interpreting perspective images a fundamental problem in computer vision is how to determine the 3 d spatial orientation of curves and surfaces appearing in an image the problem is generally underconstrained and is complicated by the fact that metric properties such as orientation and length are not invariant under projection under perspective projection the correct model for most real images the transform is nonlinear and therefore hard to invert two constructive methods are presented the first finds the orientation of parallel lines and planes by locating vanishing points and vanishing lines the second determines the orientation of planes by backprojection of two intrinsic properties of contours angle magnitude and curvature

mean first passage time of quantum transition processes abstract in this paper we consider the problem of mean first passage time mfpt in quantum mechanics the mfpt is the average time of the transition from a given initial state passing through some intermediate states to a given final state for the first time we apply the method developed in statistical mechanics for calculating the mfpt of random walks to calculate the mfpt of a transition process as applications we 1 calculate the mfpt for multiple state systems 2 discuss transition processes occurring in an environmental background 3 consider a roundabout transition in a hydrogen atom and 4 apply the approach to laser theory

fractional diffusion waiting time distributions and cattaneo type equations we discuss a generalized diffusion equation resulting from an additive two state process in combination with an asymptotically fractal asymptotic power law waiting time distribution the obtained equation is an extension to previously discussed fractional diffusion equations our description leads to a mean squared displacement which describes enhanced subballistic transport for long times the short time behavior however is of a ballistic nature this separation into two domains results from the introduction of a time scale through the asymptotically fractal waiting time distribution this is also mirrored by the observation that for small times our generalized diffusion equation reduces to the standard cattaneo equation the asymptotic probability density is of compressed gaussian type and thus differs from the l evy tail generally found for these kinds of processes

invariant properties of straight homogeneous generalized cylinders and their contours a fundamental group in computer vision is the recovery of three dimensional shape from image data while this problem is in general underconstrained the authors show that it can be simplified in the case where the objects being viewed are generalized cylinders they consider the class of straight homogeneous generalized cylinders shgcs without any further assumption on the viewing direction or the precise shape of these objects they present a rigorous mathematical study of the geometry of shgcs and characterize their gaussian curvature and occluding contours and use these results to prove several new invariant properties of the contours of shgcs these properties are in turn used in two implemented algorithms for recovering shgc descriptions from image contours several examples of segmentation of real images are given other applications are also discussed

solutions of a class of non markovian fokker planck equations we show that a formal solution of a rather general non markovian fokker planck equation can be represented in a form of an integral decomposition and thus can be expressed through the solution of the markovian equation with the same fokker planck operator this allows us to classify memory kernels into safe ones for which the solution is always a probability density and dangerous ones when this is not guaranteed the first situation describes random processes subordinated to a wiener process while the second one typically corresponds to random processes showing a strong ballistic component in this case the non markovian fokker planck equation is only valid in a restricted range of parameters initial and boundary conditions

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

retarding subdiffusion and accelerating superdiffusion governed by distributed order fractional diffusion equations we propose diffusionlike equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena whose diffusion exponent varies with time and which correspondingly cannot be viewed as self affine random processes possessing a unique hurst exponent we prove the positivity of the solutions of the proposed equations and establish their relation to the continuous time random walk theory we show that the distributed order time fractional diffusion equation describes the subdiffusion random process that is subordinated to the wiener process and whose diffusion exponent decreases in time retarding subdiffusion this process may lead to superslow diffusion with the mean square displacement growing logarithmically in time we also demonstrate that the distributed order space fractional diffusion equation describes superdiffusion phenomena with the diffusion exponent increasing in time accelerating superdiffusion

fractional fokker planck equation for nonlinear stochastic differential equations driven by non gaussian levy stable noises the fokker planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by gaussian noises however there are both theoretical and empirical reasons to consider similar equations driven by strongly non gaussian noises in particular they yield strongly non gaussian anomalous diffusion which seems to be relevant in different domains of physics in this paper we therefore derive a fractional fokker planck equation for the probability distribution of particles whose motion is governed by a nonlinear langevin type equation which is driven by a levy stable noise rather than a gaussian we obtain in fact a general result for a markovian forcing we also discuss the existence and uniqueness of the solution of the fractional fokker planck equation

analyzing skewed symmetries symmetry is pervasive in both man made objects and nature since symmetries project to skew symmetries finding axes of skew symmetry is an important vision task this paper presents a linear time algorithm for finding the axes of skew symmetry where the degree of symmetry is known first we present a review and critique of current methods for finding the axes of skew symmetry next we decompose the problem of finding skew symmetry into the subproblems of solving for the rotational parameter of a shear symmetry and recovering the shear parameter of a reflexive symmetry using this approach the authors derive a direct non heuristic moment based technique for finding the axes of skew symmetry for skew symmetric figures with degree of symmetry less than five we obtain a closed form solution the method does not rely on continuous contours but assumes there is no occlusion and requires knowing the contour s degree of symmetry it is the first algorithm to find the axes of skew symmetry ino n time where n is the number of contour points the method is especially suited to industrial applications where the degree of symmetry is often knowna priori examples of the method are presented for both real and synthetic images and an error analysis of the method is given

