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

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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)

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).

Room 1, Building XI
 
Abstract:
In 2022, East and Ruškuc published the congruence lattice of the infinite twisted partition monoid. As a by product, they established the congruence lattices of the finite $d$-twisted partition monoids. This talk is a first step in adapting the work of East and Ruškuc to the setting of the Brauer and Temperley-Lieb monoid. Specifically, it presents the newly established congruence lattice of the $0$-twisted Brauer and Temperley-Lieb monoids. With simple to grasp visual multiplication and applications in theoretical physics and representation theory, the family of diagram monoids are of particular interest to a number of fields as well are of stand alone interest.

Statistics and Risk Management Seminar & Thematic Line MatHBioS (Mathematics for Health and BioSciences)

Department of Mathematics, NOVA MATH/FCT NOVA

Title: Remodelling Selection to overcome Selective Depletion Biases

Speaker: Gabriela Gomes, University of Strathclyde and NOVA Math

Date | Time: July 10, 2025 | 14:30

Location: VIII-3.4

Abstract: Every population consists of individuals that vary in many traits, and each trait may or may not be associated with fitness. Variation in fitness traits lends population studies prone to selective depletion biases. When an ageing cohort exhibits declining mortality, it could be individuals becoming healthier or selective depletion of the frail. In an epidemic, when growth in cumulative infections decelerates, it could be individuals cautiously changing behaviour or selective depletion of the most susceptible. In microbial populations, when an isogenic population is stressed by antimicrobial treatment and some cells survive, this could be due to individual cells switching between normal and persister phenotypes or antibiotic selectively killing cells that divide faster. In each case, the first explanation invokes individuals changing (1), while the second posits selection on pre-existing variation changing (2). While explanations of type (1) are intuitive and widely adopted, those of type (2) are more neutral and rarely considered due to cognitive biases and challenges in estimating all variation that matters. While both are plausibly operating in most real systems, neglect of (2) leads to over-attribution of results to (1), wrong predictions, bad policy decisions and poor reproducibility, negatively impacting science, economics and ethics. To overcome this selective depletion bias, I have been proposing a pragmatic approach to study design and analysis whereby we infer distributions of characteristics that respond to selection and reframe theories accordingly. The approach is based on remodelling selection (mathematically by introducing key parametric distributions into population dynamic models, and empirically by measuring quantities of interest along selection gradients) and statistical inference (by fitting mathematical models to data). The procedure is being tested in systems where trait distributions can be inferred from population trends as well as reconstructed directly from individual measurements. Results of this ongoing research will be presented, and the wider applicability discussed. 
Prospects for conducting some of this research at NOVA School of Science and Technology are being assessed. Please join the discussion if you find the topic interesting…

Short Bio: Gabriela Gomes graduated in Applied Mathematics from the University of Porto in 1987 and completed her MSc and PhD in Mathematics from the University of Warwick in 1990 and 1993, respectively. In 1999, she switched to biology with a Wellcome Research Training Fellowship in Mathematical Biology. In 2002, she established an independent research group at the Gulbenkian Science Institute (IGC), initially supported by a Marie Curie Excellence Grant, with a spectrum of projects ranging from fundamental mathematical concepts to the management of population and ecosystem health, public engagement in science and development of research infrastructures. She subsequently led research programmes in the Research Centre for Biodiversity and Genetic Resources (CIBIO-InBIO), the Liverpool School of Tropical Medicine (LSTM), and is now a Professor of Mathematics and Statistics at the University of Strathclyde. Gabriela in a member of NOVA Math since 2023 where she leads the participation of the centre in the European project Inno4Vac (Innovations to accelerate vaccine development and manufacture).

Gabriela Gomes has published around 100 peer-reviewed research papers in international journals, initially in Mathematics and Physics and later in Biology, Ecology and Epidemiology. She has been a member of Editorial Boards for Nature Scientific Reports, Journal of Mathematical Biology and Journal of Theoretical Biology, and integrated the Board of Directors of the Portuguese Mathematical Society twice. She held various visiting positions in the USA and Brazil and is a Fellow of the Institute of Mathematics and its Applications (FIMA) in the UK.

