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The role of geometry on dispersive forces is investigated by calculating the energy between different spheroidal particles and planar surfaces, both with arbitrary dielectric properties. The energy is obtained in the non-retarded limit…
In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…
We focus on three distinct lines of recent developments: edge modes and boundary charges in gravitational physics, relational dynamics in classical and quantum gravity, and quantum reference frames. We argue that these research directions…
Perceiving the shape and material of an object from a single image is inherently ambiguous, especially when lighting is unknown and unconstrained. Despite this, humans can often disentangle shape and material, and when they are uncertain,…
For humans, object detection, recognition, and tracking are innate. These provide the ability for human to perceive their environment and objects within their environment. This ability however doesn't translate well in computers. In…
We present a computational model for the semantic interpretation of symmetry in naturalistic scenes. Key features include a human-centred representation, and a declarative, explainable interpretation model supporting deep semantic…
Contemporary perspectivism is viewed as a framework of scientific inquiry concerning the origin, generation and systematization of scientific knowledge of nature by focusing on the conditions under which such knowledge may arise in…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
In this paper we start with a simple question, how is it possible that humans can recognize different movements over skin with only a prior visual experience of them? Or in general, what is the representation of spatial sequences that are…
A particular science is not only defined by its object of study, but also by the point of view and method under which it considers that same object. Taking space and time as an illustrative example, our main aim here is to bring out an…
When joined the unified gauge picture of fundamental interactions, the gravitation theory leads to geometry of a space-time which is far from simplicity of pseudo-Riemannian geometry of Einstein's General Relativity. This is geometry of the…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
Education is a goal-oriented field. But if we want to treat education scientifically so we can accumulate, evaluate, and refine what we learn, then we must develop a theoretical framework that is strongly rooted in objective observations…
The world is composed of objects, the ground, and the sky. Visual perception of objects requires solving two fundamental challenges: segmenting visual input into discrete units, and tracking identities of these units despite appearance…
Computer graphics, often associated with films, games, and visual effects, has long been a powerful tool for addressing scientific challenges--from its origins in 3D visualization for medical imaging to its role in modern computational…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
This paper addresses object perception applied to mobile robotics. Being able to perceive semantically meaningful objects in unstructured environments is a key capability in order to make robots suitable to perform high-level tasks in home…
Contemporary scientific perspectivism is re-evaluated and extended to a comprehensive perspectivist methodology and 'mediated' realistic epistemology, especially, with reference to quantum mechanics. In the present study, this is realized…
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…