random walk particle tracking simulations of non fickian transport in heterogeneous media derivations of continuum nonlocal models of non fickian anomalous transport require assumptions that might limit their applicability we present a particle based algorithm which obviates the need for many of these assumptions by allowing stochastic processes that represent spatial and temporal random increments to be correlated in space and time be stationary or non stationary and to have arbitrary distributions the approach treats a particle trajectory as a subordinated stochastic process that is described by a set of langevin equations which represent a continuous time random walk ctrw convolution based particle tracking cbpt is used to increase the computational efficiency and accuracy of these particle based simulations the combined ctrw cbpt approach enables one to convert any particle tracking legacy code into a simulator capable of handling non fickian transport

an affine scaling optimal path method with interior backtracking curvilinear technique for linear constrained optimization this paper presents an affine scaling optimal path approach in association with nonmonotonic interior backtracking line search technique for nonlinear optimization subject to linear constraints we shall employ the eigensystem decomposition and affine scaling mapping to form affine scaling optimal curvilinear path very easily by using interior backtracking line search technique each iterate switches to trial step of strict interior feasibility the nonmonotone criterion is used to speed up the convergence progress in the contours of objective function with large curvature theoretical analysis is given which prove that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions the results of numerical experiments are reported to show the effectiveness of the proposed algorithm

from ornstein uhlenbeck dynamics to long memory processes and fractional brownian motion this article establishes a natural physical path leading from regular ornstein uhlenbeck dynamics to anomalous long memory processes and thereafter to fractional brownian motion considering a system composed of n different parts each part conducting its own ornstein uhlenbeck dynamics and all parts being perturbed by a common external l evy noise we show that the collective system dynamics in the limit n ensuremath rightarrow ensuremath infty converges to a temporal moving average of the driving noise the limiting moving average process in turn can posses a long memory in which case when observed over large time scales further yields fractional brownian motion the temporal correlation structure of the limiting moving average process turns out to be determined by the structural statistical variability of the system s composing parts thus the emergence of a long memory is a consequence of the intrinsic quenched disorder present at the system s formation epoch rather than the consequence of the external annealed disorder carried in continuously by the driving noise

fractional model equation for anomalous diffusion abstract in recent years the phenomenon of anomalous diffusion has attracted more and more attention one of the main impulses was initiated by de gennes idea of the ant in the labyrinth several authors presented asymptotic probability density functions for the location of a random walker on a fractal object as this density function and the time dependence of its second moment are now well established a modified diffusion equation providing the correct result is formulated the parameters of this fractional partial differential equation are uniquely determined by the fractal hausdorff dimension of the underlying object and the anomalous diffusion exponent the presented equation reduces exactly to the ordinary isotropic diffusion equation by appropriate choice of the parameters a closed form solution is given in terms of fox s h function in the asymptotic case a halved diffusion equation can be established furthermore the differences to equations considered previously are discussed

weak subordination breaking for the quenched trap model we map the problem of diffusion in the quenched trap model onto a different stochastic process brownian motion that is terminated at the coverage time s nx with nx being the number of visits to site x here 0 t t g 1 is a measure of the disorder in the original model this mapping allows us to treat the intricate correlations in the underlying random walk in the random environment the operational time s is changed to laboratory time t with a l evy time transformation investigation of brownian motion stopped at time s yields the diffusion front of the quenched trap model which is favorably compared with numerical simulations in the zero temperature limit of 0 we recover the renormalization group solution obtained by monthus phys rev e 68 036114 2003 our theory surmounts the critical slowing down that is found when 1 above the critical dimension 2 mapping the problem to a continuous time random walk becomes feasible though still not trivial

physical pictures of transport in heterogeneous media advection dispersion random walk and fractional derivative formulations 1 the basic conceptual picture and theoretical basis for development of transport equations in porous media are examined the general form of the governing equations is derived for conservative chemical transport in heterogeneous geological formations for single realizations and for ensemble averages of the domain the application of these transport equations is focused on accounting for the appearance of non fickian anomalous transport behavior the general ensemble averaged transport equation is shown to be equivalent to a continuous time random walk ctrw and reduces to the conventional forms of the advection dispersion equation ade under highly restrictive conditions fractional derivative formulations of the transport equations both temporal and spatial emerge as special cases of the ctrw in particular the use in this context of levy flights is critically examined in order to determine chemical transport in field scale situations the ctrw approach is generalized to nonstationary systems we outline a practical numerical scheme similar to those used with extended geological models to account for the often important effects of unresolved heterogeneities

a bayesian multiple hypothesis approach to edge grouping and contour segmentation a contour segmentation algorithm is presented that takes an edge map and extracts continuous curves of arbitrary smoothness correctly handling curve intersections and capable of extrapolating over significant measurement gaps the algorithm incorporates noise models of the edge detection process and limited scene statistics it is based on an explicit contour model and employs a statistical distance measure to quantify the likelihood of each segmentation hypothesis a bayesian multiple hypothesis tree organizes possible segementations making it possible to postpone grouping decisions until a sufficient amount of information is available we have demonstrated its performance on real and synthetic images

