GENERAL DESCRIPTION
The special session on mathematical modelling aims to highlight the fundamental role of mathematics in understanding and solving real-world problems. Applications in areas such as climate science, biology, health, and sustainability will be presented, demonstrating how mathematical models make it possible to analyze complex phenomena and support informed decision-making. The session will also emphasize the importance of interdisciplinary collaboration and the development of new tools that connect mathematical theory with the challenges of today’s world.
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SCHEDULE
Thursday October 8th (Pere i Joan Coromines)
11:00h Bridging scales to learn cell–cell adhesion from partial trajectory data
by Gissell Estrada Rodriguez (Universitat Politècnica de Catalunya and CRM)
11: 40h Mathematical Modelling of the 1820 Mallorca Plague Epidemic
by Pere Puig Casado (Universitat Autònoma de Barcelona i Centre de Recerca Matematica)
12:20h From Mathematical equations to Climate information
by Froila M. Palmeiro Núñez (Instituto de Geociencias (IGEO), Universidad Complutense de Madrid (CSIC‐UCM))
16:00h Dynamical systems and coherent structures
by Francisco Marques (Polytechnic University of Catalonia)
16:40h Decoupling excitatory and inhibitory synaptic conductances from single spiking neuronal recordings
by Catalina Vich Llompart (University of the Balearic Islands)
17:20h Inferring Parameters and States in Neurobiological Networks
by Daniele Avitabile (Vrije Universiteit Amsterdam)
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ABSTRACTS
Bridging scales to learn cell–cell adhesion from partial trajectory data
by Gissell Estrada Rodriguez (UPC i CRM)
Abstract
Cell–cell adhesion drives collective behaviours such as segregation, mixing, and invasion, but the underlying interaction parameters are not directly observable. We develop a Bayesian framework that infers these parameters from partial cell trajectories by linking microscopic stochastic dynamics with macroscopic population densities. The resulting likelihood enables estimation of adhesion strengths, repulsion radii, and nonlinear diffusion coefficients, with uncertainty quantified through preconditioned Crank–Nicolson MCMC sampling. We validate the method for one population and then estimate six parameters for two interacting populations across four distinct dynamical regimes. Experiments
with synthetic trajectories show accurate recovery of the main parameters, reduced uncertainty with additional trajectories, and robustness to MCMC tuning and initialisation. The framework provides a basis for inferring quantitative interaction laws from experimental cell-trajectory data
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Mathematical Modelling of the 1820 Mallorca Plague Epidemic
by Pere Puig Casado (UAB / CRM)
Abstract
The 1820 plague epidemic in Mallorca has traditionally been interpreted as an outbreak of
bubonic plague. In this talk, historical daily mortality data from Son Servera and Capdepera
are analysed using a compartmental epidemiological model combined with Bayesian
inference. The model describes the temporal dynamics of susceptible, infected, surviving,
and deceased individuals and allows the estimation of key epidemiological parameters,
including the basic reproduction number R0 and the mean infectious period. The results
reveal significant differences between the two towns, with higher transmission potential and
a longer infectious period in Son Servera (R0 ~ 1.3) than in Capdepera (R0 ~ 1.0). Overall,
the inferred dynamics are more consistent with direct human-to-human transmission,
possibly pneumonic or septicemic plague, than with a classical bubonic outbreak. This talk
illustrates how mathematical modelling and Bayesian statistical methods can be combined
with historical records to quantitatively reconstruct past epidemics and provide insights into
their underlying transmission mechanisms.
Reference: Puig, P. & Pujadas-Mora, J.M. (2026). The 1820 Mallorca plague was not a
classic bubonic outbreak. PNAS, 123(34), e2536892123.
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From Mathematical equations to Climate information
by Froila M. Palmeiro Núñez (Instituto de Geociencias (IGEO), Universidad Complutense de Madrid (CSIC‐UCM)
Abstract
Climate models are among the most mathematically complex tools in modern science. At
their core lies a system of nonlinear partial differential equations — the primitive equations
of fluid dynamics — governing the evolution of atmospheric and oceanic flows across scales
that span orders of magnitude in space and time. Solving these equations requires
sophisticated numerical schemes at a high computational cost.
Yet the mathematical challenges of climate modelling extend well beyond numerical analysis
and appear in the everyday practice of climate science. Quantifying the uncertainty in
long-term predictions requires advanced probabilistic and statistical methods. Incorporating
observational data into model states relies on modern data assimilation techniques.
