Minisymposia

Abstract: This minisymposium brings together cutting-edge advancements in mathematical modeling, machine learning, and Bayesian inference, highlighting their applications to biological systems, health data, and computational efficiency. The five presentations tackle critical challenges, proposing innovative solutions that merge theory and application in distinct but related fields.

The first talk introduces a novel ordinal decomposition-based loss function tailored for deep ordinal segmentation. Traditional segmentation methods often overlook the natural ordering of classes, leading to suboptimal results. The proposed approach integrates ordinal decompositions and regularized losses, optimizing for tasks such as glioma tumor severity assessment and depth estimation in urban driving.

The symposium then delves into a Bayesian calibration framework for complex, data-limited models. Using Gaussian processes, this approach facilitates robust uncertainty quantification in fields like steel production and glioblastoma cell culture evolution, providing efficient, computationally feasible solutions.

Next, a pioneering method for identifying transcription factors (TFs) in cellular reprogramming is presented. Using a stochastic gene regulatory network model, this approach enhances TF prediction, improving the efficiency and maturity of cell conversions, a key challenge in regenerative medicine and disease modeling.

The fourth talk focuses on the optimization of Generalized Hamiltonian Monte Carlo (GHMC) for Bayesian inference. GHMC’s potential is explored in complex biological models, from breast cancer resistance to COVID-19 epidemiological modeling. Through novel parameter tuning techniques, this work achieves improved convergence rates and sampling efficiency over traditional methods.

Finally, the age-structured dynamics of COVID-19 transmission are investigated in the Basque Country. A deterministic model stratifies the population by age, revealing the differential impacts of age on disease severity. The results offer new insights into age-based control measures, informing future pandemic response strategies.

Together, these presentations showcase the transformative potential of mathematical models and computational methods in tackling complex problems in health and biological systems.

This mini-symposium gathers a broad spectrum of innovative mathematical and computational approaches aimed at addressing the challenges of modeling, analysis and control in complex systems. Constituted by 15 talk, it encompasses applications across ecology, fluid dynamics, finance, epidemiology and social dynamics, highlighting emerging numerical methods, data-driven approaches and machine learning techniques. The focus lies on the development of methodologies that preserve key structural properties, enhance stability and ensure computational efficiency, addressing the challenges posed by high-dimensional and nonlinear dynamics. Topics include agent-based and equation-based modeling, bistability analysis, dynamic programming, isogeometric collocation, manifold learning, physics-informed neural networks, positivity-preserving integration, radial basis function interpolation and semi-Lagrangian methods. By bridging theoretical advances and computational innovation, this mini-symposium highlights the pivotal role of mathematics in addressing pressing challenges and unveiling new opportunities for modeling and controlling complex real-world systems.

Mathematical models have proven to be reliable tools in sciences and engineering. By simulating sound physical and biological systems, the models can provide insight into the understanding of complex phenomena contributing to the design of new laboratory experiments and/or the optimization of existing technologies in different areas. In this minisymposium, we aim to provide a forum for presenting new results on mathematical models based on ordinary/partial differential equations, parameter optimization and numerical analysis of numerical methods for human diseases, their diagnosis and treatment. Particular attention will be given to controlled drug delivery systems, tumors and elastography.

In recent years, plant-soil dynamics have received increasing attention from the scientific community due to their importance in preserving ecosystems’ resilience and biodiversity. Patterns, in particular, represent an established strategy adopted by vegetation to optimise the available resources and adapt to abrupt climatic variations. These spatial structures are analysed from several perspectives: ecologically, investigating the key mechanisms behind plant-soil interactions leading to their emergence and their relation with so-called tipping points; mathematically, developing new analytical and numerical tools to analyse realistic models (often based on partial differential equations, but not exclusively) and predict their longtime evolution for different environmental scenarios. Effective models can only be constructed in interdisciplinary teams, where experts share their knowledge and work hand in hand to reach a successful compromise between mathematical tractability and biological accuracy. The close collaboration between these two areas, as increasingly emerged in the last years, is therefore fundamental in order to tackle current impelling issues worldwide, such as climate change.

This minisymposium aims to provide an overview of the most recent developments in ecological and mathematical investigations of plant-soil dynamics, with a particular focus on the strict interplay between these two disciplines. Therefore, two dedicated sessions led by experts in both fields will promote interactions as well as exchange between different techniques, and foster new collaborations.

Three-dimensional (3D) bioprinting has garnered a lot of attention lately. This technique uses a numerically controlled dispensing system to deposit cells and biomaterial inks, or bioink, in a precise and regulated manner. To bridge the gap between manufactured and natural tissue constructs, 3D bioprinting techniques have become a versatile tool for fabricating or patterning functional 3D bio-structures with exact geometric designs. All these techniques play a role in the so-called “Regenerative Medicine (RM)” that, according to the definition of The USA National Institutes of Health can be defined as “the process of creating living, functional tissues to repair or replace tissue or organ function lost due to age, disease, damage, or congenital defects”.