power law correlated processes with asymmetric distributions motivated by the fact that many physical systems display sid power law correlations together with siid an asymmetry in the probability distribution we propose a stochastic process that can model both properties the process depends on only two parameters where one controls the scaling exponent of the power law correlations and the other controls the degree of asymmetry in the distributions leaving the correlations unaffected we apply the process to air humidity data and find that the statistical properties of the process are in a good agreement with those observed in the data

fractional diffusion exact representations of spectral functions for all the relevant transformed spaces i e fourier laplace and fourier laplace we present exact solutions of a fractional diffusion equation describing random transport on fractals the potential importance of such spectral representations lies in their applications to interpreting experimental measurements of anomalous diffusion processes in contrast to the well known asymptotic results the exact representations provide a much broader basis for comparison with data

diffusion equations for a markovian jumping process we consider a markovian jumping process which is defined in terms of the jump size distribution and the waiting time distribution with a position dependent frequency in the diffusion limit we assume the power law form for the frequency for small steps we derive the fokker planck equation and show the presence of the normal diffusion subdiffusion and superdiffusion for the l evy distribution of the step size we construct a fractional equation which possesses a variable coefficient and solve it in the diffusion limit then we calculate fractional moments and define the fractional diffusion coefficient as a natural extension to the cases with the divergent variance we also solve the master equation numerically and demonstrate that there are deviations from the l evy stable distribution for large wave numbers

random walks on site disordered lattices random walk models with disordered waiting times site disorder are analysed using a real space renormalisation group method anomalous diffusion is found in all dimensions whenever the first moment of the distribution of waiting times diverges above two dimensions the fixed points are described by continuous time random walks with non analytic waiting time functions below two dimensions the fixed points are themselves disordered random walks where the disorder is characterised by a stable probability distribution a fractal dimension is defined for site disordered lattices and below two dimensions a hyperscaling law is found which relates the fractal dimension the euclidean dimension and the exponent describing the displacement of the walker

anomalous diffusion in systems driven by the stable levy noise with a finite noise relaxation time and inertia dynamical systems driven by a general levy stable noise are considered the inertia is included and the noise represented by a generalized ornstein uhlenbeck process has a finite relaxation time a general linear problem the additive noise is solved the resulting distribution converges with time to the distribution for the white noise massless case moreover a multiplicative noise is discussed it can make the distribution steeper and the variance which is finite depends sublinearly on time subdiffusion for a small mass a white noise limit corresponds to the stratonovich interpretation on the other hand the distribution tails agree with the ito interpretation if the inertia is very large an escape time from the potential well is calculated

newton s method with a model trust region modification a modified newton method for unconstrained minimization is presented and analyzed the modification is based upon the model trust region approach this report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified newton iteration several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis very strong convergence results are presented concerning the minimization algorithm in particular the explicit use of second order information is justified by demonstrating that the iterates converge to a point which satisfies the second order necessary conditions for minimization with the exception of very pathological cases this occurs whenever the algorithm is applied to problems with continuous second partial derivatives

on the geometric interpretation of image contours abstract in this paper we suggest a computational model for the 3d interpretation of a 2d view based on contour classification and contour interpretation we concentrate on those contours arising from discontinuities in surface orientation we combine a generic surface description well suited for visual tasks with a model of the image formation process in order to derive image contour configurations that are likely to be interpreted in terms of surface contours next we describe a computer algorithm which attempts to interpret image contours on the following grounds first an image analysis process produces a description in terms of contours and relationships between them second among these contours we select those which form a desired configuration third the selected contours are combined with constraints available with the image formation process in order to be interpreted in terms of discontinuities in surface orientation as a consequence there is a dramatic reduction in the number of possible orientations of the associated scene surfaces

general criterion for harmonicity citation proesmans k vandebroek h van den broeck c 2017 general criterion for harmonicity physical review letters 119 14 1 5 doi 10 1103 physrevlett 119 147803

boundary layer turbulence as a kangaroo process a nonlocal mixing length theory of turbulence transport by finite size eddies is developed by means of a novel evaluation of the reynolds stress the analysis involves the contruct of a sample path space and a stochastic closure hypothesis the simplifying property of exhange strong eddies is satisfied by an analytical sampling rate model a nonlinear scaling relation maps the path space onto the semi infinite boundary layer the underlying near wall behavior of fluctuating velocities perfectly agrees with recent direct numerical simulations the resulting integro differential equation for the mixing of scalar densities represents fully developed boundary layer turbulence as a nondiffusive kubo anderson or kangaroo type of stochastic process the model involves a scaling exponent with in the diffusion limit for the partly analytical solution for the mean velocity profile excellent agreement with the experimental data yields 0 58 1995 the american physical society

stretched gaussian asymptotics of the truncated levy flights for the diffusion in nonhomogeneous media abstract the levy jumping process defined in terms of the jumping size distribution and the waiting time distribution is considered the jumping rate depends on the process value the fractional diffusion equation which contains the variable diffusion coefficient is solved in the diffusion limit that solution resolves itself to the stretched gaussian when the order parameter 2 the truncation of the levy flights in the exponential and power law form is introduced and the corresponding random walk process is simulated by the monte carlo method the stretched gaussian tails are found in both cases the time which is needed to reach the limiting distribution strongly depends on the jumping rate parameter when the cutoff function falls slowly the tail of the distribution appears to be algebraic

