temporal complexity of the order parameter at the phase transition we study a decision making model in a condition where it is equivalent to the two dimensional ising model and we show that at the onset of phase transition it generates temporal complexity namely nonstationary and nonergodic fluctuations we argue that this is a general property of criticality thereby opening the door to the application of the recently discovered phenomenon of complexity matching for an efficient transfer of information to occur a perturbing complex network must share the same temporal complexity as the perturbed complex network

distributions of time averages for weakly chaotic systems the role of infinite invariant density distributions of time averaged observables are investigated using deterministic maps with n indifferent fixed points and n state continuous time random walk processes associated with them in a weakly chaotic phase namely when separation of trajectories is subexponential maps are characterized by an infinite invariant density we find that the infinite density can be used to calculate the distribution of time averages of integrable observables with a formula recently obtained by rebenshtok and barkai as an example we calculate distributions of the average position of the particle and average occupation fractions our work provides the distributional limit theorem for time averages for a wide class of nonintegrable observables with respect to the infinite invariant density in other words it deals with the situation where the darling kac aaronson theorem does not hold

residence time distribution for a class of gaussian markov processes we study the distribution of residence time or equivalently that of mean magnetization for a family of gaussian markov processes indexed by a positive parameter alpha the persistence exponent for these processes is simply given by theta alpha but the residence time distribution is nontrivial the shape of this distribution undergoes a qualitative change as theta increases indicating a sharp change in the ergodic properties of the process we develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha for some special values of alpha we obtain closed form expressions of the distribution function s1063 651x 99 03306 1

self diffusion and visited surface in the droplet condensation problem breath figures abstract we study experimentally and theoretically new aspects of condensation growth and coalescence of droplets on a substrate we address in particular the dynamics of a marked droplet which undergoes coalescences with neighbouring droplets we find that the number of coalescences of the droplet grows as log t t is time and that the traveled distance increases as r t the average radius of the droplets at time t the fraction of the surface which was never covered by any droplet an important quantity for applications such as drug spreading or surface decontamination decays as t showing that completion occurs only slowly heuristic arguments accurate numerical simulations on simplified models which neglect polydispersity and an exact solution reported elsewhere a bray b derrida and c godreche europhys lett 27 1994 175 strongly support these findings and show that this power law decay is a generic feature common to many different situations finally the contour of the ensemble of dry sites appears fractal with dimension d 1 22 an experimental result not reproduced by the simplified models

scaling behaviour of randomly alternating surface growth processes the scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time are addressed the duration of each application of the two primary processes is assumed to be independently drawn from given distribution functions we analytically address processes in which the two primary processes are linear and extend the conclusions to nonlinear processes as well the growth scaling exponent of the average roughness with the number of applications is found to be determined by the long time tail of the distribution functions for processes in which both mean application times are finite the scaling behaviour follows that of the corresponding cyclical process in which the uniform application time of each primary process is given by its mean if the distribution functions decay with a small enough power law for the mean application times to diverge the growth exponent is found to depend continuously on this power law exponent in contrast the roughness exponent does not depend on the timing of the applications the analytical results are supported by numerical simulations of various pairs of primary processes and with different distribution functions self affine surfaces grown by two randomly alternating processes are common in nature e g due to randomly changing weather conditions and in man made devices such as rechargeable batteries

large deviations and nontrivial exponents in coarsening systems we investigate the statistics of the mean magnetization of its large deviations and persistent large deviations in simple coarsening systems in particular we consider more specifically the case of the diffusion equation of the ising chain at zero temperature and of the two dimensional voter model for the diffusion equation at large times the mean magnetization has a limit law which is studied analytically using the independent interval approximation the probability of persistent large deviations defined as the probability that the mean magnetization was for all previous times greater than some level x decays algebraically at large times with an exponent continuously varying with x when x 1 is the usual persistence exponent similar behaviour is found for the glauber ising chain at zero temperature for the two dimensional voter model large deviations of the mean magnetization are algebraic while the probability of persistent large deviations seem to behave as the usual persistence probability

convex graph invariant relaxations for graph edit distance the edit distance between two graphs is a widely used measure of similarity that evaluates the smallest number of vertex and edge deletions insertions required to transform one graph to another it is np hard to compute in general and a large number of heuristics have been proposed for approximating this quantity with few exceptions these methods generally provide upper bounds on the edit distance between two graphs in this paper we propose a new family of computationally tractable convex relaxations for obtaining lower bounds on graph edit distance these relaxations can be tailored to the structural properties of the particular graphs via convex graph invariants specific examples that we highlight in this paper include constraints on the graph spectrum as well as tractable approximations of the stability number and the maximum cut values of graphs we prove under suitable conditions that our relaxations are tight i e exactly compute the graph edit distance when one of the graphs consists of few eigenvalues we also validate the utility of our framework on synthetic problems as well as real applications involving molecular structure comparison problems in chemistry

