In this talk, we shalldiscuss the construction of infinitely many global-in-time Höldercontinuous analytically weak solutions to stochastic Euler equations inthree-dimensional periodic domain.

The proof is based on astochastic convex integration technique using Beltrami waves asbuilding blocks.

Zoom link: https://videoconf-colibri.zoom.us/j/92565611443?pwd=diOblm3Pu1aC5vYRMoN1BKd0DyktmB.1

Cayley's Theorem states that any finite monoid can be faithfully represented as a semigroup of transformations (self-maps) of a finite set. The minimum size of such a set is the (minimum transformation) degree of the monoid.

We obtain formulae for the degrees of the most well-studied families of finite diagram monoids, including the partition, Brauer, Temperley-Lieb and Motzkin monoids. For example, the partition monoid Pn has degree 1 + ( B(n + 2) - B(n + 1) + B(n) ) / 2 for n ≥ 2, where these are Bell numbers. The proofs involve constructing explicit faithful representations of the minimum degree, many of which can be realised as (partial) actions on projections.

This is joint work with Reinis Cirpons and James Mitchell, both at Univ St Andrews.

A famous result ofDelort (1991) establishes the concentration-

cancellationphenomenon for approximating solutions of 2D Euler equations

with a vortex sheetwhose vorticity maximal function has a log-decay of order

1/2 . On the otherhand, DiPerna and Majda (1987) showed that if the log-

decay assumption isstrictly larger than 1 then the lack of concentration

(and hence energyconservation) holds. Then the so-called DiPerna-Majda

gap problem asks:concentration-cancellation vs. energy conservation in the

remaining log-range(1/2,1]?

In this talk, afterreviewing earlier contributions to the DiPerna-Majda

gap problem, I willpresent a new approach to this question based on sparse-

ness. This is based onjoint projects with Mario Milman and Daniel Spector.

The talk will beself-contained, and no additional prerequisites are needed.

Abstract:

This talk examines the worst-case complexity in continuous optimization, defined as the computational effort required by an algorithm, in the worst-case scenario, to reduce a stationarity measure below a given positive threshold. We begin with an overview of foundational concepts and key results in worst-case complexity. Next, we delve into recent findings on the complexity of directional direct-search methods for nonsmooth unconstrained problems. Moving to the domain of multi-objective optimization, we highlight its distinctive challenges and recent advances. Finally, we present the worst-case complexity of a trust-region algorithm for solving (strongly) convex smooth unconstrained problems.

This talk is anontechnical overview of some topics of spectral theory of Toeplitz operatorson classical Hardy spaces and their abstract generalizations built upon Banachfunction spaces. We pay special attention to Toeplitz operators with continuousand piecewise continuous symbols.

Lab. 2.2, building VII.




Abstract:
 
We begin with a very introductory overview of classical, intuitionistic, and linear logics. Several proof translations exist between classical and intuitionistic logic (negative translations) [1, 2, 3], as well as between intuitionistic and linear logic (Girard translations) [4, 5]. These translations serve various purposes, including transferring properties between systems, simplifying proofs, facilitating the extraction of constructive computational content from proofs, and controlling the use of logical resources.
 
We will show that all these systems can be expressed as extensions of a basic logical system (essentially, intuitionistic linear logic). By establishing a common logical basis, we are able to formalize a unified approach to devising and simplifying such proof translations [6]. This approach clarifies the relationships between different logical systems, and reveals the underlying structure that connects them. Through this simplification process, we obtain the most well-known translations in the literature.
 
This is joint work with Paulo Oliva and Clarence Protin.

References:

[1] A.S. Troelstra, D. van Dalen, Constructivism in mathematics: An introduction. In Studies in Logic and the Foundations of Mathematics, volume 1, 1988.

[2] M. Heine Sørensen, P. Urzyczyn, Lectures on the Curry-Howard Isomorphism, volume 149. Elsevier, 2006.
 
[3] G. Ferreira, P. Oliva, On various negative translations, Electronic Proceedings in Theoretical Computer Science, 47:21-33, 2011.

[4] J.-Y. Girard, Linear logic, Theoretical Computer Science, 50:1–101, 1987.
 
[5] J.-Y. Girard, A tutorial on linear logic. In Substructural Logics, Studies in Logic and Computation 2, pages 327–355. Oxford Science Publications, 1994.
 
[6] G. Ferreira, P. Oliva, C. Protin, On the various translations between classical, intuitionistic and linear logic. (subm.)
https://arxiv.org/abs/2409.02249

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: On Generalized Mean Reverting Processes with Possible Structural Change

Speaker: Yunhong Lyu,Trent University, Peterborough, Canada

Date | Time: February 11, 2025 | 14h00

 Zoom: https://videoconf-colibri.zoom.us/j/88333359956

Abstract: In this presentation, we address the inference problem for the drift parameter in a generalized mean-reverting process, which is well-suited for modeling data exhibiting periodic characteristics. Additionally, we examine the case where linear constraints may be imposed on the drift parameters. We introduce three estimators: the unrestricted estimator, the restricted estimator, and the shrinkage estimator, and evaluate their relative efficiency. Furthermore, we explore change-point detection within this framework. Simulation studies validate the effectiveness of the proposed methods, which are subsequently applied to real-world environmental data. The results highlight the significance of accurate inference and timely change detection in environmental processes. Finally, the proposed methodology is expected to enhance the understanding and management of environmental systems.

Short Bio: Yunhong Lyu is an Assistant Professor in the Department of Mathematics & Statistics at Trent University, specializing in statistical modeling and structural change detection. Her research focuses on the inference problems in mean-reverting processes, such as parameter estimation, hypothesis testing and change-point detection, with applications in economics, health, and environmental studies. She holds a PhD from the University of Windsor and has published work on financial modeling, healthcare economics, and education policy. Beyond her research, she enjoys mentoring and teaching both undergraduate and graduate students.

Organizers: Mina Norouzirad & Isabel Natário

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

--------------------------------------------

  Seminar of Operations Research

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Title: A specialized second-order augmented Lagrangian method for mathematical programs with cardinality constraints

Speaker: Mariana da Rosa, UNICAMP, Brasil

Date | Time: February 12, 2025 | 15h00

Place: FCT NOVA, VII-Second Floor, Seminar room

Abstract:

In this talk, a practical and specialized second-order augmented Lagrangian method for solving mathematical programs with cardinality constraints (MPCaC) is presented. The seminar begins with a review of the stationarity conditions for MPCaC and a discussion of some augmented Lagrangian methods proposed in the literature. The presentation then considers a new approach that incorporates a second-order refinement step tailored to the structure of MPCaC. Under reasonable assumptions, the method ensures convergence to second-order stationary points, making it a potential tool for tackling this class of optimization problems.

