Fractional dynamics in financial indexes

The goal of this study is the analysis of the dynamical properties of financial data series from 32 worldwide stock market indices during the period 2000–2009 at a daily time horizon. Stock market indices are examples of complex interacting systems for which a huge amount of data exists. The methods and algorithms that have been explored for the description of physical phenomena become an effective background in the analysis of economical data. In this perspective are applied the classical concepts of signal analysis, Fourier transform and methods of fractional calculus. The results reveal classification patterns typical of fractional dynamical systems.

Complex-order forced van der Pol oscillator

In this paper we consider a complex-order forced van der Pol oscillator. The complex derivative Dα1jβ, with α, β ∈ ℝ+, is a generalization of the concept of an integer derivative, where α = 1, β = 0. The Fourier transforms of the periodic solutions of the complex-order forced van der Pol oscillator are computed for various values of parameters such as frequency ω and amplitude b of the external forcing, the damping μ, and parameters α and β. Moreover, we consider two cases: (i) b = 1, μ = {1.0, 5.0, 10.0}, and ω = {0.5, 2.46, 5.0, 20.0}; (ii) ω = 20.0, μ = {1.0, 5.0, 10.0}, and b = {1.0, 5.0, 10.0}. We verified that most of the signal energy is concentrated in the fundamental harmonic ω0. We also observed that the fundamental frequency of the oscillations ω0 varies with α and μ. For the range of tested values, the numerical fitting led to logarithmic approximations for system (7) in the two cases (i) and (ii). In conclusion, we verify that by varying the parameter values α and β of the complex-order derivative in expression (7), we accomplished a very effective way of perturbing the dynamical behavior of the forced van der Pol oscillator, which is no longer limited to parameters b and ω.

Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

Dynamics of the Dow Jones and the NASDAQ stock indexes

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indices. We analyze the Dow Jones Industrial Average ( ∧ DJI) and the NASDAQ Composite ( ∧ IXIC) indexes at a daily time horizon. The methods and algorithms that have been explored for description of physical phenomena become an effective background, and even inspiration, for very productive methods used in the analysis of economical data. We start by applying the classical concepts of signal analysis, Fourier transform, and methods of fractional calculus. In a second phase we adopt a pseudo phase plane approach.

Assessment of data-driven modeling strategies for water delivery canals

Conferência: CONTROLO’2012 - 16-18 July 2012 - Funchal

Simulation and dynamics of freeway traffic

This paper presents the new package entitled Simulator of Intelligent Transportation Systems (SITS) and a computational oriented analysis of traffic dynamics. The SITS adopts a microscopic simulation approach to reproduce real traffic conditions considering different types of vehicles, drivers and roads. A set of experiments with the SITS reveal the dynamic phenomena exhibited by this kind of system. For this purpose a modelling formalism is developed that embeds the statistics and the Laplace transform. The results make possible the adoption of classical system theory tools and point out that it is possible to study traffic systems taking advantage of the knowledge gathered with automatic control algorithms. A complementary perspective for the analysis of the traffic flow is also quantified through the entropy measure.

A cellulosic liquid crystal pool for cellulose nanocrystals: structure and molecular dynamics at high shear rates

Cellulose and its derivatives, such as hydroxypropylcellulose (HPC) have been studied for a long time but they are still not well understood particularly in liquid crystalline solutions. These systems can be at the origin of networks with properties similar to liquid crystalline (LC) elastomers. The films produced from LC solutions can be manipulated by the action of moisture allowing for instance the development of a soft motor (Geng et al., 2013) driven by humidity. Cellulose nanocrystals (CNC), which combine cellulose properties with the specific characteristics of nanoscale materials, have been mainly studied for their potential as a reinforcing agent. Suspensions of CNC can also self-order originating a liquid-crystalline chiral nematic phases. Considering the liquid crystalline features that both LC-HPC and CNC can acquire, we prepared LC-HPC/CNC solutions with different CNC contents (1,2 and 5 wt.%). The effect of the CNC into the LC-HPC matrix was determined by coupling rheology and NMR spectroscopy - Rheo-NMR a technique tailored to analyse orientational order in sheared systems. (C) 2015 Elsevier Ltd. All rights reserved.

Fractional Dynamics of Computer Virus Propagation

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

Fractional Dynamics of Computer Virus Propagation

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Evolutionary dynamics of Chlamydia trachomatis genome and identification of molecular patterns of hypothetical protein coding genes

The obligate intracellular bacterium Chlamydia trachomatis is a human pathogen of major public health significance. Strains can be classified into 15 main serovars (A to L3) that preferentially cause ocular infections (A-C), genital infections (D-K) or lymphogranuloma venereum (LGV) (L1-L3), but the molecular basis behind their distinct tropism, ecological success and pathogenicity is not welldefined. Most chlamydial research demands culture in eukaryotic cell lines, but it is not known if stains become laboratory adapted. By essentially using genomics and transcriptomics, we aimed to investigate the evolutionary patterns underlying the adaptation of C. trachomatis to the different human tissues, given emphasis to the identification of molecular patterns of genes encoding hypothetical proteins, and to understand the adaptive process behind the C. trachomatis in vivo to in vitro transition. Our results highlight a positive selection-driven evolution of C. trachomatis towards nichespecific adaptation, essentially targeting host-interacting proteins, namely effectors and inclusion membrane proteins, where some of them also displayed niche-specific expression patterns. We also identified potential "ocular-specific" pseudogenes, and pointed out the major gene targets of adaptive mutations associated with LGV infections. We further observed that the in vivo-derived genetic makeup of C. trachomatis is not significantly compromised by its long-term laboratory propagation. In opposition, its introduction in vitro has the potential to affect the phenotype, likely yielding virulence attenuation. In fact, we observed a "genital-specific" rampant inactivation of the virulence gene CT135, which may impact the interpretation of data derived from studies requiring culture. Globally, the findings presented in this Ph.D. thesis contribute for the understanding of C.trachomatis adaptive evolution and provides new insights into the biological role of C. trachomatishypothetical proteins. They also launch research questions for future functional studies aiming toclarify the determinants of tissue tropism, virulence or pathogenic dissimilarities among C. trachomatisstrains.

Dynamics of serotonergic neurons revealed by fiber photometry

This work was developed in the context of the MIT Portugal Program, area of Bioengineering Systems, in collaboration with the Champalimaud Research Programme, Champalimaud Center for the Unknown, Lisbon, Portugal. The project entitled Dynamics of serotonergic neurons revealed by fiber photometry was carried out at Instituto Gulbenkian de Ciência, Oeiras, Portugal and at the Champalimaud Research Programme, Champalimaud Center for the Unknown, Lisbon, Portugal

Simulation of OWES with five-Level converter linked to the grid: Harmonic assessment

This paper deals with a computing simulation for an offshore wind energy system taking into account the influence of the marine waves action throughout the floating platform. The wind energy system has a variable-speed turbine equipped with a permanent magnet synchronous generator and a full-power five level converter, injecting energy into the electric grid through a high voltage alternate current link. A reduction on the unbalance of the voltage in the DC-link capacitors of the five-level converter is proposed by a strategic selection of the output voltage vectors. The model for the drive train of the wind energy system is a two mass model, including the dynamics of the floating platform. A case study is presented and the assessment of the quality of the energy injected into the electric grid is discussed.

Introduction [to Contact force models for multibody dynamics]

"Series: Solid mechanics and its applications, vol. 226"