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ABACUS: Laboratorio de Matemáticas Aplicadas y Cómputo de Alto Rendimiento del Departamento de Matemáticas

Ubicación:
Centro de Formación y Desarrollo en Nutrición (CEFODEN). Universidad Mexiquense del Bicentenario
Carretera México-Toluca Km. 38.5, Ocoyoacac, Estado de México

RESEÑA DE LA TERCERA ESCUELA

MEMORIA FOTOGRÁFICA

El programa del evento puede consultarse aquí.

Actividades

  1. Tres cursos teórico-practicos como se especifica a continuación*
  2. Sesiones prácticas de implementación
  3. Panel de discusion: Big data en Mexico y el mundo
  4. Sesión de carteles

Comité organizador:
Jesús González (Cinvestav)
José Perea (Michigan State University)
Gelasio Salazar (Universidad Autónoma de San Luis Potosí) 
Victor Pérez Abreu (CIMAT)

  • José  de  Jesús  Aguirre  Tepole   
  • Víctor Andrés Amaya Carvajal
  • Érik  José  Amézquita  Morataya   
  • Octavio Arizmendi
  • Sergio  Barajas  Oviedo   
  • Leo  Betthauser   
  • Rolando Biscay
  • Peter  Bubenik   
  • Natalia  Cadavid  Aguilar   
  • Jonathan  Castillo  Ramírez   
  • Elías  Cedillo  Hernández   
  • Ricardo  Esteban  Chávez  Cáliz   
  • Samir  Chowsdhury
  • Adriana  Haydee  Contreras  Peruyero   
  • Carina  Curto  
  • Luis  Gerardo  de  la  Fraga   
  • Ángel  Emilio  De  León  Gutiérrez   
  • Enrique Dunn
  • Gilberto  Flores  Vargas   
  • Víctor  David  García  Medina   
  • Jesús González Espino Barros
  • Rafael  José  González  De  Gouevia   
  • Ricardo  José  Guerrero  Rodríguez   
  • Daniel  Guerrero  Romero
  • Bárbara  Mayera  Gutiérrez  Mejía
  • Aldo  Guzmán  Sáenz   
  • Yair  Adán  Hernández  Esparza   
  • José  María  Ibarra  Rodríguez   
  • Vladimir  Itskov  
  • Adriana  Lara  López   
  • Abraham  Martín  del  Campo  Sánchez   
  • Asael  Fabián Martínez Martínez
  • Facundo  Mémoli  
  • Daniel  Mora  de  la  Cruz   
  • Jesús  Murillo  García   
  • Miguel Nakamura
  • Raúl  Nava  Hernández   
  • Isacc  Ortigoza  Suárez
  • Alberto  Carlos  Ortíz  Argüello
  • Luis Jorge Palacios Vela
  • José  Andrés  Perea  Benitez
  • Víctor Pérez Abreu
  • Jesús Manuel Pérez Angulo
  • Marcelino  Ramírez  Ibáñez
  • Beatriz  Ramonetti  Valencia
  • Fermín  Omar  Reveles  Gurrola
  • Antonio  Peter  Rieser
  • Jesús  Iván  Rivera  Ramírez
  • Erika  Berenice  Roldán  Roa
  • Roxana  Wendoline  Ruíz  Aguilar
  • Gelasio Salazar
  • José Ángel Sánchez Gómez
  • Omar  Radhamés  Urquídez  Calvo
  • María  Alejandra  Valdez  Cabrera
  • Luis  Fernando Valenzuela Peinado 
  • Carlos  Vargas  Obieta

*Cursos

1. "Topology  for  Data  Science"
Lecturers: Peter Bubenik and Leo Betthauser (University of Florida)
References

Short description: Algebraic topology has been successful in developing machinery for synthesizing complex geometric information into global invariants. The new field of applied topology seeks to implement and build on these tools for the purpose of analyzing modern data. We will give an introduction to topological data analysis (TDA) and show how it can be combined with other approaches popular in data science. We will start by introducing the underlying mathematics, simplicial complexes and homology, and proceed to study the main tool of the subject, persistent homology. In order to allow our results to be more easily combined with statistics and machine learning, I will introduce the persistence landscape. With these tools, I will analyze a number of biological applications and see how we can combine TDA with permutation tests, principal component analysis and support vector machines. This course will include a practical component where we will use R to implement all of the above.

It is strongly recommended that attendees understand simplicial complexes and simplicial homology with coefficients in a field, and have some familiarity with persistent homology. For the tutorial, it would be helpful if participants

1. download R from https://cran.rstudio.com/
2. download RStudio from https://www.rstudio.com/products/rstudio/download3/
3. work through the R introduction at http://www.r-tutor.com/r-introduction

2. "Applications of topology to neuroscience"
Lecturers: Carina Curto y Vladimir Itskov (Pennsylvania State University)

Short description: The brain represents information via neural codes, and "cracking the neural code" is one of the fundamental challenges of neuroscience. In this course we will learn how topology can help us to understand basic properties of neural codes. We will also see how topological data analysis can be used to detect principles of neural coding from experimental recordings of neural activity. These ideas will be illustrated in a variety of systems, whose neural circuits support vision, spatial navigation, and olfaction.

3. "Network Data Analysis: Metrics and Persistent Homology"
Lecturers: Facundo Mémoli and Samir Chowdhury (Ohio State University)
References

Course description: Networks are representations of (possibly asymmetric) relationships between objects that have long been used in the sciences, and techniques for their analysis have a rich history in mathematics. In this course, we view networks as generalized metric spaces and extend the mathematical tools available for studying finite metric spaces to the setting of networks. We will show how the Gromov-Hausdorff distance between finite metric spaces can be extended to define a distance on the collection of all networks under a suitable notion of isomorphism. We will cover both the main theoretical properties of this metric and discuss the computational complexity associated with its calculation. We will then explore certain network signatures (isomorphism invariants)—the local and global spectrum—that can be used to perform clustering/classification tasks on databases of networks. As a second component of the course, in order to extend our collection of network signatures, we will consider the tool of persistent homology, and explain how it can be adapted to the setting of directed networks. We will describe the stability properties of the resulting constructions under the notion of metric alluded to above. Throughout the course we will supplement theoretical concepts with computational examples (in Matlab), demonstrations, and possible extension projects.