The Eigencurve is Proper

We prove that the Coleman-Mazur eigencurve is proper over the weight space for any prime p and tame level N.Comment: Final refereed version; to appear in Duke mathematical Journa

Potential Energy Advantage of Quantum Economy

Energy cost is increasingly crucial in the modern computing industry with the wide deployment of large-scale machine learning models and language models. For the firms that provide computing services, low energy consumption is important both from the perspective of their own market growth and the government's regulations. In this paper, we study the energy benefits of quantum computing vis-a-vis classical computing. Deviating from the conventional notion of quantum advantage based solely on computational complexity, we redefine advantage in an energy efficiency context. Through a Cournot competition model constrained by energy usage, we demonstrate quantum computing firms can outperform classical counterparts in both profitability and energy efficiency at Nash equilibrium. Therefore quantum computing may represent a more sustainable pathway for the computing industry. Moreover, we discover that the energy benefits of quantum computing economies are contingent on large-scale computation. Based on real physical parameters, we further illustrate the scale of operation necessary for realizing this energy efficiency advantage.Comment: 23 pages, many figure

A review of distributed statistical inference

The rapid emergence of massive datasets in various fields poses a serious challenge to traditional statistical methods. Meanwhile, it provides opportunities for researchers to develop novel algorithms. Inspired by the idea of divide-and-conquer, various distributed frameworks for statistical estimation and inference have been proposed. They were developed to deal with large-scale statistical optimization problems. This paper aims to provide a comprehensive review for related literature. It includes parametric models, nonparametric models, and other frequently used models. Their key ideas and theoretical properties are summarized. The trade-off between communication cost and estimate precision together with other concerns are discussed

Single-Stage Diffusion NeRF: A Unified Approach to 3D Generation and Reconstruction

3D-aware image synthesis encompasses a variety of tasks, such as scene generation and novel view synthesis from images. Despite numerous task-specific methods, developing a comprehensive model remains challenging. In this paper, we present SSDNeRF, a unified approach that employs an expressive diffusion model to learn a generalizable prior of neural radiance fields (NeRF) from multi-view images of diverse objects. Previous studies have used two-stage approaches that rely on pretrained NeRFs as real data to train diffusion models. In contrast, we propose a new single-stage training paradigm with an end-to-end objective that jointly optimizes a NeRF auto-decoder and a latent diffusion model, enabling simultaneous 3D reconstruction and prior learning, even from sparsely available views. At test time, we can directly sample the diffusion prior for unconditional generation, or combine it with arbitrary observations of unseen objects for NeRF reconstruction. SSDNeRF demonstrates robust results comparable to or better than leading task-specific methods in unconditional generation and single/sparse-view 3D reconstruction.Comment: Project page: https://lakonik.github.io/ssdner

Dimension reduction for covariates in network data

A problem of major interest in network data analysis is to explain the strength of connections using context information. To achieve this, we introduce a novel approach named network-supervised dimension reduction by projecting covariates onto low-dimensional spaces for revealing the linkage pattern, without assuming a model.We propose a new loss function for estimating the parameters in the resulting linear projection, based on the notion that closer proximity in the low-dimension projection renders stronger connections. Interestingly, the convergence rate of our estimator is shown to depend on a network effect factor which is the smallest number that can partition a graph in a way similar to the graph coloring problem. Our methodology has interesting connections to principal component analysis and linear discriminant analysis, which we exploit for clustering and community detection. The methodology developed is further illustrated by numerical experiments and the analysis of a pulsar candidates data in astronomy

Logarithmic adic spaces: some foundational results

We develop a theory of log adic spaces by combining the theories of adic spaces and log schemes, and study the Kummer \'etale and pro-Kummer \'etale topology for such spaces. We also establish the primitive comparison theorem in this context, and deduce from it some related cohomological finiteness or vanishing results.Comment: 81 pages. This paper supersedes the preprint arXiv:1709.0578

