On the Complexity of Finite-Sum Smooth Optimization under the Polyak-{\L}ojasiewicz Condition

This paper considers the optimization problem of the form $\min_{{\bf x}\in{\mathbb R}^d} f({\bf x})\triangleq \frac{1}{n}\sum_{i=1}^n f_i({\bf x})$, where $f(\cdot)$ satisfies the Polyak--{\L}ojasiewicz (PL) condition with parameter $\mu$ and $\{f_i(\cdot)\}_{i=1}^n$ is $L$-mean-squared smooth. We show that any gradient method requires at least $\Omega(n+\kappa\sqrt{n}\log(1/\epsilon))$ incremental first-order oracle (IFO) calls to find an $\epsilon$-suboptimal solution, where $\kappa\triangleq L/\mu$ is the condition number of the problem. This result nearly matches upper bounds of IFO complexity for best-known first-order methods. We also study the problem of minimizing the PL function in the distributed setting such that the individuals $f_1(\cdot),\dots,f_n(\cdot)$ are located on a connected network of $n$ agents. We provide lower bounds of $\Omega(\kappa/\sqrt{\gamma}\,\log(1/\epsilon))$, $\Omega((\kappa+\tau\kappa/\sqrt{\gamma}\,)\log(1/\epsilon))$ and $\Omega\big(n+\kappa\sqrt{n}\log(1/\epsilon)\big)$ for communication rounds, time cost and local first-order oracle calls respectively, where $\gamma\in(0,1]$ is the spectral gap of the mixing matrix associated with the network and~$\tau>0$ is the time cost of per communication round. Furthermore, we propose a decentralized first-order method that nearly matches above lower bounds in expectation

Effects of Impeller Diameter on High-Speed Rescue Pump

Impeller diameter is a crucial design parameter of high-speed rescue pumps because it affects the performance and inner flow characteristics of these pumps. In this study, a pump with an impeller diameter of 248 mm was modeled and its performance was tested. Numerical simulations were conducted under steady and unsteady states, in which the sizes of the impeller diameters were designated as 248 mm (original), 235.6 mm (5% trimmed), 223.2 mm (10% trimmed), and 210.8 mm (15% trimmed). ANSYS software was used to test the shear stress transport (SST k-ω) of the four models, and results agreed well with experimental data. Diameter size affected impeller characteristics in both steady and unsteady states. Subsequently, the differences in performance, hydraulic loss, pressure pulsation, and radial force of the impellers were evaluated. In the performance test, the head and efficiency of the pump decreased as impeller diameter was reduced. The result trends are in accordance with the trim law within the acceptable error range. In terms of hydraulic loss, the impeller and diffuser vane components presented opposite trends with flow rate increase. Finally, in terms of pressure pulsation and radial force, the amplitude diminished while periodicity improved as impeller diameter decreased

Regulation of the Optical Properties of Cellulose Nanocrystal Films by Sealed Deposition Treatment

Cellulose nanocrystal (CNC) can self-assemble and arrange at specific concentrations, imparting unique optical properties to the system. This paper investigated the effects of sealed deposition time and CNC concentration on the formation and alignment of cholesteric liquid crystals within the naturally dried films by analyzing the changes of CNC films in macroscopic color, UV-vis spectra, polarization optics, microscopic morphology, and crystal structure to elucidate the mechanism of CNC self-assembly behavior during the formation of CNC films. The results showed that when the sealed deposition time was extended to 48 h, the structural color development range and the long-range ordering of the cholesteric phase structure of CNC films were considerably enhanced. As the concentration increased, the CNC particle spacing decreased, the torsion angle between neighboring particles increased, and the pitch was compressed, decreasing from 480 nm to 344 nm. The results of polarized light microscopy analysis demonstrated that the sealed deposition treatment had a significant advantage in the formation of long-range ordered cholesteric phase structure in high-concentration CNC suspensions. The results of this research indicated that prolonging the sealed deposition time and increasing the CNC concentration could enhance the improvement of long-range orderliness in the films and promote the formation of cholesteric phase structural domains. This further improved the scientific basis for the preparation of CNC-based smart packaging materials and had a positive effect on the development of new visual food packaging and inspection materials

Developing a new generation of therapeutic dental polymers to inhibit oral biofilms and protect teeth

