hopf bifurcation in a delayed reaction diffusion advection population model abstract in this paper we investigate a reaction diffusion advection model with time delay effect the stability instability of the spatially nonhomogeneous positive steady state and the associated hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction diffusion advection model and the model can exhibit oscillatory pattern through hopf bifurcation the effect of advection on hopf bifurcation values is also considered and our results suggest that hopf bifurcation is more likely to occur when the advection rate increases

speed observation and position feedback stabilization of partially linearizable mechanical systems the problems of speed observation and position feedback stabilization of mechanical systems are addressed in this paper our interest is centered on systems that can be rendered linear in the velocities via a partial change of coordinates it is shown that the class is fully characterized by the solvability of a set of partial differential equations pdes and strictly contains the class studied in the existing literature on linearization for speed observation or control a reduced order globally exponentially stable observer constructed using the immersion and invariance methodology is proposed the design requires the solution of another set of pdes which are shown to be solvable in several practical examples it is also proven that the full order observer with dynamic scaling recently proposed by karagiannis and astolfi obviates the need to solve the latter pdes finally it is shown that the observer can be used in conjunction with an asymptotically stabilizing full state feedback interconnection and damping assignment passivity based controller preserving asymptotic stability

correlation functions cluster functions and spacing distributions for random matrices the usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants from this representation one can deduce formulas for spacing probabilities in terms of fredholm determinants of matrix valued kernels the derivations of the various formulas are somewhat involved in this article we present a direct approach which leads immediately to scalar kernels for the unitary ensembles and matrix kernels for the orthogonal and symplectic ensembles and the representations of the correlation functions cluster functions and spacing distributions in terms of them

eigenvalue significance testing for genetic association genotype eigenvectors are widely used as covariates for control of spurious stratification in genetic association significance testing for the accompanying eigenvalues has typically been based on a standard tracy widom limiting distribution for the largest eigenvalue derived under white noise assumptions it is known that even modest local correlation among markers inflates the largest eigenvalues even in the absence of true stratification in addition a few sample eigenvalues may be extreme creating further complications in accurate testing we explore several methods to identify appropriate null eigenvalue thresholds while remaining sensitive to eigenvalues corresponding to population stratification we introduce a novel block permutation approach designed to produce an appropriate null eigenvalue distribution by eliminating long range genomic correlation while preserving local correlation we also propose a fast approach based on eigenvalue distribution modeling using a simple fit criterion and the general marcenko pastur equation under a simple discrete eigenvalue model block permutation and the model based approach work well for pure simulations and for data resampled from the 1000 genomes project in contrast we find that the standard approach of computing an effective number of markers does not perform well the performance of the methods is also demonstrated for a motivating example from the international cystic fibrosis consortium

integral input to state stable systems in cascade the integral input to state stability iiss property is studied in the context of nonlinear time invariant systems in cascade some sufficient conditions for the preservation of the iiss property under a cascade interconnection are presented these are first given as growth restrictions on the supply functions of the storage function associated with each subsystem and are then expressed as solutions based requirements a lyapunov based condition guaranteeing that the cascade composed of an iiss system driven by a globally asymptotically stable gas one remains gas is also provided we also show that some of these results extend to cascades composed of more than two subsystems

some results on global and semiglobal stabilization of affine systems in this paper the relations between semiglobal stabilization and global stabilization of affine systems are investigated it is shown that for one dimensional systems the two concepts are equivalent for the n dimensional case we introduce a more restrictive concept the l semiglobal stabilization which implies global stabilization this result is applied to bilinear systems

outlier robust pca the high dimensional case principal component analysis plays a central role in statistics engineering and science because of the prevalence of corrupted data in real world applications much research has focused on developing robust algorithms perhaps surprisingly these algorithms are unequipped indeed unable to deal with outliers in the high dimensional setting where the number of observations is of the same magnitude as the number of variables of each observation and the dataset contains some arbitrarily corrupted observations we propose a high dimensional robust principal component analysis algorithm that is efficient robust to contaminated points and easily kernelizable in particular our algorithm achieves maximal robustness it has a breakdown point of 50 the best possible while all existing algorithms have a breakdown point of zero moreover our algorithm recovers the optimal solution exactly in the case where the number of corrupted points grows sublinearly in the dimension

a note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices recently johansson and johnstone proved that the distribution of the properly rescaled largest principal component of the complex real wishart matrix x x xtx converges to the tracy widom law as n p the dimensions of x tend to in some ratio n p 0 we extend these results in two directions first of all we prove that the joint distribution of the first second third etc eigenvalues of a wishart matrix converges after a proper rescaling to the tracy widom distribution second of all we explain how the combinatorial machinery developed for wigner random matrices in refs 27 38 and 39 allows to extend the results by johansson and johnstone to the case of x with non gaussian entries provided n p o p1 3 we also prove that max n1 2 p1 2 2 o p1 2 log p a e for general 0

traveling wavefronts for time delayed reaction diffusion equation ii nonlocal nonlinearity abstract in this paper we study a class of time delayed reaction diffusion equation with local nonlinearity for the birth rate for all wavefronts with the speed c c where c 0 is the critical wave speed we prove that these wavefronts are asymptotically stable when the initial perturbation around the traveling waves decays exponentially as x but the initial perturbation can be arbitrarily large in other locations this essentially improves the stability results obtained by mei so li and shen m mei j w h so m y li s s p shen asymptotic stability of traveling waves for the nicholson s blowflies equation with diffusion proc roy soc edinburgh sect a 134 2004 579 594 for the speed c 2 d m e p d m with small initial perturbation and by lin and mei c k lin m mei on travelling wavefronts of the nicholson s blowflies equations with diffusion submitted for publication for c c with sufficiently small delay time r 0 the approach adopted in this paper is the technical weighted energy method used in m mei j w h so m y li s s p shen asymptotic stability of traveling waves for the nicholson s blowflies equation with diffusion proc roy soc edinburgh sect a 134 2004 579 594 but inspired by gourley s a gourley linear stability of travelling fronts in an age structured reaction diffusion population model quart j mech appl math 58 2005 257 268 and based on the property of the critical wavefronts the weight function is carefully selected and it plays a key role in proving the stability for any c c and for an arbitrary time delay r 0

