Manolis Christodoulakis

Computation of repetitions and regularities of biologically weighted sequences.

Biological weighted sequences are used extensively in molecular biology as profiles for protein families, in the representation of binding sites and often for the representation of sequences produced by a shotgun sequencing strategy. In this paper, we address three fundamental problems in the area of biologically weighted sequences: (i) computation of repetitions, (ii) pattern matching, and (iii) computation of regularities. Our algorithms can be used as basic building blocks for more sophisticated algorithms applied on weighted sequences.

Indeterminate strings, prefix arrays & undirected graphs

An integer array y = y 1 . . n is said to be feasible if and only if y 1 = n and, for every i ? 2 . . n , i ? i + y i ? n + 1 . A string is said to be indeterminate if and only if at least one of its elements is a subset of cardinality greater than one of a given alphabet Σ; otherwise it is said to be regular. A feasible array y is said to be regular if and only if it is the prefix array of some regular string. We show using a graph model that every feasible array of integers is a prefix array of some (indeterminate or regular) string, and for regular strings corresponding to y, we use the model to provide a lower bound on the alphabet size. We show further that there is a 1-1 correspondence between labelled simple graphs and indeterminate strings, and we show how to determine the minimum alphabet size ? of an indeterminate string x based on its associated graph G x . Thus, in this sense, indeterminate strings are a more natural object of combinatorial interest than the strings on elements of Σ that have traditionally been studied.

Identifying rhythms in musical texts

A fundamental problem in music is to classify songs according to their rhythm. A rhythm is represented by a sequence of “Quick” (Q) and “Slow” (S) symbols, which correspond to the (relative) duration of notes, such that S = 2Q. In this paper, we present an efficient algorithm for locating the maximum-length substring of a music text t that can be covered by a given rhythm r.

Abelian borders in binary words

Abstract In this article we study the appearance of abelian borders in binary words, a notion closely related to the abelian period of a word. We show how many binary words have shortest border of a given length by identifying relations with Dyck words. Furthermore, we give some bounds on the number of abelian border-free words of a given length and on the number of abelian words of a given length that have at least one abelian border. Finally, using some techniques employed in a recent paper by Christodoulakis et al. (2013), we show that there exists an algorithm that finds the shortest abelian border of a binary word that is not abelian border-free in Θ ( n ) time on average.

Detection and Removal of Muscle Artifacts from Scalp EEG Recordings in Patients with Epilepsy

The Electroencephalogram (EEG) is often contaminated by muscle artifacts. EEG is a widely used recording technique for the study of many brain related diseases such as epilepsy. The detection and removal of muscle artifacts from the EEG signal poses a real challenge and is crucial for the reliable interpretation of EEG-based quantitative measures. In this paper, an automatic method for detection and removal of muscle artifacts from scalp EEG recordings, based on canonical correlation analysis (CCA), is introduced. To this end we exploit the fact that the EEG signal may exhibit altered autocorrelation structure and spectral characteristics during periods when it is contaminated by muscle activity. Therefore, we design classifiers in order to automatically discriminate between contaminated and non-contaminated EEG epochs using features based on the aforementioned quantities and examine their performance on simulated data and in scalp EEG recordings obtained from patients with epilepsy.

Automatic detection and removal of muscle artifacts from scalp EEG recordings in patients with epilepsy

Automatic detection and removal of muscle artifacts plays an important role in long-term scalp electroencephalography (EEG) monitoring, and muscle artifact detection algorithms have been intensively investigated. This paper proposes an algorithm for automatic muscle artifacts detection and removal using canonical correlation analysis (CCA) and wavelet transform (WT) in epochs from long-term EEG recordings. The proposed method first performs CCA analysis and then conducts wavelet decomposition on the canonical components within a specific frequency range and selects a subset of the wavelet coefficients for subsequent processing. A set of features, including the mean of wavelet coefficients and the canonical component autocorrelation values, are extracted from the above analysis and subsequently used as input in a random forest (RF) classifier. The RF classifier produces a similarity measure between observations and selects a subset of the most important features by comparing the original data with a set of synthetic data that is constructed based on the latter. The RF predictor output is finally used in combination with unsupervised clustering algorithms to discriminate between contaminated and non-contaminated EEG epochs. The proposed method is evaluated in epochs of 30 min from scalp EEG recordings obtained from three patients with epilepsy and yields a sensitivity of 71% and 80%, as well as a specificity of 81% and 85% for k-means and spectral clustering, respectively.

