Thursday, November 10, 2022

Field Prize Prediction 2026 - Lisa Piccirllio (comes first), Urmila Mahadev (comes 2nd), Shai Evra, W Sawin, M Weber, Kaisa Matomaki, Adam Harper, Yifeng Liu, Dr. Tang's



As a project, 3 years back, I analyzed last 50 years of papers (10 TB data) of all the field medalists & the rest of the mathematicians (a lot of unstructured text data) to predict the field medal for the 2022 event. Again, this was a graph mining & NLP (natural language processing & text mining) exercise to motivate upcoming data scientists to try something new, figure out new problems to solve, and probably unleash the power of predictive analytics & narrow AI as well. 

This required a lot of 

1. Data cleaning 

2. Defining the breakthrough of every winner  

3. Developing co-author network data 

4. look-a-like profiling based on topics, citations, embeddings, and lot of other things  

5. Developing topic models through natural language processing, the topology of networks, superimposing topology of networks with topics & changing the definition of a breakthrough with respect to the papers of the winners 

6. Deep Divergence Learning & Ricci Flow for community detection for clustering right topics with unsupervised learning 

7. Reinforcement learning & ensemble modeling 

And A Secret recipe of this predictive analytics project which came through the concept of the topology of social networks & KBGAN: Adversarial Learning for Knowledge Graph Embeddings https://arxiv.org/abs/1711.04071 

8. Ant Colony Optimization to understand amongst research coauthors has the shortest path with innovation breakthrough yield & to win the Field..


My prediction came true for Maryana Viazovska, Hugo Duminil & J Maynard while Bhargav Bhatt won New Horizon breakthrough prize. 





I am running the algorithms this time for 2026 and the initial analysis shows Lisa Piccirllio (comes first), Urmila Mahadev (comes 2nd), Melanie Weber, Shai Evra, W Sawin, Kaisa Matomaki, Adam Harper, Yifeng Liu, Dr. Tang's name  have probability over 95% to win 2026 Field prize. 


Tuesday, November 8, 2022

Ricci Curvature, Yang-Mills curvature, New letter from Dr. Yau on Stable regular solution of Einstein-Yang-Mills equation

Hi Readers,

Its 3 AM in Mumbai.. I have been writing about Ricci Curvature, Yang Mills Curvature for a while. 

Some of you might like the new letter by Dr. Yau on it with Yang-Mills curvature tensor, coordinate transformation, etc. - 

https://arxiv.org/pdf/2210.09861.pdf

This is a very simple yet a genius letter. More to come on this topic. 

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Different topic - 

I have been asked what books to read on Ricci Flow - 

The Book I recommend is Sobolev Inequalities, Heat Kernels under Ricci Flow, Poincare Conjecture by Qi S Zhang. 

Something which you might like in this book apart from my old lectures


















 

Saturday, November 5, 2022

Ricci Curvature and Field Prize prediction for 2026

Hey guys,

Here comes my new blogpost. 

1. Thank you - Thanks a lot for messages on A. my field prize prediction, B. My Ricci Flow video & C. My talk abstract which was selected for a satellite conference. 

I am building a new algorithm to predict Field Prize which is going to happen in 2026 using Graph Neural Networks, HodgeNet and Ricci Curvature. 

My Original Algorithm was - 

1. Data cleaning 

2. Defining the breakthrough of every winner  

3. Developing co-author network data 

4. look-a-like profiling based on topics, citations, embeddings, and lot of other things  

5. Developing topic models through natural language processing, the topology of networks, superimposing topology of networks with topics & changing the definition of a breakthrough with respect to the papers of the winners 

6. Deep Divergence Learning & Ricci Flow for community detection for clustering right topics with unsupervised learning 

7. Reinforcement learning & ensemble modeling 

And A Secret recipe of this predictive analytics project which came through the concept of the topology of social networks & KBGAN: Adversarial Learning for Knowledge Graph Embeddings - https://arxiv.org/abs/1711.04071 

8. Ant Colony Optimization to understand amongst research coauthors have shortest path with innovation breakthrough yield & to win field.. 


I am going to use lot of HodgeNet to analyze co-author network edges along with this original algorithm. 


More coming soon on this topic..  

Tuesday, November 1, 2022

Congratulations to Bhargav Bhatt and Field 2026

Hi Readers,

Congratulations to Bhargav Bhatt for winning Nemmers Prize this month.

While I have been using lot of dimensionality reduction techniques in my Field Prize Prediction algorithm (done 2 years before 2022 Field Prize which came true for which came true for - James Maynard, Hugo Duminil, Maryna Viazovska while Bhargav Bhatt winning New Horizons Breakthrough Prize and recently Northwestern University's Nemmers Prize - https://lnkd.in/dEs3E4ge ), I will be using HoroPCA for next Field Prize Prediction algorithm which is going to happen in 2026.



 

Wednesday, October 26, 2022

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..    










Sunday, October 16, 2022

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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Friday, October 14, 2022

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