We study the problem of localizing a configuration of points and planes from the collection of point-to-plane distances. This problem models simultaneous localization and mapping from acoustic echoes as well as the & x201C;structure from sound & x201D; app ...
Clustering is a classic topic in optimization with k-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best-known algorithm for k-means in Euclidean space with a provable guarantee is a simple local ...
We present a comparison between approximated methods for the construction of mock catalogues based on the halo-bias mapping technique. To this end, we use as reference a high-resolution N-body simulation of 38403 dark matter particles on a 400 h(-1) Mpc cu ...
Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful ...
Humans exhibit outstanding learning and adaptation capabilities while performing various types of manipulation tasks. When learning new skills, humans are able to extract important information by observing examples of a task and efficiently refine a priori ...
We obtain quantitative bounds on the mixing properties of the Hamiltonian Monte Carlo (HMC) algorithm with target distribution in d-dimensional Euclidean space, showing that HMC mixes quickly whenever the target log-distribution is strongly concave and has ...
3D objects, modeled using Computer Aided Geometric Design (CAGD) tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physic ...
We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base space, and layers are equivariant ma ...
