Giulia Menconi

Compression and Diffusion: A Joint Approach to Detect Complexity

Abstract The adoption of the Kolmogorov–Sinai entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are a manifestation of system dynamics whose rules are either unknown or too complex for a mathematical treatment, is still a challenge since the KS entropy is not computable, in general, in that case. Here we present a plan of action based on the joint action of two procedures, both related to the KS entropy, but compatible with computer implementation through fast and efficient programs. The former procedure, called compression algorithm sensitive to regularity (CASToRE), establishes the amount of order by the numerical evaluation of algorithmic compressibility. The latter, called complex analysis of sequences via scaling and randomness assessment (CASSANDRA), establishes the complexity degree through the numerical evaluation of the strength of an anomalous effect. This is the departure, of the diffusion process generated by the observed fluctuations, from ordinary Brownian motion. The CASSANDRA algorithm shares with CASToRE a connection with the Kolmogorov complexity. This makes both algorithms especially suitable to study the transition from dynamics to thermodynamics, and the case of non-stationary time series as well. The benefit of the joint action of these two methods is proven by the analysis of artificial sequences with the same main properties as the real time series to which the joint use of these two methods will be applied in future research work.

Information and dynamical systems: a concrete measurement on sporadic dynamics

Abstract We present a method for the study of dynamical systems based on the notion of quantity of information. Measuring the quantity of information of a string by using data compression algorithms, it is possible to give a notion of orbit complexity of dynamical systems. In compact ergodic dynamical systems, entropy is almost everywhere equal to orbit complexity. We have introduced a new compression algorithm called CASToRe which allows a direct estimation of the information content of the orbits in the 0-entropy case. The method is applied to a sporadic dynamical system (Manneville map).

Data compression and genomes: a two-dimensional life domain map.

We define the complexity of DNA sequences as the information content per nucleotide, calculated by means of some Lempel-Ziv data compression algorithm. It is possible to use the statistics of the complexity values of the functional regions of different complete genomes to distinguish among genomes of different domains of life (Archaea, Bacteria and Eukarya). We shall focus on the distribution function of the complexity of non-coding regions. We show that the three domains may be plotted in separate regions within the two-dimensional space where the axes are the skewness coefficient and the curtosis coefficient of the aforementioned distribution. Preliminary results on 15 genomes are introduced.

Vortex dynamics in evolutive flows: A weakly chaotic phenomenon

We make use of a wavelet method to extract, from experimental velocity signals obtained in an evolutive flow, the dominating velocity components generated by vortex dynamics. We characterize the resulting time series complexity by means of a joint use of data compression and of an entropy diffusion method. We assess that the time series emerging from the wavelet analysis of the vortex dynamics is a weakly chaotic process with a vanishing Kolmogorov-Sinai entropy and a power-law growth of the information content. To reproduce the Fourier spectrum of the experimental signal, we adopt a harmonic dependence on time with a fluctuating frequency, ruled by an inverse power-law distribution of random events. The complexity of these fluctuations is determined by studying the corresponding artificial sequences. We reproduce satisfactorily both spectral and complex properties of the experimental signal by locating the complexity of the fluctuating process at the border between the stationary and the nonstationary states.

A compression-based approach for coding sequences identification. I. Application to prokaryotic genomes.

Most of the gene prediction algorithms for prokaryotes are based on Hidden Markov Models or similar machine-learning approaches, which imply the optimization of a high number of parameters. The present paper presents a novel method for the classification of coding and non-coding regions in prokaryotic genomes, based on a suitably defined compression index of a DNA sequence. The main features of this new method are the non-parametric logic and the costruction of a dictionary of words extracted from the sequences. These dictionaries can be very useful to perform further analyses on the genomic sequences themselves. The proposed approach has been applied on some prokaryotic complete genomes, obtaining optimal scores of correctly recognized coding and non-coding regions. Several false-positive and false-negative cases have been investigated in detail, which have revealed that this approach can fail in the presence of highly structured coding regions (e.g., genes coding for modular proteins) or quasi-random non-coding regions (e.g., regions hosting non-functional fragments of copies of functional genes; regions hosting promoters or other protein-binding sequences). We perform an overall comparison with other gene-finder software, since at this step we are not interested in building another gene-finder system, but only in exploring the possibility of the suggested approach.

