hilbert space description on nonlinear discrete time dynamical systems it is shown that the linear recurrences of the form xn 1 xn where is analytic in xn can be brought down to a linear recurrence in hilbert space with the boson displacement operator

time independent invariants of motion for the quadratic system a hamiltonian method is developed to obtain first integrals of the form p qmu and p qmu rnu for a general system of two dimensional autonomous ordinary differential equations with quadratic terms where p q and r are linear or quadratic polynomials and mu nu are two real numbers it is found that there is an intimate relationship between the polynomials and the equilibrium points of the system which is useful for determining the existence of periodic orbits and asymptotic behaviour

painleve property and constants of the motion of the complex lorenz model the results of the painleve analysis and of a search for constants of the motion of the complex lorenz model are presented

speech perception in gated noise the effects of temporal resolution previous investigations have suggested that hearing impaired hi listeners have reduced masking release mr compared to normal hearing listeners nh when they listen in modulated noise the current study examined the following questions that have not been clearly answered first when hi listeners are amplified so that their performance is equal to that of nh listeners in quiet and in steady noise do hi listeners still show reduced mr with modulated noise when compared to nh listeners second is the masking release the same for sentences and cv syllables third does forward masking significantly contribute to the variability in performance among hi listeners to compensate for reduced hearing sensitivity for hi listeners the spectrum levels of both speech and noise were adjusted based on the individual hearing loss there was no significant difference between the performance of nh listeners and that of hi listeners in steady noise and in quiet however the amount of mr for sentences and for cv syllables was significantly reduced for hi listeners for sentence recognition the amount of mr seemed to be more related to hearing sensitivity for low to mid frequencies than to forward masking in contrast forward masking thresholds appear to be a major contributor to the amount of mr for syllable recognition

integrals of motion for three dimensional non hamiltonian dynamical systems the problem of finding integrals of motion of three dimensional dynamical systems is analysed the authors introduce a new type of direct method in the search of parameter values for which an integral of motion exists this method consists in proposing an ansatz for the integral that explicitly shows the dependence with respect to one of the phase space coordinates of the system they apply this procedure to the reduced three wave interaction problem and to the rabinovich system for both models new integrals of motion are found

a non linear stochastic differential equation exact critical statics and dynamics abstract the nonlinear stochastic differential equation we present is a generalization of a class of equations describing various physical and chemical systems coupled to external sources of noise the static behaviour of this system exhibits first and second order nonequilibrium transitions which are purely induced by the external noise exact analytical expressions for the time dependent solutions are found

investigation of painleve property under time singularities transformations in this paper the relation between the painleve property for ordinary differential equations and some coordinate transformations in the complex plane is investigated two sets of transformations are introduced for which the transformations of singularities structure in the complex plane are explicitly computed the first set acts only on the dependent variables while the second one acts also on the independent variables it allows for defining an extended painleve test which is coordinates invariant our results are applied on various problems arising in the singularity analysis such as the problem of negative resonances and the weak painleve conjecture the method for finding new first integrals for dynamical systems is also shown

improved multi kernel classification machine with nystrom approximation technique kernelized modification of ho kashyap algorithm with squared approximation of the misclassification errors kmhks is an effective algorithm for nonlinearly separable classification problems while kmhks only adopts one kernel function so a multi kernel classification machine with reduced complexity named nystrom approximation matrix with multiple kmhkss nmkmhks has been developed but nmkmhks has to initialize many parameters and has not an ability to deal with noise well to this end we propose an improved multi kernel classification machine with nystrom approximation technique inmkmhks inmkmhks is based on a new way of generating kernel functions and a new nystrom approximation technique the contributions of inmkmhks are that 1 avoiding the problem of setting too many parameters 2 keeping comparable space and computational complexities after comparing with nmkmhks 3 having a tighter generalization risk bound in terms of rademacher complexity analysis 4 having a better recognition than nmkmhks on average 5 possessing an ability to deal with noise and practical images highlightsavoiding the problem of setting some initial parameters keeping a comparable space and computational complexities having a tighter generalization risk bound having a better recognition than nmkmhks on average possessing an ability to deal with noise and practical images

first integrals of autonomous systems of differential equations and the prelle singer procedure the prelle singer procedure for determining elementary first integrals of two dimensional autonomous systems of ordinary differential equations is introduced and how it can be generalized to higher dimensions is discussed the application of this procedure in several dynamical systems is reported

objective measures of listener envelopment this paper reports the results of subjective studies to determine objective predictors of perceived listener envelopment in concert halls subjects seated in an anechoic room were exposed to simulated sound fields that were expected to have varied listener envelopment as independent variables the reverberation time the early to late sound ratio the overall sound level and the angular distribution of the late arriving sound levels were varied all of these factors had statistically significant effects on perceived listener envelopment the results indicate however that the angular distribution of the late arriving sound and the overall level would have the largest effects in real concert halls thus listener envelopment depends on having strong lateral reflections arriving at the listener 80 ms or more after the direct sound several objective measures correlated significantly with listener envelopment however a new measure the late lateral sound level as measured using a figure of eight microphone was found to be both conceptually simple and a very good predictor of the perceived listener envelopment of the sound fields in this experiment

