In differential geometry, a field of mathematics, a Courant algebroid is a vector bundle together with an inner product and a compatible bracket more
We introduce the Courant algebroid lift, a new construction that takes a Courant algebroid together with a vector bundle connection and produces, when the connection is flat in the image of the anchor, a Courant algebroid. In general, this lift produ...
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...
We investigate the large scale anomalies in the angular distribution of the cosmic microwave background radiation as measured by WMAP using several tests. These tests, based on the multipole vector expansion, measure correlations between the phases...
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...
A deep matching model library for recommendations & advertising. It's easy to train models and to export representation vectors which can be used for ANN search. (⭐ 2413)
We study implications for the apparent alignment of the spin axes, proper-motions, and polarization vectors of the Crab and Vela pulsars. The spin axes are deduced from recent Chandra X-ray Observatory images that reveal jets and nebular structure...
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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...