Ciprian Doru Giurcaneanu

Assessment of Linear and Nonlinear Synchronization Measures for Analyzing EEG in a Mild Epileptic Paradigm

Epilepsy is one of the most common brain disorders and may result in brain dysfunction and cognitive disturbances. Epileptic seizures usually begin in childhood without being accommodated by brain damage and are tolerated by drugs that produce no brain dysfunction. In this study, cognitive function is evaluated in children with mild epileptic seizures controlled with common antiepileptic drugs. Under this prism, we propose a concise technical framework of combining and validating both linear and nonlinear methods to efficiently evaluate (in terms of synchronization) neurophysiological activity during a visual cognitive task consisting of fractal pattern observation. We investigate six measures of quantifying synchronous oscillatory activity based on different underlying assumptions. These measures include the coherence computed with the traditional formula and an alternative evaluation of it that relies on autoregressive models, an information theoretic measure known as minimum description length, a robust phase coupling measure known as phase-locking value, a reliable way of assessing generalized synchronization in state-space and an unbiased alternative called synchronization likelihood. Assessment is performed in three stages; initially, the nonlinear methods are validated on coupled nonlinear oscillators under increasing noise interference; second, surrogate data testing is performed to assess the possible nonlinear channel interdependencies of the acquired EEGs by comparing the synchronization indexes under the null hypothesis of stationary, linear dynamics; and finally, synchronization on the actual data is measured. The results on the actual data suggest that there is a significant difference between normal controls and epileptics, mostly apparent in occipital-parietal lobes during fractal observation tests.

Genetic networks inferred from time series of gene expression data

The paper considers the problem of building genetic networks from time series of gene expression data. The class of models of interest is that of systems of differential equations specifying gene-gene interactions and the goal is to infer the network structure from experimental gene expression data. As a mean to regularize the inverse problem, we assume the biologically plausible constraint which imposes limits on the number of genes interacting with any given gene. The existing algorithms for inferring gene network structure heavily rely on the transformation of the system of differential equations into an approximative discretized system. In contrast, our proposed algorithms infer the structure of the gene networks by operating with the exact solutions of the differential equations. For the case of time series of non-uniformly sampled gene expressions, we first fit an optimal sum of exponentials model to each gene, where the best fit is defined by the minimum description length (MDL) principle, the optimal model being subsequently used for interpolating the data at a finer and equidistant grid in time. As a simulating environment we take simple genetic networks, assumed to be the ground truth, where the dynamical interactions between genes are postulated to be linear differential equations. We show that we can recover the sparse structure of the original model using the data generated by the system for a wide range of model parameters (i.e. strengths of the gene-gene interactions).

Estimation of AR and ARMA models by stochastic complexity

In this paper the stochastic complexity criterion is applied to estimation of the order in AR and ARMA models. The power of the criterion for short strings is illustrated by simulations. It requires an integral of the square root of Fisher information, which is done by Monte Carlo technique. The stochastic complexity, which is the negative logarithm of the Normalized Maximum Likelihood universal density function, is given. Also, exact asymptotic formulas for the Fisher information matrix are derived.

A decision support framework for the discrimination of children with controlled epilepsy based on EEG analysis

BackgroundIn this work we consider hidden signs (biomarkers) in ongoing EEG activity expressing epileptic tendency, for otherwise normal brain operation. More specifically, this study considers children with controlled epilepsy where only a few seizures without complications were noted before starting medication and who showed no clinical or electrophysiological signs of brain dysfunction. We compare EEG recordings from controlled epileptic children with age-matched control children under two different operations, an eyes closed rest condition and a mathematical task. The aim of this study is to develop reliable techniques for the extraction of biomarkers from EEG that indicate the presence of minor neurophysiological signs in cases where no clinical or significant EEG abnormalities are observed.MethodsWe compare two different approaches for localizing activity differences and retrieving relevant information for classifying the two groups. The first approach focuses on power spectrum analysis whereas the second approach analyzes the functional coupling of cortical assemblies using linear synchronization techniques.ResultsDifferences could be detected during the control (rest) task, but not on the more demanding mathematical task. The spectral markers provide better diagnostic ability than their synchronization counterparts, even though a combination (or fusion) of both is needed for efficient classification of subjects.ConclusionsBased on these differences, the study proposes concrete biomarkers that can be used in a decision support system for clinical validation. Fusion of selected biomarkers in the Theta and Alpha bands resulted in an increase of the classification score up to 80% during the rest condition. No significant discrimination was achieved during the performance of a mathematical subtraction task.