a geometrical method towards first integrals for dynamical systems we develop a method based on darboux s and liouville s works to find first integrals and or invariant manifolds for a physically relevant class of dynamical systems without making any assumption on these elements forms we apply it to three dynamical systems lotka volterra lorenz and rikitake

the kronecker product and stochastic automata networks this paper can be thought of as a companion paper to van loan s the ubiquitous kronecker product paper j comput appl math 123 2000 85 we collect and catalog the most useful properties of the kronecker product and present them in one place we prove several new properties that we discovered in our search for a stochastic automata network preconditioner we conclude by describing one application of the kronecker product omitted from van loan s list of applications namely stochastic automata networks

families of invariants of the motion for the lotka volterra equations the linear polynomials family the modified carleman embedding method already introduced by the authors to find first integrals invariants of the motion of polynomial form to the lotka volterra system is described in detail and its efficiency to treat the n dimensional system proved using this method an extensive investigation is performed for polynomials of the first degree which allow a classification of the integrals in three families for some systems possessing one invariant it is possible to find a second invariant using rescaling methods they represent very restrictive solutions implying that there exists a great number of conditions among the equation s coefficients to satisfy a proof is given that the volterra invariants can be deduced as a limit finally the interesting properties of the solutions of these systems are studied in detail

generalized hamiltonian structures for systems in three dimensions with a rescalable constant of motion the generalized hamiltonian structures of several three dimensional dynamical systems of interest in physical applications are considered in general hamiltonians exist only for systems that possess at least one time independent constant of motion systems with only time dependent constants of motion may sometimes be rescaled and their constant of motion made time independent when this is possible the transformed system may be cast in a generalized hamiltonian formalism with non canonical structure functions

analytical approach to initial value problems in nonlinear systems a method based on the equivalence between finite dimensional nonlinear and infinite dimensional linear systems of ordinary differential equations is presented in order to calculate the time dependent solutions of nonlinear physico chemical systems the solution is cast in the form of power series whose general term is known analytically

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

stable local dimensionality reduction approaches dimensionality reduction is a big challenge in many areas a large number of local approaches stemming from statistics or geometry have been developed however in practice these local approaches are often in lack of robustness since in contrast to maximum variance unfolding mvu which explicitly unfolds the manifold they merely characterize local geometry structure moreover the eigenproblems that they encounter are hard to solve we propose a unified framework that explicitly unfolds the manifold and reformulate local approaches as the semi definite programs instead of the above mentioned eigenproblems three well known algorithms locally linear embedding lle laplacian eigenmaps le and local tangent space alignment ltsa are reinterpreted and improved within this framework several experiments are presented to demonstrate the potential of our framework and the improvements of these local algorithms

two stage regularized linear discriminant analysis for 2 d data fisher linear discriminant analysis lda involves within class and between class covariance matrices for 2 d data such as images regularized lda rlda can improve lda due to the regularized eigenvalues of the estimated within class matrix however it fails to consider the eigenvectors and the estimated between class matrix to improve these two matrices simultaneously we propose in this paper a new two stage method for 2 d data namely a bidirectional lda blda in the first stage and the rlda in the second stage where both blda and rlda are based on the fisher criterion that tackles correlation blda performs the lda under special separable covariance constraints that incorporate the row and column correlations inherent in 2 d data the main novelty is that we propose a simple but effective statistical test to determine the subspace dimensionality in the first stage as a result the first stage reduces the dimensionality substantially while keeping the significant discriminant information in the data this enables the second stage to perform rlda in a much lower dimensional subspace and thus improves the two estimated matrices simultaneously experiments on a number of 2 d synthetic and real world data sets show that blda rlda outperforms several closely related competitors

poisson structure of dynamical systems with three degrees of freedom it is shown that the poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one form in three dimensions advantage is taken of this fact and the theory of foliations is used in discussing the geometrical structure underlying complete and partial integrability techniques for finding poisson structures are presented and applied to various examples such as the halphen system which has been studied as the two monopole problem by atiyah and hitchin it is shown that the halphen system can be formulated in terms of a flat sl 2 r valued connection and belongs to a nontrivial godbillon vey class on the other hand for the euler top and a special case of three species lotka volterra equations which are contained in the halphen system as limiting cases this structure degenerates into the form of globally integrable bi hamiltonian structures the globally integrable bi hamiltonian case is a linear and the sl 2 r structure is a quadratic unfolding of an integrable one form in 3 1 dimensions it is shown that the existence of a vector field compatible with the flow is a powerful tool in the investigation of poisson structure and some new techniques for incorporating arbitrary constants into the poisson one form are presented herein this leads to some extensions analogous to q extensions of poisson structure the kermack mckendrick model and some of its generalizations describing the spread of epidemics as well as the integrable cases of the lorenz lotka volterra may leonard and maxwell bloch systems admit globally integrable bi hamiltonian structure

