Joint meeting APDE - Machine Learning

DATE: 21st January 2021
TIME: 10:00-13:10
LOCATION: Online
Link: https://zoom.us/j/97084137138?pwd=WnNtWTNkbnlCbjdubDRNTVU3NGxFdz09
More info: https://sites.google.com/view/apdebilbao/workshops

PROGRAM

- Talk 1 - 10:00-10:25
Jonathan Heras (UR)
Title: Machine learning for biomedical imaging
Abstract: In this talk, we will present how machine learning methods, and namely deep learning techniques, are applied to analyse biomedical images. To this aim, we will first introduce the main techniques that are currently used to tackle bioimaging problems; and, subsequently, we will show how those techniques have been applied to deal with several projects conducted by members of our team in collaboration with biomedical researchers. Some of those projects are the segmentation of tumours, the detection of stoma, or the detection of neurons. Finally, we will present some common problems and limitations that are faced in this context. 


- Talk 2 - 10:30-10:55
Sergei Iakunin (BCAM)
Title: Vortex filament approximation for the reconnection process of two straight antiparallel vortices
Abstract: Reconnection of vortex tubes is a phenomena widely spread in different turbulent flows: from evolution of aircraft condensation trails to interaction of bubble-rings in water. In most experiments vortices after reconnection turn into a hairpin shape with waves running from the reconnection point. This shape looks quite similar to a solution of the vortex filament equation which describes a deformation under self induction of a single vortex filament initially shaped as a corner. In this case all the information about further evolution of vortex filament is contained in the corner tip singularity which corresponds to the reconnection point, however in the real flow it is quite challenging extract some information form this point and even to find it. We propose a modified vortex filament model which includes an interaction between vortices and as a consequence vortex stretching. This new model allows to find the reconnection moment and estimate velocity of the reconnection point before and after the reconnection and more other quantities which are useful for further comparison with the Navier-Stokes simulation of the flow and better understanding of the phenomena.  


- Talk 3 - 11:00-11:25
Renato Lucá (BCAM) 
Title: Machine learning and the Kortewegde Vries equation.
Abstract: We discuss a recent result of Di Qi and Andrew J. Majda in which the authors propose a neural network model to capture some extreme events appearing in a (truncated) Kortewegde Vries statistical framework. This models shallow water waves across an abrupt depth change.

- Break - 11:25-11:45

- Talk 4 - 11:45-12:10
Santiago Mazuelas (BCAM) 
Title: Machine learning: what, why, and how.
Abstract: Techniques developed in the field of "machine learning" are enabling numerous practical applications including recommendation systems, fraud detection, and automated translation, among many others. Such practical relevance is causing a wide coverage in the media that is often overloaded with enigmatic jargon and allusions to science fiction. In this talk I will briefly describe the basic ideas behind the techniques referred to as machine learning; from their main differences with other approaches to their mathematical foundations developed in the last decades of the 20th century.  


- Talk 5 - 12:10-12:40
Jamie Taylor (BCAM) 
Title: A design problem for surface treatments in liquid crystals.
Abstract: Liquid crystals are soft, structured materials that are encountered in a wide variety of technological and biological applications. Their softness makes their structures far more susceptible to outside effects, in contrast to (e.g.) classical crystals. Generally, control of liquid crystals can be achieved using external fields, or from surface affects at interfaces with other materials. In this talk we will discuss a multi-pronged approach to understanding how rugosity (fine scale fluctuations on a solid surface) can give "effective" surface treatments which can lead to control of behaviour in the "bulk" of the material. Furthermore, the results can be phrased as a design problem, which is solvable using techniques from machine learning. 


-Talk 6 - 12:45-13:10
José Antonio Lozano (BCAM) 
Title: Combinatorial Optimization and the Fourier Transform
Abstract: This talk deals with the solution of Combinatorial Optimization Problems. We show that while they are defined attending different ideas and criteria they can be put in a common framework by means of the Fourier transform. This is the first step on the path to taxonomize problems and algorithms. We illustrate this approach by means of permutation-based combinatorial optimization problems.