taxi trips distribution modeling based on entropy maximizing theory a case study in harbin city china abstract understanding origin destination distribution of taxi trips is very important for improving effects of transportation planning and enhancing quality of taxi services this study proposes a new method based on entropy maximizing theory to model od distribution in harbin city using large scale taxi gps trajectories firstly a k means clustering method is utilized to partition raw pick up and drop off location into different zones and trips are assumed to start from and end at zone centers a generalized cost function is further defined by considering travel distance time and fee between each od pair gps data collected from more than 1000 taxis at an interval of 30 s during one month are divided into two parts data from first twenty days is treated as training dataset and last ten days is taken as testing dataset the training dataset is used to calibrate model while testing dataset is used to validate model furthermore three indicators mean absolute error mae root mean square error rmse and mean percentage absolute error mpae are applied to evaluate training and testing performance of entropy maximizing model versus gravity model the results demonstrate entropy maximizing model is superior to gravity model findings of the study are used to validate the feasibility of od distribution from taxi gps data in urban system

bethe ansatz solution of zero range process with nonuniform stationary state the eigenfunctions and eigenvalues of the master equation for zero range process with totally asymmetric dynamics on a ring are found exactly using the bethe ansatz weighted with the stationary weights of particle configurations the bethe ansatz applicability requires the rates of hopping of particles out of a site to be the q numbers n q this is a generalization of the rates of hopping of noninteracting particles equal to the occupation number n of a site of departure the noninteracting case can be restored in the limit q ensuremath rightarrow 1 the limiting cases of the model for q 0 ensuremath infty correspond to the totally asymmetric exclusion process and the drop push model respectively we analyze the partition function of the model and apply the bethe ansatz to evaluate the generating function of the total distance traveled by particles at large time in the scaling limit in case of nonzero interaction q ensuremath ne 1 the generating function has the universal scaling form specific for the kardar parizi zhang universality class

random walk of second class particles in product shock measures we consider shock measures in a class of conserving stochastic particle systems on these shock measures have a product structure with a step like density profile and include a second class particle at the shock position we show for the asymmetric simple exclusion process for the exponential bricklayers process and for a generalized zero range process that under certain conditions these shocks and therefore the second class particles perform a simple random walk some previous results including random walks of product shock measures and stationary shock measures seen from a second class particle are direct consequences of our more general theorem multiple shocks can also be handled easily in this framework similar shock structure is also found in a nonconserving model the branching coalescing random walk where the role of the second class particle is played by the rightmost or leftmost particle

duality relations for asymmetric exclusion processes we derive duality relations for a class ofu q su 2 symmetric stochastic processes including among others the asymmetric exclusion process in one dimension like the known duality relations for symmetric hopping processes these relations express certainm point correlation functions inn particle systems n m in terms of sums of correlation functions of the same system but with onlym particles for the totally asymmetric case we obtain exact expressions for some boundary density correlation functions the dynamical exponent for these correlators isz 2 which is different from the dynamical exponent for bulk density correlations which is known to bez 3 2

dynamic analysis of traffic time series at different temporal scales a complex networks approach abstract the analysis of dynamics in traffic flow is an important step to achieve advanced traffic management and control in intelligent transportation system its complexity and periodicity are definitely two fundamental properties in traffic dynamics in this study we first measure the complexity of traffic flow data by lempel ziv algorithm at different temporal scales and the data are collected from loop detectors on freeway second to obtain more insight into the complexity and periodicity in traffic time series we then construct complex networks from traffic time series by considering each day as a cycle and each cycle as a single node the optimal threshold value of complex networks is estimated by the distribution of density and its derivative in addition the complex networks are subsequently analyzed in terms of some statistical properties such as average path length clustering coefficient density average degree and betweenness finally take 2 min aggregation data as example we use the correlation coefficient matrix adjacent matrix and closeness to exploit the periodicity of weekdays and weekends in traffic flow data the findings in this paper indicate that complex network is a practical tool for exploring dynamics in traffic time series

quenched convergence and strong local equilibrium for asymmetric zero range process with site disorder we study asymmetric zero range processes on z with nearest neighbour jumps and site disorder the jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles we prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities and dynamic local loss of mass at supercritical hydrodynamic densities our results do not assume starting from local gibbs states as byproducts of these results we prove convergence of the process from given initial configurations with an asymptotic density of particles to the left of the origin in particular we relax the weak convexity assumption of 7 8 for the escape of mass property 1 msc 2010 subject classification 60k35 82c22

