bifurcation phenomena in the optimal velocity model for traffic flow in the optimal velocity model with a time lag we show that there appear multiple exact solutions in some ranges of car density describing a metastable uniform flow a metastable congested flow and an unstable congested flow this establishes the presence of subcritical hopf bifurcations our analytical results have implications for continuum traffic flow such as hysteresis phenomena associated with discontinuous transitions between uniform and congested flow

nonlinear growth in weighted networks with neighborhood preferential attachment abstract we propose a nonlinear growing model for weighted networks with two significant characteristics i the new weights triggered by new edges at each time step grow nonlinearly with time and ii a neighborhood local world exists for local preferential attachment which is defined as one selected node and its neighbors global strength driven and local weight driven preferential attachment mechanisms are involved in our model we study the evolution process through both mathematical analysis and numerical simulation and find that the model exhibits a wide range power law distribution for node degree strength and weight in particular a nonlinear degree strength relationship is obtained this nonlinearity implies that accelerating growth of new weights plays a nontrivial role compared with accelerating growth of edges because of the specific local world model a small world property emerges and a significant hierarchical organization independent of the parameters is observed

relativistic calogero sutherland model spin generalization quantum affine symmetry and dynamical correlation functions spin generalization of the relativistic calogero sutherland model is constructed by using the affine hecke algebra and shown to possess the quantum affine symmetry the spinless model is exactly diagonalized by means of the macdonald symmetric polynomials the dynamical density density correlation function as well as the one particle green function are evaluated exactly we also investigate the finite size scaling of the model and show that the low energy behaviour is described by the c 1 gaussian theory with a new selection rule the results indicate that the excitations obey the fractional exclusion statistics and also exhibit the tomonaga luttinger liquid behaviour

twisted fourier mukai functors due to a theorem by orlov every exact fully faithful functor between the bounded derived categories of coherent sheaves on smooth projective varieties is of fourier mukai type we extend this result to the case of bounded derived categories of twisted coherent sheaves and at the same time we weaken the hypotheses on the functor as an application we get a complete description of the exact functors between the abelian categories of twisted coherent sheaves on smooth projective varieties

on the 0 dimensional cusps of the kahler moduli of a k3 surface let s be a complex algebraic k3 surface it is proved that the 0 dimensional cusps of the kahler moduli of s are in one to one correspondence with the twisted fourier mukai partners of s as a result a counting formula for the 0 dimensional cusps of the kahler moduli is obtained applications to rational maps between k3 surfaces are given when the picard number of s is 1 the bijective correspondence is calculated explicitly by using the fricke modular curve

polynomial modeling for time varying systems based on a particle swarm optimization algorithm in this paper an effective particle swarm optimization pso is proposed for polynomial models for time varying systems the basic operations of the proposed pso are similar to those of the classical pso except that elements of particles represent arithmetic operations and variables of time varying models the performance of the proposed pso is evaluated by polynomial modeling based on various sets of time invariant and time varying data results of polynomial modeling in time varying systems show that the proposed pso outperforms commonly used modeling methods which have been developed for solving dynamic optimization problems including genetic programming gp and dynamic gp an analysis of the diversity of individuals of populations in the proposed pso and gp reveals why the proposed pso obtains better results than those obtained by gp

an extended continuum traffic model with the consideration of the optimal velocity difference abstract in this letter we derived an extended continuum model from a car following model with consideration of the optimal velocity difference called the relative optimal velocity via employing the transformation relation from microscopic variables to macroscopic ones the stability condition of this continuum traffic model is obtained by performing linear stability analysis results show that the optimal velocity difference helps to improve the stability of traffic flow we make use of the upwind finite difference scheme for simulation the effects of the optimal velocity difference the relative optimal velocity and the velocity difference the optimal velocity on local clustering effect and instability are studied and compared each other respectively the spatiotemporal evolution patterns of traffic flow for the different initial density strength of the optimal velocity difference and the velocity difference are obtained their space time diagrams reveal the local clustering effect induced by the instability of traffic flow and generate the stop go traffic jams numerical simulation result indicates the unstable region is shrunken under the effect of the optimal velocity difference the relative optimal velocity and or the velocity difference the optimal velocity