Graph-theoretic analysis of scalp EEG brain networks in epilepsy — The influence of montage and volume conduction

It is well established that both the choice of recording reference (montage) and volume conduction affect the connectivity measures obtained from scalp EEG. Our purpose in this work is to establish the extent to which they influence the graph theoretic measures of brain networks in epilepsy obtained from scalp EEG. We evaluate and compare two commonly used linear connectivity measures - cross-correlation and coherence - with measures that account for volume conduction, namely corrected cross-correlation, imaginary coherence, phase lag index and weighted phase lag index. We show that the graphs constructed with cross-correlation and coherence are the most affected by volume conduction and montage; however, they demonstrate the same trend - decreasing connectivity at seizure onset, which continues decreasing in the ictal and early post-ictal period, increasing again several minutes after the seizure has ended-with all other measures except imaginary coherence. In particular, networks constructed using cross-correlation yield better discrimination between the pre-ictal and ictal periods than the measures less sensitive to volume conduction. Thus, somewhat paradoxically, although removing effects of volume conduction allows for a more accurate reconstruction of the true underlying networks this may come at the cost of discrimination ability with respect to brain state.

Implementing approximate regularities

In this paper, we study approximate regularities of strings, that is, approximate periods, approximate covers, and approximate seeds. We explore their similarities and differences and we implement algorithms for solving the smallest distance approximate period/cover/seed problem and the restricted smallest approximate period/cover/seed/ problem in polynomial time, under a variety of distance rules (the Hamming distance, the edit distance, and the weighted edit distance). Then, we analyse our experimental results to find out the time complexity of the algorithms in practice.

Periodicity in functional brain networks: Application to scalp EEG from epilepsy patients

Seizure detection and prediction studies using scalp- or intracranial-EEG measurements often focus on short-length recordings around the occurrence of the seizure, normally ranging between several seconds and up to a few minutes before and after the event. The underlying assumption in these studies is the presence of a relatively constant EEG activity in the interictal period, that is presumably interrupted by the occurrence of a seizure, at the time the seizure starts or slightly earlier. In this study, we put this assumption under test, by examining long-duration scalp EEG recordings, ranging between 22 and 72 hours, of five patients with epilepsy. For each patient, we construct functional brain networks, by calculating correlations between the scalp electrodes, and examine how these networks vary in time. The results suggest not only that the network varies over time, but it does so in a periodic fashion, with periods ranging between 11 and 25 hours.

Introducing weighted approaches to study network brain dynamics from EEG epilepsy measurements: The EigenBrain algorithm

It is fairly established that dynamic recordings of functional activity maps can naturally and efficiently be represented by functional connectivity networks. In this article we study weighted and fully-connected brain networks, created from electroencephalographic (EEG) measurements that concern patients with focal and generalized epilepsy. We introduce a totally new methodology that has never been utilized before and that investigates weighted and fully-connected networks, which includes eigen-decomposition analysis, feature extraction and quantitative comparisons among entire graph datasets. Our goal is to establish epileptic seizure detection/prediction rules, by identifying repetitive EEG activity in patients before and after each seizure onset. In the present paper we treat each brain network as a weighted and full adjacency matrix, without cutting, binarizing or ignoring any values. In this way, it is the first time that the full structure of the connectivity weighing profile is exploited. Also apart from graph theory approaches, mathematical models such as eigen-decomposition analysis are used in our research, in order to study and analyze brain networks. Finally, we present and discuss the results and conclusions of our new method, which are in line with earlier EEG epilepsy findings and demonstrate a standard EEG behavior in both the postictal and preictal period.