phase ordering and persistence in a class of stochastic processes interpolating between the ising and voter models we study the dynamics of a class of two dimensional stochastic processes depending on two parameters which may be interpreted as two different temperatures respectively associated to interfacial and to bulk noise special lines in the plane of parameters correspond to the ising model voter model and majority vote model the dynamics of this class of models may be described formally in terms of reaction diffusion processes for a set of coalescing annihilating and branching random walkers we use the freedom allowed by the space of parameters to measure by numerical simulations the persistence probability of a generic model in the low temperature phase where the system coarsens this probability is found to decay at large times as a power law with a seemingly constant exponent we also discuss the connection between persistence and the nature of the interfaces between domains

aging arcsine law in brownian motion and its generalization classical arcsine law states that the fraction of occupation time on the positive or the negative side in brownian motion does not converge to a constant but converges in distribution to the arcsine distribution here we consider how a preparation of the system affects the arcsine law i e aging of the arcsine law we derive an aging distributional theorem for occupation time statistics in brownian motion where the ratio of time when measurements start to the measurement time plays an important role in determining the shape of the distribution furthermore we show that this result can be generalized as an aging distributional limit theorem in renewal processes

statistics of the occupation time for a random walk in the presence of a moving boundary we investigate the distribution of the time spent by a random walker to the right of a boundary moving with constant velocity v for the continuous time problem brownian motion we provide a simple alternative proof of newman s recent result newman t j 2001 j phys a math gen 34 l89 using a method developed by kac we then discuss the same problem for the case of a random walk in discrete time with an arbitrary distribution of steps taking advantage of the general set of results of sparre andersen for the binomial random walk we analyse the corrections to the continuum limit on the example of the mean occupation time the case of cauchy distributed steps is also studied

statistical properties of functionals of the paths of a particle diffusing in a one dimensional random potential we present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one dimensional quenched random potential we demonstrate the implementation of the formalism in two specific examples 1 where the functional corresponds to the local time spent by the particle around the origin and 2 where the functional corresponds to the occupation time spent by the particle on the positive side of the origin within an observation time window of size t we compute the disorder average distributions of the local time the inverse local time the occupation time and the inverse occupation time and show that in many cases disorder modifies the behavior drastically

density approach to ballistic anomalous diffusion an exact analytical treatment this paper addresses the problem of deriving the probability distribution density of a diffusion process generated by a nonergodic dichotomous fluctuation using the liouville equation density method the velocity of the diffusing particles fluctuates from the value of 1 to the value of 1 and back with the distribution density of time durations of the two states proportional to 1 in the asymptotic time limit the adopted density method allows us to establish an exact analytical expression for the probability distribution density of the diffusion process generated by these fluctuations contrary to intuitive expectations the central part of the diffusion distribution density is not left empty when moving from 2 ergodic condition to cr the monomodal distribution density with a minimum at the origin is turned into a bimodal one with a central bump whose intensity increases for 2 the

extreme value theory for constrained physical systems we investigate extreme value theory for physical systems with a global conservation law which describes renewal processes mass transport models and long range interacting spin models as shown previously a special feature is that the distribution of the extreme value exhibits a nonanalytical point in the middle of the support we expose exact relationships between constrained extreme value theory and well known quantities of the underlying stochastic dynamics all valid beyond the midpoint in general i e even far from the thermodynamic limit for example for renewal processes the distribution of the maximum time between two renewal events is exactly related to the mean number of these events in the thermodynamic limit we show how our theory is suitable to describe typical and rare events which deviate from classical extreme value theory for example for the renewal process we unravel dual scaling of the extreme value distribution pointing out two types of limiting laws a normalizable scaling function for the typical statistics and a non normalized state describing the rare events

statistical models for company growth abstract we study sutton s microcanonical model for the internal organization of firms that leads to non trivial scaling properties for the statistics of growth rates we show that the growth rates are asymptotically gaussian in this model whereas empirical results suggest that the kurtosis of the distribution increases with size we also obtain the conditional distribution of the number and size of sub sectors in sutton s model we formulate and solve an alternative model based on the assumption that the sector sizes follow a power law distribution we find in this new model both anomalous scaling of the variance of growth rates and non gaussian asymptotic distributions we give some testable predictions of the two models that would differentiate them further we also discuss why the growth rate statistics at the country level and at the company level should be identical

renewal processes and the hurst effect consider a pure recurrent positive renewal process generated by some inter arrival waiting time if the waiting time has power law fall off exponent i e tail index in 1 2 and if the jump s amplitude has non zero but finite mean and finite variance the cumulative amplitude process is long range dependent with hurst exponent in 1 2 1 results in this direction have been obtained by daley under the sole assumptions that the waiting time has moment index in 1 2 if the amplitude has zero mean up to a brownian trend the cumulative amplitude process exhibits a negative dependence property with hurst exponent in 0 1 2 the case of delayed stationary renewal processes is also investigated together with two classes of limiting renewal processes the compound exponential and the levy classes these are of some interest when the average time between consecutive jumps tends to zero jointly with the probability mass of the jumps height concentrating about zero in some precise way under suitable hypothesis the hurst effect is maintained in the limit

