Tensor network approach to two-dimensional Yang–Mills theories

Hi Guys,

A short blog on what is Tensor Networks & Yang Mills. I used to write about Yang Mills, Mass Gap, Twitter, social spaces and lot of other things in this blog. 

1. What is Tensor Network and why it should be viewed as data structure - https://www.youtube.com/watch?v=S6QGgRARPYw 

2. Tensor network approach to two-dimensional Yang–Mills theories

- https://academic.oup.com/ptep/article/2021/12/123B03/6415218 

You can also refer to following links - 

1. Machine learning line bundle connections - https://openaccess.city.ac.uk/id/eprint/27860/1/1-s2.0-S037026932200106X-main.pdf 

2. Tensor network approach to two-dimensional Yang–Mills theories - https://academic.oup.com/ptep/article/2021/12/123B03/6415218 

3. The Calabi–Yau Landscape: From Geometry, to Physics, to Machine Learning - https://books.google.co.in/books?hl=en&lr=&id=rxI7EAAAQBAJ&oi=fnd&pg=PR7&ots=mZZ3378c8r&sig=mhKICovJaoULSZW81LdE3lp1jLY&redir_esc=y#v=onepage&q&f=false 

4. Emergent Attention on Yang-Mills Space of Connections - https://lukepereira.github.io/notebooks/documents/2021-moduli-attention/main.pdf 

5. Convergence of Hermitian-Yang-Mills Connections on Kähler Surfaces and mirror symmetry - https://arxiv.org/pdf/math/0301324.pdf

6. Quantum Walk Model for Idea Propagation in Social Network and Group Decision Making - https://www.researchgate.net/publication/351631537_A_Quantum_Walk_Model_for_Idea_Propagation_in_Social_Network_and_Group_Decision_Making

Einstein Yang Mill Connections, Calabi Yau, Machine Learning, Space of Connections

Hi,

I am back with a new post. A lot of readers might remember my old article (2013) on 

1. Yang Mills & Twitter Cortex, 

2. Ricci Flow & Twitter 

3. and my blog on Yang Mills, Ricci Flow, Quantum Groups etc.   

Here are few papers & books which got published after that article - 

1. Machine learning line bundle connections - https://openaccess.city.ac.uk/id/eprint/27860/1/1-s2.0-S037026932200106X-main.pdf 

2. Tensor network approach to two-dimensional Yang–Mills theories - https://academic.oup.com/ptep/article/2021/12/123B03/6415218 

3. The Calabi–Yau Landscape: From Geometry, to Physics, to Machine Learning - https://books.google.co.in/books?hl=en&lr=&id=rxI7EAAAQBAJ&oi=fnd&pg=PR7&ots=mZZ3378c8r&sig=mhKICovJaoULSZW81LdE3lp1jLY&redir_esc=y#v=onepage&q&f=false 

4. Emergent Attention on Yang-Mills Space of Connections - https://lukepereira.github.io/notebooks/documents/2021-moduli-attention/main.pdf 

5. Over-squashing, Bottlenecks, and Graph Ricci curvature - https://blog.twitter.com/engineering/en_us/topics/insights/2022/over-squashing--bottlenecks--and-graph-ricci-curvature 

Thank you, IBM-DeepRing, Neural Networks & Ricci Flow Pruning, New way of solving Yang Mills...

Hi Readers,

Thank you - Thanks a lot for messages for 

A. my field prize prediction coming true which I explained in the first post - https://researchcircle.blogspot.com/2021/12/graph-mining-network-science-topology.html 

B. My Ricci Flow video which was submission to Field Prize Math contest 

C. My talk abstract which was selected for a satellite conference on Solving PDEs using Nash Entropy optimized GANs in Dynamical & Complex systems.

Writing a new & short blog on Neural Networks, Ricci Flow, Blockchain, DeepRing etc.

There is a way to protect neural networks through Blockchain. IBM produced a great paper on it - https://openaccess.thecvf.com/content_CVPRW_2019/papers/BCMCVAI/Goel_DeepRing_Protecting_Deep_Neural_Network_With_Blockchain_CVPRW_2019_paper.pdf 

Off course, I have been talking about AWS Blockchain for a while. But, this paper from IBM is amazing. DeepRing is ensemble of Blockchain & CNN with unique architecture of Hash Vector of each Block (which I have been talking about for a while including perturbation). This is an ideal structure for chainlink which Eric Schmidt - Ex-CEO of Google is advisor on. 

One thing which this paper lacks is pruning of Neural Networks through Ricci Flow (information flow optimization inside neural networks) which I spoke in my SDSU lecture towards the end apart from Healthcare analytics & image analytics (computer vision). 

Another AI which this paper can use is TopologyGAN, QGAN (Quantum GAN) & HodgeNET. 

