resonant response in nonequilibrium steady states the time dependent probability density function of the order parameter of a system evolving toward a stationary state exhibits an oscillatory behavior if the eigenvalues of the corresponding evolution operator are complex the frequencies n with which the system reaches its stationary state correspond to the imaginary part of such eigenvalues if the system at the stationary state is further driven by a small and oscillating perturbation with a given frequency we formally prove that the linear response to the probability density function is enhanced when n for n n we prove that the occurrence of this phenomenon is characteristic of systems that are in a nonequilibrium stationary state in particular we obtain an explicit formula for the frequency dependent mobility in terms of the relaxation to the stationary state of the unperturbed probability current we test all these predictions by means of numerical simulations considering an ensemble of noninteracting overdamped particles on a tilted periodic potential

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

value at risk forecasts by a spatiotemporal model in chinese stock market abstract this paper generalizes a recently proposed spatial autoregressive model and introduces a spatiotemporal model for forecasting stock returns we support the view that stock returns are affected not only by the absolute values of factors such as firm size book to market ratio and momentum but also by the relative values of factors like trading volume ranking and market capitalization ranking in each period this article studies a new method for constructing stocks reference groups the method is called quartile method applying the method empirically to the shanghai stock exchange 50 index we compare the daily volatility forecasting performance and the out of sample forecasting performance of value at risk var estimated by different models the empirical results show that the spatiotemporal model performs surprisingly well in terms of capturing spatial dependences among individual stocks and it produces more accurate var forecasts than the other three models introduced in the previous literature moreover the findings indicate that both allowing for serial correlation in the disturbances and using time varying spatial weight matrices can greatly improve the predictive accuracy of a spatial autoregressive model

first passage and risk evaluation under stochastic volatility we solve the first passage problem for the heston random diffusion model we obtain exact analytical expressions for the survival and the hitting probabilities to a given level of return we study several asymptotic behaviors and obtain approximate forms of these probabilities which prove among other interesting properties the nonexistence of a mean first passage time one significant result is the evidence of extreme deviations which implies a high risk of default when certain dimensionless parameter related to the strength of the volatility fluctuations increases we confront the model with empirical daily data and we observe that it is able to capture a very broad domain of the hitting probability we believe that this may provide an effective tool for risk control which can be readily applicable to real markets both for portfolio management and trading strategies

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

role of the initial conditions on the enhancement of the escape time in static and fluctuating potentials we present a study of the noise driven escape of an overdamped brownian particle moving in a cubic potential profile with a metastable state we analyze the role of the initial conditions of the particle on the enhancement of the average escape time as a function of the noise intensity for fixed and fluctuating potentials we observe the noise enhanced stability effect for all the initial unstable states investigated for a fixed potential we find a peculiar initial condition xc which separates the set of the initial unstable states in two regions those which give rise to divergences from those which show nonmonotonic behavior of the average escape time for fluctuating potential at this particular initial condition and for low noise intensity we find large fluctuations of the average escape time

hitting time distributions in financial markets we analyze the hitting time distributions of stock price returns in different time windows characterized by different levels of noise present in the market the study has been performed on two sets of data from us markets the first one is composed by daily price of 1071 stocks trade for the 12 year period 1987 1998 the second one is composed by high frequency data for 100 stocks for the 4 year period 1995 1998 we compare the probability distribution obtained by our empirical analysis with those obtained from different models for stock market evolution specifically by focusing on the statistical properties of the hitting times to reach a barrier or a given threshold we compare the probability density function pdf of three models namely the geometric brownian motion the garch model and the heston model with that obtained from real market data we will present also some results of a generalized heston model r 2007 elsevier b v all rights reserved

modulated stochastic multiresonance in a single mode laser system driven by colored additive and multiplicative noises without external periodic force abstract the stochastic resonance phenomenon is studied in a single mode laser system driven by correlated multiplicative and additive colored noises without modulation by external periodic force we detect that there are multiple extrema maximum in the curve of the mean output laser intensity versus the multiplicative noise intensity this phenomenon called stochastic multiresonance reveals that the mean output laser intensity can be amplified at several values of the multiplicative noise intensity whose peaks are modulated by a sinusoidal function this kind of stochastic resonance differs with those reported by past references furthermore similar behaviors also exist in the variance and the skewness

effect of time delay on pattern dynamics in a spatial epidemic model time delay accounting for constant incubation period or sojourn times in an infective state widely exists in most biological systems like epidemiological models however the effect of time delay on spatial epidemic models is not well understood in this paper spatial pattern of an epidemic model with both nonlinear incidence rate and time delay is investigated in particular we mainly focus on the effect of time delay on the formation of spatial pattern through mathematical analysis we gain the conditions for hopf bifurcation and turing bifurcation and find exact turing space in parameter space furthermore numerical results show that time delay has a significant effect on pattern formation the simulation results may enrich the finding of patterns and may well capture some key features in the epidemic models

mean escape time in a system with stochastic volatility we study the mean escape time in a market model with stochastic volatility the process followed by the volatility is the cox ingersoll and ross process which is widely used to model stock price fluctuations the market model can be considered as a generalization of the heston model where the geometric brownian motion is replaced by a random walk in the presence of a cubic nonlinearity we investigate the statistical properties of the escape time of the returns from a given interval as a function of the three parameters of the model we find that the noise can have a stabilizing effect on the system as long as the global noise is not too high with respect to the effective potential barrier experienced by a fictitious brownian particle we compare the probability density function of the return escape times of the model with those obtained from real market data we find that they fit very well

