Related papers: Configuration Spaces for the Working Undergraduate
An S-approximation space is a novel approach to study systems with uncertainty that are not expressible in terms of inclusion relations. In this work, we further examined these spaces, mostly from a topological point of view by a…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
We supply basic tools for the study of the topological order of a multiplet which is an eigenspace of a finite-dimensional normal operator with continuous parameters. We allow intrinsic degeneracies within the multiplet where a well-known…
We give $\mathbb{Z}$-bases for the homology and cohomology of the configuration space $\operatorname{config}(n,w)$ of $n$ unit disks in an infinite strip of width $w$, first studied by Alpert, Kahle and MacPherson. We also study the way…
This work proposes a framework that generates and optimally selects task-specific assembly configurations for a large group of homogeneous modular aerial systems, explicitly enforcing bounds on inter-module downwash. Prior work largely…
Homological algebra is often understood as the translator between the world of topology and algebra. However, this branch of mathematics is worth studying by itself, given that it provides fascinating perspectives about other disciplines,…
We systematically study some basic properties of the theory of pre-topological spaces, such as, pre-base, subspace, axioms of separation, connectedness, etc. Pre-topology is also known as knowledge space in the theory of knowledge…
We investigate several topological and combinatorial properties of line arrangements. We associate to a line arrangement a link obtained by intersecting the arrangement with some sphere. Several topics are discussed: (a) some link…
This is the fourth in a series of papers math.AG/0312190, math.AG/0503029, math.AG/0410267 on configurations in an abelian category A. Given a finite partially ordered set (I,<), an (I,<)-configuration is a finite collection of objects and…
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…
This paper provides both an introduction to and a detailed overview of the principles and practice of classifier calibration. A well-calibrated classifier correctly quantifies the level of uncertainty or confidence associated with its…
For a certain class of algebras $\cal A$ we give a method for constructing Banach spaces $X$ such that every operator on $X$ is close to an operator in $\cal A$. This is used to produce spaces with a small amount of structure. We present…
We define a class of subsets of a topological space that coincides with the class of compact saturated subsets when the space is sober, and with enough good properties when the space is not sober. This class is introduced especially in view…
In this paper we study topological surfaces as gridded surfaces in the 2-dimensional scaffolding of cubic honeycombs in Euclidean and hyperbolic spaces.
This work seeks to tackle the inherent complexity of dataspaces by introducing a novel data structure that can represent datasets across multiple levels of abstraction, ranging from local to global. We propose the concept of a multilevel…
Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected…
We compute the fundamental group of various spaces of Desargues configurations in complex projective spaces: planar and non-planar configurations, with a fixed center and also with an arbitrary center.
Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and…
We study homological representations of mapping class groups, including the braid groups. These arise from the twisted homology of certain configuration spaces, and come in many different flavours. Our goal is to give a unified general…
Automatic or assisted workflow composition is a field of intense research for applications to the world wide web or to business process modeling. Workflow composition is traditionally addressed in various ways, generally via theorem proving…