coupled map lattices with complex order parameter abstract we introduce and study coupled map lattices with complex state variable the dynamical regimes of the finite length systems are classified naturally in terms of a topological invariant the overall phase shift accumulated along the whole length at fixed time a stability analysis of the spatially uniform states is presented and the results of numerical simulations of the spatio temporal dynamics are discussed we demonstrate that fast amplitude evolution including regular and chaotic spatio temporal behavior takes place on the background of a slower phase evolution for large values of the topological invariant the phase dynamics may give rise to an instability which in some cases results in a jump of the system to another value of the invariant we also consider the formation of long lived bubbles i e local domains of complicated dynamics in the spatial regions of locally reduced phase gradient our coupled map lattice model and its generalizations may be useful for understanding the dynamics in a larger range of parameters for such nonlinear dissipative media which allow small amplitude description in terms of the complex ginzburg landau equation as well as for time delay feedback systems with nonzero central frequency of the generated signal

continuity of gaussian local times continuity in the time parameter is considered for a natural version of the local time for stationary gaussian processes bounds are given for the local and uniform modulus of continuity which are applicable in cases not covered by kono notably when the incremental variance is a regularly varying function of index two

stochastic system with colored correlation between white noise and colored noise abstract a stochastic system with colored correlation between white noise and colored noise is investigated theoretically a general fokker planck equation of the system is derived by using a standard method we discuss a bistable system with colored correlation between additive white noise and multiplicative colored one it is found that the effects of the correlation time of multiplicative colored noise on the statistical properties of the bistable system are different from those of the correlation time of the correlation between additive white noise and multiplicative colored noise on the statistical properties of the bistable system

pattern recognition by affine moment invariants abstract the paper deals with moment invariants which are invariant under general affine transformation and may be used for recognition of affine deformed objects our approach is based on the theory of algebraic invariants the invariants from second and third order moments are derived and shown to be complete the paper is a significant extension and generalization of recent works several numerical experiments dealing with pattern recognition by means of the affine moment invariants as the features are described

regularity of local times of random fields abstract in this paper we study the fractional smoothness of local times of general processes starting from the occupation time formula and obtain the quasi sure existence of local times in the sense of the malliavin calculus this general result is then applied to the local times of n parameter d dimensional brownian motions fractional brownian motions and the self intersection local time of the 2 dimensional brownian motion as well as smooth semimartingales

projection based polygonality measurement measuring the degree to which a shape resembles a polygon referred to as polygonality is a difficult problem due to the intrinsic diversity in the form and distortion of shapes caused by digitization and similarity transformation this paper proposes a generic approach for this problem by performing the measurement in the projection space where the radon image of some primitive shapes which compose the shape becomes apparent the obtained measures take value in 0 1 with 1 corresponding to analytical polygons they are robust to additive noise and boundary distortion and is invariant to similarity transformation the new framework generalizes existing polygonal measures such as triangularity and quadrangularity in addition the ability to estimate polygon s geometric quantities in the projection space allows approximating a shape by analytical polygons the efficiency of the proposed approach is demonstrated through a number of experiments on both synthetic and real data sets

a new convexity measure based on a probabilistic interpretation of images in this paper we present a novel convexity measure for object shape analysis the proposed method is based on the idea of generating pairs of points from a set and measuring the probability that a point dividing the corresponding line segments belongs to the same set the measure is directly applicable to image functions representing shapes and also to gray scale images which approximate image binarizations the approach introduced gives rise to a variety of convexity measures which make it possible to obtain more information about the object shape the proposed measure turns out to be easy to implement using the fast fourier transform and we would consider this in detail finally we illustrate the behavior of our measure in different situations and compare it to other similar ones

theoreme central limite pour l intersection de deux saucisses de wiener independantes j f le gall 4 proved thatn2 times the volume of the intersection of two independent wiener sausages in 3 with radius 1 n converges inl2 asn towards a multiple of the intersection local time at 0 for the underlying brownian motions

measuring shapes with desired convex polygons in this paper we have developed a family of shape measures all the measures from the family evaluate the degree to which a shape looks like a predefined convex polygon a quite new approach in designing object shape based measures has been applied in most cases such measures were defined by exploiting some shape properties such properties are optimized e g maximized or minimized by certain shapes and based on this the new shape measures were defined an illustrative example might be the shape circularity measure derived by exploiting the well known result that the circle has the largest area among all the shapes with the same perimeter of course there are many more such examples e g ellipticity linearity elongation and squareness measures are some of them there are different approaches as well in the approach applied here no desired property is needed and no optimizing shape has to be found we start from a desired convex polygon and develop the related shape measure the method also allows a tuning parameter thus there is a new 2 fold family of shape measures dependent on a predefined convex polygon and a tuning parameter that controls the measure s behavior the measures obtained range over the interval 0 1 and pick the maximal possible value equal to 1 if and only if the measured shape coincides with the selected convex polygon that was used to develop the particular measure all the measures are invariant with respect to translations rotations and scaling transformations an extension of the method leads to a family of new shape convexity measures

