exclusion and persistence in deterministic and stochastic chemostat models abstract we first introduce and analyze a variant of the deterministic single substrate chemostat model in this model microbe removal and growth rates depend on biomass concentration with removal terms increasing faster than growth terms using a comparison principle we show that persistence of all species is possible in this scenario then we turn to modelling the influence of random fluctuations by setting up and analyzing a stochastic differential equation in particular we show that random effects may lead to extinction in scenarios where the deterministic model predicts persistence on the other hand we also establish some stochastic persistence results

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

output regulation of periodic signals for dps an infinite dimensional signal generator in this note we consider output regulation and disturbance rejection of periodic signals via state feedback in the setting of exponentially stabilizable linear infinite dimensional systems we show that if an infinite dimensional exogenous system is generating periodic reference signals solvability of the state feedback regulation problem is equivalent to solvability of the so called equations this result allows us to consider asymptotic tracking of periodic reference signals which only have absolutely summable fourier coefficients while in related existing work the reference signals are confined to be infinitely smooth we also discuss solution of the regulator equations and construct the actual feedback law to achieve output regulation in the single input single output siso case the output regulation problem is solvable if the transfer function of the stabilized plant does not have zeros at the frequencies i spl omega sub n of the periodic reference signals and if the sequence cr i spl omega sub n a bk b sup 1 spl times q spl phi sub n cr i spl omega sub n a bk p spl phi sub n sub n spl isin z spl isin l sup n2 a one dimensional heat equation is used as an illustrative example

algebraic feature extraction for image recognition based on an optimal discriminant criterion abstract a novel algebraic feature extraction method for image recognition is presented the main difference between the present method and any other existing algebraic feature extraction method is that the present method uses an optimal discriminant criterion to extract algebraic features for the given training image samples a set of optimal discriminant projection vectors is calculated according to a generalized fisher criterion function on the basis of the optimal discriminant projection vector the projective feature vectors of an image i e algebraic features are extracted by projecting the image onto all optimal discriminant projection vectors the method of calculating the set of optimal discriminant projection vectors is discussed a minimum distance classifier is also proposed for classifying projective feature vectors experimental results showed that the present method has good recognition performance an important conclusion about the present method is that the foley sammon optimal set of discriminant vectors is a special case of the set of optimal discriminant projection vectors

discrete time switching periodic adaptive control for time varying parameters with unknown periodicity abstractin this paper we address the problem of unknown periodicity for a class of discrete time nonlinear parametric systems without assuming any growth conditions on the nonlinearities the unknown periodicity hides in the parametric uncertainties which is difficult to estimate with existing techniques by incorporating a logic based switching mechanism we identify the period and bound of unknown parameter simultaneously lyapunov based analysis is given to demonstrate that a finite number of switchings can guarantee the asymptotic tracking for the nonlinear parametric systems the simulation result also shows the efficacy of the proposed switching periodic adaptive control approach

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

two group sir epidemic model with stochastic perturbation a stochastic two group sir model is presented in this paper the existence and uniqueness of its nonnegative solution is obtained and the solution belongs to a positively invariant set furthermore the globally asymptotical stability of the disease free equilibrium is deduced by the stochastic lyapunov functional method if r 0 1 which means the disease will die out while if r 0 1 we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average in addition the intensity of the fluctuation is proportional to the intensity of the white noise when the white noise is small we consider the disease will prevail at last we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments

on the realization of periodic functions abstract in this article canonical and spectrally minimal infinite dimensional state space realizations for periodic functions are considered it is shown that the periodic functions having l 1 fourier coefficients are precisely those realizable by a riesz spectral system rss in which the system operator generates a periodic strongly continuous semigroup and the observation operator is bounded this realization can easily be converted to a canonical and spectrally minimal form it is shown how the use of rss and cesaro sums of fourier series allows the construction of a state space realization for a given periodic function merely integrable over its period simple finite dimensional approximations with error bounds are derived for the rss realization regular well posed linear systems wpls are used to construct a fuhrmann type realization for a given periodic function integrable over its period it is shown that the rss realizations and wpls realizations are precisely equally good at coping with the possible ill behavior of a given bounded periodic function integrable over its period but the wpls realization is not always spectrally minimal or canonical

brief robust adaptive compensation of biased sinusoidal disturbances with unknown frequency asymptotically stable observable linear systems of order n which are not required to be minimum phase and are affected by an additive noisy biased sinusoidal disturbance with unknown bias magnitude phase and frequency are considered the problem of designing an output feedback compensator which regulates the output to zero for any initial condition and for any biased sinusoidal disturbance with no noise is addressed under the assumption that the system parameters are known this problem is solved by a 2n 6 order compensator which generates asymptotically convergent estimates of the biased sinusoidal disturbance and of its parameters including frequency the robustness of the closed loop system with respect to sufficiently small additive unmodelled noise is characterized in terms of input to state stability

