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Invited Talk
Title: Computation, Statistics, and Optimization of Random Functions
Speaker: Afonso Bandeira
Affiliation: ETH - Zurich - https://people.math.ethz.ch/~abandeira/
Abstract: When faced with a data analysis, learning, or statistical inference problem, the amount and quality of data available fundamentally determines whether such tasks can be performed with certain levels of accuracy. Indeed, many theoretical disciplines study limits of such tasks by investigating whether a dataset effectively contains the information of interest. With the growing size of datasets however, it is crucial not only that the underlying statistical task is possible, but also that is doable by means of efficient algorithms. In this talk we will discuss methods aiming to establish limits of when statistical tasks are possible with computationally efficient methods or when there is a fundamental «Statistical-to-Computational gap›› in which an inference task is statistically possible but inherently computationally hard. This is intimately related to understanding the geometry of random functions, with connections to statistical physics, study of spin glasses, random geometry; and in an important example, algebraic invariant theory.
Inverse Problems and Application in Health Sciences (PICS)
Coordinator: Paula Cerejeiras
Title: The inverse conductivity problem in the case of discontinuous conductivities
Speaker: Ivan Pombo
Abstract: In this talk, we present the inverse conductivity problem for 2D complex conductivities with jumps. Such materials have never been considered in the literature where still the case of Lipschitz conductivities are assumed. For the study of this problem, we model it as an interior transmission problem. To treat it several new concepts are required, such as an adaptation of the notion of scattering data, and the definition of admissible points, which permit the enlargement of the set of CGO incident waves. This will allow us to prove the reconstruction of the conductivity. Given that these are early results in this direction, we also present some of the footwork necessary to proceed further in this direction. Moreover, a final note on the case of 3D is made.
Members of CIDMA involved in the work presented: Ivan Pombo (CHAG), Uwe Kähler (CHAG), Paula Cerejeiras (CHAG), and Evgeny Lakshtanov (OGTCG).
Members of other Research Units of UA involved in the work presented: Sergey Mikhalev (Centre for Mechanical Engineering and Automation - TEMA)
Mathematics: Teaching and Assessment in Higher Education (MATEAS)
Coordinator: Luís Descalço
Title: Teaching and assessment in higher education and Covid-19
Speaker: Luís Descalço
Abstract: We present recent work within MATEAS strand, in particular in digital contents and software development for teaching and assessment to respond to the Covid-19 situation.
The discussion about teaching and assessment in higher education became more relevant, motivated by the need to adapt properly to distance education. This discussion and sharing of experiences is still one of the main strand activities.
We have adapted the plans of the strand to respond to this situation, implementing functionalities in the existing software to export digital contents created by members of several research groups of CIDMA, within projects MEGUA and SIACUA, for distance assessment using Moodle and PmatE.
A new Web application, MCQEditor, has been developed from scratch. This application allows the creation of parameterized multiple-choice questions for assessment in Moodle, using LaTeX, Python and SymPy and is an attempt to produce the simplest possible interface for this purpose. This work was presented in Inovação Pedagógica, and the application is freely available.
Members of CIDMA involved in the work presented: Andreia Hall (PSG), António Caetano (FAAG), Dina Seabra (FAAG), João Pedro Cruz (OGTCG), Jorge Neves (OGTCG), José Carlos Lopes (AGG), Luís Descalço (OGTCG), Nuno Bastos (SCG), Paula Carvalho (OGTCG), and Paula Oliveira (HMMEG).
Mathematics for the Industry (MI)
Coordinator: Rui Borges Lopes
Title: Forecasting in a fast-growing business
Speaker: Rui Borges Lopes
Abstract: A company recently started its activity in the liquefied petroleum gas (LPG) cylinder business. To properly manage its assets, the company sought a reliable estimation of sales and returns for the following years. To this end, a method using time series techniques, multiple linear regression models and artificial neural networks was developed and proposed.
The proposed method was able to increase the accuracy of the forecasting and has shown to be useful when facing rapid growth, where historical data are scarce and often show high variability.
Members of CIDMA involved in the work presented: Magda Monteiro (PSG) and Rui Borges Lopes (OGTCG).
Gravitational Geometry and Dynamics Group (GGDG)
Coordinator: Carlos Herdeiro
Title: Practical deep learning: from particle physics to Gravitational Waves and beyond.
Speaker: Felipe Freitas
Abstract: In this talk, we are going to explore three independent problems: detection of new physics phenomena at the Large Hadron Collider, parameter exploration of Gravitational Waves detected by LIGO and the detection of Pulmonary diseases using X-ray images (COVID-19 early detection and other applications). Where we apply deep learning tools and how the know-how of the domain scientific knowledge can flow from fundamental research to other daily problems we current face. This flow is largely facilitated due to the current usage of deep learning frameworks such as pyTorch and FastAI. We are going to see how these frameworks not only facilitate the research but also opens the door to researchers apply their domain knowledge in different fields.
Members of CIDMA involved in the work presented: António Morais, Carlos Herdeiro, Felipe Ferreira de Freitas, Nico Sanchis Gual, and Eugen Radu (all members of GGDG).
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