We prove a global version of the so-called div-curl-lemma, a crucial result for compensated compactness and in homogenization theory, for mixed tangential and normal boundary conditions in bounded weak Lipschitz domains in 3D and weak Lipschitz inter...
Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors. This thesis...
The success of Bayesian inference with MCMC depends critically on Markov chains rapidly reaching the posterior distribution. Despite the plentitude of inferential theory for posteriors in Bayesian non-parametrics, convergence properties of MCMC algor...
Quivers, gauge theories and singular geometries are of great interest in both mathematics and physics. In this note, we collect a few open questions which have arisen in various recent works at the intersection between gauge theories, representation...
Sadly, our esteemed colleague and friend Ning Cai passed away on 25th May, 2023. In his memory, Ingo Althöfer, Holger Boche, Christian Deppe, Jens Stoye, Ulrich Tamm, Andreas Winter, and Raymond Yeung have organized the "Workshop on Information Theo...
Let $G$ be a 1-connected, almost-simple Lie group over a local field and $\mathcal{S}$ a subsemigroup of $G$ with non-empty interior. The action of the regular hyperbolic elements in the interior of $\mathcal{S}$ on the flag manifold $G/P$ and on t...
Chapter 13: SOC Systems in Astrophysics --- Content list: 13.1 Theory -- 13.1.1 The Sacle-Free Probability Theorem - 13.1.2 The Fractal-Diffusive Spatio-Temporal Relationship - 13.1.3 Size Distributions of Astrophysical Observables - 13.1.4 Scaling L...
Equivocation and ambiguity in public speech are well-studied discourse phenomena, especially in political science and analysis of political interviews. Inspired by the well-grounded theory on equivocation, we aim to resolve the closely related proble...
We study the join-semilattice of constructibility real degrees in the side-by-side Sacks model, the model of set theory obtained by forcing with a countable-support product of infinitely many Sacks forcings over the constructible universe. In particu...
We investigate the destroying of charged and rotating black holes in Einstein-Maxwell-(dilaton) theory. We show that a test particle with some appropriate properties in the black hole background can turn the black hole into a naked singularity. In th...
A forward model is presented to an inverse scattering problem that arises in the application of reflective Fourier ptychographic microscopy. The model allows us to determine the 3D distributions of refractive index for weakly scattering semi-transpar...
An outstanding challenge with the Integrated Information Theory of Consciousness (IIT) is to find a way of rapidly and accurately calculating integrated information from neural data. A number of measures of integrated information based on time series...
Round-based DAGs enable high-performance Byzantine fault-tolerant consensus, yet their technical advantages remain underutilized due to their short history. While research on consensus protocols is active in both academia and industry, many studies o...
We have studied numerically the Lee-Yang singularities of the four dimensional Ising model at criticality, which is believed to be in the same universality class as the $φ_4^4$ scalar field theory. We have focused in the numerical characterization o...
Despite the extraordinary successes the two great bastions of $20^{th}$ century science (Quantum Theory and General Relativity) are troubled with serious conceptual and mathematical difficulties. As a result, further growth of fundamental science i...
In his 1918 paper 'A General Form of Integral', Percy John Daniell developed a theory of integration capable of dealing with functions on arbitrary sets. Daniell's method differs from the measure-theoretic notion of integration. Linear functionals ov...
In this note we show that a mutation theory of species with potential can be defined so that a certain class of skew-symmetrizable integer matrices have a species realization admitting a non-degenerate potential. This gives a partial affirmative answ...
Bus systems involve complex bus-bus and bus-passengers interactions. We study the problem of assigning buses to bus stops to minimise the average waiting time of passengers, W. An analytical theory for two specific cases of interactions is formulated...
We show that Shipley's "detection functor" for symmetric spectra generalizes to motivic symmetric spectra. As an application, we construct motivic strict ring spectra representing morphic cohomology, semi-topological $K$-theory, and semi-topological...
This paper is part of a series of three articles with the objective of investigating a stratified version of the homotopy hypothesis in terms of semi-model structures that interact well with classical examples of stratified spaces, such as Whitney st...