In this PhD manuscript, we explore optimisation phenomena which occur in complex neural networks through the lens of 2-layer diagonal linear networks. This rudimentary architecture, which consists of a two layer feedforward linear network with a diagonal ...
We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...
Let k be a field of positive characteristic. Building on the work of the second named author, we define a new class of k-algebras, called diagonally F-regular algebras, for which the so-called Uniform. Symbolic Topology Property (USTP) holds effectively. W ...
Diffractive optical elements (DOEs) which consist of microstructure surface relief permit the generation of the spatial distribution of light beams by using a single element. Due to their compact size, design flexibility, and mass productivity, they are us ...
We conducted atomic-scale scanning tunneling microscopy of a graphene nanosheet on graphite. In addition to a rhombus lattice representing the (root 3x root 3)R30 degrees superstructure, we resolved another quadrangle lattice similar to a rectangle in the ...
We study the behaviour of extremal eigenvalues of the Dirichlet biharmonic operator over rectangles with a given fixed area. We begin by proving that the principal eigenvalue is minimal for a rectangle for which the ratio between the longest and the shorte ...
In many countries of moderate to high seismicity, reinforced concrete (RC) core walls are used as lateral bracing systems in mid- to high-rise buildings where they typically accommodate lift shafts or stair cases. Unlike planar walls which provide horizont ...
We investigate polariton-polariton interactions in a semiconductor microcavity through two-dimensional Fourier transform (2DFT) spectroscopy. We observe, in addition to the lower-lower and the upper-upper polariton self-interactions, a lower-upper cross in ...
