Lunch
14:30 - 15:10 Daniel Graça [Universidade do Algarve]
Computational complexity: from discrete to continuous characterizations
Abstract: Classical computational complexity classes such as P, EXPTIME, or PSPACE are traditionally defined using a
discrete characterization. In this talk we will show how these classes can be characterized in a continuous manner, by using ordinary differential equations.
To achieve this purpose we will have to solve several problems, like presenting a proper notion of complexity for continuous models, among other.
Here we show how such problems can be overcome and how the above continuous characterization can be obtained.
This talk describes joint work with O. Bournez, R. Gozzi, and A. Pouly
15:15 - 15:30 Daniela Silva [CMAT-SAPOR]
Spatio-temporal variability of the distribution and abundance of sardine off the Portuguese continental
coast and relationship with environmental drivers
Abstract: Scientific tools capable of identifying the distribution patterns of species are important as they contribute
to improve knowledge of causes of species fluctuations. Species distribution data often implies residual spatial autocorrelation and temporal variability, so
both components are important to study the evolution of species distribution from an ecological point of view. This study aims to estimate the spatio-temporal
distribution of sardine (Sardina pilchardus) in the western and southern Iberian waters considering the sampling nature from different species data sources,
fishery-dependent and fishery-independent data. This talk will focus on modelling issues associated to survey data, being suggested a hierarchical two-part model
capable of dealing with zero-inflated data, different sources of uncertainty and past dependencies with the environment.
15:35 - 16:00 Irene Brito [CMAT-GTA]
Expected utility based modelling of risk decision problems
Abstract: In the context of decision making under risk, expected utility theory describes how decision makers
choose between risky prospects. Due to inconsistencies in modelling certain risk decision problems and empirical experiments, modifications of the
expected utility model have been proposed. In this talk, risk decision problems, including certainty effects, common ratio and common consequence
effects are analysed and described using a risk model based on expected utility, entropy and variance.
Coffee Break
16:40 - 17:05 José Joaquim [CMAT-ANAP]
Global exponential stability of discrete-time Hopfield neural network models with unbounded delays
Abstract: In this presentation, first, a normed vectorial space which could be used as the phase space of a difference
equation with unbounded delays is presented, then an exponential stability criterion of the zero solution of discrete-time systems with unbounded delays is given.
Based on the M-matrix theory, we establish sufficient conditions to ensure the global exponential stability of the zero equilibrium of low-order, and high-order,
discrete-time Hopfield neural network models with unbounded delays and delay in the leakage terms. At the end of this presentation, a numerical example is given,
illustrating the effectiveness of the new results.
17:10 - 17:25 Catarina Faustino [CMAT-GTA]
Directed homology of tensor products of precubical sets
Abstract: Precubical sets are combinatorial-topological objects that may be used to model concurrent systems. An important categorical
construction for precubical sets is the tensor product, which models the parallel composition of independent concurrent systems. In this talk, I will discuss two concepts of
directed homology for precubical sets and their behavior with respect to tensor products.
17:30 - 18:10 Sónia Dias [Instituto Politécnico de Viana do Castelo]
Linear Models for Distributional Data
Abstract: In the classical data framework one numerical value or one category is associated with each individual.
However, the interest of many studies lays in groups of records gathered according to characteristics of the individuals or classes of individuals.For such
situations, Symbolic Data Analysis proposes that a distribution or an interval of the individual records' values is associated with each unit,
thereby considering new variable types, named symbolic variables. One such type of symbolic variable is the histogram-valued variable,
where to each entity under analysis corresponds an empirical distribution. For this type of variables, models and methods for the representation,
analysis, interpretation and organization of the data are in development.
End
Posters
Mouse over the titles shows poster
abstracts.
Arraz, C.F., Clain, S., Brito, I.
(CMAT - UM)
Utility Clustering
Abstract: This project aims to develop a new clustering method, in which the metric is replaced by or mixed with a utility function,
commonly used in the context of Risk Theory and Decision Theory. In the traditional clustering technique, the formation of clusters is obtained through metrics, minimizing
the dissimilarities between the elements belonging to the same cluster. However, the metrics are indifferent to the specifics of the problems, therefore it may be relevant
in some models to consider characteristics that are not captured through metrics. The introduction of a utility function allows the integration of a new quantification
for clustering taking into account this piece as further information.
Azevedo, D., Azevedo, A.
(CMAT - ANAP)
Asymptotics for partial sums of the generating functions of the Fuss-Catalan numbers
Abstract: We study the asymptotic behaviour of the generating function of the (d)
Fuss- Catalan numbers.
For d=2, this was done with methods that can not be used for general d.