emd based refined composite multiscale entropy analysis of complex signals abstract multiscale entropy mse is an effective method to measure the complexity of signals from complex systems which has been applied to various fields successfully however mse may yield an inaccurate estimate of entropy and induce undefined entropy as the coarse graining procedure reduces the length of data considerably at large scales refined composite multiscale entropy rcmse is then developed to solve this problem however trends superimposed in signals may significantly affect the complexity measurement thus we introduce an empirical mode decomposition based rcmse called emd rcmse to first eliminate such effects of trends and then measure the complexity of signals it is validated from simulated signals and has good estimation in addition this method is also applied to study the complexity of traffic signals and we obtain some interesting results 1 traffic signals are more complex than the results showing from rcmse mse 2 weekday and weekend patterns different combination of trends greatly affect the results 3 complexity indices change with time at each day due to the degree of human activities

forecasting interval time series using a fully complex valued rbf neural network with dpso and pso algorithms we propose a novel interval time series its forecasting approach a fully complex valued rbf neural network is extended to address its forecasting dpso pso are used to jointly optimize the structure and parameters of the model results on simulated and real world its data confirm the efficacy of the approach interval time series prediction is one of the most challenging research topics in the field of time series modeling and prediction in view of the remarkable function approximation capability of fully complex valued radial basis function neural networks fcrbfnns we set out to investigate the possibility of forecasting interval time series by denoting the lower and upper bounds of the interval as real and imaginary parts of a complex number respectively this results in a complex valued interval we then model the resulted complex valued interval time series via a fcrbfnn furthermore we propose to evolve the fcrbfnn by using particle swarm optimization pso and discrete pso for joint optimization of the structure and parameters finally the proposed interval time series prediction approach is tested with simulated interval time series data as well as real interval stock price time series data from the new york stock exchange our experimental results indicate that it is a promising alternative for interval time series forecasting

modeling the coevolution of topology and traffic on weighted technological networks for many technological networks the network structures and the traffic taking place on them mutually interact the demands of traffic increment spur the evolution and growth of the networks to maintain their normal and efficient functioning in parallel a change of the network structure leads to redistribution of the traffic in this paper we perform an extensive numerical and analytical study extending results of wang phys rev lett 94 188702 2005 by introducing a general strength coupling interaction driven by the traffic increment between any pair of vertices our model generates networks of scale free distributions of strength weight and degree in particular the obtained nonlinear correlation between vertex strength and degree and the disassortative property demonstrate that the model is capable of characterizing weighted technological networks moreover the generated graphs possess both dense clustering structures and an anticorrelation between vertex clustering and degree which are widely observed in real world networks the corresponding theoretical predictions are well consistent with simulation results

robotic reactions delay induced patterns in autonomous vehicle systems fundamental design principles are presented for vehicle systems governed by autonomous cruise control devices by analyzing the corresponding delay differential equations it is shown that for any car following model short wavelength oscillations can appear due to robotic reaction times and that there are tradeoffs between the time delay and the control gains the analytical findings are demonstrated on an optimal velocity model using numerical continuation and numerical simulation

linear stability and nonlinear analyses of traffic waves for the general nonlinear car following model with multi time delays abstract in this paper the general nonlinear car following model with multi time delays is investigated in order to describe the reactions of vehicle to driving behavior platoon stability and string stability criteria are obtained for the general nonlinear car following model burgers equation and korteweg de vries kdv equation and their solitary wave solutions are derived adopting the reductive perturbation method we investigate the properties of typical optimal velocity model using both analytic and numerical methods which estimates the impact of delays about the evolution of traffic congestion the numerical results show that time delays in sensing relative movement is more sensitive to the stability of traffic flow than time delays in sensing host motion

a hybrid forecasting model reducing gaussian noise based on the gaussian support vector regression machine and chaotic particle swarm optimization in this paper the relationship between gaussian noise and the loss function of the support vector regression machine svrm is analyzed and then a gaussian loss function proposed to reduce the effect of such noise on the regression estimates since the e insensitive loss function cannot reduce noise a novel support vector regression machine g svrm is proposed then a chaotic particle swarm optimization cpso algorithm developed to estimate its unknown parameters finally a hybrid forecasting model combining g svrm with the cpso is proposed to forecast a multi dimensional time series the results of two experiments demonstrate the feasibility of this approach

the decomposition of level 1 irreducible highest weight modules with respect to the level 0 actions of the quantum affine algebra the level 1 irreducible highest weight modules of the quantum affine algebra uq bn are decomposed into irreducible components with respect to the level 0 u 0 q bn action previously defined in 13 the components of the decomposition are found to be the so called tame representations of u 0 q bn parametrized by the skew young diagrams of the border strip type this result verifies a recent conjecture due to kirillov et al