statistics of the occupation time for a class of gaussian markov processes we revisit the work of dhar and majumdar 1999 phys rev e 59 6413 on the limiting distribution of the temporal mean mt t 1 0tdu sign yu for a gaussian markovian process yt depending on a parameter which can be interpreted as brownian motion in the time scale t t2 this quantity the mean magnetization is simply related to the occupation time of the process that is the length of time spent on one side of the origin up to time t using the fact that the intervals between sign changes of the process form a renewal process on the time scale t we determine recursively the moments of the mean magnetization we also find an integral equation for the distribution of mt this allows a local analysis of this distribution in the persistence region mt 1 as well as its asymptotic analysis in the regime where is large finally we put the results thus found in perspective with those obtained by dhar and majumdar by another method based on a formalism due to kac

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

large deviations of ergodic counting processes a statistical mechanics approach the large deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic nonstationary statistical properties of its fluctuations here we study this formalism through a statistical mechanics approach that is with an auxiliary counting process that maximizes an entropy function associated with the thermodynamic potential we show that the realizations of this auxiliary process can be obtained after applying a conditional measurement scheme to the original ones providing is this way an alternative measurement interpretation of the thermodynamic approach general results are obtained for renewal counting processes that is those where the time intervals between consecutive events are independent and defined by a unique waiting time distribution the underlying statistical mechanics is controlled by the same waiting time distribution rescaled by an exponential decay measured by the free energy function a scale invariance shift closure and intermittence phenomena are obtained and interpreted in this context similar conclusions apply for nonrenewal processes when the memory between successive events is induced by a stochastic waiting time distribution

symmetric phase only matched filtering of fourier mellin transforms for image registration and recognition presents a new method to match a 2d image to a translated rotated and scaled reference image the approach consists of two steps the calculation of a fourier mellin invariant fmi descriptor for each image to be matched and the matching of the fmi descriptors the fmi descriptor is translation invariant and represents rotation and scaling as translations in parameter space the matching of the fmi descriptors is achieved using symmetric phase only matched filtering spomf the performance of the fmi spomf algorithm is the same or similar to that of phase only matched filtering when dealing with image translations the significant advantage of the new technique is its capability to match rotated and scaled images accurately and efficiently the innovation is the application of spomf to the fmi descriptors which guarantees high discriminating power and excellent robustness in the presence of noise this paper describes the principle of the new method and its discrete implementation for either image detection problems or image registration problems practical results are presented for various applications in medical imaging remote sensing fingerprint recognition and multiobject identification

aging and percolation dynamics in a non poissonian temporal network model we present an exhaustive mathematical analysis of the recently proposed non poissonian activity driven nopad model moinet et al phys rev lett 114 108701 2015 a temporal network model incorporating the empirically observed bursty nature of social interactions we focus on the aging effects emerging from the non poissonian dynamics of link activation and on their effects on the topological properties of time integrated networks such as the degree distribution analytic expressions for the degree distribution of integrated networks as a function of time are derived exploring both limits of vanishing and strong aging we also address the percolation process occurring on these temporal networks by computing the threshold for the emergence of a giant connected component highlighting the aging dependence our analytic predictions are checked by means of extensive numerical simulations of the nopad model

fluctuations around equilibrium laws in ergodic continuous time random walks we study occupation time statistics in ergodic continuous time random walks under thermal detailed balance conditions the average occupation time is given by the boltzmann gibbs canonical law but close to the nonergodic phase the finite time fluctuations around this mean are large and nontrivial they exhibit dual time scaling and distribution laws the infinite density of large fluctuations complements the levy stable density of bulk fluctuations neither of the two should be interpreted as a stand alone limiting law as each has its own deficiency the infinite density has an infinite norm despite particle conservation while the stable distribution has an infinite variance although occupation times are bounded these unphysical divergences are remedied by consistent use and interpretation of both formulas interestingly while the system s canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion they also control the infinite and levy stable densities of fluctuations the duality of stable and infinite densities is in fact ubiquitous for these dynamics as it concerns the time averages of general physical observables

subordinated stochastic processes with aged operational time in this paper subordinated stochastic processes are considered where the renewal process acting as the operational time it is assumed that the observation of the process begins at a certain time after the start of the renewal process a recurrence formula was derived for calculating the multipoint probability density functions of the aged renewal process two point correlation functions for certain subordinated stochastic processes particularly for the generalized ornstein uhlenbeck process were calculated a model of relaxation in a disordered medium with traps and obstacles is proposed

stationary definition of persistence for finite temperature phase ordering for the two dimensional kinetic ising model at finite temperature the local mean magnetization simply related to the fraction of time spent by a given spin in the positive direction has a limiting distribution singular at the onsager spontaneous magnetization the exponent of this singularity defines the persistence exponent we also study first passage exponents associated to persistent large deviations of and their temperature dependence