Global Mapping of DNA Conformational Flexibility on Saccharomyces cerevisiae

In this study we provide the first comprehensive map of DNA conformational flexibility in Saccharomyces cerevisiae complete genome. Flexibility plays a key role in DNA supercoiling and DNA/protein binding, regulating DNA transcription, replication or repair. Specific interest in flexibility analysis concerns its relationship with human genome instability. Enrichment in flexible sequences has been detected in unstable regions of human genome defined fragile sites, where genes map and carry frequent deletions and rearrangements in cancer. Flexible sequences have been suggested to be the determinants of fragile gene proneness to breakage; however, their actual role and properties remain elusive. Our in silico analysis carried out genome-wide via the StabFlex algorithm, shows the conserved presence of highly flexible regions in budding yeast genome as well as in genomes of other Saccharomyces sensu stricto species. Flexibile peaks in S. cerevisiae identify 175 ORFs mapping on their 3’UTR, a region affecting mRNA translation, localization and stability. (TA)n repeats of different extension shape the central structure of peaks and co-localize with polyadenylation efficiency element (EE) signals. ORFs with flexible peaks share common features. Transcripts are characterized by decreased half-life: this is considered peculiar of genes involved in regulatory systems with high turnover; consistently, their function affects biological processes such as cell cycle regulation or stress response. Our findings support the functional importance of flexibility peaks, suggesting that the flexible sequence may be derived by an expansion of canonical TAYRTA polyadenylation efficiency element. The flexible (TA)n repeat amplification could be the outcome of an evolutionary neofunctionalization leading to a differential 3’-end processing and expression regulation in genes with peculiar function. Our study provides a new support to the functional role of flexibility in genomes and a strategy for its characterization inside human fragile sites.

Mobilomics in Saccharomyces cerevisiae strains

BackgroundMobile Genetic Elements (MGEs) are selfish DNA integrated in the genomes. Their detection is mainly based on consensus-like searches by scanning the investigated genome against the sequence of an already identified MGE. Mobilomics aims at discovering all the MGEs in a genome and understanding their dynamic behavior: The data for this kind of investigation can be provided by comparative genomics of closely related organisms. The amount of data thus involved requires a strong computational effort, which should be alleviated.ResultsOur approach proposes to exploit the high similarity among homologous chromosomes of different strains of the same species, following a progressive comparative genomics philosophy. We introduce a software tool based on our new fast algorithm, called regender, which is able to identify the conserved regions between chromosomes. Our case study is represented by a unique recently available dataset of 39 different strains of S.cerevisiae, which regender is able to compare in few minutes. By exploring the non-conserved regions, where MGEs are mainly retrotransposons called Tys, and marking the candidate Tys based on their length, we are able to locate a priori and automatically all the already known Tys and map all the putative Tys in all the strains. The remaining putative mobile elements (PMEs) emerging from this intra-specific comparison are sharp markers of inter-specific evolution: indeed, many events of non-conservation among different yeast strains correspond to PMEs. A clustering based on the presence/absence of the candidate Tys in the strains suggests an evolutionary interconnection that is very similar to classic phylogenetic trees based on SNPs analysis, even though it is computed without using phylogenetic information.ConclusionsThe case study indicates that the proposed methodology brings two major advantages: (a) it does not require any template sequence for the wanted MGEs and (b) it can be applied to infer MGEs also for low coverage genomes with unresolved bases, where traditional approaches are largely ineffective.

Information of sequences and applications

In this short note, we outline some results about complexity of orbits of a dynamical system, entropy and initial condition sensitivity in weakly chaotic dynamical systems. We present a technique to estimate orbit complexity by the use of data compression algorithms. We also outline how this technique has been applied by our research group to dynamical systems and to DNA sequences.

A top-down linguistic approach to the analysis of genomic sequences: The metabotropic glutamate receptors 1 and 5 in human and in mouse as a case study

This paper presents a top-down strategy to detect features in genomic sequences. The strategys core is to exploit dictionary-based compression algorithms and analyse the content of the automatically generated dictionary. We classify the different over-represented segments and in the case study we correlate them to experimentally identified or theoretically forecasted biological features. A large spectrum analysis reveals that the only feature co-located with the a priori extracted segments is the torsional flexibility of DNA, while non-B DNA configurations are anti-localized and other features are mostly independent of the extracted sequences. This analysis unravels complex relationships between the linguistic structures investigated under our approach and some known biological features.

Non-sequential Recursive Pair Substitutions and Numerical Entropy Estimates in Symbolic Dynamical Systems

We numerically test the method of non-sequential recursive pair substitutions to estimate the entropy of an ergodic source. We compare its performance with other classical methods to estimate the entropy (empirical frequencies, return times, and Lyapunov exponent). We have considered as a benchmark for the methods several systems with different statistical properties: renewal processes, dynamical systems provided and not provided with a Markov partition, and slow or fast decay of correlations. Most experiments are supported by rigorous mathematical results, which are explained in the paper.