weighted self similar networks under preferential attachment abstract we introduce an abstract evolutionary formalism that generates weighted networks whose growth under stochastic preferential attachment triggers unrestricted weight rearrangements in existing links the class of resulting algorithms for different parameter values includes the barabasi albert and barrat barthelemy vespignani models as special cases we solve the recursions that describe the average growth to derive exact solutions for the expected degree and strength distribution the individual strength and weight development and the joint distribution of neighboring degrees we find that the network exhibits a particular form of self similarity namely every sufficiently interconnected node has on average the same constitution of small degree neighbors as any other node of large degree finally we suggest potential applications in several fields of interest

bifurcation analysis of a class of car following traffic models abstract we consider a follow the leader traffic model describing the dynamics of n cars on a circular road where each car driver chooses his acceleration according to a certain law the model is represented by a nonlinear system of ode s this model is known to have a solution with constant velocities and headways which in a certain parameter regime is stable varying the density of the cars we prove that the loss of stability is generally due to a hopf bifurcation also we investigate numerically the global bifurcation diagram for periodic solutions and obtain a complete picture of the dynamics of general optimal velocity models finally some analytical results on the stability of solutions in the case of non equal drivers are given

self adaptive mix of particle swarm methodologies for constrained optimization abstract in recent years many different variants of the particle swarm optimizer pso for solving optimization problems have been proposed however pso has an inherent drawback in handling constrained problems mainly because of its complexity and dependency on parameters furthermore one pso variant may perform well for some test problems but not obtain good results for others in this paper our purpose is to develop a new pso algorithm that can efficiently solve a variety of constrained optimization problems it considers a mix of different pso variants each of which evolves with a different number of individuals from the current population in each generation the algorithm assigns more individuals to the better performing variants and fewer to the worse performing ones also a new pso variant is developed for use in the proposed algorithm to maintain a better balance between its local and global pso versions a new methodology for adapting pso parameters is presented and the proposed self adaptive pso algorithm tested and analyzed on two sets of test problems namely the cec2006 and cec2010 constrained optimization problems based on the results the proposed algorithm shows significantly better performance than the same global and local pso variants as well as other state of the art algorithms although based on our analysis it cannot guarantee an optimal solution for any unknown problem it is expected to be able to solve a wide variety of practical problems

evolving estimators of the pointwise holder exponent with genetic programming the regularity of a signal can be numerically expressed using holder exponents which characterize the singular structures a signal contains in particular within the domains of image processing and image understanding regularity based analysis can be used to describe local image shape and appearance however estimating the holder exponent is not a trivial task and current methods tend to be computationally slow and complex this work presents an approach to automatically synthesize estimators of the pointwise holder exponent for digital images this task is formulated as an optimization problem and genetic programming gp is used to search for operators that can approximate a traditional estimator the oscillations method experimental results show that gp can generate estimators that achieve a low error and a high correlation with the ground truth estimation furthermore most of the gp estimators are faster than traditional approaches in some cases their runtime is orders of magnitude smaller this result allowed us to implement a real time estimation of the holder exponent on a live video signal the first such implementation in current literature moreover the evolved estimators are used to generate local descriptors of salient image regions a task for which a stable and robust matching is achieved comparable with state of the art methods in conclusion the evolved estimators produced by gp could help expand the application domain of holder regularity within the fields of image analysis and signal processing

constructing ordinary sum differential equations using polynomial networks data relations can define general sum partial differential equations of a composite function additive derivative model time series data observations can analogously describe an ordinary sum differential equation with time derivatives which is possible to be solved using partial derivative term substitutions of time dependent series differential polynomial neural network is a new type of neural network which constructs and substitutes for an unknown general partial differential equation from data observations developed by the author it generates sum series of convergent partial polynomial derivative terms which can describe an unknown complex function time series this type of non linear regression decomposes a system model described by the general differential equation into many partial low order derivative specifications of selected relative sum terms common soft computing techniques in general can apply input variables of only absolute interval values of a specific data range the character of relative data allows processing a wider range of test interval values than defined by a training set the characteristics of the composite sum differential equation solutions can facilitate a much greater variety of model forms than is allowed using standard soft computing methods recurrent neural network proved to form simple solid time series models most of which it is possible to describe using ordinary differential equations so the comparisons were done

analysis of optimal velocity model with explicit delay we analyze the optimal velocity model ovm with explicit delay the properties of congestion and the delay time of car motion are investigated by analytical and numerical methods it is shown that the small explicit delay time has almost no effects in the case of the large explicit delay time a new phase of congestion pattern of ovm seems to appear