hydrodynamics of confined colloidal fluids in two dimensions we apply a hybrid molecular dynamics and mesoscopic simulation technique to study the dynamics of two dimensional colloidal disks in confined geometries we calculate the velocity autocorrelation functions and observe the predicted t 1 long time hydrodynamic tail that characterizes unconfined fluids as well as more complex oscillating behavior and negative tails for strongly confined geometries because the t 1 tail of the velocity autocorrelation function is cut off for longer times in finite systems the related diffusion coefficient does not diverge but instead depends logarithmically on the overall size of the system the langevin equation gives a poor approximation to the velocity autocorrelation function at both short and long times

a cumulative entropy method for distribution recognition of model error abstract this paper develops a cumulative entropy method cem to recognize the most suitable distribution for model error in terms of the cem the levy stable distribution is employed to capture the statistical properties of model error the strategies are tested on 250 experiments of axially loaded cft steel stub columns in conjunction with the four national building codes of japan aij 1997 china dl t 1999 the eurocode 4 eu4 2004 and united states aisc 2005 the cumulative entropy method is validated as more computationally efficient than the shannon entropy method compared with the kolmogorov smirnov test and root mean square deviation the cem provides alternative and powerful model selection criterion to recognize the most suitable distribution for the model error

anomalous diffusion for a correlated process with long jumps abstract we discuss diffusion properties of a dynamical system which is characterised by long tail distributions and finite correlations the particle velocity has the stable levy distribution it is assumed as a jumping process the kangaroo process with a variable jumping rate both the exponential and the algebraic form of the covariance defined for the truncated distribution are considered it is demonstrated by numerical calculations that the stationary solution of the master equation for the case of power law correlations decays with time but a simple modification of the process makes the tails stable the main result of the paper is a finding that in contrast to the velocity fluctuations the position variance may be finite it rises with time faster than linearly the diffusion is anomalously enhanced on the other hand a process which follows from a superposition of the ornstein uhlenbeck levy processes always leads to position distributions with a divergent variance which means accelerated diffusion

fluid limit of the continuous time random walk with general levy jump distribution functions the continuous time random walk ctrw is a natural generalization of the brownian random walk that allows the incorporation of waiting time distributions psi t and general jump distribution functions eta x there are two well known fluid limits of this model in the uncoupled case for exponential decaying waiting times and gaussian jump distribution functions the fluid limit leads to the diffusion equation on the other hand for algebraic decaying waiting times psi approximately t 1 beta and algebraic decaying jump distributions eta approximately x 1 alpha corresponding to levy stable processes the fluid limit leads to the fractional diffusion equation of order alpha in space and order beta in time however these are two special cases of a wider class of models here we consider the ctrw for the most general levy stochastic processes in the levy khintchine representation for the jump distribution function and obtain an integrodifferential equation describing the dynamics in the fluid limit the resulting equation contains as special cases the regular and the fractional diffusion equations as an application we consider the case of ctrws with exponentially truncated levy jump distribution functions in this case the fluid limit leads to a transport equation with exponentially truncated fractional derivatives which describes the interplay between memory long jumps and truncation effects in the intermediate asymptotic regime the dynamics exhibits a transition from superdiffusion to subdiffusion with the crossover time scaling as tauc approximately lambda alpha beta where 1 lambda is the truncation length scale the asymptotic behavior of the propagator green s function of the truncated fractional equation exhibits a transition from algebraic decay for t tauc

fox function representation of non debye relaxation processes applying the liouville riemann fractional calculus we derive and solve a fractional operator relaxation equation we demonstrate how the exponent of the asymptotic power law decay t relates to the order of the fractional operatordv dtv 0 1 continuous time random walk ctrw models offer a physical interpretation of fractional order equations and thus we point out a connection between a special type of ctrw and our fractional relaxation model exact analytical solutions of the fractional relaxation equation are obtained in terms of fox functions by using laplace and mellin transforms apart from fractional relaxation fox functions are further used to calculate fourier integrals of kohlrausch williams watts type relaxation functions because of its close connection to integral transforms the rich class of fox functions forms a suitable framework for discussing slow relaxation phenomena

recovery of shgcs from a single intensity view generalized cylinders are a flexible loosely defined class of parametric shapes capable of modeling many real world objects straight homogeneous generalized cylinders are an important subclass of generalized cylinders whose cross sections are scaled versions of a reference curve although there has been considerable research into recovering the shape of shgcs from their contour this work has almost exclusively involved methods that couple contour and heuristic constraints a rigorous approach to the problem of recovering solid parametric shape from a single intensity view should involve at least two stages 1 deriving the contour constraints and 2 determining if additional image constraints e g intensity can be used to uniquely determine the 3d object shape in this paper the authors follow the approach just described this methodology is also important for the recovery of object classes like tubes where contour and heuristic constraints are shown to be insufficient for shape recovery first the authors prove that shgc contours generated under orthography have exactly two degrees of freedom next the authors show that the remaining free parameters can be resolved using reflectance based constraints without knowledge of the number of light sources their positions intensities the amount of ambient light or the surface albedo finally the reflectance based recovery algorithm is demonstrated on both synthetic and real shgc images

a curvilinear method based on minimal memory bfgs updates we present a new matrix free method for the computation of negative curvature directions based on the eigenstructure of minimal memory bfgs matrices we determine via simple formulas the eigenvalues of these matrices and we compute the desirable eigenvectors by explicit forms consequently a negative curvature direction is computed in such a way that avoids the storage and the factorization of any matrix we propose a modification of the l bfgs method in which no information is kept from old iterations so that memory requirements are minimal the proposed algorithm incorporates a curvilinear path and a linesearch procedure which combines two search directions a memoryless quasi newton direction and a direction of negative curvature results of numerical experiments for large scale problems are also presented

anomalous fluctuation properties we complement and extend our work on fluctuations arising in nonequilibrium systems in steady states driven by l evy noise h touchette and e g d cohen phys rev e 76 020101 r 2007 as a concrete example we consider a particle subjected to a drag force and a l evy white noise with tail index ensuremath mu 0 2 and calculate the probability distribution of the work done on the particle by the drag force as well as the probability distribution of the work dissipated by the dragged particle in a nonequilibrium steady state for 0l ensuremath mu l2 both distributions satisfy what we call an anomalous fluctuation property characterized by positive and negative fluctuations that asymptotically have the same probability for ensuremath mu 2 by contrast the work and dissipated work distributions satisfy the known conventional and extended fluctuation relations respectively which are both characterized by positive fluctuations that are exponentially more probable than negative fluctuations the difference between these different fluctuation behaviors is discussed in the context of large deviation theory experiments that could probe or reveal an anomalous fluctuation property are also discussed

analytic approach to the problem of convergence of truncated levy flights towards the gaussian stochastic process an analytic expression for characteristic function defining a truncated l evy flight is derived it is shown that the characteristic function yields results in agreement with recent simulations of truncated l evy flights by mantegna and stanley phys rev lett 73 2946 1994 with the analytic expression for the characteristic function the convergence of the l evy process towards the gaussian is demonstrated without simulations in the calculation of first return probability the simulations are replaced by numerical integration using simple quadratures

anomalous diffusion in nonhomogeneous media time subordinated langevin equation approach diffusion in nonhomogeneous media is described by a dynamical process driven by a general levy noise and subordinated to a random time the subordinator depends on the position this problem is approximated by a multiplicative process subordinated to a random time it separately takes into account effects related to the medium structure and the memory density distributions and moments are derived from the solutions of the corresponding langevin equation and compared with the numerical calculations for the exact problem both subdiffusion and enhanced diffusion are predicted distribution of the process satisfies the fractional fokker planck equation

state dependent diffusion thermodynamic consistency and its path integral formulation the friction coefficient of a particle can depend on its position as it does when the particle is near a wall we formulate the dynamics of particles with such state dependent friction coefficients in terms of a general langevin equation with multiplicative noise whose evaluation requires the introduction of specific rules two common conventions the ito and the stratonovich provide alternative rules for evaluation of the noise but other conventions are possible we show that the requirement that a particle s distribution function approach the boltzmann distribution at long times dictates that a drift term must be added to the langevin equation this drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise we explore the consequences of this result in a number of examples with spatially varying diffusion coefficients we also derive a path integral representation for arbitrary interpretation of the noise and use it in a perturbative study of correlations in a simple system

correlation cascades of levy driven random processes abstract we explore the correlation structure of a large class of random processes driven by non gaussian levy noise sources with possibly infinite variances examples of such processes include levy motions levy driven ornstein uhlenbeck motions levy driven moving average processes fractional levy motions and fractional levy noises based on the fact that non gaussian levy noises are continuum superpositions of poisson noises we unveil an underlying cascade of levy correlation functions which characterize the process distribution and the correlation structure of the processes under consideration in the case where the driving levy noise sources are fractal the resulting cascade admits a unique scale free form