compound rank k projections for bilinear analysis in many real world applications data are represented by matrices or high order tensors despite the promising performance the existing 2 d discriminant analysis algorithms employ a single projection model to exploit the discriminant information for projection making the model less flexible in this paper we propose a novel compound rank k projection crp algorithm for bilinear analysis the crp deals with matrices directly without transforming them into vectors and it therefore preserves the correlations within the matrix and decreases the computation complexity different from the existing 2 d discriminant analysis algorithms objective function values of crp increase monotonically in addition the crp utilizes multiple rank k projection models to enable a larger search space in which the optimal solution can be found in this way the discriminant ability is enhanced we have tested our approach on five data sets including uuim cvl pointing 04 usps and coil20 experimental results show that the performance of our proposed crp performs better than other algorithms in terms of classification accuracy

pulse vaccination on seir epidemic model with nonlinear incidence rate in this paper we consider an seir epidemic model with two time delays and nonlinear incidence rate and study the dynamical behavior of the model with pulse vaccination by using the floquet theorem and comparison theorem we prove that the infection free periodic solution is globally attractive when r 1

extinction and periodic solutions for an impulsive sir model with incidence rate stochastically perturbed abstract in this paper we consider an impulsive sir model with incidence rate stochastically perturbed first we prove the existence and uniqueness of the global positive solution by constructing the equivalent system without impulse second we obtain a sufficient condition which determines epidemic to extinct then we demonstrate the existence and global attraction of the boundary periodic solution under the certain condition finally we present a sufficient condition which allows the existence of a positive periodic solution

stability of a stochastic sir system abstract we propose a stochastic sir model with or without distributed time delay and we study the stability of disease free equilibrium the numerical simulation of the stochastic sir model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold stochastic value is found

on a nonlinear multivariable servomechanism problem abstract multivariable nonlinear plants with both measured and unmeasured vector disturbance signals are considered output feedback dynamic control laws are designed for the problem of tracking a constant or slowly varying reference input while rejecting constant or slowly varying disturbances

large correlation analysis in this paper a novel supervised dimensionality reduction method is developed based on both the correlation analysis and the idea of large margin learning the method aims to maximize the minimal correlation between each dimensionality reduced instance and its class label thus named as large correlation analysis lca unlike most existing correlation analysis methods such as cca ccas and cda which all maximize the total or ensemble correlation over all training instances lca devotes to maximizing the individual correlations between given instances and its associated labels and is established by solving a relaxed quadratic programming with box constraints experimental results on real world datasets from both uci and usps show its effectiveness compared to the existing canonical correlation analysis methods

on a stochastic logistic equation with impulsive perturbations a stochastic logistic model with impulsive perturbations is proposed and investigated first we give a new definition of a solution of an impulsive stochastic differential equation isde which is more convenient for use than the existing one using this definition we show that our model has a global and positive solution and obtain its explicit expression then we establish the sufficient conditions for extinction non persistence in the mean weak persistence persistence in the mean and stochastic permanence of the solution the critical value between weak persistence and extinction is obtained in addition the limit of the average in time of the sample path of the solution is estimated by two constants afterwards the lower growth rate and the upper growth rate of the solution are estimated finally sufficient conditions for global attractivity are established

nonlinear control for robust rejection of periodic disturbances consider a linear plant with a strictly proper rational transfer function and an input which is a known periodic waveform of unknown amplitude and phase in the case when the periodic waveform has infinitely many non zero harmonics it is pointed out that for a wide class of linear time invariant infinite dimensional controllers it is not possible to robustly stabilize the plant and achieve asymptotic rejection of the disturbance for a specific linear plant and a triangular wave disturbance it is shown by construction that the problem is soluble with a nonlinear controller robustness is measured using the gap metric robust stability margin

optimal discriminant plane for a small number of samples and design method of classifier on the plane abstract in a previous work zi quan hong and jing yu yang minimum distance classifier on the optimal discriminant plane we suggested and derived a method for constructing classifier on the optimal discriminant plane using minimum distance criteria in this paper the problem of solving optimal discriminant plane for a small number of samples is discussed which is based on the above paper by the same authors in the case of a small number of samples generalized eigenequation ax bx established for a large number of samples usually has no solution because within class scatter matrix is singular to obtain the solution of the generalized eigenequation a new method is suggested in which the singular value perturbation is added to the within class scatter matrix such that the matrix becomes a nonsingular matrix therefore the generalized eigenequation can be solved using existing algorithms we proved that the generalized eigenequations on the optimal discriminant plane are stable in respect of eigenvalues and the generalized eigenvectors are indeed the optimal discriminant directions if the perturbation is subject to some certain conditions the experimental results have shown that our method works well and the minimum distance classifier on the optimal discriminant plane can be constructed with high performance even in the case of a small number of samples

