Correspondence-based analogies for choosing problem representations

Mathematics and computing students learn new concepts and fortify their expertise by solving problems. The representation of a problem, be it through algebra, diagrams, or code, is key to understanding and solving it. Multiple-representation interactive environments are a promising approach, but the task of choosing an appropriate representation is largely placed on the user. We propose a new method to recommend representations based on correspondences: conceptual links between domains. Correspondences can be used to analyse, identify, and construct analogies even when the analogical target is unknown. This paper explains how correspondences build on probability theory and Gentner's structure-mapping framework; proposes rules for semi-automated correspondence discovery; and describes how correspondences can explain and construct analogies

Inspection and Selection of Representations

We present a novel framework for inspecting representations and encoding their formal properties. This enables us to assess and compare the informational and cognitive value of different representations for reasoning. The purpose of our framework is to automate the process of representation selection, taking into account the candidate representation’s match to the problem at hand and to the user’s specific cognitive profile. This requires a language for talking about representations, and methods for analysing their relative advantages. This foundational work is first to devise a computational end-to-end framework where problems, representations, and user’s profiles can be described and analysed. As AI systems become ubiquitous, it is important for them to be more compatible with human reasoning, and our framework enables just that.EPSR

Cross-domain correspondences for explainable recommendations

Humans use analogies to link seemingly unrelated domains. A mathematician might discover an analogy that allows them to use mathematical tools developed in one domain to prove a theorem in another. Someone could recommend a book to a friend, based on understanding their hobbies, and drawing an analogy between them. Recommender systems typically rely on learning statistical correlations to uncover these cross-domain correspondences, but it is difficult to generate human-readable explanations for the correspondences discovered. We formalise the notion of 'correspondence' between domains, illustrating this through the example of a simple mathematics problem. We explain how we might discover such correspondences, and how a correspondence-based recommender system could provide more explainable recommendations

The Legume–Rhizobia Symbiosis

The symbiotic nitrogen fixation (SNF) with legumes is the primary source of biologically fixed nitrogen for agricultural system. It is performed by a group of bacteria commonly called rhizobia. It is characterized by a host preference, and the differences among symbioses between rhizobial strains and legume genotypes are related to infection, nodule development and effectiveness in N2 fixation. The interaction between a rhizobia and the legume is mediated by a lipochitin oligosaccharide secreted by the rhizobia, and called “Nod factor”. It is recognized by transmembrane receptors on the root-hair cells of the legume. It can regulate the nodule organogenesis by inducing changes in the cytokinin balance of the root, during nodule initiation. N2 fixation in legume nodules is catalyzed by the nitrogenase enzyme depending upon the photosynthate supply, the O2 concentration, and the fixed-N export. Among environmental factors that influence the SNF, the temperature is essential for nodule formation; the salinity and drought decrease the nodule permeability to O2 and the photosynthate supply to the nodule, the phosphorus deficiency inhibits the nodule development and the total N2 fixation. Rhizobia strains differ in their efficiency in N2 fixation with host legume. There is evidence of genotypic variability for SNF at different levels of available P which show a possibility of selecting cultivars able to support biological N2 fixation under low P soils