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)

Program

Part I – Public transport for smart cities
September 17, 15:30 – 17:30 with a short break

Abstract: The idea of a smart city is one that utilizes IoT technologies and data analytics to optimize the efficiency of city operations and services, so as to provide a high quality of life for its citizens. Due to reduced public funding, many public transportation systems are already facing challenges to maintain their services. For a smart city, the goal of public transportation is not simply the movement of people, but to provide mobility for living. In order to provide sufficient coverage/frequency, an integrated co-ordinated multi-modal public transportation system is needed, leading to substantial increase in operational complexity. Environmental concerns and the recent pandemic may also have changed work and commuting patterns in the future. For smart cities, public transport must offer ubiquitous access, real-time response to demand, convenience and quality service, and energy-efficient operations. This talk will discuss the challenges in network design, operations planning, scheduling and management of smart public transport systems.

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)

Abstract: We study a vehicle and crew (re-)scheduling problem for a public transit system which is subject to highly stochastic travel times and disruptions. Our research is motivated by the operations of the tramways system in Hong Kong which faces severe challenges because it does not run on dedicated tracks but must share the road with vehicular traffic in heavily congested areas.  We develop a decision-support system that optimises service frequencies, meal-break delays and overtime costs, and taking stochastic time-dependent travel-time uncertainties into account. The efficiency and effectiveness are evaluated via simulation. The results identify the potential benefits of revising the schedule dynamically in real time using optimization models.

We will also discuss bus-bridging strategies to handle major disruptions.

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.

We have been studying compartmental models of infectious disease spread, considering voluntary vaccination. The law governing the dynamics of voluntary vaccination is defined such that each individual chooses whether or not to be vaccinated, influenced by their perception of the choices of other individuals and the state of the disease in the system. This is known in the literature as imitation dynamics. I will present a simple model that explains the main ideas behind the construction of this type of model. The use of imitation dynamics in this model led to the emergence of chaotic behavior. I will also present two other models, one with an age structure and the other with loss of immunity.

Free transmission problems form a class of free boundary problems in which the solution-dependent discontinuity occurs at the level of the operator. Arising naturally in the modelling of heterogeneous diffusion and related processes, these problems present genuine mathematical difficulties, especially in the fully nonlinear setting. I will discuss recent progress on the existence of viscosity solutions and on their optimal regularity, both in the interior and up to the (fixed and free) boundary. I also plan to mention a few results on the development of numerical schemes tailored to this class of problems. Time permitting, I will conclude with a selection of open questions and possible directions for future research.

Speaker: Prof. Marta Gomes, Instituto Superior Técnico, University of Lisbon

Date | Time: December 5, 2025 | 14h30

Place:NOVA FCT, Departamento de Informática , sala232

Title: Spatialmulti-criteria decision analysis for rehabilitation priority ranking: acollaborative application to heritage workforce housing sites ( Co-authors: AnaPaula Falcão, Rita Machete, Alexandre B. Gonçalves )

Abstract: This workpresents a methodology to rank heritage sites regardingrehabilitation,considering both the characteristics of building sites and ofthe urban environment in the surrounding area. The objective is to aid thedecision process of building rehabilitation byranking the sites according totheir potential for re-emergence in the affordable housing rental market. Thedeveloped methodology is based on a combination of multi-criteria decisionanalysis (MCDA) and spatial analysis of geographical data, in order toconstruct an index, the “rehabilitation potential”, which is understandable byrehabilitation technicians and land managers and is applicable to support a listof priorities of building rehabilitation interventions. The methodology wasapplied to a case study consisting of aset of 33 heritage sites of theworkforce housing typology in Lisbon. These were built in the early industrialage in Portugal and are owned by the city municipality. The application ofMCDAwas a collaborative process that brought together the expertise of the academyand of the public administration. The results included a sensitivity analysisand gave form to a recommendation of five sites, selected from the totalworkforce housing set, to be rehabilitated in the near future.