spatially nonhomogeneous equilibrium in a reaction diffusion system with distributed delay we consider a reaction diffusion system with general time delayed growth rate and kernel functions the existence and stability of the positive spatially nonhomogeneous steady state solution are obtained moreover taking minimal time delay as the bifurcation parameter hopf bifurcation near the steady state solution is proved to occur at a critical value 0 especially the hopf bifurcation is forward and the bifurcated periodic solutions are stable on the center manifold the general results are applied to competitive and cooperative systems with weak or strong kernel function respectively

local stabilization of minimum phase nonlinear systems abstract in this note we briefly review the notion of a nonlinear minimum phase system i e a system which when constrained in such a way as to produce zero output evolves with an asymptotically stable dynamics the main purpose of the paper is to show that any minimum phase nonlinear system can always be locally stabilized by smooth state feedback

planar linear systems with single saturated feedback abstract we study planar linear systems with a linear or non linear feedback global stabilizer subjected to saturation the number of open loop unstable eigenvalues characterizes the set of the equilibrium points and the shape of the asymptotic stability region asr some topological bifurcations on the shape of the asr are described

monotone traveling wavefronts of the kpp fisher delayed equation abstract in the early 2000 s gourley 2000 wu et al 2001 ashwin et al 2002 initiated the study of the positive wavefronts in the delayed kolmogorov petrovskii piskunov fisher equation u t t x u t x u t x 1 u t h x u 0 x r m since then this model has become one of the most popular objects in the studies of traveling waves for the monostable delayed reaction diffusion equations in this paper we give a complete solution to the problem of existence and uniqueness of monotone waves in eq we show that each monotone traveling wave can be found via an iteration procedure the proposed approach is based on the use of special monotone integral operators which are different from the usual wu zou operator and appropriate upper and lower solutions associated to them the analysis of the asymptotic expansions of the eventual traveling fronts at infinity is another key ingredient of our approach

optshrink an algorithm for improved low rank signal matrix denoising by optimal data driven singular value shrinkage the truncated singular value decomposition of the measurement matrix is the optimal solution to the representation problem of how to best approximate a noisy measurement matrix using a low rank matrix here we consider the unobservable denoising problem of how to best approximate a low rank signal matrix buried in noise by optimal re weighting of the singular vectors of the measurement matrix we exploit recent results from random matrix theory to exactly characterize the large matrix limit of the optimal weighting coefficients and show that they can be computed directly from data for a large class of noise models that includes the independent identically distributed gaussian noise case our analysis brings into sharp focus the shrinkage and thresholding form of the optimal weights the nonconvex nature of the associated shrinkage function on the singular values and explains why matrix regularization via singular value thresholding with convex penalty functions such as the nuclear norm will always be suboptimal we validate our theoretical predictions with numerical simulations develop an implementable algorithm optshrink that realizes the predicted performance gains and show how our methods can be used to improve estimation in the setting where the measured matrix has missing entries

a nested matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems a new infinitesimal sufficient condition is given for uniform global asymptotic stability ugas for time varying nonlinear systems it is used to show that a certain relaxed persistency of excitation condition called uniform spl delta persistency of excitation u spl delta pe is sufficient for uniform global asymptotic stability in certain situations u spl delta pe of the right hand side of a time varying differential equation is also shown to be necessary under a uniform lipschitz condition the infinitesimal sufficient condition for ugas involves the inner products of the flow field with the gradients of a finite number of possibly sign indefinite locally lipschitz lyapunov like functions these inner products are supposed to be bounded by functions that have a certain nested or triangular negative semidefinite structure this idea is reminiscent of a previous idea of matrosov who supplemented a lyapunov function having a negative semidefinite derivative with an additional function having a derivative that is definitely nonzero where the derivative of the lyapunov function is zero for this reason we call the main result a nested matrosov theorem the utility of our results on stability analysis is illustrated through the well known case study of the nonholonomic integrator

dirichlet problem for the diffusive nicholson s blowflies equation abstract the object of this paper is to consider the asymptotic behavior of solutions of the diffusive nicholson s blowflies equation under dirichlet boundary condition a new approach is developed to study the global attractivity of the positive steady state for a reaction diffusion equation with time delay when monotone or quasi monotone conditions fail to apply this approach should be applicable to other dirichlet problems as well even though our analysis is tailored to the diffusive nicholson s blowflies equation

necessary and sufficient conditions for uniform semiglobal practical asymptotic stability application to cascaded systems it is well established that for a cascade of two uniformly globally asymptotically stable ugas systems the origin remains ugas provided that the solutions of the cascade are uniformly globally bounded while this result has met considerable popularity in specific applications it remains restrictive since in practice it is often the case that the decoupled subsystems are only uniformly semiglobally practically asymptotically stable uspas recently we established that the cascade of uspas systems is uspas under a local boundedness assumption and the hypothesis that one knows a lyapunov function for the driven subsystem the contribution of this paper is twofold 1 we present a converse theorem for uspas and 2 we establish uspas of cascaded systems without the requirement of a lyapunov function compared to other converse theorems in the literature ours has the advantage of guaranteeing a specific relationship between the upper and lower bounds on the generated lyapunov function v and of providing a time invariant bound on the gradient of v which is fundamental to establish theorems for cascades

