variable delay feedback control of unstable steady states in retarded time delayed systems we study the stability of unstable steady states in scalar retarded time delayed systems subjected to a variable delay feedback control the important aspect of such a control problem is that time delayed systems are already infinite dimensional before the delayed feedback control is turned on when the frequency of the modulation is large compared to the system s dynamics the analytic approach consists of relating the stability properties of the resulting variable delay system with those of an analogous distributed delay system otherwise the stability domains are obtained by a numerical integration of the linearized variable delay system the analysis shows that the control domains are significantly larger than those in the usual time delayed feedback control and that the complexity of the domain structure depends on the form and the frequency of the delay modulation

prediction error and its estimation for subset selected models strategies are compared for development of a linear regression model and the subsequent assessment of its predictive ability simulations were performed as a designed experiment over a range of data structures approaches using a forward selection of variables resulted in slightly smaller prediction errors and less biased estimators of predictive accuracy than all possible subsets selection but often did not improve on the full model random and balanced data splitting resulted in increased prediction errors and estimators with large mean squared error to maximize predictive accuracy while retaining a reliable estimate of that accuracy it is recommended that the entire sample usually he used for model development and assessment

delay stabilization of rotating waves near fold bifurcation and application to all optical control of a semiconductor laser we consider the delayed feedback control method for stabilization of unstable rotating waves near a fold bifurcation theoretical analysis of a generic model and numerical bifurcation analysis of the rate equations model demonstrate that such orbits can always be stabilized by a proper choice of control parameters our paper confirms the recently discovered invalidity of the so called odd number limitation of delayed feedback control previous results have been restricted to the vicinity of a subcritical hopf bifurcation we now refute such a limitation for rotating waves near a fold bifurcation we include an application to all optical realization of the control in three section semiconductor lasers

actions as space time shapes human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion we regard human actions as three dimensional shapes induced by the silhouettes in the space time volume we adopt a recent approach 14 for analyzing 2d shapes and generalize it to deal with volumetric space time action shapes our method utilizes properties of the solution to the poisson equation to extract space time features such as local space time saliency action dynamics shape structure and orientation we show that these features are useful for action recognition detection and clustering the method is fast does not require video alignment and is applicable in but not limited to many scenarios where the background is known moreover we demonstrate the robustness of our method to partial occlusions nonrigid deformations significant changes in scale and viewpoint high irregularities in the performance of an action and low quality video

time delay estimation with unknown spatially correlated gaussian noise the problem of estimating the difference in arrival times of a non gaussian signal at two spatially separated sensors is considered the signal is assumed to be corrupted by spatially correlated gaussian noises of unknown cross correlation the author proposes and analyzes two new classes of methods for time delay estimation based on higher order statistics the proposed methods are conceptually very similar to the traditional cross correlation based techniques in that the proposed criteria peak at a lag value equalizing true delay since the proposed methods are based upon higher order cumulant statistics of the data they result in estimators that remain unbiased in the presence of gaussian noise

robust temporal activity templates using higher order statistics a robust theoretically founded approach for the extraction of temporal templates corresponding to areas of motion in video is presented higher order statistics kurtosis are employed to extract activity areas i e binary masks indicating which pixels in a video are active the application of the kurtosis on illumination changes modeled as gaussians and mixture of gaussians is shown to be sensitive to outliers for both models thus correctly localizing active pixels activity areas are compared to existing difference based temporal templates known as motion energy images and the robustness of both categories of temporal templates to additive noise is analyzed theoretically experiments with numerous real videos with additive noise both indoors and outdoors are conducted to compare the robustness of the activity areas and motion energy images and their temporal extensions the activity history areas and motion history images as expected from the theoretical analysis the kurtosis based activity areas prove to be more robust than the difference based templates challenging videos containing occlusions varying backgrounds and shadows are also examined and it is shown that the proposed approach outperforms the difference based method for these cases as well consistently providing reliable localization of activity under a wide range of difficult circumstances the proposed approach provides good results at a very low computational cost and without requiring prior knowledge about the scene nor training of any kind

towards easier realization of time delayed feedback control of odd number orbits we develop generalized time delayed feedback schemes for the stabilization of periodic orbits with an odd number of positive floquet exponents which are particularly well suited for experimental realization we construct the parameter regimes of successful control and validate these by numerical simulations and numerical continuation methods in particular it is shown how periodic orbits can be stabilized with symmetric feedback matrices by introducing an additional latency time in the control loop finally we show using normal form analysis and numerical simulations how our results could be implemented in a laser setup using optoelectronic feedback