A digital twin is a virtual representation of a real-world object that has dynamic, two-way connections between the real-world object and its digital twin. After being originally used by NASA in 2010, the terms ”Digital Twin” are becoming increasingly common in many different industry areas. When used in the context of medicine, since digital twins enable learning and discovering new knowledge, new hypothesis generation and testing, and “in silico” experiments and comparisons, they are poised to play a key role in formulating highly personalized treatments in the future. Then they have the power to bring about the urgently required fundamental reform of conventional medical practices contributing to preparing them for the new era of precision (and accuracy).

All of this was made possible also thanks to both 1) the availability of powerful computational resources which are crucial tools for not only processing large quantities of data and new knowledge discovery but also for doing so in a relatively small fraction of time when compared to what was needed just a few years ago; 2) the availability of mathematical tools that can effectively describe/simulate physical phenomena using such computational resources. 

This mini Symposium aims to give points of view, ideas, and suggestions about the methodologies, tools, and application examples that can benefit from the disruptive approach based on Digital Twins in Medicine.

We explore the mathematical modeling of complex, multi-agent systems in biological contexts, with a focus on kinetic and diffusive frameworks. Biological systems such as immune responses, cellular self-organization, predator-prey dynamics, and collective navigation behaviors exhibit intricate interactions driven by both local and nonlocal interactions. The talks cover a range of approaches to understanding these systems, from kinetic equations modeling the spatial organization of cells, to diffusive models that capture the dynamics of biological aggregations and multi-stable behaviors observed in population-level movements.

Presentations address dynamics in medical conditions such as autoimmune diseases, using bifurcation analysis to understand feedback loops in immune stability. Non-local advection-diffusion models analyze self-organizing behaviors such as aggregation and segregation in populations and tissues, highlighting pattern formation and stable state coexistence. Further talks cover kinetic and diffusive frameworks in wound healing, drug delivery, and cancer invasion, examining spatial interactions and boundary effects. Predator-prey dynamics and ecological restoration are studied through reaction-diffusion systems and controlled Lotka-Volterra models. Theoretical insights are supplemented with advanced numerical methods for simulating biological processes, providing a comprehensive view of how mathematical modeling supports breakthroughs in biomedical and ecological research.

This symposium will explore the role of mathematical modeling and infectious disease data in advancing our understanding of infectious disease dynamics. One focus will be the use of models and multiscale data to investigate the epidemiology of vector-borne diseases, where complex host-pathogen dynamics and transmission risks present unique challenges. Uncertainty in model parameters, due to limited or variable data, can significantly affect predictions. The mini-symposium will highlight methods for addressing this uncertainty, improving experimental design, and ensuring that models provide reliable insights. The symposium will also delve into modeling chronic infections such as hepatitis B, exploring how within-host dynamics and treatment strategies can be optimized to reduce transmission and improve outcomes. Additionally, the discussion will include an exploration of epidemic models with immunity boosting and waning, demonstrating how such models can exhibit complex behavior depending on model parameters.

Ultimately, this symposium aims to demonstrate how mathematical modeling can be a powerful tool for understanding disease dynamics, guiding intervention strategies, and informing public health responses to both emerging threats and ongoing epidemics.

Numerical models play a crucial role in the analysis and prediction of natural phenomena and real world processes in several fields, such as biology, ecology, epidemiology, population dynamics, vegetation pattern formation, diseases spread, sustainability, material science. The mini-symposium aims to cover a broad range of issues arising in the mathematical formulation and numerical solution of evolutionary problems arising in natural and applied sciences. This event will bring together experts in mathematical modelling and applied mathematics, who will present new results and emerging research trends.

The mini-symposium falls within the activities of the MUR-PRIN 2022 project 20229P2HEA Stochastic numerical modelling for sustainable innovation; and of the MUR-PRIN 2022 project 2022XZSAFN Anomalous Phenomena on Regular and Irregular Domains: Approximating Complexity for the Applied Sciences.

This session brings together recent advancements in stochastic processes and statistical inference methods applied to complex systems across biology, network theory, and physical sciences. The talks explore various models that handle nonuniform, reset-driven, and multi-stage dynamics, offering insights into practical applications, theoretical developments, and methodological challenges.

The first presentation deals with a mixed Gompertz-Lognormal diffusion process modeling sigmoidal fetal growth patterns across non-uniform biometric measurements; a hybrid Bayesian approach to impute missing data at standardized gestational ages is also introduced. The second study addresses a lognormal diffusion process with multisigmoidal growth to model real-world phenomena, like COVID-19 infection waves in Europe, where growth phases may be interrupted by random catastrophes. In network dynamics, the third study examines Markovian random walks with resets on undirected networks. Further, a two-dimensional birth-death process is introduced for studying B cell receptor (BCR) behaviours, a core component of the immune response, with the aim to better understand immune dynamics. Lastly, in the field of physical phenomena, a stochastic motion with alternating velocities and resets is studied, highlighting the probability laws and limiting behavior in systems with independent Bernoulli resets.

