robust algorithms for solving stochastic partial differential equations a robust semi implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations pdes is described this can be used for calculating correlation functions of systems of interacting stochastic fields such field equations can arise in the description of hamiltonian and open systems in the physics of nonlinear processes and may include multiplicative noise sources the algorithm can be used for studying the properties of nonlinear quantum or classical field theories the general approach is outlined and applied to a specific example namely the quantum statistical fluctuations of ultra short optical pulses in 2 parametric waveguides this example uses a non diagonal coherent state representation and correctly predicts the sub shot noise level spectral fluctuations observed in homodyne detection measurements it is expected that the methods used will be applicable for higher order correlation functions and other physical problems as well a stochastic differencing technique for reducing sampling errors is also introduced this involves solving nonlinear stochastic parabolic pdes in combination with a reference process which uses the wigner representation in the example presented here a computer implementation on mimd parallel architectures is discussed

the numerical analysis of ordinary differential equations runge kutta and general linear methods mathematical and computational introduction the euler method and its generalizations analysis of runge kutta methods general linear methods bibliography

multiple bursts multiple looks and stream coherence in the release from informational masking in the simultaneous multitone masking paradigm introduced by neff and green percept psychophys 41 409 415 1987 the masker typically is a small number of tones having frequencies and levels that are randomly drawn on every presentation large amounts of masking for a pure tone signal often occur that are thought to reflect central rather than peripheral limitations on processing previous work from this laboratory has indicated that playing a rapid succession of randomly drawn multitone maskers in each observation interval dramatically reduces the amount of masking that is observed relative to a single burst sb in this multiple bursts different mbd procedure the signal tone is the only constant frequency component during the sequence of bursts and tends to perceptually segregate from the masker in this study the number of masker bursts and the interburst interval ibi were varied the goals were to determine how the release from masking relative to the sb condition depends on the number of bursts and to examine whether increasing the ibi would cause each burst to be processed independently if the latter were true it might disrupt the perception of signal stream coherence thereby diminishing the mbd advantage however multiple independent looks could also lead to an improvement in performance for those subjects showing large amounts of informational masking in the sb condition substantial reduction in masked thresholds occurred as the number of masker bursts increased while masking increased as ibi lengthened the results were not consistent with a simple version of a multiple look model in which the information from each burst was combined optimally but instead appear to be attributable to mechanisms involved in the perceptual organization of sounds

higher order implicit strong numerical schemes for stochastic differential equations higher order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed these are based on a stochastic taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero the regions of absolute stability of these implicit and related explicit methods are also examined

solving langevin equation with the bicolour rooted tree method national basic research program of china 973 program 2007cb814800 national natural science foundation of china 10475067

universal property of the housekeeping entropy production the entropy production of a nonequilibrium system with broken detailed balance is a random variable whose mean value is nonnegative the housekeeping entropy production which is a part of total entropy production is associated with the heat dissipation in maintaining a nonequilibrium steady state we derive a langevin type stochastic differential equation for the housekeeping entropy production the equation allows us to define a housekeeping entropic time ensuremath tau remarkably it turns out that the probability distribution of the housekeeping entropy production at a fixed value of ensuremath tau is given by the gaussian distribution regardless of system details the gaussian distribution is universal for any systems whether in the steady state or in the transient state and whether they are driven by time independent or time dependent driving forces we demonstrate the universal distribution numerically for model systems

synchrony and variability induced by spatially correlated additive and multiplicative noise in the coupled langevin model the synchrony and variability of the coupled langevin model subjected to spatially correlated additive and multiplicative noise are discussed we have employed numerical simulations and the analytical augmented moment method which is the second order moment method for local and global variables h hasegawa phys rev e 67 041903 2003 it has been shown that the synchrony of an ensemble is increased decreased by a positive negative spatial correlation in both additive and multiplicative noise although the variability for local fluctuations is almost insensitive to spatial correlations that for global fluctuations is increased decreased by positive negative correlations when a pulse input is applied the synchrony is increased for the correlated multiplicative noise whereas it may be decreased for correlated additive noise coexisting with uncorrelated multiplicative noise an application of our study to neuron ensembles has demonstrated the possibility that information is conveyed by the variance and synchrony in input signals which accounts for some neuronal experiments

