text:
\section{Introduction}
Recently, the relation among complex networks,  their geometry  and evolution \cite{RMP,Newman_rev,Boccaletti2006},  and   more traditional fields of physics  such as  quantum physics and quantum communication \cite{Cirac,Calsamiglia,Sachdev,Ising,Hubbard,JCH}, quantum information \cite{Quantuminformation}, cosmology \cite{Cosmology} and quantum gravity \cite{Rovelli,Rovelli2,triangulations} are starting to attract the interest of scientists.

For instance, an interesting aspect of complex network evolution is that in major examples of realistic models for complex networks growth,
quantum statistics emerge as important distributions determining the network dynamics.
In fact, the  evolution of scale-free networks with fitness of the nodes \cite{Fitness} is described by the  Bose-Einstein statistics and this model can be therefore mapped to a Bose gas. In correspondence of the  Bose-Einstein condensation \cite{Bose} of the Bose gas, the network topology undergoes a major structural condensation transition in which a node is linked to a finite fraction of links. This model can explain the emergence of ``super-hubs" in complex networks and the  ``winner-takes-all" phenomenon.  Interestingly  the evolution of  Cayley trees with fitness  of the nodes, is determined by the Fermi-Dirac statistics \cite{Fermi,Complex}. In addition to that, it has also been found that ensembles of complex networks  have been shown to be related with quantum statistics \cite{Garlaschelli}.  Finally, it has been shown that random geometric networks on a hyperbolic space can show a scale-free network topology \cite{Hyperbolic,Navigability} and that growing networks in hyperbolic space define the  so called ``network cosmology" \cite{Cosmology}.
 From the quantum information perspective, complex networks encode relevant information in their structures, and new quantum entropy measures have been proposed in order to characterize and quantify this information \cite{Vonneuman,Garnerone,Jesus2}.Moreover, the  quantum random walk can be used to propose  different definitions of quantum PageRank on networks \cite{Garneronegoogle,Jesus1,Faccin,Zimboras,Caldarelli}.

Multiplex networks are multilayer network structures that are attracting large interest \cite{PhysicsReports,Kivela}. In fact they are able to describe several  types of interactions between the same set of nodes. For example, social networks, where the same people are connected by different means of communications, or different types of social ties, like friendship, collaboration, co-authorship, and so on are better described by multiplex networks.
Similarly,  if we want to describe diffusion in transportation networks we need to consider the multiplex nature of the underlying transportation networks, where  a given  location can be linked to other locations by different types of transportation, train, bus, airplane etc.
Finally, in brain networks the large variety of neuron types and types of interactions between them, will   not be fully understood  if the multilayer approach is not adopted \cite{Bullmore,Makse,Liaisons}.
Multilayer have a highly non trivial structure including communities \cite{Mason} and many different types of encoded structural correlations \cite{PRE,Goh,Vito}. Recently  some quantum information measures such as the Von Neumann entropy of single networks \cite{Vonneuman} have been extended to multilayer networks in order to quantify their complexity  \cite{Math}.

Multiplex networks are formed by layers that are usually scale-free and have a number of nodes that increases in time. For these reasons their evolution can be described by growing multiplex networks models \cite{Growth1,Growth2,Nonlinear}.
In single layer networks growing network models \cite{BA,Fitness,Bose} are able to explain the spontaneous emergence of scale-free degree distribution. In particular   the most fundamental growing network model, the Barab\'asi-Albert (BA) model \cite{BA} includes  only two dynamical rules: growth and preferential attachment, meaning that at each time a new node is added to the network and it attaches links preferentially to high degree nodes.
Just these two elements of the model have been shown to be responsible for a scale-free degree distribution of exponent $\gamma=3$.
An important element determining network evolution is the intrinsic quality of the nodes, determining their fitness that make them more likely to acquire new links, with respect to other nodes with the same degree \cite{Fitness}.
The dynamics of single  growing scale-free networks with fitness of the nodes can be mapped to a Bose gas \cite{Bose}  giving rise to the intriguing phenomenon of the Bose-Einstein condensation, while growing Cayley trees with fitness of the nodes  can be mapped to a Fermi gas\cite{Fermi} by using a similar mathematical formalism.

