quantum spectrum as a time series fluctuation measures the fluctuations in the quantum spectrum could be treated like a time series in this framework we explore the statistical self similarity in the quantum spectrum using the detrended fluctuation analysis dfa and random matrix theory rmt we calculate the hausdorff measure for the spectra of atoms and gaussian ensembles and study their self affine properties we show that dfa is equivalent to the delta3 statistics of rmt unifying two different approaches we exploit this connection to obtain theoretical estimates for the hausdorff measure

desynchronization in diluted neural networks the dynamical behavior of a weakly diluted fully inhibitory network of pulse coupled spiking neurons is investigated upon increasing the coupling strength a transition from regular to stochasticlike regime is observed in the weak coupling phase a periodic dynamics is rapidly approached with all neurons firing with the same rate and mutually phase locked the strong coupling phase is characterized by an irregular pattern even though the maximum lyapunov exponent is negative the paradox is solved by drawing an analogy with the phenomenon of stable chaos i e by observing that the stochasticlike behavior is limited to an exponentially long with the system size transient remarkably the transient dynamics turns out to be stationary

dynamical model and nonextensive statistical mechanics of a market index on large time windows the shape and tails of partial distribution functions pdf for a financial signal i e the s and the turbulent nature of the markets are linked through a model encompassing tsallis nonextensive statistics and leading to evolution equations of the langevin and fokker planck type a model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log returns for such a financial market index for small and large time windows and both for small and large log returns these turbulent market volatility of normalized log returns distributions can be sufficiently well fitted with a ensuremath chi 2 distribution the transition between the small time scale model of nonextensive intermittent process and the large scale gaussian extensive homogeneous fluctuation picture is found to be at ca a 200 day time lag the intermittency exponent ensuremath kappa in the framework of the kolmogorov log normal model is found to be related to the scaling exponent of the pdf moments thereby giving weight to the model the large value of ensuremath kappa points to a large number of cascades in the turbulent process the first kramers moyal coefficient in the fokker planck equation is almost equal to zero indicating no restoring force a comparison is made between normalized log returns and mere price increments

superstatistics in hydrodynamic turbulence abstract superstatistics is a statistics of a statistics relevant for driven nonequilibrium systems with fluctuating intensive parameters it contains tsallis statistics as a special case we show that probability density functions of velocity differences and accelerations measured in eulerian and lagrangian turbulence experiments are well reproduced by simple superstatistics models we compare fits obtained for log normal superstatistics and 2 superstatistics tsallis statistics

transition from localized to extended eigenstates in the ensemble of power law random banded matrices we study statistical properties of the ensemble of large n times n random matrices whose entries h ij decrease in a power law fashion h ij sim i j alpha mapping the problem onto a nonlinear sigma model with non local interaction we find a transition from localized to extended states at alpha 1 at this critical value of alpha the system exhibits multifractality and spectral statistics intermediate between the wigner dyson and poisson one these features are reminiscent of those typical for the mobility edge of disordered conductors we find a continuous set of critical theories at alpha 1 parametrized by the value of the coupling constant of the sigma model at alpha 1 all states are expected to be localized with integrable power law tails at the same time for 1 alpha 3 2 the wave packet spreading at short time scale is superdiffusive langle r rangle sim t frac 1 2 alpha 1 which leads to a modification of the altshuler shklovskii behavior of the spectral correlation function at 1 2 alpha 1 the statistical properties of eigenstates are similar to those in a metallic sample in d alpha 1 2 1 dimensions finally the region alpha 1 2 is equivalent to the corresponding gaussian ensemble of random matrices alpha 0 the theoretical predictions are compared with results of numerical simulations

two tandem queues with general renewal input i diffusion approximation and integral representations we consider two tandem queues with exponential servers arrivals to the first queue are governed by a general renewal process if the arrivals were also exponentially distributed this would be a simple example of a jackson network however the structure of the model is much more complicated for general arrivals we analyze the joint steady state queue length distribution for this network in the heavy traffic limit where the arrival rate is only slightly less than the service rates we formulate and solve the boundary value problem for the diffusion approximation to this model we obtain simple integral representations for the asymptotic steady state queue length distribution

nonextensive random matrix theory approach to mixed regular chaotic dynamics we apply tsallis q indexed entropy to formulate a nonextensive random matrix theory which may be suitable for systems with mixed regular chaotic dynamics the joint distribution of the matrix elements is given by folding the corresponding quantity in the conventional random matrix theory by a distribution of the inverse matrix element variance it keeps the basis invariance of the standard theory but violates the independence of the matrix elements we consider the subextensive regime of q more than unity in which the transition from the wigner to the poisson statistics is expected to start we calculate the level density for different values of the entropic index our results are consistent with an analogous calculation by tsallis and collaborators we calculate the spacing distribution for mixed systems with and without time reversal symmetry comparing the result of calculation to a numerical experiment shows that the proposed nonextensive model provides a satisfactory description for the initial stage of the transition from chaos towards the poisson statistics

