comments on distributed control of spatially invariant systems the central theme of the paper is theory of spatially invariant partial differential systems on an infinite domain that can be reduced to the study of a family of finite dimensional systems parameterized by e r which can then be analyzed pointwise

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

sparse principal component analysis via rotation and truncation sparse principal component analysis sparse pca aims at finding a sparse basis to improve the interpretability over the dense basis of pca while still covering the data subspace as much as possible in contrast to most existing work that addresses the problem by adding sparsity penalties on various objectives of pca we propose a new method sparse pca via rotation and truncation spcart which finds a rotation matrix and a sparse basis such that the sparse basis approximates the basis of pca after the rotation the algorithm of spcart consists of three alternating steps 1 rotating the pca basis 2 truncating small entries and 3 updating the rotation matrix its performance bounds are also given the spcart is efficient with each iteration scaling linearly with the data dimension parameter choice is simple due to explicit physical explanations we give a unified view to several existing sparse pca methods and discuss the connections with spcart some ideas from spcart are extended to gpower a popular sparse pca algorithm to address its limitations experimental results demonstrate that spcart achieves the state of the art performance along with a good tradeoff among various criteria including sparsity explained variance orthogonality balance of sparsity among loadings and computational speed

an investigation of multiple solutions yielded by the equivalent linearization method abstract the equivalent linearization method is a standard technique for the approximate solution of non linear random vibration problems it is known that in some cases the method can yield multiple stable solutions for the mean value and the standard deviation of the system response the validity and accuracy of this type of solution is investigated here by considering a single degree of freedom system for which the multiple solutions which are obtained may be compared with the exact response statistics it is found that the multiple solutions correspond to distinguishable states which occur in the response of the system a state is defined here as a form of response which persists for some time and whose local temporal statistics differ from the ensemble statistics of the complete response the accuracy of the equivalent linearization method is found to be variable

algebraic characterization of approximate controllability of behaviours of spatially invariant systems we give algebraic characterizations of the properties of autonomy and of controllability of behaviours of spatially invariant dynamical systems consisting of distributional solutions w that are periodic in the spatial variables to a system of partial differential equations corresponding to a polynomial matrix m g c 1 d mxn

the response envelope probability density function of a duffing oscillator with random narrow band excitation abstract a duffing oscillator excited by narrow band random noise can exhibit multi valued behaviour with random jumps between two pseudo stable states in this paper an approximate form of the probability density function or the envelope of the response is obtained state equations for the response envelope with the random excitation envelope as input are obtained by stochastic averaging the joint probability density function of response envelope and input envelope can be found approximately for certain ranges of the system parameters the response envelope probability density function shows two maxima in the cases where the response is multi valued numerical simulation confirms the results

multiple time scaling of the response of a duffing oscillator to narrow band random excitation the response of a duffing oscillator to narrow band random excitation is considered two approaches multiple time scaling and stochastic averaging are used both lead to the same set of three state equations for the slowly varying local mean square response or envelope and two other variables the stationary solution of these equations is similar to results previously obtained by using statistical linearization the stationary and nonstationary from the three state equations results compare favourably with digital simulations random jumps are shown to occur if the excitation bandwidth is sufficiently small

beam beam interaction models under narrow band random excitation abstract the aim of this paper is to continue our previous investigations on beam beam interaction models in particle accelerators by considering these models under narrow band random excitation in this investigation the multiple scale and the moment methods are used the equations of modulation of the amplitude and the phase are derived and perturbation techniques are used to seek approximate steady state solutions two special cases are considered to illustrate this study and excellent agreement is found between analytical and numerical results other cases can be similarly studied the effects of noise and detuning parameters are examined numerically and theoretically and we find that the system demonstrates a diffused limit cycle as the intensity of noise increases the numerical results show that the multiple scale method is effective for these stochastic systems

