relating continuous and discrete pepa models of signalling pathways pepa and its semantics have recently been extended to model biological systems in order to cope with massive quantities of processes as is usually the case when considering biological reactions the model is interpreted in terms of a small set of coupled ordinary differential equations odes instead of a large state space continuous time markov chain ctmc so far the relationship between these two semantics of pepa had not been established this is the goal of the present paper after introducing a new extension of pepa denoted email protected that allows models to capture both mass action law and bounded capacity law cooperations the relationship between these two semantics is demonstrated the result relies on kurtz s theorem that expresses that a set of odes can be in some sense considered as the limit of pure jump markov processes

fluid computation of passage time distributions in large markov models recent developments in the analysis of large markov models facilitate the fast approximation of transient characteristics of the underlying stochastic process fluid analysis makes it possible to consider previously intractable models whose underlying discrete state space grows exponentially as model components are added in this work we show how fluid approximation techniques may be used to extract passage time measures from performance models we focus on two types of passage measure passage times involving individual components as well as passage times which capture the time taken for a population of components to evolve specifically we show that for models of sufficient scale global passage time distributions can be well approximated by a deterministic fluid derived passage time measure where models are not of sufficient scale we are able to generate upper and lower approximations for the entire cumulative distribution function of these passage time random variables using moment based techniques additionally we show that for passage time measures involving individual components the cumulative distribution function can be directly approximated by fluid techniques finally using the gpa tool we take advantage of the rapid fluid computation of passage times to show how a multi class client server system can be optimised to satisfy multiple service level agreements

algorithmic product form approximations of interacting stochastic models a large variety of product form solutions for continuous time markovian models can be derived by checking a set of structural properties of the underlying stochastic processes and a condition on their reversed rates in previous work marin and vigliotti 2010 9 we have shown how to derive a large class of product form solutions using a different formulation of the reversed compound agent theorem grcat we continue this line of work by showing that it is possible to exploit this result to approximate the steady state distribution of non product form model interactions by means of product form ones

a fluid analysis framework for a markovian process algebra markovian process algebras such as pepa and stochastic p calculus bring a powerful compositional approach to the performance modelling of complex systems however the models generated by process algebras as with other interleaving formalisms are susceptible to the state space explosion problem models with only a modest number of process algebra terms can easily generate so many states that they are all but intractable to traditional solution techniques previous work aimed at addressing this problem has presented a fluid flow approximation allowing the analysis of systems which would otherwise be inaccessible to achieve this systems of ordinary differential equations describing the fluid flow of the stochastic process algebra model are generated informally in this paper we show formally that for a large class of models this fluid flow analysis can be directly derived from the stochastic process algebra model as an approximation to the mean number of component types within the model the nature of the fluid approximation is derived and characterised by direct comparison with the chapman kolmogorov equations underlying the markov model furthermore we compare the fluid approximation with the exact solution using stochastic simulation and we are able to demonstrate that it is a very accurate approximation in many cases for the first time we also show how to extend these techniques naturally to generate systems of differential equations approximating higher order moments of model component counts these are important performance characteristics for estimating for instance the variance of the component counts this is very necessary if we are to understand how precise the fluid flow calculation is in a given modelling situation

noise reduction in surface reconstruction from a given gradient field we present a gradient space technique for noise reduction in surfaces reconstructed from a noisy gradient field we first analyze the error sources in the recovered gradient field of a surface using a three image photometric stereo method based on this analysis we propose an additive noise model to describe the errors in the surface gradient estimates we then use a vector space formulation and construct a multiscale orthonormal expansion for gradient fields using the sparse representation properties of this expansion we develop techniques for reducing the gradient field noise by coefficient selection with thresholding the simulation results indicate that the proposed technique provides significant improvement on the noise levels of both the estimated gradient fields and the reconstructed surfaces under heavy noise levels furthermore the experiments using noisy photometric stereo image triplets of real range data suggest that the additive model remains viable after the nonlinear photometric stereo operation to provide accurate noise removal

activity spectrum from waiting time distribution in high frequency financial data not only returns but also waiting times between trades are random variables in this work we analyze the spectra of the waiting time processes for tick by tick trades the numerical problem strictly related with the real inversion of laplace transforms is analyzed by using tikhonov s regularization method we also analyze these spectra by a rough method using a comb of dirac s delta functions

nonextensivity and natural time the case of seismicity nonextensive statistical mechanics pioneered by tsallis has recently achieved a generalization of the gutenberg richter law for earthquakes this remarkable generalization is combined here with natural time analysis which enables the distinction of two origins of self similarity i e the process memory and the process increments infinite variance by using also detrended fluctuation analysis for the detection of long range temporal correlations we demonstrate the existence of both temporal and magnitude correlations in real seismic data of california and japan natural time analysis reveals that the nonextensivity parameter q in contrast to some published claims cannot be considered as a measure of temporal organization but the tsallis formulation does achieve a satisfactory description of real seismic data for japan for q 1 66 when supplemented by long range temporal correlations

