superdiffusivity in first passage percolation in standard first passage percolation on bbb z d with d geq 2 the time minimizing paths from a point to a plane at distance l are expected to have transverse fluctuations of order l xi it has been conjectured that xi d geq 1 2 with the inequality strict superdiffusivity at least for low d and with xi 2 2 3 we prove versions of xi d geq 1 2 for all d and xi 2 geq 3 5

power law shot noise the behavior of power law shot noise for which the associated impulse response functions assume a decaying power law form is explored expressions are obtained for the moments moment generating functions amplitude probability density functions autocorrelation functions and power spectral densities for a variety of parameters of the process for certain parameters the power spectral density exhibits 1 f type behavior over a substantial range of frequencies so that the process serves as a source of 1 f sup alpha shot noise for alpha in the range 0

schmitt trigger a solvable model of stochastic resonance an ideal schmitt trigger st is the simplest two state system available for realization of stochastic resonance sr an exact solution is found for the st driven by exponentially correlated gaussian noise plus a weak periodic signal the signal to noise ratio is shown to pass through a maximum at a specific value of the noise intensity a qualitative classification is given for a class of noise models which either exhibit sr or do not

application of computational mechanics to the analysis of natural data an example in geomagnetism we discuss how the ideal formalism of computational mechanics can be adapted to apply to a noninfinite series of corrupted and correlated data that is typical of most observed natural time series specifically a simple filter that removes the corruption that creates rare unphysical causal states is demonstrated and the concept of effective soficity is introduced we believe that computational mechanics cannot be applied to a noisy and finite data series without invoking an argument based upon effective soficity a related distinction between noise and unresolved structure is also defined noise can only be eliminated by increasing the length of the time series whereas the resolution of previously unresolved structure only requires the finite memory of the analysis to be increased the benefits of these concepts are demonstrated in a simulated times series by a the effective elimination of white noise corruption from a periodic signal using the expletive filter and b the appearance of an effectively sofic region in the statistical complexity of a biased poisson switch time series that is insensitive to changes in the word length memory used in the analysis the new algorithm is then applied to an analysis of a real geomagnetic time series measured at halley antarctica two principal components in the structure are detected that are interpreted as the diurnal variation due to the rotation of the earth based station under an electrical current pattern that is fixed with respect to the sun earth axis and the random occurrence of a signature likely to be that of the magnetic substorm in conclusion some useful terminology for the discussion of model construction in general is introduced

network amplification of local fluctuations causes high spike rate variability fractal firing patterns and oscillatory local field potentials we investigate a model for neural activity in a two dimensional sheet of leaky integrate and fire neurons with feedback connectivity consisting of local excitation and surround inhibition each neuron receives stochastic input from an external source independent in space and time as recently suggested by softky and koch 1992 1993 independent stochastic input alone cannot explain the high interspike interval variability exhibited by cortical neurons in behaving monkeys we show that high variability can be obtained due to the amplification of correlated fluctuations in a recurrent network furthermore the cross correlation functions have a dual structure with a sharp peak on top of a much broader hill this is due to the inhibitory and excitatory feedback connections which cause hotspots of neural activity to form within the network these localized patterns of excitation appear as clusters or stripes that coalesce disintegrate or fluctuate in size while simultaneously moving in a random walk constrained by the interaction with other clusters the synaptic current impinging upon a single neuron shows large fluctuations at many time scales leading to a large coefficient of variation cv for the interspike interval statistics the power spectrum associated with single units shows a 1 f decay for small frequencies and is flat at higher frequencies while the power spectrum of the spiking activity averaged over many cells equivalent to the local field potential shows no 1 f decay but a prominent peak around 40 hz in agreement with data recorded from cat and monkey cortex gray et al 1990 eckhorn et al 1993 firing rates exhibit self similarity between 20 and 800 msec resulting in 1 f like noise consistent with the fractal nature of neural spike trains teich 1992

fluctuations of extensive functions of quenched random couplings an extensive quantity is a family of functions v of random parameters indexed by the finite regionsv subsets of d over which v are additive up to corrections satisfying the boundary estimate stated below it is shown that unless the randomness is nonessential in the sense that lim v v has a unique value in the absolute i e not just probabilistic sense the variance of such a quantity grows as the volume ofv of particular interest is the free energy of a system with random couplings for such v bounds are derived also for the generating functione et in a separate application variance bounds are used for an inequality concerning the characteristic exponents of directed polymers in a random environment

