exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

on g inverses and the nonsingularity of a bordered matrixabc0 abstract we consider the bordered matrix m a b c 0 with the rank additivity condition and g c 1 c 2 c 3 c 4 which is a g inverse of m we give the necessary and sufficient conditions for c 1 to be a g inverse outer inverse reflexive g inverse and moore penrose inverse of a as a special case we give necessary and sufficient conditions for m to be nonsingular and explicit expressions of c i in m 1 moreover we give a method for computing any outer inverse of a matrix

jam phases in a two dimensional cellular automaton model of traffic flow the jam phases in a two dimensional cellular automaton model of traffic flow are investigated by computer simulations two different types of jam phases are found the spatially diagonal long range correlation obeys a power law at the low density jam configurations the diagonal correlation exponentially decays at the high density jam the exponent of the short range correlation in the diagonal direction is introduced to define the transition between these two phases we also discuss the stability of the jams

recurrent neural network for computing the drazin inverse this paper presents a recurrent neural network rnn for computing the drazin inverse of a real matrix in real time this recurrent neural network rnn is composed of n independent parts subnetworks where n is the order of the input matrix these subnetworks can operate concurrently so parallel and distributed processing can be achieved in this way the computational advantages over the existing sequential algorithms can be attained in real time applications the rnn defined in this paper is convenient for an implementation in an electronic circuit the number of neurons in the neural network is the same as the number of elements in the output matrix which represents the drazin inverse the difference between the proposed rnn and the existing ones for the drazin inverse computation lies in their network architecture and dynamics the conditions that ensure the stability of the defined rnn as well as its convergence toward the drazin inverse are considered in addition illustrative examples and examples of application to the practical engineering problems are discussed to show the efficacy of the proposed neural network

characterizations iterative method sign pattern and perturbation analysis for the dmp inverse with its applications abstract this paper is a study on main properties and characterizations of the dmp inverse also corresponding representations and computational procedures are derived particularly an upgrade of the bordering method to the case of the dmp inverse is considered as well as applications of the dmp inverse in solving singular linear systems also the dmp inverse of an upper block triangular matrix and its sign pattern are investigated furthermore several computational procedures aimed to approximating the dmp inverse are developed implemented and tested the main of them are the limit representation a revised successive matrix squaring iterations and the gradient neural network gnn dynamical system finally some perturbation bounds and continuity of the dmp inverse are studied

recurrent neural networks for computing pseudoinverses of rank deficient matrices three recurrent neural networks are presented for computing the pseudoinverses of rank deficient matrices the first recurrent neural network has the dynamical equation similar to the one proposed earlier for matrix inversion and is capable of moore penrose inversion under the condition of zero initial states the second recurrent neural network consists of an array of neurons corresponding to a pseudoinverse matrix with decaying self connections and constant connections in each row or column the third recurrent neural network consists of two layers of neuron arrays corresponding respectively to a pseudoinverse matrix and a lagrangian matrix with constant connections all three recurrent neural networks are also composed of a number of independent subnetworks corresponding to the rows or columns of a pseudoinverse the proposed recurrent neural networks are shown to be capable of computing the pseudoinverses of rank deficient matrices

the representation and approximation for the weighted moore penrose inverse in hilbert space we present a unified representation theorem of the weighted moore penrose inverse in hilbert space specific expressions and computational procedures for the weighted moore penrose inverse in hilbert space can be uniformly derived

on integral representation of the generalized inverse at s 2 we present a general integral representation for the generalized inverse a t s 2 which extends earlier result on the moore penrose inverse weighted moore penrose inverse and drazin inverse

the iterative methods for computing the generalized inverse at s 2 of the bounded linear operator between banach spaces in this paper we present the iterative methods for computing the generalized inverse a t s 2 over banach spaces and also for computing the generalized drazin inverses of banach algebra elements moreover we estimate the error bounds of the iterative methods for approximating a t s 2

the 2 inverse with applications in statistics an inverse g of a given matrix a which satisfies the property gag g is known as a 2 inverse this paper presents a three phase inversion procedure for which the 2 inverse is a special case we present the geometry of 2 inverses and show that starting from 2 inverses various types of generalized inverses can be derived two examples of the occurrence of 2 inverses in statistics are given one concerning the constrained least squares estimator the other concerning a necessary and sufficient condition for a quadratic form of singular multivariate normal variates to follow a chi square distribution