bifurcations and multiple traffic jams in a car following model with reaction time delay we investigate an optimal velocity car following model for n cars on a circular singlelane road where reaction time delay of drivers is taken into account the stability of the uniform ow equilibrium is studied analytically while bifurcating periodic solutions for difierent wave numbers are investigated with numerical continuation techniques this reveals that the periodic solution with the smallest wave number may be stable and all other periodic solutions are unstable as n is increased periodic solutions develop stop and go fronts that correspond to rapid deceleration and acceleration between regions of uniformly owing and stagnant tra c in terms of the positions of all cars on the ring these fronts are associated with tra c jams all tra c jams form a tra c pattern that evolves under time due to slow motion of the fronts the tra c pattern corresponding to the stable periodic motion of cars is the only stable one however we flnd that other periodic orbits may be unstable only so weakly that they give rise to transient tra c jams that may persist for long times eventually such tra c jams either merge with one another or disperse until the stable tra c pattern is reached

kink soliton characterizing traffic congestion we study traffic congestion by analyzing a one dimensional traffic flow model developing an asymptotic method to investigate the long time behavior near a critical point we derive the modified korteweg de vries mkdv equation as the lowest order model there is an infinite number of kink solitons to the mkdv equation while it has been found by numerical simulations that the kink pattern arising in traffic congestion is uniquely determined irrespective of initial conditions in order to resolve this selection problem we consider higher order corrections to the mkdv equation and find that there is a kink soliton that can deform continuously with the perturbation represented by the addition of these corrections with numerical confirmation we show that this continuously deformable kink soliton characterizes traffic congestion we also discuss the relationship between traffic congestion and the slugging phenomenon in granular flow

nonlinear analysis of the optimal velocity difference model with reaction time delay abstract we investigate the effect of reaction time delay of drivers upon traffic flow analytically and numerically we extend the optimal velocity difference model by taking reaction time delay of drivers into account the stability condition is obtained the burgers korteweg de vries kdv and modified korteweg de vries mkdv equations are derived in the stable metastable and unstable regions the results show that the increase of reaction time delay of drivers leads to the unrealistic traffic phenomena and unstable traffic flow by adjusting the coefficient of the velocity and optimal velocity difference the unrealistic traffic phenomena and unstable traffic flow can disappear

one dimensional unstable eigenfunction and manifold computations in delay differential equations in this paper we present a new numerical technique for computing the unstable eigenfunctions of a saddle periodic orbit in a delay differential equation this is used to obtain the necessary starting data for an established algorithm for computing one dimensional 1d unstable manifolds of an associated saddle fixed point of a suitable poincare map to illustrate our method we investigate an intermittent transition to chaos in a delay system describing a semiconductor laser subject to phase conjugate feedback

inference of differential equation models by genetic programming this paper describes an evolutionary method for identifying a causal model from the observed time series data we use a system of ordinary differential equations odes as the causal model this approach is known to be useful for practical applications e g bioinformatics chemical reaction models control theory etc to explore the search space more effectively in the course of evolution the right hand sides of odes are inferred by genetic programming gp and the least mean square lms method is used along with the ordinary gp we apply our method to several target tasks and empirically show how successfully gp infers the systems of odes we also describe an extension of the approach to the inference of differential equation systems with transcendental functions

effects of accelerating growth on the evolution of weighted complex networks many real systems possess accelerating statistics where the total number of edges grows faster than the network size in this paper we propose a simple weighted network model with accelerating growth we derive analytical expressions for the evolutions and distributions for strength degree and weight which are relevant to accelerating growth we also find that accelerating growth determines the clustering coefficient of the networks interestingly the distributions for strength degree and weight display a transition from scale free to exponential form when the parameter with respect to accelerating growth increases from a small to large value all the theoretical predictions are successfully contrasted with numerical simulations

numerical stability analysis of a large scale delay system modeling a lateral semiconductor laser subject to optical feedback this paper highlights the use of advanced numerical tools to study the stability of large scale systems of delay differential equations ddes specifically we consider a model describing a semiconductor laser subject to conventional optical feedback and lateral carrier diffusion the symmetry of the governing rate equations allows external cavity mode solutions ecms to be computed as steady state solutions using the software package dde biftool branches of ecms are computed as a function of varying feedback strength the stability along these branches is computed by solving eigenvalue problems the size of which is governed by a step length heuristic in this paper we employ an improved heuristic which substantially reduces the size of these eigenvalue problems this approach makes the stability analysis of large scale systems of ddes computationally feasible