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

excitable systems with noise and delay with applications to control renewal theory approach we present an approach for the analytical treatment of excitable systems with noise induced dynamics in the presence of time delay an excitable system is modeled as a bistable system with a time delay while another delay enters as a control term taken after pyragas k pyragas phys lett a 170 421 1992 as a difference between the current system state and its state tau time units before this approach combines the elements of renewal theory to estimate the essential features of the resulting stochastic process as functions of the parameters of the controlling term

a simplified proof of the relation between scaling exponents in first passage percolation in a recent breakthrough work chatterjee 5 proved a long standing conjecture that relates the transversal exponentand the fluctuation exponentin first passage percolation on z d the purpose of this paper is to introduce a new and intuitive idea that replaces the main argument of 5 and gives an alternative proof of this relation specifically we show that under the assumption that exponents defined in 5 exist one has the relation 2 1 one advantage of our argument is that it does not require the nearly gamma assumption of 5

power spectrum of mass and activity fluctuations in a sandpile we consider a directed abelian sandpile on a strip of size 2 ifmmode times else texttimes fi n driven by adding a grain randomly at the left boundary after every t timesteps we establish the exact equivalence of the problem of mass fluctuations in the steady state and the number of zeros in the ternary base representation of the position of a random walker on a ring of size 3 n we find that while the fluctuations of mass have a power spectrum that varies as 1 f for frequencies in the range 3 ensuremath 2n ensuremath ll f ensuremath ll 1 t the activity fluctuations in the same frequency range have a power spectrum that is linear in f

including long range dependence in integrate and fire models of the high interspike interval variability of cortical neurons many different types of integrate and fire models have been designed in order to explain how it is possible for a cortical neuron to integrate over many independent inputs while still producing highly variable spike trains within this context the variability of spike trains has been almost exclusively measured using the coefficient of variation of interspike intervals however another important statistical property that has been found in cortical spike trains and is closely associated with their high firing variability is long range dependence we investigate the conditions if any under which such models produce output spike trains with both interspike interval variability and long range dependence similar to those that have previously been measured from actual cortical neurons we first show analytically that a large class of high variability integrate and fire models is incapable of producing such outputs based on the fact that their output spike trains are always mathematically equivalent to renewal processes this class of models subsumes a majority of previously published models including those that use excitation inhibition balance correlated inputs partial reset or nonlinear leakage to produce outputs with high variability next we study integrate and fire models that have nonpoissonian renewal point process inputs instead of the poisson point process inputs used in the preceding class of models the confluence of our analytical and simulation results implies that the renewal input model is capable of producing high variability and long range dependence comparable to that seen in spike trains recorded from cortical neurons but only if the interspike intervals of the inputs have infinite variance a physiologically unrealistic condition finally we suggest a new integrate and fire model that does not suffer any of the previously mentioned shortcomings by analyzing simulation results for this model we show that it is capable of producing output spike trains with interspike interval variability and long range dependence that match empirical data from cortical spike trains this model is similar to the other models in this study except that its inputs are fractional gaussian noise driven poisson processes rather than renewal point processes in addition to this model s success in producing realistic output spike trains its inputs have long range dependence similar to that found in most subcortical neurons in sensory pathways including the inputs to cortex analysis of output spike trains from simulations of this model also shows that a tight balance between the amounts of excitation and inhibition at the inputs to cortical neurons is not necessary for high interspike interval variability at their outputs furthermore in our analysis of this model we show that the superposition of many fractional gaussian noise driven poisson processes does not approximate a poisson process which challenges the common assumption that the total effect of a large number of inputs on a neuron is well represented by a poisson process

fractal renewal processes two relatively simple renewal processes whose power spectral densities vary as 1 f sup d are constructed 1 a standard renewal point process with 0