segmented minimum noise fraction transformation for efficient feature extraction of hyperspectral images in this paper a segmented minimum noise fraction mnf transformation is proposed for efficient feature extraction of hyperspectral images hsis the original bands can be partitioned into several highly correlated subgroups based on the correlation matrix image of the hyperspectral data the mnf is implemented separately on each subgroup of the data and then the bhattacharyya distance is used as the band separability measure for feature extraction consequently the extracted features can then be significantly classified using state of art classifiers i e k nn or svm experiments on two benchmark hsis collected by aviris and rosis demonstrate that the proposed method significantly reduces the transformation time in comparison with the conventional mnf the fisher scalars criterion shows that the class separability with the segmented mnf is the best and the extracted features even exhibit higher classification accuracy compared with the pca or mnf highlightsa segmented minimum noise fraction mnf transformation is proposed for efficient feature extraction of hyperspectral images hsis the proposed method significantly reduces the transformation time in comparison with the conventional mnf the class separability of the extracted features is improved the extracted features by smnf even exhibit higher classification accuracy compared with the pca or mnf

optimal fisher discriminant analysis using the rank decomposition abstract the fisher optimal discriminant vector is a very efficient means in high dimensional pattern analysis in the case of a small number of samples the within class scatter matrix s w is singular therefore the calculation of the fisher optimal discriminant vector becomes very important in this paper the conception of the rank decomposition of matrices is first introduced and a new method for calculating the fisher optimal discriminant vector is presented which is particularly well suited to the case of a small number of samples in the sense that the scatter matrices are rank deficient the new method is compared with the pseudoinverse and perturbation methods in tian j opt soc am a 5 1670 1672 1988 and hong and yang pattern recognition 24 317 324 1991 an important conclusion is proved in the three methods our method is the best one for calculating the fisher optimal discriminant vectors in the cases of both a large and a small number of samples the experimental results have also shown that our method can give the highest recognition rate in the case of a small number of samples among the three methods

brief paper asymptotic rejection of asymmetric periodic disturbances in output feedback nonlinear systems this paper deals with asymptotic rejection of periodic disturbances which may have asymmetric basic wave patterns this class of disturbances covers asymmetric wave forms in the half period such as alternating sawtooth wave form some disturbances which are generated from nonlinear oscillation such as van de pol oscillators as well as disturbances with symmetric half period wave forms such as sinusoidal disturbances and triangular disturbances etc the systems considered in this paper can be transformed to the nonlinear output feedback form the amplitude and phase of the disturbances are unknown the novel concept of integral phase shift is introduced together with the newly introduced half period integration operator to investigate the invariant properties of asymmetric periodic disturbances they are used for the estimation of unknown disturbances in the systems together with observer design techniques to deal with nonlinearity the proposed control design with the disturbance estimation asymptotically rejects the unknown disturbance and ensures the overall stability of the system

a novel feature extraction method for image recognition based on similar discriminant function sdf abstract the extraction of image features is the most fundamental and important problem in image recognition in this paper a similarity measure of matrices is first presented and a similar discriminant function sdf of images is established based on the discriminant function we further propose a novel feature extraction method for image recognition for each class of training image samples an optimal projection axis maximizing the similarity among these training image samples for the class is calculated unlike the common methods of feature extraction we extract a projective feature vector for a training image sample by projecting the image on the optimal projection axis of the class itself and a set of projective feature vectors for a testing image sample by projecting the image on all the optimal projection axes finally a hierarchical classifier in the optimal discriminant space is designed to recognize images in order to test the efficiency of our method it is used to recognize human faces and english characters experimental results have shown that our method has good recognition performance and the extracted projective feature vectors contain more recognition information than commonly used image features

algebraic feature extraction of image for recognition abstract the extraction of image features is one of the fundamental tasks in image recognition up until now there have been several kinds of features to be used for the purpose of image recognition as follows 1 visual features 2 statistical features of pixel 3 transform coefficient features in addition there is another kind of feature which the author believes is very useful i e 4 algebraic features which represent intrinsic attributions of an image singular values sv of image are this kind of feature in this paper we prove that sv feature vector has some important properties of algebraic and geometric invariance and insensitiveness to noise these properties are very useful for the description and recognition of images as an example sv feature vector is used for the problem of recognizing human facial images in this paper using sv feature vector samples of facial images a normal pattern bayes classification model based on sammon s optimal descriminant plane is constructed the experimental result shows that sv feature vector has good performance of class separation

description and discrimination of planar shapes using shape matrices a shape descriptor has been developed which can describe a shape independent of its translation rotation and scaling the description is in the form of a matrix and it is obtained by a polar quantization of a shape the quantization process takes into consideration not only a shape s outer geometry but its inner geometry as well the descriptor is information preserving and if the quantization parameters are selected properly it is possible to reconstruct an original shape from its description in this technique shape discrimination is possible by a simple exclusive or operation on shape descriptions

a stochastic differential equation sis epidemic model in this paper we extend the classical susceptible infected susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation sde for the number of infectious individuals i t we then prove that this sde has a unique global positive solution i t and establish conditions for extinction and persistence of i t we discuss perturbation by stochastic noise in the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance the results are illustrated by computer simulations including two examples based on real life diseases

the threshold of a stochastic sis epidemic model with vaccination this paper is concerned with the long time behavior of a stochastic sis epidemic model with vaccination sufficient conditions for extinction and persistence in mean are obtained we find a threshold of the stochastic model which determines the outcome of the disease in case the white noises are small at last some numerical simulations are carried out to support our results

classification of partial 2 d shapes using fourier descriptors we present a method for the classification of 2 d partial shapes using fourier descriptors we formulate the problem as one of estimating the fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments the method used for obtaining the estimates of the fourier descriptors minimizes a sum of two terms the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2 area of the unknown shape experiments with synthetic and real boundaries show that estimates closer to the true values of fourier descriptors of complete boundaries are obtained also classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20 30 percent of the data is missing

novel fisher discriminant classifiers at the present several applications need to classify high dimensional points belonging to highly unbalanced classes unfortunately when the training set cardinality is small compared to the data dimensionality small sample size problem the classification performance of several well known classifiers strongly decreases similarly the classification accuracy of several discriminative methods decreases when non linearly separable and unbalanced classes are treated in this paper we firstly survey state of the art methods that employ improved versions of linear discriminant analysis lda to deal with the above mentioned problems secondly we propose a family of classifiers based on the fisher subspace estimation which efficiently deal with the small sample size problem non linearly separable classes and unbalanced classes the promising results obtained by the proposed techniques on benchmark datasets and the comparison with state of the art predictors show the efficacy of the proposed techniques

asymptotic rejection of unmatched general periodic disturbances with nonlinear lipschitz internal models this article deals with asymptotic rejection of general periodic disturbances in a class of nonlinear systems by exploiting observer design with lipschitz output nonlinearities for the internal model design it is shown that a class of general periodic distances can be modelled as outputs of linear systems with nonlinear output functions based on this observation a nonlinear observer design with output lipschitz nonlinearities is investigated and integrated for the internal model design to estimate the phase and amplitude of the desired feedforward input for asymptotic disturbance rejection in a class of nonlinear systems with input to state stable zero dynamics a number of problems on disturbance rejection can be formulated in the disturbance rejection form shown in this article to which the proposed nonlinear lipschitz internal model can be applied two examples are included to demonstrate the proposed design strategies

dimensionality reduction of image features using the canonical contextual correlation projection a linear discriminative supervised technique for reducing feature vectors extracted from image data to a lower dimensional representation is proposed it is derived from classical linear discriminant analysis lda extending this technique to cases where there is dependency between the output variables i e the class labels and not only between the input variables the latter can readily be dealt with in standard lda the novel method is useful for example in supervised segmentation tasks in which high dimensional feature vectors describe the local structure of the image the principal idea is that where standard lda merely takes into account a single class label for every feature vector the new technique incorporates class labels of its neighborhood in the analysis as well in this way the spatial class label configuration in the vicinity of every feature vector is accounted for resulting in a technique suitable for e g image data this extended lda that takes spatial label context into account is derived from a formulation of standard lda in terms of canonical correlation analysis the novel technique is called the canonical contextual correlation projection cccp an additional drawback of lda is that it cannot extract more features than the number of classes minus one in the two class case this means that only a reduction to one dimension is possible our contextual lda approach can avoid such extreme deterioration of the classification space and retain more than one dimension the technique is exemplified on a pixel based medical image segmentation problem in which it is shown that it may give significant improvement in segmentation accuracy