backlund transformations for nonlinear evolution equations hilbert space approach abstract a new method of determining backlund transformations for nonlinear partial differential equations of the evolution type is introduced using the hilbert space approach the problem of finding backlund transformations is brought down to the solution of an abstract equation in hilbert space

painleve analysis yoshida s theorems and direct methods in the search for integrable hamiltonians treating as an example two dimensional similarity invariant hamiltonians with polynomial velocity dependent potentials the authors show how painleve analysis yoshida s theorems and direct methods can be combined in the search for integrable hamiltonians new integrable systems are found one of which has a polynomial second invariant of fifth order in the momenta most of the necessary calculations have been performed by applying various reduce packages developed for that purpose

symmetries and first integrals for dissipative systems the connection between symmetries time independent and time dependent first integrals for autonomous systems of first order ordinary differential equations is discussed several new results which have been obtained by applying a reduce package are reported

systems of ordinary differential equations with nonlinear superposition principles abstract this work is concerned with the derivation of superposition rules which express the general solution of ordinary differential equations x x t x r n t r in terms of a finite number of particular solutions the point of departure is lie s criterion according to which such a rule exists if and only if the vector fields x t generate a finite dimensional lie algebra we provide three different constructive methods for deriving superposition rules and apply them to systems of coupled riccati equations of the projective and conformal types based respectively on the lie algebra sl n 1 r and o p 1 n p 1

comments on global dynamics of the generalized lorenz systems having invariant algebraic surfaces abstract in the recent paper global dynamics of the generalized lorenz systems having invariant algebraic surfaces published in physica d the authors study the generalized lorenz system x a y x y b x c y x z z d z x y and consider the subclass of these systems which have an invariant algebraic surface within this subclass they present their global dynamics via the blow up and poincare compactification in this comment we argue that the results presented in the commented paper can be directly obtained from the well known results on global dynamics of the lorenz system having invariant algebraic surfaces to achieve it we use the equivalence existing under generic conditions c 0 between the lorenz system and the generalized lorenz system by means of a linear scaling in time and coordinates on the other hand their study is not complete because a case is missed in the list of six invariant algebraic surfaces in the generalized lorenz system considered by the authors we also analyze here the global dynamics in this seventh situation

necessary and sufficient conditions for finite time singularities in ordinary differential equations abstract this paper gives a theorem which provides necessary and sufficient conditions for the existence of a real finite value of the independent variable at which the general solution of a certain class of ordinary differential equations diverges to infinity this class is a large subset of the set of all autonomous non linear polynomial ordinary differential equation these conditions involve the asymptotic form of the local series representation for the general solutions around the singularities and can be checked algorithmically

solutions in closed form and as power series to the real lorenz equations using the method of the lie theory of extended groups and for the parameter values b 1 and r 0 we construct explicitly the general exact solution to the real lorenz equations in terms of jacobian elliptic functions in the context of our approach further possible completely integrable cases of the lorenz system are discussed by considering the result of the painleve analysis for 1 b 2 and r 1 9 and negative values of r the latter case r 0 and 0 not following from the painleve test for other positive parameter values and in the form of appropriate power series we find some particular exact solutions which do not possess the painleve property

invariant algebraic surfaces of the lorenz system in this paper we provide a complete classification of the darboux invariants of the irreducible darboux polynomials of the rational first integrals and of the algebraic integrability for the classical lorenz system s y x rx y xz z bz xy in the proofs we use the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations

dynamics of the lorenz system having an invariant algebraic surface in this paper we characterize all dynamics of the lorenz system x s y x y rx xz y z xy bz having an invariant algebraic surface

extracting the optimal dimensionality for local tensor discriminant analysis supervised dimensionality reduction with tensor representation has attracted great interest in recent years it has been successfully applied to problems with tensor data such as image and video recognition tasks however in the tensor based methods how to select the suitable dimensions is a very important problem since the number of possible dimension combinations exponentially increases with respect to the order of tensor manually selecting the suitable dimensions becomes an impossible task in the case of high order tensor in this paper we aim at solving this important problem and propose an algorithm to extract the optimal dimensionality for local tensor discriminant analysis experimental results on a toy example and real world data validate the effectiveness of the proposed method

nonlinear dynamical systems and classical orthogonal polynomials it is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract schrodinger equation in hilbert space with boson hamiltonian the fourier coefficients of the expansion of solutions to the schrodinger equation in the particular occupation number representation are expressed by means of the classical orthogonal polynomials the introduced formalism amounts to a generalization of the classical methods for linearization of nonlinear differential equations such as the carleman embedding technique and koopman approach