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

approximation of subadditive functions and convergence rates in limiting shape results for a nonnegative subadditive function h on mathbb z d with limiting approximation g x lim n h nx n it is of interest to obtain bounds on the discrepancy between g x and h x typically of order x nu with nu 1 for certain subadditive h x particularly those which are expectations associated with optimal random paths from 0 to x in a somewhat standardized way a more natural and seemingly weaker property can be established every x is in a bounded multiple of the convex hull of the set of sites satisfying a similar bound we show that this convex hull property implies the desired bound for all x applications include rates of convergence in limiting shape results for first passage percolation standard and oriented and longest common subsequences and bounds on the error in the exponential decay approximation to the off axis connectivity function for subcritical bernoulli bond percolation on the integer lattice

chaotic resonance two state model with chaos induced escape over potential barrier we consider the resonant effects of chaotic fluctuations on a strongly damped particle in a bistable potential driven by weak sinusoidal perturbation we derive analytical expressions of chaos induced transition rate between the neighboring potential wells based on the inhomogeneous smoluchowski equation our first order analysis reveals that the transition rate has the form of the kramers escape rate except for a perturbed prefactor this modification to the prefactor is found to arise from the statistical asymmetry of the chaotic noise by means of the two state model and the chaos induced transition rate we arrive at an analytical expression of the signal to noise ratio snr our first order snr shows that chaotic resonance can correspond directly to stochastic resonance

regular and stochastic behavior of parkinsonian pathological tremor signals abstract regular and stochastic behavior in the time series of parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non markov stochastic processes and flicker noise spectroscopy we have developed a new method of analyzing and diagnosing parkinson s disease pd by taking into consideration discreteness fluctuations long and short range correlations regular and stochastic behavior markov and non markov effects and dynamic alternation of relaxation modes in the initial time signals the spectrum of the statistical non markovity parameter reflects markovity and non markovity in the initial time series of tremor the relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states the local time behavior of the initial time correlation function and the first point of the non markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series the obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a pd patient generally the method allows one to assess the efficacy of the medical treatment for a group of pd patients

scaling of swimming sequences in copepod behavior data analysis and simulation abstract we consider symbolic sequences of copepod behavior classified as break and slow swimming states successive residence times for each state have been recorded for 327 symbolic times series obtained from 52 different trajectories we performed a symbolic dynamics analysis of the succession of states and showed that the probability densities of the duration of each state obey power laws for large times we analyzed the transition between states and showed as expected the non markovian properties of this dynamics we further simulate a copepod trajectory using an alternate renewal process for the generation of the sequence time series and using a brownian motion for the copepod motion during swimming periods

stochastic resonance in ion channels characterized by information theory we identify a unifying measure for stochastic resonance sr in voltage dependent ion channels which comprises periodic conventional aperiodic and nonstationary sr within a simplest setting the gating dynamics is governed by two state conductance fluctuations which switch at random time points between two values the corresponding continuous time point process is analyzed by virtue of information theory in pursuing this goal we evaluate for our dynamics the tau information the mutual information and the rate of information gain as a main result we find an analytical formula for the rate of information gain that solely involves the probability of the two channel states and their noise averaged rates for small voltage signals it simplifies to a handy expression our findings are applied to study sr in a potassium channel we find that sr occurs only when the closed state is predominantly dwelled upon upon increasing the probability for the open channel state the application of an extra dose of noise monotonically deteriorates the rate of information gain i e no sr behavior occurs

