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1 vote

Mathematical physics without partial derivatives

One way for reformulating all of (classical) mechanics is Peridynamics, which does away with derivatives. It is essentially a non-local reformulation. Javili, Ali, et al. "Peridynamics review." Mathem …
Piyush Grover's user avatar
6 votes
Accepted

Physical interpretation of the Manifold Hypothesis

Q: Might there be a reason why stable physical processes would tend to have low-dimensional phase spaces. Yes. One reason is physical processes have dissipation. E.g., turbulence is "known" to be cha …
Piyush Grover's user avatar
10 votes

How useful is differential geometry and topology to deep learning?

Topological data analysis is already pretty popular in "data science", so much so that there are companies built on this idea. See: 1). https://en.wikipedia.org/wiki/Topological_data_analysis 2).htt …
Piyush Grover's user avatar
52 votes
1 answer
5k views

Mathematics of imaging the black hole

The first ever black hole was "pictured" recently, per an announcement made on 10th April, 2019. See for example: https://www.bbc.com/news/science-environment-47873592 . It has been claimed that stat …
Piyush Grover's user avatar