Computational Aspects of Optional P\'{o}lya Tree

Optional P\'{o}lya Tree (OPT) is a flexible non-parametric Bayesian model for density estimation. Despite its merits, the computation for OPT inference is challenging. In this paper we present time complexity analysis for OPT inference and propose two algorithmic improvements. The first improvement, named Limited-Lookahead Optional P\'{o}lya Tree (LL-OPT), aims at greatly accelerate the computation for OPT inference. The second improvement modifies the output of OPT or LL-OPT and produces a continuous piecewise linear density estimate. We demonstrate the performance of these two improvements using simulations

A FARM-TO-DOOR DELIVERY MODE FOR ORGANIC VEGETABLES UNDER MOBILE COMMERCE IN METROPOLISES OF CHINA

This paper presents a farm-to-door delivery mode for organic vegetables, which connects farmers and customers directly, under the circumstance of mobile commerce (M-commerce). In recent years, the need of organic vegetables is growing constantly in China. Meanwhile, the farm-to-door delivery mode widely spread in metropolises as people there barely have time to go to food markets on weekdays. However, the terrible traffic condition makes it impossible to conduct the delivery in day time. So vegetables have to be delivered very early in the morning (usually 3:00-7:00 A.M.), which makes the owner unable to attend delivery. And in the traditional delivery mode, the absence of delivery may lead to the package missing in China. Aiming at solving these practical issues in China, an SMS-based interaction system is integrated in the delivery mode for informing, endorsing, confirming, tracing and complaining. Intelligent cupboards are used as a buffer to realize the asynchronously endorsement. This is a new business mode that extends the frontiers of the M-commerce. It can greatly reduce the intermediate links of vegetable distribution and simplify the food purchasing in people’s daily life. This application of mobile technology would have a huge potential in market

Effective g-factors of carriers in inverted InAs/GaSb bilayers

We perform tilt-field transport experiment on inverted InAs/GaSb which hosts quantum spin Hall insulator. By means of coincidence method, Landau level (LL) spectra of electron and hole carriers are systematically studied at different carrier densities tuned by gate voltages. When Fermi level stays in the conduction band, we observe LL crossing and anti-crossing behaviors at odd and even filling factors respectively, with a corresponding g-factor of 11.5. It remains nearly constant for varying filling factors and electron densities. On the contrary, for GaSb holes only a small Zeeman splitting is observed even at large tilt angles, indicating a g-factor of less than 3.Comment: 16 pages containing 4 figure

Taming Gradient Variance in Federated Learning with Networked Control Variates

Federated learning, a decentralized approach to machine learning, faces significant challenges such as extensive communication overheads, slow convergence, and unstable improvements. These challenges primarily stem from the gradient variance due to heterogeneous client data distributions. To address this, we introduce a novel Networked Control Variates (FedNCV) framework for Federated Learning. We adopt the REINFORCE Leave-One-Out (RLOO) as a fundamental control variate unit in the FedNCV framework, implemented at both client and server levels. At the client level, the RLOO control variate is employed to optimize local gradient updates, mitigating the variance introduced by data samples. Once relayed to the server, the RLOO-based estimator further provides an unbiased and low-variance aggregated gradient, leading to robust global updates. This dual-side application is formalized as a linear combination of composite control variates. We provide a mathematical expression capturing this integration of double control variates within FedNCV and present three theoretical results with corresponding proofs. This unique dual structure equips FedNCV to address data heterogeneity and scalability issues, thus potentially paving the way for large-scale applications. Moreover, we tested FedNCV on six diverse datasets under a Dirichlet distribution with {\alpha} = 0.1, and benchmarked its performance against six SOTA methods, demonstrating its superiority.Comment: 14 page

Two-parameter estimation with three-mode NOON state in a symmetric three-well

We propose a theoretical scheme to realize two-parameter estimation via a Bose-Einstein condensates confined in a symmetric triple-well. The three-mode NOON state is prepared adiabatically as the initial state. Two phase differences between the wells are two parameters to be estimated. With the help of classical and quantum Fisher information, we study the sensitivity of the triple-well on estimating two phase parameters simultaneously. The result shows that the precision of simultaneous estimation of two parameters in a triple-well system can reach the Heisenberg scaling