Spectrum of Linear Difference Operators and the Solvability of Nonlinear Discrete Problems

Let T∈ℕ with T>5. Let 𝕋:={1,…,T}. We study the Fučik spectrum Σ of the discrete problem Δ2u(t-1)+λu+(t)-μu-(t)=0, t∈𝕋, u(0)=u(T+1)=0, where u+(t)=max⁡{u(t),0}, u-(t)=max⁡{-u(t),0}. We give an expression of Σ via the matching-extension method. We also use such discrete spectrum theory to study nonlinear boundary value problems of difference equations at resonance

Design of Unsigned Approximate Hybrid Dividers based on Restoring Array and Logarithmic Dividers

Approximate computer arithmetic has been extensively studied due to its advantages to further reduce power consumption and increase performance at reduced accuracy. Although a number of approximate adders and multipliers have been studied, only a few approximate dividers have been proposed. A logarithmic divider (LD) has low complexity and accuracy, while an exact array divider (EXD) has a high complexity. Therefore, in this paper, an approximate hybrid divider (AXHD) is proposed. It takes advantage of both LD and EXD to achieve a tradeoff between hardware performance and accuracy. Exact restoring divider cells are used to generate the most significant bits (MSBs) of the quotient for attaining a high accuracy while the other quotient digits are generated by using a LD as an approximate scheme to improve figures of merit such as power consumption, area and delay. To further save hardware resources, a so-called eliminated approximate hybrid divider (E-AXHD) based on AXHD is also proposed. In this improved design, a reduced width divider is used to replace the EXD in AXHD. Specifically, for a 16-by-8 design, n=(n + 1) array division is used to replace the n=8 array division (n < 8). The proposed AXHD and E-AXHD are evaluated and analyzed using error and hardware metrics. The proposed designs are also compared with EXD, LD and previous approximate dividers. The results show that the proposed designs outperform previous approximate dividers by considering both energy and error. The proposed hybrid dividers are of particular interest for error tolerant applications such as image processing and machine learning

Design and Evaluation of Approximate Logarithmic Multipliers for Low Power Error-Tolerant Applications

In this work, the designs of both non-iterative and iterative approximate logarithmic multipliers (LMs) are studied to further reduce power consumption and improve performance. Non-iterative approximate LMs (ALMs) that use three inexact mantissa adders, are presented. The proposed iterative approximate logarithmic multipliers (IALMs) use a set-one adder in both mantissa adders during an iteration; they also use lower-part-or adders and approximate mirror adders for the final addition. Error analysis and simulation results are also provided; it is found that the proposed approximate LMs with an appropriate number of inexact bits achieve a higher accuracy and lower power consumption than conventional LMs using exact units. Compared with conventional LMs with exact units, the normalized mean error distance (NMED) of 16-bit approximate LMs is decreased by up to 18% and the power-delay product (PDP) has a reduction of up to 37%. The proposed approximate LMs are also compared with previous approximate multipliers; it is found that the proposed approximate LMs are best suitable for applications allowing larger errors, but requiring lower energy consumption and low power. Approximate Booth multipliers fit applications with less stringent power requirements, but also requiring smaller errors. Case studies for error-tolerant computing applications are provided

How to Determine the Most Powerful Pre-trained Language Model without Brute Force Fine-tuning? An Empirical Survey

Transferability estimation has been attached to great attention in the computer vision fields. Researchers try to estimate with low computational cost the performance of a model when transferred from a source task to a given target task. Considering the effectiveness of such estimations, the communities of natural language processing also began to study similar problems for the selection of pre-trained language models. However, there is a lack of a comprehensive comparison between these estimation methods yet. Also, the differences between vision and language scenarios make it doubtful whether previous conclusions can be established across fields. In this paper, we first conduct a thorough survey of existing transferability estimation methods being able to find the most suitable model, then we conduct a detailed empirical study for the surveyed methods based on the GLUE benchmark. From qualitative and quantitative analyses, we demonstrate the strengths and weaknesses of existing methods and show that H-Score generally performs well with superiorities in effectiveness and efficiency. We also outline the difficulties of consideration of training details, applicability to text generation, and consistency to certain metrics which shed light on future directions.Comment: Accepted by Findings of EMNLP 202

Enzyme Biosensors for Point-of-Care Testing

Biosensors are devices that integrate a variety of technologies, containing biology, electronics, chemistry, physics, medicine, informatics, and correlated technology. Biosensors act as transducer with a biorecognition element and transform a biochemical reaction on the transducer surface directly into a measurable signal. The biosensors have the advantages of rapid analysis, low cost, and high precision, which are widely used in many fields, such as medical care, disease diagnosis, food detection, environmental monitoring, and fermentation industry. The enzyme biosensors show excellent application value owing to the development of fixed technology and the characteristics of specific identification, which can be combined with point-of-care testing (POCT) technology. POCT technology is attracting more and more attention as a very effective method of clinic detection. We outline the recent advances of biosensors in this chapter, focusing on the principle and classification of enzyme biosensor, immobilization method of biorecognition layers, and fabrication of amperometric biosensors, as well as the applications of POCT. A summary of glucose biosensor development and integrated setups is included. The latest applications of enzyme biosensors in diagnostic applications focusing on POCT of biomarkers in real samples were described

Ethyne Reducing Metal-Organic Frameworks to Control Fabrications of Core/shell Nanoparticles as Catalysts

An approach using cobalt metal-organic frameworks (Co-MOF) as precursors is established for the fabrication of cobalt nanoparticles in porous carbon shells (core/shell Co@C). Chemical vapor deposition of ethyne is used for controlling the reduction of cobalt nanoclusters in the MOF and the spontaneous formation of the porous carbon shells. The metallic cobalt cores formed are up to 4 - 6 nm with the crystal phase varying between hexagonally-close-packed (hcp) and face-centre-packed (fcc). The porous carbon shells change from amorphous to graphene with the ethyne deposition temperature increasing from 400 to 600 oC. The core/shell Co@C nanoparticles exhibit high catalytic activity in selectively converting syngas (CTY: 254.1 - 312.1 μmolCO·gCo-1·s-1) into hydrocarbons (4.0 - 5.2 gHC·g-cat-1·h-1) at 260 oC. As well as the crystal size and phase, the coordination numbers of the cobalt to oxygen and to other cobalt atoms on the surface of the cobalt nanoparticles, and the permeability of the porous carbon shell have been related to the catalytic performance in FTS reactions

Relationship Between Outdoor Air Pollutant Exposure and Premature Delivery in China- Systematic Review and Meta-Analysis

Objective: Preterm birth (PTB) is considered as a public health problem and one of the main risk factors related to the global disease burden. The purpose of this study aims to explore the influence of exposure to major air pollutants at different pregnancies on PTB.Methods: The relationship between air pollutants and PTB in China was collected from cohort studies and case-control studies published before 30 April 2022. Meta-analysis was carried out with STATA 15.0 software.Results: A total of 2,115 papers were retrieved, of which 18 papers met the inclusion criteria. The comprehensive effect of pollutant exposure and PTB were calculated. PM2.5 during entire pregnancy and O3 exposure during third trimester were positively associated with preterm birth. Every 10 μg/m3 increase in the average concentration of PM2.5 during the whole pregnancy will increase the risk of premature delivery by 4%, and every 10 μg/m3 increase in the average concentration of O3 in the third trimester will increase the risk of premature delivery by 1%.Conclusion: Exposure to PM2.5 entire prenatal pregnancy and O3 in third trimester is associated with an increased risk of preterm birth occurrence