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Linearization around unstable travelling waves in excitable systems can be used to approximate strength-extent curves in the problem of initiation of excitation waves for a family of spatially confined perturbations to the rest state. This…
Spatiotemporal control of excitable media is of paramount importance in the development of new applications, ranging from biology to physics. To this end we identify and describe a qualitative property of excitable media that enables us to…
We present an extension of the canonical coupled mode theory of electromagnetic waves to the case of pulses and spatio-temporal perturbations in complex media. Unlike previous attempts to derive such a model, our approach involves no…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…
We analyze the effects of spatially extended periodic forcing on the dynamics of one-dimensional excitation waves. Entrainment of unstable primary waves has been studied numerically for different amplitudes and frequencies of additional…
We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly…
In this work we demonstrate the efficacy of neural networks in the characterization of dispersive media. We also develop a neural network to make predictions for input probe pulses which propagate through a nonlinear dispersive medium,…
This work develops a quantitative homogenization theory for random suspensions of rigid particles in a steady Stokes flow, and completes recent qualitative results. More precisely, we establish a large-scale regularity theory for this…
We study linear stability of planar travelling waves for a scalar reaction-diffusion equation with non-linear anisotropic diffusion. The mathematical model is derived from the full thermo-hydrodynamical model describing the process of…
The paper formulates the concept of persistence of excitation for discrete-time linear switched systems, and provides sufficient conditions for an input signal to be persistently exciting. Persistence of excitation is formulated as a…
A quantitative description of pulses and wave trains in the spatially discrete Hodgkin-Huxley model for myelinated nerves is given. Predictions of the shape and speed of the waves and the thresholds for propagation failure are obtained. Our…
The impulse response of a flame to acoustic velocity perturbations is a key quantity for predicting thermoacoustic stability, but its identification from sparse, noisy observations requires solving an ill-posed inverse convolution problem.…
We study linear perturbations of classically stable Q-balls in theories admitting analytic solutions. Although the corresponding boundary value problem is non-Hermitian, the analysis of perturbations can also be performed analytically in…
The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…
An analytical prediction is established of how an isolated many-body quantum system relaxes towards its thermal long-time limit under the action of a time-independent perturbation, but still remaining sufficiently close to a reference case…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
This work deals with the problem of simultaneous regulation and model parameter estimation in adaptive model predictive control. We propose an adaptive model predictive control and conditions which guarantee a persistently exciting closed…
The extremely regular, periodic radio emission from millisecond pulsars makes them useful tools for studying neutron star astrophysics, general relativity, and low-frequency gravitational waves. These studies require that the observed pulse…
Within the current uncertainties in the treatment of the coupling between pulsation and convection, limiting amplitude, nonlinear, convective models appear the only viable approach for providing theoretical predictions about the intrinsic…