DALiuGE: A Graph Execution Framework for Harnessing the Astronomical Data Deluge

The Data Activated Liu Graph Engine - DALiuGE - is an execution framework for processing large astronomical datasets at a scale required by the Square Kilometre Array Phase 1 (SKA1). It includes an interface for expressing complex data reduction pipelines consisting of both data sets and algorithmic components and an implementation run-time to execute such pipelines on distributed resources. By mapping the logical view of a pipeline to its physical realisation, DALiuGE separates the concerns of multiple stakeholders, allowing them to collectively optimise large-scale data processing solutions in a coherent manner. The execution in DALiuGE is data-activated, where each individual data item autonomously triggers the processing on itself. Such decentralisation also makes the execution framework very scalable and flexible, supporting pipeline sizes ranging from less than ten tasks running on a laptop to tens of millions of concurrent tasks on the second fastest supercomputer in the world. DALiuGE has been used in production for reducing interferometry data sets from the Karl E. Jansky Very Large Array and the Mingantu Ultrawide Spectral Radioheliograph; and is being developed as the execution framework prototype for the Science Data Processor (SDP) consortium of the Square Kilometre Array (SKA) telescope. This paper presents a technical overview of DALiuGE and discusses case studies from the CHILES and MUSER projects that use DALiuGE to execute production pipelines. In a companion paper, we provide in-depth analysis of DALiuGE's scalability to very large numbers of tasks on two supercomputing facilities.Comment: 31 pages, 12 figures, currently under review by Astronomy and Computin

Cohomological Hall algebras, vertex algebras and instantons

We define an action of the (double of) Cohomological Hall algebra of Kontsevich and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We identify this action with the one of the affine Yangian of $\mathfrak{gl}(1)$. Based on that we derive the vertex algebra at the corner $\mathcal{W}_{r_1,r_2,r_3}$ of Gaiotto and Rapcak. We conjecture that our approach works for a big class of Calabi-Yau categories, including those associated with toric Calabi-Yau $3$-folds.Comment: 72 pages, 4 figures, v2: Added some clarifications and updated references 73 pages, 4 figures, v3: Corrected typos and clarified some minor point

The quotient in preorder theories

Seeking the largest solution to an expression of the form Ax 64 B is a common task in several domains of engineering and computer science. This largest solution is commonly called quotient. Across domains, the meanings of the binary operation and the preorder are quite different, yet the syntax for computing the largest solution is remarkably similar. This paper is about finding a common framework to reason about quotients. We only assume we operate on a preorder endowed with an abstract monotonic multiplication and an involution. We provide a condition, called admissibility, which guarantees the existence of the quotient, and which yields its closed form. We call preordered heaps those structures satisfying the admissibility condition. We show that many existing theories in computer science are preordered heaps, and we are thus able to derive a quotient for them, subsuming existing solutions when available in the literature. We introduce the concept of sieved heaps to deal with structures which are given over multiple domains of definition. We show that sieved heaps also have well-defined quotients

The C++0x "Concepts" Effort

C++0x is the working title for the revision of the ISO standard of the C++ programming language that was originally planned for release in 2009 but that was delayed to 2011. The largest language extension in C++0x was "concepts", that is, a collection of features for constraining template parameters. In September of 2008, the C++ standards committee voted the concepts extension into C++0x, but then in July of 2009, the committee voted the concepts extension back out of C++0x. This article is my account of the technical challenges and debates within the "concepts" effort in the years 2003 to 2009. To provide some background, the article also describes the design space for constrained parametric polymorphism, or what is colloquially know as constrained generics. While this article is meant to be generally accessible, the writing is aimed toward readers with background in functional programming and programming language theory. This article grew out of a lecture at the Spring School on Generic and Indexed Programming at the University of Oxford, March 2010

The Quotient in Preorder Theories

Seeking the largest solution to an expression of the form A x <= B is a common task in several domains of engineering and computer science. This largest solution is commonly called quotient. Across domains, the meanings of the binary operation and the preorder are quite different, yet the syntax for computing the largest solution is remarkably similar. This paper is about finding a common framework to reason about quotients. We only assume we operate on a preorder endowed with an abstract monotonic multiplication and an involution. We provide a condition, called admissibility, which guarantees the existence of the quotient, and which yields its closed form. We call preordered heaps those structures satisfying the admissibility condition. We show that many existing theories in computer science are preordered heaps, and we are thus able to derive a quotient for them, subsuming existing solutions when available in the literature. We introduce the concept of sieved heaps to deal with structures which are given over multiple domains of definition. We show that sieved heaps also have well-defined quotients.Comment: In Proceedings GandALF 2020, arXiv:2009.0936

On Some Quadratic Algebras I 12\frac{1}{2}: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials

We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations. One can find more details about the content of present paper in Extended Abstract.Comment: Dedicated to the memory of Alain Lascoux (1944-2013). Preprint RIMS-1817, 172 page