a practical guide to heavy tails statistical techniques and applications part 1 applications heavy tailed probability distributions in the world wide web m e crovella et al self similarity and heavy tails structural modelling of network traffic w willinger et al heavy tails in high frequency financial data u a muller et al stable paretian modelling in finance some empirical and theoretical aspects s mittnik et al risk management and quantile estimation f bassi et al part 2 time series analyzing stable time series r j adler et al inference for linear processes with stable noise m calder r a davis on estimating the intensity of long range dependence in finite and infinite variance time series m s taqqu v teverovsky why non linearities can ruin the heavy tailed modeller s day s i resnick periodogram estimates from heavy tailed data t mikosch bayesian inference for time series with infinite variance stable innovations n ravishanker z qiou part 3 heavy tail estimation hill bootstrap and jackknife estimators for heavy tails o v pictet et al characteristic function based estimation of stable distribution parameters s m kogan d b williams part 4 regression bootstrapping signs and permutations for regression with heavy tailed errors a robust resampling r lepage et al linear regression with stable disturbances j h mcculloch part 5 signal processing deviation from normality in statistical signal processing parameter estimation with alpha stable distributions p tsakalides c l nikias statistical modelling and receiver design for multi user communication networks g a tsihrintzis part 6 model structures subexponential distributions c m goldie c kluppelberg structure of stationary stable processes j rosinski tail behaviour of some shot noise processes g samorodnitsky part 7 numerical procedures numerical approximation of the symmetric stable distribution and density j h mcculloch table of the maximally skewed stable distributions j h mcculloch d b panton multivariate stable distributions approximation estimation simulation and identification j p nolan univariate stable distributions parametrizations and software j p nolan

analysis and design of impulsive control systems some sufficient conditions for asymptotic stability of impulsive control systems with impulses at fixed times have recently been presented in this paper we derive some less conservative conditions for asymptotic stability of such impulsive control systems and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also extended

power law statistics and universal scaling in the absence of criticality critical states are sometimes identified experimentally through power law statistics or universal scaling functions we show here that such features naturally emerge from networks in self sustained irregular regimes away from criticality in these regimes statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics we thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates and found the same power law statistics indicating that these are not sufficient to establish criticality we rather suggest that these are universal features of large scale networks when considered macroscopically these results put caution on the interpretation of scaling laws found in nature

impulsive control in this paper the concept and principles of impulsive control are presented impulsive control can be applied to a class of systems whose state variables are changeable in a very short time period in particular the asymptotic stability of the impulsive control of a nonlinear system is given

impulsive control of lurie systems in this paper the impulsive control scheme of lurie systems is represented using lyapunov s direct method and comparison technique we present novel conditions under which impulsively controlled lurie systems are asymptotically stable and give the estimate of the upper bound of impulse interval in particular globally exponential stability of impulsive control of lurie systems is presented impulsive controller design with examples is provided to show the feasibility and effectiveness of our method finally

radial structure of the internet the structure of the internet at the autonomous system as level has been studied by the physics mathematics and computer science communities we extend this work to include features of the core and the periphery taking a radial perspective on as network structure new methods for plotting as data are described and they are used to analyse datasets that have been extended to contain edges missing from earlier collections the average distance from one vertex to the rest of the network is used as the baseline metric for investigating radial structure common vertex specific quantities are plotted against this metric to reveal distinctive characteristics of central and peripheral vertices two datasets are analysed

two dimensional elliptic grid solver using boundary grid control and curvature correction the thompson method of explicitly evaluating control function of the elliptic grid solver is employed to improve local grid quality around convex and concave boundaries the curvature correction is principally added to the grid lines around a boundary and is quickly attenuated as the grid points move inward the algebraic advancing front method is employed to estimate two levels of orthogonal grids for evaluating the control functions at the boundary if the grid equation based on the cauchy riemann relation with and as independent variables is employed numerical examinations show that a lengthy trial and error procedure is required to get a satisfactory grid distribution in contrast the method based on the cauchy riemann relation with x and y as independent variables which benefits from the maximum principle not only removes the undesired grid clustering and diluting easily but also effectively improves overall grid smoothness and slightly enhances boundary grid orthogonality