fractal renewal processes generate 1 f noise 1 mathit f mathit d noise occurs in an impressive variety of physical systems and numerous complex theories have been proposed to explain it we construct two relatively simple renewal processes whose power spectral densities vary as 1 mathit f mathit d i a standard renewal point process with 0d1 and ii a finite valued alternating renewal process with 0d2 the resulting event number statistics coincidence rates minimal coverings and autocorrelation functions are shown also to follow power law forms these fractal characteristics derive from interevent time probability density functions which themselves decay in a power law fashion a number of applications are considered trapping in amorphous semiconductors electronic burst noise movement in systems with fractal boundaries the digital generation of 1 mathit f mathit d noise and ionic currents in cell membranes

statistical properties of one dimensional binary sequences with power law power spectrum abstract by the fourier filtering method we generate one dimensional binary sequences from coarse grained continuous sequences with preset exponents 0 using the spectrum analysis we find that the corresponding binary sequences have pure 1 f power spectrum and spectrum exponents 0 0 2 0 where f is the frequency we evaluate numerically the relation between and 0 using the autocorrelation function analysis the detrended fluctuation analysis the duration time analysis and the entropy analysis we investigate extensively the statistical properties of such binary sequences we find that the statistical properties are basically different for 1 and 1 and binary sequences become more and more ordered as increases

drift and diffusion in periodically driven renewal processes we consider the drift and diffusion properties of periodically driven renewal processes these processes are defined by a periodically time dependent waiting time distribution which governs the interval between subsequent events we show that the growth of the cumulants of the number of events is asymptotically periodic and develop a theory which relates these periodic growth coefficients to the waiting time distribution defining the periodic renewal process the first two coefficients which are the mean frequency and effective diffusion coefficient of the number of events are considered in greater detail they may be used to quantify stochastic synchronization

stochastic origins of the long range correlations of ionic current fluctuations in membrane channels an explicit stochastic representation of a stationary ionic current signal recorded from a single channel of a biological membrane is presented in the framework of the proposed approach we show how the dichotomous time structure of the signal leads to the non markovian character of the channel current the rescaled range hurst and detrended fluctuation analyses confirm the theoretical result to investigate the ionic current fluctuations we introduce the orey index as a statistical method providing additional information on the properties of stochastic processes in order to reveal any differences between the experimental and reconstructed signals we apply also the statistical tests to the model based simulations of the channel action

universal generation of 1 f noises this paper establishes a universal mechanism for the generation of 1 f noises the mechanism is based on a signal superposition model which superimposes signals transmitted from independent sources all sources transmit a statistically common yet arbitrary stochastic signal pattern each source has its own random transmission parameters amplitude frequency and initiation epoch we explore randomizations of the transmission parameters which render the power spectrum of the super imposed signal invariant with respect of the stochastic signal pattern transmitted analysis shows that the aforementioned randomizations yield superimposed signals which are 1 f noises the result obtained is in effect a randomized central limit theorem for 1 f noises

dry friction avalanches experiment and theory experimental evidence and theoretical models are presented supporting the conjecture that dry friction stick slip is described by self organized criticality we use the data obtained with a pin on disk tribometer set to measure lateral force to examine the variation of the friction force as a function of time we study nominally flat surfaces of matching aluminum and steel the probability distribution of force drops follows a negative power law with exponents ensuremath mu in the range 3 2 3 5 the frequency power spectrum follows a 1 f ensuremath alpha pattern with ensuremath alpha in the range 1 1 8 we first compare these experimental results with the well known robin hood model of self organized criticality we find good agreement between theory and experiment for the force drop distribution but not for the power spectrum we explain this on a physical basis and propose a model which takes explicitly into account the stiffness and inertia of the tribometer specifically we numerically solve the equation of motion of a block on a friction surface pulled by a spring and show that for certain spring constants the motion is characterized by the same power law spectrum as in experiments we propose a physical picture relating the fluctuations of the force drops to the microscopic geometry of the surface

