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.

System Modeling and Control Through Fractional-Order Algorithms

The theory of fractional calculus goes back to the beginning of thr throry of differential calculus but its inherent complexity postponed the applications of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of automaticcontrol preliminary work has already been carried out but the proposed algorithms are restricted to the frequency domain. The paper discusses the design of fractional-order discrete-time controllers. The algorithms studied adopt the time domein, which makes them suited for z-transform analusis and discrete-time implementation. The performance of discrete-time fractional-order controllers with linear and non-linear systems is also investigated.

Fractional Dynamics in Forest Fires

Every year forest fires consume large areas, being a major concern in many countries like Australia, United States and Mediterranean Basin European Countries (e.g., Portugal, Spain, Italy and Greece). Understanding patterns of such events, in terms of size and spatiotemporal distributions, may help to take measures beforehand in view of possible hazards and decide strategies of fire prevention, detection and suppression. Traditional statistical tools have been used to study forest fires. Nevertheless, those tools might not be able to capture the main features of fires complex dynamics and to model fire behaviour [1]. Forest fires size-frequency distributions unveil long range correlations and long memory characteristics, which are typical of fractional order systems [2]. Those complex correlations are characterized by self-similarity and absence of characteristic length-scale, meaning that forest fires exhibit power-law (PL) behaviour. Forest fires have also been proved to exhibit time-clustering phenomena, with timescales of the order of few days [3]. In this paper, we study forest fires in the perspective of dynamical systems and fractional calculus (FC). Public domain forest fires catalogues, containing data of events occurred in Portugal, in the period 1980 up to 2011, are considered. The data is analysed in an annual basis, modelling the occurrences as sequences of Dirac impulses. The frequency spectra of such signals are determined using Fourier transforms, and approximated through PL trendlines. The PL parameters are then used to unveil the fractional-order dynamics characteristics of the data. To complement the analysis, correlation indices are used to compare and find possible relationships among the data. It is shown that the used approach can be useful to expose hidden patterns not captured by traditional tools.

Effects of Soil Compaction and Organic Carbon Content on Preferential Flow in Loamy Field Soils

Abstract: Preferential flow and transport through macropores affect plant water use efficiency and enhance leaching of agrochemicals and the transport of colloids, thereby increasing the risk for contamination of groundwater resources. The effects of soil compaction, expressed in terms of bulk density (BD), and organic carbon (OC) content on preferential flow and transport were investigated using 150 undisturbed soil cores sampled from 15 × 15–m grids on two field sites. Both fields had loamy textures, but one site had significantly higher OC content. Leaching experiments were conducted in each core by applying a constant irrigation rate of 10 mm h−1 with a pulse application of tritium tracer. Five percent tritium mass arrival times and apparent dispersivities were derived from each of the tracer breakthrough curves and correlated with texture, OC content, and BD to assess the spatial distribution of preferential flow and transport across the investigated fields. Soils from both fields showed strong positive correlations between BD and preferential flow. Interestingly, the relationships between BD and tracer transport characteristics were markedly different for the two fields, although the relationship between BD and macroporosity was nearly identical. The difference was likely caused by the higher contents of fines and OC at one of the fields leading to stronger aggregation, smaller matrix permeability, and a more pronounced pipe-like pore system with well-aligned macropores.

Comparison Among Aerobic Exercise and Other Types of Interventions to Treat Depression: A Systematic Review

Depression is a common and disabling disease that affects over 100 million people worldwide and can have a significant impact on physical and mental health, reducing their quality of life. Thus, the aim of this article was to provide information on research results and key chains related to the therapeutic effects of chronic aerobic exercise compared with other types of interventions to treat depression, which may become a useful clinical application in a near future. Researches have shown the effectiveness of alternative treatments, such as physical exercise, minimizing high financial costs and minimizing side effects. In this review, the data analyzed allows us to claim that alternative therapies, such as exercise, are effective on controlling and reducing symptoms. 69.3% of the studies that investigated the antidepressant effects of exercise on depressive were significant, and the other 30.7% of the studies improved only in general physiological aspects, such as increased oxygen uptake, increased use of blood glucose and decreased body fat percentage, with no improvement on symptoms of depression. From the sample analyzed, 71.4% was composed of women, and regarding the severity of symptoms, 85% had mild to moderate depression and only 15% had moderate to severe depression. However, there is still disagreement regarding the effect of exercise compared to the use of antidepressants in symptomatology and cognitive function in depression, this suggests that there is no consensus on the correct intensity of aerobic exercise as to achieve the best dose-response, with intensities high to moderate or moderate to mild.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Tuning metadata for better movie content-based recommendation systems

The increasing number of television channels, on-demand services and online content, is expected to contribute to a better quality of experience for a costumer of such a service. However, the lack of efficient methods for finding the right content, adapted to personal interests, may lead to a progressive loss of clients. In such a scenario, recommendation systems are seen as a tool that can fill this gap and contribute to the loyalty of users. Multimedia content, namely films and television programmes are usually described using a set of metadata elements that include the title, a genre, the date of production, and the list of directors and actors. This paper provides a deep study on how the use of different metadata elements can contribute to increase the quality of the recommendations suggested. The analysis is conducted using Netflix and Movielens datasets and aspects such as the granularity of the descriptions, the accuracy metric used and the sparsity of the data are taken into account. Comparisons with collaborative approaches are also presented.