on albanese torsors and the elementary obstruction we show that the elementary obstruction to the existence of 0 cycles of degree 1 on an arbitrary variety x over an arbitrary field can be expressed in terms of the albanese 1 motives associated with dense open subsets of x arithmetic applications are given

bandwidth selection for kernel density estimation the problem of automatic bandwidth selection for a kernel density estimator is considered it is well recognized that the bandwidth estimate selected by the least squares cross validation is subject to large sample variation this difficulty limits the application of the cross validation estimate based on characteristic functions an important expression for the cross validation bandwidth estimate is obtained the expression clearly points out the source of variation to stabilize the variation a simple bandwidth selection procedure is proposed it is shown that the stabilized bandwidth selector gives a strongly consistent estimate of the optimal bandwidth under commonly used smoothness conditions the stabilized bandwidth estimate has a faster convergence rate than the convergence rate of the cross validation estimate for sufficiently smooth density functions it is shown that the stabilized bandwidth estimate is asymptotically normal with a relative convergence rate n 1 2 instead of the rate n 1 10 of the cross validation estimate a plug in estimate and an adjusted plug in estimate are also proposed and their asymptotic distributions are obtained it is noted that the plug in estimate is asymptotically efficient the adjusted plug in bandwidth estimate and the stabilized bandwidth estimate are shown to be asymptotically equivalent the simulation results verify that the proposed procedures perform much better than the cross validation for finite samples

characterization of escape times of josephson junctions for signal detection the measurement of the escape time of a josephson junction might be used to detect the presence of a sinusoidal signal embedded in noise when use of standard signal processing tools can be prohibitive due to the extreme weakness of the source or to the huge amount of data in this paper we show that the prescriptions for the experimental setup and some physical behaviors depend on the detection strategy more specifically by exploitation of the sample mean of escape times to perform detection two resonant regions are identified at low frequencies there is a stochastic resonance or activation phenomenon while near the plasma frequency a geometric resonance appears furthermore detection performance in the geometric resonance region is maximized at the prescribed value of the bias current the naive sample mean detector is outperformed in terms of error probability by the optimal likelihood ratio test the latter exhibits only geometric resonance showing monotonically increasing performance as the bias current approaches the junction critical current in this regime the escape times are vanishingly small and therefore performance is essentially limited by measurement electronics the behavior of the likelihood ratio and sample mean detector for different values of incoming signal to noise ratio is discussed and a relationship with the error probability is found detectors based on the likelihood ratio test could be employed also to estimate unknown parameters in the applied input signal as a prototypical example we study the phase estimation problem of a sinusoidal current which is accomplished by using the filter bank approach finally we show that for a physically feasible detector the performances are found to be very close to the cramer rao theoretical bound applications might be found for example in some astronomical detection problems where the all sky gravitational and or radio wave search for pulsars requires the analysis of nearly sinusoidal long lived waveforms at very low signal to noise ratio or to analyze weak signals in the subterahertz range where the traditional electronics counterpart is difficult to implement

populations in a periodically changing habitat comparison of two extended models abstract we investigate the dynamics of a population in periodically changing external conditions and we determine the survival chance as a function of the selection pressure and changeability we compare two extended models in one an individual is characterized by its genetic structure from which a phenotype follows while in the second model an individual is described by a real number directly representing the phenotype we show that although the models exhibit in general similar behavior the simpler model could in some special conditions give incorrect results

minimal condition number for positive definite hankel matrices using semidefinite programming abstract we present a semidefinite programming approach for computing optimally conditioned positive definite hankel matrices of order n unlike previous approaches our method is guaranteed to find an optimally conditioned positive definite hankel matrix within any desired tolerance since the condition number of such matrices grows exponentially with n this is a very good test problem for checking the numerical accuracy of semidefinite programming solvers our tests show that semidefinite programming solvers using fixed double precision arithmetic are not able to solve problems with n 30 moreover the accuracy of the results for 24 n 30 is questionable in order to accurately compute minimal condition number positive definite hankel matrices of higher order we use a mathematica 6 0 implementation of the sdpha solver that performs the numerical calculations in arbitrary precision arithmetic by using this code we have validated the results obtained by standard codes for n 24 and we have found optimally conditioned positive definite hankel matrices up to n 100

role of the noise on the transient dynamics of an ecosystem of interacting species abstract we analyze the transient dynamics of an ecosystem described by generalized lotka volterra equations in the presence of a multiplicative noise and a random interaction parameter between the species we consider specifically three cases i two competing species ii three interacting species one predator two preys iii n interacting species the interaction parameter in case i is a stochastic process which obeys a stochastic differential equation we find noise delayed extinction of one of two species which is akin to the noise enhanced stability phenomenon other two noise induced effects found are temporal oscillations and spatial patterns of the two competing species in case ii the noise induces correlated spatial patterns of the predator and of the two preys concentrations finally in case iii we find the asymptotic behavior of the time average of the ith population when the ecosystem is composed of a great number of interacting species

on optimal data based bandwidth selection in kernel density estimation a bandwidth selection method is proposed for kernel density estimation this is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth but with two important modifications the result is a bandwidth selector with the by nonparametric standards extremely fast asymptotic rate of convergence of n where n denotes sample size comparison is given to other bandwidth selection methods and small sample impact is investigated

