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.

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.

Cystoscopy in the diagnosis and follow-up of urinary schistosomiasis in Brazilian soldiers returning from Mozambique, Africa

The assessment of urinary schistosomiasis in individuals coming from endemic areas often requires diagnostic resources not used in areas of exposure in order to determine complications or to establish more precise criteria of cure. Cystoscopy and 24-hour urine examination were performed, after treatments with praziquantel 40 mg/kg body weight, single dose, on 25 Brazilian military men who were part of a United Nations peace mission to Mozambique in 1994. The median age of the individuals was 29 years and all presented a positive urine parasitological exam. The alterations detected by cystoscopy were hyperemia and granulomas in the vesical submucosa in 59.1% of the individuals and only granulomas in 40.9%. A vesical biopsy revealed granulomas in all patients and viable eggs in 77.3% even after a period during which the patients no longer excreted eggs in urine. Cystoscopy after treatment, followed by biopsy and histopathological evaluation, performed in areas where the evolution of the disease can be better monitored, was found to be a safe criterion of parasitological cure.

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.

Unilateral Versus Bilateral Prostatic Arterial Embolization for Lower Urinary Tract Symptoms in Patients with Prostate Enlargement

PURPOSE: This study was designed to compare baseline data and clinical outcome between patients with prostate enlargement/benign prostatic hyperplasia (PE/BPH) who underwent unilateral and bilateral prostatic arterial embolization (PAE) for the relief of lower urinary tract symptoms (LUTS). METHODS: This single-center, ambispective cohort study compared 122 consecutive patients (mean age 66.7 years) with unilateral versus bilateral PAE from March 2009 to December 2011. Selective PAE was performed with 100- and 200-μm nonspherical polyvinyl alcohol (PVA) particles by a unilateral femoral approach. RESULTS: Bilateral PAE was performed in 103 (84.4 %) patients (group A). The remaining 19 (15.6 %) patients underwent unilateral PAE (group B). Mean follow-up time was 6.7 months in group A and 7.3 months in group B. Mean prostate volume, PSA, International prostate symptom score/quality of life (IPSS/QoL) and post-void residual volume (PVR) reduction, and peak flow rate (Qmax) improvement were 19.4 mL, 1.68 ng/mL, 11.8/2.0 points, 32.9 mL, and 3.9 mL/s in group A and 11.5 mL, 1.98 ng/mL, 8.9/1.4 points, 53.8 mL, and 4.58 mL/s in group B. Poor clinical outcome was observed in 24.3 % of patients from group A and 47.4 % from group B (p = 0.04). CONCLUSIONS: PAE is a safe and effective technique that can induce 48 % improvement in the IPSS score and a prostate volume reduction of 19 %, with good clinical outcome in up to 75 % of treated patients. Bilateral PAE seems to lead to better clinical results; however, up to 50 % of patients after unilateral PAE may have a good clinical outcome.

Embolisation of Prostatic Arteries as Treatment of Moderate to Severe Lower Urinary Symptoms (LUTS) Secondary to Benign Hyperplasia: Results of Short- and Mid-Term Follow-Up

OBJECTIVES: To evaluate the short- and medium-term results of prostatic arterial embolisation (PAE) for benign prostatic hyperplasia (BPH). METHODS: This was a prospective non-randomised study including 255 patients diagnosed with BPH and moderate to severe lower urinary tract symptoms after failure of medical treatment for at least 6 months. The patients underwent PAE between March 2009 and April 2012. Technical success is when selective prostatic arterial embolisation is completed in at least one pelvic side. Clinical success was defined as improving symptoms and quality of life. Evaluation was performed before PAE and at 1, 3, 6 and every 6 months thereafter with the International Prostate Symptom Score (IPSS), quality of life (QoL), International Index of Erectile Function (IIEF), uroflowmetry, prostatic specific antigen (PSA) and volume. Non-spherical polyvinyl alcohol particles were used. RESULTS: PAE was technically successful in 250 patients (97.9 %). Mean follow-up, in 238 patients, was 10 months (range 1-36). Cumulative rates of clinical success were 81.9 %, 80.7 %, 77.9 %, 75.2 %, 72.0 %, 72.0 %, 72.0 % and 72.0 % at 1, 3, 6, 12, 18, 24, 30 and 36 months, respectively. There was one major complication. CONCLUSIONS: PAE is a procedure with good results for BPH patients with moderate to severe LUTS after failure of medical therapy. KEY POINTS: • Prostatic artery embolisation offers minimally invasive therapy for benign prostatic hyperplasia. • Prostatic artery embolisation is a challenging procedure because of vascular anatomical variations. • PAE is a promising new technique that has shown good results.

