Dynamical Systems & Applications
Registration : Please fill the form for the semester 2024.1 (April-June 2024) here
(Mandatory to attend the lectures)
- Students can enroll for credit or as auditing participants
- If a student of UFRJ is taking the school as a credit course, he/she has also to register on the SIGA platform
- Evaluation : students who are taking the school for edit are required to do an oral presentation at the end of the semester. At this purpose, students will be divided in groups and presentations are going to be group presentations
- Time schedule : professors from Europe have 5 hours difference with respect Brazil, so we had to move the time to 2pm-3pm (Rio de Janeiro time) which corresponds to 7pm-8pm in Barcelona.
- Certificates : students who are taking the course for credit and are not from UFRJ can receive a certificate from the Program of Pós graduação of IM, UFRJ. Students who are participating as auditing can receive a certificate of participation, still from the same program.
Contact e-mail : stefanella.boatto at matematica.ufrj.br
Welcome to the International School on Dynamical Systems & Applications.
The school is structured in a series of minicourses of 3-4 hours each, one week per month, starting at the end of April.
The main purpose is to provide an interdisciplinary environment where students have access and learn how to use a variety of tools from dynamical systems used in several applications, ranging from Physics to Biology.
We shall start addressing some of the tools used in Celestial Mechanics and Neuroscience.
Organizing committee :
Stefanella Boatto
Mathematical Institute
Universidade Federal do Rio de Janeiro (UFRJ)
Brazil
Jaqueline Siqueira
Mathematical Institute
Universidade Federal do Rio de Janeiro (UFRJ)
Brazil
Humberto Viglioni
Universidade Federal de Sergipe, Aracaju (UFS)
Brazil
Rodrigo Schaefer
Jagiellonian University Poland
Upcoming minicourses :
Minicurse 20 : Isabel Serra
Universitat Autònoma de Barcelona (Catalunya, Spain)
& President of the Catalonian Society of Statistics
Universitat Autònoma de Barcelona (Catalunya, Spain)
& President of the Catalonian Society of Statistics
2, 7, 9, 14 of May
Learning statistics for machine learning
11am-12pm (Rio de Janeiro )
Learning statistics for AI/ML
Statistics, as a field, serves as the backbone of modern data analysis, providing the means to distill complex information into meaningful insights and predictions. Throughout its evolutionary journey, statistics has continually adapted and refined its methodologies to meet the ever-growing demands of an increasingly data-driven world.
From its humble origins as a tool for summarizing data sets, statistics has evolved into a powerful framework for inference. Its role in quantifying uncertainty has been fundamental in shaping our understanding of the world around us. Whether in the realm of science, economics, sociology, or beyond, statistics has proven indispensable in extracting knowledge.
The advent of the digital age has heralded a new era in statistical analysis, with the proliferation of computing technology enabling the handling of massive datasets with unprecedented ease. This has paved the way for the rise of artificial intelligence (AI) and machine learning (ML) algorithms, which leverage statistical principles to extract meaningful insights from complex data structures. The synergy between statistics and AI/ML has revolutionized fields as diverse as healthcare, finance, and marketing, driving innovation and transformation at an unprecedented pace. Concretaly, while traditional statistics has indeed largely centered its developments around characterizing uncertainty through patterns or mean values, other dimensions within this discipline, notably the study of extreme values, are now offering profound insights.
Prof. Isabel Serra's short biography
Isabel Serra has a Ph.D. in mathematics. She is a professor at the Autonomous University of Barcelona and researches in the Statistical Modeling of Extreme Events and Health Risks group founded by the Spanish government. She is a collaborating researcher in the Complex Systems Group of the Center for Mathematical Research (CRM) since 2014 and in the CAOS group of the BSC since 2018. She was dedicated to the transfer of mathematical knowledge and therefore worked as Head of the Knowledge and Technology Transfer Unit in CRM until 2022. Her main line of research within mathematics is the Theory of Extreme Values and her scientific interest focuses on the study of Complex Systems together with physical researchers and Critical Systems together with engineering researchers. She has worked on several interdisciplinary projects and has published in journals in different fields.
