statistical mechanical analogies for space dependent epidemics abstract a statistical mechanical model for the propagation of a space dependent epidemic is suggested based on the following assumptions 1 the population is made up of three types of individuals susceptibles infectives and recovered the total population size is constant and confined in a given region of d s dimensional euclidean space d s 1 2 3 2 an infected individual has a constant probability of recovery and an immune recovered individual has a constant probability of resensibilization 3 any infected individual from a given neighborhood of a susceptible individual has a probability p r of transmitting the disease which depends on the distance r between the two individuals 4 the individuals migrate from one position to another with a rate depending on the displacement vector between the two positions a statistical mechanical description of the epidemic spreading is given in terms of a set of grand canonical probability densities for the positions and states of the individuals an exact nonlinear evolution equation is derived for these probability densities and a self consistent procedure of solving it is suggested an explicit computation is presented for the case of very fast migration based on the adiabatic elimination of the coordinates of the individuals an eikonal approximation for the fluctuations of the different types of individuals irrespective of their positions is developed in the limit of very large systems with constant total population density resulting in a hamilton jacobi equation for the logarithm of the probability density of the proportions of susceptibles infective and recovered the deterministic equations of the process are identified with the evolution equations for the most probable fluctuation paths if the individuals are confined at discrete positions in space this approach leads to the ordinary differential equation description of cellular automata epidemics presented in the literature a continuous space alternative description is also presented it is shown that the logarithm of the probability density of population fluctuations is a liapunov function for the deterministic evolution equations this liapunov function is used for developing a generalized thermodynamic formalism of the epidemic process similar to the thermodynamic and stochastic theory of ross hunt and hunt from nonequilibrium thermodynamics of transport processes and reaction diffusion systems

stochastic renormalization group approach to random point processes a fractal generalization of poisson statistics a generalization of the shlesinger hughes stochastic renormalization method is suggested for random point processes a decimation procedure is introduced in terms of two parameters the probability that a decimation step takes place and the probability that during a decimation step a random dot is removed from the process at each step a random number of dots are removed by this procedure a chain of point processes is generated the renormalized point process is a superposition of the intermediate processes attached to the different steps for a statistical ensemble the fraction lq of systems for which q decimation steps occur is a power function of the fraction q of points which survive q decimation steps lq q 1 df where df 1 ln ln 1 is a fractal exponent smaller than unity df 1 if the random points are initially independent then a complete analysis is possible in this case explicit expressions for the renormalized janossy densities the joint densities and the generating functional of

industrial replacement communication networks and fractal time statistics abstract three models for the fractal time statistics of renewal processes are suggested the first two models are related to the industrial replacement a model assumes that the state of an industrial aggregate is described by a continuous positive variable x which is a measure of its complexity the failure probability exponentially decreases as the complexity of the aggregate increases a renewal process is constructed by assuming that after the occurrence of a breakdown event the defective aggregate is replaced by a new aggregate whose complexity is a random variable selected from an exponential probability law we show that the probability density of the lifetime of an aggregate has a long tail t t 1 h as t where the fractal exponent h is the ratio between the average complexity of an aggregate which leaves the system and the average complexity of a new aggregate the asymptotic behavior of all moments of the number n of replacement events occurring in a large time interval may be evaluated analytically for 1 h 0 the mean and the dispersion of n behave as n t t h and n 2 t t 2 h as t which outlines the intermittent character of the fluctuations a second model gives a discrete description of industrial replacement the aggregates are assumed to be made up of variable numbers of basic units each basic unit has a probability to be associated in an aggregate and a probability of being in an active state an aggregate can work if at least a basic unit is in active state the mechanism of replacement is the same as in the first model the number of basic units from an aggregate playing the role of a complexity measure the probability density of the lifetime has a long tail modulated by a periodic function in ln t t t 1 h ln t where h ln ln 1 and ln t is a periodic function of ln t with a period ln 1 a third model is related to the transmission errors in communication networks a network is made up of a large number of communication channels each channel has a probability to be open and a probability of transmitting a message the number of open channels is a random variable which is kept constant as far as the transmission is possible if a failure occurs then the number of open channels is changed in a random way we show that this model is approximately isomorphic with the second one the probability density of the time between two succesive errors has also an inverse power tail modulated by a periodic function in ln t the general implications of these models for the physics of fractal time are analysed

