RESUMO
Assessing Granger causality (GC) intended as the influence, in terms of reduction of variance of surprise, that a driver variable exerts on a given target, requires a suitable treatment of 'instantaneous' effects, i.e. influences due to interactions whose time scale is much faster than the time resolution of the measurements, due to unobserved confounders or insufficient sampling rate that cannot be increased because the mechanism of generation of the variable is inherently slow (e.g. the heartbeat). We exploit a recently proposed framework for the estimation of causal influences in the spectral domain and include instantaneous interactions in the modelling, thus obtaining (i) a novel index of undirected instantaneous causality and (ii) a novel measure of GC including instantaneous effects. An effective procedure to speed up the optimization of parameters in this frame is also presented. After illustrating the proposed formalism in a theoretical example, we apply it to two datasets of cardiovascular and respiratory time series and compare the values obtained within the frequency bands of physiological interest by the proposed total measure of causality with those derived from the standard GC analysis. We find that the inclusion of instantaneous causality allows us to correctly disentangle the baroreflex mechanism from the effects related to cardiorespiratory interactions. Moreover, studying how controlling the respiratory rhythm acts on cardiovascular interactions, we document an increase of the direct (non-baroreflex mediated) influence of respiration on the heart rate in the respiratory frequency band when switching from spontaneous to paced breathing. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.
Assuntos
Algoritmos , Barorreflexo , Simulação por Computador , Frequência CardíacaRESUMO
Dynamical models implemented on the large scale architecture of the human brain may shed light on how a function arises from the underlying structure. This is the case notably for simple abstract models, such as the Ising model. We compare the spin correlations of the Ising model and the empirical functional brain correlations, both at the single link level and at the modular level, and show that their match increases at the modular level in anesthesia, in line with recent results and theories. Moreover, we show that at the peak of the specific heat (the critical state), the spin correlations are minimally shaped by the underlying structural network, explaining how the best match between the structure and function is obtained at the onset of criticality, as previously observed. These findings confirm that brain dynamics under anesthesia shows a departure from criticality and could open the way to novel perspectives when the conserved magnetization is interpreted in terms of a homeostatic principle imposed to neural activity.
Assuntos
Anestesia , Conectoma , Modelos Neurológicos , Vigília/fisiologia , Encéfalo/fisiologia , HumanosRESUMO
We consider the formalism of information decomposition of target effects from multisource interactions, i.e., the problem of defining redundant and synergistic components of the information that a set of source variables provides about a target, and apply it to the two-dimensional Ising model as a paradigm of a critically transitioning system. Intuitively, synergy is the information about the target variable that is uniquely obtained by taking the sources together, but not considering them alone; redundancy is the information which is shared by the sources. To disentangle the components of the information both at the static level and at the dynamical one, the decomposition is applied respectively to the mutual information and to the transfer entropy between a given spin, target, and a pair of neighboring spins (taken as the drivers). We show that a key signature of an impending phase transition (approached from the disordered size) is the fact that the synergy peaks in the disordered phase, both in the static and in the dynamic case: The synergy can thus be considered a precursor of the transition. The redundancy, instead, reaches its maximum at the critical temperature. The peak of the synergy of the transfer entropy is far more pronounced than those of the static mutual information. We show that these results are robust with respect to the details of the information decomposition approach, as we find the same results using two different methods; moreover, with respect to previous literature rooted in the notion of global transfer entropy, our results demonstrate that considering as few as three variables is sufficient to construct a precursor of the transition, and provide a paradigm for the investigation of a variety of systems prone to crisis, such as financial markets, social media, or epileptic seizures.
RESUMO
We propose a method of analysis of dynamical networks based on a recent measure of Granger causality between time series, based on kernel methods. The generalization of kernel-Granger causality to the multivariate case, here presented, shares the following features with the bivariate measures: (i) the nonlinearity of the regression model can be controlled by choosing the kernel function and (ii) the problem of false causalities, arising as the complexity of the model increases, is addressed by a selection strategy of the eigenvectors of a reduced Gram matrix whose range represents the additional features due to the second time series. Moreover, there is no a priori assumption that the network must be a directed acyclic graph. We apply the proposed approach to a network of chaotic maps and to a simulated genetic regulatory network: it is shown that the underlying topology of the network can be reconstructed from time series of node's dynamics, provided that a sufficient number of samples is available. Considering a linear dynamical network, built by preferential attachment scheme, we show that for limited data use of the bivariate Granger causality is a better choice than methods using L1 minimization. Finally we consider real expression data from HeLa cells, 94 genes and 48 time points. The analysis of static correlations between genes reveals two modules corresponding to well-known transcription factors; Granger analysis puts in evidence 19 causal relationships, all involving genes related to tumor development.
