Entropy analysis of DNA code dynamics in human chromosomes

Deoxyribonucleic acid, or DNA, is the most fundamental aspect of life but present day scientific knowledge has merely scratched the surface of the problem posed by its decoding. While experimental methods provide insightful clues, the adoption of analysis tools supported by the formalism of mathematics will lead to a systematic and solid build-up of knowledge. This paper studies human DNA from the perspective of system dynamics. By associating entropy and the Fourier transform, several global properties of the code are revealed. The fractional order characteristics emerge as a natural consequence of the information content. These properties constitute a small piece of scientific knowledge that will support further efforts towards the final aim of establishing a comprehensive theory of the phenomena involved in life.

Root-locus practical sketching rules for fractional-order system

For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

Analysis of Forest Fires by means of Pseudo Phase Plane and Multidimensional Scaling Methods

Forest fires dynamics is often characterized by the absence of a characteristic length-scale, long range correlations in space and time, and long memory, which are features also associated with fractional order systems. In this paper a public domain forest fires catalogue, containing information of events for Portugal, covering the period from 1980 up to 2012, is tackled. The events are modelled as time series of Dirac impulses with amplitude proportional to the burnt area. The time series are viewed as the system output and are interpreted as a manifestation of the system dynamics. In the first phase we use the pseudo phase plane (PPP) technique to describe forest fires dynamics. In the second phase we use multidimensional scaling (MDS) visualization tools. The PPP allows the representation of forest fires dynamics in two-dimensional space, by taking time series representative of the phenomena. The MDS approach generates maps where objects that are perceived to be similar to each other are placed on the map forming clusters. The results are analysed in order to extract relationships among the data and to better understand forest fires behaviour.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

Dynamical Analysis and Visualization of Tornadoes Time Series

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.

Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

In this paper we study several natural and man-made complex phenomena in the perspective of dynamical systems. For each class of phenomena, the system outputs are time-series records obtained in identical conditions. The time-series are viewed as manifestations of the system behavior and are processed for analyzing the system dynamics. First, we use the Fourier transform to process the data and we approximate the amplitude spectra by means of power law functions. We interpret the power law parameters as a phenomenological signature of the system dynamics. Second, we adopt the techniques of non-hierarchical clustering and multidimensional scaling to visualize hidden relationships between the complex phenomena. Third, we propose a vector field based analogy to interpret the patterns unveiled by the PL parameters.

Fractional State Space Analysis of Temperature Time Series

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.

Constructing Cultural Policies in Romania. A possible model for communicating the national value system

The premise of this paper is that a model for communicating the national value system must start from a strategy aimed at the identification, the cultivation and communication of values that give consistency to the value system. The analysis concentrates on the elements of such strategies and on the implications of applying a value communication program on the identity architecture of the community. The paper will also discuss the role of the national value system in the context of the emerging global culture, where the individual has the power to create his/her own hybrid cultural model.

Analysis of financial indices by means of the windowed Fourier transform

The goal of this study is to analyze the dynamical properties of financial data series from nineteen worldwide stock market indices (SMI) during the period 1995–2009. SMI reveal a complex behavior that can be explored since it is available a considerable volume of data. In this paper is applied the window Fourier transform and methods of fractional calculus. The results reveal classification patterns typical of fractional order systems.

Cutting forces and wear analysis of Si3N4 diamond coated tools in high speed machining

Si3N4 tools were coated with a thin diamond film using a Hot-Filament Chemical Vapour Deposition (HFCVD) reactor, in order to machining a grey cast iron. Wear behaviour of these tools in high speed machining was the main subject of this work. Turning tests were performed with a combination of cutting speeds of 500, 700 and 900 m min−1, and feed rates of 0.1, 0.25 and 0.4 mm rot−1, remaining constant the depth of cut of 1 mm. In order to evaluate the tool behaviour during the turning tests, cutting forces were analyzed being verified a significant increase with feed rate. Diamond film removal occurred for the most severe set of cutting parameters. It was also observed the adhesion of iron and manganese from the workpiece to the tool. Tests were performed on a CNC lathe provided with a 3-axis dynamometer. Results were collected and registered by homemade software. Tool wear analysis was achieved by a Scanning Electron Microscope (SEM) provided with an X-ray Energy Dispersive Spectroscopy (EDS) system. Surface analysis was performed by a profilometer.