numerical simulations of stochastic differential equations a simple very accurate algorithm for numerical simulation of stochastic differential equations is described its relationship to colored noise is elucidated and exhibited by explicit results the especially delicate problem of mean first passage times is highlighted and highly accurate agreement between the numerical simulations and analytic results are shown

the measurement problem in level discrimination there is disagreement among theorists over the exact measure to be used to quantify auditory level discrimination it has been proposed that for level discrimination tasks the measure that is most linearly related to the sensitivity index d will be the correct measure the level difference l and the weber fraction are both candidates though the latter is sensitive to the physical unit in which it is expressed e g pressure or intensity while the former is not psychometric functions for level discrimination were obtained at a number of pedestal levels for 10 ms sinusoids either 1000 or 6500hz and broadband noise bursts these functions were used to assess which of three measures l p p or i i is most nearly linearly related to d the results suggest that p p is the measure that comes closest to being linearly related to d

dependence of post masking on masker duration and its relation to temporal effects in loudness temporal masking of tones by noise was investigated using a post forward masking paradigm the masker level and duration were varied for every masker level employed the rate of decay of masking was found to depend on the duration of the masker specific loudness values were computed from the forward masking functions and an electronic device which simulates these loudness functions is presented in the simulation a series of integrators or a single integration with one long time constant was utilized the effect of the proposed integrators on loudness meters is discussed

population rate codes carried by mean fluctuation and synchrony of neuronal firings abstract a population of firing neurons is expected to carry information not only by the mean firing rate but also by fluctuation and synchrony among neurons in order to examine this possibility we have studied responses of neuronal ensembles to three kinds of inputs mean fluctuation and synchrony driven inputs the generalized rate code model including additive and multiplicative noise h hasegawa phys rev e 75 2007 051904 has been studied by direct simulations dss and the augmented moment method amm in which equations of motion for mean firing rate fluctuation and synchrony are derived results calculated by the amm are in good agreement with those by dss the independent component analysis ica of our results has shown that mean firing rate fluctuation or variability and synchrony may carry independent information in the population rate code model the input output relation of mean firing rates is shown to have higher sensitivity for larger multiplicative noise as recently observed in prefrontal cortex a comparison is made between results obtained by the integrate and fire if model and our rate code model

informational masking for simultaneous nonspeech stimuli psychometric functions for fixed and randomly mixed maskers sensitivity d and response bias were measured as a function of target level for the detection of a 1000 hz tone in multitone maskers using a one interval two alternative forced choice 1i 2afc paradigm ten such maskers each with eight randomly selected components in the region 200 5000 hz with 800 1250 hz excluded to form a protected zone were presented under two conditions the fixed condition in which the same eight component masker is used throughout an experimental run and the random condition in which an eight component masker is chosen randomly trial to trial from the given set of ten such maskers differences between the results obtained with these two conditions help characterize the listener s susceptibility to informational masking im the d results show great intersubject variability but can be reasonably well fit by simple energy detector models in which internal noise and filter bandwidth are used as fitting parameters in contrast the results are not well fit by these models in addition to presentation of new data and its relation to energy detector models this paper provides comments on a variety of issues problems and research needs in the im area 2005 acoustical society of america doi 10 1121 1 2032748

particle smoothing in continuous time a fast approach via density estimation we consider the particle smoothing problem for state space models where the transition density is not available in closed form in particular for continuous time nonlinear models expressed via stochastic differential equations sdes conventional forward backward and two filter smoothers for the particle filter require a closed form transition density with the linear gaussian euler maruyama discretization usually applied to the sdes to achieve this we develop a pair of variants using kernel density approximations to relieve the dependence and in doing so enable use of faster and more accurate discretization schemes such as runge kutta in addition the new methods admit arbitrary proposal distributions providing an avenue to deal with degeneracy issues experimental results on a functional magnetic resonance imaging fmri deconvolution task demonstrate comparable accuracy and significantly improved runtime over conventional techniques

a fourth order algorithm for solving the multi dimensional kramers equation in langevin form we propose a new fourth order numerical method for solving the multi dimensional kramers equation in standard and overdamped regimes the algorithm is developed for modelling the trajectories of airborne particles propagating through porous media such as three dimensional fibre networks it disentangles the deterministic and stochastic parts of the solution so that standard fourth order numerical methods can be used to calculate the deterministic component the stochastic correction to the solution is obtained using a perturbative expansion of the stochastic force in the overdamped regime our method avoids the need for extremely small time steps required by conventional methods we compare the convergence rate of our algorithm to that of other methods by solving the one dimensional duffing equation the proposed algorithm is finally used to evaluate the performance of various filters made from fibres of two different sizes