alternative multiview maximum entropy discrimination maximum entropy discrimination med is a general framework for discriminative estimation based on maximum entropy and maximum margin principles and can produce hard margin support vector machines under some assumptions recently the multiview version of med multiview med mvmed was proposed in this paper we try to explore a more natural mvmed framework by assuming two separate distributions p 1 theta 1 over the first view classifier parameter theta 1 and p 2 theta 2 over the second view classifier parameter theta 2 we name the new mvmed framework as alternative mvmed amvmed which enforces the posteriors of two view margins to be equal the proposed amvmed is more flexible than the existing mvmed because compared with mvmed which optimizes one relative entropy amvmed assigns one relative entropy term to each of the two views thus incorporating a tradeoff between the two views we give the detailed solving procedure which can be divided into two steps the first step is solving our optimization problem without considering the equal margin posteriors from two views and then in the second step we consider the equal posteriors experimental results on multiple real world data sets verify the effectiveness of the amvmed and comparisons with mvmed are also reported

toward optimal manifold hashing via discrete locally linear embedding binary code learning also known as hashing has received increasing attention in large scale visual search by transforming high dimensional features to binary codes the original euclidean distance is approximated via hamming distance more recently it is advocated that it is the manifold distance rather than the euclidean distance that should be preserved in the hamming space however it retains as an open problem to directly preserve the manifold structure by hashing in particular it first needs to build the local linear embedding in the original feature space and then quantize such embedding to binary codes such a two step coding is problematic and less optimized besides the off line learning is extremely time and memory consuming which needs to calculate the similarity matrix of the original data in this paper we propose a novel hashing algorithm termed discrete locality linear embedding hashing dllh which well addresses the above challenges the dllh directly reconstructs the manifold structure in the hamming space which learns optimal hash codes to maintain the local linear relationship of data points to learn discrete locally linear embedding codes we further propose a discrete optimization algorithm with an iterative parameters updating scheme moreover an anchor based acceleration scheme termed anchor dllh is further introduced which approximates the large similarity matrix by the product of two low rank matrices experimental results on three widely used benchmark data sets i e cifar10 nus wide and youtube face have shown superior performance of the proposed dllh over the state of the art approaches

on loss of accuracy and non uniqueness of solutions generated by equivalent linearization and cumulant neglect methods abstract the equivalent linearization the gaussian closure and the non gaussian cumulant neglect closure schemes are used to analyze responses of a non linear system with multiple potential wells under random external excitations the resulting response statistics are compared with those obtained from monte carlo simulations and exact stationary solutions to the corresponding fokker planck kolmogorov equation the question of uniqueness of mean square responses for different approximation methods is also examined and discussed the results presented show that accuracies of these approximation techniques vary depending on the nature and strength of non linearity of the system and the intensity of excitation for certain conditions the exact mean square responses are underestimated by a factor of ten or more the gaussian closure technique and the equivalent linearization method lead to identical results which are somewhat less accurate than those obtained by the non gaussian cumulant neglect closure scheme it is also shown that the solution generated by these techniques may not be unique

stabilizability and controllability of spatially invariant p d e systems in this paper we derive new readily testable criteria for exponential stabilizability approximate controllability and exact controllability for multiplicative systems arising from linear partial differential equations on an infinite domain these multiplicative systems have an unbounded semigroup generator but bounded input and output operators the theoretical results are illustrated by several examples in particular explicit easily verifiable conditions for exponential stabilizability approximate and exact controllability are given for second order p d e systems dual results for exponential detectability approximate and exact observability are also included

uncorrelated component analysis based hashing the approximate nearest neighbor ann search problem is important in applications such as information retrieval several hashing based search methods that provide effective solutions to the ann search problem have been proposed however most of these focus on similarity preservation and coding error minimization and pay little attention to optimizing the precision recall curve or receiver operating characteristic curve in this paper we propose a novel projection based hashing method that attempts to maximize precision and recall we first introduce an uncorrelated component analysis uca transformation by examining precision and recall and then propose a uca based hashing method the proposed method is evaluated with a variety of data sets the results show that uca based hashing outperforms state of the art methods and has computationally efficient training and encoding processes

supervised discrete hashing with relaxation data dependent hashing has recently attracted attention due to being able to support efficient retrieval and storage of high dimensional data such as documents images and videos in this paper we propose a novel learning based hashing method called supervised discrete hashing with relaxation sdhr based on supervised discrete hashing sdh sdh uses ordinary least squares regression and traditional zero one matrix encoding of class label information as the regression target code words thus fixing the regression target in sdhr the regression target is instead optimized the optimized regression target matrix satisfies a large margin constraint for correct classification of each example compared with sdh which uses the traditional zero one matrix sdhr utilizes the learned regression target matrix and therefore more accurately measures the classification error of the regression model and is more flexible as expected sdhr generally outperforms sdh experimental results on two large scale image data sets cifar 10 and mnist and a large scale and challenging face data set frgc demonstrate the effectiveness and efficiency of sdhr

