optimal network configuration for maximal coherence resonance in excitable systems we analyze the coherence resonance phenomenon in an ensemble of noise driven excitable neurons giving special attention to the role of the interaction topology the neural architecture is modeled using a spatially embedded network in which we can tune the network organization between scale free like with dominating long range connections and a network with mostly adjacent neurons connected we found that besides an optimal noise intensity also an optimal network configuration exists at which the largest average coherence of noise induced spikes is achieved furthermore we show that long as well as short range interactions between neurons should exist in order to achieve the optimal response of the neuronal network

stochastic resonance in an ensemble of bistable systems under stable distribution noises and nonhomogeneous coupling in this paper stochastic resonance of an ensemble of coupled bistable systems driven by noise having an stable distribution and nonhomogeneous coupling is investigated the stable distribution considered here is characterized by four intrinsic parameters 0 2 is called the stability parameter for describing the asymptotic behavior of stable densities 1 1 is a skewness parameter for measuring asymmetry 0 is a scale parameter for measuring the width of the distribution and is a location parameter for representing the mean value it is demonstrated that the resonant behavior is optimized by an intermediate value of the diversity in coupling strengths we show that the stability parameter and the scale parameter can be well selected to generate resonant effects in response to external signals in addition the interplay between the skewness parameter and the location parameter on the resonance effects is also studied we further show that the asymmetry of a l evy stable distribution resulting from the skewness parameter and the location parameter can enhance the resonance effects both theoretical analysis and simulation are presented to verify the results of this paper

multiplicative noise induced coherence resonance via two different mechanisms in bistable neural models the bistable fitzhugh nagumo fhn neural model driven by two multiplicative noises and one additive noise is investigated two different potential mechanisms for enhancing coherence of bistable fhn model are presented that is the first multiplicative noise changes the system from the bistable to the oscillatory regime and the second multiplicative noise can enhance the symmetry of two stable states of the system the two mechanisms are analytically or numerically explained at any level of the second multiplicative noise a maximal coherence have been found at some intermediate noise intensity of the first multiplicative noise only when the first multiplicative noise intensity is less than 0 0001 can a maximal coherence be obtained at some intermediate noise intensity of the second multiplicative noise these coherence resonance phenomena have been understood in terms of the presented mechanisms

variability in noise driven integrator neurons neural variability in the presence of noise has been studied mainly in resonator neurons such as hodgkinhuxley or fitzhugh nagumo models here we investigate this variability for integrator neurons whose excitability is due to a saddle node bifurcation of the rest state instead of a hopf bifurcation using simple theoretical expressions for the interspike times distributions we obtain coefficients of variation in good agreement with numerical calculations in realistic neuron models the main features of this coefficient as a function of noise depend on the refractory period and on the presence of bistability the bistability is responsible for the existence of two different time scales in the spiking behavior giving an antiresonance effect

noise memory induced excitability and pattern formation in oscillatory neural models we report a noise memory induced phase transition in an array of oscillatory neural systems which leads to the suppression of synchronous oscillations and restoration of excitable dynamics this phenomenon is caused by the systematic contributions of temporally correlated parametric noise i e possessing a memory which stabilizes a deterministically unstable fixed point changing the noise correlation time a reentrant phase transition to noise induced excitability is observed in a globally coupled array since noise induced excitability implies the restoration of the ability to transmit information associated spatiotemporal patterns are observed afterwards furthermore an analytic approach to predict the systematic effects of exponentially correlated noise is presented and its results are compared with the simulations

eigenvalue distributions for a class of covariance matrices with application to bienenstock cooper munro neurons under noisy conditions we analyze the effects of noise correlations in the input to or among bienenstock cooper munro neurons using the wigner semicircular law to construct random positive definite symmetric correlation matrices and compute their eigenvalue distributions in the finite dimensional case we compare our analytic results with numerical simulations and show the effects of correlations on the lifetimes of synaptic strengths in various visual environments these correlations can be due either to correlations in the noise from the input lateral geniculate nucleus neurons or correlations in the variability of lateral connections in a network of neurons in particular we find that for fixed dimensionality a large noise variance can give rise to long lifetimes of synaptic strengths this may be of physiological significance

internal noise stochastic resonance for intracellular calcium oscillations in a cell system by constructing a mesoscopic stochastic model for intracellular calcium oscillations in a cell system we have investigated how the internal noise would influence the calcium oscillations of such a system using stochastic simulation methods and chemical langevin method it is found that stochastic calcium oscillations appear when the internal noise is considered while the deterministic model only yields steady state the performance of such oscillations undergoes a maximum with the variation of the internal noise level indicating the occurrence of internal noise stochastic resonance interestingly we find that the optimal system size matches well with the real cell size when the control parameter is tuned near the left hopf bifurcation point and such a match is robust to the variation of the control parameters

partial synchronization in coupled chemical chaotic oscillators in this paper we investigate the problem of partial synchronization in diffusively coupled chemical chaotic oscillators with zero flux boundary conditions the dynamical properties of the chemical system which oscillates with uniform phase evolution yet has chaotic amplitudes upca are first discussed by combining numerical and analytical methods the impossibility of full global synchronization in a network of two or three coupled chemical oscillators is discovered mathematically stable partial synchronization corresponds to convergence to a linear invariant manifold of the global state space the sufficient conditions for exponential stability of the invariant manifold in a network of three coupled chemical oscillators are obtained via the nonlinear contraction principle

entrainment of coupled oscillators on regular networks by pacemakers we study kuramoto oscillators driven by one pacemaker on d dimensional regular topologies with nearest neighbor interactions we derive the analytical expressions for the common frequency in the case of phase locked motion and for the critical frequency of the pacemaker placed at an arbitrary position in the lattice so that above the critical frequency no phase locked motion is possible we show that the mere change in topology from an open chain to a ring induces synchronization for a certain range of pacemaker frequencies and couplings while keeping the other parameters fixed moreover we demonstrate numerically that the critical frequency of the pacemaker decreases as a power of the linear size of the lattice with an exponent equal to the dimension of the system this leads in particular to the conclusion that for infinite dimensional topologies the critical frequency for having entrainment decreases exponentially with increasing size of the system or more generally with increasing depth of the network that is the average distance of the oscillators from the pacemaker