Polymeric tooth-colored restorations are increasingly popular in dentistry. However, restoration failures remain a major challenge, and more than 50% of all operative work was devoted to removing and replacing the failed restorations. This is a heavy burden, with the expense for restoring dental cavities in the U.S. exceeding $46 billion annually. In addition, the need is increasing dramatically as the population ages with increasing tooth retention in seniors. Traditional materials for cavity restorations are usually bioinert and replace the decayed tooth volumes. This article reviews cutting-edge research on the synthesis and evaluation of a new generation of bioactive dental polymers that not only restore the decayed tooth structures, but also have therapeutic functions. These materials include polymeric composites and bonding agents for tooth cavity restorations that inhibit saliva-based microcosm biofilms, bioactive resins for tooth root caries treatments, polymers that can suppress periodontal pathogens, and root canal sealers that can kill endodontic biofilms. These novel compositions substantially inhibit biofilm growth, greatly reduce acid production and polysaccharide synthesis of biofilms, and reduce biofilm colony-forming units by three to four orders of magnitude. This new class of bioactive and therapeutic polymeric materials is promising to inhibit tooth decay, suppress recurrent caries, control oral biofilms and acid production, protect the periodontium, and heal endodontic infections

Research progress in cell therapy for oral diseases: focus on cell sources and strategies to optimize cell function

In recent years, cell therapy has come to play an important therapeutic role in oral diseases. This paper reviews the active role of mesenchymal stem cells, immune cell sources, and other cells in oral disorders, and presents data supporting the role of cell therapy in oral disorders, including bone and tooth regeneration, oral mucosal disorders, oral soft tissue defects, salivary gland dysfunction, and orthodontic tooth movement. The paper will first review the progress of cell optimization strategies for oral diseases, including the use of hormones in combination with stem cells, gene-modified regulatory cells, epigenetic regulation of cells, drug regulation of cells, cell sheets/aggregates, cell-binding scaffold materials and hydrogels, nanotechnology, and 3D bioprinting of cells. In summary, we will focus on the therapeutic exploration of these different cell sources in oral diseases and the active application of the latest cell optimization strategies

Yb-ASE Suppression in Single-Frequency Hybrid Double Cladding Erbium–Ytterbium Co-Doped Fiber Amplifier with SMS Structure

A hybrid double cladding erbium–ytterbium co-doped fiber (EYDF) amplifier with a single-mode-multimode-single-mode (SMS) active fiber is demonstrated in this study. The hybrid gain fiber with an SMS structure is composed of two kinds of EYDFs with 6 and 12 μm core diameters. The transmission spectra of the SMS fiber structure were theoretically analyzed and the simulation results indicated that the maximum loss in the 1~1.1 μm band where the Yb-band amplified spontaneous emission (Yb-ASE) located, was much larger than that of the 1.5-μm band because of the wavelength difference. The power performance and spectra properties of the hybrid fiber amplifier were theoretically and experimentally analyzed and compared with a typical uniform fiber amplifier under the same conditions. The experimental results demonstrated that this hybrid fiber amplifier can suppress the Yb-ASE by over 12 dB and increase the slope efficiency by more than 2%, but the ASE in the 1.5-μm band increases by 2~3 dB. This work provides a possible method to enable EYDF amplifiers to suppress the Yb-ASE and overcome the pump bottleneck effect

Recent Progresses of Superhydrophobic Coatings in Different Application Fields: An Overview

With the development of material engineering and coating industries, superhydrophobic coatings with exceptional water repellence have increasingly come into researchers’ horizons. The superhydrophobic coatings with corrosion resistance, self-cleaning, anti-fogging, drag-reduction, anti-icing properties, etc., meet the featured requirements from different application fields. In addition, endowing superhydrophobic coatings with essential performance conformities, such as transparency, UV resistance, anti-reflection, water-penetration resistance, thermal insulation, flame retardancy, etc. plays a remarkable role in broadening their application scope. Various superhydrophobic coatings were fabricated by diverse technologies resulting from the fundamental demands of different fields. Most past reviews, however, provided only limited information, and lacked detailed classification and presentation on the application of superhydrophobic coatings in different sectors. In the current review, we will highlight the recent progresses on superhydrophobic coatings in automobile, marine, aircraft, solar energy and architecture-buildings fields, and discuss the requirement of prominent functionalities and performance conformities in these vital fields. Poor durability of superhydrophobic coating remains a practical challenge that needs to be addressed through real-world application. This review serves as a good reference source and provides insight into the design and optimization of superhydrophobic coatings for different applications