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Fitting data with dynamical models: ten lessons on mathematical field work
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From October 24, 2023 to December 05, 2023
ICM-CRM Meeting (2023)
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Harmonic Measure and free Boundary Problems
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9th Computational and Systems Neuroscience Retreat
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Valuation Theory and the OM Algorithm
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Satellite ECM 2024 Conference: Climate-Inclusive Ecosystem Modeling: Understanding the Dynamics of Ecosystems in a Changing World
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BIMR - Escola estiu - Barcelona Introduction to Mathematical Research
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Fluid Dynamics, Geometry and Computer Science in interaction Exploration of new horizons
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La explotación de las matemáticas para ayudar en el diseño de columnas de adsorción

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selected videos

Centre de Recerca Matemàtica

Centre de Recerca Matemàtica
Session 2 (Lluís Alsedà). Introduction to data fitting methods. Mathematical models are essential for understanding and predicting the behaviour of dynamical processes in a wide range of fields, from physics and engineering to biology and social sciences. A mathematical model is a set of equations that describe the evolution of a system over time, based on certain assumptions and simplifications. By formulating a mathematical model, scientists can gain insight into the underlying mechanisms of a dynamical process and test hypotheses that would be difficult or impossible to investigate experimentally. Moreover, mathematical models allow scientists to make predictions about the behaviour of a system under different conditions and to design interventions that optimize its performance. In addition to their explanatory and predictive power, mathematical models are also a valuable tool for communication and collaboration between scientists from different fields. By using a common language of mathematics, scientists can share ideas, test each other’s models, and build on each other’s work. This interdisciplinary approach has led to many breakthroughs in science and technology, from the development of new drugs and materials to the design of more efficient and sustainable systems. Overall, mathematical modeling is an indispensable tool for advancing our understanding of the world around us and for solving some of the most pressing problems of our time. Fitting mathematical models to real data is a crucial step in scientific research and engineering applications as it allows us to quantitatively describe and understand the observed phenomena. By fitting models to data, we can extract important parameters that characterize the system under study and test the validity of the model assumptions. Furthermore, fitting models to data enables us to make predictions about the behaviour of the system under different conditions, estimate the uncertainties in the predictions, and design experiments to test the model predictions. In this way, fitting models to data provides a powerful tool for hypothesis testing, model selection, and decision-making in a wide range of scientific fields. In this course, given a time series of observed data, we will model their time evolution using dynamical systems theory with the objective of determining the possible sets of parameters such that the time trajectories generated by the model fit the time series of the observed data. To do so, we will provide different modelling approaches based on mathematical and/or computational models and a variety of different tools for data fitting. In summary, we aim to design models that describe observed data and validate them.
Fitting Data with Dynamical Systems: Session 2 (25/10/23)
Session 1 (Josep Sardanyés). Introduction to mathematical and computational tools to investigate dynamical processes. Mathematical models are essential for understanding and predicting the behaviour of dynamical processes in a wide range of fields, from physics and engineering to biology and social sciences. A mathematical model is a set of equations that describe the evolution of a system over time, based on certain assumptions and simplifications. By formulating a mathematical model, scientists can gain insight into the underlying mechanisms of a dynamical process and test hypotheses that would be difficult or impossible to investigate experimentally. Moreover, mathematical models allow scientists to make predictions about the behaviour of a system under different conditions and to design interventions that optimize its performance. In addition to their explanatory and predictive power, mathematical models are also a valuable tool for communication and collaboration between scientists from different fields. By using a common language of mathematics, scientists can share ideas, test each other’s models, and build on each other’s work. This interdisciplinary approach has led to many breakthroughs in science and technology, from the development of new drugs and materials to the design of more efficient and sustainable systems. Overall, mathematical modeling is an indispensable tool for advancing our understanding of the world around us and for solving some of the most pressing problems of our time. Fitting mathematical models to real data is a crucial step in scientific research and engineering applications as it allows us to quantitatively describe and understand the observed phenomena. By fitting models to data, we can extract important parameters that characterize the system under study and test the validity of the model assumptions. Furthermore, fitting models to data enables us to make predictions about the behaviour of the system under different conditions, estimate the uncertainties in the predictions, and design experiments to test the model predictions. In this way, fitting models to data provides a powerful tool for hypothesis testing, model selection, and decision-making in a wide range of scientific fields. In this course, given a time series of observed data, we will model their time evolution using dynamical systems theory with the objective of determining the possible sets of parameters such that the time trajectories generated by the model fit the time series of the observed data. To do so, we will provide different modelling approaches based on mathematical and/or computational models and a variety of different tools for data fitting. In summary, we aim to design models that describe observed data and validate them.
