Related papers: Weak Simplicial Bisimilarity for Polyhedral Models…
The work described in this paper builds on the polyhedral semantics of the Spatial Logic for Closure Spaces (SLCS) and the geometric spatial model checker PolyLogicA. Polyhedral models are central in domains that exploit mesh processing,…
Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability…
This work explores the potential of spatial model checking of polyhedral models on a number of selected examples. In computer graphics polyhedral models can be found in the form of triangular surface meshes of tetrahedral volume meshes…
Based on the concept of weakly meet $s_{Z}$-continuouity put forward by Xu and Luo in \cite{qzm}, we further prove that if the subset system $Z$ satisfies certain conditions, a poset is $s_{Z}$-continuous if and only if it is weakly meet…
These lectures contain an introduction to the theory and practice of weak-scale supersymmetry. They begin with a discussion of the hierarchy problem and the motivation for weak-scale supersymmetry. They continue by developing the coset…
Poly-bicategories generalise planar polycategories in the same way as bicategories generalise monoidal categories. In a poly-bicategory, the existence of enough 2-cells satisfying certain universal properties (representability) induces…
Our aim is to investigate spaces with sigma-discrete and meager dense sets, as well as selective versions of these properties. We construct numerous examples to point out the differences between these classes while answering questions of…
Closure spaces are a generalisation of topological spaces obtained by removing the idempotence requirement on the closure operator. We adapt the standard notion of bisimilarity for topological models, namely Topo-bisimilarity, to closure…
Lensing studies are typically carried out around high density regions, such as groups and clusters, where the lensing signals are significant and indicative of rich density structures. However, a more comprehensive test of the cosmological…
Suppose that $S_1$ and $S_2$ are nonempty subsets of a complete metric space $(\mathcal{M},d)$ and $\phi,\psi:S_1\to S_2$ are mappings. The aim of this work is to investigate some conditions on $\phi$ and $\psi$ such that the two functions,…
Closure spaces, a generalisation of topological spaces, have shown to be a convenient theoretical framework for spatial model checking. The closure operator of closure spaces and quasi-discrete closure spaces induces a notion of…
Bilinear models has been shown to achieve impressive performance on a wide range of visual tasks, such as semantic segmentation, fine grained recognition and face recognition. However, bilinear features are high dimensional, typically on…
In this work, we have introduced and studied some basic geometric properties of extended weakly symmetric spaces. After classification of this structure we have also established the existence of such a space by presenting a non-trivial…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
We present a new approach to simple homotopy theory of polyhedra using finite topological spaces. We define the concept of collapse of a finite space and prove that this new notion corresponds exactly to the concept of a simplicial…
We show that any weakly separated Bessel system of model spaces in the Hardy space on the unit disc is a Riesz system and we highlight some applications to interpolating sequences of matrices. This will be done without using the recent…
We analyse the low--multipole components of the weak-lensing convergence field in a FLRW universe. The low--multipole convergence field, encodes the largest-angle coherent potential gradients, essential for assessment of large-angle…
The ATLAS collaboration has recently performed a vast scan of the phenomenological Minimal Supersymmetric Standard Model (pMSSM) with a focus on the electroweak-ino sector, and analysed how their Run 2 searches for electroweak production of…
The aim of this paper is to investigate weakly developable spaces. For a comparison with semi-metrizable spaces, we introduce and study a class of spaces among those of weakly developable spaces, semimetrizable spaces and first countable…
Given any model category, or more generally any category with weak equivalences, its simplicial localization is a simplicial category which can rightfully be called the "homotopy theory" of the model category. There is a model category…