A common and intuitive way of identifying the proximity relationship between two entities is to use the preposition ‘near’ (e.g. ‘near (inn, village)’). However, the ‘near’ relation is vague, often asymmetric and context-dependent, and hence incorporating factors such as the effect of type, size and scale of reference object and associated features is required for cognitive modeling. In this work, we interpreted spatial proximity as described in the historic Corpus of Lake District Writing comprising travel narratives as early as the 16th century. At a time when modern transportation modes were not available, it is interesting to explore how proximity has been perceived and recounted with various context factors explicit or implied. We utilized pre-trained BERT and its variants to first identify the broader semantics of ‘near’ and generate contextual embeddings. We further identified the contextual factors of spatial nearness. Finally, we used quantitative distances between entities to measure the departure of context-dependent proximities from objective notions of distance.

Abstract—Large Language Models (LLMs) suffer from inherent stochasticity, limiting their utility in high-stakes enterprise environments where determinism and auditability are required. This paper introduces the MFOUR Vibe Framework (MVF), a platform-agnostic architectural standard that transforms probabilistic natural language intent into deterministic software artifacts. We define a five-layer topology, comprising the Kernel Identity, Synaptic Routing, Interface Contracts, Context Anchoring, and the Mirror Test. Furthermore, we introduce The Vibe Integrity Score (VIS), a quantitative metric for evaluating the structural adherence of generative outputs. This specification provides the foundational schema and logic protocols for building "Glass Box" AI systems that are observable, secure, and commercially viable.

We generalize the well-known correspondence between partitions and equivalence relations on a set to the case of graphs and hypergraphs. This is motivated by the role that partitions and equivalence relations play in Rough Set Theory and the results provide some of the foundations needed to develop a theory of rough graphs. We use one notion of a partition of a hypergraph, which we call a graphical partition, and we show how these structures correspond to relations on a hypergraph having additional properties. In the case of a hypergraph with only nodes and no edges these properties are exactly the usual reflexivity, symmetry and transitivity properties required for equivalence relations on a set. We present definitions for upper and lower approximations of a subgraph with respect to a graphical partition. These generalize the well-known approximations in Rough Set Theory. We establish fundamental properties of our generalized approximations and provide examples of these constructions on some graphs.

As locative media and augmented reality spread into the everyday world so it becomes important to create aesthetic visual markers at scale. We explore a designer-centred approach in which skilled designers handcraft seed designs that are automatically recombined to create many markers as subtle variants of a common theme. First, we extend the d-touch topological approach to creating visual markers that has previously been shown to support creative design with two new techniques: area order codes and visual checksums. We then show how the topological structure of such markers provides the basis for recombining designs to generate many variations. We demonstrate our approach through the creation of beautiful, personalized and interactive wallpaper. We reflect on how technologies must enable designers to balance goals of scalability, aesthetics and reliability in creating beautiful interactive decoration.

We consider a modal logic based on mathematical morphology which allows the expression of mereotopological relations between subgraphs in the setting of the discrete space. A specific form of topological closure for graphs can be expressed in the logic, as a combination of the negation and its bi-intuitionistic dual, as well as a modality, using the stable relation Q, which describes the incidence structure of the graph. By working in this context we have been able to define qualitative spatial relations between discrete regions, and to compare them with earlier works in mereotopology, both in the discrete and in the continuous space.