相关论文: An Episode in The Old Mathematical Intelligencer

Some historical data and geometrical representations about Stormer and Van-der-Pol long delayed echoes.

Any empirical data can be approximated to one of Pearson distributions using the first four moments of the data (Elderton and Johnson, 1969; Pearson, 1895; Solomon and Stephens, 1978). Thus, Pearson distributions made statistical analysis…

We show that Ahmed's Integral is closely related to the fourth power of the Probability Integral

Introduction to deep neural networks and their history.

Deep Learning has attracted significant attention in recent years. Here I present a brief overview of my first Deep Learner of 1991, and its historic context, with a timeline of Deep Learning highlights.

Lecture given Friday 7 April 1995 at the Santa Fe Institute, Santa Fe, New Mexico. The lecture was videotaped; this is an edited transcript.

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

The game of Cops and Robbers is a well known game played on graphs. In this paper we consider the class of graphs of bounded diameter. We improve the strategy of cops and previously used probabilistic method which results in an improved…

This paper presents a new anytime algorithm for the marginal MAP problem in graphical models. The algorithm is described in detail, its complexity and convergence rate are studied, and relations to previous theoretical results for the…

The aim of this paper is to describe the origin, first solutions, further progress, the state of art, and a new ansatz in the treatment of a problem dating back to the 1920's, which still has not found a satisfactory solution and deserves…

Mastermind is a popular board game released in 1971, where a codemaker chooses a secret pattern of colored pegs, and a codebreaker has to guess it in several trials. After each attempt, the codebreaker gets a response from the codemaker…

The article considers strategies of coalitions that are based on intelligence information about moves of some of the other agents. The main technical result is a sound and complete logical system that describes the interplay between…

Historical map legends are critical for interpreting cartographic symbols. However, their inconsistent layouts and unstructured formats make automatic extraction challenging. Prior work focuses primarily on segmentation or general optical…

In this note, we try to trace the birth of importance sampling (IS) back to 1949. We found the classical formulation of IS in a paper from Kahn in June 1949. As for the appearance of the expression importance sampling itself, it may have…

The notion of an individual random sequence goes back to von Mises. We describe the evolution of this notion, especially the use of martingales (suggested by Ville), and the development of algorithmic information theory in 1960s and 1970s…

In this paper, we prove some refined estimate in the neck region when a sequence of harmonic maps from surfaces blow up. The new estimate allows us to see the shape of the center of the neck region. As an application, we prove an inequality…

In this paper we have investigated some old issues concerning four color map problem. We have given a general method for constructing counter-examples to Kempe's proof of the four color theorem and then show that all counterexamples can be…

In this note we fill a gap in the proof of the main theorem (Theorem 1.2) of our paper 'Surfaces in 4-manifolds', Math. Res. Letters 4 (1997), 907-914.

We show that if $n=7k/i$ with $i \in \{1,2,3\}$ then the cop number of the generalised Petersen graph $GP(n,k)$ is $4$, with some small previously-known exceptions. It was previously proved by Ball et al. (2015) that the cop number of any…

Mirror graphs were introduced by Bre\v{s}ar et al. in 2004 as an intriguing class of graphs: vertex-transitive, isometrically embeddable into hypercubes, having a strong connection with regular maps and polytope structure. In this article…