This paper explores some applications of a two-moment inequality for the integral of the $r$-th power of a function, where $0 < r< 1$. The first contribution is an upper bound on the Rényi entropy of a random vector in terms of the two different mom...
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an even sma...
This paper addresses the question of when projections of a high-dimensional random vector are approximately Gaussian. This problem has been studied previously in the context of high-dimensional data analysis, where the focus is on low-dimensional pro...
For a hyperplane arrangement in a real vector space, the coefficients of its Poincaré polynomial have many interpretations. An interesting one is provided by the Varchenko-Gel'fand ring, which is the ring of functions from the chambers of the arrang...
We are interested in computing a simple eigenpair $(λ,{\bf x})$ of a large non-Hermitian matrix $A$, by a general harmonic Rayleigh-Ritz projection method. Given a search subspace $\mathcal{K}$ and a target point $τ$, we focus on the convergence of...
For a given subspace, the Rayleigh-Ritz method projects the large quadratic eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar to the Rayleigh-Ritz method for the linear eigenvalue problem, the Rayleigh-Ritz method defines...
For an arbitrary self-adjoint operator $B$ in a Hilbert space $H$, we present direct and inverse theorems establishing the relationship between the degree of smoothness of a vector $x \in H$ with respect to the operator $B$, the rate of convergence...
A simple tool to extract motion vectors from h264 encoded videos. (⭐ 122)
Brain fiber tracts are widely used in studying brain diseases, which may lead to a better understanding of how disease affects the brain. The segmentation of brain fiber tracts assumed enormous importance in disease analysis. In this paper, we propos...
This paper proves a linear algebra result that has to do with the geometry of "widgets". For us a widget is a collection of n pairs of points in a vector space. (The pairs represent the different possible spin states of a particle.) We investigate li...
A Mall bundle on a Hopf manifold H is a holomorphic vector bundle whose pullback to the universal cover of H is trivial. We define resonant and non-resonant Mall bundles, generalizing the notion of the resonance in ODE, and prove that a non-resonant...
A geometric version of the Poincaré Lemma is established for the topological vector space of differential chains. In particular, every differential k-cycle with compact support in a contractible open subset U of a smooth n-manifold M is the boundary...
Ticks are important vectors of emerging zoonotic diseases. While adults of many tick species parasitize mammals, immature ticks are often found on wild birds. In the tropics, difficulties in species-level identification of immature ticks hinder studi...
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...
Gather/scatter is a type of memory addressing that at once collects (gathers) from, or stores (scatters) data to, multiple arbitrary memory indices. Examples
Debating over conflicting issues is a necessary first step towards resolving conflicts. However, intrinsic perspectives of an arguer are difficult to overcome by persuasive argumentation skills. Proceeding from a debate to a deliberative process, whe...
A plotter is a machine that produces vector graphics drawings. Plotters draw lines on paper using a pen, or in some applications, use a knife to cut a
?️?Create, Customize and Talk to your AI Character/Companion in Realtime (All in One Codebase!). Have a natural seamless conversation with AI everywhere (mobile, web and terminal) using LLM OpenAI GPT3.5/4, Anthropic Claude2, Chroma Vector DB, Whisper Speech2T…
MicroCanvas is a 2D Graphics Engine built for ESP32 to make portable GUI, Video Games, Vector Graphics for any display. You can add support for any display in port layer. Contributions are always welcome :) (⭐ 56)
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