Therefore, we used another approach: techniques of holonomic sequences.
We were able to prove that, for all d the sequence of the partial sums
of the series is holonomic of order 2 and degree d-1.
After that, we establish the asymptotic behaviour of the generating
function, whenever it diverges (the series diverges (i.e.
|x|>(d-1)^(d-1)/d^d).
Dias, A., Menezes, R., Feijó, D., Silva, A.
(CMAT - SAPOR, IPMA - DivRP)
Analysis of regional and temporal patterns in seine fishing of the landings in Continental Portugal
Abstract: In Continental Portugal, 50% of the fish landed comes from seine fishing, known as “sardine fishing”.
With the reduction of the sardine stock to unsustainable levels, fishing opportunities have recently been reduced for this species, and fishermen have had to find
solutions to maintain similar levels of profitability, such as catching mackerel, anchovy and horse mackerel.
The present work intends to analyze the regional and temporal patterns in the landings of pelagic fish, using official landings data from the seine fishing fleet.
To assist in this analysis, a graphical application in the R environment will be developed.
Leitão A.M., Severino, R.J.M.
(CMAT, FMH, Lisbon University; CMAT - ANAP)
A different kind of complex dynamics: FLOW
Abstract: In 1980s, Stephen Wolfram introduced the concept of complexity to classify the dynamics that some elementary
cellular automata (Boolean, one-dimensional systems, with periodic boundary conditions) were capable of.
After the order and disorder kind of ECA dynamics have been identified, wolfram found that some ECAs did not fit that classification. indeed, some ECAs showed
dynamics with order and disorder characteristics, and a new kind of dynamics was needed. since then, the idea of complex dynamics in cellular automata has been
strongly associated with the characteristics found for these 1D systems.
The aim of our work is to introduce a different kind of complex dynamics, something not possible for 1D systems: the idea of FLOW.
Monte, C., Brito, I.
(CMAT - GTA)
Classification and Optimization of Portfolios
Abstract: In the context of risk classification, several risk measures and models depending on expected utility, entropy,
variance or loss probability have been proposed. This work aims to apply different risk measures to the classification of portfolio stocks and to implement the mean-variance
optimization model developed by Markowitz to obtain efficient portfolios. A dataset consisting of historical stock data of the Portuguese stock market PSI index,
from July 17, 2017, to July 16, 2021, is considered, and numerical results obtained with both classification and optimization methodologies are compared.
Ralha, R.
(CMAT - ALC)
Increasing parallelism in the bisection method for symmetric tridiagonals
Abstract: For a symmetric tridiagonal matrix $T$ with diagonal entries $a_i, \; i=1, \cdots n$ and off-diagonal
entries $b_i, \; i=1, \cdots n-1$, let $count(x)$ denote the number of negative terms in the sequence
\begin{equation} \label{sturm2}
\begin{array} {l}
q_1(x)=a_1-x \\
q_i(x)=(a_i-x)-b_{i-1}^2/q_{i-1}(x), \; \; i=2, \cdots, n
\end{array}
\end{equation}
This gives the number of eigenvalues smaller than $x$ and is the basis of the bisection algorithm which computes eigenvalues of $T$ very accuratelly.
In a parallel computer many of these sequences may be computed simultaneously for different trial points $x$. In a parallel bisection algorithm, $x$ is the middle
point of an interval containing an eigenvalue. In this approach the number of sequences that may be processed in parallel is limited by the number of eigenvalues to be computed.
To increase parallelism one may use multisection of intervals but this is rather inefficient as compared to bisection. To solve these problems we propose an algorithm for the
parallel computation of $count(x)$.
Teixeira, A.P., Tavares, I.O., Almeida, R.
(CMAT - SAPOR, ANAP)
Mathematics on the cancer research: a first overview
Abstract: Cancer has been a topic of interest to the scientific community and several works where mathematical
techniques play an important role in the research of this disease have been published.
In this study, a research concerning publications on the cancer topic and involving mathematical techniques is performed; the collected data is described and characterized.
Tavares, I.O., Almeida, R. Teixeira, A.P.
(CMAT - ANAP, SAPOR)
Probability and statistics technics on the cancer research
Abstract: Cancer is one of the leading causes of mortality today, causing the death of nearly 10 million people in 2020.
However, it is a disease that, if detected at an early stage and effectively treated, can be cured. Scientific studies have been used as one of the strategies to combat
and prevent this disease, being the use of methods and models under the scope of probability and statistics frequently used.
In this study, a database considering relevant publications on the research of cancer that use probability and statistics technics is being built; the main characteristics
of these works are described.