FREQUENCY, URINALYSIS AND SUSCEPTIBILITY PROFILE OF PATHOGENS CAUSING URINARY TRACT INFECTIONS IN ENUGU STATE, SOUTHEAST NIGERIA

Objective: This study was designed to determine the frequency and causative agent(s) of urinary tract infections (UTIs) in individuals with symptoms of urinary tract infections in Enugu State of Southeast Nigeria, and to determine the antibiotic susceptibility pattern of microbial agents isolated from urine culture.Methods: The study involved 211 individuals (149 females and 62 males) clinically suspected for UTI. Urine samples were collected by the mid-stream ‘clean catch’ method and tested using standard procedures. Antibiotic susceptibility of the isolated pathogens was tested using the Kirby-Bauer technique according to the Clinical and Laboratory Standards Institute (CLSI) guidelines.Results: Microscopy of centrifuged urine samples showed 16 patients had pyuria while 54 had pus cells. Calcium oxalate crystals were found in 14 samples. Urinalysis performed with urine samples showed 17 had protein; seven were nitrite positive and three had moderate to high glucose concentration. Fifty-four urine samples (36.2%) from females and 12 (19.4%) from males showed significant growth upon culture. Gram stain and biochemical tests identified nine different organisms with Escherichia coli as the most common isolated species. Forty three randomly selected strains were further tested for their susceptibility against a panel of antibiotics. Thirty isolates (81.08%) were resistant to four or more antibiotics with the highest resistance shown by E. coli (76.67%). All the Gram- negative isolates were resistant to Ampicilox, Cefuroxime and Amoxicillin.Conclusion: Urinary tract infections were found more in females in the area under study. As found in other studies, E. coli was the most predominant isolate, although other organisms seem to be on the increase.

THE EFFECT OF HOOKWORM INFECTION AND URINARY SCHISTOSOMIASIS ON BLOOD HEMOGLOBIN CONCENTRATION OF SCHOOLCHILDREN LIVING IN NORTHERN MOZAMBIQUE

This study aims to assess the association between schistosomiasis and hookworm infection with hemoglobin levels of schoolchildren in northern Mozambique. Through a cross-sectional survey, 1,015 children from five to 12 years old in the provinces of Nampula, Cabo Delgado and Niassa were studied. Hookworm infection and urinary schistosomiasis were diagnosed, through Ritchie and filtration methods, with a prevalence of 31.3% and 59.1%, respectively. Hemoglobin levels were obtained with a portable photometer (Hemocue®). The average hemoglobin concentration was 10.8 ± 1.42 g/dL, and 62.1% of the children presented levels below 11.5 g/dL, of which 11.8% of the total number of children had hemoglobin levels below 9 g/dL. A multiple linear regression analysis demonstrated negative interactions between hemoglobin levels and ancylostomiasis, this being restricted to the province of Cabo Delgado (β = -0.55; p < 0.001) where an independent interaction between hemoglobin levels and urinary schistosomiasis was also observed (β = -0.35; p = 0.016). The logistical regression model indicated that hookworm infection represents a predictor of mild (OR = 1.87; 95% CI = 1.17-3.00) and moderate/severe anemia (OR = 2.71; 95% CI = 1.50 - 4.89). We concluded that, in the province of Cabo Delgado, hookworm and Schistosoma haematobium infections negatively influence hemoglobin levels in schoolchildren. Periodical deworming should be considered in the region. Health education and improvements in sanitary infrastructure could achieve long-term and sustainable reductions in soil-transmitted helminthiases and schistosomiasis prevalence rates.