Video of Lecture 1, 2 of May 2024
Video of Lecture 2, 7 of May 2024
Video of Lecture 3 9 of May 2024
Video of Lecture 4, 14 of May 2024
Dept. of Mathematics, San Francisco State University - SFSU, USA
Microscopic and Global Dynamics of piecewise isometry
August 2024
Past minicourses :
Minicourse 19: Carolina Charalambous
PUC Santiago of Chile (Chile)
ccharalambous at astro.puc.cl
2, 4, 25 of April 2024
Dynamics of planetary systems
1pm-2pm (Rio de Janeiro)
Abstract: In this mini-course we will delve into the intersection of dynamics and astrophysics, elucidating the instrumental role dynamics plays in resolving diverse astrophysical problems. Beginning with a general overview of the Solar System and understanding how planets form, we will cover general problems observed in extrasolar systems as a consequence of their dynamic evolution. We will focus on resonant systems and how these specific configurations might help us understand the origins of planetary systems. The course will be divided into the "chronological" phases of planet formation: early stages when there was still gas in the protoplanetary disk, and for the long term evolution we will analyse the dissipative effects that the star produces on the planets as well as the interactions between the planets themselves. The goal is to have some basic techniques of solar system dynamics together with their application to actual problems, and have some analytical and numerical tools.
Dr. Carolina Charalambous's short biography:
She is originally from Buenos Aires, Argentina. In 2015 she obtained my degree in Astronomy at the National University of La Plata.
She finished her Ph.D. in April 2020 in Celestial Mechanics and Planetary Sciences at the University of Cordoba, Argentina, were she also did a 1 year post-doc in the Institute for Theoretical and Experimental Astronomy, both with a fellowship from CONICET.
During 2021 and 2022 she did a postdoc at the University of Namur, Belgium, and she is currently a FONDECYT postdoctoral fellow since January 2023 at the Pontificia Universidad Catolica, Chile.
Her personal website and her linkedin profile:
https://sites.google.com/view/carolina-charalambous
https://www.linkedin.com/in/carolina-charalambous/
Video of Lecture 1 : 2 of Aprli 2024
Video of Lecture 2 : 4 of April 2024
Video od Lecture 3 : 25 of April 2023
Minicourse 18: Mattia Frasca
& Lucia Valentina Gambuzza
Dept. Electrical Engineering Electronics and Computer Science,
Università di Catania (Italy)
mattia.frasca at dieei.unict.it gambuzza at dees.unict.it
17, 29, 24, & 26 October 2023
1pm-2pm (Rio de Janeiro's time)
Synchronization of coupled dynamical systems
Lecture 1. Synchronization and the mathematical models used to study it Video 17 October 2023
Lecture 2. The Master Stability Function for synchronization of complex networks Video 19 October 2023
Lecture 3. Beyond complete synchronization Video 24 October 2023
Lecture 4. Synchronization in simplicial complexes Video 2 November 2023
(video bis)
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Abstract: In this mini-course we will discuss some fundamentals on synchronization of coupled dynamical systems. We will start with a short introduction on the synchronization phenomenon and the systems where it is relevant. We will then present an overview of the mathematical models used for studying synchronization. Then, we will move to the general model of identical dynamical systems coupled on a complex network and illustrate the main tool for the study of the stability of synchronization in these systems, that is, the Master Stability Function. Then, we will discuss the different regimes of synchronization that may appear in a network, namely the scenarios where not all the units synchronize each other, giving rise to patterns of synchronization such as remote and chimera states. Finally, we will show how synchronization emerges when the dynamical units interact not only in pairs, but in groups of two or more units.