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

stochastic resonance of drawdown risk in energy market prices abstract we investigate the stochastic resonance dynamic behavior characteristics of price drawdown time series driven by internal and external periodic information and discuss the influence of information resonance on price drawdown risk based on price drawdown periodic heston model and signal power amplification a theoretical model of the periodic price drawdown time series is proposed to describe the energy price drawdown time series with the periodic heston model then the signal power amplification spa is employed to measure the stochastic resonance phenomenon in the internal and external periodic information environment of complex energy dynamics system combined with the real data of wti spot price of nymex the least square method of drawdown time series distribution is used to estimate the parameters of the model the probability density functions of drawdown between the theoretical model and the real data are compared and a good agreement can be found between both the simulated data from the proposed model and the real data after the stochastic simulation of signal power amplification under internal and external periodic information respectively the results show that i in the functions of spa versus price volatility parameters noise correlation strength or periodic information strength inverse resonance phenomenon can be observed that is to say there is the best system price volatility parameter noise correlation strength and information strength corresponding to the least risk of the price drawdown ii in the spa versus amplitude of volatility fluctuations the correlation induce multiple inverse stochastic resonance phenomenon can be observed iii the increase of growth rate strengthens spa and weakens drawdown risk of energy market prices

dynamic behaviors and measurements of financial market crash rate abstract this paper proposes the conditional crash rate ccr to study the degree of financial market crisis and evaluate the risk of financial market crash based on maximum drawdown and escape rate it is found that the ccr of stock price in financial market is equivalent to the escape rate of the drawdown time series corresponding to price series based on the mean escape rate the analytical solution of ccr of financial market of stock price described by black scholes model is obtained for the ccr empirical researches show that the theoretical results of the heston model are in good agreement with the results of the real financial data of the sp ii we can find critical phenomena resonance and inverse resonance behaviors in the function of ccr vs mean reversion of volatility ii the parameter variation induces the appearance of noise enhancement stability in the function of ccr vs amplitude of volatility fluctuation

on the section conjecture in anabelian geometry let x be a smooth projective curve of genus 1 over a field k which is finitely generated over the rationals the section conjecture in grothendieck s anabelian geometry says that the sections of the canonical projection from the arithmetic fundamental group of x onto the absolute galois group of k are up to conjugation in one to one correspondence with k rational points of x the birational variant conjectures a similar correspondence where the fundamental group is replaced by the absolute galois group of the function field k x the present paper proves the birational section conjecture for all x when k is replaced e g by the field of p adic numbers it disproves both conjectures for the field of real or p adic algebraic numbers and it gives a purely group theoretic characterization of the sections induced by k rational points of x in the birational setting over almost arbitrary fields as a biproduct we obtain galois theoretic criteria for radical solvability of polynomial equations in more than one variable and for a field to be pac to be large or to be hilbertian

a discrete time version for models of population dynamics in the presence of an infection we present a set of difference equations which represents the discrete counterpart of a large class of continuous model concerning the dynamics of an infection in an organism or in a host population the limiting behavior of the discrete model is studied and a threshold parameter playing the role of the basic reproduction number is derived

on the nesterov todd direction in semidefinite programming we study different choices of search direction for primal dual interior point methods for semidefinite programming problems one particular choice we consider comes from a specialization of a class of algorithms developed by nesterov and todd for certain convex programming problems we discuss how the search directions for the nesterov todd nt method can be computed efficiently and demonstrate how they can be viewed as newton directions this last observation also leads to convenient computation of accelerated steps using the mehrotra predictor corrector approach in the nt framework we also provide an analytical and numerical comparison of several methods using different search directions and suggest that the method using the nt direction is more robust than alternative methods

noise induced escape in an excitable system we consider the stochastic dynamics of escape in an excitable system the fitzhugh nagumo fhn neuronal model for different classes of excitability we discuss first the threshold structure of the fhn model as an example of a system without a saddle state we then develop a nonlinear nonlocal stability approach based on the theory of large fluctuations including a finite noise correction to describe noise induced escape in the excitable regime we show that the threshold structure is revealed via patterns of most probable optimal fluctuational paths the approach allows us to estimate the escape rate and the exit location distribution we compare the responses of a monostable resonator and monostable integrator to stochastic input signals and to a mixture of periodic and stochastic stimuli unlike the commonly used local analysis of the stable state our nonlocal approach based on optimal paths yields results that are in good agreement with direct numerical simulations of the langevin equation

stochastic resonance in a mono stable system with multiplicative and additive noise the stochastic resonance in a biased mono stable system subject to multiplicative and additive noise is investigated based on the adiabatic approximation theory the analytic expression of the signal to noise ratio snr is obtained it is shown that the snr is a non monotonic function of the intensities of the multiplicative and additive noise as well as the parameters of the mono stable system

