synchrony of neural oscillators induced by random telegraphic currents when a neuron receives a randomly fluctuating input current its reliability of spike generation improves compared with the case of a constant input current mainen and sejnowski science 268 1503 1995 this phenomenon can be interpreted as phase synchronization between uncoupled nonlinear oscillators subject to a common external input we analyze this phenomenon using dynamical models of neurons assuming the input current to be a simple random telegraphic signal that jumps between two values and the neuron to be always purely self oscillatory the internal state of the neuron randomly jumps between two limit cycles corresponding to the input values which can be described by random phase maps when the switching time of the input current is sufficiently long using such a random map description we discuss the synchrony of neural oscillators subject to fluctuating inputs especially when the phase maps are monotonic we can generally show that the lyapunov exponent is negative namely phase synchronization is stable and reproducibility of spike timing improves

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

quantifying phase synchronization using instances of hilbert phase slips abstract we propose to quantify phase synchronization between two signals x t and y t by calculating variance in the hilbert phase of y t at instances of phase slips exhibited by x t the proposed approach is tested on numerically simulated coupled chaotic roessler systems and second order autoregressive processes furthermore we compare the performance of the proposed and original approaches using uterine electromyogram signals and show that both approaches yield consistent results a standard phase synchronization approach which involves unwrapping the hilbert phases 1 t and 2 t of the two signals and analyzing the variance in the n 1 t m 2 t mod 2 n and m are integers was used for comparison the synchronization indexes obtained from the proposed approach and the standard approach agree reasonably well in all of the systems studied in this work our results indicate that the proposed approach unlike the traditional approach does not require the non invertible transformations unwrapping of the phases and calculation of mod 2 and it can be used to reliably to quantify phase synchrony between two signals

a generalized henon heiles system and related integrable newton equations a detailed description is given of integrable cases of the generalized henon heiles systems which differs from the standard h h ones by the term q22 their connection with fifth order one component soliton equations is discussed lax representations are constructed and the bi hamiltonian formulation of dynamics is given it is also shown that the gh h system can be mapped onto another system of newton equations with a nonstandard hamiltonian structure

shape from recognition a novel approach for 3 d face shape recovery in this paper we develop a novel framework for robust recovery of three dimensional 3 d surfaces of faces from single images the underlying principle is shape from recognition i e the idea that pre recognizing face parts can constrain the space of possible solutions to the image irradiance equation thus allowing robust recovery of the 3 d structure of a specific part parts of faces like nose lips and eyes are recognized and localized using robust expansion matching filter templates under varying pose and illumination specialized backpropagation based neural networks are then employed to recover the 3 d shape of particular face parts representation using principal components allows to efficiently encode classes of objects such as nose lips etc the specialized networks are designed and trained to map the principal component coefficients of the part images to another set of principal component coefficients that represent the corresponding 3 d surface shapes to achieve robustness to viewing conditions the network is trained with a wide range of illumination and viewing directions a method for merging recovered 3 d surface regions by minimizing the sum squared error in overlapping areas is also derived quantitative analysis of the reconstruction of the surface parts in varying illumination and pose show relatively small errors indicating that the method is robust and accurate several examples showing recovery of the complete face also illustrate the efficacy of the approach

generalized lenard chains separation of variables and superintegrability we show that the notion of generalized lenard chains naturally allows formulation of the theory of multiseparable and superintegrable systems in the context of bi hamiltonian geometry we prove that the existence of generalized lenard chains generated by a hamiltonian function defined on a four dimensional n manifold guarantees the separation of variables as an application we construct such chains for the henon heiles systems and for the classical smorodinsky winternitz systems new bi hamiltonian structures for the kepler potential are found

surface topography using shape from shading abstract this paper demonstrates how a recently reported shape from shading scheme can be used to extract topographic information from 2d intensity imagery worthington and hancock ieee trans pattern anal mach intell 21 1999 1250 1267 the shape from shading scheme has two important features which enhance the recovered surface description firstly it uses a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint this not only improves the data closeness of the recovered needle map but also removes the necessity for extensive parameter tuning secondly we use curvature information to impose topographic constraints on the recovered needle map the topographic information is captured using the shape index of koenderink and van doorn image vision comput 10 1992 557 565 and consistency is imposed using a robust error function we show that the new shape from shading scheme leads to a meaningful topographic labelling of 3d surface structures moreover the resulting topographic information proves to be useful in a simple histogram based object recognition scheme

the quasi bi hamiltonian formulation of the lagrange top starting from the tri hamiltonian formulation of the lagrange top lt in a six dimensional phase space we discuss the possible reductions of the poisson tensors the vector field and its hamiltonian functions on a four dimensional space we show that the vector field of the lt possesses on the reduced phase space a quasi bi hamiltonian formulation which provides a set of separation variables for the corresponding hamilton jacobi equation

exact results for the kuramoto model with a bimodal frequency distribution we analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed the dynamics of this system has been the subject of long standing interest in 1984 kuramoto proposed several conjectures about its behavior ten years later crawford obtained the first analytical results by means of a local center manifold calculation nevertheless many questions have remained open especially about the possibility of global bifurcations here we derive the system s stability diagram for the special case where the bimodal distribution consists of two equally weighted lorentzians using an ansatz recently discovered by ott and antonsen we show that in this case the infinite dimensional problem reduces exactly to a flow in four dimensions depending on the parameters and initial conditions the long term dynamics evolves to one of three states incoherence where all the oscillators are desynchronized partial synchrony where a macroscopic group of phase locked oscillators coexists with a sea of desynchronized ones and a standing wave state where two counter rotating groups of phase locked oscillators emerge analytical results are presented for the bifurcation boundaries between these states similar results are also obtained for the case in which the bimodal distribution is given by the sum of two gaussians