RESUMO
OBJECTIVE: Event-related potentials (ERPs) are usually obtained by averaging thus neglecting the trial-to-trial latency variability in cognitive electroencephalography (EEG) responses. As a consequence the shape and the peak amplitude of the averaged ERP are smeared and reduced, respectively, when the single-trial latencies show a relevant variability. To date, the majority of the methodologies for single-trial latencies inference are iterative schemes providing suboptimal solutions, the most commonly used being the Woody's algorithm. APPROACH: In this study, a global approach is developed by introducing a fitness function whose global maximum corresponds to the set of latencies which renders the trial signals most aligned as possible. A suitable genetic algorithm has been implemented to solve the optimization problem, characterized by new genetic operators tailored to the present problem. MAIN RESULTS: The results, on simulated trials, showed that the proposed algorithm performs better than Woody's algorithm in all conditions, at the cost of an increased computational complexity (justified by the improved quality of the solution). Application of the proposed approach on real data trials, resulted in an increased correlation between latencies and reaction times w.r.t. the output from RIDE method. SIGNIFICANCE: The above mentioned results on simulated and real data indicate that the proposed method, providing a better estimate of single-trial latencies, will open the way to more accurate study of neural responses as well as to the issue of relating the variability of latencies to the proper cognitive and behavioural correlates.
Assuntos
Algoritmos , Encéfalo/fisiologia , Eletroencefalografia/métodos , Potenciais Evocados/fisiologia , Tempo de Reação/fisiologia , Humanos , Processamento de Sinais Assistido por ComputadorRESUMO
We study the phase diagram of a generalized Winfree model. The modification is such that the coupling depends on the fraction of synchronized oscillators, a situation which has been noted in some experiments on coupled Josephson junctions and mechanical systems. We let the global coupling k be a function of the Kuramoto order parameter r through an exponent z such that z=1 corresponds to the standard Winfree model, z<1 strengthens the coupling at low r (low amount of synchronization), and at z>1 , the coupling is weakened for low r . Using both analytical and numerical approaches, we find that z controls the size of the incoherent phase region and that one may make the incoherent behavior less typical by choosing z<1 . We also find that the original Winfree model is a rather special case; indeed, the partial locked behavior disappears for z>1 . At fixed k and varying gamma , the stability boundary of the locked phase corresponds to a transition that is continuous for z<1 and first order for z>1 . This change in the nature of the transition is in accordance with a previous study of a similarly modified Kuramoto model.
RESUMO
OBJECTIVE: We aimed to perform a quantitative analysis of event-related modulation of EEG activity, resulting from a not-warned and a warned paradigm of painful laser stimulation, in migraine patients and controls, by the use of a novel analysis, based upon a parametric approach to measure predictability of short and noisy time series. METHODS: Ten migraine patients were evaluated during the not-symptomatic phase and compared to seven age and sex matched controls. The dorsum of the right hand and the right supraorbital zone were stimulated by a painful CO(2) laser, in presence or in absence of a visual warning stimulus. An analysis time of 1s after the stimulus was submitted to a time-frequency analysis by a complex Morlet wavelet and to a cross-correlation analysis, in order to detect the development of EEG changes and the most activated cortical regions. A parametric approach to measure predictability of short and noisy time series was applied, where time series were modeled by leave-one-out (LOO) error. RESULTS: The averaged laser-evoked potentials features were similar between the two groups in the alerted and not alerted condition. A strong reset of the beta rhythms after the painful stimuli was seen for three groups of electrodes along the midline in patients and controls: the predictability of the series induced by the laser stimulus changed very differently in controls and patients. The separation was more evident after the warning signal, leading to a separation with P-values of 0.0046 for both the hand and the face. DISCUSSION: As painful stimulus causes organization of the local activity in cortex, EEG series become more predictable after stimulation. This phenomenon was less evident in migraine, as a sign of an inadequate cortical reactivity to pain. SIGNIFICANCE: The LOO method enabled to show in migraine subtle changes in the cortical response to pain.
