Related papers: Four redundant axiomatics
A generalized quintessence model is presented which corresponds to a richer vacuum structure that, besides a time-dependent, slowly varying scalar field, contains a varying cosmological term. From first principles we determine a number of…
Given a real closed field $R$, we identify exactly four proper reducts of $R$ which expand the underlying (unordered) $R$-vector space structure. Towards this theorem we introduce a new notion, of strongly bounded reducts of linearly…
We provide a summary of the mathematical and computational techniques that have enabled learning reductions to effectively address a wide class of problems, and show that this approach to solving machine learning problems can be broadly…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
We consider all theories with eight supersymmetries whose reduction to three dimensions gives rise to scalars that parametrise symmetric manifolds. We conjecture that these theories are non-linear realisations of very-extended Kac-Moody…
We show tight lower bounds for the entire trade-off between space and query time for the Approximate Near Neighbor search problem. Our lower bounds hold in a restricted model of computation, which captures all hashing-based approaches. In…
In this essay, we immerse into the framework of normed division algebras as a suitable arena to accommodate the standard model of elementary particles, and we explore some applications to cosmology. Remarkably, they permit interesting…
We undertake the construction of quadratic parity-violating terms involving the curvature in the four-dimensional metric-affine gravity. We demonstrate that there are only 12 linearly independent scalars, plus an additional one that can be…
In Real Analysis, Littlewood's three principles are known as heuristics that help teach the essentials of measure theory and reveal the analogies between the concepts of topological space and continuos function on one side and those of…
We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…
We introduce the notion of scale to generalize and compare different invariants of metric spaces and their measures. Several versions of scales are introduced such as Hausdorff, packing, box, local and quantization. They moreover are…
We extend the Marsden-Weinstein-Meyer symplectic reduction theorem to the setting of multisymplectic manifolds. In this context, we investigate the dependence of the reduced space on the reduction parameters. With respect to a distinguished…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
In this second part of the paper, dedicated to theories with extra dimensions, a new physical notion about the "tensor length scale" is introduced, based on the gravitational theories with covariant and contravariant metric tensor…
The quotient shape types of normed vectorial spaces(over the same field) with respect to Banach spaces reduce to those of Banach spaces. The finite quotient shape type of normed spaces is an invariant of the (algebraic) dimension, but not…
We consider the extension of static dimensional reduction to real-time. For a scalar field theory it is shown that in the high-temperature limit this leads to an effective classical theory. Quantum corrections to the leading classical…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
We investigate the space of simplices in Euclidean Space
Here we briefly describe some topics along the lines of projective spaces and related geometric constructions connected to linear algebra, which provide fundamental examples in classical geometry and analysis.