influence of spatiotemporally correlated noise on structure formation in excitable media we discuss the influence of additive spatiotemporally correlated i e colored noise on pattern formation in a two dimensional network of excitable systems the signature of spatiotemporal stochastic resonance stsr is analyzed using cross correlation and information theoretic measures it is found that the stsr behavior is affected by both the spatial and temporal correlations of the noise due to an interplay with the length scales of the deterministic network increasing the spatiotemporal noise correlation shifts the occurrence of stsr to smaller values of the noise variance additionally if the spatial correlation of the noise exceeds that of the network the excitation patterns disappear in favor of cloudy structures directly rendering the underlying spatial noise field

correlated noise induced spatiotemporal coherence resonance in a square lattice network abstract the effects of additive correlated noise which is composed of common gaussian white noise and local gaussian colored noise on a square lattice network locally modelled by the rulkov map are studied we focus on the ability of noise to induce pattern formation in a resonant manner it is shown that local gaussian colored noise is able to induce pattern formation which is more coherent at some noise intensity or correlation time so it is able to induce spatiotemporal coherence resonance in the network when common gaussian white noise is applied in addition it is seen that the correlated noise can induce coherent spatial structures at some intermediate noise correlation while this is not the case for smaller and larger noise intensities the mechanism of the observed spatiotemporal coherence resonance is discussed it is also found that the correlation time of local colored noise has no evident effect on the optimal value of the noise strength for spatiotemporal coherence resonance in the network

cooperative dynamics in a network of stochastic elements with delayed feedback networks of globally coupled noise activated bistable elements with connection time delays are considered the dynamics of these systems is studied numerically using a langevin description and analytically using 1 a gaussian approximation as well as 2 a dichotomous model the system demonstrates ordering phase transitions and multistability that is for a strong enough feedback it exhibits nontrivial stationary states and oscillatory states whose frequencies depend only on the mean of the time delay distribution function other observed dynamical phenomena include coherence resonance and in the case of nonuniform coupling strengths amplitude death and chaos furthermore an increase of the stability of the trivial equilibrium with increasing nonuniformity of the time delays is observed

np completeness of st orientations for plane graphs an st orientation or bipolar orientation of a 2 connected graph g is an orientation of its edges to generate a directed acyclic graph with a single source s and a single sink t given a plane graph g and two exterior vertices s and t the problem of finding an optimum st orientation i e an st orientation in which the length of a longest st path is minimized was first proposed indirectly by rosenstiehl and tarjan in and then later directly by he and kao in in this paper we prove that given a 2 connected plane graph g two exterior vertices s t and a positive integer k the decision problem of whether g has an st orientation where the maximum length of an st path is k is np complete this solves a long standing open problem on the complexity of optimum st orientations for plane graphs as a by product we prove that the np completeness result holds for planar graphs as well

collapse of ordered spatial pattern in neuronal network abstract spatiotemporal systems can emerge some regular spatial patterns due to self organization or under external periodical pacing while external attack or intrinsic collapse can destroy the regularity in the spatial system for an example the electrical activities of neurons in nervous system show regular spatial distribution under appropriate coupling and connection it is believed that distinct regularity could be induced in the media by appropriate forcing or feedback while a diffusive collapse induced by continuous destruction can cause breakdown of the media in this paper the collapse of ordered spatial distribution is investigated in a regular network of neurons morris lecar hindmarsh rose in two dimensional array a stable target wave is developed regular spatial distribution emerges by imposing appropriate external forcing with diversity or generating heterogeneity parameter diversity in space the diffusive invasion could be produced by continuous parameter collapse or switch in local area e g the diffusive poisoning in ion channels of potassium in morris lecar neurons causes breakdown in conductance of channels it is found that target wave dominated regularity can be suppressed when the collapsed area is diffused in random statistical correlation functions for sampled nodes neurons are defined to detect the collapse of ordered state by series analysis

type i membranes phase resetting curves and synchrony type i membrane oscillators such as the connor model connor et al 1977 and the morris lecar model morris and lecar 1981 admit very low frequency oscillations near the critical applied current hansel et al 1995 have numerically shown that synchrony is difficult to achieve with these models and that the phase resetting curve is strictly positive we use singular perturbation methods and averaging to show that this is a general property of type i membrane models we show in a limited sense that so called type ii resetting occurs with models that obtain rhythmicity via a hopf bifurcation we also show the differences between synapses that act rapidly and those that act slowly and derive a canonical form for the phase interactions

two distinct mechanisms of coherence in randomly perturbed dynamical systems we carefully examine two mechanisms coherence resonance and self induced stochastic resonance by which small random perturbations of excitable systems with large time scale separation may lead to the emergence of new coherent behaviors in the form of limit cycles we analyze what controls the degree of coherence in these two mechanisms and classify their very different properties in particular we show that coherence resonance arises only at the onset of bifurcation and is rather insensitive against variations in the noise amplitude and the time scale separation ratio in contrast self induced stochastic resonance may arise away from bifurcations and the properties of the limit cycle it induces are controlled by both the noise amplitude and the time scale separation ratio

a tour of the theory of absolutely minimizing functions a detailed analysis of the class of absolutely minimizing functions in euclidean spaces and the relationship to the infinity laplace equation

