Refined scale-dependent permutation entropy to analyze systems complexity

Multiscale entropy (MSE) has become a prevailing method to quantify the complexity of systems. Unfortunately, MSE has a temporal complexity in O(N2)O(N2), which is unrealistic for long time series. Moreover, MSE relies on the sample entropy computation which is length-dependent and which leads to large variance and possible undefined entropy values for short time series. Here, we propose and introduce a new multiscale complexity measure, the refined scale-dependent permutation entropy (RSDPE). Through the processing of different kinds of synthetic data and real signals, we show that RSDPE has a behavior close to the one of MSE. Furthermore, RSDPE has a temporal complexity in O(N)O(N). Finally, RSDPE has the advantage of being much less length-dependent than MSE. From all this, we conclude that RSDPE over-performs MSE in terms of computational cost and computational accuracy

Refined composite multiscale permutation entropy to overcome multiscale permutation entropy length dependence

Multiscale permutation entropy (MPE) has recently been proposed to evaluate complexity of time series. MPE has numerous advantages over other multiscale complexity measures, such as its simplicity, robustness to noise and its low computational cost. However, MPE may loose statistical reliability as the scale factor increases, because the coarse-graining procedure used in the MPE algorithm reduces the length of the time series as the scale factor grows. To overcome this drawback, we introduce the refined composite MPE (RCMPE). Through applications on both synthetic and real data, we show that RCMPE is much less dependent on the signal length than MPE. In this sense, RCMPE is more reliable than MPE. RCMPE could therefore replace MPE for short times series or at large scale factors

SUSY Ward identities for multi-gluon helicity amplitudes with massive quarks

We use supersymmetric Ward identities to relate multi-gluon helicity amplitudes involving a pair of massive quarks to amplitudes with massive scalars. This allows to use the recent results for scalar amplitudes with an arbitrary number of gluons obtained by on-shell recursion relations to obtain scattering amplitudes involving top quarks.Comment: 22 pages, references adde

Refined multiscale Hilbert-Huang spectral entropy and its application to central and peripheral cardiovascular data

Objective: Spectral entropy has been applied in variety of fields. Multiscale spectral entropy (MSSE) has also recently been proposed to take into account structures on several scales. However, MSSE has some drawbacks, such as the coarse-graining procedure performed in the time domain. In this study, we propose a new framework to compute MSSE. This framework is also adapted for nonstationary data. Methods: Our work relies on processing steps performed directly in the frequency domain. For nonstationary signals, the evolution of entropy values with scales is observed along time. Our algorithm is herein evaluated both on synthetic time series (stationary and non-stationary signals) and on data from the cardiovascular system (CVS). For this purpose, heart rate variability (from the central CVS), laser Doppler flowmetry, and laser speckle contrast data (both from the peripheral CVS) are analyzed. Results: The results show that our framework has better performances than the existing algorithms to compute MSSE, both in terms of reliability and computational cost. Moreover, it is able to reveal repetitive patterns on central and peripheral CVS signals. These patterns may be linked to physiological activities. Furthermore, from the processing of microvascular data, it is able to distinguish young from elderly subjects. Conclusion: Our framework outperforms other algorithms to compute MSSE. It also has the advantage of revealing physiological information. Significance: By showing better performances than existing algorithms to compute MSSE, our work is a new and promising way to compute an entropy measure from the spectral domain. It also has the advantage of stressing physiologically linked phenomena

Recursion relations, Helicity Amplitudes and Dimensional Regularization

Using the method of on-shell recursion relations we compute tree level amplitudes including D-dimensional scalars and fermions. These tree level amplitudes are needed for calculations of one-loop amplitudes in QCD involving external quarks and gluons.Comment: 28 pages, 6 figures, clarifications adde

A direct proof of the CSW rules

Using recursion methods similar to those of Britto, Cachazo, Feng and Witten (BCFW) a direct proof of the CSW rules for computing tree-level gluon amplitudes is given.Comment: 11 pages, uses axodraw.st

The role of betaines in alkaline extracts of Ascophyllum nodosum in the reduction of Meloidogyne javanica and M. incognita infestations of tomato plants

L'application sur les racines de plants de tomates d'un extrait alcalin de l'algue brune #Ascophyllum nodosum, disponible dans le commerce, produit une réduction significative du nombre de juvéniles de deuxième stade de #Meloidogyne javanica et #M. incognita$ pénétrant dans les racines, en comparaison avec des plants de tomates traités uniquement avec de l'eau. Le nombre d'oeufs récupérés sur les plants traités par l'extrait d'algue est également significativement plus faible. Lorsque les trois bétaïnes essentielles (bétaïne d'acide-gamma-aminobutyrique, bétaïne d'acide delta-aminovalérique, glycine bétaïne) présentes dans l'extrait d'algue sont appliquées - à des concentrations équivalent à celles de l'extrait - on observe également une réduction significative de l'infestation par les nématodes et du nombre d'oeufs récupérés. Il peut donc être conclu que les bétaïnes présentes dans l'extrait d'algue jouent un rôle important dans le processus occasionnant les effets observés. Lorsque le sol est humidifée par une application des constituants inorganiques de l'extrait, on observe également une réduction significative du nombre d'oeufs récupérés, cette réduction étant plus faible que celle produite par application de bétaïnes. (Résumé d'auteur

Harmonic assessment based adjusted current total harmonic distortion

Power systems suffer from harmonic distortion and extra ohmic losses associated with them. Moreover, all harmonic frequencies are mostly assumed to have the same effect on the system losses. However, the frequency-dependency of the resistances should be taken into account, so that the apparent power and the power factor have to considerably reflect power losses under nonsinusoidal conditions. In this paper, the difference between unweighted and weighted non-sinusoidal losses, is addressed. A new harmonic-adjusted total harmonic distortion definition is proposed for both voltage and current. Besides, a new formula that relates the proposed harmonic-adjusted total harmonic distortion and a generalised harmonic derating factor definition of the frequency dependent losses of the power transmission and distribution equipment, is derived. An optimal C-type passive filter design for harmonic mitigation and power factor correction based on the minimisation of the proposed harmonic-adjusted total harmonic distortion for a balanced nonsinusoidal system is introduced. A comparative study of the proposed filter design based on the new harmonic-adjusted definition, and a conventional filter design based on standard total harmonic distortion definition, is presented