effect of nonlinear correlations on the statistics of return intervals in multifractal data sets we study the statistics of return intervals between events above a certain threshold in multifractal data sets without linear correlations we find that nonlinear correlations in the record lead to a power law i decay of the autocorrelation function of the return intervals ii increase in the conditional return period and iii decay in the probability density function of the return intervals we show explicitly that all the observed quantities depend both on the threshold value and system size and hence there is no simple scaling observed we also demonstrate that this type of behavior can be observed in real economic records and can be used to improve considerably risk estimation

branching ratio approximation for the self exciting hawkes process we introduce a model independent approximation for the branching ratio of hawkes self exciting point processes our estimator requires knowing only the mean and variance of the event count in a sufficiently large time window statistics that are readily obtained from empirical data the method we propose greatly simplifies the estimation of the hawkes branching ratio recently proposed as a proxy for market endogeneity and formerly estimated using numerical likelihood maximization we employ our method to support recent theoretical and experimental results indicating that the best fitting hawkes model to describe s futures price changes is in fact critical now and in the recent past in light of the long memory of financial market activity

model checking single agent behaviours by fluid approximation in this paper we investigate a potential use of fluid approximation techniques in the context of stochastic model checking of csl formulae we focus on properties describing the behaviour of a single agent in a large population of agents exploiting a limit result known also as fast simulation in particular we will approximate the behaviour of a single agent with a time inhomogeneous ctmc which depends on the environment and on the other agents only through the solution of the fluid differential equation and model check this process we will prove the asymptotic correctness of our approach in terms of satisfiability of csl formulae we will also present a procedure to model check time inhomogeneous ctmc against csl formulae

diffusion of epicenters of earthquake aftershocks omori s law and generalized continuous time random walk models the epidemic type aftershock sequence etas model is a simple stochastic process modeling seismicity based on the two best established empirical laws the omori law power law decay ensuremath sim 1 t 1 ensuremath theta of seismicity after an earthquake and gutenberg richter law power law distribution of earthquake energies in order to describe also the space distribution of seismicity we use in addition a power law distribution ensuremath sim 1 r 1 ensuremath mu of distances between triggered and triggering earthquakes the etas model has been studied for the last two decades to model real seismicity catalogs and to obtain short term probabilistic forecasts here we present a mapping between the etas model and a class of ctrw continuous time random walk models based on the identification of their corresponding master equations this mapping allows us to use the wealth of results previously obtained on anomalous diffusion of ctrw after translating into the relevant variable for the etas model we provide a classification of the different regimes of diffusion of seismic activity triggered by a mainshock specifically we derive the relation between the average distance between aftershocks and the mainshock as a function of the time from the mainshock and of the joint probability distribution of the times and locations of the aftershocks the different regimes are fully characterized by the two exponents ensuremath theta and ensuremath mu our predictions are checked by careful numerical simulations we stress the distinction between the bare omori law describing the seismic rate activated directly by a mainshock and the renormalized omori law taking into account all possible cascades from mainshocks to aftershocks of aftershock of aftershock and so on in particular we predict that seismic diffusion or subdiffusion occurs and should be observable only when the observed omori exponent is less than 1 because this signals the operation of the renormalization of the bare omori law also at the origin of seismic diffusion in the etas model we present predictions and insights provided by the etas to ctrw mapping which suggest different ways for studying seismic catalogs finally we discuss the present evidence for our predicted subdiffusion of seismicity triggered by a main shock stressing the caveats and limitations of previous empirical works

existence and uniqueness in photometric stereo we analyze the problem of recovering the shape of a smooth lambertian surface from two images obtained by consecutive illumination of the surface by distant point light sources from two different directions we discuss the issues of existence and uniqueness for the corresponding system of two first order nonlinear partial differential equations we show that generically this system has up to a constant a unique solution we also examine exceptional cases for which there is no such uniqueness

aftershocks in coherent noise models the decay pattern of aftershocks in the so called coherent noise models m e j newman and k sneppen phys rev e54 6226 1996 is studied in detail analytical and numerical results show that the probability to nd a large event at timet after an initial major event decreases as t for smallt with the exponent ranging from 0 to values well above 1 this is in contrast to sneppen und newman who stated that the exponent is about 1 independent of the microscopic details of the simulation numerical simulations of an extended model c wilke t martinetz phys rev e56 7128 1997 show that the power law is only a generic feature of the original dynamics and does not necessarily appear in a more general context finally the implications of the results to the modeling of earthquakes are discussed