spatial temporal patterns of a two age structured population model with spatial non locality abstract the spatial temporal patterns of the solutions to a differential equation with non local delayed feedback that models the population dynamics of a two stage species have been studied in this paper the effects of the maturation time and immature mobility constant on the existence and stability of both spatially homogeneous and inhomogeneous periodic solutions are investigated by studying the hopf bifurcation at the spatially homogeneous steady state and computing center manifold our results show that the bifurcated homogeneous periodic solutions are stable while inhomogeneous periodic solutions will eventually tend to homogeneous periodic solutions after transient oscillations furthermore increasing of the immature mobility constant will weaken the periodic oscillation and shorten the transient oscillation time numerical simulations are given at last to verify our results

large complex correlated wishart matrices fluctuations and asymptotic independence at the edges we study the asymptotic behavior of eigenvalues of large complex correlated wishart matrices at the edges of the limiting spectrum in this setting the support of the limiting eigenvalue distribution may have several connected components under mild conditions for the population matrices we show that for every generic positive edge of that support there exists an extremal eigenvalue which converges almost surely towards that edge and fluctuates according to the tracy widom law at the scale n 2 3 moreover given several generic positive edges we establish that the associated extremal eigenvalue fluctuations are asymptotically independent finally when the leftmost edge is the origin we prove that the smallest eigenvalue fluctuates according to the hard edge tracy widom law at the scale n 2 as an application an asymptotic study of the condition number of large correlated wishart matrices is provided

global robust stabilization of nonlinear cascaded systems this paper gives a sufficient condition for a class of nonlinear cascaded systems to be globally stabilizable via state feedback in the presence of uncertainty which does not necessarily satisfy the so called matching condition the authors result is an extension of the former stabilization results which treated systems without uncertainty in the sense that the uncertainty is taken into account

reduction theorems for stability of closed sets with application to backstepping control design we present a solution to the following reduction problem for asymptotic stability of closed sets in nonlinear systems given two closed positively invariant subsets of the state space of a nonlinear system c 1 c 2 assuming that c 1 is asymptotically stable relative to c 2 find conditions under which c 1 is asymptotically stable we also investigate analogous reduction problems for stability and attractivity we illustrate the implications of our results on the stability of sets for cascade connected systems and on a hierarchical control design problem for upper triangular control systems we present a reduction based backstepping technique that does not require the knowledge of a lyapunov function and mitigates the problem of controller complexity arising in classical backstepping design

on uniform boundedness of parameterized discrete time systems with decaying inputs applications to cascades a framework for controller design of sampled data nonlinear systems via their approximate discrete time models has been established recently within this framework naturally arises the need to investigate stability properties of parameterized discrete time systems further results that guarantee appropriate stability of the parameterized family of discrete time systems that is used within this framework have been also established for systems with cascaded structure a fundamental condition that is required in this framework is uniform boundedness of solutions of the cascade however this is difficult to check in general in this paper we provide a range of sufficient conditions for uniform boundedness that are easier to check these results further contribute to the toolbox for controller design of sampled data nonlinear systems via their approximate discrete time models

on the distribution of the largest eigenvalue in principal components analysis let x 1 denote the square of the largest singular value of an n p matrix x all of whose entries are independent standard gaussian variates equivalently x 1 is the largest principal component variance of the covariance matrix x x or the largest eigenvalue of a p variate wishart distribution on n degrees of freedom with identity covariance consider the limit of large p and n with n p gamma ge 1 when centered by mu p sqrt n 1 sqrt p 2 and scaled by sigma p sqrt n 1 sqrt p 1 sqrt n 1 1 sqrt p 1 3 the distribution of x 1 approaches the tracey widom law of order 1 which is defined in terms of the painleve ii differential equation and can be numerically evaluated and tabulated in software simulations show the approximation to be informative for n and p as small as 5 the limit is derived via a corresponding result for complex wishart matrices using methods from random matrix theory the result suggests that some aspects of large p multivariate distribution theory may be easier to apply in practice than their fixed p counterparts

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

on the distribution of the length of the longest increasing subsequence of random permutations let sn be the group of permutations of 1 2 n if 7r e sn we say that 7 i1 7f ik is an increasing subsequence in 7r if il i2 ik and 7r ii 7r i2 7r ik let 1n r be the length of the longest increasing subsequence for example if n 5 and 7r is the permutation 5 1 3 2 4 in one line notation thus 7r 1 5 7r 2 1 then the longest increasing subsequences are 1 2 4 and 1 3 4 and n 3 equip sn with uniform distribution

hopf bifurcations in a reaction diffusion population model with delay effect abstract a reaction diffusion population model with a general time delayed growth rate per capita is considered the growth rate per capita can be logistic or weak allee effect type from a careful analysis of the characteristic equation the stability of the positive steady state solution and the existence of forward hopf bifurcation from the positive steady state solution are obtained via the implicit function theorem where the time delay is used as the bifurcation parameter the general results are applied to a food limited population model with diffusion and delay effects as well as a weak allee effect population model