Seminar of Analysis

Speaker:   Prof. Manil T. Mohan (Department of Mathematics, Indian Institute of Technology Roorkee, India)

Date/time:   02/19/2025 (Wednesday), at 14:15

Location:   Online via Zoom.

Please find the details below:

Link:  https://videoconf-colibri.zoom.us/j/94188507343?pwd=cbH0CTpLYuAxa5haPOm2DcAYKN0DJQ.1

Meeting ID:  941 8850 7343 

Passcode:  229621

Title:   Navier-Stokes equations-The Million Dollar Problem

Abstract:   The Navier-Stokes equations describe the motion of viscous fluids, which can be expressed mathematically in terms of conservation of momentum and conservation of mass for Newtonian fluids. A fundamental problem in analysis is to decide whether smooth, physically reasonable solutions exist for the three-dimensional Navier-Stokes equations (Navier-Stokes existence and uniqueness problem). In May 2000, the Clay Mathematics Institute announced this problem as one of its seven Millennium prize problems in Mathematics. The aim of this talk is to shed lights on this million dollar open problem in Mathematics.

Joint Seminar  Analysis Group & Mathematics for Health and Life Sciences Thematic Line 

 Speaker:   Nico Stollenwerk (Basque Center for Applied Mathematics)

Date/time:   02/26/2025 (Wednesday), at 14:15

Location:  Room 1.16, VII

[15:00 - 15:15 Coffee break ]

Joint Seminar  Analysis Group & Mathematics for Health and Life Sciences Thematic Line 

 Speaker:  Maíra Aguiar (Basque Center for Applied Mathematics & Ikerbasque - Basque Foundation for Science)

Date/time:   02/26/2025 (Wednesday), at 15:15

Location:  Room 1.16, VII

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

~ PhD Program in Mathematics Seminars ~

Titles:
Title 1:  Da Geração de uma Carteira de Mercado Sintética à Escolha de Resseguro: Uma Abordagem Empírica à Criação de um Fundo Sísmico em Portugal
Title 2: Introduction on the role of catastrophe models in measuring flood risks under climate change conditions

Speakers: João Correia & Beatriz Curioso, PDM & NOVA Math

Date | Time: February 26, 2025 | 14h30
Place: FCT NOVA, VII-Second Floor, Seminar room

Abstracts:
Abstract 1:  Um dos principais trabalhos a desenvolver na tese de doutoramento, prende-se com o estudo de estruturas de resseguro para o grupo de ramos de incêndio e outros danos – o mais exposto a catástrofes naturais – na perspetiva nacional. Assim, um dos objetivos iniciais passou pela construção de um simulador capaz de avaliar e comparar performances de diferentes estruturas de resseguro tradicionais, face a cenários de catástrofe. Para tal, relevou-se necessário colmatar a falta de informação disponível, gerando uma carteira de apólices sintética (recorrendo, essencialmente, a leitura de imagens e otimização linear), cujas suas propriedades reflitam a realidade nacional, plasmada em dados públicos. Por fim, incluiu-se uma metodologia de apoio à decisão (SMART e Trident), hierarquizando o valor acrescentado de cada esquema de resseguro com base em critérios e preferências estabelecidas pelo decisor. Como demonstração, é feito um caso de estudo no contexto de avaliação de vários modelos possíveis para a criação de um sistema de proteção contra fenómenos sísmicos para Portugal (Fundo Sísmico).

Abstract 2: In this talk, I will present the initial research made for my PhD thesis: an overview of the flooding phenomenon, focussing on the underlying risks, and a literature review on flood catastrophe models, including the usual procedures when building this type of models for the insurance sector.

Bios:

Bio1: João Correia: Licenciei-me em Matemática Aplicada à Economia e à Gestão pela Universidade do Algarve (2020) e sou mestre em Matemática Atuarial na NOVA FCT (2023), onde dissertei sobre a realidade atual da cobertura do risco sísmico no setor segurador nacional (em colaboração com a Autoridade de Supervisão de Seguros e Fundos de Pensões (ASF)). Após o mestrado ingressei nos quadros da ASF, no Departamento de Análise de Riscos e Solvência, como atuário, com uma das funções principais associada à realização dos estudos quantitativos de suporte à preparação de uma proposta para a criação de um sistema de proteção contra fenómenos sísmicos, incumbida pelo Governo. Atualmente, enquanto aluno de doutoramento, procuro prosseguir a minha especialização no âmbito das ciências atuariais, nomeadamente em resseguro e gestão de risco para catástrofes, em perfeita simbiose com a minha posição profissional.

Bio2: Beatriz Curioso is currently a PhD student in Mathematics with specialisation in Statistics and Risk Management at NOVA FCT. She completed the BSc in Mathematics in 2018, the MSc in Mathematics and Applications with specialisation in Pure Mathematics in 2021, and the MSc in Actuarial Mathematics in 2024, at the same institution. She has over three years of professional experience in the Pension Funds sector and has recently started working as an Actuary in Non-Life Insurance at Fidelidade.

Organizers: Isabel Natário & Mina Norouzirad & Rui Cardoso

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

~ PhD Program in Mathematics Seminars ~

Title: Modeling Mobility Data during COVID-19 in Portugal

Speaker: André Brito, PDM & NOVA Math

Date | Time: March 5, 2025 | 14h30
Place: FCT NOVA, VII-Second Floor, Lab. 2.2

Zoom:  https://videoconf-colibri.zoom.us/j/88333359956

Abstract: The COVID-19 pandemic highlighted the crucial role of statistical modeling in understanding infectious disease dynamics. This study investigates the spatio-temporal dependencies of viral respiratory infections by incorporating non-traditional data sources, particularly human mobility data. Traditional epidemiological models rely on clinical and surveillance data, but integrating mobility patterns provides a deeper understanding of disease spread. Using publicly available Google Community Mobility Reports, this research analyzes population movement across districts in Portugal. We employ statistical modeling to explain mobility including movement stringency and temperature as predictors. The study explores how mobility metrics evolved throughout the pandemic and their predictive value for epidemiological surveillance. This research underscores the importance of dynamic modeling approaches that account for temporal and spatial variations in mobility patterns. The results contribute to improved public health decision-making, providing a framework for leveraging mobility data in future epidemic responses.

