At the project end the following results can be summarised:
Training
The wide variety of training activities organised and carried out by the BIGMATH team focused on enhancing ESRs soft skills and familiarity with both the academic and industrial landscape: presentations at conferences and scientific events have been fostered together with a close cooperation with companies through team work, brand presentations and R&I activities.
Research
Most of the ESRs had long periods of industrial secondments (in some cases performed in smart working from remote, due to the Covid19 restrictions), during which they worked in strict collaboration between the industrial and the academic partners and experienced the work habits in a business oriented environment. In some cases, extensions of existing theories and their mathematical study was needed, together with the development of ad hoc algorithms and related software. The ESRs have been assisted by the advisors in this process. Main obtained results:
• Human face reconstruction: from the research of ESR3 we were able to set up and study the mathematical properties of a full pipeline to reconstruct complex shapes, like that of an ear,in a realistic way. The pipeline has a high degree of flexibility to be adapted also to other use cases, posing thus the first step towards general purpose morphable models. From the research of ESR1 and ESR2 new methods, with computational advantages and a higher degree of interpretability of the existing ones, have been studied, which allow to create more and more realistic virtual humans, to be employed in the entertainment industry.
• Finance: ESR4 and ESR5 developed new classification methods in presence of unbalanced samples, with the double aim of estimating credit risk, or of predicting commercial trade volumes or unexploited capital of investment of clients of a company. Such problems required the development of techniques of discriminant analysis which rely on suitable techniques of matrix decompositions in large scale linear algebra, or on supervised machine learning techniques that had to be adapted to the case of datasets with imbalanced labels.
• Industry 4.0: ESR6 studied statistical techniques able to identify patterns in multivariate time series with binary outputs, which are able to predict the occurrence of specific events, like failures in a production line. Multinomial urn models, models based on Latent Dirichlet Allocation and models based on survival analysis have been tested on a specific industrial problem. The tests have highlighted which kind of information is crucial to collect to solve the problem. ESR7 developed some new distributed optimization techniques that may be applied to complex problems which occur frequently when many different “entities” (like sensors, individuals, etc.) can exchange information only with their neighbours, but the entire system formed by such entities must be optimized to perform a task.
Impact
The impact of the Action can be measured in terms of enhancing the career perspectives and employability of ESRs and contribution to their skills development. More specifically the ESRs learned to work on challenging industrial problems; to develop skills in interdisciplinary and international team-working; to increase their ability to apply tailor-made solutions; to leverage on long-term collaboration opportunities, and on contacts with leading researchers and networks of mathematicians. Additionally the project had a positive impact on knowledge transfer to industry. In fact all the research streams followed by the ESRs can be translated into business solutions, immediately or in a near future.
