Programme
October 25th, 2024
09h30 - 09h45 Welcoming & Opening Session
09h45 - 10h45 Rita Guerra (Former student) - Fourier-type operators, properties and applications
10h45 - 11h15 Coffee-Break
11h15 - 11h45 Paulo Monteiro - Computational experiments on Lehman matrices, mni and their cores
11h45 - 12h15 Manisha Jain - Adding concurrency to Quantum dynamic logic
12h15 -12h45 Zita Abreu - Pseudo-MDP convolutional codes
12h45 - 14h30 Lunch-Break
14h30 - 15h30 Daniel Figueiredo (Former student) - Relation-changing structures (and applications to Health decision-making)
15h30 - 16h00 Marta Maltez - New developments in analysing multivariate compositional data
16h00 - 16h30 Rui Martins - A C++ library for sensitivity analysis of ODEs
16h30- 17h00 Chen Liang - Axisymmetric Bosonic Stars: bifurcations with spherical bosonic stars
Chairs: Juliana Cunha and Miguel Almeida
Rita Guerra
Title: Fourier-type operators, properties and applications
Abstract: The class of integral transforms of Fourier-type has been studied for more than a century. There is a very extensive list of their applications and operators generated by them. Nevertheless, this type of transforms continues to be a topic of interest for many researchers, namely in what concerns to generalizations and applications. In this talk, we focus our attention on some generalizations of the Fourier transform, their properties and also some convolutions. Moreover, we explore some applications of this type of operators.
Paulo Monteiro
Title: Computational experiments on Lehman matrices, mni and their cores
Abstract: See here!
Manisha Jain
Title: Adding concurrency to Quantum dynamic logic
Abstract: This work focuses on quantum programming language and logics for quantum programs.We extend the standard quantum programming language with a parallel operator and an await command. Our extended quantum dynamic logic provides a more robust framework for reasoning about the behaviors and properties of quantum programs that utilize these new constructs.
Zita Abreu
Title: Pseudo-MDP convolutional codes
Abstract: In this talk, I will introduce a new construction of convolutional codes and examine their erasure correction capabilities. MDP convolutional codes are known for their optimal correction performance when decoding is performed sequentially. However, few constructions of MDP convolutional codes exist, and those that do typically require a large finite field. To address this, I will propose a new method by taking an encoder from an MDP convolutional code and repeating one of its (matrix) coefficients. The resulting code, which I refer to as Pseudo-MDP, is defined over the same finite field as the original code. While it may not be an MDP code, it demonstrates improved erasure correction performance compared to the original.
Daniel Figueiredo
Title: Relation-changing structures (and applications to Health decision-making)
Abstract: State-transition models are graph-like strucutures that can be used to describe a wide range of phenomena. While the accessibility relation (set of edges) is usually fixed, in the last years, some author have been proposing relation-changing structures. These strcutures consider dynamic updates on the accessibility relation based, for instance, in the edges previously crossed. Because of this, this class of structure is called "reactive" by some authors. In this session, we revisit some concepts and languages to reason about these reactive models and explore concepts such as model-checking. During the presentation, we show how these structures can more accurately design processes/protocols on Health decision-making.
Marta Maltez
Title: New developments in analysing multivariate compositional data
Abstract: Principal component analysis aims to summarize the multivariate data structure and is known for its dimension reduction, which achieves maximum variability. Compositional data are constrained positive data that reflect an overall composition, such as histograms of categorical variables or percentages of parts within a whole. An observation defined by a composition of p D-compositional variables (i.e. p variables each with D-part compositional components) is a compositional data. This type of multivariate observation is called a (p-dimensional) compositional data vector. Since each vector can be thought of as two-dimensional, a dataset formed by these compositional data vectors can be seen as a three-way array.
The methodology under development divides the data into two parts: the total data and the partial data, corresponding to R different geographical regions. Each region is a three-dimensional structure (n*p*D). Since the total can be considered with the same structure and corresponds to the sum of the R regions, a dimensionality reduction is performed on the total, by PCA for compositional data vectors. The eigenvectors of the previous procedure are used in each region, corresponding to the partial. The scores of the main principal component are obtained. Finally, longitudinal plots are constructed using the clr coefficients and pivot coordinates, where each part of the composition is given by an age group, explaining how each group behaves over time.
Rui Martins
Title: A C++ library for sensitivity analysis of ODEs
Abstract: In this presentation, I will talk about an implementation of the discrete adjoint sensitivity analysis method in C++. This method is designed to perform sensitivity analysis of optimisation problems involving ODEs. In particular, this implementation leverages automatic adjoint differentiation (AAD) and Single Instruction, Multiple Data (SIMD) vectorization, presenting a small performance enhancement relative to state-of-the-art sensitivity analysis methods when the optimisation problems involve few objective functions and many parameters.
Chen Liang
Title: Axisymmetric Bosonic Stars: bifurcations with spherical bosonic stars
Abstract: A physical system may remain stable under certain perturbations or evolve in a new direction. In other words, the solutions to the equations describing the system may develop new branches under specific perturbations. Such bifurcation phenomena can occur in systems ranging from small droplets to compact astrophysical objects like black holes, on a cosmic scale. We find that exotic compact objects, composed of Einstein gravity minimally coupled to spin-0 and spin-1 massive bosonic fields, exhibit similar bifurcation phenomena. Under specific axisymmetric perturbations, spherically symmetric excited-state bosonic stars branch into two new solutions: chain-like and ring-like axisymmetric bosonic stars. Given that most studies of perturbations on exotic compact objects have only considered spherical perturbations, this work provides new insights into the behavior of such objects under axisymmetric perturbations.