Related papers: Martin Gardner's Mistake
The sudden appearance of modern machine learning (ML) phenomena like double descent and benign overfitting may leave many classically trained statisticians feeling uneasy -- these phenomena appear to go against the very core of statistical…
We define outliers as a set of observations which contradicts the proposed mathematical (statistical) model and we discuss the frequently observed types of the outliers. Further we explore what changes in the model have to be made in order…
Recently, the covariant formulation of the geometric bifurcation theory, developed in a previous paper, has been applied to two elementary problems: the study of limit cycles of dynamical systems and the second part of Hilbert's sixteenth…
The Oberwolfach problem, posed by Ringel in 1967, asks for a decomposition of $K_{2n+1}$ into edge-disjoint copies of a given $2$-factor. We show that this can be achieved for all large $n$. We actually prove a significantly more general…
We present an analysis of a coin-tossing problem posed by Daniel Litt which has generated some popular interest. We demonstrate a recursive identity which leads to relatively simple formulas for the excess number of wins for one player over…
The very early dismissal of Schwarzschild's original solution and manifold, and the rise, under Schwarzschild's name, of the inequivalent solution and manifold found instead by Hilbert, are scrutinised and commented upon, in the light of…
More than 30 years ago, Shiloach published an algorithm to solve the minimum linear arrangement problem for undirected trees. Here we fix a small error in the original version of the algorithm and discuss its effect on subsequent…
Providing explanations about how machine learning algorithms work and/or make particular predictions is one of the main tools that can be used to improve their trusworthiness, fairness and robustness. Among the most intuitive type of…
There has been growing interest in generalization performance of large multilayer neural networks that can be trained to achieve zero training error, while generalizing well on test data. This regime is known as 'second descent' and it…
In the seminal book M\'echanique analitique, Lagrange, 1788, the notion of a Lagrange multiplier was first introduced in order to study a smooth minimization problem subject to equality constraints. The idea is that, under some regularity…
We review some recent work on removing hidden confounding and causal regularization from a unified viewpoint. We describe how simple and user-friendly techniques improve stability, replicability and distributional robustness in…
We re-address the problem of construction of new infinite-dimensional completely integrable systems on the basis of known ones, and we reveal a working mechanism for such transitions. By splitting the problem's solution in two steps, we…
Crowdsourcing has emerged as an effective platform for labeling large amounts of data in a cost- and time-efficient manner. Most previous work has focused on designing an efficient algorithm to recover only the ground-truth labels of the…
In this article, we study the Piltz divisor problem, which is sometimes called the generalized Dirichlet divisor problem, over number fields. We establish an identity akin to Vorono\"i's formula concerning the error term in the Dirichlet…
In this article, the issue of choice cuts made to a rectangular region are considered and explored. Results show that this problem is not trivial. Outcomes for teaching and learning are considered.
This note corrects an erroneous article by M.W. Evans on his GCUFT theory which he took over in his GCUFT book. Due to Evans' bad habit of suppressing seemingly unimportant indices type match errors occur that cannot be removed. In addition…
We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that is…
The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix $C$. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of $p$-dimensional…
Kane and Mertz's 2012 AMS Notices article "Debunking Myths about Gender and Mathematics Performance" claims to have debunked the greater male variability hypothesis with respect to mathematics abilities. The logical and statistical…
In the 1930's, Tarski introduced his plank problem at a time when the field Discrete Geometry was about to born. It is quite remarkable that Tarski's question and its variants continue to generate interest in the geometric and analytic…