universality of accelerating change abstract on large time scales the progress of human technology follows an exponential growth trend that is termed accelerating change the exponential growth trend is commonly considered to be the amalgamated effect of consecutive technology revolutions where the progress carried in by each technology revolution follows an s curve and where the aging of each technology revolution drives humanity to push for the next technology revolution thus as a collective mankind is the intelligent designer of accelerating change in this paper we establish that the exponential growth trend and only this trend emerges universally on large time scales from systems that combine together two elements randomness and amalgamation hence the universal generation of accelerating change can be attained by systems with no intelligent designer

stability analysis and design of impulsive control systems with time delay a class of impulsive control systems with time varying delays is considered by establishing an impulsive delay differential inequality we analyze the global exponential stability of the impulsive delay systems and estimate the exponential convergence rate on the basis of the analysis a design procedure of impulsive controller is presented the designed impulsive controller not only can globally exponentially stabilize the time delay systems but also can control the exponential convergence rate of the systems two numerical examples are given to illustrate the effectiveness of the method

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

a new look at q exponential distributions via excess statistics q exponential distributions play an important role in nonextensive statistics they appear as the canonical distributions i e the maximum generalized q entropy distributions under mean constraint their relevance is also independently justified by their appearance in the theory of superstatistics introduced by beck and cohen in this paper we provide a third and independent rationale for these distributions we indicate that q exponentials are stable by a statistical normalization operation and that pickands extreme values theorem plays the role of a clt like theorem in this context this suggests that q exponentials can arise in many contexts if the system at hand or the measurement device introduces some threshold moreover we give an asymptotic connection between excess distributions and maximum q entropy we also highlight the role of generalized pareto distributions in many applications and present several methods for the practical estimation of q exponential parameters

impulsive control of a nuclear spin generator in this paper several new theorems on the stability of impulsive control systems are presented these theorems are then used to find the conditions under which the nuclear spin generator can be asymptotically controlled to the equilibrium point by using impulsive control given the parameters of the nuclear spin generator and the impulsive control law we also present a theory of impulsive synchronization of two nuclear spin generators moreover a larger upper bound of impulsive intervals for the stabilization and synchronization can be obtained

a novel hyperbolic grid generation procedure with inherent adaptive dissipation abstract this paper reports a novel hyperbolic grid generation with an inherent adaptive dissipation hgad which is capable of inn proving the oscillation and overlapping of grid lines in the present work upwinding differencing is applied to discretize the hyperbolic system and thereby to develop the adaptive dissipation coefficient complex configurations with the features of geometric discontinuity exceptional concavity and convexity are used as the test cases for comparison of the present hgad procedure with the conventional hyperbolic and elliptic ones the results reveal that the hgad method is superior in orthogonality and smoothness of the grid system in addition the computational efficiency of the flow solver may be improved by using the present hgad procedure

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

the effects of pulse vaccination on seir model with two time delays abstract in this paper impulsive vaccination has been applied to control the spread and transmission of an infectious disease an seir epidemic model with two time delays and pulse vaccination is formulated the exact infection free periodic solution of the impulsive epidemic system is obtained moreover we show that if the vaccination rate is larger than the infectious population disappear so the disease dies out while if the vaccination rate is less than the infectious population persist our results indicate that a large vaccination rate or a short period of pulsing or a long latent period of the disease is a sufficient condition for the eradication of the disease

moore s clock abstract considering a stochastic clock a chronograph that ticks randomly according to an underpinning ticking rate we address the durations between its successive ticking epochs and ask when are the inter ticking durations independent of each other we establish that this question has two answers equilibrium and non equilibrium the equilibrium answer is termed benchmark clock it is characterized by a constant ticking rate and it corresponds to the time flow of a steady state universe model the non equilibrium answer is termed moore s clock it is characterized by an exponential ticking rate and it corresponds to the time flow of a big bang universe model in the context of stochastic clocks moore s clock is the manifestation of moore s law of accelerating change this paper explores the rich statistical structure of moore s clock and pinpoints the dramatic differences between the stationary benchmark clock and the non stationary moore s clock