statistics of occupation times and connection to local properties of nonhomogeneous random walks we consider the statistics of occupation times the number of visits at the origin and the survival probability for a wide class of stochastic processes which can be classified as renewal processes we show that the distribution of these observables can be characterized by a single exponent that is connected to a local property of the probability density function of the process viz the probability of occupying the origin at time t p t we test our results for two different models of lattice random walks with spatially inhomogeneous transition probabilities one of which of non markovian nature and find good agreement with theory we also show that the distributions depend only on the occupation probability of the origin by comparing them for the two systems when p t shows the same long time behavior each observable follows indeed the same distribution

nonergodicity of a time series obeying levy statistics time averaged autocorrelation functions of a dichotomous random process switching between 1 and 0 and governed by wide power law sojourn time distribution are studied such a process called a levy walk describes dynamical behaviors of many physical systems fluorescence intermittency of semiconductor nanocrystals under continuous laser illumination being one example when the mean sojourn time diverges the process is non ergodic in that case the time average autocorrelation function is not equal to the ensemble averaged autocorrelation function instead it remains random even in the limit of long measurement time several approximations for the distribution of this random autocorrelation function are obtained for different parameter ranges and favorably compared to monte carlo simulations nonergodicity of the power spectrum of the process is briefly discussed and a nonstationary wiener khintchine theorem relating the correlation functions and the power spectrum is presented the considered situation is in full contrast to the usual assumptions of ergodicity and stationarity

limit theorems for levy walks in d dimensions rare and bulk fluctuations we consider super diffusive levy walks in dimensions when the duration of a single step i e a ballistic motion performed by a walker is governed by a power law tailed distribution of infinite variance and finite mean we demonstrate that the probability density function pdf of the coordinate of the random walker has two different scaling limits at large times one limit describes the bulk of the pdf it is the d dimensional generalization of the one dimensional levy distribution and is the counterpart of the central limit theorem clt for random walks with finite dispersion in contrast with the one dimensional levy distribution and the clt this distribution does not have a universal shape the pdf reflects anisotropy of the single step statistics however large the time is the other scaling limit the so called infinite density describes the tail of the pdf which determines second dispersion and higher moments of the pdf this limit repeats the angular structure of the pdf of velocity in one step a typical realization of the walk consists of anomalous diffusive motion described by anisotropic d dimensional levy distribution interspersed with long ballistic flights described by infinite density the long flights are rare but due to them the coordinate increases so much that their contribution determines the dispersion we illustrate the concept by considering two types of levy walks with isotropic and anisotropic distributions of velocities furthermore we show that for isotropic but otherwise arbitrary velocity distributions the d dimensional process can be reduced to a one dimensional levy walk we briefly discuss the consequences of non universality for the d 1 dimensional fractional diffusion equation in particular the non uniqueness of the fractional laplacian

statistics of the occupation time of renewal processes we present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time according to the nature of the distribution of time intervals the probability density functions of these random variables have very different scalings in time we analyze successively the cases where this distribution is narrow where it is broad with index 1 and finally where it is broad with index 1 2 the methods introduced in this work provide a basis for the investigation of the statistics of the occupation time of more complex stochastic processes see joint paper by g de smedt c godreche and j m luck 26

fingerprint ridge distance computation methodologies abstract the average ridge distance of fingerprint images is used in many problems and applications it is used in fingerprint filter design or in identification and classification procedures this paper addresses the problem of local average ridge distance computation this computation is based on a two step procedure first the average distance is defined in each significant portion of the image and then this information is propagated onto the remaining regions to complete the computation two methods are considered in the first step geometric and spectral in the geometric approach the central points of ridges are estimated on a regular grid and straight lines passing through these points and parallel to the ridge directions are used the second method is based on the computation of harmonic coefficients leading to effective estimates of the average ridge period in order to complete the average distance map a diffusion equation is used so that maps with minimum variations are favored finally some experimental results on nist sdb4 are reported

the class of a torus in the grothendieck ring of varieties we establish a formula for the classes of certain tori in the grothendieck ring of varieties expressing them in terms of the natural lambda structure on the grothendieck ring more explicitly we will see that if l is the torus of invertible elements in the n dimensional separable k algebra l then the class of l can be expressed as an alternating sum of the images of the spectrum of l under the lambda operations multiplied by powers of the lefschetz class this formula is suggested from the cohomology of the torus illustrating a heuristic method that can be used in other situations to prove the formula will require some rather explicit calculations in the grothendieck ring to be able to perform these we introduce a homomorphism from the burnside ring of the absolute galois group of k to the grothendieck ring of varieties over k in the process we obtain some information about the structure of the subring generated by zero dimensional varieties

infinite invariant density in a semi markov process with continuous state variables we report on a fundamental role of a non normalized formal steady state i e an infinite invariant density in a semi markov process where the state is determined by the interevent time of successive renewals the state describes certain observables found in models of anomalous diffusion e g the velocity in the generalized levy walk model and the energy of a particle in the trap model in our model the interevent time distribution follows a fat tailed distribution which makes the state value more likely to be zero because long interevent times imply small state values we find two scaling laws describing the density for the state value which accumulates in the vicinity of zero in the long time limit these laws provide universal behaviors in the accumulation process and give the exact expression of the infinite invariant density moreover we provide two distributional limit theorems for time averaged observables in these nonstationary processes we show that the infinite invariant density plays an important role in determining the distribution of time averages

