Dynamic Analysis of a Two-Language Competitive Model with Control Strategies

The dynamic behavior of a two-language competitive model is analyzed systemically in this paper. By the linearization and the Bendixson-Dulac theorem on dynamical system, some sufficient conditions on the globally asymptotical stability of the trivial equilibria and the existence and the stability of the positive equilibrium of this model are presented. Nextly, in order to protect the endangered language, an optimal control problem relative to this model is explored. We derive some necessary conditions to solve the optimal control problem and present some numerical simulations using a Runge-Kutta fourth-order method. Finally, the languages competitive model is extended to this model assessing the impact of state-dependent pulse control strategy. Using the Poincaré map, differential inequality, and method of qualitative analysis, we prove the existence and stability of positive order-1 periodic solution for this control model. Numerical simulations are carried out to illustrate the main results and the feasibility of state-dependent impulsive control strategy.This paper has been partially supported by the Scientific Research Programmes of Colleges in Xinjiang (Grant no. XJEDU2011S08), the Natural Science Foundation of Xinjiang (Grant no. 2011211B08), the National Natural Science Foundation of China (Grants nos. 11001235, 11271312, and 11261056), the China Postdoctoral Science Foundation (Grants nos. 20110491750 and 2012T50836), and the Ministerio de Economia y Competitividad (Spain), Project no. MTM2010-15314 and has been co-financed by the European Community Fund FEDERS

Analysis of an age-structured dengue model with multiple strains and cross immunity

Dengue fever is a typical mosquito-borne infectious disease, and four strains of it are currently found. Clinical medical research has shown that the infected person can provide life-long immunity against the strain after recovering from infection with one strain, but only provide partial and temporary immunity against other strains. On the basis of the complexity of transmission and the diversity of pathogens, in this paper, a multi-strain dengue transmission model with latency age and cross immunity age is proposed. We discuss the well-posedness of this model and give the terms of the basic reproduction number R0 = max{R1, R2} , where Ri is the basic reproduction number of strain i (i = 1, 2). Particularly, we obtain that the model always has a unique diseasefree equilibrium P0 which is locally stable for R0 1, the strain-i dominant equilibrium Pi is locally stable for Rj < R∗ i (i, j = 1, 2, i 6= j). Additionally, the threshold criteria on the uniformly persistence, the existence and global asymptotically stability of coexistence equilibrium are also obtained. Finally, these theoretical results and interesting conclusions are illustrated with some numerical simulations

Harnessing the Wisdom in Colloidal Chemistry to Make Stable Single-Atom Catalysts

Research on single‐atom catalysts (SACs), or atomically dispersed catalysts, has been quickly gaining momentum over the past few years. Although the unique electronic structure of singly dispersed atoms enables uncommon—sometimes exceptional—activities and selectivities for various catalytic applications, developing reliable and general procedures for preparing stable, active SACs in particular for applications under reductive conditions remains a major issue. Herein, the challenges associated with the synthesis of SACs are highlighted semiquantitatively and three stabilization techniques inspired by colloidal science including steric, ligand, and electrostatic stabilization are proposed. Some recent examples are discussed in detail to showcase the power of these strategies in the synthesis of stable SACs without compromising catalytic activity. The substantial further potential of steric, ligand, and electrostatic effects for developing SACs is emphasized. A perspective is given to point out opportunities and remaining obstacles, with special attention given to electrostatic stabilization where little is done so far. The stabilization strategies presented herein have a wide applicability in the synthesis of a series of new SACs with improved performances

Baichuan 2: Open Large-scale Language Models

Large language models (LLMs) have demonstrated remarkable performance on a variety of natural language tasks based on just a few examples of natural language instructions, reducing the need for extensive feature engineering. However, most powerful LLMs are closed-source or limited in their capability for languages other than English. In this technical report, we present Baichuan 2, a series of large-scale multilingual language models containing 7 billion and 13 billion parameters, trained from scratch, on 2.6 trillion tokens. Baichuan 2 matches or outperforms other open-source models of similar size on public benchmarks like MMLU, CMMLU, GSM8K, and HumanEval. Furthermore, Baichuan 2 excels in vertical domains such as medicine and law. We will release all pre-training model checkpoints to benefit the research community in better understanding the training dynamics of Baichuan 2.Comment: Baichuan 2 technical report. Github: https://github.com/baichuan-inc/Baichuan

Copy Number Variation in CNP267 Region May Be Associated with Hip Bone Size

Osteoporotic hip fracture (HF) is a serious global public health problem associated with high morbidity and mortality. Hip bone size (BS) has been identified as one of key measurable risk factors for HF, independent of bone mineral density (BMD). Hip BS is highly genetically determined, but genetic factors underlying BS variation are still poorly defined. Here, we performed an initial genome-wide copy number variation (CNV) association analysis for hip BS in 1,627 Chinese Han subjects using Affymetrix GeneChip Human Mapping SNP 6.0 Array and a follow-up replicate study in 2,286 unrelated US Caucasians sample. We found that a copy number polymorphism (CNP267) located at chromosome 2q12.2 was significantly associated with hip BS in both initial Chinese and replicate Caucasian samples with p values of 4.73E-03 and 5.66E-03, respectively. An important candidate gene, four and a half LIM domains 2 (FHL2), was detected at the downstream of CNP267, which plays important roles in bone metabolism by binding to several bone formation regulator, such as insulin-like growth factor-binding protein 5 (IGFBP-5) and androgen receptor (AR). Our findings suggest that CNP267 region may be associated with hip BS which might influence the FHL2 gene downstream

2D Black Phosphorus: from Preparation to Applications for Electrochemical Energy Storage

Black phosphorus (BP) is rediscovered as a 2D layered material. Since its first isolation in 2014, 2D BP has triggered tremendous interest in the fields of condensed matter physics, chemistry, and materials science. Given its unique puckered monolayer geometry, 2D BP displays many unprecedented properties and is being explored for use in numerous applications. The flexibility, large surface area, and good electric conductivity of 2D BP make it a promising electrode material for electrochemical energy storage devices (EESDs). Here, the experimental and theoretical progress of 2D BP is presented on the basis of its preparation methods. The structural and physiochemical properties, air instability, passivation, and EESD applications of 2D BP are discussed systemically. Specifically, the latest research findings on utilizing 2D BP in EESDs, such as lithium‐ion batteries, supercapacitors, and emerging technologies (lithium–sulfur batteries, magnesium‐ion batteries, and sodium‐ion batteries), are summarized. On the basis of the current progress, a few personal perspectives on the existing challenges and future research directions in this developing field are provided