Motivated by the work of Colin de Verdière and Saint-Raymond on spectral theory for zeroth-order pseudodifferential operators tori, we consider viscosity limits in which operators, P, are replaced P + iν Δ, ν > 0. By adapting Helffer–Sjöstrand scattering resonances, show that, a complex neighbourhood continuous spectrum, eigenvalues Δ have as goes to In simplified setting this justifies claims ...

We propose and analyze a randomized zeroth-order optimization method based on approximating the exact gradient by finite differences computed in set of orthogonal random directions that changes with each iteration. A number previously proposed methods are recovered as special cases including spherical smoothing, coordinate descent, well discretized descent. Our main contribution is proving conv...

The paper establishes some new bounds for Randic and GA indices.

Let Tn denote the set of all unrooted and unlabeled trees with n vertices, and (i, j) a double-star. By assuming that every tree of Tn is equally likely, we show that the limiting distribution of the number of occurrences of the double-star (i, j) in Tn is normal. Based on this result, we obtain the asymptotic value of Randić index for trees. Fajtlowicz conjectured that for any connected graph ...

Most student modelling systems seek to develop a model of the internal operation of the cognitive system. In contrast, Input-Output Agent Modelling (IOAM) models an agent in terms of relationships between the inputs and outputs of the cognitive system. Previous IOAM systems have demonstrated high predictive accuracy in the domain of elementary subtraction. These systems use zeroth-order inducti...

Saddle-point problems have recently gained increased attention from the machine learning community, mainly due to applications in training Generative Adversarial Networks using stochastic gradients. At same time, some only a zeroth-order oracle is available. In this paper, we propose several algorithms solve smooth (strongly) convex-concave saddle-point oracles and estimate their convergence ra...

A prism grating using polymer stabilized liquid crystal was fabricated and its diffraction characteristics evaluated. Such a prism grating exhibits not only a periodic grating structure but also a prism-like gradient refractive index within each grating period. As a result, the diffraction behavior is asymmetric. The first order exhibits high diffraction efficiency while the zeroth order has a ...