detection of couplings in ensembles of stochastic oscillators the problem of detection and quantitative characterization of directional couplings in an ensemble of noisy oscillators from a time series is addressed we suggest estimators for the strengths of couplings which are based on modeling the observed oscillations with a set of stochastic phase oscillators and easily interpreted from a physical viewpoint moreover we present an analytic formula for a statistical significance level allowing to reveal an architecture of couplings reliably from a relatively short time series the technique applies to weakly coupled nonsynchronized oscillators it is introduced for oscillators with close basic frequencies but can be readily generalized to the case of arbitrary frequencies efficiency of the technique is demonstrated in numerical experiments

on subordinacy and spectral multiplicity for a class of singular differential operators the spectral multiplicity of self adjoint operators h associated with singular differential expressions of the form is investigated based on earlier work of i s kac and recent results on subordinacy complete sets of necessary and sufficient conditions for the spectral multiplicity to be one or two are established in terms of i the boundary behaviour of titchmarsh weyl m functions and ii the asymptotic properties of solutions of lu u at the endpoints a and b in particular it is shown that h has multiplicity two if and only if l is in the limit point case at both a and b and the set of all for which no solution of lu u is subordinate at either a or b has positive lebesgue measure the results are completely general subject only to minimal restrictions on the coefficients p r q r and w r and the assumption of separated boundary conditions when l is in the limit circle case at both endpoints

a robust method for detecting interdependences application to intracranially recorded eeg we present a measure for characterizing statistical relationships between two time sequences in contrast to commonly used measures like cross correlations coherence and mutual information the proposed measure is non symmetric and provides information about the direction of interdependence it is closely related to recent attempts to detect generalized synchronization however we do not assume a strict functional relationship between the two time sequences and try to define the measure so as to be robust against noise and to detect also weak interdependences we apply our measure to intracranially recorded electroencephalograms of patients suffering from severe epilepsies

synchronization likelihood an unbiased measure of generalized synchronization in multivariate data sets the study of complex systems consisting of many interacting subsystems requires the use of analytical tools which can detect statistical dependencies between time series recorded from these subsystems typical examples are the electroencephalogram eeg and magnetoencephalogram meg which may involve the simultaneous recording of 150 or more time series coherency which is often used to study such data is only sensitive to linear and symmetric interdependencies and cannot deal with non stationarity recently several algorithms based upon the concept of generalized synchronization have been introduced to overcome some of the limitations of coherency estimates e g physica d 134 1999 419 brain res 792 1998 24 however these methods are biased by the degrees of freedom of the interacting subsystems physica d 134 1999 419 physica d 148 2001 147 we propose a novel measure for generalized synchronization in multivariate data sets which avoids this bias and can deal with non stationary dynamics

spectral properties of a class of reflectionless schrodinger operators abstract we prove that one dimensional reflectionless schrodinger operators with spectrum a homogeneous set in the sense of carleson belonging to the class introduced by sodin and yuditskii have purely absolutely continuous spectra this class includes all earlier examples of reflectionless almost periodic schrodinger operators in addition we construct examples of reflectionless schrodinger operators with more general types of spectra given by the complement of a denjoy widom type domain in c which exhibit a singular component

synchronous chaos in coupled oscillator systems we investigate the synchronization of chaotic oscillations in coupled oscillator systems both theoretically and in analog electronic circuits particular attention is paid to deriving and testing general conditions for the stability of synchronous chaotic behavior in cases where the coupled oscillator array possesses a shift invariant symmetry these cases include the well studied cases of nearest neighbor diffusive coupling and all to all or global coupling an approximate criterion is developed to predict the stability of synchronous chaotic oscillations in the strong coupling limit when the oscillators are coupled through a single coordinate scalar coupling this stability criterion is illustrated numerically in a set of coupled r ossler like oscillators synchronization experiments with coupled r ossler like oscillator circuits are also carried out to demonstrate the applicability of the theory to real systems

detecting synchronization clusters in multivariate time series via coarse graining of markov chains synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series starting from a matrix r of bivariate synchronization indices a previous method utilized the eigenvectors of r for cluster identification analogous to several recent attempts at group identification using eigenvectors of the correlation matrix all of these approaches assumed a one to one correspondence of dominant eigenvectors and clusters which has however been shown to be wrong in important cases we clarify the usefulness of eigenvalue decomposition for synchronization cluster analysis by translating the problem into the language of stochastic processes and derive an enhanced clustering method harnessing recent insights from the coarse graining of finite state markov processes we illustrate the operation of our method using a simulated system of coupled lorenz oscillators and we demonstrate its superior performance over the previous approach finally we investigate the question of robustness of the algorithm against small sample size which is important with regard to field applications

