Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

Energetic Electron Pitch Angle Diffusion due to Whistler Wave during Terrestrial Storms

A concise and elegant expression of cyclotron harmonic resonant quasi-pure pitch-angle diffusion is constructed for the parallel whistler mode waves, and the quasi-linear diffusion coefficient is prescribed in terms of the whistler mode wave spectral intensity. Numerical computations are performed for the specific case of energetic electrons interacting with a band of frequency of whistler mode turbulence at L ≈ 3. It is found that the quasi-pure pitch-angle diffusion driven by the whistler mode scatters energetic electrons from the larger pitch-angles into the loss cone, and causes pitch-angle distribution to evolve from the pancake-shaped before the terrestrial storms to the flat-top during the main phase. This probably accounts for the quasi-isotropic pitch-angle distribution observed by the combined release and radiation effects satellite spacecraft at L ≈ 3.

An Extended Model for Interaction Between Left-hand Superluminous Waves and Magnetospheric Electrons

The left-hand superluminous electromagnetic waves, L-O mode and L-X mode, can be excited and observed in the auroral cavity of the Earth during the magnetic storms. The two modes can propagate into outer radiation zone and encounter enhanced resonant interactions with the trapped energetic electrons over a wide range of magnetosphere. A current first-order resonant model is extended to evaluate the stochastic acceleration of electrons by the L-O mode and L-X mode at the higher-order resonance. Similar to the first-order resonance, L-O mode can produce significant acceleration of electrons at the higher harmonic resonances over a wide range of wave normal angles and spatial regions. However, the higher harmonic resonance＇s contribution for significant electron acceleration by L-X mode is less than that of the first order resonance, with the requirement of higher minimum energies, e.g., -1 MeV in the outer radiation belt. This indicates that L-O mode may be one of the efficient mechanisms for the stochastic acceleration of electrons within the outer radiation zone.

Stochastic motion of the untrapped particle in electrostatic mode

The stochastic energy diffusion of the untrapped particle in the electrostatic mode is investigated analytically. We find that the equilibrium electrostatic field of periodical structure plays the same role as the usual focusing magnetic field to lead the test particle to stochastic motion. The resonance overlapping criterion for the random state is given, and also the Fokker-Planek-Kohnogorov approach to diffusion is considered for our system.

An Accelerated Method for Simulating Population Dynamics

We present an accelerated method for stochastically simulating the dynamics of heterogeneous cell populations.The algorithm combines a Monte Carlo approach for simulating the biochemical kinetics in single cells with a constant-number Monte Carlo method for simulating the reproductive fitness and the statistical characteristics of growing cell populations.To benchmark accuracy and performance,we compare simulation results with those generated from a previously validated population dynamics algorithm.The comparison demonstrates that the accelerated method accurately simulates population dynamics with significant reductions in runtime under commonly invoked steady-state and symmetric cell division assumptions.Considering the increasing complexity of cell population models,the method is an important addition to the arsenal of existing algorithms for simulating cellular and population dynamics that enables efficient,coarse-grained exploration of parameter space.