The Persistence of Memory

This paper analyzes several natural and man-made complex phenomena in the perspective of dynamical systems. Such phenomena are often characterized by the absence of a characteristic length-scale, long range correlations and persistent memory, which are features also associated to fractional order systems. For each system, the output, interpreted as a manifestation of the system dynamics, is analyzed by means of the Fourier transform. The amplitude spectrum is approximated by a power law function and the parameters are interpreted as an underlying signature of the system dynamics. The complex systems under analysis are then compared in a global perspective in order to unveil and visualize hidden relationships among them.

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

Análise de tecnologias de impermeabilização e isolamento em reabilitação da envolvente de edifícios

Neste trabalho é abordado o estágio efectuado por um período de sete meses na E.A. (Engenheiros Associados) e um estudo de caso sobre as tecnologias aplicadas no isolamento térmico de paredes exteriores. Na primeira parte deste relatório é efectuada uma breve caracterização da empresa e da sua actividade no mercado. A Engenheiros e Associados tem a sua estrutura assente nos seguintes sectores: Técnico-Comercial, de Aprovisionamento e de Gestão Administrativa; da qual foi efectuada uma descrição do trabalho desenvolvido em cada um desses sectores, nomeadamente a permanência na obra e as visitas e diligências às obras. A segunda parte deste relatório, que é a parte fulcral do trabalho desenvolvido, assenta sobre o sistema de ETICS (External Thermal Insulation Composite System), ou seja, o sistema de reboco delgado armado sobre isolamento térmico. Foi utilizado o sistema Cappotto na Obra de Requalificação da Urbanização de Vila d’Este – 1ª Fase. Após uma breve apresentação e evolução da história do ETICS ao longo do tempo, é exposta a caracterização da obra onde vai ser aplicado o sistema, que recai sobre a tipologia dos edifícios. Refira-se que, neste relatório, os edifícios por serem de construção túnel se dividem em três tipos: tipo plana ou corrente, tipo ângulo e tipo topo. Na Analise de Patologias efectuada evidenciam-se as fissuras e a humidade presentes em quase toda a extensão dos referidos edifícios antes do tratamento, tornando-as assim as principais anomalias destes edifícios. Foram elemento de foco as anomalias existentes nos edifícios, como: Deterioração do fibrocimento; Insuficiência das caleiras; Deficiências das impermeabilizações; Ausência de rufos; Deficiência das ligações; Degradação do revestimento e pintura; Fissuração do reboco; Degradação dos forros exteriores; Deterioração das padieiras; Deterioração dos peitoris; Deterioração das juntas de dilatação; Infiltrações e condensações; Ruptura das canalizações; Deslocamentos; Deficiências de ventilação; Deficiências de estanqueidade; Inexistência de Sistema de combate a incêndios. Para estas patologias são apresentadas as propostas de solução de forma a eliminar as mesmas. Sendo o ETICS escolhido por ser o sistema que elimina a maior parte destas patologias, tendo em conta uma relação de qualidade/preço, é abordada de uma forma detalhada e extensiva da aplicação do sistema antes, durante e depois da obra em si. Assim como, é feita uma descrição pormenorizada do material utilizado para a implementação do sistema. A análise dos pontos críticos refere-se a zonas sensíveis onde há a necessidade de reforço do sistema com vista a eliminar o aparecimento posterior de patologias, como por exemplo as características de suporte. Após a aplicação do sistema podem aparecer algumas patologias das quais se destaca o facto dos produtos serem preparados em obra, o erro humano nas dosagens do fabricante e no acrescento de água sem necessidade e a par das condições climatéricas, são as causas mais comuns do aparecimento de anomalias no sistema de ETICS, provocando fissurações e infiltrações, que são descritas neste relatório. É também abordada a manutenção e reparação do sistema, onde a manutenção refere-se à lavagem e à remoção de microorganismos das paredes e posterior pintura. A reparação dos danos divide-se em dois tipos, áreas até 2 cm2 e áreas maiores que 2 cm2. Por fim, são apresentados alguns rendimentos, que foram possíveis obter ao longo do desenvolvimento do trabalho, dos materiais e da mão-de-obra, dando origem aos custos directos. Sendo também abordadas as vantagens e desvantagens do sistema desde o seu início até à sua conclusão.

Some applications of fractional calculus in engineering

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, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. 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 FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.