eliminating finite size effects and detecting the amount of white noise in short records with long term memory long term memory is ubiquitous in nature and has important consequences for the occurrence of natural hazards but its detection often is complicated by the short length of the considered records and additive white noise in the data here we study synthetic gaussian distributed records x i of length n that consist of a long term correlated component 1 ensuremath a y i characterized by a correlation exponent ensuremath gamma 0l ensuremath gamma l1 and a white noise component a ensuremath eta i 0 ensuremath le a ensuremath le 1 we show that the autocorrelation function c n s has the general form c n s c ensuremath infty s ensuremath e a 1 ensuremath e a where c ensuremath infty 0 1 c ensuremath infty sg0 b a s ensuremath ensuremath gamma and e a 2 b a 2 ensuremath ensuremath gamma 1 ensuremath ensuremath gamma n ensuremath ensuremath gamma o n ensuremath 1 the finite size parameter e a also occurs in related quantities for example in the variance ensuremath delta n 2 s of the local mean in time windows of length s ensuremath delta n 2 s ensuremath delta ensuremath infty 2 s ensuremath e a 1 ensuremath e a for purely long term correlated data b 0 ensuremath cong 2 ensuremath ensuremath gamma 1 ensuremath ensuremath gamma 2 yielding e 0 ensuremath cong n ensuremath ensuremath gamma and thus c n s frac 2 ensuremath ensuremath gamma 1 ensuremath ensuremath gamma 2 s ensuremath ensuremath gamma ensuremath n ensuremath ensuremath gamma 1 ensuremath n ensuremath ensuremath gamma and ensuremath delta n 2 s s ensuremath ensuremath gamma ensuremath n ensuremath ensuremath gamma 1 ensuremath n ensuremath ensuremath gamma we show how to estimate e a and c ensuremath infty s from a given data set and thus how to obtain accurately the exponent ensuremath gamma and the amount of white noise a

fractional fokker planck equation solution and application recently metzler et al phys rev lett 82 3563 1999 introduced a fractional fokker planck equation ffpe describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field and a boltzmann thermal heat bath in this paper we present the solution of the ffpe in terms of an integral transformation the transformation maps the solution of ordinary fokker planck equation onto the solution of the ffpe and is based on levy s generalized central limit theorem the meaning of the transformation is explained based on the known asymptotic solution of the continuous time random walk ctrw we investigate in detail i a force free particle ii a particle in a uniform field and iii a particle in a harmonic field we also find an exact solution of the ctrw and compare the ctrw result with the corresponding solution of the ffpe the relation between the fractional first passage time problem in an external nonlinear field and the corresponding integer first passage time is given an example of the one dimensional fractional first passage time in an external linear field is investigated in detail the ffpe is shown to be compatible with the scher montroll approach for dispersive transport and thus is applicable in a large variety of disordered systems the simple ffpe approach can be used as a practical tool for a phenomenological description of certain types of complicated transport phenomena

simple jumping process with memory transport equation and diffusion we present a stochastic jumping process defined in terms of jump size probability density and jumping rate which is a generalization of the well known kangaroo process the definition takes into account two process values after and before the jump therefore the process is able to preserve memory about its previous values it possesses a simple stationary limit its master equation is interpreted as the kinetic equation with variable collision rate the process can be easily applied to model systems which relax to distributions other than maxwellian the case of a constant jumping rate corresponds to the diffusion process either normal or ballistic

an extremum principle for shape from contour an extremum principle is developed that determines three dimensional surface orientation from a two dimensional contour the principle maximizes the ratio of the area to the square of the perimeter a measure of the compactness or symmetry of the three dimensional surface the principle interprets regular figures correctly and it interprets skew symmetries as oriented real symmetries the maximum likelihood method approximates the principle on irregular figures but we show that it consistently overestimates the slant of an ellipse

subdiffusion and localization in the one dimensional trap model we study a one dimensional generalization of the exponential trap model using both numerical simulations and analytical approximations we obtain the asymptotic shape of the average diffusion front in the subdiffusive phase our central result concerns the localization properties we find the dynamical participation ratios to be finite but different from their equilibrium counterparts therefore the idea of a partial equilibrium within the limited region of space explored by the walk is not exact even for long times where each site is visited a very large number of times we discuss the physical origin of this discrepancy and characterize the full distribution of dynamical weights we also study two different two time correlation functions which exhibit different aging properties one is sub aging whereas the other one shows full aging therefore two diverging time scales appear in this model we give intuitive arguments and simple analytical approximations that account for these differences and obtain new predictions for the asymptotic short time and long time behavior of the scaling functions finally we discuss the issue of multiple time scalings in this model

fractional diffusion equation for a power law truncated levy process abstract truncated levy flights are stochastic processes which display a crossover from a heavy tailed levy behavior to a faster decaying probability distribution function pdf putting less weight on long flights overcomes the divergence of the levy distribution second moment we introduce a fractional generalization of the diffusion equation whose solution defines a process in which a levy flight of exponent is truncated by a power law of exponent 5 a closed form for the characteristic function of the process is derived the pdf of the displacement slowly converges to a gaussian in its central part showing however a power law far tail possible applications are discussed

a new affine scaling interior point algorithm for nonlinear optimization subject to linear equality and inequality constraints in this paper we propose a new interior affine scaling region algorithm with nonmonotonic interior point backtracking technique for nonlinear optimization subject to linear equality and inequality constraints the trust region subproblem in the proposed algorithm is defined by minimizing a quadratic function subject only to an affine scaling ellipsoidal constraint in a null subspace of the extended equality constraints using both trust region strategy and line search technique the affine scaling trust region subproblem at each iteration generates backtracking interior step to obtain a new accepted step the global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions a nonmonotonic criterion should bring about speeding up the convergence progress in some ill conditioned cases