the influence of noise on the logistic model the behavior of the logistic system which is generated by the functionf x ax 1 x changes in an interesting way if it is perturbed by external noise it turns out that the chaotic behavior which was predicted by li and yorke for orbits of period 3 becomes visible and that a sequence of mergence transitions occurs at the critical parameter the change of the invariant probability density and the lyapunov exponents are examined numerically the power spectrum for the period 3 orbit for different fluctuations is calculated and a recursion formula for the time evolution of the probability density is presented as a discrete time analog of a chapman kolmogorov equation

exactly solvable nonlinear model with two multiplicative gaussian colored noises abstract an overdamped system with a linear restoring force and two multiplicative colored noises is considered noise amplitudes depend on the system state x as x and x an exactly soluble model of a system is constructed due to consideration of a specific relation between noises exact expressions for the time dependent univariate probability distribution function and the fractional moments are derived their long time asymptotic behavior is investigated analytically it is shown that anomalous diffusion and stochastic localization of particles not subjected to a restoring force can occur

approximate fokker planck equation of system driven by multiplicative colored noises with colored cross correlation abstract using the hanggi ansatz to truncate the evolution equation for probability density an approximate fokker planck equation afpe is derived this afpe is valid for one dimensional general systems driven by two multiplicative colored noises 1 0 and 2 0 that are correlated in color 3 0 under the condition for 1 2 and 3 to satisfy some inequalities we apply this afpe to a symmetrical bistable potential system driven by a colored multiplicative noise and a white additive noise with white cross correlation to verify the validity of our analytical approximation the numerical simulations for this system is performed we discovered a new phenomenon that the symmetry of stationary probability density broken by the correlation between the noises can be gradually recovered as the noise self correlation time is increased

an efficiently computable metric for comparing polygonal shapes a method for comparing polygons that is a metric invariant under translation rotation and change of scale reasonably easy to compute and intuitive is presented the method is based on the l sub 2 distance between the turning functions of the two polygons it works for both convex and nonconvex polygons and runs in time o mn log mn where m is the number of vertices in one polygon and n is the number of vertices in the other some examples showing that the method produces answers that are intuitively reasonable are presented

effects of self correlation time and cross correlation time of additive and multiplicative colored noises for dynamical properties of a bistable system considering a bistable system driven by additive and multiplicative colored noises with colored cross correlation we obtain the analytic expressions of the stationary probability distribution pst x the linear relaxation time tc and the correlated function c s the effects of the noise intensity the self correlation time and the cross correlation time for the bistable system are discussed the noise intensity d speeds up relaxation of the system from unstable points which when d q the effects are damped the self correlation time 1 and 2 make the stationary probability distribution of the dynamical variable x be shaper and speed up the fluctuation decay of the dynamical variable x on the contrary the cross correlation time 3 makes the stationary probability distribution of the dynamical variable x be flatter and slows down the fluctuation decay of the dynamical variable x the effect of the self correlation time is more projecting than the effect of the cross correlation time

measuring linearity of planar point sets our goal is to design algorithms that give a linearity measure for planar point sets there is no explicit discussion on linearity in literature although some existing shape measures may be adapted we are interested in linearity measures which are invariant to rotation scaling and translation these linearity measures should also be calculated very quickly and be resistant to protrusions in the data set the measures of eccentricity and contour smoothness were adapted from literature the other five being triangle heights triangle perimeters rotation correlation average orientations and ellipse axis ratio the algorithms are tested on 30 sample curves and the results are compared against the linear classifications of these curves by human subjects it is found that humans and computers typically easily identify sets of points that are clearly linear and sets of points that are clearly not linear they have trouble measuring sets of points which are in the gray area in between although they appear to be conceptually very different approaches we prove theoretically and experimentally that eccentricity and rotation correlation yield exactly the same linearity measurements they however provide results which are furthest from human measurements the average orientations method provides the closest results to human perception while the other algorithms proved themselves to be very competitive

