Fractional generalization of memristor and higher order elements

Fractional calculus generalizes integer order derivatives and integrals. Memristor systems generalize the notion of electrical elements. Both concepts were shown to model important classes of phenomena. This paper goes a step further by embedding both tools in a generalization considering complex-order objects. Two complex operators leading to real-valued results are proposed. The proposed class of models generate a broad universe of elements. Several combinations of values are tested and the corresponding dynamical behavior is analyzed.

Acrescentar valor à organização com a auditoria interna

Dissertação de Mestrado Apresentado ao Instituto de Contabilidade e Administração do Porto para a obtenção do grau de Mestre em Auditoria, sob orientação de Doutora Alcina Portugal Dias

Phonological and articulation treatment approaches in Portuguese children with speech and language impairments: a randomized controlled intervention study

Background: In Portugal, the routine clinical practice of speech and language therapists (SLTs) in treating children with all types of speech sound disorder (SSD) continues to be articulation therapy (AT). There is limited use of phonological therapy (PT) or phonological awareness training in Portugal. Additionally, at an international level there is a focus on collecting information on and differentiating between the effectiveness of PT and AT for children with different types of phonologically based SSD, as well as on the role of phonological awareness in remediating SSD. It is important to collect more evidence for the most effective and efficient type of intervention approach for different SSDs and for these data to be collected from diverse linguistic and cultural perspectives. Aims: To evaluate the effectiveness of a PT and AT approach for treatment of 14 Portuguese children, aged 4.0–6.7 years, with a phonologically based SSD. Methods & Procedures: The children were randomly assigned to one of the two treatment approaches (seven children in each group). All children were treated by the same SLT, blind to the aims of the study, over three blocks of a total of 25 weekly sessions of intervention. Outcome measures of phonological ability (percentage of consonants correct (PCC), percentage occurrence of different phonological processes and phonetic inventory) were taken before and after intervention. A qualitative assessment of intervention effectiveness from the perspective of the parents of participants was included. Outcomes & Results: Both treatments were effective in improving the participants’ speech, with the children receiving PT showing a more significant improvement in PCC score than those receiving the AT. Children in the PT group also showed greater generalization to untreated words than those receiving AT. Parents reported both intervention approaches to be as effective in improving their children’s speech. Conclusions & Implications: The PT (combination of expressive phonological tasks, phonological awareness, listening and discrimination activities) proved to be an effective integrated method of improving phonological SSD in children. These findings provide some evidence for Portuguese SLTs to employ PT with children with phonologically based SSD

Complex-order forced van der Pol oscillator

In this paper we consider a complex-order forced van der Pol oscillator. The complex derivative Dα1jβ, with α, β ∈ ℝ+, is a generalization of the concept of an integer derivative, where α = 1, β = 0. The Fourier transforms of the periodic solutions of the complex-order forced van der Pol oscillator are computed for various values of parameters such as frequency ω and amplitude b of the external forcing, the damping μ, and parameters α and β. Moreover, we consider two cases: (i) b = 1, μ = {1.0, 5.0, 10.0}, and ω = {0.5, 2.46, 5.0, 20.0}; (ii) ω = 20.0, μ = {1.0, 5.0, 10.0}, and b = {1.0, 5.0, 10.0}. We verified that most of the signal energy is concentrated in the fundamental harmonic ω0. We also observed that the fundamental frequency of the oscillations ω0 varies with α and μ. For the range of tested values, the numerical fitting led to logarithmic approximations for system (7) in the two cases (i) and (ii). In conclusion, we verify that by varying the parameter values α and β of the complex-order derivative in expression (7), we accomplished a very effective way of perturbing the dynamical behavior of the forced van der Pol oscillator, which is no longer limited to parameters b and ω.

Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

Complex order biped rhythms

Animal locomotion is a complex process, involving the central pattern generators (neural networks, located in the spinal cord, that produce rhythmic patterns), the brainstem command systems, the steering and posture control systems and the top layer structures that decide which motor primitive is activated at a given time. Pinto and Golubitsky studied an integer CPG model for legs rhythms in bipeds. It is a four-coupled identical oscillators' network with dihedral symmetry. This paper considers a new complex order central pattern generator (CPG) model for locomotion in bipeds. A complex derivative Dα±jβ, with α, β ∈ ℜ+, j = √-1, is a generalization of the concept of an integer derivative, where α = 1, β = 0. Parameter regions where periodic solutions, identified with legs' rhythms in bipeds, occur, are analyzed. Also observed is the variation of the amplitude and period of periodic solutions with the complex order derivative.

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.

Bipedal Locomotion: A Fractional CPG for Generating Patterns

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

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?

Deciding Kleene Algebra Terms Equivalence in Coq

This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.

O planeamento estratégico como instrumento de melhoria da comunicação organizacional interna

O planeamento estratégico é uma ferramenta usada pelas empresas, como forma de contribuir para a melhoria do seu desempenho, preconizando a concretização de objetivos. A comunicação organizacional interna é um o instrumento que, para além de traduzir uma mensagem enviada aos vários indivíduos da empresa, ajuda a interpretação dessa mensagem. Este estudo tem como objetivo perceber se, o planeamento estratégico pode ser um instrumento de melhoria conceptual e de gestão da comunicação organizacional interna. Neste trabalho utilizamos uma metodologia de estudo de caso único, suportada através do método qualitativo, com recurso a entrevistas, e do método quantitativo, através de questionários estruturados. As entrevistas aos quadros superiores da empresa foram realizadas com recuso a uma análise de conteúdo, verificando-se ser de extrema importância para a gestão, tanto o planeamento estratégico, como a comunicação interna. Os instrumentos de medida usados permitiram concluir que existem, ainda, algumas lacunas de planeamento e comunicação da empresa analisada. Da análise do caso em estudo é percetível que o planeamento estratégico, como a comunicação organizacional interna, são instrumentos usados com um nível de sucesso suficiente para colocar a empresa no rumo certo e estável de mercado. Por último, entendemos que no âmbito da conciliação dos dois temas, o planeamento estratégico facilita uma comunicação mais fluída, podendo, assim, ser um instrumento de melhoria da comunicação interna. Como limitações deste trabalho relatamos, em especial, a necessária precaução da generalização dos resultados obtidos e a dificuldade em realizar uma análise mais ampla na discussão de resultados, devido aos parcos trabalhos internacionais e, sobretudo, nacionais. A principal originalidade deste estudo decorre de ser utilizada uma análise com triangulação metodológica e o facto de a unidade de análise em estudo ser uma empresa líder na sua área de negócio e setor.