multidimensional reflected brownian motions having exponential stationary distributions on considere la distribution stationnaire d un mouvement brownien reflechi dans un domaine d dimensionnel g on etudie deux classes de processus de ce type

some consequences of exchangeability in random matrix theory properties of infinite sequences of exchangeable random variables result directly in explicit expressions for calculating asymptotic densities of eigenvalues of any ensemble of random matrices h whose distribution depends only on tr h h where h is the hermitian conjugate of h for real symmetric matrices and for hermitian matrices the densities are constructed by summing up wigner semicircles with varying radii and weights as confirmed by monte carlo simulations extensions to more general matrix ensembles are also considered

semiclassical level spacings when regular and chaotic orbits coexist the authors calculate semiclassical limiting level spacing distributions p s for systems whose classical energy surface is divided into a number of separate region in which motion is regular or chaotic in the calculation it is assumed that the spectrum is the superposition of statistically independent sequences of levels from each of the classical phase space regions sequences from regular regions having poisson distributions and those from irregular regions having wigner distributions the formulae for p s depend on the sum of the liouville measures of all the classical regular regions and on the separate liouville measures of the significant chaotic regions

family of solvable generalized random matrix ensembles with unitary symmetry we construct a very general family of characteristic functions describing random matrix ensembles rme having a global unitary invariance and containing an arbitrary one variable probability measure which we characterize by a spread function various choices of the spread function lead to a variety of possible generalized rmes which show deviations from the well known gaussian rme originally proposed by wigner we obtain the correlation functions of such generalized ensembles exactly and show examples of how particular choices of the spread function can describe ensembles with arbitrary eigenvalue densities as well as critical ensembles with multifractality

on the diffusion approximation to two parallel queues with processor sharing a two dimensional queuing model is considered in which the server in the second queue helps the server in the first queue during periods when the second queue is empty the system is analyzed in the heavy traffic limit and explicit approximate solutions are obtained to the resulting diffusion equations using singular perturbation methods approximate asymptotic formulas are obtained for the stationary distribution of the number of customers as well as for some first passage time problems associated with the busy period it is shown that these formulas reduce to the asymptotic expansions of the exact solutions when the latter are available

computing moments of the exit time distribution for markov processes by linear programming we provide a new approach to the numerical computation of moments of the exit time distribution of markov processes the method relies on a linear programming formulation of a process exiting from a bounded domain the lp formulation characterizes the evolution of the process through the moments of the induced occupation measure and naturally provides upper and lower bounds for the exact values of the moments the conditions the moments have to satisfy are derived directly from the generator of the markov process and are not based on some approximation of the process excellent software is readily available because the computations involve finite dimensional linear programs

random matrix ensembles from nonextensive entropy the classical gaussian ensembles of random matrices can be constructed by maximizing boltzmann gibbs shannon s entropy s text bgs ensuremath ensuremath int d mathbf h p mathbf h mathrm ln p mathbf h with suitable constraints here we construct and analyze random matrix ensembles arising from the generalized entropy s q 1 ensuremath ensuremath int d mathbf h p mathbf h q q ensuremath 1 thus s 1 s text bgs the resulting ensembles are characterized by a parameter q measuring the degree of nonextensivity of the entropic form making q ensuremath rightarrow 1 recovers the gaussian ensembles if q ensuremath ne 1 the joint probability distributions p mathbf h cannot be factorized i e the matrix elements of mathbf h are correlated in the limit of large matrices two different regimes are observed when ql1 p mathbf h has compact support and the fluctuations tend asymptotically to those of the gaussian ensembles anomalies appear for qg1 both p mathbf h and the marginal distributions p h ij show power law tails numerical analyses reveal that the nearest neighbor spacing distribution is also long tailed not wigner dyson and after proper scaling very close to the result for the 2 ifmmode times else texttimes fi 2 case char22 a generalization of wigner s surmise we discuss connections of these nonextensive ensembles with other non gaussian ones such as the so called l evy ensembles and those arising from soft confinement

classical dynamics of a family of billiards with analytic boundaries the classical dynamics of a billiard which is a quadratic conformal image of the unit disc is investigated the author gives the stability analysis of major periodic orbits present the poincare maps demonstrate the mixing properties by following the evolution of a small element in phase space show the existence of homoclinic points and calculate the lyapunov exponent and the kolmogorov entropy h it turns out that the system becomes strongly chaotic positive h for sufficiently large deformations of the unit disc the system shows a generic stochastic transition the computations suggest that the system is mixing if the boundary is not convex

family of generalized random matrix ensembles using the generalized maximum entropy principle based on the nonextensive q entropy a family of random matrix ensembles is generated this family unifies previous extensions of random matrix theory rmt and gives rise to an orthogonal invariant stable levy ensemble with new statistical properties some of them are analytically derived

