Divulga-se a abertura de concurso para a atribuição de **6 (seis) Bolsas de Investigação para Licenciados **inscritos num curso de 2º ciclo nas áreas da Matemática, das Ciências da Computação ou da Estatística, da Universidade do Minho**, **no âmbito do financiamento UIDB/00013/2020 - Financiamento Base do Centro de Matemática (CMAT) da Escola de Ciências da Universidade do Minho, financiado pela Fundação para a Ciência e Tecnologia (FCT) através de fundos nacionais, cujo aviso de abertura está publicado no portal *Euraxess* com a **referência ****37/ECUM/CMAT/2023- UIDB/00013/2020 (6 vagas).**

O __concurso encontra-se aberto até ao dia 04/07/2023__.

O edital encontra-se disponível no Portal Euraxess Europa:

https://euraxess.ec.europa.eu/jobs/119139

Propostas:

**[Proposal BI2023-A]** Automated Metadata Extraction from Geological Research Articles

Supervisor: Cecília Castro (cecilia@math.uminho.pt)

Target audience: students of the Master in Mathematics and Computation

Work plan: This project aims to design, develop, and implement an automated system for extracting metadata from scientific articles, with a focus on the field of geology. The primary goal is to identify and catalog the most frequently cited geological sites in the scientific literature. The information extraction procedure should be capable of retrieving the geolocation of each site from a variety of formats, which can range from text, such as names, to images, like maps. This implies the use of image processing techniques and pattern recognition to identify and extract the desired coordinates. Furthermore, other relevant information should also be gathered, including the authors' names, nationalities, and institutional affiliations, as well as the publication date of the articles referencing the site. By automatically storing this type of information in a structured format, it becomes possible to gain an understanding of the variety of known and studied geological sites worldwide and their importance. Additionally, this stored data provides valuable insights into research trends, author collaborations, and the impact of individual studies on the broader scientific discourse. This project has the collaboration of Professor José Brilha, full professor of the School of Sciences, University of Minho.

**[Project BI2023-B]** Study of species distribution models incorporating spatial correlation

Supervisor: Raquel Menezes (rmenezes@math.uminho.pt)

Target audience: 2^{nd}-year students of the Master in Statistics for Data Science

Work plan: Sardines and other pelagic fish are of great cultural and economic importance in Portugal. Species Distribution Models allow the learning of environmental factors that favor or hinder the occurrence and abundance of species in a region. Recently, methods have been developed that allow the estimation of their spatial distribution and evolution over time, by incorporating random effects with spatial correlation. This project proposes to study these methods, applying them to real data, in order to generate knowledge about these resources in the current context.

**[Project BI2023-C]** Semigroups of transformations with an invariant set

Supervisor: Suzana Mendes Gonçalves (smendes@math.uminho.pt)

Target audience: 1^{st} -year students of the Master in Mathematics and Computation

Work plan: Given a non-empty set X, the set of all transformations α:X→X, under composition, is a semigroup, usually denoted by T(X). This semigroup, as well of several of its subsemigroups, has been studied by many authors, since every semigroup S is embeddable in a semigroup T(Z), for some set Z. The principal aim of this project is to study the structure of subsemigroups of T(X) whose elements are transformations that leave invariant a certain set: for example, the semigroup of all transformations α:X→X such that Yα⊆Y, where Y is a fixed subset of X.

**[Project BI2023-D]** Machine Learning Approach for Combinatorial Optimization of Time-Series Analysis

Supervisors: Fernanda Costa (mfc@math.uminho.pt), Flora Ferreira (fjferreira@math.uminho.pt)

Target audience: 1st -year students of the Master in Mathematics and Computation

Work plan: Abstract: When analyzing time-series data, multiple categorical dimensions can be present. These dimensions offer the option to either split the data or aggregate it without considering these dimensions. However, exhaustive splitting across all dimensions becomes impractical due to the exponential increase in the number of time-series to analyze. Conversely, fully aggregating the data into a single time-series diminishes valuable information and yields suboptimal analysis results. This project proposes the development of an optimization algorithm, utilizing machine learning techniques, to determine the optimal approach for aggregating or splitting a time-series dataset along various dimensions. The aim is to enhance unsupervised anomaly detection in time-series analysis.

