1.Yang-Mills, 2.Job Postings 3.Calabi-Yau 4.EconoPhysics, Divergent Recovery, TopologyGAN, Ricci Flow, Hodge theory

Hi Readers,

Yang Mills - First of all, lot of people must have seen my old orchestration on Yang Mills & Social Collider - Kdnuggets (and Neural Networks & Ricci Flow my old blog) - Here comes the absolutely brilliant paper on Yang Mills almost depicting the same - Emergent Attention on Yang-Mills Space of Connections - https://lukepereira.github.io/notebooks/documents/2021-moduli-attention/main.pdf (from Universidade Federal Fluminense .... Brazil & India is where so much of mathematical innovation is happening right ) Btw, you should watch my Ricci Flow video on Community detection & clustering to before reading this paper - https://www.youtube.com/watch?v=z_pjsJisdHQ 

Job Postings - This is an absolutely brilliant paper by Pratik Kothari on
Job Postings and Aggregate Stock Returns A much needed paper in today's time especially when CNBC announced Stock futures bounce as investors assess start of new quarter, bond market recession ( https://www.cnbc.com/2022/03/31/stock-market-futures-open-to-close-news.html ) 
- https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3223141

Calabi Yau - While I am impressed with the Inception Neural Network for Complete Intersection Calabi-Yau 3-folds - inspired by Google’s Inception model to compute the Hodge number I am still waiting for application on DeepSwarm in Calabi Yau. 

EconoPhysics - Dr. Gita Gopinath mentions Divergent Recovery in her IMF blog. How to make it optimum can be a very cool question to solve through EconoPhysics?

Most of you might have read my previous blog on Ricci Curvature & Market Failure ( https://researchcircle.blogspot.com/2022/02/job-posting-paper-ricci-flow-economics.html ). And some of you might have seen my recent tweet on Hodge Theory & Trading Networks in the evening. ( https://twitter.com/Prasad_Kothari/status/1509634908125335559 )

The following figure is from Sandhu's paper (w.r.t. Average Ricci curvature over a 15-year span of the S&P 500 - Choosing a window of T = 22 days )

I have mentioned portrait divergence in the following orchestration to compare sub-topologies between the economic & trade networks.  

Reference - 

1. Symmetry perception with spiking neural networks -  https://www.nature.com/articles/s41598-021-85232-3

2. Comparing methods for comparing networks -  https://www.nature.com/articles/s41598-019-53708-y

3. Ricci Curvature-Based Semi-Supervised Learning on an Attributed Network - https://ui.adsabs.harvard.edu/abs/2021Entrp..23..292W/abstract

4. Controlling Entropy via Discrete Ricci Flow Over Networks - https://arxiv.org/abs/1910.04560

The most interesting thing which I have not mentioned in this solution (apart from the code) is Thermodynamic Entropy in Quantum Statistics for Stock Market Networks from Shanghai University which talks about - Asian Financial Crisis (what could have been cool is use of HodgeNet (Graph Neural Networks for Edge Data) in it - https://ieeexplore.ieee.org/document/9049000

Edge entropy distribution of network structure before, during, and after the 1997 Asian financial crisis. (a)-(e) Bose-Einstein statistics. (d)-(f) Fermi-Dirac statistics.

  

Mirror Symmetry, Swarm Intelligence, Calibi Yau, GAN, SNNs, Econophysics

Hey Readers,

I am back again with a new blogpost on Saturday morning 5:30 AM. I got lot of inquiries about Dennis Sullivan and his amazing victory on Abel Prize. One of the best papers I have read by Dennis Sullivan is Circle Packing (off course my NLP, Reinforcement Learning, Ant Colony Optimization, Profiling etc. based prediction on last 50 years of math research papers is taking shape with Bhargav Bhatt's Hodge Theory, Maryna Viazovska's sphere packing etc. while off course Terence Tao has just published another paper on Sphere packing.. Sphere packing seems trend of the year while I am already thinking Duck pack algorithm — A new swarm intelligence algorithm for route planning based on imprinting behavior).. 

I also used to write a lot about Econophysics, String Theory (M-Theory etc. as I was big fan of Stephen Hawkings and probably had entire Brief History of Time by heart that time) Hodge Theory, Hodge Decomposition of information flow in networks & its impact on markets. 

Perelman's 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. 