optimal control of a co rotating vortex pair averaging and impulsive control abstract the problem of controlling the position of a pair of point vortices using a strain field or a field of a single source sink is considered the problem dimension is reduced by averaging over the fast rotation of vortices around the center of vorticity control is assumed to be function of rotation phase only for the case of the strain field actuation optimal control problem is posed in three different settings control input whose integral over a cycle of vortex rotation is bounded bounded control input and mixed problem where both integral over a cycle and control magnitude are bounded it is shown that optimal solutions in integral setting are impulsive they consist of dirac delta functions applied at optimal phases during the cycle of vortex rotation if a bound on the control magnitude is added to the constraints the mixed problem a solution is obtained for which control is at the maximum amplitude except possibly for intervals during which it is zero these results are obtained by direct optimization for the case of a source sink field we pose the optimal control problem of the averaged equations through the use of the pontryagin maximum principle an obtained solution is a set of dirac delta pulses at optimal phases of the vortex rotation cycle a discussion of these results in the context of vortex merger control is given impulsive control arises here naturally as an optimal control design once averaging method is used

robust stability of impulsive takagi sugeno fuzzy systems with parametric uncertainties this paper presents a kind of time varying impulsive takagi sugeno t s fuzzy model with parametric uncertainties in which each subsystem of the model is time varying several robust stabilities of time varying systems with parametric uncertainties such as general robust stability robustly asymptotical stability and exponential stability are studied using uniformly positive definite matrix functions and the lyapunov method specifically robust stability conditions of time invariant impulsive t s fuzzy systems are also derived in the formulation of quasi linear matrix inequalities qlmis and an iterative lmis algorithm is designed for solving qlmis finally a unified chaotic system with continuous periodic switch and a unified time invariant chaotic system are used for demonstrating the effectiveness of our respective results

finite element approximations of impulsive optimal control problems for heat equations abstract in this paper we study the priori error analysis for semidiscrete galerkin finite element approximation of the impulsive optimal control problem governed by linear heat equation with control constraint we first derive pontryagin s maximum principle and construct the semidiscrete finite element approximation scheme for our impulsive optimal control problem then the error estimates for optimal control u the related state y and the adjoint state will be obtained finally an efficient algorithm for our numerical experiment is designed which verifies the theoretical results obtained in this paper

on some simple estimates of an exponent of regular variation summary we present a class of simple estimates of an exponent of regular variation unlike those proposed recently by de haan and resnick 1980 ours converge at an algebraic rather than a logarithmic rate and unlike those considered by teugels 1980 their form does not depend on the unknown exponent

non linear impulsive dynamical systems part i stability and dissipativity in this paper we develop lyapunov and invariant set stability theorems for non linear impulsive dynamical systems furthermore we generalize dissipativity theory to non linear dynamical systems with impulsive effects specifically the classical concepts of system storage functions and supply rates are extended to impulsive dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy dissipated energy over the continuous time system dynamics and dissipated energy over the resetting instants furthermore extended kalman yakubovich popov conditions in terms of the impulsive system dynamics characterizing dissipativeness via system storage functions are derived finally the framework is specialized to passive and non expansive impulsive systems to provide a generalization of the classical notions of passivity and non expansivity for non linear impulsive systems these results are used in the second part of this paper to develop extensions of the small gain and p

less conservative conditions for asymptotic stability of impulsive control systems this note studies the stability of impulsive control systems a new comparison theorem for asymptotic stability of impulsive differential system is presented based on the new result we derive some less conservative conditions for asymptotic stability of impulsive control systems with impulses at fixed times and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also enlarged

on the fractal characterization of paretian poisson processes abstract paretian poisson processes are poisson processes which are defined on the positive half line have maximal points and are quantified by power law intensities paretian poisson processes are elemental in statistical physics and are the bedrock of a host of power law statistics ranging from pareto s law to anomalous diffusion in this paper we establish evenness based fractal characterizations of paretian poisson processes considering an array of socioeconomic evenness based measures of statistical heterogeneity we show that amongst the realm of poisson processes which are defined on the positive half line and have maximal points paretian poisson processes are the unique class of fractal processes exhibiting scale invariance the results established in this paper are diametric to previous results asserting that the scale invariance of poisson processes with respect to physical randomness based measures of statistical heterogeneity is characterized by exponential poissonian intensities

