Bessel Functions in Mass Action. Modeling of Memories and Remembrances

Data from experimental observations of a class of neurological processes (Freeman K-sets) present functional distribution reproducing Bessel function behavior. We model such processes with couples of damped/amplified oscillators which provide time dependent representation of Bessel equation. The root loci of poles and zeros conform to solutions of K-sets. Some light is shed on the problem of filling the gap between the cellular level dynamics and the brain functional activity. Breakdown of time-reversal symmetry is related with the cortex thermodynamic features. This provides a possible mechanism to deduce lifetime of recorded memory.Comment: 16 pages, 9 figures, Physics Letters A, 2015 in pres

A Variational Perspective on Accelerated Methods in Optimization

Accelerated gradient methods play a central role in optimization, achieving optimal rates in many settings. While many generalizations and extensions of Nesterov's original acceleration method have been proposed, it is not yet clear what is the natural scope of the acceleration concept. In this paper, we study accelerated methods from a continuous-time perspective. We show that there is a Lagrangian functional that we call the \emph{Bregman Lagrangian} which generates a large class of accelerated methods in continuous time, including (but not limited to) accelerated gradient descent, its non-Euclidean extension, and accelerated higher-order gradient methods. We show that the continuous-time limit of all of these methods correspond to traveling the same curve in spacetime at different speeds. From this perspective, Nesterov's technique and many of its generalizations can be viewed as a systematic way to go from the continuous-time curves generated by the Bregman Lagrangian to a family of discrete-time accelerated algorithms.Comment: 38 pages. Subsumes an earlier working draft arXiv:1509.0361

Instabilities in tensorial nonlocal gravity

We discuss the cosmological implications of nonlocal modifications of general relativity containing tensorial structures. Assuming the presence of standard radiation- and matter-dominated eras, we show that, except in very particular cases, the nonlocal terms contribute a rapidly growing energy density. These models therefore generically do not have a stable cosmological evolution.Comment: 10 pages, 2 figures. v2: version published in PR

Viscous damping of r-modes: Large amplitude saturation

We analyze the viscous damping of r-mode oscillations of compact stars, taking into account non-linear viscous effects in the large-amplitude regime. The qualitatively different cases of hadronic stars, strange quark stars, and hybrid stars are studied. We calculate the viscous damping times of r-modes, obtaining numerical results and also general approximate analytic expressions that explicitly exhibit the dependence on the parameters that are relevant for a future spindown evolution calculation. The strongly enhanced damping of large amplitude oscillations leads to damping times that are considerably lower than those obtained when the amplitude dependence of the viscosity is neglected. Consequently, large-amplitude viscous damping competes with the gravitational instability at all physical frequencies and could stop the r-mode growth in case this is not done before by non-linear hydrodynamic mechanisms.Comment: 18 pages, 17 figures, changed convention for the r-mode amplitude, version to be published in PR