spurious detection of phase synchronization in coupled nonlinear oscillators coupled nonlinear systems under certain conditions exhibit phase synchronization which may change for different frequency bands or with the presence of additive system noise in both cases fourier filtering is traditionally used to preprocess data we investigate to what extent the phase synchronization of two coupled r ossler oscillators depends on 1 the broadness of their power spectrum 2 the width of the bandpass filter and 3 the level of added noise we find that for identical coupling strengths oscillators with broader power spectra exhibit weaker synchronization further we find that within a broad bandwidth range bandpass filtering reduces the effect of noise but can lead to a spurious increase in the degree of phase synchronization with narrowing bandwidth even when the coupling between the two oscillators remains the same

experimental synchronization of circuit oscillations induced by common telegraph noise experimental realization and quantitative investigation of common noise induced synchronization of limit cycle oscillations subject to random telegraph signals are performed using an electronic oscillator circuit based on our previous formulation k nagai et al phys rev e 71 036217 2005 dynamics of the circuit is described as random phase mappings between two limit cycles lyapunov exponents characterizing the degree of synchronization are estimated from experimentally determined phase maps and compared with linear damping rates of phase differences measured directly noisy on off intermittency of the phase difference as predicted by the theory is also confirmed experimentally

phase synchronization in temperature and precipitation records abstract we study phase synchronization between atmospheric variables such as daily mean temperature and daily precipitation records we find significant phase synchronization between records of oxford and vienna as well as between the records of precipitation and temperature in each city to find the time delay in the synchronization between the records we study the time lag phase synchronization when the records are shifted by a variable time interval of days we also compare the results of the method with the classical cross correlation method and find that in certain cases the phase synchronization yields more significant results

statistical approach to shape from shading reconstruction of three dimensional face surfaces from single two dimensional images the human visual system is proficient in perceiving three dimensional shape from the shading patterns in a two dimensional image how it does this is not well understood and continues to be a question of fundamental and practical interest in this paper we present a new quantitative approach to shape from shading that may provide some answers we suggest that the brain through evolution or prior experience has discovered that objects can be classified into lower dimensional object classes as to their shape extraction of shape from shading is then equivalent to the much simpler problem of parameter estimation in a low dimensional space we carry out this proposal for an important class of three dimensional 3d objects human heads from an ensemble of several hundred laser scanned 3d heads we use principal component analysis to derive a low dimensional parameterization of head shape space an algorithm for solving shape from shading using this representation is presented it works well even on real images where it is able to recover the 3d surface for a given person maintaining facial detail and identity from a single 2d image of his face this algorithm has applications in face recognition and animation

noise induced synchronization of uncoupled nonlinear systems we derive a recursion formulae of transition probability of the noise induced synchronization arising in a pair of identical uncoupled logistic maps linked by common noisy excitation only the formulae has a delta type stationary solution which represents the perfect synchronization with probability 1 the stationary solution maintains under chaotic bifurcation while the escape times to reach the perfect synchronization increase in the chaotic region the escape times analysis implies existence of lower dimensional dynamics around the perfect synchronization we also provide a physical implementation of the synchronization

learning driver response relationships from synchronization patterns we test recent claims that causal driver response relationships can be deduced from interdependencies between simultaneously measured time series we apply two recently proposed interdependence measures that should give results similar to cross predictabilities used by previous authors the systems that we study are asymmetrically coupled simple models lorenz roessler and henon models the couplings being such that they lead to generalized synchronization if the data were perfect noise free infinitely long we should be able to detect at least in some cases which of the coupled systems is the driver and which the response this might no longer be true if the time series has finite length instead estimated interdependencies depend strongly on which of the systems has a higher effective dimension at the typical neighborhood sizes used to estimate them and causal relationships are more difficult to detect we also show that slightly different variants of the interdependence measure can have quite different sensitivities

families of quasi bi hamiltonian systems and separability it is shown how to construct an infinite number of families of quasi bi hamiltonian qbh systems by means of the constrained flows of soliton equations three explicit qbh structures are presented for the first three families of the constrained flows the nijenhuis coordinates defined by the nijenhuis tensor for the corresponding families of qbh systems are proved to be exactly the same as the separated variables introduced by mean of the lax matrices for the constrained flows

linear transmitter with correlated noises abstract a linear transmitter with correlated gaussian white additive and multiplicative noises and a periodic signal coupled either additively or multiplicatively is considered the correlations have a weak destructive effect in case of the additive signal and a strong constructive effect in case of the multiplicative one analytical results for the linear transmitter with the additive signal agree with those obtained previously by a different approach we also show how to analytically calculate certain expectation values involving exponentials of gaussian processes

fast facial shape recovery from a single image with general unknown lighting by using tensor representation in this paper we propose a fast 3 d facial shape recovery algorithm from a single image with general unknown lighting in order to derive the algorithm we formulate a nonlinear least square problem with two parameter vectors which are related to personal identity and light conditions we then combine the spherical harmonics for the surface normals of a human face with tensor algebra and show that in a certain condition the dimensionality of the least square problem can be further reduced to one tenth of the regular subspace based model by using tensor decomposition n mode svd which greatly speeds up the computations in order to enhance the shape recovery performance we have incorporated prior information in updating the parameters in the experiment the proposed algorithm takes less than 0 4s to reconstruct a face and shows a significant performance improvement over other reported schemes

