstationary process in a forced van der pol system a model describing the angles behavior for a dynamical system under weak quasiperiodic forcing with an arbitrary number of independent frequencies is derived to establish from experimental data whether or not two or more interacting processes are synchronized is an old and important problem in the absence of noise the existence of synchronization between two processes in interacting limit cycle oscillators was originally taken to imply that their basic frequencies of oscillation are related as integer numbers i e are rationally connected 1 2 and that their instantaneous phases are permanently locked this definition suggests that the detection of whether or not synchronization exists can be established by computation of the ratio of basic frequencies in the fourier spectrum of the signal from one of the sub systems involved even in this simplest case however the finite observation time and the discreteness of the digitiza tion steps used in practice will make it appear that all fre quencies are rationally connected thereby complicating the reliable estimation of their ratio furthermore the noise that is invariably present in all real macroscopic systems means that only effective synchronization 3 can normally take place meaning that the phases can remain locked only dur ing finite time intervals and that the basic frequencies may no longer be rationally connected 4 serious difficulties may also arise due to the nonstationarity of experimental data in view of these problems modern techniques for estab lishing the presence or absence of synchronization are based on the assumption that the behavior of each subsystem can be considered separately and that their individual time series can be compared by a variety of techniques e g by compu tation of the phase difference between them this approach has been justified theoretically 3 6 and is widely used to detect synchronization not only in periodic noisy but also in

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

spatial statistics and bayesian computation on wednesday may 6th 1992 professor b w silverman in the chair summary markov chain monte carlo mcmc algorithms such as the gibbs sampler have provided a bayesian inference machine in image analysis and in other areas of spatial statistics for several years founded on the pioneering ideas of ulf grenander more recently the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a markov random field has opened the way to the use of mcmc in general bayesian computation in this paper we trace the early development of mcmc in bayesian inference review some recent computational progress in statistical physics based on the introduction of auxiliary variables and discuss its current and future relevance in bayesian applications we briefly describe a simple mcmc implementation for the bayesian analysis of agricultural field experiments with which we have some practical experience

minimal attractors and bifurcations of random dynamical systems we consider attractors for certain types of random dynamical systems these are skew product systems whose base transformations preserve an ergodic invariant measure we discuss definitions of invariant sets attractors and invariant measures for deterministic and random dynamical systems under assumptions that include for example iterated function systems but that exclude stochastic differential equations we demonstrate how random attractors can be seen as examples of milnor attractors for a skew product system we discuss the minimality of these attractors and invariant measures supported by them as a further connection between random dynamical systems and deterministic dynamical systems we show how dynamical or d bifurcations of random attractors with multiplicative noise can be seen as blowout bifurcations and we relate the issue of branching at such d bifurcations to branching at blowout bifurcations

multivariate aspects of shape theory sis and thus provide a comprehensive view of shape distributions when landmark coordinates are gaussian distributed this work allows the statistical analysis of shape to be carried out using standard techniques of multivariate analysis the paper includes some new results in all dimensions and a general gaussian approximation to the size and shape distribution we also discuss some inference problems and give a numerical example

information theoretic image formation the emergent role of information theory in image formation is surveyed unlike the subject of information theoretic communication theory information theoretic imaging is far from a mature subject the possible role of information theory in problems of image formation is to provide a rigorous framework for defining the imaging problem for defining measures of optimality used to form estimates of images for addressing issues associated with the development of algorithms based on these optimality criteria and for quantifying the quality of the approximations the definition of the imaging problem consists of an appropriate model for the data and an appropriate model for the reproduction space which is the space within which image estimates take values each problem statement has an associated optimality criterion that measures the overall quality of an estimate the optimality criteria include maximizing the likelihood function and minimizing mean squared error for stochastic problems and minimizing squared error and discrimination for deterministic problems the development of algorithms is closely tied to the definition of the imaging problem and the associated optimality criterion algorithms with a strong information theoretic motivation are obtained by the method of expectation maximization related alternating minimization algorithms are discussed in quantifying the quality of approximations global and local measures are discussed global measures include the mean squared error and discrimination between an estimate and the truth and probability of error for recognition or hypothesis testing problems local measures include fisher information

segmentation registration and measurement of shape variation via image object shape a model of object shape by nets of medial and boundary primitives is justified as richly capturing multiple aspects of shape and yet requiring representation space and image analysis work proportional to the number of primitives metrics are described that compute an object representation s prior probability of local geometry by reflecting variabilities in the net s node and link parameter values and that compute a likelihood function measuring the degree of match of an image to that object representation a paradigm for image analysis of deforming such a model to optimize a posteriori probability is described and this paradigm is shown to be usable as a uniform approach for object definition object based registration between images of the same or different imaging modalities and measurement of shape variation of an abnormal anatomical object compared with a normal anatomical object examples of applications of these methods in radiotherapy surgery and psychiatry are given

