Tootfinder

I love the commitment to experimenting with input devices: a mechanical keyboard, but for toes.
https://www.reddit.com/r/ErgoMechKeyboards/comments/1m218cz/toepad_a_keyboard_for_your_feet/

Nouvelle application sur #LaForgeEdu : FlashMD est un outil libre et gratuit qui permet la création de flashcards Š imprimer ou Š utiliser en ligne.
On crée les flashcards en Markdown : un titre 2 pour l'idée Š expliquer, la suite du contenu pour l'explication. C'est très rapide ! La mise en page est calculée automatiquement.
C'est une version simplifiée de CartesMD, mais avec d'autres options, comme la possibilité de réviser en ligne les flashcards
http://flashmd.forge.apps.education.fr/

Enjoyed "We, the Fleet" by Alex T. Singer in this month's Clarkesworld
A cyborg, self-replicating probes, family and friendship
#amreading #scifi

This https://arxiv.org/abs/2409.19908 has been replaced.
link: https://scholar.google.com/scholar?q=a

Independent Sets in Hypergraphs
A theorem of Shearer states that every $n$-vertex triangle-free graph of maximum degree $d \geq 2$ contains an independent set of size at least $(d\log d - d + 1)/(d - 1)^2 \cdot n$. Ajtai, Komlós, Pintz, Spencer and Szemerédi proved that every $(r + 1)$-uniform $n$-vertex ``uncrowded'' hypergraph of maximum degree $d \geq 1$ has an independent set of size at least $c_r(\log d)^{1/r}/d^{1/r} \cdot n$ for some $c_r > 0$ depending only on $r$. Shearer asked whether his method for triangle-free …

This https://arxiv.org/abs/1811.03437 has been replaced.
link: https://scholar.google.com/scholar?q=a

Integrating Project Spatial Coordinates into Pavement Management Prioritization
To date, pavement management software products and studies on optimizing the prioritization of pavement maintenance and rehabilitation (M&R) have been mainly focused on three parameters; the pre-treatment pavement condition, the rehabilitation cost, and the available budget. Yet, the role of the candidate projects' spatial characteristics in the decision-making process has not been deeply considered. Such a limitation, predominately, allows the recommended M&R projects' schedule to involve simu…

This https://arxiv.org/abs/2111.14384 has been replaced.
link: https://scholar.google.com/scholar?q=a

Zero cycles, Mennicke symbols and $\mathrm{K}_1$-stability of certain real affine algebras
Let $R$ be a reduced real affine algebra of (Krull) dimension $d \ge 2$ such that either $R$ has no real maximal ideals, or the intersection of all real maximal ideals in $R$ has height at least one. In this article, we prove the following: (1) the $d$-th Euler class group $\text{E}^d(R)$, defined by Bhatwadekar-R.~Sridharan, is canonically isomorphic to the Levine-Weibel Chow group of zero cycles $\text{CH}_0(\text{Spec}(R))$; (2) the universal Mennicke symbol $\text{MS}_{d+1}(R)$ is canonical…

This https://arxiv.org/abs/2112.12859 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Countable, Dense, Dedekind-Complete Subset of $\mathbb{R}$ Constructed by Extending $\mathbb{Q}$ via Simultaneous Marking of Closed Intervals with Rational Endpoints
This article explores the model-dependent nature of set cardinality, emphasizing that cardinality is not absolute but varies across different axiomatic frameworks. Although Cantor's diagonal argument shows the real numbers are non-denumerable within ZF (Zermelo-Fraenkel set theory), the precise cardinality of the continuum remains unsettled and depends critically on model assumptions. For instance, under Gödel's inner-model axiom V=Ultimate L, the Continuum Hypothesis (CH) holds, whereas Marti…

This https://arxiv.org/abs/2004.09217 has been replaced.
link: https://scholar.google.com/scholar?q=a

Vanishing Chern classes for numerically flat Higgs bundles
I consider Higgs bundles satisfying a notion of ampleness that was introduce Bruzzo, Graña Otero and Hernández Ruipérez, and prove that the Chern classes of rank $r$ H-ample Higgs bundles over dimension $n$, polarized, smooth, complex, projective varieties are positive under opportune hypothesis. I extend this to non-negativeness of Chern classes of all numerically effective Higgs bundles; and use this condition to prove the vanishing of Chern classes of numerically flat Higgs bundles.

This https://arxiv.org/abs/2212.00636 has been replaced.
link: https://scholar.google.com/scholar?q=a

Newman's conjecture for the partition function modulo integers with at least two distinct prime divisors
Let $M$ be a positive integer and $p(n)$ be the number of partitions of a positive integer $n$. Newman's Conjecture asserts that for each integer $r$, there are infinitely many positive integers $n$ such that \[ p(n)\equiv r \pmod{M}. \] For a positive integer $d$, let $B_{d}$ be the set of positive integers $M$ such that the number of prime divisors of $M$ is $d$. In this paper, we prove that for each positive integer $d$, the density of the set of positive integers $M$ for which Newman's Conj…

This https://arxiv.org/abs/2210.12988 has been replaced.
link: https://scholar.google.com/scholar?q=a