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

synchronization of self sustained oscillators by common white noise abstract we study the stability of self sustained oscillations under the influence of external noise for small noise amplitude a phase approximation for the langevin dynamics is valid a stationary distribution of the phase is used for an analytic calculation of the maximal lyapunov exponent we demonstrate that for small noise the exponent is negative which corresponds to synchronization of oscillators

the dynamics of chimera states in heterogeneous kuramoto networks abstract we study a variety of mixed synchronous incoherent chimera states in several heterogeneous networks of coupled phase oscillators for each network the recently discovered ott antonsen ansatz is used to reduce the number of variables in the partial differential equation pde governing the evolution of the probability density function by one resulting in a time evolution pde for a variable with as many spatial dimensions as the network bifurcation analysis is performed on the steady states of these pdes the results emphasise the commonality of the dynamics of the different networks and provide stability information that was previously inferred

correlation anti correlation transition by state dependent poisson noise noise may induce some degrees of order in many biological and complex systems we present an example of a noise dependent transition from correlation to anti correlation of the states of a bivariate system coupled by state dependent poisson noises by varying the degree of dependence of the rate of jumps on the other variable the system undergoes different degrees of correlation from independence to perfect correlation which in this case coincides with perfect synchronization in the limit of the deterministic periodic case

class ii neurons display a higher degree of stochastic synchronization than class i neurons we describe the relationship between the shape of the phase resetting curve prc and the degree of stochastic synchronization observed between a pair of uncoupled general oscillators receiving partially correlated poisson inputs in addition to inputs from independent sources we use perturbation methods to derive an expression relating the shape of the prc to the probability density function pdf of the phase difference between the oscillators we compute various measures of the degree of synchrony and cross correlation from the pdf s and use the same to compare and contrast differently shaped prcs with respect to their ability to undergo stochastic synchronization since the shape of the prc depends on underlying dynamical details of the oscillator system we utilize the results obtained from the analysis of general oscillator systems to study specific models of neuronal oscillators it is shown that the degree of stochastic synchronization is controlled both by the firing rate of the neuron and the membership of the prc type i or type ii it is also shown that the circular variance for the integrate and fire neuron and the generalized order parameter for a hippocampal interneuron model have a nonlinear relationship to the input correlation

a robust real time algorithm for facial shape recovery from a single image containing cast shadow under general unknown lighting it is difficult to find a non iterative solution for statistical shape from shading sfs for a single image containing cast shadow under unknown arbitrary light conditions this is because it is not trivial to find a mapping from a convex cone in the image space to a point in the depth space to find a non iterative solution for the statistical sfs which has not been done yet to our knowledge we show that it is possible to approximate a cone of images illumination cone to a polytope by a nonlinear function which is a transform from cartesian coordinates to hyperspherical coordinates the images of a subject form a convex cone in the image space and it can be better to use the direction of an image in hyperspherical coordinates as an input feature for the mapping rather than the image itself the maximum error occurs on one of the vertices of the polytope if we choose the objective function to be the squared error of a linear function in the hyperspherical space hence we can solve the least square problem using the cost only for the vertices in deriving the solution we use the generalized rayleigh quotient canonical correlation analysis cca and prior information on input images to reduce the solution space and improve 3 d reconstruction performance in experiments the proposed scheme performs robustly under light variations and is fast enough for real time applications

antireliability of noise driven neurons we demonstrate within the framework of the fitzhugh nagumo model that a firing neuron can respond to a noisy driving in a nonreliable manner the same gaussian white noise acting on identical neurons evokes different patterns of spikes the effect is characterized via calculations of the lyapunov exponent and the event synchronization correlations we construct a theory that explains the antireliability as a combined effect of a high sensitivity to noise of some stages of the dynamics and nonisochronicity of oscillations geometrically the antireliability is described by a random noninvertible one dimensional map

understanding dynamics of the system using hilbert phases an application to study neonatal and fetal brain signals the hilbert phase phi t of a signal x t exhibits slips when the magnitude of their successive phase difference phi t i 1 phi t i exceeds pi by applying this approach to periodic uncorrelated and long range correlated data we show that the standard deviation of the time difference between the successive phase slips deltatau normalized by the percentage of slips in the data is characteristic of the correlation in the data we consider a 50x50 square lattice and model each lattice point by a second order autoregressive ar2 process further we model a subregion of the lattice using a different set of ar2 parameters compared to the rest by applying the proposed approach to the lattice model we show that the two distinct parameter regions introduced in the lattice are clearly distinguishable finally we demonstrate the application of this approach to spatiotemporal neonatal and fetal magnetoencephalography signals recorded using 151 superconducting quantum interference device sensors to identify the sensors containing the neonatal and fetal brain signals and discuss the improved performance of this approach over the traditionally used spectral approach

synchronization of uncoupled oscillators by common gamma impulses from phase locking to noise induced synchronization nonlinear oscillators can mutually synchronize when they are driven by common external impulses two important scenarios are i synchronization resulting from phase locking of each oscillator to regular periodic impulses and ii noise induced synchronization caused by the poisson random impulses but their difference has not been fully quantified here we analyze a pair of uncoupled oscillators subject to common random impulses with gamma distributed intervals which can be smoothly interpolated between the regular periodic and the random poisson impulses their dynamics are characterized by phase distributions frequency detuning lyapunov exponents and information theoretic measures which clearly reveal the differences between the two synchronization scenarios