level 0 structure of level 1 uq sl2 modules and macdonald polynomials the level 1 integrable highest weight modules of uq sl2 admit a level 0 action of the same algebra this action is defined using the affine hecke algebra and the basis of the level 1 module generated by components of vertex operators each level 1 module is a direct sum of finite dimensional irreducible level 0 modules whose highest weight vector is expressed in terms of macdonald polynomials this decomposition leads to the fermionic character formula for the level 1 modules

derivation of continuum traffic flow models from microscopic follow the leader models in this paper we establish a connection between a microscopic follow the leader model based on ordinary differential equations and a semidiscretization of a macroscopic continuum model based on a c

a method based on pso and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts abstract group decision making is a type of decision problem in which multiple experts acting collectively analyze problems evaluate alternatives and select a solution from a collection of alternatives as the natural language is the standard representation of those concepts that humans use for communication it seems natural that they use words linguistic terms instead of numerical values to provide their opinions however while linguistic information is readily available it is not operational and thus it has to be made usable though expressing it in terms of information granules to do so granular computing which has emerged as a unified and coherent framework of designing processing and interpretation of information granules can be used the aim of this paper is to present an information granulation of the linguistic information used in group decision making problems defined in heterogeneous contexts i e where the experts have associated importance degrees reflecting their ability to handle the problem the granulation of the linguistic terms is formulated as an optimization problem solved by using the particle swarm optimization in which a performance index is maximized by a suitable mapping of the linguistic terms on information granules formalized as sets this performance index is expressed as a weighted aggregation of the individual consistency achieved by each expert

age based model for weighted network with general assortative mixing abstract in this paper we propose an evolutionary model for weighted networks by introducing an age based mutual selection mechanism our model generates power law distributions of degree weight and strength which are confirmed by analytical predictions and are consistent with real observations the investigation of the relationship between clustering and the connectivity of nodes suggests hierarchical organization in the weighted networks furthermore both assortative and disassortative properties can be naturally obtained by tuning a parameter which controls the strength of age based preferential attachments since the age information of nodes is easier to acquire than the degree and strength of nodes and almost all empirically observed structural and weighted properties can be reproduced by the simple evolutionary regulation our model may reveal some underlying mechanisms that are key for the evolution of weighted complex networks

on first order fuzzy ricatti difference equation this paper deals with the existence the boundedness and the asymptotic behavior of the positive solutions to a first order fuzzy ricatti difference equation xn 1 a xnb xn n 0 1 where xn is a sequence of positive fuzzy numbers a b and the initial value x0 are positive fuzzy numbers moreover an example is given to demonstrate the effectiveness of the results obtained

on a functional differential equation arising from a traffic flow model we provide a derivation in the context of a traffic flow model as well as both analytical and numerical studies of the functional differential equation z s alpha 2 z s beta z s z s z s here alpha and beta are positive parameters and we are in particular investigating the existence and properties of nonconstant traveling wave type solutions

dynamic weight evolution network with preferential attachment abstract a dynamic weight evolution network with preferential attachment is introduced the network includes two significant characteristics i topological growth triggered by newly added node with m links at each time step each new edge carries an initial weight growing nonlinearly with time ii weight dynamics the weight between two existing nodes experiences increasing or decreasing in a nonlinear way by using continuum theory and mean field method we study the strength the degree the weight and their distributions we find that the distributions exhibit a power law feature in particular the relationship between the degree and the strength is nonlinear and the power law exponents of the three are the same all the theoretical predictions are successfully contrasted with numerical simulations

from unweighted to weighted networks with local information abstract in this paper we analyze an evolving model with local information which can generate a class of networks by choosing different values of the parameter p the model introduced exhibits the transition from unweighted networks to weighted networks because the distribution of the edge weight can be widely tuned with the increase in the local information the degree correlation of the network transforms from assortative to disassortative we also study the distribution of the degree strength and edge weight which all show crossover between exponential and scale free finally an application of the proposed model to the study of the synchronization is considered it is concluded that the synchronizability is enhanced when the heterogeneity of the edge weight is reduced