shock fluctuations in asymmetric simple exclusion the one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the burgers equation we study the process with rates of jumpsp q to the right and left respectively and with initial product measure with densities to the left and right of the origin respectively with shock initial conditions we prove that a second class particle added to the system at the origin at time zero identifies microscopically the shock for all later times if this particle is added at another site then it describes the behavior of a characteristic of the burgers equation for vanishing left density 0 we prove in the scale t1 2 that the position of the shock at timet depends only on the initial configuration in a region depending ont the proofs are based on laws of large numbers for the second class particle

a technique for the numerical solution of initial value problems based on a class of birkhoff type interpolation method in this paper a class of birkhoff type interpolation problems on arbitrary nodal points is studied the explicit representation characterization the uniqueness and the error function are explicitly given furthermore we apply the obtained birkhoff type interpolation method to find i the numerical solution of high order initial value problems ivps and the corresponding error of this approximation ii the approximation of some special functions with their explicit error functions and iii new interpolatory type quadrature formulae of precision degree at least m n 1 and m kn 1 m n email protected n n k 2 numerical examples are included to demonstrate the validity and applicability of the technique proposed in this paper and a comparison is made with the existing results the results reveal that the new method is effective simple and accurate

microscopic shape of shocks in a domain growth model considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities e g the inviscid burgers equation for the simple exclusion process the physical solutions of these partial differential equations develop discontinuities called shocks the microscopic structure of these shocks is of much interest and far from being well understood we introduce a domain growth model in which we find a stationary in time product measure for the model as seen from a defect tracer or second class particle traveling with the shock we also show that under some natural assumptions valid for a wider class of domain growth models no other model has stationary product measure as seen from the moving defect tracer

shocks in the asymmetric exclusion process with internal degree of freedom we determine all families of markovian three state lattice gases with pair interaction and a single local conservation law one such family of models is an asymmetric exclusion process where particles exist in two different nonconserved states we derive conditions on the transition rates between the two states such that the shock has a particularly simple structure with minimal intrinsic shock width and random walk dynamics we calculate the drift velocity and diffusion coefficient of the shock

self duality for the two component asymmetric simple exclusion process we study a two component asymmetric simple exclusion process asep that is equivalent to the asep with second class particles we prove self duality with respect to a family of duality functions which are shown to arise from the reversible measures of the process and the symmetry of the generator under the quantum algebra uq x1d524 x1d529 3 we construct all invariant measures in explicit form and discuss some of their properties we also prove a sum rule for the duality functions

euler hydrodynamics of one dimensional attractive particle systems we consider attractive irreducible conservative particle systems on z without necessarily nearest neighbor jumps or explicit invariant measures we prove that for such systems the hydrodynamic limit under euler time scaling exists and is given by the entropy solution to some scalar conservation law with lipschitz continuous flux our approach is a generalization of bahadoran et al stochastic process appl 99 2002 1 30 from which we relax the assumption that the process has explicit invariant measures

multiple shocks in bricklayers model in bricklayers model which is a generalization of the misanthrope processes we show that a nontrivial class of product distributions is closed under the time evolution of the process this class also includes measures fitting to shock data of the limiting pde in particular we show that shocks of this type with discontinuity of size one perform ordinary nearest neighbor random walks only interacting in an attractive way via their jump rates our results are related to those of belitsky and schutz 4 on the simple exclusion process although we do not use quantum formalism as they do the structures we find are described from a fixed position similar ones were found in balazs 2 valak as seen from the random position of the second class particle

on the dirichlet problem for asymmetric zero range process on increasing domains in order to obtain hitting time estimates for the asymmetric zero range process azrp on d in dimensions d 3 we characterize the principal eigenvalue of the generator of the azrp with dirichlet boundary on special domains we obtain a donsker varadhan variational representation and show that the corresponding eigenfunction is unique in a natural class of functions

how to initialize a second class particle we identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric interacting particle systems with established hydrodynamic behavior respectively including zero range misanthrope and many other models the initial condition is a step profile which in some classical cases of asymmetric models gives rise to a rarefaction fan scenario we also point out a model with nonconcave nonconvex hydrodynamics where the rescaled second class particle distribution has both continuous and discrete counterparts the results follow from a substantial generalization of ferrari and kipnis arguments ann inst h poincare 31 1995 143 154 for the totally asymmetric simple exclusion process the main novelty is the introduction of a signed coupling measure as initial data which nevertheless results in a proper probability initial distribution for the site of the second class particle and makes the extension possible we also reveal in full generality a very interesting invariance property of the one site marginal distribution of the process underneath the second class particle which in particular proves the intrinsicality of our choice for the initial distribution finally we give a lower estimate on the probability of survival of a second class particle antiparticle pair