mitigating the effects of measurement noise on granger causality computing granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years such causal relations if correctly estimated can yield significant insights into the dynamical organization of the system being investigated since experimental measurements are inevitably contaminated by noise it is thus important to understand the effects of such noise on granger causality estimation the first goal of this paper is to provide an analytical and numerical analysis of this problem specifically we show that due to noise contamination 1 spurious causality between two measured variables can arise and 2 true causality can be suppressed the second goal of the paper is to provide a denoising strategy to mitigate this problem specifically we propose a denoising algorithm based on the combined use of the kalman filter theory and the expectation maximization algorithm numerical examples are used to demonstrate the effectiveness of the denoising approach

on off intermittency power spectrum and fractal properties of time series abstract some dynamical systems possess invariant submanifolds such that the dynamics restricted to the invariant submanifold is chaotic this situation arises in systems with a spatial symmetry or in the synchronization of chaotic oscillators the invariant submanifold could become unstable to perturbations in the transverse directions when a parameter of the system is changed through a critical blow out value this could result in an extreme form of temporally intermittent bursting called on off intermittency we propose a model that incorporates the universal features of systems that display on off intermittency we study this model both with and without additive noise and we derive scaling results for the power spectral density of the on off intermittent process and for the box counting dimension for the set of time intervals when the process takes on values above a given threshold we then present numerical simulations realizing these results

synchronization of chaotic structurally nonequivalent systems synchronization features are explored for a pair of chaotic high dimensional bidirectionally coupled structurally nonequivalent systems we find two regimes of synchronization in dependence on the coupling strength creation of a lower dimensional chaotic state and for larger coupling a transition toward a stable periodic motion we characterize this new state showing that it is associated with an abrupt transition in the lyapunov spectrum the robustness of this state against noise is discussed and the use of this dynamical property as a possible approach for the control of chaos is outlined

synchronization with positive conditional lyapunov exponents synchronization of chaotic systems may occur only when the largest conditional lyapunov exponent of the driven system is negative the synchronization with positive conditional lyapunov exponents reported in a recent paper phys rev e 56 2272 1997 is a combined result of the contracting region of the system and the finite precision in computer simulations

a coupled statistical model for face shape recovery from brightness images we focus on the problem of developing a coupled statistical model that can be used to recover facial shape from brightness images of faces we study three alternative representations for facial shape these are the surface height function the surface gradient and a fourier basis representation we jointly capture variations in intensity and the surface shape representations using a coupled statistical model the model is constructed by performing principal components analysis on sets of parameters describing the contents of the intensity images and the facial shape representations by fitting the coupled model to intensity data facial shape is implicitly recovered from the shape parameters experiments show that the coupled model is able to generate accurate shape from out of training sample intensity images

averaging approach to phase coherence of uncoupled limit cycle oscillators receiving common random impulses populations of uncoupled limit cycle oscillators receiving common random impulses show various types of phase coherent states which are characterized by the distribution of phase differences between pairs of oscillators we develop a theory to predict the stationary distribution of pairwise phase differences from the phase response curve which quantitatively encapsulates the oscillator dynamics via averaging of the frobeniusperron equation describing the impulse driven oscillators the validity of our theory is confirmed by direct numerical simulations using the fitzhugh nagumo neural oscillator receiving common poisson impulses as an example

the reliability of the stochastic active rotator the reliability of firing of excitable oscillating systems is studied through the response of the active rotator a neuronal model evolving on the unit circle to white gaussian noise a stochastic return map is introduced that captures the behavior of the model this map has two fixed points one stable and the other unstable iterates of all initial conditions except the unstable point tend to the stable fixed point for almost all input realizations this means that to a given input realization there corresponds a unique asymptotic response in this way repetitive stimulation with the same segment of noise realization evokes after possibly a transient time the same response in the active rotator in other words this model responds reliably to such inputs it is argued that this results from the nonuniform motion of the active rotator around the unit circle and that similar results hold for other neuronal models whose dynamics can be approximated by phase dynamics similar to the active rotator

stability of incoherence in a population of coupled oscillators we analyze a mean field model of coupled oscillators with randomly distributed frequencies this system is known to exhibit a transition to collective oscillations for small coupling the system is incoherent with all the oscillators running at their natural frequencies but when the coupling exceeds a certain threshold the system spontaneously synchronizes we obtain the first rigorous stability results for this model by linearizing the fokker planck equation about the incoherent state an unexpected result is that the system has pathological stability properties the incoherent state is unstable above threshold butneutrally stable below threshold we also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise

a method for enforcing integrability in shape from shading algorithms an approach for enforcing integrability a particular implementation of the approach an example of its application to extending an existing shape from shading algorithm and experimental results showing the improvement that results from enforcing integrability are presented a possibly nonintegrable estimate of surface slopes is represented by a finite set of basis functions and integrability is enforced by calculating the orthogonal projection onto a vector subspace spanning the set of integrable slopes the integrability projection constraint was applied to extending an iterative shape from shading algorithm of m j brooks and b k p horn 1985 experimental results show that the extended algorithm converges faster and with less error than the original version good surface reconstructions were obtained with and without known boundary conditions and for fairly complicated surfaces

state dependent fire models and related renewal processes we introduce a general class of stochastic processes forced by instantaneous random fires i e jumps that reset the state variable x to a given value since in many physical systems the fire activity is often dependent on the actual value of the state variable as in the case of natural fires in ecosystems and firing dynamics in neuronal activity the frequency of fire occurrence is assumed to be state dependent such dynamics leads to independent interfire statistics i e to renewal point processes various functions relating the frequency of fire occurrence to x t are analyzed and compared the relation between the probabilistic dynamics of x t and the interfire statistics is derived and some exact probability distribution of both x t and the interfire times are obtained for systems with different degrees of complexity after studying processes in which the fire activity is coupled only to a deterministic drift we also analyze processes forced by either additive or multiplicative gaussian white noise

