A formal proof of the Kepler conjecture

This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project

BLOOM: A 176B-Parameter Open-Access Multilingual Language Model

Large language models (LLMs) have been shown to be able to perform new tasks based on a few demonstrations or natural language instructions. While these capabilities have led to widespread adoption, most LLMs are developed by resource-rich organizations and are frequently kept from the public. As a step towards democratizing this powerful technology, we present BLOOM, a 176B-parameter open-access language model designed and built thanks to a collaboration of hundreds of researchers. BLOOM is a decoder-only Transformer language model that was trained on the ROOTS corpus, a dataset comprising hundreds of sources in 46 natural and 13 programming languages (59 in total). We find that BLOOM achieves competitive performance on a wide variety of benchmarks, with stronger results after undergoing multitask prompted finetuning. To facilitate future research and applications using LLMs, we publicly release our models and code under the Responsible AI License

Possible Monitoring and Removal of As(III) by an Integrated System of Electrochemical Sensor and Nanocomposite Materials

In this study, nanocomposites composed of magnetite nanoparticles (MNPs) coated with polyaniline fabricated by in situ polymerization were prepared for arsenic adsorption. Properties of particular MNPs and their nanocomposites were characterized with scanning electron microscopy, X-ray diffraction spectroscopy, and Fourier transform infrared spectroscopy. The As(III) concentration before and after adsorption on nanocomposites was detected by atomic absorption spectroscopy method and then compared with the results measured by a self-developed potentiostat system with anodic stripping voltammetry method. The polyaniline coating resulted in an improvement for As(III) adsorption ability of magnetite nanoparticles, and among the three compositions of PAni/MNP nanocomposites, the 5 wt% PAni showed the highest capability of As(III) adsorption (or removal) of 50 mg/g. Performing pH investigation, the concentration of remaining As decreased when pH increased from 2 to 5 and reached saturation value at higher pH. Above all, the electronic device can be integrated with As(III) removal system using PAni/MNP nanocomposites, proving to act as an independent monitoring system, and even more the adsorbent on the composites could be removed and the recyclability of the material was also investigated

A FORMAL PROOF OF THE KEPLER CONJECTURE

Contains fulltext : 176365.pdf (publisher's version ) (Open Access

Optimizing the Partial Gear Ratios of the Two-stage Worm Gearbox for Minimizing Total Gearbox Cost

Optimizing the design of a worm gearbox is complex to get due to considering multiple objectives and numerous main design parameters. Hence, a more consistent and robust optimization technique will be considered in obtaining the optimized results. This paper presents the optimization process of the Two-Stage Worm Gearbox with the objective function of minimizing total gearbox cost. Ten main design parameters are chosen as input parameters for evaluating their impacts on the response of the partial gear ratio u2. In this study, the simulation experiments were used, which do not need cost to perform all potential tests. In order to do this, a 2^(10-3) model and using 1/16 fractional model were selected due to the limitation of the built-in function in Minitab@18. Moreover, the screening experiments are purposely used to determine the number of parameters, which has a minor influence on the response. Compared to using the Taguchi technique, the model of 2^11 corresponding to L32 or 32 tests is a simple method to achieve the objectives. The results show that Total gearbox ratio exhibits the biggest effect on the response compared to others. Furthermore, the interactions between these factors to the remaining are significant. The high reliability of the proposed model is verified by simulation experiments. The random tendency of data shows that u2 is not crucially influenced by other than the input parameters. The data in versus order prove that the response is not varied to the time factor. Moreover, the coefficients of adjusted R2 and R2 are both greater than 99 %, it can be concluded that the proposed regression model is appropriate. The proposed optimization process in this study is reliable and the optimal design method can provide a useful reference on performance improvement of other worm gears