lumping based equivalences in markovian automata algorithms and applications to product form analyses abstract in this paper we consider two relations over stochastic automata named lumpable bisimulation and exact equivalence that induce a strong and an exact lumping respectively on the underlying markov chains we show that an exact equivalence over the states of a non synchronising automaton is indeed a lumpable bisimulation for the corresponding reversed automaton and then it induces a strong lumping on the time reversed markov chain underlying the model this property allows us to prove that the class of quasi reversible models is closed under exact equivalence quasi reversibility is a pivotal property to study product form models hence exact equivalence turns out to be a theoretical tool to prove the product form of models by showing that they are exactly equivalent to models which are known to be quasi reversible algorithms for computing both lumpable bisimulation and exact equivalence are introduced case studies as well as performance tests are also presented

turning back time in markovian process algebra product form solutions in markovian process algebra mpa are constructed using properties of reversed processes the compositionality of mpas is directly exploited allowing a large class of hierarchically constructed systems to be solved for their state probabilities at equilibrium the paper contains new results on both reversed stationary markov processes as well as mpa itself and includes a mechanisable proof in mpa notation of jackson s theorem for product form queueing networks several examples are used to illustrate the approach

impossible and ambiguous shading patterns a smooth object depicted in a monochrome image will often exhibit brightness variation or shading a problem much studied in computer vision has been that of how object shape may be recovered from image shading when the imaging conditions are such that an overhead point source illuminates a smooth lambertian surface the problem may be formulated as that of finding a solution to an eikonal equation this article will focus on the existence and uniqueness of such solutions reporting recent results obtained with regard to existence shading patterns are exhibited for which there is no corresponding object shape specifically a necessary and sufficient condition is presented for a circularly symmetric eikonal equation to admit exclusively unbounded solutions additionally a sufficient condition is given for an eikonal equation to have no solution whatsoever in connection with uniqueness we consider eikonal equations defined over a disc such that the euclidean norm of the gradient of any solution is circularly symmetric vanishes exactly at the disc center and diverges to infinity as the circumference of the disc is approached contrary to earlier influential work a class of such eikonal equations is shown to possess simultaneously circularly symmetric and noncircularly symmetric bounded smooth solutions

clustering of extreme and recurrent events in deterministic chaotic systems we study the nontrivial clustering properties of extreme or recurrent events in the context of deterministic chaotic systems we find that correlations between return times of such events can depend nonmonotonically on the threshold used to define the events which leads to counterintuitive behavior in particular the distribution of the conditional return intervals can indicate clustering as well as repelling of extreme events for the same condition but different thresholds in sharp contrast to what has been observed for stochastic processes with long range correlations as well as for independent and identically distributed random variables this has important implications for the time dependent hazard assessment of extreme events indicating that possible threshold dependencies should always be taken into account

random neural networks with negative and positive signals and product form solution we introduce a new class of random neural networks in which signals are either negative or positive a positive signal arriving at a neuron increases its total signal count or potential by one a negative signal reduces it by one if the potential is positive and has no effect if it is zero when its potential is positive a neuron fires sending positive or negative signals at random intervals to neurons or to the outside positive signals represent excitatory signals and negative signals represent inhibition we show that this model with exponential signal emission intervals poisson external signal arrivals and markovian signal movements between neurons has a product form leading to simple analytical expressions for the system state

a tutorial on empa a theory of concurrent processes with nondeterminism priorities probabilities and time we give an overview of empa a process algebra for modeling and analyzing concurrent systems where nondeterminism priorities probabilities and time are present aiming at a reasonable trade off between the expressive power of the calculus and the complexity of its underlying theory

effects of diversity and procrastination in priority queuing theory the different power law regimes empirical analyses show that after the update of a browser or the publication of the vulnerability of a software or the discovery of a cyber worm the fraction of computers still using the older browser or software version or not yet patched or exhibiting worm activity decays as a power law ensuremath sim 1 t ensuremath alpha with 0l ensuremath alpha ensuremath le 1 over a time scale of years we present a simple model for this persistence phenomenon framed within the standard priority queuing theory of a target task which has the lowest priority compared to all other tasks that flow on the computer of an individual we identify a time deficit control parameter ensuremath beta and a bifurcation to a regime where there is a nonzero probability for the target task to never be completed the distribution of waiting time mathcal t until the completion of the target task has the power law tail ensuremath sim 1 t 1 2 resulting from a first passage solution of an equivalent wiener process taking into account a diversity of time deficit parameters in a population of individuals the power law tail is changed into 1 t ensuremath alpha with ensuremath alpha 0 5 ensuremath infty including the well known case 1 t we also study the effect of procrastination defined as the situation in which the target task may be postponed or delayed even after the individual has solved all other pending tasks this regime provides an explanation for even slower apparent decay and longer persistence