Bio: André Martins Brito is a PhD student in Applied Mathematics at NOVA School of Science and Technology, specializing in Statistics and Risk Management. His research focuses on epidemiology and the modeling of mobility-incidence relationships. With a strong academic background, he holds a master’s degree in Applied Mathematics with a specialization in Actuarial Sciences, Statistics, and Operations Research, and a bachelor’s degree in Mathematics Applied to Economics and Management. His research experience includes a scholarship in epidemiology, contributing to a nationwide project on extreme weather event risk assessment in Portugal. Professionally, he has worked as a Data Analyst/Manager at the Bernhard Nocht Institute for Tropical Medicine, where he managed research databases and statistical analyses and worked as an A&H Regional Underwriting Analyst at AIG Europe, applying statistical methods to risk analysis.

Organizers: Isabel Natário & Mina Norouzirad & Rui Cardoso

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

Seminar of Analysis

Speaker:  Alina Shalukhina (Department of Mathematics, NOVA FCT, Portugal)

Date/time:  12/03/2025 (Wednesday), from 14:15 to 15:15.

Location:  Room 1.16, Building VII.

Title:  On interpolation of variable Lebesgue spaces over spaces of homogeneous type

Abstract:  We show that the Hardy--Littlewood maximal operator $M$ is bounded on a variable Lebesgue space $L^{p(\cdot)}(X)$, $1<p_-\leq p_+<\infty$, over a space of homogeneous type $X$ if and only if, for every $q\in(1,\infty)$, the exponent $p(\cdot)$ can be represented as

                          $\frac{1}{p(x)}=\frac{\theta}{q}+\frac{1-\theta}{r(x)},      x \in X,$

so that $M$ is bounded on $L^{r(\cdot)}(X)$ for all sufficiently small $\theta>0$. This is an extension of the analogous result by Diening, Karlovych and Shargorodsky from the Euclidean spaces to spaces
of homogeneous type. Results of this kind are applied for transferring properties like
compactness of linear operators from standard Lebesgue spaces to the variable ones.

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

~ PhD Program in Mathematics Seminars ~

Title: Statistical disclosure control and quality evaluation of synthetic data generated by non-parametric methods

Speaker: Vítor Augusto, PDM & NOVA Math

Date | Time: March 12, 2025 | 14h30
Place: FCT NOVA, VII-Second Floor, Lab. 2.2

Abstract: This PhD aims to continue the work in statistical disclosure control by improving the quality of synthetic data generated through non-parametric methods (such as GAN or CART). To achieve this, it will be necessary to extend existing exact inferential procedures for data generated by single imputation to cases of multiple imputation, perform the computational refinement of the degrees of freedom defined in asymptotic inferential procedures for vectors used in their adaptation to matrix inference, and adapt GAN methods for generating partially or completely synthetic data for a sequence of sensitive variables describing a profile. Finally, simulations will be carried out, along with the application to a real database.

Bio:  Vítor Augusto is a PhD student in Mathematics with a specialization in Statistics and Risk Management at NOVA School of Science and Technology. He also completed his Bachelor's degree in Mathematics and his Master's in Mathematics and Applications, specializing in Actuarial Science, Statistics, and Operational Research at the same institution. Professionally, before starting his PhD, he worked as a Maths teacher in elementary and high schools.

Organizers: Isabel Natário & Mina Norouzirad & Rui Cardoso

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: Using R Shiny for teaching statistical methods

Speaker: Alexandra Daub, Lars Knieper & Sophie Potts, Georg-August-University, Goettingen, Germany

Date | Time: March 19, 2025 | 14h00

 Zoom: https://videoconf-colibri.zoom.us/j/88333359956

Abstract: It is challenging to introduce statistical concepts to a heterogeneous student population with diverse backgrounds. Visualizations are often used in lectures and associated exercises. As these are usually done on lecture slides or (digital) notes, they remain static. In addition, the immediate programming of statistical concepts is a hindrance for students, as usually a basic understanding of the methodology is needed in advance.
In order to provide interactive visualizations combined with explanations and further give the opportunity to adjust parameters of statistical methods, webapps for teaching purposes are developed. Therefore, the R-Shiny framework is employed. It enables users to program interactive web apps directly with R while still being flexible enough to incorporate HTML, Javascript and CSS. It offers the potential to teach statistical concepts visually and interactively. Further, students are able to get a low-barrier intuition of statistical concepts before programming and applying these themselves.

Short Bio: Alexandra Daub, Lars Knieper and Sophie Potts are PhD students at the Chair of Spatial Data Science and Statistical Learning led by Prof. Dr. Elisabeth Bergherr at the University of Goettingen (Germany). Alexandra Daub and Lars Knieper both work on gradient-based boosting methods for estimating statistical models, with Lars Knieper focusing on the estimation of random and spatial effects and Alexandra Daub on generalized additive models for location, scale and shape. Sophie Potts is working on statistical modelling (currently a joint model for longitudinal and time-to-event data) with a special focus on their application in social sciences. During the first years of their PhDs, all three worked on a project on digital teaching material, which founded the chair's collection of Shiny applications. Both, their in-class teaching activities as well as the work on digital teaching material encompasses various areas of statistics including undergraduate statistics, statistical inference, spatial statistics and multivariate statistics.

Organizers: Mina Norouzirad & Isabel Natário

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

Recommender Systems (RSs) are pivotal in diverse domains such as e-commerce, music streaming, and social media.

The first part of the seminar presents a comparative analysis of key loss functions in recommender systems: Binary Cross-Entropy (BCE), Categorical Cross-Entropy (CCE), and Bayesian Personalized Ranking (BPR), which distinguish between positive items (interacted by users) and negative items. While previous studies have empirically shown that CCE outperforms BCE and BPR with the full set of negative items, we provide a theoretical explanation by proving that CCE offers the tightest lower bound on ranking metrics like Normalized Discounted Cumulative Gain (NDCG). Given that using the full set of negatives is computationally expensive, we derive bounds for these losses in negative sampling settings, establishing a probabilistic lower bound for NDCG. Our analysis shows that BPR's bound on NDCG is weaker than BCE’s, challenging the common belief that BPR is superior to BCE in recommender system training.