an exactly solvable nonlinear model constructive effects of correlations between gaussian noises abstract a system with two correlated gaussian white noises is analysed this system can describe both stochastic localization and long tails in the stationary distribution correlations between the noises can lead to a nonmonotonic behaviour of the variance as function of the intensity of one of the noises and to a stochastic resonance a method for improving the transmission of external periodic signal by tuning parameters of the system discussed in this paper is proposed

information transfer with rate modulated poisson processes a simple model for nonstationary stochastic resonance stochastic resonance in a simple model of information transfer is studied for sensory neurons and ensembles of ion channels an exact expression for the information gain is obtained for the poisson process with the signal modulated spiking rate this result allows one to generalize the conventional stochastic resonance sr problem with periodic input signal to the arbitrary signals of finite duration nonstationary sr moreover in the case of a periodic signal the rate of information gain is compared with the conventional signal to noise ratio the paper establishes the general nonequivalence between both measures notwithstanding their apparent similarity in the limit of weak signals

analytically solvable autocorrelation function for weakly correlated interevent times long term temporal correlations observed in event sequences of natural and social phenomena have been characterized by algebraically decaying autocorrelation functions such temporal correlations can be understood not only by heterogeneous interevent times iets but also by correlations between iets in contrast to the role of heterogeneous iets on the autocorrelation function little is known about the effects due to the correlations between iets to rigorously study these effects we derive an analytical form of the autocorrelation function for the arbitrary iet distribution in the case with weakly correlated iets where the farlie gumbel morgenstern copula is adopted for modeling the joint probability distribution function of two consecutive iets our analytical results are confirmed by numerical simulations for exponential and power law iet distributions for the power law case we find a tendency of the steeper decay of the autocorrelation function for the stronger correlation between iets our analytical approach enables us to better understand long term temporal correlations induced by the correlations between iets

frequency analysis of binary oscillators triggered by a random noise abstract the frequency analysis of a bistable binary oscillator triggered by a stationary random signal is performed by analyzing the expression for the power spectrum of its output the oscillator state changes when the input noise exceeds a fixed threshold which occurs in correspondence of the events produced by an ordinary renewal process after each state change a fixed refractory time t is to be passed before the output performs a new transition a theoretical study shows that a coherence resonance cr effect appears in the output square wave if the threshold is lower than a positive real value when the overcoming of the input threshold occurs according to a poisson process with exponential parameter the regularity is present at the output only if the product t exceeds 2 1 the value of the characteristic frequency increases rapidly with t towards its asymptotic value 1 2 t the same probabilistic approach is then adopted to perform the spectral analysis of a set of uncoupled binary oscillators sharing the same refractory time t and the same input random signal under mild assumptions the whole system behaves as a single oscillator whose output is amplified proportionally to the number of elements involved

robust stochastic resonance for simple threshold neurons simulation and theoretical results show that memoryless threshold neurons benefit from small amounts of almost all types of additive noise and so produce the stochastic resonance or sr effect input output mutual information measures the performance of such threshold systems that use subthreshold signals the sr result holds for all possible noise probability density functions with finite variance the only constraint is that the noise mean must fall outside a forbidden threshold related interval that the user can control a new theorem shows that this condition is also necessary a corollary and simulations show that the sr effect occurs for right sided beta and weibull noise as well these sr results further hold for the entire uncountably infinite class of alpha stable probability density functions alpha stable noise densities have infinite variance and infinite higher order moments and often model impulsive noise environments the stable noise densities include the special case of symmetric bell curve densities with thick tails such as the cauchy probability density the sr result for alpha stable noise densities shows that the sr effect in threshold and thresholdlike systems is robust against occasional or even frequent violent fluctuations in noise regression analysis reveals both an exponential relationship for the optimal noise dispersion as a function of the alpha bell curve tail thickness and an approximate linear relationship for the sr maximal mutual information as a function of the alpha bell curve tail thickness