models of intermediate spectral statistics based on numerical results it is conjectured that the spectral statistics of certain pseudointegrable billiards have a special form similar to that of the anderson model at the transition point a simple theoretical model where such statistics can be obtained analytically is briefly discussed a few models with similar behavior are considered in particular we analytically found the eigenvalue statistics of a poisson distributed matrix perturbed by a rank one matrix which is a good model for spectral statistics of a singular billiard

wireframe projections physical realisability of curved objects and unambiguous reconstruction of simple polyhedra the reconstruction of an object from a single 2d projection of a 3d wireframe model is a vision problem with applications in cad cam and computer graphics we propose an algorithm for the interpretation of wireframe projections based on assigning semantic and numerical depth labels to lines this method allows us to state necessary and sufficient conditions for the physical realisability of a wireframe projection of a curved object the presence of linear features provides further constraints on the positions of object vertices for example each straight line gives rise to a coplanarity constraint between a set of object vertices we show that extra information such as vanishing points parallel lines or user entered depth parity information is sufficient to uniquely determine the face circuits in wireframe projections of polyhedra with simple trihedral vertices in fact a polyhedron with simple trihedral vertices can be unambiguously reconstructed from its 3d wireframe model

a heavy traffic limit theorem for networks of queues with multiple customer types the central result of this paper is a heavy traffic limit theorem for the vector of total station workloads in an open network of queues with multiple customer types under first come first served and priority disciplines the limit process is a regulated brownian motion on the nonnegative orthant with parameters specified from the first two moments of the interarrival and service time distributions and a matrix of reduced routing information through the phenomenon of state space collapse associated limit results for queue length workload and sojourn time processes by customer type are obtained jointly as simple transformations of the total workload limit process diffusion approximations based on the theorem are discussed

equilibria for diffusion models of pairs of communicating computers symmetric case the steady state queueing behavior of interacting computers is basic to computer network theory equilibrium properties are determined for the diffusion model for the special case of a symmetrically disposed pair of communicaling computers in the mathematical model arrivals to the system can represent the presentation of programming jobs and each service represents the completion of a stage of processing the exogenous arrivals and the services during the busy period are permitted to be arbitrary renewal processes computer interaction arises as follows when each stage of processing is completed a certain probability exists that the entire job is complete however with the complementary probability the job is input to the other computer for an additional stage of processing in the space of all systems we find an infinite set of curves whereon the joint equilibrium density reduces to a very simple form for the general case a direct formal infinite series representation of the joint equilibrium density is found using conformal mapping the moment generating function is obtained rational expressions for the mean queue size and delay are given the mean queue size for poisson arrivals is interpreted a simple expression for the tail exponent for the queue size marginal is found the nature of the joint density in the neighborhood of the origin is delineated the connection to delay equilibria is mentioned extensions to a larger class of communicating computer pairs is indicated

generalized superstatistics of nonequilibrium markovian systems abstract the paper is devoted to the construction of the superstatistical description for nonequilibrium markovian systems it is based on kirchhoff s diagram technique and the assumption on the system under consideration to possess a wide variety of cycles with vanishing probability fluxes the latter feature enables us to introduce equivalence classes called channels within which detailed balance holds individually then stationary probability as well as flux distributions are represented as some sums over the channels the latter construction actually forms the superstatistical description which however deals with a certain superposition of equilibrium subsystems rather than a formal expansion of the nonequilibrium steady state distribution into terms of the boltzmann type

overcoming superstrictness in line drawing interpretation presents an algorithm for correcting incorrect line drawings incorrect projections of a polyhedral scene such incorrect drawings arise e g when an image of a polyhedral world is taken the edges and vertices are extracted and a drawing is synthesized along the way the true positions of the vertices in the 2d projection are perturbed due to digitization errors and the preprocessing as most available algorithms for interpreting line drawings are superstrict they judge these noisy inputs as incorrect and fail to reconstruct a three dimensional scene from them the presented method overcomes this problem by moving the positions of all vertices until a very close correct drawing is found the closeness criterion is to minimize the sum of squared distances from each vertex in the input drawing to its corrected position with this tool any superstrict method for line drawing interpretation is now practical as it can be applied to the corrected version of the input drawing

random matrix theory within superstatistics we propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics spectral characteristics of systems with mixed regular chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable we illustrate the method by calculating the level density the nearest neighbor spacing distributions and the two level correlation functions for systems in transition from order to chaos the calculated spacing distribution fits the resonance statistics of random binary networks obtained in a recent numerical experiment