a branched chain approach to fractal time abstract a branched chain description of fractal time is suggested within its framework the long time tails are the result of a stochastic renormalization procedure the jumps are grouped into blocks of random size the blocks of blocks etc the size of a block being described by a branching chain process the block formation ends up after a random number of steps according to a scale invariant probability law the general scaled form of a multi state waiting time density function is derived as expected this function has a long tail for large times the shlesinger hughes time scaling physica a 109 1981 597 is recovered as a particular case of our approach the fluctuation analysis outlines an essential feature of the theory due to jump clustering the correlation functions have also long tails however unlike the case of true chain reactions the system has the tendency to smooth the fluctuations

analogies between colored levy noise and random channel approach to disordered kinetics we point out some interesting analogies between colored levy noise and the random channel approach to disordered kinetics these analogies are due to the fact that the probability density of the levy noise source plays a similar role as the probability density of rate coefficients in disordered kinetics although the equations for the two approaches are not identical the analogies can be used for deriving new useful results for both problems the random channel approach makes it possible to generalize the fractional uhlenbeck ornstein processes fuo for space and time dependent colored noise we describe the properties of colored noise in terms of characteristic functionals which are evaluated by using a generalization of huber s approach to complex relaxation phys rev b 31 6070 1985 we start out by investigating the properties of symmetrical white noise and then define the levy colored noise in terms of a langevin equation with a levy white noise source we derive exact analytical expressions for the various characteristic functionals which characterize the noise and a functional fractional fokker planck equation for the probability density functional of the noise at a given moment in time second by making an analogy between the theory of colored noise and the random channel approach to disordered kinetics we derive fractional equations for the evolution of the probability densities of the random rate coefficients in disordered kinetics these equations serve as a basis for developing methods for the evaluation of the statistical properties of the random rate coefficients from experimental data special attention is paid to the analysis of systems for which the observed kinetic curves can be described by linear or nonlinear stretched exponential kinetics

state maps for linear systems modeling of physical systems consists of writing the equations describing a phenomenon and yields as a result a set of differential algebraic equations as such state space models are not a natural starting point for modeling while they have utmost importance in the simulation and control phase the paper addresses the problem of computing state variables for systems of linear differential algebraic equations of various forms the point of view from which the problem is considered is the behavioral one as put forward in j c willems automatica j ifac 22 1986 pp 561 580 dynamics reported 2 1989 pp 171 269 ieee trans automat control 36 1991 pp 259 294

on the rationality of knorr s virtually irreducible lattices abstract it was established by reinhard knorr that the half of brauer s height zero conjecture which assumes an abelian defect group would follow from the nonexistence of certain integral representations of abelian p groups we establish nonexistence of such representations of rank less than 14 for the elementary abelian group of order 8 and believe these to be the first results of this kind the result is made possible by imposing a simple rationality condition

fractals in physics applications and theoretical developments abstract we report about the developments in two subjects in which we have been recently active the first one refers to a reanalysis of the distribution of galaxies and clusters with the methods of modern statistical mechanics contrary to the usual picture of a relatively smooth distribution at large scale we find that fractal and multifractal properties extend up to the observational limits this result should have deep implications also in relation to the recently observed anisotropy of the microwave background radiation the second subject concerns the attempts to develop a theory of fractal growth based on the new concept of the fixed scale transformation we discuss the instructive example of the percolating cluster in which the fst program can be fully implemented we then compare this example with the more complex cases of dla and dbm for which the identification of the scale invariant growth rules is much more complex in this respect the fst points to the key concept that is the scale invariance of screening and noise reduction the state of the art and the main open problems will be critically discussed