a random telegraph signal of mittag leffler type a general method is presented to explicitly compute autocovariance functions for non poisson dichotomous noise based on renewal theory the method is specialized to a random telegraph signal of mittag leffler type analytical predictions are compared to monte carlo simulations non poisson dichotomous noise is non stationary and standard spectral methods fail to describe it properly as they assume stationarity

relationship between dynamical heterogeneities and stretched exponential relaxation we identify dynamical heterogeneities as an essential prerequisite for stretched exponential relaxation in dynamically frustrated systems this heterogeneity takes the form of ordered domains of finite but diverging lifetime for particles in atomic or molecular systems or spin states in magnetic materials at the onset of the dynamical heterogeneity the distribution of time intervals spent in such domains or traps becomes stretched exponential at long times we rigorously show that once this is the case the autocorrelation function of the renewal process formed by these time intervals is also a stretched exponential at long times

weakly non ergodic statistical physics for weakly non ergodic systems the probability density function of a time average observable overline mathcal o is f alpha overline mathcal o 1 over pi lim epsilon to 0 mbox im sum j 1 l p mathrm eq j overline mathcal o mathcal o j i epsilon alpha 1 over sum j 1 l p mathrm eq j overline mathcal o mathcal o j i epsilon alpha where mathcal o j is the value of the observable when the system is in state j 1 l pjeq is the probability that a member of an ensemble of systems occupies state j in equilibrium for a particle undergoing a fractional diffusion process in a binding force field with thermal detailed balance conditions pjeq is boltzmann s canonical probability within the unbiased sub diffusive continuous time random walk model the exponent 0 1 is the anomalous diffusion exponent x2 t found for free boundary conditions when 1 ergodic statistical mechanics is recovered lim alpha to 1 f alpha overline mathcal o delta overline mathcal o langle mathcal o rangle we briefly discuss possible physical applications in single particle experiments

stability in a system subject to noise with regulated periodicity the stability of a simple dynamical system subject to multiplicative one side pulse noise with hidden periodicity is investigated both analytically and numerically the stability analysis is based on the exact result for the characteristic functional of the renewal pulse process the influence of the memory effects on the stability condition is analyzed for two cases i the dead time distorted poissonian process and ii the renewal process with pareto distribution we show that for fixed noise intensity the system can be stable when the noise is characterized by high periodicity and unstable at low periodicity

fractional feynman kac equation for weak ergodicity breaking the continuous time random walk ctrw is a model of anomalous subdiffusion in which particles are immobilized for random times between successive jumps a power law distribution of the waiting times 1 leads to subdiffusion x 2 t for 0 1 in closed systems the long stagnation periods cause time averages to divert from the corresponding ensemble averages which is a manifestation of weak ergodicity breaking the time average of a general observable u t 1 t 0 t u x d is a functional of the path and is described by the well known feynman kac equation if the motion is brownian here we derive forward and backward fractional feynman kac equations for functionals of ctrw in a binding potential we use our equations to study two specific time averages the fraction of time spent by a particle in half box and the time average of the particle s position in a harmonic field in both cases we obtain the probability density function of the time averages for t and the first two moments our results show that both the occupation fraction and the time averaged position are random variables even for long times except for 1 when they are identical to their ensemble averages using our fractional feynman kac equation we also study the dynamics leading to weak ergodicity breaking namely the convergence of the fluctuations to their asymptotic values

algebraic independence in the grothendieck ring of varieties we give sufficient cohomological criteria for the classes of given varieties over a field k to be algebraically independent in the grothendieck ring of varieties over k and construct some examples

anomalous metapopulation dynamics on scale free networks we model transport of individuals across a heterogeneous scale free network where a few weakly connected nodes exhibit heavy tailed residence times using the empirical law of the axiom of cumulative inertia and fractional analysis we show that anomalous cumulative inertia overpowers highly connected nodes in attracting network individuals this fundamentally challenges the classical result that individuals tend to accumulate in high order nodes the derived residence time distribution has a nontrivial u shape which we encounter empirically across human residence and employment times

fingerprint identification using graph matching abstract a new algorithm for automated fingerprint encoding and matching is presented the algorithm is intended to be insensitive to imperfections introduced during fingerprint registration such as noise distortion and displacement a fingerprint is represented in the form of a graph whose nodes correspond to ridges in the print edges of the graph connect nodes that represent neighboring or intersecting ridges hence the graph structure captures the topological relationships within the fingerprint the algorithm has been implemented and tested using a library of real life fingerprint images