pacemaker guided noise induced spatial periodicity in excitable media we study the impact of subthreshold periodic pacemaker activity and internal noise on the spatial dynamics of excitable media for this purpose we examine two systems that both consist of diffusively coupled units in the first case the local dynamics of the units is driven by a simple one dimensional model of excitability with a piece wise linear potential in the second case a more realistic biological system is studied and the local dynamics is driven by a model for calcium oscillations internal noise is introduced via the leap stochastic integration procedure and its intensity is determined by the finite size of each constitutive system unit we show that there exists an intermediate level of internal stochasticity for which the localized pacemaker activity maps best into coherent periodic waves whose spatial frequency is uniquely determined by the local subthreshold forcing via an analytical treatment of the simple minimal model for the excitable spatially extended system we explicitly link the pacemaker activity with the spatial dynamics and determine necessary conditions that warrant the observation of the phenomenon in excitable media our results could prove useful for the understanding of interplay between local and global agonists affecting the functioning of tissue and organs

absolutely minimal lipschitz extension of tree valued mappings we prove that every lipschitz function from a subset of a locally compact length space to a metric tree has a unique absolutely minimal lipschitz extension amle we relate these extensions to a stochastic game called politics a generalization of a game called tug of war that has been used in peres et al j am math soc 22 1 167 210 2009 to study real valued amles

coauthorship networks and patterns of scientific collaboration by using data from three bibliographic databases in biology physics and mathematics respectively networks are constructed in which the nodes are scientists and two scientists are connected if they have coauthored a paper we use these networks to answer a broad variety of questions about collaboration patterns such as the numbers of papers authors write how many people they write them with what the typical distance between scientists is through the network and how patterns of collaboration vary between subjects and over time we also summarize a number of recent results by other authors on coauthorship patterns

a mechanism of synchronization in interacting multi cell genetic systems abstract we investigate a general coupled noisy system with time delays which may be applied to biologically plausible systems for cell cell communication in a simplified context the main conclusion is that appropriate noise intensities and coupling strengths are capable of driving the system to be synchronous we first provide an analytical treatment for the synchronization process based on the essential phase locking mechanism and then derive sufficient conditions which if satisfied ensure existence of the synchrony solution finally a multi cell system with a synthetic gene regulatory network which contains both intracellular and extracellular noises and time delays is adopted to demonstrate effects of extracellular noises and couplings on synchronization

light noise induced suprathreshold circadian oscillations and coherent resonance in drosophila based on a reduced circadian oscillator model in drosophila smolen biophys j 83 2349 2002 the effects of light noise and time delay on a circadian oscillator near a hopf bifurcation are studied by using numerical computation when the light controlled parameter is suprathreshold it was found that the circadian oscillations can be induced by light fluctuation there is an optimal light noise intensity at which a remarkable coherent circadian oscillation is observed which implies a significant resonance phenomenon in the sense of preferred biological circadian oscillations time delay can control the coherence of noise induced circadian oscillations and the strength of coherent resonance achieves a maximum under a moderate time delay

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

effects of non gaussian noise near supercritical hopf bifurcation abstract we have studied the effects of non gaussian colored noise in a chemical oscillation system the well known brusselator model in the parameter region close to the supercritical hopf bifurcation with the variation of the parameter q which quantifies the deviation from gaussian character the signal to noise ratio of noise induced oscillation exhibits a bell shaped change indicating the presence of resonant activity the cooperative effects of q and the correlation time on the performance of noise induced oscillation are also investigated interestingly resonance like behavior can be induced by either q or when the other parameter is properly fixed stochastic normal form theory is used to analyze these nontrivial effects and the simulation results are well reproduced this work provides us comprehensive understanding of how non gaussian noise influences the dynamics in chemical oscillation systems

encoding with bursting subthreshold oscillations and noise in mammalian cold receptors mammalian cold thermoreceptors encode steady state temperatures into characteristic temporal patterns of action potentials we propose a mechanism for the encoding process it is based on plant s ionic model of slow wave bursting to which stochastic forcing is added the model reproduces firing patterns from cat lingual cold receptors as the parameters most likely to underlie the thermosensitivity of these receptors varied over a 25 c range the sequence of firing patterns goes from regular bursting to simple periodic to stochastically phase locked firing or skipping the skipping at higher temperatures is shown to necessitate an interaction between noise and a subthreshold endogenous oscillation in the receptor the basic period of all patterns is robust to noise further noise extends the range of encodable stimuli an increase in firing irregularity with temperature also results from the loss of stability accompanying the approach by the slow dynamics of a reverse hopf bifurcation the results are not dependent on the precise details of the plant model but are generic features of models where an autonomous slow wave arises through a hopf bifurcation the model also addresses the variability of the firing patterns across fibers an alternate model of slow wave bursting chay and fan 1993 in which skipping can occur without noise is also analyzed here in the context of cold thermoreception our study quantifies the possible origins and relative contribution of deterministic and stochastic dynamics to the coding scheme implications of our findings for sensory coding are discussed

stochastic resonance in models of neuronal ensembles two recently suggested mechanisms for the neuronal encoding of sensory information involving the effect of stochastic resonance with aperiodic time varying inputs are considered it is shown using theoretical arguments and numerical simulations that the nonmonotonic behavior with increasing noise of the correlation measures used for the so called aperiodic stochastic resonance asr scenario does not rely on the cooperative effect typical of stochastic resonance in bistable and excitable systems rather asr with slowly varying signals is more properly interpreted as linearization by noise consequently the broadening of the resonance curve in the multineuron stochastic resonance without tuningscenario can also be explained by this linearization computation of the input output correlation as a function of both signal frequency and noise for the model system further reveals conditions where noise induced firing with aperiodic inputs will benefit from stochastic resonance rather than linearization by noise thus our study clarifies the tuning requirements for the optimal transduction of subthreshold aperiodic signals it also shows that a single deterministic neuron can perform as well as a network when biased into a suprathreshold regime finally we show that the inclusion of a refractory period in the spike detection scheme produces a better correlation between instantaneous firing rate and input signal s1063 651x 97 01102 1

