Path signature has unique advantages on extracting high-order differential features of sequential data. Our team has been studying the path signature theory and actively applied it to various applications, including infant cognitive score prediction, human motion recognition, hand-written character recognition, hand-written text line recognition and writer identification etc. In this talk, I will share our most recent works on infant cognitive score prediction using deep path signature. The cognitive score can reveal individual’s abilities on intelligence, motion, language abilities. Recent research discovered that the cognitive ability is closely related with individual’s cortical structure and its development. We have proposed two frameworks to predict the cognitive score with different path signature features. For the first framework, we construct the temporal path signature along the age growth and extract signature features of developmental infant cortical features. By incorporating the cortical path signature into the multi-stream deep learning model, the individual cognitive score can be predicted with missing data issues. For the second framework, we propose deep path signature algorithm to compute the developmental feature and obtain the developmental connectivity matrix. Then we have designed the graph convolutional network for the score prediction. These two frameworks have been tested on two in-house cognitive data sets and reached the state-of-the-art results.

The Temperley-Lieb algebra is a diagrammatic algebra - defined on a basis of "string diagrams" with multiplication given by "joining the diagrams together".  It first arose as an algebra of operators in statistical mechanics but quickly found application in knot theory (where Jones used it to define his famed polynomial) and the representation theory of $sl_2$.  From the outset, the representation theory of the Temperley-Lieb algebra itself has been of interest from a physics viewpoint and in characteristic zero it is well understood.  In this talk we will explore the representation theory over mixed characteristic (i.e. over positive characteristic fields and specialised at a root of unity).  This gentle introduction will take the listener through the beautifully fractal-like structure of the algebras and their cell modules with plenty of examples.

The complementarity and substitutability between products are essential concepts in retail and marketing. Qualitatively, two products are said to be substitutable if a customer can replace one product by the other, while they are complementary if they tend to be bought together. In this article, we take a network perspective to help automatically identify complements and substitutes from sales transaction data. Starting from a bipartite product-purchase network representation, with both transaction nodes and product nodes, we develop appropriate null models to infer significant relations, either complements or substitutes, between products, and design measures based on random walks to quantify their importance. The resulting unipartite networks between products are then analysed with community detection methods, in order to find groups of similar products for the different types of relationships. The results are validated by combining observations from a real-world basket dataset with the existing product hierarchy, as well as a large-scale flavour compound and recipe dataset.

arXiv link: https://arxiv.org/abs/2103.02042