model for interevent times with long tails and multifractality in human communications an application to financial trading social technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure it is well known that the interevent statistics observed in these contexts differs from the poissonian profile by being long tailed distributed with resting and active periods interwoven understanding mechanisms generating consistent statistics has therefore become a central issue the approach we present is taken from the continuous time random walk formalism and represents an analytical alternative to models of nontrivial priority that have been recently proposed our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions we here analyze the intertransaction time intervals of several financial markets we observe that empirical data describe a subtle multifractal behavior our model explains this structure by taking the pausing time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks a stretched exponential kernel provides a multifractal profile valid for a certain limited range a suggested heuristic analytical profile is capable of covering a broader region

solution of the nonlinear theory and tests of earthquake recurrence times we develop an efficient numerical scheme to solve accurately the set of nonlinear integral equations derived previously in a saichev and d sornette j geophys res 112 b04313 2007 which describes the distribution of interevent times in the framework of a general model of earthquake clustering with long memory detailed comparisons between the linear and nonlinear versions of the theory and direct synthetic catalogs show that the nonlinear theory provides an excellent fit to the synthetic catalogs while there are significant biases resulting from the use of the linear approximation we then address the suggestions proposed by some authors to use the empirical distribution of interevent times to obtain a better determination of the so called clustering parameter our theory and tests against synthetic and empirical catalogs find a rather dramatic lack of power for the distribution of interevent times to distinguish between quite different sets of parameters casting doubt on the usefulness of this statistic for the specific purpose of identifying the clustering parameter

statistics of superior records we study statistics of records in a sequence of random variables these identical and independently distributed variables are drawn from the parent distribution the running record equals the maximum of all elements in the sequence up to a given point we define a superior sequence as one where all running records are above the average record expected for the parent distribution we find that the fraction of superior sequences s n decays algebraically with sequence length n s n n in the limit n interestingly the decay exponent is nontrivial being the root of an integral equation for example when is a uniform distribution with compact support we find 0 450265 in general the tail of the parent distribution governs the exponent we also consider the dual problem of inferior sequences where all records are below average and find that the fraction of inferior sequences i n decays algebraically albeit with a different decay exponent i n n we use the above statistical measures to analyze earthquake data language en

memory in the occurrence of earthquakes we study the statistics of the recurrence times ensuremath tau between earthquakes above a certain magnitude m in six one global and five regional earthquake catalogs we find that the distribution of the recurrence times strongly depends on the previous recurrence time ensuremath tau 0 such that small and large recurrence times tend to cluster in time this dependence on the past is reflected in both the conditional mean recurrence time and the conditional mean residual time until the next earthquake which increase monotonically with ensuremath tau 0 as a consequence the risk of encountering the next event within a certain time span after the last event depends significantly on the past an effect that has to be taken into account in any effective earthquake prognosis

on complete integrals and uniqueness in shape from shading in this paper we analyze the problem of representing solutions of a first order partial differential equation in terms of complete integrals we show that some of the existing results referring to the representability problem are incomplete additionally we analyze in the context of complete integrals the uniqueness problem for the shape recovery of a smooth lambertian surface from an image obtained by illuminating this surface by an overhead distant point light source specifically we revisit the uniqueness results already existing in the shape from shading literature that concern eikonal equations corresponding to the images of a lambertian hemisphere and a lambertian plane we show that the latter results are incomplete and indicate how to fill the gaps in the corresponding proofs

theory of earthquakes interevent times applied to financial markets abstract we analyze the probability density function pdf of waiting times between financial loss exceedances the empirical pdfs are fitted with the self excited hawkes conditional poisson process with a long power law memory kernel the hawkes process is the simplest extension of the poisson process that takes into account how past events influence the occurrence of future events by analyzing the empirical data for 15 different financial assets we show that the formalism of the hawkes process used for earthquakes can successfully model the pdf of interevent times between successive market losses

exact fluid lumpability in markovian process algebra quantitative analysis by means of discrete state stochastic processes is hindered by the well known phenomenon of state space explosion whereby the size of the state space may have an exponential growth with the number of agents of the system under scrutiny when the stochastic process underlies a markovian process algebra model this problem may be alleviated by suitable notions of behavioural equivalence that induce lumping at the underlying continuous time markov chain establishing an exact relation between a potentially much smaller aggregated chain and the original one for the analysis of massively parallel systems however lumping techniques may not be sufficient to yield a computationally tractable problem recently much work has been directed towards forms of fluid techniques that provide a set of ordinary differential equations odes approximating the expected path of the stochastic process unfortunately even fluid models of realistic systems may be too large for feasible analysis this paper studies a behavioural relation for process algebra with fluid semantics called projected label equivalence which is shown to yield an exactly fluid lumpable model i e an aggregated ode system which can be related to the original one without any loss of information project label equivalence relates sequential components of a process term in general for any two sequential components that are related in the fluid sense nothing can be said about their relationship from the stochastic viewpoint we define and study a notion of well posedness which allows us to relate fluid lumpability to the stochastic notion of semi isomorphism which is a weaker version of the common notion of isomorphism between the doubly labelled transition systems at the basis of the markovian interpretation