A Multi–Agent Brokerage Platform for Media Content Recommendation

Near real time media content personalisation is nowadays a major challenge involving media content sources, distributors and viewers. This paper describes an approach to seamless recommendation, negotiation and transaction of personalised media content. It adopts an integrated view of the problem by proposing, on the business-to-business (B2B) side, a brokerage platform to negotiate the media items on behalf of the media content distributors and sources, providing viewers, on the business-to-consumer (B2C) side, with a personalised electronic programme guide (EPG) containing the set of recommended items after negotiation. In this setup, when a viewer connects, the distributor looks up and invites sources to negotiate the contents of the viewer personal EPG. The proposed multi-agent brokerage platform is structured in four layers, modelling the registration, service agreement, partner lookup, invitation as well as item recommendation, negotiation and transaction stages of the B2B processes. The recommendation service is a rule-based switch hybrid filter, including six collaborative and two content-based filters. The rule-based system selects, at runtime, the filter(s) to apply as well as the final set of recommendations to present. The filter selection is based on the data available, ranging from the history of items watched to the ratings and/or tags assigned to the items by the viewer. Additionally, this module implements (i) a novel item stereotype to represent newly arrived items, (ii) a standard user stereotype for new users, (iii) a novel passive user tag cloud stereotype for socially passive users, and (iv) a new content-based filter named the collinearity and proximity similarity (CPS). At the end of the paper, we present off-line results and a case study describing how the recommendation service works. The proposed system provides, to our knowledge, an excellent holistic solution to the problem of recommending multimedia contents.

Effects of microcurrents and physical exercise on the abdominal fat in patients with coronary artery disease

Introduction Coronary artery disease is associated with decreased levels of physical activity, contributing to increases in abdominal fat and consequently increasing metabolic risk. The innovative use of microcurrents may be an effective method to increase the lipolytic rate of abdominal adipocytes. This study aimed to investigate the effects of utilizing microcurrents in a home-based exercise program in subjects with coronary artery disease to assess changes in total, subcutaneous and visceral abdominal adipose tissue. Methods This controlled trial included 44 subjects with myocardial infarction, randomly divided into Intervention Group 1 (IG1; n = 16), Intervention Group 2 (IG2; n = 12) and Control Group (CG; n = 16). IG1 performed a specific exercise program at home during 8 weeks, and IG2 additionally used microcurrents on the abdominal region before the exercise program. All groups were given health education sessions. Computed tomography was used to evaluate abdominal, subcutaneous and visceral fat, accelerometers to measure habitual physical activity and the semi-quantitative food frequency questionnaire for dietary intake. Results After 8 weeks, IG2 showed a significantly decrease in subcutaneous fat (p ≤ 0.05) when compared to CG. Concerning visceral fat, both intervention groups showed a significant decrease in comparison to the CG (p ≤ 0.05). No significant changes were found between groups on dietary intake and habitual physical activity, except for sedentary activity that decreased significantly for IG2 in comparison with CG (p ≤ 0.05). Conclusion This specific home-based exercise program using microcurrent therapy for individuals with coronary artery disease showed improvements in visceral and subcutaneous abdominal fat.

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.

Matrix fractional systems

This paper addresses the matrix representation of dynamical systems in the perspective of fractional calculus. Fractional elements and fractional systems are interpreted under the light of the classical Cole–Cole, Davidson–Cole, and Havriliak–Negami heuristic models. Numerical simulations for an electrical circuit enlighten the results for matrix based models and high fractional orders. The conclusions clarify the distinction between fractional elements and fractional systems.

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.