Organizers: Isabel Natário and Paula Patrício

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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)

Room 1, Building XI
 
Abstract:
We provide a brief introduction to (C1,C2)-clonoids, which are sets of functions of several arguments closed under right composition with a clone C1 and under left composition with another clone C2. Our primary focus is on clonoids of Boolean functions, and we present classifications of (C1,C2)-clonoids in the spirit of Post's classification of clones. Moreover, we propose refinements and strengthenings to Sparks's theorem on the cardinalities of clonoid lattices.

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: Exploring Household Income in EU Countries: A Three-Parameter Distribution Perspective

Speaker: Kamila Trzcińska, University of University of Lodz, Poland

Date | Time: July 24, 2025 | 14:00

Location: VIII-3.4

Abstract: Household income is a key economic variable that reflects the living standards and material well-being of different social groups. Understanding its distribution is essential for analyzing inequality and economic structure. This study applies three-parameter income distribution models, known for their flexibility and strong statistical properties, to data from EU countries.The focus is on evaluating how well these theoretical models, including the Zenga distribution (2010), approximate empirical income data. The goodness of fit is assessed using measures such as the coefficient of similarity, the Mortara index, and a newly proposed metric based on the comparison of empirical and theoretical cumulative distribution functions. Additionally, basic statistical characteristics derived from the models are compared with their empirical counterparts.

Short Bio: Kamila Trzcińska is Assistant Professor at the Faculty of Economics and Sociology, University of Lodz. Her academic work focuses on the statistical analysis of income and wealth distributions, with particular emphasis on measuring and understanding income inequality, poverty, and the concentration of wealth among households. She conducts in both theoretical and applied research, contributing to the broader discussion on socio-economic disparities and their quantitative assessment. Her studies explore statistical tools to analyze income dynamics and economic well-being.

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Organizers: Isabel Natário and Mina Norouzirad and Frederico Caeiro

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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)

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: Ambiguity When Comparing Brands: Caution and Monopolistic Competition

Speaker: Jaime Velasco Sanchez, PhD at the University of Surrey, United Kingdom

Date | Time: September 4, 2025 | 15:00

Location: To be announced

Abstract: When consumers are not sure how to compare brands, caution creates monopolistic competition. This is addressed by looking at an exchange economy with countably many differentiated goods and analyzing the price impact of a coalition of countably many agents withholding their endowments. Such impact persists even when making the coalition smaller and smaller.

Organizers: Isabel Natário and Mina Norouzirad and Marta Faias

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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)

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: Directional Statistics in modelling high volatility

Speaker: Ashis SenGupta, CSIR Emeritus Scientist, Govt of India; Augusta University, Georgia, USA; METU, Turkey

Date | Time: September 18, 2025 | 14:30

Location: To be announced

Teams: https://www.google.com/url?q=https://teams.microsoft.com/l/meetup-join/19%253ameeting_NDJjM2M4YzYtZTNhMC00OGJiLThiYmYtOGMwMGI5MWY5OTMx%2540thread.v2/0?context%3D%257b%2522Tid%2522%253a%2522ae7e50a2-ed26-41f7-bd75-f49683f2433a%2522%252c%2522Oid%2522%253a%25224fb0e073-941c-4a18-993a-8d7d76f8978e%2522%257d%26launchAgent%3DGSuiteAddOn%26correlationId%3D41bdd273-e8bf-4abd-b9ce-a371e68581bc&sa=D&source=calendar&usg=AOvVaw0cnzRZzZVob8K6dY8HOBr8

Abstract: Modern data in many areas of applied science are characterized by high volatility, e.g. long tails as well as high kurtosis or peakedness. They also exhibit asymmetry and multimodality. Classical families of distributions with well-defined probability density functions are inadequate to model such data. On the other hand, families that may be good contenders for modelling high volatility do not in general admit probability density functions on the Euclidean manifold. But these families often can be mapped onto non-Euclidean manifolds, through deep results involving characteristic functions, for which the densities can have elegant Fourier series representations. This connection also immensely helps in statistical inference for the associated parameters. Also, on their own these families provide ample flexibilities in modelling data on non-Euclidean manifolds. We first develop the related theories for deriving these highly flexible families. Next, optimal inference procedures are outlined. Finally, emerging real-life examples from both Euclidean and non-Euclidean manifolds are presented to illustratethe results.