asymptotic rejection of unmatched general periodic disturbances in a class of non minimum phase non linear systems this article deals with asymptotic rejection of unmatched general periodic disturbances in nonminimum phase non linear output feedback systems the steady state responses are defined for unstable systems subject to general periodic disturbances and the generalised gain and phase are defined for stable systems subject to general periodic disturbances based on the new definitions new results are obtained for the equivalent input disturbance and disturbance estimation an lp convergent estimate of the equivalent input disturbance is incorporated in the control design to ensure the asymptotic rejection of unmatched general periodic disturbances while maintaining the stability of the non linear system

a stochastic sis epidemic model with saturating contact rate abstract in this paper we formulate and investigate the dynamics of a sis epidemic model with saturating contact rate and its corresponding stochastic differential equation version for the deterministic epidemic model we show that the disease free equilibrium is global asymptotically stable if the basic reproduction number is less than unity and if the basic reproduction number is greater than unity model 1 2 admits a unique endemic equilibrium which is locally asymptotically stable by analyzing the corresponding characteristic equations for the stochastic epidemic model the existence and uniqueness of the positive solution are proved by employing the lyapunov analysis method the basic reproduction number r 0 s is proved to be a sharp threshold which determines whether there is an endemic outbreak or not if r 0 s 1 and under mild extra conditions the disease can be eradicated almost surely whereas if r 0 s 1 it has a stationary distribution which leads to the stochastic persistence of the disease finally numerical simulations are presented to illustrate our theoretical results

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

harmonic generation in adaptive feedforward cancellation schemes the paper investigates the generation of harmonics in adaptive feedforward cancellation schemes specifically it is shown that an algorithm designed to reject a certain number of frequency components may in fact be capable of reducing higher order harmonics as well this effect originates in the time variation of the adaptive parameters a consequence is that the adaptive system may perform better than the algorithm with the fixed ideal parameters surprisingly the response to higher order harmonics can be calculated precisely using a laplace transform analysis the origin of the numerical procedure is in the equivalence between the adaptive feedforward cancellation scheme and a control scheme based on the internal model principle the implication of the results on design and implementation issues is discussed

adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequency abstract two algorithms are presented for the rejection of sinusoidal disturbances with unknown frequency the first is an indirect algorithm where the frequency of the disturbance is estimated and the estimate is used in another adaptive algorithm that adjusts the magnitude and phase of the input needed to cancel the effect of the disturbance a direct algorithm that uses the concept of a phase locked loop is also presented in which frequency estimation and disturbance cancellation are performed simultaneously approximate analyses are presented for both schemes and the results are found useful for the selection of the design parameters simulations are given which demonstrate the validity of the analytical results and the ability of the algorithms to reject sinusoidal disturbances with unknown frequency the indirect algorithm is found to have a larger capture region for the parameter estimates whereas the direct algorithm has superior convergence properties locally about the optimum parameter estimates

a generalized optimal set of discriminant vectors abstract a generalized optimal set of discriminant vectors for linear feature extraction is presented first the criteria of selecting the generalized optimal discriminant vectors are introduced and then a unified solving method is derived to solve the vectors of the generalized optimal set in both cases of a large number of samples and a small number of samples the experimental results show that the present method is superior to the foley sammon method foley and sammon ieee trans comput 24 281 289 1975 the positive pseudoinverse method tian et al opt engng 25 7 834 839 1986 the perturbation method hong and yang pattern recognition 24 317 324 1991 and the matrix rank decomposition method cheng et al pattern recognition 25 101 111 1992 in terms of correct classification rate

asymptotic rejection of general periodic disturbances in output feedback nonlinear systems this note deals with asymptotic rejection of general periodic disturbances in nonlinear systems a novel approach based on integrations over the half of disturbance period is proposed to estimate disturbances which may not be harmonic or even smooth the proposed algorithm uses the period and the knowledge of the basic disturbance patterns while the amplitude and phase of the disturbances are unknown and they are estimated based on the estimated disturbance the disturbance rejection algorithm is then proposed for linear systems and nonlinear systems in the output feedback format which asymptotically rejects the periodical disturbances the proposed algorithm extends asymptotic rejection of unknown disturbances from sinusoidal disturbances to a more general class of periodical disturbances which includes zero mean square waves symmetric triangular waves etc

learning control for nonlinear systems in output feedback form abstract the class of single input single output minimum phase nonlinear time invariant systems with unknown output dependent nonlinearities unknown parameters and known relative degree is considered the output regulation problem is addressed and solved in the presence of unknown periodic reference and or disturbance signals of known common period a simple learning control algorithm is designed which guarantees asymptotic output tracking for any initial condition belonging to any given connected compact set it can be interpreted as a generalization of the classical pid 1 control which solves the regulator problem when reference and disturbance signals are constant as far as linear systems are concerned global results are achieved