recurrent neural network for computing outer inverse two linear recurrent neural networks for generating outer inverses with prescribed range and null space are defined each of the proposed recurrent neural networks is based on the matrix valued differential equation a generalization of dynamic equations proposed earlier for the nonsingular matrix inversion the moore penrose inversion as well as the drazin inversion under the condition of zero initial state the application of the first approach is conditioned by the properties of the spectrum of a certain matrix the second approach eliminates this drawback though at the cost of increasing the number of matrix operations the cases corresponding to the most common generalized inverses are defined the conditions that ensure stability of the proposed neural network are presented illustrative examples present the results of numerical simulations

recurrent neural network approach based on the integral representation of the drazin inverse in this letter we present the dynamical equation and corresponding artificial recurrent neural network for computing the drazin inverse for arbitrary square real matrix without any restriction on its eigenvalues conditions that ensure the stability of the defined recurrent neural network as well as its convergence toward the drazin inverse are considered several illustrative examples present the results of computer simulations

neural network approach to computing outer inverses based on the full rank representation abstract the first intention of this paper is to emphasize equivalence between two well known general representations of outer inverses with prescribed range and null space of a given matrix two dynamical state equations corresponding to particular expressions which are included in these representations are defined within the second objective in this way two gradient based neural networks initiated by introduced dynamical equations are exploited in generating the class of outer inverses the results corresponding to most common generalized inverses are obtained in particular cases numerical results are presented

the representation and approximation for drazin inverse we present a unified representation theorem for drazin inverse specific expression and computational procedures for drazin inverse can be uniformly derived numerical examples are tested and the application to the singular linear equations is also considered

the green wave model of two dimensional traffic transitions in the flow properties and in the geometry of the traffic jam abstract we carried out computer simulations to study the green wave model gwm the parallel updating version of the two dimensional traffic model of biham et al the better convergence properties of the gwm together with a multi spin coding technique enabled us to extrapolate to the infinite system size which indicates a nonzero density transition from the free flow to the congested state jamming transition in spite of the sudden change in the symmetry of the correlation function at the transition point finite size scaling and temporal scaling seems to hold at least above the threshold density there is a second transition point at a density deep in the congested phase where the geometry of the cluster of jammed cars changes from linear to branched just at this transition point this cluster has fractal geometry with dimension 1 58 the jamming transition is also described within the mean field approach

recurrent neural networks for computing weighted moore penrose inverse1this project is supported by the national nature science foundation of china doctoral point foundation of china and youth science foundation of universities in shanghai of china 1 three recurrent neural networks are presented for computing the weighted moore penrose inverse of rank deficient matrices the first recurrent neural network has the dynamical equation similar to the one proposed earlier for matrix inversion and is capable of weighted moore penrose inverse under the condition of zero initial states the second recurrent neural network consists of an array of neurons corresponding to a weighted moore penrose inverse matrix with decaying self connections and constant connections in each row or column the third recurrent neural network consists of two layers of neuron arrays corresponding respectively to a weighted moore penrose inverse and a lagrangian matrix with constant connections

theoretical approach to two dimensional traffic flow models in this paper we present a theoretical analysis of a recently proposed two dimensional cellular automata model for traffic flow in cities with the ingredient of a turning capability numerical simulations of this model show that there is a transition between a freely moving phase with high velocity to a jammed state with low velocity we study the dynamics of such a model starting with the microscopic evolution equation which will serve as a basis for further analysis it is shown that a kinetic approach based on the boltzmann assumption is able to provide a reasonably good description of the jamming transition we further introduce a space time continuous phenomenological model leading to two partial differential equations whose preliminary results agree rather well with the numerical simulations

metastable states in a microscopic model of traffic flow it is a well known fact that metastable states of very high throughput and hysteresis effects exist in traffic flow which the simple cellular automaton model of traffic flow and its continuous generalization fail to reproduce it is shown that the model can be generalized to give a one parametric family of models a part of which reproduces the metastable states and the hysteresis the models that have that property and those that do not that are separated by a transition that can be clearly identified