indirect adaptive type 2 fuzzy impulsive control of nonlinear systems in this paper a novel indirect adaptive interval type 2 fuzzy tracking control is proposed strategy with impulsive and lyapunov synthesis approach it handles the training data corrupted by noise or rule uncertainties for linear and nonlinear systems involving external disturbances in comparison with conventional methods the advocated approach guarantees closed loop stability the output tracking error of the overall system will converge to zero asymptotically by the generalized barbalat s lemma numerical simulations are given to illustrate the effectiveness of the proposed techniques

understanding the determinants of volatility clustering in terms of stationary markovian processes abstract volatility is a key variable in the modeling of financial markets the most striking feature of volatility is that it is a long range correlated stochastic variable i e its autocorrelation function decays like a power law for large time lags in the present work we investigate the determinants of such feature starting from the empirical observation that the exponent of a certain stock s volatility is a linear function of the average correlation of such stock s volatility with all other volatilities we propose a simple approach consisting in diagonalizing the cross correlation matrix of volatilities and investigating whether or not the diagonalized volatilities still keep some of the original volatility stylized facts as a result the diagonalized volatilities result to share with the original volatilities either the power law decay of the probability density function and the power law decay of the autocorrelation function this would indicate that volatility clustering is already present in the diagonalized un correlated volatilities we therefore present a parsimonious univariate model based on a non linear langevin equation that well reproduces these two stylized facts of volatility the model helps us in understanding that the main source of volatility clustering once volatilities have been diagonalized is that the economic forces driving volatility can be modeled in terms of a smoluchowski potential with logarithmic tails

modeling statistics and kinetics of the natural aggregation structures and processes with the solution of generalized logistic equation abstract the generalized logistic equation is proposed to model kinetics and statistics of natural processes such as earthquakes forest fires floods landslides and many others this equation has the form d n a d a s 1 n a n a q a q 0 and a 0 is the size of an element of a structure and 0 the equation contains two exponents and q taking into account two important properties of elements of a system their fractal geometry and their ability to interact either to enhance or to damp the process of aggregation the function n a can be understood as an approximation to the number of elements the size of which is less than a the function d n a d a where n a is the general solution of this equation for q 1 is a product of an increasing bounded function and power law function with stretched exponential cut off the relation with tsallis non extensive statistics is demonstrated by solving the generalized logistic equation for q 0 in the case 0 q 1 the equation models super additive and the case q 1 it models sub additive structures the gutenberg richter g r formula results from interpretation of empirical data as a straight line in the area of stretched exponent with small the solution is applied for modeling distribution of foreshocks and aftershocks in the regions of napa valley 2014 and sumatra 2004 earthquakes fitting the observed data well both qualitatively and quantitatively

fully exponential laplace approximations to expectations and variances of nonpositive functions abstract tierney and kadane 1986 presented a simple second order approximation for posterior expectations of positive functions they used laplace s method for asymptotic evaluation of integrals in which the integrand is written as f exp nh and the function h is approximated by a quadratic the form in which they applied laplace s method however was fully exponential the integrand was written instead as exp nh log f this allowed first order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second order expansion for the ratio other second order expansions hartigan 1965 johnson 1970 lindley 1961 1980 mosteller and wallace 1964 require computation of more derivatives of the log likelihood function in this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions to obtain a second order approximation to an expectation e g we use the fully exponential method to approximate

noniterative parabolic grid generation for parabolized equations generation de grilles curvilignes generalisees tridimensionnelles pour des corps cartesien cylindriques et spheriques a l aide d equations aux derivees partielles paraboliques les equations de grilles parabolisees sont resolues de maniere non iterative en avancant dans deux directions

frequency of frequencies distributions and size dependent exchangeable random partitions abstractmotivated by the fundamental problem of modeling the frequency of frequencies fof distribution this paper introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random count and its exchangeable random partitions a cluster structure naturally arising from a completely random measure mixed poisson process allows the probability distribution of the random partitions of a subset of a population to be dependent on the population size a distinct and motivated feature that makes it more flexible than a partition structure this allows it to model an entire fof distribution whose structural properties change as the population size varies a fof vector can be simulated by drawing an infinite number of poisson random variables or by a stick breaking construction with a finite random number of steps a generalized negative binomial process model is proposed to generate a cluster structure where in the prior the number of clusters is f

