Rodolfo Rosa

Circular codes revisited: A statistical approach

In 1996 Arquès and Michel [1996. A complementary circular code in the protein coding genes. J. Theor. Biol. 182, 45-58] discovered the existence of a common circular code in eukaryote and prokaryote genomes. Since then, circular code theory has provoked great interest and underwent a rapid development. In this paper we discuss some theoretical issues related to the synchronization properties of coding sequences and circular codes with particular emphasis on the problem of retrieval and maintenance of the reading frame. Motivated by the theoretical discussion, we adopt a rigorous statistical approach in order to try to answer different questions. First, we investigate the covering capability of the whole class of 216 self-complementary, C(3) maximal codes with respect to a large set of coding sequences. The results indicate that, on average, the code proposed by Arquès and Michel has the best covering capability but, still, there exists a great variability among sequences. Second, we focus on such code and explore the role played by the proportion of the bases by means of a hierarchy of permutation tests. The results show the existence of a sort of optimization mechanism such that coding sequences are tailored as to maximize or minimize the coverage of circular codes on specific reading frames. Such optimization clearly relates the function of circular codes with reading frame synchronization.

New resampling method to assess the accuracy of the maximal Lyapunov exponent estimation

Abstract In this paper, we propose a novel method to assess standard errors and confidence intervals for the maximal Lyapunov exponent estimated on time continuous chaotic systems. The method is based on resampling the original series by means of spline interpolation in the time domain. In such a way, new time series of increased size are obtained, and the sample distribution of the estimators is constructed. The method is explained and tested on the basis of computer simulations both for clean and noisy series. We give evidence that the distribution of the maximal Lyapunov exponent calculated by this method fairly agrees with the one obtained by true series with different initial conditions. An empirical criterion for the choice of the parameters of the resampling is also suggested .

The Merli-Missiroli-Pozzi Two-Slit Electron-Interference Experiment.

In 2002 readers of Physics World voted Young’s double-slit experiment with single electrons as “the most beautiful experiment in physics” of all time. Pier Giorgio Merli, Gian Franco Missiroli, and Giulio Pozzi carried out this experiment in a collaboration between the Italian Research Council and the University of Bologna almost three decades earlier. I examine their experiment, place it in historical context, and discuss its philosophical implications.

DNA, dichotomic classes and frame synchronization: a quasi-crystal framework.

In this article, we show how a new mathematical model of the genetic code can be exploited for investigating the almost periodic properties of DNA and mRNA protein-coding sequences. We present the main mathematical features of the model and highlight its connections with both number theory and group theory. The group theoretic framework presents interesting analogies with the theory of crystals. Moreover, we exploit the information provided by dichotomic classes, binary variables naturally derived from the mathematical model, in order to build statistical classifiers for retrieving and predicting the normal reading frame used by the ribosome in protein synthesis. The results show that coding sequences possess a local informational structure that can be related to frame synchronization processes. The information for retrieving the normal reading frame, which implies the existence of short-range correlations and almost periodic structures related to the organization of codons, offers an interesting analogy with the properties of quasi-crystals. From a theoretical point of view, our results might contribute to clarifying the relation between biological information and shape in nucleic acids and proteins. Also, from the point of view of applications, we present new promising tools for designing efficient algorithms for frame synchronization, which plays a crucial role in faithful synthesis of proteins.

A Novel Monte-Carlo Based Method for Quantitative Thin Film X-Ray Microanalysis

Abstract. A novel approach to the quantitative analysis of thinned samples, which exploits the finite and variable width of the incident beam of an analytical electron microscope (AEM), is reported. For a binary alloy AB, the method requires two measurements of the I(AKα)/I(BKα) X-ray intensity ratios, obtained with two different beam diameters. The digital image of the beam is also recorded by a slow-scan CCD camera; its pixel intensities are converted into probability densities by our Monte Carlo code, which has been modified to simulate the electron trajectories crossing the vertical boundaries of the sample. The result of the simulation consists of two thickness t vs concentration C matrices for the two different spot sizes; the unique t-C combination, corresponding to the analyzed region, is obtained through the convergence routine described in our previous papers.This method has been applied to the analysis of Si-Ge alloys in AEM cross sections of Si/Si1−xGex/Si heterostructures. The Ge concentrations obtained by this method on samples of different composition and thickness are in agreement with those deduced from other experimental techniques.