vehicular traffic through a self similar sequence of traffic lights abstract we study the dynamical behavior of vehicular traffic through a sequence of traffic lights positioned self similarly on a highway where all traffic lights turn on and off simultaneously with cycle time t s the signals are positioned self similarly by cantor set the nonlinear map model of vehicular traffic controlled by self similar signals is presented the vehicle exhibits the complex behavior with varying cycle time the tour time is much lower such that signals are positioned periodically with the same interval the arrival time t x at position x scales as t x x x d f where d f is the fractal dimension of cantor set the landscape in the plot of t x x against cycle time t s shows a self affine fractal with roughness exponent 1 d f

traffic flow of mobile objects through obstacles turning and translational objects abstract we study the unidirectional flow of mobile objects through obstacles on a square lattice two models are presented one is the lattice gas model consisting of translational particles and the other is that of turning particles fundamental diagrams for the two models are presented the traffic flow of translational particles is compared with that of turning particles in the traffic flow of translational particles the fundamental diagram shows a trapezoid shape in the random configuration of obstacles while it shows a parabolic shape in the periodic configuration of obstacles the traffic flow of turning particles with a back step shows a similar behavior to that of translational particles in the traffic flow of turning particles without backward moves the current becomes zero when the density is higher than a critical density in the traffic flow of turning particles without a back step the dynamical transition between free traffic and a perfectly jammed state occurs at the critical density while dynamical transition does not occur in traffic flow of translational particles

representation and approximation of the outer inverse at s 2 of a matrix a abstract in this paper we establish a basic representation and a representation theorem for the outer inverse a t s 2 of a matrix a which is the matrix x satisfying xax x r x t and n x s we develop several specific representations and iterative methods for a t s 2 we show that this representation includes many of the traditional generalized inverses and outer inverses and the relation of our results to these outer inverses will be explored

scaling behaviour in discrete traffic models we investigate the noisy discrete single lane highway traffic model proposed by nagel and schreckenberg 1992 and demonstrate by computer simulations that as a function of the car density there is a dynamical transition from laminar flow to jammed traffic in the system related to the divergence of the relaxation time of average car velocity the critical density is close to the position of the maximum in the fundamental diagram we give estimates of the critical exponents related to this jamming transition the critical density of the geometrical 1 1 dimensional percolation transition of jammed regions can be rather far from the jamming point depending on the strength of the noise which indicates that cooperativity leading to the jamming transition can be long range in character

resonances near the real axis for transparent obstacles the purpose of this paper is to study the resonances for the transmission problem for a strictly convex obstacle in r n n 2 if the speed of propagation in the interior of the body is strictly less than that in the exterior we obtain an infinite sequence of resonances tending rapidly to the real axis these resonances are associated with a quasimode for the transmission problem the main ingredient of the paper is the construction of a quasimode the frequency support of which coincides with the corresponding gliding manifold to do this we first find a global symplectic normal form for pairs of glancing hypersurfaces in a neighborhood of and then we separate the variables microlocally near the whole glancing manifold

jamming transition in two dimensional pedestrian traffic abstract jamming transitions of pedestrian traffic are investigated under the periodic boundary condition on the square lattice by the use of the lattice gas model of biased random walkers without the back step the two cases are presented the one with two types of walkers and the other with four types of walkers in the two types of walkers the first is the random walker going to the right and the second is the random walker going up in the four types of walkers the first second third and fourth are respectively the random walkers going to the right left up and down it is found that the dynamical jamming transitions occur at the critical densities the transition points do not depend on the system size for large system but depend strongly on the strength of drift the jamming transitions are compared with that obtained by the cellular automaton model of car traffic

passenger s fluctuation and chaos on ferryboats abstract we study the fluctuation of shipping passengers on a few ferryboats which shuttle between an origin and a destination repeatedly we present the dynamical model for the ferryboats the model is described in terms of nonlinear maps defined from the vectors ti n and wi n i 1 2 n for n ferryboats where ti n is the arrival time of ferryboat i at the origin on trip n and wi n the number of passengers waiting at the origin on trip n we clarify the fluctuations of shipping passengers and tour time for the ferry schedule it is found that the dynamical transitions among the regular periodic and chaotic motions occur by varying the ferry s capacity fmax headway tmin and loading parameter even if the second ferryboat follows the leader first ferryboat keeping the constant headway the passengers shipping on the second fluctuate highly when the parameters take specific values

