An important operation in generalized complex geometry is the Courant bracket which extends the Lie bracket that acts only on vectors to a pair given by a vector and a p-form. We explore the possibility of promoting the elements of the Courant brac...
We introduce canonical weight normalization for convolutional neural networks. Inspired by the canonical tensor decomposition, we express the weight tensors in so-called canonical networks as scaled sums of outer vector products. In particular, we tr...
We prove concentration inequalities for $f\left( X\right) $ about its median, where $X$ is a random vector in $\mathbb{R}^n$ with independent heavy tailed coordinates of Weibull or power type, and $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a locally Li...
This paper proposes a novel class of block quasi-Newton methods for convex optimization which we call symmetric rank-$k$ (SR-$k$) methods. Each iteration of SR-$k$ incorporates the curvature information with~$k$ Hessian-vector products achieved from...
A vector graphics application for structured SVG editing, available on all major desktop platforms and on web. Currently in late alpha. (⭐ 2314)
We study the Grain Boundary (GB) migration based on the underlying disconnection structure and mechanism. Disconnections are line defects that lie solely within a GB and are characterized by both a Burgers vector and a step height, as set by the GB b...
I'm in Linear Algebra right now and we're mostly just working with vector spaces, but they're introducing us to the basic concepts of fields and groups in preparation taking for Abstract Algebra la...
In this bachelor thesis, we show how four different machine learning methods (Long Short-Term Memory, Random Forest, Support Vector Machine Regression, and k-Nearest Neighbor) perform compared to already successfully applied trading strategies such a...
It is well known that for Gaussian channels, a nearest neighbor decoding rule, which seeks the minimum Euclidean distance between a codeword and the received channel output vector, is the maximum likelihood solution and hence capacity-achieving. Near...
We derive a vector generalization of the square root embedding-based curvature-corrected Cramér--Rao bound (CRB) previously considered by the same author in \cite{srk} with scalar parameters. A \emph{directional} curvature correction is established...
We elevate the field theoretical similarities between Maxwell and Weyl vector fields into a full local scale/gauge invariant Weyl/Maxwell mutual sourcing theory. In its preliminary form, and exclusively in four dimensions, the associated Lagrangian i...
A compatible associative algebra is a vector space equipped with two associative multiplication structures that interact in a certain natural way. This article presents the classification of these algebras with dimension less than four, as well as th...
Open-source Large Language Models enable projects such as NASA SciX (i.e., NASA ADS) to think out of the box and try alternative approaches for information retrieval and data augmentation, while respecting data copyright and users' privacy. However,...
An infinite integer matrix A is called image partition regular if, whenever the natural numbers are finitely coloured, there is an integer vector x such that Ax is monochromatic. Given an image partition regular matrix A, can we also insist that each...
A 3D almost-Riemannian manifold is a generalized Riemannian manifold defined locally by 3 vector fields that play the role of an orthonormal frame, but could become collinear on some set $\Zz$ called the singular set. Under the Hormander condition, a...
Understanding mind-brain-environment relations is one of the key topics in psychology. Kurt Lewin, inspired by theoretical physics, tried to establish topological and vector psychology analyzing patterns of interaction between the individual and her/...
Iris recognition systems transform an iris image into a feature vector. The seminal pipeline segments an image into iris and non-iris pixels, normalizes this region into a fixed-dimension rectangle, and extracts features which are stored and called a...
In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators,
Fork of Duane Merrill Merge-based Parallel Sparse Matrix-Vector Multiplication Artifact (⭐ 6)
We discuss a conjecture concerning the enumeration of nonsingular matrices over a finite field that are block companion and whose order is the maximum possible in the corresponding general linear group. A special case is proved using some recent resu...