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Ensemble modeling has been widely used to solve complex problems as it helps to improve overall performance and generalization. In this paper, we propose a novel TemporalAugmenter approach based on ensemble modeling for augmenting the…
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…
Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons…
The diffusion equation is extended by including spatial-temporal memory in such a manner that the conservation of the concentration is maintained. The additional memory term gives rise to the formation of non-trivial stationary solutions.…
We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
We consider the electrons of a molecule in the adiabatic time-dependent density functional theory approximation. We establish the well-posedness of the time evolution and its linear response close to a non-degenerate ground state, and prove…
We study both analytically and numerically the effects of including refractory periods in the Hopfield model for associative memory. These periods are introduced in the dynamics of the network as thresholds that depend on the state of the…
We propose a description of nonequilibrium systems via a simple protocol that combines exchange-correlation potentials from density functional theory with self-energies of many-body perturbation theory. The approach, aimed to avoid double…
Post-exponential decay of the probability density of a quantum particle leaving a trap can be reproduced accurately, except for interference oscillations at the transition to the post-exponential regime, by means of an ensemble of classical…
How do neuronal populations encode time-dependent stimuli in their population firing rate? To address this question, I consider the quasi-renewal equation and the event-based expansion, two theoretical approximations proposed recently, and…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
We present a novel approach within the functional renormalization group framework for computing critical exponents that characterize the time evolution of out-of-equilibrium many-body systems. Our approach permits access to quantities…
We apply the time-dependent current-density functional theory to the study of the relaxation of a closed many-electron system evolving from an non-equilibrium initial state. We show that the self-consistent unitary time evolution generated…
Failure times of a machinery cannot always be assumed independent and identically distributed, e.g. if after reparations the machinery is not restored to a same-as-new condition. Framed within the renewal processes approach, a…
We study the possibility of accommodating both early and late-time tensions using a novel reinforcement learning technique. By applying this technique, we aim to optimize the evolution of the Hubble parameter from recombination to the…
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…
We derive a Markovian master equation that models the evolution of systems subject to driving and control fields. Our approach combines time rescaling and weak-coupling limits for the system-environment interaction with a secular…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one…