相关论文: Martin Gardner's Mistake

We provide details of the error Gabor Ellmann found in 2004 in a heuristic argument of Guy and Kelly on this problem. This led to a correction of their conjectured upper bound for the no-three-in-line problem. However, details of the issue…

In this paper, I will demonstrate a new perspective on the Two Envelope Problem. I hope to show with convincing clarity how the paradox results from an inherent problem pertaining to the interpretation of Bayesian probability. Specifically,…

One can notice that quite often difference between so-called "standard students" and "gifted" ones is not because that first are less smart, but they have different "orientation", they consider subject as a collections of rules which should…

Credit allocation in the mainstream bibliometrics is fundamentally flawed and the popular indicators have been misleading science for decades. Originally a simple technical mistake has become an integral part of our culture and is very…

It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a…

The multi-answer phenomenon, where a question may have multiple answers scattered in the document, can be well handled by humans but is challenging enough for machine reading comprehension (MRC) systems. Despite recent progress in…

O. Einstein (2008) proved Bollob\'as-type theorems on intersecting families of ordered sets of finite sets and subspaces. Unfortunately, we report that the proof of a theorem on ordered sets of subspaces had a mistake. We prove two weaker…

The notion of concept drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time; as a consequence machine learning models may become inaccurate and need adjustment. While there do exist…

For general memoryless systems, the typical information theoretic solution - when exists - has a "single-letter" form. This reflects the fact that optimum performance can be approached by a random code (or a random binning scheme),…

Classification is one of the most important tasks of machine learning. Although the most well studied model is the two-class problem, in many scenarios there is the opportunity to label critical items for manual revision, instead of trying…

The problem of the malicious ma\^{i}tre d' is introduced and solved by Peter Winkler in his book Mathematical Puzzles: A Connoisseur's Collection [1]. This problem is about a ma\^{i}tre d' seating diners around a table, trying to maximize…

A recent Comment by W. T. Kranz is shown to be plagued by a serious mathematical error which makes its conclusions invalid.

By creating a new method, the author proved the well-known world's baffling problems Goldbach conjecture, twin primes conjecture, the Proposition (C) and the Proposition $n^2+1$.

The many-normal-means problem is a classic example that motivates the development of many important inferential procedures in the history of statistics. In this short note, we consider a further special case of the problem, which involves…

This is a work in two parts devoted to solutions of the so-called {\em four Landau's problems} in Number Theory, listed by Edmund Landau at the 1912 International Congress of Mathematics. In Part I the {\em Goldbach's conjecture} is proved.…

We consider the common-knowledge paradox raised by Halpern and Moses: common knowledge is necessary for agreement and coordination, but common knowledge is unattainable in the real world because of temporal imprecision. We discuss two…

We consider mixed model of traffic flow distribution in large networks (BMW model, 1954 & Stable Dynamic model, 1999). We build dual problem and consider primal-dual mirror descent method for the dual problem. There are two ways to recover…

The notion of concept drift refers to the phenomenon that the distribution generating the observed data changes over time. If drift is present, machine learning models can become inaccurate and need adjustment. While there do exist methods…

We present a variation of the proof in the first author's "Mob families and mad families" of Con(b<a), which in particular removes some of the obstacles to generalising the argument to uncountable cardinals.

In this article, I focus on the resiliency of the P=?NP problem. The main point to deal with is the change of the underlying logic from first to second-order logic. In this manner, after developing the initial steps of this change, I can…