Assuntos
Ritmo beta , Lasers , Enxaqueca sem Aura/fisiopatologia , Dor/fisiopatologia , Adulto , Potenciais Evocados Visuais , Feminino , Humanos , Masculino , Enxaqueca sem Aura/diagnóstico , Modelos Neurológicos , Dor/diagnóstico , Valor Preditivo dos Testes , Tempo de Reação/fisiologiaRESUMO
In this paper, we consider systolic arterial pressure time series from healthy subjects and chronic heart failure patients, undergoing paced respiration, and show that different physiological states and pathological conditions may be characterized in terms of predictability of time series signals from the underlying biological system. We model time series by the regularized least-squares approach and quantify predictability by the leave-one-out error. We find that the entrainment mechanism connected to paced breath, that renders the arterial blood pressure signal more regular and thus more predictable, is less effective in patients, and this effect correlates with the seriousness of the heart failure. Using a Gaussian kernel, so that all orders of nonlinearity are taken into account, the leave-one-out error separates controls from patients (probability less than 10(-7)), and alive patients from patients for whom cardiac death occurred (probability less than 0.01).
Assuntos
Algoritmos , Pressão Sanguínea , Diagnóstico por Computador/métodos , Insuficiência Cardíaca/diagnóstico , Insuficiência Cardíaca/fisiopatologia , Modelos Biológicos , Respiração , Sístole , Feminino , Humanos , Masculino , Pessoa de Meia-Idade , Reprodutibilidade dos Testes , Medição de Risco/métodos , Fatores de Risco , Sensibilidade e Especificidade , Índice de Gravidade de Doença , Estatística como AssuntoRESUMO
We analyze by means of Granger causality the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. Whilst fully conditioned Granger causality is not affected by synergy, the pairwise analysis fails to put in evidence synergetic effects. We show that maximization of the total Granger causality to a given target, over all the possible partitions of the set of driving variables, puts in evidence redundant multiplets of variables influencing the target, provided that an unnormalized definition of Granger causality is adopted. Along the same lines we also introduce a pairwise index of synergy (w.r.t. to information flow to a third variable) which is zero when two independent sources additively influence a common target; thus, this definition differs from previous definitions of synergy.
Assuntos
Análise Multivariada , Dinâmica não LinearRESUMO
Brain Functional Connectivity (FC) quantifies statistical dependencies between areas of the brain. FC has been widely used to address altered function of brain circuits in control conditions compared to different pathological states, including epilepsy, a major neurological disorder. However, FC also has the as yet unexplored potential to help us understand the pathological transformation of the brain circuitry. Our hypothesis is that FC can differentiate global brain interactions across a time-scale of days. To this end, we present a case report study based on a mouse model for epilepsy and analyze longitudinal intracranial electroencephalography data of epilepsy to calculate FC changes from the initial insult (status epilepticus) and over the latent period, when epileptogenic networks emerge, and at chronic epilepsy, when unprovoked seizures occur as spontaneous events. We found that the overall network FC at low frequency bands decreased immediately after status epilepticus was provoked, and increased monotonously later on during the latent period. Overall, our results demonstrate the capacity of FC to address longitudinal variations of brain connectivity across the establishment of pathological states.
RESUMO
We consider the dynamics of diluted neural networks with clipped and adapting synapses. Unlike previous studies, the learning rate is kept constant as the connectivity tends to infinity: the synapses evolve on a time scale intermediate between the quenched and annealing limits and all orders of synaptic correlations must be taken into account. The dynamics is solved by mean-field theory, the order parameter for synapses being a function. We describe the effects, in the double dynamics, due to synaptic correlations.
Assuntos
Modelos Neurológicos , Rede Nervosa/fisiologia , Sinapses/fisiologia , Fenômenos Biofísicos , Biofísica , Aprendizagem/fisiologia , Processos EstocásticosRESUMO
We study the phase-synchronization properties of systolic and diastolic arterial pressure in healthy subjects. We find that delays in the oscillatory components of the time series depend on the frequency bands that are considered, in particular we find a change of sign in the phase shift going from the very low frequency band to the high frequency band. This behavior should reflect a collective behavior of a system of nonlinear interacting elementary oscillators. We prove that some models describing such systems, e.g., the Winfree and the Kuramoto models, offer a clue to this phenomenon. For these theoretical models there is a linear relationship between phase shifts and the difference of natural frequencies of oscillators and a change of sign in the phase shift naturally emerges.
