Ricardo Mansilla

Universality of Rank-Ordering Distributions in the Arts and Sciences

Searching for generic behaviors has been one of the driving forces leading to a deep understanding and classification of diverse phenomena. Usually a starting point is the development of a phenomenology based on observations. Such is the case for power law distributions encountered in a wealth of situations coming from physics, geophysics, biology, lexicography as well as social and financial networks. This finding is however restricted to a range of values outside of which finite size corrections are often invoked. Here we uncover a universal behavior of the way in which elements of a system are distributed according to their rank with respect to a given property, valid for the full range of values, regardless of whether or not a power law has previously been suggested. We propose a two parameter functional form for these rank-ordered distributions that gives excellent fits to an impressive amount of very diverse phenomena, coming from the arts, social and natural sciences. It is a discrete version of a generalized beta distribution, given by f(r) = A(N+1-r)b/ra, where r is the rank, N its maximum value, A the normalization constant and (a, b) two fitting exponents. Prompted by our genetic sequence observations we present a growth probabilistic model incorporating mutation-duplication features that generates data complying with this distribution. The competition between permanence and change appears to be a relevant, though not necessary feature. Additionally, our observations mainly of social phenomena suggest that a multifactorial quality resulting from the convergence of several heterogeneous underlying processes is an important feature. We also explore the significance of the distribution parameters and their classifying potential. The ubiquity of our findings suggests that there must be a fundamental underlying explanation, most probably of a statistical nature, such as an appropriate central limit theorem formulation.

On the behavior of journal impact factor rank-order distribution

An empirical law for the rank-order behavior of journal impact factors is found. Using an extensive data base on impact factors including journals on education, agrosciences, geosciences, mathematics, chemistry, medicine, engineering, physics, biosciences and environmental, computer and material sciences, we have found extremely good fittings outperforming other rank-order models. Based in our results, we propose a two-exponent Lotkaian Informetrics. Some extensions to other areas of knowledge are discussed.

Algorithmic Complexity of Real Financial Markets

A new approach to the understanding of complex behavior of financial markets index using tools from thermodynamics and statistical physics is developed. Physical complexity, a quantity rooted in the Kolmogorov–Chaitin theory is applied to binary sequences built up from real time series of financial markets indexes. The study is based on NASDAQ and Mexican IPC data. Different behaviors of this quantity are shown when applied to the intervals of series placed before crashes and to intervals when no financial turbulence is observed. The connection between our results and the efficient market hypothesis is discussed.

Stewart-Lyth inverse problem

During inflation, the inflaton and graviton fields undergo quantum fluctuations. These fluctuations generated theseeds for the large-scale structure of the Universe and left their imprints in the anisotropies currently observed in theCosmic Microwave Background Radiation (CMBR) (for detailed explanation see Refs. [1] and [2]).The Stewart and Lyth equations [3] are the state of the art for predicting the anisotropies for most inflationarymodels [4]. Anticipating the near future launching of satellites able to measure the CMBR anisotropies with unprece-dented accuracy, we would like to find out whether the inflationary potential can be obtained from the Stewart-Lythequations by using as input observationalinformation about the density perturbations and gravitationalwavesspectra.

The mutual information theory for the certification of rice coding sequences.

We report here the use of the mutual information theory for the certification of annotated rice coding sequences of both GenBank and TIGR databases. Considering coding sequences larger than 600 bp, we successfully screened out genes with aberrant compositional features. We found that they represent about 10% of both datasets after cleaning for gene redundancy. Most of the rejected accessions showed a different trend in GC3% vs GC2% plot compared to the set of accessions that have been published in international journals. This suggests the existence of a bias in the pattern recognition algorithms used by gene prediction programs.

