Lunch
14:00 - 14:30 Yulin Zhang [CMAT-ALC]
Stable pairs and stable matrix rays
Abstract: A is called (positive) stable if all its eigenvalues have positive real part. The question of when the sum of two stable matrices A, B is stable arises in
the analysis of price stability in the consolidation of two markets. When A, B and A + B are stable, A, B is called a stable pair. The ray A + tB, t = 0, is called stable if A, tB is a stable pair for all t = 0.
In our work, we considered the conditions for a ray may fail. The density of stable directions and the frequency of stable pairs are also discussed.
14:35 - 14:55 Laid Boudjellal [CMAT-ANAP]
Delay differential equations modelling the tumor-immune system dynamics
Abstract: Advances in mathematical modeling can enable to understand the interactions among cancer cells and cells of the immune system and their response to treatment,
thereby promoting the progress towards targeted and effective therapies for this highly complex disease. According to [1] and references therein cited, the tumor-immune system interactions can be summarized in
three relevant phases, namely the clearance phase, the equilibrium phase, and the escape phase. In particular, during the escape phase, tumor cells exhibit an accelerated expansion and growth than in other
phases. Moreover, one of the most effective immunotherapy that helps immune system against tumor cells during the escape phase is the adoptive cellular therapy. For that reason, our main interest is studying the
dynamical behavior of tumor-immune cells interactions during this critical escape phase. Starting from our previous ODE model [2], we propose a delay differential equations model that describes the rivalry among
tumor and immune cells during the escape phase, in the presence of adoptive cell therapy and interleukin. The delay is incorporated in the model to represent the time lag by the adaptive immune cells in
responding after recognizing the tumor cells [3]. The delay introduces some complexities in the dynamics but has the novelty of capturing the memory of the cells. For the delay model, we prove the consistency
between the model solution and the biological context, including existence, uniqueness, positivity, and boundedness of the solution. We study the stability of the equilibrium states, and investigate the existence
of bifurcations in the parameter space. We complement our study with various numerical simulations that show different behaviours of the solution. Finally, we compare the results obtained for the delay model with
those for the ODE model in order to evaluate the effect of the time delay on the dynamics. Joint work with A.J. Soares and M.J. Torres, from Centre of Mathematics, University of Minho.
15:00 - 15:20 Ana Moreira [CMAT-SAPOR]
Variable selection for mixtures of linear regression models by L1-penalized estimation.
Abstract: : Finite Mixture Regression (FMR) models provide a flexible tool for modelling data that arise from a heterogeneous population, where the relationship between
the dependent and explanatory variables varies across different subpopulations. Given the often large number of explanatory variables considered in such models, variable selection assumes critical importance.
Traditional subset selection methods are computationally demanding. Therefore, more efficient techniques, such as penalty-based methods, have been developed. The Least Absolute Shrinkage and Selection
Operator (LASSO), Adaptive LASSO (ALASSO), and Relaxed LASSO (RLASSO) are some examples of these methods. This study compares the performance of LASSO, ALASSO, and RLASSO in the context of variable selection for
mixtures of linear regression models, employing the Expectation-Maximization (EM) and Classification Expectation-Maximization (CEM) algorithms for parameter estimation. Extensive simulation analyses highlight
the impact of various scenarios on the performance of these methods, with the ALASSO method demonstrating superior overall effectiveness in selecting the most relevant explanatory variables.
15:25 - 15:45 Ana Catarina Sousa[CMAT-ALC]
Proof terms in the study of proof search.
Abstract: We propose a methodology for the theoretical study of proof search where the representation of partial (i.e., incomplete) proofs and their conversion into
finished proofs is central. Slightly extending the Curry-Howard paradigm [3] of representation of finished proofs by means of proof terms, we introduce partial proof terms, which are proof terms expressing gaps
in incomplete derivations with the help of formal sequents, that is, sequents occurring as proper components of the syntax of proof terms.A given proof system S with proof terms is extended to S?, with partial
proof terms, and including: (1) a rewriting system acting on partial proof terms, expressing a proof search procedure, such that: there is a proof of a sequent in S, represented by t, if and only if the formal
version of the sequent reduces to t; and (2) a “typing system” for partial proof terms, which is a logical system handling partial sequents. These comprise a sequent of S, a partial proof term t, and the list of
formal sequents occurring in t. Such partial sequents implement the fundamental concept of proof state, understood as comprising: a goal sequent, a record of the history of the search, and a list of proof
obligations. The rewriting system and the typing systems are linked by a “subject reduction” theorem, and so, whenever a partial proof term reduces, the goal sequent is preserved and the proof obligations are
updated. In this talk, we illustrate our methodology with a proof system for intuitionistic logic: the focused sequent calculus LJT [2, 1], whose proof search follows the focusing discipline.