lifetime enhancement of scroll rings by spatiotemporal fluctuations the dynamics of three dimensional scroll rings with spatiotemporal random excitability is investigated numerically using the fitzhugh nagumo model depending on the correlation time and length scales of the fluctuations the lifetime of the ring filament is enlarged and a resonance effect between the time scale of the scroll ring and the time correlation of the noise is observed numerical results are interpreted in terms of a simplified stochastic model derived from the kinematical equations for three dimensional excitable waves

scale free brain functional networks functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites analysis of the resulting networks in different tasks shows that a the distribution of functional connections and the probability of finding a link versus distance are both scale free b the characteristic path length is small and comparable with those of equivalent random networks and c the clustering coefficient is orders of magnitude larger than those of equivalent random networks all these properties typical of scale free small world networks reflect important functional information about brain states

a general theorem of existence of quasi absolutely minimal lipschitz extensions in this paper we consider a wide class of generalized lipschitz extension problems and the corresponding problem of finding absolutely minimal lipschitz extensions we prove that if a minimal lipschitz extension exists then under certain other mild conditions a quasi absolutely minimal lipschitz extension must exist as well here we use the qualifier quasi to indicate that the extending function in question nearly satisfies the conditions of being an absolutely minimal lipschitz extension up to several factors that can be made arbitrarily small

spatial coherence resonance in excitable media we study the phenomenon of spatial coherence resonance in a two dimensional model of excitable media with fitzhugh nagumo local dynamics in particular we show that there exists an optimal level of additive noise for which an inherent spatial scale of the excitable media is best pronounced we argue that the observed phenomenon occurs due to the existence of a noise robust excursion time that is characteristic for the local dynamics whereby the diffusion constant representing the rate of diffusive spread determines the actual resonant spatial frequency additionally biological implications of presented results in the field of neuroscience are outlined

sup inf explicit formulas for minimal lipschitz extensions for 1 fields on r n abstract we study the relationship between the lipschitz constant of 1 field introduced in 12 and the lipschitz constant of the gradient canonically associated with this 1 field moreover we produce two explicit formulas which are two extremal minimal lipschitz extensions for 1 fields as a consequence of the previous results for the problem of minimal extension by lipschitz continuous functions from r m to r n we produce explicit formulas similar to those of bauschke and wang see 7 finally we show that wells s extensions see 24 of 1 fields are absolutely minimal lipschitz extensions when the domain of 1 field to expand is finite we provide a counter example showing that this result is false in general

stochastic resonance on weakly paced scale free networks we study the impact of additive gaussian noise and weak periodic forcing on the dynamics of a scale free network of bistable overdamped oscillators the periodic forcing is introduced to a single oscillator and therefore acts as a pacemaker trying to impose its rhythm on the whole ensemble we show that an intermediate intensity of temporally and spatially uncorrelated noise is able to optimally assist the pacemaker in achieving this goal thus providing evidence for stochastic resonance on weakly paced scale free networks because of the inherent degree inhomogeneity of individual oscillators forming the scale free network the placement of the pacemaker within the network is thereby crucial as two extremes we consider separately the introduction of the pacemaker to the oscillator with the highest degree and to one of the oscillators having the lowest degree in both cases the coupling strength plays a crucial role since it determines to what extent the whole network will follow the pacemaker on the expense of a weaker correlation between the pacemaker and the units that are directly linked with the paced oscillator higher coupling strengths facilitate the global outreach of the pacemaker but require higher noise intensities for the optimal response in contrast lower coupling strengths and comparatively low noise intensities localize the optimal response to immediate neighbors of the paced oscillator if the pacemaker is introduced to the main hub the transition between the locally and globally optimal responses is characterized by a double resonance that postulates the existence of an optimal coupling strength for the transmission of weak rhythmic activity across scale free networks we corroborate the importance of the inhomogeneous structure of scale free networks by additionally considering regular networks of oscillators with different degrees of coupling

dynamics of gompertzian tumour growth under environmental fluctuations abstract we investigate the effect of correlated additive and multiplicative gaussian white noise on the gompertzian growth of tumours our results are obtained by solving numerically the time dependent fokker planck equation fpe associated with the stochastic dynamics in our numerical approach we have adopted b spline functions as a truncated basis to expand the approximated eigenfunctions the eigenfunctions and eigenvalues obtained using this method are used to derive approximate solutions of the dynamics under study we perform simulations to analyze various aspects of the probability distribution of the tumour cell populations in the transient and steady state regimes more precisely we are concerned mainly with the behaviour of the relaxation time to the steady state distribution as a function of i of the correlation strength between the additive noise and the multiplicative noise and ii as a function of the multiplicative noise intensity d and additive noise intensity it is observed that both the correlation strength and the intensities of additive and multiplicative noise affect the relaxation time

regular edge labeling of 4 connected plane graphs and its applications in graph drawing problems abstract in this paper we extend the concept of the regular edge labeling for general plane graphs and for triconnected triangulated plane graphs to 4 connected triangulated plane graphs we present two different linear time algorithms for constructing such a labeling by using regular edge labeling we present a new linear time algorithm for constructing rectangular dual of planar graphs our algorithm is simpler than previously known algorithms the coordinates of the rectangular dual constructed by our algorithm are integers while the one constructed by known algorithms are real numbers our second regular edge labeling algorithm is based on canonical ordering of 4 connected triangulated plane graphs by using this technique we present a new algorithm for constructing visibility representation of 4 connected planar graphs our algorithm reduces the size of the representation by a factor of 2 for such graphs