isoperimetry in two dimensional percolation we study isoperimetric sets i e sets with minimal boundary for a prescribed volume on the unique infinite connected component of supercritical bond percolation on the square lattice in the limit of the volume tending to infinity properly scaled isoperimetric sets are shown to converge in the hausdorff metric to the solution of an isoperimetric problem in 2 with respect to a particular norm as part of the proof we also show that the anchored isoperimetric profile as well as the cheeger constant of the giant component in finite boxes scale to deterministic quantities this settles a conjecture of itai benjamini for the square lattice 2015 wiley periodicals inc

informational and causal architecture of continuous time renewal processes we introduce the minimal maximally predictive models epsilon text machines of processes generated by certain hidden semi markov models their causal states are either discrete mixed or continuous random variables and causal state transitions are described by partial differential equations as an application we present a complete analysis of the epsilon text machines of continuous time renewal processes this leads to closed form expressions for their entropy rate statistical complexity excess entropy and differential information anatomy rates

stochastic resonance in discrete time nonlinear ar 1 models this paper deals with stochastic resonance this nonlinear physical phenomenon generally occurs in bistable systems excited by random input noise plus a sinusoid through its internal dynamics such a system forces cooperation between the input noise and the input sine provided the existence of fine tuning between the power noise and the dynamics the system reacts periodically at the frequency of the sine of particular interest is the fact that the local output signal to noise ratio presents a maximum when plotted against the input noise power the system resounds stochastically continuous time systems have already been studied we study the ability of intrinsically discrete time systems general nonlinear ar 1 models to produce stochastic resonance it is then suggested that such discrete systems can be used in signal processing

divergence of shape fluctuations in two dimensions we consider stochastic growth models such as standard first passage percolation on z d where to leading order there is a linearly growing deterministic shape under natural hypotheses we prove that for d 2 the shape fluctuations grow at least logarithmically in all directions although this bound is far from the expected power law behavior with exponent 1 3 it does prove divergence with additional hypotheses we obtain inequalities involving and the related exponent which is expected to equal 2 3 for d 2 combining these inequalities with previously known results we obtain for standard first passage percolation the bounds 1 8 for d 2 and 3 4 for all d

fractional brownian motors and stochastic resonance we study fluctuating tilt brownian ratchets based on fractional subdiffusion in sticky viscoelastic media characterized by a power law memory kernel unlike the normal diffusion case the rectification effect vanishes in the adiabatically slow modulation limit and optimizes in a driving frequency range it is shown also that the anomalous rectification effect is maximal stochastic resonance effect at optimal temperature and can be of surprisingly good quality moreover subdiffusive current can flow in the counterintuitive direction upon a change of temperature or driving frequency the dependence of anomalous transport on load exhibits a remarkably simple universality

theory of frequency and phase synchronization in a rocked bistable stochastic system we investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked overdamped bistable potential driven by white gaussian noise the archetype description of stochastic resonance we present an approach to the stochastic counting process of noise induced switching events starting from the markovian dynamics of the nonstationary continuous particle dynamics one finds upon contraction onto two states a non markovian renewal dynamics a proper definition of an output discrete phase is given and the time rate of change of its noise average determines the corresponding output frequency the phenomenon of noise assisted phase synchronization is investigated in terms of an effective instantaneous phase diffusion the theory is applied to rectangular shaped rocking signals versus increasing input noise strengths in this case for an appropriate choice of the parameter values the system exhibits a noise induced frequency locking accompanied by a very pronounced suppression of the phase diffusion of the output signal precise numerical simulations corroborate very favorably our analytical results the novel theoretical findings are also compared with prior ones

