Time-Delay Identification Using Multiscale Ordinal Quantifiers

Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon.

Robust spike timing in an excitable cell with delayed feedback

The initiation and regeneration of pulsatile activity is a ubiquitous feature observed in excitable systems with delayed feedback. Here, we demonstrate this phenomenon in a real biological cell. We establish a critical role of the delay resulting from the finite propagation speed of electrical impulses in the emergence of persistent multiple-spike patterns. We predict the coexistence of a number of such patterns in a mathematical model and use a biological cell subject to dynamic clamp to confirm our predictions in a living mammalian system. Given the general nature of our mathematical model and experimental system, we believe that our results capture key hallmarks of physiological excitability that are fundamental to information processing.

Euler-Bernoulli cantilever beam bending considering the inner diffusion flows finite propagation speed

Исследуются нестационарные колебания балки Эйлера-Бернулли с учетом массопереноса. Используется модель упругой диффузии для многокомпонентных сред. Для получения решения задачи используются вариационный принцип Даламбера и метод эквивалентный граничных условий. Unsteady vibrations of the Euler-Bernoulli beam are studied taking into account mass transfer. The model of elastic diffusion for multicomponent media is used. To obtain a solution to the problem, the d’Alembert variational principle and the equivalent boundary conditions method are used.

Linear relativistic thermoelastic rod

We derive and analyze the linearized hyperbolic equations describing a relativistic heat-conducting elastic rod. We construct a decreasing energy integral for these equations, compute the associated characteristic propagation speeds and prove that the solutions decay in time by using a Fourier decomposition. For comparison purposes, we obtain analogous results for the classical system with heat waves, in which the finite propagation speed of heat is kept but the other relativistic terms are neglected and also for the usual classical system.

Some local questions for hyperbolic systems with non-regular time dependent coefficients

We investigate local properties for microlocally symmetrizable hyperbolic systems with just time dependent coefficients. Thanks to Paley–Wiener theorem, we establish finite propagation speed by showing precise estimates on the evolution of the support of the solution in terms of suitable norms of the coefficients of the operator and of the symmetrizer. From this result, local existence and uniqueness follow by quite standard methods. Our argument relies on the use of Fourier transform, and it cannot be extended to operators whose coefficients depend also on the space variables. On the other hand, it works under very mild regularity assumptions on the coefficients of the operator and of the symmetrizer.

Operational calculus and integral transforms for groups with finite propagation speed

Let

Local existence and singularities formation for isothermal relativistic radiation hydrodynamics equations

We study the Cauchy problem for multi-dimensional compressible relativistic hydrodynamics in the presence of a radiation field. First, based on the theory of quasilinear symmetric hyperbolic, we establish the local existence of smooth solutions for both non-vacuum and vacuum cases. Next, in the spirit of Sideris’ work [T. Sideris, Formation of singularities of solutions to nonlinear hyperbolic equations, Arch. Ration. Mech. Anal. 86 (1984) 369–381; T. Sideris, Formation of singularities in three-dimensional compressible fluids, Comm. Math. Phys. 101 (1985) 475–485], we show that smooth solutions blow-up in finite time if the initial data is compactly supported and large enough. Compared with the previous work, the main difficulties of the first problem lie in two aspects, we must first deal with the source terms relying on radiative quantities, and we also need to solve out the new coefficients matrices under the Lorentz transformation for vacuum case. The second difficulty arises on how to verifying that the smooth solution has finite propagation speed..