Homología persistente

Hay 7 posts etiquetados con Homología persistente.

Homología persistente como herramienta de análisis de redes neuronales

Ponente: José Manuel Ros Rodrigo (Universidad de La Rioja).

Lugar: Seminario Mirian Andrés (Edificio CCT).

Hora: miércoles 16 de noviembre de 2022, 11:00.

Resumen: Esta presentación está dedicada al estudio de la homología persistente como herramienta matemática para su aplicación sobre redes neuronales. La herramienta fue introducida, de manera pionera, por S. Watanabe en el artículo «Topological measurement of deep neural networks» que constituye la base de este trabajo. Durante la revisión del artículo han surgido una serie de dificultades que han originado dos interpretaciones diferentes de los contenidos del mismo: la interpretación global y la interpretación local. Este estudio  pretende ser un primer paso para comprender, por medio de herramientas matemáticas, la riqueza estructural de los modelos de deep learning.

Nota: puedes acceder a las transparencias de la charla a través del siguiente enlace.

Processing Biomedical Images for the Study of Treatments Related to Neurodegenerative Diseases

 

Ponente: Gadea Mata Martínez (Universidad de La Rioja)

Lugar: Salón de Actos (Edificio CCT)

Hora: martes 5 de septiembre, 12:00

Resumen: The study of neuronal cell morphology and function in neurodegenerative disease processes is essential in order to develop suitable treatments. In fact, studies such as the quantification of either synapses or the neuronal density are instrumental in measuring the evolution and the behaviour of neurons under the effects of certain physiological conditions.

In order to analyse this data, fully automatic methods are required. To this end, we have studied and developed methods inspired by Computational Algebraic Topology and Machine Learning techniques. Notions such as the definition of connected components, or others related to the persistent homology and zigzag persistence theory have been used to compute the synaptic density or to recognise the neuronal structure. In addition, machine learning methods have been used to determine where neurons are located in large images and to ascertain which are the best features to describe this kind of cells.

Nota: la charla se trata de una prueba de tiempo para la presentación de la Tesis, que tendrá lugar el viernes 15 de septiembre a las 12:00 en el mismo Salón de Actos del CCT.

Spectral sequences for multidimensional persistence

 

Ponente: Andrea Guidolin (Politecnico di Torino)

Lugar: Seminario Mirian Andrés (Edificio CCT)

Hora: lunes 23 de enero, 12:30

Abstract: Persistent homology is a largely used technique in topological data analysis which allows to extract topological information from data. Its success is due to the wide range of situations where it can be applied, from classification of digital images to networks, from biological data to analysis of sensor fields. In short, a filtration of simplicial complexes is constructed from given data, and through the use of homology one obtains a “topological signature” of the data set.

Another mathematical object related to filtrations of simplicial complexes is the spectral sequence, whose relationship with persistent homology has been made clear during the last few years. We consider multidimensional persistence, an n-dimensional generalization of persistent homology, and we introduce a suitable generalization of spectral sequences, explaining the relation between the two concepts and pointing out the advantages of this new approach.

The slides of the talk are available through this link.