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Diffstat (limited to 'doc/latex/latex/dynamics')
5 files changed, 118 insertions, 0 deletions
diff --git a/doc/latex/latex/dynamics/Ising/multiplex_ising.tex b/doc/latex/latex/dynamics/Ising/multiplex_ising.tex new file mode 100644 index 0000000..ec87454 --- /dev/null +++ b/doc/latex/latex/dynamics/Ising/multiplex_ising.tex @@ -0,0 +1,22 @@ +%%% +%%% Layer activity +%%% + +\myprogram{{multiplex\_ising}} + {compute the coupled ising model in a multiplex with $2$ layers.} + {$<$layer1$>$ $<$layer2$>$ $<$T$>$ $<$J$>$ $<\gamma>$ $<h^{[1]}>$ $<h^{[2]}>$ $<p_1>$ $<p_2>$ $<num epochs>$} + +\mydescription{Compute and print the output of the ising dynamics on two coupled layers of a multiplex network. + Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. + + $T$ is the value of thermal noise in the system, $J$ the value of peer pressure, $\gamma$ the relative ratio between internal coupling and peer pressure, $h^{[1]}$ and $h^{[2]}$ the external fields acting on the two layers, $p_1$ the probability for a spin on layer $1$ at $t=0$ to be up, $p_2$ the same probability for spins on layer $2$, $num epochs$ the number of epochs for the simulation.} + +\myreturn{One line, reporting all controlling parameter, the value of consensus in layer $1$ $m^{[1]}$, the value of consensus in layer $2$ $m^{[2]}$ and the coherence $C$.} + +\myreference{\refising} diff --git a/doc/latex/latex/dynamics/randomwalks/entropyrate2add.tex b/doc/latex/latex/dynamics/randomwalks/entropyrate2add.tex new file mode 100644 index 0000000..98a432b --- /dev/null +++ b/doc/latex/latex/dynamics/randomwalks/entropyrate2add.tex @@ -0,0 +1,24 @@ +%%% +%%% Layer activity +%%% + +\myprogram{{entropyrate2add}} + {compute the entropy rate of additive biased walks in a multiplex with $2$ layers.} + {$<$layer1$>$ $<$layer2$>$ $<overlapping network>$ $<$N$>$ $b_1$ $b_2$} + +\mydescription{Compute and print the entropy rate of an additive biased walk in a multiplex with $2$ layers and bias parameters $b_1$ and $b_2$. + Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. + + The file \textit{overlapping network} has also a third column indicating the number of times two nodes are connected across all layers. + + $N$ is the number of nodes, $b_1$ is the degree-biased exponent for layer $1$, $b_2$ is the degree-biased exponent for layer $2$.} + +\myreturn{One line, reporting the value of the entropy rate $h$ of an additive biased random walks with $b_1$ and $b_2$ as bias exponents, $b_1$ and $b_2$.} + +\myreference{\refbiased} diff --git a/doc/latex/latex/dynamics/randomwalks/entropyrate2int.tex b/doc/latex/latex/dynamics/randomwalks/entropyrate2int.tex new file mode 100644 index 0000000..8a337f4 --- /dev/null +++ b/doc/latex/latex/dynamics/randomwalks/entropyrate2int.tex @@ -0,0 +1,24 @@ +%%% +%%% Layer activity +%%% + +\myprogram{{entropyrate2int}} + {compute the entropy rate of intensive biased walks in a multiplex with $2$ layers.} + {$<$layer1$>$ $<$layer2$>$ $<overlapping network>$ $<$N$>$ $b_1$ $b_2$} + +\mydescription{Compute and print the entropy rate of an intensive biased walks in a multiplex with $2$ layers and bias parameters $b_p$ and $b_o$. + Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. + + The file \textit{overlapping network} has also a third column indicating the number of times two nodes are connected across all layers. + + $N$ is the number of nodes, $b_p$ is the biased exponent on the participation coefficient, $b_o$ is the biased exponent on the overlapping degree.} + +\myreturn{One line, reporting the value of the entropy rate $h$ of an intensive biased random walks with $b_p$ and $b_o$ as bias exponents, $b_p$ and $b_o$.} + +\myreference{\refbiased} diff --git a/doc/latex/latex/dynamics/randomwalks/entropyrate2mult.tex b/doc/latex/latex/dynamics/randomwalks/entropyrate2mult.tex new file mode 100644 index 0000000..7abfecd --- /dev/null +++ b/doc/latex/latex/dynamics/randomwalks/entropyrate2mult.tex @@ -0,0 +1,24 @@ +%%% +%%% Layer activity +%%% + +\myprogram{{entropyrate2mult}} + {compute the entropy rate of multiplicative biased walks in a multiplex with $2$ layers.} + {$<$layer1$>$ $<$layer2$>$ $<overlapping network>$ $<$N$>$ $b_1$ $b_2$} + +\mydescription{Compute and print the entropy rate of a multiplicative biased walk in a multiplex with $2$ layers and bias parameters $b_1$ and $b_2$. + Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. + + The file \textit{overlapping network} has also a third column indicating the number of times two nodes are connected across all layers. + + $N$ is the number of nodes, $b_1$ is the degree-biased exponent for layer $1$, $b_2$ is the degree-biased exponent for layer $2$.} + +\myreturn{One line, reporting the value of the entropy rate $h$ of an multiplicative biased random walks with $b_1$ and $b_2$ as bias exponents, $b_1$ and $b_2$.} + +\myreference{\refbiased} diff --git a/doc/latex/latex/dynamics/randomwalks/statdistr2.tex b/doc/latex/latex/dynamics/randomwalks/statdistr2.tex new file mode 100644 index 0000000..09c1bc2 --- /dev/null +++ b/doc/latex/latex/dynamics/randomwalks/statdistr2.tex @@ -0,0 +1,24 @@ +%%% +%%% Layer activity +%%% + +\myprogram{{statdistr2}} + {compute the stationary distribution of additive, multiplicative and intensive biased walks in a multiplex with $2$ layers.} + {$<$layer1$>$ $<$layer2$>$ $<overlapping network>$ $<$N$>$ $b_1$ $b_2$} + +\mydescription{Compute and print the stationary distribution of additive, multiplicative and intensive biased walks in a multiplex with $2$ layers. + Files \textit{layer1}, \textit{layer2}, contain the (undirected) edge list of the two layer, and each + line is in the format: + + \hspace{0.5cm}\textit{src\_ID} \textit{dest\_ID} + + where \textit{src\_ID} and \textit{dest\_ID} are the IDs of the two + endpoints of an edge. + + The file \textit{overlapping network} has also a third column indicating the number of times two nodes are connected across all layers. + + $N$ is the number of nodes, $b_1$ is the first bias exponent (the bias exponent for layer $1$ for additive and multiplicative walks, the bias exponent on the participation coefficient for intensive walks), $b_2$ is the second bias exponent (the bias exponent for layer $1$ for additive and multiplicative walks, the bias exponent on the participation coefficient for intensive walks).} + +\myreturn{N lines. In the n-th line we report the node ID, the stationary distribution of that node for additive walks with exponents $b_1$ and $b_2$, the stationary distribution for multiplicative walks with exponents $b_1$ and $b_2$, the stationary distribution for multiplicative walks with exponents $b_1$ and $b_2$, the values of the bias exponents $b_1$ and $b_2$.} + +\myreference{\refbiased} |