In the context of multiplex networks, growing multiplex networks models have been shown   to generate multiplex networks with different degree distributions in the different layers, and different pattern of correlations \cite{PRE, Goh,Vito} between the degrees of the same node in different layers \cite{Growth1,Growth2,Nonlinear}. Nevertheless the role of the fitness of the nodes on growing multiplex networks models has not yet been explored.
Here we combine the process of link addition and the process of rewiring of the links in presence of an intrinsic fitness of the nodes. We show that the network growth can  exploit the symmetries of the multiplex networks and we can  generate scale-free supersymmetric multiplex networks described by coupled Fermi-Dirac and Bose-Einstein statistics. Moreover, we explore  the information content of these structures with quantum information tools by extending the definition of entanglement entropy of single networks \cite{Garnerone} to multiplex structures. To this end we map each each network in a given layer to a quantum network state and we  describe the complexity of each layer of the  multiplex networks by calculating the entanglement entropies of these quantum states. Finally  we relate  the entanglement entropies  of the layers of the supersymmetric multiplex network to  the entropy rate of the multiplex network.
The entropy rate \cite{Entropyrate} of the supersymmetric multiplex model  describes the rate at which the typical number of multiplex networks, which can be realized during the dynamics, grows in time.
Therefore here we show  that the entanglement entropies of the layers of the supersymmetric network, which  extract information  form a snapshot of the multiplex network using quantum information tools,  have a very simple relation with the entropy rate of the same supersymmetric  multiplex network, describing the classical non-equilibrium dynamics of the multilayer structure.

The paper is structured as follows:
In section II we define the supersymmetric multiplex model and we provide its mean-field solution.
In section III we characterize the supersymmetric multiplex structural properties.
In section IV we define the entropy rate of the supersymmetric multiplex network.
In section V evaluate the  entanglement entropies of the layers  of the supersymmetric multiplex network.
In section VI we relate the entanglement entropies of the layers of the supersymmetric multiplex network  with its entropy rate.
Finally in section VII we give the conclusions.

We note here that for simplicity in  the main text of the paper  we consider only the case of a duplex (i.e. a multiplex with $M=2$), but the analysis can be easily extended to a multiplex with a generic value of the number of layers $M$.
Therefore in  the appendix the extension to supersymmetric multiplex networks with generic value of $M$ is discussed.
\section{ supersymmetric multiplex network model}
\subsection{The supersymmetric multiplex evolution}
A multiplex network is a multilayer system  formed by $N$ nodes having a copy (or replica) in each of the  $M$ layers, and $M$ layers formed by different networks of interactions between the $N$ nodes.
Here we assume that each node $i$ has quenched quality quantified by the  quenched parameter $\epsilon_i\in (0,1)$ called the energy of the node and we indicate by
\begin{eqnarray}
\eta_i=e^{-\beta\epsilon_i}
\end{eqnarray}
the fitness of the node $i$, determined both by its energy and a global parameter $\beta>0$.
On single layers it has been shown \cite{Fitness,Bose} that the fitness of the nodes is able to explain how some nodes (the more fit) acquire links at a faster rate than others, as observed in a variety of complex networks, including the Internet and the World-Wide-Web.
In particular, in these models it is assumed that  each new node links preferentially to nodes of high degree and high fitness, with a probability $\Pi_i$ that it attaches a new link to a node $i$ given by
\begin{eqnarray}
\Pi_i=\frac{\eta_i k_i}{\sum_j \eta_jk_j}=\frac{e^{-\beta\epsilon_i}k_i}{\sum_j e^{-\beta\epsilon_j}k_j},
\end{eqnarray}
where $k_i$ is the degree of node $i$, in this way generalizing the dynamics of the famous BA model \cite{BA} in which the preferential attachment is only driven by the degree of the nodes.