a random walk approach to spiral motion the paper deals with random spiral motion described in polar coordinates the trajectory of a particle is described by the distance r from a given point as a function of the angle theta relative to a given direction a stochastic description of the spiral shapes generated by the random variations of r and theta is suggested based on the following assumptions a the ray r is made up of additive contributions corresponding to certain jump processes b the angle phi between two jumps is a random variable selected from a given probability law g phi d phi with finite or infinite moments c the contributions rho 1 rho 2 of the different jumps to the ray r are independent random variables selected from a probability law p rho d rho with finite moments an expression for the generating functional of a random spiral r theta is given in the form of an infinite series which can be used to evaluate the stochastic properties of the ray r the asymptotic properties of the random spiral shapes depend on the function g phi d phi if all moments of the angle between two jumps exist and are finite the average shape is a linear archimedean spiral r theta approximately theta as theta to infinity and the dispersion of the ray increases linearly with the angle delta r2 theta approximately theta as theta to infinity if g phi has a long tail g phi approximately phi 1 h as phi to infinity with 1 h 0 the average shape is a nonlinear fractal archimedean spiral r theta approximately theta h as phi to infinity and the fluctuations of the ray have an intermittent behaviour delta r2 theta approximately theta 2h as phi to infinity a complete analysis is possible in a markovian like case for which the angle between two jumps is exponentially distributed in this case a closed expression tor the generating functional is available and all cumulants of the ray can be computed exactly the mth cumulant which expresses the correlations among the rays at different angles theta 1 theta m is proportional to the minimum angle min theta 1 theta m and the intermittent behaviour is missing an alternative stochastic description is suggested based on the assumption that the number of jumps in a given angle interval is distributed according to an inhomogeneous poisson law this model is also analytically tractable it is less restrictive in the sense that the average shape corresponds to a broader class of spirals including the linear and the fractal archimedean and the logarithmic ones however it cannot be used to describe the intermittent behaviour

on 1 f noise and other distributions with long tails abstract it is shown following shockley shockley w 1957 proc ire 45 279 290 that when a population is engaged in tasks whose completion requires the successful conclusion of many independent subtasks the distribution function for successes in the primary task is log normal it is also shown that when the dispersion of the log normal distribution is large the distribution is mimicked by a 1 x distribution over a wide range of x this argument provides a generic set of processes that yields the much observed 1 x distribution and will also lead to a 1 f noise spectrum it is commonly found that distributions that seem to be log normal over a broad range say to the 95th percentile of a population change to an inverse fractional power pareto distribution for the last few percentile annual income distributions are examples with this structure the very wealthy generally achieve their superwealth through amplification processes that are not available to most we have introduced a simple amplification model to characterize the transition from a log normal distribution to an inverse power pareto tail

fractional oscillator driven by a gaussian noise abstract the time dependent response is studied of a fractional oscillator driven by a gaussian white noise applying the method of characteristic functionals combined with the technique of integral transforms we derive explicit formulas for the variances of position and velocity and the asymptotic power spectrum of the oscillator the effects of the order of fractional derivative on statistical characteristics of the oscillator are analyzed numerically

mass action law versus local contagion dynamics a mean field statistical approach with application to the theory of epidemics a mean field approach for epidemic processes with high migration is suggested by analogy with non equilibrium statistical mechanics for large systems a limit of the thermodynamic type is introduced for which both the total size of the system and the total number of individuals tend to infinity but the population density remains constant in the thermodynamic limit the infection rate is proportional to the product of the proportion of individuals susceptible to infection and the average probability of infection the limit form of the average probability of infection is insensitive to the detailed behaviour of the fluctuations of the number of infectious individuals and may belong to two universality classes 1 if the fluctuation of the number of infectives is non intermittent it increases with the increase of the partial density of infectives and approaches exponentially the asymptotic value one for large densities 2 for intermittent fluctuations obeying a power law scaling the average probability of infection also displays a saturation effect for large densities of infectives but the asymptotic value one is approached according to a power law rather than exponentially for low densities of infectives both expressions for the average probability of infection are linear functions of the proportion of infectives and the infection rate is given by the mass action law