Coffee Break
16:25 - 16:55 Carlos Rito [CMAT-GTA]
On fake planes and fake quadrics.
Abstract: In this talk I will explain what fake planes and fake quadric surfaces are, say a few words about the state of the art and then I will report on some ongoing projects related to these
surfaces.
17:00 - 17:40 Diogo Oliveira e Silva, [Universidade de Lisboa / University of Birmingham]
Sharp extension inequalities on finite fields.
Abstract: Sharp restriction theory and the finite field extension problem have both received much attention in the last two decades, but so far they have not
intersected. In this talk, we discuss our first results on sharp restriction theory on finite fields. Even though our methods for dealing with paraboloids and cones borrow some inspiration from their euclidean
counterparts, new phenomena arise which are related to the underlying arithmetic and discrete structures. The talk is based on recent joint work with Cristian González-Riquelme
(https://arxiv.org/abs/2405.16647)
End
Posters
Mouse over the titles shows poster
abstracts.
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André Mendes (MMC) and Pedro Patrício (CMAT)
Quantum Compilation and the Sub-graph Isomorphism Problem: Challenges and Strategies
Abstract: In quantum computing, instructions cannot be applied directly between arbitrary hardware registers; instead, like in classical computers, programs must
be compiled to the architectural constraints of the target device. Layout selection is one of the steps in quantum compilation. In this stage, given a program's interaction graph, the compiler must attempt
to locate the best set of qubits in the target machine's coupling map that best fits the program's interaction graph. This can be boiled down to the Sub-Graph Isomorphism Problem, in which, given two graphs:
a query and a target graph one must find if the target graph contains a sub-graph that is isomorphic to the query graph.
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Assis Azevedo (CMAT), Davide Azevedo (CMAT), Mário Bessa (CMUP) and Maria Joana Torres (CMAT)
Volume preserving Sobolev weak Lusin theorem
Abstract: Let $d\geq 2$, $X$ be a closed connected $d$-dimensional manifold and $p$ between $0$ and $1$. We obtain a weak version of Lusin's theorem in the closure of volume
preserving Lipschitz homeomorphisms in $W^{1,p}(X,X)$. This result is crucial to prove such conservative homeomorphisms are ergodic from a generic viewpoint. This establishes a version of Oxtoby and Ulam
theorem for this Sobolev class.
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Fernando Miranda (CMAT), Gonçalo Carvalho (UTAD) and Maria Irene Falcão (CMAT)
Appell Polynomials and Applications
Abstract: : In 1880, Appell introduced and studied sequences of polynomials, now referred to as Appell polynomials, which exhibit interesting properties and have
various important applications in mathematics, physics, and engineering. This work, conducted under the UMINHO/BII/2023/13 scholarship, explores some key properties characterizing Appell polynomials. As a
practical application, we construct a new family of polynomials, termed Appell-Fibonacci polynomials, whose properties are quite remarkable. In this context, we have published a sequence in the Online
Encyclopedia of Integer Sequences (A374917) corresponding to the inverse of the Fibonacci sequence (beginning 1,1) with respect to binomial convolution.
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Catarina Faustino (CMAT)
On the topology of concurrent systems
Abstract: As amply demonstrated in the literature, concepts and methods from algebraic topology can be profitably employed in concurrency theory, the field of
computer science that studies systems of simultaneously executing processes. A powerful combinatorial-topological model for concurrent systems is given by higher-dimensional automata, i.e., pointed labeled
precubical sets. The purpose of this work is to show that the topology of an HDA model of a concurrent system can be arbitrarily complex. More precisely, we show that for every connected polyhedron there exists
an accessible transition system that admits an HDA model with the same homotopy type as the polyhedron. This is joint work with T. Kahl and R. Lopes.
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Emmanuela Villar (LCD), Cecília Coelho (CMAT), Maria Fernanda Costa (CMAT), Luís L. Ferrás (CMAT)
Predicting Miranda's Hydropower Plant Inflow with Neural Networks
Abstract: Hydropower Plants are a very important renewable energy resource, however optimizing their management is difficult. In this work we propose using a neural
network to predict the water inflow per hour and day for the Miranda Hydropower Plant in the Araguari lake, Brazil.