I see few papers published on this topic these days -

1. Trading networks and Hodge theory - https://iopscience.iop.org/article/10.1088/2399-6528/abd1c2/pdf

2. Semiparametric Estimates of Monetary Policy Effects: String Theory Revisited - https://economics.mit.edu/files/13030

3. Ricci Solitons & Black Holes - http://dspace.rri.res.in/bitstream/2289/3857/2/Chapter_7.pdf

4. Entropy of Reissner–Nordström 3D Black Hole in Roegenian Economics - https://www.semanticscholar.org/paper/Entropy-of-Reissner%E2%80%93Nordstr%C3%B6m-3D-Black-Hole-in-Udriste-Ferrara/fb2052f27e6700fed05ae259d63232639b465643

 

I used to write a lot about swarm intelligence (ant colony optimization etc.) on Google Plus, G-spaces long time back on this blog to give mathematical meaning to Google Plus (Hodge Cycle, Supersymmetric Yang Mills, Social Collider etc.) & also give some movie meaning to it. Also, I wrote a lot about Ricci Flow (Used to prove Poincare Conjecture) -

1. Meet the parents, Circle of Trust and Google Plus - https://www.kdnuggets.com/2013/10/circle-trust-google-plus.html

2. Yang-Mills: A million dollar connection between Twitter and quantum physics - https://www.kdnuggets.com/2013/11/yang-mills-million-dollar-connection-twitter-quantum-physics.html

3. A lot about Ricci Flow, Group theory, Quantum Groups (remember Sir Atiyah's 1984 paper with TIFR which I cited few blogposts back)

4. I also wrote a lot about applications of deep learning & swarm intelligence to solve mathematical conjectures 

Hence the new orchestration which Cao & Zhao might like (as I see their paper on Calabi Yau, Machine Learning and Convolutional Neural Networks .. I would like to see possible use of Geodesic Convolutional Neural Networks) on Yang Mills which also uses Maryam Mirzakhani's concept on Mirror Symmetry in Spiking Neural Networks... 

SYZ conjecture, Maryam Mirzakhani - AI, Geodesics, Riemannian surfaces, Dennis Sullivan

Hey readers,

Everyone must have seen my last comment on Andrica's conjecture & Firoozbakht's conjecture and how looking at prime numbers as dynamical system is a smarter way to solve this. I also have a way to look at it further in terms of How to use GANs - Generative Adversarial Networks (with optimum convergence while leveraging Nash entropy) to solve PDEs in Dynamical & Chaotic systems generated by prime numbers.

There was this beautiful paper from Maryam Mirzakhani (field prize winner 2014) - Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces (2005) - https://www.math.stonybrook.edu/~mlyubich/Archive/Geometry/Teichmuller%20Space/Mirz3.pdf

A lot of my discussions during my evening time in 2010 happened on how to apply her paper in AI. So, I came up with an orchestration in 2011 on Geodesics CNN on Riemannian Surface (I used to write a same blog by the name of DataHulk - which I deleted in 2017 and restarted this year).

Here is a very interesting paper which got published in Switzerland on the same topic - Geodesic convolutional neural networks on Riemannian manifolds - https://arxiv.org/pdf/1501.06297.pdf . The most interesting part of this paper was heat diffusion on manifolds, Heat kernel signature etc.

This was followed by my 2 lectures & video on

1. Ricci Flow (heat diffusion equation with derivative form) in Networks ( https://www.kdnuggets.com/2014/05/poincare-conjecture-perelman-topology-social-networks.html )

2. Some part of my lecture in SDSU which focused on Pruning of Neural Networks using Ricci Flow after which University of Cambridge published a new paper on 
RicciNets: Curvature-guided Pruning of High-performance Neural Networks Using Ricci Flow - https://arxiv.org/abs/2007.04216

3. You might like my video on Ricci Flow & its use in use in community detection  - https://www.youtube.com/watch?v=z_pjsJisdHQ&t=23s  

Here is one way to look at SYZ conjecture -

By the way you might like the old paper - THE HOMOLOGY THEORY OF THE CLOSED GEODESIC PROBLEM MICHELINE VIGUE-POIRRIER & DENNIS SULLIVAN - https://www.math.stonybrook.edu/~dennis/publications/PDF/DS-pub-0034.pdf  ( Dennis Sullivan won Abel prize on 24th March for amazing circle packing work )

Edited - Zhiren Wang, associate professor of mathematics at Penn State, has been award the 11th Brin Prize in Dynamical Systems MAY 24, 2022 

PK the genius, Misinformation detection in networks including Vimeo, TopologyGANs, HodgeNet, Duck Swarm intelligence

Hey readers, 

Happy Sunday morning! A lot of my readers liked my blogpost on Econophysics, Ricci Flow and Gita Gopinath's post on Divergent Recovery ( https://researchcircle.blogspot.com/2022/02/ricci-flow-geomstats-lie-groups-on.html ) 

Also, Lot of my readers liked my video on Ricci Flow Animation - 

https://www.youtube.com/watch?v=z_pjsJisdHQ&t=16s 

Also lot of people liked my previous blog about Duck Swarm Intelligence, Ricci Flow (my tweet few months back on TopologyGANs & HodgeNet).. 