a successive projection method it is of both theoretical and practical interest to find the projection of a point to the intersection of a finite number of closed convex sets by a sequence of projections to the individual sets successively in this paper we study such a method and analyze its convergence properties a main feature of the method is its capability to decompose the projection problem into several small ones for some structured sparse problems these small subproblems can be solved independently and the presented method has a potential use in parallel computation

exponential distribution of financial returns at mesoscopic time lags a new stylized fact we study the probability distribution of stock returns at mesoscopic time lags return horizons ranging from about an hour to about a month while at shorter microscopic time lags the distribution has power law tails for mesoscopic times the bulk of the distribution more than 99 of the probability follows an exponential law the slope of the exponential function is determined by the variance of returns which increases proportionally to the time lag at longer times the exponential law continuously evolves into gaussian distribution the exponential to gaussian crossover is well described by the analytical solution of the heston model with stochastic volatility r 2004 elsevier b v all rights reserved

escape times in fluctuating metastable potential and acceleration of diffusion in periodic fluctuating potentials abstract the problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered for the overdamped brownian particle moving in a piecewise linear dichotomously fluctuating metastable potential we obtain the mean first passage time as a function of the potential parameters the noise intensity and the mean rate of switchings of the dichotomous noise we find noise enhanced stability phenomenon in the system investigated and the parameter region of the fluctuating potential where the effect can be observed for the diffusion of the overdamped brownian particle in a fast fluctuating symmetric periodic potential we obtain that the effective diffusion coefficient depends on the mean first passage time as discovered for fixed periodic potential the effective diffusion coefficients for sawtooth sinusoidal and piecewise parabolic potentials are calculated in closed analytical form

mean field limit of systems with multiplicative noise a detailed study of the mean field solution of langevin equations with multiplicative noise is presented three different regimes depending on noise intensity weak intermediate and strong noise are identified by performing a self consistent calculation on a fully connected lattice the most interesting strong noise regime is shown to be intrinsically unstable with respect to the inclusion of fluctuations as a ginzburg criterion shows on the other hand the self consistent approach is shown to be valid only in the thermodynamic limit while for finite systems the critical behavior is found to be different in this last case the self consistent field itself is broadly distributed rather than taking a well defined mean value its fluctuations described by an effective zero dimensional multiplicative noise equation govern the critical properties these findings are obtained analytically for a fully connected graph and verified numerically both on fully connected graphs and on random regular networks the results presented here shed some doubt on what is the validity and meaning of a standard mean field approach in systems with multiplicative noise in finite dimensions where each site does not see an infinite number of neighbors but a finite one the implications of all this on the existence of a finite upper critical dimension for multiplicative noise and kardar parisi zhang problems are briefly discussed

stochastic resonance in a trapping overdamped monostable system the response of a trapping overdamped monostable system to a harmonic perturbation is analyzed in the context of stochastic resonance phenomenon we consider the dynamics of a brownian particle moving in a piecewise linear potential with a white gaussian noise source based on linear response theory and laplace transform technique analytical expressions of signal to noise ratio snr and signal power amplification spa are obtained we find that the snr is a nonmonotonic function of the noise intensity while the spa is monotonic theoretical results are compared with numerical simulations

the cuspidalisation of sections of arithmetic fundamental groups abstract in this paper which is a sequel to 7 we investigate the theory of cuspidalisation of sections of arithmetic fundamental groups of hyperbolic curves to cuspidally i th and 2 p th step prosolvable arithmetic fundamental groups as a consequence we exhibit two necessary and sufficient conditions for sections of arithmetic fundamental groups of hyperbolic curves over p adic local fields to arise from rational points we also exhibit a class of sections of arithmetic fundamental groups of p adic curves which are orthogonal to pic and which satisfy unconditionally one of the above conditions

arithmetic of p adic curves and sections of geometrically abelian fundamental groups let x be a proper smooth and geometrically connected curve of genus g x ge 1 over a p adic local field we prove that there exists an effectively computable open affine subscheme u subset x with the property that text period x 1 and text index x equals 1 or 2 resp text period x text index x 1 assuming text period x text index x if resp if and only if the exact sequence of the geometrically abelian fundamental group of usplits we compute the torsor of splittings of the exact sequence of the geometrically abelian absolute galois group associated to x and give a new characterisation of sections of arithmetic fundamental groups of curves over p adic local fields which are orthogonal to text pic 0 resp text pic wedge as a consequence we observe that the non geometric geometrically pro p section constructed by hoshi 3 is orthogonal to text pic 0

the influences of delay time on the stability of a market model with stochastic volatility abstract the effects of the delay time on the stability of a market model are investigated by using a modified heston model with a cubic nonlinearity and cross correlated noise sources these results indicate that i there is an optimal delay time o which maximally enhances the stability of the stock price under strong demand elasticity of stock price and maximally reduces the stability of the stock price under weak demand elasticity of stock price ii the cross correlation coefficient of noises and the delay time play an opposite role on the stability for the case of the delay time o and the same role for the case of the delay time o moreover the probability density function of the escape time of stock price returns the probability density function of the returns and the correlation function of the returns are compared with other literatures

