summaryrefslogtreecommitdiff
path: root/doc/latex/latex/models/nullmodels
diff options
context:
space:
mode:
Diffstat (limited to 'doc/latex/latex/models/nullmodels')
-rw-r--r--doc/latex/latex/models/nullmodels/model_MDM.tex37
-rw-r--r--doc/latex/latex/models/nullmodels/model_MSM.tex38
-rw-r--r--doc/latex/latex/models/nullmodels/model_hypergeometric.tex33
-rw-r--r--doc/latex/latex/models/nullmodels/model_layer_growth.tex46
4 files changed, 154 insertions, 0 deletions
diff --git a/doc/latex/latex/models/nullmodels/model_MDM.tex b/doc/latex/latex/models/nullmodels/model_MDM.tex
new file mode 100644
index 0000000..dd754b8
--- /dev/null
+++ b/doc/latex/latex/models/nullmodels/model_MDM.tex
@@ -0,0 +1,37 @@
+\myprogram{{model\_MDM.py}}
+ {Multi-activity Deterministic Model.}
+ {$<$Bi\_file$>$ $<$M$>$}
+
+\mydescription{This is the Multi-activity Deterministic Model (MDM).
+ In this model each node $i$ is considered active if it was
+ active in the reference multiplex, maintains the same value
+ of node activity $B_i$ (i.e., the number of layers in which
+ it was active) and is associated an activity vector sampled
+ uniformly at random from the $M\choose{B_i}$ possible
+ activity vectors with $B_i$ non-null entries.
+
+ The file \textit{Bi\_file} is in the format:
+
+ \hspace{0.5cm} \textit{Bi N(Bi)}
+
+ where \textit{Bi} is a value of node activity
+ and \textit{N(Bi)} is the number of nodes which had node
+ activity equaly to \textit{Bi} in the reference multiplex.
+
+ The parameter \textit{M} is the number of layers in the
+ multiplex.
+}
+
+
+\myreturn{The program prints on \texttt{stdout} a distribution of
+ bit-strings, in the format:
+
+ \hspace{0.5cm} \textit{Bi bitstring count}
+
+ where \textit{bitstring} is the activity
+ bitstring, \textit{Bi} is the number of non-zero entries
+ of \textit{bitstring} and \textit{count} is the number of
+ times that \textit{bitstrings} appear in the null model.}
+
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/models/nullmodels/model_MSM.tex b/doc/latex/latex/models/nullmodels/model_MSM.tex
new file mode 100644
index 0000000..e3c8abf
--- /dev/null
+++ b/doc/latex/latex/models/nullmodels/model_MSM.tex
@@ -0,0 +1,38 @@
+\myprogram{{model\_MSM.py}}
+ {Multi-activity Stochastic Model.}
+ {$<$node\_Bi\_file$>$ $<$M$>$}
+
+\mydescription{This is the Multi-activity Stochastic Model (MSM).
+ In this model each node $i$ is considered active if it was
+ active in the reference multiplex, and is activated on
+ each layer with a probability equal to $B_i/M$ where $B_i$
+ was the activity of node $i$ in the reference multiplex.
+
+ The file \textit{node\_Bi\_file} is in the format:
+
+ \hspace{0.5cm} \textit{node\_i Bi)}
+
+ where \textit{Bi} is the value of node activity
+ of \textit{node\_i} in the reference multiplex.
+
+
+ The parameter \textit{M} is the number of layers in the
+ multiplex.
+}
+
+\myreturn{The program prints on \texttt{stdout} a node-layer list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{node\_i layer\_i}
+
+ where \textit{node\_i} is the ID of a node and \textit{layre\_i} is
+ the ID of a layer. This list indicates which nodes are active in
+ which layer. For instance, the line:
+
+ \hspace{0.5cm} \textit{24 3}
+
+ indicates that the node with ID \textit{24} is active on
+ layer \textit{3}.
+}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/models/nullmodels/model_hypergeometric.tex b/doc/latex/latex/models/nullmodels/model_hypergeometric.tex
new file mode 100644
index 0000000..0315c7b
--- /dev/null
+++ b/doc/latex/latex/models/nullmodels/model_hypergeometric.tex
@@ -0,0 +1,33 @@
+\myprogram{{model\_hypergeometric.py}}
+ {Hypergeometric node activity null model.}
+ {$<$layer\_N\_file$>$ $<$N$>$}
+
+\mydescription{This is the hypergeometric model of node activation. In
+ this model each layer has exactly the same number of active
+ node of a reference multiplex network, but nodes on each
+ layer are activated uniformly at random, thus destroying all
+ inter-layer activity correlation patterns.
+
+ The file \textit{layer\_N\_file} reports on the n-th line
+ the number of active nodes on the n-th layer (starting from
+ zero). The second parameter \textit{N} is the total number
+ of active nodes in the multiplex.
+ }
+
+
+\myreturn{The program prints on \texttt{stdout} a node-layer list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{node\_i layer\_i}
+
+ where \textit{node\_i} is the ID of a node and \textit{layre\_i} is
+ the ID of a layer. This list indicates which nodes are active in
+ which layer. For instance, the line:
+
+ \hspace{0.5cm} \textit{24 3}
+
+ indicates that the node with ID \textit{24} is active on
+ layer \textit{3}.
+}
+
+\myreference{\refcorrelations}
diff --git a/doc/latex/latex/models/nullmodels/model_layer_growth.tex b/doc/latex/latex/models/nullmodels/model_layer_growth.tex
new file mode 100644
index 0000000..9c0bb12
--- /dev/null
+++ b/doc/latex/latex/models/nullmodels/model_layer_growth.tex
@@ -0,0 +1,46 @@
+\myprogram{{model\_layer\_growth.py}}
+ {Layer growth with preferential activation model.}
+ {$<$layer\_N\_file$>$ $<$N$>$ $<$M0$>$ $<$A$>$ [RND]}
+
+\mydescription{This is the model of layer growth with preferential
+ node activation. In this model an entire new layer arrives
+ at time $t$ and a number of nodes $N_t$ is activated ($N\_t$
+ is equal to the number of nodes active on that layer in the
+ reference multiplex). Then, each node $i$ of the new layer
+ is activated with a probability:
+
+ \begin{equation*}
+ P_i(t) \propto A + B_i(t)
+ \end{equation*}
+
+ where $B_i(t)$ is the activity of node $i$ at time $t$
+ (i.e., the number of layers in which node $i$ is active at
+ time $t$) while $A>0$ is an intrinsic attractiveness.
+
+ The file \textit{layer\_N\_file} reports on the n-th line
+ the number of active nodes on the n-th layer.
+
+ The parameter \textit{N} is the number of nodes in the
+ multiplex, \textit{M0} is the number of layers in the
+ initial network, \textit{A} is the value of
+ node attractiveness.
+
+ If the user specifies \texttt{RND} as the last parameter,
+ the sequence of layers is }
+
+\myreturn{The program prints on \texttt{stdout} a node-layer list of lines in the
+ format:
+
+ \hspace{0.5cm} \textit{node\_i layer\_i}
+
+ where \textit{node\_i} is the ID of a node and \textit{layre\_i} is
+ the ID of a layer. This list indicates which nodes are active in
+ which layer. For instance, the line:
+
+ \hspace{0.5cm} \textit{24 3}
+
+ indicates that the node with ID \textit{24} is active on
+ layer \textit{3}.
+}
+
+\myreference{\refcorrelations}