discontinuous transition from free flow to synchronized flow induced by short range interaction between vehicles in a three phase traffic flow model abstract in this paper we incorporate a limitation on the interaction range between neighboring vehicles into the cellular automaton model proposed by gao and jiang et al k gao r jiang s x hu b h wang and q s wu phys rev e 76 2007 026105 which was established within the framework of kerner s three phase traffic theory and has been shown to be able to reproduce the three phase traffic flow this modification eliminates an unrealistic phenomenon found in the previous model where the velocity adaptation effect between neighboring vehicles can exist even if those vehicles are infinitely far away from each other therefore in the improved model we regulate that such interactions can only occur within a finite distance for simplicity we suppose a constant value to describe this distance in this paper as a result when compared to the previous model the improved model mainly simulates the following results which are believed to be an improvement 1 the improved model successfully reproduces the expected discontinuous transition from free flow to synchronized flow and the related moving synchronized flow pattern which are both absent in the original model but have been observed in real traffic 2 the improved model simulates the correlation functions time headway distributions and optimal velocity functions which are all more consistent with the empirical data than the previous model and most of the other models published before 3 together with the previous two models considering the velocity difference effect this model finally accomplishes a significative process of developing traffic flow models from the traditional fundamental diagram approach to the three phase traffic theory this process should be helpful for us to understand the traffic dynamics and mechanics further and deeper

a class of bounded component analysis algorithms for the separation of both independent and dependent sources bounded component analysis bca is a recent approach which enables the separation of both dependent and independent signals from their mixtures in this approach under the practical source boundedness assumption the widely used statistical independence assumption is replaced by a more generic domain separability assumption this article introduces a geometric framework for the development of bounded component analysis algorithms two main geometric objects related to the separator output samples namely principal hyper ellipsoid and bounding hyper rectangle are introduced the maximization of the volume ratio of these objects and its extensions are introduced as relevant optimization problems for bounded component analysis the article also provides corresponding iterative algorithms for both real and complex sources the numerical examples illustrate the potential advantage of the proposed bca framework in terms of correlated source separation capability as well as performance improvement for short data records

emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces olshausen and field 1996 applied the principle of independence maximization by sparse coding to extract features from natural images this leads to the emergence of oriented linear filters that have simultaneous localization in space and in frequency thus resembling gabor functions and simple cell receptive fields in this article we show that the same principle of independence maximization can explain the emergence of phase and shift invariant features similar to those found in complex cells this new kind of emergence is obtained by maximizing the independence between norms of projections on linear subspaces instead of the independence of simple linear filter outputs the norms of the projections on such independent feature subspaces then indicate the values of invariant features

nonnegative matrix factorization for spectral data analysis data analysis is pervasive throughout business engineering and science very often the data to be analyzed is nonnegative and it is often preferable to take this constraint into account in the analysis process here we are concerned with the application of analyzing data obtained using astronomical spectrometers which provide spectral data which is inherently nonnegative the identification and classification of space objects that cannot be imaged in the normal way with telescopes is an important but difficult problem for tracking thousands of objects including satellites rocket bodies debris and asteroids in orbit around the earth in this paper we develop an effective nonnegative matrix factorization algorithm with novel smoothness constraints for unmixing spectral reflectance data for space object identification and classification purposes promising numerical results are presented using laboratory and simulated datasets

joint independent subspace analysis using second order statistics this paper deals with a novel generalization of classical blind source separation bss in two directions first relaxing the constraint that the latent sources must be statistically independent this generalization is well known and sometimes termed independent subspace analysis isa second jointly analyzing several isa problems where the link is due to statistical dependence among corresponding sources in different mixtures when the data are one dimensional i e multiple classical bss problems this model known as independent vector analysis iva has already been studied in this paper we combine iva with isa and term this new model joint independent subspace analysis jisa we provide full performance analysis of jisa including closed form expressions for minimal mean square error mse fisher information and cramer rao lower bound in the separation of gaussian data the derived mse applies also for non gaussian data when only second order statistics are used we generalize previously known results on iva including its ability to uniquely resolve instantaneous mixtures of real gaussian stationary data and having the same arbitrary permutation at all mixtures numerical experiments validate our theoretical results and show the gain with respect to two competing approaches that either use a finer block partition or a different norm

