Fractional Analysis of the DNA Information

Proceedings of the 12th Conference on 'Dynamical Systems -Theory and Applications'

A Multidimensional scaling perspective of Rostow's forecasts with the Track-record (1960s-2011) of "pioneers" and "latecomers"

Proceedings of the 12th Conference on Dynamical Systems -Theory and Applications

Bipedal Locomotion: A Fractional CPG for Generating Patterns

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

Fractional Dynamics Representation in the Pseudo Phase Plane

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

Application of Fractional Calculus in Mechatronics

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of mechanical systems.

Implicit methods for qualitative modeling of gene regulatory networks.

Advancements in high-throughput technologies to measure increasingly complex biological phenomena at the genomic level are rapidly changing the face of biological research from the single-gene single-protein experimental approach to studying the behavior of a gene in the context of the entire genome (and proteome). This shift in research methodologies has resulted in a new field of network biology that deals with modeling cellular behavior in terms of network structures such as signaling pathways and gene regulatory networks. In these networks, different biological entities such as genes, proteins, and metabolites interact with each other, giving rise to a dynamical system. Even though there exists a mature field of dynamical systems theory to model such network structures, some technical challenges are unique to biology such as the inability to measure precise kinetic information on gene-gene or gene-protein interactions and the need to model increasingly large networks comprising thousands of nodes. These challenges have renewed interest in developing new computational techniques for modeling complex biological systems. This chapter presents a modeling framework based on Boolean algebra and finite-state machines that are reminiscent of the approach used for digital circuit synthesis and simulation in the field of very-large-scale integration (VLSI). The proposed formalism enables a common mathematical framework to develop computational techniques for modeling different aspects of the regulatory networks such as steady-state behavior, stochasticity, and gene perturbation experiments.

Dynamic Criteria: a Longitudinal Analysis of Professional Basketball Players" Outcomes

This paper describes the fluctuations of temporal criteria dynamics in the context of professional sport. Specifically, we try to verify the underlying deterministic patterns in the outcomes of professional basketball players. We use a longitudinal approach based on the analysis of the outcomes of 94 basketball players over ten years, covering practically players" entire career development. Time series were analyzed with techniques derived from nonlinear dynamical systems theory. These techniques analyze the underlying patterns in outcomes without previous shape assumptions (linear or nonlinear). These techniques are capable of detecting an intermediate situation between randomness and determinism, called chaos. So they are very useful for the study of dynamic criteria in organizations. We have found most players (88.30%) have a deterministic pattern in their outcomes, and most cases are chaotic (81.92%). Players with chaotic patterns have higher outcomes than players with linear patterns. Moreover, players with power forward and center positions achieve better results than other players. The high number of chaotic patterns found suggests caution when appraising individual outcomes, when coaches try to find the appropriate combination of players to design a competitive team, and other personnel decisions. Management efforts must be made to assume this uncertainty.

Diferencias en la dimensionalidad electroencefalograma entre vigilia y sueño profundo

Differences in dimensionality of electroencephalogram during awake and deeper sleep stages. The nonlinear dynamical systems theory provides some tools for the analysis of electroencephalogram (EEG) at different sleep stages. Its use could allow the automatic monitoring of the states of the sleep and it would also contribute an explanatory level of the differences between stages. The goal of the present paper is to address this type of analysis, focusing on the most different stages. Estimations of dimensionality were compared when six subjects were awake and in a deep sleep stage. Greater dimensionality involves more complexity because the system receives more external influences. If this dimensionality is maximum, we can consider that the time series is a noisy one. A smaller dimensionality involves lower complexity because the system receives fewer inputs. We hypothesized that we would find greater dimensionality when subjects were awake than in a deep sleep stage. Results show a noisy time series during the awake stage, whereas in the sleep stage, dimensionality is smaller, confirming our hypothesis. This result is similar to the findings reached previously by other authors.

Dynamic patterns of flow in the workplace: characterizing within-individual variability using a complexity science approach

As a result of the growing interest in studying employee well-being as a complex process that portrays high levels of within-individual variability and evolves over time, this present study considers the experience of flow in the workplace from a nonlinear dynamical systems approach. Our goal is to offer new ways to move the study of employee well-being beyond linear approaches. With nonlinear dynamical systems theory as the backdrop, we conducted a longitudinal study using the experience sampling method and qualitative semi-structured interviews for data collection; 6981 registers of data were collected from a sample of 60 employees. The obtained time series were analyzed using various techniques derived from the nonlinear dynamical systems theory (i.e., recurrence analysis and surrogate data) and multiple correspondence analyses. The results revealed the following: 1) flow in the workplace presents a high degree of within-individual variability; this variability is characterized as chaotic for most of the cases (75%); 2) high levels of flow are associated with chaos; and 3) different dimensions of the flow experience (e.g., merging of action and awareness) as well as individual (e.g., age) and job characteristics (e.g., job tenure) are associated with the emergence of different dynamic patterns (chaotic, linear and random).

Time series analysis for minority game simulations of financial markets

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolution. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Local dimension and finite time prediction in coupled map lattices

Forecasting, for obvious reasons, often become the most important goal to be achieved. For spatially extended systems (e.g. atmospheric system) where the local nonlinearities lead to the most unpredictable chaotic evolution, it is highly desirable to have a simple diagnostic tool to identify regions of predictable behaviour. In this paper, we discuss the use of the bred vector (BV) dimension, a recently introduced statistics, to identify the regimes where a finite time forecast is feasible. Using the tools from dynamical systems theory and Bayesian modelling, we show the finite time predictability in two-dimensional coupled map lattices in the regions of low BV dimension. © Indian Academy of Sciences.

Catastrophic regime shift in water reservoirs and São Paulo water supply crisis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A new entropy measure based on the Renyi entropy rate using Gaussian kernels

The concept of entropy rate is well defined in dynamical systems theory but is impossible to apply it directly to finite real world data sets. With this in mind, Pincus developed Approximate Entropy (ApEn), which uses ideas from Eckmann and Ruelle to create a regularity measure based on entropy rate that can be used to determine the influence of chaotic behaviour in a real world signal. However, this measure was found not to be robust and so an improved formulation known as the Sample Entropy (SampEn) was created by Richman and Moorman to address these issues. We have developed a new, related, regularity measure which is not based on the theory provided by Eckmann and Ruelle and proves a more well-behaved measure of complexity than the previous measures whilst still retaining a low computational cost.

Passivity Framework for Modeling, Composing and Mitigating Cyber Attacks

Thesis (Ph.D.)--University of Washington, 2016-08

Hamilton Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.