paradigms and puzzles in the theory of dynamical systems a self contained exposition is given of an approach to mathematical models in particular to the theory of dynamical systems the basic ingredients form a triptych with the behavior of a system in the center and behavioral equations with latent variables as side panels the author discusses a variety of representation and parametrization problems in particular questions related to input output and state models the proposed concept of a dynamical system leads to a new view of the notions of controllability and observability and of the interconnection of systems in particular to what constitutes a feedback control law the final issue addressed is that of system identification it is argued that exact system identification leads to the question of computing the most powerful unfalsified model

generating functional approach to space and time dependent colored noise a stochastic model for time and space dependent colored noise is suggested based on the following assumptions 1 the noise field is generated by a random number of point events corresponding to a correlated point process 2 the contributions of the different events to the noise field are additive each contribution being a random function selected from the same probability density functional an analytical treatment of the noise field described by these assumptions is possible the generating functional of the noise field as well as the corresponding cumulants can be computed exactly all cumulants are explicitly evaluated when the contribution of an event is given by a diffusion equation a detailed analysis of the asymptotic behavior is made for time homogeneous and translationally invariant processes a gaussian random field colored in space and time emerges for very frequent independent events of very small intensities provided that the central moments of the contribution of an event to the noise field are finite and fast decreasing in space the correlations among events lead to corrections of the gauss limit law however the cumulants of the random fields are also finite if the central moments of an event are slowly decreasing in space a different type of asymptotic behavior occurs the cumulants of the noise field become infinite and the resulting field is described by a non gaussian stable law of the l evy type the theory may be applied to the study of stochastic gravitational fluctuations in galactic systems to the analysis of concentration fluctuations for diffusion processes in disordered systems and for the analysis of the influence of environmental fluctuations in continuum mechanics and electrodynamics

state representations of arma models a state representation of an arbitrary arma model is computed explicitly it is shown then that every arma model is homotopy equivalent to its state representation and that two state models are homotopy equivalent if and only if they are similar

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

knorr lattices their characters and some subsets of fpd examples of positive height cyclic knorr lattices for elementary abelian p groups are constructed and bounds relating the height of such lattices to the size of the group are given the problem is formulated in terms of finite geometry when p 2 certain examples are shown to arise from difference sets

on the state of behaviors the theme of the present paper is the study of the concept of state and the corresponding state maps in the context of willems behavioral theory we concentrate on markovian system and their representation in terms of first order difference or differential systems we follow by a full analysis of the special case of state systems the embedding of a linear system in a state system via the use of state maps arriving at state representations or equivalently to a realization theory for behaviors minimality is defined and characterized and a state space isomorphism theorem is established realization procedures based on the shift realization are developed as well as a rigorous analysis of the construction of state maps the paper owes much to rapisarda and willems p rapisarda j c willems state maps for linear systems siam j contr optim 35 1997 1053 1091

nonequilibrium fluctuation dissipation relations for independent random rate processes with dynamical disorder a class of rate processes with dynamical disorder is investigated based on the two following assumptions a the system is composed of a random number of particles or quasiparticles which decay according to a first order kinetic law b the rate coefficient of the process is a random function of time with known stochastic properties the formalism of characteristic functionals is used for the direct computation of the dynamical averages the suggested approach is more general than the other approaches used in the literature it is not limited to a particular type of stochastic process and can be applied to any type of random evolution of the rate coefficient we derive an infinity of exact fluctuation dissipation relations which establish connections among the moments of the survival function and the moments of the number of surviving particles the analysis of these fluctuation dissipation relations leads to the unexpected result that in the thermodynamic limit the fluctuations of the number of partic

arma models and their equivalences the classical theory of strict system equivalence of rosenbrock and fuhrmann is presented in a very general setting namely in the setting of arma models defined over an arbitrary commutative ring

maximum entropy formalism fractals scaling phenomena and 1 f noise a tale of tails in this report on examples of distribution functions with long tails we a show that the derivation of distributions with inverse power tails from a maximum entropy formalism would be a consequence only of an unconventional auxilliary condition that involves the specification of the average value of a complicated logarithmic function b review several models that yield log normal distributions c show that log normal distributions may mimic 1 f noise over a certain range and d present an amplification model to show how log normal personal income distributions are transformed into inverse power pareto distributions in the high income range