nonparametric detection of signals by information theoretic criteria performance analysis and an improved estimator determining the number of sources from observed data is a fundamental problem in many scientific fields in this paper we consider the nonparametric setting and focus on the detection performance of two popular estimators based on information theoretic criteria the akaike information criterion aic and minimum description length mdl we present three contributions on this subject first we derive a new expression for the detection performance of the mdl estimator which exhibits a much closer fit to simulations in comparison to previous formulas second we present a random matrix theory viewpoint of the performance of the aic estimator including approximate analytical formulas for its overestimation probability finally we show that a small increase in the penalty term of aic leads to an estimator with a very good detection performance and a negligible overestimation probability

high dimensional analysis of semidefinite relaxations for sparse principal components principal component analysis pca is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix however pca is well known to behave poorly in the large p small n setting in which the problem dimension p is comparable to or larger than the sample size n this paper studies pca in this high dimensional regime but under the additional assumption that the maximal eigenvector is sparse say with at most k nonzero components we consider a spiked covariance model in which a base matrix is perturbed by adding a k sparse maximal eigenvector and we analyze two computationally tractable methods for recovering the support set of this maximal eigenvector as follows a a simple diagonal thresholding method which transitions from success to failure as a function of the rescaled sample size dia n p k n k 2 log p k and b a more sophisticated semidefinite programming sdp relaxation which succeeds once the rescaled sample size sdp n p k n klog p k is larger than a critical threshold in addition we prove that no method including the best method which has exponential time complexity can succeed in recovering the support if the order parameter sdp n p k is below a threshold our results thus highlight an interesting trade off between computational and statistical efficiency in high dimensional inference

suboptimal decentralized control over noisy communication channels a b s t r a c t in this paper we present a technique for the design of decentralized controllers for mean square stability of a large scale system with cascaded clusters of subsystems each subsystem is linear and time invariant and both system and measurement are subject to gaussian noise for stability analysis of this system we consider the effects of additive white gaussian noise awgn channels used for exchanging information between subsystems

eigenvalue ratio test for the number of factors this paper proposes two new estimators for determining the number of factors r in static approximate factor models we exploit the well known fact that the r largest eigenvalues of the variance matrix of n response variables grow unboundedly as n increases while the other eigenvalues remain bounded the new estimators are obtained simply by maximizing the ratio of two adjacent eigenvalues our simulation results provide promising evidence for the two estimators

a unifying integral iss framework for stability of nonlinear cascades we analyze nonlinear cascades in which the driven subsystem is integral input to state stable iss and we characterize the admissible integral iss gains for stability this characterization makes use of the convergence speed of the driving subsystem and allows a larger class of gain functions when the convergence is faster we show that our integral iss gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem the result is used to develop a new observer based backstepping design in which the growth of the nonlinear damping terms is reduced

a rotation test to verify latent structure in multivariate regression models we have the opportunity to look for hidden structure unrelated to the observed predictors however when one fits a model involving such latent variables it is important to be able to tell if the structure is real or just an artifact of correlation in the regression errors we develop a new statistical test based on random rotations for verifying the existence of latent variables the rotations are carefully constructed to rotate orthogonally to the column space of the regression model we find that only non gaussian latent variables are detectable a finding that parallels a well known phenomenon in independent components analysis we base our test on a measure of non gaussianity in the histogram of the principal eigenvector components instead of on the eigenvalue the method finds and verifies some latent dichotomies in the microarray data from the agemap consortium

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

stability of cascaded fuzzy systems and observers a large class of nonlinear systems can be well approximated by takagi sugeno ts fuzzy models with linear or affine consequents it is well known that the stability of these consequent models does not ensure the stability of the overall fuzzy system therefore several stability conditions have been developed for ts fuzzy systems we study a special class of nonlinear dynamic systems that can be decomposed into cascaded subsystems which are represented as ts fuzzy models we analyze the stability of the overall ts system based on the stability of the subsystems and prove that the stability of the subsystems implies the stability of the overall system the main benefit of this approach is that it relaxes the conditions imposed when the system is globally analyzed thereby solving some of the feasibility problems another benefit is that by using this approach the dimension of the associated linear matrix inequality lmi problem can be reduced for naturally distributed applications such as multiagent systems the construction and tuning of a centralized observer may not be feasible therefore we also extend the cascaded approach to the observer design and use fuzzy observers to individually estimate the states of these subsystems a theoretical proof of stability and simulation examples are presented the results show that the distributed observer achieves the same performance as the centralized one while leading to increased modularity reduced complexity lower computational costs and easier tuning applications of such cascaded systems include multiagent systems distributed process control and hierarchical large scale systems

non parametric detection of the number of signals hypothesis testing and random matrix theory detection of the number of signals embedded in noise is a fundamental problem in signal and array processing this paper focuses on the non parametric setting where no knowledge of the array manifold is assumed first we present a detailed statistical analysis of this problem including an analysis of the signal strength required for detection with high probability and the form of the optimal detection test under certain conditions where such a test exists second combining this analysis with recent results from random matrix theory we present a new algorithm for detection of the number of sources via a sequence of hypothesis tests we theoretically analyze the consistency and detection performance of the proposed algorithm showing its superiority compared to the standard minimum description length mdl based estimator a series of simulations confirm our theoretical analysis

hopf bifurcation in a reaction diffusion equation with distributed delay and dirichlet boundary condition abstract the stability and hopf bifurcation of the positive steady state to a general scalar reaction diffusion equation with distributed delay and dirichlet boundary condition are investigated in this paper the time delay follows a gamma distribution function through analyzing the corresponding eigenvalue problems we rigorously show that hopf bifurcations will occur when the shape parameter n 1 and the steady state is always stable when n 0 by computing normal form on the center manifold the direction of hopf bifurcation and the stability of the periodic orbits can also be determined under a general setting our results show that the number of critical values of delay for hopf bifurcation is finite and increasing in n which is significantly different from the discrete delay case and the first hopf bifurcation value is decreasing in n examples from population biology and numerical simulations are used to illustrate the theoretical results

