Equilibrium distributions of discrete non-autonomous graphs

We introduce the notions of equilibrium distribution and time of convergence in discrete non-autonomous graphs. Under some conditions we give an estimate to the convergence time to the equilibrium distribution using the second largest eigenvalue of some matrices associated with the system.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

Simulation of default events in a CDX and estimation of the spread

The portfolio generating the iTraxx EUR index is modeled by coupled Markov chains. Each of the industries of the portfolio evolves according to its own Markov transition matrix. Using a variant of the method of moments, the model parameters are estimated from a data set of Standard and Poor's. Swap spreads are evaluated by Monte-Carlo simulations. Along with an actuarially fair spread, at least squares spread is considered.

Slaughterhouses fungal burden assessment: a contribution for the pursuit of a better assessment strategy

In slaughterhouses, the biological risk is present not only from the direct or indirect contact with animal matter, but also from the exposure to bioaerosols. Fungal contamination was already reported from the floors and walls of slaughterhouses. This study intends to assess fungal contamination by cultural and molecular methods in poultry, swine/bovine and large animal slaughterhouses. Air samples were collected through an impaction method, while surface samples were collected by the swabbing method and subjected to further macro- and micro-scopic observations. In addition, we collected air samples using the impinger method in order to perform real-time quantitative PCR (qPCR) amplification of genes from specific fungal species, namely A. flavus, A. fumigatus and A. ochraceus complexes. Poultry and swine/bovine slaughterhouses presented each two sampling sites that surpass the guideline of 150 CFU/m3. Scopulariopsis candida was the most frequently isolated (59.5%) in poultry slaughterhouse air; Cladosporium sp. (45.7%) in the swine/bovine slaughterhouse; and Penicillium sp. (80.8%) in the large animal slaughterhouse. Molecular tools successfully amplified DNA from the A. fumigatus complex in six sampling sites where the presence of this fungal species was not identified by conventional methods. This study besides suggesting the indicators that are representative of harmful fungal contamination, also indicates a strategy as a protocol to ensure a proper characterization of fungal occupational exposure.

Fusional vergence measurements for eso versus exo deviations: is there a difference?

Purpose: The aims of this study were to compare angle of deviation, fusional vergence measurements and fusion reserve ratio between esophoria and exophoria. Methods: A cross-sectional study was performed in children with best-corrected visual acuity of 0.0 LogMAR in either eye, compensated heterophoria within 10 prism dioptres (PD), full ocular rotations, presence of fusional vergence and stereopsis (60 seconds of arc or better). Fusional amplitudes were compared between angle of deviation (2, 4, 6, 8 and 10 PD) in esophoria and exophoria. The fusion reserve ratio was calculated (to assess the effect of the underlying angle of deviation) as fusional convergence divided by prism alternating cover test measurements. Results: Two-hundred and eleven children (7.65±1.16 years) were recruited to this study. Exophoria was most common for near (n=181; 85.8%) and distance (n=20; 9.5%). Esophoria was present in 22 children for near (10.4%) and in 1 child for distance (0.5%). No significant differences were found between fusional amplitudes and angle of deviation for near (p>0.05). Children with exophoria of 10PD had a slight, but not, significant (p=0.264) increase in fusional convergence from 2PD (19.95±5.09) to 10PD (26.67±5.77). In esophoric children the variation of fusional convergence was smaller from 2P (25.00±0.00) to 10PD (22.50±3.54) and non significant (p=0.185). The fusion reserve ratio was significantly smaller in children with higher deviations (i.e. 10PD) for both esophoria (p=0.003) and exophoria (p>0.001). The fusion reserve ratio ranged between 12.50 (2PD) and 2.25±0.35 (10PD) for esophoria and between 9.98±2.55 (2PD) and 2.67±0.58 (10PD) for exophoria. Conclusions: Angle of deviation is not an efficient measure to predict fusional amplitudes. The fusion reserve ratio appears to be a better measurement to assess the effect of the underlying angle of deviation on fusional convergence. More studies are necessary to understand better the relationship between fusion amplitudes and angle of deviation.