spin and pseudospin symmetry along with orbital dependency of the dirac hulthen problem abstract the role of the hulthen potential on the spin and pseudospin symmetry solutions is investigated systematically by solving the dirac equation with attractive scalar s r and repulsive vector v r potentials the spin and pseudospin symmetry along with orbital dependency pseudospin orbit and spin orbit dependent couplings of the dirac equation are included to the solution by introducing the hulthen square approximation this effective approach is based on forming the spin and pseudo centrifugal kinetic energy term from the square of the hulthen potential the analytical solutions of the dirac equation for the hulthen potential with the spin orbit and pseudospin orbit dependent couplings are obtained by using the nikiforov uvarov nu method the energy eigenvalue equations and wave functions for various degenerate states are presented for several spin orbital pseudospin orbital and radial quantum numbers under the condition of the spin and pseudospin symmetry

separation theorem for independent subspace analysis and its consequences independent component analysis ica the theory of mixed independent non gaussian sources has a central role in signal processing computer vision and pattern recognition one of the most fundamental conjectures of this research field is that independent subspace analysis isa the extension of the ica problem where groups of sources are independent can be solved by traditional ica followed by grouping the ica components the conjecture called isa separation principle i has been rigorously proven for some distribution types recently ii forms the basis of the state of the art isa solvers iii enables one to estimate the unknown number and the dimensions of the sources efficiently and iv can be extended to generalizations of the isa task such as different linear controlled post nonlinear complex valued partially observed problems as well as to problems dealing with nonparametric source dynamics here we shall review the advances on this field

from traffic and pedestrian follow the leader models with reaction time to first order convection diffusion flow models in this work we derive first order continuum traffic flow models from a microscopic delayed follow the leader model these are applicable in the context of vehicular traffic flow as well as pedestrian traffic flow the microscopic model is based on an optimal velocity function and a reaction time parameter the corresponding macroscopic formulations in eulerian or lagrangian coordinates result in first order convection diffusion equations more precisely the convection is described by the optimal velocity while the diffusion term depends on the reaction time a linear stability analysis for homogeneous solutions of both continuous and discrete models is provided the conditions match those of the car following model for specific values of the space discretization the behavior of the novel model is illustrated thanks to numerical simulations transitions to collision free self sustained stop and go dynamics are obtained if the reaction time is sufficiently large the results show that the dynamics of th

l p nested symmetric distributions in this paper we introduce a new family of probability densities called lp nested symmetric distributions the common property shared by all members of the new class is the same functional form x f x where f is a nested cascade of lp norms x p xi p 1 p lp nested symmetric distributions thereby are a special case of spherical distributions for which f is only required to be positively homogeneous of degree one while both spherical and lp nested symmetric distributions contain many widely used families of probability models such as the gaussian spherically and elliptically symmetric distributions lp spherically symmetric distributions and certain types of independent component analysis ica and independent subspace analysis isa models spherical distributions are usually computationally intractable here we demonstrate that lp nested symmetric distributions are still computationally feasible by deriving an analytic expression for its normalization constant gradients for maximum likelihood estimation analytic expressions for certain types of marginals as well as an exact and efficient sampling algorithm we discuss the tight links of lp nested symmetric distributions to well known machine learning methods such as ica isa and mixed norm regularizers and introduce the nested radial factorization algorithm nrf which is a form of non linear ica that transforms any linearly mixed non factorial lp nested symmetric source into statistically independent signals as a corollary we also introduce the uniform distribution on the lp nested unit sphere

any l state solutions of the hulthen potential by the asymptotic iteration method in this paper we present the analytical solution of the radial schrodinger equation for the hulthen potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any l states we obtain the energy eigenvalues and corresponding eigenfunctions for different screening parameters the wavefunctions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different values in order to demonstrate this the results of the asymptotic iteration method are compared with the results of the supersymmetry numerical integration variational and shifted 1 n expansion methods