formal and analytic integrability of the lorenz system the well known lorenz system can be written as and here we study the first integrals of the lorenz system that can be described by formal power series in particular if s 0 and either b is not a negative rational number or b is a negative rational number and k1b k2 1 s 0 for all k1 and k2 non negative integers with k1 k2 0 then the lorenz system has no analytic first integrals in a neighbourhood of the origin

lorenz integrable system moves a la poinsot a transformation is derived which takes the lorenz integrable system into the well known euler equations of a torque free rigid body about a fixed point i e the famous motion a la poinsot the proof is based on lie group analysis applied to two third order ordinary differential equations admitting the same two dimensional lie symmetry algebra lie s classification of two dimensional symmetry algebras in the plane is used if the same transformation is applied to the lorenz system with any values of the parameters then one obtains euler equations of a rigid body about a fixed point subjected to a torsion depending on time and angular velocity the numerical solution of this system yields a three dimensional picture which looks like a tornado the cross section of which has a butterfly shape thus lorenz s butterfly has been transformed into a tornado

discriminative embedded clustering a framework for grouping high dimensional data in many real applications of machine learning and data mining we are often confronted with high dimensional data how to cluster high dimensional data is still a challenging problem due to the curse of dimensionality in this paper we try to address this problem using joint dimensionality reduction and clustering different from traditional approaches that conduct dimensionality reduction and clustering in sequence we propose a novel framework referred to as discriminative embedded clustering which alternates them iteratively within this framework we are able not only to view several traditional approaches and reveal their intrinsic relationships but also to be stimulated to develop a new method we also propose an effective approach for solving the formulated nonconvex optimization problem comprehensive analyses including convergence behavior parameter determination and computational complexity together with the relationship to other related approaches are also presented plenty of experimental results on benchmark data sets illustrate that the proposed method outperforms related state of the art clustering approaches and existing joint dimensionality reduction and clustering methods

carleman embedding and lyapunov exponents we investigate the solutions of those autonomous systems with quadratic nonlinearities in a n dimensional vector space together with the solutions of their first variational equation systems by means of the carleman embedding an iterative procedure based on this result is developed to evaluate the lyapunov exponents of the considered systems we test the method by giving some results for the lyapunov exponents of the lorenz model

structure of normal form series for non analytical vector fields and generalized resonances this paper is devoted to the study of normal form transformations and resonances the usual theory of normal forms is formulated in a more general context the quasi monomial formalism in which negative and non integer exponents are accepted the general coefficient of the poincareseries is explicitly constructed in the non resonant case for any qm system from there arises the necessity to generalize resonances to non analytical vector fields using particular changes of parameterization we extend this resonance relation to the nonlinear part of the vector field the changes of variables that arise from this provide approximations of the solutions far from the fixed point

a novel multi view learning developed from single view patterns the existing multi view learning mvl learns how to process patterns with multiple information sources in generalization this mvl is proven to have a significant advantage over the usual single view learning svl however in most real world cases we only have single source patterns to which the existing mvl is unable to be directly applied this paper aims to develop a new mvl technique for single source patterns to this end we first reshape the original vector representation of single source patterns into multiple matrix representations in doing so we can change the original architecture of a given base classifier into different sub ones each newly generated sub classifier can classify the patterns represented with the matrix here each sub classifier is taken as one view of the original base classifier as a result a set of sub classifiers with different views are come into being then one joint rather than separated learning process for the multi view sub classifiers is developed in practice the original base classifier employs the vector pattern oriented ho kashyap classifier with regularization learning called mhks as a paradigm which is not limited to mhks thus the proposed joint multi view learning is named as multiv mhks finally the feasibility and effectiveness of the proposed multiv mhks is demonstrated by the experimental results on benchmark data sets more importantly we have demonstrated that the proposed multi view approach generally has a tighter generalization risk bound than its single view one in terms of the rademacher complexity analysis

integrating the nonintegrable analytic structure of the lorenz system revisited abstract a study of the complex time analytic structure of the lorenz system in nonintegrable parameter regimes reveals the special sets of parameter values for which one time dependent integral of motion exists furthermore the analysis yields the exact form of the part of the integral with the highest homogeneous weight and a method to construct the rest of the integral recursive clustering of singularities in the chaotic regimes of the system is observed in computer studies and explained by a simple analytic argument the analytic techniques used in these studies a systematic resummation of a logarithmic psi series appears to be quite general and can provide explicit representations of a solution even in the chaotic regimes in the neighborhood of a given movable singularity furthermore we suggest that this technique provides a type of renormalization program to study a wide class of nonintegrable systems