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Bios
Mattia Frasca graduated in Electronics Engineering in 2000 and received the Ph.D. in Electronics and Automation Engineering in 2003, at the University of Catania, Italy, where is now associate professor and teaches process control, complex adaptive systems, and automatic control. Since November 2022 he is the President of the Master Degree in Automation Engineering and Control of Complex Systems. Since September 2023 he is the Erasmus Istitutional Coordinator of the University of Catania. His scientific interests include nonlinear systems and chaos, analysis and control of complex networks, bio-inspired robotics, and epidemic modeling. He is Editor of Chaos, Solitons and Fractals, Associate Editor of the Journal of Complex Networks, and served as Associate Editor for IEEE Transactions on Circuits and Systems I in 2012-15. He was one of the organizers of the 10th "Experimental Chaos Conference", co-chair of the "4th International Conference on Physics and Control" and chair of the "European Conference on Circuit Theory and Design 2017". He published six books and more than 300 papers on refereed international journals and proceedings and is co-author of two international patents. He has been President of the Italian Society for Chaos and Complexity (SICC) for the period 2018-2021.
Lucia Valentina Gambuzza received the Master degree in Automation Engineering and Control of Complex Systems in 2010 from the University of Catania and the Ph.D degree in Systems Engineering in 2014. Since 2014 to 2021 she held a post-doc position in the same university. She is currently a research associate (RTD-B) at the University of Catania where she also teaches control systems technologies and process modeling and control. Her interests are complex systems; control and synchronization of complex systems; nonlinear dynamics and chaos. She has published more than 50 papers on the topic. She has been, and currently is, involved in several research projects, with national and international collaborations. Since January 2017 she is Associate Editor of Chaos Solitons, Fractals and since November 2017 of Complexity and since July 2023 is Associate Editor for Frontiers in Physics. She regularly serves as Referee for many international journals, among which: Int. Journal of Bifurcation and Chaos, Nonlinear Dynamics, International Journal of Adaptive Control and Signal Processing, IEEE Trans. Automatic Control, IEEE Trans. Control of Network Systems and IEEE Transactions on Circuits and Systems I.
Minicourse 17: Raphaël Kevin Tinarrage
FGV (Brazil)
raphael.tinarrage at fgv.br
26, 28 September & 3, 5 October 2023
1pm-2pm (Rio de Janeiro's time)
An introduction to Topological Data Analysis
Video of Lecture 1 : 26 September 2023
Video of Lecture 2 : 28 September 2023
Video of Lecture 3 : 3 October 2023
Video of Lecture 4 : 5 October 2023
Abstract of the course: In this course, I will present Topological Data Analysis (TDA), and in particular persistent homology. This theory, born in the early 2000s, has now largely invested in the field of computational geometry and data analysis in general. In a few words, in TDA, we seek to discover and understand the topology – that is to say, the shape – of datasets. Rather than applying rigid models to the data, we preserve their inherent complexity, which we explore through topological invariants. By illuminating data analysis from a new angle, TDA opens the door to new insights and discoveries. In order to present both the mathematical and practical aspects of TDA, the course will be divided into four sessions. In the first one, I'll explain what topology means, what topological invariants are, and how they can help us understand datasets. During the second session, we will focus on the practical estimation of these invariants, from a computational geometric perspective. Persistent homology and its famous persistence diagrams will come into play in the third session. We'll finish with a programming session in Python: I invite everyone to come with the library Gudhi installed (available on pip).
Bio: I did most of my mathematical training at the Institut de Mathématiques d'Orsay in the south of Paris. I went on to the ENS Saclay, where I obtained my diploma d'agrégation (teaching diploma). I then followed a research master's degree in mathematics and life sciences. I did a PhD in Topological Data Analysis, under the supervision of Frédéric Chazal and Marc Glisse in the DataShape team (INRIA Saclay). I developed variations of persistent homology theory to solve topological inference problems. I am now a postdoc at EMAp, pursuing my missions to develop and apply TDA. Besides researching mathematics, I enjoy teaching mathematics (in particular confronting young students with research), understanding the topology of the world around me, and playing capoeira.
