# Random Thoughts

## A list of brief questions and thoughts

^{99} MISC

Published: 2020-10-08

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Summary: Plasticity Related to Neurogenisis and PCD Ryu20161 have found neurogenisis in adult mammalian brains. Combined with programmed cell death (PCD), this can serve as plasticity on a large timescale.
Origami and Neuron Activities I attended a talk on 01/18/2018. The speaker presented his research on the relation between cosmic web, spiderweb, and origami. The idea is that cosmic web is like origami folding in phase space (position, and velocity). He started with a grid and used Zeldovich approach to move the vertices around to simulate the condensation of dark matter.

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^{9} Cosmic Rays and Neuroscience

Published: 2020-10-08

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Summary: References Parihar, V. K., Allen, B. D., Caressi, C., Kwok, S., Chu, E., Tran, K. K., … Limoli, C. L. (2016). Cosmic radiation exposure and persistent cognitive dysfunction. Scientific Reports, 6(June), 1–14. Parihar, V. K., Allen, B., Tran, K. K., Macaraeg, T. G., Chu, E. M., Kwok, S. F., … Limoli, C. L. (2015). What happens to your brain on the way to Mars. Science Advances, 1(4), e1400256.

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^{8} Factor Graph

Published: 2020-10-08

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Summary: In the propagation of information, we are usually dealing with such relations that some system (factor) $ f$ is related to some inputs (variable) $ x$.
Factor graph builds such networks of relations. In such a graph, we use boxes to represent factors, and circles to represent variables.
From Factor Graph @ Wikipedia
Suppose we need to find out the probability of factor $ f_4$, we have to take in the two variables $ X_2$ and $ X_3$.

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^{7} Spin Glass

Published: 2020-10-08

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Summary: In the realm of physics, Ising model has been and probably will be an useful model for our intuition. Naively speaking, our world is full of local interactions yet the consequences are very likely to be long range through long range correlations. The famous Ising model is a key model of such concepts.
Ising model deals with a system of spins and their interactions. To build up the dynamics of a system, we need the configuration of it as well as the interactions.

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^{6} Mean-field Method

Published: 2020-10-08

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Summary: Mean-field is a concept in statistical mechanics to approximately treat the many body problem. It is an effective theory.
Paramagnetic Material In paramagnetic materials, the “polarized” spins $ {s_i}$ determine the overall “magnetization” of the material. When the spins are all aligned, we get the maximium “magnetization”. If the directions of the spins are completely random, the material is not “magnetized”. In other words, we can use a quantity $ m=\langle s \rangle$, which is called magnetization, to represent how well the overall “magnetization” of the material is.

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^{5} Neuron2vec

Published: 2020-10-08

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Summary: Embedding is the key.
What is neuron2vec? The story starts from word2vec. In language processing, they developed a method to represent words in vectors so that we can actually calculate how similar two words are or even predict the next word using a given context.
Suppose we have found the vector representations of two words dog and cat, which are $\mathbf v_1$ and $\mathbf v_2$, the similarity between these two words are calculated as

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^{4} Logic Decomposition of Networks

Published: 2020-10-08

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Summary: In the ink notes I have explained the basics of the idea. However, I didn’t derive an relation between the network connection coefficients and the logic unit coefficients.
We’ll only consider spin 1/2 nodes, hence Ising model but the spins could be fully connect.
Review of Ink Notes Basically, the equation we need to solve is
$$ \begin{align} &\sum_{ij} J_{ij}s_is_j + \sum_i K_i s_i\\ =& \sum_{ij}A_{ij}(1+s_i s_j) \\ &+ \sum_{ijk} B_{ijk} \left( 3 + (-s_i -s_j + 2s_k) + s_i s_j - 2 s_i s_k -2 s_j s_k \right)\\ &+\sum_{ijk} C_{ijk} \left( 3 - (-s_i -s_j + 2s_k) + s_i s_j - 2 s_i s_k -2 s_j s_k \right) \end{align} $$ In this expression, $A_{ij}$ is the coefficient for NOT logic calculation, $B_{ijk}$ is the coefficient for AND logic calculation, and $C_{ijk}$ is the coefficient for OR logic calculation.

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^{3} Binary Human Model

Published: 2020-10-08

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Summary: Han has been discussing with me about building human dynamics by making analogy to neural systems.
The idea is to treat every human as an activation function which is connected to each other to form a large network. The trouble was how to deal with information input and output from outside of the group which is similar to external stimulation in neural systems.
A Simplified Model Here we develop a model for wechat groups instead of general human dynamics.

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^{2} Why Can We Understand the Universe?

Published: 2020-10-08

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Summary: Our brain contains significantly less degrees of freedom than the whole universe. Yet we are developing a very good understanding of whole universe.
One of the interesting points is that the universe doesn’t go through all the possible states of its configuration. There are many constraints on the universe that forbids it from developing into many other states. Thus we could understand the restrictions thus grasp the key of the state of the universe.

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^{1} Pan-Intelligence

Published: 2020-10-08

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Summary: Biological neural networks give us human intelligence. Are biological neural networks special out of the numerous different kinds of network systems, e.g., internet, social networks, and artifical neural networks?
I prefer to believe they are not special just with the right topology.
So what is a list of all systems that could function as a neural network?
Social networks. We could model the society as an information processing network. It is extremely complicated, at least more complicated than the models in physics.

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