multiple rank multi linear svm for matrix data classification matrices or more generally multi way arrays tensors are common forms of data that are encountered in a wide range of real applications how to classify this kind of data is an important research topic for both pattern recognition and machine learning in this paper by analyzing the relationship between two famous traditional classification approaches i e svm and stm a novel tensor based method i e multiple rank multi linear svm mrmlsvm is proposed different from traditional vector based and tensor based methods multiple rank left and right projecting vectors are employed to construct decision boundary and establish margin function we reveal that the rank of transformation can be regarded as a tradeoff parameter to balance the capacity of learning and generalization in essence we also proposed an effective approach to solve the proposed non convex optimization problem the convergence behavior initialization computational complexity and parameter determination problems are analyzed compared with vector based classification methods mrmlsvm achieves higher accuracy and has lower computational complexity compared with traditional supervised tensor based methods mrmlsvm performs better for matrix data classification promising experimental results on various kinds of data sets are provided to show the effectiveness of our method highlightswe have proposed a novel method i e mrmlsvm for matrix data classification we have revealed the essence of mrmlsvm from the view of learning theory we have provided an effective way to solve the proposed non convex problem our proposed approach is a common model and mrmlsvm is just an instance

exponential factors and darbouxian first integrals of the lorenz system in this article we characterize all the exponential factors and the darbouxian first integrals for the lorenz system s y x rx y xz z bz xy in the proofs we use the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations

connection between the existence of first integrals and the painleve property in two dimensional lotka volterra and quadratic systems taking advantage of the considerable amount of work done in the search for first integrals invariants for the two dimensional lotka volterra system and the quadratic system lvs and qs we compare the relations needed to exhibit invariants one for the lvs at least three for the qs to the two conditions of the painleve test index and compatibility we find that eventually restricting the invariants to those which are analytic all exponents integers and thereby adding new constraints these constraints always coalesce with the two painleve conditions we conclude that straightforward application of the painleve test picks up only these simple analytic invariants and that possession of the painleve property is too strong a condition for the existence of the invariants

occurrence of secular terms in the carleman embedding secular terms occur in many perturbative solutions of nonlinear equation systems in this work an investigation is made of which cases they may occur in as the result of the application of the linear carleman embedding to a system of nonlinear equations the solution for the embedded system is written in a form that makes it convenient to see how these terms originate their occurrence for the general case is discussed and the results are exemplified by working out the henon heiles system

complex singularities and the lorenz attractor the lorenz attractor is one of the best known examples of applied mathematics however much of what is known about it is a result of numerical calculations and not of mathemat ical analysis as a step toward mathematical analysis we allow the time variable in the three dimensional lorenz system to be complex hoping that solutions that have resisted analysis on the real line will give up their secrets in the complex plane knowledge of singularities being fundamental to any investigation in the complex plane we build upon earlier work and give a complete and consistent formal development of complex singular ities of the lorenz system using the psi series the psi series contain two undetermined constants in addition the location of the singularity is undetermined as a consequence of the autonomous nature of the lorenz system we prove that the psi series converge using a technique that is simpler and more powerful than that of hille thus implying a two parameter family of singular solutions of the lorenz system we pose three ques tions answers to which may bring us closer to understanding the connection of complex singularities to lorenz dynamics

linearization transformations for non linear dynamical systems hilbert space approach abstract a new method for the linearization of non linear dynamical systems with both a finite and an infinite number of degrees of freedom is introduced using the hilbert space approach the problem of finding the linearization transformations is reduced to the solution of abstract linear equations in hilbert space

space time memory functions and solution of nonlinear evolution equations a new approach is presented for solving a certain class of nonlinear partial differential equations a space time memory function r t is introduced to exactly convert a given nonlinear evolution equation into the following linear form t f r t r f r t t0dt dr r r t t f r t a markovian integro differential operator r and the memory function r t reflect the nonlinearity and are determined depending on a given initial condition the approach is useful if higher order memory functions associated with are insensitive to approximation the korteweg de vries equation is treated as an example for certain initial profiles the memory function is shown to be identically zero and we find exact linear partial differential equations leading to the single and the two soliton solution in the case of the three soliton solution the second order memory function vanishes exactly and r t is found to be a single exponential function of t a new approach is presented for solving a certain class of nonlinear partial differential equations a space time memory function r t is introduced to exactly convert a given nonlinear evolution equation into the following linear form t f r t r f r t t0dt dr r r t t f r t a markovian integro differential operator r and the memory function r t reflect the nonlinearity and are determined depending on a given initial condition the approach is useful if higher order memory functions associated with are insensitive to approximation the korteweg de vries equation is treated as an example for certain initial profiles the memory function is shown to be identically zero and we find exact linear partial differential equations leading to the single and the two soliton solution in the case of the three soliton solution the second order memory function vanishes exactly and r t is found to be a single exponential function of t