Mini-course 16: Jerôme Daquin
Dept. Mathematics & naXys, Université de Namur, Belgium
Dept. Mathematics & naXys, Université de Namur, Belgium
Chaos and computational methods for portraying phase spaces
2, 4, 9, 11 May 2023
1pm-2pm (Rio de Janeiro's time)
2, 4, 9, 11 May 2023
1pm-2pm (Rio de Janeiro's time)
Video of Lecture 1 - 2 of May 2023
Video of Lecture 2 - 4 of May 2023
These lectures, intended to a broad audience, will present introductory concepts and aspects of chaotic dynamical systems. We will start by examining qualitatively what is meant by ``chaos" using the paradigmatic logistic family as guiding model. In most applications, chaos is associated to a positive largest Lyapunov characteristic exponent, for which close orbits diverge exponentially. Computational methods to compute characteristic exponents, and others modern variational and non-variational finite-time chaos indicators apt to portray phase portraits, will be reviewed.
Mini-course 15: Lorenzo Giambagli
Dept. Physics,Univ. di Firenze, Italy- Dept. Mathematics, Univ. de Namur, Belgium
Spectral Analysis of Deep Neural Networks
6, 11, 13, 25 April 2023
1pm (Rio de Janeiro's time)
Video of Lecture 1 : 6 of April 2023
Video of Lecture 2 : 11 of April 2023
Video of Lecture 3 : 13 of April 2023
Video of Lecture 4 : 25 of April 2023
Deep Neural Networks are an extremely powerful and flexible function approximation which, in the last decades, has seen an exponential growth in applications. Despite being very easy to use and implement in a wide variety of contexts, these are tools which somehow lack in interpretability and error control.
In this short curse we will start from the basis of automatic supervised learning and we will proceed toward the training and analysis of a Deep Neural Network.
Minicourse 14: Cynthia de Oliveira Lage Ferreira
ICMC, USP, São Carlos, Brazil
A topologia por trás das redes complexas.
22, 29 November & 1 December, 1pm-2:30 pm (Rio de Janeiro's time)
Neste minicurso, apresentaremos uma breve introdução dos aspectos topológicos das redes complexas.
Estudaremos os modelos básicos de redes como, por exemplo, as redes aleatórias e as redes de Barabási-Albert e, também, algumas medidas de centralidade como grau, betweenness e clustering coefficient.
Além disso, veremos como as ferramentas da análise topológica de dados (TDA) podem contribuir para a compreensão da topologia das redes.
Para ilustrar os conceitos abordados, faremos algumas aplicações com dados reais em Python utilizando a plataforma Google Colab.
Video of Lecture 1 - 22 of November 2022
Video of Lecture 2 - 29 of November 2022
Video of Lecture 3- 1 of December 2022
Mini-course 13 : Riccardo Muolo
Dept. of Mathematics, Université de Namur, Belgium
4, 6, 11 & 13 of October, 1pm-2:30pm (Rio de Janeiro's time)
Turing patterns on networks: from lattices to non-normal topologies.
In 1952 the British mathematician Alan Turing published a work on morphogenesis that is now a milestone in the study of pattern formation. For reaction-diffusion systems of two species, he showed that by pertubing a stable homogeneous equilibrium, the system could become unstable as driven by diffusion and then exhibit patterns.
In this mini-course, we will start from Turing's original work, to then focus on its extension on lattices and complex networks. We will study how to pass from a continuous support to a discrete one and how in such framework the diffusion role is played by the Laplacian matrix. Then, we will proceed in studyi
ng how different network topologies affect the formation of Turing patterns, with particular focus on non-normal networks, i.e., networks whose adjacency matrix does not commute with its adjoint.
In the last part, we will study two recent modifications of the reaction-diffusion framework: the first one relies on putting an upper bound to the signal propagation, the second one further extends the reaction-diffusion setting, showing that patterns can be obtained even without diffusion.
