We present a new approach for parsing twodimensional input using relational grammars and fuzzy sets. A fast, incremental parsing algorithm is developed, motivated by the two-dimensional structure of written mathematics. The approach reports all identifiable parses of the input. The parses are represented as a fuzzy set, in which the membership grade of a parse measures the similarity between it and the handwritten input. To identify and report parses efficiently, we adapt and apply existing techniques such as rectangular partitions and shared parse forests, and introduce new ideas such as relational classes and interchangeability. We also present a correction mechanism that allows users to navigate parse results and choose the correct interpretation in case of recognition errors or ambiguity. Such corrections are incorporated into subsequent incremental recognition results. Finally, we include two empirical evaluations of our recognizer. One uses a novel user-oriented correction count metric, while the other replicates the CROHME 2011 math recognition contest. Both evaluations demonstrate the effectiveness of our proposed approach.

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The deep ocean is the largest ecosystem on the planet, constituting greater than 90% of all habitable space. Over three-quarters of countries globally have deep ocean within their Exclusive Economic Zones. While maintaining deep-ocean function is key to ensuring planetary health, deficiencies in knowledge and governance, as well as inequitable global capacity, challenge our ability to safeguard the resilience of this vast realm, leaving the fate of the deep ocean in the hands of a few. Historically, deep-ocean scientific exploration and research have been the purview of a limited number of nations, resulting in most of humankind not knowing the deep ocean within their national jurisdiction or beyond. In this article, we highlight the inequities and need for increased deep-ocean knowledge generation, and discuss experiences in piloting an innovative project ‘My Deep Sea, My Backyard’ toward this goal. Recognizing that many deep-ocean endeavours take place in countries without deep-ocean access, this project aimed to reduce dependency on external expertise and promote local efforts in two small island developing states, Trinidad and Tobago and Kiribati, to explore their deep-sea backyards using comparatively low-cost technology while building lasting in-country capacity. We share lessons learned so future efforts can bring us closer to achieving this goal. This article is part of the theme issue ‘Nurturing resilient marine ecosystems’.

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Recognizing handwritten mathematics is a challenging classification problem, requiring simultaneous identification of all the symbols comprising an input as well as the complex two-dimensional relationships between symbols and subexpressions. Because of the ambiguity present in handwritten input, it is often unrealistic to hope for consistently perfect recognition accuracy. We present a system which captures all recognizable interpretations of the input and organizes them in a parse forest from which individual parse trees may be extracted and reported. If the top-ranked interpretation is incorrect, the user may request alternates and select the recognition result they desire. The tree extraction step uses a novel probabilistic tree scoring strategy in which a Bayesian network is constructed based on the structure of the input, and each joint variable assignment corresponds to a different parse tree. Parse trees are then reported in order of decreasing probability. Two accuracy evaluations demonstrate that the resulting recognition system is more accurate than previous versions (which used non-probabilistic methods) and other academic math recognizers.