相关论文: A Shape Dynamics Tutorial

Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…

This article is a review of modern approaches to gravity that treat the gravitational interaction as a type of gauge theory. The purpose of the article is twofold. First, it is written in a colloquial style and is intended to be a…

Suppose one seeks to free oneself from a symmetric absolute space by quotienting out its symmetry group. This in general however fails to erase all memory of this absolute space's symmetry properties. Stratification is one major reason for…

A general diffeomorphism invariant SU(2) gauge theory is a gravity theory with two propagating polarizations of the graviton. We develop this description of gravity, in particular for future applications to the perturbative quantization.…

Faddeev variant of embedding theory is an example of using the embedding approach for the description of gravity. In the original form of the embedding approach, the gravity is described by an embedding function of a four-dimensional…

Many modern theories which try to unify gravity with the Standard Model of particle physics, as e.g. string theory, propose two key modifications to the commonly known physical theories: i) the existence of additional space dimensions; ii)…

This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…

Modified Newtonian Dynamics (MOND) is an alternative to the dark matter hypothesis that attempts to explain the "missing gravity" problem in astrophysics and cosmology through a modification to objects' dynamics. Since its conception in…

We provide a general algorithm to construct a Hamiltonian, such that its dynamical flow covariantly defines any given spherically symmetric and static metric. This Hamiltonian is defined as a linear combination of the standard (general…

The curvature invariants have been subject of interest due to the debate concerning the notions of intrinsic/extrinsic frame-dragging, the use of the electromagnetic analogy in such classification, and the question of whether there is a…

Smoothed Particle Hydrodynamics (SPH) is a unique numerical method widely used for astrophysical problems since it involves no spatial grid. Rather, fluid quantities are carried by a set of Lagrangian `particles' which move with the flow,…

The introduction of General Relativity (GR) in 1915 revolutionized our understanding of gravity, but over time, its limitations in explaining phenomena like dark energy, dark matter, and quantum gravity have motivated alternative theories.…

Robot simulators are indispensable tools across many fields, and recent research has significantly improved their functionality by incorporating additional gradient information. However, existing differentiable robot simulators suffer from…

I present the first analytical study of gravitational collapse in a compact CMC foliation with $S^3$ spatial topology. The solutions I find, in this context, will be both solutions of Shape Dynamics and General Relativity. The aim is to…

Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime…

A suite of relational notions of shape are presented at the level of configuration space geometry, with corresponding new theories of shape mechanics and shape statistics. These further generalize two quite well known examples: --1)…

Reconstructing the surfaces of deformable objects from correspondences between a 3D template and a 2D image is well studied under Shape-from-Template (SfT) methods; however, existing approaches break down when topological changes accompany…

Domain generalization aims to address the domain shift between training and testing data. To learn the domain invariant representations, the model is usually trained on multiple domains. It has been found that the gradients of network…

We give a brief summary of the formalism of invariants in general scalar-tensor and multiscalar-tensor gravities without derivative couplings. By rescaling of the metric and reparametrization of the scalar fields, the theory can be…

A class of theories of gravitation that naturally incorporates preferred frames of reference is presented. The underlying space-time geometry consists of a partial parallelization of space-time and has properties of Riemann-Cartan as well…