The strong chromatic index of 1-planar graphs

The chromatic index $\chi'(G)$ of a graph $G$ is the smallest $k$ for which $G$ admits an edge $k$-coloring such that any two adjacent edges have distinct colors. The strong chromatic index $\chi'_s(G)$ of $G$ is the smallest $k$ such that $G$ has a proper edge $k$-coloring with the condition that any two edges at distance at most 2 receive distinct colors. A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, we show that every graph $G$ with maximum average degree $\bar{d}(G)$ has $\chi'_{s}(G)\le (2\bar{d}(G)-1)\chi'(G)$. As a corollary, we prove that every 1-planar graph $G$ with maximum degree $\Delta$ has $\chi'_{\rm s}(G)\le 14\Delta$, which improves a result, due to Bensmail et al., which says that $\chi'_{\rm s}(G)\le 24\Delta$ if $\Delta\ge 56$

Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches

Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity distribution of an object from measurements taken on its boundary. It is severely ill-posed, necessitating advanced computational methods for accurate image reconstructions. Recent years have witnessed significant progress, driven by innovations in analytic-based approaches and deep learning. This review explores techniques for solving the EIT inverse problem, focusing on the interplay between contemporary deep learning-based strategies and classical analytic-based methods. Four state-of-the-art deep learning algorithms are rigorously examined, harnessing the representational capabilities of deep neural networks to reconstruct intricate conductivity distributions. In parallel, two analytic-based methods, rooted in mathematical formulations and regularisation techniques, are dissected for their strengths and limitations. These methodologies are evaluated through various numerical experiments, encompassing diverse scenarios that reflect real-world complexities. A suite of performance metrics is employed to assess the efficacy of these methods. These metrics collectively provide a nuanced understanding of the methods' ability to capture essential features and delineate complex conductivity patterns. One novel feature of the study is the incorporation of variable conductivity scenarios, introducing a level of heterogeneity that mimics textured inclusions. This departure from uniform conductivity assumptions mimics realistic scenarios where tissues or materials exhibit spatially varying electrical properties. Exploring how each method responds to such variable conductivity scenarios opens avenues for understanding their robustness and adaptability

Synergistic and Antagonistic Drug Combinations Depend on Network Topology

Drug combinations may exhibit synergistic or antagonistic effects. Rational design of synergistic drug combinations remains a challenge despite active experimental and computational efforts. Because drugs manifest their action via their targets, the effects of drug combinations should depend on the interaction of their targets in a network manner. We therefore modeled the effects of drug combinations along with their targets interacting in a network, trying to elucidate the relationships between the network topology involving drug targets and drug combination effects. We used three-node enzymatic networks with various topologies and parameters to study two-drug combinations. These networks can be simplifications of more complex networks involving drug targets, or closely connected target networks themselves. We found that the effects of most of the combinations were not sensitive to parameter variation, indicating that drug combinational effects largely depend on network topology. We then identified and analyzed consistent synergistic or antagonistic drug combination motifs. Synergistic motifs encompass a diverse range of patterns, including both serial and parallel combinations, while antagonistic combinations are relatively less common and homogenous, mostly composed of a positive feedback loop and a downstream link. Overall our study indicated that designing novel synergistic drug combinations based on network topology could be promising, and the motifs we identified could be a useful catalog for rational drug combination design in enzymatic systems

A multiobjective single bus corridor scheduling using machine learning-based predictive models

Many real-life optimisation problems, including those in production and logistics, have uncertainties that pose considerable challenges for practitioners. In spite of considerable efforts, the current methods are still not satisfactory. This is primarily caused by a lack of effective methods to deal with various uncertainties. Existing literature comes from two isolated research communities, namely the operations research community and the machine learning community. In the operations research community, uncertainties are often modelled and solved through techniques like stochastic programming or robust optimisation, which are often criticised for their over conservativeness. In the machine learning community, the problem is formulated as a dynamic control problem and solved through techniques like supervised learning and/or reinforcement learning, which could suffer from being myopic and unstable. In this paper, we aim to fill this research gap and develop a novel framework that takes advantages of both short-term accuracy from mathematical models and high-quality future forecasts from machine learning modules. We demonstrate the practicality and feasibility of our approach for a real-life bus scheduling problem and two controlled bus scheduling instances that are generated artificially. To our knowledge, the proposed framework represents the first multi-objective bus-headway-optimisation method for non-timetabled bus schedule with major practical constraints being considered. The advantages of our proposed methods are also discussed, along with factors that need to be carefully considered for practical applications. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group