Short Bio: Professor Ashis Sengupta holds a Ph.D. from Ohio State University, under the supervision of Professor C. R. Rao. He advised 17 Ph.G. students in India, turkey and USA and he has more than 120 publications, including 12 books and volumes in Multivariate Analysis, Directional Statistics, Statistical Machine Learning, Financial Statistics and Reliability Inference. He is an Emeritus Scientist at the Indian Institute of Technology, Kharagpur, Advisor/Consultant at the Indian Statistical Institute, Adjunct Professor at Augusta University, Georgia, USA, a Distinguished Professor at the Middle East Technical University in Turkey and an Advisor at Analythium, Canada. He was a Visiting Professor in several Universities, including Stanford University, University of California-Santa Barbara and Riverside, University of Wisconsin-Madison, University of Missouri- Columbia, Michigan State University, Concordia University, Institute of Statistical Mathematics and Keio University (Japan), Haceteppe University (Turkey), University of Malaya (Malaysia), Daegu University (South Korea), Academia Sinica (Republic of China), as well as other Universities in Canada, Belgium, Sweden, Germany and Israel. He is an ex Editor-in-Chief of Environmental and Ecological Statistics (Springer, USA), and of the Journal of the Indian Society for Probability and Statistics and an Associate Editor for the Book series of the Forum of International Mathematics, Springer. He visited mainland China as Citizen Ambassador from American Statistical Association and is the recipient of several International and National recognitions, including 2 Lifetime Achievements and Distinguished Statistician Awards. He was elected President of the Mathematical Sciences section of the Indian Science Congress in 2011-2012 and he is an Elected Member of the International Statistical Institute, Fellow of the National Academy of Sciences, India and, of the Indian Society for Probability and Statistics and of the American Statistical Association – currently the only working statistician in India with this recognition. 

Organizers: Isabel Natário and Mina Norouzirad and Carlos Agra Coelho

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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)

In recent decades, differential equations with nonstandard growth conditions have attracted increasing attention from researchers. Such problems arise in various branches of applied mathematics and physics, including image restoration and digital processing, electrorheological or thermo-rheological fluid flows, and elasticity. At the intersection of these areas lies the study of problems involving the p(x)-bilaplacian operator. In this seminar, we investigate a parabolic partial differential equation with the p(x)-bilaplacian operator. By performing a change of variables, the original problem is reformulated as a system of two second-order equations. We discretize this system with respect to the variables t and x, leading to the semidiscrete and discrete problems, respectively. We establish existence, uniqueness, and a priori estimates for both the semidiscrete and the discrete solutions. Furthermore, we prove that the resulting system of second-order equations admits a unique weak solution. A detailed study of the convergence order of the semidiscrete and discrete solutions toward the weak solution is also presented. Finally, we present numerical examples in one-dimensional and two-dimensional spatial domains using MATLAB software.

My talk is about the effects of small-scale turbulence on large-scale motion by using a stochastic scaling and singular limits. Many works have been done in recent years using the scaling limit in both scalar and vector cases. The second one is characterized by the presence of stretching, which is  an incremental detail over the scalar case. Our (with F. Flandoli) aim in [arXiv:2410.00520] is to understand the stretching mechanism of stochastic models of turbulence acting on a simple model of polymer. Namely, we investigate a scaling limit problem, under suitable intensity assumption. The polymer density equation, initially an SPDE converges (in the first step) weakly to a limit deterministic equation with a new degenerate term with some singular parameter. Recently, in [arXiv:2503.18143] we investigate the singular limit in the spirit of the hydrodynamic limit techniques. One consequence is that the limiting density shows a power-law decay in the polymer length, which is consistent with physical predictions.

The activities mentioned herein were performed in the framework of the project: EU-HORIZON EUROPE ERC-2021-ADG "Noise in Fluids" (NoisyFluid), no. 101053472

This talk provides an overview of Evolutionarily Stable Strategies (ESS) in population games and addresses some common misconceptions found in the classical literature. We focus specifically on Locally Superior Strategies (LSS), which represent a very special case of ESS, examining them in contexts with both finite and infinite action sets. Locally Superior Strategies are particularly significant among evolutionary stability concepts because they act as attractors under the Replicator Dynamic. The main result I will present unifies the finite and infinite frameworks by establishing a necessary and sufficient condition for an ESS to be a LSS.