similarity uncertainty and masking in the identification of nonspeech auditory patterns this study examined whether increasing the similarity between informational maskers and signals would increase the amount of masking obtained in a nonspeech pattern identification task the signals were contiguous sequences of pure tone bursts arranged in six narrow band spectro temporal patterns the informational maskers were sequences of multitone bursts played synchronously with the signal tones the listener s task was to identify the patterns in a 1 interval 6 alternative forced choice procedure three types of multitone maskers were generated according to different randomization rules for the least signal like informational masker the components in each multitone burst were chosen at random within the frequency range of 200 6500 hz excluding a protected region around the signal frequencies for the intermediate masker the frequency components in the first burst were chosen quasirandomly but the components in successive bursts were constrained to fall in narrow frequency bands around the frequencies of the components in the initial burst within the narrow bands the frequencies were randomized this masker was considered to be more similar to the signal patterns because it consisted of a set of narrow band sequences any one of which might be mistaken for a signal pattern the most signal like masker was similar to the intermediate masker in that it consisted of a set of synchronously played narrow band sequences but the variation in frequency within each sequence was sinusoidal completing roughly one period in a sequence this masker consisted of discernible patterns but not patterns that were part of the set of signals in addition masking produced by gaussian noise bursts thought to produce primarily peripherally based energetic masking was measured and compared to the informational masking results for the three informational maskers more masking was produced by the maskers comprised of narrow band sequences than for the masker in which the frequencies were not constrained to narrow bands also the slopes of the performance level functions for the three informational maskers were much shallower than for the gaussian noise masker or for no masker the findings provided qualified support for the hypothesis that increasing the similarity between signals and maskers or parts of the maskers causes greater informational masking however it is also possible that the greater masking was a consequence of increasing the number of perceptual streams that had to be evaluated by the listener

numerical integration of stochastic differential equations several numerical methods for treating stochastic differential equations are considered both the convergence in the mean square limit and the convergence of the moments is discussed and the generation of appropriate random numbers is treated the necessity of simulations at various time steps with an extrapolation to time step zero is emphasized and demonstrated by a simple example

mean square and asymptotic stability of the stochastic theta method stability analysis of numerical methods for ordinary differential equations odes is motivated by the question for what choices of stepsize does the numerical method reproduce the characteristics of the test equation we study a linear test equation with a multiplicative noise term and consider mean square and asymptotic stability of a stochastic version of the theta method we extend some mean square stability results in saito and mitsui siam j numer anal 33 1996 pp 2254 2267 in particular we show that an extension of the deterministic a stability property holds we also plot mean square stability regions for the case where the test equation has real parameters for asymptotic stability we show that the issue reduces to finding the expected value of a parametrized random variable we combine analytical and numerical techniques to get insights into the stability properties for a variant of the method that has been proposed in the literature we obtain precise analytic expressions for the asymptotic stability region this allows us to prove a number of results the technique introduced is widely applicable and we use it to show that a fully implicit method suggested by kloeden and platen numerical solution of stochastic differential equations springer verlag 1992 has an asymptotic stability extension of the deterministic a stability property we also use the approach to explain some numerical results reported in milstein platen and schurz siam j numer anal 35 1998 pp 1010 1019

excitation based and informational masking of a tonal signal in a four tone masker this study examined contributions of peripheral excitation and informational masking to the variability in masking effectiveness observed across samples of multi tonal maskers detection thresholds were measured for a 1000 hz signal presented simultaneously with each of 25 four tone masker samples using a two interval forced choice adaptive task thresholds were measured with each sample fixed throughout trial blocks for ten listeners average thresholds differed by as much as 26 db across samples an excitation based model of partial loudness moore b c j et al 1997 j audio eng soc 45 224 237 was used to predict thresholds these predictions accounted for a significant portion of variance in the data of several listeners but no relation between the model and data was observed for many listeners moreover substantial individual differences on the order of 41 db were observed for some maskers the largest individual differences were found for maskers predicted to produce minimal excitat