renewal modulation and superstatistics in times series we consider two different approaches to which we refer to as renewal and modulation to generate time series with a nonexponential distribution of waiting times we show that different time series with the same waiting time distribution are not necessarily statistically equivalent and might generate different physical properties renewal generates aging and anomalous scaling while modulation yields no significant aging and either ordinary or anomalous diffusion according to the dynamic prescription adopted we show in fact that the physical realization of modulation generates two classes of events the events of the first class are determined by the persistent use of the same exponential time scale for an extended lapse of time and consequently are numerous the events of the second class are identified with the abrupt changes from one to another exponential prescription and consequently are rare the events of the second class although rare determine the scaling of the diffusion process and for this reason we term them as crucial events according to the prescription adopted to produce modulation the distribution density of the time distances between two consecutive crucial events might have or not a diverging second moment in the former case the resulting diffusion process although going through a transition regime very extended in time will eventually become anomalous in conclusion modulation rather than ruling out the action of renewal events produces crucial events hidden by clouds of exponential events thereby setting the challenge for their identification

exact occupation time distribution in a non markovian sequence and its relation to spin glass models we compute exactly the distribution of the occupation time in a discrete non markovian toy sequence that appears in various physical contexts such as the diffusion processes and ising spin glass chains the non markovian property makes the results nontrivial even for this toy sequence the distribution is shown to have non gaussian tails characterized by a nontrivial large deviation function that is computed explicitly an exact mapping of this sequence to an ising spin glass chain via a gauge transformation raises an interesting question for a generic finite sized spin glass model at a given temperature what is the distribution over disorder of the thermally averaged number of spins that are aligned to their local fields we show that this distribution remains nontrivial even at infinite temperature and can be computed explicitly in few cases such as in the sherrington kirkpatrick model with gaussian disorder

mean first passage times in confined media from markovian to non markovian processes we review recent theoretical works that enable the accurate evaluation of the mean first passage time mfpt of a random walker to a target in confinement for markovian memory less and non markovian walkers for the markovian problem we present a general theory which allows one to accurately evaluate the mfpt and its extensions to related first passage observables such as splitting probabilities and occupation times we show that this analytical approach provides a universal scaling dependence of the mfpt on both the volume of the confining domain and the source target distance in the case of general scale invariant processes this analysis is applicable to a broad range of stochastic processes characterized by length scale invariant properties and reveals the key role that can be played by the starting position of the random walker we then present an extension to non markovian walks by taking the specific example of a tagged monomer of a polymer chain looking for a target in confinement we show that the mfpt can be calculated accurately by computing the distribution of the positions of all the monomers in the chain at the instant of reaction such a theory can be used to derive asymptotic relations that generalize the scaling dependence with the volume and the initial distance to the target derived for markovian walks finally we present an application of this theory to the problem of the first contact time between the two ends of a polymer chain and review the various theoretical approaches of this nonmarkovian problem

linear response to perturbation of nonexponential renewal processes we study the linear response of a two state stochastic process obeying the renewal condition by means of a stochastic rate equation equivalent to a master equation with infinite memory we show that the condition of perennial aging makes the response to coherent perturbation vanish in the long time limit

algebraic theory of dicritical divisors the topological theory of dicritical divisors is algebracized which makes it valid for nonzero characteristic as well as mixed characteristic

ergodic transitions in continuous time random walks we consider continuous time random walk models described by arbitrary sojourn time probability density functions we find a general expression for the distribution of time averaged observables for such systems generalizing some recent results presented in the literature for the case where sojourn times are identically distributed independent random variables our results shed some light on the recently proposed transitions between ergodic and weakly nonergodic regimes on the other hand for the case of nonidentical trapping time densities over the lattice points the distribution of time averaged observables reveals that such systems are typically nonergodic in agreement with some recent experimental evidences on the statistics of blinking quantum dots some explicit examples are considered in detail our results are independent of the lattice topology and dimensionality

aging in mortal superdiffusive levy walkers a growing body of literature examines the effects of superdiffusive subballistic movement premeasurement aging or time lag on observations arising from single particle tracking a neglected aspect is the finite lifetime of these levy walkers be they proteins cells or larger structures we examine the effects of aging on the motility of mortal walkers and discuss the means by which permanent stopping of walkers may be categorized as arising from natural death or experimental artifacts such as low photostability or radiation damage this is done by comparison of the walkers mean squared displacement msd with the front velocity of propagation of a group of walkers which is found to be invariant under time lags for any running time distribution of a mortal random walker the msd is tempered by the stopping rate this provides a physical interpretation for truncated heavy tailed diffusion processes and serves as a tool by which to better classify the underlying running time distributions of random walkers tempering of aged msds raises the issue of misinterpreting superdiffusive motion which appears brownian or subdiffusive over certain time scales

arcsine laws and interval partitions derived from a stable subordinator levy discovered that the fraction of time a standard one dimensional brownian motion b spends positive before time t has arcsine distribution both for a fixed time when b t 0 almost surely and for t an inverse local time when b t 0 almost surely this identity in distribution is extended from the fraction of time spent positive to a large collection of functionals derived from the lengths and signs of excursions of b away from 0 similar identities in distribution are associated with any process whose zero set is the range of a stable subordinator for instance a bessel process of dimension d for 0 d 2