a method of sieves for multiresolution spectrum estimation and radar imaging a method of sieves using splines is proposed for regularizing maximum likelihood estimates of power spectra this method has several important properties including the flexibility to be used at multiple resolution levels the resolution level is defined in terms of the support of the polynomial b splines used an expression for the optimal rate of growth of the sieve is derived using a discrepancy measure derived from the kullback leibler divergence of parameterized density functions while the sieves may be defined on nonuniform grids in the case of uniform grids the optimal sieve size corresponds to an optimal resolution iterative algorithms for obtaining the maximum likelihood sieve estimates are derived applications to spectrum estimation and radar imaging are proposed

an efficient and provably correct algorithm for the multiscale estimation of image contours by means of polygonal lines a large portion of image contours is characterized by local properties such as sharp variations of the image intensity across the contour the integration of local image descriptors estimated by using these local properties into curvilinear descriptors is a difficult problem from a theoretical viewpoint because of the combinatorially large number of possible curvilinear descriptors to deal with this difficulty the notion of compressible graphs is introduced and a contour data model is defined leading to an efficient linear time algorithm which provably recovers contours with an upper bound on the approximation error

bayesian segmentation via asymptotic partition functions asymptotic approximations to the partition function of gaussian random fields are derived textures are characterized via gaussian random fields induced by stochastic difference equations determined by finitely supported stationary linear difference operators adjusted to be nonstationary at the boundaries it is shown that as the scale of the underlying shape increases the log normalizer converges to the integral of the log spectrum of the operator inducing the random field fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the differential operator induced random field model matrix analysis techniques are proposed for handling textures with variable orientation examples of texture parameters estimated from training data via asymptotic maximum likelihood are shown isotropic models involving powers of the laplacian and directional models involving partial derivative mixtures are explored parameters are estimated for mitochondria and actin myocin complexes in electron micrographs and clutter in forward looking infrared images deformable template models are used to infer the shape of mitochondria in electron micrographs with the asymptotic approximation allowing easy recomputation of the partition function as inference proceeds

wasserstein distances in the analysis of time series and dynamical systems abstract a new approach based on wasserstein distances which are numerical costs of an optimal transportation problem allows us to analyze nonlinear phenomena in a robust manner the long term behavior is reconstructed from time series resulting in a probability distribution over phase space each pair of probability distributions is then assigned a numerical distance that quantifies the differences in their dynamical properties from the totality of all these distances a low dimensional representation in a euclidean space is derived in which the time series can be classified and statistically analyzed this representation shows the functional relationships between the dynamical systems under study it allows us to assess synchronization properties and also offers a new way of numerical bifurcation analysis the statistical techniques for this distance based analysis of dynamical systems are presented filling a gap in the literature and their application is discussed in a few examples of datasets arising in physiology and neuroscience and in the well known henon system

affine permutation invariance of 2 d shapes shapes provide a rich set of clues on the identity and topological properties of an object in many imaging environments however the same object appears to have different shapes due to distortions such as translation rotation reflection scaling or skewing further the order by which the object s feature points are scanned changes i e the order of the pixels may be permuted relating two dimensional shapes of the same object distorted by different affine and permutation transformations is a challenge we introduce a shape invariant that we refer to as the intrinsic shape of an object and describe an algorithm blaiser to recover it the intrinsic shape is invariant to affine permutation distortions it is a uniquely defined representative of the equivalence class of all affine permutation distortions of the same object blaiser computes the intrinsic shape from any arbitrarily affine permutation distorted image of the object without prior knowledge regarding the distortions or the undistorted shape of the object the critical step of blaiser is the determination of the shape orientation and we provide a detailed discussion on this topic the operations of blaiser are based on low order moments of the input shape and thus robust to error and noise examples illustrate the performance of the algorithm

invariant graphs for forced systems abstract many applications of nonlinear dynamics involve forced systems we consider the case where for a fixed input the driven system is contracting this is for instance the situation in certain classes of filters and in the study of synchronization when such contraction is uniform it is well known that there exists a globally attracting invariant set which is the graph of a function from the driving state space to the driven state space if the contraction is sufficiently strong then is smooth we describe the theoretical framework for such results and discuss a number of applications to the filtering of time series to synchronization and to quasiperiodically forced systems we go on to give recent generalizations to the case of non uniform contraction that is contraction measured by lyapunov exponent like quantities we conclude with a number of new results for quasiperiodic forcing a corollary of these is that a strange non chaotic attractor for such a system cannot be the graph of a continuous function nor roughly speaking can it have as open attracting neighbourhood in other words its closure must contain some repelling orbits