some remarks on the shape from shading problem in computer vision the shape from shading problem in computer vision see horn 11 deals with the reconstruction of the shape of an object from a two dimensional image we consider an object illuminated by a point source the reflected light being recorded on a photographic plate at a fixed position the intensity of the reflected light is a function of the position of the source the position of the plate and the normal to the surface of the object if the surface is given as u u x jj this leads see horn i to a first order partial differential equation of the form

improved risk estimation in multifractal records application to the value at risk in finance we suggest a risk estimation method for financial records that is based on the statistics of return intervals between events above below a certain threshold q and is particularly suited for multifractal records the method is based on the knowledge of the probability w q t ensuremath delta t that within the next ensuremath delta t units of time at least one event above q occurs if the last event occurred t time units ago we propose an analytical estimate of w q and show explicitly that the proposed method is superior to the conventional precursory pattern recognition technique widely used in signal analysis which requires considerable fine tuning and is difficult to implement we also show that the estimation of the value at risk which is a standard tool in finances can be improved considerably by the method

hybrid dynamics of stochastic programs we provide stochastic concurrent constraint programming sccp a stochastic process algebra based on ccp with a semantics in terms of hybrid automata we associate with each sccp program both a stochastic and a non deterministic hybrid automaton then we compare such automata with the standard stochastic semantics given by a continuous time markov chain and the one based on ordinary differential equations obtained by a fluid flow approximation technique we discuss in detail two case studies repressilator and the circadian clock with particular regard to the robustness exhibited by the different semantic models and to the effect of discreteness in dynamical evolution of such systems

bio pepa a framework for the modelling and analysis of biological systems in this work we present bio pepa a process algebra for the modelling and the analysis of biochemical networks it is a modification of pepa originally defined for the performance analysis of computer systems in order to handle some features of biological models such as stoichiometry and the use of general kinetic laws bio pepa may be seen as an intermediate formal compositional representation of biological systems on which different kinds of analyses can be carried out bio pepa is enriched with some notions of equivalence specifically the isomorphism and strong bisimulation for pepa have been considered and extended to our language finally we show the translation of a biological model into the new language and we report some analysis results

separable solutions for markov processes in random environments abstract in this paper we address the problem of efficiently deriving the steady state distribution for a continuous time markov chain ctmc s evolving in a random environment e the process underlying e is also a ctmc s is called markov modulated process markov modulated processes have been widely studied in literature since they are applicable when an environment influences the behaviour of a system for instance this is the case of a wireless link whose quality may depend on the state of some random factors such as the intensity of the noise in the environment in this paper we study the class of markov modulated processes which exhibits separable product form stationary distribution we show that several models that have been proposed in literature can be studied applying the extended reversed compound agent theorem ercat and also new product forms are derived we also address the problem of the necessity of ercat for product forms and show a meaningful example of product form not derivable via ercat

self similarity of waiting times in fracture systems experimental and numerical results are presented for a fracture experiment carried out on a fiber reinforced element under flexural loading and a statistical analysis is performed for acoustic emission waiting time distributions by an optimization procedure a recently proposed scaling law describing these distributions for different event magnitude scales is confirmed by both experimental and numerical data thus reinforcing the idea that fracture of heterogeneous materials has scaling properties similar to those found for earthquakes analysis of the different scaling parameters obtained for experimental and numerical data leads us to formulate the hypothesis that the type of scaling function obtained depends on the level of correlation among fracture events in the system

unified scaling law in the coherent noise model abstract the waiting time distribution between successive events and the unified scaling law is studied using the coherent noise model it is shown that although this model generates uncorrelated event sizes and does not exhibit criticality it still provides the unified scaling law we argue the role of characteristic kink observed in the unified scaling law and the meaning of the parameter c used to fix the peak of the kink to unity our results indicate that the parameter c is indeed a physical quantity localizing the end of the linear tendency in the scaling law which corresponds to the completion of the dominance of correlated events in time