on abelian birational sections for a smooth and geometrically irreducible variety x over a field k the quotient of the absolute galois group gk x by the commutator subgroup of g k x projects onto gk we investigate the sections of this projection we show that such sections correspond to infinite divisions of the elementary obstruction of colliot thelene and sansuc if k is a number field and the tate shafarevich group of the picard variety of x is finite then such sections exist if and only if the elementary obstruction vanishes for curves this condition also amounts to the existence of divisors of degree 1 finally we show that the vanishing of the elementary obstruction is not preserved by extensions of scalars

statistics of the occupation time of renewal processes we present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time according to the nature of the distribution of time intervals the probability density functions of these random variables have very different scalings in time we analyze successively the cases where this distribution is narrow where it is broad with index 1 and finally where it is broad with index 1 2 the methods introduced in this work provide a basis for the investigation of the statistics of the occupation time of more complex stochastic processes see joint paper by g de smedt c godreche and j m luck 26

the elementary obstruction and homogeneous spaces let k be a field of characteristic zero and let k be an algebraic closure of k for a geometrically integral variety x over k we write k x for the function field of x x k k if x has a smooth k point the natural embedding of multiplicative groups k k x admits a galois equivariant retraction in the first part of this article equivalent conditions to the existence of such a retraction are given over local and then over global fields those conditions are expressed in terms of the brauer group of x in the second part of the article we restrict attention to varieties that are homogeneous spaces of connected but otherwise arbitrary algebraic groups with connected geometric stabilizers for k local or global and for such a variety x in many situations but not all the existence of a galois equivariant retraction to k k x ensures the existence of a k rational point on x for homogeneous spaces of linear algebraic groups the technique also handles the case where k is the function field of a complex surface resume soient k un corps de caracteristique nulle et k une cloture algebrique de k pour une k variete x geometriquement integre on note k x le corps des fonctions de x x k k si x possede un k point lisse le plongement naturel de groupes multiplicatifs k k x admet une retraction equivariante pour l action du groupe de galois de k sur k dans la premiere partie de l article sur les corps locaux puis sur les corps globaux on donne des conditions equivalentes a l existence d une telle retraction equivariante ces conditions s expriment en terme du groupe de brauer de la variete x dans la seconde partie de l article on considere le cas des espaces homogenes de groupes algebriques connexes non necessairement lineaires avec groupes d isotropie duke mathematical journal vol 141 no 2 c 2008 received 6 november 2006 revision received 23 april 2007 2000 mathematics subject classification primary 14g05 11g99 12g05 secondary 11e72 14f22 14k15

aging and rejuvenation with fractional derivatives we discuss a dynamic procedure that makes fractional derivatives emerge in the time asymptotic limit of non poisson processes we find that two state fluctuations with an inverse power law distribution of waiting times finite first moment and divergent second moment namely with the power indexm in the interval 2 m 3 yield a generalized master equation equivalent to the sum of an ordinary markov contribution and a fractional derivative term we show that the order of the fractional derivative depends on the age of the process under study if the system is infinitely old the order of the fractional derivative o is given by o 3 m a brand new system is characterized by the degree o m 2 if the system is prepared at time ta 0 and the observation begins at time t 0 we derive the following scenario for times 0 t ta the system is satisfactorily described by the fractional derivative with o 3 m upon time increase the system undergoes a rejuvenation process that in the time limit t ta yields o m 2 the intermediate time regime is probably incompatible with a picture based on fractional derivatives or at least with a mono order fractional derivative

colored noise induced discontinuous transitions in symbiotic ecosystems a symbiotic ecosystem is studied by means of the lotka volterra stochastic model using the generalized verhulst self regulation the effect of fluctuating environment on the carrying capacity of a population is taken into account as dichotomous noise the study is a follow up of our investigation of symbiotic ecosystems subjected to three level trichotomous noise r mankin a ainsaar a haljas and e reiter phys rev e 65 051108 2002 relying on the mean field theory an exact self consistency equation for stationary states is derived in some cases the mean field exhibits hysteresis as a function of noise parameters it is established that random interactions with the environment can cause discontinuous transitions the dependence of the critical coupling strengths on the noise parameters is found and illustrated by phase diagrams predictions from the mean field theory are compared with the results of numerical simulations our results provide a possible scenario for catastrophic shifts of population sizes observed in nature

effect of time delay in fitzhugh nagumo neural model with correlations between multiplicative and additive noises abstract we study the effect of time delay in the fitzhugh nagumo neural model with correlations between multiplicative and additive noise terms based on the corresponding fokker planck equation the explicit expressions of the stationary probability distribution function spdf the mean first passage time mfpt and the signal to noise ratio snr are obtained respectively research results show that i the system undergoes a succession of two phase transitions i e the reentrance phenomenon as the noise correlation parameter is increased and a single phase transition as the time delay is increased ii the mfpt as a function of the multiplicative noise intensity exhibits a maximum this maximum for mfpt identifies the noise enhanced stability nes effect the noise correlation parameter intensifies the nes effect while the time delay and the additive noise intensity weakens it iii the existence of a maximum in the snr as a function of the multiplicative noise intensity is the identifying characteristic of the stochastic resonance sr phenomenon the noise correlation parameter enhances the sr while the time delay and the additive noise intensity weaken it

stability measures in metastable states with gaussian colored noise we present a study of the escape time from a metastable state of an overdamped brownian particle in the presence of colored noise generated by ornstein uhlenbeck process we analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity we observe the noise enhanced stability effect for all the initial unstable states used and for all values of the correlation time tau c investigated we can distinguish two dynamical regimes characterized by weak and strong correlated noises depending on the value of tau c with respect to the relaxation time of the system