Bacterial genomes lacking long-range correlations may not be modeled by low-order Markov chains

We examine the relationship between exponential correlation functions and Markov models in a bacterial genome in detail. Despite the well known fact that Markov models generate sequences with correlation function that decays exponentially, simply constructed Markov models based on nearest-neighbor dimer (first-order), trimer (second-order), up to hexamer (fifth-order), and treating the DNA sequence as being homogeneous all fail to predict the value of exponential decay rate. Even reading-frame-specific Markov models (both first- and fifth-order) could not explain the fact that the exponential decay is very slow. Starting with the in-phase coding-DNA-sequence (CDS), we investigated correlation within a fixed-codon-position subsequence, and in artificially constructed sequences by packing CDSs with out-of-phase spacers, as well as altering CDS length distribution by imposing an upper limit. From these targeted analyses, we conclude that the correlation in the bacterial genomic sequence is mainly due to a mixing of heterogeneous statistics at different codon positions, and the decay of correlation is due to the possible out-of-phase between neighboring CDSs. There are also small contributions to the correlation from bases at the same codon position, as well as by non-coding sequences. These show that the seemingly simple exponential correlation functions in bacterial genome hide a complexity in correlation structure which is not suitable for a modeling by Markov chain in a homogeneous sequence. Other results include: use of the (absolute value) second largest eigenvalue to represent the 16 correlation functions and the prediction of a 10-11 base periodicity from the hexamer frequencies.

On the scaling of the distribution of daily price fluctuations in the Mexican financial market index

In this paper, a statistical analysis of log-return fluctuations of the IPC, the Mexican Stock Market Index is presented. A sample of daily data covering the period from 04/09/2000–04/09/2010 was analyzed, and fitted to different distributions. Tests of the goodness of fit were performed in order to quantitatively asses the quality of the estimation. Special attention was paid to the impact of the size of the sample on the estimated decay of the distributions tail. In this study a forceful rejection of normality was obtained. On the other hand, the null hypothesis that the log-fluctuations are fitted to a α-stable Levy distribution cannot be rejected at the 5% significance level.

Protein surface roughness accounts for binding free energy of Plasmepsin II-ligand complexes

The calculation of absolute binding affinities for protein‐inhibitor complexes remains as one of the main challenges in computational structure‐based ligand design. The present work explored the calculations of surface fractal dimension (as a measure of surface roughness) and the relationship with experimental binding free energies of Plasmepsin II complexes. Plasmepsin II is an attractive target for novel therapeutic compounds to treat malaria. However, the structural flexibility of this enzyme is a drawback when searching for specific inhibitors. Concerning that, we performed separate explicitly solvated molecular dynamics simulations using the available high‐resolution crystal structures of different Plasmepsin II complexes. Molecular dynamics simulations allowed a better approximation to systems dynamics and, therefore, a more reliable estimation of surface roughness. This constitutes a novel approximation in order to obtain more realistic values of fractal dimension, because previous works considered only x‐ray structures. Binding site fractal dimension was calculated considering the ensemble of structures generated at different simulation times. A linear relationship between binding site fractal dimension and experimental binding free energies of the complexes was observed within 20 ns. Previous studies of the subject did not uncover this relationship. Regression model, coined FD model, was built to estimate binding free energies from binding site fractal dimension values. Leave‐one‐out cross‐validation showed that our model reproduced accurately the absolute binding free energies for our training set (R2 = 0.76; <|error|> =0.55 kcal/mol; SDerror = 0.19 kcal/mol). The fact that such a simple model may be applied raises some questions that are addressed in the article.

Chronotherapy of cancer: periodic perturbations in vascular growth and metastasis

Abstract A non-autonomous model was developed for vascular tumor growth and cancer metastasis under periodic perturbations that simulate chronotherapy. It was found that for a critical amplitude and a perturbation frequency of twice the autonomous frequency in vascular growth, less complex and therefore less robust states are reached and the tumor population decreases. In metastasis, similar results were found for a perturbation frequency equal to the autonomous frequency. In metastasis, similar behaviors occur, for a perturbation’s frequency equal to the fundamental frequency of system.

Dose and frequency in cancer therapy. Theoretical non-autonomous model of p53 network

Abstract A non-autonomous model for the regulation of apoptosis by p53 is proposed as a model for cancer chronotherapy. A perturbation is introduced that simulates damage caused to DNA in a periodic regime. To characterize the resulting system dynamics, the techniques used were stroboscopic analysis, Poincare section and power spectrum. The complexity of the time series was determined using the LZ index. Periodic and quasi-periodic dynamics were obtained as the control parameters were varied. The less complex states are those corresponding to higher values of the amplitude which indicates a strict control of the dose is required on periodic treatments.