discontinuous condensation transition and nonequivalence of ensembles in a zero range process we study a zero range process where the jump rates do not only depend on the local particle configuration but also on the size of the system rigorous results on the equivalence of ensembles are presented characterizing the occurrence of a condensation transition in contrast to previous results the phase transition is discontinuous and the system exhibits ergodicity breaking and metastable phases this leads to a richer phase diagram including nonequivalence of ensembles in certain phase regions the paper is motivated by results from granular clustering where these features have been observed experimentally

existence of the zero range process and a deposition model with superlinear growth rates we give a construction of the zero range and bricklayers processes in the totally asymmetric attractive case the novelty is that we allow jump rates to grow exponentially earlier constructions have permitted at most linearly growing rates we also show the invariance and extremality of a natural family of i i d product measures indexed by particle density extremality is proved with an approach that is simpler than existing ergodicity proofs

large deviations of interacting particle systems in infinite volume we prove a large deviation theorem from the hydrodynamical limit for the empirical measure of ginzburg landau and zero range processes in infinite volume starting from deterministic initial configurations in the ginzburg landau case the main tool is the study of the evolution of the h 1 norm and in the zero range case the attractiveness which allows couplings

invariant measures for a two species asymmetric process we consider a process of two classes of particles jumping on a one dimensional lattice the marginal system of the first class of particles is the one dimensional totally asymmetric simple exclusion process when classes are disregarded the process is also the totally asymmetric simple exclusion process the existence of a unique invariant measure with product marginals with density and for the first and first plus second class particles respectively was shown by ferrari kipnis and saada recently derrida janowsky lebowitz and speer have computed this invariant measure for finite boxes and performed the infinite volume limit based on this computation we give a complete description of the measure and derive some of its properties in particular we show that the invariant measure for the simple exclusion process as seen from a second class particle with asymptotic densities and is equivalent to the product measure with densities to the left of the origin and to the right of the origin

from duality to determinants for q tasep and asep we prove duality relations for two interacting particle systems the q deformed totally asymmetric simple exclusion process q tasep and the asymmetric simple exclusion process asep expectations of the duality functionals correspond to certain joint moments of particle locations or integrated currents respectively duality implies that they solve systems of odes these systems are integrable and for particular step and half stationary initial data we use a nested contour integral ansatz to provide explicit formulas for the systems solutions and hence also the moments we form laplace transform like generating functions of these moments and via residue calculus we compute two different types of fredholm determinant formulas for such generating functions for asep the first type of formula is new and readily lends itself to asymptotic analysis as necessary to reprove gue tracy widom distribution fluctuations for asep while the second type of formula is recognizable as closely related to tracy and widom s asep formula comm math phys 279 2008 815 844 j stat phys 132 2008 291 300 comm math phys 290 2009 129 154 j stat phys 140 2010 619 634 for q tasep both formulas coincide with those computed via borodin and corwin s macdonald processes probab theory related fields 2014 158 225 400 both q tasep and asep have limit transitions to the free energy of the continuum directed polymer the logarithm of the solution of the stochastic heat equation or the hopf cole solution to the kardar parisi zhang equation thus q tasep and asep are integrable discretizations of these continuum objects the systems of odes associated to their dualities are deformed discrete quantum delta bose gases and the procedure through which we pass from expectations of their duality functionals to characterizing generating functions is a rigorous version of the replica trick in physics

asymptotic convergence of cubic hermite collocation method for parabolic partial differential equation in this paper the asymptotic convergence of cubic hermite collocation method in continuous time for the parabolic partial differential equation is established of order oh 2 the linear combination of cubic hermite basis taken as approximating function is evaluated using the zeros of chebyshev polynomials as collocation points the theoretical results are verified for two test problems

internal dla and the stefan problem generalized internal diffusion limited aggregation is a stochastic growth model on the lattice in which a finite number of sites act as poisson sources of particles which then perform symmetric random walks with an attractive zero range interaction until they reach the first site which has been visited by fewer than alpha particles at which point they stop sites on which particles are frozen constitute the occupied set we prove that in appropriate regimes the particle density has a hydrodynamic limit which is the one phase stefan problem this is then used to study the asymptotic behavior of the occupied set in two dimensions when the walks are independent with one source at the origin and alpha 1 we obtain in particular that the occupied set is asymptotically a disc of radius k sqrt t where k is the solution of exp k 2 4 pi k 2 settling a conjecture of lawler bramson and griffeath

