Related papers: A Formal Algebra for OLAP
With the rapid development of IT operations, it has become increasingly crucial to efficiently manage and analyze large volumes of data for practical applications. The techniques of Natural Language Processing (NLP) have shown remarkable…
Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications. We present a…
This paper uses typed linear algebra (LA) to represent data and perform analytical querying in a single, unified framework. The typed approach offers strong type checking (as in modern programming languages) and a diagrammatic way of…
Large Language Models (LLMs) are increasingly used in empirical software engineering (ESE) to automate or assist annotation tasks such as labeling commits, issues, and qualitative artifacts. Yet the reliability and reproducibility of such…
In this paper, we present our ongoing work and initial results on the formal specification and verification of MiniMaple (a substantial subset of Maple with slight extensions) programs. The main goal of our work is to find behavioral errors…
In recent years there has been increased use of machine learning (ML) techniques within mathematics, including symbolic computation where it may be applied safely to optimise or select algorithms. This paper explores whether using…
Understanding micro-architectural behavior is profound in efficiently using hardware resources. Recent work has shown that, despite being aggressively optimized for modern hardware, in-memory online transaction processing (OLTP) systems…
In this paper, we use the language of operads to study open dynamical systems. More specifically, we study the algebraic nature of assembling complex dynamical systems from an interconnection of simpler ones. The syntactic architecture of…
We continue the investigation of analytic spaces from the perspective of computable structure theory. We show that if $p \geq 1$ is a computable real, and if $\Omega$ is a nonzero, non-atomic, and separable measure space, then every…
We define computational atoms named "actions" equipped primarily with three operations: reduction, collection, and inspection. We show how actions can be used for decision-making algorithms from simple axioms. We describe the encodings of…
This research addresses a new tool for data analysis known as Topological Data Analysis TDA It underlies an area of Mathematics known as Combinatorial Algebra or more recently Algebraic Topology which through making strong use of…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
Today, huge amount of data is available on the web. Now there is a need to convert that data in knowledge which can be useful for different purposes. This paper depicts the use of data mining process, OLAP with the combination of multi…
The heterogeneity of data poses a great challenge when data from different sources is to be merged for one application. Solutions for this are offered, for example, by ontology-based data management (OBDM). A challenge of OBDM is the…
A new model of quantum computing has recently been proposed which, in analogy with a classical lambda-calculus, exploits quantum processes which operate on other quantum processes. One such quantum meta-operator takes N unitary…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
We show how the basic operations of quantum computing can be expressed and manipulated in a clear and concise fashion using a multiparticle version of geometric (aka Clifford) algebra. This algebra encompasses the product operator formalism…
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…
We introduce a symmetric operad whose algebras are the Operator Product Expansion (OPE) Algebras of quantum fields. There is a natural classical limit for the algebras over this operad and they are commutative associative algebras with…
Large Language Models (LLMs) show promise for automated code optimization but struggle without performance context. This work introduces Opal, a modular framework that connects performance analytics insights with the vast body of published…