weak signal transmission in complex networks and its application in detecting connectivity we present a network model of coupled oscillators to study how a weak signal is transmitted in complex networks through both theoretical analysis and numerical simulations we find that the response of other nodes to the weak signal decays exponentially with their topological distance to the signal source and the coupling strength between two neighboring nodes can be figured out by the responses this finding can be conveniently used to detect the topology of unknown network such as the degree distribution clustering coefficient and community structure etc by repeatedly choosing different nodes as the signal source through four typical networks i e the regular one dimensional small world random and scale free networks we show that the features of network can be approximately given by investigating many fewer nodes than the network size thus our approach to detect the topology of unknown network may be efficient in practical situations with large network size

chemical langevin equation a path integral view of gillespie s derivation in 2000 gillespie rehabilitated the chemical langevin equation cle by describing two conditions that must be satisfied for it to yield a valid approximation of the chemical master equation cme in this work we construct an original path integral description of the cme and show how applying gillespie s two conditions to it directly leads to a path integral equivalent to the cle we compare this approach to the path integral equivalent of a large system size derivation and show that they are qualitatively different in particular both approaches involve converting many sums into many integrals and the difference between the two methods is essentially the difference between using the euler maclaurin formula and using riemann sums our results shed light on how path integrals can be used to conceptualize coarse graining biochemical systems and are readily generalizable

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

whitney type extension theorems for jets generated by sobolev functions abstract let l p m r n 1 p be the homogeneous sobolev space and let e r n be a closed set for each p n and each non negative integer m we give an intrinsic characterization of the restrictions d f e m to e of m jets generated by functions f l p m 1 r n our trace criterion is expressed in terms of variations of corresponding taylor remainders of m jets evaluated on a certain family of well separated two point subsets of e for p this result coincides with the classical whitney glaeser extension theorem for m jets our approach is based on a representation of the sobolev space l p m 1 r n p n as a union of c m d r n spaces where d belongs to a family of metrics on r n with certain nice properties here c m d r n is the space of c m functions on r n whose partial derivatives of order m are lipschitz functions with respect to d this enables us to show that for every non negative integer m and every p n the very same classical linear whitney extension operator as in 31 provides an almost optimal extension of m jets generated by l p m 1 functions

algorithms for computing a parameterized st orientation st orientations st numberings or bipolar orientations of undirected graphs are central to many graph algorithms and applications several algorithms have been proposed in the past to compute an st orientation of a biconnected graph in this paper we present new algorithms that compute such orientations with certain parameterized characteristics in the final st oriented graph such as the length of the longest path this work has many applications including graph drawing and network routing where the length of the longest path is vital in deciding certain features of the final solution this work applies to other difficult problems as well such as graph coloring and of course longest path we present extended theoretical and experimental results which show that our technique is efficient and performs well in practice

excitability transitions and wave dynamics under spatiotemporal structured noise we present an analytic and numerical study of the effects of external fluctuations in active media our analytical methodology transforms the initial stochastic partial differential equations into an effective set of deterministic reaction diffusion equations as a result we are able to explain and make quantitative predictions on the systematic and constructive effects of the noise for example target patterns created out of noise and traveling or spiral waves sustained by noise our study includes the case of realistic noises with temporal and spatial structures

non markovian approach to globally coupled excitable systems we consider stochastic excitable units with three discrete states each state is characterized by a waiting time density function this approach allows for a non markovian description of the dynamics of separate excitable units and of ensembles of such units we discuss the emergence of oscillations in a globally coupled ensemble with excitatory coupling in the limit of a large ensemble we derive the non markovian mean field equations nonlinear integral equations for the populations of the three states we analyze the stability of their steady solutions collective oscillations are shown to persist in a large parameter region beyond supercritical and subcritical hopf bifurcations we compare the results with simulations of discrete units as well as of coupled fitzhugh nagumo systems

target patterns in two dimensional heterogeneous oscillatory reaction diffusion systems properties of target patterns created by pacemakers representing local regions with the modified oscillation frequency are studied for twodimensional oscillatory reaction diffusion systems described by the complex ginzburg landau equation an approximate analytical solution based on the phase dynamics approximation is constructed for a circular core and compared with numerical results for circular and square cores the dependence of the wavenumber and frequency of generated waves on the size and frequency shift of the pacemaker is discussed instabilities of target patterns involving repeated creations of ring shaped amplitude defects are further considered c 2006 elsevier b v all rights reserved

noise induced intermittency in a model of a turbulent boundary layer abstract the presence of attracting heteroclinic cycles in a set of truncated ordinary differential equations for the modal amplitudes in a proper orthogonal decomposition of the navier stokes equations leads to burst like intermittent phenomenon in the reconstructed velocity field the time between bursts or the cycle time is effectively randomized by the addition of small random perturbations in this case taking the form of irregular pressure fluctuations from the outer flow this suggests that interaction of the inner and outer flow is important in the generation and triggering of these burst events a scaling law is developed for the time between burst events as well as an expression for the probability distribution of these time intervals

stochastic resonance in an autonomous system with a nonuniform limit cycle in a recent numerical study gang et al phys rev lett 71 807 1993 presented the first example of stochastic resonance in an autonomous system they considered a two variable model in which a limit cycle is born as some parameter is varied their numerical experiments revealed various noise induced effects including a noise induced shift in the frequency of the limit cycle oscillations and noise induced oscillations in the absence of a deterministic limit cycle we show that both of these effects are simple consequences of the nonuniformity of the motion along the limit cycle

a model for fast computer simulation of waves in excitable media abstract starting from a two variable system of reaction diffusion equations an algorithm is devised for efficient simulation of waves in excitable media the spatio temporal resolution of the simulation can be varied continuously for fine resolutions the algorithm provides accurate solution of the underlying reaction diffusion equations for coarse resolutions the algorithm provides qualitative simulations at small computational cost