weak second order splitting schemes for lagrangian monte carlo particle methods for the composition pdf fdf transport equations we study a class of methods for the numerical solution of the system of stochastic differential equations sdes that arises in the modeling of turbulent combustion specifically in the monte carlo particle method for the solution of the model equations for the composition probability density function pdf and the filtered density function fdf this system consists of an sde for particle position and a random differential equation for particle composition the numerical methods considered advance the solution in time with weak second order accuracy with respect to the time step size the four primary contributions of the paper are i establishing that the coefficients in the particle equations can be frozen at the mid time while preserving second order accuracy ii examining the performance of three existing schemes for integrating the sdes iii developing and evaluating different splitting schemes which treat particle motion reaction and mixing on different sub steps and iv developing the method of manufactured solutions mms to assess the convergence of monte carlo particle methods tests using mms confirm the second order accuracy of the schemes in general the use of frozen coefficients reduces the numerical errors otherwise no significant differences are observed in the performance of the different sde schemes and splitting schemes

stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise a microscopic approach abstract we have studied the stochastic resonance sr of bistable systems coupled to a bath with a nonlinear system bath interaction by using the microscopic generalized caldeira leggett cl model the adopted cl model yields the non markovian langevin equation with nonlinear dissipation and state dependent multiplicative diffusion which preserve the fluctuation dissipation relation fdr results of our simulations are given as follows 1 the spectral power amplification spa exhibits sr not only for a and b but also for while the stationary probability distribution function is independent of them where a and b denote magnitudes of multiplicative and additive noises respectively and expresses the relaxation time of ornstein uhlenbeck ou colored noise 2 the spa for coexisting additive and multiplicative noises has a single peak but two peak structure as functions of a b and or results 1 and 2 are qualitatively different from previous ones obtained by phenomenological langevin models where the fdr is not held or indefinite these show an importance of the fdr in a study on sr of open bistable systems

signal uncertainty and psychometric functions in profile analysis experiment 1 was conducted to compare the effects of signal frequency uncertainty on the detection of a change in spectral shape and on the detection of a tone in wideband noise results indicate that for both tasks the uncertainty effect was small being on average about 3 db in a second experiment psychometric functions were measured for the detection of changes in the spectral shape of multicomponent complexes psychometric functions for profile tasks have a 25 db range and are similar to those measured for the detection of an increment in the level of a single sinusoid these psychometric functions are different from those found when detecting a signal in noise which typically have a 10 db range three equations for the shape of the psychometric functions were compared the difference in the resulting fits was small thus preventing an unambiguous choice of functional form

numerical procedures for sample structures on stochastic differential equations procedures are discussed for the numerical construction of sample processes on stochastic differential equations structures of a relevant class of gaussian white noise functionals are analyzed to some closed forms and new numerical algorithms for single noise problems are presented up to the accuracy of o h3 or within errors of o h7 2 in the sense of the mean square norm

numerical integration of multiplicative noise stochastic differential equations a two stage runge kutta algorithm for vector ito and by transform also stratonovich stochastic differential equations with multiplicative noise has been developed the method is second order accurate but for vanishing drift the algorithm yields a martingale independent of step size several examples are included to illustrate our method a discussion of errors shows that sample size can be as important as truncation

strategies used to detect auditory signals in small sets of random maskers detection performance for a masked auditory signal of fixed frequency can be substantially degraded if there is uncertainty about the frequency content of the masker a quasimolecular psychophysical approach was used to examine response strategies in masker uncertainty conditions and to investigate the influence of uncertainty when the number of different masker samples was limited to ten or fewer the task of the four listeners was to detect a 1000 hz signal that was presented simultaneously with one of ten ten tone masker samples the masker sample was either fixed throughout a block of two interval forced choice trials or was randomized across or within trials the primary results showed that 1 when the signal level was low and the masker sample differed between the two intervals of a trial most listeners based their responses more on the presence of specific masker samples than on the signal 2 the detrimental effect of masker uncertainty was clearly evident when only four maskers were randomly presented and grew as the size of the masker set was increased from two to ten 3 the slopes of psychometric functions measured with the same masker samples differed among the fixed and two random masker conditions 4 there were large differences in the influence of masker uncertainty across masker samples and listeners these data demonstrate the great susceptibility of human listeners to the influence of masker uncertainty and the ability of quasimolecular investigations to reveal important aspects of behavior in uncertainty condition

