Oscillation of second order self-conjugate differential equation with impulses

AbstractIn this paper, we investigate the oscillation of second-order self-conjugate differential equation with impulses(1)(a(t)(x(t)+p(t)x(t-τ))′)′+q(t)x(t-σ)=0,t≠tk,t⩾t0,(2)x(tk+)=(1+bk)x(tk),k=1,2,…,(3)x′(tk+)=(1+bk)x′(tk),k=1,2,…,where a,p,q are continuous functions in [t0,+∞), q(t)⩾0, a(t)>0, ∫t0∞(1/a(s))ds=∞, τ>0, σ>0, bk>-1, 0<t0<t1 <t2<⋯<tk<⋯ and limk→∞tk=∞. We get some sufficient conditions for the oscillation of solutions of Eqs. (1)–(3)

Progressive-Hint Prompting Improves Reasoning in Large Language Models

The performance of Large Language Models (LLMs) in reasoning tasks depends heavily on prompt design, with Chain-of-Thought (CoT) and self-consistency being critical methods that enhance this ability. However, these methods do not fully exploit the answers generated by the LLM to guide subsequent responses. This paper proposes a new prompting method, named Progressive-Hint Prompting (PHP), that enables automatic multiple interactions between users and LLMs by using previously generated answers as hints to progressively guide toward the correct answers. PHP is orthogonal to CoT and self-consistency, making it easy to combine with state-of-the-art techniques to further improve performance. We conducted an extensive and comprehensive evaluation to demonstrate the effectiveness of the proposed method. Our experimental results on six benchmarks show that combining CoT and self-consistency with PHP significantly improves accuracy while remaining highly efficient. For instance, with text-davinci-003, we observed a 4.2% improvement on GSM8K with greedy decoding compared to Complex CoT, and a 46.17% reduction in sample paths with self-consistency. With GPT-4 and PHP, we achieve state-of-the-art performances on SVAMP (91.9%), GSM8K (95.5%) and AQuA (79.9%).Comment: Tech Repor

Backward Reasoning in Large Language Models for Verification

Chain-of-Though (CoT) prompting has shown promising performance in various reasoning tasks. Recently, Self-Consistency \citep{wang2023selfconsistency} proposes to sample a diverse set of reasoning chains which may lead to different answers while the answer that receives the most votes is selected. In this paper, we propose a novel method to use backward reasoning in verifying candidate answers. We mask a token in the question by ${\bf x}$ and ask the LLM to predict the masked token when a candidate answer is provided by \textit{a simple template}, i.e., ``\textit{\textbf{If we know the answer of the above question is \{a candidate answer\}, what is the value of unknown variable ${\bf x}$?}}'' Intuitively, the LLM is expected to predict the masked token successfully if the provided candidate answer is correct. We further propose FOBAR to combine forward and backward reasoning for estimating the probability of candidate answers. We conduct extensive experiments on six data sets and three LLMs. Experimental results demonstrate that FOBAR achieves state-of-the-art performance on various reasoning benchmarks.Comment: Preprin

Nanocomposite hydrogel fibers in the field of diagnosis and treatment

In the past few decades, many researchers have focused their research interests on nanocomposite hydrogel fibers (NHFs). These practitioners have developed and optimized techniques for preparing nanofiber membranes such as the template method, microfluidic spinning, electrospinning, wet spinning and three-dimensional printing (3D printing). NHFs have important applications in wearable monitoring, diagnosis and nursing due to their various excellent properties (such as high-water content, porous morphology, flexibility, braiding and rich active functional groups). In this paper, the latest progress of NHFs in pose monitoring, continuous monitoring of physiological indicators, diagnosis, wearables, nursing, drug delivery and dressings are reviewed. This paper also aims to review their key operational parameters, advantages and disadvantages of NHFs in the above fields, including sensitivity, working range and other special properties. Specifically, NHFs can be used for continuous monitoring of biological postures (such as gestures) or physiological indicators (such as blood sugar) in vitro and in vivo. NHFs also can be used for long-term monitoring of related indicators in the wearable field. NHFs can be used in tissue engineering and drug delivery. Finally, we look forward to the development prospects, challenges and opportunities of the next generation of NHFs. We confirm that the emergence of NHFs in the field of diagnosis and treatment has opened up a new vision for human health. Researchers have optimized the template method, microfluidic spinning, electrospinning, wet spinning and 3D printing

MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (e.g., LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called MetaMathQA. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (i.e., GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves 66.4% on GSM8K and 19.4% on MATH, exceeding the state-of-the-art models of the same size by 11.5% and 8.7%. Particularly, MetaMath-70B achieves an accuracy of 82.3% on GSM8K, slightly better than GPT-3.5-Turbo. We release all the MetaMathQA dataset, the MetaMath models with different model sizes and the training code for public use.Comment: Technical Report, Work in Progress. Project Page: https://meta-math.github.io

Graphene-wrapped reversible reaction for advanced hydrogen storage

Here, we report the fabrication of a graphene-wrapped nanostructured reactive hydride composite, i.e., 2LiBH4-MgH2, made by adopting graphene-supported MgH2 nanoparticles (NPs) as the nanoreactor and heterogeneous nucleation sites. The porous structure, uniform distribution of MgH2 NPs, and the steric confinement by flexible graphene induced a homogeneous distribution of 2LiBH4-MgH2 nanocomposite on graphene with extremely high loading capacity (80 wt%) and energy density. The well-defined structural features, including even distribution, uniform particle size, excellent thermal stability, and robust architecture endow this composite with significant improvements in its hydrogen storage performance. For instance, at a temperature as low as 350 °C, a reversible storage capacity of up to 8.9 wt% H2, without degradation after 25 complete cycles, was achieved for the 2LiBH4-MgH2 anchored on graphene. The design of this three-dimensional architecture can offer a new concept for obtaining high performance materials in the energy storage field

Selectively enhanced expression of prophenoloxidase activating enzyme 1 (PPAE1) at a bacteria clearance site in the white shrimp, Litopenaeus vannamei

<p>Abstract</p> <p>Background</p> <p>The prophenoloxidase-activating (PO activating) system plays an important role in the crustacean innate immunity, particularly in wound healing and pathogen defense. A key member of this system is prophenoloxidase-activating enzyme (PPAE), which is the direct activator of prophenoloxidase (proPO). Despite their importance in crustacean PO activating system, the studies on them remain limited.</p> <p>Results</p> <p>Here we report on a PPAE of white shrimp, <it>Litopenaeus vannamei </it>(lvPPAE1), which showed 94% similarity to PPAE1 of <it>Penaeus monodon</it>. We found that lvPPAE1 in fluid hemocytes was down regulated after challenge by <it>Vibrio harveyi </it>but was enhanced when shrimps were exposed to a bacteria-rich environment for long-term. In <it>vivo </it>gene silence of lvPPAE1 by RNAi can significantly reduce the phenoloxidase activity (PO) and increase the susceptibility of shrimps to <it>V. harveyi</it>. Although lvPPAE1 was down-regulated in fluid hemocytes by <it>Vibrio </it>challenge, its expression increased significantly in gill after bacteria injection, which is the primary bacteria-clearance tissue.</p> <p>Conclusion</p> <p>Suppressed expression in fluid hemocytes and enhanced expression in gill indicates selectively enhanced expression at the bacterial clearance site. This is a novel feature for PPAE expression. The results will contribute to our understanding of the PO activating system in crustaceans.</p

Multi-source excited travelling-wave bowtie antenna based on a meander series of YBCO bicrystal Josephson junctions

Series superconducting Josephson junctions (JJs), as terahertz (THz) mixers, have attracted increasing attentions due to their advantages in solving the saturation problem of superconducting mixers, achieving higher mixing harmonics and higher sensitivity in THz band. However, the normal-state resistances of the series JJs are so low that there exists an impedance mismatch between the coupled antenna and the JJs. In this paper, a meander embedding travelling-wave bowtie antenna is proposed for a series of bicrystal JJs. With this antenna, not only the problem of impedance mismatch can be solved, but also more series JJs can be inserted into the antenna. Five and even seven series JJs in the meander match the proposed antenna well. Furthermore, combined current distribution, far-field radiation patterns and parameter study are investigated in the numerical simulation to analyze this antenna

A Review of Modeling and Control of Piezoelectric Stick-Slip Actuators

Piezoelectric stick-slip actuators with high precision, large actuating force, and high displacement resolution are currently widely used in the field of high-precision micro-nano processing and manufacturing. However, the non-negligible, non-linear factors and complexity of their characteristics make its modeling and control quite difficult and affect the positioning accuracy and stability of the system. To obtain higher positioning accuracy and efficiency, modeling and control of piezoelectric stick-slip actuators are meaningful and necessary. Firstly, according to the working principle of stick-slip drive, this paper introduces the sub-models with different characteristics, such as hysteresis, dynamics, and friction, and presents the comprehensive modeling representative piezoelectric stick-slip actuators. Next, the control approaches suggested by different scholars are also summarized. Appropriate control strategies are adopted to reduce its tracking error and position error in response to the influence of various factors. Lastly, future research and application prospects in modeling and control are pointed out