matrixized learning machine with modified pairwise constraints matrix pattern oriented classifier design matcd has been demonstrated to be effective in terms of the classification performance since it utilizes two sided weight vectors to constrain the matrix based patterns however the existing matcd might not be able to acquire the prior distribution knowledge such as the relationship between two patterns inspired by the pairwise constraints pc method i e must links and cannot links between the patterns this paper introduces a new regularization term named rp with a modified pc method into matcd the new classifier design strategy is expected to not only learn the structural information of each pattern itself but also acquire the prior distribution knowledge about each constrained pair with both the discrimination metric from the traditional pc and the spatial distance measure from the heat kernel method in practice this paper selects one typical matrixized classifier named matmhks as the basic building block and introduces the term rp into it the newly proposed classifier is named mlmmpc and the subsequent experiments validate the effectiveness of it two major contributions of this paper can be concluded as 1 improving the existing matrix pattern oriented classifier design techniques and 2 modifying the traditional pc method by combining the discrimination metric and the distance measure together highlightsa novel matrix oriented classification algorithm named mlmmpc is proposed to improve the original matrix learning framework by a new regularization term r p to combine pairwise constraints and spatial measure together in r p implementability is demonstrated on both image and vector based datasets

forward and simultaneous masked thresholds in bandlimited maskers in subjects with normal hearing and cochlear hearing loss forward and simultaneous masked thresholds were measured at 0 5 and 2 0 khz in bandpass maskers as a function of masker bandwidth and in a broadband masker with the goal of estimating psychophysical suppression suppression was operationally defined in two ways 1 as a change in forward masked threshold as a function of masker bandwidth and 2 as a change in effective masker level with increased masker bandwidth taking into account the nonlinear growth of forward masking subjects were younger adults with normal hearing and older adults with cochlear hearing loss thresholds decreased as a function of masker bandwidth in forward masking which was attributed to effects of suppression thresholds remained constant or increased slightly with increasing masker bandwidth in simultaneous masking for subjects with normal hearing slightly larger estimates of suppression were obtained at 2 0 khz rather than at 0 5 khz for hearing impaired subjects suppression was reduced in regions of hearing loss the magnitude of suppression was strongly correlated with the absolute threshold at the signal frequency but did not vary with thresholds at frequencies remote from the signal the results suggest that measuring forward masked thresholds in bandlimited and broadband maskers may be an efficient psychophysical method for estimating suppression

forward masking adaptation or integration the aim of this study was to attempt to distinguish between neural adaptation and persistence or temporal integration as possible explanations of forward masking thresholds were measured for a sinusoidal signal as a function of signal duration for conditions where the delay between the masker offset and the signal offset the offset offset interval was fixed the masker was a 200 ms broadband noise presented at a spectrum level of 40 db re 20 pa and the signal was a 4 khz sinusoid gated with 2 ms ramps the offset offset interval was fixed at various durations between 4 and 102 ms and signal thresholds were measured for a range of signal durations at each interval a substantial decrease in thresholds was observed with increasing duration for signal durations up to about 20 ms at short offset offset intervals the amount of temporal integration exceeded that normally found in quiet the results were simulated using models of temporal integration the temporal window model and adaptation for both models the inclusion of a peripheral nonlinearity similar to that observed physiologically in studies of the basilar membrane was essential in producing a good fit to the data both models were about equally successful in accounting for the present data however the temporal window model provided a somewhat better account of similar data from a simultaneous masking experiment using the same parameters this suggests that the linear time invariant properties of the temporal window approach are appropriate for modeling forward masking overall the results confirm that forward masking can be described in terms of peripheral nonlinearity followed by linear temporal integration at higher levels in the auditory system however the difference in predictions between the adaptation and integration models is relatively small meaning that influence of adaptation cannot be ruled out

integrals of motion for the lorenz system a direct method is proposed for determining the conditions under which the lorenz system is integrable this method uses only leading singular behavior to recover all known integrals of motion together with a few new ones

psychophysical suppression measured with bandlimited noise extended below and or above the signal effects of age and hearing loss the objectives of this study were to measure suppression with bandlimited noise extended below and above the signal at lower and higher signal frequencies between younger and older subjects and between subjects with normal hearing and cochlear hearing loss psychophysical suppression was assessed by measuring forward masked thresholds at 0 8 and 2 0 khz in bandlimited maskers as a function of masker bandwidth bandpass masker bandwidth was increased by introducing noise components below and above the signal frequency while keeping the noise centered on the signal frequency and also by adding noise below the signal only and above the signal only subjects were younger and older adults with normal hearing and older adults with cochlear hearing loss for all subjects suppression was larger when noise was added below the signal than when noise was added above the signal consistent with some physiological evidence of stronger suppression below a fiber s characteristic frequency than above for subjects

cuing effects for informational masking the detection of a tone added to a random frequency multitone masker can be very poor even when the maskers have little energy in the frequency region of the signal this paper examines the effects of adding a pretrial cue to reduce uncertainty for the masker or the signal the first two experiments examined the effect of cuing a fixed frequency signal as the number of masker components and presentation methods were manipulated cue effectiveness varied across observers but could reduce thresholds by as much as 20 db procedural comparisons indicated observers benefited more from having two masker samples to compare with or without a signal cue than having a single interval with one masker sample and a signal cue the third experiment used random frequency signals and compared no cue signal cue and masker cue conditions and also systematically varied the time interval between cue offset and trial onset thresholds with a cued random frequency signal remained higher than for a cued fixed frequency signal for time intervals between the cue and trial of 50 ms or longer thresholds were approximately the same with a signal or a masker cue and lower than when there was no cue without a cue or with a masker cue analyses of possible decision strategies suggested observers attended to the potential signal frequencies particularly the highest signal frequency with a signal cue observers appeared to attend to the frequency of the subsequent signal