mean phase coherence as a measure for phase synchronization and its application to the eeg of epilepsy patients abstract we apply the concept of phase synchronization of chaotic and or noisy systems and the statistical distribution of the relative instantaneous phases to electroencephalograms eegs recorded from patients with temporal lobe epilepsy using the mean phase coherence as a statistical measure for phase synchronization we observe characteristic spatial and temporal shifts in synchronization that appear to be strongly related to pathological activity in particular we observe distinct differences in the degree of synchronization between recordings from seizure free intervals and those before an impending seizure indicating an altered state of brain dynamics prior to seizure activity

symmetric shape from shading using self ratio image in this paper we present a symmetric shape from shading sfs approach to recover both shape and albedo for symmetric objects lambertian surfaces with unknown varying albedo and orthographic projections are assumed in our formulation of symmetric sfs we have two image irradiance equations one is the standard equation used in sfs and the other is a self ratio image irradiance equation this new image irradiance equation relates the self ratio image which is defined as the ratio of two halves of the input image to light source and surface shape the introduction of the self ratio image facilitates the direct use of symmetry cue based on the self ratio image a new model based symmetric source from shading algorithm is also presented we then propose symmetric sfs algorithms to recover both shape and albedo from a single image and present experimental results the new symmetric sfs scheme has one important property the existence of a unique global solution which consists of unique local solutions at each point simultaneously obtained using the intensity information at that point and the surrounding local region and the assumption of a cal c 2 surface proofs for the existence of a unique solution in the cases of unknown constant and non constant albedos are provided

new constraints on data closeness and needle map consistency for shape from shading this paper makes two contributions to the problem of needle map recovery using shape from shading first we provide a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint this not only improves the data closeness of the recovered needle map but also removes the necessity for extensive parameter tuning second we exploit the improved ease of control of the new shape from shading process to investigate various types of needle map consistency constraint the first set of constraints are based on needle map smoothness the second avenue of investigation is to use curvature information to impose topographic constraints third we explore ways in which the needle map is recovered so as to be consistent with the image gradient field in each case we explore a variety of robust error measures and consistency weighting schemes that can be used to impose the desired constraints on the recovered needle map we provide an experimental assessment of the new shape from shading framework on both real world images and synthetic images with known ground truth surface normals the main conclusion drawn from our analysis is that the data closeness constraint improves the efficiency of shape from shading and that both the topographic and gradient consistency constraints improve the fidelity of the recovered needle map

type ii phase resetting curve is optimal for stochastic synchrony the phase resetting curve prc describes the response of a neural oscillator to small perturbations in membrane potential its usefulness for predicting the dynamics of weakly coupled deterministic networks has been well characterized however the inputs to real neurons may often be more accurately described as barrages of synaptic noise effective connectivity between cells may thus arise in the form of correlations between the noisy input streams we use constrained optimization and perturbation methods to prove that the prc shape determines susceptibility to synchrony among otherwise uncoupled noise driven neural oscillators prcs can be placed into two general categories type i prcs are non negative while type ii prcs have a large negative region here we show that oscillators with type ii prcs receiving common noisy input synchronize more readily than those with type i prcs

synchronization and desynchronization of self sustained oscillators by common noise we consider the effect of external noise on the dynamics of limit cycle oscillators the lyapunov exponent becomes negative under influence of small white noise what means synchronization of two or more identical systems subject to common noise we analytically study the effect of small nonidentities in the oscillators and in the noise and derive statistical characteristics of deviations from the perfect synchrony large white noise can lead to desynchronization of oscillators provided they are nonisochronous this is demonstrated for the van der pol duffing system

dynamics of limit cycle oscillators subject to general noise the phase description is a powerful tool for analyzing noisy limit cycle oscillators the method however has found only limited applications so far because the present theory is applicable only to gaussian noise while noise in the real world often has non gaussian statistics here we provide the phase reduction method for limit cycle oscillators subject to general colored and non gaussian noise including a heavy tailed one we derive quantifiers like mean frequency diffusion constant and the lyapunov exponent to confirm consistency of the results applying our results we additionally study a resonance between the phase and noise

time scale synchronization of chaotic oscillators this paper presents the result of the investigation of chaotic oscillator synchronization a new approach to detect the synchronized behaviour of chaotic oscillators has been proposed this approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators this approach has been applied for the coupled rossler and lorenz systems

synchronized spatiotemporal chaos and spatiotemporal on off intermittency in a nonlinear ring cavity we numerically study the transverse ikeda system describing a ring cavity with a saturable absorber nonlinearity which is driven by a coherent input field the gaussian shape of the input beam favors the solutions to have space inversion symmetry these solutions bifurcate into states of synchronized spatiotemporal chaos where synchronization refers to the identical dynamics of the two beam halves we demonstrate that the breakdown of this synchronized chaotic state is caused by on off intermittency the qualitative and quantitative features of the transition are studied in particular the scaling behavior of the transition in the space domain is investigated the results display a qualitative similarity with the scaling behavior of spatiotemporal intermittency textcopyright 1996 the american physical society