continuous time random walk with generic waiting time and external force we derive an integrodifferential diffusion equation for decoupled continuous time random walk that is valid for a generic waiting time probability density function and external force using this equation we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential a combination of power law and generalized mittag leffler function and a sum of exponentials under the influence of a harmonic trap we show that first two waiting time probability density functions can reproduce the results of the ordinary and fractional diffusion equations for all the time regions from small to large times but the third one shows a much more complicated pattern furthermore from the integrodifferential diffusion equation we show that the second einstein relation can hold for any waiting time probability density function

multiplicative levy processes ito versus stratonovich interpretation langevin equation with a multiplicative stochastic force is considered that force is uncorrelated it has the levy distribution and the power law intensity the fokker planck equations which correspond both to the ito and stratonovich interpretation are presented they are solved for the case without drift and for the harmonic oscillator potential the variance is evaluated it is always infinite for the ito case whereas for the stratonovich one it can be finite and rise with time slower that linearly which indicates subdiffusion analytical results are compared with numerical simulations

anomalous diffusion in stochastic systems with nonhomogeneously distributed traps the stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed the particle is subjected to a stochastic stimulation obeying a general levy stable statistics and experiences long rests due to nonhomogeneously distributed traps the memory is taken into account by subordination of that process to a random time then the subordination equation is position dependent the problem is approximated by a decoupling of the medium structure and memory and exactly solved for a power law position dependence of the memory in the case of the gaussian statistics the density distribution and moments are derived depending on geometry and memory parameters the system may reveal both the subdiffusion and enhanced diffusion the similar analysis is performed for the levy flights where the finiteness of the variance follows from a variable noise intensity near a boundary two diffusion regimes are found in the bulk and near the surface the anomalous diffusion exponent as a function of the system parameters is derived

fractional fokker planck equation for levy flights in nonhomogeneous environments the fractional fokker planck equation which contains a variable diffusion coefficient is discussed and solved it corresponds to the l evy flights in a nonhomogeneous medium for the case with the linear drift the solution is stationary in the long time limit and it represents the l evy process with a simple scaling the solution for the drift term in the form ensuremath lambda text text sgn x possesses two different scales which correspond to the l evy indexes ensuremath mu and ensuremath mu 1 ensuremath mu l1 the former component of the solution prevails at large distances but it diminishes with time for a given x the fractional moments as a function of time are calculated they rise with time and the rate of this growth increases with ensuremath lambda

modeling of financial data comparison of the truncated levy flight and the arch 1 and garch 1 1 processes we compare our results on empirical analysis of nancia l data with simulations of two stochastic models of the dynamics of stock market prices the two models are i the truncated l evy igh t recently introduced by us and ii the arch 1 and garch 1 1 processes we n d that the tlf well describes the scaling and its breakdown observed in empirical data while it is not able to properly describe the uctuation s of volatility empirically detected the arch 1 and garch 1 1 models are able to describe the probability density function of price changes at a given time horizon but both fail to describe the scaling properties of the pdfs for short time horizons c 1998 elsevier science b v all rights reserved

recovery of 3 d objects with multiple curved surfaces from 2 d contours abstract inference of 3 d shape from 2 d contours in a single image is an important problem in machine vision often techniques to solve this problem examine each surface in the scene separately whereas our perception of their shapes clearly depends on the interplay between them as well in this paper we describe a technique that attempts to recover the shapes of all the surfaces of an object simultaneously though it is limited to objects made of zero gaussian curvature surfaces our technique is based on an analysis of three kinds of symmetries defined in the paper and the constraints that derive from them and from other boundaries this technique uses some of the constraints developed in an earlier paper that was limited to examining a zero gaussian curvature surface cut by parallel planes this restriction has been removed here and the constraints have been reformulated to allow integration of constraints from all the neighboring surfaces results on some complex examples are shown

analytical solutions for diffusion on fractal objects a generalization of the euclidean diffusion equation is proposed for diffusion on fractals on the basis of a scaling argument a renormalization group theory for the green s function and numerical tests conjectures on the applicability to natural fractals such as porous media are presented

straight homogeneous generalized cylinders differential geometry and uniqueness results it is well known that certain objects like ellipsoids or spheres admit several sometimes many different parameterizations by generalized cylinders under what conditions does a given surface admit at most one description by a straight homogeneous generalized cylinder shgc under what other conditions does a surface admit at most a few such descriptions to answer these questions it is first necessary to understand the geometry and intrinsic properties of shgc s in this paper a necessary and sufficient condition for the regularity of the surface described by an shgc is given the gaussian curvature of this surface is calculated and it is proved that its parabolic lines are either meridians or parallels of the associated shgc these results are used in the second part of the paper to prove several new uniqueness results it is first proved that if a surface is described by two shgc s with the same cross section plane and axis then these shgc s are necessarily deduced from each other through inverse scalings of their cross sections and sweeping rule curve and that the surface associated with an shgc with at least two parabolic meridians and two parabolic parallels cannot be described by a different shgc shafer s pivot and slant theorems are then extended to prove that the surface associated with a non linear shgc does not have any different shgc parameterization with the same cross section plane or the same axis finally it is shown that a surface with at least two parabolic lines admits at most three different shgc descriptions and that a surface with at least four parabolic lines admits at most one shgc description in particular a closed surface with at least one concave point admits at most three different shgc descriptions

