A note on additive complements of the squares

Let $\mathcal{S}=\{1^2,2^2,3^2,...\}$ be the set of squares and $\mathcal{W}=\{w_n\}_{n=1}^{\infty} \subset \mathbb{N}$ be an additive complement of $\mathcal{S}$ so that $\mathcal{S} + \mathcal{W} \supset \{n \in \mathbb{N}: n \geq N_0\}$ for some $N_0$. Let $\mathcal{R}_{\mathcal{S},\mathcal{W}}(n) = \#\{(s,w):n=s+w, s\in \mathcal{S}, w\in \mathcal{W}\}$. In 2017, Chen-Fang \cite{C-F} studied the lower bound of $\sum_{n=1}^NR_{\mathcal{S},\mathcal{W}}(n)$. In this note, we improve Cheng-Fang's result and get that $$\sum_{n=1}^NR_{\mathcal{S},\mathcal{W}}(n)-N\gg N^{1/2}.$$ As an application, we make some progress on a problem of Ben Green problem by showing that $$\limsup_{n\rightarrow\infty}\frac{\frac{\pi^2}{16}n^2-w_n}{n}\ge \frac{\pi}{4}+\frac{0.193\pi^2}{8}.$$Comment: The new version significantly improves the result of the former on

When STING meets viruses: Sensing, trafficking and response

To effectively defend against microbial pathogens, the host cells mount antiviral innate immune responses by producing interferons (IFNs), and hundreds of IFN-stimulated genes (ISGs). Upon recognition of cytoplasmic viral or bacterial DNAs and abnormal endogenous DNAs, the DNA sensor cGAS synthesizes 2\u27,3\u27-cGAMP that induces STING (stimulator of interferon genes) undergoing conformational changes, cellular trafficking, and the activation of downstream factors. Therefore, STING plays a pivotal role in preventing microbial pathogen infection by sensing DNAs during pathogen invasion. This review is dedicated to the recent advances in the dynamic regulations of STING activation, intracellular trafficking, and post-translational modifications (PTMs) by the host and microbial proteins

Mechanism of crack propagation for K9 glass

In order to study the mechanism of crack propagation, the varied cutting-depth scratch experiment is carried out and smoothed particle hydrodynamics (SPH) simulation method is used to assistant the investigation. The SPH simulation results reveal that crack will propagate in the direction where stress concentration exceeds the fracture toughness of K9 glass. The initial crack length in critical transition depth is calculated by combining the critical stress of fracture and the fracture toughness of K9 glass. Based on the effective plastic strain, the relation between scratching depth and crack depth is obtained. The recovery of crack tip is found and explained from the relationship between cutting depth and crack depth. Using the energy balance theory of Griffith, the variation of material internal energy is revealed. Comparing the scratching forces obtained from experiment and simulation, the validity of simulation results is verified. The phenomenon of crack delayed propagation is found in both experiment and simulation. The explanation of mechanism is given

Passivity-based tracking control of an omnidirectional mobile robot using only one geometrical parameter

This paper presents an output feedback tracking control scheme for a three-wheeled omnidirectional mobile robot, based on passivity property and a modified generalized proportional integral (GPI) observer. The proposed control approach is attractive from an implementation point of view, since only one robot geometrical parameter (i.e., contact radius) is required. Firstly, a nominal dynamic model is given and the passivity property is analyzed. Then the controller is designed based on passivity property and a modified GPI observer. The controller design objective is to preserve the passivity property of the robot system in the closed-loop system, which is conceptually different from the traditional model-based control methodology. Particularly, the designed control system takes full advantage of the robot natural damping. Therefore, only considerably small or non differential feedback is needed. In addition, theoretical analysis is given to show the closed-loop stability behavior. Finally, experiments are conducted to validate the effectiveness of the proposed control system design in both tracking and robustness performance

Active Disturbance Rejection Control of Euler-Lagrange Systems Exploiting Internal Damping.

