Refined Asymptotics of the Finite-Size Magnetization via a New Conditional Limit Theorem for the Spin

We study the fluctuations of the spin per site around the thermodynamic magnetization in the mean-field Blume-Capel model. Our main theorem generalizes the main result in a previous paper (Ellis, Machta, and Otto) in which the first rigorous confirmation of the statistical mechanical theory of finite-size scaling for a mean-field model is given. In that paper our goal is to determine whether the thermodynamic magnetization is a physically relevant estimator of the finite-size magnetization. This is done by comparing the asymptotic behaviors of these two quantities along parameter sequences converging to either a second-order point or the tricritical point in the mean-field Blume-Capel model. The main result is that the thermodynamic magnetization and the finite-size magnetization are asymptotic when the parameter $\alpha$ governing the speed at which the sequence approaches criticality is below a certain threshold $\alpha_0$. Our main theorem in the present paper on the fluctuations of the spin per site around the thermodynamic magnetization is based on a new conditional limit theorem for the spin, which is closely related to a new conditional central limit theorem for the spin.Comment: 78 pages, 2 figure

SheetCopilot: Bringing Software Productivity to the Next Level through Large Language Models

Computer end users have spent billions of hours completing daily tasks like tabular data processing and project timeline scheduling. Most of these tasks are repetitive and error-prone, yet most end users lack the skill to automate these burdensome works. With the advent of large language models (LLMs), directing software with natural language user requests become a reachable goal. In this work, we propose a SheetCopilot agent that takes natural language task and control spreadsheet to fulfill the requirements. We propose a set of atomic actions as an abstraction of spreadsheet software functionalities. We further design a state machine-based task planning framework for LLMs to robustly interact with spreadsheets. We curate a representative dataset containing 221 spreadsheet control tasks and establish a fully automated evaluation pipeline for rigorously benchmarking the ability of LLMs in software control tasks. Our SheetCopilot correctly completes 44.3\% of tasks for a single generation, outperforming the strong code generation baseline by a wide margin. Our project page:https://sheetcopilot.github.io/.Comment: Accepted to NeurIPS 202

Latency Minimization for Multiuser Computation Offloading in Fog-Radio Access Networks

This paper considers computation offloading in fog-radio access networks (F-RAN), where multiple user equipments (UEs) offload their computation tasks to the F-RAN through a number of fog nodes. Each UE can choose one of the fog nodes to offload its task, and each fog node may simultaneously serve multiple UEs. Depending on the computation burden at the fog nodes, the tasks may be computed by the fog nodes or further offloaded to the cloud via capacity-limited fronthaul links. To compute all UEs tasks as fast as possible, joint optimization of UE-Fog association, radio and computation resources of F-RAN is proposed to minimize the maximum latency of all UEs. This min-max problem is formulated as a mixed integer nonlinear program (MINP). We first show that the MINP can be reformulated as a continuous optimization problem, and then employ the majorization minimization (MM) approach to finding a solution for it. The MM approach that we develop herein is unconventional in that---each MM subproblem is inexactly solved with the same provable convergence guarantee as the conventional exact MM. In addition, we also consider a cooperative offloading model, where the fog nodes compress-and-forward their received signals to the cloud. Under this model, a similar min-max latency optimization problem is formulated and tackled again by the inexact MM approach. Simulation results show that the proposed algorithms outperform some heuristic offloading strategies, and that the cooperative offloading is generally better than the non-cooperative one.Comment: 11 pages, 8 figure

Degradation assessment of waterlogged wood at Haimenkou site

Haimenkou site is the largest railing-enclosed wooden architecture settlement site on the waterfrontin current China. This research conducts degradation assessment of waterlogged wood at Haimenkou site withvarious methods, including maximum moisture content analysis, basic density analysis, shrinkage measurement,swelling analysis, chemical composition analysis, measurement of compression strength parallel to grain, SEMmicrostructure analysis and measurement of crystallinity, providing scientific guidance for the subsequentformulation of proper methods of reinforcement