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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...
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,
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...
A spread code is a set of vector spaces of a fixed dimension over a finite field Fq with certain properties used for random network coding. It can be constructed in different ways which lead to different decoding algorithms. In this work we present a...
We will prove that for piecewise smooth and concave domains Korn's first inequality holds for vector fields satisfying homogeneous normal or tangential boundary conditions with explicit Korn constant square root of 2....
Given a dataset of individuals each described by a covariate vector, a treatment, and an observed outcome on the treatment, the goal of the individual treatment effect (ITE) estimation task is to predict outcome changes resulting from a change in tre...
Dynamically Interactive Visualization (DIVI) is a novel approach for orchestrating interactions within and across static visualizations. DIVI deconstructs Scalable Vector Graphics charts at runtime to infer content and coordinate user input, decoupli...
Python machine learning applications in image processing, recommender system, matrix completion, netflix problem and algorithm implementations including Co-clustering, Funk SVD, SVD++, Non-negative Matrix Factorization, Koren Neighborhood Model, Koren Integrat…
Coordinate systems are defined on general metric spaces with the purpose of generalizing vector fields on a manifold. Conversion formulae are available between metric and Cartesian coordinates on a Hilbert space. Nagumo's Invariance Theorem is invo...
We study theoretically the shapes of a dividing epithelial monolayer of cells lying on top of an elastic stroma. The negative tension created by cell division provokes a buckling instability at a finite wave vector leading to the formation of periodi...
Use the "Paint collection" feature and change the color of the whole collection or do it icon by icon. Download your collections in the code format compatible with all browsers, and use icons on your …
Use the "Paint collection" feature and change the color of the whole collection or do it icon by icon. Download your collections in the code format compatible with all browsers, and use icons on your …