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The aim of the SIJIMAT seminar is to bring together young researchers from the Centre de Recerca Matemàtica in order to promote the interaction between the different research areas present at the centre. Through informal talks of 45 minutes plus a 15 minutes discussion, PhD students and postdoctoral fellows will have the opportunity to learn about the research done by their colleagues.
All talks are expected to have an introductory section that helps non-expert participants understand the main questions and goals of the field in which the speaker works. A second section might introduce the main tools used by the speaker to tackle those questions. Finally, in the last section, the speaker will provide a brief summary of her current research project.
Can the memory loss help to study
the propagation of a disease?
Date: Thursday 30th, March 2023.
Place: Aula petita CRM.
Mathematical models applied to the field of biology and, in particular, epidemiology are currently of great interest due to the pandemic generated by COVID-19. However, their study to describe the spread of a disease has a long history. It dates back to the research on smallpox inoculation carried out by Bernoulli in the 18th century. Since then, both deterministic and stochastic models have been considered and many factors have been taken into account: infectious agents, mode of transmission, latency periods, temporary or partial immunity, quarantine periods, etc.
The aim of this talk is to present a SIR-type stochastic model, which is an extension of the one proposed by Tuckwell and Williams in 2007. It is a discrete-time Markovian model in which the total population remains constant and individuals meet a random number of other individuals at each time step. One of its innovative aspects is the time dependence of this parameter.
An analytic description of the model and its dynamics will be provided.
In order to better comprehend them, a brief introduction to Markov chains will be given and their connection with memory loss will be explained. Finally, with the aid of some simulations, it will be shown how the evolution of a disease is affected by the time dependence of the number of daily encounters.
These results are part of a work carried out with M. Besalú.
Postdoctoral researcher at UAB
Giulia Binotto obtained a PhD in mathematics by the Unviersitat de Barcelona in 2018. She has been an adjunct lecturer in the department of Information and Communication Technologies Engineering (ETIC) at Universitat Pompeu Fabra and is currently a postdoctoral fellow in the Advanced Stochastic Modelling research group at UAB.
- Besalú, M.; Binotto, G.; Rovira, C. (2020)
Convergence of delay equations driven by a Hölder continuous function of order β ∈ (1/3, 1/2)
Electronic Journal of Differential Equations), No. 65, pp. 1–27
- Binotto, G.; Nourdin, I.; Nualart, D. (2018)
Weak symmetric integrals with respect to the fractional Brownian motion
Annals of Probability, Volume 46, Number 4, 2243-2267
- Bardina, X.; Binotto, G.; Rovira, C. (2016)
The complex Brownian motion as a strong limit of processes constructed from a Poisson process
Journal of Mathematical Analysis and Applications. Vol 444, Issue 1, pp 700-720.
16/03/23 | Blai Vidiella Postdoctoral researcher at CSIC – Institut de Biologia Evolutiva
ABSTRACT: Since the dawn of humanity, scientists have been captivated by the intricate and complex systems found in nature. From the movements of celestial bodies to the behavior of microorganisms, we have sought to understand and explain the phenomena we observe in the natural world. Today, as we face increasing challenges such as climate change and ecosystem degradation, our understanding of these systems has never been more important. In this talk, I will explore the power of mathematical modeling in helping us to gain a deeper understanding of the biological systems that make up the biosphere. Specifically, I will focus the application of mathematical rules to understand evolutionary questions, such as punctuated equilibria; the role of mathematical modeling in studying anthropogenic ecology; and the concept of ‘ghost ecosystems’ resulting from climate change. Through this discussion, I hope to shed light on the exciting possibilities that lie ahead for those working at the intersection of mathematics and biology.
02/03/2023 | Manuel Molano (CRM) | Investigating how rats make decisions
ABSTRACT: In this talk I will briefly explain how neuroscientists investigate the strategies used by animals to make decisions and the neural mechanisms underlying such strategies. I will then provide an example in which we have studied the behavior of rats performing a task in which they have to listen to an auditory stimulus and decide between two alternatives basing their decision on the information provided by the stimulus. By tracking the position of the rats using a machine learning tool we were able to characterize how they combine their previous experience with the incoming stimulus information, and show that they flexibly update an initial decision by incorporating new incoming information.
19/01/23 | Giovanni Dalmasso (CRM) | 4D reconstruction of developmental trajectories using spherical harmonics
ABSTRACT: Normal organogenesis cannot be recapitulated in vitro for mammalian organs, unlike in species including Drosophila and zebrafish. Available 3D data in the form of ex vivo images only provide discrete snapshots of the development of an organ morphology. Here, we present a computer-based approach to recreate its continuous evolution in time and space from a set of 3D volumetric images. This method is based on the remapping of shape data into the space of the coefficients of a spherical harmonics expansion where a smooth interpolation over time is simpler. This approach had been tested on mouse limb buds and embryonic hearts. A key advantage of this method is that the resulting 4D trajectory can take advantage of all the available data while also being able to interpolate well through time intervals for which there are little or no data. This allows for a quantitative, data-driven 4D description of mouse limb morphogenesis.
15/12/22 | Alfonso Garmendia (CRM) | Deformation Quantization
ABSTRACT: The goal of quantization is to associate a C*-algebra (a quantum space) to any Poisson manifold (a classical space) in a way that preserves the symmetries. This talk tries to convey the motivation and a summary on deformation quantization with examples.
01/12/22 | Angelica Torres (CRM) | Algebraic Geometry and line reconstruction in Computer Vision
ABSTRACT: The 3D image reconstruction problem aims to create a 3D model of a scene or object starting from 2D images. This process is done in four stages: Feature identification in the images, point and line matching, camera estimation and triangulation, and construction of the 3D model. Stages two and three of the process deal mainly with geometric information that can be studied algebraically. This is precisely where Algebraic Geometry comes into play. In this talk I will introduce the 3D image reconstruction problem and the algebraic tools that allow to model the cameras and image features, I will also define the point and line Multiview varieties, and finally mention some algebraic results on the geometry of points and lines that can be reconstructed effectively.
18/11/22 | Mar Giralt-Miron (UPC) | Chaotic dynamics, exponentially small phenomena and Celestial Mechanics
ABSTRACT: A fundamental problem in dynamical systems is to prove that a given model has chaotic dynamics. One of the methods employed to prove this type of motions is to verify the existence of transversal intersections between the stable and unstable manifolds of certain objects. Then, there exists a theorem (the Smale-Birkhoff homoclinic theorem) which ensures the existence of chaotic motions.
In this talk we present a method to analyze the distance and transversality between certain stable and unstable manifolds when a small perturbation is added to an integrable system. In particular, we consider the case where the distance between manifolds is exponentially small. This implies that this difference cannot be detected by expanding the manifolds into a series with respect to the small perturbation parameter. Therefore, classical perturbation theory cannot be applied.
Finally, we apply these techniques to a celestial mechanics problem. In particular, we study the Lagrange point L 3 in the restricted planar circular 3-body problem.
|Giovanni Dalmasso||CRM Postdoctoral Researcher | Cancer Modelling Lab|
|Gerard Farré||CRM Postdoctoral Researcher | Dynamical Systems|
|Roser Homs||CRM Postdoctoral Researcher | Computational & Mathematical Biology|
|Manuel Molano||CRM Postdoctoral Researcher | Computational Neuroscience|