Detecting structure in parity binary sequences

In this article, we investigate the possible existence of error-detection/correction mechanisms in the genetic machinery by means of a recently proposed coding strategy. On this basis, we numerically code exons, creating binary parity strings and successively we study their dependence structure by means of rigorous statistical methods (moving block bootstrap, and a new entropy-based method). The results show that parity sequences display complex dependence patterns enforcing the hypothesis of the existence of deterministic error-correction mechanisms grounded on this particular parity coding.

Markov Chain Monte Carlo in Stastical Mechanics

The appearance of the article by N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller marked the birth of the Monte Carlo method for the study of statistical-mechanical systems and of a specific form of “importance sampling”—namely, Markov chain Monte Carlo. After nearly 40 years of statistical usage, this technique has had a profound impact on statistical theory, on both Bayesian and classical statistics. Markov chain Monte Carlo is used essentially to estimate integrals in high dimensions. This article addresses the accuracy of such estimation. Through computer experiments performed on the two-dimensional Ising model, we compare the most common method for error estimates in statistical mechanics. It appears that the moving-block bootstrap outperforms other methods based on subseries values when the number of observations is relatively small and the time correlation between successive configurations decays slowly. Moreover, the moving-block bootstrap enables estimates of the standard error to be made not only for the averages of directly obtained data but also for estimates derived from sophisticated numerical procedures.

The non-power model of the genetic code: a paradigm for interpreting genomic information.

In this article, we present a mathematical framework based on redundant (non-power) representations of integer numbers as a paradigm for the interpretation of genomic information. The core of the approach relies on modelling the degeneracy of the genetic code. The model allows one to explain many features and symmetries of the genetic code and to uncover hidden symmetries. Also, it provides us with new tools for the analysis of genomic sequences. We review briefly three main areas: (i) the Euplotid nuclear code, (ii) the vertebrate mitochondrial code, and (iii) the main coding/decoding strategies used in the three domains of life. In every case, we show how the non-power model is a natural unified framework for describing degeneracy and deriving sound biological hypotheses on protein coding. The approach is rooted on number theory and group theory; nevertheless, we have kept the technical level to a minimum by focusing on key concepts and on the biological implications.

FIB Preparation of a NiO Wedge-Lamella and STEM X-Ray Microanalysis for the Determination of the Experimental k (O-Ni) Cliff-Lorimer Coefficient

A method for the fabrication of a wedge-shaped thin NiO lamella by focused ion beam is reported. The starting sample is an oxidized bulk single crystalline, <100> oriented, Ni commercial standard. The lamella is employed for the determination, by analytical electron microscopy at 200 kV of the experimental k(O-Ni) Cliff-Lorimer (G. Cliff & G.W. Lorimer, J Microsc 103, 203-207, 1975) coefficient, according to the extrapolation method by Van Cappellen (E. Van Cappellen, Microsc Microstruct Microanal 1, 1-22, 1990). The result thus obtained is compared to the theoretical k(O-Ni) values either implemented into the commercial software for X-ray microanalysis quantification of the scanning transmission electron microscopy/energy dispersive spectrometry equipment or calculated by the Monte Carlo method. Significant differences among the three values are found. This confirms that for a reliable quantification of binary alloys containing light elements, the choice of the Cliff-Lorimer coefficients is crucial and experimental values are recommended.

TESTING CHAOTIC DYNAMICS IN SYSTEMS WITH TWO POSITIVE LYAPUNOV EXPONENTS: A BOOTSTRAP SOLUTION

The present paper is devoted to the problem of detecting the presence of two positive Lyapunov exponents in time series data. In order to accomplish this task the accuracy of the estimates is essential, but existing estimation approaches do not provide it. We present a procedure exploiting resampling methods for building a statistical test for the presence of two positive exponents of comparable magnitudes through rigorous assessment of confidence intervals. The problem is studied by means of computer experiments performed in a variety of conditions on coupled Lorenz systems. Then, a case study regarding the time series of the cardiovascular activity of the toad Bufo Arenarum is presented. A comparison with other estimator algorithms is also shown.