a characterization and representation of the generalized inverse a 2 t s and its applications abstract this paper presents an explicit expression for the generalized inverse a 2 t s based on this we established the characterization the representation theorem and the limiting process for a 2 t s as an application we estimate the error bound of the iterative method for approximating a 2 t s

effect of partition line on jamming transition in pedestrian counter flow abstract the effect of partition line on the pedestrian counter flow is investigated under the open boundaries by using the lattice gas model of biased random walkers there are two types of walkers without the back step the one is the walker going to the right and the other is the walker going to the left the right left walker prefers to move within outside the partition line right walkers interfere with left walkers near the partition line when the density of right walkers increases under a constant value of left walker density the jamming transition between the freely moving phase and the stopped state occurs at a critical density depending on the left walker density the critical density is compared with that without the partition line the partition line has an important effect on the jamming transition

neumann resonances in linear elasticity for an arbitrary body we study resonances scattering poles associated to the elasticity operator in the exterior of an arbitrary obstacle inr3 with neumann boundary conditions we prove that there exists a sequence of resonances tending rapidly to the real axis

clogging transition of pedestrian flow in t shaped channel abstract pedestrian flow is investigated under the open boundaries in a t shaped channel where the branch flow joins the main flow at the junction the pedestrian merging flow is simulated by the use of the lattice gas model of biased random walkers when the main flow rate increases under the constant value of branch flow rate the clogging transitions occur at the main flow or branch flow or both flows it is shown that the dynamical phase transitions depend on both inlet densities the four distinct phases are found the phase diagram is presented for the distinct phases the scaling of saturated flow rate and transition point is shown the flow rate exhibits the universal scaling form

pedestrian behaviors in a lattice gas model with large maximum velocity abstract in this paper the lattice gas model for pedestrian flow is extended to large maximum velocity v max 1 it is shown that at large v max the critical density corresponding to the maximum flow rate of fundamental diagram is in good agreement with empirical results the counter flow is studied and it is found that with the increase of v max the jam transition threshold decreases this is explained by the attachment rate to jam and detachment rate from jam the fundamental diagram of mixed pedestrian flow is also investigated and the dependence of the flow rate on the ratio of fast pedestrians is simulated finally the counter flow of mixed pedestrians is studied and it is found the more homogeneous the mixed pedestrians are distributed the smaller the jam transition threshold is

full rank representation of generalized inverse at s 2 and its application in this paper we introduce a full rank representation of the generalized inverse a t s 2 of a given complex matrix a which is based on an arbitrary full rank decomposition of g where g is a matrix such that r g t and n g s using this representation we introduce the minor of the generalized inverse a t s 2 as a special case of the minor a determinantal representation of the generalized inverse a t s 2 is obtained as an application we use an example to demonstrate that this representation is correct

successive matrix squaring algorithm for computing outer inverses abstract in this paper we derive a successive matrix squaring sms algorithm to approximate an outer generalized inverse with prescribed range and null space of a given matrix a c r m n we generalize the results from the papers l chen e v krishnamurthy i macleod generalized matrix inversion and rank computation by successive matrix powering parallel computing 20 1994 297 311 y wei successive matrix squaring algorithm for computing drazin inverse appl math comput 108 2000 67 75 y wei h wu j wei successive matrix squaring algorithm for parallel computing the weighted generalized inverse a mn appl math comput 116 2000 289 296 and obtain an algorithm for computing various classes of outer generalized inverses of a instead of particular matrices used in these articles we use an appropriate matrix r c s n m s r numerical examples are presented

complex valued zhang neural network for online complex valued time varying matrix inversion abstract in this paper a new complex valued recurrent neural network cvrnn called complex valued zhang neural network cvznn is proposed and simulated to solve the complex valued time varying matrix inversion problems such a cvznn model is designed based on a matrix valued error function in the complex domain and utilizes the complex valued first order time derivative information of the complex valued time varying matrix for online inversion superior to the conventional complex valued gradient based neural network cvgnn and its related methods the state matrix of the resultant cvznn model can globally exponentially converge to the theoretical inverse of the complex valued time varying matrix in an error free manner moreover by exploiting the design parameter 1 superior convergence can be achieved for the cvznn model to solve such complex valued time varying matrix inversion problems as compared with the situation without design parameter involved i e the situation with 1 computer simulation results substantiate the theoretical analysis and further demonstrate the efficacy of such a cvznn model for online complex valued time varying matrix inversion

