What is a degree of freedom? Configuration spaces and their topology
March 23, 2023
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Physics
Mathematics
Classical Physics
Mathematical Physics
Mathematical Physics
Understanding degrees of freedom in classical mechanics is fundamental to
characterizing physical systems. Counting them is usually easy, especially if
we can assign them a clear meaning. However, the precise definition of a degree
of freed...
DiffMesh: A Motion-aware Diffusion Framework for Human Mesh Recovery
from Videos
March 23, 2023
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Computer Science
Computer Vision and Pattern Recognition
Artificial Intelligence
Human-Computer Interaction
Multimedia
Human mesh recovery (HMR) provides rich human body information for various
real-world applications. While image-based HMR methods have achieved impressive
results, they often struggle to recover humans in dynamic scenarios, leading to
tempo...
Image segmentation relies heavily on neural networks which are known to be
overconfident, especially when making predictions on out-of-distribution (OOD)
images. This is a common scenario in the medical domain due to variations in
equipment...
Hypodifferentials of nonsmooth convex functions and their applications
to nonsmooth convex optimization
March 23, 2023
Mathematics
Optimization and Control
A hypodifferential is a compact family of affine mappings that defines a
local max-type approximation of a nonsmooth convex function. We present a
general theory of hypodifferentials of nonsmooth convex functions defined on a
Banach space. ...
Normalized Laplacian eigenvalues of hypergraphs
March 23, 2023
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Mathematics
Combinatorics
In this paper, we give tight bounds for the normalized Laplacian eigenvalues
of hypergraphs that are not necessarily uniform, and provide an edge version
interlacing theorem, a Cheeger inequality, and a discrepancy inequality that
are relat...
Evaluation of Boltzmann's H-function for Particles with Orientational
Degrees of Freedom
March 23, 2023
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Physics
Statistical Mechanics
Boltzmann's H-function H(t) holds a venerable place in the history of
science. However, it seems never to have been evaluated for particles with
orientational degrees of freedom. We generalize Boltzmann's H-function to a gas
of molecules th...
Bootstrap-Assisted Inference for Generalized Grenander-type Estimators
March 23, 2023
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Mathematics
Economics
Statistics
Statistics Theory
Econometrics
Methodology
Statistics Theory
Westling and Carone (2020) proposed a framework for studying the large sample
distributional properties of generalized Grenander-type estimators, a versatile
class of nonparametric estimators of monotone functions. The limiting
distribution...
Type-II Saddles and Probabilistic Stability of Stochastic Gradient
Descent
March 23, 2023
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Computer Science
Mathematics
Physics
Machine Learning
Optimization and Control
Data Analysis, Statistics and Probability
Characterizing and understanding the dynamics of stochastic gradient descent
(SGD) around saddle points remains an open problem. We first show that saddle
points in neural networks can be divided into two types, among which the
Type-II sadd...
Extremal Black Holes as Relativistic Systems with Kepler Dynamics
March 23, 2023
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Physics
Mathematics
General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
Dynamical Systems
Mathematical Physics
The recent detection of gravitational waves emanating from inspiralling black
hole binaries has triggered a renewed interest in the dynamics of relativistic
two-body systems. The conservative part of the latter are given by Hamiltonian
syst...
AdaCL:Adaptive Continual Learning
March 23, 2023
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Computer Science
Machine Learning
Computer Vision and Pattern Recognition
Class-Incremental Learning aims to update a deep classifier to learn new
categories while maintaining or improving its accuracy on previously observed
classes. Common methods to prevent forgetting previously learned classes
include regulari...