random matrix ensembles with an effective extensive external charge recent theoretical studies of chaotic scattering have encountered ensembles of random matrices in which the eigenvalue probability density function contains a one body factor with an exponent proportional to the number of eigenvalues two such ensembles have been encountered an ensemble of unitary matrices specified by the so called poisson kernel and the laguerre ensemble of positive definite matrices here we consider various properties of these ensembles jack polynomial theory is used to prove a reproducing property of the poisson kernel and a certain unimodular mapping is used to demonstrate that the variance of a linear statistic is the same as in the dyson circular ensemble for the laguerre ensemble the scaled global density is calculated exactly for all even values of the parameter while for random matrices with unitary symmetry the neighbourhood of the smallest eigenvalue is shown to be in the soft edge universality class

controller design for nonlinear affine systems by control lyapunov functions abstract this paper addresses the stabilization problems for nonlinear affine systems first of all the explicit feedback controller is developed for a nonlinear multiple input affine system by assuming that there exists a control lyapunov function next based upon the homogeneous property sufficient conditions for the continuity of the derived controller are developed and then the developed control design methodology is applied to stabilize a class of nonlinear affine cascaded systems it is shown that under some homogeneous assumptions on control lyapunov functions and the interconnection term the cascaded system can be globally stabilized finally some interesting results of finite time stabilization for nonlinear affine systems are also obtained

global convergence of nonlinear cascade flows with morse bott zero dynamics abstract we derive a sufficient condition that a flow captures the dynamics on an invariant submanifold this leads to a refinement of the lasalle invariance principle as a consequence we generalize a well known global asymptotic stability result of nonlinear cascade systems to show global convergence to a compact invariant set this includes the case where a globally asymptotically stable system is coupled to a morse bott flow

cascade and locally dissipative realizations of linear quantum systems for pure gaussian state covariance assignment this paper presents two realizations of linear quantum systems for covariance assignment corresponding to pure gaussian states the first one is called a cascade realization given any covariance matrix corresponding to a pure gaussian state we can construct a cascaded quantum system generating that state the second one is called a locally dissipative realization given a covariance matrix corresponding to a pure gaussian state if it satisfies certain conditions we can construct a linear quantum system that has only local interactions with its environment and achieves the assigned covariance matrix both realizations are illustrated by examples from quantum optics

distribution functions for random variables for ensembles of positive hermitian matrices distribution functions for random variables that depend on a parameter are computed asymptotically for ensembles of positive hermitian matrices the inverse fourier transform of the distribution is shown to be a fredholm determinant of a certain operator that is an analogue of a wiener hopf operator the asymptotic formula shows that up to the terms of order o 1 the distributions are gaussian

a new approach to cholesky based covariance regularization in high dimensions summary in this paper we propose a new regression interpretation of the cholesky factor of the covariance matrix as opposed to the well known regression interpretation of the cholesky factor of the inverse covariance which leads to a new class of regularized covariance estimators suitable for high dimensional problems regularizing the cholesky factor of the covariance via this regression interpretation always results in a positive definite estimator in particular one can obtain a positive definite banded estimator of the covariance matrix at the same computational cost as the popular banded estimator of bickel levina 2008b which is not guaranteed to be positive definite we also establish theoretical connections between banding cholesky factors of the covariance matrix and its inverse and constrained maximum likelihood estimation under the banding constraint and compare the numerical performance of several methods in simulations and on a sonar data example

a lyapunov approach to cascade interconnection of integral input to state stable systems this technical note deals with the stability of cascade interconnection of integral input to state iiss time varying systems a new technique to construct smooth lyapunov functions of cascaded systems is proposed from the construction sufficient conditions for internal stability and stability with respect to external signals are derived one of the derived conditions is a trade off between slower convergence of the driving system and steeper input growth of the driven system the trade off is no more necessary if the speed of convergence of the driven system is not radially vanishing the results are related to trajectory based approaches and small gain techniques for feedback interconnection the difference between the feedback case and the cascade case is viewed from the requirement on convergence speed of autonomous parts

longest increasing subsequences from patience sorting to the baik deift johansson theorem we describe a simple one person card game patience sorting its analysis leads to a broad circle of ideas linking young tableaux with the longest increasing subsequence of a random permutation via the schensted correspondence a recent highlight of this area is the work of baik deift johansson which yields limiting probability laws via hard analysis of toeplitz determinants

the distribution and moments of the smallest eigenvalue of a random matrix of wishart type abstract given a random rectangular m n matrix with elements from a normal distribution what is the distribution of the smallest singular value to pose an equivalent question in the language of multivariate statistics what is the distribution of the smallest eigenvalue of a matrix from the central wishart distribution in the null case we give new results giving the distribution as a simple recursion this includes the more difficult case when n m is an even integer without resorting to zonal polynomials and hypergeometric functions of matrix arguments with the recursion one can obtain exact expressions for the density and the moments of the distribution in terms of functions usually no more complicated than polynomials exponentials and at worst ordinary hypergeometric functions we further elaborate on the special cases when n m 0 1 2 and 3 and give a numerical table of the expected values for 2 m 25 and 0 n m 25

