Symbolic fractional dynamics

Fractional dynamics reveals long range memory properties of systems described by means of signals represented by real numbers. Alternatively, dynamical systems and signals can adopt a representation where states are quantified using a set of symbols. Such signals occur both in nature and in man made processes and have the potential of a aftermath as relevant as the classical counterpart. This paper explores the association of Fractional calculus and symbolic dynamics. The results are visualized by means of the multidimensional technique and reveal the association between the fractal dimension and one definition of fractional derivative.

Complex dynamics of financial indices

This paper presents a novel method for the analysis of nonlinear financial and economic systems. The modeling approach integrates the classical concepts of state space representation and time series regression. The analytical and numerical scheme leads to a parameter space representation that constitutes a valid alternative to represent the dynamical behavior. The results reveal that business cycles can be clearly revealed, while the noise effects common in financial indices can elegantly be filtered out of the results.

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.

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.

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.

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.

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.

Introduction [to Contact force models for multibody dynamics]

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

Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' Threshold Theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.

Perturbation theory for classical thermodynamic Green's functions

A systematic time-dependent perturbation scheme for classical canonical systems is developed based on a Wick's theorem for thermal averages of time-ordered products. The occurrence of the derivatives with respect to the canonical variables noted by Martin, Siggia, and Rose implies that two types of Green's functions have to be considered, the propagator and the response function. The diagrams resulting from Wick's theorem are "double graphs" analogous to those introduced by Dyson and also by Kawasaki, in which the response-function lines form a "tree structure" completed by propagator lines. The implication of a fluctuation-dissipation theorem on the self-energies is analyzed and compared with recent results by Deker and Haake.

Classical predictive electrodynamics of two charges with radiation: General framework. I.

Outgoing radiation is introduced in the framework of the classical predictive electrodynamics using LorentzDiracs equation as a subsidiary condition. In a perturbative scheme in the charges the first radiative self-terms of the accelerations, momentum and angular momentum of a two charge system without external field are calculated.

Manual reaction times and brain dynamics after 'awake surgery' of slow-growing tumors invading the parietal area. A case report

Primary objectives: Awake surgeries of slow-growing tumours invading the brain and guided by direct electrical stimulation induce major brain reorganizations accompanied with slight impairments post-operatively. In most cases, these deficits are so slight after a few days that they are often not detectable on classical neuropsychological evaluations. Consequently, this study investigated whether simple visuo-manual reaction time paradigms would sign some level of functional asymmetries between both hemispheres. Importantly, the visual stimulus was located in the saggital plane in order to limit attentional biases and to focus mainly on the inter-hemispheric asymmetry. Methods and procedures: Three patients (aged 41, 59 and 59 years) after resections in parietal regions and a control group (age¼44, SD¼6.9) were compared during simple uni- and bimanual reaction times (RTs). Main outcomes and results: Longer RTs were observed for the contralesional compared to the ipsilesional hand in the unimanual condition. This asymmetry was reversed for the bimanual condition despite longer RTs. Conclusion and clinical implications: Reaction time paradigms are useful in these patients to monitor more precisely their functional deficits, especially their level of functional asymmetry, and to understand brain (re)organization following slowgrowing lesions.

On the origin of the inertia: the modified Newtonian dynamics theory

The sameness between the inertial mass and the gravitational mass is an assumption and not a consequence of the equivalent principle is shown. In the context of the Sciama’s inertia theory, the sameness between the inertial mass and the gravitational mass is discussed and a certain condition which must be experimentally satisfied is given. The inertial force proposed by Sciama, in a simple case, is derived from the Assis’ inertia theory based in the introduction of a Weber type force. The origin of the inertial force is totally justified taking into account that the Weber force is, in fact, an approximation of a simple retarded potential, see [18, 19]. The way how the inertial forces are also derived from some solutions of the general relativistic equations is presented. We wonder if the theory of inertia of Assis is included in the framework of the General Relativity. In the context of the inertia developed in the present paper we establish the relation between the constant acceleration a0 , that appears in the classical Modified Newtonian Dynamics (M0ND) theory, with the Hubble constant H0 , i.e. a0 ≈ cH0 .

Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)10.1088/1751-8113/44/39/395004]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.

NMR chemical shifts of the rhodopsin chromophore in the dark state and in bathorhodopsin: a hybrid QM/MM molecular dynamics study.

We investigate nuclear magnetic resonance (NMR) parameters of the rhodopsin chromophore in the dark state of the protein and in the early photointermediate bathorhodopsin via first-principles molecular dynamics simulations and NMR chemical shift calculations in a hybrid quantum/classical (QM/MM) framework. NMR parameters are particularly sensitive to structural properties and to the chemical environment, which allows us to address different questions about the retinal chromophore in situ. Our calculations show that both the 13C and the 1H NMR chemical shifts are rather insensitive to the protonation state of Glu181, an ionizable amino acid side chain located in the vicinity of the isomerizing 11-cis bond. Thus, other techniques should be better suited to establish its protonation state. The calculated chemical shifts for bathorhodopsin further support our previously published theoretical structure, which is in very good agreement with more recent X-ray data.