the roles of mean residence time on herd behavior in a financial market abstract we investigate the herd behavior of stock prices in a finance system with the heston model based on parameter estimation of the heston model obtained by minimizing the mean square deviation between the theoretical and empirical return distributions we simulate mean residence time of positive return mrtpr plots of mrtpr against the amplitude or mean reversion of volatility demonstrate a phenomenon of herd behavior for a positive cross correlation between noise sources of the heston model also for a negative cross correlation a phenomenon of herd behavior is observed in plots of mrtpr against the long run variance by increasing amplitude or mean reversion of volatility

stability in a system subject to noise with regulated periodicity the stability of a simple dynamical system subject to multiplicative one side pulse noise with hidden periodicity is investigated both analytically and numerically the stability analysis is based on the exact result for the characteristic functional of the renewal pulse process the influence of the memory effects on the stability condition is analyzed for two cases i the dead time distorted poissonian process and ii the renewal process with pareto distribution we show that for fixed noise intensity the system can be stable when the noise is characterized by high periodicity and unstable at low periodicity

local global principles for 1 motives building upon our arithmetic duality theorems for 1 motives we prove that the manin obstruction related to a finite subquotient x of the brauer group is the only obstruction to the hasse principle for rational points on torsors under semiabelian varieties over a number field assuming the finiteness of the tate shafarevich group of the abelian quotient this theorem answers a question by skorobogatov in the semiabelian case and is a key ingredient of recent work on the elementary obstruction for homogeneous spaces over number fields we also establish a cassels tate type dual exact sequence for 1 motives and give an application to weak approximation

sizing and least change secant methods oren and luenberger introduced in 1974 a strategy for replacing hessian approximations by their scalar multiples and then performing quasi newton updates generally least change secant updates such as the bfgs or dfp updates oren and luenberger management sci 20 1974 pp 845 862 in this paper the function omega a left frac operatorname trace a n operatorname det a 1 n right is shown to be a measure of change with a direct connection to the oren luenberger strategy this measure is interesting because it is related to the ell 2 condition number but it takes all the eigenvalues of a into account rather than just the extremes if the class of possible updates is restricted to the broyden class i e scalar premultiples are not allowed then the optimal update depends on the dimension of the problem it may or may not be in the convex class but it becomes the bfgs update as the dimension increases this seems to be yet another explanation for why

theory of stochastic resonance for small signals in weakly damped bistable oscillators the response of a weakly damped bistable oscillator to an external periodic force is considered theoretically in the approximation of weak signals we can write a linearized equation for the signal and the corresponding nonlinear equation for the noise these equations contain two unknown parameters an effective stiffness and an additional damping factor in the case of the weakly damped bistable oscillator considered here the two dimensional fokker planck equation corresponding to the equation for the noise can be solved approximately by changing to a slow variable energy and applying a method of successive approximation this approach allows us to find the unknown parameters and to calculate the amplitude ratio of the output and input signals i e the gain factor

solving hankel matrix approximation problem using semidefinite programming positive semidefinite hankel matrices arise in many important applications some of their properties may be lost due to rounding or truncation errors incurred during evaluation the problem is to find the nearest matrix to a given matrix to retrieve these properties the problem is converted into a semidefinite programming problem as well as a problem comprising a semidefined program and second order cone problem the duality and optimality conditions are obtained and the primal dual algorithm is outlined explicit expressions for a diagonal preconditioned and crossover criteria have been presented computational results are presented a possibility for further improvement is indicated

solving semidefinite quadratic linear programs using sdpt3 this paper discusses computational experiments with linear optimization problems involving semidefinite quadratic and linear cone constraints sqlps many test problems of this type are solved using a new release of sdpt3 a matlab implementation of infeasible primal dual path following algorithms the software developed by the authors uses mehrotra type predictor corrector variants of interior point methods and two types of search directions the hkm and nt directions a discussion of implementation details is provided and computational results on problems from the sdplib and dimacs challenge collections are reported

galois sections for abelianized fundamental groups given a smooth projective curve x of genus at least 2 over a number field k grothendieck s section conjecture predicts that the canonical projection from the etale fundamental group of x onto the absolute galois group of k has a section if and only if the curve has a rational point we show that there exist curves where the above map has a section over each completion of k but not over k in the appendix victor flynn gives explicit examples in genus 2 our result is a consequence of a more general investigation of the existence of sections for the projection of the etale fundamental group with abelianized geometric part onto the galois group we also point out the relation to the elementary obstruction of colliot thelene and sansuc