Short bio: Prof. Marta Gomes is anAssistant Professor at Instituto Superior Técnico (IST), Department of CivilEngineering, Architecture and Environment, and a researcher at CERIS. She holdsa PhD in Systems Engineering (2007) from IST and has extensive expertise inoperations research, optimization, discrete-event simulation, multi-criteriadecision analysis, and large-scale data analytics, with applications acrosscivil engineering, industrial engineering, mechanical and aerospace systems.Her career includes a strong record of publications and collaborative research projects inmaintenance optimization, transport systems, pavement engineering, and urbanand environmental planning. 

Title: Fractional Derivatives: Applications in data fitting and Artificial Neural Networks.

Speaker: Prof. Hamza El Mahjour (Abdelmalek Essaâdi University, MA).

Date | Time: December 10, 2025 | from 14:00 to 14:30.

Place: Room 2.23 - Building IX.

Abstract: Fractional calculus introduces non-integer-order derivatives with a built-in memory effect, enabling more accurate modeling of history-dependent phenomena than classical integer-order derivatives.This talk focuses on that memory property and its practical impact. A clear example is the work of Barros et al. (2021): a fractional Caputo SIR model for COVID-19 that incorporates transmission hysteresis and reduces fitting errors by 10-20\% on real data (Italy, South Korea) compared to the standard SIR model, using an adapted Adams–Bashforth–Moulton scheme.I will also briefly review the integration of fractional derivatives into artificial neural networks. By employing Caputo-type fractional operators, these networks gain memory-dependent dynamics and additional tunable parameters (the fractional orders), leading to improved accuracy, stability, adaptability, and ability to capture long-range dependencies in tasks from control and modeling to image processing and medicine.Overall, the memory effect of fractional derivatives provides tangible advantages in both epidemiological modeling and next-generation neural networks, making complex systems easier to represent and control.

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Title: An Introduction to Fractional Calculus: Theory and Challenges.

Speaker: Prof. Aadil Lahrouz (Abdelmalek Essaâdi University, MA).

Date | Time: December 10, 2025 | from 14:30 to 15:00.

Place: Room 2.23 - Building IX.

Abstract: This talk gives an introduction to fractional calculus, which extends classical calculus to non-integer orders. We start with the basic concepts, including the definitions of fractional integrals and fractional derivatives. We focus mainly on two approaches: the Riemann-Liouville and Caputo definitions. We explain their main properties and the key differences between these formulations in different function spaces. Next, we present the main theory of fractional differential equations. We cover existence and uniqueness results, continuation and blow-up theorems. We also explain how fractional differential equations differ from classical ones, particularly in their memory effects and non-local behavior. Throughout the presentation, we point out several important theoretical challenges and open questions in the field.

MatHBioS Workshop

Title: Initiation to Neural Networks with PyTorch.

Speaker: Prof. Hamza El Mahjour (Abdelmalek Essaâdi University, MA).

Date: December 9, 2025 | from 10:00 to 12:00 and from 14:30 to 15:30.
          December 10, 2025 | from 10:00 to 12:00.
          December 11, 2025 | from 14:30 to 15:30.

Place: Room 2.23 - Building IX.

Abstract: This training is designed for PhD students with prior Python experience. It is a five-hour workshop that introduces participants to the practical implementation of neural networks using PyTorch, with a strong emphasis on hands-on coding and real-time model development. Designed for those already familiar with Python, the sessions will guide you from foundational concepts to building, training, and evaluating deep learning models. Through interactive exercises, participants will gain confidence in using PyTorch as a flexible and powerful framework for research applications.

