In this paper, two different n -order topological circuit networks are connected by diodes to establish a unified network model, which is a previously unexplored problem. The network model includes not only five resistive elements but also diode devices, so the network contains many different network types. This problem can be solved through three main steps: First, the network is simplified into two different equivalent circuit models. Second, the nonlinear difference equation model is established by applying Kirchhoff’s law. Finally, the two equations with similar structures are processed uniformly, and the general solutions of the nonlinear difference equations are obtained by using the transformation technique. As an example, several interesting specific results are deduced. Our study on the network model has significant value, as it can be applied to relevant interdisciplinary research.

Abstract In clinical medicine, the pain feeling is a significant indicator for the medical condition of patients. Of late, automatic pain assessment methods have received more and more interests. Many researchers proposed corresponding methods and achieved impressive results. However, they always ignore the locality and individual differences of painful expression. Therefore, a locality and identity aware network (LIAN) for pain assessment is presented here. Concretely, for the locality characteristic, a locality aware module consisting of a two‐branch structure, feature and attention branches, is presented. The former learns pain features by a deep network, while the latter guides the pain features to focus on the discriminational regions of pain. As for the individual differences, an identity aware module with a multi‐task method is proposed to represent identity‐related information to achieve identity‐invariant pain assessment. Extensive experiments on public databases show the superiority of LIAN in pain assessment.

The semantics of mathematical formulae depend on their spatial structure, and they usually exist in layout presentations such as PDF, LaTeX, and Presentation MathML, which challenges previous text index and retrieval methods. This paper proposes an innovative mathematics retrieval system along with the novel algorithms, which enables efficient formula index and retrieval from both webpages and PDF documents. Unlike prior studies, which require users to manually input formula markup language as query, the new system enables users to "copy" formula queries directly from PDF documents. Furthermore, by using a novel indexing and matching model, the system is aimed at searching for similar mathematical formulae based on both textual and spatial similarities. A hierarchical generalization technique is proposed to generate sub-trees from the semi-operator tree of formulae and support substructure match and fuzzy match. Experiments based on massive Wikipedia and CiteSeer repositories show that the new system along with novel algorithms, comparing with two representative mathematics retrieval systems, provides more efficient mathematical formula index and retrieval, while simplifying user query input for PDF documents.

The explosive growth of the internet and electronic publishing has led to a huge number of scientific documents being available to users, however, they are usually inaccessible to those with visual impairments and often only partially compatible with software and modern hardware such as tablets and e-readers. In this paper we revisit Maxtract, a tool for analysing and converting documents into accessible formats, and combine it with two advanced segmentation techniques, statistical line identification and machine learning formula identification. We show how these advanced techniques improve the quality of both Maxtract's underlying document analysis and its output. We re-run and compare experimental results over a number of datasets, presenting a qualitative review of the improved output and drawing conclusions.

Text line detection is a prerequisite procedure of mathematical formula recognition, however, many incorrectly segmented text lines are often produced due to the two-dimensional structures of mathematics when using existing segmentation methods such as Projection Profiles Cutting or white space analysis. In consequence, mathematical formula recognition is adversely affected by these incorrectly detected text lines, with errors propagating through further processes. Aimed at mathematical formula recognition, we propose a text line detection method to produce reliable line segmentation. Based on the results produced by PPC, a learning based merging strategy is presented to combine incorrectly split text lines. In the merging strategy, the features of layout and text for a text line and those between successive lines are utilised to detect the incorrectly split text lines. Experimental results show that the proposed approach obtains good performance in detecting text lines from mathematical documents. Furthermore, the error rate in mathematical formula identification is reduced significantly through adopting the proposed text line detection method.

This paper presents a performance evaluation system for mathematical formula identification. First, a ground-truth dataset is constructed to facilitate the performance comparison of different mathematical formula identification algorithms. Statistics analysis of the dataset shows the diversities of the dataset to reflect the real-world documents. Second, a performance evaluation metric for mathematical formula identification is proposed, including the error type definitions and the scenario-adjustable scoring. The proposed metric enables in-depth analysis of mathematical formula identification systems in different scenarios. Finally, based on the proposed evaluation metric, a tool is developed to automatically evaluate mathematical formula identification results. It is worth noting that the ground-truth dataset and the evaluation tool are freely available for academic purpose.

Recognizing mathematical expressions in PDF documents is a new and important field in document analysis. It is quite different from extracting mathematical expressions in image-based documents. In this paper, we propose a novel method by combining rule-based and learning-based methods to detect both isolated and embedded mathematical expressions in PDF documents. Moreover, various features of formulas, including geometric layout, character and context content, are used to adapt to a wide range of formula types. Experimental results show satisfactory performance of the proposed method. Furthermore, the method has been successfully incorporated into a commercial software package for large-scale Chinese e-Book production.