When considering the evolution of technological, social or transportation multilayer networks, a similar mechanism can be taken into account.
Nevertheless t,he new links of  a given layer might be added also according to a preferential attachment mechanism deriving from the popularity of a node in another layer. This model the case in which   a popular node in one layer  attracts also links in another layer.  Moreover, it can also happen that, instead, the popularity of a node in a layer is modulated by a process of rewiring of the links, and that links attached to popular nodes in one layer are more likely to be rewired. This could mimic the case in which the connectivities of hubs are damped by the process of  link rewiring.
We consider for simplicity a multiplex networks formed by $M=2$ layers and we describe its evolution as a growing multiplex network model in which each node has a given energy and corresponding fitness.  Specifically, we consider the case in which in the dynamics in the two networks is not symmetrical. In one layer new links are exclusively added according to a generalized preferential attachment which rewards high fitness nodes of high degree in either one of the layers, and  in the other layer the links are attached but also rewired in such a way to reduce the growth of the degree of high fitness nodes in that layer. This model can be generalized to a multiplex networks with larger number of layers in which the layer can be divided in two groups, each group of layer behaving in a similar way. In order to keep the description of the model simple we now focus on the case in which $M=2$, discussing in the appendix  the generalization to the general value of $M$.
We   start at $t=0$ from a small set of nodes $N_0$ connected in both layers.
Each node $i$ of the network has degrees $k^{[1]}_i,k^{[2]}_i$ respectively in layer 1 and layer 2, and energy $\epsilon_i$ drawn from a $g(\epsilon)$ distribution.
At each time  $t$ we add a node  to the multiplex network, each node has two replicas nodes, one on each layer. Moreover, each replica node is  initially attached to $m$ existing nodes in the same layer. In the following we will  indicate with $l$ the number of network changes, i.e. links additions or link rewirings,  occurring in each layer  starting from time $t=1$. After time $t$ we will have $l=mt$.
For each   network change in layer 1  we follow the subsequent procedure:
\begin{itemize}
\item We extract a number $\sigma^{[1]}_l=1,2$. The event $\sigma^{[1]}_l=1$ occurs  with  probability  $p^{[1]}(1)=\alpha$ while the event $\sigma_l^{[1]}=2$ occurs with probability   $p^{[1]}(2)=1-\alpha$.
\item If $\sigma^{[1]}_l=1$   the new node is attached  in layer 1  to a node $i^{[1]}_l$ chosen with probability
\begin{eqnarray}
\Pi^{[1,1]}\left(i_l^{[1]}=i\right)=\frac{e^{-\beta \epsilon_i}k_i^{[1]}}{\sum_j e^{-\beta \epsilon_j}k_j^{[1]}},
\end{eqnarray}
i.e. it will be attached preferentially to nodes with low energy and high degree in layer 1,  according to a generalized preferential attachment.
Instead, if $\sigma^{[1]}_l=2$ the new  node  is attached in layer 1 to a node $i^{[1]}_l$ chosen with probability
 \begin{eqnarray}
\Pi^{[1,2]}\left(i_l^{[1]}=i\right)=\frac{e^{-\beta \epsilon_i}k_i^{[2]}}{\sum_j e^{-\beta \epsilon_j}k_j^{[2]}},
\end{eqnarray}
i.e. will be attached preferentially to nodes with low energy and high degree in layer 2,  according to  a generalized preferential attachment.
\end{itemize}
For each  network change in layer 2 we follow the subsequent procedure:
\begin{itemize}
\item  We extract a number $\sigma^{[2]}_l=1,2$.
 The event $\sigma^{[2]}_l=1$ occurs  with  probability  $p^{[2]}(1)=1-\alpha$ while the event $\sigma_l^{[2]}=2$ occurs with probability   $p^{[2]}(2)=\alpha$.
\item If $\sigma^{[2]}_l=1$  the new node will be attached, in  layer 2, to a node $i_l^{[2]}$ chosen with probability
\begin{eqnarray}
\Pi^{[2,1]}\left(i_l^{[2]}=i\right)=\frac{e^{-\beta \epsilon_i}k_i^{[1]}}{\sum_j e^{-\beta \epsilon_j}k_j^{[1]}}.
\end{eqnarray}
Instead, if $\sigma^{[2]}_l=2$ a random link of a node $i^{[2]}_l$ chosen with probability
\begin{eqnarray}
\Pi^{[2,2]}\left(i_l^{[2]}=i\right)=\frac{e^{-\beta \epsilon_i}k_i^{[2]}}{\sum_j e^{-\beta \epsilon_j}k_j^{[2]}}
\end{eqnarray}
 is rewired, i.e. it is detached from node $i_l^{[2]}$ and attached to the new node of the network.
\end{itemize}
Therefore the network is  determined by the sequence of the values $\{\sigma^{[1]}_l,i_l^{[1]}\sigma^{[2]}_l,i_l^{[2]}\}$ that fully determines the evolution of the multiplex network given the initial condition.

