Abstracts

Workshops

Pedro Reis Costa (IPMA and CCMAR University of Algarve)

Marine Biotoxins and Seafood Safety: Advances and Current Challenges

Analyzing Shellfish production contributes to the economic sustainability of coastal regions and responds to the increasing demand for seafood. However, shellfish can accumulate high levels of naturally occurring toxins produced by harmful algal blooms (HABs), posing a risk to consumers. To protect public health, most coastal countries implement monitoring programs for toxic phytoplankton and shellfish toxicity, aiming to minimize the risk of acute intoxications and ensure seafood quality. Changes in climate conditions, human activities, and technological advancements are commonly pointed out to justify the increasing occurrence, frequency, and intensity of HABs and the subsequent contamination of marine resources. Understanding the oceanographic and ecological mechanisms that trigger HABs and developing new tools for their early detection are crucial for forecasting HAB contamination in shellfish farms. The current goals of developing aquaculture as a sustainable and economically viable industry involve predicting, characterizing, and mitigating the impacts of these natural phenomena.

Raquel Lucas (Instituto de Saúde Pública da Universidade do Porto-ISPUP)

The population burden of musculoskeletal disorders: how to address the elephant in the room?

Rheumatic and musculoskeletal disorders are the major cause of disability worldwide. At ISPUP, we conduct epidemiologic research on musculoskeletal health, including bone physical properties and fragility fractures, sagittal postural patterns, and chronic musculoskeletal pain. Conceptually, we aim to bring together material, spatial and subjective dimensions of musculoskeletal health. Etiologically, we explore constitutional and contextual influences that shape the development of musculoskeletal traits in the general population.

Most disability due to musculoskeletal disorders is caused by chronic pain. Yet, there is a well-known dissociation between the extent of identifiable organic lesions and the severity of the subjective experience of pain. This concept supports an understanding of chronic musculoskeletal pain as a syndrome - rather than a symptom - that develops throughout life, results from organic as well as psychosocial influences, and features physical suffering as a main manifestation. Chronic pain is as much a population as an individual problem, and our research focuses on finding ways to address it as such. I will go through examples where Mathematics is central to address our research questions:

Modeling chronic pain onset and recurrence throughout life outside clinical settings
Comparing the performance of different experimental pain responses in the context of safety constraints to data collection
Quantifying competing effects of different public health trends and policies on musculoskeletal health outcomes
Selecting nuanced alternatives to null hypothesis significance testing for policy-making

Invited talks

Sílvia Barbeiro (CMUC, Department of Mathematics, University of Coimbra)

Mathematical modeling in ophthalmology

Optical coherence tomography (OCT) is a non-invasive imaging modality widely used in ophthalmology. Optical coherence elastography (OCE) uses OCT images to measure tissue displacement following mechanical stimulation, allowing to map its mechanical properties.

Starting with a brief presentation of these imaging modalities, in this talk we will we will discuss a robust mathematical model for the reconstruction of the mechanical properties of the retina using OCE. Moreover, motivated by the corneal opacity problem, we will develop a suitable model of the corneal stroma and simulate light scattering in the human cornea to mimic the real OCT imaging system. The talk is furnished with some numerical examples representing real applications.

Estela Bicho (Algoritmi, Dep. Eletrónica Industrial, University of Minho)

A Neuro-dynamics approach to Robots as Socially Intelligent Assistants/Co-workers: from the mathematics & neurocognitive basis of joint action in humans to human-robot collaboration

As robot systems are moving as assistants into human everyday life, the question how to design robots capable of acting as sociable partners in collaborative joint activity becomes increasingly important. The capacity to anticipate and take into account action goals of a partner is considered a fundamental cognitive capacity for successful cooperative behaviour in a shared task. We will report about our bio-inspired approach towards creating socially intelligent robots that is heavily based on findings about the neurocognitive mechanisms underlying joint action in humans. We believe that designing cognitive control architectures on this basis will lead to more natural and efficient human-robot interaction/collaboration since the teammates will become more predictable for each other. Central to our approach, we use neuro-dynamics as a theoretical language to model cognition, learning, decision making and action. The robot control architecture is formalized by a coupled system of dynamic neural fields representing a distributed network of local but connected neural populations with specific functionalities. Different pools of neurons encode task relevant information about action means, action goals and context in form of self-sustained activation patterns. These patterns are triggered by input from connected populations and evolve continuously in time under the influence of recurrent interactions. The dynamic control architecture has been validated in tasks in which an anthropomorphic robot acts as a personal assistant in joint action tasks. We show that the context dependent mapping from action observation onto appropriate complementary actions allows the robot to cope with dynamically changing joint action situations. More specifically, the results illustrate crucial cognitive capacities for efficient and successful human-robot collaboration such as goal inference, error monitoring, anticipatory action selection, emotion inference, adaptation and learning.