three methods for estimating a range of vehicular interactions abstract we present three different approaches how to estimate the number of preceding cars influencing a decision making procedure of a given driver moving in saturated traffic flows the first method is based on correlation analysis the second one evaluates quantitatively deviations from the main assumption in the convolution theorem for probability and the third one operates with advanced instruments of the theory of counting processes statistical rigidity we demonstrate that universally accepted premise on short ranged traffic interactions may not be correct all methods introduced have revealed that minimum number of actively followed vehicles is two it supports an actual idea that vehicular interactions are in fact middle ranged furthermore consistency between the estimations used is surprisingly credible in all cases we have found that the interaction range the number of actively followed vehicles drops with traffic density whereas drivers moving in congested regimes with lower density around 30 vehicles per kilometer react on four or five neighbors drivers moving in high density flows respond to two predecessors only

a unifying view of wiener and volterra theory and polynomial kernel regression volterra and wiener series are perhaps the best understood nonlinear system representations in signal processing although both approaches have enjoyed a certain popularity in the past their application has been limited to rather low dimensional and weakly nonlinear systems due to the exponential growth of the number of terms that have to be estimated we show that volterra and wiener series can be represented implicitly as elements of a reproducing kernel hilbert space by using polynomial kernels the estimation complexity of the implicit representation is linear in the input dimensionality and independent of the degree of nonlinearity experiments show performance advantages in terms of convergence interpretability and system sizes that can be handled

a fast fixed point algorithm for independent component analysis we introduce a novel fast algorithm for independent component analysis which can be used for blind source separation and feature extraction we show how a neural network learning rule can be transformed into a fixedpoint iteration which provides an algorithm that is very simple does not depend on any user defined parameters and is fast to converge to the most accurate solution allowed by the data the algorithm finds one at a time all nongaussian independent components regardless of their probability distributions the computations can be performed in either batch mode or a semiadaptive manner the convergence of the algorithm is rigorously proved and the convergence speed is shown to be cubic some comparisons to gradient based algorithms are made showing that the new algorithm is usually 10 to 100 times faster sometimes giving the solution in just a few iterations

a recurrence formula for obtaining certain matrix elements in the base of eigenfunctions of the hamiltonian for a particular screened potential a recurrence formula for obtaining matrix elements of products of powers of exp nu r and 1 exp nu r is derived the matrix elements are calculated in the base of eigenfunctions of the hamiltonian for the effective potential lambda exp nu r 1 exp nu r mu exp nu r 1 exp nu r 2 where lambda nu and mu are positive constants this potential can be considered as a generalisation of a potential suggested by hylleraas and risberg 1941 and by hulthen 1942 in the limit of the parameter nu tending to zero the recurrence formula is transformed into a recurrence formula is transformed into a recurrence formula given by badawi et al 1973 for matrix elements of powers of r for the hydrogen atom

a new image representation algorithm inspired by image submodality models redundancy reduction and learning in biological vision we develop a new biologically motivated algorithm for representing natural images using successive projections into complementary subspaces an image is first projected into an edge subspace spanned using an ica basis adapted to natural images which captures the sharp features of an image like edges and curves the residual image obtained after extraction of the sharp image features is approximated using a mixture of probabilistic principal component analyzers mppca model the model is consistent with cellular functional information theoretic and learning paradigms in visual pathway modeling we demonstrate the efficiency of our model for representing different attributes of natural images like color and luminance we compare the performance of our model in terms of quality of representation against commonly used basis like the discrete cosine transform dct independent component analysts ica and principal components analysis pca based on their entropies chrominance and luminance components of images are represented using codes having lower entropy than dct ica or pca for similar visual quality the model attains considerable simplification for learning from images by using a sparse independent code for representing edges and explicitly evaluating probabilities in the residual subspace

extended supersymmetry for the bound states of the generalized hulthen potential hierarchy using the associated hypergeometric differential equation we analytically solve the bound states corresponding to a hierarchy of the radial potential v0 e r 1 e r c e r 1 e r 2 as a generalization of the hulth n potential then an analytic solution corresponding to a special case for which the parameter c is expected to be in terms of l l 1 is also derived meanwhile without introducing a superpotential and in the framework of supersymmetric quantum mechanics it is shown that these bound states can be calculated by two different algebraic methods based on these two approaches it is noted that the bound states realize an extended supersymmetry structure

