experimental evidence of stochastic resonance without tuning due to non gaussian noises in order to test theoretical predictions we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non gaussian noise in agreement with the theoretical predictions our main findings are an enhancement of the sensibility of the system together with a remarkable widening of the response robustness this implies that even a single resonant unit can reach a marked reduction in the need for noise tuning

spatio temporal patterns in population dynamics abstract the transient dynamics of interacting biological species extracted from two ecosystems is investigated we model the environment interaction by a multiplicative noise and the temperature oscillations by a periodic forcing we find noise induced effects such as enhanced temporal oscillations spatial patterns and noise delayed extinction for the model of two competing species we extend our analysis to an ecosystem of three interacting species namely one predator and two preys we find spatial patterns induced by the noise

mechanism of stochastic resonance enhancement in neuronal models driven by 1 f noise noise can assist neurons in the detection of weak signals via a mechanism known as stochastic resonance sr in a previous study phys lett a 243 281 1998 we showed that when colored noise with 1 f ensuremath beta spectrum is added to the fitzhugh nagumo fhn neuronal model the optimal noise variance for sr could be minimized with ensuremath beta ensuremath approx 1 in this study we investigate analytically how the noise color ensuremath beta affects the sr profile in a linearized version of the fhn model we demonstrate that the aforementioned effect of 1 f noise is related to the dynamical characteristics of the model neuron i e the refractory period the low pass filtering effect of the membrane capacitance and the high pass filtering effect of the recovery variable

analog study of the first passage time problem driven by power law distributed noise abstract in this work we develop an analog circuit to generate a stochastic signal with stationary distribution exhibiting a tunable power law tail the proposed circuit design is a variant of a recently introduced one based on a differential equation with both multiplicative and additive noises here the circuit is carefully designed in order to ensure that all components operate within their specific regimes we provide a detailed characterization of the output signal including the power law exponent dependence on the tunable component we apply the present circuit to study the first passage time problem in a simple integrate fire model of neural dynamics driven by a non gaussian noise

stochastic resonance in neuron models periodically stimulated sensory neurons typically exhibit a kind of statistical phase locking to the stimulus they tend to fire at a preferred phase of the stimulus cycle but not at every cycle hence the histogram of interspike intervals isih i e of times between successive firings is multimodal for these neurons with peaks centered at integer multiples of the driving period a particular kind of residence time histogram for a large class of noisy bistable systems has recently been shown to exhibit the major features of the neural data in the present paper we show that an excitable cell model the fitzhugh nagumo equations also reproduces these features when driven by additive periodic and stochastic forces this model exhibits its own brand of stochastic resonance as the peaks of the isih successively go through a maximum when the noise intensity is increased further the presence of a noise induced limit cycle introduces a third time scale in the problem this limit cycle is found to modify qualitatively the phase locking picture e g by suppressing certain peaks in the isih finally the role of noise and possibly of stochastic resonance sr in the neural encoding of sensory information is discussed

fully measurable grand lebesgue spaces abstract using variable exponents we build a new class of rearrangement invariant banach function spaces independent of the variable lebesgue spaces whose function norm is f ess sup x 0 1 p x x f where p x denotes the norm of the lebesgue space of exponent p x assumed measurable and possibly infinite and is measurable too such class contains some known banach spaces of functions among which are the classical and the grand lebesgue spaces and the exp spaces 0 we analyze the function norm and we prove a boundedness result for the hardy littlewood maximal operator via a hardy type inequality

stochastic bifurcation for a tumor immune system with symmetric levy noise abstract in this paper we investigate stochastic bifurcation for a tumor immune system in the presence of a symmetric non gaussian levy noise stationary probability density functions will be numerically obtained to define stochastic bifurcation via the criteria of its qualitative change and bifurcation diagram at parameter plane is presented to illustrate the bifurcation analysis versus noise intensity and stability index the effects of both noise intensity and stability index on the average tumor population are also analyzed by simulation calculation we find that stochastic dynamics induced by gaussian and non gaussian levy noises are quite different

enhancement of stochastic resonance the role of non gaussian noises abstract we have analyzed the phenomenon of stochastic resonance in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation that enables us to get through the two state theory analytical expressions for the signal to noise ratio finding an enhancement of this quantity when the system departs from gaussian behavior this finding is supported by extensive numerical simulations we discuss the relation of these results to some experiments in sensory systems

