Related papers: On Model Theory of Valued Vector Spaces
The correspondence of single-field cosmological models based on Einstein gravity to modern observational data is considered. A method is proposed to determine possible types of dynamics based on extreme values of the scalar field. It is…
We develop a field theoretical approach based on the temporary basis description as a tool to investigate the transmission properties of a time-driven quantum device. It employs a perturbative scheme for the calculation of the transmission…
This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector budles, giving a detailed comparison with the moduli scheme obtained via…
Machine learning enables powerful cosmological inference but typically requires many high-fidelity simulations covering many cosmological models. Transfer learning offers a way to reduce the simulation cost by reusing knowledge across…
We improve results of Belair, Macintyre, and Scanlon on valued fields with a valuation preserving automorphism by weakening their assumptions on the residue difference field. In the equicharacteristic zero case we also determine the induced…
Latent space model plays a crucial role in network analysis, and accurate estimation of latent variables is essential for downstream tasks such as link prediction. However, the large number of parameters to be estimated presents a…
Reasoning systems with too simple a model of the world and human intent are unable to consider potential negative side effects of their actions and modify their plans to avoid them (e.g., avoiding potential errors). However, hand-encoding…
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
Following the work of Semyon Alesker in the scalar valued case and of Thomas Wannerer in the vector valued case, the dimensions of the spaces of continuous translation invariant and unitary equivariant tensor valuations are computed. In…
We present bases for certain spaces of meromorphic vector-valued rational-weight mock modular forms constructed using Rademacher sums.
We introduce and study in detail the notion of compatibility between valuations and orderings in real hyperfields. We investigate their relation with valuations and orderings induced on factor and residue hyperfields. Much of the theory…
We define Hecke operators on vector valued modular forms transforming with the Weil representation associated to a discriminant form. We describe the properties of the corresponding algebra of Hecke operators and study the action on modular…
A relationship between real, complex, and quaternionic vector fields on spheres is given by using a relationship between the corresponding standard inner products. The number of linearly independent complex vector fields on the standard…
We give an overview of the implementation of the soft-bootstrap method applied to the landscape of theories where the Special Galileon couples to a massless vector particle. We also describe the corresponding traditional Lagrangian approach…
We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucidate the Lie theory relating these objects, i.e., their…
We show how to obtain a ``heavy'' meson effective lagrangian for the case where the number of heavy particles is not conserved. We apply the method in a simple example at tree level and perform then the reduction for the case of vector…
The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case…
In this paper I shall consider various possible scalar-vector-tensor field theories which might be used to describe the Universe. After imposing numerous constraints of a physical and mathematical nature on the theories under consideration,…
A vector composition of a vector $\mathbf{\ell}$ is a matrix $\mathbf{A}$ whose rows sum to $\mathbf{\ell}$. We define a weighted vector composition as a vector composition in which the column values of $\mathbf{A}$ may appear in different…
Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They…