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Found 12 papers, 4 papers with code
On Manifold Learning in Plato's Cave: Remarks on Manifold Learning and Physical Phenomena
Many techniques in machine learning attempt explicitly or implicitly to infer a low-dimensional manifold structure of an underlying physical phenomenon from measurements without an explicit model of the phenomenon or the measurement apparatus.
Using VAEs to Learn Latent Variables: Observations on Applications in cryo-EM
Variational autoencoders (VAEs) are a popular generative model used to approximate distributions.
Geometric Ergodicity in Modified Variations of Riemannian Manifold and Lagrangian Monte Carlo
Unlike Euclidean Hamiltonian Monte Carlo (EHMC) and the Metropolis-adjusted Langevin algorithm (MALA), the geometric ergodicity of these Riemannian algorithms has not been extensively studied.
Methods for Cryo-EM Single Particle Reconstruction of Macromolecules having Continuous Heterogeneity
Macromolecules change their shape (conformation) in the process of carrying out their functions.
Manifold Density Estimation via Generalized Dequantization
For instance, some kinds of data may be known to lie on the surface of a sphere.
Magnetic Manifold Hamiltonian Monte Carlo
We introduce magnetic manifold HMC, an HMC algorithm on embedded manifolds motivated by the physics of particles constrained to a manifold and moving under magnetic field forces.
Spectral Flow on the Manifold of SPD Matrices for Multimodal Data Processing
Our approach combines manifold learning, which is a class of nonlinear data-driven dimension reduction methods, with the well-known Riemannian geometry of symmetric and positive-definite (SPD) matrices.
Non-Canonical Hamiltonian Monte Carlo
Hamiltonian Monte Carlo is typically based on the assumption of an underlying canonical symplectic structure.
Hyper-Molecules: on the Representation and Recovery of Dynamical Structures, with Application to Flexible Macro-Molecular Structures in Cryo-EM
We introduce the ``hyper-molecule'' framework for modeling structures across different states of heterogeneous molecules, including continuums of states.
Numerical Algorithms for the Computation of Generalized Prolate Spheroidal Functions
The purpose of this paper is to review the elements of computing GPSFs and associated eigenvalues.
Numerical Analysis Numerical Analysis 42A38, 65T99, 33F05, 65D20
Continuously heterogeneous hyper-objects in cryo-EM and 3-D movies of many temporal dimensions
One of the great opportunities in cryo-EM is to recover the structure of macromolecules in heterogeneous samples, where multiple types or multiple conformations are mixed together.
A Representation Theory Perspective on Simultaneous Alignment and Classification
One of the difficulties in 3D reconstruction of molecules from images in single particle Cryo-Electron Microscopy (Cryo-EM), in addition to high levels of noise and unknown image orientations, is heterogeneity in samples: in many cases, the samples contain a mixture of molecules, or multiple conformations of one molecule.