travelling wave fronts in reaction diffusion systems with spatio temporal delays this paper deals with the existence of travelling wave fronts in reaction diffusion systems with spatio temporal delays our approach is to use monotone iterations and a nonstandard ordering for the set of profiles of the corresponding wave system new iterative techniques are established for a class of integral operators when the reaction term satisfies different monotonicity conditions following this the existence of travelling wave fronts for reaction diffusion systems with spatio temporal delays is established finally we apply the main results to a single species diffusive model with spatio temporal delay and obtain some existence criteria of travelling wave fronts by choosing different kernels

limits of spiked random matrices ii given a large high dimensional sample from a spiked population the top sample covariance eigenvalue is known to exhibit a phase transition we show that the largest eigenvalues have asymptotic distributions near the phase transition in the rank one spiked real wishart setting and its general analogue proving a conjecture of baik et al ann probab 33 1643 1697 2005 we also treat shifted mean gaussian orthogonal and ensembles such results are entirely new in the real case in the complex case we strengthen existing results by providing optimal scaling assumptions one obtains the known limiting random schrodinger operator on the half line but the boundary condition now depends on the perturbation we derive several characterizations of the limit laws in which appears as a parameter including a simple linear boundary value problem this pde description recovers known explicit formulas at 2 4 yielding in particular a new and simple proof of the painleve representations for these tracy widom distributions

uniform semiglobal practical asymptotic stability for non autonomous cascaded systems and applications it is due to the modularity they provide that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on adding integrators nevertheless the standing assumptions in most of the present literature on cascaded systems is that when decoupled the subsystems constituting the cascade are uniformly globally asymptotically stable ugas hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable uspas this situation is often encountered in control practice e g in control of physical systems with external perturbations measurement noise unmodelled dynamics etc after giving a rigorous framework for the analysis of such stability properties this paper generalizes previous results for cascades by establishing that under a uniform boundedness condition on its solutions the cascade of two uspas systems remains uspas an analogous result is derived for uniformly semiglobally asymptotically stable usas systems in cascade furthermore we show the utility of our results in the pid control of mechanical systems affected by unknown non dissipative forces and considering the dynamics of the dc motors

global asymptotic stabilisation of non linear systems in this article the problem of global asymptotic stabilisation of non linear systems is considered first of all the global asymptotic stability of a class of non linear systems is considered it is proved that the class of non linear systems is globally asymptotically stable under certain appropriate conditions secondly based on the result obtained the global asymptotic stabilisation of a class of non linear systems is investigated and the feedback control laws which globally stabilise the class of systems are designed thirdly by the coordinate change and the results obtained the global stabilisation of the affine non linear systems are studied and then some sufficient conditions of stabilisation are presented finally the global asymptotic stabilisation of partially linear cascade non linear system is considered the sufficient conditions of global stabilisation are obtained and the corresponding feedback control laws which stabilise the non linear systems are designed in addition some

dynamics of nonlinear parabolic systems with time delays abstract the dynamics of a coupled system of semilinear parabolic equations with discrete time delays is investigated using the method of upper and lower solutions it is shown that if the reaction function in the system possesses a mixed quasimonotone property and the corresponding elliptic system has a pair of coupled upper and lower solutions then there is a monotone iteration process which yields a pair of quasisolutions of the elliptic system and the sector between the quasisolutions is an attractor of the delayed parabolic system under some additional conditions this sector is a global attractor and the solution of the parabolic system converges to a true solution of the elliptic system the same conclusions are obtained for a coupled system of parabolic ordinary equations with time delays applications are given to three model problems arising from ecology and nuclear engineering these model problems possess multiple steady state solutions and sufficient conditions are given to ensure the stability and instability of these solutions

asymptotic behavior of support vector machine for spiked population model for spiked population model we investigate the large dimension n and large sample size m asymptotic behavior of the support vector machine svm classification method in the limit of n m at fixed m n we focus on the generalization performance by analytically evaluating the angle between the normal direction vectors of svm separating hyperplane and corresponding bayes optimal separating hyperplane this is an analogous result to the one shown in paul 2007 and nadler 2008 for the angle between the sample eigenvector and the population eigenvector in random matrix theorem we provide not just bound but sharp prediction of the asymptotic behavior of svm that can be determined by a set of nonlinear equations based on the analytical results we propose a new method of selecting tuning parameter which significantly reduces the computational cost a surprising finding is that svm achieves its best performance at small value of the tuning parameter under spiked population model these results are confirmed to be correct by comparing with those of numerical simulations on finite size systems we also apply our formulas to an actual dataset of breast cancer and find agreement between analytical derivations and numerical computations based on cross validation

on global uniform asymptotic stability of nonlinear time varying systems in cascade abstract in this short paper we deal with the stability analysis problem of nonautonomous nonlinear systems in cascade in particular we give sufficient conditions to guarantee that i a globally uniformly stable gus nonlinear time varying nltv system remains gus when it is perturbed by the output of a globally uniformly asymptotically stable guas nltv system under the assumption that the perturbing signal is absolutely integrable ii if in addition the perturbed system is guas it remains guas under the cascaded interconnection iii two guas systems yield a guas cascaded system under some growth restrictions over the lyapunov function our proofs rely on the second method of lyapunov roughly speaking on a e stability analysis

brief growth rate conditions for uniform asymptotic stability of cascaded time varying systems in the last decade several results on cascaded autonomous systems have appeared in the literature the sufficient conditions for the stability and stabilizability of these systems are often related to certain growth rate conditions on the functions which define the dynamics of the system in this paper we analyze three complementary classes of nonlinear time varying systems according to these growth rates for each case we give further results to guarantee uniform global asymptotic stability of the cascade and relate our contributions to input to state stability and other growth rate conditions previously reported the advantage of this type of analysis is that it is often easier to verify such conditions than to find a lyapunov function with a negative definite derivative