Fitting Data with Dynamical Systems: Session 1 (24/10/23)
September 4, 2023 Institut d’Estudis Catalans (IEC) ABSTRACT In this lecture, I will describe the progress made in the last 15 years, in our understanding of the long-time behaviour of large solutions to the energy-critical focusing nonlinear wave equation. In the last part of the lecture, I will concentrate on progress (with Collot, Duyckaerts, Martel and Merle) on the asymptotic simplification for large time, into sums of modulated static solutions plus a linear term, in all dimensions, in the radial case. INVITED SPEAKER Carlos Kenig University of Chicago Louis Block Distinguished Service Professor Carlos Eduardo Kenig is an Argentine-American mathematician and the Louis Block Distinguished Service Professor at the University of Chicago’s Department of Mathematics. His work in harmonic analysis and partial differential equations is well recognised. Kenig earned his PhD in 1978 from the University of Chicago under the guidance of Alberto Calderón. He has worked at Princeton University and the University of Minnesota since then, until returning to the University of Chicago in 1985. He has a strong background in elliptic and dispersive partial differential equations. Since 2014, he has been a member of the National Academy of Sciences. Zhongwei Shen, Kin Ming Hui, Gigliola Staffilani, and Panagiota Daskalopoulos are among his students.
Colloquium 2023 | Asymptotic simplification for nonlinear wave equations | Carlos Kenig (UChicago)
Eduardo Sáenz de Cabezón es matemático y profesor de lenguajes y sistemas informáticos en la Universidad de La Rioja. Desarrolla su investigación en el área del álgebra computacional, a la que ha contribuido con 25 publicaciones de investigación y colaboraciones con matemáticos españoles y europeos como Henry P. Wynn.<br /><br />Sáenz de Cabezón también es conocido por difundir las matemáticas a través de conferencias, espectáculos y charlas para personas de todas las edades en todo el mundo. Fue ganador del concurso de monólogos científicos en Famelab Spain (2013) y en la Fundación Aquae (2014), y también quedó finalista en el Cheltenham Science Festival (Reino Unido). Es miembro fundador de BigVan, autor del libro Matematical Intelligence (Plataforma Editorial) y colaborador del programa de radio La Ventana (SER). La más conocida de sus charlas es "Math is forever", que ha sido vista por casi un millón y medio de personas en TED.<br /><br />Lo podéis ver hablando de matemáticas en su canal de YouTube Derivando (https://www.youtube.com/derivando).
Entrevista a Eduardo Sáenz de Cabezón (Universidad de La Rioja)
To speak about science to broad audience means being able to connect a certain content to a certain audience. We will explore some general techniques to stablish this connection in different ways. We will give practical advice, study some examples and address the main issues one faces when trying to communicate science or math. This talk is aimed at PhD and Postdoctoral researchers. Speaker: Eduardo Saénz de Cabezón Universidad de La Rioja Eduardo Sáenz de Cabezón is a Spanish mathematician, and professor of computer languages and systems at the Universidad de La Rioja since 2001. He is a recognized specialist in scientific monologues. He develops his research in the area of computational algebra, to which he has contributed 25 research publications and collaborations with Spanish and European mathematicians such as Henry P. Wynn. Cabezón is also known for disseminating mathematics through conferences, shows and talks for people of all ages around the world. He was the winner of competition for scientific monologues at Famelab Spain (2013) and at the Aquae Foundation (2014), also becoming a finalist at the Cheltenham Science Festival (United Kingdom). He is a founding member of BigVan, author of the book “Mathematical Intelligence” (Plataforma Editorial) and collaborator at the La Ventana radio show (SER). The best known of his talks is “Math is forever” which has been seen by almost a million and a half people at TED. You can see him talking about mates on his YouTube channel Derivando.
