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Time and place: , Rest area, 10th floor, NH Abels Hus
Time and place: , Rest area, 10th floor NHA

 

In my talk I will discuss the use of topological methods in the analysis of neural data. The key idea is to associate a space to the data set and then determine its shape by using persistent homology. In this way we have obtained good state spaces for Head Direction Cells and Grid Cells. Topological decoding shows how neural firing patterns determine behaviour.This is an interesting local to global situation which gives rise to some reflections. Based on very recent experimental results from the Moser-Lab at NTNU we show that the state space of a population of grid cells is a two dimensional torus!

 

Coffee, tea and biscuits from 14.00

Time and place: , Rest area, 10th floor NHA

Abstract:

In 1823 Niels Henrik Abel published a paper with title "Oplösning af et par opgaver ved hjelp af bestemte integraler," (Solution of a couple of problems by means of definite integrals), Magazin for Naturviden-skaberne, Aargang I, Bind 2, Christiania, which did not appear in French translation until 1881. Here he presented a complete framework for fractional-order calculus with appropriate notation for non-integer-order integration and differentiation. This seems to have been unknown until discussed in Podlubny, Magin, Trymorush, "Niels Henrik Abel and the birth of fractional calculus," Fractional Calculus and Applied Analysis, pp. 1068-1075, 2017.

I will give an introduction to non-integer order calculus and Abel's derivation of it. This will be done by going through his 1823 paper showing how he assumes a generalization of both Cauchy's formula for repeated integration and the fundamental theorem of calculus. In addition I will show how fractional calculus can be used to derive fractional-order partial differential wave equations. They have solutions with power-law attenuation which matches measurements in the complex media of medical ultrasound and elastography as well as in sediment acoustics and seismics.

Time and place: , Rest area, 10th floor NHA

Abstract:

A well-studied problem in computer vision is "structure from motion", where 3D structures and camera poses are reconstructed from given 2D images taken by the unknown cameras. The most classical instance is the 5-point problem: given 2 images of 5 points, the 3D coordinates of the points and the 2 camera poses can be reconstructed. In fact, given 2 generic images of 5 points, this problem has 20 solutions (i.e., 3D coordinates + 2 camera poses) over the complex numbers. Reconstruction problems which have a finite positive number of solutions given generic input images, such as the 5-point problem, are called "minimal". These are the most relevant problem instances for practical algorithms, in particular those with a small generic number of solutions. 

We formally define minimal problems from the point of view of algebraic geometry. Our algebraic techniques lead to a classification of all minimal problems for point-line arrangements and any number of cameras. We compute their generic number of solutions with symbolic and numerical methods.

This is joint work with Timothy Duff, Anton Leykin, and Tomas Pajdla.​

 

NB! Coffee/Tea/Biscuits from 14.00.