An extended log-normal method of moments (ELNMOM) is presented in this study for solving the population balance equation (PBE) for Brownian coagulation. The method is an extension of the log-normal method of moments (LNMOM) proposed by Lee in 1983. The ELNMOM uses the superposition of log-normal subdistributions to represent the size distribution. Unlike previous modal studies, the subdistributions are not independent modes but flexible components in this study and the closure of this method is achieved by introducing additional higher-order moment equations. Based on some simplifying assumptions, the ELNMOM is implemented with only four adjustable parameters for a preliminary exploration. The method is then validated by comparing the size distribution parameters predicted by this method with those predicted by the LNMOM and other numerical methods for Brownian coagulation in the continuum regime and the free-molecular regime. The results show that the ELNMOM more accurately predicts the total particle number concentration, the geometric standard deviation and the geometric mean particle volume than the LNMOM while not taking much more computation time.

Color image binarization plays a pivotal role in image preprocessing work and significantly impacts subsequent tasks, particularly for text recognition. This paper concentrates on document image binarization (DIB), which aims to separate an image into a foreground (text) and background (non-text content). We thoroughly analyze conventional and deep-learning-based approaches and conclude that prevailing DIB methods leverage deep learning technology. Furthermore, we explore the receptive fields of pre- and post-network training to underscore the Transformer model’s advantages. Subsequently, we introduce a lightweight model based on the U-Net structure and enhanced with the MobileViT module to capture global information features in document images better. Given its adeptness at learning both local and global features, our proposed model demonstrates competitive performance on two standard datasets (DIBCO2012 and DIBCO2017) and good robustness on the DIBCO2019 dataset. Notably, our proposed method presents a straightforward end-to-end model devoid of additional image preprocessing or post-processing, eschewing the use of ensemble models. Moreover, its parameter count is less than one-eighth of the model, which achieves the best results on most DIBCO datasets. Finally, two sets of ablation experiments are conducted to verify the effectiveness of the proposed binarization model.

Declarative models help improve the reliability of software systems: models can be used to convey requirements, analyze system designs and verify implementation properties. Alloy is a commonly used modeling language. A key strength of Alloy is the Analyzer, Alloy's integrated development environment (IDE), which allows users to write and execute models by leveraging a fully automatic SAT based analysis engine. Unfortunately, writing correct constraints of complex properties is difficult. To help users identify fault locations, AlloyFL is a fault localization technique that takes as input a faulty Alloy model and a fault-revealing test suite. As output, AlloyFL returns a ranked list of locations from most to least suspicious. This paper describes our Java implementation of AlloyFL as an extension to the Analyzer. Our experimental results show AlloyFL is capable of detecting the location of real world faults and works in the presence of multiple faulty locations. The demo video for AlloyFL can be found at https://youtu.be/ZwgP58Nsbx8.