separable equilibrium state probabilities via time reversal in markovian process algebra the reversed compound agent theorem rcat is a compositional result that uses markovian process algebra mpa to derive the reversed process of certain interactions between two continuous time markov chains at equilibrium from this reversed process together with the given forward process the joint state probabilities can be expressed as a product form although no general algorithm has previously been given this paper first generalises rcat to multiple more than two cooperating agents which removes the need for multiple applications and inductive proofs in cooperations of an arbitrary number of processes a new result shows a simple stochastic equivalence between cooperating synchronised processes and corresponding parallel asynchronous processes this greatly simplifies the proof of the new multi agent theorem which includes a statement of the desired product form solution itself as a product of given state probabilities in the parallel components the reversed process and product form thus derived rely on a solution to certain rate equations and it is shown for the first time that a unique solution exists under mild conditions certainly for queueing networks and g networks

recurrence intervals between earthquakes strongly depend on history we study the statistics of the recurrence times between earthquakes above a certain magnitude m in california we find that the distribution of the recurrence times strongly depends on the previous recurrence time tau 0 as a consequence the conditional mean recurrence time between two events increases monotonically with tau 0 for tau 0 well below the average recurrence time is smaller than while for is greater than also the mean residual time until the next earthquake does not depend only on the elapsed time but also strongly on tau 0 the larger tau 0 is the larger is the mean residual time the above features should be taken into account in any earthquake prognosis language en

geometric fluid approximation for general continuous time markov chains fluid approximations have seen great success in approximating the macro scale behaviour of markov systems with a large number of discrete states however these methods rely on the continuous time markov chain ctmc having a particular population structure which suggests a natural continuous state space endowed with a dynamics for the approximating process we construct here a general method based on spectral analysis of the transition matrix of the ctmc without the need for a population structure specifically we use the popular manifold learning method of diffusion maps to analyse the transition matrix as the operator of a hidden continuous process an embedding of states in a continuous space is recovered and the space is endowed with a drift vector field inferred via gaussian process regression in this manner we construct an ordinary differential equation whose solution approximates the evolution of the ctmc mean mapped onto the continuous space known as the fluid limit

height and gradient from shading the method described here for recovering the shape of a surface from a shaded image can deal with complex wrinkled surfaces integrability can be enforced easily because both surface height and gradient are represented the robustness of the method stems in part from linearization of the reflectance map about the current estimate of the surface orientation at each picture cell the new scheme can find an exact solution of a given shape from shading problem even though a regularizing term is included this is a reflection of the fact that shape from shading problems are it not ill posed when boundary conditions are available or when the image contains singular points

self similar branching of aftershock sequences abstract in this paper we propose a branching aftershock sequence bass model for seismicity we suggest that the bass model is a preferred alternative to the widely studied epidemic type aftershock sequence etas model in the bass model an initial or seed earthquake is specified the subsequent earthquakes are obtained from the statistical distributions of magnitude time and location the magnitude scaling is based on a combination of the gutenberg richter scaling relation and the modified bath s law for the scaling relation of aftershocks relative to the magnitude of the seed earthquake omori s law specifies the distribution of earthquake times and a modified form of omori s law specifies the distribution of earthquake locations since the bass model is specified by the four scaling relations it is fully self similar this is not the case for etas we also give a deterministic version of bass and show that it satisfies tokunaga side branching statistics in a similar way to diffusion limited aggregation dla

dynamics of book sales endogenous versus exogenous shocks in complex networks we present an extensive study of the foreshock and aftershock signatures accompanying peaks of book sales the time series of book sales are derived from the ranking system of amazon com we present two independent ways of classifying peaks one based on the acceleration pattern of sales and the other based on the exponent of the relaxation they are found to be consistent and reveal the coexistence of two types of sales peaks exogenous peaks occur abruptly and are followed by a power law relaxation while endogenous sale peaks occur after a progressively accelerating power law growth followed by an approximately symmetrical power law relaxation which is slower than for exogenous peaks we develop a simple epidemic model of buyers connected within a network of acquaintances which propagates rumors and opinions on books the comparison between the predictions of the model and the empirical data confirms the validity of the model and suggests in addition that social networks have evolved to converge very close to criticality here in the sense of critical branching processes of opinion spreading we test in detail the evidence for a power law distribution of book sales and confirm a previous indirect study suggesting that the fraction of books density distribution p s of sales s is a power law p s ensuremath sim 1 s 1 ensuremath mu with ensuremath mu ensuremath approx 2

probabilistic approximations of odes based bio pathway dynamics bio chemical networks are often modeled as systems of ordinary differential equations odes such systems will not admit closed form solutions and hence numerical simulations will have to be used to perform analyses however the number of simulations required to carry out tasks such as parameter estimation can become very large to get around this we propose a discrete probabilistic approximation of the odes dynamics we do so by discretizing the value and the time domain and assuming a distribution of initial states w r t the discretization then we sample a representative set of initial states according to the assumed initial distribution and generate a corresponding set of trajectories through numerical simulations finally using the structure of the signaling pathway we encode these trajectories compactly as a dynamic bayesian network this approximation of the signaling pathway dynamics has several advantages first the discretized nature of the approximation helps to bridge the gap between the accuracy of the results obtained by ode simulation and the limited precision of experimental data used for model construction and verification second and more importantly many interesting pathway properties can be analyzed efficiently through standard bayesian inference techniques instead of resorting to a large number of ode simulations we have tested our method on ode models of the egf ngf signaling pathway 1 and the segmentation clock pathway 2 the results are very promising in terms of accuracy and efficiency