*Those who are interested are invited to complete the form at this link: (https://docs.google.com/forms/d/e/1FAIpQLSckWV1aZjUmXXaW8xieqpTDuxkQSl74OqzZM6cmgQvWWeqdkw/viewform?pli=1)

In this talk, we revisit compartmental models, given by systems of ordinary differential equations, that describe the transmission dynamics of specific infectious diseases. These models are then generalized through hybrid frameworks and complex networks, enabling their application to a large number of evolution problems in fields such as sociology, economics, geography and epidemiology. Optimal control methods are applied to these models and complex networks aiming to mitigate epidemic outbreaks. In the second part of the talk, we propose a controlled complex network of Lotka-Volterra systems, where the strength of the migrations of biological populations are represented by control functions, reproducing the implementation of ecological corridors. We establish synchronization-type results, and the solutions to the optimal control problems demonstrate the potential to restore biodiversity in heterogeneous habitats. This is achieved by reaching either a global coexistence equilibrium or, in a more favorable scenario, a global limit cycle-ensuring sustained biological oscillations and vibrant ecological dynamics.

We investigate the unbounded operator obtained from the finite Hilbert transform when it acts from $L^1(-1, 1)$ into itself. A full inversion theorem is established for this operator, together with suitable extended versions of the Parseval and Poincaré-Bertrand formulae.

The talk is based on joint papers with Oleksiy Karlovych. We consider multidimensional generalisations of Wiener-Hopf operators and show that, under mild restrictions on the underlying Banach function space, their norm is estimated below by the L^infinity norm of the symbol, while their Kuratowski measure of noncompactness is estimated below by half that norm. Additionally, we show that for a classical Wiener-Hopf operator on a (separable) translation-invariant Banach function space over the half-line, its Hausdorff measure of noncompactness, its essential norm, and its norm are all equal.

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: Estimation of Above-Ground Biomass in Forests Using Satellite Data

Speaker: Ricardo Coelho, PhD Student, NOVA SST, Caparica, Portugal

Date | Time: January 22, 2026 | 14:30

Location: To be announced

Teams: https://teams.microsoft.com/meet/32754086330496?p=nspp91z49enhjNBXTR

Abstract: Monitoring carbon sequestration is essential for climate policy, carbon markets, and ecosystem assessment. Above-Ground Biomass (AGB) is a key indicator of carbon storage, where it can be estimated using direct or indirect methods. Direct methods involve the destruction of the trees, while indirect methods, like allometric equations, require the collection of forest inventory data, which is a time-consuming and costly process. With technological advances, a faster and more cost-effective alternative is to estimate AGB through remote sensing, combining satellite data with field measurements, which can lead to more accurate estimates.Machine learning (ML) models have been widely applied for AGB prediction, but many do not account for spatial autocorrelation and fail to quantify prediction uncertainty. Hybrid approaches that combine spatial statistical models with ML have emerged to address these limitations, leveraging both predictive power and spatial dependency modelling. This study first presents a simulation experiment to systematically compare the predictive performance of ML, hybrid, and spatial statistical methods under controlled geostatistical scenarios. We then apply these approaches to estimate AGB in a region of Spain, using GEOSAT-2 remote sensing data, including reflectance bands, vegetation indices, and texture metrics. 

Short Bio: Ricardo Coelho is a PhD student in the Mathematical Doctoral Programme at the NOVA School of Science and Technology (FCT-NOVA). His research work is focused on predicting forest biomass, through statistical models, using field and remote sensing data. Before enrolling in his PhD, he did a MSc in Mathematics and Applications at FCT-NOVA and a BSc in Mathematics at the same university. 

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 UID/00297/2025 (\url{https://doi.org/10.54499/UID/00297/2025}) and UID/PRR/00297/2025 (\url{https://doi.org/10.54499/UID/PRR/00297/2025}) (Center for Mathematics and Applications)

We study a class of degenerate fully nonlinear elliptic equations consisting of a pure equation and an associated transmission-type free boundary problem. We first propose a regularization of the pure equation and derive a numerical method for the regularized problem. The regularization plays a crucial role in ensuring the monotonicity of the numerical scheme. We prove that the method is monotone, consistent, and stable. As a consequence, the Barles–Souganidis framework guarantees the convergence of the numerical approximation. Once the numerical treatment of the pure equation is established, we show how a similar approach can be extended to the free boundary transmission problem. Finally, we present numerical experiments that support the theoretical results.