Nets of lines with the combinatorics of the square grid and with touching inscribed conics. (arXiv:1911.08477v1 [math.AG])

In the projective plane, we consider congruences of straight lines with the combinatorics of the square grid and with all elementary quadrilaterals possessing touching inscribed conics. The inscribed conics of two combinatorially neighbouring quadrilaterals have the same touching point on their common edge-line. We suggest that these nets are a natural projective generalisation of incircular…

Solitons in fluctuating hydrodynamics of diffusive processes. (arXiv:1911.08489v1 [cond-mat.stat-mech])

We demonstrate that fluid mechanical systems arising from large fluctuations of one-dimensional statistical processes generically exhibit solitons and nonlinear waves. We derive the explicit form of these solutions and examine their properties for the specific cases of the Kipnis-Marchioro-Presutti model (KMP) and the Symmetric Exclusion Process (SEP). We show that the two fluid systems are…

Subliminal aspects concerning the Lounesto’s classification. (arXiv:1911.08506v1 [math-ph])

In the present communication we employ a split programme applied to spinors belonging to the regular and singular sectors of the Lounesto’s classification, looking towards to unveil how it can be built or defined upon two spinors arrangement. We separate the spinors into two distinct parts and investigate to which class within the Lounesto’s classification…

Optimal Complexity and Certification of Bregman First-Order Methods. (arXiv:1911.08510v1 [math.OC])

We provide a lower bound showing that the $O(1/k)$ convergence rate of the NoLips method (a.k.a. Bregman Gradient) is optimal for the class of functions satisfying the $h$-smoothness assumption. This assumption, also known as relative smoothness, appeared in the recent developments around the Bregman Gradient method, where acceleration remained an open issue. On the way,…

Topological properties of secure wireless sensor networks under the q-composite key predistribution scheme with unreliable links. (arXiv:1911.08513v1 [cs.NI])

Security is an important issue in wireless sensor networks (WSNs), which are often deployed in hostile environments. The q-composite key predistribution scheme has been recognized as a suitable approach to secure WSNs. Although the q-composite scheme has received much attention in the literature, there is still a lack of rigorous analysis for secure WSNs operating…

Justification of the discrete nonlinear Schr\”odinger equation from a parametrically driven damped nonlinear Klein-Gordon equation and numerical comparisons. (arXiv:1911.08514v1 [nlin.PS])

We consider a damped, parametrically driven discrete nonlinear Klein-Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces the equation into a discrete nonlinear Schr\”odinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error…

The nonsmooth landscape of blind deconvolution. (arXiv:1911.08526v1 [math.OC])

The blind deconvolution problem aims to recover a rank-one matrix from a set of rank-one linear measurements. Recently, Charisopulos et al. introduced a nonconvex nonsmooth formulation that can be used, in combination with an initialization procedure, to provably solve this problem under standard statistical assumptions. In practice, however, initialization is unnecessary. As we demonstrate numerically,…

Projected Gradient Method for Decentralized Optimization over Time-Varying Networks. (arXiv:1911.08527v1 [math.OC])

Decentralized distributed optimization over time-varying graphs (networks) is nowadays a very popular branch of research in optimization theory and consensus theory. One of the motivations to consider such networks is an application to drone networks. However, the first theoretical results in this branch appeared only five years ago (Nedic, 2014). The first results about the…

Stability of logarithmic Sobolev inequalities under a noncommutative change of measure. (arXiv:1911.08533v1 [quant-ph])

We generalize Holley-Stroock’s perturbation argument from commutative to quantum Markov semigroups. As a consequence, results on (complete) modified logarithmic Sobolev inequalities and logarithmic Sobolev inequalities for self-adjoint quantum Markov process can be used to prove estimates on the exponential convergence in relative entropy of quantum Markov systems which preserve a fixed state. This leads to…