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Some of my readers might remember my old article - 2013 on Yang Mills & Social Collider (across social networks). Things have progressed in positive way after writing that article (ref - https://researchcircle.blogspot.com/2022/04/yang-mills-social-collider-machine.html ) 

1. Ricci Yang Mills Flow on surface

2. Emergent Attention on Yang-Mills Space of Connections - https://lukepereira.github.io/notebooks/documents/2021-moduli-attention/main.pdf

3. Yang-Mills theory in highly multiple-connected topologies - https://www.researchgate.net/publication/321462498_Yang-Mills_theory_in_highly_multiple-connected_topologies

4. A Quantum Walk Model for Idea Propagation in Social Network and Group Decision Making - https://www.researchgate.net/publication/351631537_A_Quantum_Walk_Model_for_Idea_Propagation_in_Social_Network_and_Group_Decision_Making

5. Yang-Mills-Higgs connections on Calabi-Yau manifolds -
https://arxiv.org/abs/1412.7738 (coupled with Use of CNNs - Convolutional Neural Networks on Calabi-Yau in CERN paper)

Partnerships on Yang Mills -

A. Simons Foundation announces new collaboration on confinement and QCD strings - https://www.eurekalert.org/news-releases/960218

B. Research Fellow (David Wilkowski 's Group), Centre for Quantum Technologies - https://www.timeshighereducation.com/unijobs/listing/304528/research-fellow-david-wilkowski-s-group-centre-for-quantum-technologies/

Stable Blackholes, Perelman, Ricci Curvature, Why not CurvGAN for Ricci Curvature for Lemma calculation..

Hi guys,

I am superhappy today. It's has been proven today that block holes are stable In a 912-page paper posted online on May 30, Szeftel, Elena Giorgi of Columbia University and Sergiu Klainerman of Princeton University ( https://arxiv.org/abs/2205.14808 ) Dr. Yau from Harvard has announced this paper as breakthrough of the century. Reminds me of my U of A-NASA LPL RA days, when I used to analyze pixel data sent by Mars Rover in Mars Mission.

I have been talking about Ricci Curvature & Blackholes since a lot=ng time which you can find in my blog. This paper uses some of those concepts Ricci Curvature, Hawking vector field. 

For reference you can see my blog 1. https://researchcircle.blogspot.com/2022/03/maryam-mirzakhani-mirror-symmetry-swarm.html  - 

Perelman's 2008 paper (a small note) 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 was writing about Tensors, Ricci Curvature, Hawking vectorfield, Ramanujan Sparce Neural Networks, CurvGAN. etc. 

2. https://researchcircle.blogspot.com/2022/04/2-papers-on-einstein-rosenberg-bridge.html - 

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. 

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

Most importantly, this paper could have been shorter using some of the AI & ML techniques such as 

1. CurvGANs for Ricci Curvature - Curvature Graph Generative Adversarial Networks - https://arxiv.org/pdf/2203.01604.pdf 

2. Causal Future Prediction in a Minkowski Space-Time - https://thanosvlo.github.io/publication/cones/

3. Some Swarm intelligence for tensor calculation

Applications in Econophysics - I have written a lot about Ricci Curvature & Econophysics in my previous posts. Some of the papers in Econophysics which can leverage the Lemma calculation methods in. the paper are - 

A. Semiparametric Estimates of Monetary Policy Effects: String Theory Revisited - https://economics.mit.edu/files/13030
B. Ricci Solitons & Black Holes - http://dspace.rri.res.in/bitstream/2289/3857/2/Chapter_7.pdf
C. 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
D. Network geometry and market instability -https://royalsocietypublishing.org/doi/10.1098/rsos.201734

Ollivier persistent Ricci curvature, Molecular design, CurvGAN...

Hey guys & some fans,

A short blog on molecular design & Ricci Curvature ... (Hey Russia, I am still taking Perelman's side..) 

1. I have done some work on drug discovery & molecular design using AI. I know lot of you have liked my Forbes comments on COVID when no drug/vaccine was available in the market..

2. I know some of you liked my Ricci Flow (used to solve Poincare Conjecture) & Community detection video which was my submission to Field prize math contest ( https://www.youtube.com/watch?v=z_pjsJisdHQ&t=22s )

Hence, suggesting new way of molecular design using Ollivier Ricci curvature for a graph network, Graph Neural Networks tested on PDBbind-CN Database (http://pdbbind.org.cn/) with bit of a twist using CurvGANs to predict next molecular structure, affinity binding data etc.  

Here are couple of papers which my fans can read - 

1. Ollivier persistent Ricci curvature (OPRC) based molecular representation for drug design - https://arxiv.org/pdf/2011.10281.pdf

2. Curvature Graph Generative Adversarial Networks - https://arxiv.org/pdf/2203.01604.pdf 

I will upload the code later in Julia or Python. 

One company which can use this algorithm is 22nd Century Group based in New York (CEO James Mish). 

Thank you, Chainlinks, Hyperbolic Embeddings, Melanie Weber...

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. 

2. Chainlinks - A lot of you are wondering about my tweet on Hodge Decomposition of information flow over complex networks - The reason was hodge decomposition of information flow over 2 narrow networks - regular economy and crypto economy (including my new favourite ChainLinks) hence EconoPhysics 

3. Hyperbolic Embeddings - https://dawn.cs.stanford.edu/2018/03/19/hyperbolics/ Created by Stanford (I often use this in my projects since it has been pre-trained on UMLS). 

This has also been pre-trained on embeddings from MusicBrainz. Apps & companies like Gaana, Saregamapa - might get some help in improving their recommendation system - The Indian music industry is valued at Rs 1500 Cr and has grown at 10.3% CAGR in the past five years... Spotify, YouTube Music might use this apart from reinforcement learning on user data.

4. Melanie Weber - This paper by Melanie Weber is really good as an application of Ricci Flow in big data - Forman-Ricci Flow for Change Detection in Large Dynamic Data Sets - https://web.math.princeton.edu/~mw25/publication/axioms/