Ricci Flow, Pruning & Convergence, Interconnectedness of Financial Systems, CytoScape

Hey Readers,

I have been superbusy lately. If some of my readers remember.. I used to write a lot about Spin Bayesian Neural Networks a decade back. Here it comes in the hardware industry in the applied way
1. All-Spin Bayesian Neural Networks - https://arxiv.org/abs/1911.05828
2. Hardware implementation of Bayesian network building blocks with stochastic spintronic devices - https://www.nature.com/articles/s41598-020-72842-6

 

Coming back to the blog... this blogpost which is divided into 2 parts -

1. Ricci Flow & Convergence
2. Amazing & brilliant article by Joseph Stiglitz on interconnectedness between banks & recovery

1. Ricci Flow & Convergence -
Gradient inequality and convergence to steady-states of the normalized Ricci flow on surfaces - This study the problem of convergence of the normalized Ricci flow evolving on compact Riemannian surfaces without boundary - https://www.sciencedirect.com/science/article/pii/S0362546X22000797

Ricci flow and a sphere theorem for Ln/2-pinched Yamabe metrics - differential sphere and Ricci flow convergence theorem for positive scalar curvature Yamabe metrics with Ln/2 -pinched curvature in general dimensions n - https://www.sciencedirect.com/science/article/pii/S000187082100493X

For more reference on EconoPhysics, you should read my earlier blog on Ricci Flow & market Fragility - https://researchcircle.blogspot.com/2022/02/job-posting-paper-ricci-flow-economics.html 

(which talks about Ricci curvature: An economic indicator for market fragility and systemicrisk - https://www.researchgate.net/publication/303600815_Ricci_curvature_An_economic_indicator_for_market_fragility_and_systemic_risk which is an analysis based on geometric feature extraction on network data of daily returns from a set of stocks & market topology comprising the Standard and Poor’s 500 (S&P 500) over a 15-year span to highlight the fact that corresponding changes in Ricci curvature, is negatively correlated to increases in network fragility)

Ricci Flow & Local Fragility 

I will talk more about Marc Cuban's DogeSphere, market fragility, Nash equilibrium of twitterSphere later along with market fragility - convergence to steady-states of the normalized Ricci flow & Yamabe Metric later. 

2. A brilliant article by Nobel Laureate Joseph Stiglitz which talks about The interconnected structure of the financial system which has been a focal point of debate among policymakers - https://voxeu.org/article/collective-moral-hazard-and-interbank-market

This column offers a theory to help explain the structure of the financial system and its consequences for risk-taking and systemic risk through network sciences & graph mining (implied through study of interconnectedness of the banks & financial institutions).

 

Gita Gopinath would agree with this brilliant article on based on her IMF blogs on asynchronous yet divergent recovery & capital flows. The Nash Equilibrium during a crisis, the government optimally bails out bank which is interconnected to prevent the inefficiencies associated with their failure (The optimum path to recovery that I have been writing about in this blog). This can be a very cool exercise for CytoScape. 

This article also talks about Channels of interconnectedness - 

The first channel through which interconnectedness alters risk-taking is represented by the top arrow in Figure. Since downside risk is implicitly insured by the government, the interbank market channels fund investment opportunities with high upside risk. As a result, the institutions which become large and interconnected (SIFIs) are those with relatively risky portfolios. 

The second channel through which interconnectedness alters risk-taking, represented by the middle arrow in Figure, is that the implicit insurance offered by a SIFI's liabilities (through the endogenously determined contracts) enables smaller, peripheral institutions to hold excessively risky assets, even though they do not directly benefit from bailouts themselves. This channel causes the resources of smaller, peripheral banks to be concentrated in excessively risky projects. Through these two channels, interconnectedness may lead to widespread excessive risk-taking, increasing the risk of crisis.

This makes me think of channel pruning (from Point 1 & Point 2) of channels through Ricci Flow - Curvature-guided Pruning of High-performance Networks Using Ricci Flow for optimum recovery. 

This is kind of inspiration from my 2017 SDSU lecture on Ricci Flow & Neural Networks Pruning (and a paper which followed that on
RicciNets: Curvature-guided Pruning of High-performance Neural Networks Using Ricci Flow) applied towards financial interconnected networks which almost behave in the similar way..

Also think about a convergence to steady states of financial systems through Ricci Flow & EconoPhysics..