Optimal and parameter-free gradient minimization methods for convex and nonconvex optimization

We propose novel optimal and parameter-free algorithms for computing an approximate solution with small (projected) gradient norm. Specifically, for computing an approximate solution such that the norm of its (projected) gradient does not exceed $\varepsilon$, we obtain the following results: a) for the convex case, the total number of gradient evaluations is bounded by $O(1)\sqrt{L\|x_0 - x^*\|/\varepsilon}$, where $L$ is the Lipschitz constant of the gradient and $x^*$ is any optimal solution; b) for the strongly convex case, the total number of gradient evaluations is bounded by $O(1)\sqrt{L/\mu}\log(\|\nabla f(x_0)\|/\epsilon)$, where $\mu$ is the strong convexity modulus; and c) for the nonconvex case, the total number of gradient evaluations is bounded by $O(1)\sqrt{Ll}(f(x_0) - f(x^*))/\varepsilon^2$, where $l$ is the lower curvature constant. Our complexity results match the lower complexity bounds of the convex and strongly cases, and achieve the above best-known complexity bound for the nonconvex case for the first time in the literature. Moreover, for all the convex, strongly convex, and nonconvex cases, we propose parameter-free algorithms that do not require the input of any problem parameters. To the best of our knowledge, there do not exist such parameter-free methods before especially for the strongly convex and nonconvex cases. Since most regularity conditions (e.g., strong convexity and lower curvature) are imposed over a global scope, the corresponding problem parameters are notoriously difficult to estimate. However, gradient norm minimization equips us with a convenient tool to monitor the progress of algorithms and thus the ability to estimate such parameters in-situ

Numerical investigation on hydrodynamic performance of a novel shaftless rim-driven counter-rotating thruster considering gap fluid

Shaftless rim-driven thruster (RDT) has recently become the research focus for marine propulsion, primarily due to low vibration, low noise, and energy saving as its advantage. This study is based on CFD theory and used the Ansys-Fluent software to examine the hydrodynamic performance of a novel rim-driven counter-rotating thruster (RDCRT). It takes a No.19A+Ka4-70 duct propeller and a 20 kW RDT as examples, as it verifies the feasibility of the simulation method. It establishes three geometric models for RDCRT's hydrodynamic performance to determine whether it is necessary to consider the motor stator/rotor gap. It examines the flow distribution characteristics of the gap fluid friction force and flow channel and investigates the gap's influence on the hydrodynamic performance. Relevant case studies indicate that, when considering the gap, the calculation outcomes of the simulation model are between the stationary model and the rotational model of the rotor inner wall when ignoring the gap. In the Forward and Aft regions, the total frictional power of the gap channel correspondingly accounts for 1.7% and 1.35% of the rated power. Additionally, compared to situations with a gap, the pressure coefficient of the inner surface of the Forward and Aft rim without a gap is more significant. Thus, the hydrodynamic simulation model should not ignore the gap. For the RDCRT, the thrust coefficient, the torque coefficient, and the maximum efficiency value are more significant than those of the single-propeller RDT, hence validating its advantages

Short-range interaction of strongly nonlocal spatial optical solitons

A novel phenomenon is discovered that the short-range interaction between strongly nonlocal spatial solitons depends sinusoidally on their phase difference. The two neighbouring solitons at close proximate can be inter-trapped via the strong nonlocality, and propagate together as a whole. The trajectory of the propagation is a straight line with its slope controlled by the phase difference. The experimental results carried out in nematic liquid crystals agree quantitatively with the prediction. Our study suggests that the phenomenon to steer optical beams by controlling the phase difference could be used in all-optical information processing.Comment: 4 pages 6 figure

Covalently immobilized lipase on a thermoresponsive polymer with an upper critical solution temperature as an efficient and recyclable asymmetric catalyst in aqueous media

This work was financially supported by the National Natural Science Foundation of China (Grant No. 21203102), the Tianjin Municipal Natural Science Foundation (Grant No. 14JCQNJC06000), China Scholarship Council (Grant No. 201606200087), MOE (IRT13R30) and 111 Project (B12015).A thermoresponsive lipase catalyst with an upper critical solution temperature (UCST) of about 26 °C was exploited by covalent immobilization of an enzyme, Pseudomonas cepacia lipase (PSL), onto poly(acrylamide-co-acrylonitrile) via glutaraldehyde coupling. The experimental conditions for the PSL immobilization were optimized. The immobilized PSL was much more stable for wide ranges of temperature and pH than the free PSL. The material was also evaluated as an asymmetric catalyst in the kinetic resolution of racemic α-methylbenzyl butyrate at 55 °C in an aqueous medium and exhibited high catalytic performance and stability. Up to 50% conversion and 99.5% product enantiomeric excess were achieved, thus providing highly pure enantiomers. More importantly, this biocatalyst could be easily recovered by simple decantation for reuse based on temperature-induced precipitation. It showed good reusability and retained 80.5% of its original activity with a well reserved enantioselectivity in the 6th cycle. This work would shed light on the future development of new UCST-type enzyme catalysts.PostprintPeer reviewe

PLM-ARG: antibiotic resistance gene identification using a pretrained protein language model

Motivation: Antibiotic resistance presents a formidable global challenge to public health and the environment. While considerable endeavors have been dedicated to identify antibiotic resistance genes (ARGs) for assessing the threat of antibiotic resistance, recent extensive investigations using metagenomic and metatranscriptomic approaches have unveiled a noteworthy concern. A significant fraction of proteins defies annotation through conventional sequence similarity-based methods, an issue that extends to ARGs, potentially leading to their under-recognition due to dissimilarities at the sequence level. Results: Herein, we proposed an Artificial Intelligence-powered ARG identification framework using a pretrained large protein language model, enabling ARG identification and resistance category classification simultaneously. The proposed PLM-ARG was developed based on the most comprehensive ARG and related resistance category information (>28K ARGs and associated 29 resistance categories), yielding Matthew’s correlation coefficients (MCCs) of 0.983 ± 0.001 by using a 5-fold cross-validation strategy. Furthermore, the PLM-ARG model was verified using an independent validation set and achieved an MCC of 0.838, outperforming other publicly available ARG prediction tools with an improvement range of 51.8%–107.9%. Moreover, the utility of the proposed PLM-ARG model was demonstrated by annotating resistance in the UniProt database and evaluating the impact of ARGs on the Earth's environmental microbiota. Availability and implementation: PLM-ARG is available for academic purposes at https://github.com/Junwu302/PLM-ARG, and a user-friendly webserver (http://www.unimd.org/PLM-ARG) is also provided