Differences

This shows you the differences between two versions of the page.

--- jy:results [2018/07/26 02:04] – [7.24.18 Inverse Problem] yiling
+++ jy:results [2019/09/16 09:22] (current) – [2019-09-16 :Case N1: long tail antiferromagentic] yiling
@@ Line 1: / Line 1: @@
+[[namespace:page#here|2019-09-16 :Case N1: long tail antiferromagentic]]
 ====== 2018-07-2 :The solutions to the inverse Ising problem  ======
@@ Line 93: / Line 97: @@
 ====== 7.19.18 Inverse Problem  ======
-The mean field theory (nMF):
+{{page>dynstat:mean-field}}
-$\mathbf{J}^\text{nMF}=-\mathbf{C}^{-1}, (i \neq j) $,
-$h_{i}^\text{nMF}=\tanh^{-1}\left< s_{i} \right>-\sum_{j=1}^{N} J{ij}^\text{nMF}\left< s_{j} \right> $ .
-The independent-pair theory (IP):
-$J_{ij}^\text{pair}=0.25*\ln\left[ \frac{(1+m_{i}+m_{j}+C_{ij}^{*}) (1-m_{i}-m_{j}+C_{ij}^{*})} {(1-m_{i}+m_{j}-C_{ij}^{*})(1+m_{i}-m_{j}-C_{ij}^{*})} \right]$, with $C_{ij}^{*}=C_{ij}+m_{i}m_{j} , (i \neq j)$
-$h_{i}^\text{pair}=0.5*\ln\left( \frac{1+m_{i}} {1-m_{i}} \right)-\sum_{j=1}^{N} J_{ij}^\text{pair} m_{j}$.
-The Thouless-Anderson-Palmer theory (TAP):
-$\mathbf{C}^{-1}+J_{ij}^\text{TAP}+2(J_{ij}^\text{TAP})^{2}m_{i}m_{j}=0 , (i \neq j)$
-$h_{i}^\text{TAP}=h_{i}^\text{nMF}-m_{i}\sum_{i=1}^{N} (J_{ij}^\text{TAP})^{2} (1-m_{j})^{2}$.
-The Sessak and Monasson theory (SM):
-$J_{ij}^\text{SM}=J_{ij}^\text{nMF}+J_{ij}^\text{pair}-\frac{C_{ij}}{(1-m_{i}^{2})(1-m_{j}^{2})-C_{ij}^{2}} , (i \neq j)$
-$h_{i}^\text{SM}=0.5*\ln\left( \frac{1+m_{i}} {1-m_{i}} \right)-\sum_{j=1}^{N} J_{ij}^\text{SM} m_{j}$.
 The coefficient of $R^{2}$ is:
@@ Line 324: / Line 303: @@
 {{jy:h20_0.22t1.png}}
 {{jy:j20_0.22t1.png}}
+====== 7.30.18 Inverse Problem data ======
+{{jy:j78.png}}
+{{jy:ha78.png?450}}
+{{jy:ja78.png?450}}
+{{jy:j781.png}}
+{{jy:h78a1.png?450}}
+{{jy:j78a1.png?450}}

Lab Comp Bio Net

User Tools

Differences