Beyond loss function analysis, we turn our attention to the robustness of Sequential Recommender Systems against data perturbations. Traditional similarity measures, such as Rank-Biased Overlap, prove inadequate for evaluating ranking stability in finite-length sequences. To address this, we introduce Finite Rank-Biased Overlap, a novel similarity measure tailored for practical scenarios. Through empirical analysis of item removal at different positions in temporally ordered sequences, we demonstrate that the impact on recommendation quality is highly position-dependent, with removals at the end of sequences leading to significant performance degradation.

Seminarof Analysis

Speaker:  Prof. Fernanda Cipriano (NOVA Math andDepartment of Mathematics, NOVA FCT, Portugal)

Date/time: 26/03/2025 (Wednesday), from 14:15 to 15:15.

Location:  Room 112, Building IV.

Title:  Weak solution for stochasticDegasperis-Procesi equation

Abstract:  Thiswork is concerned with the existence of solution to the stochastic Degasperis-Procesiequation with an infinite dimensional multiplicative noise and integrableinitial data. Writing the equation as a system composed of a stochasticnonlinear conservation law and an elliptic equation, we are able to develop amethod based on the conjugation of kinetic theory with stochastic compactnessarguments. More precisely, we apply the stochastic Jakubowski-Skorokhodrepresentation theorem to show the existence of a weak kinetic martingalesolution. In this framework, the solution is a stochastic process with samplepaths in Lebesgue spaces, which are compatible with peakons and wave breakingphysical phenomenon.

This is ajoint work with Nikolai Chemetov.

This course provides a comprehensive overview of neural recommender systems, focusing on their foundations, state-of-the-art advancements, and practical challenges. It covers essential deep learning architectures and techniques that power modern recommender systems, exploring their role in personalizing user experiences across various domains such as e-commerce, entertainment, and social media. Key topics include sequence-based models, which capture sequential user behavior, and Transformer-based approaches, which leverage attention mechanisms for better context understanding. The course also delves into graph-based recommendation models, which model relationships between users and items in complex networks. By the end of the course, students will gain a strong understanding of neural recommender systems, their applications, and the challenges of deploying them in real-world settings.

The course is designed for graduate students and researchers with a foundational understanding of machine learning and deep learning. Familiarity with basic neural network architectures (e.g., CNNs, RNNs) is recommended.

The course will appeal to students from related areas such as natural language processing, and computer vision, and optimization, given its focus on domain-specific applications. The emphasis on ethical considerations and explainability will also interest students working on Safe, Explainable, and Trustworthy AI.

This course provides a comprehensive overview of neural recommender systems, focusing on their foundations, state-of-the-art advancements, and practical challenges. It covers essential deep learning architectures and techniques that power modern recommender systems, exploring their role in personalizing user experiences across various domains such as e-commerce, entertainment, and social media. Key topics include sequence-based models, which capture sequential user behavior, and Transformer-based approaches, which leverage attention mechanisms for better context understanding. The course also delves into graph-based recommendation models, which model relationships between users and items in complex networks. By the end of the course, students will gain a strong understanding of neural recommender systems, their applications, and the challenges of deploying them in real-world settings.

The course is designed for graduate students and researchers with a foundational understanding of machine learning and deep learning. Familiarity with basic neural network architectures (e.g., CNNs, RNNs) is recommended.

Yes, the course will appeal to students from related areas such as natural language processing, and computer vision, and optimization, given its focus on domain-specific applications. The emphasis on ethical considerations and explainability will also interest students working on Safe, Explainable, and Trustworthy AI.

This course provides a comprehensive overview of neural recommender systems, focusing on their foundations, state-of-the-art advancements, and practical challenges. It covers essential deep learning architectures and techniques that power modern recommender systems, exploring their role in personalizing user experiences across various domains such as e-commerce, entertainment, and social media. Key topics include sequence-based models, which capture sequential user behavior, and Transformer-based approaches, which leverage attention mechanisms for better context understanding. The course also delves into graph-based recommendation models, which model relationships between users and items in complex networks. By the end of the course, students will gain a strong understanding of neural recommender systems, their applications, and the challenges of deploying them in real-world settings.

The course is designed for graduate students and researchers with a foundational understanding of machine learning and deep learning. Familiarity with basic neural network architectures (e.g., CNNs, RNNs) is recommended.

Yes, the course will appeal to students from related areas such as natural language processing, and computer vision, and optimization, given its focus on domain-specific applications. The emphasis on ethical considerations and explainability will also interest students working on Safe, Explainable, and Trustworthy AI.

Zoom link: 
https://videoconf-colibri.zoom.us/j/92261549490
 
Abstract:
The purpose of this talk is to revisit the story of semilattices decompositions of semigroups, starting from the basic notions, that date to the early days of semigroup theory, and up to very recent applications of the theory (to certain non-regular semigroups, but also regular rings).

Seminarof Analysis

Speaker:  Dr. Yashveer Kumar (INESC-ID, IST-ULisbon,Portugal)

Date/time: 02/04/2025 (Wednesday), from 14:15 to 15:15.

Location:  Room 112, Building IV.

Title:  Numerical wavelet approximation scheme fordistributed order fractional differential equations

Abstract:  In thistalk, we introduce a new method for solving distributed-order fractionaldifferential equations using Legendre wavelets. Our approach works for bothsingle-variable and two-variable cases. We combine the Legendre Gaussquadrature formula with the Tau technique to build an operational matrix forthese wavelets. This matrix helps convert complex differential problems intosimpler linear algebraic equations. To show how well our method works, wepresent several test examples.

Abstract:
In this work, we introduce two frameworks for derivative-free bilevel optimization. We consider both the upper and lower-level problems with bound constraints on the variables, as well as general nonlinear constraints, assuming that first-order information is either unavailable or impractical to obtain. Furthermore, we allow both the objective functions and constraints to be nonsmooth. The lower-level problem is solved with an accuracy that is progressively refined during the optimization process.We first propose a line-search-based method for problems where the upper-level is only bound-constrained, analyzing convergence to Clarke-Jahn stationary points when accuracy is allowed to reach its maximum. If a stricter bound is imposed on the refinement process, we prove convergence to approximate stationary points using an extended notion of Goldstein stationarity.We then extend this analysis to a MADS-type approach, initially for bound-constrained problems, investigating both cases: full accuracy refinement and bounded accuracy. For this framework, we provide a convergence analysis similar to that of the line-search-based method. Finally, we discuss how more complex constraints can be handled through an exact penalty function approach embedded in both frameworks, extending convergence results to Clarke-Jahn and approximate stationarity.