Conforming an Extracorporeal Lithotripter System for Video Urodynamic Studies

Objectives: This study aimed to evaluate the efficiency using existing fluoroscopic unit and lithotripter table of an extracorporeal lithotripter system for video urodynamic studies (VUDS) to determine anatomical abnormalities in patients with neurogenic lower urinary tract dysfunction (NLUTD). Methods: The extracorporeal lithotripsy system was adapted to obtain optimum fluoroscopic view according to body shape and observed organs of patients. We reviewed the VUDS data of 25 patients with NLUTD. Results: “Christmas tree bladder” (CTB) was found in 5 (20%) patients. Vesicoureteral reflux (VUR) and external detrusor sphincter dyssynergia (DESD) were detected in 3 (12%) and 4 (16%) patients, respectively. Four (16%) patients with normal coordination between detrusor contraction and external sphincter relaxation were proven by VUDS. CTB, VUR, or DESD was not observed in 10 (40%) patients with flaccid bladder. Hematuria, urinary tract infection, or autonomic dysreflexia did not occur in any of the patients. Conclusions: VUDS can discern anatomical abnormalities of the urinary tract, and patients in undeveloped areas of the world who have NLUTD can have easier access to VUDS because of the decreasing capital cost of VUDS

Research on the Evolution of Journal Topic Mining Based on the BERT-LDA Model

Scientific papers are an important form for researchers to summarize and display their research results. Information mining and analysis of scientific papers can help to form a comprehensive understanding of the subject. Aiming at the ignorance of contextual semantic information in current topic mining and the uncertainty of screening rules in association evolution research, this paper proposes a topic mining evolution model based on the BERT-LDA model. First, the model combines the contextual semantic information learned by the BERT model with the word vectors of the LDA model to mine deep semantic topics. Then construct topic filtering rules to eliminate invalid associations between topics. Finally, the relationship between themes is analyzed through the theme evolution, and the complex relationship between the themes such as fusion, diffusion, emergence, and disappearance is displayed. The experimental results show that, compared with the traditional LDA model, the topic mining evolution model based on BERTLDA can accurately mine topics with deep semantics and effectively analyze the development trend of scientific and technological paper topics

Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems

Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where deep learning algorithms are used to solve problems in mathematics. The latter has popularised the field of scientific machine learning where deep learning is applied to problems in scientific computing. Specifically, more and more neural network architectures have been developed to solve specific classes of partial differential equations (PDEs). Such methods exploit properties that are inherent to PDEs and thus solve the PDEs better than standard feed-forward neural networks, recurrent neural networks, or convolutional neural networks. This has had a great impact in the area of mathematical modeling where parametric PDEs are widely used to model most natural and physical processes arising in science and engineering. In this work, we review such methods as well as their extensions for parametric studies and for solving the related inverse problems. We equally proceed to show their relevance in some industrial applications

A Hybrid Algorithm of Traffic Accident Data Mining on Cause Analysis

Road traffic accident databases provide the basis for road traffic accident analysis, the data inside which usually has a radial, multidimensional, and multilayered structure. Traditional data mining algorithms such as association rules, when applied alone, often yield uncertain and unreliable results. An improved association rule algorithm based on Particle Swarm Optimization (PSO) put forward by this paper can be used to analyze the correlation between accident attributes and causes. The new algorithm focuses on characteristics of the hyperstereo structure of road traffic accident data, and the association rules of accident causes can be calculated more accurately and in higher rates. A new concept of Association Entropy is also defined to help compare the importance between different accident attributes. T-test model and Delphi method were deployed to test and verify the accuracy of the improved algorithm, the result of which was a ten times faster speed for random traffic accident data sampling analyses on average. In the paper, the algorithms were tested on a sample database of more than twenty thousand items, each with 56 accident attributes. And the final result proves that the improved algorithm was accurate and stable