Embeddings between generalized weighted Lorentz spaces
We give a new characterization of a continuous embedding between two function spaces of type $GΓ$. Such spaces are governed by functionals of type \begin{equation*} \|f\|_{GΓ(r,q;w,δ)} := \left(\int_{0}^{L} \left( \frac1{Δ(t)} \int_0^t f^*(s)^r δ(s) ds \right)^{\frac{q}{r}} w(t) dt \right)^\frac1{q}, \end{equation*} in which $f^*$ is the nonincreasing rearrangement of $f$, $L\in(0,\infty]$, $r,q \in (0, \infty)$, $w, δ$ are weights on $(0,L)$ and $Δ(t)=\int_{0}^{t}δ(s)\,ds$ fo…

This https://arxiv.org/abs/2209.05806 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Weyl tube theorem for Kähler manifolds
As sharpened in terms of Alesker's theory of valuations on manifolds, a classic theorem of Weyl asserts that the coefficients of the tube polynomial of an isometrically embedded riemannian manifold $M \hookrightarrow \mathbb R^n$ constitute a canonical finite dimensional subalgebra $\mathcal {L K}(M)$ of the algebra $\mathcal{V} (M)$ of all smooth valuations on $M$, isomorphic to the algebra of valuations on Euclidean space that are invariant under rigid motions. We construct an analogous, larg…

This https://arxiv.org/abs/2401.08063 has been replaced.
link: https://scholar.google.com/scholar?q=a

An Infinite Double Bubble Theorem
The classical double bubble theorem characterizes the minimizing partitions of $\mathbb{R}^n$ into three chambers, two of which have prescribed finite volume. In this paper we prove a variant of the double bubble theorem in which two of the chambers have infinite volume. Such a configuration is an example of a (1,2)-cluster, or a partition of $\mathbb{R}^n$ into three chambers, two of which have infinite volume and only one of which has finite volume. A $(1,2)$-cluster is locally minimizing wit…

This https://arxiv.org/abs/2109.06078 has been replaced.
link: https://scholar.google.com/scholar?q=a

BV Functions and Sets of Finite Perimeter on Configuration Spaces
This paper contributes to foundations of the geometric measure theory in the infinite dimensional setting of the configuration space over the Euclidean space $\mathbb R^n$ equipped with the Poisson measure $π$. We first provide a rigorous meaning and construction of the $m$-codimensional Poisson measure -- formally written as "$(\infty-m)$-dimensional Poisson measure" -- on the configuration space. We then show that our construction is consistent with potential analysis by establishing the abs…

"Looser privacy rules will not fix our problems."
https://mastodon.social/@ScienceScholar/114592301397747952

I don’t get a lot of deep sleep and I’ve had tinnitus for years https://mastodon.social/@ScienceScholar/114762150898062416

This https://arxiv.org/abs/2410.14073 has been replaced.
link: https://scholar.google.com/scholar?q=a

Digesting Gibbs Sampling Using R
In general, the statistical simulation approaches are referred to as the Monte Carlo methods as a whole. The broad class of the Monte Carlo methods involves the Markov chain Monte Carlo (MCMC) techniques that attract the attention of researchers from a wide variety of study fields. The main focus of this report is to provide a framework for all users who are interested in implementing the MCMC approaches in their investigations, especially the Gibbs sampling. I have tried, if possible, to elimi…

This https://arxiv.org/abs/2207.01061 has been replaced.
link: https://scholar.google.com/scholar?q=a

Computing Vanishing Ideals for Toric Codes
Motivated by applications to the theory of error-correcting codes, we give methods for computing a generating set for the ideal generated by $β$-graded polynomials vanishing on certain subsets of a simplicial complete toric variety $X$ over a finite field $\mathbb{F}_q$, where $β$ is a $d\times r$ matrix whose columns generate a subsemigroup $\mathbb{N}β$ of $\mathbb{N}^d$. We also give a method for computing the vanishing ideal of the set of $\mathbb{F}_q$-rational points of $X$. When $β=[…

This https://arxiv.org/abs/2012.13515 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Boundaries of $\varepsilon$-neighbourhoods of Planar Sets: Singularities, Global Structure, and Curvature
We study the geometry, topological properties and smoothness of the boundaries of closed $\varepsilon$-neighbourhoods $E_\varepsilon = \{x \in \mathbb{R}^2 \, : \, \textrm{dist}(x, E) \leq \varepsilon \}$ of compact planar sets $E \subset \mathbb{R}^2$. We develop a novel technique for analysing the boundary, and use this to obtain a classification of singularities (i.e.~non-smooth points) on $\partial E_\varepsilon$ into eight categories. We show that the set of singularities is either countab…

If this mechanism is indeed involved in the origin of life, then a form of life is likely to be present on innumerable habitable planets throughout the universe. Which is expected, of course, and will no-doubt be found at some point.
https://mastodon.social/@ScienceScholar/114734…

This https://arxiv.org/abs/2107.07544 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Boundaries of $\varepsilon$-neighbourhoods of Planar Sets, Part II: Global Structure and Curvature
We study the global topological structure and smoothness of the boundaries of $\varepsilon$-neighbourhoods $E_\varepsilon = \{x \in \mathbb{R}^2 \, : \, \textrm{dist}(x, E) \leq \varepsilon \}$ of planar sets $E \subset \mathbb{R}^2$. We show that for a compact set $E$ and $\varepsilon > 0$ the boundary $\partial E_\varepsilon$ can be expressed as a disjoint union of an at most countably infinite union of Jordan curves and a possibly uncountable, totally disconnected set of singularities. We al…