Zero123++: a Single Image to Consistent Multi-view Diffusion Base Model

We report Zero123++, an image-conditioned diffusion model for generating 3D-consistent multi-view images from a single input view. To take full advantage of pretrained 2D generative priors, we develop various conditioning and training schemes to minimize the effort of finetuning from off-the-shelf image diffusion models such as Stable Diffusion. Zero123++ excels in producing high-quality, consistent multi-view images from a single image, overcoming common issues like texture degradation and geometric misalignment. Furthermore, we showcase the feasibility of training a ControlNet on Zero123++ for enhanced control over the generation process. The code is available at https://github.com/SUDO-AI-3D/zero123plus

One-2-3-45++: Fast Single Image to 3D Objects with Consistent Multi-View Generation and 3D Diffusion

Recent advancements in open-world 3D object generation have been remarkable, with image-to-3D methods offering superior fine-grained control over their text-to-3D counterparts. However, most existing models fall short in simultaneously providing rapid generation speeds and high fidelity to input images - two features essential for practical applications. In this paper, we present One-2-3-45++, an innovative method that transforms a single image into a detailed 3D textured mesh in approximately one minute. Our approach aims to fully harness the extensive knowledge embedded in 2D diffusion models and priors from valuable yet limited 3D data. This is achieved by initially finetuning a 2D diffusion model for consistent multi-view image generation, followed by elevating these images to 3D with the aid of multi-view conditioned 3D native diffusion models. Extensive experimental evaluations demonstrate that our method can produce high-quality, diverse 3D assets that closely mirror the original input image. Our project webpage: https://sudo-ai-3d.github.io/One2345plus_page

Physical activity and weight loss among adults with type 2 diabetes and overweight or obesity: a post hoc analysis of the Look AHEAD trial

Importance: Prior findings from the Look AHEAD trial showed no significant reduction in the risk of cardiovascular events by lifestyle-induced weight loss among individuals with type 2 diabetes (T2D) and overweight or obesity. However, physical activity (PA) may modify the changes in cardiovascular risk associated with weight loss. Objective: To examine the joint association of weight loss and PA with the risk of adverse cardiovascular events in patients with T2D and overweight or obesity. Design, Setting, and Participants: This cohort study was a post hoc analysis of the Look AHEAD randomized clinical trial, which compared the cardiovascular effects of weight loss by intensive lifestyle intervention vs diabetes support and education among individuals with T2D and overweight or obesity. The study was conducted from June 2001 to September 2012, and participants were patients in the substudy of accelerometry-measured PA from 8 locations in the United States. Data were analyzed from June to August 2023. Exposures: Body weight change and accelerometer-derived PA volume across the first 4 years. Main Outcomes and Measures: The primary outcome was a composite cardiovascular outcome including cardiovascular death, nonfatal myocardial infarction, nonfatal stroke, or hospitalization for angina. Results: Among a total of 1229 participants (mean [SD] age, 60 [7] years; 533 male [43%]), 333 (27%) achieved and maintained weight loss for the first 4 years. Among the individuals who maintained weight loss, 105 (32%) maintained high PA volume. During a median of 9.5 years of follow-up, 198 participants (16.1%) experienced the primary outcome. Compared with those with low PA volume and no weight loss (105 [15.8%]), maintaining high PA volume and weight loss was associated with a 61% lower risk of the primary end point (hazard ratio, 0.39; 95% CI, 0.19-0.81; P = .01). However, there was no significant difference in the risk of the primary end point among those with either weight loss only or high PA only. The multiplicative interaction between weight loss and PA for the risk of cardiovascular events was also significant (P for interaction = .01). Conclusions and Relevance: In this cohort study, maintaining weight loss and higher PA volume was associated with a lower risk of the composite cardiovascular outcome. The findings suggest that the cardiovascular benefits of PA may vary and be enhanced by weight loss among individuals with T2D and overweight or obesity