Classes of random walks on temporal networks with competing timescales

Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the co-existence of different timescales in the system. Here, we introduce random walks on general stochastic temporal networks allowing for lasting interactions, with up to three competing timescales. We then compare the mean resting time and stationary state of different models. We also discuss the accuracy of the mathematical analysis depending on the random walk model and the structure of the underlying network, and pay particular attention to the emergence of non-Markovian behaviour, even when all dynamical entities are governed by memoryless distributions.Comment: 16 pages, 5 figure

First principles calculation of the phonons modes in the hexagonal YMnO3\rm YMnO_3 ferroelectric and paraelectric phases

The lattice dynamics of the $\rm YMnO_3$ magneto-electric compound has been investigated using density functional calculations, both in the ferroelectric and the paraelectric phases. The coherence between the computed and experimental data is very good in the low temperature phase. Using group theory, modes continuity and our calculations we were able to show that the phonons modes observed by Raman scattering at 1200K are only compatible with the ferroelectric $P6_{3} cm$ space group, thus supporting the idea of a ferroelectric to paraelectric phase transition at higher temperature. Finally we proposed a candidate for the phonon part of the observed electro-magnon. This mode, inactive both in Raman scattering and in Infra-Red, was shown to strongly couple to the Mn-Mn magnetic interactions

The Road to Understanding the Confrontation Clause: Ohio v. Clark Makes a U-Turn

The article discusses the Confrontation Clause and summarizes the state of the law before the U.S. Supreme Court\u27s decision in the case Ohio v. Clark. Topics discussed include problems that the decision caused and how these problems affect the admissibility of statements into evidence; and ways in which use of Confrontation Clause teat can eliminate confusion related to issue

Delay induced Turing-like waves for one species reaction-diffusion model on a network

A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an external non homogenous perturbation. These are generalized Turing-like waves that materialize in a single species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time delayed differential equation. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz networks and with the inclusion of the delay

Random walk on temporal networks with lasting edges

We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time of edges activation. We first propose a comprehensive analytical and numerical treatment on directed acyclic graphs. Once cycles are allowed in the network, non-Markovian trajectories may emerge, remarkably even if the walker and the evolution of the network edges are governed by memoryless Poisson processes. We then introduce a general analytical framework to characterize such non-Markovian walks and validate our findings with numerical simulations.Comment: 18 pages, 18 figure

Eddies and interface deformations induced by optical streaming

We study flows and interface deformations produced by the scattering of a laser beam propagating through non-absorbing turbid fluids. Light scattering produces a force density resulting from the transfer of linear momentum from the laser to the scatterers. The flow induced in the direction of the beam propagation, called 'optical streaming', is also able to deform the interface separating the two liquid phases and to produce wide humps. The viscous flow taking place in these two liquid layers is solved analytically, in one of the two liquid layers with a stream function formulation, as well as numerically in both fluids using a boundary integral element method. Quantitative comparisons are shown between the numerical and analytical flow patterns. Moreover, we present predictive simulations regarding the effects of the geometry, of the scattering strength and of the viscosities, on both the flow pattern and the deformation of the interface. Finally, theoretical arguments are put forth to explain the robustness of the emergence of secondary flows in a two-layer fluid system