Short Bio:

Edoardo Cesaroni earned his Master’s degree in Management Engineering (Decision Models for Management Engineering curriculum) in July 2023 from Sapienza University of Rome. Since November of the same year, he has been a Ph.D. student in the ABRO doctoral program, specializing in Operations Research (MATH-06/A ex MAT/09), at the Department of Computer, Control, and Management Engineering Antonio Ruberti (DIAG) at Sapienza University of Rome, under the supervision of Professor Giampaolo Liuzzi. His main research interests focus on derivative-free optimization and the application of optimization techniques to machine learning problems. During his first year of doctoral studies, he focused on applying optimization techniques to real-world case-studies, specifically working on the optimal sizing of batteries in railway systems and the identification of risk factors for gastric neoplastic lesions in collaboration with medical researchers from Sant'Andrea Hospital.

Zoom link: https://videoconf-colibri.zoom.us/j/92261549490
 
Abstract:
This talk will explore the connection between combinatorial group theory and cryptographic protocols, particularly in the context of key exchange mechanisms, where two parties seek to establish a common group element (key) by making use of the difficulty encoded by an algorithmic problem [5]. These protocols not only provide practical cryptographic applications but also drive the theoretical study of algorithmic problems, such as the conjugacy problem or the decomposition problem, and the study of properties of particular groups, such as the probability of two elements being conjugate, motivating the identification of groups that enhance the security of the protocol.

To ensure secure communication, it is crucial that protocols minimize the information revealed about the final key. We will examine the main criteria that define protocol security and investigate the group-theoretic properties that enhance it. In particular, we will introduce the concepts as the degree of commutativity [4, 1] and the conjugacy ratio [3].

This talk will conclude with a discussion of future research, including potential contributions to existing problems in group theory and possible extensions to semigroup theory. By bridging algebraic structures with cryptographic challenges, this work aims to further the understanding of secure communication protocols and their mathematical foundations.

References:
[1] Y. Antolı́n, A. Martino, E. Ventura. Degree of Commutativity of Infinite Groups. Proc. Amer. Math. Soc, 145(2): 479-485, 2017.
[2] J. Araújo, M. Kinyon, J. Konieczny, A. Malheiro. Three Notions of Conjugacy for Abstract Semigroups, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2015.
[3] L. Ciobanu, C. G. Cox, and A. Martino. The conjugacy ratio of groups, Proc. Edinb. Math. Soc., 62:895-911, 2019.
[4] W. H. Gustafson. What is the probability that two group elements commute?. Amer. Math, Monthly, 80:1031-1034, 1973.

[5] A. Myasnikov, V. Shpilrain, and A. Ushakov. Group-based Cryptography, Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser Verlag, Basel, 2008.

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: Estimation and Testing in Some Mean-Reverting Processes

Speaker: Severien Nkurunziza, University of Windsor, Windsor, Canada

Date | Time: April 23, 2025 | 14h00

 Zoom: https://videoconf-colibri.zoom.us/j/88333359956

Abstract: We consider inference problem concerning the drift parameter in some generalized mean-reverting processes with unknown change-points in the context where the target parameter is suspected to satisfy some restrictions. We generalize some recent findings in five ways. First, the established method incorporates the uncertain prior knowledge. Second, we derive the unrestricted estimator (UE) and the restricted estimator (RE) as well as their asymptotic properties. Third, we propose a test for testing the hypothesized restrictions and we establish its asymptotic power. Fourth, we construct a class of shrinkage estimators (SEs) which includes as special cases the UE, RE, andclassical SEs. Fifth, we study the relative performance of the proposed class of SEs, and we prove that James-Stein type estimators dominate the UE. Beyond such interesting findings, the additional novelty of the derived results consists in the fact that the dimensions of the proposed estimators are random. Because of that, the asymptotic power of the proposed test and the relative efficiencies do not follow
from classical methods. To overcome this problem, we derive an asymptotic result which is useful in its own.

Short Bio: Dr. Sévérien Nkurunziza is a Professor of Statistics in the Department of Mathematics and Statistics at the University of Windsor. He joined the department in July 2005 as an Assistant Professor, after completing his PhD in statistics at the Université du Québec à Montréal. Since 2006, he has been funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) and since 2017, he is Elected Member of International Statistical Institute. His research topics include the models with breakpoints, shrinkage-type estimators and asymptotic theory in Statistics. In particular, he focuses on statistical methods that may have applications in survival analysis, in financial mathematics as well as in brain imaging. More details about Dr. S. Nkurunziza’s research contributions can be found at https://www.uwindsor.ca/science/math/711/faculty-dr-s%C3%A9v%C3%A9rien-nkurunziza.

Organizers: Mina Norouzirad & Isabel Natário

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This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

Seminarof Analysis

Speaker:  Prof. Arbaz Khan (Department of Mathematics,Indian Institute of Technology Roorkee, India)

Date/time: 30/04/2025 (Wednesday), from 14:15 to 15:15 Lisbon time (18:45pm to19:45pm IST)

Location:  Online via Zoom.

Please findthe details below:

Link: https://videoconf-colibri.zoom.us/j/91434648600?pwd=xhjPqgsVnEEQSQqMa6VYWkRFe6KJIl.1

MeetingID: 914 3464 8600

Passcode: 418037

Title:  Uncertainty Quantification in Poroelasticity:Methods and Error Control

Abstract:  Linearporoelasticity models play a crucial role in various applications acrossbiology and geophysics. A prominent example is the Biot consolidation model,which captures the coupled behavior between the elastic deformation of afluid-saturated porous medium and the diffusive flow of the fluid within it,under the assumption of small deformations. This model forms a foundationalframework for computational simulations in medicine (e.g., organ modeling) andgeomechanics (e.g., deformation of permeable rocks).

In the first part of this talk, we present anovel locking-free stochastic Galerkin mixed finite element method (SG-MFEM)for the Biot consolidation model incorporating uncertainties in the Young'smodulus and hydraulic conductivity fields. Starting from a five-field mixedvariational formulation, we describe the stochastic Galerkin approximation andestablish the well-posedness of the resulting system. Emphasis is placed on thedevelopment of efficient linear algebra techniques, including a new preconditionerfor the MINRES algorithm, for which we derive spectral bounds. Numericalexperiments illustrate the robustness and efficiency of the proposed solver.

The second part of the talk focuses on thedevelopment of a posteriori error estimators for the SG-MFEM applied tothe Biot model with uncertain parameters. These estimators form the basis foradaptive refinement strategies that enhance computational efficiency whilepreserving accuracy.