robust multicategory support matrix machines we consider the classification problem when the input features are represented as matrices rather than vectors to preserve the intrinsic structures for classification a successful method is the support matrix machine smm in 19 which optimizes an objective function with a hinge loss plus a so called spectral elastic net penalty however the issues of extending smm to multicategory classification still remain moreover in practice it is common to see the training data contaminated by outlying observations which can affect the robustness of existing matrix classification methods in this paper we address these issues by introducing a robust angle based classifier which boils down binary and multicategory problems to a unified framework benefitting from the use of truncated hinge loss functions the proposed classifier achieves certain robustness to outliers the underlying optimization model becomes nonconvex but admits a natural dc difference of two convex functions representation we develop a new and efficient algorithm by incorporating the dc algorithm and primal dual first order methods together the proposed dc algorithm adaptively chooses the accuracy of the subproblem at each iteration while guaranteeing the overall convergence of the algorithm the use of primal dual methods removes a natural complexity of the linear operator in the subproblems and enables us to use the proximal operator of the objective functions and matrix vector operations this advantage allows us to solve large scale problems efficiently theoretical and numerical results indicate that for problems with potential outliers our method can be highly competitive among existing methods

groupwise retargeted least squares regression in this brief we propose a new groupwise retargeted least squares regression grelsr model for multicategory classification the main motivation behind grelsr is to utilize an additional regularization to restrict the translation values of relsr so that they should be similar within same class by analyzing the regression targets of relsr we propose a new formulation of relsr where the translation values are expressed explicitly on the basis of the new formulation discriminative least squares regression can be regarded as a special case of relsr with zero translation values moreover a groupwise constraint is added to relsr to form the new grelsr model extensive experiments on various machine leaning data sets illustrate that our method outperforms the current state of the art approaches

tensor rank preserving discriminant analysis for facial recognition facial recognition one of the basic topics in computer vision and pattern recognition has received substantial attention in recent years however for those traditional facial recognition algorithms the facial images are reshaped to a long vector thereby losing part of the original spatial constraints of each pixel in this paper a new tensor based feature extraction algorithm termed tensor rank preserving discriminant analysis trpda for facial image recognition is proposed the proposed method involves two stages in the first stage the low dimensional tensor subspace of the original input tensor samples was obtained in the second stage discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition on the one hand the proposed trpda algorithm fully utilizes the natural structure of the input samples and it applies an optimization criterion that can directly handle the tensor spectral analysis problem thereby decreasing the computation cost compared those traditional tensor based feature selection algorithms on the other hand the proposed trpda algorithm extracts feature by finding a tensor subspace that preserves most of the rank order information of the intra class input samples experiments on the three facial databases are performed here to determine the effectiveness of the proposed trpda algorithm

lie symmetries of the lorenz model abstract we study the generalized symmetries of the lorenz model to find the parameter values at which one or more time dependent integrals of motion exist in these cases the integrals are found trivially from the symmetries themselves a complete study of the one completely algebraically integrable case shows a the dynamics can be integrated exactly by reducing it first to a lower dimensional system b the symmetry vector field is hamiltonian these facts hold for other dissipative completely integrable dynamical systems as well the analytic study of a natural two form reveals that it is an entire function of time the foliation of phase space induced by the two form for the partially integrable cases has a simple description in terms of the coefficients occurring in the laurent series expansions of the dependent variables

integrability partial integrability and nonintegrability for systems of ordinary differential equations the integrability of systems of ordinary differential equations with polynomial vector fields is investigated by using the singularity analysis methods three types of results are obtained first a general relationship between the degrees of first integrals and the so called kowalevskaya exponents is derived second it is shown that all solutions of algebraically integrable systems can be expanded in puiseux series third a new method to study partially integrable systems is studied these different aspects allow us to study algorithmically the integrability partial integrability and nonintegrability of differential systems

multilinear discriminant analysis for face recognition there is a growing interest in subspace learning techniques for face recognition however the excessive dimension of the data space often brings the algorithms into the curse of dimensionality dilemma in this paper we present a novel approach to solve the supervised dimensionality reduction problem by encoding an image object as a general tensor of second or even higher order first we propose a discriminant tensor criterion whereby multiple interrelated lower dimensional discriminative subspaces are derived for feature extraction then a novel approach called k mode optimization is presented to iteratively learn these subspaces by unfolding the tensor along different tensor directions we call this algorithm multilinear discriminant analysis mda which has the following characteristics 1 multiple interrelated subspaces can collaborate to discriminate different classes 2 for classification problems involving higher order tensors the mda algorithm can avoid the curse of dimensionality dilemma and alleviate the small sample size problem and 3 the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in k mode optimization we provide extensive experiments on orl cmu pie and feret databases by encoding face images as second or third order tensors to demonstrate that the proposed mda algorithm based on higher order tensors has the potential to outperform the traditional vector based subspace learning algorithms especially in the cases with small sample sizes