tracking the direction of arrival of multiple moving targets the authors focus on the problem of tracking the direction of arrival doa of multiple moving targets the targets are assumed to be moving with constant accelerations subject to minor random perturbations and emitting narrow band signals that impinge on an array of passive sensors estimates of the doa vector of the targets are obtained from the sensor data based on the maximum likelihood ml principle in such a way that the association between the estimates made at different time points is maintained at each stage the current ml estimates of doa are treated as measurements and refined via a kalman filter tracking is accomplished without the need to perform unduly heavy computations an efficient strategy for dealing with closely spaced targets is also presented finally the performance of the tracking algorithm is illustrated via computer simulations

selecting nonlinear stochastic process rate models using information criteria we demonstrate how unknown process rates within a stochastic modelling framework based on markov processes can be approximated from time series data using polynomial basis functions the problem of model selection is considered by adapting basis function selection methods and the minimum description length information criteria which have previously been developed for nonlinear autoregressive models of time series under gaussian noise assumptions we investigate the effectiveness of the methods with application to stochastic biological population models

invariant trajectory classification of dynamical systems with a case study on ecg an invariant pattern recognition framework for classification of phase space trajectories of nonlinear dynamical systems is presented using statistical shape theory known external influences can be discriminated from true changes of the system the external effects are modeled as a transformation group acting on the phase space and variation of the trajectories not explained by the transformations is accounted for using principal component analysis the approach suggested is highly adaptable to a wide range of situations and individual differences the methodology presented is applied to detect abnormalities in electrocardiograms results based on measured data indicate that the model developed is resistant to the effects of respiration and body position changes which are abundant in ambulatory conditions and cause significant morphological artifacts in the signal the results also show that the detection of an artificially induced acute myocardial infarction is achieved with high performance due to its low computational complexity the method developed can be implemented in real time the method developed also adapts to morphological changes caused by various heart conditions

the complex bingham distribution and shape analysis summary a complex version of the bingham distribution is defined on the unit complex sphere in ck various statistical properties including asymptotic normality under high concentration are derived symmetries in the distribution make it a natural tool for the analysis of the shape of landmark data in two dimensions strengths and weaknesses of this approach are investigated links and contrasts with bookstein co ordinates are discussed a hybrid approach to principal component analysis based on complex and real co ordinates is suggested

generic observability of differentiable systems a dynamical system consists of a smooth vectorfield defined on a differentiable manifold and a smooth mapping from the manifold to the real numbers the vectorfield represents the dynamics of a physical system the mapping stands for a measuring device by which experimental information on the dynamics is made available the information itself is modeled as a sampled version of the image of the state trajectory under the smooth mapping in this paper the observability of this set up is discussed from the viewpoint of genericity first the observability property is expressed in terms of transversality conditions then the theory of transversal intersection is called upon to yield the desired results it is shown that almost any measuring device will combine with a given physical system to form an observable dynamical system if 2n 1 samples are taken and not fewer where n is the dimension of the manifold dually it is shown that almost any physical system will combine with a given measuring device

maximum likelihood narrow band direction finding and the em algorithm generalized em expectation maximization algorithms have been derived for the maximum likelihood estimation of the direction of arrival of multiple narrowband signals in noise both deterministic and stochastic signal models are considered the algorithm for the deterministic model yields estimates of the signal amplitudes while that for the stochastic model yields estimates of the powers of the signal both algorithms have the properties that their limit points are stable and satisfy the necessary maximizer conditions for maximum likelihood estimators it is shown via simulation that the maximum likelihood method allows for the resolution of the directions of arrival of signals at angular separation and noise levels for which other high resolution methods will not work algorithm convergence does depend on initial conditions however convergence to a global maximum has been observed in simulation when the initial estimates are within a significant fraction if one beamwidth componentwise of this maximum simulations also show that the deterministic model has a significant impact on the angle estimator performance

entropies and combinatorics of random branching processes and context free languages the entropies and combinatorics of trees that branch according to fixed but finite numbers of rules are studied context free grammars are used to categorize the ways in which nodes branch to yield daughter nodes thus providing an organized setting to examine the entropies for random branching processes whose realizations are trees and whose probabilities are determined by probabilities associated with the substitution rules of the grammar normalized entropy rates h are derived for the critical branching rate and supercritical branching rate processes an equipartition theorem is proved for the supercritical processes a strong departure from classical theorems for markov sources occurs for supercritical branching processes as the typical sets have supergeometric growth rates the combinatorics of the set of all trees that can be generated from the context free substitution rules is also studied

boundary finding with parametrically deformable models segmentation using boundary finding is enhanced both by considering the boundary as a whole and by using model based global shape information the authors apply flexible constraints in the form of a probabilistic deformable model to the problem of segmenting natural 2 d objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form the parametric model is based on the elliptic fourier decomposition of the boundary probability distributions on the parameters of the representation bias the model to a particular overall shape while allowing for deformations boundary finding is formulated as an optimization problem using a maximum a posteriori objective function results of the method applied to real and synthetic images are presented including an evaluation of the dependence of the method on prior information and image quality