Masterclass BGSMath: How to Speak about Mathematics to Broad Audiences
CRM researcher Josep Sardanyés presents the project 'MPA4Sustainability: Enhancing MPAs’ role in restoring biodiversity while maintaining access to ecosystem services' (Reference Number: BiodivRestore-424). Marine Protected Areas (MPAs) will play a crucial role in the successful implementation of the European Biodiversity Strategy and the European Green Deal. They are locations where we can concentrate efforts to restore biodiversity and support the diversification of the blue economy to boost the sustainable use of marine resources. We have paid a lot of attention to the best ways to design and establish MPAs; yet with more than 17,000 MPAs now designated globally, less than a quarter have a clear management plan. Managing complex socioecological systems (SES) is harder and navigating them towards sustainability is even harder. That is particularly the case for MPAs for which biodiversity targets and the exploitation of regional ecosystem services have to be balanced. This project aims to find practical solutions to guide MPA managers in the best approaches to yield positive biodiversity outcomes while maintaining the ability of neighbouring communities to benefit from marine ecosystem services sustainably. Managers of MPAs in Madeira, France, Denmark and Sweden will together with scientists co-create the insights needed to develop this guide, based on a global synthesis of MPA data and detailed functional analyses at three case study sites. We will use data science and statistical modelling to determine the structure of interactions between biodiversity and the provision of ecosystem services (ES) in all current MPAs depending on their SES characteristics. We will then extend recent advances in theoretical ecological modelling to these socio-ecological networked systems to understand how management actions can tip MPA SES towards favorable states using three MPA case studies to benchmark models. With this insight, we will determine the characteristics that will yield desirable SES states. Monitoring is crucial to guide adaptive management plans along this MPA restoration journey. We will determine whether readily available biodiversity and ES indicators can be integrated with rapid sampling to develop a standardized ‘citizen monitoring’ approach that can provide the necessary and sufficient level of information needed to manage the transformative change at MPAs. Finally, we will tackle the policy interaction hurdles managers face when developing plans in regions where multiple MPAs have been designated with varied policy targets. We will determine how best to manage these MPA networks to add value for regional biodiversity and ES targets. This project will produce a decision support system for MPA managers, which we will make available in a user-friendly format complementing current international MPA guidelines to help increase the uptake of management plans for existing MPA networks. In addition, it will produce tangible advice on integrative governance for our practitioners that will meet current urgent needs for the three case study regions. PARTNERS OF THE PROJECT Coordinator: Aquatic Resources, Technical University of Denmark, Kgs. Lyngby, Denmark Island Research and Environmental Observatory (CRIOBE), EPHE/CNRS/Perpignan University, Perpignan, France Research, Madeira Whale Museum-Municipality of Machico, Caniçal Machico – Madeira, Portugal Evolutionary Biology, Spanish National Research Council, Barcelona, Spain Nonlinear Dynamics and Evolution, Mathematical Research Center, Cerdanyola del Valles, Spain Aquatic Resources, Swedish University of Agricultural Sciences, Lysekil, Sweden + Information: https://www.biodiversa.org/2034/download Josep Sardanyés @ CRM: https://www.crm.cat/person/37/sardanyes-cayuela-josep/
MPA4sustainability | Josep Sardanyés - CRM Mathematical Biology group

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