An Improved Indexing and Matching Method for Mathematical Expressions Based on Inter-Relevant Successive Tree

In recent years, a growing number of math contents are available on the Web. When conventional search engines deal with mathematical expressions, the two-dimen- sion-al structure of mathematical expressions is lost, which results in a low performance of math retrieval. While the retrieval technology specifically designed for mathematical expressions is not mature currently. Aiming at these problems, an improved mathematical expression indexing and matching method was proposed through employing full text index method to deal with the two-dimensional structure of mathematical expressions. Firstly, through the fully consideration of LaTeX formulae’ characteristics, a feature representation method of mathematical expressions and a clustering method of feature keywords were put forward. Then, an improved inter-relevant successive trees index model was applied to the construction of the mathematical expression index, in which the cluster algorithm of mathematical expression features was employed to solve the problem of the quantity growth of the trees in processing large amount of formulae. Finally, the matching algorithms of mathematical expressions were given which provide four query modes called exact matching, compatible matching, sub-expression matching and fuzzy matching. In browser/server mode, 110027 formulae were used as experimental samples. The index file size was 29.02 Mb. The average time of retrieval was 1.092 seconds. The experimental result shows the effectiveness of the method.

Computer-based Creativity Enhanced Conceptual Design Model for Non-routine Design of Mechanical Systems

Computer-based conceptual design for routine design has made great strides, yet non-routine design has not been given due attention, and it is still poorly automated. Considering that the function-behavior-structure（FBS） model is widely used for modeling the conceptual design process, a computer-based creativity enhanced conceptual design model（CECD） for non-routine design of mechanical systems is presented. In the model, the leaf functions in the FBS model are decomposed into and represented with fine-grain basic operation actions（BOA）, and the corresponding BOA set in the function domain is then constructed. Choosing building blocks from the database, and expressing their multiple functions with BOAs, the BOA set in the structure domain is formed. Through rule-based dynamic partition of the BOA set in the function domain, many variants of regenerated functional schemes are generated. For enhancing the capability to introduce new design variables into the conceptual design process, and dig out more innovative physical structure schemes, the indirect function-structure matching strategy based on reconstructing the combined structure schemes is adopted. By adjusting the tightness of the partition rules and the granularity of the divided BOA subsets, and making full use of the main function and secondary functions of each basic structure in the process of reconstructing of the physical structures, new design variables and variants are introduced into the physical structure scheme reconstructing process, and a great number of simpler physical structure schemes to accomplish the overall function organically are figured out. The creativity enhanced conceptual design model presented has a dominant capability in introducing new deign variables in function domain and digging out simpler physical structures to accomplish the overall function, therefore it can be utilized to solve non-routine conceptual design problem.

Synthetic Data Generation and Shuffled Multi-Round Training Based Offline Handwritten Mathematical Expression Recognition

Offline handwritten mathematical expression recognition is a challenging optical character recognition(OCR)task due to various ambiguities of handwritten symbols and complicated two-dimensional structures.Recent work in this area usually constructs deeper and deeper neural networks trained with end-to-end approaches to improve the performance.However,the higher the complexity of the network,the more the computing resources and time required.To improve the performance without more computing requirements,we concentrate on the training data and the training strategy in this paper.We propose a data augmentation method which can generate synthetic samples with new LaTeX notations by only using the official training data of CROHME.Moreover,we propose a novel training strategy called Shuffled Multi-Round Training(SMRT)to regularize the model.With the generated data and the shuffled multi-round training strategy,we achieve the state-of-the-art result in expression accuracy,i.e.,59.74%and 61.57%on CROHME 2014 and 2016,respectively,by using attention-based encoder-decoder models for offline handwritten mathematical expression recognition.