Collectively, these studies demonstrate the versatility of stochastic processes in capturing complex growth, reset, and network behaviors across fields, underscoring their value in modeling real-world systems with non-uniform dynamics and renewal structures.

This session features recent analytical results inspired from or devoted to models of interest, for instance, in biology, medicine, epidemiology, vehicular traffic and collective dynamics. Results consist in rigorous proofs of well posedness, of specific qualitative properties or of answers to optimal management problems. Typically, analytical techniques rely on those of non linear hyperbolic partial differential equations that, due to the peculiarities of the applications, contain also integral terms accounting for non local interactions. In this area, numerical integrations allow to show qualitative properties of solutions. At the same time, new questions pose new requirements on numerical methods, asking the development of better algorithms.

Mathematical modeling plays a central role in decoding complex systems, offering tools to uncover patterns, forecast behaviors, and inform decision-making across a wide range of fields, including ecology, economics, and environmental science. This minisymposium is structured into two sessions: the first explores ecological applications, while the second focuses on economic and environmental challenges.

In the first session, ecological models of diffusion and instability provide critical insights into population dynamics, spatial pattern formation, and ecosystem interactions, helping to explain how species adapt, compete, and coexist. Through approaches such as anomalous diffusion and cross-diffusion, these models uncover aspects of stability and spatial distribution, revealing the mechanisms behind the formation of ecological patterns and predator-prey relationships.

The second session emphasizes the importance of mathematical modeling in addressing complex sustainability, economic, and environmental issues. As concerns around ecological conservation, resource management, and economic stability become more pressing, these models provide valuable insights into dynamic systems, supporting effective decision-making and sustainable development. In economics, frameworks such as game theory and data-driven methods address questions of pricing, sustainability, and resource allocation. Incorporating elements like circular economy practices and wastewater management, these models simulate policy impacts, forecast outcomes, and optimize resources on both local and global scales. From consumer-driven sustainability to managing invasive species and enhancing agricultural water use, the versatility of mathematical modeling is evident across diverse applications, demonstrating its value in promoting resource efficiency and societal well-being.

By bridging theory with applications, the minisymposium provides essential tools for addressing global challenges, from biodiversity conservation to sustainable economic practices, making mathematical modeling essential for a balanced, resilient future.

Mathematical biophysics is a polymorph discipline that spans in multiple scientific highways. 

In this minisymposium, we  particularly focus on its application in the study of population dynamics of different nature. Indeed, mathematical biophysics is at the hearth of the development and implementation of mathematical methodologies to model and analyse the dynamics of complex systems in observed biological and natural sciences. Thus, we fill imperative to show the most recent and innovative advancements conceived in Europe and in particular in Italy.

The contributions presented in this minisymposium deal with disparate biophysical problems, ranging from the modelling of bacterial aggregation and inhibitor factors, to the optimal design of radio frequency pulses in magnetic resonance, up to the control of infectious disease spread, including the effects of human behavioral changes. 

The presented works are the results of a synergic approach to unifying the expertises from a wide range of fields, including mathematics, physics, bioengineering, biology, ecology and social sciences.

Human behavior is at the center of epidemics: it determines the effectiveness of interventions (through compliance) or the self-regulation of exposure where governments have no jurisdiction. The almost whimsical way that individuals make up their minds (in decisions that range drastically different timescales) determines the course of epidemics. Understanding the drivers and effects of such phenomena is thus crucial.

In this mini-symposium, we aim to study and showcase the effect of different mechanisms for human behavior in epidemics --- especially those where behavior is one of the central mechanisms, with the example of COVID-19-like diseases (i.e., where compliance plays a major role) and sexually transmitted infections (STI, where voluntary self-regulation of exposure plays a major role). Specifically, the confirmed participants of this mini-symposium will present research on:

1. Optimal mitigation strategies to minimize societal costs (proxy for behavior at the society scale, Müller et al).

2. The effect of polarization and homophily in epidemic in structured societies (Sartori and Mäs). 

3.  Imitation-driven vaccination and complex dynamics in epidemics (Doutor). 

4. Behavior-induced complex feedbacks in HIV-Chlamydia spread, considering HIV Pre-Exposure Prophylaxis (PrEP, Contreras et al)

We will focus on the consequences of such behaviors (or modeling choices) on the observed epidemic dynamics and present real-world examples of where these may be observed and relevant. Thereby, we aim to open lively discussions around the topics and foster scientific exchange in the community. 

Structured population models are often used in biology and epidemiology when the individual state can be characterized by a continuous variable that evolves continuously in time. Examples of structuring variables can be demographic or infection age, body size, and immunity level. The resulting models usually take the form of hyperbolic partial integro-differential equations or renewal equations, and generate infinite-dimensional dynamical systems whose analysis and numerical solution are notably complex. This minisymposium is devoted to recent advances in the development of modelling and computational strategies in structured population dynamics.