synchronization induced by periodic inputs in finite n unit bistable langevin models the augmented moment method we have studied the synchronization induced by periodic inputs applied to a finite n unit coupled bistable langevin model which is subjected to cross correlated additive and multiplicative noises the effects on the synchronization of the system size n the coupling strength and the cross correlation between additive and multiplicative noise have been investigated using the semi analytical augmented moment method amm which is a second order moment approximation for local and global variables h hasegawa phys rev e 67 2003 041903 a linear analysis of the stationary solution of the amm equations shows that the stability is improved degraded by positive negative couplings results of the nonlinear bistable langevin model are compared to those of the linear langevin model

proprietes d intersection des marches aleatoires i convergence vers le temps local d intersection we study intersection properties of multi dimensional random walks letx andy be two independent random walks with values in d d 3 satisfying suitable moment assumptions and letin denote the number of common points to the paths ofx andy up to timen the sequence in suitably normalized is shown to converge in distribution towards the intersection local time of two independent brownian motions results are applied to the proof of a central limit theorem for the range of a two dimensional recurrent random walk thus answering a question raised by n c jain and w e pruitt

a local time approach to the self intersections of brownian paths in space we study the brownian functional alpha x b int limits b int delta x w t w s dsdt wherewt is a brownian path in two or three dimensions forb off the diagonal we identify x b with a local time and establish the holder continuity of x b in bothx andb

effect of multiplicative and additive noise on genetic transcriptional regulatory mechanism abstract a multiplicative noise and an additive noise are introduced in the kinetic model of smolen baxter byrne p smolen d a baxter j h byrne amer j physiol cell physiol 274 1998 531 in which the expression of gene is controlled by protein concentration of transcriptional activator the fokker planck equation is solved and the steady state probability distribution is obtained numerically it is found that the multiplicative noise converts the bistability to monostability that can be regarded as a noise induced transition the additive noise reduces the transcription efficiency the correlation between the multiplicative noise and the additive noise works as a genetic switch and regulates the gene transcription effectively

harmonic analysis of additive levy processes let x1 xn denote n independent d dimensional levy processes and consider the n parameter random field mathfrak x t x 1 t 1 cdots x n t n first we demonstrate that for all nonrandom borel sets f subseteq bf r d the minkowski sum mathfrak x bf r n oplus f of the range mathfrak x bf r n of mathfrak x with f can have positive d dimensional lebesgue measure if and only if a certain capacity of f is positive this improves our earlier joint effort with yuquan zhong by removing a certain condition of symmetry in khoshnevisan et al ann probab 31 2 1097 1141 2003 moreover we show that under mild regularity conditions our necessary and sufficient condition can be recast in terms of one potential densities this rests on developing results in classical non probabilistic harmonic analysis that might be of independent interest as was shown in khoshnevisan et al ann probab 31 2 1097 1141 2003 the potential theory of the type studied here has a large number of consequences in the theory of levy processes presently we highlight a few new consequences

sur la saucisse de wiener et les points multiples du mouvement brownien on considere b t t 0 un mouvement brownien a valeurs dans l espace euclidien a d dimensions r d d 2 issu de o on s interesse a la probabilite que b penetre avant un instant donne t dans une petite boule de l espace

the intersection local time of the westwater process in this paper self intersection properties of the westwater process are investigated as a result we obtain that the westwater process has an intersection local time bar alpha x 0 s t 1 which is holder continuous with respect tox s t r3 0 1 2 1 2 1 and the hausdorff dimension of the double time set is 1 2 as for brownian motion inr3

stochastic resonance in an asymmetric bistable system with coloured noises and periodic rectangular signal abstract in this paper we consider the phenomenon of stochastic resonance sr in an asymmetric bistable system with coloured noises and periodic rectangular signal expression of the signal to noise ratio snr has been obtained under the adiabatic limit we investigate the effect of any system parameter such as p q r 1 2 on the snr the plot of snr 1 shows sr for some values of the additive noise self correlation time 2 but not for the whole range of 2 the system bias r suppresses the snr when the intensity of additive noise q is increased the sr phenomenon disappears in the plot of snr p but the plot of snr q presents sr for almost all values of the multiplicative noise intensity p

colored noise enhanced stability in a tumor cell growth system under immune response in this paper we investigate a mathematical model for describing the growth of tumor cell under immune response which is driven by cross correlation between multiplicative and additive colored noises as well as the nonzero cross correlation in between the expression of the mean first passage time mfpt is obtained by virtue of the steepest descent approximation it is found i when the noises are negatively cross correlated 0 then the escape is slower than in the case with no correlation moreover in the case of positive cross correlation the escape time has a maximum for a certain intensity of one of the noises i e the maximum for mfpt identifies the noise enhanced stability of the cancer state ii the effect of the cross correlation time 3 on the mfpt is completely opposite for 0 and 0 iii the self correlation times 1 and 2 of colored noises can enhance stability of the cancer state while the immune rate can reduce it