bifurcation analysis of traffic flow through an improved car following model considering the time delayed velocity difference abstract in this paper a new car following model with consideration of time delayed velocity difference is proposed to investigate the effect of time delayed velocity on traffic flow via bifurcation analysis based on this model the linear stability analysis is carried out and the corresponding stability condition is obtained then the hopf bifurcation analysis is performed in term of theoretical analysis and numerical simulation the result shows that there exist hopf bifurcation critical points and the position of the critical points is found to be located on the boundary of the instability region finally the influence of the delay time and sensitivity of velocity difference on hopf bifurcation is discussed respectively

on pattern formation in a class of traffic models abstract we consider a simple microscopic follow the leader model of n identical cars on a circular road in the classical setting a car is not allowed to reach its leader if it happens at a particular time t e we propose to extend the model beyond this time t e the idea is to define a physically reasonable leader for each car mathematically the resulting model is a kind of filippov system the objective is to study a long time behavior of the model in case n 3 we observed several invariant patterns which apparently exhibit spatial temporal symmetries we managed to classify and identify two kinds of rotating waves the classification exploits symbolic dynamical notions

updated semi discretization method for periodic delay differential equations with discrete delay an updated version of the semi discretization method is presented for periodic systems with a single discrete time delay the delayed term is approximated as a weighted sum of two neighbouring discrete delayed state values and the transition matrix over a single period is determined stability charts are constructed for the damped and delayed mathieu equation for different time period time delay ratios the convergence of the method is investigated by examples stability charts are constructed for 1 and 2 degree of freedom milling models the codes of the algorithm are also attached in the appendix copyright 2004 john wiley sons ltd

metastable patterns in solutions of ut ϵ2uxx f u we consider the equation in question on the interval 0 x 1 having neumann boundary conditions with f u f u where f is a double well energy density with equal minima at u 1 the only stable states of the system are patternless constant solutions but given two phase initial data a pattern of interfacial layers typically forms far out of equilibrium the ensuing nonlinear relaxation process is extremely slow patterns persist for exponentially long times proportional to exp a l where a f 1 and l is the minimum distance between layers physically a tiny potential jump across a layer drives its motion we prove the existence and persistence of these metastable patterns and characterise accurately the equations governing their motion the point of view is reminiscent of center manifold theory a manifold parametrising slowly evolving states is introduced a neighbourhood is shown to be normally attracting and the parallel flow is characterised to high relative accuracy proofs involve a detailed study of the dirichlet problem spectral gap analysis and energy estimates

equivalences of twisted k3 surfaces we prove that two derived equivalent twisted k3 surfaces have isomorphic periods the converse is shown for k3 surfaces with large picard number it is also shown that all possible twisted derived equivalences between arbitrary twisted k3 surfaces form a subgroup of the group of all orthogonal transformations of the cohomology of a k3 surface

numerical bifurcation analysis of delay differential equations numerical methods for the bifurcation analysis of delay differential equations ddes have only recently received much attention partially because the theory of ddes smoothness boundedness stability of solutions is more complicated and less established than the corresponding theory of ordinary differential equations as a consequence no established software packages exist at present for the bifurcation analysis of ddes we outline existing numerical methods for the computation and stability analysis of steady state solutions and periodic solutions of systems of ddes with several constant delays

stochastic master equation approach to aggregation in freeway traffic in analogy to the usual aggregation phenomena such as the formation of liquid droplets in a supersaturated vapor the nucleation growth and condensation of car clusters are considered in a one lane freeway traffic flow model the clustering behavior known as congestion in an initially homogeneous traffic stream is described by a master equation the construction of the stochastic equation is given as well as its relationship to other dynamical models numerical experiments in heavy traffic with well explained transition probabilities show the transition from the initial free particle situation free jet of vehicles to the final congested cluster state where one big aggregate of cars is formed the results are presented analytically in dependence of the stable cluster size from car concentration and numerically as stochastic trajectories

global bifurcation investigation of an optimal velocity traffic model with driver reaction time we investigate an optimal velocity model which includes the reflex time of drivers after an analytical study of the stability and local bifurcations of the steady state solution we apply numerical continuation techniques to investigate the global behavior of the system specifically we find branches of oscillating solutions connecting hopf bifurcation points which may be super or subcritical depending on parameters this analysis reveals several regions of multistability

isomorphism of two realizations of quantum affine algebra u_q widehat mathfrak g mathfrak l text n text we establish an explicit isomorphism between two realizations of the quantum affine algebra u q widehat mathfrak g mathfrak l text n text given previously by drinfeld and reshetikhin semenov tian shansky our result can be considered as an affine version of the isomorphism between the drinfield jimbo and the faddeev reshetikhin takhtajan constructions of the quantum algebra u q mathfrak g mathfrak l n