pseudo regular oscillations induced by external noise an examination of the effect of noise on a general system at a saddle node bifurcation has revealed that in the limit of weak noise the probability density of the time to pass through the saddle node has a universal shape the specific kinetics of the particular system serving only to set the time scale this probability density is displayed and its salient features are explicated in the case of a saddle node bifurcation leading to relaxation oscillations this analysis leads to the prediction of the existence of noise induced oscillations which appear much less random than might at first be expected the period of these oscillations has a well defined nonzero most probable value the inverse of which is a noise induced frequency this frequency can be detected as a peak in power spectra from numerical simulations of such a system this is the first case of the prediction and detection of a noise induced frequency of which the authors are aware

use of recurrence plot and recurrence quantification analysis in taiwan unemployment rate time series abstract the aim of the article is to answer the question if the taiwan unemployment rate dynamics is generated by a non linear deterministic dynamic process this paper applies a recurrence plot and recurrence quantification approach based on the analysis of non stationary hidden transition patterns of the unemployment rate of taiwan the case study uses the time series data of the taiwan s unemployment rate during the period from 1978 01 to 2010 06 the results show that recurrence techniques are able to identify various phases in the evolution of unemployment transition in taiwan

minimal model for spatial coherence resonance we show that a planar medium locally modeled by a simple one dimensional excitable system with a piece wise linear potential can serve as a minimal model for spatial coherence resonance via an analytical treatment of the spatially extended system we derive the dependence of the resonant wave number on several crucial system parameters ranging from the diffusion coefficient to the local excursion time of constitutive excitable units thus we provide vital insights into mechanisms that enable the emergence of exclusively noise induced spatial periodicity in excitable media

effects of colored noise and noise delay on a calcium oscillation system abstract as a calcium oscillations system is in steady state the effects of colored noise and noise delay on the system is investigated using stochastic simulation methods the results indicate that 1 the colored noise can induce coherence bi resonance phenomenon 2 there exist three peaks in the r 0 r is the reciprocal coefficient of variance and 0 is the self correlation time of the colored noise curves for the same noise intensity q 1 the gaussian colored noise can induce calcium spikes but the white noise cannot do this 3 the delay time can improve noise induced spikes regularity as 0 is small and r has a significant minimum with increasing as 0 is large 4 large values of reduce noise induced spikes regularity

strong effects of network architecture in the entrainment of coupled oscillator systems random networks of coupled phase oscillators representing an approximation for systems of coupled limit cycle oscillators are considered entrainment of such networks by periodic external forcing applied to a subset of their elements is numerically and analytically investigated for a large class of interaction functions we find that the entrainment window with a tongue shape becomes exponentially narrow for networks with higher hierarchical organization however the entrainment is significantly facilitated if the networks are directionally biased i e closer to the feedforward networks furthermore we show that the networks with high entrainment ability can be constructed by evolutionary optimization processes the neural network structure of the master clock of the circadian rhythm in mammals is discussed from the viewpoint of our results

compact visibility representation of 4 connected plane graphs the visibility representation vr for short is a classical representation of plane graphs the vr has various applications and has been extensively studied in the literature a main focus of the study is to minimize the size of the vr it is known that there exists a plane graph g with n vertices where any vr of g requires a size at least 2n3 x 4n3 3 for upper bounds it is known that every plane graph has a vr with size at most 23n x 2n 5 and a vr with size at most n 1 x 43n it has been an open problem to find a vr with both height and width simultaneously bounded away from the trivial upper bounds namely of size c hnxc wn with c h 1 and c w 2 in this paper we provide the first vr construction for a non trivial graph class that simultaneously bounds both the height and the width we prove that every 4 connected plane graph has a vr with height 3n4 2 n 4 and width 3n2 our vr algorithm is based on an st orientation of 4 connected plane graphs with special properties the area of the vr presented in this paper is larger than the area of some of the previous results for this graph class however bounding one dimension of the vr only requires finding a good st orientation or a good dual s t orientation of g on the other hand bounding both dimensions of the vr requires finding a good st orientation and a good dual s t orientation of g at the same time and hence is far more challenging since the st orientation is a very useful concept in other applications this result may be of independent interest reducing the height the width respectively of the vr is the same as reducing the length of the longest path in an st orientation of g dual st orientation respectively we show that it s np complete to find an st orientation of a 2 connected plane graph that minimizes the sum of the length of the longest path in the orientation and the length of the longest path in its dual orientation

global asymptotic stability of stochastic bam neural networks with distributed delays and reaction diffusion terms this paper is concerned with global asymptotic stability of a class of reaction diffusion stochastic bi directional associative memory bam neural networks with discrete and distributed delays based on suitable assumptions we apply the linear matrix inequality lmi method to propose some new sufficient stability conditions for reaction diffusion stochastic bam neural networks with discrete and distributed delays the obtained results are easy to check and improve upon the existing stability results an example is also given to demonstrate the effectiveness of the obtained results

a phase model of temperature dependent mammalian cold receptors we present a tractable stochastic phase model of the temperature sensitivity of a mammalian cold receptor using simple linear dependencies of the amplitude frequency and bias on temperature the model reproduces the experimentally observed transitions between bursting beating and stochastically phase locked firing patterns we analyze the model in the deterministic limit and predict using a strutt map the number of spikes per burst for a given temperature the inclusion of noise produces a variable number of spikes per burst and also extends the dynamic range of the neuron both of which are analyzed in terms of the strutt map our analysis can be readily applied to other receptors that display various bursting patterns following temperature changes

system size stochastic resonance in a model for opinion formation we study a model for opinion formation which incorporates three basic ingredients for the evolution of the opinion held by an individual imitation influence of fashion and randomness we show that in the absence of fashion the model behaves as a bistable system with random jumps between the two stable states with a distribution of times following kramer s law we also demonstrate the existence of system size stochastic resonance by which there is an optimal value for the number of individuals n for which the average opinion follows better the fashion