Bestregards,

On behalf of organizers of theAnalysis Seminar,

Kush Kinra

Joint Seminarof Analysis & MatHBioS Thematic Line

Speaker:  Prof.Fabio Chalub (NOVA Math, Universidade NOVA de Lisboa, Portugal)

Date/time: 07/05/2025 (Wednesday), from 14:15 to 15:15.

Location:  Room 1, Building XI.

Title:  Group centrality in optimal and suboptimalvaccination for epidemic models in contact networks

Abstract:  The pursuitof strategies that minimize the number of individuals needing vaccination tocontrol an outbreak is a well-established area of study in mathematicalepidemiology. However, when vaccines are in short supply, public policy tendsto prioritize immunizing vulnerable individuals over epidemic control. As aresult, optimal vaccination strategies may not always be practical forinforming real-world public policies. In this work, we focus on a disease thatresults in long-term immunity and spreads through a heterogeneous population,represented by a contact network. We study four well-known group centralitymeasures and show that the GED-Walk offers a reliable means of estimating theimpact of vaccinating specific groups of individuals, even in suboptimal cases.Additionally, we depart from the search for target individuals to be vaccinatedand provide proxies for identifying optimal groups for vaccination. While theGED-Walk is the most useful centrality measure for suboptimal cases, thebetweenness (a related, but different centrality measure) stands out whenlooking for optimal groups. This indicates that optimal vaccination is notconcerned with breaking the largest number of transmission routes, butinterrupting geodesic ones.

This is a joint work with Jorge O. Cerdeira andMatheus Hansen (NOVA Math, Universidade NOVA de Lisboa, Portugal)

Description: By linking conceptual theories with observed data, transparent hierarchical generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular biology, microbiome studies, and resource allocation in epidemiology. These lectures will survey some applications of transparent generative models and show how they inform experimental design, iterative model refinement, goodness-of-fit evaluation, and agent based simulation. We emphasize a modular view of generative mechanisms and discuss how they can be flexibly recombined in new problem contexts. 

Current research in generative models is currently split across several islands of activity, and we highlight opportunities lying at disciplinary intersections. We will study both coded applications that go over these ideas and the applications will be done using R. All attendees will be asked to have a recent version of R installed on their laptop so we can do hands-on activities together.

We will go over the principles of:

- hierarchical mixture models (https://www.huber.embl.de/msmb/)

- latent variables for microbiome (https://doi.org/10.6084/m9.figshare.c.6922510.v1)

- machine learning for goodness of fit

( https://github.com/krisrs1128/generative_review. )

Registration can be completed here.

Description: By linking conceptual theories with observed data, transparent hierarchical generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular biology, microbiome studies, and resource allocation in epidemiology. These lectures will survey some applications of transparent generative models and show how they inform experimental design, iterative model refinement, goodness-of-fit evaluation, and agent based simulation. We emphasize a modular view of generative mechanisms and discuss how they can be flexibly recombined in new problem contexts. 

Current research in generative models is currently split across several islands of activity, and we highlight opportunities lying at disciplinary intersections. We will study both coded applications that go over these ideas and the applications will be done using R. All attendees will be asked to have a recent version of R installed on their laptop so we can do hands-on activities together.

We will go over the principles of:

- hierarchical mixture models (https://www.huber.embl.de/msmb/)

- latent variables for microbiome (https://doi.org/10.6084/m9.figshare.c.6922510.v1)

- machine learning for goodness of fit

( https://github.com/krisrs1128/generative_review. )

Registration can be completed here.

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: Everything is Connected: Space, Time, EVT, and Graph Neural Networks

Speaker: Tanujit Chakraborty, Sorbonne University and Sorbonne Centre for Artificial Intelligence, Abu Dhabi and Paris

Date | Time: May 13, 2025 | 14h00

 Zoom: https://videoconf-colibri.zoom.us/j/88333359956

Abstract: Air quality forecasting is a vital space-time challenge with profound implications for public health and environmental management. In this talk, I will introduce E-STGCN (Extreme Spatiotemporal Graph Convolutional Networks), a novel approach that integrates graph convolutional networks with extreme value theory to predict air quality at unprecedented accuracy levels. We will delve into the mathematical underpinnings of E-STGCN, including its ability to capture complex spatiotemporal dependencies across dynamic networks. Emphasis will be placed on how the model processes extreme events, handles multi-scale relationships, and achieves state-of-the-art results on Delhi's air quality data.

Short Bio: Tanujit Chakraborty is an Associate Professor of Statistics and Data Science at Sorbonne University and Sorbonne Centre for Artificial Intelligence (Abu Dhabi and Paris). He received his MS and Ph.D. degrees from the Indian Statistical Institute, Kolkata. His research interests include statistical learning, neural networks, time series forecasting, and health data sciences. He was also a visiting faculty member at Duke-NUS Medical School, National University of Singapore. He has served as a statistical consultant at PharmaACE Analytics, Bajaj FinServ, and ITC Limited.

Organizer: Isabel Natário

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This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

Seminarof Analysis

Speaker: Prof. ZdzislawBrzezniak (Department of Mathematics, University of York)

Date/time: 14/05/2025 (Wednesday), from 14:15 to 15:15.

Location:  Online via Zoom.

Please findthe details below:

Link: https://videoconf-colibri.zoom.us/j/98576468310?pwd=Onlqd9Yz2ioDQfAAbP4qmdIrvQYSJY.1

MeetingID: 985 76468310

Passcode: 971632

Title:  Weak martingale solutions to stochasticNavier-Stokes-Cahn-Hilliard system with transport noise

Abstract:  In thistalk, we investigate the weak solvability of an initial boundary value problemknown as the Navier-Stokes-Cahn-Hilliard system, which describes the dynamicsof a homogeneous, incompressible and isothermal mixture of two immiscibleNewtonian fluids flowing in a bounded  2Dor 3D domain under stochastic perturbations.

We assume that the density and viscosity of themixture are constants and, to prove the existence result, we consider anapproximation problem and use the Jakubowski-Skorohod Theorem to prove that thelaws of the corresponding solutions on a certain non-metric topological space$Z_T$ have a sequence weakly convergent to a new probability

measure on $Z_T$.

Now, by following the argument of Mikuleviciusand Rozovskii in their paper (Ann. Probab. 33(1) (2005), 137--176) with somemodifications, we prove that the canonical process on the space $Z_T$ is infact a martingale solution of our problem with respect to the new measure.

The approach is quite interesting compared tothe existence approach in the literature, since we combine both theJakubowski-Skorohod theorem and the Mikulevicius and Rozovskii argument to dealwith our problem.

