相关论文: The On-Line Encyclopedia of Integer Sequences
We consider sigma-words, which are words used by Evdokimov in the construction of the sigma-sequence. We then find the number of occurrences of certain patterns and subwords in these words.
In the paper we present a description of complex systems in terms of self-organization processes of prime integer relations. A prime integer relation is an indivisible element made up of integers as the basic constituents following a single…
Permutations that avoid given patterns have been studied in great depth for their connections to other fields of mathematics, computer science, and biology. From a combinatorial perspective, permutation patterns have served as a unifying…
The sequence A000975 in OEIS can be defined by $A_1=1$, $A_{n+1}=2A_n$ if $n$ is odd, and $A_{n+1}=2A_n+1$ if $n$ is even. This sequence satisfies other recurrence relations, admits some closed formulas, and is known to enumerate several…
Most modern Information Extraction (IE) systems are implemented as sequential taggers and only model local dependencies. Non-local and non-sequential context is, however, a valuable source of information to improve predictions. In this…
PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. It includes a versatile formula macro system and supports the creation of documents that intersperse macro definitions, reasoner invocations and…
In the following pages we discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata. We have divided our paper into seven parts which are more or less self-contained. Needless…
We present an approach for recursively splitting and rephrasing complex English sentences into a novel semantic hierarchy of simplified sentences, with each of them presenting a more regular structure that may facilitate a wide variety of…
We arrange the orders in an algebraic number field in a tree. This tree can be used to enumerate all orders of bounded index in the maximal order as well as the orders over some given order.
We generalize the notion of a de Bruijn sequence to a "multi de Bruijn sequence": a cyclic or linear sequence that contains every k-mer over an alphabet of size q exactly m times. For example, over the binary alphabet {0,1}, the cyclic…
The universe is a vast heterogeneous network of interconnected entities that continuously generate and exchange information through various forms of interactions, some of which are yet to be discovered. Internet of Everything (IoE)…
In the field of ontology matching, the most systematic evaluation of matching systems is established by the Ontology Alignment Evaluation Initiative (OAEI), which is an annual campaign for evaluating ontology matching systems organized by…
We describe the design of Comlex Syntax, a computational lexicon providing detailed syntactic information for approximately 38,000 English headwords. We consider the types of errors which arise in creating such a lexicon, and how such…
The age of information (AoI) has been studied actively in recent years as a performance measure for systems that require real-time performance, such as remote monitoring systems via communication networks. The theoretical analysis of the…
Several explanation methods such as Integrated Gradients (IG) can be characterised as path-based methods, as they rely on a straight line between the data and an uninformative baseline. However, when applied to language models, these…
Longest Increasing Subsequence (LIS) is a fundamental statistic of a sequence, and has been studied for decades. While the LIS of a sequence of length $n$ can be computed exactly in time $O(n\log n)$, the complexity of estimating the…
This paper presents the first publicly available treebank of Odia, a morphologically rich low resource Indian language. The treebank contains approx. 1082 tokens (100 sentences) in Odia selected from "Samantar", the largest available…
This note provides very simple, efficient algorithms for computing the number of distinct longest common subsequences of two input strings and for computing the number of LCS embeddings.
Open Information Extraction (OpenIE) aims to extract structured relational tuples (subject, relation, object) from sentences and plays critical roles for many downstream NLP applications. Existing solutions perform extraction at sentence…
In this paper we introduce the concept of completeness of sets. We study this property on the set of integers. We examine how this property is preserved as we carry out various operations compatible with sets. We also introduce the problem…