learning intermediate level representations of form and motion from natural movies we present a model of intermediate level visual representation that is based on learning invariances from movies of the natural environment the model is composed of two stages of processing an early feature representation layer and a second layer in which invariances are explicitly represented invariances are learned as the result of factoring apart the temporally stable and dynamic components embedded in the early feature representation the structure contained in these components is made explicit in the activities of second layer units that capture invariances in both form and motion when trained on natural movies the first layer produces a factorization or separation of image content into a temporally persistent part representing local edge structure and a dynamic part representing local motion structure consistent with known response properties in early visual cortex area v1 this factorization linearizes statistical dependencies among the first layer units making them learnable by the second layer the second layer units are split into two populations according to the factorization in the first layer the form selective units receive their input from the temporally persistent part local edge structure and after training result in a diverse set of higher order shape features consisting of extended contours multiscale edges textures and texture boundaries the motion selective units receive their input from the dynamic part local motion structure and after training result in a representation of image translation over different spatial scales and directions in addition to more complex deformations these representations provide a rich description of dynamic natural images and testable hypotheses regarding intermediate level representation in visual cortex

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

infinite hidden markov models for unusual event detection in video we address the problem of unusual event detection in a video sequence invariant subspace analysis isa is used to extract features from the video and the time evolving properties of these features are modeled via an infinite hidden markov model ihmm which is trained using ldquonormalrdquo ldquotypicalrdquo video the ihmm retains a full posterior density function on all model parameters including the number of underlying hmm states anomalies unusual events are detected subsequently if a low likelihood is observed when associated sequential features are submitted to the trained ihmm a hierarchical dirichlet process framework is employed in the formulation of the ihmm the evaluation of posterior distributions for the ihmm is achieved in two ways via markov chain monte carlo and using a variational bayes formulation comparisons are made to modeling based on conventional maximum likelihood based hmms as well as to dirichlet process based gaussian mixture models

interpreting the wide scattering of synchronized traffic data by time gap statistics based on the statistical evaluation of experimental single vehicle data we propose a quantitative interpretation of the erratic scattering of flow density data in synchronized traffic flows a correlation analysis suggests that the dynamical flow density data are well compatible with the so called jam line characterizing fully developed traffic jams if one takes into account the variation of their propagation speed due to the large variation of the netto time gaps the inhomogeneity of traffic flow the form of the time gap distribution depends not only on the density but also on the measurement cross section the most probable netto time gap in congested traffic flow upstream of a bottleneck is significantly increased compared to uncongested freeway sections moreover we identify different power law scaling laws for the relative variance of netto time gaps as a function of the sampling size while the exponent is 1 in free traffic corresponding to statistically independent time gaps the exponent is about 2 3 in congested traffic flow because of correlations between queued vehicles

recovery of sparse translation invariant signals with continuous basis pursuit we consider the problem of decomposing a signal into a linear combination of features each a continuously translated version of one of a small set of elementary features although these constituents are drawn from a continuous family most current signal decomposition methods rely on a finite dictionary of discrete examples selected from this family e g shifted copies of a set of basic waveforms and apply sparse optimization methods to select and solve for the relevant coefficients here we generate a dictionary that includes auxiliary interpolation functions that approximate translates of features via adjustment of their coefficients we formulate a constrained convex optimization problem in which the full set of dictionary coefficients represents a linear approximation of the signal the auxiliary coefficients are constrained so as to only represent translated features and sparsity is imposed on the primary coefficients using an l1 penalty the basis pursuit denoising bp method may be seen as a special case in which the auxiliary interpolation functions are omitted and we thus refer to our methodology as continuous basis pursuit cbp we develop two implementations of cbp for a one dimensional translation invariant source one using a first order taylor approximation and another using a form of trigonometric spline we examine the tradeoff between sparsity and signal reconstruction accuracy in these methods demonstrating empirically that trigonometric cbp substantially outperforms taylor cbp which in turn offers substantial gains over ordinary bp in addition the cbp bases can generally achieve equally good or better approximations with much coarser sampling than bp leading to a reduction in dictionary dimensionality

topographic independent component analysis in ordinary independent component analysis the components are assumed to be completely independent and they do not necessarily have any meaningful order relationships in practice however the estimated independent components are often not at all independent we propose that this residual dependence structure could be used to define a topographic order for the components in particular a distance between two components could be defined using their higher order correlations and this distance could be used to create a topographic representation thus we obtain a linear decomposition into approximately independent components where the dependence of two components is approximated by the proximity of the components in the topographic representation