oblique derivative boundary conditions and the image method the image method of solving boundary value problems is extended to oblique derivative boundary conditions on plane boundaries for a class of equations including the wave equation the heat equation and laplace s equation this generalizes the recent result of gilbarg and trudinger elliptic partial differential equations of second order springer verlag berlin 1977 for laplace s equation the usefulness of the method is illustrated by solving with it both the wave equation and the heat equation in a half space with an initial point source and an oblique derivative boundary condition in both cases a surface wave is found for the wave equation there is a region near the boundary where the surface wave is the first arrival for the heat equation the surface wave is the largest wave in this region for small values of the time

reflected brownian motion in a wedge semimartingale property in this paper the object of study is reflected brownian motion in a two dimensional wedge with constant direction of reflection on each side of the wedge the basic question considered here is when is this process a semimartingale it is first shown that a related process defined by specifying the corner of the wedge to be an absorbing state rather than an instantaneous one is a semimartingale conditions for the existence and uniqueness of the process for which the corner is an instantaneous state were given by vardhan and williams brownian motion in a wedge with oblique reflection comm pure appl math to appear under these conditions it is shown that starting away from the corner the process is a semimartingale if and only if there is a convex combination of the directions of reflection that points into the wedge this equivalence is also shown to hold starting from the corner except in one unresolved case for which the wedge angle exceeds and the directions of reflection are exactly opposed

non gaussian probability distribution functions from maximum entropy principle considerations in this work we develop the recently suggested concept of superstatistics c beck and e g d cohen physica a 322 267 2003 face the problem of devising a viable way for estimating the correct statistics for a system in the absence of sufficient knowledge of its microscopical dynamics and suggest to solve it through the maximum entropy principle as an example we deduce the probability distribution function for velocity fluctuations in turbulent fluids which is slightly different from the form suggested by c beck phys rev lett 87 180601 2001

spectral fluctuations of billiards with mixed dynamics from time series to superstatistics a statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards one with mushroomlike shape and the other from the family of the limacon billiards is presented these billiards have mixed regular chaotic dynamics but different structures in their classical phase spaces the spectrum of each billiard is represented as a time series where the level order plays the role of time two most important findings follow from the time series analysis first the spectra can be characterized by two distinct relaxation lengths this is a prerequisite for the validity of the superstatistical approach which is based on the folding of two distribution functions second the shape of the resulting probability density function of the so called superstatistical parameter is reasonably approximated by an inverse chi2 distribution this distribution is used to compute nearest neighbor spacing distributions and compare them with those of the resonance frequencies of billiards with mixed dynamics within the framework of superstatistics the obtained spacing distribution is found to present a good description of the experimental ones and is of the same or even better quality as a number of other spacing distributions including the one from berry and robnik however in contrast to other approaches toward a theoretical description of spectral properties of systems with mixed dynamics superstatistics also provides a description of properties of the eigenfunctions in terms of a superstatistical generalization of the porter thomas distribution indeed the inverse chi2 parameter distribution is found suitable for the analysis of experimental resonance strengths in the limacon billiards within the framework of superstatistics

plane based optimization for 3d object reconstruction from single line drawings in previous optimization based methods of 3d planar faced object reconstruction from single 2d line drawings the missing depths of the vertices of a line drawing and other parameters in some methods are used as the variables of the objective functions a 3d object with planar faces is derived by finding values for these variables that minimize the objective functions these methods work well for simple objects with a small number tv of variables as n grows however it is very difficult for them to find the expected objects this is because with the nonlinear objective functions in a space of large dimension the search for optimal solutions can easily get trapped into local minima in this paper we use the parameters of the planes that pass through the planar faces of an object as the variables of the objective function this leads to a set of linear constraints on the planes of the object resulting in a much lower dimensional null space where optimization is easier to achieve we prove that the dimension of this null space is exactly equal to the minimum number of vertex depths that define the 3d object since a practical line drawing is usually not an exact projection of a 3d object we expand the null space to a larger space based on the singular value decomposition of the projection matrix of the line drawing in this space robust 3d reconstruction can be achieved compared with the two most related methods our method not only can reconstruct more complex 3d objects from 2d line drawings but also is computationally more efficient

open queueing networks in heavy traffic this paper presents heavy traffic limit theorems for the queue length and sojourn time processes associated with open queueing networks these limit theorems state that properly normalized sequences of queue length and sojourn time processes converge weakly to a certain diffusion as the network traffic intensity converges to unity the limit diffusion is reflected brownian motion on the nonnegative orthant this process behaves like brownian motion on the interior of its state space and reflects instantaneously on the boundaries the reflection direction is a constant for each boundary hyperplane

