Related papers: The OEIS: A Fingerprint File for Mathematics
Infinite sequences are of tremendous theoretical and practical importance, and in the Information Age sequences of 0s and 1s are of particular interest. Over the past century, the field of symbolic dynamics has developed to study sequences…
An oriented hypergraph is an oriented incidence structure that extends the concept of a signed graph. We introduce hypergraphic structures and techniques central to the extension of the circuit classification of signed graphs to oriented…
Let $\beta$ be any permutation on $n$ symbols and let $c(k, \beta)$ be the number of permutations that $k$-commute with $\beta$. The cycle type of a permutation $\beta$ is a vector $(c_1, \dots, c_n)$ such that $\beta$ has exactly $c_i$…
To every integer monic polynomial of degree m can be associated m integer sequences having interesting properties to the roots of the polynomial. These sequences can be used to find the real roots of any integer monic polynomial by using…
This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college…
High-quality ordinary differential equation (ODE) solver libraries have a long history, going back to the 1970s. Over the past several years we have implemented, on top of the PETSc linear and nonlinear solver package, a new…
A software for managing simulation jobs and results, named "OACIS", is presented. It controls a large number of simulation jobs executed in various remote servers, keeps these results in an organized way, and manages the analyses on these…
The integration of Artificial Intelligence (AI) into automation systems has the potential to enhance efficiency and to address currently unsolved existing technical challenges. However, the industry-wide adoption of AI is hindered by the…
Higher-order interactions (HOIs) are ubiquitous in real-world complex systems and applications. Investigation of deep learning for HOIs, thus, has become a valuable agenda for the data mining and machine learning communities. As networks of…
We propose a semester-long Bayesian statistics course for undergraduate students with calculus and probability background. We cultivate students' Bayesian thinking with Bayesian methods applied to real data problems. We leverage modern…
Open Information Extraction (OIE) aims to extract factual relational tuples from open-domain sentences. Downstream tasks use the extracted OIE tuples as facts, without examining the certainty of these facts. However, uncertainty/speculation…
Indicators of Compromise (IOCs) are artifacts observed on a network or in an operating system that can be utilized to indicate a computer intrusion and detect cyber-attacks in an early stage. Thus, they exert an important role in the field…
An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of $+1$ or $-1$. We define the adjacency, incidence and Laplacian matrices of an oriented hypergraph and study each of them. We extend several matrix…
An elementary description of the Eightfold Way for the non-specialist is presented. This article, for publication in {\it Macmillan Encylopedia of Physics, Supplement: Elementary Particle Physics}, is being submitted to the Archive for…
Bayesian statistics has gained great momentum since the computational developments of the 1990s. Gradually, advances in Bayesian methodology and software have made Bayesian techniques much more accessible to applied statisticians and, in…
Recognition of handwritten mathematical expressions allows to transfer scientific notes into their digital form. It facilitates the sharing, searching, and preservation of scientific information. We introduce MathWriting, the largest online…
In this paper we describe a procedure for calculating the number of regular octahedrons that have vertices with coordinates in the set {0,1,...,n}. As a result, we introduce a new sequence in ``The Online Encyclopedia of Integer Sequences"…
The paper is an introduction to intuitionistic mathematics.
We explore the possibility of using machine learning to identify interesting mathematical structures by using certain quantities that serve as fingerprints. In particular, we extract features from integer sequences using two empirical laws:…
Expanded lecture notes. Preliminary version, comments are welcome.