fluctuation bounds in the exponential bricklayers process this paper is the continuation of our earlier paper balazs et al in ann inst henri poincare probab stat 48 1 151 187 2012 where we proved t1 3 order of current fluctuations across the characteristics in a class of one dimensional interacting systems with one conserved quantity we also claimed two models with concave hydrodynamic flux which satisfied the assumptions which made our proof work in the present note we show that the totally asymmetric exponential bricklayers process also satisfies these assumptions hence this is the first example with convex hydrodynamics of a model with t1 3 order current fluctuations across the characteristics as such it further supports the idea of universality regarding this scaling

blockage hydrodynamics of one dimensional driven conservative systems we consider an arbitrary one dimensional conservative particle system with finite range interactions and finite site capacity governed on the hydrodynamic scale by a scalar conservation law with lipschitz continuous flux h a finite size perturbation restricts the local current to some maximum value we show that the perturbed hydrodynamic behavior is entirely determined by if inf h is first nondecreasing and then nonincreasing which we believe is a necessary condition

exact shock measures and steady state selection in a driven diffusive system with two conserved densities we study driven 1d lattice gas models with two types of particles and nearest neighbor hopping we find the most general case when there is a shock solution with a product measure which has a density profile of a step function for both densities the position of the shock performs a biased random walk we calculate the microscopic hopping rates of the shock we also construct the hydrodynamic limit of the model and solve the resulting hyperbolic system of conservation laws in case of open boundaries the selected steady state is given in terms of the boundary densities

orthogonal stochastic duality functions from lie algebra representations we obtain stochastic duality functions for specific markov processes using representation theory of lie algebras the duality functions come from the kernel of a unitary intertwiner between representations which provides generalized orthogonality relations for the duality functions in particular we consider representations of the heisenberg algebra and mathfrak su 1 1 both cases lead to orthogonal self duality functions in terms of hypergeometric functions for specific interacting particle processes and interacting diffusion processes

between equilibrium fluctuations and eulerian scaling perturbation of equilibrium for a class of deposition models we investigate propagation of perturbations of equilibrium states for a wide class of 1d interacting particle systems the class of systems considered incorporates zero range k exclusion misanthropic bricklayers models and much more we do not assume attractivity of the interactions we apply yau s relative entropy method rather than coupling arguments the result is partial extension of t seppalainen s recent paper for 0 1 5 fixed we prove that rescaling microscopic space and time by n respectively n1 the macroscopic evolution of perturbations of microscopic order n of the equilibrium states is governed by burgers equation the same statement should hold for 0 1 2 as in seppalainen s cited paper but our method does not seem to work for 1 5

existence of hydrodynamics for the totally asymmetric simple k exclusion process in a totally asymmetric simple k exclusion process particles take nearest neighbor steps to the right on the lattice z under the constraint that each site contain at most k particles we prove that such processes satisfy hydrodynamic limits under euler scaling and that the limit of the empirical particle profile is the entropy solution of a scalar conservation law with a concave flux function our technique requires no knowledge of the invariant measures of the process which is essential because the equilibria of asymmetric k exclusion are unknown but we cannot calculate the flux function precisely the proof proceeds via a coupling with a growth model on the two dimensional lattice in addition to the basic k exclusion with constant exponential jump rates we treat the site disordered case where each site has its own jump rate randomly chosen but frozen for all time the hydrodynamic limit under site disorder is new even for the simple exclusion process the case k 1 our proof makes no use of the markov property so at the end of the paper we indicate how to treat the case with arbitrary waiting times

processus des misanthropes we consider a system of identical interacting particles moving on the lattice d the rate at which a particle at the site x jumps to the site y is p y x b x y where p is an irreducible probability on d and b x y is an increasing resp decreasing function of the number x resp y of particles at site x resp y we study the convergence of the system to equilibrium and describe the invariant measures

asymptotic behaviour of the galerkin and the finite element collocation methods for a parabolic equation the asymptotic convergence of the solution of a parabolic equation is proved the proof is based on two methods namely the galerkin method expressed in terms of linear splines and the finite element collocation method expressed by cubic spline basis functions both methods are considered in continuous time the asymptotic rate of convergence for the two methods is found to be of order o h 2

some properties of k step exclusion processes we introduce k step exclusion processes as generalizations of the simple exclusion process we state their main equilibrium properties when the underlying stochastic matrix corresponds to a random walk or is positive recurrent and reversible finally we prove laws of large numbers for tagged and second class particles

