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In spacetime dimensions of 4 (i.e., 3+1) and higher, topological orders exhibit spatially extended excitations like loops and membranes, which support diverse topological data characterizing braiding, fusion, and shrinking processes,…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
Assembly of large scale structural systems in space is understood as critical to serving applications that cannot be deployed from a single launch. Recent literature proposes the use of discrete modular structures for in-space assembly and…
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…
Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this…
Learning the embedding space, where semantically similar objects are located close together and dissimilar objects far apart, is a cornerstone of many computer vision applications. Existing approaches usually learn a single metric in the…
Tabular foundation models aim to learn universal representations of tabular data that transfer across tasks and domains, enabling applications such as table retrieval, semantic search and table-based prediction. Despite the growing number…
Clones of functions play a foundational role in both universal algebra and theoretical computer science. In this work, we introduce clone merge monoids (cm-monoids), a unifying one-sorted algebraic framework that integrates abstract clones,…
Nested parallelism exists in scientific codes that are searching multi-dimensional spaces. However, implementations of nested parallelism often have overhead and load balance issues. The Orbital Analysis code we present exhibits a sparse…
The main contribution of this dissertation is the introduction of new or improved approximation algorithms and data structures for several similarity search problems. We examine the furthest neighbor query, the annulus query, distance…
Curved algebras are a generalization of differential graded algebras which have found numerous applications recently. The goal of this foundational article is to introduce the notion of a curved operad, and to develop the operadic calculus…
With web and mobile platforms becoming more prominent devices utilized in data analysis, there are currently few systems which are not without flaw. In order to increase the performance of these systems and decrease errors of data…
The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement, then by an advanced study launched by the Direction de la Recherche et des Etudes Technologiques in France in…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…
Graph databases have been the subject of significant research and development. Problems such as modularity, centrality, alignment, and clustering have been formalized and solved in various application contexts. In this paper, we focus on…
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…
How do analysts think about grouping and spatial operations? This overarching question incorporates a number of points for investigation, including understanding how analysts begin to explore a dataset, the types of grouping/spatial…
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…