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

angular factorization of matrices let q denote a selfadjoint matrix or operator of finite rank the factorization of i q into the form i q i w d i w is considered the well known case where w is constrained to be lower triangular while d is diagonal is extended to quadrangular and other generalized canonical forms the case where q is not selfadjoint is also developed applications for these results may be found in the realm of multivariate stochastic approximation and signal extraction

linear response to perturbation of nonexponential renewal process a generalized master equation approach the work by barbi bologna and grigolini phys rev lett 95 220601 2005 discusses a response to alternating external field of a non markovian two state system where the waiting time between the two attempted changes of state follows a power law it introduced a new instrument for description of such situations based on a stochastic master equation with reset in the present brief report we provide an alternative description of the situation within the framework of a generalized master equation the results of our analytical approach are corroborated by direct numerical simulations of the system

linear and nonlinear experimental regimes of stochastic resonance we investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode the experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an interval of values spanning several orders of magnitude we observe both a regime described by the linear response theory and the nonlinear deviation from it in the nonlinear regime we detect saturation of the power spectral density of the output signal detected at the frequency of the modulating signal and a dip in the noise level of the same spectral density when these effects are observed we detect a phase and frequency synchronization between the stochastic output and the deterministic input

effects of time delay on transient behavior of a time delayed metastable system subjected to cross correlated noises abstract the effects of time delay on the transient properties of a time delayed metastable system subjected to cross correlated noises are studied by means of a stochastic simulation method it is found that i both additive noise and multiplicative noise can produce the noise enhanced stability nes effect ii the time delay induces critical behavior on the nes i e there is a critical value of the delay time c 1 2 2 above which the time delay increases the stability of the system enhanced by the additive noise and below which the nes effect induced by the additive noise disappears iii there exists another critical value of the delay time c 2 3 0 above which the time delay increases the stability of the system enhanced by the multiplicative noise and below which the time delay decreases it

dynamics of two competing species in the presence of levy noise sources we consider a lotka volterra system of two competing species subject to multiplicative stable levy noise the interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence both of a periodic driving term and an additive stable levy noise we study the species dynamics which is characterized by two different regimes exclusion of one species and coexistence of both we find quasiperiodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species analyzing the role of the levy noise sources

the role of abstract algebra in structured estimation theory an attempt is made to formalize both structured covariance estimation and autoregressive process parameter estimation in terms of the underlying abstract jordan algebra an algebra that differs from the usual noncommutative but associative matrix algebra the investigation puts one on a firm footing from which to attack future problems in statistical signal processing rather in the same manner that the introduction of lie algebra and lie groups in control theory made a variety of new ideas and developments possible

noise enhanced stability of periodically driven metastable states we study the effect of noise enhanced stability of periodically driven metastable states in a system described by piecewise linear potential we find that the growing of the average escape time with the intensity of the noise is depending on the initial condition of the system we analytically obtain the condition for the noise enhanced stability effect and verify it by numerical simulations

roles of capital flow on the stability of a market system abstract the roles of capital flow in an ensemble composed of sub markets are investigated a modified heston model and recycled noises are employed to describe the dynamics of stock price and capital flow in the ensemble respectively the mean escape times of two sub markets with a cubic nonlinearity are calculated by using numerical simulation the results evidence that i there is a worst delay time or rate of capital inflow concerning the minimal stability of stock price and an optimal delay time or rate of capital outflow concerning the maximal stability of stock price when 0 denotes strength of correlation between two wiener processes of the stock price and the volatility ii when 0 the stability of stock price is maximally enhanced by an optimal delay time or rate of capital inflow and reduced by a worst rate of capital outflow but monotonously strengthened by delay time of capital outflow

coherence resonance like and efficiency of financial market abstract we study the coherent resonance phenomenon of stock market returns and volatility and discuss the effectiveness of financial market based on the coherent resonance theory of statistical physics in this paper we use the heston model to give the series describing the return and volatility considering the limited data of csi 300 index the bayesian estimation parameters of the proposed model are given by combining bayesian parameter estimation and realized volatility the characteristic correlation time cct and normalized fluctuations of pulse durations r p are employed to further explore the coherent resonance behavior of stock market price returns and volatility based on the stochastic simulation of the estimated parameters we can observe the phenomena of coherent resonance like and anti coherent resonance in cct and r p as a function of long run variance and amplitude of volatility we can also observe the critical phenomenon there is a critical mean reversion of volatility on both sides of the critical value the opposite characteristics of coherent and anti coherent resonance can be observed the enhanced long run variance of volatility and weakened amplitude of volatility both cause coherent like resonance in cct and r p vs the mean reversion of volatility in addition it can be seen that the market efficiency is lower when coherent resonance occurs and higher when anti coherence resonance occurs

an algorithm for restricted least squares regression abstract a commonly occurring problem in statistics is that of minimizing a least squares expression subject to side constraints here a simple iterative algorithm is presented and shown to converge to the desired solution several examples are presented including finding the closest concave convex function to a set of points and other general quadratic programming problems the dual problem to the basic problem is also discussed and a solution for it is given in terms of the algorithm finally extensions to expressions other than least squares are given

