‘Big Mathematics for Big Data’, a seminar by University of Oxford Guest Speaker, Professor Vidit Nanda.5 March 2019
Professor Vidit Nanda started his seminar with us on Friday 1st of March. He Began his talk by showing some theoretical results (theorems) of topological data analysis, explaining the validity of them in association to his work and following on to demonstrate that the pattern your data creates, reflects its performance. An example Vidit gave was using data that created an ellipse, looking for the calculations for the ellipse and assessing the elliptical regression and linear regression.
He progresses through his seminar by discussing the importance of how going through data can determine techniques which have already been used before, referring to Greek myth of Odysseus and its relation to linearity and non-linearity. Following this, he then uses a comical definition for Topology, describing it as the result of taking away measurements (landmarks) and statistics from analysts and geometers. To connect this, he makes the audience aware of geometry history, its familiarity/link to Topology and how the Euler characteristic were the birth of Topology.
He then proceeded by talking about Chain Complex, is a sequence of vector spaces and linear maps and example to relate to this would be the boundary of three edges on a triangle, creating a compose of 0. Vidit continues to explain the homology of this chain complex and how/why it is the quotient vector space which reflects the topology, showing examples of betti numbers and referring to its association to the Euler characteristic through diagrams.
Vidit would use his computer to work out the image through the points and use an alternative way to look at data that connects Topology and Homology, using a scale of life and death to reflect the position of the void being filled and emptied. With persistence diagrams and homology being used to compute connected components at 1D and 2D scales, a new breast cancer was discovered by comparing hamming distance to tabulate the slots that disagreed. The new breast cancer which was discovered, CMY-B, had a 100% survival rate and was recoverable but was originally being treated with methods for other forms of cancer.
Another application of Persistent Homology he discussed was mobile sensor coverage criterion, the easiest way to escape the sensors would be to use Topology to find a section of constant white which exists negative space. Measuring would be invalid for this hypothesis. This continued to protein compressibility, estimating the compressibility changes of pressure with a fixed temperature. Without measuring the atom centres, growing balls from the core would determine the distance between atoms as the edges of the growing circles would intersect to reveal the distance, this would reveal the compressibility. A life and death of points in persistent diagram were shown at the end of the seminar to reflect the points found of the proteins, revealing 19 compressibility outliners, 2 were measured at 25 at either end of the scale and 1 was measured in the centre at 0.
Our guest speaker from The University of Oxford, Professor Vidit Nanda, gave us a better understanding of his research and progress in Persistent Homology. This seminar also gave students and staff the opportunity to benefit from the discussion of ‘Big Mathematics for Big Data’, possibly incorporating the new knowledge into their own research. For individuals who may be considering a course in computing or for those who may have a general interest, these discussions provide an insight into current students’ research and where it will lead them.
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Find out more about Professor Vidit Nanda and his future seminars.