hydrodynamic friction and the capacitance of arbitrarily shaped objects the translational friction coefficient and the capacitance of a variety of objects are calculated with a probabilistic method involving hitting the probed objects with random walks launched from an enclosing spherical surface this method is applied to exactly solvable examples to test the program accuracy and to physically important and analytically intractable examples cube chain of spheres at the vertices of self avoiding and random walks etc large fluctuations in the friction of polymer chains with a random coil structure are found to give large deviations from the mean field kirkwood riseman theory and hydrodynamic fluctuation effects are found to diminish with the chain swelling accompanying excluded volume interaction capacity applications are reviewed and our probabilistic estimates of polymer friction are compared with previous calculations using alternative methods transients to the capacity and related properties are expressed in terms of fluctuations in the wiener sausage volume volume swept out by a brownian particle where a repeated visit to a spatial region does not contribute to the volume increase in time

self intersection local times occupation fields and stochastic integrals where functions 6 converge to 6 as jo it turns out that b d co for every open set d which intersects with the diagonal t t2 however varadhan v has shown that b d u log s converges to a finite limit as e jo if d 0 s t u rosen r2 has found an expression for the limit in terms 1 of ito s stochastic integrals the integrals 0 1 and their renormalizations have been studied also in y 1 l 1 l2 and for the brownian motion in lr3 in rl r3 w y23 0 2 in this paper we investigate more general self intersection local times

internal fluctuations period doubling and chemical chaos the effects of internal molecular fluctuations on period doubling bifurcations and chaotic band merging are studied in a well stirred reactive chemical system where spatial degrees of freedom play no role the calculations are carried out using a stochastic model based on reactive lattice gas cellular automata molecular fluctuations arising from reactive collisions are incorporated in the model and the mass action rate equations are recovered in the mean field limit large system sizes can be studied and permit the investigation of the internal noise scaling structure in the periodic and chaotic regimes for the willamowski r ossler system the noise scaling exponent is consistent with that found for one dimensional quadratic maps subject to external noise the model provides a means to study small non equilibrium reacting systems where fluctuations may not be neglected

reactive lattice gas automata abstract a probabilistic lattice gas cellular automaton model of a chemically reacting system is constructed microdynamical equations for the evolution of the system are given the continuous and discrete boltzmann equations are developed and their reduction to a generalized reaction diffusion equation is discussed the microscopic reactive dynamics is consistent with any polynomial rate law up to the fourth order in the average particle density it is shown how several microscopic ca rules are consistent with a given rate law as most ca systems the present one has spurious properties whose effects are shown to be unimportant under appropriate conditions as an explicit example of the general formalism a ca dynamics is constructed for an autocatalytic reactive scheme known as the schlogl model simulations show that in spite of the simplicity of the underlying discrete dynamics the model exhibits the phase separation and wave propagation phenomena expected for this system because of the microscopic nature of the dynamics the role of internal fluctuations on the evolution process can be investigated

the measurement of circularity and ellipticity on a digital grid abstract a new method is presented based on the discrete fourier transform of an ordered sequence of boundary points for measuring the circularity and ellipticity of object boundaries together with a parametric description of their best fitting circles or ellipses techniques for rapid computation are discussed an analysis of quantization error with verification by computer experiment is presented

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

stochastic time delayed systems driven by correlated noises steady state analysis abstract in the present paper a class of stochastic time delayed systems driven by correlated gaussian white noises are considered novikov s theorem is used to derive delay fokker planck equations in the case of small time delays approximate stationary solutions are obtained as a special case the delay fokker planck equation and the approximate stationary probability density function is obtained for a bistable system numerical simulations show that the small delay approximation is a good approximation in the case of small delay furthermore the effects of the correlated noises and the feedback are investigated the critical curve separating the unimodal and bimodal regions of the stationary probability distribution is shown to be affected by the degree of the correlation of the noises and e the strength of the feedback both and e can change the curve of the stationary probability density function from a bimodal to a unimodal structure

geometric moment invariants this paper derives moment invariants in an intuitive way by multiple integrals of invariant geometric primitives like distance area and volume many existing 2 d and 3 d moment invariants are re expressed to prove the correctness of this method furthermore this construction method can be easily extended to higher dimensional space and get higher order moment invariants explicit expressions of 3 d moment invariants are generated automatically with the help of symbolic computation software and can be regarded as a kind of shape descriptor for the representation of solid objects

