Tuesday, August 2, 2022

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/  


Saturday, July 23, 2022

Chainlinks, CyberGAN, Graph link prediction in computer networks

Hey guys,

Some of my readers have missed me. I have been superbusy. Here is a short blog -

1. I like Chainlink as a blockchain infrastructure. Eric Schmidt has invested in it heavily. Optimization of verification system in a very cost effective way is something Chainlink is really good at. 

A good network science algorithm with strong non zero sum game algo, rock solid cybersecurity system and lot of B2B applications.

2. For basics, one paper which chainlink fellows might like is by Sanna Passino, Turcotte Mellissa et.
Graph link prediction in computer networks using Poisson matrix factorisation ( https://spiral.imperial.ac.uk/handle/10044/1/89018 ) for its algorithm for cybersecurity. Off course, CyberGANs are much better suited for such projects :) 

Something, the ChainLinks fellows program should think about. 

3. Ideally, There can be ensemble of ColombGAN & CyberGAN to achieve good convergence in the model. 

Lot to come later. 





Saturday, July 9, 2022

busy in emergencies but ignored topic - NS & Information geometry

 Since lack of time & busy in emergencies…. This is one of my unpublished articles I wrote in 2013. Some datahulk fans might like it. Should be read along with the new paper The Computational Challenge of Amartya Sen’s Social Choice Theory in Formal Philosophy https://www.researchgate.net/publication/339022300_The_Computational_Challenge_of_Amartya_Sen's_Social_Choice_Theory_in_Formal_Philosophy

(Blockchain missing from the paper which could have been a huge help)


Coming back to 2013 -

Predicting virality social media messages through NavierStokes (node2vec & confusion2Vec we’re not algorithms yet)… Also I am not setting up a game & Nash entropy between stubborn & non-stubborn players…before Facebook’s work on mechanism design for social good….. not any GANs.. No CurvGAN, No TopologyGAN also not using Ricci flow ( https://youtu.be/z_pjsJisdHQ  )but Gibb’s energy & Navier Stokes in information geometry in a very very simple English…. 

Assume that information flows through the social networks. Information flow through social networks can be measured in terms of Gibbs entropy. When it comes to complex networks, information flow can be measured in terms of nash entropy or Perelman entropy. Now, is there connection between Shannon entropy and navier stokes equation?

About Navier Stokes 

Waves follow our boat as we meander across the lake, and turbulent air currents follow our flight in a modern jet. Mathematicians and physicists believe that an explanation for and the prediction of both the breeze and the turbulence can be found through an understanding of solutions to the Navier-Stokes equations. Although these equations were written down in the 19th Century, our understanding of them remains minimal. The challenge is to make substantial progress toward a mathematical theory which will unlock the secrets hidden in the Navier-Stokes equations.

Turbulence in social networks – Whenever a social media campaign is run, the turbulence and push of the information is created in specific nodes of social networks and information flows through the pipes connecting different nodes. Can we identify which nodes the information will flow through and calculate the turbulence which we call as social buzz created by the campaign? It is highly possible. 

1. The way fluid changes its properties get changed when pressure and temperature is changed in the fluid system. Fluid can be lost to some extend during the curvature of the flow etc. 
2. Similar way, when information flow is pushed through different nodes of the social media or social network, information fluid changes its properties. The information message can miss few bits of information while getting forwarded. 





 

Combining all three formulas, depending on your initial node, we can calculate through which nodes information will flow at what viscosity and velocity and identify whether your post/message on facebook or twitter will go viral or not.

We can also calculate which nodes (nano influencers) are supposed to be tapped in order to make your post viral and identify natural pockets where information can be fed from where there will be free fluid flow and your message can reach millions.

This exercise is very specific to the node from which you are sending the information in social network, what is your message about and the surrounding nodes/social media profiles to your node or social media profile. Also how distant are the natural pockets/nodes which can distribute your information effectively and the pressure required from social media campaign to push your message or information flow to these nodes.


References:

1. Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces - http://arxiv.org/abs/1012.0119
2. Stability Result for Navier–Stokes Equations with Entropy Transport - http://link.springer.com/article/10.1007%2Fs00021-015-0205-x
3. Entropy measures for complex networks: Toward an information theory of complex topologies - http://arxiv.org/abs/0907.1514
4. On Maximizing the Entropy of Complex Networks - http://www.sciencedirect.com/science/article/pii/S1877050911003875

 





Thursday, July 7, 2022

Next Post- Thank you & DeepWalk

 Hey guys,

Thank you for showering congratulations on me predicting field prize do accurately. And my Ricci Flow video. 



You can see my ensemble here including Swarm Intelligence & Ant colony optimization - https://researchcircle.blogspot.com/2021/12/graph-mining-network-science-topology.html?m=1 

I am going to write new blog on Deepwalk, Quantum walk in social networks, Yang mills, TopologyGAN, ColombGAN, Ricci Flow, very soon. And also on blockchain analytics, GANs in hybrid clinical trials and lot of other things  

I have been superbusy with lot of work, emergencies, and tons of other things. 