\subsection{Mean-field solution of   the supersymmetric multiplex  model}
When studying growing networks with preferential attachment, in general large attention is given to the degree sequence of the network.
In order to predict the degree distribution of these models, mean-field approaches have been extensively studied, finding that in general they give a very good prediction of the structural properties  of the network \cite{Doro_book}.
In this paper we analyse the supersymmetric multiplex model  with the mean-field theory  leaving to subsequent works the analysis with the master equation approach. In order to check the validity of the approach we then compare the analytical results to simulations as discussed in Section \ref{sim}.
In the mean-field approach, one assumes that the degree of each node has no fluctuations, and therefore identifies the degrees $k^{[1]}_i,k^{[2]}_i$ at time $t$ with their average over the multiplex network realization. Moreover this approximation is also called the continuous approximation because it is assumed that both the degrees of the nodes and the time are continuous variables.
Therefore the mean-field equations for the supersymmetric multiplex model read
\begin{eqnarray}
\frac{dk_i^{[1]}}{dt}=me^{-\beta \epsilon_i}\left[\frac{\alpha}{\sum_j e^{-\beta\epsilon_j}k_j^{[1]}}k_i^{[1]}+\frac{(1-\alpha)}{\sum_j e^{-\beta\epsilon_j}k_j^{[2]}}k_i^{[2]}\right],\nonumber \\
\frac{dk_i^{[2]}}{dt}=me^{-\beta \epsilon_i}\left[\frac{(1-\alpha)}{\sum_j e^{-\beta\epsilon_j}k_j^{[1]}}k_i^{[1]}-\frac{\alpha}{\sum_j e^{-\beta\epsilon_j}k_j^{[2]}}k_i^{[2]}\right].
\label{mf0}
\end{eqnarray}
Using an approach similar to the one used in the Bianconi-Barab\'asi model \cite{Bose}, we will assume self consistently that
\begin{eqnarray}
\lim_{t\to \infty}\frac{\sum_j e^{-\beta\epsilon_j}k_j^{[1]}}{mt}&=&c_1, \nonumber \\
\lim_{t\to \infty}\frac{\sum_j e^{-\beta\epsilon_j}k_j^{[2]}}{mt}&=&c_2,
\label{selfc0}
\end{eqnarray}
where $c_1$ and $c_2$ are constants independent of the network realization.
Therefore, asymptotically in time we have
\begin{eqnarray}
\sum_j e^{-\beta\epsilon_j}k_j^{[1]}&\simeq& mtc_1,\nonumber \\
\sum_j e^{-\beta\epsilon_j}k_j^{[2]}& \simeq &mtc_2.
\label{asymptotics}
\end{eqnarray}

If we define the vector of the degree of each node as
\begin{eqnarray}
{\bf k}_i=\left(\begin{array}{c} k^{[1]}_i(t)\nonumber \\ k^{[2]}_i(t)\end{array}\right),
\end{eqnarray}
and we substitute for $t\gg1$ the asymptotic expression for the normalization sums Eq. $(\ref{asymptotics})$ we obtain that the mean-field Eqs. $(\ref{mf0})$ can be written as