graph completions for impulsive feedback controls abstract the paper considers impulsive control systems where the evolution equation depends linearly on the time derivatives of the control function the basic theory of graph completions is here extended to control functions in feedback form in the case where the control u u t x is piecewise smooth with a jump along a hypersurface in the t x space results are proved on the existence and uniqueness of solutions and on their approximation by means of smooth feedbacks the paper is concluded with a couple of examples concerning the feedback control of mechanical systems by means of active constraints

hyperbolic equation method of grid generation for enclosed regions in a recent study the authors combined the grid front marching method and the parabolic equation method in this study a similar idea is applied to extend the cordeva and barth hyperbolic equation method to enclosed regions

enhancements of a three dimensional hyperbolic grid generation scheme a hyperbolic grid generation scheme formulated from grid orthogonality and cell volume specification has been significantly enhanced so that high quality three dimensional grids can be obtained for a wide variety of geometries while the speed of the scheme remains one to two orders of magnitude faster than typical elliptic grid generation methods the robustness of the scheme has been greatly improved over previous applications of the three dimensional hyperbolic grid generation procedure enhancements included the use of spatially variable smoothing coefficient metric correction procedures local treatment of severe convex corners and new extrapolation treatments of floating and axis boundaries the versatility of the new hyperbolic grid generation scheme is demonstrated by three dimensional grids generated for external components of the integrated space shuttle vehicle and the sofia telescope

marching grid generation using parabolic partial differential equations abstract the unique aspect of grid generation in computational fluid dynamics is that the grid generation equations have no physical meanings so any equation may be used for this purpose if the grids generated are useful this aspect provides a vast freedom in developing new methods of grid generation this paper explores feasibility of using parabolic partial differential equations for grid generation the advantages of using parabolic partial differential equations are as follows 1 parabolic equations are initial value problems so grids are generated by a marching algorithm like the hyperbolic grid generation method 2 the parabolic partial differential equations have most properties of the elliptic equations particularly the diffusion effect which smooths out any singularity of the inner boundary condition if any and 3 the prescribed outer boundary conditions may be satisfied the importance of the marching algorithm stated above is twofold first computational time required is only a very small fraction of that for the elliptic grid generation equations second the fast memory space required during grid generation can be substantially reduced from that required by the elliptic grid generation method the authors consider the grid generation for a two dimensional airfoil flow calculations for simplicity of discussions although the method described in this paper is not restricted to two dimensions or airfoil problems

growing networks of overlapping communities with internal structure we introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks the model comprises two complementary mechanisms one mechanism accounts for the evolution of the internal link structure of a single community and the second mechanism coordinates the growth of multiple overlapping communities the first mechanism is based on the assumption that each node establishes links with its neighbors and introduces new nodes to the community at different rates we demonstrate that this simple mechanism gives rise to an effective maximal degree within communities this observation is related to the anthropological theory known as dunbar s number i e the empirical observation of a maximal number of ties which an average individual can sustain within its social groups the second mechanism is based on a recently proposed generalization of preferential attachment to community structure appropriately called structural preferential attachment spa the combination of these two mechanisms into a single model spa allows us to reproduce a number of the global statistics of real networks the distribution of community sizes of node memberships and of degrees the spa model also predicts a three qualitative regimes for the degree distribution within overlapping communities and b strong correlations between the number of communities to which a node belongs and its number of connections within each community we present empirical evidence that support our findings in real complex networks

on the bias of traceroute sampling or power law degree distributions in regular graphs understanding the graph structure of the internet is a crucial step for building accurate network models and designing efficient algorithms for internet applications yet obtaining this graph structure can be a surprisingly difficult task as edges cannot be explicitly queried for instance empirical studies of the network of internet protocol ip addresses typically rely on indirect methods like traceroute to build what are approximately single source all destinations shortest path trees these trees only sample a fraction of the network s edges and a paper by lakhina et al 2003 found empirically that the resulting sample is intrinsically biased further in simulations they observed that the degree distribution under traceroute sampling exhibits a power law even when the underlying degree distribution is poisson in this article we study the bias of traceroute sampling mathematically and for a very general class of underlying degree distributions explicitly calculate the distribution that will be observed as example applications of our machinery we prove that traceroute sampling finds power law degree distributions in both regular and poisson distributed random graphs thus our work puts the observations of lakhina et al on a rigorous footing and extends them to nearly arbitrary degree distributions