universality at the edge of the spectrum in wigner random matrices we prove universality at the edge for rescaled correlation functions of wigner random matrices in the limit n as a corollary we show that after proper rescaling the 1th 2nd 3rd etc eigenvalues of wigner random hermitian resp real symmetric matrix weakly converge to the distributions established by tracy and widom in g u e g o e cases

global stabilization of nonlinear cascade systems abstract we present sufficient conditions for the global stabilizability of two cascade connected nonlinear systems these are based on general results concerning global asymptotic stability of triangular systems which are proved in the last section for polynomial systems in particular the stabilizing feedback is given explicitly

stability and bifurcation in a reaction diffusion model with nonlocal delay effect in this paper the existence stability and multiplicity of spatially nonhomogeneous steady state solution and periodic solutions for a reaction diffusion model with nonlocal delay effect and dirichlet boundary condition are investigated by using lyapunov schmidt reduction moreover we illustrate our general results by applications to models with a single delay and one dimensional spatial domain

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

the optimal hard threshold for singular values is 4 sqrt 3 we consider recovery of low rank matrices from noisy data by hard thresholding of singular values in which empirical singular values below a threshold are set to 0 we study the asymptotic mean squared error amse in a framework where the matrix size is large compared with the rank of the matrix to be recovered and the signal to noise ratio of the low rank piece stays constant the amse optimal choice of hard threshold in the case of n by n matrix in white noise of level is simply 4 3 n 2 309 n when is known or simply 2 858 y med when is unknown where y med is the median empirical singular value for nonsquare m by n matrices with m n the thresholding coefficients 4 3 and 2 858 are replaced with different provided constants that depend on m n asymptotically this thresholding rule adapts to unknown rank and unknown noise level in an optimal manner it is always better than hard thresholding at any other value and is always better than ideal truncated singular value decomposition tsvd which truncates at the true rank of the low rank matrix we are trying to recover hard thresholding at the recommended value to recover an n by n matrix of rank r guarantees an amse at most 3 nr 2 in comparison the guarantees provided by tsvd optimally tuned singular value soft thresholding and the best guarantee achievable by any shrinkage of the data singular values are 5 nr 2 6 nr 2 and 2 nr 2 respectively the recommended value for hard threshold also offers among hard thresholds the best possible amse guarantees for recovering matrices with bounded nuclear norm empirical evidence suggests that performance improvement over tsvd and other popular shrinkage rules can be substantial for different noise distributions even in relatively small n

stable subspace tracking algorithm based on a signed urv decomposition subspace estimation and tracking are of fundamental importance in many signal processing algorithms the class of schur subspace estimators provides a complete parametrization of all principal subspace estimates defined as the column spans of corresponding low rank matrix approximants that lie within a specified 2 norm distance of a given matrix the parametrization is found in terms of a two sided hyperbolic decomposition hyperbolic urv or hurv which can be computed using hyperbolic rotations unfortunately such rotations are commonly associated with numerical instabilities in this paper we present a numerically stable non iterative algorithm to compute the hurv called the signed urv surv algorithm we show that this algorithm implicitly imposes certain constraints on the hurv such that important norm bounds that guarantee stability are satisfied the constraints also restrict the parametrization of the subspace estimate such that it becomes close to the principal subspace provided by the svd which is a special case within this class the complexity of the algorithm is of the same order as that of a qr update updating and downdating are of the same complexity and are both numerically stable surv is proven to provide rank estimates consistent with the svd with the same rank threshold it can replace an svd where only subspace estimation is needed typical applications would e g be the detection of the number of signals in array signal processing and subspace estimation for source separation and interference mitigation such as the first step in music and esprit type algorithms simulation results demonstrate the numerical stability and confirm that this algorithm provides exact rank estimates and good principal subspace estimates as compared to the svd

comments on the stabilization of nonlinear systems by adding an integrator we present a new proof of the result that static stabilizability implies dynamic stabilizability the goal is to show how to compute explicitly the stabilizing feedback in some cases when the classical proof shows only the existence new results on dynamic feedback stabilization are proposed

stability and hopf bifurcation in a diffusive logistic population model with nonlocal delay effect abstract a reaction diffusion model with logistic type growth nonlocal delay effect and dirichlet boundary condition is considered and combined effect of the time delay and nonlocal spatial dispersal provides a more realistic way of modeling the complex spatiotemporal behavior the stability of the positive spatially nonhomogeneous positive equilibrium and associated hopf bifurcation are investigated for the case of near equilibrium bifurcation point and the case of spatially homogeneous dispersal kernel

dynamic generalized controllability and observability functions with applications to model reduction and sensor deployment in this paper we introduce the notion of dynamic generalized controllability and observability functions for nonlinear systems these functions are called dynamic and generalized since they make use of additional states dynamic extension and are such that partial differential inequalities are solved in place of equations the presence of the dynamic extension permits the construction of classes of canonical controllability and observability functions without relying on the solution of any partial differential equation or inequality the effectiveness of the proposed concept is validated by means of two applications the model reduction problem via balancing and the sensor deployment problem in a continuous stirred tank reactor cstr

reliable control of nonlinear systems in this paper we extend veillette s results 1995 to the study of reliable linear quadratic regulator problem for nonlinear systems this is achieved by employing the hamilton jacobi inequality in the nonlinear case instead of algebraic riccati equation in the linear one the proposed state feedback controllers are shown to be able to tolerate the outage of actuators within a prespecified subset of actuators both the gain margins of guaranteeing system stability and retaining a performance bound are estimated