a note on the validity of statistical bootstrapping for estimating the uncertainty of tensor parameters in diffusion tensor images diffusion tensors are estimated from magnetic resonance images mris that are diffusion weighted and those images inherently contain noise therefore noise in the diffusion weighted images produces uncertainty in estimation of the tensors and their derived parameters which include eigenvalues eigenvectors and the trajectories of fiber pathways that are reconstructed from those eigenvalues and eigenvectors although repetition and wild bootstrap methods have been widely used to quantify the uncertainty of diffusion tensors and their derived parameters we currently lack theoretical derivations that would validate the use of these two bootstrap methods for the estimation of statistical parameters of tensors in the presence of noise the aim of this paper is to examine theoretically and numerically the repetition and wild bootstrap methods for approximating uncertainty in estimation of diffusion tensor parameters under two different schemes for acquiring diffusion weighted images whether these bootstrap methods can be used to quantify uncertainty in some diffusion tensor parameters such as fractional anisotropy fa depends critically on the morphology of the diffusion tensor that is being estimated the wild and repetition bootstrap methods in particular cannot quantify uncertainty in the principal direction pd of isotropic or oblate tensor we also examine the use of bootstrap methods in estimating tensors in a voxel containing multiple tensors demonstrating their limitations when quantifying the uncertainty of tensor parameters in those locations simulation studies are also used to understand more thoroughly our theoretical results our findings raise serious concerns about the use of bootstrap methods to quantify the uncertainty of fiber pathways when those pathways pass through voxels that contain either isotropic tensors oblate tensors or multiple tensors

grand bochner lebesgue space and its associate space abstract our aim is to introduce the grand bochner lebesgue space in the spirit of iwaniec sbordone spaces also known as grand lebesgue spaces and prove some of its properties we will also deal with the associate space for grand bochner lebesgue spaces

multiplicative processes and power laws takayasu sato and takayasu phys rev lett 79 966 1997 revisited the question of stochastic processes with multiplicative noise which have been studied in several different contexts over the past decades we focus on the regime found for a generic set of control parameters in which stochastic processes with multiplicative noise produce intermittency of a special kind characterized by a power law probability density distribution we briefly explain the physical mechanism leading to a power law probability distribution function and provide a list of references for these results dating back from a quarter of century we explain how the formulation in terms of the characteristic function developed by takayasu sato and takayasu can be extended to exponents ensuremath mu g2 which explains the reason for the lucky coincidence the multidimensional generalization of the results of takayasu sato and takayasu and the present status of the problem are briefly summarized the discovery of stretched exponential tails in the presence of the cutoff introduced by takayasu sato and takayasu is explained theoretically we end by briefly listing applications

non gaussian noise weakened stability in a foraging colony system with time delay abstract in this paper the dynamical properties in a foraging colony system with time delay and non gaussian noise were investigated using delay fokker planck approach the stationary probability distribution spd the associated relaxation time art and normalization correlation function ncf are obtained respectively the results show that i the time delay and non gaussian noise can induce transition from a single peak to double peaks in the spd i e a type of bistability occurring in a foraging colony system where time delay and non gaussian noise not only cause transitions between stable states but also construct the states themselves numerical simulations are presented and are in good agreement with the approximate theoretical results ii there exists a maximum in the art as a function of the noise intensity this maximum for art is identified as the characteristic of the non gaussian noise weakened stability of the foraging colonies in the steady state iii the art as a function of the noise correlation time exhibits a maximum and a minimum where the minimum for art is identified as the signature of the non gaussian noise enhanced stability of the foraging colonies and iv the time delay can enhance the stability of the foraging colonies in the steady state while the departure from gaussian noise can weaken it namely the time delay and departure from gaussian noise play opposite roles in art or ncf

effective markovian approximation for non gaussian noises a path integral approach abstract we have analyzed diffusion in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation to the initially non markovian problem such an approximation allows us to get analytical expressions for the mean first passage time that has been tested against extensive numerical simulations

coherence enhancement in nonlinear systems subject to multiplicative ornstein uhlenbeck noise we show that for two biologically relevant models with self sustained oscillations under the action of a multiplicative ornstein uhlenbeck process their coherence response behaves nonmonotonically with the process correlation time there is a correlation time for which the quality factor is optimized this phenomenon is a consequence of the interplay between the correlation time and the system s periodicity this relation is evidenced through a power law relation with an exponent close to 1 2

resampling inference with complex survey data abstract methods for standard errors and confidence intervals for nonlinear statistics such as ratios regression and correlation coefficients have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement in particular the important special case of two sampled clusters per stratum these methods include the customary linearization or taylor method and resampling methods based on the jackknife and balanced repeated replication brr unlike the jackknife or the brr the linearization method is applicable to general sampling designs but it involves a separate variance formula for each nonlinear statistic thereby requiring additional programming efforts both the jackknife and the brr use a single variance formula for all nonlinear statistics but they are more computing intensive the resampling methods developed here retain these features of the jackknife and the brr yet permit extension to more complex designs involving sampling without replace