Identifying robust signals of climate change against a background of natural variability
requires rigorous statistical testing. And the growing use of Artificial Intelligence brings new
challenges regarding physical consistency and model interpretability. This presentation aims
to illustrate how applied mathematics bridges past climate reconstructions, present-day
predictions, and future climate projections.
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Decoupling excitatory and inhibitory synaptic conductances from single spiking neuronal recordings
by Catalina Vich Llompart (University of the Balearic Islands)
Abstract
Joint work with Rosa M. Delicado-Moll, Antonio E. Teurel, Antoni Guillamon.
Maintaining a tight, instant-to-instant balance between excitatory and
inhibitory (E/I) synaptic conductances is a fundamental homeostatic mechanism that
regulates neuronal excitability and neural network stability. Disruptions in this
dynamic E/I balance alter cellular computation and are linked to severe
neurodegenerative and psychiatric disorders, such as Alzheimer’s and Parkinson’s
diseases. Quantifying how these time-varying synaptic inputs evolve at high
temporal resolution is essential to deciphering learning rules, spatial navigation, and
motor control. However, direct experimental measurements of separate synaptic
conductances are technically challenging in vivo. This constraint creates a critical
need for accurate mathematical inverse methods capable of inferring these
unobservable conductances from a single, readily measurable quantity: the
membrane potential trace. While partial solutions exist for subthreshold regimes,
reconstructing distinct E/I time courses within the non-linear, active spiking regime
remains an open problem in mathematical biology.
In this work, we develop a novel computational inverse strategy designed to
decouple and estimate the continuous time course of both excitatory and inhibitory
conductances from a single spiking membrane potential trace. Moving away from
traditional multi-trial experimental requirements, our method maps the underlying
non-linear relationship between constant synaptic drives and two discrete observable
metrics: the interspike intervals (oscillatory period) and the spike amplitudes. This
high-dimensional relationship is solved dynamically within small temporal windows
by implementing a two-dimensional numerical Newton’s method coupled with
continuous bivariate cubic spline interpolations to refine the discretized grid
estimates. We validate the accuracy and robustness of the algorithm using
simulations of a conductance-based stellate cell model across diverse physiological
scenarios, including varying frequencies, in-phase and anti-phase configurations,
and stochastic noise perturbations. Finally, we introduce a cross-correlation
realignment post-processing step to correct systematic horizontal time lags. This
adjustment brings the precision of the estimated inhibitory conductances to a level
comparable to the excitatory ones, providing a robust, data-efficient computational
framework for tracking local functional connectivity.
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Dynamical systems and coherent structures
by Francisco Marques (UPC)
Abstract
The talk will focus on the importance of Dynamical Systems theory for
understanding the interaction between the different types of fluid flows, both stable and
unstable, and the sudden changes (bifurcations) that occur when modifying the problem
parameters. A brief introduction to Dynamical Systems theory will be presented, describing
the generic bifurcations that occur in both continuous and discrete dissipative systems.
Discrete systems naturally arise when studying the stability of periodic flows using the
Poincaré map. These bifurcations will be illustrated with various examples that the
Barcelona UPC group has studied over the years, and especially recently. The presence of
multiple successive bifurcations and the role of codimension-two bifurcations as organizing
centers of the dynamics will be analyzed. Various pathways leading to spatially and
temporally complex states (routes to chaos), which eventually transition to fully turbulent
states, will be illustrated.
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Inferring Parameters and States in Neurobiological Networks
by Daniele Avitabile (VU Amsterdam)
Abstract
he study of cortical dynamics during different states such as decision making,
sleep and movement, is an important topic in Neuroscience. Modelling efforts aim to relate
the neural rhythms present in cortical recordings to the underlying dynamics responsible for
their emergence. We present an effort to characterise the neural activity from the cortex of a
mouse during natural sleep, captured through local field potential measurements. Our
approach relies on using a discretised Wilson–Cowan Amari neural field model for neural
activity, along with a data assimilation method that allows the Bayesian joint estimation of the
state and parameters. We demonstrate the feasibility of our approach on synthetic
measurements before applying it to a dataset available in literature. Our findings suggest the
potential of our approach to characterize the stimulus received by the cortex from other brain
regions, while simultaneously inferring a state that aligns with the observed signal.