Measuring and Controlling the Chaotic Motion of Profits

The study of economic systems has generated deep interest in exploring the complexity of chaotic motions in economy. Due to important developments in nonlinear dynamics, the last two decades have witnessed strong revival of interest in nonlinear endogenous business chaotic models. The inability to predict the behavior of dynamical systems in the presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we study a specific economic model from the literature. More precisely, a system of three ordinary differential equations gather the variables of profits, reinvestments and financial flow of borrowings in the structure of a firm. Firstly, using results of symbolic dynamics, we characterize the topological entropy and the parameter space ordering of kneading sequences, associated with one-dimensional maps that reproduce significant aspects of the model dynamics. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. Finally, we show that complicated behavior arising from the chaotic firm model can be controlled without changing its original properties and the dynamics can be turned into the desired attracting time periodic motion (a stable steady state or into a regular cycle). The orbit stabilization is illustrated by the application of a feedback control technique initially developed by Romeiras et al. [1992]. This work provides another illustration of how our understanding of economic models can be enhanced by the theoretical and numerical investigation of nonlinear dynamical systems modeled by ordinary differential equations.

The influence of genetic polymorphisms in XRCC3 and ADH5 genes on the frequency of genotoxicity biomarkers in workers exposed to formaldehyde

The International Agency for Research on Cancer classified formaldehyde as carcinogenic to humans because there is “sufficient epidemiological evidence that it causes nasopharyngeal cancer in humans”. Genes involved in DNA repair and maintenance of genome integrity are critically involved in protecting against mutations that lead to cancer and/or inherited genetic disease. Association studies have recently provided evidence for a link between DNA repair polymorphisms and micronucleus (MN) induction. We used the cytokinesis-block micronucleus (CBMN assay) in peripheral lymphocytes and MN test in buccal cells to investigate the effects of XRCC3 Thr241Met, ADH5 Val309Ile, and Asp353Glu polymorphisms on the frequency of genotoxicity biomarkers in individuals occupationally exposed to formaldehyde (n = 54) and unexposed workers (n = 82). XRCC3 participates in DNA double-strand break/recombination repair, while ADH5 is an important component of cellular metabolism for the elimination of formaldehyde. Exposed workers had significantly higher frequencies (P < 0.01) than controls for all genotoxicity biomarkers evaluated in this study. Moreover, there were significant associations between XRCC3 genotypes and nuclear buds, namely XRCC3 Met/Met (OR = 3.975, CI 1.053–14.998, P = 0.042) and XRCC3 Thr/Met (OR = 5.632, CI 1.673–18.961, P = 0.005) in comparison with XRCC3 Thr/Thr. ADH5 polymorphisms did not show significant effects. This study highlights the importance of integrating genotoxicity biomarkers and genetic polymorphisms in human biomonitoring studies.

Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

Clinical and genetic factors predicting response to therapy in patients with Crohn’s disease

Aim - To identify clinical and/or genetic predictors of response to several therapies in Crohn’s disease (CD) patients. Methods - We included 242 patients with CD (133 females) aged (mean ± standard deviation) 39 ± 12 years and a disease duration of 12 ± 8 years. The single-nucleotide polymorphisms (SNPs) studied were ABCB1 C3435T and G2677T/A, IL23R G1142A, C2370A, and G9T, CASP9 C93T, Fas G670A and LgC844T, and ATG16L1 A898G. Genotyping was performed with real-time PCR with Taqman probes. Results - Older patients responded better to 5-aminosalicylic acid (5-ASA) and to azathioprine (OR 1.07, p = 0.003 and OR 1.03, p = 0.01, respectively) while younger ones responded better to biologicals (OR 0.95, p = 0.06). Previous surgery negatively influenced response to 5-ASA compounds (OR 0.25, p = 0.05), but favoured response to azathioprine (OR 2.1, p = 0.04). In respect to genetic predictors, we observed that heterozygotes for ATGL16L1 SNP had a significantly higher chance of responding to corticosteroids (OR 2.51, p = 0.04), while homozygotes for Casp9 C93T SNP had a lower chance of responding both to corticosteroids and to azathioprine (OR 0.23, p = 0.03 and OR 0.08, p = 0.02,). TT carriers of ABCB1 C3435T SNP had a higher chance of responding to azathioprine (OR 2.38, p = 0.01), while carriers of ABCB1 G2677T/A SNP, as well as responding better to azathioprine (OR 1.89, p = 0.07), had a lower chance of responding to biologicals (OR 0.31, p = 0.07), which became significant after adjusting for gender (OR 0.75, p = 0.005). Conclusions - In the present study, we were able to identify a number of clinical and genetic predictors of response to several therapies which may become of potential utility in clinical practice. These are preliminary results that need to be replicated in future pharmacogenomic studies.

Optimal location of supports in beam structures using genetic algorithms

Real structures can be thought as an assembly of components, as for instances plates, shells and beams. This later type of component is very commonly found in structures like frames which can involve a significant degree of complexity or as a reinforcement element of plates or shells. To obtain the desired mechanical behavior of these components or to improve their operating conditions when rehabilitating structures, one of the eventual parameters to consider for that purpose, when possible, is the location of the supports. In the present work, a beam-type structure is considered, and for a set of cases concerning different number and types of supports, as well as different load cases, the authors optimize the location of the supports in order to obtain minimum values of the maximum transverse deflection. The optimization processes are carried out using genetic algorithms. The results obtained, clearly show a good performance of the approach proposed. © 2014 IEEE.

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.