distribution of first return times in correlated stationary signals we present an analytical expression for the first return time frt probability density function of a stationary correlated signal precisely we start by considering a stationary discrete time ornstein uhlenbeck ou process with exponential decaying correlation function the first return time distribution for this process is derived by adopting a well known formalism typically used in the study of the frt statistics for nonstationary diffusive processes then by a subordination approach we treat the case of a stationary process with power law tail correlation function and diverging correlation time we numerically test our findings obtaining in both cases a good agreement with the analytical results we notice that neither in the standard ou nor in the subordinated case a simple form of waiting time statistics like stretched exponential or similar can be obtained while it is apparent that long time transient may shadow the final asymptotic behavior

a poissonian explanation for heavy tails in e mail communication abstract patterns of deliberate human activity and behavior are of utmost importance in areas as diverse as disease spread resource allocation and emergency response because of its widespread availability and use e mail correspondence provides an attractive proxy for studying human activity recently it was reported that the probability density for the inter event time between consecutively sent e mails decays asymptotically as with 1 the slower than exponential decay of the inter event time distribution suggests that deliberate human activity is inherently non poissonian here we demonstrate that the approximate power law scaling of the inter event time distribution is a consequence of circadian and weekly cycles of human activity we propose a cascading nonhomogeneous poisson process that explicitly integrates these periodic patterns in activity with an individual s tendency to continue participating in an activity using standard statistical techniques we show that our model is consistent with the empirical data our findings may also provide insight into the origins of heavy tailed distributions in other complex systems complex systems human activity hypothesis testing point process

predictability of the coherent noise model and its applications we study the threshold distribution function of the coherent noise model for the case of infinite number of agents this function is piecewise constant with a finite number of steps n the latter exhibits a 1 f behavior as a function of the order of occurrence of an avalanche and hence versus natural time an analytic expression of the expectation value mathcal e s for the size s of the next avalanche is obtained and used for the prediction of the next avalanche apart from mathcal e s the number of steps n can also serve for this purpose this enables the construction of a similar prediction scheme which can be applied to real earthquake aftershock data

reversed processes product forms and a non product form the equilibrium joint state probabilities of interacting markov processes are obtained in a hierarchical way by finding the reversed process of the interaction in terms of the reversed processes of its components from a reversed process a product form solution for the joint state probabilities follows directly the method uses a markovian process algebra formalism and generalises the recent reversed compound agent theorem rcat to solve a diverse class of concurrent systems this class includes processes with shared exclusive resources a customer oriented specification of a last come first served lcfs queue with coxian service times and an extended ps queue with a non product form solution from these results a new very short proof of the bcmp theorem ensues the principal advantage of the methodology is its potential for mechanisation and symbolic implementation indeed many non standard product forms have emerged directly from the compositional approach

universal local versus unified global scaling laws in the statistics of seismicity the unified scaling law for earthquakes proposed by bak christensen danon and scanlon is shown to hold worldwide as well as for areas as diverse as japan new zealand spain or new madrid the scaling functions that account for the rescaled recurrence time probability densities show a power law behavior for long times with a universal exponent about minus 2 2 another decreasing power law governs short times but with an exponent that may change from one area to another this is in contrast with a local time homogenized version of bak et al s procedure which seems to present a universal scaling behavior

return interval distribution of extreme events and long term memory the distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines it is well known that many physical processes in nature and society display long range correlations hence in the last few years considerable research effort has been directed towards studying the distribution of return intervals for long range correlated time series based on numerical simulations it was shown that the return interval distributions are of stretched exponential type in this paper we obtain an analytical expression for the distribution of return intervals in long range correlated time series which holds good when the average return intervals are large we show that the distribution is actually a product of power law and a stretched exponential form we also discuss the regimes of validity and perform detailed studies on how the return interval distribution depends on the threshold used to define extreme events

missing data in aftershock sequences explaining the deviations from scaling laws in this paper we extend the branching aftershock sequence model to study the role of missing data at short times and small amplitudes after a mainshock we apply this model which contains three parameters characterizing the missing data to the magnitude and temporal statistics of four aftershock sequences in california we find that the observed time dependent deviations of the frequency magnitude scaling from the gutenberg richter power law dependency can be described quantitatively by the model we also show that for the same set of parameters the model is able to explain quantitatively the observed magnitude dependent deviations of the temporal decay of aftershocks from omori s law in addition we show that the same sets of data can also reproduce quite well the various functional forms of the probability density functions of the return times between consecutive events with magnitudes above a prescribed threshold as well as the violation of scaling at short and intermediate time scales