stickiness in hamiltonian systems from sharply divided to hierarchical phase space we investigate the dynamics of chaotic trajectories in simple yet physically important hamiltonian systems with nonhierarchical borders between regular and chaotic regions with positive measures we show that the stickiness to the border of the regular regions in systems with such a sharply divided phase space occurs through one parameter families of marginally unstable periodic orbits and is characterized by an exponent ensuremath gamma 2 for the asymptotic power law decay of the distribution of recurrence times generic perturbations lead to systems with hierarchical phase space where the stickiness is apparently enhanced due to the presence of infinitely many regular islands and cantori in this case we show that the distribution of recurrence times can be composed of a sum of exponentials or a sum of power laws depending on the relative contribution of the primary and secondary structures of the hierarchy numerical verification of our main results are provided for area preserving maps mushroom billiards and the newly defined magnetic mushroom billiards

description of chaos order transition with random matrices within the maximum entropy principle the deformed gaussian orthogonal ensemble introduced earlier is developed here for large dimensional matrices both the spacing and eigenvector distributions are studied and compared to other ones suggested for the chaos order transition problem the concept of a universal lower entropy with respect to the gaussian orthogonal ensemble entropy is proved very useful

interpolation approximations of sojourn time distributions we present a method for approximating sojourn time distributions in open queueing systems based on light and heavy traffic limits the method is consistent with and generalizes the interpolation approximations for moments previously presented by m i reiman and b simon the method is applicable to the class of systems for which both light and heavy traffic limits can be computed which currently includes markovian networks of priority queues with a unique bottleneck node we illustrate the method of generating closed form analytic approximations for the sojourn time distribution of the m m 1 queue with bernoulli feedback the m m 1 processor sharing queue a priority queue with feedback and the m ek 1 queue empirical evidence suggests that the method works well on a large and identifiable class of priority queueing models

reflected brownian motion with skew symmetric data in a polyhedral domain this paper is concerned with the characterization and invariant measures of certain reflected brownian motions rbm s in polyhedral domains the kind of rbm studied here behaves like d dimensional brownian motion with constant drift in the interior of a simple polyhedron and is instantaneously reflected at the boundary in directions that depend on the face that is hit under the assumption that the directions of reflection satisfy a certain skew symmetry condition first introduced in harrison williams 9 it is shown that such an rbm can be characterized in terms of a family of submartingales and that it reaches non smooth parts of the boundary with probability zero in 9 a purely analytic problem associated with such an rbm was solved here the exponential form solution obtained in 9 is shown to be the density of an invariant measure for the rbm furthermore if the density is integrable over the polyhedral state space then it yields the unique stationary distribution for the rbm in the proofs of these results a key role is played by a dual process for the rbm and by results in 9 for reflected brownian motions on smooth approximating domains

spectral statistics in the quantized cardioid billiard the spectral statistics of the strongly chaotic cardioid billiard is studied the analysis is based on the first 11 000 quantal energy levels for both odd and even symmetry it is found that the level spacing distribution is in good agreement with the gaussian orthogonal ensemble distribution of random matrix theory in the cases of the number variance and rigidity we observe agreement with the random matrix model for short range correlations only whereas for long range correlations both statistics saturate in agreement with semiclassical expectations furthermore the conjecture that for classically chaotic systems the normalized mode fluctuations have a universal gaussian distribution with unit variance is tested and found to be in very good agreement for both symmetry classes by means of the gutzwiller trace formula the trace of the cosine modulated heat kernel is studied since the billiard boundary is focusing there are conjugate points that give rise to zeros instead of exclusively at gaussian peaks at the locations of the periodic orbits

the effect of pitchfork bifurcations on the spectral statistics of hamiltonian systems we present a quantitative semiclassical treatment of the effects of bifurcations on the spectral rigidity and the spectral form factor of a hamiltonian quantum system defined by two coupled quartic oscillators which on the classical level exhibits mixed phase space dynamics we show that the signature of a pitchfork bifurcation is two fold beside the known effect of an enhanced periodic orbit contribution due to its peculiar hbar dependence at the bifurcation we demonstrate that the orbit pair born at the bifurcation gives rise to distinct deviations from universality slightly above the bifurcation this requires a semiclassical treatment beyond the so called diagonal approximation our semiclassical predictions for both the coarse grained density of states and the spectral rigidity are in excellent agreement with corresponding quantum mechanical results

from time series to superstatistics complex nonequilibrium systems are often effectively described by a statistics of a statistics in short a superstatistics we describe how to proceed from a given experimental time series to a superstatistical description we argue that many experimental data fall into three different universality classes chi2 superstatistics tsallis statistics chi2 inverse superstatistics and log normal superstatistics we discuss how to extract the two relevant well separated superstatistical time scales tau and t the probability density of the superstatistical parameter beta and the correlation function for beta from the experimental data we illustrate our approach by applying it to velocity time series measured in turbulent taylor couette flow which is well described by log normal superstatistics and exhibits clear time scale separation

