Dynamical Systems, May P. Dolciani Prize etc.

I have been working a lot of Nash Entropy and Ricci Flow optimized GANs to solve PDEs in Dynamical and Chaotic systems. 

One update about this topic.. Diana M. Thomas is going to receive 2023 Mary P. Dolciani Prize for excellence in research and Math. Her primary topic being Number theory and dynamical systems. 

More to come on this topic later... 

Breakthrough Prize in Mathematics, Optimizing Neural Networks through Yang Mills Flow

A very short blog for everyone who has previously read my blogposts on Ricci Flow ....  

I am looking for a co-author to publish a new Neural Network architecture on Yang Mills Flow, Vector Bundles, GANs (Torus GANs), Nash Flow, DeepWalk & Markov Chains

A hint - When we pass from holomorphic vector bundles to complex manifolds, the Yang-Mills flow is replaced by the Ricci flow. Reverse is true as well. 

If I ever write my next book, it is going to cover Maryam Mirzakhani,
Firoozbakht, Einstein, Godel, Bernoulli, Jacob Jacobi, Levi Civita and lot of other mathematicians..

Mathematics, data & AI makes history.. something to remember since my Field prize prediction came true..

Also, heartiest congratulations to Daniel Spielman for $3 million Breakthrough Prize in Mathematics. His graph theory principles were used in my field prize prediction.

My old book on GANs, DCGANs, QGANs, InfoGANs, GANs & RNNs, DGANs+CNNs+RNNs, GraphGANs, Reinforcement Learning, Deepfake detection using CNNs including self driving cars which I never published..

This was the book I was going to write on GANs in 2017... I was looking for coauthor... but, my readers would like the index, business use cases and the syllabus...  

Ricci-Yang-Mills flow, DeepWalk, GANs, Markov Chains

Hi Readers, 

Those who have been following my articles & blog on Ricci flow, Ricci Curavture on applications which Perelman used to solve Poincaré conjecture including 'my field prize math contest video' - https://www.youtube.com/watch?v=z_pjsJisdHQ on Ricci Flow & community detection, my accepted lecture in satellite conference on solving PDEs through Nash entropy & Ricci Flow optimized GANs in dynamical systems apart from my field prize prediction which came true (Hugo, Maynard, Maryana.. Bhargav Bhatt missing it out of millions of mathematicians but winning Clay Award..), my special congratulations email to Nikolai 1 year back... Here comes Twitter talking about Ricci Curvature - https://blog.twitter.com/engineering/en_us/topics/insights/2022/over-squashing--bottlenecks--and-graph-ricci-curvature

I am looking for a co-author to write a new Network Science paper on 

1. Ricci-Yang-Mills flow, 

2. GANs (Torus GANs), Nash Flow

3. DeepWalk & 

4. Markov Chains

Here is a wonderful blog on DeepWalk by IIT Roorkee  - https://dsgiitr.com/blogs/deepwalk/ 

Congratulations to 2022 physics Nobel Laureates for Quantum Entanglement & Quantum Information Processing

Hi Readers,

I have been writing a ton on Quantum Information Processing, Quantum entanglement, Quantum Game Theory, Ricci Flow etc. including my poster/talk at Purdue University few years back. Here is an abstract of the talk -

Complex networks including social networks, protein-protein networks, etc. have always alluded to us for a very long time. Quantum computers hold key to the evolving problem of community detection. Obviously, D-wave has been used with superconducting flux qubits while Universal quantum computer leverages the limited number of qubits with still exponential speed available. The further algorithms used on quantum computers have been mainly modularity graph clustering or modules available in tools such as Gurobi with graph optimization. This talk intends to stir the conversation towards a new method of community detection on quantum computers. quantum machine learning has been used to analyze Weyl spaces, Banach spaces, and Hilbert spaces. Using geometric decomposition if we apply discrete Ricci flow, the evolution of communities in the network can be analyzed and community detection becomes more accurate. Ricci flow has been known as a leading tool for smooth manifold decomposition. Many of the times, Communities detected Lie groups on Riemannian manifolds. Using Perelman entropy functional or Nash entropy functional, along with Weyl vector and quantum mass density function, Ricci flow can be further expressed in terms of entanglement. Using Ricci flow and quantum game theory, the study of communities, the way they are entangled with key players, and the payoffs of entanglement prove to be a significant breakthrough in network analysis. 

This year's Physics Nobel has been given to Aspect, Clauser and Zeilinger for Quantum Entanglement, Quantum Information Processing etc. Heartiest congratulations to all 3 for their wonderful research. 

Few papers which I really liked from Dr. Aspect (since I am a huge fan of Einstein - Niels Bohr Debates .. Einsten - God plays a Dice..Niel's Bohr - Don't tell god what to do with his dice! etc.. randomness etc.) - 

1. From the Einstein-Bohr debate to quantum information: the second quantum revolution (Orale) - https://hal.archives-ouvertes.fr/hal-01724593/
2. 14 From Einstein, Bohr, Schrödinger to Bell and Feynman: a New Quantum Revolution? -  https://www.degruyter.com/document/doi/10.1051/978-2-7598-2265-2.c021/html

Also, my movie submission to Harvard Math Department - Copenhagen - A BBC documentary and a dialogue between Niels Bohr and Werner Heisenberg    https://people.math.harvard.edu/~knill/various/copenhagen/index.html

I think it's a win for entire Quantum Computing community including me. 

