Nonholonomic Einstein systems, Perelman Entropy, Ricci Flow

Hi Readers,

Happy Diwali! I am in Mumbai these days.. I have been speaking about nonholonomic diffusion in Einstein Systems, Ricci Flow, Yang Mills Flow, topological game theory in social networks and neural networks since 2010 with some mathematicians.

Perelman's (Field Medalist in 2010 who rejected Field Medal first time in 150 years after solving Poincare Conjecture which was unsolved for 100 years) 2008 paper The entropy formula for the Ricci flow and its geometric applications says that he did not know enough about Blackholes & (pseudo)- Riemannian geometry, Ricci Flow, Black Hole Thermodynamics, etc https://arxiv.org/pdf/math/0211159.pdf

Hence, I thought a perfect way to apply Perelman's work was AI, Data Science (please see my Ricci Flow- https://www.youtube.com/watch?v=z_pjsJisdHQ&t=26s ) & Econophysics using black hole thermodynamics etc. 

Anyway......

Here comes a state of the art paper on Perelman Entropy and Quantum Information systems - Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies - https://dl.acm.org/doi/abs/10.1007/s11128-021-03287-7

Obviously CERN has produced a great paper on application of Convolutional Neural Networks in Einstein Sasaki Vol Min. - https://arxiv.org/abs/1706.03346

But this paper Quantum Geometric Information Flows changes the way, I have analyzed GANs through Perelman Entropy and Ricci Flow in my SDSU-UCSD lecture for better convergence of GANs (the original lecture was on Image and Video Analytics/Computer Vision in Healthcare). 

This paper also gives lot of room for new research on on Ricci Flow,  Yang Mills and Social Collider articles (2 articles in KDnuggets). Twitter has recently published a blog on Ricci Curvature and Graph Neural Networks, while Univ of Cambridge has published a paper on RicciNets after my lecture.

This also changes the way I was going to apply Ricci Flow & Nash Entropy Optimized GANs to solve PDEs in Dynamical and Chaotic systems in certain way. 

More to come soon.. 

Happy Diwali again! Every Diwali brings lot of peace of mind and some good memories..    

Ricci Yamabe Flow, Neural Networks

Hi Readers,

Anyone using Ricci Yamabe flow in Neural Networks.. instead of Ricci Flow for Pruning/Optimization of neural networks.. 

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Ricci Flow, Markov Chain, Torus GAN, Yang Mills..

Hi guys,

It is 3 AM Friday Night. Few hints on Yang Mills & Calibi Yau since I have been writing a lot on these topics apart from 

1. CERN project to analyze Calabi Yau data 

2. Google project on Inception Neural Networks to analyze Calabi Yau 

3. A Julia Code on Machine learning of Vector Bundles (TBR)

4. Sobolev training of Neural Networks from Deepmind

My vision for Yang Mills was Mathematical Analogy which I developed working in the nights through 

1. Twitter and Social Collider, 

2. Use of Quantum Neural Nets - (recently published paper - Neural quantum states for supersymmetric quantum gauge theories sponsored by NTT  - https://arxiv.org/pdf/2112.05333.pdf

3. Projected Spaces, 

4. Ricci Flow and Markov chain, 

5. Vector Bundles (Gang Tian has published some awesome work in Vector Bundles and Ricci Flow in 2014), 

6. Random Vector - Salt vector (Salt vector was available in the encryption system of the banking software I was working on along with Convolutional Neural Networks etc. in 2011)... 

7. and  along with Twitter Cortex for Graph Neural Networks to analyze it Further..

.. part of which was later on published in Kdnuggets in 2013 in a very simplified format and visual way...  - https://www.kdnuggets.com/2013/11/yang-mills-million-dollar-connection-twitter-quantum-physics.html

What is yet to be seen is - 

1. Use of GraphGANs, TopologyGANs, Vector Bundles and CurvGANs for analyzing social Networks 

2. Ricci Flow to Analyze Social Networks - Available in my animation video on Ricci Flow (used to prove $1 million Poincare Conjecture) & its application in  Community detection in social networks which was an entry in Field Prize Math video Contest with your friends and colleagues 

3. Ricci Curvature and Markov Chain to Analyze social Networks along with HodgeNet for Link Prediction  

4. TorusGANs to analyze clusters in social networks further after running Ricci Flow Surgery as shown in my video of "PK - me - Prasad Kothari - giving answers to Grigori Perelman" - https://www.youtube.com/watch?v=z_pjsJisdHQ

 

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