For now please feel free to read this primer on DeepWalk from IIT Roorkeehttps://dsgiitr.com/blogs/deepwalk/ 

But, afterall DataHulk in me never takes rest 😉



Thursday, June 9, 2022

Deepwalk, Link Prediction & reinforcement learning

A simple question- 

Can you predict topic of my next blog through topic modeling, Node2Vec,  Deepwalk for Link Prediction & Reinforcement Learning by analyzing previous blogposts… 

3 more hints after 2 weeks  - 

1. 

Interacting topological edge channels - 

 https://www.nature.com/articles/s41567-019-0692-4 

2. Hodgenet, Hodge theory & trading networks 

3. Geometric PDE: Prescribed Curvature Problems, the Ricci Flow, and Yang-Mills Theory - https://smp.uq.edu.au/project/geometric-pde-prescribed-curvature-problems-ricci-flow-and-yang-mills-theory



Tuesday, May 10, 2022

ICM 2018, Hodge theory of Teichmuller curves, CurvGAN, Hodge Loci, Schrodinger Flows, ColombGAN, Yang Mill Connections

Hey Readers,

I used to write a lot about Teichmuller Curves, Hodge Theory, Machine Learning, Schrodinger Flows, Nash Entropy Optimized GANs, Yang Mills & Social Colliderhttps://www.kdnuggets.com/2013/11/yang-mills-million-dollar-connection-twitter-quantum-physics.html ) in 2010 - 2013 on weekends. I expected the following papers/talks will come in in the coming decade using the information topology of research papers of the last 50 years.. and here they come...  

1. Here is an amazing lecture from Anna Wienhard in ICM 2018 on Teichmuller Theory (what was missing in this Field Medal - ICM lecture was mention of CurvGAN, ColombGAN & TopologyGAN for analyzing Hodge, Teichmuller Curves, and other conjectures/topological entities) - 


2. Here is a cool application of CurvGAN on Hodge theory of Teichmuller curves (which becomes really important in analyzing Teichmuller curves through AI & analyze Hodge conjecture, Hodge Loci, etc.) - https://www.uni-frankfurt.de/50569475/Generic_50569475.pdf

with some interesting insights and way to solve Hodge Conjecture.

3. Here is the coolest paper on Schrodinger Flows & Bayesian learning (which has amazing applications in social networks & learning through social networks)https://arxiv.org/abs/2111.10510 

Another application of this is DeepWalk & learning across the networks through optimized navigation (check out some amazing applications of DeepWalk by IIT Roorkee). 

4. Why are we not using TopologyGAN, CurvGAN & ColombGAN to analyze  Yang-Mills?  

So far the latest we have seen after my publication of Yang-Mills & Social Collider... - 

Hermitian–Yang-Mills Connections on Collapsing Elliptically Fibered K3 Surfaces - https://link.springer.com/article/10.1007/s12220-021-00808-9 

  • Emergent Attention on Yang-Mills Space of Connections - https://lukepereira.github.io/notebooks/documents/2021-moduli-attention/main.pdf
  • Yang-Mills theory in highly multiple-connected topologies - https://www.researchgate.net/publication/321462498_Yang-Mills_theory_in_highly_multiple-connected_topologies 
  • The Hyperbolic Yang–Mills Equation for Connections in an Arbitrary Topological Class - https://link.springer.com/article/10.1007/s00220-018-3205-x 





Wednesday, May 4, 2022

12th May, TopologyGAN, CurvGAN..

Hey Readers,

It's Tuesday night 1 AM. It's going to be 12th May next week - Maryam Mirzakhani's Birthday & I am going to celebrate it with some cool blog on Teichmüller theory

First of all, Congrats Gigliola Staffilani
.. Her work on Schrodinger flows in Hyperbolic spaces, Nonlinear dispersive equations is very cool & she just won the National Academy of Sciences awards. If you want to read more about data driven vector soliton solutions of coupled nonlinear vector soliton Schrödinger equation, please read my Jan 10 blog.. - https://researchcircle.blogspot.com/2022/01/interesting-case-of-schrodinger.html

Coming back to Ricci Curvature & GANs, there is a very interesting paper on
CurvGANs & Ricci Curvature by Jianxin Li - https://arxiv.org/abs/2203.01604

The importance of this paper on CurvGANs along with TopologyGAN in applied sense is as follows - 

1. Predicting link in market topology & market failure to further my concept of Ricci Curvature - https://researchcircle.blogspot.com/2022/02/job-posting-paper-ricci-flow-economics.html 

2. Predicting information flow in social networks using Ricci Curvature & Ricci Flow as explained in my previous blogs. 

3. This can also be applied on another paper on Schrödinger equation in a general curved spacetime geometry to predict curvature of the spacetime geometry, Schwarzschild black hole & solve information paradox - https://www.worldscientific.com/doi/10.1142/S0218271822500183

4. Also, to further the analysis of an old paper (1949) by Abel Prize winner John Milnor by on Total Curvature of Knots.. Yes.. at least 73 years back. 
 

5. There might be possible applications of TopologyGAN & CurvGAN in Pointwise Convergence of the Schrödinger Flow which is portrayed & further researched in the following paper - https://arxiv.org/abs/1907.11192