self similar potentials in random media fractal evolutionary landscapes and kimura s neutral theory of molecular evolution abstract a general method for constructing self similar scalar fractal random fields is suggested based on the assumption that the fields are generated by a broad distribution of punctual sources the method is illustrated by a problem of population biology the evolution on a random fitness landscape a random fitness landscape is constructed based on the following hypotheses the landscape is defined by the dependence of a fitness variable on the state vector x of the individuals x the corresponding hypersurface has a large number of local maxima characterized by a local probability law with variable parameters these maxima are uniformly randomly distributed throughout the state space of the individuals from generation to generation the heights and the shapes of these local maxima can change this change is described in terms of two probabilities p and that an individual modification occurs and that the process of variation as a whole stops respectively a general method for computing the stochastic properties of the evolutionary landscape is suggested based on the use of characteristic functionals an explicit computation of the fourier spectrum of the cumulants of the evolutionary landscape is performed in a limit of the thermodynamic type for which the number of maxima and the volume of the state space of the individuals tend to infinity but the density of maxima remains constant it is shown that although a typical realization of the evolutionary landscape is very rough its average properties expressed by the fourier spectrum of its cumulants are smooth and characterized by scaling laws of the power law type the average landscape which is made up of the frozen contributions of the changes corresponding to different generations is flat a result which is consistent with the kimura s theory of molecular evolution some general implications of the suggested approach for the statistical physics of systems with random ultrametric topology are also investigated

on behavior homomorphisms and system equivalence in this paper we introduce the concept of a behavior homomorphisms and isomorphisms and use it to present a uni ed approach to the study of equivalence of di erent behavior representations concentrating on a special representation we call normalized arma narma representation c 2001 elsevier science b v all rights reserved

duality in g algebras keywords finite group complete discrete valuation ring symmetric g algebra symmetric bilinear form projective ideal symmetric algebra rg lattice unimodular symmetric g algebra almost projective ideal almost split sequences block defect groups virtually irreducible lattices splitting trace lattices reference ctg article 1988 005doi 10 1007 bf01161746 record created on 2008 12 16 modified on 2017 05 12

some cyclic virtually irreducible lattices abstract virtually irreducible lattices which satisfy a simple rationality condition and have positive height are constructed for elementary abelian 2 groups the non existence of such lattices would have implied part of brauer s height zero conjecture a characterization of rank 6 lattices for the elementary abelian group of size 16 is given

on two dimensional fractional brownian motion and fractional brownian random field as a generalization of one dimensional fractional brownian motion 1dfbm we introduce a class of two dimensional self similar strongly correlated random walks whose variance scales with power law we report analytical results on the statistical size and shape and segment distribution of its trajectory in the limit of large n the relevance of these results to polymer theory is discussed we also study the basic properties of a second generalization of 1dfbm the two dimensional fractional brownian random field 2dfbrf it is shown that the product of two 1dfbms is the only 2dfbrf which satisfies the self similarity defined by sinai

a physical interpretation of age dependent master equations abstract physical systems described by fast and slow relaxing variables are considered the underlying microscopic equations are assumed to be markovian considering that the macroscopic state of the system is characterized by the set of slow relaxing variables we show that the age state probability density obeys a system of age dependent master equations with time and age dependent transition rates if the time scales attached to the slow and fast relaxing variables are well differentiated there is a strong correlation between the age of a fluctuation state and the corresponding number of transition events an alternative approach based on haken s slaving principle is developed for time homogeneous microscopic equations the adiabatic elimination of fast relaxing variables leads to a system of age dependent master equations with time independent and age dependent transition rates these equations are equivalent to a generalized master equation with an inhomogeneous term