Miroslaw Lachowicz (Institute of Applied Mathematics and Mechanics, University of Warsaw, Poland, II CoSysM3 Meeting)

Space-nonlocal movement

My talk is dedicated to discussion of importance of space-nonlocal modeling of biological phenomena. Space-nonlocal models in terms of integro--differential equations and their applications in description of movement of cells as well as the invasion of cancer cells into surrounding tissue will be presented. The talk bases on recent papers Ref. [1], Ref. [2] and uses some techniques from Ref. [3].

[1] Lachowicz, M. Matusik, K.A. Topolski, "Space-nonlocal description of cell movement", to appear.

[2] Z. Szymanska, M. Lachowicz, N. Sfakianakis, M.A.J. Chaplain, "Mathematical modelling of cancer invasion: Phenotypic transitioning provides insight into multifocal foci formation", J. Computat. Science, 75, 102175 (2024).

[3] M. Lachowicz, H. Leszczynski, E. Puzniakowska-Galuch, "Diffusive and anti-diffusive behavior for kinetic models of opinion dynamics", Symmetry, 11, 1024 (2019).

Luís Meira-Machado (Centre of Mathematics, University of Minho)

Advanced Techniques and Tools for Complex Survival Data Analysis

Analyzing survival data involves navigating intricate challenges that require specialized techniques. This talk addresses these complexities, focusing on key contemporary topics. We highlight the importance of understanding different types of censoring and emphasize using appropriate methods to handle incomplete data, ensuring accuracy and reliability in survival analysis. Additionally, we delve into multi-state models, offering a robust framework for analyzing complex survival data. Our discussion covers multistate regression and the estimation of transition probabilities, emphasizing the Markov condition and methods for incorporating covariates. Furthermore, we showcase software solutions, including tools developed by the authors, which play a crucial role in simplifying the analysis of complex survival datasets.

Alexandre Rodrigues (ISEG - Lisbon School of Economics & Management, Centro de Matemática Aplicada e Previsão Económica, University of Lisbon)

Pulse vaccination in a SIR model: Global dynamics, bifurcations and seasonality

In this talk, I analyze a periodically forced dynamical system inspired by the SIR model with impulsive vaccination. I characterize its dynamics according to the proportion of vaccinated individuals and the time between doses. I draw the associated bifurcation diagram. I also explore analytically and numerically chaotic dynamics by adding seasonality to the disease transmission rate. This is a joint work with João Maurício de Carvalho (University of Porto).

César Silva (Centre of Mathematics and Applications, University of Beira Interior)

Stability criteria for delay systems with applications to neural network models

In this talk, for general families of delay differential equations and delay difference equations, we derive stability criteria that can be applied to establish the stability of several neural network models discussed in the literature. In the continuous-time setting, we investigate the global exponential stability for non-autonomous Cohen-Grossberg neural network models with both discrete time-varying and infinite distributed delays. We also discuss the existence of periodic solutions when the system is periodic. In the discrete-time setting, we present a global exponential stability criterion, with the proof based on an induction argument. Additionally, when the difference equation is periodic, we prove the existence of a periodic solution by constructing a type of Poincaré map. Specifically, we obtain stability criteria for both low-order and high-order Hopfield and BAM discrete neural network models. This presentation is based on two recent papers: one co-authored with Joaquim Oliveira and António Bento, and the other with Joaquim Oliveira and Ahmed Elmwafy.

Contributed talks

Paulo Barbosa (Centre of Mathematics, University of Minho)

Developing a Lateral Inhibition Plasticity Learning Rule in Dynamic Neural Field Models