Blog
Density of states and non-smooth Lyapunov exponent in the localized phase
Localization of wave functions in the disordered models can be characterized by the Lyapunov exponent, which is zero in the extended phase and nonzero in the localized phase. Previous studies have shown that this exponent is a smooth function of eigenenergy in...
Bridging Econometrics and AI: VaR Estimation via Reinforcement Learning and GARCH Models
In an environment of increasingly volatile financial markets, the accurate estimation of risk remains a major challenge. Traditional econometric models, such as GARCH and its variants, are based on assumptions that are often too rigid to adapt to the complexity of the...
Existence and uniqueness of Leray-Hopf weak solution for the inhomogeneous 2D Navier–Stokes equations without vacuum
We prove the existence and uniqueness of weak solutions of the inhomogeneous incompressible Navier–Stokes equations without vacuum using the relative energy method. We present a novel and direct proof of the existence of weak solutions based on approximation with more regular solutions....
$H^1$ local exact controllability of some one-dimensional bilinear Schr{ö}dinger equations
The local exact controllability of the one-dimensional bilinear Schr{\”o}dinger equation with Dirichlet boundary conditions has been extensively studied in subspaces of H 3 since the seminal work of K. Beauchard. Our first objective is to revisit this result and establish the controllability...
Hitting and Covering Affine Families of Convex Polyhedra, with Applications to Robust Optimization
Geometric hitting set problems, in which we seek a smallest set of points that collectively hit a given set of ranges, are ubiquitous in computational geometry. Most often, the set is discrete and is given explicitly. We propose new variants of these...
Medium-induced coherent gluon radiation for $2\to 2$ processes with general kinematics
High-energy proton-nucleus (pA) collisions have provided various clues for the role of cold nuclear matter effects in hadron production. In particular, multiple rescatterings of an incoming parton by the nuclear target are known to induce the radiation of many soft gluons, with...
PP-Tac: Paper Picking Using Tactile Feedback in Dexterous Robotic Hands
Robots are increasingly envisioned as human companions, assisting with everyday tasks that often involve manipulating deformable objects. Although recent advances in robotic hardware and embodied AI have expanded their capabilities, current systems still struggle with handling thin, flat, and deformable objects such...
Small Alfvén Number Limit for the Global-in-time Solutions of Incompressible MHD Equations with General Initial Data
The small Alfv\’en number (denoted by $\varepsilon$) limit (one type of large parameter limits, i.e. singular limits) in magnetohydrodynamic (abbr. MHD) equations was first proposed by Klainerman–Majda in (Comm. Pure Appl. Math. 34: 481–524, 1981). Recently Ju–Wang–Xu mathematically verified that the \emph{local-in-time}...
Photo-generated charge-transfer excitons in NiO revealed by ultrafast time-resolved resonant inelastic x-ray scattering
Strong electronic correlation can lead to insulating behavior and to the opening of large optical gaps, even in materials with partly filled valence shells. Although the non-equilibrium optical response encodes both local (quasi atomic) and collective (long range) responses, optical spectroscopy is...
A Time Series Dataset of NIR Spectra and RGB and NIR-HSI Images of the Barley Germination Process
We provide an open-source dataset of RGB and NIR-HSI (near-infrared hyperspectral imaging) images with associated segmentation masks and NIR spectra of 2242 individual malting barley kernels. We imaged every kernel pre-exposure to moisture and every 24 hours after exposure to moisture for...