Few years back I met Raghuram Rajan at Chicago Booth to discuss his book & I also told him that I am working on new & innovative approach to detect misinformation over networks (I know there are lot of approaches but nothing like this one & yes this is different from the one I wrote about Inorganic Social Network Growth through Ant Colony Optimization in my old DataHullk - researchcircles blog.. I will write more about it in my next one). 

Every social network including Vimeo faces a problem of Misinformation. Here is my new orchestration to detect misinformation in social networks (I have mentioned about Hodge Decomposition of information Flow over narrow or complex networks) 

- 

Ricci Flow, Market Fragility, Market Topology, Influencers & Game Theory, Ramanujan graph+Block Sparse Neural Networks, Hodge decomposition of information flow, RNNs

Hi Readers,

I know lot of readers missed me for last few days. I have been really busy with projects & proposals. 

But, here continues my blog to teach everyone new ways of using Hamilton & Perelman's Ricci Flow since 2009 ( Please refer - https://www.kdnuggets.com/2014/05/poincare-conjecture-perelman-topology-social-networks.html )

Also, refer to my video on Ricci Flow & Community Detection - https://www.youtube.com/watch?v=z_pjsJisdHQ&t=12s 

1. When I was in Chicago, I wrote a lot about Ramanujan Graph in the night but never published, 

2. I used to write a lot about G-spaces on this datahulk blog in 2011 also lot about Ricci Curvatures, market topology, 

3. Stubborn & Non-Stubborn players in Game theory and social networks to identify right influencers

4. Hodge Decomposition of information flow 

5. Ricci Curvatures of network graph, network topology, Ricci Solitons

Here is my new orchestration (which kind of predicted Google stock going down on Friday & Monday) - 

Ricci Flow, Nash Entropy, Cigar Soliton, Lie groups, Sobolev inequality

Hey readers,

Its 3 AM.. Friday Night... dark outside.. I miss Sweet-greens, Joes and Juice, Roti in Chicago.. Wait.. actually I miss everything and everyone in Chicago. Coming back to Ricci Flow... If my fans/followers/readers remember from 2011.. I had written a lot of orchestrations on 

• Lie groups, 
• Ricci Flow, 
• Nash Entropy of Ricci Flow & 
• Convergence

..And also possibility of applying machine learning methods such as CNNs on or on Calabi Yau & Sasaki-Einstein base manifolds.. (Yeah Yeah.. just like Geoff Hinton's Boltzmann Machine's 1970s paper, I wanted to apply in drug discovery in 2006..which was a great project btw..)... 

Here are few papers which my readers might like -

1. One the Diagonalization of the Ricci Flow on Lie Groups ( https://arxiv.org/abs/1110.4003 ) - This is an amazing paper by Cynthia Will on Nilpotent Lie algebra which finally provides a good example on a left-invariant metric on a 4-dimensional nilpotent Lie group whose Ricci flow is not diagonal. Also, please see a special mention of

• Asymptotic behavior of some nil-solitons
• Ricci operator & Jacobi identity

2. On the Chern-Ricci Flow and Its Solitons for Lie Groups ( https://arxiv.org/pdf/1311.0832.pdf )- One of the best things about this paper is use of Levi Civita connection & Chern connection 

By the way, Just to show how important Levi Civita was - One day Einstein wrote to Levi Civita - I admire the elegance of your method of computation; it must be nice to ride through these fields upon the horse of true mathematics while the like of us have to make our way laboriously on foot). Off course, The opinion expressed by Einstein was not shared by many of the Levi-Civita contemporaries and also by many scientists nowadays. Indeed many do not believe that the abstraction required to use the absolute tensor calculus is justified by the obtained results, as these last can be deduced by classical and simpler procedures.. 

• Book - When Einstein Walked with Godel - https://www.goodreads.com/book/show/36794489-when-einstein-walked-with-g-del
• Levi-Civita,Tullio Francesco Dell’Isola, Emilio Barchiesi, Luca Placidi - https://hal.archives-ouvertes.fr/hal-02099661/document

3. A uniform Sobolev inequality for ancient Ricci flows with bounded Nash entropy - Special thing about this paper is ( https://arxiv.org/pdf/2107.01419v1.pdf )-

- Lie derivative
- Nash Entropy of Ricci Flow
- Convergence of Nash Entropy
- Cigar Soliton - Witten's black hole 

(if you remember Perelman's 2nd paper on Poincare conjecture in the series of 3 papers which mentioned blackholes in the Notes.. this is what has happened in last 9 years - Cigar Soliton & Witten's black hole)..