spatial structures and periodic travelling waves in an integro differential reaction diffusion population model an integro differential reaction diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase it is claimed that this is inherently more realistic than the usual kind of reaction diffusion model for mobile populations three kinds of bifurcation from the uniform steady state solution are considered i to steady spatially periodic structures ii to periodic standing wave solutions and iii to periodic travelling wave solutions these correspond to aggregation and motion of populations

traveling wave fronts for generalized fisher equations with spatio temporal delays we study the existence of traveling wave fronts for a reaction diffusion equation with spatio temporal delays and small parameters the equation reduces to a generalized fisher equation if small parameters are zero we present two results in the first one we deal with the equation with very general kernels and show the persistence of fisher wave fronts for all sufficiently small parameters in the second one we deal with some particular kernels with which the nonlocal equation can be reduced to a system of singularly perturbed odes and we are then able to apply the geometric singular perturbation theory and phase plane arguments to this system to show the existence of the minimal wave speed the existence of a continuum of wave fronts and the global uniqueness of the physical wave front with each wave speed

penalized discriminant analysis fisher s linear discriminant analysis lda is a popular data analytic tool for studying the relationship between a set of predictors and a categorical response in this paper we describe a penalized version of lda it is designed for situations in which there are many highly correlated predictors such as those obtained by discretizing a function or the grey scale values of the pixels in a series of images in cases such as these it is natural efficient and sometimes essential to impose a spatial smoothness constraint on the coefficients both for improved prediction performance and interpretability we cast the classification problem into a regression framework via optimal scoring using this our proposal facilitates the use of any penalized regression technique in the classification setting the technique is illustrated with examples in speech recognition and handwritten character recognition

permanent magnet synchronous motors are globally asymptotically stabilizable with pi current control this note shows that the industry standard desired equilibrium for permanent magnet synchronous motors i e maximum torque per ampere can be globally asymptotically stabilized with a pi control around the current errors provided some viscous friction possibly small is present in the rotor dynamics and the proportional gain of the pi is suitably chosen instrumental to establish this surprising result is the proof that the map from voltages to currents of the incremental model of the motor satisfies some passivity properties the analysis relies on basic lyapunov theory making the result available to a wide audience

deterministic parallel analysis an improved method for selecting factors and principal components factor analysis and principal component analysis are used in many application areas the first step choosing the number of components remains a serious challenge our work proposes improved methods for this important problem one of the most popular state of the art methods is parallel analysis pa which compares the observed factor strengths with simulated strengths under a noise only model the paper proposes improvements to pa we first derandomize it proposing deterministic pa which is faster and more reproducible than pa both pa and deterministic pa are prone to a shadowing phenomenon in which a strong factor makes it difficult to detect smaller but more interesting factors we propose deflation to counter shadowing we also propose to raise the decision threshold to improve estimation accuracy we prove several consistency results for our methods and test them in simulations we also illustrate our methods on data from the human genome diversity project where they significantly improve the accuracy

normal forms and hopf bifurcation for partial differential equations with delays the paper addresses the computation of normal forms for some partial functional differential equations pfdes near equilibria the analysis is based on the theory previously developed for autonomous retarded functional differential equations and on the existence of center or other invariant manifolds as an illustration of this procedure two examples of pfdes where a hopf singularity occurs on the center manifold are considered

traveling waves for non local delayed diffusion equations via auxiliary equations in this paper we study the existence of traveling wave solutions for a class of delayed non local reaction diffusion equations without quasi monotonicity the approach is based on the construction of two associated auxiliary reaction diffusion equations with quasi monotonicity and a profile set in a suitable banach space by using the traveling wavefronts of the auxiliary equations under monostable assumption by using the schauder s fixed point theorem we then show that there exists a constant c 0 such that for each c c the equation under consideration admits a traveling wavefront solution with speed c which is not necessary to be monotonic

stability and bifurcations in a nonlocal delayed reaction diffusion population model abstract a nonlocal delayed reaction diffusion equation with dirichlet boundary condition is considered in this paper it is shown that a positive spatially nonhomogeneous equilibrium bifurcates from the trivial equilibrium the stability instability of the bifurcated positive equilibrium and associated hopf bifurcation are investigated providing us with a complete picture of the dynamics

lyapunov functions for stable cascades and applications to global stabilization generalizes lyapunov constructions for a cascade of two nonlinear systems one of which is stable rather than asymptotically stable a new cross term construction in the lyapunov function allows us to replace earlier growth conditions by a necessary boundedness condition this method is instrumental in the global stabilization of feedforward systems and new stabilization results are derived from the generalized construction

nonsmooth stabilization of a class of nonlinear cascaded systems a global nonsmooth stabilization scheme is presented for a class of nonlinear cascaded systems with uncontrollable linearization a stepwise constructive control methodology is proposed for the driving subsystem by using the adding a power integrator technique under suitable conditions and based on homogeneous properties it is proved that the stabilization of the driving subsystem implies the stabilization of the overall cascaded system due to the versatility of the adding a power integrator technique and homogeneous properties the proposed controller not only can be used to stabilize the cascaded system asymptotically but also is able to lead to an interesting result of finite time stabilization under appropriate conditions

global stabilization of a certain class of nonlinear systems abstract systems are considered which can be reduced to a regular form and possess an invariant manifold such that the restriction of the system to the manifold is globally asymptotically stable gas we construct a feedback which renders the manifold globally attracting it was proved that in this situation boundedness of all orbits is necessary and sufficient for the control system to be gas a lyapunov type condition for the latter property adapted to the situation in question is given results of andreini bacciotti and stefani are shown to be a special case of our result