globally flat coordinates in which we have a constant metric g μ ν = η μ ν {\displaystyle g_{\mu \nu }=\eta _{\mu \nu }} where in space with signature (
Generalization of the Rouse model without any use of the postulates concerning the Gaussian distribution of the vector connecting the ends of segments is advanced. In the initial (in general, nonlinear) Langevin equations, self-averaging over conti...
Frequencies of $k$-mers in sequences are sometimes used as a basis for inferring phylogenetic trees without first obtaining a multiple sequence alignment. We show that a standard approach of using the squared-Euclidean distance between $k$-mer vector...
We discuss the classification of 2-solvable Frobenius Lie algebras. We prove that every 2-solvable Frobenius Lie algebra splits as a semidirect sum of an n-dimensional vector space V and an n-dimensional maximal Abelian subalgebra (MASA) of the full...
Let $V$ be a braided vector space of diagonal type. Let $\mathfrak B(V)$, $\mathfrak L^-(V)$ and $\mathfrak L(V)$ be the Nichols algebra, Nichols Lie algebra and Nichols braided Lie algebra over $V$, respectively. We show that a monomial belongs to $...
We study the LHC phenomenology of a couple of mass-degenerate heavy new gauge bosons with the quantum numbers of the Z and photon. We give a leading-order estimate of the number of events expected in Drell-Yan processes in terms of the parameters of...
In this paper, I propose a new framework for representing multidimensional incomplete preferences through zonotope-valued utilities, addressing the shortcomings of traditional scalar and vector-based models in decision theory. Traditional approaches...
The training covers introduction to Julia, vector and array operations in Julia, followed by introductory machine learning techniques and applications. The course then takes a deep dive into introducing …
We study some physical properties of black holes in Null Aether Theory (NAT)--a vector-tensor theory of gravity. We first review the black hole solutions in NAT and then derive the first law of black hole thermodynamics. The temperature of the black...
The training covers introduction to Julia, vector and array operations in Julia, followed by introductory machine learning techniques and applications. The course then takes a deep dive into introducing …
We completely characterize the finite dimensional subsets A of any separable Hilbert space for which the notion of A-hypercyclicity coincides with the notion of hypercyclicity, where an operator T on a topological vector space X is said to be A-hyper...
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Vector representations of gene co-expression in single cell RNAseq. (⭐ 36)
This note defines a flag vector for $i$-graphs. The construction applies to any finite combinatorial object that can be shelled. Two possible connections to quantum topology are mentioned. Further details appear in the author's "On quantum topology...
4 days ago · With Vector Search, you can create two types of indexes, depending on how you plan to update them with your data. You can create an index designed for batch updates, or an index …
Our main result states that whenever we have a non-Euclidean norm $\|\cdot\|$ on a two-dimensional vector space $X$, there exists some $x\neq 0$ such that for every $λ\neq 1, λ>0$, there exist $y, z\in X$ verifying that $\|y\|=λ\|x\|$, $z\neq 0$,...
We address the problem of self-supervised learning on discrete event sequences generated by real-world users. Self-supervised learning incorporates complex information from the raw data in low-dimensional fixed-length vector representations that coul...
We propose a novel convolutional method for the detection and identification of vertebrae in whole spine MRIs. This involves using a learnt vector field to group detected vertebrae corners together into individual vertebral bodies and convolutional i...
num Systems. The idea behind the condition involves solving an n n system of equations Ax = b, where x is an n 1 (\column vector") of unknowns, b is a given n 1 (the \constants" of the equation or \system …
The goal is to verify the Hodge conjecture (and some related conjectures) for certain moduli spaces. It is shown that the (generalized) Hodge conjecture holds for the projective moduli spaces of vector bundles over an abelian or K3 surface or a cur...