stochastic calculus in physics the relationship of the ito stratonovich stochastic calculus to studies of weakly colored noise is explained a functional calculus approach is used to obtain an effective fokker planck equation for the weakly colored noise regime in a smooth limit this representation produces the stratonovich version of the ito stratonovich calculus for white noise it also provides an approach to steady state behavior for strongly colored noise numerical simulation algorithms are explored and a novel suggestion is made for efficient and accurate simulation of white noise equations

a model of auditory pattern analysis based on component relative entropy recently results from detection and information theory have been used to predict performance of human observers in experiments involving the discriminability of changes in individual components of unfamiliar or uncertain tone patterns r a lutfi j acoust soc am 91 3391 3401 1992 in this paper the theoretical analysis is expanded to yield a general rule of pattern analysis that accounts for nearly all of the major results of such experiments conducted over the last 18 years the rule can be stated as follows component discriminability in an unfamiliar tone pattern profile or sequence is a linearly increasing function of the component s relative entropy core in the pattern ancillary the threshold for detection of a change decreases by one order of magnitude factor of 10 for each one bit increase in core this precise relation of threshold to core is demonstrated repeatedly in a review of past studies and is shown to account for the relative effects of a variety of important variables and their interactions such variables include the total duration of the pattern the number of tones in the pattern the number of tones subject to change the relative level and duration of individual tones in the pattern the relative variability and the physical dimension of the tones parameters that are subject to change the number and position of targets in the pattern the psychophysical procedure used method of adjustment versus same different the type of discrimination task frequency versus intensity discrimination and the manner of presentation of the tones simultaneous or sequential the core rule seems to reflect a general property of auditory analysis wherein the perception of patterns in an ensemble is dominated by those features that dominate the variance of the ensemble

an integral algorithm for numerical integration of one dimensional additive colored noise problems we present an integral closed algorithm for solving a langevin equation driven by an additive colored noise both the mean first passage time in a bistable system and the diffusion current in a titled periodic potential are calculated and the comparison with existing algorithms is carried out the dependence of the numerical results on the time steps is studied our algorithm is shown to have high accuracy and stability

stochastic calculus application to dynamic bifurcations and threshold crossings for the dynamic pitchfork bifurcation in the presence of white noise the statistics of the last time at zero are calculated as a function of the noise level and the rate of change of the parameter the threshold crossing problem used for example to model the firing of a single cortical neuron is considered concentrating on quantities that may be experimentally measurable but have so far received little attention expressions for the statistics of pre threshold excursions occupation density and last crossing time of zero are compared with results from numerical generation of paths

accurate monte carlo tests of the stochastic ginzburg landau model with multiplicative colored noise an accurate and fast monte carlo algorithm is proposed for solving the ginzburg landau equation with multiplicative colored noise the stable cases of solution for choosing time steps and trajectory numbers are discussed

psychometric functions for multicomponent maskers with spectral uncertainty previous experiments used a two alternative forced choice adaptive procedure to measure thresholds for a 1000 hz signal in the presence of maskers composed of multiple sinusoids these sinusoids were drawn at random from a 300 to 3000 hz range excluding the signal frequency and frequencies within a critical band around the signal this experiment examined psychometric functions for 50 of the original 200 maskers with 10 components using signal levels from 10 80 db spl the psychometric functions were well fitted in d by signal level coordinates but individual functions typically spanned a 30 to 40 db range corresponding adaptive thresholds did not differ from thresholds based on 200 maskers and were in agreement with the average of the predicted thresholds across the 50 maskers although individual maskers could differ in effectiveness by 10 15 db the majority produced similar masking overall the adaptive procedure adequately characterizes performance in these conditions work supported by nih

exponential timestepping with boundary test for stochastic differential equations we present new numerical methods for scalar stochastic differential equations successive time increments are independent random variables with an exponential distribution we perform numerical experiments using a double well potential exponential timestepping algorithms are efficient for escape time problems because a simple boundary test can be performed at the end of each step

balanced implicit methods for stiff stochastic systems this paper introduces some implicitness in stochastic terms of numerical methods for solving stiff stochastic differential equations and especially a class of fully implicit methods the balanced methods their order of strong convergence is proved numerical experiments compare the stability properties of these schemes with explicit ones

correlation coefficients and correlation ratios as estimates of observer weights in multiple observation tasks advantages of correlational methods are described for estimating the relative reliance or weight observers give to different elements of a complex display when performing auditory or visual discriminations correlational methods differ from other such methods by providing a least squares estimate of weights rather than a maximum likelihood estimate based on a presumed model the main benefit is that these methods can be generally applied in cases where the statistical properties of elements are unknown where correlations exist between elements or where it is necessary to evaluate decision models that are inherently nonlinear

