Dynamical systems theory for music dynamics

We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\it temporal dynamics} in music. (i) Phase space portraits are constructed from the time series wherefrom the dimensionality is evaluated as a measure of the {\pit global} dynamics of each piece. (ii) Spectral analysis of the time series yields power spectra ($\sim f^{-\nu}$) close to {\pit red noise} ($\nu \sim 2$) in the low frequency range. (iii) We define an information entropy which provides a measure of the {\pit local} dynamics in the musical piece; the entropy can be interpreted as an evaluation of the degree of {\it complexity} in the music, but there is no evidence of an analytical relation between local and global dynamics. These findings are based on computations performed on eighty sequences sampled in the music literature from the 18th to the 20th century.Comment: To appear in CHAOS. Figures and Tables (not included) can be obtained from [email protected]

Modelling performance in a Balanced Scorecard : findings from a case study

Cet article s'intéresse à la mise en place de l'approche dite du "Balanced Scorecards" dans des unités opérationnelles plutôt qu'au niveau d'une direction générale. Il s'appuie sur une étude de cas. On propose de traiter les questions relatives à la coordination, à la fixation des objectifs et au contrôle en s'appuyant sur une méthodologie originale pour construire le modèle d'interaction entre les différentes entités de l'organisation. Cette méthodologie fait une part importante à l'apprentissage organisationnel permettant ainsi une compréhension mutuelle des degrés de liberté individuels et une meilleure observation réciproque. Cette approche "horizontale" est mieux adaptée à ce type de contexte que l'approche "verticale" plus traditionnelle du BCS.Pilotage;Tableaux de bord;Incitations;Apprentissage organisationnel

Complex resonance frequencies of a finite, circular radiating duct with an infinite flange

Radiation by solid or fluid bodies can be characterized by resonance modes. They are complex, as well as resonance frequencies, because of the energy loss due to radiation. For ducts, they can be computed from the knowledge of the radiation impedance matrix. For the case of a flanged duct of finite length radiating on one side in an infinite medium, the expression of this matrix was given by Zorumski, using a decomposition in duct modes. In order to calculate the resonance frequencies, the formulation used in Zorumski's theory must be modified as it is not valid for complex frequencies. The analytical development of the Green's function in free space used by Zorumski depends on the integrals of Bessel functions which become divergent for complex frequencies. This paper proposes first a development of the Green's function which is valid for all frequencies. Results are applied to the calculation of the complex resonance frequencies of a flanged duct, by using a formulation of the internal pressure based upon cascade impedance matrices. Several series of resonance modes are found, each series being shown to be related to a dominant duct mode. Influence of higher order duct modes and the results for several fluid densities is presented and discussed

Wavelet analysis of the multivariate fractional Brownian motion

The work developed in the paper concerns the multivariate fractional Brownian motion (mfBm) viewed through the lens of the wavelet transform. After recalling some basic properties on the mfBm, we calculate the correlation structure of its wavelet transform. We particularly study the asymptotic behavior of the correlation, showing that if the analyzing wavelet has a sufficient number of null first order moments, the decomposition eliminates any possible long-range (inter)dependence. The cross-spectral density is also considered in a second part. Its existence is proved and its evaluation is performed using a von Bahr-Essen like representation of the function \sign(t) |t|^\alpha. The behavior of the cross-spectral density of the wavelet field at the zero frequency is also developed and confirms the results provided by the asymptotic analysis of the correlation

Statistical identification of geometric parameters for high speed train catenary

Pantograph/catenary interaction is known to be strongly dependent on the static geometry of the catenary, this research thus seeks to build a statistical model of this geometry. Sensitivity analyses provide a selection of relevant parameters affecting the geometry. After correction for the dynamic nature of the measurement, provide a database of measurements. One then seeks to solve the statistical inverse problem using the maximum entropy principle and the maximum likelihood method. Two methods of multivariate density estimations are presented, the Gaussian kernel density estimation method and the Gaussian parametric method. The results provide statistical information on the significant parameters and show that the messenger wire tension of the catenary hides sources of variability that are not yet taken into account in the model