on subordinacy and analysis of the spectrum of schrodinger operators with two singular endpoints the theory of subordinacy is extended to all one dimensional schrodinger operatorsfor which the corresponding differential expression l d 2 dr 2 v r is in the limit point case at both ends of an interval a b with v r locally integrable this enables a detailed classification of the absolutely continuous and singular spectra to be established in terms of the relative asymptotic behaviour of solutions of lu xu x e as r a and r b the result provides a rigorous but straightforward method of direct spectral analysis which has very general application and somefurther properties of the spectrum are deduced from the underlying theory

mixing properties of the rossler system and consequences for coherence and synchronization analysis cross spectral and synchronization analysis of two independent identical chaotic rossler systems suggest a coupling although there is no interaction this spuriously detected interaction can either be explained by the absence of mixing or by finite size effects to decide which alternative holds the phase dynamics is studied by a model of the fluctuations derived from the system s equations the basic assumption of the model is a diffusive character for the system which corresponds to mixing comparison of theoretical properties of the model with empirical properties of the rossler system suggests that the system is mixing but the rate of mixing appears to be rather low

the xi function despite the fact that spectral and inverse spectral properties of one dimensional schrsdinger operators h d2 dx2 have been extensively studied for seventy five years there remain large areas where our knowledge is limited for example while the inverse theory for operators on l2 co co is well understood in case v is periodic 12 24 25 35 39 42 49 it is not understood in case limjx o v x co and h has discrete spectrum our goal here is to introduce a special function x a on r associated to h which we believe will be a valuable tool in the spectral and inverse spectral theory in a sense we will make precise it complements the weyl m functions m x a a main application of which we will make here concerns a generalization of the trace formula for schrsdinger operators to general v s recall the well known trace formula for periodic potentials let v x v x t 1 then by floquet theory see e g 10 37 44

synchronization between main rhythmic processes in the human cardiovascular system for the cases of spontaneous respiration and paced respiration with a fixed frequency and linearly increasing frequency we investigate synchronization between three main rhythmic processes governing the cardiovascular dynamics in humans namely the main heart rhythm respiration and the process whose fundamental frequency is close to 0 1 hz the analysis of the experimental records reveals synchronous regimes of different orders n m between all the three main rhythms the influence of the regime of breathing and the magnitude of heart rate variability on the degree of synchronization is considered

on a theorem of kac and gilbert we prove a general operator theoretic result that asserts that many multiplicity two selfadjoint operators have simple singular spectrum

entanglement and nonclassical properties of hypergraph states hypergraph states are multiqubit states that form a subset of the locally maximally entangleable states and a generalization of the well established notion of graph states mathematically they can conveniently be described by a hypergraph that indicates a possible generation procedure of these states alternatively they can also be phrased in terms of a nonlocal stabilizer formalism in this paper we explore the entanglement properties and nonclassical features of hypergraph states first we identify the equivalence classes under local unitary transformations for up to four qubits as well as important classes of five and six qubit states and determine various entanglement properties of these classes second we present general conditions under which the local unitary equivalence of hypergraph states can simply be decided by considering a finite set of transformations with a clear graph theoretical interpretation finally we consider the question of whether hypergraph states and their correlations can be used to reveal contradictions with classical hidden variable theories we demonstrate that various noncontextuality inequalities and bell inequalities can be derived for hypergraph states

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

on subordinacy and analysis of the spectrum of one dimensional schrodinger operators abstract by considering the behaviour as n of the ratio of l2 0 n norms of solutions of d 2 dr 2 v r u xu 0 r x r a characterisation of the absolutely continuous and singular spectra of one dimensional schrodinger operators is deduced the analysis is applicable to all operators for which l d 2 dr 2 v r is regular at 0 and in the limit point case at infinity with v r locally integrable

equality of the spectral and dynamical definitions of reflection for full line jacobi matrices schrodinger operators and cmv matrices we show that being reflectionless in the sense of the well known property of m functions is equivalent to a lack of reflection in the dynamics in the sense that any state that goes entirely to x as t goes entirely to x as t this allows us to settle a conjecture of deift and simon from 1983 regarding ergodic jacobi matrices

a peak synchronization measure for multiple signals peaks signify important events in a signal in a pair of signals how peaks are occurring with mutual correspondence may offer us significant insights into the mutual interdependence between the two signals based on important events in this work we proposed a novel synchronization measure between two signals called peak synchronization which measures the simultaneity of occurrence of peaks in the signals we subsequently generalized it to more than two signals we showed that our measure of synchronization is largely independent of the underlying parameter values a time complexity analysis of the algorithm has also been presented we applied the measure on intracranial eeg signals of epileptic patients and found that the enhanced synchronization during an epileptic seizure can be modeled better by the new peak synchronization measure than the classical amplitude correlation method

