Research
Research
Research
Research
1,938+ open-access research outputs.
We introduce the ARCH-m(X) model, a semiparametric extension of the ARCH-X framework in which the effect of a multivariate exogenous covariate vector X on the conditional variance is modeled through a…
In this paper we develop a consistent variable selection procedure for GARCH-X models that identifies the truly relevant exogenous covariates influencing volatility dynamics. The proposed method is ba…
Foundation segmentation models such as the Segment Anything Model (SAM) have demonstrated strong generalization across natural images; however, their robustness under clinically realistic medical imag…
We propose a density-valued vector autoregressive model with latent factors for multivariate time series of density functions. Motivated by weekly regional distributions of SARS-CoV-2 cycle threshold …
We establish the approximate controllability in $L^2$ for the nonlinear Benjamin-Ono equation on torus via two-dimensional control input. Our proof is based on adaptations of geometric control approac…
Let $-\Delta_{\mathbb{H}}+V$ be the Schr\"odinger operator on $\mathbb{H}$ where $V \in L^p(\mathbb{H}) \cap L^\infty(\mathbb{H})$ for some $p > 0$. If $(X_n)$ is a uniformly discrete sequence of comp…
In this paper, we first extend the explicit formula \cite{gerard2023explicit} for the classical Benjamin-Ono equation to each flow of the Benjamin-Ono hierarchy on line. We then use this representatio…
We investigate the Benjamin-Feir instability of small-amplitude gravity-capillary Stokes waves in deep water for the full water wave equations. While modulational instability has been classically pred…
In this paper, we tackle the Multiple Watchman Route Problem (MWRP), which aims to find a set of paths that M watchmen can follow such that every location on the map can be seen by at least one watchm…
We develop a framework for the fifth-order Kadomtsev--Petviashvili equation on $\mathbb{T}_x \times \mathbb{R}_y$ within a mean-zero KP-adapted Sobolev scale. A localized high-order feedback acting on…
Conformal selection (CS) uses calibration data to identify test inputs whose unobserved outcomes are likely to satisfy a pre-specified minimal quality requirement, while controlling the false discover…
We study two conjectures posed in the analysis of Boolean functions $f : \{-1, 1\}^n \to \{-1, 1\}$, in both of which, the Majority function plays a central role: the "Majority is Least Stable" (Benja…
Multimodal deep learning models that fuse whole-slide histopathology images with genomic data have achieved strong discriminative performance for cancer survival prediction, as measured by the concord…
In this paper, we introduce the concepts of the $u$-bracket, finite multiple harmonic $u$-series, and $u$-multiple zeta values via the Carlitz module. These objects serve as function field counterpart…
This article is concerned with Kronecker flows on the infinite torus. The work is partly motivated by the fact that many Hamiltonian PDEs and systems on infinite lattices admit invariant tori, of poss…
Daily probability changes in Kalshi macro prediction markets forecast cryptocurrency realized volatility through two distinct channels. The monetary policy channel, measured by Fed rate repricing on K…
For first passage percolation (FPP) on Euclidean lattices $\mathbb{Z}^d$ with $d\ge 2$, it is expected that the variance of the first passage time between two points grows sublinearly in the distance …
We prove that for almost all symmetric spaces $X$ and for any sequence of compact locally symmetric spaces $Y_n$ which is uniformly discrete, has a uniform spectral gap, and converges in the sense of …
The classical Goodstein process, defined via hereditary base-$k$ exponential normal form, is a well-known example of a principle unprovable in Peano Arithmetic. In this paper, we generalize this frame…
We carry out an extended symmetry analysis of the multi-layer quasi-geostrophic problem. This model is given by a system of an arbitrary number of coupled barotropic vorticity equations. Conservation …
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