rank optimized logistic matrix regression toward improved matrix data classification while existing logistic regression suffers from overfitting and often fails in considering structural information we propose a novel matrix based logistic regression to overcome the weakness in the proposed method 2d matrices are directly used to learn two groups of parameter vectors along each dimension without vectorization which allows the proposed method to fully exploit the underlying structural information embedded inside the 2d matrices further we add a joint norm on two parameter matrices which are organized by aligning each group of parameter vectors in columns this added co regularization term has two roles enhancing the effect of regularization and optimizing the rank during the learning process with our proposed fast iterative solution we carried out extensive experiments the results show that in comparison to both the traditional tensor based methods and the vector based regression methods our proposed solution achieves better performance for matrix data classifications

msdlsr margin scalable discriminative least squares regression for multicategory classification in this brief we propose a new margin scalable discriminative least squares regression msdlsr model for multicategory classification the main motivation behind the msdlsr is to explicitly control the margin of dlsr model we first prove that the dlsr is a relaxation of the traditional l 2 support vector machine based on this fact we further provide a theorem on the margin of dlsr with this theorem we add an explicit constraint on dlsr to restrict the number of zeros of dragging values so as to control the margin of dlsr the new model is called msdlsr theoretically we analyze the determination of the margin and support vectors of msdlsr extensive experiments illustrate that our method outperforms the current state of the art approaches on various machine leaning and real world data sets

lda qr an efficient and effective dimension reduction algorithm and its theoretical foundation lda qr a linear discriminant analysis lda based dimension reduction algorithm is presented it achieves the efficiency by introducing a qr decomposition on a small size matrix while keeping competitive classification accuracy its theoretical foundation is also presented

bi hamiltonian structure in frenet serret frame abstract we reduce the problem of constructing bi hamiltonian structure in three dimensions to the solutions of a riccati equation in moving coordinates of frenet serret frame all explicitly constructed examples in the literature are exhausted by constant solutions we conclude that in three dimensions vector fields which are not eigenvectors of the curl operator are locally bi hamiltonian

invariant hyperplanes and darboux integrability of polynomial vector fields this paper is composed of two parts in the first part we provide an upper bound for the number of invariant hyperplanes of the polynomial vector fields in n variables this result generalizes those given in artes et al 1998 pac j math 184 207 30 and llibre and rodriguez 2000 bull sci math 124 599 619 the second part gives an extension of the darboux theory of integrability to polynomial vector fields on algebraic varieties

a general time dependent invariant for and integrability of the quadratic system we derive a general time dependent invariant first integral for the quadratic system qs that requires only one condition on the coefficients of the qs the general invariant could yield asymptotic behaviour of phase space trajectories with more conditions imposed on the coefficients the general invariant reduces to polynomial form and is equivalent to polynomial invariants found using a direct method for the special case of a linear polynomial invariant where one of the variables is analytically invertible the solution of the qs is reduced to a quadrature

hilbert space description of classical dynamical systems ii abstract it is shown that classical dynamical systems can be described by a hilbert space schrodinger like equation with the hamiltonian a non hermitian one expressed in terms of bose creation and annihilation operators the presented formalism includes the carleman embedding as the special case

efficient image classification via multiple rank regression the problem of image classification has aroused considerable research interest in the field of image processing traditional methods often convert an image to a vector and then use a vector based classifier in this paper a novel multiple rank regression model mrr for matrix data classification is proposed unlike traditional vector based methods we employ multiple rank left projecting vectors and right projecting vectors to regress each matrix data set to its label for each category the convergence behavior initialization computational complexity and parameter determination are also analyzed compared with vector based regression methods mrr achieves higher accuracy and has lower computational complexity compared with traditional supervised tensor based methods mrr performs better for matrix data classification promising experimental results on face object and hand written digit image classification tasks are provided to show the effectiveness of our method

growth of forward masking for sinusoidal and noise maskers as a function of signal delay implications for suppression in noise the first two experiments were designed to determine whether mutual suppression in broadband noise increases in strength with increasing overall level in experiment i masking functions signal threshold versus masker level were measured in forward masking as a function of the delay time of a 10 ms signal both for a broadband noise masker low pass filtered at 8 khz and for sinusoidal maskers at 1 2 and 4 khz in the latter case the signal frequency equaled the masker frequency for short signal delays the masking functions were steeper for the sinusoidal masker than for the noise masker at longer delays the slopes for both masker types decreased and the slopes for the two masker types became more nearly equal in experiment ii we investigated the effect of gating a low level noise cue with the sinusoidal masker at the longer signal delays the masking functions had equal slopes for the broadband noise masker and the sinusoidal masker with cue at short signal delays the masking functions for sinuso