additive risk models for survival data with high dimensional covariates as a useful alternative to cox s proportional hazard model the additive risk model assumes that the hazard function is the sum of the baseline hazard function and the regression function of covariates this article is concerned with estimation and prediction for the additive risk models with right censored survival data especially when the dimension of the covariates is comparable to or larger than the sample size principal component regression is proposed to give unique and numerically stable estimators asymptotic properties of the proposed estimators component selection based on the weighted bootstrap and model evaluation techniques are discussed this approach is illustrated with analysis of the primary biliary cirrhosis clinical data and the diffuse large b cell lymphoma genomic data it is shown that this methodology is numerically stable and effective in dimension reduction while still being able to provide satisfactory prediction and classification results

better subset regression using the nonnegative garrote a new method called the nonnegative nn garrote is proposed for doing subset regression it both shrinks and zeroes coefficients in tests on real and simulated data it produces lower prediction error than ordinary subset selection it is also compared to ridge regression if the regression equations generated by a procedure do not change drastically with small changes in the data the procedure is called stable subset selection is unstable ridge is very stable and the nn garrote is intermediate simulation results illustrate the effects of instability on prediction error

motion recognition using nonparametric image motion models estimated from temporal and multiscale co occurrence statistics a new approach for motion characterization in image sequences is presented it relies on the probabilistic modeling of temporal and scale co occurrence distributions of local motion related measurements directly computed over image sequences temporal multiscale gibbs models allow us to handle both spatial and temporal aspects of image motion content within a unified statistical framework since this modeling mainly involves the scalar product between co occurrence values and gibbs potentials we can formulate and address several fundamental issues model estimation according to the ml criterion hence model training and learning and motion classification we have conducted motion recognition experiments over a large set of real image sequences comprising various motion types such as temporal texture samples human motion examples and rigid motion situations

large vector autoregression for multilayer spatially correlated time series one of the most commonly used methods for modeling multivariate time series is the vector autoregressive model var var is generally used to identify lead lag and contemporaneous relationships describing granger causality within and between time series in this article we investigate the var methodology for analyzing data consisting of multilayer time series that are spatially interdependent when modeling var relationships for such data the dependence between time series is both a curse and a blessing the former because it requires modeling the between time series correlation or the contemporaneous relationships which may be challenging when using likelihood based methods the latter because the spatial correlation structure can be used to specify the lead lag relationships within and between time series within and between layers to address these challenges we propose an l1 l2 regularized likelihood estimation method the lead lag and contemporaneous relationships are estimated using an effic

controlling variable selection by the addition of pseudovariables we propose a new approach to variable selection designed to control the false selection rate fsr defined as the proportion of uninformative variables included in selected models the method works by adding a known number of pseudovariables to the real dataset running a variable selection procedure and monitoring the proportion of pseudovariables falsely selected information obtained from bootstrap like replications of this process is used to estimate the proportion of falsely selected real variables and to tune the selection procedure to control the fsr

motion estimation using higher order statistics the objective of this paper is to introduce a fourth order cost function of the displaced frame difference dfd capable of estimating motion even for small regions or blocks using higher than second order statistics is appropriate in case the image sequence is severely corrupted by additive gaussian noise some results are presented and compared to those obtained from the mean kurtosis and the mean square error of the dfd

beyond the odd number limitation a bifurcation analysis of time delayed feedback control we investigate the normal form of a subcritical hopf bifurcation subjected to time delayed feedback control bifurcation diagrams which cover time dependent states as well are obtained by analytical means the computations show that unstable limit cycles with an odd number of positive floquet exponents can be stabilized by time delayed feedback control contrary to incorrect claims in the literature the model system constitutes one of the few examples where a nonlinear time delay system can be treated entirely by analytical means

a simulation of biased estimation and subset selection regression techniques this study compared three biased estimation and four subset selection regression techniques to least squares in a large scale simulation the parameters relevant to a comparison of the techniques involved were systematically varied over wide ranges a parameter of importance not used in previous major simulations of subset techniques the proportion of independent variables in the data that were superfluous was included the major result is that neither biased estimation nor subset selection demonstrated a consistent superiority over the other excluding stepwise and principal component regression both of which performed poorly