This talk is based on a joint research withAristide Ndongmo Ngana (York).

Room 4.6, Building VIII
 
 
Abstract:
The Chu-Vandermonde formula and its q-analogue admit a generalization, due to Bender, in which one parameter in the sum is replaced by a sequence with the property that its successive differences are each equal to 0 or 1. For this formula I will present a non-terminating extension and several other generalizations, each of which reduces to a classical result when a particular choice is made for the sequence involved. One of the results I will describe is a generalization of Bender's type for the q-binomial theorem. For this I will give a combinatorial proof in terms of overpartitions.

Seminar of Analysis

Speaker:  Prof. Pierre-A. Vuillermot (Department of Mathematics, University of Lisbon and Institut Élie Cartan de Lorraine).

Date/time:  21/05/2025 (Wednesday), from 14:15 to 15:15.

Location:   Room 4.7, Building VIII.

Title:  On a new class of weighted Orlicz-Sobolev spaces and their embeddings

Abstract:  In this talk, I will introduce a new scale of weighted Orlicz-Sobolev spaces and discuss the existence of various continuous and compact embeddings for them. Continuous embeddings are relatively easy to come by, I will show that the way to compactness is more tortuous as it is based on the combination of the existence of a Schauder basis in the spaces under consideration with a condition on the generating Orlicz functions regarding their local behavior at the origin. I will illustrate the results by means of several examples.

Abstract:

The Center of Intelligent Systems (CIS), from the Institute of Mechanical Engineering (IDMEC), focuses the research and development activities in the design and analysis of complex engineering problems. The main research areas of CIS are "Control Systems and Advanced Robotics” and "Intelligent Automation, Data Modeling and Optimization”. This research line focuses on new methodologies in automation and systems integration, systems design in mechatronic systems, data analysis for prediction, decision making and decision support systems based on intelligent methodologies, and optimization using bio-inspired metaheuristics in energy, transports, aerospace, health, manufacturing and logistics. This seminar will focus on the most recent developments of CIS in optimization applied to real-world problems. Which ones? Be there to see these ‘details' :).

Short Bio:

Prof. João M. Costa Sousa is Full Professor in the Dept. Mechanical Engineering, Instituto Superior Técnico (IST), Universidade de Lisboa, Portugal. He is the Coordinator of the Center of Intelligent Systems, IDMEC. He received the MSc in mechanical engineering from IST in 1992, and the PhD in electrical engineering from Delft University of Technology, the Netherlands, 1998. He has authored one book and more than two hundred papers in journals and conference proceedings. He has supervised more than 100 PhD and MSc students. He participated in more than 20 research projects, being the Principal Researcher in seven, five of them with industry in intelligent automation and machine learning. He was the PI of an Industry 5.0 project with the pharmaceutical industry. Prof. Sousa is an Associate Editor of IEEE Transactions on Fuzzy Systems, Mathematics and Computers in Simulation, Sensors, and Fuzzy Sets and Systems. He is past Chair of the Fuzzy Systems Technical Committee, IEEE Computational Intelligence Society. See: https://scholar.google.com/citations?user=ciBwHqsAAAAJ&hl=en

Room 4.7, Building VIII

Abstract:
Ramsey theory is a branch of combinatorics that seeks to find patterns in disorganized situations. One of its main achievements, Szemeredi’s theorem on arithmetic progressions, got an ergodic theoretic proof in 1977 when Furstenberg devised a Correspondence Principle to encode combinatorial information about sets of integers into a dynamical system. Since then ergodic methods have been very successful in obtaining new Ramsey theoretic results, some of which still have no purely combinatorial proof.
I will survey some of the history of how ergodic theory and Ramsey theory are interconnected, and explore some recent developments.

This seminar takes place within the scope of the master's course "Seminário em Matemática Pura". This is a public session where a presentation is made by the student.
 
Room 4.6, Building VIII

Abstract:
For germs of plane curves, Zariski proved that an irreducible plane curve germ is analytically equivalent to an irreducible plane curve germ with finite Puiseux parametrization. Germs of plane curve germs represent the simplest instance of quasi-ordinary hypersurfaces in dimension two. Zariski’s algebraic techniques cannot be applied to the general case. We show that, for some types of quasi-ordinary surfaces, these techniques can indeed be applied in the context of contact geometry. This is an ongoing work for my thesis.

Online seminar

Abstract:
Coding theory, originated in the late 1940s, is driven by the need toensure reliable communication over noisy channels. Linearerror-correcting codes, in particular, became central to the fielddue to their algebraic structure and practical utility. These codescan be studied via combinatorial, algebraic, and geometric methods:to each code one associates a matroid from its generator orparity-check matrix, and the independent sets of the matroid define asimplicial complex whose Stanley–Reisner ring captures the code’scombinatorial structure. The Betti numbers of this ring encode keyinvariants of the code. Computing them is difficult in general, butthey reflect important parameters and offer new perspectives on thecode’s structure. In this talk, we will focus on the homologicalinvariants of certain families of BCH codes. BCH codes are regardedas one of the most useful codes in the theory of error-correctingcodes. Despite their prominence, basic properties such as dimensionand minimum distance remain unresolved in many cases. Timepermitting, we will discuss open problems such as Charpin’sconjecture regarding the minimum distance of primitive BCH codes.

Room: 4.6, ed. VIII

Abstract: The concept of a determinant associated with a finite group originates in the work of Dedekind and Frobenius in the late 19\textsuperscript{th} century. This idea was later extended to finite semigroups, where the determinant of the semigroup algebra captures deep structural information. For commutative semigroups, Steinberg provided a factorization of the semigroup determinant, and more recently, the theory has been developed for broader classes, such as semigroups in the pseudovariety $\ensuremath{\mathsf{ECom}}$, where all idempotents commute.

In this talk, we trace the development of computing determinants for finite semigroups, from its classical origins to more recent results. We focus on semigroups whose structure enables determinant computation via partial orders and canonical decompositions, particularly using the notion of $\ll$-smoothness. These developments highlight both the possibilities and limitations in extending the theory beyond commutative and idempotent-commuting settings.

We also discuss recent progress in identifying broader classes of semigroups where determinant computations remain tractable, even when full $\ll$-transitivity is absent. This opens new directions for understanding the algebraic and combinatorial properties that govern the behavior of semigroup determinants.