wavelet analysis and scaling properties of time series we propose a wavelet based method for the characterization of the scaling behavior of nonstationary time series it makes use of the built in ability of the wavelets for capturing the trends in a data set in variable window sizes discrete wavelets from the daubechies family are used to illustrate the efficacy of this procedure after studying binomial multifractal time series with the present and earlier approaches of detrending for comparison we analyze the time series of averaged spin density in the 2d ising model at the critical temperature along with several experimental data sets possessing multifractal behavior

conformal mapping solution of laplace s equation on a polygon with oblique derivative boundary conditions we consider laplace s equation in a polygonal domain together with the boundary conditions that along each side the derivative in the direction at a specified oblique angle from the normal should be zero first we prove that solutions to this problem can always be constructed by taking the real part of an analytic function that maps the domain onto another region with straight sides oriented according to the angles given in the boundary conditions then we show that this procedure can be carried out successfully in practice by the numerical calculation of schwarz christoffel transformations the method is illustrated by application to a hall effect problem in electronics and to a reflected brownian motion problem motivated by queueing theory

superstatistics in random matrix theory abstract using the superstatistics method we propose an extension of the random matrix theory to cover systems with mixed regular chaotic dynamics unlike most of the other works in this direction the ensembles of the proposed approach are basis invariant but the matrix elements are not statistically independent spectral characteristics of the mixed systems are expressed by averaging the corresponding quantities in the standard random matrix theory over the fluctuations of the inverse variance of the matrix elements we obtain analytical expressions for the level density and the nearest neighbor spacing distributions for four different inverse variance distributions the resulting expressions agree with each other for small departures from chaos measured by an effective non extensivity parameter our results suggest among other things that superstatistics is suited only for the initial stage of transition from chaos to regularity

on the diffusion approximation to a fork and join queueing model the use of singular perturbation methods to obtain approximate analytic solutions to the types of diffusion equations that are used to model queueing networks is shown as an example a two dimensional fork and join model is considered approximations to the stationary distribution of the number of customers in the system as well as the residual busy period are computed the formulas obtained clearly show the dependence of the solution on the variables and the parameters of the model

distribution of resonance strengths in microwave billiards of mixed and chaotic dynamics a new measure for statistical properties of the wave function components of quantum systems the distribution of the product of two partial widths is introduced it is tested with data obtained in analog experiments with microwave billiards where the product of two partial widths equals the resonance strengths in the microwave spectra the billiards are from the family of the limacons one with chaotic and two with mixed classical dynamics for completely chaotic systems the partial widths generically obey a porter thomas distribution we show that in this case the distribution of their product equals a k0 distribution while we find deviations of the experimental strength distribution from the k0 distribution for the billiards with mixed dynamics the distributions agree perfectly for the chaotic billiard when taking into account the experimental threshold of detection in the theoretical description hence the strength distribution provides another stringent test for the connection between statistical properties of systems with classical chaotic dynamics and random matrix theory

a shape from shading method of polyhedral objects using prior information we propose a new method for recovering the 3d shape of a polyhedral object from its single 2d image using the shading information contained in the image and the prior information on the object in a strict sense we cannot recover the shape of a polyhedron from an incorrect line drawing even if it is practically almost correct in order to overcome this problem we propose a flexible face positioning method that can permit inconsistencies in the recovered shape that arise from vertex position errors contained in incorrect line drawings also we propose to use prior information about the horizontality and verticality of special faces and the convex and concave properties of the edges in order to attain good solutions and present a method of formulating such prior information as physical constraints the shape from shading method is formulated as a minimization problem of a nonlinear cost function with the nonlinear constraints and its solution is searched by a global optimization algorithm in the experiments with a synthetic image and three kinds of real images shapes that are similar to those of the actual objects were recovered in all cases as a result the proposed method has proven to be effective in the shape recovery of simple shape polyhedral objects

approximate analysis of fork join synchronization in parallel queues an approximation technique called scaling approximation is introduced and applied to the analysis of homogeneous fork join queuing systems consisting of k or 2 servers the development of the scaling approximation technique is guided by both experimental and theoretical considerations the approximation is based on the observation that there exist upper and lower bounds on the mean response time that grow at the same rate as a function of k simple closed form approximate expressions for the mean response time are derived and compared to simulation results the relative error in the approximation is less than 5 for k

workload models for stochastic networks value functions and performance evaluation this paper concerns control and performance evaluation for stochastic network models structural properties of value functions are developed for controlled brownian motion cbm and deterministic fluid workload models leading to the following conclusions outside of a null set of network parameters the following hold i the fluid value function is a smooth function of the initial state under further minor conditions the fluid value function satisfies the derivative boundary conditions that are required to ensure it is in the domain of the extended generator for the cbm model exponential ergodicity of the cbm model is demonstrated as one consequence ii the fluid value function provides a shadow function for use in simulation variance reduction for the stochastic model the resulting simulator satisfies an exact large deviation principle while a standard simulation algorithm does not satisfy any such bound iii the fluid value function provides upper and lower bounds on performance for the cbm model this follows from an extension of recent linear programming approaches to performance evaluation

