相关论文: Martin Gardner's Mistake

It is sometimes claimed that the twin "paradox" requires general relativity for a resolution. This paper presents a simple, exact resolution using only special relativity and the equivalence principle. Two earlier approximate solutions are…

In this short article, we present a solution to one of the probability puzzles that Daniel Litt, a mathematician at the University of Toronto, posted on his X account earlier this year. The main goal of this note is to show how some of the…

In this paper we present a heuristic method to provide individual explanations for those elements in a dataset (data points) which are wrongly predicted by a given classifier. Since the general case is too difficult, in the present work we…

We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any concept, the so-called…

In 1926, Jarn\'ik introduced the problem of drawing a convex $n$-gon with vertices having integer coordinates. He constructed such a drawing in the grid $[1,c\cdot n^{3/2}]^2$ for some constant $c>0$, and showed that this grid size is…

We correct a 1957 combinatorial enumeration by the linguist J. Greenberg. The desired count, the Bell number B(25), supported using his Mass Comparison method for language classification. In 1987, he used this method to classify indigenous…

A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…

In this article we establish certain variants of the Inverse Cluster Size problem. We introduce the notion of primitive extensions and establish the Primitive variant of the problem. Precisely, we prove the existence of primitive extensions…

Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…

In this paper we consider the two-armed bandit problem, which often naturally appears per se or as a subproblem in some multi-armed generalizations, and serves as a starting point for introducing additional problem features. The…

The occurrence of Simpson's paradox (SP) in $2\times 2$ contingency tables has been well studied. The present work comprehensively revisits this problem using a combination of philosophical reflections, causal considerations, and…

Throughout the whole year of 1874, C. Jordan and L. Kronecker were quarrelling over two theorems. On the one hand, Jordan had stated in 1870 a canonical form theorem for substitutions of linear groups; on the other hand, Karl Weierstrass…

We provide a list of (mainly unsolved) problems in ordered and orderable groups. These were originally compiled 10 years ago by the last two authors. New problems have been added to the list. Progress on some of these is noted and…

Missing data is a common problem in medical research, and is commonly addressed using multiple imputation. Although traditional imputation methods allow for valid statistical inference when data are missing at random (MAR), their…

Many studies on the cost-sensitive learning assumed that a unique cost matrix is known for a problem. However, this assumption may not hold for many real-world problems. For example, a classifier might need to be applied in several…

DY Gao solely or together with some of his collaborators applied his Canonical duality theory (CDT) for solving a class of unconstrained optimization problems, getting the so-called "triality theorems". Unfortunately, the "double-min…

Given an observed random variable, consider the problem of recovering its distribution among a family of candidate ones. The two-point inequality, Fano's lemma and more recently an inequality due to Venkataramanan and Johnson (2018) allow…

The Locker Problem is frequently used in introducing some topics in elementary number theory like divisors and multiples. It appears in many curricula ranging from elementary, secondary and up to tertiary level. In this paper, I will…

During the course of verifying the results of Ramanujan on hypergeometric series, Berndt in his notebooks, Part II mentioned corrected forms of two of the Ramanujan's results. The aim of this short research note is to point out that one of…

These lecture notes are meant to accompany two lectures given at the CDM 2016 conference, about the Kadison-Singer Problem. They are meant to complement the survey by the same authors (along with Spielman) which appeared at the 2014 ICM. In…