**[Project BI2023-E]** The chaotic dynamics of Smale's horseshoe application

Supervisor: Davide Azevedo (davidemsa@math.uminho.pt)

Target audience: students of the Master in Mathematics and Computation

Work plan: The horseshoe application is defined from a region S of the plane, consisting of a square and two semicircles connected to it on the left and on the right. It is a diffeomorphism of S, which contracts the domain in the vertical direction, stretches it in the horizontal direction and then folds it into a horseshoe shape contained in S. The aim is to study the dynamics of this map, which has a rich structure. For this, another dynamical system that is easier to study will be used as support. This project is accessible to students from both specialization areas and does not require prior knowledge of dynamical systems.

**[Project BI2023-F]** Stability of discrete neural network models

Supervisor: José Joaquim Martins Oliveira (jjoliveira@math.uminho.pt)

Target audience: students of the Master in Mathematics and Computation (specialization area in Mathematics, Pure Mathematics Profile)

Work plan: In this project, in the first moment, it is intended to study the main types of discrete-time neural network models with delays and describe the main known stability criteria. In a second moment, it is intended that the scholarship holder study the existing techniques for obtaining the global stability of Hopfield-type models and try to find out to what extent new stability criteria can be obtained for other types of discrete neural networks models, such as BAM (bidirectional associative memory) models, Cohen-Grossberg models, and/or higher order Hopfield models.

**[Project BI2023-G]** Modeling HIV test utilization in the Lisbon cohort of men who have sex with men and associated factors

Supervisors: Carla Moreira (d8434@math.uminho.pt), Luís Machado (lmachado@math.uminho.pt)

Target audience: students of the Master in Statistics for Data Science

Work plan: In 2019, the HIV incidence was 7.6 cases per 100,000 people, with the majority in men. Of the cases diagnosed in individuals under 30 years of age, 65.2% were diagnosed in MSM. In Portugal, laboratory screening for HIV infection is recommended annually for MSM, or more frequently if they present a clinical picture compatible with primary infection or if they remain at high risk of exposure to HIV. This study aims to identify the frequency of HIV testing in HIV-negative men who have sex with men.

**[Project BI2023-H]** Inverse function theorem

Supervisor: José Manuel Ribeiro Oliveira (jmo@math.uminho.pt)

Target audience: 1^{st} or 2^{nd}-year students of the Master in Mathematics and Computation

Work plan: It is well known that the inverse function theorem states that a smooth mapping, in which its derivative at a point of its domain is a linear isomorphism, admits a restriction which is a diffeomorphism. When the derivative of the mapping is not necessarily bijective, it is also possible to characterize properties of the mapping under lighter hypotheses such as surjective derivative or injective derivative. This work embraces the study of some properties of smooth mappings between two smooth manifolds in which its derivatives are injective mappings or surjective mappings, enhancing the construction of submanifolds as inverse images of regular values of smooth mappings.

**[Project BI2023-I]** Inductive Logic Programming: logical foundations and computational systems

Supervisors: José Carlos Espírito Santo ( jes@math.uminho.pt), Luís Pinto (luis@math.uminho.pt)

Target audience: 1^{st} -year students of the Master in Mathematics and Computation

Work plan: Inductive logic programming (ILP) offers an alternative machine learning paradigm, based on logic and inductive reasoning, where the goal is to induce a hypothesis (a logic program), capable of generalizing prior knowledge and a collection of training examples. In this project, it is intended, on the one hand, to study the logical foundations of ILP and inductive reasoning, including techniques such as abduction, subsumption or inverse resolution, and, on the other hand, to get acquainted with computational systems based on ILP, such as, for example, ILASP or Popper.

**[Project BI2023-J]** Generalized Linear Mixed Models

Supervisor: Susana Faria (sfaria@math.uminho.pt)

Target audience: 1^{st} -year students of the Master in Statistics for Data Science

Work plan: Generalized Linear Mixed Models (GLMMs) are particularly useful for describing the relationship between a response variable and one or more explanatory variables in grouped data according to one or more factors, such as longitudinal data, repeated measurements, and data with a hierarchical structure. This study aims to address the problem of parameter estimation and variable selection in GLMMs. Additionally, we intend to apply these models to a real dataset.