the effect of correlated observations on the performance of distributed estimation estimating unknown signal in wireless sensor networks wsns requires sensor nodes to transmit their observations of the signal over a multiple access channel to a fusion center fc the fc uses the received observations which is corrupted by observation noise and both channel fading and noise to find the minimum mean square error mse estimate of the signal in this paper we investigate the effect of the source node correlation the correlation between sensor node observations and the source signal and the inter node correlation the correlation between sensor node observations on the performance of the linear minimum mean square error lmmse estimator for three correlation models in the presence of channel fading first we investigate the asymptotic behavior of the achieved distortion i e mse resulting from both the observation and channel noise in a non fading channel then the effect of channel fading is considered and the corresponding distortion outage probability the probability that the distortion exceeds a certain value is found by representing the distortion as a ratio of indefinite quadratic forms a closed form expression is derived for the outage probability that shows its dependency on the correlation finally the new representation of the outage probability allows us to propose an iterative solution for the power allocation problem to minimize the outage probability under total and individual power constraints numerical simulations are provided to verify our analytic results

quantifying time varying coordination of multimodal speech signals using correlation map analysis this paper demonstrates an algorithm for computing the instantaneous correlation coefficient between two signals the algorithm is the computational engine for analyzing the time varying coordination between signals which is called correlation map analysis cma correlation is computed around any pair of points in the two input signals thus coordination can be assessed across a continuous range of temporal offsets and be detected even when changing over time due to temporal fluctuations the correlation algorithm has two major features i it is structurally similar to a tunable filter requiring only one parameter to set its cutoff frequency and sensitivity ii it can be applied either uni directionally computing correlation based only on previous samples or bi directionally computing correlation based on both previous and future samples computing instantaneous correlation for a range of time offsets between two signals produces a 2d correlation map in which correlation is characterized as

local spectral properties of reflectionless jacobi cmv and schrodinger operators we prove that jacobi cmv and schrodinger operators which are reflectionless on a homogeneous set e in the sense of carleson under the assumption of a blaschke type condition on their discrete spectra accumulating at e have purely absolutely continuous spectrum on e

local unitary symmetries of hypergraph states hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well studied class of graph states graph states are important in applications such as measurement based quantum computation and quantum error correction the study of hypergraph states with their richer multipartite entanglement and other nonlocal properties has a promising outlook for new insight into multipartite entanglement we present results analyzing local unitary symmetries of hypergraph states including both continuous and discrete families of symmetries in particular we show how entanglement types can be detected and distinguished by certain configurations in the hypergraphs from which hypergraph states are constructed

electroencephalograms in epilepsy analysis and seizure prediction within the framework of lyapunov theory abstract epileptic seizures are defined as the clinical manifestation of excessive and hypersynchronous activity of neurons in the cerebral cortex and represent one of the most frequent malfunctions of the human central nervous system therefore the search for precursors and predictors of a seizure is of utmost clinical relevance and may even guide us to a deeper understanding of the seizure generating mechanisms we extract chaos indicators such as lyapunov exponents and kolmogorov entropies from different types of electroencephalograms eegs this covers mainly intracranial eegs semi invasive and invasive recording techniques but also scalp eegs from the surface of the skin among the analytical methods we tested up to now we find that the spectral density of the local expansion exponents is best suited to predict the onset of a forthcoming seizure we also evaluate the time evolution of the dissipation in these signals it exhibits strongly significant variations that clearly relate to the time relative to a seizure onset this article is mainly devoted to an assessment of these methods with respect to their sensitivity to eeg changes e g prior to a seizure further we investigate interictal eegs i e far away from a seizure in order to characterize their more general properties such as the convergence of the reconstructed quantities with respect to the number of phase space dimensions generally we use multichannel reconstruction but we also present a comparison with the delay embedding technique

extreme violation of local realism in quantum hypergraph states hypergraph states form a family of multiparticle quantum states that generalizes the well known concept of greenberger horne zeilinger states cluster states and more broadly graph states we study the nonlocal properties of quantum hypergraph states we demonstrate that the correlations in hypergraph states can be used to derive various types of nonlocality proofs including hardy type arguments and bell inequalities for genuine multiparticle nonlocality moreover we show that hypergraph states allow for an exponentially increasing violation of local realism which is robust against loss of particles our results suggest that certain classes of hypergraph states are novel resources for quantum metrology and measurement based quantum computation

analysis of quantum error correction with symmetric hypergraph states graph states have been used to construct quantum error correction codes for independent errors hypergraph states generalize graph states and symmetric hypergraph states have been shown to allow for the correction of correlated errors in this paper it is shown that symmetric hypergraph states are not useful for the correction of independent errors at least for up to 30 qubits furthermore error correction for error models with protected qubits is explored a class of known graph codes for this scenario is generalized to hypergraph codes