Related papers: A Modular First Formalisation of Combinatorial Des…
Formalised libraries of combinatorial mathematics have rapidly expanded over the last five years, but few use one of the most important tools: probability. How can often intuitive probabilistic arguments on the existence of combinatorial…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
This set of theories presents a formalisation in Isabelle/HOL+Isar of data dependencies between components. The approach allows to analyse system structure oriented towards efficient checking of system: it aims at elaborating for a concrete…
When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL…
The paper describes multistage design of composite (modular) systems (i.e., design of a system trajectory). This design process consists of the following: (i) definition of a set of time/logical points; (ii) modular design of the system for…
The formalisation of mathematics is continuing rapidly, however combinatorics continues to present challenges to formalisation efforts, such as its reliance on techniques from a wide range of other fields in mathematics. This paper presents…
This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…
Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…
Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work,…
Computability theory is traditionally conceived as the theoretical basis of informatics. Nevertheless, numerous proposals transcend computability theory, in particular by emphasizing interaction of modules, or components, parts,…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
During modeling of dynamical systems, often two or more model architectures are combined to obtain a more powerful or efficient model regarding a specific application area. This covers the combination of multiple machine learning…
A number of machine learning models have been proposed with the goal of achieving systematic generalization: the ability to reason about new situations by combining aspects of previous experiences. These models leverage compositional…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…
Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…
We study problems related to indecomposability of modules over certain local finite dimensional trivial extension algebras. We do this by purely combinatorial methods. We introduce the concepts of graph of cyclic modules, of combinatorial…
The aim of this research is to introduce a novel structural design process that allows architects and engineers to extend their typical design space horizon and thereby promoting the idea of creativity in structural design. The theoretical…
This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…