effective properties of multicomponent simultaneous maskers under conditions of uncertainty when more than one sinusoid is used as a masker more masking is observed than would be predicted by a simple combination of their individual effects this masking is dramatically increased when the masker components vary in frequency and intensity with each presentation these studies manipulated several masker parameters under conditions of high masker uncertainty examining the effect of excluding critical band components fixing or randomizing component amplitudes and frequencies and narrowing the frequency range of the components the signal was always a 200 ms 1000 hz sinusoid presented simultaneously with the 200 ms masker removing critical band components reduced the amount of masking but considerable masking remained that appears to be nonperipheral in origin fixing masker frequencies across the two intervals of a trial greatly reduced the masking observed whereas fixing masker amplitudes had no effect reducing the frequency range from 5000 to 2700 hz generally increased the masking obser

cuing effects for informational masking the detection of a tone added to a random frequency multitone masker can be very poor even when the maskers have little energy in the frequency region of the signal this paper examines the effects of adding a pretrial cue to reduce uncertainty for the masker or the signal the first two experiments examined the effect of cuing a fixed frequency signal as the number of masker components and presentation methods were manipulated cue effectiveness varied across observers but could reduce thresholds by as much as 20 db procedural comparisons indicated observers benefited more from having two masker samples to compare with or without a signal cue than having a single interval with one masker sample and a signal cue the third experiment used random frequency signals and compared no cue signal cue and masker cue conditions and also systematically varied the time interval between cue offset and trial onset thresholds with a cued random frequency signal remained higher than for a cued fixed frequency signal for time intervals between the cue and trial of 50 ms or longer thresholds were approximately the same with a signal or a masker cue and lower than when there was no cue without a cue or with a masker cue analyses of possible decision strategies suggested observers attended to the potential signal frequencies particularly the highest signal frequency with a signal cue observers appeared to attend to the frequency of the subsequent signal

statistical mechanics of kinks for quasi exactly solvable potentials we study the thermodynamics of kinks in the presence of quasi exactly solvable qes potentials using a langevin code implemented on a massively parallel computer specifically we study the potential v 2 1 2 for which certain exact solutions of the schrodinger equation are known provided the parameters and satisfy certain constraints for 1 this potential has two degenerate minima otherwise it has only one minimum thus a system with this potential is capable of describing a second order phase transition a la the 4 model however no exact solutions of the schrodinger equation for this potential exist we have obtained an exact solution for the kink in this model in addition we have calculated in a 1d model such quantities as the probability density function pdf field configuration and field field correlation functions both above and below the transition temperature tc for several temperatures these quantities help us understand the contribution to the specific heat from coherent structures such as domain walls kinks as opposed to the contribution from lattice vibrations we have calibrated our results against known exact solutions for limiting cases with very high accuracy

theoretical analysis for critical fluctuations of relaxation trajectory near a saddle node bifurcation a langevin equation whose deterministic part undergoes a saddle node bifurcation is investigated theoretically it is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle node bifurcation point in the weak noise limit while the final value of the deterministic solution changes discontinuously at the point a systematic formulation for analyzing a path probability measure is constructed on the basis of a singular perturbation method in this formulation the critical nature turns out to originate from the neutrality of exiting time from a saddle point the theoretical calculation explains results of numerical simulations

second order algorithm for simulating stochastic differential equations with white noises abstract the second order algorithm for simulating stochastic differential equations with gaussian white noises is presented these stochastic differential equations are universal type among these gaussian white noises come from different sources specifically the proposed algorithm extends previous first order algorithm for stochastic differential equations with different white noises and second order algorithm for stochastic differential equations with same white noise in practice it is proved that this algorithm is scientific

relative estimates of combination weights decision criteria and internal noise based on correlation coefficients a means by which relative combination weights may be determined is described for a signal detection model in which the decision variable is a weighted linear combination of several independent normally distributed random variables xi s the first theorem presents the correlation between the binary response variables signal versus no signal and the component xi the second theorem presents a parallel result for the case that additive internal noise is present thus in psychophysical experiments the relative combination weights may be obtained by correlating the observers responses and the input random variables third three numerical methods which allow the evaluation of the relative magnitude of the decision criterion and the variance of a hypothetical additive internal noise are considered