\begin{eqnarray}
\frac{d {\bf k}_i}{dt}=\frac{e^{-\beta\epsilon_i}}{t}{\bf A} {\bf k}_i,
\label{mfs}
\end{eqnarray}
where the matrix ${\bf A}$ is defined as
\begin{eqnarray}
{\bf A}&=&\left(\begin{array}{cc}\alpha/c_1 & (1-\alpha)/c_2\nonumber\\ (1-\alpha)/c_1&-\alpha/c_2\end{array}\right).
\end{eqnarray}
The solution of Eq. $(\ref{mfs})$ is given in terms of the eigenvalue and the eigenvector of the matrix ${\bf A}$.These eigenvalue are respectively  positive and  negative for every value of the parameter $\alpha$ of the model.
 We will indicate the eigenvalues of ${\bf A}$ as   $\lambda_{+}$ and $\lambda_{-}$ in correspondence of their sign.
These eigenvalues are given by
\begin{eqnarray}
\lambda_{+}=\frac{1}{2}\left[\left(\frac{\alpha}{c_1}-\frac{\alpha}{c_2}\right)+ \sqrt{\Delta}\right],\nonumber \\
\lambda_{-}=\frac{1}{2}\left[\left(\frac{\alpha}{c_1}-\frac{\alpha}{c_2}\right)- \sqrt{\Delta}\right],
\end{eqnarray}
with
\begin{eqnarray}
\Delta=\left(\frac{\alpha}{c_1}-\frac{\alpha}{c_2}\right)^2+4\frac{\alpha^2+(1-\alpha)^2}{c_1c_2}.
\end{eqnarray}
We have therefore that the constants $c_1$ and $c_2$ can be expressed as a function of $\lambda_{+}$ and $\lambda_-$ as
\begin{eqnarray}
c_1&=&\frac{(1-\alpha)^2+\alpha^2}{2\alpha}\left[\left(\frac{1}{\lambda_+}+\frac{1}{\lambda_-}\right)+\sqrt{\Lambda}\right],\nonumber \\
c_2&=&\frac{(1-\alpha)^2+\alpha^2}{2\alpha}\left[-\left(\frac{1}{\lambda_+}+\frac{1}{\lambda_-}\right)+\sqrt{\Lambda}\right],
\end{eqnarray}
with
\begin{eqnarray}
\Lambda&=&\left(\frac{1}{\lambda_+}+\frac{1}{\lambda_-}\right)^2-\frac{4\alpha^2}{[(1-\alpha)^2+\alpha^2]}\frac{1}{\lambda_+\lambda_-}.
\end{eqnarray}
Moreover,  we  indicate by ${\bf u^+}=(u_1^{+},u_2^{+})$ and ${\bf u^-}=(u_1^-,u_2^-)$ the eigenvectors corresponding respectively to the eigenvalues $\lambda_{+}$ and $\lambda_-$.
The components of these eigenvectors are given by
\begin{eqnarray}
u^{+}_{1}&=&\frac{c_1}{2(1-\alpha)}\left(\frac{\alpha}{c_2}+\frac{\alpha}{c_1}+\sqrt{\Delta}\right), \nonumber \\
u^{+}_{2}&=&1,\nonumber \\
u^{-}_1&=&\frac{c_1}{2(1-\alpha)}\left(\frac{\alpha}{c_2}+\frac{\alpha}{c_1}-\sqrt{\Delta}\right),\nonumber \\
u^{-}_2&=&1.
\end{eqnarray}
Therefore, solving the Eqs. $(\ref{mfs})$ the  degrees of node $i$ in the two layers can be calculated in the mean-field approximation to be
\begin{eqnarray}
{\bf k}_i(t)=d^+ {\bf u^{+}}\left(\frac{t}{t_i}\right)^{e^{-\beta \epsilon_i}\lambda_{+}}+d^{-} {\bf u^{-}}\left(\frac{t}{t_i}\right)^{-e^{-\beta\epsilon_i}\lambda_{-}},
\label{k1}
\end{eqnarray}
where $t_i$ is the time at which the node $i$ is arrived in the network and
where $d^-$ and $d^+$ are constants determined by the initial condition ${\bf k}_i(t_i)=m{\bf 1}$ where ${\bf 1}$ is the column vector of components $(1,1)$. Starting from Eq. $(\ref{k1})$, the initial condition can be also written as
\begin{eqnarray}
{\bf k}_i(t_i)=m{\bf 1}={\bf U}{\bf d},
\end{eqnarray}
where ${\bf U}$ is the matrix with column vectors given by the eigenvectors ${\bf u}^{+}$ and ${\bf u}^{-}$ i.e.