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Jhonathan Barrios (CMAT), Wolfram Erlhagen (CMAT), Miguel F. Gago (ICVS), Flora Ferreira (CMAT)
Investigating the Effects of Levodopa Medication on Gait Dynamics in Parkinson's Disease using Topological Data Analysis
Abstract: : Topological data analysis (TDA) has been applied to extract features that differentiate gait patterns and improve the performance of machine learning
models in detecting gait-related disorders. Given the nonlinear nature of human gait dynamics, TDA provides advanced topological and geometric methods for analyzing time series data. This study aims to use TDA
to investigate the topological features of gait time series in individuals with Parkinson's disease. Gait data were collected from 29 patients, including 15 with idiopathic Parkinson's disease (IPD) and 14 with
vascular parkinsonism (VaP), during “Off” (off medication) and “On” (post-Levodopa) phases using Physilog sensors. Time series data of variables such as stride length, cycle duration were analyzed using
computational topology techniques, focusing on persistence diagrams, extracting different these features were compared to traditional measures such as mean and coefficient of variation. Wilcoxon test was used
to compare differences between “Off” and “On” phases in various patient subgroups, assessing statistical significance of features compared to traditional measures. Preliminary findings suggest that response to
levodopa influences topological features of stride length patterns in patients with parkinsonism. In addition, descriptors such as Betti curves, persistence landscapes, and silhouette landscapes using
persistence homology were extracted from time series. These descriptors were employed in binary classification tasks to distinguish between “On” and “Off” states for both IPD and VaP patients.
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José Oliveira (CMAT) and Ana Sofia Teixeira (MMC)
New global stability criterion for a discrete-time Hopfield neural network model with unbounded delays
Abstract: Stability in neural network models is crucial for ensuring consistent and reliable results, both during the training process and inference. Furthermore,
stability mitigates issues such as divergence during training and overfitting, where the model memorizes data rather than learning from it. In this poster, we present sufficient conditions for the global
asymptotic stability of a discrete-time Hopfield neural network model with unbounded delays and delays in the leakage terms. The obtained stability criteria are based in M-matrix theory, where, unlike typical
results in the literature, singular M-matrices are considered. To the best of our knowledge, this is the first time that a stability criterion involving singular M-matrices has been established for a neural
network model with unbounded activation functions and infinite delays. A numerical example is provided to illustrate the effectiveness of new results.
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Luisa Novais (DMAT) and Susana Faria (CMAT)
Comparing Information and Classification Criteria for Estimating the Number of Components in Mixture of Regression Models with Random Effects
Abstract: Choosing the number of components for mixture models has long been considered an important but difficult research problem. In this study, we investigate
the problem of determining the number of components in mixtures of regression models with random effects, investigating the performance of a variety of information and classification criteria through a
simulation study.
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Marta Ferreira (CMAT) and Elisa Moreira (LCD)
Looking for the tails of a distribution
Abstract: : Extreme value theory provides statistical tools for inference at values as unusual or even more than ever observed. Extreme value models are intended
to model tails, whose behaviour is essentially determined by a shape parameter, known as the tail index. Other extremal parameters depend on it, such as high quantiles (e.g., Value-at-Risk), probability of
exceeding an extreme level (e.g., probability of ruin) or an upper limit of support (e.g., human life span). A crucial and much studied aspect in this framework is determining where the tail of a distribution
begins. This will be the topic of the present work, in which we analyse a methodology introduced in [1]. A simulation study will allow us to evaluate the performance of the method, followed by an illustration
with financial data.
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Paulo Barbosa (CMAT), Estela Bicho, Flora Ferreira (CMAT), Wolfram Erlhagen (CMAT)
Lateral Inhibition Learning Rule for Self-Sustained Bump Solutions in Dynamic Neural Field Models
Abstract: Dynamic Neural Field (DNF) models describe the spatio-temporal dynamics of neural population activity, enabling exploration of cortical phenomena like
traveling waves, localized bumps, and oscillatory patterns. We propose a cortical plasticity learning rule to develop lateral inhibition coupling and generate self-sustained bumps, where excitatory dynamics
follow a modified Hebbian rule and inhibitory dynamics are governed by a homeostatic rule that balances excitatory inputs.
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Sérgio Vieira (MECD) and Raquel Menezes (CMAT)
Species Distribution Models Incorporating Spatial Correlation: The Case of Anchovy Presence on the Portuguese Coast
Abstract: The anchovy (Engraulis encrasicolus) is a species of high commercial importance in the coastal waters of Portugal. The spatial distribution of this
species is influenced by various environmental factors, such as sea surface temperature (SST), chlorophyll concentration (CHL), and depth. However, in addition to these factors, spatial correlation between
adjacent areas also plays a crucial role in understanding distribution patterns. In this study, Species Distribution Models (SDMs) incorporating spatial correlation were employed using the spmodel library to
model anchovy presence along the portuguese coast. The analysis was performed using environmental data combined with fishing landing information. To account for spatial correlation, a spatial mixed model
approach was used, capturing autocorrelation between geographically close locations. Based on the analyses, it was found that sea surface temperature and depth of observation are the most relevant variables for
anchovy presence. A graphical application in R was developed to visualize the spatial distribution patterns of the species and their relationships with environmental variables.
