{"id":20445,"date":"2026-04-29T19:15:30","date_gmt":"2026-04-29T17:15:30","guid":{"rendered":"https:\/\/scm.iec.cat\/?post_type=sessions&p=20445"},"modified":"2026-10-05T12:33:37","modified_gmt":"2026-10-05T10:33:37","slug":"bmd-2026-mathematical-modelling","status":"publish","type":"sessions","link":"https:\/\/scm.iec.cat\/eng\/sessions\/bmd-2026-mathematical-modelling\/","title":{"rendered":"BMD 2026 \u2013 Mathematical Modelling"},"content":{"rendered":"

GENERAL DESCRIPTION<\/strong><\/h3>\n

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\u2019s world.<\/p>\n

_______________________________________________________________________________________________________<\/p>\n

SCHEDULE<\/strong><\/h3>\n
Thursday October 8th (Pere i Joan Coromines)<\/h5>\n

11:00<\/strong>h\u00a0 Bridging scales to learn cell\u2013cell adhesion from partial trajectory data
\n<\/em>by Gissell Estrada Rodriguez<\/strong> (Universitat Polit\u00e8cnica de Catalunya and CRM)<\/p>\n

11: 40<\/strong>h Mathematical Modelling of the 1820 Mallorca Plague Epidemic
\n<\/em>by Pere Puig Casado<\/strong> (Universitat Aut\u00f2noma de Barcelona i Centre de Recerca Matematica)<\/p>\n

12:20<\/strong>h\u00a0 From Mathematical equations to Climate information
\n<\/em>by Froila M. Palmeiro N\u00fa\u00f1ez<\/strong> (Instituto de Geociencias (IGEO), Universidad Complutense de Madrid (CSIC\u2010UCM))<\/p>\n

16:00<\/strong>h Dynamical systems and coherent structures
\n<\/em>by Francisco Marques<\/strong> (Polytechnic University of Catalonia)<\/p>\n

16:40<\/strong>h Decoupling excitatory and inhibitory synaptic conductances from single spiking neuronal recordings
\n<\/em>by Catalina Vich Llompart<\/strong> (University of the Balearic Islands)<\/p>\n

17:20<\/strong>h Inferring Parameters and States in Neurobiological Networks
\n<\/em>by Daniele Avitabile<\/strong> (Vrije Universiteit Amsterdam)<\/p>\n

____________________________________________________________________<\/p>\n

ABSTRACTS<\/strong><\/h3>\n
Bridging scales to learn cell\u2013cell adhesion from partial trajectory data<\/em>
\n<\/strong>by Gissell Estrada Rodriguez<\/strong> (UPC i CRM)<\/h5>\n

Abstract<\/strong><\/p>\n

Cell\u2013cell adhesion drives collective behaviours such as segregation, mixing, and invasion, but the underlying interaction parameters are not directly observ\u0002able. 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\u2013Nicolson MCMC sampling. We vali\u0002date the method for one population and then estimate six parameters for two interacting populations across four distinct dynamical regimes. Experiments
\nwith synthetic trajectories show accurate recovery of the main parameters, re\u0002duced uncertainty with additional trajectories, and robustness to MCMC tuning and initialisation. The framework provides a basis for inferring quantitative in\u0002teraction laws from experimental cell-trajectory data<\/p>\n

____________________________________________________________________<\/p>\n

Mathematical Modelling of the 1820 Mallorca Plague Epidemic<\/em>
\n<\/strong>by Pere Puig Casado<\/strong> (UAB \/ CRM)<\/h5>\n

Abstract<\/strong><\/p>\n

The 1820 plague epidemic in Mallorca has traditionally been interpreted as an outbreak of
\nbubonic plague. In this talk, historical daily mortality data from Son Servera and Capdepera
\nare analysed using a compartmental epidemiological model combined with Bayesian
\ninference. The model describes the temporal dynamics of susceptible, infected, surviving,
\nand deceased individuals and allows the estimation of key epidemiological parameters,
\nincluding the basic reproduction number R0 and the mean infectious period. The results
\nreveal significant differences between the two towns, with higher transmission potential and
\na longer infectious period in Son Servera (R0 ~ 1.3) than in Capdepera (R0 ~ 1.0). Overall,
\nthe inferred dynamics are more consistent with direct human-to-human transmission,
\npossibly pneumonic or septicemic plague, than with a classical bubonic outbreak. This talk
\nillustrates how mathematical modelling and Bayesian statistical methods can be combined
\nwith historical records to quantitatively reconstruct past epidemics and provide insights into
\ntheir underlying transmission mechanisms.<\/p>\n

Reference: Puig, P. & Pujadas-Mora, J.M. (2026). The 1820 Mallorca plague was not a
\nclassic bubonic outbreak. PNAS, 123(34), e2536892123.<\/p>\n

____________________________________________________________________<\/p>\n

From Mathematical equations to Climate information<\/em>
\n<\/strong>by Froila M. Palmeiro N\u00fa\u00f1ez<\/strong> (Instituto de Geociencias (IGEO), Universidad Complutense de Madrid (CSIC\u2010UCM)<\/h5>\n

Abstract<\/strong><\/p>\n

Climate models are among the most mathematically complex tools in modern science. At
\ntheir core lies a system of nonlinear partial differential equations \u2014 the primitive equations
\nof fluid dynamics \u2014 governing the evolution of atmospheric and oceanic flows across scales
\nthat span orders of magnitude in space and time. Solving these equations requires
\nsophisticated numerical schemes at a high computational cost.
\nYet the mathematical challenges of climate modelling extend well beyond numerical analysis
\nand appear in the everyday practice of climate science. Quantifying the uncertainty in
\nlong-term predictions requires advanced probabilistic and statistical methods. Incorporating
\nobservational data into model states relies on modern data assimilation techniques.
\nIdentifying robust signals of climate change against a background of natural variability
\nrequires rigorous statistical testing. And the growing use of Artificial Intelligence brings new
\nchallenges regarding physical consistency and model interpretability. This presentation aims
\nto illustrate how applied mathematics bridges past climate reconstructions, present-day
\npredictions, and future climate projections.<\/p>\n

