Related papers: Rainbow Thresholds
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the…
Fix $k\ge 11$ and a rainbow $k$-clique $R$. We prove that the inducibility of $R$ is $k!/(k^k-k)$. An extremal construction is a balanced recursive blow-up of $R$. This answers a question posed by Huang, that is a generalization of an old…
The locating rainbow connection number of a graph is defined as the minimum number of colors required to color vertices such that every two vertices there exists a rainbow vertex path and every vertex has a distinct rainbow code. This…
The rainbow arborescence conjecture posits that if the arcs of a directed graph with $n$ vertices are colored by $n-1$ colors such that each color class forms a spanning arborescence, then there is a spanning arborescence that contains…
We obtain some new inequalities of Chebyshev Type.
This study provides a summary of the theory which enables the analysis of extreme values, i.e., of measurements acquired from the observation of extraordinary/rare physical phenomena. The formalism is developed in a transparent way,…
We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that…
We suggest a new color distance based on two observations. First, perceptual color differences were designed to be used to compare very similar colors. They do not capture human perception for medium and large color differences well.…
We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential…
We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…
In this paper, new upper and lower bounds for the Trapezoid inequality of absolutely continuous functions are obtained. Applications to some special means are provided as well.
An exact r-coloring of a set $S$ is a surjective function $c:S \rightarrow \{1, 2, \ldots,r\}$. A rainbow solution to an equation over $S$ is a solution such that all components are a different color. We prove that every 3-coloring of…
Language models famously improve under a smooth scaling law, but some specific capabilities exhibit sudden breakthroughs in performance. Advocates of "emergence" view these capabilities as unlocked at a specific scale, but others attribute…
More precise unification predictions require going beyond the lowest order, including 2-loop running of the couplings and a correct treatment of threshold effects. Here we revised two different approaches to deal with light thresholds,…
We introduce a novel approach to finite sample robustness that avoids the pessimism of traditional breakdown analyses. We define the threshold breakdown point, the smallest contamination fraction needed to induce a prescribed deviation, and…
We apply a framework for the description of random tilings without height representation, which was proposed recently, to the special case of quasicrystalline random tilings. Several important examples are discussed, thereby demonstrating…
It is shown that the recent determination of the various proton charge extensions is compatible with Standard Model expectations.
We improve the previuosly known bound for some vertex Folkman numbers.
In 2017, Ron Aharoni made the following conjecture about rainbow cycles in edge-coloured graphs: If $G$ is an $n$-vertex graph whose edges are coloured with $n$ colours and each colour class has size at least $r$, then $G$ contains a…