assessing statistical significance of phase synchronization index an application to study baroreflex function in critically ill infants abstract phase differences of two signals in perfect synchrony exhibit a narrow band distribution whereas the phase differences of two asynchronous signals exhibit uniform distribution we assess the statistical significance of the phase synchronization between two signals by using a signed rank test to compare the distribution of their phase differences to the theoretically expected uniform distribution for two asynchronous signals using numerical simulation of a second order autoregressive ar2 process we show that the proposed approach correctly identifies the coupling between the ar2 process and the driving white noise we also identify the optimal p value that distinguishes coupled scenarios from uncoupled ones to identify the limiting cases we study the phase synchronization between two independent white noises as a function of bandwidth of the filter in a different second simulation we identify the frequency bandwidth below which the proposed approach fails and suggest using a data driven approach for those scenarios finally we demonstrate the application of this approach to study the coupling between beat to beat cardiac intervals and continuous blood pressure obtained from critically ill infants to characterize the baroreflex function

two degrees of freedom quasi bi hamiltonian systems starting from the classical example of the henon heiles integrable hamiltonian system we show that it admits a slightly different formulation from the classical bi hamiltonian system we introduce the general notion of a quasi bi hamiltonian system qbhs and study some of its basic properties only in the case of two degrees of freedom in particular we give the general form of this structure in the nijenhuis coordinates which are constructed using the eigenvalues of the nijenhuis operator of the system and show how they serve to separate the hamilton jacobi equation in the last section we look at the problem of the semi local existence of such structures

detecting phase synchronization in noisy data from coupled chaotic oscillators two schemes are proposed to detect phase synchronization from chaotic data contaminated by noise the first is a neighborhood based method which links time delay embedding with instantaneous phase estimation the second adopts the local projection method as a preprocessing filter to noisy data both schemes utilize the state recurrence an important feature of chaotic data the proposed schemes are applied to data measured from two typical chaotic systems i e the coupled rossler systems and the coupled lorenz systems respectively the results show that phase synchronization which may be buried by noise is detected even when the noise level is high moreover the overestimation of the degree of phase synchronization which may be introduced by the hilbert transform combined with a traditional linear bandpass filter can be avoided when the data are contaminated by only measurement noise

quasi bi hamiltonian systems and separability two quasi bi hamiltonian systems with three and four degrees of freedom are presented these systems are shown to be separable in terms of nijenhuis coordinates moreover the most general pfaffian quasi bi hamiltonian system with an arbitrary number of degrees of freedom is constructed in terms of nijenhuis coordinates and its separability is proved

correlation transfer in stochastically driven neural oscillators over long and short time scales in the absence of synaptic coupling two or more neural oscillators may become synchronized by virtue of the statistical correlations in their noisy input streams recent work has shown that the degree of correlation transfer from input currents to output spikes depends not only on intrinsic oscillator dynamics but also on the length of the observation window over which the correlation is calculated in this paper we use stochastic phase reduction and regular perturbations to derive the correlation of the total phase elapsed over long time scales a quantity that provides a convenient proxy for the spike count correlation over short time scales we derive the spike count correlation directly using straightforward probabilistic reasoning applied to the density of the phase difference our approximations show that output correlation scales with the autocorrelation of the phase resetting curve over long time scales we also find a concise expression for the influence of the shape of the phase resetting curve on the initial slope of the output correlation over short time scales these analytic results together with numerical simulations provide new intuitions for the recent counterintuitive finding that type i oscillators transfer correlations more faithfully than do type ii over long time scales while the reverse holds true for the better understood case of short time scales

stochastic phase transition operator in this study a markov operator is introduced that represents the density evolution of an impulse driven stochastic biological oscillator the operator s stochastic kernel is constructed using the asymptotic expansion of stochastic processes instead of solving the fokker planck equation the markov operator is shown to successfully approximate the density evolution of the biological oscillator considered the response of the oscillator to both periodic and time varying impulses can be analyzed using the operator s transient and stationary properties furthermore an unreported stochastic dynamic bifurcation for the biological oscillator is obtained by using the eigenvalues of the product of the markov operators

the complete whittaker theorem for two dimensional integrable systems and its application the authors prove for a particle moving in a plane under the influence of a conservative force that when the motion is constrained by a second invariant quadratic in the velocities then the potential allows separability of the hamilton jacobi equation in rectangular polar elliptical cylinder or parabolic cylinder coordinates this link shows the intimate connection between quadratic invariants and the two dimensional hamilton jacobi equation they give examples of the utility of parabolic cylinder coordinates in cases of recent study

amplitude death in an array of limit cycle oscillators we analyze a large system of limit cycle oscillators with mean field coupling and randomly distributed natural frequencies we prove that when the coupling is sufficiently strong and the distribution of frequencies has sufficiently large variance the system undergoes amplitude death the oscillators pull each other off their limit cycles and into the origin which in this case is astable equilibrium point for the coupled system we determine the region in couplingvariance space for which amplitude death is stable and present the first proof that the infinite system provides an accurate picture of amplitude death in the large but finite system

chaos noise and synchronization reconsidered in a recent paper maritan and banavar phys rev lett 72 1451 1994 reported the synchronization of identical chaotic systems by additive noise we relate such a synchronization to the maximum lyapunov exponent of a single system and discuss the underlying mechanisms of the effect in the case of the lorenz equations the nonvanishing mean of the noise mimics a parameter change leading to synchronization for the logistic map a state dependence of the fluctuations is induced by the boundary conditions