a study of behaviors abstract the paper presents the results of the study of behavior theory as developed by j c willems from the point of view of polynomial and rational models considering behaviors in the discrete time case to be generalizations of rational models a natural focal point becomes the concept of a behavior homomorphism we give a characterization of behavior homomorphisms and analyze their invertibility properties in terms of embeddings in unimodular polynomial matrices these results which are of intrinsic interest are then applied to the uniform derivation of a large number of results for equivalence in different classes of behavior representations to a certain extent these are generalizations of the strict system equivalence concept for the class of polynomial matrix description of systems in the style of rosenbrock a study of behavioral controllability is undertaken and gives some new insights into connections with geometric control theory

a hopf like equation and perturbation theory for differential delay equations we extend techniques developed for the study of turbulent fluid flows to the statistical study of the dynamics of differential delay equations because the phase spaces of differential delay equations are infinite dimensional phase space densities for these systems are functionals we derive a hopf like functional differential equation governing the evolution of these densities the functional differential equation is reduced to an infinite chain of linear partial differential equations using perturbation theory a necessary condition for a measure to be invariant under the action of a nonlinear differential delay equation is given finally we show that the evolution equation for the density functional is the fourier transform of the infinite dimensional version of the kramers moyal expansion

generating functional approach to multichannel parallel relaxation with application to the problem of direct energy transfer in fractal systems with dynamic disorder a model for multichannel parallel relaxation is suggested based on the following assumptions a an individual channel is characterized by a set of continuous state variables the corresponding relaxation rate is a function of the state variables as well as of the time interval for which the channel is open b the number of channels is a random variable described by a correlated point process defined in the space of state parameters of an individual channel analytical expressions for the generating functional of the overall relaxation rate and for the average survival function are derived in terms of the generating functional of the point process the general formalism is applied to the problem of direct energy transfer from excited donors to acceptors in fractal systems with dynamic disorder it is assumed that the number of acceptors obeys a poissonian distribution law with a constant average density in a df dimensional fractal structure embedded in a ds dimensional euclidean space ds 1 2 3 and th

realization of autoregressive equations in pencil and descriptor form a linear system described by autoregressive equations with a given input output structure cannot be transformed to standard state space form if the implied input output relation is nonproper instead a realization in descriptor form must be used in this paper it is shown how to obtain minimal descriptor realizations from autoregressive equations without separating finite and infinite frequencies and without going through a reduction process external equivalence is used so that even situations in which there is no transfer matrix can be considered the approach is based on the so called pencil representation of linear systems and it is shown that there is a natural realization of autoregressive equations in pencil form in this way the link between the realization theories of willems and fuhrmann can also be clarified

evolution towards ergodic behavior of stationary fractal random processes with memory application to the study of long range correlations of nucleotide sequences in dna abstract the possible occurrence of ergodic behavior for large times is investigated in the case of stationary random processes with memory it is shown that for finite times the time average of a state function is generally a random variable and thus two types of cumulants can be introduced for the time average and for the statistical ensemble respectively in the limit of infinite time a transition from the random to the deterministic behavior of the time average may occur resulting in an ergodic behavior the conditions of occurrence of this transition are investigated by analyzing the scaling behavior of the cumulants of the time average a general approach for the computation of these cumulants is developed explicit computations are presented both for short and long memory in the particular case of separable stationary processes for which the cumulants of a statistical ensemble can be factorized into products of functions depending on binary time differences in both cases the ergodic behavior emerges for large times provided that the cumulants of a statistical ensemble decrease to zero as the time differences increase to infinity the analysis leads to the surprising conclusion that the scaling behavior of the cumulants of the time average is relatively insensitive to the type of memory considered both for short and long memory the cumulants of the time average obey inverse different from zero for large time differences then the time averaage is random even as the length of the total time interval tends to infinity and the ergodic behavior no longer holds the theory is applied to the study of long range correlations of nucleotide sequences in dna in this case the length t of a sequence of nucleotides plays the role of the time variable a proportionality relationship is established between the cumulants of the pyrimidine excess in a sequence of length t and the cumulants of the time length average of the probability of occurrence of a pyrimidine it is shown that the statistical analysis of the dna data presented in the literature is consistent with the occurrence of the ergodic behavior for large lengths the implications of the approach to the analysis of the large time behavior of stochastic cellular automata and of fractional brownian motion are also investigated

universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder dynamical generalizations of stretched exponential the asymptotic behavior of multichannel parallel relaxation processes for systems with dynamical disorder is investigated in the limit of a very large number of channels an individual channel is characterized by a state vector x which due to dynamical disorder is a random function of time a limit of the thermodynamic type in the x space is introduced for which both the volume available and the average number of channels tend to infinity but the average volume density of channels remains constant scaling arguments combined with a stochastic renormalization group approach lead to the identification of two different types of universal behavior of the relaxation function corresponding to nonintermittent and intermittent fluctuations respectively for nonintermittent fluctuations a dynamical generalization of the static huber s relaxation equation is derived which depends only on the average functional density of channels w t d w t the channels being classified according to their different relaxation rates w w t which are random functions of time for intermittent fluctuations a more complicated relaxation equation is derived which in addition to the average density of channels w t d w t depends also on a positive fractal exponent h which characterizes the fluctuations of the density of channels the general theory is applied for constructing dynamical analogs of the stretched exponential relaxation function for nonintermittent fluctuations the type of relaxation is determined by the regression dynamics of the fluctuations of the relaxation rate if the regression process is fast and described by an exponential attenuation function then after an initial stretched exponential behavior the relaxation process slows down and it is not fully completed even in the limit of very large times for self similar regression obeying a negative power law the relaxation process is less sensitive to the influence of dynamical disorder both for small and large times the relaxation process is described by stretched exponentials with the same fractal exponent as for systems with static disorder for large times the efficiency of the relaxation process is also slowed down by fluctuations similar patterns are found for intermittent fluctuations with the difference that for very large times and a slow regression process a crossover from a stretched exponential to a self similar algebraic relaxation function occurs some implications of the results for the study of relaxation processes in

a fractal time approach to continuous flow systems with stagnancy abstract a statistical mechanical approach to continuous flow systems is suggested the fractal time behavior of these systems is described by means of a succession of recycle events at each step a random fraction of the outlet flux of the precedent step is recycled into the system the volume involved in the process of fluid exchange increasing from step to step by assuming that the flow pattern is the same for all cycles we show that the overall residence time distribution obeys a self similar scaling equation its solution has a long time tail and yields infinite moments although the model is formulated in terms of the residence time distribution theory it might be possible that the results would be of interest for the physics of fractal time in general

analogs of renormalization group transformations in random processes abstract we review the properties of a real space renormalization group transformation of the free energy including the existence of oscillatory terms multiplying the non analytic part of the free energy we then construct stochastic processes which incorporate into probability distributions the features of the free energy scaling equation the essential information is obtainable from the scaling equation and a direct solution for a probability is not necessary these random processes are shown to be generated directly from cantor sets in a spatial representation the ensuing random process exhibits a transition between gaussian and fractal behavior in the fractal regime the trajectories will in an average sense form self similar clusters in a temporal representation the random process exhibits a transition between an asymptotically constant renewal rate and fractal behavior the fractal regime represents a frozen state with only transient effects allowed and is related to charge transport in glasses

on levy or stable distributions and the williams watts model of dielectric relaxation this paper is concerned with the levy or stable distribution function defined by the fourier transform q alpha left z right frac 1 2 pi int infty infty exp left izu left u right alpha right du with 0 alpha leqslant 2 when 2 it becomes the gauss distribution function and when 1 the cauchy distribution when 2 the distribution has a long inverse power tail q alpha left z right sim frac gamma left 1 alpha right sin tfrac 1 2 pi alpha pi left z right 1 alpha in the regime of small if logz 1 the distribution is mimicked by a log normal distribution we have derived rapidly converging algorithms for the numerical calculation ofq z for various in the range 0 1 the functionq z appears naturally in the williams watts model of dielectric relaxation in that model one expresses the normalized dielectric parameter as in n left omega right equiv in n left omega right i in n left omega right int 0 infty e i omega t left d phi left t right mathord left vphantom d phi left t right dt right kern nulldelimiterspace dt right dt with phi left t right exp left t mathord left vphantom t tau right kern nulldelimiterspace tau right alpha it has been found empirically by various authors that observed dielectric parameters of a wide variety of materials of a broad range of frequencies are fitted remarkably accurately by using this form of t e n is shown to be directly related toq z it is also shown that if the williams watts exponential is expressed as a weighted average of exponential relaxation functions exp left t mathord left vphantom t tau right kern nulldelimiterspace tau right alpha int 0 infty g left lambda alpha right e lambda t dt the weight functiong is expressible as a stable distribution some suggestions are made about physical models that might lead to the williams watts form of t