response amplitude probability functions of a hardening duffing oscillator subjected to filtered white noise the problem of estimating the probability distribution of the response amplitude of a hardening duffing oscillator subjected to narrow band excitation is addressed a method is presented which is based on a quasi static approximation of system behaviour and is capable of reproducing the resulting concave shape of probability functions when a jump phenomenon occurs predictions are compared with those obtained via stochastic averaging techniques and with digital simulations

iterative quantization a procrustean approach to learning binary codes for large scale image retrieval this paper addresses the problem of learning similarity preserving binary codes for efficient similarity search in large scale image collections we formulate this problem in terms of finding a rotation of zero centered data so as to minimize the quantization error of mapping this data to the vertices of a zero centered binary hypercube and propose a simple and efficient alternating minimization algorithm to accomplish this task this algorithm dubbed iterative quantization itq has connections to multiclass spectral clustering and to the orthogonal procrustes problem and it can be used both with unsupervised data embeddings such as pca and supervised embeddings such as canonical correlation analysis cca the resulting binary codes significantly outperform several other state of the art methods we also show that further performance improvements can result from transforming the data with a nonlinear kernel mapping prior to pca or cca finally we demonstrate an application of itq to learning binary attributes or classemes on the imagenet data set

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

asymptotics and approximation of large systems of ordinary differential equations abstract in this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations under the mild assumption that the so called characteristic function of our system is completely monotonic we obtain a drastically simplified condition which ensures boundedness of the associates semigroup if the characteristic function satisfies certain additional conditions we deduce sharp rates of convergence to equilibrium we moreover address the important and delicate issue of the role of the infinite system in understanding the asymptotic behaviour of large but finite systems and we provide a precise way of obtaining size independent rates of convergence for families of finite dimensional systems finally we illustrate our abstract results in the setting of the well known platoon problem

random superharmonic and subharmonic response multiple time scaling of a duffing oscillator narrowband random third order superharmonic and one third order subharmonic response of a duffing oscillator is discussed a multiple time scale approach is used the work is a more rigorous approach than that already published on random superharmonic response by the authors and the results obtained corroborate the previous ones in particular random jumps in amplitude can occur but are less likely to occur as the bandwidth of the excitation is increased the results are further corroborated by comparison with digital simulation in addition new results on random subharmonic response are also presented obtained by using the same approach

retargeted least squares regression algorithm this brief presents a framework of retargeted least squares regression relsr for multicategory classification the core idea is to directly learn the regression targets from data other than using the traditional zero one matrix as regression targets the learned target matrix can guarantee a large margin constraint for the requirement of correct classification for each data point compared with the traditional least squares regression lsr and a recently proposed discriminative lsr models relsr is much more accurate in measuring the classification error of the regression model furthermore relsr is a single and compact model hence there is no need to train two class binary machines that are independent of each other the convex optimization problem of relsr is solved elegantly and efficiently with an alternating procedure including regression and retargeting as substeps the experimental evaluation over a range of databases identifies the validity of our method

phase plane for narrow band random excitation of a duffing oscillator abstract the response of a duffing oscillator to narrow band random excitation is consedered it is shown that multiple values of the response can occur at some frequencies for very narrow excitation bandwidths but these reduce to a single value as the bandwidth is increased time histories of quantities such as mean square displacement are obtained from the time dependent fokker planck equation smoothed time histories of mean square velocity and displacement are plotted on a phase plane the phase plane can show either one sink or two sinks and a saddle point as in the sinusoidal case but again excitation bandwith determines whether or not multiple sinks occur

stochastic response and stability of the duffing oscillator under narrowband excitation the duffing equation under narrowband gaussian excitation is studied almost sure asymptotic stability analysis is used to discuss the realizability of multivalued steady states the theoretical predictions are supported by numerical simulation results