tug of war and the infinity laplacian we consider a class of zero sum two player stochastic games called tug of war and use them to prove that every bounded real valued lipschitz function f on a subset y of a length space x admits a unique absolutely minimal am extension to x i e a unique lipschitz extension u x for which lip u u lip u u for all open u x y

proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systems we show that chaotic states situated in the proximity of periodic windows in bifurcation diagrams are eligible for the observation of coherence resonance in particular additive gaussian noise of appropriate intensity can enhance the temporal order in such chaotic states in a resonant manner results obtained for the logistic map and the lorenz equations suggest that the presented mechanism of coherence resonance is valid beyond particularities of individual systems we attribute the findings to the increasing attraction of imminent periodic orbits and the ability of noise to anticipate their existence and use a modified wavelet analysis to support our arguments

predictability of noise controlled dynamics abstract noise controlled dynamics runs counter to usual intuition the larger the noise the more regular the solutions we present numerical and analytical results for a set of three stochastic partial differential equations in one space dimension motivated by the intermittent destabilization of tall thin convection cells by horizontal shear time series are predictable in the sense that they follow limit cycles with a small variation in amplitude from cycle to cycle closer inspection reveals that the amplitude is determined by very small amounts of noise

uniqueness of lipschitz extensions minimizing the sup norm of the gradient in this paper we examine the problem of minimizing the sup norm of the gradient of a function with prescribed boundary values geometrically this can be interpreted as finding a minimal lipschitz extension due to the weak convexity of the functional associated to this problem solutions are generally nonunique by adopting g aronsson s notion of absolutely minimizing we are able to prove uniqueness by characterizing minimizers as the unique solutions of an associated partial differential equation in fact we actually prove a weak maximum principle for this partial differential equation which in some sense is the euler equation for the minimization problem this is significantly difficult because the partial differential equation is both fully nonlinear and has very degenerate ellipticity to overcome this difficulty we use the weak solutions of m g crandall and p l lions also known as viscosity solutions in conjunction with some arguments using integration by parts

estimating the active dimension of cardiac pacemaking dynamics abstract although there exist several different models for the excitability of cardiac and nerve cells the number of ionic currents that determine this excitability is not clearly known on the other hand the chaotic behavior of excitable cells has recently been demonstrated the science of complex dynamics provides tools for the reconstruction of the original dynamics from a time series of observed data we determined the degrees of freedom for the excitability of a single cardiac pacemaker cell by chaotic analysis of a time series of action potentials aps recorded from the rabbit sinus node we provide evidence that at least 12 variables are needed to determine the ap from our findings we conclude that a new model for the cardiac pacemaker mechanism may be needed because previous models could deal only with fewer than 12 variables our approach based on our observation of a time series offers a powerful tool for constructing a model for the underlying biological mechanism

analytic expressions for rate and cv of a type i neuron driven by white gaussian noise we study the one dimensional normal form of a saddle node system under the influence of additive gaussian white noise and a static bias current input parameter a model that can be looked upon as the simplest version of a type i neuron with stochastic input this is in contrast with the numerous studies devoted to the noise driven leaky integrate and fire neuron we focus on the firing rate and coefficient of variation cv of the interspike interval density for which scaling relations with respect to the input parameter and noise intensity are derived quadrature formulas for rate and cv are numerically evaluated and compared to numerical simulations of the system and to various approximation formulas obtained in different limiting cases of the model we also show that caution must be used to extend these results to the neuron model with multiplicative gaussian white noise the correspondence between the first passage time statistics for the saddle node model and the neuron model is obtained only in the stratonovich interpretation of the stochastic neuron model while previous results have focused only on the ito interpretation the correct stratonovich interpretation yields cvs that are still relatively high although smaller than in the ito interpretation it also produces certain qualitative differences especially at larger noise intensities our analysis provides useful relations for assessing the distance to threshold and the level of synaptic noise in real type i neurons from their firing statistics we also briefly discuss the effect of finite boundaries finite values of threshold and reset on the firing statistics

vector valued optimal lipschitz extensions consider a bounded open set and a lipschitz function does this function always have a canonical optimal lipschitz extension to all of u we propose a notion of optimal lipschitz extension and address existence and uniqueness in some special cases in the case n m 2 we show that smooth solutions have two phases in one they are conformal and in the other they are variants of infinity harmonic functions called infinity harmonic fans we also prove existence and uniqueness for the extension problem on finite graphs 2011 wiley periodicals inc

transport and its enhancement caused by coupling using the weiss mean field approximation theory and the particles transport theory for the spatially periodic stochastic systems we derive an exact analytical expression for the stationary probability current of a coupled lattice system driven by dichotomous noise it is shown that for this coupled lattice system the spatial asymmetry of the system the asymmetry of the dichotomous noise and the coupling among nearest neighbors are the ingredients for the stationary probability current by applying our theory to two special models we find that 1 the coupling can lead to the directional transport of the particles even when the potential and the dichotomous noise are symmetric and 2 the coupling among nearest neighbors can enhance the transport of the particles in some circumstances our results are applied to a device of two dimensional josephson junction arrays and a large protein motors cluster

noise stabilized random attractor a two dimensional flow model is introduced with deterministic behavior consisting of bursts that become successively larger with longer interburst time intervals between them the system is symmetric in one variable and there are bursts on either side of separated by the presence of an invariant manifold at in the presence of arbitrarily small additive noise in the direction the successive bursts have bounded amplitudes and interburst intervals this system with noise is proposed as a model for edge localized modes in tokamaks with noise the bursts can switch from positive to negative and vice versa the probability distribution of burst heights and interburst periods is studied as is the dependence of the statistics on the noise variance the modification of this behavior as the symmetry in is broken is studied showing qualitatively similar behavior if the symmetry breaking is small enough experimental observations of a nonlinear circuit governed by the same equations are presented showing good agreement