blocks of defect zero and products of elements of orderp abstract suppose thatgis a finite group and thatfis a field of characteristicp 0 which is a splitting field for all subgroups ofg lete0be the sum of the block idempotents of defect zero infg and let be the set of solutions togp 1 ing we show thate0 2 whenpis odd ande0 3 whenp 2 in the latter case 2 r whereris the set of real elements of 2 defect zero soe0 r r 2 we also show thate0 4 4 2 whenp 2 where 4is the set of solutions tog4 1 these results give us various criteria for the existence ofp blocks of defect zero

shlesinger hughes stochastic renormalization iterated logarithmic tails and multiple hierarchical fractal aggregation abstract the multiple hierarchical fractal aggregation is used as an illustration for a new type of asymptotic behavior of fractal random processes defined in terms of a multiple shlesinger hughes renormalization procedure the joint probability distributions of aggregate sizes for a multiple association process are analyzed based on the following set of assumptions a the system contains basic units of different types however each aggregate is made up of a single type of units b the size of a single aggregate obeys a geometrical distribution of the flory type c the aggregation process occurs in a hierarchical way i e each aggregate of a given type triggers the generation of a complex of another type a chain of joint size probability distributions is introduced we show that these probability distributions depend on the probabilities that a unit from a given aggregate is active that is that it may trigger the aggregation process of basic units of another type these probabilities generate a chain of fractal exponents which characterize the asymptotic behavior of the size probability distributions the probability distribution attached to a succession of q 2 aggregation processes has a very long tail with a logarithmic shape it is an inverse power of the q th iterate logarithm of size n ln ln ln n this decay law is much slower than the inverse power laws characteristic for the usual statistical fractals

singular state models and singular ltid systems in this paper we offer a systematic development of state representation theory for singular linear systems in the behavioural setting of willems

spatiotemporal correlation of colored noise we calculated the noise correlation in a gaussian stochastic process that is non ensuremath delta function correlated in both space and time the colored noise obeys a linear reaction diffusion langevin equation with gaussian white noise our result is a generalization of the ornstein uhlenbeck process to take into account finite correlation in space as well as in time for colored noise

g algebras jacobson radical and almost split sequences keywords finite group indecomposable kg module sas sequence almost split exact sequences restriction relative jacobson radicals local criterion multiplicity module vertex source indecomposable projective module twisted group algebra induction reference ctg article 1988 006doi 10 1007 bf01393690 record created on 2008 12 16 modified on 2017 05 12

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

a renormalization approach to a class of exponential random processes with application to the bronchial tree abstract a new stochastic renormalization approach for multi step decay phenomena is developed a simple physical interpretation of the renormalization method is suggested it consists in grouping successions of variable numbers of decay events into blocks the law of probability multiplication leads to an exponential random process y yx1 x2 0 where both the exponents x1 x2 and the basis y0 are random variables the physically consistent solution of the model corresponds to a super strong renormalization regime the dependence of the moments of the decay parameter on the number of decay steps q can be exactly determined it consists in a linear superposition of inverse power laws in q modulated by periodic functions in in q having different periods the theory is applied to the renormalization of the bronchial tree our computation shows that the lung structure is very tolerant to fluctuations this result supports the mechanism of morphogenesis of fractal biological organs suggested by west ann biomed eng 18 1990 135 the possibilities of application to the scattering phenomena in one dimensional disordered media are also investigated