Pseudo Phase Plane and Fractional Calculus Modelling of Western Global Economic Downturn

This paper applies Pseudo Phase Plane (PPP) and Fractional Calculus (FC) mathematical tools for modeling world economies. A challenging global rivalry among the largest international economies began in the early 1970s, when the post-war prosperity declined. It went on, up to now. If some worrying threatens may exist actually in terms of possible ambitious military aggression, invasion, or hegemony, countries’ PPP relative positions can tell something on the current global peaceful equilibrium. A global political downturn of the USA on global hegemony in favor of Asian partners is possible, but can still be not accomplished in the next decades. If the 1973 oil chock has represented the beginning of a long-run recession, the PPP analysis of the last four decades (1972–2012) does not conclude for other partners’ global dominance (Russian, Brazil, Japan, and Germany) in reaching high degrees of similarity with the most developed world countries. The synergies of the proposed mathematical tools lead to a better understanding of the dynamics underlying world economies and point towards the estimation of future states based on the memory of each time series.

Fractional Calculus: Quo Vadimus? (Where Are We Going?)

Discussions under this title were held during a special session in frames of the International Conference “Fractional Differentiation and Applications” (ICFDA ’14) held in Catania (Italy), 23-25 June 2014, see details at http://www.icfda14.dieei.unict.it/. Along with the presentations made during this session, we include here some contributions by the participants sent afterwards and also by few colleagues planning but failed to attend. The intention of this special session was to continue the useful traditions from the first conferences on the Fractional Calculus (FC) topics, to pose open problems, challenging hypotheses and questions “where to go”, to discuss them and try to find ways to resolve.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Per-unit royalty and fixed-fee licensing in a differentiated Stackelberg model

In the present paper we consider a differentiated Stackelberg model, when the leader firm engages in an R&D process that gives an endogenous cost-reducing innovation. The aim is to study the licensing of the cost-reduction by a per-unit royalty and a fixed-fee. We analyse the implications of these types of licensing contracts over the R&D effort, the profits of the firms, the consumer surplus and the social welfare. By using comparative static analysis, we conclude that the degree of the differentiation of the goods plays an important role in the results.

Fractional Calculus: Application in modeling 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.

Electrical Skin Phenomena: A Fractional Calculus Analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenomas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

A Fractional Calculus Perspective in the Evolutionary Design of Combinational Circuits

This paper analyses the performance of a genetic algorithm (GA) in the synthesis of digital circuits using two novel approaches. The first concept consists in improving the static fitness function by including a discontinuity evaluation. The measure of variability in the error of the Boolean table has similarities with the function continuity issue in classical calculus. The second concept extends the static fitness by introducing a fractional-order dynamical evaluation.

Short-Circuit Impedance of Power Transformers: the Fractional Order Calculus Approach

First IFAC Workshop on Fractional Differentiation and Its Application - 19-21 July 2004, Enseirb, Bordeaux, France - FDA'04

On the Estimation of the Short-Circuit Impedance of Power Transformers Using Fractional Order Calculus

This paper reports investigation on the estimation of the short circuit impedance of power transformers, using fractional order calculus to analytically study the influence of the diffusion phenomena in the windings. The aim is to better characterize the medium frequency range behavior of leakage inductances of power transformer models, which include terms to represent the magnetic field diffusion process in the windings. Comparisons between calculated and measured values are shown and discussed.

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.

Routine Transthoracic Echocardiography in a General Intensive Care Unit: an 18 Month Survey in 704 Patients

The authors analyzed 704 transthoracic echocardiographic (TTE) examinations, performed routinely to all admitted patients to a general 16-bed Intensive Care Unit (ICU) during an 18-month period. Data acquisition and prevalence of abnormalities of cardiac structures and function were assessed, as well as the new, previously unknown severe diagnoses. A TTE was performed within the first 24 h of admission on 704 consecutive patients, with a mean age of 61.5+/-17.5 years, ICU stay of 10.6+/-17.1 days, APACHE II 22.6+/-8.9, and SAPS II 52.7+/-20.4. In four patients, TTE could not be performed. Left ventricular (LV) dimensions were quantified in 689 (97.8%) patients, and LV function in 670 (95.2%) patients. Cardiac output (CO) was determined in 610 (86.7%), and mitral E/A in 399 (85.9% of patients in sinus rhythm). Echocardiographic abnormalities were detected in 234 (33%) patients, the most common being left atrial (LA) enlargement (n=163), and LV dysfunction (n=132). Patients with these alterations were older (66+/-16.5 vs 58.1+/-17.4, p<0.001), presented a higher APACHE II score (24.4+/-8.7 vs 21.1+/-8.9, p<0.001), and had a higher mortality rate (40.1% vs 25.4%, p<0.001). Severe, previously unknown echocardiographic diagnoses were detected in 53 (7.5%) patients; the most frequent condition was severe LV dysfunction. Through a multivariate logistic regression analysis, it was determined that mortality was affected by tricuspid regurgitation (p=0.016, CI 1.007-1.016) and ICU stay (p<0.001, CI 1-1.019). We conclude that TTE can detect most cardiac structures in a general ICU. One-third of the patients studied presented cardiac structural or functional alterations and 7.5% severe previously unknown diagnoses.