exported oscillator competition a concept to analyze complex rhythms we study the interaction between two independent nonlinear oscillators competing through a neutral excitable element the first oscillator completely deterministic acts as a normal pacemaker sending pulses to the neutral element which fires when it is excited by these pulses the second oscillator endowed with some randomness though unable to make the excitable element to beat leads to the occasional suppression of its firing the missing beats or errors are registered and their statistics analyzed in terms of the noise intensity and the periods of both oscillators this study is inspired in some complex rhythms such as a particular class of heart arrhythmia

collections of heteroclinic cycles in the kuramoto sivashinsky equation abstract we study the kuramoto sivashinky equation with periodic boundary conditions in the case of low dimensional behavior we analyze the bifurcations that occur in a six dimensional 6d approximation of its inertial manifold we mainly focus on the attracting and structurally stable heteroclinic connections that arise for these parameter values we reanalyze the ones that were previously described via a 4d reduction to the center unstable manifold ambruster et al 1988 1989 we also find a parameter region for which a manifold of structurally stable heteroclinic cycles exist the existence of such a manifold is responsible for an intermittent behavior which has some features of unpredictability

delayed stochastic resonance with a 1 d ring abstract we study here a simple one dimensional ring composed of stochastic binary elements with delayed interaction with this model we can analytically compute interspike interval histograms and show how resonance or rhythmic behaviors arise with only noise and delay

intermittent diffusion in the presence of noise abstract the diffusion coefficient for intermittent diffusion in the presence of weak additive gaussian white noise is calculated the recent result by tsimring physica d 63 1993 41 is shown to be correct only in a certain limit of the parameter values

stochastic resonance in coupled threshold elements on a barabasi albert network abstract stochastic resonance is investigated in a system of threshold elements located at nodes and coupled along edges of a barabasi albert network driven by a common subthreshold periodic signal and independent noises array enhanced stochastic resonance is observed i e increase of the spectral power amplification evaluated from the mean output of the network due to proper coupling this enhancement occurs though the response of individual threshold elements to the periodic signal is very diverse due to a power law distribution of their connectivity numerical results are qualitatively explained using simple linear response theory in the mean field approximation

synchronization processes in complex networks we present an extended analysis based on the dynamics towards synchronization of a system of coupled oscillators of the hierarchy of communities in complex networks in the synchronization process different structures corresponding to well defined communities of nodes appear in a hierarchical way the analysis also provides a useful connection between synchronization dynamics complex networks topology and spectral graph analysis

synchronization of rossler oscillators on scale free topologies abstract we study the synchronization of rossler oscillators as prototypes of chaotic systems on scale free complex networks as it turns out the underlying topology crucially affects the global synchronization properties in particular we show that the existence of loops facilitates the synchronizability of the system whereas rossler oscillators do not synchronize on tree like topologies beyond a certain size moreover it is not the mere number of loops that counts for synchronization but also the type of loops by considering cayley trees modified by additional loops in different ways we find out that also the distribution of shortest path lengths between two oscillators plays an important role for the global synchronization

synchronization transition in degenerate optical parametric oscillators induced by nonlinear coupling in this paper the synchronization of certain degenerate optical parametric oscillators is investigated in detail complete and or partial synchronization can be reached when linear controller constructed by the real part or imaginary part of the subharmonic mode is imposed on the chaotic degenerate optical parametric oscillators with appropriate coupling intensity the lyapunov exponents under different coupling coefficients are calculated to find the critical condition for complete synchronization transition from complete synchronization to partial synchronization is observed when nonlinear coupling is introduced into the two chaotic oscillators it is found that synchronization of chaotic oscillators keeps robust when the intensity of the nonlinear coupling is less than the intensity of the linear coupling the complete synchronization state is destructed and transient period for partial synchronization is in certain delay when the intensity of the nonlinear coupling is beyond the intensity of the linear coupling

noise enhanced excitability in bistable activator inhibitor media we show that external fluctuations induce excitable behavior in a bistable spatially extended system with activator inhibitor dynamics of the fitzhugh nagumo type this can be understood as a mechanism for sustained signal propagation in bistable media the phase diagram of the stochastic system is analytically obtained and numerically verified for small noise intensities front propagation becomes unstable and excitable pulses arise as the only possible spatiotemporal behavior of the system for large noise intensities on the other hand the system enters an effective regime of oscillatory behavior where it exhibits spontaneous nucleation of pulses and synchronized firing

extrinsic periodic information interpolates between monostable and bistable states in intracellular calcium dynamics abstract extrinsic periodic information including physiological cyclical and circadian replacement would affect inevitably a real cell in this paper we investigate the effect of extrinsic periodic information on intracellular calcium dynamics by means of second order algorithm for stochastic simulation colored noises by simulating time evolutions and stationary probability distribution of intracellular ca2 concentrations the results show i intracellular calcium oscillation between cytosol and calcium store shows synchronous and anti synchronous oscillation as intensity and frequency of extrinsic periodic information vary ii extrinsic periodic information interpolates stability from bistable state monostable state bistable state monostable state as frequency of extrinsic periodic information increases iii extrinsic periodic information interpolates stability from monostable state bistable state as intensity of extrinsic periodic information increases

extracting topological features from dynamical measures in networks of kuramoto oscillators the kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of nonequilibrium transitions between an incoherent and a synchronized state here we analyze populations of almost identical oscillators in arbitrary interaction networks our aim is to extract topological features of the connectivity pattern from purely dynamical measures based on the fact that in a heterogeneous network the global dynamics is not only affected by the distribution of the natural frequencies but also by the location of the different values in order to perform a quantitative study we focused on a very simple frequency distribution considering that all the frequencies are equal but one that of the pacemaker node we then analyze the dynamical behavior of the system at the transition point and slightly above it as well as very far from the critical point when it is in a highly incoherent state the gathered topological information ranges from local features such as the single node connectivity to the hierarchical structure of functional clusters and even to the entire adjacency matrix

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