Related papers: A Modular First Formalisation of Combinatorial Des…

Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…

Urban systems are intrinsically complex, involving different dimensions and scales, and consequently various approaches and scientific disciplines. In that context, urban simulation models have been coined as essential for the construction…

In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…

This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…

This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…

Ramsey theory looks for regularities in large objects. Model theory studies algebraic structures as models of theories. The structural Ramsey theory combines these two fields and is concerned with Ramsey-type questions about certain…

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

In recent work, comonads and associated structures have been used to analyse a range of important notions in finite model theory, descriptive complexity and combinatorics. We extend this analysis to Hybrid logic, a widely-studied extension…

An objective of the theory of combinatorial groupoids is to introduce concepts like "holonomy", "parallel transport", "bundles", "combinatorial curvature" etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes,…

The aim of this study is to construct and compose an instructional design in combinatorial learning, particularly in the concept of counting. A composed design is expected to optimize students' combinatorial-thinking skill. This research…

We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…

Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…

This article provides formal definitions characterizing well-formed composition of components in order to guarantee their safe deployment and execution. Our work focuses on the structural aspects of component composition; it puts together…

We study modules over the ring $\widetilde{\C}$ of complex generalized numbers from a topological point of view, introducing the notions of $\widetilde{\C}$-linear topology and locally convex $\widetilde{\C}$-linear topology. In this…

In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to…

This dissertation builds a compositional cyber-physical systems theory to develop concrete semantics relating the above diverse views necessary for safety and security assurance. In this sense, composition can take two forms. The first is…

The increasing relevance of areas such as real-time and embedded systems, pervasive computing, hybrid systems control, and biological and social systems modeling is bringing a growing attention to the temporal aspects of computing, not only…

Much work has been done on generalising results about uniform spaces to the pointfree context. However, this has almost exclusively been done using classical logic, whereas much of the utility of the pointfree approach lies in its…

We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…