multifractal random walk we introduce a class of multifractal processes referred to as multifractal random walks mrws to our knowledge it is the first multifractal process with continuous dilation invariance properties and stationary increments mrws are very attractive alternative processes to classical cascadelike multifractal models since they do not involve any particular scale ratio the mrws are indexed by four parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments we briefly explain how in the same way one can build stationary multifractal processes or positive random measures

universality of market superstatistics we use a key concept of the continuous time random walk formalism i e continuous and fluctuating interevent times in which mutual dependence is taken into account to model market fluctuation data when traders experience excessive or superthreshold losses or excessive or superthreshold profits we analytically derive a class of superstatistics that accurately model empirical market activity data supplied by bogachev ludescher tsallis and bunde that exhibit transition thresholds we measure the interevent times between excessive losses and excessive profits and use the mean interevent discrete or step time as a control variable to derive a universal description of empirical data collapse our dominant superstatistic value is a power law corrected by the lower incomplete gamma function which asymptotically tends toward robustness but initially gives an exponential we find that the scaling shape exponent that drives our superstatistics subordinates itself and a superscaling configuration emerges thanks to the weibull copula function our approach reproduces the empirically proven dependence between successive interevent times we also use the approach to calculate a dynamic risk function and hence the dynamic var which is significant in financial risk analysis our results indicate that there is a functional but not literal balance between excessive profits and excessive losses that can be described using the same body of superstatistics but different calibration values and driving parameters we also extend our original approach to cover empirical seismic activity data e g given by corral the interevent times of which range from minutes to years superpositioned superstatistics is another class of superstatistics that protects power law behavior both for short and long time behaviors these behaviors describe well the collapse of seismic activity data and capture so called volatility clustering phenomena

fractional calculus and continuous time finance ii the waiting time distribution we complement the theory of tick by tick dynamics of financial markets based on a continuous time random walk ctrw model recently proposed by scalas et al 4 and we point out its consistency with the behaviour observed in the waiting time distribution for bund future prices traded at liffe london

impact of interactions on human dynamics abstract queueing theory has been recently proposed as a framework to model the heavy tailed statistics of human activity patterns the main predictions are the existence of a power law distribution for the interevent time of human actions and two decay exponents 1 and 3 2 current models lack however a key aspect of human dynamics i e several tasks require or are determined by interactions between individuals here we introduce a minimal queueing model of human dynamics that already takes into account human human interactions to achieve large scale simulations we obtain a coarse grained version of the model allowing us to reach large interevent times and reliable scaling exponents estimations using this we show that the interevent distribution of interacting tasks exhibit the scaling exponents 2 3 2 and a series of numerable values between 3 2 and 1 this work demonstrates that within the context of queueing models of human dynamics interactions change the exponent of the power law distributed interevent times beyond the study of human dynamics these results are relevant to systems where the event of interest consists of the simultaneous occurrence of two or more events

memory effects in the statistics of interoccurrence times between large returns in financial records we study the statistics of the interoccurrence times between events above some threshold q in two kinds of multifractal data sets multiplicative random cascades and multifractal random walks with vanishing linear correlations we show that in both data sets the relevant quantities probability density functions and the autocorrelation function of the interoccurrence times as well as the conditional return period are governed by power laws with exponents that depend explicitly on the considered threshold by studying a large number of representative financial records market indices stock prices exchange rates and commodities we show explicitly that the interoccurrence times between large daily returns follow the same behavior in a nearly quantitative manner we conclude that this kind of behavior is a general consequence of the nonlinear memory inherent in the multifractal data sets

q exponential relaxation of the expected avalanche size in the coherent noise model abstract recently sarlis and christopoulos 2012 the threshold distribution function p t h r e s k x of the coherent noise model for infinite number of agents after the k th avalanche has been studied as a function of k and hence natural time an analytic expression of the expectation value e s k 1 for the size s k 1 of the next avalanche has been obtained in the case that the coherent stresses are exponentially distributed with an average value here by using a statistical ensemble of initially identical systems we investigate the relaxation of the average e s k 1 versus k for k values smaller than k max f the numerical results indicate that e s k 1 collapses to the q exponential tsallis 1988 as a function of k for larger k values the ensemble average can be effectively described by the time average threshold distribution function obtained by newman and sneppen 1996 an estimate k 0 f k max f of this transition is provided this ensemble of coherent noise models may be considered as a simple prototype following q exponential relaxation the resulting q values are compatible with those reported in the literature for the coherent noise model