Fractional central pattern generators for bipedal locomotion

Locomotion has been a major research issue in the last few years. Many models for the locomotion rhythms of quadrupeds, hexapods, bipeds and other animals have been proposed. This study has also been extended to the control of rhythmic movements of adaptive legged robots. In this paper, we consider a fractional version of a central pattern generator (CPG) model for locomotion in bipeds. A fractional derivative D α f(x), with α non-integer, is a generalization of the concept of an integer derivative, where α=1. The integer CPG model has been proposed by Golubitsky, Stewart, Buono and Collins, and studied later by Pinto and Golubitsky. It is a network of four coupled identical oscillators which has dihedral symmetry. We study parameter regions where periodic solutions, identified with legs’ rhythms in bipeds, occur, for 0<α≤1. We find that the amplitude and the period of the periodic solutions, identified with biped rhythms, increase as α varies from near 0 to values close to unity.

Design optimization of cruciform specimens for biaxial fatigue loading

In order to correctly assess the biaxial fatigue material properties one must experimentally test different load conditions and stress levels. With the rise of new in-plane biaxial fatigue testing machines, using smaller and more efficient electrical motors, instead of the conventional hydraulic machines, it is necessary to reduce the specimen size and to ensure that the specimen geometry is appropriated for the load capacity installed. At the present time there are no standard specimen’s geometries and the indications on literature how to design an efficient test specimen are insufficient. The main goal of this paper is to present the methodology on how to obtain an optimal cruciform specimen geometry, with thickness reduction in the gauge area, appropriated for fatigue crack initiation, as a function of the base material sheet thickness used to build the specimen. The geometry is optimized for maximum stress using several parameters, ensuring that in the gauge area the stress is uniform and maximum with two limit phase shift loading conditions. Therefore the fatigue damage will always initiate on the center of the specimen, avoiding failure outside this region. Using the Renard Series of preferred numbers for the base material sheet thickness as a reference, the reaming geometry parameters are optimized using a derivative-free methodology, called direct multi search (DMS) method. The final optimal geometry as a function of the base material sheet thickness is proposed, as a guide line for cruciform specimens design, and as a possible contribution for a future standard on in-plane biaxial fatigue tests. © 2014, Gruppo Italiano Frattura. All rights reserved.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

The K-Th derivatives of the immanant and the X-symmetric power of an operator

In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.

Travelling wave profiles in some models with nonlinear diffusion

We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.

Consumo de benzodiazepinas por idosos institucionalizados: inapropriação, qualidade de sono e contributo para a segurança na medicação

A racionalização do uso de medicamentos constitui-se como um fator contribuinte para a melhoria da segurança do doente, particularmente no que respeita à segurança na medicação, tendo-se tornado prioritária para as organizações e instituições de saúde. A avaliação do uso de medicamentos inapropriados no idoso constitui-se como uma medida que concorre para evitar, prevenir ou corrigir eventos adversos associados ao seu uso. As benzodiazepinas são uma das classes de medicamentos mais prescritas em idosos. No entanto, e apesar de sua utilidade clínica, algumas benzodiazepinas são consideradas inapropriadas nesta faixa etária por potenciarem o efeito sedativo e aumentar a incidência de quedas e fraturas. A longo prazo, na promoção da qualidade do sono, a sua efetividade é discutível já que a toma de uma benzodiazepina para a resolução de um problema como o sono, muitas vezes pontual, passa a ser um problema crónico de exigência de toma contínua, sem que a qualidade deste seja restabelecida, pondo em risco a segurança do doente. Este estudo tem como objetivo caracterizar o consumo de benzodiazepinas por idosos institucionalizados, numa instituição de longa permanência do concelho de Sesimbra, sua inapropriação e a relação com a qualidade de sono. Foi desenvolvido um estudo descritivo e transversal, assente no paradigma qualitativo, com a recolha de dados a decorrer em três momentos: registo de informação em grelha própria da caracterização sociodemográfica e da caracterização do consumo de benzodiazepinas; aplicação do índice de Katz para determinar a funcionalidade dos participantes; aplicação do questionário adaptado do Pittsburgh Sleep Quality Index para avaliação da qualidade do sono. A inapropriação foi avaliada pela aplicação dos critérios de Beers. Após aplicação dos critérios de inclusão (idade superior a 65 anos e capacidade funcional) aos 97 utentes da instituição, a amostra foi constituída por 51 utentes. Foi recolhido consentimento informado de todos os participantes. Os resultados obtidos mostram que 46% das benzodiazepinas consumidas são de duração intermédia de ação, observando-se ainda um valor considerável de consumo de benzodiazepinas de longa duração de ação (36%). Estes valores correspondem a um grau elevado de inapropriação, potenciando os riscos para a segurança do doente nesta faixa etária. O lorazepam 2,5mg é a benzodiazepina mais utilizada como hipnótico. Mas, apesar do consumo deste grupo de medicamentos 81,6% dos idosos que consumem benzodiazepinas não apresentam boa qualidade de sono (PSQI>5), enquanto 77% dos idosos que não consomem benzodiazepinas apresentam boa qualidade de sono (PSQI≤5). Nos idosos que consomem benzodiazepinas, a média de tempo despendido na cama até adormecer foi de cerca de 55 minutos, valor superior ao grupo que não consome benzodiazepinas, onde a média é de 27 minutos. Neste grupo de idosos, o consumo de benzodiazepinas não só é inapropriado como não contribuiu para uma melhoria na qualidade de sono nem para a segurança do doente, como são os consumidores de benzodiazepinas que apresentam uma pior qualidade de sono, nas suas várias dimensões.

Effect of fractional orders in the velocity control of a servo system

The application of fractional-order PID controllers is now an active field of research. This article investigates the effect of fractional (derivative and integral) orders upon system's performance in the velocity control of a servo system. The servo system consists of a digital servomechanism and an open-architecture software environment for real-time control experiments using MATLAB/Simulink tools. Experimental responses are presented and analyzed, showing the effectiveness of fractional controllers. Comparison with classical PID controllers is also investigated.

Comments on ‘‘Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions

Applied Mathematical Modelling, Vol.33

Fractional central differences and derivatives

Journal of Vibration and Control, Vol. 14, Nº 9-10

Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

On the relation between the fractional Brownian motion and the fractional derivatives

Physics Letters A, vol. 372; Issue 7

Synthesis of organometallic Ruthenium(II) complexes with strong activity against several human canceer cell lines

A new family of "RuCp" (Cp=eta(5)-C5H5) derivatives with bidentate N,O and N,N'-heteroaromatic ligands revealed outstanding cytotoxic properties against several human cell lines namely, A2780, A2780CisR, HT29, MCF7, MDAMB231, and PD. IC50 values were much lower than those found for cisplatin. Crystal structure of compound 4 was determined by X-ray diffraction studies. Density functional theory (DFT) calculations performed for compound 1 showed electronic flow from the ruthenium center to the coordinated bidentate ligand, in agreement with the electrochemical studies and the existence of a metal-to-ligand charge-transfer (MLCT) band evidenced by spectroscopic data.

A coherent approach to non-integer order derivatives

Signal Processing, vol. 86, nº 10

A new least-squares approach to differintegration modeling

Signal Processing, Vol. 86, nº 10

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006