A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We study completeness properties of the Sobolev diffeomorphism groups Ds(M) endowed with strong right-invariant Riemannian metrics when the underlying manifold M is Rd or compact without boundary. The main result is that for s>dimM/2+1, the group Ds(M) is geodesically and me…
Templates are branched 2-manifolds with semi-flows used to model `chaotic' hyperbolic invariant sets of flows on 3-manifolds. Knotted orbits on a template correspond to those in the original flow. Birman and Williams conjectured that for any given template the number of prime factors of the knots realized would be boun…
We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the space of probability densities and right-invariant metrics on the infinite-dimension…
We consider the use of the Joint Clustering and Matching (JCM) procedure for the supervised classification of a flow cytometric sample with respect to a number of predefined classes of such samples. The JCM procedure has been proposed as a method for the unsupervised classification of cells within a sample into a numbe…
Dasgupta and Shulman showed that a two-round variant of the EM algorithm can learn mixture of Gaussian distributions with near optimal precision with high probability if the Gaussian distributions are well separated and if the dimension is sufficiently high. In this paper, we generalize their theory to learning mixture…
We describe the Williams zeta functions and the twist zeta functions of sub-Lorenz templates generated by renormalizable Lorenz maps, in terms of the corresponding zeta-functions of the sub-Lorenz templates generated by the renormalized map and by the map that determines the renormalization type.
Neural production systems learn visual dynamics by applying rule templates to entities.
problem Modeling interactions among entities in structured visual environments.
method Inspired by production systems, the paper uses rule templates to bind placeholder variables to specific entities, scoring and applying the best fitting rules to update entity properties.
result The architecture achieves robust future-state prediction and extrapolation from simple to complex environments, outperforming GNNs.
With increasing concerns about security, the need for highly secure physical biometrics-based authentication systems utilizing \emph{cancelable biometric} technologies is on the rise. Because the problem of cancelable template generation deals with the trade-off between template security and matching performance, many …
A flexible machine learning model infers the morphology of the Galactic Center Excess.
problem Inferring the unknown morphology of the Galactic Center Excess using Fermi gamma-ray data.
method Used a Gaussian process (GP) to model the Galactic Center Excess (GCE) as a flexible, non-parametric machine learning model.
result The best-fit GP contains morphological features not typically associated with traditional GCE studies, such as a localized bright source and a diagonal arm.
Registration, which aims to find an optimal 1-1 correspondence between shapes, is an important process in different research areas. Conformal mappings have been widely used to obtain a diffeomorphism between shapes that minimizes angular distortion. Conformal registrations are beneficial since it preserves the local ge…
The fact that the modular template coincides with the Lorenz template, discovered by Ghys, implies modular knots have very peculiar properties. We obtain a generalization of these results to other Hecke triangle groups. In this context, the geodesic flow can never be seen as a flow on a subset of S3, and one is led …
The paper extends LDDMM framework to include Lie group actions in large deformation shape registration.
problem Modeling smooth, invertible transformations between shapes using Lie groups and diffeomorphisms.
method Develops a registration model that decouples the actions of Lie groups and diffeomorphisms, using semidirect products and right-invariant sub-Riemannian structures.
result Joint optimization over both deformation groups improves registration accuracy and disentangles contributions.