Active disturbance rejection control (ADRC) is an efficient control technique to accommodate both internal uncertainties and external disturbances. In the typical ADRC framework, however, the design philosophy is to "force" the system dynamics into a double-integral form by an extended state observer (ESO) and then the controller is designed. Especially, the systems' physical structure has been neglected in such a design paradigm. In this article, a new ADRC framework is proposed by incorporating at a fundamental level the physical structure of the Euler-Lagrange (EL) systems. In particular, the differential feedback gain can be selected considerably small or even 0, due to the effective exploitation of the system's internal damping. The design principle stems from an analysis of the energy balance of EL systems, yielding a physically interpretable design. Moreover, the exploitation of the system's internal damping is thoroughly discussed, which is of practical significance for applications of the proposed design. Besides, a sliding-mode ESO is designed to improve the estimation performance over traditional linear ESO. Finally, the proposed control framework is illustrated through tracking control of an omnidirectional mobile robot. Extensive experimental tests are conducted to verify the proposed design as well as the discussions

Economic dispatch of community-integrated energy system considering demand-side coordinated response

There are a large number of potential schedulable resources in the integrated energy system of electricity, heat, cold, and gas. However, most of these energy sources are currently operated separately, with low system flexibility, low energy utilization rate, and serious abandonment of wind and solar energy. In order to improve the flexibility of integrated energy systems and the capacity of renewable energy consumption, an economic dispatch of community-integrated energy systems considering demand-side coordinated response is proposed. Firstly, according to various energy characteristics, mathematical models of various energy forms are established, including wind energy, photovoltaic, gas turbine, gas boiler, and other component characteristics modeling. Secondly, an economic optimal scheduling model of community-integrated energy system considering demand side response is established, including the constraints and objective functions of the optimization model, and the optimization model is solved based on the Yalmip toolbox and Cplex solver in Matlab software. Finally, the effectiveness of the proposed strategy is verified by a simulation example

LdsConv : learned depthwise separable convolutions by group pruning

Standard convolutional filters usually capture unnecessary overlap of features resulting in a waste of computational cost. In this paper, we aim to solve this problem by proposing a novel Learned Depthwise Separable Convolution (LdsConv) operation that is smart but has a strong capacity for learning. It integrates the pruning technique into the design of convolutional filters, formulated as a generic convolutional unit that can be used as a direct replacement of convolutions without any adjustments of the architecture. To show the effectiveness of the proposed method, experiments are carried out using the state-of-the-art convolutional neural networks (CNNs), including ResNet, DenseNet, SE-ResNet and MobileNet, respectively. The results show that by simply replacing the original convolution with LdsConv in these CNNs, it can achieve a significantly improved accuracy while reducing computational cost. For the case of ResNet50, the FLOPs can be reduced by 40.9%, meanwhile the accuracy on the associated ImageNet increases

Trends in admission rates of primary angle closure diseases for the urban population in China, 2011–2021

BackgroundCataract surgery and laser peripheral iridotomy (LPI) are effective approaches for preventing primary angle closure diseases (PACDs), as well as acute primary angle closure (APAC). Due to the development of population screening and increases in cataract surgery rates, this study aimed to examine trends in the admission rates of PACD among the urban population in China.MethodsThis cross-sectional study examined patients who were admitted to a hospital for PACD, and who underwent cataract surgery or LPI operations. The data were obtained from the Yinzhou Regional Health Information Platform (YRHIP) from 2011 to 2021. The annual rates of PACD and APAC admissions, cataract surgery and LPI were analyzed, with the number of cases used as numerators and the annual resident population in Yinzhou district used as denominators.ResultsA total of 2,979 patients with PACD admissions, 1,023 patients with APAC admissions, 53,635 patients who underwent cataract surgery and 16,450 patients who underwent LPI were included. The number of annual admissions for PACD gradually increased from 22 cases (1.6/100000) in 2011 to 387 cases (30.8/100000) in 2016, after which it decreased to 232 cases (16.2/100000) in 2019 and then increased to 505 cases (30.6/100000) in 2021. The number of cataract surgeries gradually increased from 1728 (127.7/100000) in 2011 to 7002 (424.9/100000) in 2021. Similarly, the number of LPI gradually increased from 109 (8.0/100000) in 2011 to 3704 (224.8/100000) in 2021.ConclusionThe admission rates of PACD for the urban population in China have declined in recent years after a long increasing trend in the rates of cataract surgery and LPI. However, it increased rapidly during the COVID-19 epidemic. The national health database should be further utilized to investigate temporal trends in the prevalence of PACD