stochastic resonance reverse resonance and resonant activation induced by a multi state noise abstract in this paper we investigate the periodic response for a linear system driven by a multiplicative multi state noise which is composed of the multiplication of two dichotomous noises to an input temporal oscillatory signal and the escape of brownian particles over the fluctuating potential barrier for a system with a piece wise linear potential and driven by an additive multi state noise which is also composed of the multiplication of two dichotomous noises for the first system we get the stochastic resonance phenomenon for the amplitude of the periodic response vs the two dichotomous noise strengths and the phenomenon of reverse resonance for the amplitude of the periodic response vs k which represents the asymmetry degree of the dichotomous noises for the second system we obtain the resonant activation phenomenon for which the mean first passage time of the brownian particles over the fluctuating potential barrier shows a minimum as the function of the transition rates of the multi state noise

asymptotic power law of moments in a random multiplicative process with weak additive noise it is well known that a random multiplicative process with weak additive noise generates a power law probability distribution it has recently been recognized that this process exhibits another type of power law the moment of the stochastic variable scales as a function of the additive noise strength we clarify the mechanism for this power law behavior of moments by treating a simple langevin type model both approximately and exactly and argue this mechanism is universal we also discuss the relevance of our findings to noisy on off intermittency and to singular spatio temporal chaos recently observed in systems of non locally coupled elements

a direct approach to the duality of grand and small lebesgue spaces abstract in this paper we show by elementary methods that the quasinorms of the grand and small lebesgue spaces f l p sup 0 t 1 1 log t 1 p t 1 f s p d s 1 p 1 p f l q 0 1 1 log t 1 q 0 t f s q d s 1 q d t t q p p 1 found by fiorenza and karadzhov in a fiorenza g e karadzhov grand and small lebesgue spaces and their analogs z anal anwendungen 23 4 2004 657 681 by using deeply extrapolation interpolation techniques are associate each other in other terms the sharp holder s type inequality 0 1 f g d x c p f l q g l p is proven where the sharpness means that l q is the smallest quasinorm up to equivalences such that the inequality holds the method is based entirely on integral estimates makes use of asymptotic properties of euler s gamma function and gives an explicit estimate of the constant c p all the results are expressed in terms of the more general spaces l p and l q 0

stochastic resonance of a periodically driven neuron under non gaussian noise abstract we investigate the first passage time statistics of the integrate fire neuron model driven by a sub threshold harmonic signal superposed with a non gaussian noise here we considered the noise as the result of a random multiplicative process displaced from the origin by an additive term such a mechanism generates a power law distributed noise whose characteristic decay exponent can be finely tuned we performed numerical simulations to analyze the influence of the noise non gaussian character on the stochastic resonance condition we found that when the noise deviates from gaussian statistics the resonance condition occurs at weaker noise intensities achieving a minimum at a finite value of the distribution function decay exponent we discuss the possible relevance of this feature to the efficiency of the firing dynamics of biological neurons as the present result indicates that neurons would require a lower noise level to detect a sub threshold signal when its statistics departs from gaussian

comparison of bootstrap approaches for estimation of uncertainties of dti parameters bootstrap is an empirical non parametric statistical technique based on data resampling that has been used to quantify uncertainties of diffusion tensor mri dti parameters useful in tractography and in assessing dti methods the current bootstrap method repetition bootstrap used for dti analysis performs resampling within the data sharing common diffusion gradients requiring multiple acquisitions for each diffusion gradient recently wild bootstrap was proposed that can be applied without multiple acquisitions in this paper two new approaches are introduced called residual bootstrap and repetition bootknife we show that repetition bootknife corrects for the large bias present in the repetition bootstrap method and therefore better estimates the standard errors like wild bootstrap residual bootstrap is applicable to single acquisition scheme and both are based on regression residuals called model based resampling residual bootstrap is based on the assumption that non constant variance of measured diffusion attenuated signals can be modeled which is actually the assumption behind the widely used weighted least squares solution of diffusion tensor the performances of these bootstrap approaches were compared in terms of bias variance and overall error of bootstrap estimated standard error by monte carlo simulation we demonstrate that residual bootstrap has smaller biases and overall errors which enables estimation of uncertainties with higher accuracy understanding the properties of these bootstrap procedures will help us to choose the optimal approach for estimating uncertainties that can benefit hypothesis testing based on dti parameters probabilistic fiber tracking and optimizing dti methods

