Multifractals via recurrence times ?

This letter is a comment on an article by T.C. Halsey and M.H. Jensen in Nature about using recurrence times as a reliable tool to estimate multifractal dimensions of strange attractors. Our aim is to emphasize that in the recent mathematical literature (not cited by these authors), there are positive as well as negative results about the use of such techniques. Thus one may be careful in using this tool in practical situations (experimental data).Comment: This is a very short and non-technical note written after an article published in Nature by T.C. Halsey and M.H. Jense

Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for the Poincare maps of a large class of singular hyperbolic flows. From this we deduce logarithm laws for these flows.Comment: 39 pages; 03 figures; proof of Theorem 1 corrected; many typos corrected; improvements on the statements and comments suggested by a referee. Keywords: singular flows, singular-hyperbolic attractor, exponential decay of correlations, exact dimensionality, logarithm la

Fault-Tolerant Control of a Three-Phase Permanent Magnet Synchronous Motor for Lightweight UAV Propellers via Central Point Drive

This paper deals with the development and the performance characterization of a novel Fault-Tolerant Control (FTC) aiming to the diagnosis and accommodation of electrical faults in a three-phase Permanent Magnet Synchronous Motor (PMSM) employed for the propulsion of a modern lightweight fixed-wing UAV. To implement the fault-tolerant capabilities, a four-leg inverter is used to drive the reference PMSM, so that a system reconfiguration can be applied in case of a motor phase fault or an inverter fault, by enabling the control of the central point of the three-phase connection. A crucial design point is to develop Fault-Detection and Isolation (FDI) algorithms capable of minimizing the system failure transients, which are typically characterized by high-amplitude high-frequency torque ripples. The proposed FTC is composed of two sections: in the first, a deterministic model-based FDI algorithm is used, based the evaluation of the current phasor trajectory in the Clarke’s plane; in the second, a novel technique for fault accommodation is implemented by applying a reference frame transformation to post-fault commands. The FTC effectiveness is assessed via detailed nonlinear simulation (including sensors errors, digital signal processing, mechanical transmission compliance, propeller loads and electrical faults model), by characterizing the FDI latency and the post-fault system performances when open circuit faults are injected. Compared with reports in the literature, the proposed FTC demonstrates relevant potentialities: the FDI section of the algorithm provides the smallest ratio between latency and monitoring samples per electrical period, while the accommodation section succeeds in both eliminating post-fault torque ripples and maintaining the mechanical power output with negligible efficiency degradation

Novel approach to fault-tolerant control of inter-turn short circuits in permanent magnet synchronous motors for UAV propellers

This paper deals with the development of a novel fault‐tolerant control technique aiming at the diagnosis and accommodation of inter‐turn short circuit faults in permanent magnet synchronous motors for lightweight UAV propulsion. The reference motor is driven by a four‐leg converter, which can be reconfigured in case of a phase fault by enabling the control of the central point of the motor Y‐connection. A crucial design point entails the development of fault detection and isolation (FDI) algorithms capable of minimizing the failure transients and avoiding the short circuit extension. The proposed fault‐tolerant control is composed of two sections: the first one applies a novel FDI algorithm for short circuit faults based on the trajectory tracking of the motor current phasor in the Clarke plane; the second one implements the fault accommodation, by applying a reference frame transformation technique to the post‐fault commands. The control effectiveness is assessed via nonlinear simulations by characterizing the FDI latency and the post‐fault performances. The proposed technique demonstrates excellent potentialities: the FDI algorithm simultaneously detects and isolates the considered faults, even with very limited extensions, during both stationary and unsteady operating conditions. In addition, the proposed accommodation technique is very effective in minimizing the post‐fault torque ripples

Statistical properties of Lorenz like flows, recent developments and perspectives

We comment on mathematical results about the statistical behavior of Lorenz equations an its attractor, and more generally to the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statisitcal behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated to the existence of physical measures: \emph{in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure}. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors.Comment: 40 pages; 10 figures; Keywords: sensitive dependence on initial conditions, physical measure, singular-hyperbolicity, expansiveness, robust attractor, robust chaotic flow, positive Lyapunov exponent, large deviations, hitting and recurrence times. Minor typos corrected and precise acknowledgments of financial support added. To appear in Int J of Bif and Chaos in App Sciences and Engineerin

Integrative organelle-based functional proteomics: in silico prediction of impaired functional annotations in SACS KO cell model

Autosomal recessive spastic ataxia of Charlevoix-Saguenay (ARSACS) is an inherited neurodegenerative disease characterized by early-onset spasticity in the lower limbs, axonal-demyelinating sensorimotor peripheral neuropathy, and cerebellar ataxia. Our understanding of ARSACS (genetic basis, protein function, and disease mechanisms) remains partial. The integrative use of organelle-based quantitative proteomics and whole-genome analysis proposed in the present study allowed identifying the affected disease-specific pathways, upstream regulators, and biological functions related to ARSACS, which exemplify a rationale for the development of improved early diagnostic strategies and alternative treatment options in this rare condition that currently lacks a cure. Our integrated results strengthen the evidence for disease-specific defects related to bioenergetics and protein quality control systems and reinforce the role of dysregulated cytoskeletal organization in the pathogenesis of ARSACS

Infinite ergodic theory and Non-extensive entropies

We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropie