Lunch
14:00 - 14:30 Luís Machado [CMAT-SAPOR]
New approaches to clustering curves for censored data
Abstract: Survival analysis encompasses various methods for analyzing time-to-event data, with a key goal being the
comparison of survival curves among different groups. If more than one type of endpoint is present, these endpoints are called competing risks since the observation
of a particular event prevents an individual from observing any other type of event. One basic but important goal in the analysis of survival and competing risk
data is the comparison of survival curves and cumulative incidence functions, for which limited literature exists. When rejecting the null hypothesis of equal curves,
indicating differences between at least one curve, it becomes important to determine if groups of curves can be formed or if all curves are distinct from one another.
To address these challenges, we propose new clustering methods specifically tailored for survival and competing risk data.
14:35 - 15:05 José Carlos Espírito Santo [CMAT-ALC]
Modal embeddings and functional calling paradigms
Abstract: : Modal embeddings are interpretations of intuitionistic logic into some modal logic which preserve and reflect
provability. The first modal embedding was due to Goedel, and another important one is due to Girard. In order to understand the difference between these two
interpretations, we have, first, to move from the level of provability (i.e. existence of proof) to the level of proofs and their normalization; and, second,
to interpret proof normalization as reduction in the lambda-calculus, which is a model of execution of functional programs. In this way, the alternative between
modal embeddings is connected to the alternative between two "calling paradigms" of functional programming, call-by-name and call-by-value. This connection has been
worked out for interpretations into linear logic. Our contribution and proposal is that, by taking the two modal embeddings as interpretations into modal logic S4,
they produce a unification of those two calling paradigms as "call by box", the paradigm followed by a new modal lambda-calculus. Joint work with Luís Pinto and
Tarmo Uustalu.
15:10 - 15:30 Elsa Soares [CMAT - SAPOR]
Prediction Methods for Longitudinal Data
Abstract: Longitudinal data are originated when different individuals are measured repeatedly over time for some variable
of interest. These data, after being collected and organized in databases, prove to be very valuable to understand and predict the behavior of individuals in
various areas, such as health and economics. This presentation will give a brief introduction to advanced statistical and machine learning methods that deal with
real-time predictions. The results obtained with the application of these models can assist in making relevant decisions for specific populations.
15:35 - 15:55 Ricardo Brasil [CMAT-GTA]
Some maps between Grassmannians
Abstract: For positive integers k=n, the Grassmannian Gr(k, n) is the manifold of linear subspaces of dimension k in
euclidean space R^n. In particular, Gr(2,n) is the manifold of linear planes in R^n and Gr(1,n) is the projective space of dimension n-1. In this talk, we will use
the quartenions and octonions to construct examples of maps from Gr(2,n) to Gr(1,m), where m is less than the dimension of Gr(2,n), that is, less than 2(n-2). Some
of these maps yield new results regarding the Lusternik-Schnirelmann category of Gr(2,n).
Coffee Break
16:30 - 17:10 Pedro V. Silva [Universidade do Porto]
Algorithmic problems for rational subsets of free inverse monoids
Abstract: The theorems of Benois and Anisimov and Seifert provide information and algorithms on the rational subsets of
free groups, but the case of free inverse monoids is much harder and several problems remain open in the general case. In this talk, we report on some recent
progress in this direction. We can prove that the membership problem for rational subsets of a finite $\J$-above monoid is decidable, covering the case of free
inverse monoids. Moreover, the equality problem is decidable for rational subsets of the monogenic free inverse monoid $F$. It is also decidable whether or not a
rational subset of $F$ is recognizable. Finally, a submonoid of $F$ is rational if and only if it is finitely generated
17:15 - 17:45 Eurica Henriques [CMAT-ANAP]
Recent results on Anisotropic Diffusion Equations
Abstract: In this talk we will focus on the study of fluids whose diffusion process takes a different form in each spacial
direction - known as anisotropic diffusion. Namely, we will discuss the recent joint works regarding singular anisotropic evolutionary differential equations related
to the porous medium type equation and to the p-Laplacean equation.
End
Posters
-
Ana Maria Leitão, Ricardo Severino
(INET-md, CMAT - UMinho)
Dynamics of a family of celullar automata suggested by performing arts
Abstract:
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Beatriz Paulo Teixeira, Ana Paula Teixeira, Regina de Almeida
(CMAT - UTAD)
Mathematics in skin cancer
Abstract:
This event is supported by Portuguese
funds through the CMAT - Research Centre of Mathematics of the
University of Minho - and the Portuguese Foundation for Science and
Technology ("FCT-Fundação para a Ciência e a Tecnologia"), within
projects UIDB/MAT/00013/2020 and UIDP/MAT/00013/2020.