yang baxter equation in long range interacting systems we consider the su p spin chains with long range interactions and the spin generalization of the calogero sutherland models we show that their properties derive from a transfer matrix obeying the yang baxter equation we obtain the expression of the conserved quantities of the dynamical models and we diagonalise them in the spin chain case we establish the connection between the degeneracies of the spectrum and the representation theory of the yangians we use a correspondence with the dynamical models to diagonalise the hamiltonian finally we extend the previous results to the case of a trigonometric r matrix

improved stability bound for steady state flow in a car following model of road traffic on a circular route this note revisits a car following model of road traffic on a circular route that was studied in recent literature and improves a stability result for steady state flows that was obtained in this literature it will be shown through a counter example that the stability bound obtained in the literature only gives a sufficient condition for stability which only becomes necessary when the number of cars on the route tends to infinity we will further present a result that gives a necessary and sufficient condition for stability

invariant manifolds for metastable patterns in ut e2uxx f u we consider the above equation on the interval 0 x 1 subject to neumann boundary conditions with f u f u where f is a double well energy density function with equal minima our previous work 3 proved the existence and persistence of very slowly evolving patterns metastable states in solutions with two phase initial data here we characterise these metastable states in terms of the global unstable manifolds of equilibria as conjectured by fusco and hale 6

lyapunov vectors and assimilation in the unstable subspace theory and applications based on a limited number of noisy observations estimation algorithms provide a complete description of the state of a system at current time estimation algorithms that go under the name of assimilation in the unstable subspace aus exploit the nonlinear stability properties of the forecasting model in their formulation errors that grow due to sensitivity to initial conditions are efficiently removed by confining the analysis solution in the unstable and neutral subspace of the system the subspace spanned by lyapunov vectors with positive and zero exponents while the observational noise does not disturb the system along the stable directions the formulation of the aus approach in the context of four dimensional variational assimilation 4dvar aus and the extended kalman filter ekf aus and its application to chaotic models is reviewed in both instances the aus algorithms are at least as efficient but simpler to implement and computationally less demanding than their original counterparts as predicted by the theory when error dynamics is linear the optimal subspace dimension for 4dvar aus is given by the number of positive and null lyapunov exponents while the ekf aus algorithm using the same unstable and neutral subspace recovers the solution of the full ekf algorithm but dealing with error covariance matrices of a much smaller dimension and significantly reducing the computational burden examples of the application to a simplified model of the atmospheric circulation and to the optimal velocity model for traffic dynamics are given this article is part of a special issue of journal of physics a mathematical and theoretical devoted to lyapunov analysis from dynamical systems theory to applications

a traffic flow model with overtaking as a filippov system abstract we investigate microscopic models of road traffic in particular we consider a car following model for a single line traffic flow of n identical cars on a circular road the classical differentiable model breaks down at the time instant when two cars collide however the natural action of a driver would be to overtake a slower car in our previous work we proposed a model which simulates the overtaking we observed a large variety of oscillatory solutions oscillatory patterns of the model in the present contribution we formulate our model as a particular filippov system i e odes with discontinuous right hand sides hence we can identify our problem with a well defined solution class we define oscillatory patterns as invariant objects of this filippov system

subcritical hopf bifurcations in a car following model with reaction time delay a nonlinear car following model of highway traffic is considered which includes the reaction time delay of drivers linear stability analysis shows that the uniform flow equilibrium of the system loses its stability via hopf bifurcations and thus oscillations can appear the stability and amplitudes of the oscillations are determined with the help of normal form calculations of the hopf bifurcation that also handles the essential translational symmetry of the system we show that the subcritical case of the hopf bifurcation occurs robustly which indicates the possibility of bistability we also show how these oscillations lead to spatial wave formation as can be observed in real world traffic flows

consensus problems with distributed delays with application to traffic flow models this paper focuses on consensus problems for a class of linear systems with distributed delay that are encountered in modeling traffic flow dynamics in the application problems the distributed delay whose kernel is a gamma distribution with a gap represents the human drivers behavior in the average the aim of the paper is to give a characterization of the regions in the corresponding delay parameter space where a consensus is reached for all initial conditions the structure and properties of the system are fully exploited which leads to explicit and computationally tractable expressions as a by product a stability theory for distributed delay systems with a gamma distribution kernel is developed also explicit expressions for the consensus function al of time delay systems with constant and distributed delays that solve a consensus problem are provided several illustrative examples complete the presentation