exploring dynamic property of traffic flow time series in multi states based on complex networks phase space reconstruction versus visibility graph abstract a new method based on complex network theory is proposed to analyze traffic flow time series in different states we use the data collected from loop detectors on freeway to establish traffic flow model and classify the flow into three states based on k means method we then introduced two widely used methods to convert time series into networks phase space reconstruction and visibility graph furthermore in phase space reconstruction we discuss how to determine delay time constant and embedding dimension and how to select optimal critical threshold in terms of cumulative degree distribution in the visibility graph we design a method to construct network from multi variables time series based on logical or finally we study and compare the statistic features of the networks converted from original traffic time series in three states based on phase space and visibility by using the degree distribution network structure correlation of the cluster coefficient to betweenness and degree degree correlation

q zero range has random walking shocks but no other surprises in the zero range world we check all nearest neighbour 1 dimensional asymmetric zero range processes for random walking product shock measures as demonstrated already for a few cases in the literature we find the totally asymmetric version of the celebrated q zero range process as the only new example besides an already known model of doubly infinite occupation numbers and exponentially increasing jump rates we also examine the interaction of shocks which appears somewhat more involved for q zero range than in the already known cases

a computationally efficient technique for solving two point boundary value problems in porous media a numerical technique for solving two point boundary value problems in the porous media is presented the technique is the combination of orthogonal collocation and finite element methods one provides the accuracy whereas the other provides the stability to the numerical results the technique is much simpler and the computer codes can be easily developed the numerical results are compared with the analytic results for verification the numerical results are found to match the analytic ones for more than four decimal places the method can be applied to the stiff problems without any limit on the range of parameters

absorbing state phase transition for driven dissipative stochastic dynamics on ℤ we study the long time behavior of conservative interacting particle systems in the activated random walk model for reaction diffusion systems and the stochastic sandpile we prove that both systems undergo an absorbing state phase transition

characterizing traffic time series based on complex network theory abstract a complex network is a powerful tool to research complex systems traffic flow being one of the most complex systems in this paper we use complex network theory to study traffic time series which provide a new insight into traffic flow analysis firstly the phase space which describes the evolution of the behavior of a nonlinear system is reconstructed using the delay embedding theorem secondly in order to convert the new time series into a complex network the critical threshold is estimated by the characteristics of a complex network which include degree distribution cumulative degree distribution and density and clustering coefficients we find that the degree distribution of associated complex network can be fitted with a gaussian function and the cumulative degree distribution can be fitted with an exponential function density and clustering coefficients are then researched to reflect the change of connections between nodes in complex network and the results are in accordance with the observation of the plot of an adjacent matrix consequently based on complex network analysis the proper range of the critical threshold is determined finally to mine the nodes with the closest relations in a complex network the modularity is calculated with the increase of critical threshold and the community structure is detected according to the optimal modularity the work in our paper provides a new way to understand the dynamics of traffic time series

condensation in stochastic particle systems with stationary product measures we study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities we review previous work on the stationary behaviour and put it in the context of the equivalence of ensembles providing a general characterization of the condensation transition for homogeneous and inhomogeneous systems in the thermodynamic limit this leads to strengthened results on weak convergence for subcritical systems and establishes the equivalence of ensembles for spatially inhomogeneous systems under very general conditions extending previous results which focused on attractive and finite systems we use relative entropy techniques which provide simple proofs making use of general versions of local limit theorems for independent random variables

stationary blocking measures for one dimensional nonzero mean exclusion processes the product bernoulli measures with densities a a e 0 1 are the extremal translation invariant stationary measures for an exclusion process with irreducible random walk kernel p in d 1 stationary measures that are not translation invariant are known to exist for specific p satisfying x xp x 0 these measures are concentrated on configurations that are completely occupied by particles far enough to the right and are completely empty far enough to the left that is they are blocking measures here we show stationary blocking measures exist for all exclusion processes in d 1 with p having finite range and x xp x 0

shock profiles for the asymmetric simple exclusion process in one dimension the asymmetric simple exclusion process asep on a one dimensional lattice is a system of particles which jump at rates p and 1 p here p 1 2 to adjacent empty sites on their right and left respectively the system is described on suitable macroscopic spatial and temporal scales by the inviscid burgers equation the latter has shock solutions with a discontinuous jump from left density rho to right density rho rho sqrt rho 1 rho rho 1 rho for a special value of the asymmetry given by p 1 p rho 1 rho rho 1 rho the measure is bernoulli with density rho on the left and rho on the right in the weakly asymmetric limit 2p 1 to0 the microscopic width of the shock diverges as 2p 1 1 the stationary measure is then essentially a superposition of bernoulli measures corresponding to a convolution of a density profile described by the viscous burgers equation with a well defined distribution for the location of the second class particle