Related papers: Deriving diffeomorphism symmetry
We investigate (local) automorphisms of parabolic geometries that generalize geodesic symmetries. We show that many types of parabolic geometries admit at most one generalized geodesic symmetry at a point with non-zero harmonic curvature.…
Symmetry is omnipresent in nature and perceived by the visual system of many species, as it facilitates detecting ecologically important classes of objects in our environment. Symmetry perception requires abstraction of long-range spatial…
In this survey, symmetry provides a framework for classification of manifolds with differential-geometric structures. We highlight pseudo-Riemannian metrics, conformal structures, and projective structures. A range of techniques have been…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
Because physical phenomena on Earth's surface occur on many different length scales, it makes sense when seeking an efficient approximation to start with a crude global approximation, and then make a sequence of corrections on finer and…
A group theory justification of one dimensional fractional supersymmetry is proposed using an analogue of a coset space, just like the one introduced in $1D$ supersymmetry. This theory is then gauged to obtain a local fractional…
Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The projection matrix is then learned on the…
When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…
Ground texture based localization methods are potential prospects for low-cost, high-accuracy self-localization solutions for robots. These methods estimate the pose of a given query image, i.e. the current observation of the ground from a…
Mutual localization provides a consensus of reference frame as an essential basis for cooperation in multirobot systems. Previous works have developed certifiable and robust solvers for relative transformation estimation between each pair…
We use the techniques developed in [1] to study the local average of random fields with spectral density $1/f^{\alpha}$. We study their scaling properties and show that the self-similarity of $1/f$ random fields is preserved under the local…
Computing the state-space topology of a dynamical system from scalar data requires accurate reconstruction of those dynamics and construction of an appropriate simplicial complex from the results. The reconstruction process involves a…
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…
By generalizing the notion of linearization, a concept originally arising from microlocal analysis and symbolic calculus, to diffeological spaces, we make a first proposal setting for optimization problems in this category. We show how…
Photometric Stereo methods seek to reconstruct the 3d shape of an object from motionless images obtained with varying illumination. Most existing methods solve a restricted problem where the physical reflectance model, such as Lambertian…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
In this note, we address formally the issue of symmetry for probabilities of different dynamical pathways in the forward and reverse directions of a conformational transition. Our discussion is based on a decomposition of equilibrium into…
The concept of local symmetry is a powerful tool in predicting complex transport phenomena in aperiodic media. A nonlocal continuity formalism reveals how local symmetries are encoded into the dynamics of light propagation in discrete…
Polymorphism offers rich and virtually unexplored space for discovering novel functional materials. To harness this potential approaches capable of both exploring the space of polymorphs and assessing their realizability are needed. One…