time delayed feedback control of unstable periodic orbits near a subcritical hopf bifurcation we show that the pyragas delayed feedback control can stabilize an unstable periodic orbit upo that arises from a generic subcritical hopf bifurcation of a stable equilibrium in an n dimensional dynamical system this extends results of fiedler et al b fiedler v flunkert m georgi p hovel e scholl refuting the odd number limitation of time delayed feedback control phys rev lett 98 11 2007 114101 who demonstrated that such a feedback control can stabilize the upo associated with a two dimensional subcritical hopf normal form the pyragas feedback requires an appropriate choice of a feedback gain matrix for stabilization as well as knowledge of the period of the targeted upo we apply feedback in the directions tangent to the two dimensional center manifold we parameterize the feedback gain by a modulus and a phase angle and give explicit formulae for choosing these two parameters given the period of the upo in a neighborhood of the bifurcation point we show first heuristically and then rigorously by a center manifold reduction for delay differential equations that the stabilization mechanism involves a highly degenerate hopf bifurcation problem that is induced by the time delayed feedback when the feedback gain modulus reaches a threshold for stabilization both of the genericity assumptions associated with a two dimensional hopf bifurcation are violated the eigenvalues of the linearized problem do not cross the imaginary axis as the bifurcation parameter is varied and the real part of the cubic coefficient of the normal form vanishes our analysis reveals two qualitatively distinct cases when the degenerate bifurcation is unfolded in a two parameter plane in each case the pyragas type feedback successfully stabilizes the branch of small amplitude upos in a neighborhood of the original bifurcation point provided that the feedback phase angle satisfies a certain restriction

time domain tests for gaussianity and time reversibility statistical signal processing algorithms often rely upon gaussianity and time reversibility two important notions related to the probability structure of stationary random signals and their symmetry parametric models obtained via second order statistics sos are appropriate when the available data is gaussian and time reversible on the other hand evidence of nonlinearity non gaussianity or time irreversibility favors the use of higher order statistics hos in order to validate gaussianity and time reversibility and quantify the tradeoffs between sos and hos consistent time domain chi squared statistical tests are developed exact asymptotic distributions are derived to estimate the power of the tests including a covariance expression for fourth order sample cumulants a modification of existing linearity tests in the presence of additive gaussian noise is discussed briefly the novel gaussianity statistic is computationally attractive leads to a constant false alarm rate test and is well suited for parametric modeling because it employs the minimal hos lags which uniquely characterize arma processes simulations include comparisons with an existing frequency domain approach and an application to real seismic data time reversibility tests are also derived and their performance is analyzed both theoretically and experimentally

stabilizing unstable periodic orbits in the lorenz equations using time delayed feedback control for many years it was believed that an unstable periodic orbit with an odd number of real floquet multipliers greater than unity cannot be stabilized by the time delayed feedback control mechanism of pyragas a recent paper by fiedler et al phys rev lett 98 114101 2007 uses the normal form of a subcritical hopf bifurcation to give a counterexample to this theorem using the lorenz equations as an example we demonstrate that the stabilization mechanism identified by fiedler et al for the hopf normal form can also apply to unstable periodic orbits created by subcritical hopf bifurcations in higher dimensional dynamical systems our analysis focuses on a particular codimension two bifurcation that captures the stabilization mechanism in the hopf normal form example and we show that the same codimension two bifurcation is present in the lorenz equations with appropriately chosen pyragas type time delayed feedback this example suggests a possible strategy for choosing the feedback gain matrix in pyragas control of unstable periodic orbits that arise from a subcritical hopf bifurcation of a stable equilibrium in particular our choice of feedback gain matrix is informed by the fiedler et al example and it works over a broad range of parameters despite the fact that a center manifold reduction of the higher dimensional problem does not lead to their model problem

delay and periodicity systems with time delay play an important role in modeling of many physical and biological processes in this paper we describe generic properties of systems with time delay which are related to the appearance and stability of periodic solutions in particular we show that delay systems generically have families of periodic solutions which are reappearing for infinitely many delay times as delay increases the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions we also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers we show that the spectrum of multipliers can be split into two parts pseudocontinuous and strongly unstable the pseudocontinuous part of the spectrum mediates destabilization of periodic solutions

comparison of prediction methods when only a few components are relevant abstract we consider prediction in a multiple regression model where we also look on the explanatory variables as random if the number of explanatory variables is large then the common least squares multiple regression solution may not be the best one we give a methodology for comparing certain alternative prediction methods by asymptotic calculations and perform such a comparisons for four specific methods the results indicate that none of these methods dominates the others and that the difference between the methods typically but not always is small when the number of observations is large in particular principal component regression does well when the eigenvalues corresponding to components not correlated with the dependent variables i e the irrelevant eigenvalues are extremely small or extremely large partial least squares regression does well for intermediate irrelevant eigenvalues a maximum likelihood type method dominates the others asymptotically at least in the case of one relevan

putting background information about relative risks into conjugate prior distributions in bayesian and empirical bayes analyses of epidemiologic data the most easily implemented prior specifications use a multivariate normal distribution for the log relative risks or a conjugate distribution for the discrete response vector this article describes problems in translating background information about relative risks into conjugate priors and a solution traditionally conjugate priors have been specified through flattening constants an approach that leads to conflicts with the true prior covariance structure for the log relative risks one can however derive a conjugate prior consistent with that structure by using a data augmentation approximation to the true log relative risk prior although a rescaling step is needed to ensure the accuracy of the approximation these points are illustrated with a logistic regression analysis of neonatal death risk