Assuntos
Relógios Biológicos/fisiologia , Pressão Sanguínea/fisiologia , Diástole/fisiologia , Modelos Cardiovasculares , Fluxo Pulsátil/fisiologia , Sístole/fisiologia , Simulação por Computador , Humanos , Pessoa de Meia-Idade , PeriodicidadeRESUMO
When evaluating causal influence from one time series to another in a multivariate data set it is necessary to take into account the conditioning effect of the other variables. In the presence of many variables and possibly of a reduced number of samples, full conditioning can lead to computational and numerical problems. In this paper, we address the problem of partial conditioning to a limited subset of variables, in the framework of information theory. The proposed approach is tested on simulated data sets and on an example of intracranial EEG recording from an epileptic subject. We show that, in many instances, conditioning on a small number of variables, chosen as the most informative ones for the driver node, leads to results very close to those obtained with a fully multivariate analysis and even better in the presence of a small number of samples. This is particularly relevant when the pattern of causalities is sparse.
Assuntos
Causalidade , Bases de Dados Factuais , Análise Multivariada , Interpretação Estatística de Dados , Eletroencefalografia/estatística & dados numéricos , Epilepsia/diagnóstico , Epilepsia/fisiopatologia , Humanos , Teoria da Informação , Modelos LinearesRESUMO
We propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by a large contribution to the expansion are associated to the informational circuits present in the system, with an informational character which can be associated to the sign of the contribution. For the sake of computational complexity, we adopt the assumption of Gaussianity and use the corresponding exact formula for the conditional mutual information. We report the application of the proposed methodology on two electroencephalography (EEG) data sets.
RESUMO
We propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by an high value will be associated to informational circuits present in the system, with an informational character (synergetic or redundant) which can be associated to the sign of the contribution. We also present preliminary results on fMRI and EEG data sets.
Assuntos
Eletroencefalografia , Entropia , Teoria da Informação , Imageamento por Ressonância Magnética , HumanosRESUMO
We discuss the use of multivariate Granger causality in presence of redundant variables: the application of the standard analysis, in this case, leads to under estimation of causalities. Using the un-normalized version of the causality index, we quantitatively develop the notions of redundancy and synergy in the frame of causality and propose two approaches to group redundant variables: (i) for a given target, the remaining variables are grouped so as to maximize the total causality and (ii) the whole set of variables is partitioned to maximize the sum of the causalities between subsets. We show the application to a real neurological experiment, aiming to a deeper understanding of the physiological basis of abnormal neuronal oscillations in the migraine brain. The outcome by our approach reveals the change in the informational pattern due to repetitive transcranial magnetic stimulations.
RESUMO
We introduce a novel method for identifying the modular structures of a network based on the maximization of an objective function: the ratio association. This cost function arises when the communities detection problem is described in the probabilistic autoencoder frame. An analogy with kernel k-means methods allows us to develop an efficient optimization algorithm, based on the deterministic annealing scheme. The performance of the proposed method is shown on real data sets and on simulated networks.
RESUMO
Dynamical scaling in a two-dimensional lattice model of chaotic maps, in contact with a thermal bath at temperature T, is numerically studied. The model here proposed is equivalent to a conserved Ising model with couplings that fluctuate over the same time scale as spin moves. When coupling fluctuations and thermal fluctuations are both important, this model does not belong to the class of universality of a Langevin equation known as model B; the scaling exponents are continuously varying with T and depend on the map used. The universal behavior of model B is recovered when thermal fluctuations are dominant.
RESUMO
A new, to our knowledge, algorithm for the phase unwrapping (PU) problem that is based on stochastic relaxation is proposed and analyzed. Unlike regularization schemes previously proposed to handle this problem, our approach dispells the following two assumptions about the solution: a Gaussian model for noise and the magnitude of the true phase-field gradient's being less than pi everywhere. We formulate PU as a constrained optimization problem for the field of integer multiples of 2pi, which must be added to the wrapped phase gradient to recover the true phase gradient. By solving the optimization problem using simulated annealing with constraints, one can obtain a consistent solution under difficult conditions resulting from noise and undersampling. Results from synthetic test images are reported.
RESUMO
Time evolution of diluted neural networks with a nonmonotonic transfer function is analytically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviors: fixed-point, periodicity, and chaos. We examine in detail the structure of the strange attractor and in particular we study the main features of the stable and unstable manifolds, the hyperbolicity of the attractor, and the existence of homoclinic intersections. We also discuss the problem of the robustness of the chaos and we prove that in the present model chaotic behavior is fragile (chaotic regions are densely intercalated with periodicity windows), according to a recently discussed conjecture. Finally we perform an analysis of the microscopic behavior and in particular we examine the occurrence of damage spreading by studying the time evolution of two almost identical initial configurations. We show that for any choice of the parameters the two initial states remain microscopically distinct.