Related papers: "A Handbook of Integer Sequences" Fifty Years Late…
A Sturmian sequence is an infinite nonperiodic string over two letters with minimal subword complexity. In two papers, the first written by Morse and Hedlund in 1940 and the second by Coven and Hedlund in 1973, a surprising correspondence…
The purpose of this memoir is to discuss two very interesting properties of integer sequences. One is the law of apparition and the other is the law of repetition. Both have been extensively studied by mathematicians such as Ward, Lucas,…
Handwritten text recognition for historical documents is an important task but it remains difficult due to a lack of sufficient training data in combination with a large variability of writing styles and degradation of historical documents.…
This paper presents combinatorial facts dealing with the number of unlabeled partially ordered sets (posets) refined by the number of arcs in the Hasse diagram (sequence A342447 in OEIS). The main result is that the differences with respect…
In 1957 Leo Moser published a problem in American Mathematical Monthly asking whether knowing the set of all pairwise sums of five numbers one could determine the original numbers. Problem was quickly generalized as "Is it always possible…
One of the central problems in additive combinatorics is to determine how large a subset of the first $N$ integers can be before it is forced to contain $k$ elements forming an arithmetic progression. Around 25 years ago, Gowers proved the…
In 1914, Kempner proved that the series 1/1 + 1/2 + ... + 1/8 + 1/10 + 1/11 + ... + 1/18 + 1/20 + 1/21 + ... where the denominators are the positive integers that do not contain the digit 9, converges to a sum less than 90. The actual sum…
Existing work on Entity Linking mostly assumes that the reference knowledge base is complete, and therefore all mentions can be linked. In practice this is hardly ever the case, as knowledge bases are incomplete and because novel concepts…
We describe the results of the computation of aliquot sequences with small starting values. In particular all sequences with starting values less than a million have been computed until either termination occurred (at 1 or a cycle), or an…
Script identification plays a vital role in applications that involve handwriting and document analysis within a multi-script and multi-lingual environment. Moreover, it exhibits a profound connection with human cognition. This paper…
The difference between two consecutive prime numbers is called the distance between the primes. We study the statistical properties of the distances and their increments (the difference between two consecutive distances) for a sequence…
In this article I present IEAD, a new interface for astronomical science databases. It is based on a powerful, yet simple, syntax designed to completely abstract the user from the structure of the underlying database. The programming…
How can an end-user provide feedback if a deployed structured prediction model generates inconsistent output, ignoring the structural complexity of human language? This is an emerging topic with recent progress in synthetic or constrained…
The complexity $f(n)$ of an integer was introduced in 1953 by Mahler & Popken: it is defined as the smallest number of $1$'s needed in conjunction with arbitrarily many +, * and parentheses to write an integer $n$ (for example, $f(6) \leq…
We report results on benchmarking Open Information Extraction (OIE) systems using RelVis, a toolkit for benchmarking Open Information Extraction systems. Our comprehensive benchmark contains three data sets from the news domain and one data…
It's hard to imagine human life in the digital and AI age without polynomials because they are everywhere but mostly invisible to ordinary people: in data trends, on computer screens, in the shapes around us, and in the very fabric of…
Indexes are models: a B-Tree-Index can be seen as a model to map a key to the position of a record within a sorted array, a Hash-Index as a model to map a key to a position of a record within an unsorted array, and a BitMap-Index as a model…
Machine learning approaches achieve high accuracy for text recognition and are therefore increasingly used for the transcription of handwritten historical sources. However, using machine learning in production requires a streamlined…
We propose a multi-scale analysis method for studying arithmetic properties of integer sets, such as primality. Our approach organizes information through a hierarchy of nested sequences, where each level enables a hierarchical expression…
In 2002, the UCR time series classification archive was first released with sixteen datasets. It gradually expanded, until 2015 when it increased in size from 45 datasets to 85 datasets. In October 2018 more datasets were added, bringing…