fingerprint matching using an orientation based minutia descriptor we introduce a novel fingerprint representation scheme that relies on describing the orientation field of the fingerprint pattern with respect to each minutia detail this representation allows the derivation of a similarity function between minutiae that is used to identify corresponding features and evaluate the resemblance between two fingerprint impressions a fingerprint matching algorithm based on the proposed representation is developed and tested with a series of experiments conducted on two public domain collections of fingerprint images the results reveal that our method can achieve good performance on these data collections and that it outperforms other alternative approaches implemented for comparison

renewal theory with fat tailed distributed sojourn times typical versus rare renewal processes with heavy tailed power law distributed sojourn times are commonly encountered in physical modeling and so typical fluctuations of observables of interest have been investigated in detail to describe rare events the rate function approach from large deviation theory does not hold and new tools must be considered here we investigate the large deviations of the number of renewals the forward and backward recurrence times the occupation time and the time interval straddling the observation time we show how non normalized densities describe these rare fluctuations and how moments of certain observables are obtained from these limiting laws numerical simulations illustrate our results showing the deviations from arcsine dynkin darling kac l evy and lamperti laws

on convex relaxation of graph isomorphism graphs are a ubiquitous mathematical abstraction used in numerous problems in science and engineering of particular importance is the need to find the best structure preserving matching of graphs since graph matching gm is a computationally intractable problem numerous heuristics exist to approximate its solution an important class of gm heuristics is relaxation techniques based on replacing the original problem by a continuous convex program conditions for applicability or inapplicability of such convex relaxations are poorly understood in this study we propose easy to check spectral properties to characterize a wide family of graphs for which we prove equivalence of convex relaxation to the exact gm

fractional feynman kac equation with space dependent anomalous exponent to describe the distribution of functionals for inhomogeneous subdiffusion in space and time dependent force field we derive forward and backward time fractional feynman kac equations with space dependent anomalous exponent based on the space jump random walk model in our examples we get the statistic of occupation fraction and first passage time for anomalous infiltration of free particles in disordered systems by applying the backward version

a randomized approach with geometric constraints to fingerprint verification abstract in this paper a fuzzy bipartite weighted graph model is proposed to solve fingerprint verification problem a fingerprint image is preprocessed first to form clusters of feature points which are called feature point clusters twenty four attributes are extracted for each feature point cluster the attributes are characterized by fuzzy values attributes of an input image to be verified are considered as the set of left nodes in a fuzzy bipartite weighted graph and the attributes of claimed template fingerprint image are considered as the set of right nodes in the graph the fingerprint verification problem is thus converted into a fuzzy bipartite weighted graph matching problem a matching algorithm is proposed for the fuzzy bipartite weighted graph model to find an optimal matching with a goodness score experimental results reveal the feasibility of the proposed approach in fingerprint verification

coarsening and persistence in the voter model the voter model is a simple model for coarsening with a nonconserved scalar order parameter we investigate coarsening and persistence in the voter model by introducing the quantity pn t defined as the fraction of voters who changed their opinion n times up to time t we show that pn t exhibits scaling behavior that strongly depends on the dimension as well as on the initial opinion concentrations exact results are obtained for the average number of opinion changes n and the autocorrelation function a t 21 n pn t 2d 2 in arbitrary dimension d these exact results are complemented by a mean field theory heuristic arguments and numerical simulations for dimensions d 2 the system does not coarsen and the opinion changes follow a nearly poissonian distribution in agreement with mean field theory for dimensions d 2 the distribution is given by a different scaling form which is characterized by nontrivial scaling exponents for unequal opinion concentrations an unusual situation occurs where different scaling functions correspond to the majority and the minority as well as for even and odd n

ageing first passage time density in continuous time random walks and quenched energy landscapes we study the first passage dynamics of an ageing stochastic process in the continuous time random walk ctrw framework in such ctrw processes the test particle performs a random walk in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function an ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time ta the time elapsed between its preparation and the start of the observation subdiffusive ageing ctrws with describe systems such as charge carriers in amorphous semiconducters tracer dispersion in geological and biological systems or the dynamics of blinking quantum dots we derive the exact forms of the first passage time density for an ageing subdiffusive ctrw in the semi infinite confined and biased case finding different scaling regimes for weakly intermediately and strongly aged systems these regimes with different scaling laws are also found when the scaling exponent is in the range for sufficiently long ta we compare our results with the ageing motion of a test particle in a quenched energy landscape we test our theoretical results in the quenched landscape against simulations only when the bias is strong enough the correlations from returning to previously visited sites become insignificant and the results approach the ageing ctrw results with small bias or without bias the ageing effects disappear and a change in the exponent compared to the case of a completely annealed landscape can be found reflecting the build up of correlations in the quenched landscape