a new approach to practical stability of impulsive functional differential equations in terms of two measures in this work we consider a new approach to the practical stability theory of impulsive functional differential equations with lyapunov functionals and razumikhin technique we use a new technique in the division of lyapunov functions given by shunian zhang and obtain conditions sufficient for the uniform practical asymptotical stability of impulsive delay differential equations an example is also discussed to illustrate the advantage of the proposed results

p moment stability of stochastic differential equations with impulsive jump and markovian switching this paper introduces some new concepts of p moment stability for stochastic differential equations with impulsive jump and markovian switching some stability criteria of p moment stability for stochastic differential equations with impulsive jump and markovian switching are obtained by using liapunov function method an example is also discussed to illustrate the efficiency of the obtained results

power law distribution of degree degree distance a better representation of the scale free property of complex networks whether real world complex networks are scale free or not has long been controversial recently in broido and clauset a d broido a clauset nat commun 10 1017 2019 it was claimed that the degree distributions of real world networks are rarely power law under statistical tests here we attempt to address this issue by defining a fundamental property possessed by each link the degree degree distance the distribution of which also shows signs of being power law by our empirical study surprisingly although full range statistical tests show that degree distributions are not often power law in real world networks we find that in more than half of the cases the degree degree distance distributions can still be described by power laws to explain these findings we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted two way selection process the model does not always produce solid power law distributions but predicts that the degree degree distance distribution exhibits stronger power law behavior than the degree distribution of a finite size network especially when the network is dense we test the strength of our model and its predictive power by examining how real world networks evolve into an overly dense stage and how the corresponding distributions change we propose that being scale free is a property of a complex network that should be determined by its underlying mechanism e g preferential attachment rather than by apparent distribution statistics of finite size we thus conclude that the degree degree distance distribution better represents the scale free property of a complex network

impulsive differential equations this paper deals with the periodic solutions problem for impulsive differential equations by using lyapunov s second method and the contraction mapping principle some conditions ensuring the existence and global attractiveness of unique periodic solutions are derived which are given from impulsive control and impulsive perturbation points of view as an application the existence and global attractiveness of unique periodic solutions for hopfield neural networks are discussed finally two numerical examples are provided to demonstrate the effectiveness of the proposed results

dynamical generalized hurst exponent as a tool to monitor unstable periods in financial time series we investigate the use of the hurst exponent dynamically computed over a weighted moving time window to evaluate the level of stability instability of financial firms financial firms bailed out as a consequence of the 2007 2008 credit crisis show a neat increase with time of the generalized hurst exponent in the period preceding the unfolding of the crisis conversely firms belonging to other market sectors which suffered the least throughout the crisis show opposite behaviors we find that the multifractality of the bailed out firms increase at the crisis suggesting that the multi fractal properties of the time series are changing these findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm in this paper we introduce a method to compute the generalized hurst exponent which assigns larger weights to more recent events with respect to older ones in this way large fluctuations in the remote past are less likely to influence the recent past we also investigate the scaling associated with the tails of the log returns distributions and compare this scaling with the scaling associated with the hurst exponent observing that the processes underlying the price dynamics of these firms are truly multi scaling

estimating heavy tail exponents through max self similarity in this paper a novel approach to the problem of estimating the heavy tail exponent 0 of a distribution is proposed it is based on the fact that block maxima of size m scale at a rate m1 for independent as well as for a number of dependent data this scaling rate can be captured well by the max spectrum plot of the data that leads to regression based estimators for consistency and asymptotic normality of these estimators is established for independent data under mild conditions on the behavior of the tail of the distribution the proposed estimators have an important computational advantage over existing methods namely they can be calculated and updated sequentially in an on line fashion without having to store the entire data set practical issues on the automatic selection of tuning parameters for the estimators and corresponding confidence intervals are also addressed extensive numerical simulations show that the proposed method is competitive for both small and large sample sizes robust to contaminants and continues to work under the presence of substantial amount of dependence the proposed estimators are used to illustrate the close connection between long range dependence and heavy tails over an internet traffic trace