Chronic hepatitis C: hepatic iron content does not correlate with response to antiviral therapy

The complex interaction between hepatitis C virus infection, iron homeostasis and the response to antiviral treatment remains controversial. The aim of this study was to evaluate the influence of hepatic iron concentration (HIC) on the sustained virological response (SVR) to antiviral therapy in patients with chronic hepatitis C. A total of 50 patients who underwent pretreatment liver biopsy with assessment of HIC by graphite furnace atomic absorption spectroscopy and were subsequently submitted to antiviral treatment with interferon/peginterferon and ribavirin were included in the study. Patients with alcoholism, history of multiple blood transfusion, chronic kidney disease, hemolytic anemia and parenteral iron therapy were excluded. The iron related markers and HIC were compared between those who achieved an SVR and non-responders (NR) patients. The mean age was 45.7 years and the proportion of patients' gender was not different between SVR and NR patients. The median serum iron was 138 and 134 µg/dL (p = 0.9), the median serum ferritin was 152.5 and 179.5 ng/mL (p = 0.87) and the median HIC was 9.9 and 8.2 µmol/g dry tissue (p = 0.51), for SVR and NR patients, respectively. Thus, hepatic iron concentration, determined by a reliable quantitative method, was not a negative predictive factor of SVR in patients with chronic hepatitis C presenting mild to moderate hepatic iron accumulation.

Produção de biodiesel a partir de pastas de gordura e resíduo de glicerol

O principal objectivo deste trabalho consistiu na produção de biodiesel a partir de resíduos fornecidos pela Empresa SOCIPOLE, S.A. Esta, forneceu, pastas de gordura (depósito formado nos óleos usados), só aproveitadas pela empresa para a produção de sabões, e resíduo de glicerol proveniente da produção de biodiesel. Com as pastas de gordura, foi feito um estudo onde se variaram alguns parâmetros, tais como: o tipo de reactor, catalisador, temperatura, agitação, tempo de reacção, razão molar gordura:metanol e condições de secagem. O estudo mais pormenorizado foi efectuado com o NaOH, como catalisador. Foram feitos vários ensaios para os tempos de reacção de 30minutos, 1hora e 2horas, a 65ºC e razão molar gordura:metanol 1:6, tendo-se obtido respectivamente 86,7; 88,1 e 87,5% para o teor de ésteres. No caso da resina catiónica forte como catalisador, aparentemente não houve reacção ao fim de 12h, enquanto no ensaio que utilizou o ácido sulfúrico, o teor de ésteres foi de 82,6%, ao fim de 12h com razão molar gordura:metanol igual a 1:11. Quanto à produção de biodiesel a partir do resíduo de ácidos gordos resultante da purificação do resíduo de glicerol, foi feito um estudo preliminar usando diferentes catalisadores, uma resina catiónica forte, ácido sulfúrico e zircónia sulfatada. Este resíduo continha cerca de 60% de ácidos gordos e aproximadamente 39% de ésteres metílicos. Dos três catalisadores usados, o que permitiu obter maior teor de ésteres foi a zircónia sulfatada, tendo-se obtido 82,9% trabalhando a 60ºC durante 18horas com agitação de 230rpm e razão molar ácidos gordos:metanol de 1:12 . O ensaio em que se obteve menor percentagem de ésteres (56,4%) foi com resina catiónica. Com as duas matérias-primas obteve-se sempre um teor de ésteres, no produto final, abaixo dos 96,5% estabelecidos pela Norma Europeia EN 14103. Estes resultados reflectem provavelmente a composição complexa das matérias-primas. As pastas de gordura podem conter compostos não esterificáveis, solúveis no biodiesel, ou mais dificilmente esterificáveis nas condições operacionais usadas. Já o resíduo de ácidos gordos apresenta uma cor escura o que indica a existência de compostos corados, talvez polímeros. Portanto, para se tirar conclusões fundamentadas é necessário fazer análises mais completas das pastas de gordura e do resíduo de ácidos gordos, assim como ao biodiesel produzido de forma a identificar as possíveis contaminações existentes nos produtos com esta proveniência.

High-Content Analysis of Breast Cancer Using Single-Cell Deep Transfer Learning

High-content analysis has revolutionized cancer drug discovery by identifying substances that alter the phenotype of a cell, which prevents tumor growth and metastasis. The high-resolution biofluorescence images from assays allow precise quantitative measures enabling the distinction of small molecules of a host cell from a tumor. In this work, we are particularly interested in the application of deep neural networks (DNNs), a cutting-edge machine learning method, to the classification of compounds in chemical mechanisms of action (MOAs). Compound classification has been performed using image-based profiling methods sometimes combined with feature reduction methods such as principal component analysis or factor analysis. In this article, we map the input features of each cell to a particular MOA class without using any treatment-level profiles or feature reduction methods. To the best of our knowledge, this is the first application of DNN in this domain, leveraging single-cell information. Furthermore, we use deep transfer learning (DTL) to alleviate the intensive and computational demanding effort of searching the huge parameter's space of a DNN. Results show that using this approach, we obtain a 30% speedup and a 2% accuracy improvement.