The wild bootstrap for multilevel models

In this paper we study the performance of the most popular bootstrap schemes for multilevel data. Also, we propose a modified version of the wild bootstrap procedure for hierarchical data structures. The wild bootstrap does not require homoscedasticity or assumptions on the distribution of the error processes. Hence, it is a valuable tool for robust inference in a multilevel framework. We assess the finite size performances of the schemes through a Monte Carlo study. The results show that for big sample sizes it always pays off to adopt an agnostic approach as the wild bootstrap outperforms other techniques

Multilevel Models with Stochastic Volatility for Repeated Cross-Sections: an Application to tribal Art Prices

In this paper we introduce a multilevel specification with stochastic volatility for repeated cross-sectional data. Modelling the time dynamics in repeated cross sections requires a suitable adaptation of the multilevel framework where the individuals/items are modelled at the first level whereas the time component appears at the second level. We perform maximum likelihood estimation by means of a nonlinear state space approach combined with Gauss-Legendre quadrature methods to approximate the likelihood function. We apply the model to the first database of tribal art items sold in the most important auction houses worldwide. The model allows to account properly for the heteroscedastic and autocorrelated volatility observed and has superior forecasting performance. Also, it provides valuable information on market trends and on predictability of prices that can be used by art markets stakeholders

On the origin of the mitochondrial genetic code: Towards a unified mathematical framework for the management of genetic information

The origin of the genetic code represents one of the most challenging problems in molecular evolution. The genetic code is an important universal feature of extant organisms and indicates a common ancestry of different forms of life on earth. Known variants of the genetic code can be mainly divided in mitochondrial and nuclear classes. Here we provide a new insight on the origin of the mitochondrial genetic code: we found that its degeneracy distribution can be explained by using a mathematical approach recently developed for the description of the Euplotes nuclear variant of the genetic code. The results point to a primeval mitochondrial genetic code composed of four base codons, which we call tesserae, that, among other features, exhibit outstanding error detection capabilities. The theoretical description suggests also a formulation of a plausible biological theory about the origin of protein coding. Such theory is based on the symmetry properties of hypothetical primeval chemical adaptors between nucleic acids and amino acids (ancient tRNA’s). Our paper provides a unified mathematical framework for different hypotheses on the origin of genetic coding. Also, it contributes to revisit our present view about the evolutionary steps that led to extant genetic codes by giving a new first-principles perspective on the difficult problem of the origin of the genetic code, and consequently, on the origin of life on earth

Entropy-Based Tests for Complex Dependence in Economic and Financial Time Series with the R Package tseriesEntropy

Testing for complex serial dependence in economic and financial time series is a crucial task that bears many practical implications. However, the linear paradigm remains pervasive among practitioners as the autocorrelation function, because, despite its known shortcomings, it is still one of the most used tools in time series analysis. We propose a solution to the problem, by introducing the R package tseriesEntropy, dedicated to testing for serial/cross dependence and nonlinear serial dependence in time series, based on the entropy metric S-rho. The package implements tests for both continuous and categorical data. The nonparametric tests, based on S-rho, rely on minimal assumptions and have also been shown to be powerful for small sample sizes. The measure can be used as a nonlinear auto/cross-dependence function, both as an exploratory tool, or as a diagnostic measure, if computed on the residuals from a fitted model. Different null hypotheses of either independence or linear dependence can be tested by means of resampling methods, backed up by a sound theoretical background. We showcase our methods on a panel of commodity price time series. The results hint at the presence of a complex dependence in the conditional mean, together with conditional heteroskedasticity, and indicate the need for an appropriate nonlinear specification

A role for circular code properties in translation

Circular codes represent a form of coding allowing detection/correction of frame-shift errors. Building on recent theoretical advances on circular codes, we provide evidence that protein coding sequences exhibit in-frame circular code marks, that are absent in introns and are intimately linked to the keto-amino transformation of codon bases. These properties strongly correlate with translation speed, codon influence and protein synthesis levels. Strikingly, circular code marks are absent at the beginning of coding sequences, but stably occur 40 codons after the initiator codon, hinting at the translation elongation process. Finally, we use the lens of circular codes to show that codon influence on translation correlates with the strong-weak dichotomy of the first two bases of the codon. The results can lead to defining new universal tools for sequence indicators and sequence optimization for bioinformatics and biotechnological applications, and can shed light on the molecular mechanisms behind the decoding process

On the origin of the mitochondrial genetic code: Towards a unified mathematical framework for the management of genetic information

The origin of the genetic code represents one of the most challenging problems in molecular evolution. The genetic code is an important universal feature of extant organisms and indicates a common ancestry of different forms of life on earth. Known variants of the genetic code can be mainly divided in mitochondrial and nuclear classes. Here we provide a new insight on the origin of the mitochondrial genetic code: we found that its degeneracy distribution can be explained by using a mathematical approach recently developed for the description of the Euplotes nuclear variant of the genetic code. The results point to a primeval mitochondrial genetic code composed of four base codons, which we call tesserae, that, among other features, exhibit outstanding error detection capabilities. The theoretical description suggests also a formulation of a plausible biological theory about the origin of protein coding. Such theory is based on the symmetry properties of hypothetical primeval chemical adaptors between nucleic acids and amino acids (ancient tRNA's). Our paper provides a unified mathematical framework for different hypotheses on the origin of genetic coding. Also, it contributes to revisit our present view about the evolutionary steps that led to extant genetic codes by giving a new first-principles perspective on the difficult problem of the origin of the genetic code, and consequently, on the origin of life on earth

Chemobrionics: from self-assembled material architectures to the origin of life

Self-organizing precipitation processes, such as chemical gardens forming biomimetic micro- and nanotubular forms, have the potential to show us new fundamental science to explore, quantify, and understand nonequilibrium physicochemical systems, and shed light on the conditions for life's emergence. The physics and chemistry of these phenomena, due to the assembly of material architectures under a flux of ions, and their exploitation in applications, have recently been termed chemobrionics. Advances in understanding in this area require a combination of expertise in physics, chemistry, mathematical modeling, biology, and nanoengineering, as well as in complex systems and nonlinear and materials sciences, giving rise to this new synergistic discipline of chemobrionics