Towards the fast scrambling conjecture

Many proposed quantum mechanical models of black holes include highly nonlocal interactions. The time required for thermalization to occur in such models should reflect the relaxation times associated with classical black holes in general relativity. Moreover, the time required for a particularly strong form of thermalization to occur, sometimes known as scrambling, determines the time scale on which black holes should start to release information. It has been conjectured that black holes scramble in a time logarithmic in their entropy, and that no system in nature can scramble faster. In this article, we address the conjecture from two directions. First, we exhibit two examples of systems that do indeed scramble in logarithmic time: Brownian quantum circuits and the antiferromagnetic Ising model on a sparse random graph. Unfortunately, both fail to be truly ideal fast scramblers for reasons we discuss. Second, we use Lieb-Robinson techniques to prove a logarithmic lower bound on the scrambling time of systems with finite norm terms in their Hamiltonian. The bound holds in spite of any nonlocal structure in the Hamiltonian, which might permit every degree of freedom to interact directly with every other one.Comment: 34 pages. v2: typo correcte

ENM2020: A Free Online Course and Set of Resources on Modeling Species' Niches and Distributions

The field of distributional ecology has seen considerable recent attention, particularly surrounding the theory, protocols, and tools for Ecological Niche Modeling (ENM) or Species Distribution Modeling (SDM). Such analyses have grown steadily over the past two decades-including a maturation of relevant theory and key concepts-but methodological consensus has yet to be reached. In response, and following an online course taught in Spanish in 2018, we designed a comprehensive English-language course covering much of the underlying theory and methods currently applied in this broad field. Here, we summarize that course, ENM2020, and provide links by which resources produced for it can be accessed into the future. ENM2020 lasted 43 weeks, with presentations from 52 instructors, who engaged with >2500 participants globally through >14,000 hours of viewing and >90,000 views of instructional video and question-and-answer sessions. Each major topic was introduced by an "Overview" talk, followed by more detailed lectures on subtopics. The hierarchical and modular format of the course permits updates, corrections, or alternative viewpoints, and generally facilitates revision and reuse, including the use of only the Overview lectures for introductory courses. All course materials are free and openly accessible (CC-BY license) to ensure these resources remain available to all interested in distributional ecology

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

A hierarchical feature-based methodology to perform cervical cancer classification

Prevention of cervical cancer could be performed using Pap smear image analysis. This test screens pre-neoplastic changes in the cervical epithelial cells; accurate screening can reduce deaths caused by the disease. Pap smear test analysis is exhaustive and repetitive work performed visu-ally by a cytopathologist. This article proposes a workload-reducing algorithm for cervical cancer detection based on analysis of cell nuclei features within Pap smear images. We investigate eight traditional machine learning methods to perform a hierarchical classification. We propose a hierarchical classification methodology for computer-aided screening of cell lesions, which can recommend fields of view from the microscopy image based on the nuclei detection of cervical cells. We evaluate the performance of several algorithms against the Herlev and CRIC databases, using a varying number of classes during image classification. Results indicate that the hierarchical classification performed best when using Random Forest as the key classifier, particularly when compared with decision trees, k-NN, and the Ridge methods