Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.

A simple approach to numerical modelling of propane combustion in fluidized beds

A mathematical model is proposed for the evolution of temperature, chemical composition, and energy release in bubbles, clouds, and emulsion phase during combustion of gaseous premixtures of air and propane in a bubbling fluidized bed. The analysis begins as the bubbles are formed at the orifices of the distributor, until they explode inside the bed or emerge at the free surface of the bed. The model also considers the freeboard region of the fluidized bed until the propane is thoroughly burned. It is essentially built upon the quasi-global mechanism of Hautman et al. (1981) and the mass and heat transfer equations from the two-phase model of Davidson and Harrison (1963). The focus is not on a new modeling approach, but on combining the classical models of the kinetics and other diffusional aspects to obtain a better insight into the events occurring inside a fluidized bed reactor. Experimental data are obtained to validate the model by testing the combustion of commercial propane, in a laboratory-scale fluidized bed, using four sand particle sizes: 400–500, 315–400, 250–315, and 200–250 µm. The mole fractions of CO2, CO, and O2 in the flue gases and the temperature of the fluidized bed are measured and compared with the numerical results.

Fractional calculus: application in modelling and control

This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control.

Strength prediction of single- and double-lap joints by standard and extended finite element modelling

The structural integrity of multi-component structures is usually determined by the strength and durability of their unions. Adhesive bonding is often chosen over welding, riveting and bolting, due to the reduction of stress concentrations, reduced weight penalty and easy manufacturing, amongst other issues. In the past decades, the Finite Element Method (FEM) has been used for the simulation and strength prediction of bonded structures, by strength of materials or fracture mechanics-based criteria. Cohesive-zone models (CZMs) have already proved to be an effective tool in modelling damage growth, surpassing a few limitations of the aforementioned techniques. Despite this fact, they still suffer from the restriction of damage growth only at predefined growth paths. The eXtended Finite Element Method (XFEM) is a recent improvement of the FEM, developed to allow the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom with special displacement functions, thus overcoming the main restriction of CZMs. These two techniques were tested to simulate adhesively bonded single- and double-lap joints. The comparative evaluation of the two methods showed their capabilities and/or limitations for this specific purpose.

A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry

Fractional order modeling of biological systems has received significant interest in the research community. Since the fractal geometry is characterized by a recurrent structure, the self-similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. To demonstrate the link between the recurrence of the respiratory tree and the appearance of a fractional-order model, we develop an anatomically consistent representation of the respiratory system. This model is capable of simulating the mechanical properties of the lungs and we compare the model output with in vivo measurements of the respiratory input impedance collected in 20 healthy subjects. This paper provides further proof of the underlying fractal geometry of the human lungs, and the consequent appearance of constant-phase behavior in the total respiratory impedance.

Persistence characteristics in financial prices: evidence from the portuguese stock market returns

The objective of this article is to provide additional knowledge to the discussion of long-term memory, leaning over the behavior of the main Portuguese stock index. The first four moments are calculated using time windows of increasing size and sliding time windows of fixed size equal to 50 days and suggest that daily returns are non-ergodic and non-stationary. Seeming that the series is best described by a fractional Brownian motion approach, we use the rescaled-range analysis (R/S) and the detrended fluctuation analysis (DFA). The findings indicate evidence of long term memory in the form of persistence. This evidence of fractal structure suggests that the market is subject to greater predictability and contradicts the efficient market hypothesis in its weak form. This raises issues regarding theoretical modeling of asset pricing. In addition, we carried out a more localized (in time) study to identify the evolution of the degree of long-term dependency over time using windows 200-days and 400-days. The results show a switching feature in the index, from persistent to anti-persistent, quite evident from 2010.

