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The SQL group-by operator plays an important role in summarizing and aggregating large datasets in a data analytic stack.While the standard group-by operator, which is based on equality, is useful in several applications, allowing…

Data analysis applications typically aggregate data across many dimensions looking for anomalies or unusual patterns. The SQL aggregate functions and the GROUP BY operator produce zero-dimensional or one-dimensional aggregates. Applications…

The execution logs that are used for process mining in practice are often obtained by querying an operational database and storing the result in a flat file. Consequently, the data processing power of the database system cannot be used…

Industry-grade database systems are expected to produce the same result if the same query is repeatedly run on the same input. However, the numerous sources of non-determinism in modern systems make reproducible results difficult to…

Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equations. The main idea behind existing SBP operators is that the…

Summation-by-parts (SBP) operators allow us to systematically develop energy-stable and high-order accurate numerical methods for time-dependent differential equations. Until recently, the main idea behind existing SBP operators was that…

As graph representations of data emerge in multiple domains, data analysts need to be able to intelligently select among a magnitude of different data graphs based on the effects different graph operators have on them. Exhaustive execution…

In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…

In this paper, we motivated the need for relational database systems to support subset query processing. We defined new operators in relational algebra, and new constructs in SQL for expressing subset queries. We also illustrated the…

The goal of this paper is to provide a strong integration between constraint modelling and relational DBMSs. To this end we propose extensions of standard query languages such as relational algebra and SQL, by adding constraint modelling…

Many applications rely on solving time-dependent partial differential equations (PDEs) that include second derivatives. Summation-by-parts (SBP) operators are crucial for developing stable, high-order accurate numerical methodologies for…

Aggregate computation in relational databases has long been done using the standard unary aggregation and binary join operators. These implement the classical model of computing joins between relations two at a time, materializing the…

We address a fundamental question concerning spatio-temporal database systems: ``What are exactly spatio-temporal queries?'' We define spatio-temporal queries to be computable mappings that are also generic, meaning that the result of a…

Consider a general machine learning setting where the output is a set of labels or sequences. This output set is unordered and its size varies with the input. Whereas multi-label classification methods seem a natural first resort, they are…

Recent advances in graph databases (GDBs) have been driving interest in large-scale analytics, yet current systems fail to support higher-order (HO) interactions beyond first-order (one-hop) relations, which are crucial for tasks such as…

Quite much recent studies has been attracted to the operated algebra since it unifies various notions such as the differential algebra and the Rota-Baxter algebra. An $\Omega$-operated algebra is a an (associative) algebra equipped with a…

Separate programming models for data transformation (declarative) and computation (procedural) impact programmer ergonomics, code reusability and database efficiency. To eliminate the necessity for two models or paradigms, we propose a…

The theory of "subalgebra basis" analogous to standard basis (the generalization of Gr\"{o}bner bases to monomial ordering which are not necessarily well ordering \cite{GP1}.) for ideals in polynomial rings over a field is developed. We…

A long standing problem of Gian-Carlo Rota for associative algebras is the classification of all linear operators that can be defined on them. In the 1970s, there were only a few known operators, for example, the derivative operator, the…

With the dramatic increase in the amount of the text-based data which commonly contains misspellings and other errors, querying such data with flexible search patterns becomes more and more commonplace. Relational databases support the LIKE…