Stochastic Complexity for the Detection of Periodically Expressed Genes

The problem we address in this study is to decide, based on the available measurements, if a particular gene exhibits a periodic behavior. To this end we propose a principled method relying on the Stochastic Complexity (SC) whose computation is discussed for the generalized Gaussian distribution. We also investigate the relationship between SC, the well-known Minimum Description Length (MDL) formula, and the Bayesian Information Criterion (BIC). The performances of the SC-based approach are compared for simulated and real data with methods that are widely accepted in the bioinformatics community.

Clustering time series gene expression data based on sum-of-exponentials fitting

This paper presents a method based on fitting a sum-of-exponentials model to the nonuniformly sampled data, for clustering the time series of gene expression data. The structure of the model is estimated by using the minimum description length (MDL) principle for nonlinear regression, in a new form, incorporating a normalized maximum-likelihood (NML) model for a subset of the parameters. The performance of the structure estimation method is studied using simulated data, and the superiority of the new selection criterion over earlier criteria is demonstrated. The accuracy of the nonlinear estimates of the model parameters is analyzed with respect to the Cramér-Rao lower bounds. Clustering examples of gene expression data sets from a developmental biology application are presented, revealing gene grouping into clusters according to functional classes.

Low-complexity transform coding with integer-to-integer transforms

We propose the application of a new transform-based coding method in conjunction with Golomb-Rice (G-R) codes to lower significantly the complexity, which can be used in various applications, e.g. the multiple description coding. The theoretical evaluations predict no important loss in compression performance, while the complexity is considerably reduced. Since GR codes are very fast and well suited for exponentially decaying distributions, they were implemented during the last decade in image and audio compressors. In all these schemes, the selection of the code parameter is performed presuming Laplacian distribution of prediction errors. We derive the selection method for the GR code parameter also for the case of Gaussian inputs.

On the use of Kolmogorov structure function for periodogram smoothing

In a recent series of papers, it was shown how the periodogram can be smoothed by thresholding the estimated cepstral coefficients either with a carefully designed uniformly most powerful unbiased test (UMPUT), or with the Bayesian information criterion (BIC). In this paper, we devise a fully automatic scheme that selects the threshold by using the Kolmogorov structure function (KSF). For the numerical examples taken from the previous literature, the newly proposed method compares favorably with the existing schemes.

Optimally Distinguishable Distributions: a New Approach to Composite Hypothesis Testing With Applications to the Classical Linear Model

The newest approach to composite hypothesis testing proposed by Rissanen relies on the concept of optimally distinguishable distributions (ODD). The method is promising, but so far it has only been applied to a few simple examples. We derive the ODD detector for the classical linear model. In this framework, we provide answers to the following problems that have not been previously investigated in the literature: i) the relationship between ODD and the widely used Generalized Likelihood Ratio Test (GLRT); ii) the connection between ODD and the information theoretic criteria applied in model selection. We point out the strengths and the weaknesses of the ODD method in detecting subspace signals in broadband noise. Effects of the subspace interference are also evaluated.

Composite hypothesis testing by optimally distinguishable distributions

Relying on optimally distinguishable distributions (ODD), it was defined very recently a new framework for the composite hypothesis testing. We resort to the linear model to investigate the performances of the ODD detector and to compare it with the widely used generalized likelihood ratio test (GLRT). As the ODD concept is very new, its application to models with nuisance parameters was not discussed in the previous literature. The present study attempts to fill the gap by proposing a modified ODD criterion to accommodate the practical case of unknown noise variance.