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The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions…

This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…

In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on…

Hyperspectral images provide much more information than conventional imaging techniques, allowing a precise identification of the materials in the observed scene, but because of the limited spatial resolution, the observations are usually…

Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies…

Material functionality can be strongly determined by structure extending only over nanoscale distances. The pair distribution function presents an opportunity to shift structural studies beyond idealized crystal models and investigate…

If supersymmetry exists at the electroweak scale, then it should be discovered at the LHC. Determining masses, of supersymmetric particles however, is more difficult. In this paper, methods are discussed to determine combinations of masses…

Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…

This document offers a concise introduction to the mathematical theory and practical application of the Hausdorff Measure and Dimension. The primary objective is to clarify and rigorously detail the two most common methods used for…

We consider random geometric graphs on the plane characterized by a non-uniform density of vertices. In particular, we introduce a graph model where $n$ vertices are independently distributed in the unit disc with positions, in polar…

Heterogeneous materials consisting of different phases are ideally suited to achieve a broad spectrum of desirable bulk physical properties by combining the best features of the constituents through the strategic spatial arrangement of the…

We study the propagation of waves in a set of absorbing subwavelength scatterers positioned on a stealth hyperuniform point pattern. We show that spatial correlations in the disorder substantially enhance absorption compared to a fully…

We consider Uncertainty Principles which take into account the role of gravity and the possible existence of extra spatial dimensions. Explicit expressions for such Generalized Uncertainty Principles in 4+n dimensions are given and their…

[First paragraph] In a recent paper Yamada et al. propose the novel concept of "pinched flow fractionation" (PFF) for the continuous size separation and analysis of particles in microfabricated lab-on-a-chip devices. In their description of…

Many theories describing physics beyond the Standard Model rely on a large separation of scales. Large scale separation arises in models with mass-split flavors if the system is conformal in the ultraviolet but chirally broken in the…

A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension $d\in\mathbb{N}$. It is a regularised and inertial version of the…

This work concentrates on numerical simulations of Photonic Crystal structures using basis-expansion methods, with a main focus on simulating disorder. The plane-wave and guided-mode expansions are outlined as tools to compute the Bloch…

While the light transmission of photonic crystals is characterized by the photonic band gap, the one of disordered photonic structures is typified by a multiplicity of transmission depths. The total transmission over a range of wavelengths…

In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational…

We propose a high-precision numerical quadrature framework based on local Fourier extension (LFE) approximations. The method constructs, on each subinterval, a truncated-SVD stabilized local Fourier continuation of the integrand on an…