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

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

resonant activation in piecewise linear asymmetric potentials this work analyzes numerically the role played by the asymmetry of a piecewise linear potential in the presence of both a gaussian white noise and a dichotomous noise on the resonant activation phenomenon the features of the asymmetry of the potential barrier arise by investigating the stochastic transitions far behind the potential maximum from the initial well to the bottom of the adjacent potential well because of the asymmetry of the potential profile together with the random external force uniform in space we find for the different asymmetries 1 an inversion of the curves of the mean first passage time in the resonant region of the correlation time of the dichotomous noise for low thermal noise intensities 2 a maximum of the mean velocity of the brownian particle as a function of and 3 an inversion of the curves of the mean velocity and a very weak current reversal in the miniratchet system obtained with the asymmetrical potential profiles investigated an inversion of the mean first passage time curves is also observed by varying the amplitude of the dichotomous noise behavior confirmed by recent experiments

escape problem under stochastic volatility the heston model we solve the escape problem for the heston random diffusion model from a finite interval of span l we obtain exact expressions for the survival probability which amounts to solving the complete escape problem as well as for the mean exit time we also average the volatility in order to work out the problem for the return alone regardless of volatility we consider these results in terms of the dimensionless normal level of volatility a ratio of the three parameters that appear in the heston model and analyze their form in several asymptotic limits thus for instance we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower depending on the value of the normal level we compare our results with those of the wiener process and show that the assumption of stochastic volatility in an apparently paradoxical way increases survival and prolongs the escape time we finally observe that the model is able to describe the main exit time statistics of the dow jones daily index

periodic trend and fluctuations the case of strong correlation abstract we study the effects of an external periodic perturbation on a poisson rate process with special attention to the perturbation induced sojourn time patterns we show that these patterns correspond to turning a memory less sequence into a sequence with memory the memory effects are stronger the slower the perturbation the adoption of a de trending technique applied with no caution might generate the impression that no fluctuation periodicity correlation exists we find that this is due to the fact that the perturbation induced memory is a global property and that the result of a local in time analysis would not find any memory effect insofar as the process under study is locally a poisson process we find that an efficient way to detect this memory effect is to analyze the moduli of the de trended sequence we turn the sequence to analyze into a diffusion process and we evaluate the shannon entropy of the resulting diffusion process we find that both the original sequence and the suitably processed de trended sequence yield the same dependence of entropy on time namely an initial scaling larger than ordinary scaling and a sequel of weak oscillations which are a clear signature of the external perturbation in both cases this is a clear indication of the fluctuation periodicity correlation

statistics of residence time for levy flights in unstable parabolic potentials we analyze the residence time problem for an arbitrary markovian process describing nonlinear systems without a steady state we obtain exact analytical results for the statistical characteristics of the residence time for diffusion in a fully unstable potential profile in the presence of levy noise we get the conditional probability density of the particle position and the average residence time the noise enhanced stability phenomenon is observed in the system investigated results from numerical simulations are in very good agreement with analytical ones

multiple cross correlation noise induced transition in a stochastic bistable system abstract based on the stochastic equivalent rules the fokker planck equation for a general one dimensional nonlinear system subjected to n component noises and cross correlation noises is derived and the greatest advantage of the method lies in its simplicity applying this method the effects of multiple sources of noise and the correlation forms of noises among them i e two multiplicative noises an additive noise and the correlation between the three noises on the steady state properties and the mean first passage time mfpt of a stochastic bistable system are discussed in details the results show rich transition phenomena such as the reentrance like noise induced phenomenon and the switch between the bimodal and the unimodal structure for different noise intensities moreover the effects of the cross correlation among the three noise sources on the mfpt are also discussed and the noise enhanced stability phenomenon and the resonant activation phenomenon are observed the numerical results are in basic agreement with the theoretical predictions

variety and volatility in financial markets we study the price dynamics of stocks traded in a financial market by considering the statistical properties of both a single time series and an ensemble of stocks traded simultaneously we use the n stocks traded on the new york stock exchange to form a statistical ensemble of daily stock returns for each trading day of our database we study the ensemble return distribution we find that a typical ensemble return distribution exists in most of the trading days with the exception of crash and rally days and of the days following these extreme events we analyze each ensemble return distribution by extracting its first two central moments we observe that these moments fluctuate in time and are stochastic processes themselves we characterize the statistical properties of ensemble return distribution central moments by investigating their probability density functions and temporal correlation properties in general time averaged and portfolio averaged price returns have different statistical properties we infer from these differences information about the relative strength of correlation between stocks and between different trading days last we compare our empirical results with those predicted by the single index model and we conclude that this simple model cannot explain the statistical properties of the second moment of the ensemble return distribution

different delays induced regime shifts in a stochastic insect outbreak dynamics abstract considering time delays in the deterministic and stochastic forces we construct stochastic delayed differential equations to investigate the regime shifts in an insect ecosystem the stationary probability distribution spd and mean first passage time mfpt are obtained respectively our main results show i the multiplicative noise positive cross correlation noise between two noises and time delays can induce the regime shifts from the boom outbreak state to the bust one but the additive noise and negative cross correlation can induce the regime shifts from the bust outbreak state to the boom one ii for the negative cross correlation the mfpt as a function of noise strengths exhibits one maximum which shows the characteristic of the noise delayed switching for the boom outbreak state but for the no cross correlation or positive cross correlation the mfpt decreases with the noise strengths iii two different types of time delays play same roles on the maximal mfpt with additive noise and play opposite roles on the maximal mfpt with multiplicative noise the mechanisms for noises and delays induced regime shifts between two states can be explained physically through the effective potential of ecological model

smallest eigenvalues of hankel matrices for exponential weights abstract we obtain the rate of decay of the smallest eigenvalue of the hankel matrices i t j k w 2 t dt j k 0 n for a general class of even exponential weights w2 exp 2q on an interval i more precise asymptotics for more special weights have been obtained by many authors