volatility driven market in a generalized lotka voltera formalism abstract the generalized lotka voltera glv formalism has been introduced in order to explain the power law distributions in the individual wealth w i t pareto law and financial markets returns fluctuations r as a result of the auto catalytic multiplicative random character of the individual capital dynamics as long as the multiplicative random factor is extracted from the same probability distribution for all the individuals the exponent of the power laws turns out to be independent on the time variations of the average this explains also the stability over the past century of experimentally measured pareto exponent in contrast to the scaling properties of the single time unconditional probability distributions the auto correlations between observables measured at different times are not correctly reproduced by the original glv if the variance 2 of is time independent in the glv formalism the volatility r 2 auto correlations decay exponentially while the measurements in real markets indicate a power law with a very small exponent we show in the present paper that by making the variance of the individual wealth changes 2 a function of the market volatility r 2 one correctly reproduces the market volatility long range correlations moreover we show that this non trivial feedback loop between the market price volatility and the variance of the investors wealth leads to non trivial patterns in the overall market trends if the feedback is too strong it may even endanger the market stability

time interval between successive trading in foreign currency market from microscopic to macroscopic abstract recently it has been shown that inter transaction interval iti distribution of foreign currency rates has a fat tail in order to understand the statistical property of the iti dealer model with n interactive agents is proposed from numerical simulations it is confirmed that the iti distribution of the dealer model has a power law tail the random multiplicative process rmp can be approximately derived from the iti of the dealer model consequently we conclude that the power law tail of the iti distribution of the dealer model is a result of the rmp

grand lebesgue spaces with respect to measurable functions abstract let 1 p given r n a measurable set of finite lebesgue measure the norm of the grand lebesgue spaces l p is given by f l p sup 0 e p 1 e 1 p e 1 f p e d x 1 p e in this paper we consider the norm f l p obtained replacing e 1 p e by a generic nonnegative measurable function e we find necessary and sufficient conditions on in order to get a functional equivalent to a banach function norm and we determine the interesting class b p of functions with the property that every generalized function norm is equivalent to a function norm built with b p we then define the l p spaces prove some embedding results and conclude with the proof of the generalized hardy inequality

fully measurable small lebesgue spaces abstract we build a new class of banach function spaces whose function norm is p f inf f k 1 f k k 1 ess inf x 0 1 p x x 1 f k where p x denotes the norm of the lebesgue space of exponent p x assumed measurable and possibly infinite constant with respect to the variable of f and is measurable too such class contains some known banach spaces of functions among which are the classical and the small lebesgue spaces and the orlicz space l log l 0 furthermore we prove the following holder type inequality 0 1 f g d t p f p g where p f is the norm of fully measurable grand lebesgue spaces introduced by anatriello and fiorenza in 2 for suitable choices of p x and x it reduces to the classical holder s inequality for the spaces e x p 1 and l log l 0

power law distributions in random multiplicative processes with non gaussian colored multipliers abstract one class of universal mechanisms that generate power law probability distributions is that of random multiplicative processes in this paper we consider a multiplicative langevin equation driven by non gaussian colored multipliers we analytically derive a formula that relates the power law exponent to the statistics of the multipliers and numerically confirm its validity using multiplicative noise generated by chaotic dynamical systems and by a two valued markov process we also investigate the relationship between our treatment and the large deviation analysis of time series and demonstrate the appearance of log periodic fluctuations superimposed on the power law distribution due to the non gaussian nature of the multipliers

bootstrap procedures under some non i i d models it is shown in this article that the classical i i d bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location as long as the random observations are independently drawn from distributions with essentially a common location this may be viewed as a robust property of the classical i i d bootstrap also included is a study of the second order properties of a different bootstrap procedure proposed by wu in the context of heteroscedasticity in regression

bootstrap white matter tractography boot trac white matter tractography is a noninvasive method for estimating and visualizing the white matter connectivity patterns in the human brain using diffusion tensor imaging dti data sources of experimental noise may induce errors in the measured fiber directions which will reduce the accuracy of the estimated white matter trajectories in this study a statistical nonparametric bootstrap method is described for estimating the dispersion and other errors in white matter tractography results prior studies have derived models of tractography error using the signal to noise ratio snr and diffusion anisotropy of the dti data tractography errors measured using bootstrap methods were generally consistent with an analytic model of tractography error except in areas where branching was evident white matter tractography with bootstrap resampling is also applied to estimate the probabilities of connection between brain regions the approach was used to generate probabilistic connectivity maps between the cerebral peduncles and specific cortical regions