Optimal Procurement Design: A Reduced Form Approach
Standard procurement models assume that the buyer knows the quality of the good at the time of procurement; however, in many settings, the quality is learned only long after the transaction. We study procurement problems in which the buyer’s valuation of the...
Dynamical mean-field analysis of adaptive Langevin diffusions: Propagation-of-chaos and convergence of the linear response
Motivated by an application to empirical Bayes learning in high-dimensional regression, we study a class of Langevin diffusions in a system with random disorder, where the drift coefficient is driven by a parameter that continuously adapts to the empirical distribution of the...
Dynamical mean-field analysis of adaptive Langevin diffusions: Replica-symmetric fixed point and empirical Bayes
In many applications of statistical estimation via sampling, one may wish to sample from a high-dimensional target distribution that is adaptively evolving to the samples already seen. We study an example of such dynamics, given by a Langevin diffusion for posterior sampling...
High-sensitivity and high-resolution collaborative determination of birefringence coefficient using weak measurement
We present a high-sensitivity and high-resolution birefringence coefficient determination system for nm-level membrane films based on weak measurement, addressing the sensitivity-resolution trade-off. A tunable bandwidth light source is exploited to achieve complementary momentum (P-pointer) and intensity (I-pointer) measurements,enabling calibration-free operation across various...
Global Solutions for 5D Quadratic Fourth-Order Schrödinger Equations
We prove small data scattering for the fourth-order Schr\”odinger equation with quadratic nonlinearity \begin{equation*} i\partial_t u+\Delta^2 u+\alpha u^2 + \beta \bar{u}^2=0\qquad\text{in }\mathbb{R}^5 \end{equation*} for $\alpha, \beta \in \mathbb{R}$. We extend the space-time resonance method, originally introduced by Germain, Masmoudi, and Shatah, to...
Exploring the User Experience of AI-Assisted Sound Searching Systems for Creative Workflows
Locating the right sound effect efficiently is an important yet challenging topic for audio production. Most current sound-searching systems rely on pre-annotated audio labels created by humans, which can be time-consuming to produce and prone to inaccuracies, limiting the efficiency of audio...
Real-Time Optimal Design of Experiment for Parameter Identification of Li-Ion Cell Electrochemical Model
Accurately identifying the parameters of electrochemical models of li-ion battery (LiB) cells is a critical task for enhancing the fidelity and predictive ability. Traditional parameter identification methods often require extensive data collection experiments and lack adaptability in dynamic environments. This paper describes...
A characterization of closed subfunctors through $3\times 3$-lemma property in extriangulated categories
Given an extriangulated category $(\mathcal{C},\mathbb{E},\mathfrak{s})$, we introduce the $3 \times 3$-lemma property for subfunctors of $\mathbb{E}$ and prove that an additive subfunctor $\mathbb{F}$ of $\mathbb{E}$ is closed if, and only if, it satisfies this condition. This characterization extends a well known result...
On the Price of Differential Privacy for Hierarchical Clustering
Hierarchical clustering is a fundamental unsupervised machine learning task with the aim of organizing data into a hierarchy of clusters. Many applications of hierarchical clustering involve sensitive user information, therefore motivating recent studies on differentially private hierarchical clustering under the rigorous framework...
Central limit theorems and moderate deviations for additive functionals of SSEP on regular trees
In this paper, we are concerned with the symmetric simple exclusion process (SSEP) on the regular tree $\mathcal{T}_d$. A central limit theorem and a moderate deviation principle of the additive functional of the process are proved, which include the CLT and the...