traffic jamming on hexagonal lattice abstract a traffic model on hexagonal lattice is studied the moving objects are modeled as biased random walkers on hexagonal lattice the hexagonal lattice traffic model is an extension of the square lattice traffic model proposed by muramatsu et al physica a 267 1999 487 the hexagonal and square models are compared it is found that hexagonal and square models have a phase transition from freely moving state to jammed state at a critical density the critical density of hexagonal model is greater than that of square model when the drift of moving objects is high the difference between the critical densities of hexagonal and square models decreases when the drift decreases

a statistical approach to vehicular traffic abstract a two dimensional cellular automaton is introduced to model the flow and jamming of vehicular traffic in cities each site of the automaton represents a crossing where a finite number of cars can wait approaching the crossing from each of the four directions the flow of cars obeys realistic traffic rules we investigate the dependence of the average velocity of cars on the global traffic density at a critical threshold for the density the average velocity reduces drastically caused by jamming for the low density regime we provide analytical results which agree with the numerical results

scaling of pedestrian channel flow with a bottleneck abstract pedestrian channel flow at a bottleneck is investigated under the open boundaries by using the lattice gas model of biased random walkers it is shown that a dynamical phase transition occurs from the free flow to the choking flow at a critical density pc with increasing density the flow rate saturates at higher density than the critical density in the choking flow region a scaling behavior is found as follows the saturated flow rate js scales as js d0 93 0 02 and the critical density pc scales as pc d w 1 16 0 02 where d is the width of the bottleneck and w is the width of channel the plot of the rescaled flow rate against the rescaled density collapses onto a single curve

iterative methods for computing the generalized inverses a 2 t s of a matrix a abstract in this paper the iterative methods for computing the generalized inverse a t s 2 the unique matrix x such that xax x r x t and n x s are established and the iterative methods for computing many important generalized inverses of matrices such as a a mn a d a a d w a l 1 a l and ap l are constructed

on the resonances of the laplacian on waveguides abstract the resonances for the dirichlet and neumann laplacian are studied on compactly perturbed waveguides in the absence of resonances an upper bound is proven for the localised resolvent this is then used to prove that the existence of a quasimode whose asymptotics is bounded away from the thresholds implies the existence of resonances converging to the real axis the following upper bound to the number of resonances is also proven k j res dist k j physical plane k j 2 k j 3

iterative method for computing the moore penrose inverse based on penrose equations an iterative algorithm for estimating the moore penrose generalized inverse is developed the main motive for the construction of the algorithm is simultaneous usage of penrose equations 2 and 4 convergence properties of the introduced method as well as their first order and second order error terms are considered numerical experiment is also presented

the generalized bott duffin inverse and its applications abstract the generalized bott duffin inverse a l of a with respect to a subspace l is defined and by means of it a unified treatment of a class of linear systems and extreme value problems with equality constraints is given

jamming transition in pedestrian counter flow a lattice gas model with biased random walkers is presented to mimic the pedestrian counter flow in a channel under the open boundary condition of constant density there are two types of walkers without the back step the one is the random walker going to the right and the other is the random walker going to the left it is found that a dynamical jamming transition from the freely moving state at low density to the stopped state at high density occurs at the critical density the transition point is given by pc 0 45 0 01 not depending on the system size the transition point depends on the strength of drift and decreases with increasing drift also we present the extended model to take into account the traffic rule in which a pedestrian walks preferably on the right hand side of the channel

generalized inverse a 2 t s and a rank equation in this paper the rank equationrankabcx rank a is considered in the sense that b and c are characterized when a 2 t s is solution to this equation as the special cases similar results for a a m n a d and a g are also derived this contributes to certain recent results in the literature including that obtained by grosz linear algebra appl 289 1999 127 and thome and wei appl math comput 141 2003 471