numerical treatment of stochastic differential equations we define general runge kutta approximations for the solution of stochastic differential equations sde these approximations are proved to converge in quadratic mean to the solution of an sde with a corrected drift the explicit form of the correction term is given concerning the order of convergence we show that in general it is impossible for the quadratic mean of the one step error to be of an order greater than o h 3 this order is attained e g by the stochastic analogue of heun s method in the n dimensional case the highest order of convergence is in general only o h 2 attained by euler s method the order o h 3 can only be reached if nabla x sigma r sigma s nabla x sigma s sigma r for the diffusion matrix

computer simulations of multiplicative stochastic differential equations a class of robust algorithms for the computer simulation of stochastic differential equations with multiplicative noise is investigated excellent agreement is obtained with the known analytic behaviour of the kubo oscillator in the white noise limit the algorithms include a known first order one dimensional explicit method as well as implicit methods of increased stability a distinction is drawn between classes of stochastic differential equations depending on the type of spatial variation or curvature defined by the diffusion tensor this allows greatly simplified numerical implementations of the new algorithms in certain cases the results of different techniques are compared for the case of the kubo oscillator where a semi implicit technique gives the greatest accuracy

statistical mechanics of double sinh gordon kinks abstract we study the classical thermodynamics of the double sinh gordon dshg theory in 1 1 dimensions this model theory has a double well potential v cosh2 n 2 when n thus allowing for the existence of kinks and antikinks though it is non integrable the dshg model is remarkably amenable to analysis below we obtain exact single kink and kink lattice solutions as well as the asymptotic kink antikink interaction in the continuum limit finding the classical partition function is equivalent to solving for the ground state of a schrodinger like equation obtained via the transfer integral method for the dshg model this equation turns out to be quasi exactly solvable we exploit this property to obtain exact energy eigenvalues and wavefunctions for several temperatures both above and below the symmetry breaking transition temperature provided n 1 2 6 the availability of exact results provides an excellent testing ground for large scale langevin simulations the probability distribution function pdf calculated from langevin dynamics is found to be in striking agreement with the exact pdf obtained from the ground state wavefunction this validation points to the utility of a pdf based computation of thermodynamics utilizing langevin methods in addition to the pdf field field and field fluctuation correlation functions were computed and also found to be in excellent agreement with the exact results

computation of lyapunov spectra effect of interactive noise and application to a chemical oscillator abstract a refined version of the sano sawada algorithm to compute lyapunov spectra has been implemented and tested with several models which include periodic chaotic and hyperchaotic attractors under conditions designed to mimic experimental situations it was found that reliable lyapunov exponents can be obtained for time series of moderate length and point density also in the presence of interactive noise as long as its amplitude does not exceed 1 of the oscillation amplitude the algorithm was then applied to experimental data from the co oxidation on pt 110 clearly showing the occurrence of chaos as well as hyperchaos

on possible cues in profile analysis identification of the incremented component the ability to identify the frequency of the incremented component in a multitone complex was assessed in two conditions both using the same 11 tone complexes fixed frequency equilog spaced random phases in the standard plus signal complex all components had equal level except one of the inner nine which was incremented in level by an in phase addition of a sinusoid of the same frequency the signal the overall level and signal position were randomly varied on each presentation in the standard absent condition the standard plus signal complex was presented first and it was followed by a single sinusoid either at the signal frequency or at that of an adjacent component below or above in the standard present condition a complex with equal level components the standard complex was also presented on each trial either before or after the standard plus signal complex in random order these two complexes were followed by the single sinusoid in both conditions the subjects had to indica

numerical simulations of generalized langevin equations with deeply asymptotic parameters a unified algorithm for solving langevin equations with deeply asymptotic parameters is proposed and tested the method consists of identifying solvable linear friction and implementing the force evaluations by use of the runge kutta method we apply the present scheme to the periodic motion of an overdamped particle subjected to a multiplicative white noise the accurate calculations for the temporal velocity of the particle and its correlation function can be realized by introducing an inertial term it is shown that the fluctuation around the steady quantity increases with decreasing time step in the overdamped white noise algorithm however a massive white noise technique greatly reduces this spurious drift and the result can converge to the correct value if the added inertia approaches zero the other application is the simulation of generalized langevin equation with an exponential memory friction this allows us to treat a weak non markovian process