evolutionary search for faces from line drawings single 2d line drawing is a straightforward method to illustrate 3d objects the faces of an object depicted by a line drawing give very useful information for the reconstruction of its 3d geometry two recently proposed methods for face identification from line drawings are based on two steps finding a set of circuits that may be faces and searching for real faces from the set according to some criteria the two steps however involve two combinatorial problems the number of the circuits generated in the first step grows exponentially with the number of edges of a line drawing these circuits are then used as the input to the second combinatorial search step when dealing with objects having more faces the combinatorial explosion prevents these methods from finding solutions within feasible time this paper proposes a new method to tackle the face identification problem by a variable length genetic algorithm with a novel heuristic and geometric constraints incorporated for local search the hybrid ga solves the two combinatorial problems simultaneously experimental results show that our algorithm can find the faces of a line drawing having more than 30 faces much more efficiently in addition simulated annealing for solving the face identification problem is also implemented for comparison

new class of random matrix ensembles with multifractal eigenvectors department of physics university of florida gainesville florida 32611 february 1 2008 three recently suggested random matrix ensembles rme are linked together to represent a class of rme with multifrac tal eigenfunction statistics the generic form of the two levelcorrelation function for the case of weak and extremely strongmultifractality is suggested pacs numbers 71 25 s 72 15 rn 05 45 b

the interpretation of line drawings with contrast failure and shadows in line drawings derived from real images lines may be missing due to contrast failure and objects with curved surfaces may cast shadows from multiple light sources this paper shows that it is the presence of shadows rather than contrast failure that renders the line drawing labelling problem np complete however shadows are a valuable visual cue since their presence is formally shown to reduce the average ambiguity of drawings this is especially true when constraints concerning shadow formation are employed to differentiate shadow and non shadow lines the extended junction constraint concerning straight lines colinear with junctions compensates the loss of information caused by contrast failure in fact we observe the contrast failure paradox a drawing is sometimes less ambiguous when lines are partly missing due to contrast failure it is known that the coplanarity of sets of object vertices can be deduced from the presence of straight lines in the drawing this paper shows that these coplanarity constraints are robust to the presence of contrast failure

reflected brownian motion on an orthant we consider a k dimensional diffusion process z whose state space is the nonnegative orthant on the interior of the orthant z behaves like a kdimensional brownian motion with arbitrary covariance matrix and drift vector at each of the k 1 dimensional hyperplanes that form the boundary of the orthant z reflects instantaneously in a direction that is constant over that hyperplane there is no extant theory of multidimensional diffusion that applies to this process because the boundary of its state space is not smooth we adopt an approach that requires a restriction on the directions of reflection but reiman has shown that this restriction is met by all diffusions z arising as heavy traffic limits in open k station queuing networks our process z is defined as a path to path mapping of k dimensional brownian motion from this construction it follows that z is a continuous markov process and a semimartingale using the latter property we obtain a change of variable formula from which one can develop a complete analytical theory for the process z

statistics of the eigenvalues of tsallis matrices abstract the statistics of the eigenvalues of symmetric random matrices composed by real and statistically independent elements following the distribution that maximizes tsallis s entropy is carried numerically in the limit of large matrices for entropic indexes in the interval 5 3 by using a convenient rescale of variables it is possible to show that such matrices fall in the same class of the gaussian orthogonal ensemble goe for the entropic index 5 3 q the density of eigenvalues and the distribution of level spacings do not seem to follow a simple rescale of variables involving different values of q and exhibit a behavior very distinct from the goe both quantities present long tails for 5 3 q 2 and such long tails die out when q 2 the density of eigenvalues appears to be symmetric around zero exhibiting a peak at the origin that becomes steeper for increasing values of q approaching a delta function at the origin when q 3 the distribution of level spacings displays a form that resembles the well known wigner s surmise augmented by a long tail for q slightly greater than 5 3 but gets deformed for increasing values of q approaching an exponential decay for q 2 for q close to 3 our results resemble those of very sparse random matrices characterized by many zero matrix elements

multiparameter generalization of nonextensive statistical mechanics we show that the stochastic interpretation of tsallis s thermostatistics given recently by beck phys rev lett 87 180601 2001 leads naturally to a multiparameter generalization the resulting class of distributions is able to fit experimental results which cannot be reproduced within boltzmann s or tsallis s formalism

superstatistical random matrix theory approach to transition intensities in mixed systems we study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory which is based on beck and cohen s superstatistics we obtain an analytic expression for the distribution of the reduced transition probabilities that applies to systems undergoing a transition out of chaos the obtained distribution fits the results of a previous nuclear shell model calculations for some electromagnetic transitions that deviate from the porter char21 thomas distribution it agrees with the experimental reduced transition probabilities for the 26 mathrm al nucleus better than the commonly used ensuremath chi 2 distribution

