Pedro A. Morettin

A method to produce evolving functional connectivity maps during the course of an fMRI experiment using wavelet-based time-varying Granger causality.

Functional magnetic resonance imaging (fMRI) is widely used to identify neural correlates of cognitive tasks. However, the analysis of functional connectivity is crucial to understanding neural dynamics. Although many studies of cerebral circuitry have revealed adaptative behavior, which can change during the course of the experiment, most of contemporary connectivity studies are based on correlational analysis or structural equations analysis, assuming a time-invariant connectivity structure. In this paper, a novel method of continuous time-varying connectivity analysis is proposed, based on the wavelet expansion of functions and vector autoregressive model (wavelet dynamic vector autoregressive-DVAR). The model also allows identification of the direction of information flow between brain areas, extending the Granger causality concept to locally stationary processes. Simulation results show a good performance of this approach even using short time intervals. The application of this new approach is illustrated with fMRI data from a simple AB motor task experiment.

Frequency domain connectivity identification: An application of partial directed coherence in fMRI

Functional magnetic resonance imaging (fMRI) has become an important tool in Neuroscience due to its noninvasive and high spatial resolution properties compared to other methods like PET or EEG. Characterization of the neural connectivity has been the aim of several cognitive researches, as the interactions among cortical areas lie at the heart of many brain dysfunctions and mental disorders. Several methods like correlation analysis, structural equation modeling, and dynamic causal models have been proposed to quantify connectivity strength. An important concept related to connectivity modeling is Granger causality, which is one of the most popular definitions for the measure of directional dependence between time series. In this article, we propose the application of the partial directed coherence (PDC) for the connectivity analysis of multisubject fMRI data using multivariate bootstrap. PDC is a frequency domain counterpart of Granger causality and has become a very prominent tool in EEG studies. The achieved frequency decomposition of connectivity is useful in separating interactions from neural modules from those originating in scanner noise, breath, and heart beating. Real fMRI dataset of six subjects executing a language processing protocol was used for the analysis of connectivity. Hum Brain Mapp, 2009.

A wavelet analysis for time series

In this paper we develop a wavelet spectral analysis for a stationary discrete process. Some basic ideas on wavelets are given and the concept of wavelet spectrum is introduced. Asymptotic properties of the discrete wavelet transform of a sample of observed values from the process are derived and the wavelet periodogram is considered as an estimator of the wavelet spectrum. Applications to real and simulated series are given.

Time-varying modeling of gene expression regulatory networks using the wavelet dynamic vector autoregressive method

MOTIVATION A variety of biological cellular processes are achieved through a variety of extracellular regulators, signal transduction, protein-protein interactions and differential gene expression. Understanding of the mechanisms underlying these processes requires detailed molecular description of the protein and gene networks involved. To better understand these molecular networks, we propose a statistical method to estimate time-varying gene regulatory networks from time series microarray data. One well known problem when inferring connectivity in gene regulatory networks is the fact that the relationships found constitute correlations that do not allow inferring causation, for which, a priori biological knowledge is required. Moreover, it is also necessary to know the time period at which this causation occurs. Here, we present the Dynamic Vector Autoregressive model as a solution to these problems. RESULTS We have applied the Dynamic Vector Autoregressive model to estimate time-varying gene regulatory networks based on gene expression profiles obtained from microarray experiments. The network is determined entirely based on gene expression profiles data, without any prior biological knowledge. Through construction of three gene regulatory networks (of p53, NF-kappaB and c-myc) for HeLa cells, we were able to predict the connectivity, Granger-causality and dynamics of the information flow in these networks. SUPPLEMENTARY INFORMATION Additional figures may be found at http://mariwork.iq.usp.br/dvar/.

Wavelet based time-varying vector autoregressive modelling

Vector autoregressive (VAR) modelling is one of the most popular approaches in multivariate time series analysis. The parameters interpretation is simple, and provide an intuitive identification of relationships and Granger causality among time series. However, the VAR modelling requires stationarity conditions which could not be valid in many practical applications. Locally stationary or time dependent modelling seem attractive generalizations, and several univariate approaches have already been proposed. In this paper we propose an estimation procedure for time-varying vector autoregressive processes, based on wavelet expansions of autoregressive coefficients. The asymptotic properties of the estimator are derived and illustrated by computer intensive simulations. We also present an application to brain connectivity identification using functional magnetic resonance imaging (fMRI) data sets.

Estimation of Time Varying Linear Systems

Based on kernel and wavelet estimators of the evolutionary spectrum and cross-spectrum we propose nonlinear wavelet estimators of the time varying coefficients of a linear system, whose input and output are locally stationary processes, in the sense of Dahlhaus (1997). We obtain large sample properties of these estimators, present some simulated examples and derive results on the L2-risk for the wavelet threshold estimators, assuming that the coefficients belong to some smoothness class.

Seasonality of suicide in the city of Sao Paulo, Brazil, 1979-2003

OBJECTIVE To evaluate suicide seasonality in the city of São Paulo within an urban area and tropical zone. METHOD Suicides were evaluated using the chi-square test and analysis of variance (ANOVA) by comparing monthly, quarterly and half-yearly variations, differentiating by gender. Analyses of time series were carried out using the autocorrelation function and periodogram, while the significance level for seasonality was confirmed with the Fishers test. RESULTS The suicides of the period between 1979 and 2003 numbered 11,434 cases. Differences were observed in suicides occurring in Spring and Autumn for the total sample (ANOVA: p-value = 0.01), and in the male sample (ANOVA: p-value = 0.02). For the analysis of time series, seasonality was significant only for the period of 7 months in the male sample (p-value = 0.04). DISCUSSION In this study, no significant seasonal differences were observed in the occurrences of suicides, with the exception of the male sample. The differences observed did not correspond with the pattern described in studies carried out in temperate zones. Some of the climatic particularities of the tropical zone might explain the atypical pattern of seasonality of suicides found in large populations within an urban area and tropical zone.

Modelling and Forecasting Linear Combinations of Time Series

Summary This paper reviews and extends several aspects of the analysis of linear combinations of time series. Special cases are temporal and contemporaneous aggregations and systematic sampling. We present some simple examples, a unified notation, references to the literature, and some general results for linear combinations of scalar and vector time series. For basic time series following ARIMA models in scalar cases we derive the ARIMA models of the linear combinations as functions of those of the basic series in both the nonseasonal and seasonal cases. For vector time series we compare the forecast efficiencies of two alternative approaches: first model and forecast and then form the linear combination, and first form the linear combination and then model and forecast; for this analysis we use the moving average representation of a stationary time series. A final section contains an application to monthly data on milk production and milk productivity series for the State of Siio Paulo, Brazil.

From Fourier to Wavelet Analysis of Time Series

It is well known that Fourier analysis is suited to the analysis of stationary series. If {Xt,t = 0, ± 1, …} is a weakly stationary process, it can be decomposed into a linear combination of sines and cosines. Formally,