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Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...
How a stimulus is processed is at the very heart of all vision research. However, there is only little research about how long the processing of a stimulus lasts. One reason is that visual processing is often explicitly or implicitly thought to be feedforw ...
Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep lear ...
We consider the Vlasov–Poisson system with repulsive interactions. For initial data a small, radial, absolutely continuous perturbation of a point charge, we show that the solution is global and disperses to infinity via a modified scattering along traject ...
We consider rank-1 lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fourier space and the non-periodic cosine space and Chebyshev space, via tent ...
Recently, remarkable progress has been made in the application of machine learning (ML) techniques (e.g., neural networks) to transformer fault diagnosis. However, the diagnostic processes employed by these techniques often suffer from a lack of interpreta ...
We study the solution of the two-temperature Fokker-Planck equation and rigorously analyse its convergence towards an explicit non-equilibrium stationary measure for long time and two widely separated time scales. The exponential rates of convergence are e ...
Isogeometric analysis (IGA) was introduced to integrate methods for analysis and computer-aided design (CAD) into a unified process. High-quality parameterization of a physical domain plays a crucial role in IGA. However, obtaining high-quality parameteriz ...
Given a group Gamma, we establish a connection between the unitarisability of its uniformly bounded representations and the asymptotic behaviour of the isoperimetric constants of Cayley graphs of Gamma for increasingly large generating sets. The connection ...
Two-dimensional (2D) hexagonal lattices of Cu disks are shown to induce orientation-dependent magnonic crystal (MC) modes for propagating forward volume spin waves in a single-crystal yttrium iron garnet (YIG) film. The width and depth of the magnonic band ...