____________________________________________________________________<\/p>\n

Decoupling excitatory and inhibitory synaptic conductances from single spiking neuronal recordings<\/em>
\n<\/strong>by Catalina Vich Llompart<\/strong> (University of the Balearic Islands)<\/h5>\n

Abstract<\/strong><\/p>\n

Joint work with Rosa M. Delicado-Moll, Antonio E. Teurel, Antoni Guillamon.
\nMaintaining a tight, instant-to-instant balance between excitatory and
\ninhibitory (E\/I) synaptic conductances is a fundamental homeostatic mechanism that
\nregulates neuronal excitability and neural network stability. Disruptions in this
\ndynamic E\/I balance alter cellular computation and are linked to severe
\nneurodegenerative and psychiatric disorders, such as Alzheimer’s and Parkinson’s
\ndiseases. Quantifying how these time-varying synaptic inputs evolve at high
\ntemporal resolution is essential to deciphering learning rules, spatial navigation, and
\nmotor control. However, direct experimental measurements of separate synaptic
\nconductances are technically challenging in vivo. This constraint creates a critical
\nneed for accurate mathematical inverse methods capable of inferring these
\nunobservable conductances from a single, readily measurable quantity: the
\nmembrane potential trace. While partial solutions exist for subthreshold regimes,
\nreconstructing distinct E\/I time courses within the non-linear, active spiking regime
\nremains an open problem in mathematical biology.
\nIn this work, we develop a novel computational inverse strategy designed to
\ndecouple and estimate the continuous time course of both excitatory and inhibitory
\nconductances from a single spiking membrane potential trace. Moving away from
\ntraditional multi-trial experimental requirements, our method maps the underlying
\nnon-linear relationship between constant synaptic drives and two discrete observable
\nmetrics: the interspike intervals (oscillatory period) and the spike amplitudes. This
\nhigh-dimensional relationship is solved dynamically within small temporal windows
\nby implementing a two-dimensional numerical Newton’s method coupled with
\ncontinuous bivariate cubic spline interpolations to refine the discretized grid
\nestimates. We validate the accuracy and robustness of the algorithm using
\nsimulations of a conductance-based stellate cell model across diverse physiological
\nscenarios, including varying frequencies, in-phase and anti-phase configurations,
\nand stochastic noise perturbations. Finally, we introduce a cross-correlation
\nrealignment post-processing step to correct systematic horizontal time lags. This
\nadjustment brings the precision of the estimated inhibitory conductances to a level
\ncomparable to the excitatory ones, providing a robust, data-efficient computational
\nframework for tracking local functional connectivity.<\/p>\n

____________________________________________________________________<\/p>\n

Dynamical systems and coherent structures<\/em>
\n<\/strong>by Francisco Marques<\/strong> (UPC)<\/h5>\n

Abstract<\/strong><\/p>\n

The talk will focus on the importance of Dynamical Systems theory for
\nunderstanding the interaction between the different types of fluid flows, both stable and
\nunstable, and the sudden changes (bifurcations) that occur when modifying the problem
\nparameters. A brief introduction to Dynamical Systems theory will be presented, describing
\nthe generic bifurcations that occur in both continuous and discrete dissipative systems.
\nDiscrete systems naturally arise when studying the stability of periodic flows using the
\nPoincar\u00e9 map. These bifurcations will be illustrated with various examples that the
\nBarcelona UPC group has studied over the years, and especially recently. The presence of
\nmultiple successive bifurcations and the role of codimension-two bifurcations as organizing
\ncenters of the dynamics will be analyzed. Various pathways leading to spatially and
\ntemporally complex states (routes to chaos), which eventually transition to fully turbulent
\nstates, will be illustrated.<\/p>\n

____________________________________________________________________<\/p>\n

Inferring Parameters and States in Neurobiological Networks<\/em>
\n<\/strong>by Daniele Avitabile<\/strong> (VU Amsterdam)<\/h5>\n

Abstract<\/strong><\/p>\n

he study of cortical dynamics during different states such as decision making,
\nsleep and movement, is an important topic in Neuroscience. Modelling efforts aim to relate
\nthe neural rhythms present in cortical recordings to the underlying dynamics responsible for
\ntheir emergence. We present an effort to characterise the neural activity from the cortex of a
\nmouse during natural sleep, captured through local field potential measurements. Our
\napproach relies on using a discretised Wilson\u2013Cowan Amari neural field model for neural
\nactivity, along with a data assimilation method that allows the Bayesian joint estimation of the
\nstate and parameters. We demonstrate the feasibility of our approach on synthetic
\nmeasurements before applying it to a dataset available in literature. Our findings suggest the
\npotential of our approach to characterize the stimulus received by the cortex from other brain
\nregions, while simultaneously inferring a state that aligns with the observed signal.<\/p>","protected":false},"parent":0,"template":"","categoria_sessions_conferences":[238],"class_list":["post-20445","sessions","type-sessions","status-publish","hentry","categoria_sessions_conferences-bmd-2026"],"acf":[],"_links":{"self":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/sessions\/20445","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/sessions"}],"about":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/types\/sessions"}],"wp:attachment":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/media?parent=20445"}],"wp:term":[{"taxonomy":"categoria_sessions_conferences","embeddable":true,"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/categoria_sessions_conferences?post=20445"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}