interpreting line drawings as three dimensional surfaces understanding how line drawings convey tri dimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too complex to model analytically we put forward here a computational model for interpreting line drawings as three dimensional surfaces based on constraints on local surface orientation along extremal and discontinuity boundaries specific techniques are described for two key processes recovering the three dimensional conformation of a space curve e g a surface boundary from its two dimensional projection in an image and interpolating smooth surfaces from orientation constraints along extremal boundaries the relevance of the model to a general theory of low level vision is discussed

solving the chapman kolmogorov equation for a jumping process a general solution to the chapman kolmogorov equation for a jumping process called the kangaroo process is derived a special case of algebraic dependences is discussed in detail in particular simple asymptotic formulas for probability distribution are presented it is demonstrated that there are two different classes of limiting stationary distributions an expression for the covariance is also derived

fractional diffusion in inhomogeneous media starting from the continuous time random walk ctrw scheme with the space dependent waiting time probability density function pdf we obtain the time fractional diffusion equation with varying in space fractional order of time derivative as an example we study the evolution of a composite system consisting of two separate regions with different subdiffusion exponents and demonstrate the effects of non trivial drift and subdiffusion whose laws are changed in the course of time

non markovian levy diffusion in nonhomogeneous media we study the diffusion equation with a position dependent power law diffusion coefficient the equation possesses the riesz weyl fractional operator and includes a memory kernel it is solved in the diffusion limit of small wave numbers two kernels are considered in detail the exponential kernel for which the problem resolves itself to the telegrapher s equation and the power law one the resulting distributions have the form of the l evy process for any kernel the renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system

models of anomalous diffusion the subdiffusive case abstract the paper discusses a model for anomalous diffusion processes their one point probability density functions p d f are exact solutions of fractional diffusion equations the model reflects the asymptotic behavior of a jump anomalous random walk process with random jump sizes and random inter jump time intervals with infinite means and variances which do not satisfy the law of large numbers in the case when these intervals have a fractional exponential p d f the fractional komogorov feller equation for the corresponding anomalous diffusion is provided and methods of finding its solutions are discussed finally some statistical properties of solutions of the related langevin equation are studied the subdiffusive case is explored in detail the emphasis is on a rigorous presentation which however would be accessible to the physical sciences audience

nonlinear stochastic equations with multiplicative levy noise the langevin equation with a multiplicative levy white noise is solved the noise amplitude and the drift coefficient have a power law form a validity of ordinary rules of the calculus for the stratonovich interpretation is discussed the solution has the algebraic asymptotic form and the variance may assume a finite value for the case of the stratonovich interpretation the problem of escaping from a potential well is analyzed numerically predictions of different interpretations of the stochastic integral are compared

complex fractal dimension of the bronchial tree the architecture of the mammalian lung has been shown to be correctly described using a fractal model with a complex dimension related to a cantor set with random errors for four different species here we provide an interpretation of that model that has implications for biological evolution we argue that fractals are more error tolerant than other structures and therefore have an evolutionary advantage

a trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints a trust region and affine scaling interior point method tram is proposed for a general nonlinear minimization with linear inequality constraints in 8 in the proposed approach a newton step is derived from the complementarity conditions based on this newton step a trust region subproblem is formed and the original objective function is monotonically decreased explicit sufficient decrease conditions are proposed for satisfying complementarity dual feasibility and second order optimality the objective of this paper is to establish global and local convergence properties of the proposed trust region and affine scaling interior point method it is shown that the proposed decrease conditions are sufficient for achieving complementarity dual feasibility and second order optimality respectively it is also established that a trust region solution is asymptotically in the interior of the proposed trust region subproblem and a damped trust region step can achieve quadratic convergence

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

levy flights in nonhomogeneous media distributed order fractional equation approach a jumping process defined in terms of the l evi distributed jumping size and the poissonian position dependent waiting time with the algebraic jumping rate is discussed on the assumption that parameters of both distributions are themselves random variables which are determined from given probability distributions the fractional equation for the distributed l evy order parameter ensuremath mu is derived and solved the solution is of the form of a combination of the fox functions and simple scaling is lacking the problem of accelerated diffusion is also discussed the case of the distributed waiting time parameter ensuremath theta is similarly solved and the solution offers a possibility to manage processes which are characterized by more general forms of the jumping rate not only algebraic moreover we mention a possibility that the parameters ensuremath mu and ensuremath theta are mutually dependent

langevin equations for continuous time levy flights we consider the combined effects of a power law l evy step distribution characterized by the step index f and a power law waiting time distribution characterized by the time index g on the long time behavior of a random walker the main point of our analysis is a formulation in terms of coupled langevin equations which allows in a natural way for the inclusion of external force fields in the anomalous case for f2 and g1 the dynamic exponent z locks onto the ratio f g drawing on recent results on l evy flights in the presence of a random force field we also find that this result is independent of the presence of weak quenched disorder for d below the critical dimension mathit d mathit c 2f 2 the disorder is relevant corresponding to a nontrivial fixed point for the force correlation function