Exploiting sensor redundancy for the calculation of fractional derivatives in the presence of noise

In this paper a new method for the calculation of the fractional expressions in the presence of sensor redundancy and noise, is presented. An algorithm, taking advantage of the signal characteristics and the sensor redundancy, is tuned and optimized through genetic algorithms. The results demonstrate the good performance for different types of expressions and distinct levels of noise.

Design, synthesis and biologival evaluation of novel isoniazid derivatives with potente antitubercular activity

The disturbing emergence of multidrug-resistant strains of Mycobacterium tuberculosis (Mtb) has been driving the scientific community to urgently search for new and efficient antitubercular drugs. Despite the various drugs currently under evaluation, isoniazid is still the key and most effective component in all multi-therapeutic regimens recommended by the WHO. This paper describes the QSAR-oriented design, synthesis and in vitro antitubercular activity of several potent isoniazid derivatives (isonicotinoyl hydrazones and isonicotinoyl hydrazides) against H37Rv and two resistant Mtb strains. QSAR studies entailed RFs and ASNNs classification models, as well as MLR models. Strict validation procedures were used to guarantee the models' robustness and predictive ability. Lipophilicity was shown not to be relevant to explain the activity of these derivatives, whereas shorter N-N distances and lengthy substituents lead to more active compounds. Compounds I, 2, 4, 5 and 6, showed measured activities against H37Rv higher than INH (i.e., MIC <= 0.28 mu M), while compound 9 exhibited a six fold decrease in MIC against the katG (S315T) mutated strain, by comparison with INH (Le., 6.9 vs. 43.8 mu M). All compounds were ineffective against H37Rv(INH) (Delta katG), a strain with a full deletion of the katG gene, thus corroborating the importance of KatG in the activation of INH-based compounds. The most potent compounds were also shown not to be cytotoxic up to a concentration 500 times higher than MIC. (C) 2014 Elsevier Masson SAS. All rights reserved.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

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.

Fractional central differences and derivatives

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

Approximating fractional derivatives through the generalized mean

This paper addresses the calculation of fractional order expressions through rational fractions. The article starts by analyzing the techniques adopted in the continuous to discrete time conversion. The problem is re-evaluated in an optimization perspective by tacking advantage of the degree of freedom provided by the generalized mean formula. The results demonstrate the superior performance of the new algorithm.

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

Calculation of fractional derivatives of noisy data with genetic algorithms

This paper addresses the calculation of derivatives of fractional order for non-smooth data. The noise is avoided by adopting an optimization formulation using genetic algorithms (GA). Given the flexibility of the evolutionary schemes, a hierarchical GA composed by a series of two GAs, each one with a distinct fitness function, is established.

A coherent approach to non-integer order derivatives

Signal Processing, vol. 86, nº 10

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

Using fractional derivatives for the joint ontrol of hexapod robots

This article studies several Fractional Order Control algorithms used for joint control of a hexapod robot. Both Padé and series approximations to the fractional derivative are considered for the control algorithm. The walking performance is evaluated through two indices: The mean absolute density of energy used per unit distance travelled, and the control effort. A set of simulation experiments reveals the influence of the different approximations upon the proposed indices. The results show that the fractional proportional and derivative algorithm, implemented using the Padé approximation with a small number of terms, gives the best results.

Analysis of the Van der Pol oscillator containing derivatives of fractional order

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.

Fractional central differences and derivatives

Journal of Vibration and Control, 14(9–10): 1255–1266, 2008