Related papers: A Modular First Formalisation of Combinatorial Des…
This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings,…
We propose a set of compositional design patterns to describe a large variety of systems that combine statistical techniques from machine learning with symbolic techniques from knowledge representation. As in other areas of computer science…
In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
LF has been designed and successfully used as a meta-logical framework to represent and reason about object logics. Here we design a representation of the Isabelle logical framework in LF using the recently introduced module system for LF.…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
Recent progress in time-series forecasting has led to rapidly increasing architectural complexity, yet many reported State-of-the-Art gains are statistically fragile or misattributed. We argue that progress requires a shift from model…
Generally, combinatorial design concerns with the arrangement of a finite set of elements into patterns (subsets, words, arrays) according to specified rules. The usefulness of this design method is that the number of input combination can…
We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…
Combinatorial designs have been studied for nearly 200 years. Fifty years ago, Cameron, Delsarte, and Ray-Chaudhury started investigating their q-analogs, also known as subspace designs or designs over finite fields. Designs can be defined…
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
We give a combinatorial description of shape theory using finite topological $T_0$-spaces (finite partially ordered sets). This description may lead to a sort of computational shape theory. Then we introduce the notion of core for inverse…
In this PhD thesis we will discuss some aspects in Commutative Algebra which have interactions with Algebraic Geometry, Representation Theory and Combinatorics. In particular, in the first chapter we will focus on understanding when certain…
We define and study a class of finite topological spaces, which model the cell structure of a space obtained by gluing finitely many Euclidean convex polyhedral cells along congruent faces. We call these finite topological spaces,…
We implement a novel representation of model search spaces as diagrams over a category of models, where we have restricted attention to a broad class of models whose structure is presented by \C-sets. (Co)limits in these diagram categories…
Compositionality is a key strategy for addressing combinatorial complexity and the curse of dimensionality. Recent work has shown that compositional solutions can be learned and offer substantial gains across a variety of domains, including…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…