on the distribution of multidimensional reflected brownian motion let z z t t 0 be a reflected brownian motion on the k dimensional nonnegative orthant with the direction of reflection constant over each boundary surface such processes arise in heavy traffic theory for k station networks of queues this paper continues our study of the diffusion process z with attention restricted to the case k 2 for simplicity most of the results extend directly to higher dimensions our notation and style of argument are designed to suggest appropriate generalizations for arbitrary k wherever possible the backward equation for the transition density function with boundary and initial conditions the corresponding forward equation and the equation for the steady state distribution are all derived informally also presented are various calculations relating to steady state distributions including a moment formula and the derivation of a condition involving the drifts and directions of reflection that we conjecture to be necessary and sufficient for existence

beyond the berry robnik regime a random matrix study of tunneling effects we consider the energy spectra of quantum hamilton systems whose classical dynamics is of mixed type i e regular for some initial conditions in the classical phase space and chaotic for the complementary initial conditions in the strict semiclassical limit when the effective planck constant eff is sufficiently small the berry robnik br statistics applies while at larger values of eff or smaller energies one sees deviations from br due to localization and tunneling effects we derive a two level random matrix model which describes these effects and can be treated analytically in a closed form the coupling between the regular and chaotic levels due to tunneling is assumed to be gaussian distributed this two level model describes most of the features of matrices of large dimensions here n 1000 which we treat numerically and is predicted to apply in mixed type systems at low energies the proposed analytical level spacing distribution function has two parameters the br parameter characterizing the classical phase space and the coupling antenna distortion or tunneling parameter between states localization effects so far are not included in our analysis except in the special case where can be replaced by some effective eff

spectral fluctuation characterization of random matrix ensembles through wavelets a recently developed wavelet based approach is employed to characterize the scaling behaviour of spectral fluctuations of random matrix ensembles as well as complex atomic systems our study clearly reveals anti persistent behaviour and supports the fourier power spectral analysis it also finds evidence for multi fractal nature in the atomic spectra the multi resolution and localization nature of the discrete wavelets ideally characterizes the fluctuations in these time series some of which are not stationary

analysis of models reducible to a class of diffusion processes in the positive quarter plane this paper is concerned with the two dimensional generalization of the single server queue diffusion approximation this model consists of a stochastic process in mathbb r times mathbb r being a diffusion in the open quarter plane with absorption on the boundaries 0 times mathbb r cup mathbb r times 0 and jumps back into this open domain on the boundary this process is a linear diffusion with absorption on 0 0 and jumps back into the x or y axis this model describes within the same framework such phenomena as coupling of processors or simultaneous arrivals of jobs which do not preserve the classical product form solutions first we exhibit a pathwise construction of the process which leads to the existence the uniqueness and the markov property from this we derive a functional equation for the laplace transform of the steady state distribution the solution of this functional equation is obtained by reduction to a boundary value problem on the righ

identifying faces in a 2d line drawing representing a manifold object a straightforward way to illustrate a 3d model is to use a line drawing faces in a 2d line drawing provide important information for reconstructing its 3d geometry manifold objects belong to a class of common solids and most solid systems are based on manifold geometry in this paper a new method is proposed for finding faces from single 2d line drawings representing manifolds the face identification is formulated based on a property of manifolds each edge of a manifold is shared exactly by two faces the two main steps in our method are 1 searching for cycles from a line drawing and 2 searching for faces from the cycles in order to speed up the face identification procedure a number of properties most of which relate to planar manifold geometry in line drawings are presented to identify most of the cycles that are or are not real faces in a drawing thus reducing the number of unknown cycles in the second searching schemes to deal with manifolds with curved faces and manifolds each represented by two or more disjoint graphs are also proposed the experimental results show that our method can handle manifolds previous methods can handle as well as those they cannot

an algebraic approach to shape from image problems abstract this paper presents a new method for recovering three dimensional shapes of polyhedral objects from their single view images the problem of recovery is formulated in a constrained optimization problem in which the constraints reflect the assumption that the scene is composed of polyhedral objects and the objective function to be minimized is a weighted sum of quadric errors of surface information such as shading and texture for practical purpose it is decomposed into the two more tractable problems a linear programming problem and an unconstrained optimization problem in the present method the global constraints placed by the polyhedron assumption are represented in terms of linear algebra whereas similar constraints have usually been represented in terms of a gradient space moreover superstrictness of the constraints can be circumvented by a new concept position free incidence structure for this reason the present method has several advantages it can recover the polyhedral shape even if image data are incorrect due to vertex position errors it can deal with perspective projection as well as orthographic projection the number of variables in the optimization problem is very small three or a little greater than three and any kinds of surface information can be incorporated in a unifying manner