brief paper riccati equations for second order spatially invariant partial differential systems recently the class of spatially invariant systems was introduced with motivating examples of partial differential equations on an infinite domain for these it was shown that by taking fourier transforms one obtains infinitely many finite dimensional systems with a scalar parameter the idea is that for the lqr controller design for these systems one can solve the parameterized lqr riccati equation pointwise while for simple first order systems like the heat equations this approach works for second order systems like wave or beam equations it is easy to construct examples for which this approach fails here we give a correct formulation for second order partial differential systems including wave and beam type equations

ldahash improved matching with smaller descriptors sift like local feature descriptors are ubiquitously employed in computer vision applications such as content based retrieval video analysis copy detection object recognition photo tourism and 3d reconstruction feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations in particular affine and intensity scale transformations however real transformations that an image can undergo can only be approximately modeled in this way and thus most descriptors are only approximately invariant in practice second descriptors are usually high dimensional e g sift is represented as a 128 dimensional vector in large scale retrieval and matching problems this can pose challenges in storing and retrieving descriptor data we map the descriptor vectors into the hamming space in which the hamming metric is used to compare the resulting representations this way we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples we show extensive experimental validation demonstrating the advantage of the proposed approach

response of a strongly non linear oscillator to narrowband random excitations abstract the principal resonance of a van der pol duffing oscillator subject to narrowband random excitations has been studied by introducing a new expansion parameter e e e u 0 the method of multiple scales is adapted for the strongly non linear system the behavior of steady state responses together with their stability and the effects of system damping and the detuning and magnitude of the random excitation on steady state responses are analyzed in detail theoretical analyses are verified by some numerical results it is found that when the random noise intensity increases the steady state solution may change form a limit cycle to a diffused limit cycle and the system may have two different stable steady state solutions for the same excitation under certain conditions the results obtained for the strongly non linear oscillator complement previous results in the literature for weakly non linear systems

responses of discretized systems under narrow band nonstationary random excitations part 2 nonlinear problems in a companion paper the extended stochastic central difference escd method was presented for computation of responses of linear multi degrees of freedom mdof systems under narrow band stationary and nonstationary random excitations the present paper is concerned with the generalization of the escd method for computation of nonlinear mdof systems the generalization is based on a combination of the escd method with statistical linearization sl technique modified adaptive time scheme ats and time coordinate transformation tct unlike the conventional sl technique the generalized escd method is applicable to mdof systems with large nonlinearities comparison is made of the computed results applying the generalized escd method to those obtained by the monte carlo simulation mcs excellent agreements were obtained it was observed that the proposed method is very efficient compared with the mcs

first passage time of nonlinear ship rolling in narrow band non stationary random seas the generalized extended stochastic central difference gescd method is applied to study the response statistics and first passage time of nonlinear ship rolling in narrow band stationary and non stationary random seas the gescd method is based on a combination of the extended stochastic central difference method with a statistical linearization technique modified adaptive time scheme and time coordinate transformation the extended stochastic central difference method is however an extension of the stochastic central difference method for the determination of the recursive mean square or covariance of responses of systems under narrow band stationary and non stationary random disturbances approximate first passage probabilities of nonlinear systems based on the modified mean rate of various crossings proposed earlier by the first author were determined it is concluded that the gescd method is very accurate simple and efficient to apply compared with monte carlo simulation the proposed method is applicable to cases with large nonlinearities and intensive random excitations the approximate first passage probabilities of the nonlinear system determined by the proposed approach are very accurate as they are in excellent agreement with those evaluated by the monte carlo simulation it is believed that the model considered in this paper is a closer representation to reality than those reported earlier in the literature

non linear resonance in strings under narrow band random excitation part i planar response and stability non linear planar response of a string to planar narrow band random excitation is investigated in this paper a response equation for the mean square deflection 2 is obtained under a single mode approximation by using the equivalent linearization technique it is shown that the response is triple valued as in the case of harmonic excitation if the centre frequency of excitation lies in a certain specified range the triple valued response occurs only if the excitation bandwidth is smaller than a critical value crit which is a monotonically increasing function of the intensity of excitation an approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the 2 plane have been charted it is shown that planar response can become unstable either due to an unbounded growth of the in plane component of motion or due to a spontaneous appearance of an out of plane component