transitions induced by time delays and cross correlated sine wiener noises in a tumor immune system interplay abstract a model of tumor immune system interplay with time delays and cross correlated sine wiener noises is investigated by numerical simulations for the stationary probability distribution spd and stationary mean value x s t of tumor cell population results show that i the structure of the spd transfers from bimodal to unimodal as the reaction time of the cell population to environmental constraints increases ii conversely as the time of immune system to develop specific immune competence and the correlation time of noises increase the structure of the spd transfers from unimodal to bimodal iii as the cross correlated intensity between noises increases the transitions induced by are suppressed

rate laws of the self induced aggregation kinetics of brownian particles abstract in this paper we have studied the self induced aggregation kinetics of brownian particles in the presence of both multiplicative and additive noises in addition to the drift due to the self aggregation process the environment may induce a drift term in the presence of a multiplicative noise then there would be an interplay between the two drift terms it may account qualitatively the appearance of the different laws of aggregation process at low strength of white multiplicative noise the cluster number decreases as a gaussian function of time if the noise strength becomes appreciably large then the variation of cluster number with time is fitted well by the mono exponentially decaying function of time for additive noise driven case the decrease of cluster number can be described by the power law but in case of multiplicative colored driven process cluster number decays multi exponentially however we have explored how the rate constant in the mono exponentially cluster number decaying case depends on strength of interference of the noises and their intensity we have also explored how the structure factor at long time depends on the strength of the cross correlation cc between the additive and the multiplicative noises

multiple intersection local time of planar brownian motion as a particular hida distribution abstract subspaces of the space of hida distributions are quantified in which the multiple intersection local time of planar brownian motion renormalized by taking off the term of order zero in its chaos decomposition lives this is done by means of a new formula expressing the expectation of higher products of multiple wiener ito integrals by certain functions of the scalar products of their kernels

intrinsic fluctuations in chaotic dynamics abstract the multivariate master equation of a chemical system exhibiting spatio temporal chaos is investigated it is shown that the probability distribution in the presence of fluctuations remains centered on the underlying deterministic attractor

cross correlation enhanced stability in a tumor cell growth model with immune surveillance driven by cross correlated noises the transient properties of a tumor cell growth model with immune surveillance driven by cross correlated multiplicative and additive noises are investigated the explicit expression of extinction rate from the state of a stable tumor to the state of extinction is obtained based on the numerical computations we find the following i the intensity of multiplicative noise d and the intensity of additive noise enhance the extinction rate for the case of 0 i e denotes cross correlation intensity between two noises but for the case of 0 a critical noise intensity d or exists at which the extinction rate is the smallest d and at first weaken the extinction rate and then enhance it ii the immune rate and the cross correlation intensity play opposite roles on the extinction rate i e enhances the extinction rate of the tumor cell while weakens the extinction rate of the tumor cell namely the immune rate can enhance the extinction of the tumor cell and the cross correlation between two noises can enhance stability of the cancer state

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

effect of correlated dichotomous noises on stochastic resonance in a linear system a linear system driven by correlated asymmetric dichotomous noises and periodic signal was investigated in the overdamped case the exact expressions of output signal amplitude and signal to noise ratio snr of the system were derived by means of numerical calculations we found that i at some fixed multiplicative noise intensities the output signal amplitude with frequency exhibits the structure of a weak peak even no peak as the dichotomous noise is asymmetric ii in the case of asymmetric dichotomous noise the signal frequency can cause non monotonous behavior of the output signal amplitude with respect to multiplicative noise intensity iii the curve of snr with frequency has a weak peak and a trough in the case of symmetric dichotomous noise but no peak with asymmetric iv whether the multiplicative noise is symmetric or asymmetric the noise can enhance response of the system v the snr increases with the correlation strength between the two noises decreasing in addition the plane of multiplicative noise intensity versus noise symmetric parameter was plotted

dynamical properties of a logistic growth model with cross correlated noises abstract a logistic growth model driven by additive and multiplicative noises which are correlated with each other is investigated using the novikov theorem and the projection operator method we obtain the analytic expressions of the stationary probability distribution p s t x the relaxation time t c and the normalized correlation function c s of this system the computational results show that the relaxation time t c increases as the cross correlated time increases but decreases while the cross correlated strength increases the relationship between the relaxation time c s and the decay time s is given correlation time and correlation strength play an opposite role on dynamic properties in this logistic growth model

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

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