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.

A Multiple Criteria Utility-based Approa h for the Unit Commitment with Wind Power and Pumped Storage Hydro

The integration of wind power in eletricity generation brings new challenges to unit commitment due to the random nature of wind speed. For this particular optimisation problem, wind uncertainty has been handled in practice by means of conservative stochastic scenario-based optimisation models, or through additional operating reserve settings. However, generation companies may have different attitudes towards operating costs, load curtailment, or waste of wind energy, when considering the risk caused by wind power variability. Therefore, alternative and possibly more adequate approaches should be explored. This work is divided in two main parts. Firstly we survey the main formulations presented in the literature for the integration of wind power in the unit commitment problem (UCP) and present an alternative model for the wind-thermal unit commitment. We make use of the utility theory concepts to develop a multi-criteria stochastic model. The objectives considered are the minimisation of costs, load curtailment and waste of wind energy. Those are represented by individual utility functions and aggregated in a single additive utility function. This last function is adequately linearised leading to a mixed-integer linear program (MILP) model that can be tackled by general-purpose solvers in order to find the most preferred solution. In the second part we discuss the integration of pumped-storage hydro (PSH) units in the UCP with large wind penetration. Those units can provide extra flexibility by using wind energy to pump and store water in the form of potential energy that can be generated after during peak load periods. PSH units are added to the first model, yielding a MILP model with wind-hydro-thermal coordination. Results showed that the proposed methodology is able to reflect the risk profiles of decision makers for both models. By including PSH units, the results are significantly improved.

Lack of methicillin-resistant Staphylococcus aureus nasal carriage among patients at a primary-healthcare unit in Porto Alegre, Brazil

INTRODUCTION: Community-associated methicillin-resistant Staphylococcus aureus (MRSA) has emerged as a pathogen in individuals without traditional risk factors. MATERIAL AND METHODS: MRSA nasal carriage was assessed in individuals consulting at a Primary Health Unit in Brazil. RESULTS: A total of 336 individuals were included: 136 were tested only for MRSA and 200 for any S. aureus. No MRSA was found among the 336 individuals and 23 (11.5%) of 200 were colonized by S. aureus. DISCUSSION: Low prevalence rates have been found in non-hospitalized individuals, but MRSA surveillance should be encouraged to monitor clinical and molecular epidemiology of CA- MRSA.

HIV-1-mother-to-child transmission and associated characteristics in a public maternity unit in Presidente Prudente, Brazil

In children, vertical transmission is the main form of HIV infection. Our aim was to determine the prevalence of HIV-1 vertical transmission in mother-infant pairs in a public maternity ward in Presidente Prudente, SP. Additionally; we sought to identify characteristics associated with this form of transmission. The files of 86 HIV-1-infected mothers and their newborns referred to a Public Hospital from March 2002 to March 2007 were analyzed. The HIV-1-RNA viral load of the newborns was determined by bDNA. The HIV-1 vertical-transmission rate was 4.6%. Children that were born in the pre-term period and breastfed were at a higher risk of HIV-1 infection (p = 0.005 and p = 0.017 respectively) than children born at term and not breastfed. Prophylactic therapy with zidovudine after birth for newborns was associated with a lower risk of infection (p = 0.003). The number of newborns weighing < 2,500 g was significantly higher for infected children (p = 0.008) than for non-infected newborns. About 22.9% of mothers did not know the HIV-1 status of their newborns eight months after delivery. The study suggests that it is necessary to increase the identification of HIV-1 infection in pregnant women and their newborns as well as to offer and explain the benefits of ARV prophylaxis.