Poincare, Perelman & Ricci Flow - Business to Blackholes

Hey guys,

In a rare interview, Perelman mentioned - The Poincare conjecture also gives an answer to the question about the shape of the Universe ( https://www.maa.org/news/math-news/perelman-calls-poincare-conjecture-formula-of-the-universe ). 

Not really. But, this blog has made sure that Ricci Flow, Ricci Curvature & Poincare conjecture have lot of applications in this business world & Black hole stability. 

1. NNs & Ricci Flow, Quantum Walk, Ricci-Yamabe maps for Riemannian flows, Drone Programming using Ricci Flow - https://researchcircle.blogspot.com/2022/04/nns-ricci-flow-quantum-walk-ricci.html?m=1 .

2. Ricci Flow, Market Fragility, Market Topology, Influencers & Game Theory, Ramanujan graph+Block Sparse Neural Networks, Hodge decomposition of information flow, RNNs - https://researchcircle.blogspot.com/2022/03/ricci-flow-market-fragility-market.html?m=1 .

3. Ricci Flow, Nash Entropy, Cigar Soliton, Lie groups, Sobolev inequality -  https://researchcircle.blogspot.com/2022/03/ricci-flow-nash-entropy-cigar-soliton.html?m=1 .

4. Ricci Flow, Economics, COVID outbreak prediction and Drug Design - https://researchcircle.blogspot.com/2022/02/ricci-flow-economics-covid-outbreak.html?m=1 .

5. Ricci Flow, Neural Networks, Nash Entropy, Ricci Yang-Mills flow - https://researchcircle.blogspot.com/2022/02/ricci-flow-neural-networks-nash-entropy.html?m=1 .

6. Security, Topological Game Theory & Ricci Flow - https://researchcircle.blogspot.com/2022/02/security-topological-game-theory-ricci.html?m=1 .

7. Ricci Flow, Geomstats, Lie Groups on Julia & EconoPhysics - https://researchcircle.blogspot.com/2022/02/security-topological-game-theory-ricci.html?m=1 .

8. Ricci Flow, Economics & a brilliant blog by Gita Gopinath - https://researchcircle.blogspot.com/2022/02/job-posting-paper-ricci-flow-economics.html?m=1 .

9. 4 interesting papers on Ricci Flow & Deep Learning - https://researchcircle.blogspot.com/2022/01/4-interesting-papers-on-ricci-flow-deep.html?m=1 . 

10. Ricci Curvature, Hawking's Vector and BlackHole Stability - https://researchcircle.blogspot.com/2022/08/stable-blackholes-perelman-ricci.html

11. Betti Numbers, Ricci Flow, Neural Network capacity, Graph Mining $ 1 million competition - https://researchcircle.blogspot.com/2022/09/betti-numbers-ricci-flow-neural-network.html 

12. Thank you, IBM-DeepRing, Neural Networks & Ricci Flow Pruning, New way of solving Yang Mills - https://researchcircle.blogspot.com/2022/08/thank-you-ibm-deepring-neural-networks.html 

13. Ollivier persistent Ricci curvature, Molecular design, CurvGAN - https://researchcircle.blogspot.com/2022/08/ollivier-persistent-ricci-curvature.html 

B-S-D Conjecture, Yang Mills, Machine Learning

Hey Readers, 

I used to write a lot about B-S-D conjecture and Yang mills (my favourite word being - SuperSymmetric Yang Mills - N = 4 -> N - 6) in this topological space called "Research Circles" (in 2010). Also, I used to write a lot on different machine learning approaches including NNs & Geoff Hionton's computer vision models.. CNNs etc.. to solve these 2 problems or rather a different way to look at these problems to generalize Ns. 

Few updates on these 2 problems -

BSD Conjecture -  

1. Machine learning invariants of arithmetic curves - https://www.sciencedirect.com/science/article/pii/S0747717122000839 

2. Ranks of elliptic curves and deep neural networks - https://arxiv.org/abs/2207.06699

Yang Mills -

1. Neural quantum states for supersymmetric quantum gauge theories - https://ml4physicalsciences.github.io/2021/files/NeurIPS_ML4PS_2021_46.pdf 

Ideally, I used to write a lot about machine learning and Q neural networks. The paper suggests that these supersymmetric matrix models could become challenging benchmark tasks for developing new neural ansatz architectures and algorithms. On such benchmark tasks one could tune the difficulty by choosing the number of bosons (and even add fermions) and the gauge group algebra, and some tasks also have exact results or analytical predictions (e.g. at very large N). At large N and strong coupling, the wave function should contain details of quantum gravity, and hence an efficient numerical method would be both powerful and exciting 

2. Preserving gauge invariance in neural networks - https://inspirehep.net/literature/1995502