nth order fuzzy linear differential equations in this paper a numerical method for solving nth order linear differential equations with fuzzy initial conditions is considered the idea is based on the collocation method the existence theorem of the fuzzy solution is considered this method is illustrated by solving several examples

time series forecasting using a system of ordinary differential equations this paper presents a hybrid evolutionary method for identifying a system of ordinary differential equations odes to predict the small time scale traffic measurements data we used the tree structure based evolutionary algorithm to evolve the architecture and a particle swarm optimization pso algorithm to fine tune the parameters of the additive tree models for the system of ordinary differential equations we also illustrate some experimental comparisons with genetic programming gene expression programming and a feedforward neural network optimized using pso algorithm experimental results reveal that the proposed method is feasible and efficient for forecasting the small scale traffic measurements data

swarm based translation invariant morphological prediction method for financial time series forecasting in this paper we present a method to overcome the random walk rw dilemma for financial time series forecasting called swarm based translation invariant morphological prediction stmp method it consists of a hybrid model composed of a modular morphological neural network mmnn combined with a particle swarm optimizer pso which searches for the best time lags to optimally describe the time series phenomenon as well as estimates the initial sub optimal parameters of the mmnn weights architecture and number of modules an additional optimization is performed with each particle of the pso population a distinct mmnn using the back propagation bp algorithm after the mmnn parameters adjustment we use a behavioral statistical test and a phase fix procedure to adjust time phase distortions observed in financial time series finally we conduct an experimental analysis with the proposed method using four real world stock market time series where five well known performance metrics and a fitness function are used to assess the prediction performance the obtained results are compared with those generated by classical models presented in the literature

learning symbolic representations of hybrid dynamical systems a hybrid dynamical system is a mathematical model suitable for describing an extensive spectrum of multi modal time series behaviors ranging from bouncing balls to air traffic controllers this paper describes multi modal symbolic regression mmsr a learning algorithm to construct non linear symbolic representations of discrete dynamical systems with continuous mappings from unlabeled time series data mmsr consists of two subalgorithms clustered symbolic regression a method to simultaneously identify distinct behaviors while formulating their mathematical expressions and transition modeling an algorithm to infer symbolic inequalities that describe binary classification boundaries these subalgorithms are combined to infer hybrid dynamical systems as a collection of apt mathematical expressions mmsr is evaluated on a collection of four synthetic data sets and outperforms other multi modal machine learning approaches in both accuracy and interpretability even in the presence of noise furthermore the versatility of mmsr is demonstrated by identifying and inferring classical expressions of transistor modes from recorded measurements

density waves in a traffic flow model with reaction time delay abstract density waves are investigated analytically and numerically in the optimal velocity model with reaction time delay of drivers the stability condition of this model is obtained by using the linear stability theory the results show that the decrease of reaction time delay of drivers leads to the stabilization of traffic flow the burgers korteweg de vries kdv and modified korteweg de vries mkdv equations are derived to describe the density waves in the stable metastable and unstable regions respectively the triangular shock waves soliton waves and kink antikink waves appearing respectively in the three distinct regions are derived to describe the traffic jams the numerical simulations are given

deterministic weighted scale free small world networks abstract we propose a deterministic weighted scale free small world model for considering pseudofractal web with the co evolution of topology and weight considering the fluctuations in traffic flow constitute a main reason for congestion of packet delivery and poor performance of communication networks we suggest a recursive algorithm to generate the network which restricts the traffic fluctuations on it effectively during the evolutionary process we provide a relatively complete view of topological structure and weight dynamics characteristics of the networks such as weight and strength distribution degree correlations average clustering coefficient and degree cluster correlations as well as the diameter

a discrete particle swarm optimization method for feature selection in binary classification problems abstract this paper investigates the feature subset selection problem for the binary classification problem using logistic regression model we developed a modified discrete particle swarm optimization pso algorithm for the feature subset selection problem this approach embodies an adaptive feature selection procedure which dynamically accounts for the relevance and dependence of the features included the feature subset we compare the proposed methodology with the tabu search and scatter search algorithms using publicly available datasets the results show that the proposed discrete pso algorithm is competitive in terms of both classification accuracy and computational performance

twisted fourier mukai number of a k3 surface we give a counting formula for the twisted fourier mukai partners of a projective k3 surface as an application we describe all twisted fourier mukai partners of a projective k3 surface of picard number 1