scaling identity for crossing brownian motion in a poissonian potential we consider d dimensional brownian motion in a truncated poissonian potential d 2 if brownian motion starts at the origin and ends in the closed ball with center y and radius 1 then the transverse fluctuation of the path is expected to be of order y whereas the distance fluctuation is of order y physics literature tells us that and should satisfy a scaling identity 2 1 we give here rigorous results for this conjecture

spectral 1 f noise derived from extremized physical information we consider the evolution of a temporal signal x t that is an intrinsic random field of order zero in the sense of a certain measurement estimation experiment the state of disorder of x t should increase toward an equilibrium state the disorder of x t is measured by its physical information scri and the equilibrium state is determined by the condition that scri be an extremum the equilibrium state is shown to have a power spectrum s ensuremath omega of the form mathrm ensuremath omega mathrm ensuremath mathrm ensuremath alpha 1 ensuremath le ensuremath alpha ensuremath le 2 that of 1 f noise

theory of non markovian stochastic resonance we consider a two state model of non markovian stochastic resonance sr within the framework of the theory of renewal processes residence time intervals are assumed to be mutually independent and characterized by some arbitrary nonexponential residence time distributions which are modulated in time by an externally applied signal making use of a stochastic path integral approach we obtain general integral equations governing the evolution of conditional probabilities in the presence of an input signal these equations generalize earlier integral renewal equations by cox and others to the case of driving induced nonstationarity on the basis of these equations a response theory of two state renewal processes is formulated beyond the linear response approximation moreover a general expression for the linear response function is derived the connection of the developed approach with the phenomenological theory of linear response for manifest non markovian sr put forward i goychuk and p hanggi phys rev lett 91 070601 2003 is clarified and its range of validity is scrutinized the theory is then applied to sr in symmetric non markovian systems and to the class of single ion channels possessing a fractal kinetics

symbolic strings and spatial 1 f spectra abstract some string dynamics which are expected to show non trivial correlations are proposed and studied it is because we were motivated by the observation that some dna sequences show spatial 1 f correlation our model is based on a rule by which one string is split into two parts in the middle and another string is inserted between them when the strings are made longer the basic model shows long range correlations with a structure characteristic of cyclic patterns on the log log plot of the spectrum the effects of string cross over and point mutation are also studied the cross over destroys the structures appearing in the basic model and makes 1 f like correlation clear the point mutation makes the power spectrum flat as is expected from the white noise nature the analogy of the cross over model with real dna evolution dynamics is suggested

estimating the intermittency of point processes with applications to human activity and viral dna abstract the intermittency of a point process is the extent to which the number of events in a time window has pronounced departures from typical values combining point process and multifractal formalisms indicates that the correlation codimension can be used to quantify intermittency the correlation codimension is easily estimated and is simply related to other second order scaling exponents such as those of the fano factor and spectral density the correlation codimensions are derived for various uncorrelated fractal and fractal rate point processes in addition the estimation of intermittency as the correlation codimension of experimental events is illustrated with applications to experimental data human activity during bed rest is highly intermittent while other human activity and viral dna composition are non intermittent

noise sensitivity of phase synchronization time in stochastic resonance theory and experiment recent numerical and heuristic arguments have revealed that the average phase synchronization time between the input and the output associated with stochastic resonance is highly sensitive to noise variation in particular there is evidence that this average time exhibits a cusplike behavior as the noise strength varies through the optimal value here we present an explicit formula for the average phase synchronization time in terms of the phase diffusion coefficient and the average frequency difference between the input and the output signals we also provide experimental evidence for the cusplike behavior by using a bistable microelectronic circuit system

transversal fluctuations for increasing subsequences on the plane consider a realization of a poisson process in 2 with intensity 1 and take a maximal up right path from the origin to n n consisting of line segments between the points where maximal means that it contains as many points as possible the number of points in such a path has fluctuations of order n where 1 3 bdj here we show that typical deviations of a maximal path from the diagonal x y is of order n with 2 3 this is consistent with the scaling identity 2 1 which is believed to hold in many random growth models