stabilization of a steady state in network oscillators by using diffusive connections with two long time delays the present study shows that diffusive connections with two long time delays can induce the stabilization of a steady state in network oscillators a linear stability analysis shows that if the two delay times retain a proportional relation with a certain bias the stabilization can be achieved independent of the delay times furthermore a simple systematic procedure for designing the coupling strength and the delay times in the connections is proposed the procedure has the following two advantages one can employ time delays as long as one wants and the stabilization can be achieved independently of its network topology our analytical results are applied to the well known double scroll circuit model on a small world network

on time delay estimation with unknown spatially correlated gaussian noise using fourth order cumulants and cross cumulants the problem of estimating the difference in arrival times of a linear non gaussian signal at two spatially separated sensors is considered the signal is assumed to be corrupted by spatially correlated gaussian noises of unknown cross correlation a parameter estimation approach is adopted and the fourth order cumulant statistics of the noisy measurements are exploited to obtain the time delay estimate specific and mild sufficient conditions are given for time delay identifiability via a persistence of excitation condition illustrative monte carlo simulation examples are also presented

spatial and temporal feedback control of traveling wave solutions of the two dimensional complex ginzburg landau equation previous work has shown that benjamin feir unstable traveling waves of the complex ginzburg landau equation cgle in two spatial dimensions cannot be stabilized using a particular time delayed feedback control mechanism known as time delay autosynchronization in this paper we show that the addition of similar spatial feedback terms can be used to stabilize such waves this type of feedback is a generalization of the time delay method of pyragas k pyragas continuous control of chaos by self controlling feedback phys lett a 170 1992 421 428 and has been previously used to stabilize waves in the one dimensional cgle by montgomery and silber k montgomery m silber feedback control of traveling wave solutions of the complex ginzburg landau equation nonlinearity 17 6 2004 2225 2248 we consider two cases in which the feedback contains either one or two spatial terms we focus on how the spatial terms may be chosen to select the direction of travel of the plane waves numerical linear stability calculations demonstrate the results of our analysis c 2007 elsevier b v all rights reserved

asymptotic analysis of subcritical hopf homoclinic bifurcation abstract this paper discusses the mathematical analysis of a codimension two bifurcation determined by the coincidence of a subcritical hopf bifurcation with a homoclinic orbit of the hopf equilibrium our work is motivated by our previous analysis of a hodgkin huxley neuron model which possesses a subcritical hopf bifurcation j guckenheimer r harris warrick j peck a willms j comput neurosci 4 1997 257 277 in this model the hopf bifurcation has the additional feature that trajectories beginning near the unstable manifold of the equilibrium point return to pass through a small neighborhood of the equilibrium that is the hopf bifurcation appears to be close to a homoclinic bifurcation as well this model of the lateral pyloric lp cell of the lobster stomatogastric ganglion was analyzed for its ability to explain the phenomenon of spike frequency adaptation in which the time intervals between successive spikes grow longer until the cell eventually becomes quiescent the presence of a subcritical hopf bifurcation in this model was the one identified mechanism for oscillatory trajectories to increase their period and finally collapse to a non oscillatory solution the analysis presented here explains the apparent proximity of homoclinic and hopf bifurcations we also develop an asymptotic theory for the scaling properties of the interspike intervals in a singularly perturbed system undergoing subcritical hopf bifurcation that may be close to a codimension two subcritical hopf homoclinic bifurcation

regressions by leaps and bounds this paper describes several algorithms for computing the residual sums of squares for all possible regressions with what appears to be a minimum of arithmetic less than six floating point operations per regression and shows how two of these algorithms can be combined to form a simple leap and bound technique for finding the best subsets without examining all possible subsets the result is a reduction of several orders of magnitude in the number of operations required to find the best subsets

image motion estimation algorithms using cumulants a class of algorithms is presented that estimates the displacement vector from two successive image frames consisting of signal plus noise in the model the signals are assumed to be either non gaussian or quasistationary deterministic and via a consistency result for cumulant estimators the authors unify the stochastic and deterministic signal viewpoints the noise sources are assumed to be gaussian perhaps spatially and temporally correlated and of unknown covariance viewing image motion estimation as a 2d time delay estimation problem the displacement vector of a moving object is estimated by solving linear equations involving third order auto cumulants and cross cumulants additionally a block matching algorithm is developed that follows from a cumulant error optimality criterion finally the displacement vector for each pel is estimated using a recursive algorithm that minimizes a mean 2d fourth order cumulant criterion simulation results are presented and discussed