synchronization of spectral components and its regularities in chaotic dynamical systems the chaotic synchronization regime in coupled dynamical systems is considered it has been shown that theonset of a synchronous regime is based on the appearance of a phase relation between the interacting chaoticoscillator frequency components of fourier spectra the criterion of synchronization of spectral components aswell as the measure of synchronization has been discussed the universal power law has been described themain results are illustrated by coupled rossler systems van der pol and van der pol duf ng oscillators doi 10 1103 physreve 71 056204 pacs numberssd 05 45 xt 05 45 tpi introduction

cross correlation of instantaneous phase increments in pressure flow fluctuations applications to cerebral autoregulation we investigate the relationship between the blood flow velocities bfv in the middle cerebral arteries and beat to beat blood pressure bp recorded from a finger in healthy and post stroke subjects during the quasisteady state after perturbation for four different physiologic conditions supine rest head up tilt hyperventilation and co2 rebreathing in upright position to evaluate whether instantaneous bp changes in the steady state are coupled with instantaneous changes in the bfv we compare dynamical patterns in the instantaneous phases of these signals obtained from the hilbert transform as a function of time we find that in post stroke subjects the instantaneous phase increments of bp and bfv exhibit well pronounced patterns that remain stable in time for all four physiologic conditions while in healthy subjects these patterns are different less pronounced and more variable we propose an approach based on the cross correlation of the instantaneous phase increments to quantify the coupling between bp and bfv signals we find that the maximum correlation strength is different for the two groups and for the different conditions for healthy subjects the amplitude of the cross correlation between the instantaneous phase increments of bp and bfv is small and attenuates within 3 5 heartbeats in contrast for post stroke subjects this amplitude is significantly larger and cross correlations persist up to 20 heartbeats further we show that the instantaneous phase increments of bp and bfv are cross correlated even within a single heartbeat cycle we compare the results of our approach with three complementary methods direct bp bfv cross correlation transfer function analysis and phase synchronization analysis our findings provide insight into the mechanism of cerebral vascular control in healthy subjects suggesting that this control mechanism may involve rapid adjustments within a heartbeat of the cerebral vessels so that bfv remains steady in response to changes in peripheral bp

phase coherence in an ensemble of uncoupled limit cycle oscillators receiving common poisson impulses an ensemble of uncoupled limit cycle oscillators receiving common poisson impulses shows a range of nontrivial behavior from synchronization desynchronization to clustering the group behavior that arises in the ensemble can be predicted from the phase response of a single oscillator to a given impulsive perturbation we present a theory based on phase reduction of a jump stochastic process describing a poisson driven limit cycle oscillator and verify the results through numerical simulations and electric circuit experiments we also give a geometrical interpretation of the synchronizing mechanism a perturbative expansion to the stationary phase distribution and the diffusion limit of our jump stochastic model

bi hamiltonian structure of an integrable henon heiles system by making use of the system of coordinates in which the separation of the variables in the hamilton jacobi equation takes place we find a bi hamiltonian stmclure of a two degrees of freedom hamiltmian system corresponding to the integrable henon

analysis of a solvable model of a phase oscillator network on a circle with infinite range mexican hat type interaction interaction with the zeroth and first fourier components we give detailed derivations of the auxiliary equations for the phases and self consistent equations for the amplitudes we solve these equations and characterize the nontrivial solutions in terms of order parameters and the rotation number furthermore we derive the boundaries of the bistable regions and study the bifurcation structures in detail expressions for location dependent resultant frequencies and entrained phases are also derived secondly we treat a different interaction that is composed of mth and nth fourier components where m n and we study its nontrivial solutions in both cases the results of numerical simulations agree quite well with the theoretical results

incorporating illumination constraints in deformable models for shape from shading and light direction estimation we present a method for the integration of nonlinear holonomic constraints in deformable models and its application to the problems of shape and illuminant direction estimation from shading experimental results demonstrate that our method performs better than previous shape from shading algorithms applied to images of lambertian objects under known illumination it is also more general as it can be applied to non lambertian surfaces and it does not require knowledge of the illuminant direction in this paper 1 we first develop a theory for the numerically robust integration of nonlinear holonomic constraints within a deformable model framework in this formulation we use lagrange multipliers and a baumgarte stabilization approach 1972 2 we also describe a fast new method for the computation of constraint based forces in the case of high numbers of local parameters 3 we demonstrate how any type of illumination constraint from the simple lambertian model to more complex highly nonlinear models can be incorporated in a deformable model framework 4 we extend our method to work when the direction of the light source is not known we couple our shape estimation method with a method for light estimation in an iterative process where improved shape estimation results in improved light estimation and vice versa 5 we perform a series of experiments

new bi hamiltonian systems on the plane we discuss several new bi hamiltonian integrable systems on the plane with integrals of motion of third fourth and sixth orders in momenta the corresponding variables of separation separated relations compatible poisson brackets and recursion operators are also presented in the framework of the jacobi method

synchrony of limit cycle oscillators induced by random external impulses the mechanism of phase synchronization between uncoupled limit cycle oscillators induced by common random impulsive forcing is analyzed by reducing the dynamics of the oscillator to a random phase map it is shown that phase synchronization generally occurs when the oscillator is driven by weak random impulsive forcing in the limit of large interimpulse intervals the case where the interimpulse intervals are finite is also analyzed perturbatively for small impulse intensity for weak poisson impulses it is shown that the phase synchronization persists up to the first order approximation