Material about the course can be found at the drobox
Video of Lecture 1 - 4 of October 2022
Video of Lecture 2 - 6 of October 2022
Video of Lecture 3 - 11 of October 2022
Video of Lecture 4 - 13 of October 2022
2022.1 - Abril-July
Mini-course 12 : Lucia Brandão Dias & Angelo Alberti
Continuação analitica de Poincaré: versão clássica & versão via Arnstorf, com aplicações
Continuação analitica de Poincaré: versão clássica & versão via Arnstorf, com aplicações
Video of Lecture 1
Video of Lecture 2
Video of Lecture 3
Minicourse 11:
Gladston Duarte - AGH University of Science and Technology, Kraków, Poland
7 & 9 of June 2022
2pm-3:30 pm
(1 hour lecture + 30 minutes questions)
Title: Cálculo de Seções de Poincaré em Mapas e Fluxos: Alguns Exemplos
(minicurso em Portuguese)
7 & 9 of June 2022
2pm-3:30 pm
(1 hour lecture + 30 minutes questions)
Title: Cálculo de Seções de Poincaré em Mapas e Fluxos: Alguns Exemplos
(minicurso em Portuguese)
Video of Lecture 1 - 7 June 2022
Video of Lecture 2 - 9 June 2022
Minicourse 10:
Jean-Luc Thiffeault - University of Wisconsin, Madison, USA
3, 5, 10, 17 of May 2022
2pm-3:30 pm (1 hour lecture + 30 minutes questions)
3, 5, 10, 17 of May 2022
2pm-3:30 pm (1 hour lecture + 30 minutes questions)
Video of Lecture 1 - 3 of May
Video of Lecture 2 - 5 of May
Video of Lecture 3 - 10 of May
Video of Lecture 4 - 17 of May
Title : Braids and dynamics: From taffy pullers to data analysis
Video of Lecture 2 - 5 of May
Video of Lecture 3 - 10 of May
Video of Lecture 4 - 17 of May
Title : Braids and dynamics: From taffy pullers to data analysis
rio2022_lectures.pdfMinicourse 9 - Howie Weiss - Huck Institute of Live Sciences,
The Pennsylvania State University, USA
19, 26 & 28 of April 2022
2pm-3:30 pm (1 hour lecture + 30 minutes questions)
The Pennsylvania State University, USA
19, 26 & 28 of April 2022
2pm-3:30 pm (1 hour lecture + 30 minutes questions)
Title : Perspectives on Mathematical Modeling in Population Biology
Students registered from 25 countries :
Aix Marseille Université, CPT , France
Université Paris-Saclay, France
Université de Namur, Belgium
McMaster University, Canada
Emory University, USA
Georgia Institute of Technology (GATECH), USA
University of California San Diego, USA
University of Toledo, USA
Instituto Federal do Maranhão (IFMA), Brazil
Universidade Estadual de Campinas (UNICAMP), Brazil
Universidade Federal de Campina Grande (UFCG), Brazil
Universidade Federal de Goiás (UFG), Brazil
Universidade Federal de Minas Gerais (UFMG), Brazil
Universidade Federal do Pernambuco (UFPE), Brazil
Universidade Federal de Rio de Janeiro (UFRJ), Brazil
Universidade Federal de Rondônia (UFR), Brazil
Universidade Federal do Sergipe (UFS), Brazil
Universidade Federal Fluminense (UFF), Brazil
Universidade de São Paulo (USP), Brazil
Universidade Tecnológica Federal do Paraná (UTFPR), Brazil
Università di Bologna, Italy
Universitá di Milano, Italy
Università di Pisa, Italy
Università di Salerno , Italy
Instituto Superior Técnico (IST), Portugal
Universidade de Lisboa, Portugal
Universitat Autònoma de Barcelona (UAB), Catalunya, Spain
Universitat de Barcelona, Catalunya, Spain
Universitat Politècnica de Catalunya (UPC), Spain
Universidad de Granada, Spain
Imperial College, UK
Moscow Institute of Physics and Technology (MIPT), Russia
Kadir Has University, Turkey
Ordu University, Turkey
Khalifa University of Science and Technology, United Arab Emirates
Birzeit University, Palestine
ORT Braude College, Israel
Telaviv University, Israel
University of HENG Samrin Thboungkhum, Cambodia
University of Iceland, Iceland
Quaid -i-Azam university Islamabad, Pakistan
University Ibn Zohr, Taroudant, Morocco
Australia National University, Australia