Urban land use change analysis and modelling: a case study of Setubal-Sesimbra, Portugal

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies

Pseudo-fractional ARMA modelling using a double Levinson recursion

IET Control Theory & Applications, Vol. 1, Nº 1

Long-term dependence in financial prices: evidence from the Belgian stock market returns

This article aims to contribute to the discussion of long-term dependence, focusing on the behavior of the main Belgian stock index. Non-parametric analyzes of the general characteristics of temporal frequency show that daily returns are non-ergodic and non-stationary. Therefore, we use the rescaled-range analysis (R/S) and the detrended fluctuation analysis (DFA), under the fractional Brownian motion approach, and we found slight evidence of long-term dependence. These results refute the random walk hypothesis with i.i.d. increments, which is the basis of the EMH in its weak form, and call into question some theoretical modeling of asset pricing. Other more localized complementary study, to identify the evolution of the degree of dependence over time windows, showed that the index has become less persistent from 2010. This may mean a maturing market by the extension of the effects of current financial crisis.

Human and climatic change impact modelling on the habitat suitability for the chimpanzee (Pan troglodytes ellioti) – Case study: The proposed Mount Cameroon National Park

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies

Dynamical modelling of a genetic algorithm

This work addresses the signal propagation and the fractional-order dynamics during the evolution of a genetic algorithm (GA). In order to investigate the phenomena involved in the GA population evolution, the mutation is exposed to excitation perturbations during some generations and the corresponding fitness variations are evaluated. Three distinct fitness functions are used to study their influence in the GA dynamics. The input and output signals are studied revealing a fractional-order dynamic evolution, characteristic of a long-term system memory.

Modelling text file evaluation processes

Text file evaluation is an emergent topic in e-learning that responds to the shortcomings of the assessment based on questions with predefined answers. Questions with predefined answers are formalized in languages such as IMS Question & Test Interoperability Specification (QTI) and supported by many e-learning systems. Complex evaluation domains justify the development of specialized evaluators that participate in several business processes. The goal of this paper is to formalize the concept of a text file evaluation in the scope of the E-Framework – a service oriented framework for development of e-learning systems maintained by a community of practice. The contribution includes an abstract service type and a service usage model. The former describes the generic capabilities of a text file evaluation service. The later is a business process involving a set of services such as repositories of learning objects and learning management systems.

Modelling an e-learning environment for learning programming languages

It is widely accepted that solving programming exercises is fundamental to learn how to program. Nevertheless, solving exercises is only effective if students receive an assessment on their work. An exercise solved wrong will consolidate a false belief, and without feedback many students will not be able to overcome their difficulties. However, creating, managing and accessing a large number of exercises, covering all the points in the curricula of a programming course, in classes with large number of students, can be a daunting task without the appropriated tools working in unison. This involves a diversity of tools, from the environments where programs are coded, to automatic program evaluators providing feedback on the attempts of students, passing through the authoring, management and sequencing of programming exercises as learning objects. We believe that the integration of these tools will have a great impact in acquiring programming skills. Our research objective is to manage and coordinate a network of eLearning systems where students can solve computer programming exercises. Networks of this kind include systems such as learning management systems (LMS), evaluation engines (EE), learning objects repositories (LOR) and exercise resolution environments (ERE). Our strategy to achieve the interoperability among these tools is based on a shared definition of programming exercise as a Learning Object (LO).

Modelling a network of heterogeneous e-learning systems

In recent years emerged several initiatives promoted by educational organizations to adapt Service Oriented Architectures (SOA) to e-learning. These initiatives commonly named eLearning Frameworks share a common goal: to create flexible learning environments by integrating heterogeneous systems already available in many educational institutions. However, these frameworks were designed for integration of systems participating in business like processes rather than on complex pedagogical processes as those related to automatic evaluation. Consequently, their knowledge bases lack some fundamental components that are needed to model pedagogical processes. The objective of the research described in this paper is to study the applicability of eLearning frameworks for modelling a network of heterogeneous eLearning systems, using the automatic evaluation of programming exercises as a case study. The paper surveys the existing eLearning frameworks to justify the selection of the e-Framework. This framework is described in detail and identified the necessary components missing from its knowledge base, more precisely, a service genre, expression and usage model for an evaluation service. The extensibility of the framework is tested with the definition of this service. A concrete model for evaluation of programming exercises is presented as a validation of the proposed approach.