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

facial shape from shading and recognition using principal geodesic analysis and robust statistics the aim in this paper is to use principal geodesic analysis to model the statistical variations for sets of facial needle maps we commence by showing how to represent the distribution of surface normals using the exponential map shape deformations are described using principal geodesic analysis on the exponential map using ideas from robust statistics we show how this deformable model may be fitted to facial images in which there is significant self shadowing moreover we demonstrate that the resulting shape from shading algorithm can be used to recover accurate facial shape and albedo from real world images in particular the algorithm can effectively fill in the facial surface when more than 30 of its area is subject to self shadowing to investigate the utility of the shape parameters delivered by the method we conduct experiments with illumination insensitive face recognition we present a novel recognition strategy in which similarity is measured in the space of the principal geodesic parameters we also use the recovered shape information to generate illumination normalized prototype images on which recognition can be performed finally we show that from a single input image we are able to generate the basis images employed by a number of well known illumination insensitive recognition algorithms we also demonstrate that the principal geodesics provide an efficient parameterization of the space of harmonic basis images

recovering facial shape using a statistical model of surface normal direction in this paper we show how a statistical model of facial shape can be embedded within a shape from shading algorithm we describe how facial shape can be captured using a statistical model of variations in surface normal direction to construct this model we make use of the azimuthal equidistant projection to map the distribution of surface normals from the polar representation on a unit sphere to cartesian points on a local tangent plane the distribution of surface normal directions is captured using the covariance matrix for the projected point positions the eigenvectors of the covariance matrix define the modes of shape variation in the fields of transformed surface normals we show how this model can be trained using surface normal data acquired from range images and how to fit the model to intensity images of faces using constraints on the surface normal direction provided by lambert s law we demonstrate that the combination of a global statistical constraint and local irradiance constraint yields an efficient and accurate approach to facial shape recovery and is capable of recovering fine local surface details we assess the accuracy of the technique on a variety of images with ground truth and real world images

gender discriminating models from facial surface normals in this paper we show how to use facial shape information to construct discriminating models for gender classification we represent facial shapes using 2 5d fields of facial surface normals and investigate three different methods to improve the gender discriminating capacity of the model constructed using the standard eigenspace method the three methods are novel variants of principal geodesic analysis pga namely a weighted pga b supervised weighted pga and c supervised pga our starting point is to define a weight map over the facial surface that indicates the importance of different locations in discriminating gender we show how to compute the relevant weights and how to incorporate the weights into the 2 5d model construction we evaluate the performance of the alternative methods using facial surface normals extracted from 3d range images or recovered from brightness images experimental results demonstrate the effectiveness of our methods moreover the classification accuracy which is as high as 97 demonstrates the effectiveness of using facial shape information for gender classification

existence of hysteresis in the kuramoto model with bimodal frequency distributions we investigate the transition to synchronization in the kuramoto model with bimodal distributions of the natural frequencies previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one due to the shallowness of the central dip here we show that proximity to the unimodal bimodal border does not necessarily imply hysteresis when the width but not the depth of the central dip tends to zero we draw this conclusion from a detailed study of the kuramoto model with a suitable family of bimodal distributions

intertime jump statistics of state dependent poisson processes a method to obtain the probability distribution of the interarrival times of jump occurrences in systems driven by state dependent poisson noise is proposed such a method uses the survivor function obtained by a modified version of the master equation associated to the stochastic process under analysis a model for the timing of human activities shows the capability of state dependent poisson noise to generate power law distributions the application of the method to a model for neuron dynamics and to a hydrological model accounting for land atmosphere interaction elucidates the origin of characteristic recurrence intervals and possible persistence in state dependent poisson models

on the integrability of stationary and restricted flows of the kdv hierarchy a bi hamiltonian formulation for stationary flows of the kdv hierarchy is derived in an extended phase space a map between stationary flows and restricted flows is constructed in one case it connects an integrable henon heiles system and the garnier system moreover a new integrability scheme for hamiltonian systems is proposed that holds in the standard phase space

global synchronization in two dimensional lattices of discrete belousov zhabotinsky oscillators abstract macroscopic synchronization was investigated experimentally in the belousov zhabotinsky reaction with a two dimensional lattice arrangement of coupled chemical oscillators the natural frequency of each oscillator was distributed randomly and the spacing distance d between beads was varied where the coupling strength between two oscillators was controlled by changing d at small d beyond a certain critical value the oscillators synchronized spontaneously with each other global synchronization in the lattice was described as a function of d the critical coupling strength for global synchronization depends on the total number of oscillators when noisy light was applied uniformly to whole oscillators the order of synchronization was maximized at optimal noise intensity noise synchronization was observed

synchronization of randomly driven nonlinear oscillators when nonlinear oscillators with stable limit cycles are subject to periodic forces these oscillators may become entrained or mode locked to the driving force remarkably a similar phenomenon occurs when the nonlinear oscillators are driven by a random force in particular when nonlinear oscillators with different initial conditions are strongly driven with the same random force their fluctuating behavior may reliably converge to an identical synchronized response analytical estimates are derived for the conditions rates and structural stability for synchronization of a broad class of randomly driven nonlinear oscillators which suggest different experimental procedures for assessing the nonlinear response of biological chemical and physical oscillators to fluctuating inputs

evaluation of entrainment of a nonlinear neural oscillator to white noise the lyapunov exponent for a one dimensional neural oscillator model the theta neuron is computed for white noise forcing using the steady state solution to the associated fokker planck equation the latter is mildly singular due to the nature of the multiplicative input in agreement with previous results with similar models the exponent is negative for all forcing amplitudes but here it is shown to be small relative to that for periodic drive in a range of forcing strengths thus the synchronization of an ensemble of independent neurons receiving common but random input can be slow moreover this implies that aperiodic input may be suboptimal in some contexts for preserving the reliability of fine spike timing a potentially important component of the neural code