Tensor computation extends the principles of linear algebra and numerical analysis to higher-dimensional data structures, allowing for efficient processing of complex data. Tensors play a central role in a variety of disciplines, from machine learning to scientific simulations. Tensors are among the most versatile and powerful mathematical tools available, with applications in many disciplines such as physics, computer science, engineering, graphs, and machine learning.

The mini-course is designed as a comprehensive introduction to tensors and their applications, bridging theory and practice. It seeks to demystify the subject for beginners while offering valuable insights for those with more advanced knowledge. Our focus is twofold: 

Conceptual Understanding: By presenting tensors in a clear and accessible manner, we aim to equip the  course attendees with a solid grasp of the core principles. 

Practical Applications: With numerous examples and case studies, we plan to illustrate how tensors are used to address real-world challenges, from simulating physical systems to enabling breakthroughs in artificial intelligence.

Registration can be completed here.

Tensor computation extends the principles of linear algebra and numerical analysis to higher-dimensional data structures, allowing for efficient processing of complex data. Tensors play a central role in a variety of disciplines, from machine learning to scientific simulations. Tensors are among the most versatile and powerful mathematical tools available, with applications in many disciplines such as physics, computer science, engineering, graphs, and machine learning.

The mini-course is designed as a comprehensive introduction to tensors and their applications, bridging theory and practice. It seeks to demystify the subject for beginners while offering valuable insights for those with more advanced knowledge. Our focus is twofold: 

Conceptual Understanding: By presenting tensors in a clear and accessible manner, we aim to equip the  course attendees with a solid grasp of the core principles. 

Practical Applications: With numerous examples and case studies, we plan to illustrate how tensors are used to address real-world challenges, from simulating physical systems to enabling breakthroughs in artificial intelligence.

Registration can be completed here.

Seminarof Analysis

Speaker: Prof. Lahcen Laayouni (School of Science and Engineering, Al AkhawaynUniversity).

Date/time: 25/06/2025 (Wednesday), from 14:15 to 15:15.

Location:  Room 4.6, Building VIII.

Title:  Optimized Schwarz Methods: Challenges andPromises at Continuous and Algebraic Levels

Abstract:  Optimized Schwarz methods are a class ofdomain decomposition techniques designed to improve the convergence ofiterative solvers for partial differential equations (PDEs) by imposingoptimized transmission conditions. This talk explores the challenges and promisesof these methods at both continuous and algebraic levels. At the continuouslevel, we address the design of effective transmission conditions, theirdependence on problem-specific parameters. At the algebraic level, we examinethe construction of algebraic block transmission conditions for robustpreconditioners. Through theoretical and numerical results, we show thepotential of optimized Schwarz methods to handle large-scale PDE problems.

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: Illuminating Distributions: Wavelet-Based Quantile Density Estimation with Applications in Auction Theory

Speaker: Hassan Doosti, Macquarie University's School of Mathematical and Physical Sciences, Sidney, Australia

Date | Time: June 26, 2025 | 14:00

Zoom: https://videoconf-colibri.zoom.us/j/88333359956

Abstract: Quantile density functions, which capture the local structure of probability distributions, have emerged as powerful tools in fields ranging from risk analysis to economic modeling. In this talk, we delve into advanced nonparametric strategies for estimating quantile density functions, spotlighting the versatility and precision of wavelet-based techniques. We investigate a range of estimators—including linear, hard thresholding, and block thresholding approaches—within both unbiased and length-biased sampling frameworks. A key focus is placed on the challenges introduced by sampling bias and the use of adaptive wavelet methods for effective bias correction. Through the lens of auction theory, we demonstrate how quantile-driven insights can unravel bidder behavior and valuation dynamics. Supported by simulation studies and real-world case examples, the presentation underscores the power of wavelet methods in handling complex and irregular data landscapes.

Short Bio: Dr. Hassan Doosti is a Senior Lecturer in Statistics at Macquarie University's School of Mathematical and Physical Sciences. He also serves as the Program Director for the Master of Data Science program. Dr. Doosti specializes in flexible modeling techniques, particularly in nonparametric curve estimation, focusing on scenarios involving incomplete or biased data. His research encompasses areas such as probability density, quantile density, and regression functions. With a prolific publication record exceeding 70 research papers, he has contributed significantly to the field. Dr. Doosti has also edited volumes, including Flexible Nonparametric Curve Estimation and Ethics in Statistics: Opportunities and Challenges. His work bridges theoretical advancements with practical applications across various domains, including medical studies and business analytics.

Organizers: Isabel Natário and Mina Norouzirad

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

Seminar of Analysis

Speaker: Prof. João Carvalho (Centre for Mathematics, University of Porto &Prince Henry Portucalense University).

Date/time: 04/07/2025 (Friday), from 14:15 to 15:15.

Location:  Room 4.7, Building VIII.

Title: Nonlinear dynamics and bifurcationsin epidemic models

Abstract:  In thefirst part we analyze a periodically forced SIR model. We prove that for $R0< 1$ the system exhibits multiple endemic equilibria -- backwardbifurcation. Using the theory of strange attractors, we prove the persistenceof strange attractors for an open subset in the parameter space where R0 < 1.

In the second part, we address a modified SIRmodel with a constant vaccination strategy and the bifurcations it unfolds. Weexplicitly prove that the endemic equilibrium is a codimension two singularityin the parameter space (R0, p), where R0 is the basic reproduction number and pis the proportion of susceptible individuals successfully vaccinated at birth.The analytical expressions of the bifurcation curves as a function of R0 and pestimate the proportion of vaccinated susceptible individuals necessary for thedisease to be eliminated from the population.

In the third part we present our ongoing work.We focus on two main topics: (i) in the absence of seasonality, the endemic(and unique) equilibrium point undergoes supercritical and subcritical Hopfbifurcations; (ii) in the presence of seasonality, we conjecture that, via thetorus breakdown theory, the system exhibits chaotic dynamics.

In the fourth and final part, we present arecent model describing the coinfection dynamics of HIV and SARS-CoV-2 underhighly active antiretroviral therapy (HAART). Unlike previous models, ourformulation incorporates the effect of HAART on both infections. We derive thebasic reproduction numbers for each virus and show that transcriticalbifurcations occur when these values cross the threshold of one. We alsoestablish stability conditions for the disease-free equilibria. Numericalsimulations reveal that HAART, although targeting HIV, may also reduceSARS-CoV-2 proliferation in coinfected individuals -- suggesting a potentialindirect benefit not widely addressed in the existing literature.

This is joint work with Professor Alexandre Rodrigues (ISEG).