Related papers: The On-Line Encyclopedia of Integer Sequences
Deep Learning and Machine Learning based models have become extremely popular in text processing and information retrieval. However, the non-linear structures present inside the networks make these models largely inscrutable. A significant…
In this paper we construct families of bit sequences using combinatorial methods. Each sequence is derived by con- verting a collection of numbers encoding certain combinatorial nu- merics from objects exhibiting symmetry in various…
Knowledge graphs (KGs) such as DBpedia, Freebase, YAGO, Wikidata, and NELL were constructed to store large-scale, real-world facts as (subject, predicate, object) triples -- that can also be modeled as a graph, where a node (a subject or an…
Open Information Extraction (OpenIE) is the task of extracting (subject, predicate, object) triples from natural language sentences. Current OpenIE systems extract all triple slots independently. In contrast, we explore the hypothesis that…
We introduce a class of stochastic integer sequences. In these sequences, every element is a sum of two previous elements, at least one of which is chosen randomly. The interplay between randomness and memory underlying these sequences…
Beame et al. [ITCS 2018 & TALG 2021] introduced and used the Bipartite Independent Set (BIS) and Independent Set (IS) oracle access to an unknown, simple, unweighted and undirected graph and solved the edge estimation problem. The…
The palindromic tree (a.k.a. eertree) is a data structure that provides access to all palindromic substrings of a string. In this paper, we propose a dynamic version of eertree, called double-ended eertree, which supports online operations…
Operators on probability distributions can be expressed as operators on the associated moment sequences, and so correspond to operators on integer sequences. Thus, there is an opportunity to apply each theory to the other. Moreover,…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense…
\emph{Uncertain Graph} (also known as \emph{Probabilistic Graph}) is a generic model to represent many real\mbox{-}world networks from social to biological. In recent times analysis and mining of uncertain graphs have drawn significant…
Novel dynamic programming algorithms to count the set $D(n)$ of zero-free degree sequences of length $n$, the set $D_c(n)$ of degree sequences of connected graphs on $n$ vertices and the set $D_b(n)$ of degree sequences of biconnected…
Integrated organic inference (IOI) is discussed in a concise and informal way with the aim that the reader is given the gist of what this approach to statistical inference is about as well as given pointers to further reading.
Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…
Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only…
We characterize exactly the lengths of binary circular words containing no squares other than 00, 11, and 0101. Key words: combinatorics on words, circular words, necklaces, square-free words, non-repetitive sequences
Recent breakthroughs in natural language processing and computer vision, driven by efficient pre-training on large datasets, have enabled foundation models to excel on a wide range of tasks. However, this potential has not yet been fully…
Time series with non-uniform intervals occur in many applications, and are difficult to model using standard recurrent neural networks (RNNs). We generalize RNNs to have continuous-time hidden dynamics defined by ordinary differential…
Recently, the one dimensional model of $N$ spins with $S=\frac{1}{2}$ on a circle, interacting with an exchange that falls off with the inverse square of the separation: $H_{\rm ISE} =\sum_{i\neq j} \frac{1}{[\frac{N}{\pi}…
The comma sequence (1, 12, 35, 94, ...) is the lexicographically earliest sequence such that the difference of consecutive terms equals the concatenation of the digits on either side of the comma separating them. The behavior of a…