record statistics of a strongly correlated time series random walks and levy flights we review recent advances on the record statistics of strongly correlated time series whose entries denote the positions of a random walk or a l evy flight on a line after a brief survey of the theory of records for independent and identically distributed random variables we focus on random walks during the last few years it was indeed realized that random walks are a very useful laboratory to test the effects of correlations on the record statistics we start with the simple one dimensional random walk with symmetric jumps both continuous and discrete and discuss in detail the statistics of the number of records as well as of the ages of the records i e the lapses of time between two successive record breaking events then we review the results that were obtained for a wide variety of random walk models including random walks with a linear drift continuous time random walks constrained random walks like the random walk bridge and the case of multiple independent random walkers finally we discuss further observables related to records like the record increments as well as some questions raised by physical applications of record statistics like the effects of measurement error and noise

aging generates regular motions in weakly chaotic systems using intermittent maps with infinite invariant measures we investigate the universality of time averaged observables under aging conditions according to aaronson s darling kac theorem in non aged dynamical systems with infinite invariant measures the distribution of the normalized time averages of integrable functions converges to the mittag leffler distribution this well known theorem holds when the start of observations coincides with the start of the dynamical processes introducing a concept of the aging limit where the aging time t a and the total measurement time t goes to infinity while the aging ratio t a t is kept constant we obtain a novel distributional limit theorem of time averaged observables integrable with respect to the infinite invariant density applying the theorem to the lyapunov exponent in intermittent maps we find that regular motions and a weakly chaotic behavior coexist in the aging limit this mixed type of dynamics is controlled by the aging ratio and hence is very different from the usual scenario of regular and chaotic motions in hamiltonian systems the probability of finding regular motions in non aged processes is zero while in the aging regime it is finite and it increases when system ages

geometric framework for fingerprint image classification given a digitized fingerprint image we would like to classify it into one of several types already established in the literature in this paper we consider five types for classification double loop whorl left loop right loop and arch we illustrate the use of a geometric framework for a systematic top down classification of the foregoing types from the double loop type down to the arch type in the order given above the framework employs both a geometric grouping and a global geometric shape analysis of fingerprint ridges to accomplish the required task these processes are based on the framework s underlying b spline representation and interpretation of the ridges

a fast projected fixed point algorithm for large graph matching we propose a fast algorithm for approximate matching of large graphs previous graph matching algorithms suffer from high computational complexity and therefore do not have good scalability by using a new doubly stochastic projection for matching two weighted graphs of n nodes our algorithm has time complexity only o n 3 per iteration and space complexity o n 2 we proved that our algorithm converges at a super logarithmic rate experiments on large synthetic and real graphs over 1000 nodes were conducted to evaluate the performance of various algorithms results show that due to its fast convergence our algorithm is more than an order of magnitude faster than the previous state of the art algorithms while maintaining comparable accuracy in large graph matching highlightslow time complexity o n3 iteration for two graphs of n nodes super logarithm convergence guarantee large graph matching experiments

on distributions of functionals of anomalous diffusion paths functionals of brownian motion have diverse applications in physics mathematics and other fields the probability density function pdf of brownian functionals satisfies the feynman kac formula which is a schrodinger equation in imaginary time in recent years there is a growing interest in particular functionals of non brownian motion or anomalous diffusion but no equation existed for their pdf here we derive a fractional generalization of the feynman kac equation for functionals of anomalous paths based on sub diffusive continuous time random walk we also derive a backward equation and a generalization to levy flights solutions are presented for a wide number of applications including the occupation time in half space and in an interval the first passage time the maximal displacement and the hitting probability we briefly discuss other fractional schrodinger equations that recently appeared in the literature

first passage and first exit times of a bessel like stochastic process we study a stochastic process x t which is a particular case of the rayleigh process and whose square is the bessel process with various applications in physics chemistry biology economics finance and other fields the stochastic differential equation is dx t nd x t dt 2d dw t where w t is the wiener process the drift term can arise from a logarithmic potential or from taking x t as the norm of a multidimensional random walk due to the singularity of the drift term for x t 0 different natures of boundary at the origin arise depending on the real parameter n entrance exit and regular for each of them we calculate analytically and numerically the probability density functions of first passage times or first exit times nontrivial behavior is observed in the case of a regular boundary

residence time statistics for normal and fractional diffusion in a force field we investigate statistics of occupation times for an over damped brownian particle in an external force field using a backward fokker planck equation introduced by majumdar and comtet for an arbitrary potential field the distribution of occupation times is expressed in terms of solutions of the corresponding first passage time problem this general relationship between occupation times and first passage times is valid for normal markovian diffusion and for non markovian sub diffusion the latter modeled using the fractional fokker planck equation for binding potential fields we find in the long time limit ergodic behavior for normal diffusion while for the fractional framework weak ergodicity breaking is found in agreement with previous results of bel and barkai on the continuous time random walk on a lattice for non binding cases rich physical behaviors are obtained and classification of occupation time statistics is made possible according to whether or not the underlying random walk is recurrent and the averaged first return time to the origin is finite our work establishes a link between fractional calculus and ergodicity breaking