informational masking by everyday sounds tone in noise detection is severely degraded when only a few spectral components of the noise are presented at random on each trial neff and green percept psychophys 41 409 415 1987 the elevations in threshold are attributed to uncertainty regarding the noise caused by sparse sampling of noise components informational masking is the term used to describe the result the present experiment was undertaken to determine how informational masking is affected when sparse sampling is from a set of common everyday sounds instead of noise on each presentation a different masker waveform of constant total power was synthesized from the magnitude and phase of a fixed number m of spectral components m 2 921 across blocks of trials the components were selected at random from 1 of 50 common environmental sounds e g baby crying door slamming phone ringing or 1 of 50 samples of gaussian noise masked thresholds for a 1 0 khz signal in the presence of both types of maskers were obtained using an adaptive two interval forced choice procedure results with noise replicated earlier results showing largest elevations in threshold for 10 20 sampled components results with everyday sounds showed a similar pattern with thresholds elevated above those for noise by as much as 10 db at the larger values of m the differences in masked thresholds were systematically related to differences in the ensemble variance of masker spectra as predicted by a model previously applied to noise lutfi j acoust soc am 94 748 758 1993 not predicted was the result of a subsequent trial by trial analysis in which 9 11 db less masking was observed for samples from everyday sounds rated as easily recognized by listeners the results suggest that listeners fail to exploit lawful dependencies among spectral components of everyday sounds to aid detection unless enough information is available for the sound to be easily recognized

stationary solutions of linear stochastic delay differential equations applications to biological systems recently k uchler and mensch stochastics stochastics rep 40 23 1992 derived exact stationary probability densities for linear stochastic delay differential equations this paper presents an alternative derivation of these solutions by means of the fokker planck approach introduced by guillouzic phys rev e 59 3970 1999 61 4906 2000 applications of this approach which is argued to have greater generality are discussed in the context of stochastic models for population growth and tracking movements

molecular modeling of proteins and mathematical prediction of protein structure this paper discusses the mathematical formulation of and solution attempts for the so called protein folding problem the static aspect is concerned with how to predict the folded native tertiary structure of a protein given its sequence of amino acids the dynamic aspect asks about the possible pathways to folding and unfolding including the stability of the folded protein from a mathematical point of view there are several main sides to the static problem the selection of an appropriate potential energy function the parameter identification by fitting to experimental data and the global optimization of the potential the dynamic problem entails in addition the solution of because of multiple time scales very stiff ordinary or stochastic differential equations molecular dynamics simulation or in case of constrained molecular dynamics of differential algebraic equations a theme connecting the static and dynamic aspect is the determination and formation of secondary structure motifs the present paper gives a self contained introduction to the necessary background from physics and chemistry and surveys some of the literature it also discusses the various mathematical problems arising some deficiencies of the current models and algorithms and possible past and future attacks to arrive at solutions to the protein folding problem

numerical solution of the kardar parisi zhang equation in one two and three dimensions abstract on a course grained level a family of microscopic growth processes may be described by a stochastic differential equation which is solved numerically for surface dimensions d 1 2 and 3 dimensional analysis shows that the spatial discretization parameter has the meaning of an effective coupling constant the numerical stability of the euler integration scheme is discussed for the strong coupling exponents defined by surface width time the following effective values were obtained d 1 0 330 0 004 and d 2 0 24 0 005 considering the width and its ensemble fluctuations at constant dimensionless time the transition between strong and weak coupling phases is located in d 3 for the largest coupling for which reliable data are available we obtain an effective exponent close to the best estimates on discrete models d 3 0 17

growth of forward masking for sinusoidal and noise maskers as a function of signal delay implications for suppression in noise the first two experiments were designed to determine whether mutual suppression in broadband noise increases in strength with increasing overall level in experiment i masking functions signal threshold versus masker level were measured in forward masking as a function of the delay time of a 10 ms signal both for a broadband noise masker low pass filtered at 8 khz and for sinusoidal maskers at 1 2 and 4 khz in the latter case the signal frequency equaled the masker frequency for short signal delays the masking functions were steeper for the sinusoidal masker than for the noise masker at longer delays the slopes for both masker types decreased and the slopes for the two masker types became more nearly equal in experiment ii we investigated the effect of gating a low level noise cue with the sinusoidal masker at the longer signal delays the masking functions had equal slopes for the broadband noise masker and the sinusoidal masker with cue at short signal delays the masking functions for sinuso