\begin{eqnarray}
{\bf U}=\left(\begin{array}{cc}u_{1}^{+}& u_{1}^{-}\nonumber \\
u_{2}^{+}&u_{2}^{-}\end{array}\right),
\end{eqnarray}
and the column vector ${\bf d}$ has components ${\bf d}=(d^{+},d^{-})$.
This equation can  always be solved finding that the constants $d^{+}$ and $d^{-}$ are given by
\begin{eqnarray}
{\bf d}&=&m{\bf U}^{-1}{\bf 1}\nonumber \\
&=&\frac{m}{u_1^{+}u_2^{-}-u_1^{-}u_2^{+}}\left(\begin{array}{c}u_2^{-}-u_1^{-} \nonumber \\ u_1^{+}-u_2^{+}\end{array}\right).
\label{dp}
\end{eqnarray}
Note that the denominator of Eq. $(\ref{dp})$ is always positive definite and never singular  since we have $u_2^{-}>0,u_2^{+}>0,u_1^{+}>0$ but $u_1^{-}<0$.
Having fixed the constant $d^{+}$ and $d^{-}$,
we can rewrite Eq.~$(\ref{k1})$ as
\begin{eqnarray}
{\bf k}_i={\bf B}{\bf v}_i
\label{k2}
\end{eqnarray}
with ${\bf v}_i$ indicating the column vector
\begin{eqnarray}
{\bf v}_i=\left(\begin{array}{c} \left(\frac{t}{t_i}\right)^{e^{-\beta \epsilon_i}\lambda_+}\\\left(\frac{t}{t_i}\right)^{e^{-\beta \epsilon_i}\lambda_-}\end{array}\right),
\end{eqnarray}
and the matrix ${\bf B}$ given by
\begin{eqnarray}
{\bf B}=\left(\begin{array}{cc} d^{+}u_1^{+} & d^{-}u_1^{-}\nonumber \\
d^{+}u_2^{+} & d^{-}u_2^{-}\end{array}\right).
\end{eqnarray}
Therefore we have also that
\begin{eqnarray}
{\bf v}_i={\bf B}^{-1}{\bf k}_i
\label{lin}
\end{eqnarray}
with
\begin{eqnarray}
{\bf B}^{-1}=\frac{1}{m}\left(\begin{array}{cc} \frac{u_2^{-}}{u_2^{-}-u_1^{-}} & -\frac{u_1^{-}}{u_2^{-}-u_1^{-}}\nonumber \\ -\frac{u_2^{+}}{u_1^{+}-u_2^{+}} &\frac{u_1^{+}}{u_1^{+}-u_2^{+}}\end{array}\right)
\end{eqnarray}
which is always well defined except for values in parameter space of zero Lebesgue measure where $u^{+}_1=1$.
Since $\lambda_+$ and $\lambda_-$have respectively positive and negative sign,  Eq.~$(\ref{lin})$ defines the two linear combination of the degrees $k^{[1]}$ and $k^{[2]}$ that respectively increases and decreases as a power-law of time.
Therefore we have found the solution of the model, once the constants $c_1$ and $c_2$ are given.
In order to find the correct values of the constants $c_1$ and $c_2$ given by Eqs.$(\ref{selfc0})$, we need to close our self-consistent argument.
Since we have assumed that the constants $c_1$ and $c_2$ are independent on the network realization, determined in the mean-field approximation by the quenched disorder of the assignment of the energies to the nodes,  the constants $c_1$ and $c_2$ can be  evaluated performing the following limits:

\begin{eqnarray}
\lim_{t\to \infty}\frac{\Avg{\sum_j e^{-\beta\epsilon_j}k_j^{[1]}}}{mt}&=&c_1, \nonumber \\
\lim_{t\to \infty}\frac{\Avg{\sum_j e^{-\beta\epsilon_j}k_j^{[2]}}}{mt}&=&c_2,
\label{selfc1}
\end{eqnarray}
where in Eqs.~$(\ref{selfc1})$ the average is performed over the distribution of the energies of the nodes.
Therefore, by  multiplying each equation of Eq. $(\ref{k2})$ by $e^{-\beta\epsilon_i}$, integrating over the continuous time $t_i$, and averaging over the $g(\epsilon)$ distribution we get that  the self consistent equations determining the constants $c_1$ and $c_2$, or equivalently $\lambda_+$ and $\lambda_-$, are given by
\begin{eqnarray}
m{\bf c}={\bf B}{\bf J}
\label{dir}
\end{eqnarray}
where the column vector ${\bf J}=(J_+,J_-)$ has component given by
\begin{eqnarray}
J_+&=&\int d\epsilon g(\epsilon)\frac{1/\lambda_{+}}{e^{\beta\epsilon}/\lambda_{+}-1},\nonumber \\
J_-&=&\int d\epsilon g(\epsilon)\frac{1/\lambda_{-}}{e^{\beta\epsilon}/\lambda_{-}-1}.
\end{eqnarray}
Inverting  Eqs.~$(\ref{dir})$ we can express ${\bf J}$ as
\begin{eqnarray}
{\bf J}&=&m{\bf B}^{-1}{\bf c}=\left(\begin{array}{c}\frac{(c_1u_2^{-}-c_2u_1^{-})}{u_2^{-}-u_1^{-}}\nonumber\\ \frac{(c_2u_1^{+}-c_1u_2^{+})}{u_1^{+}-u_2^{+}}\\\end{array}\right).
\end{eqnarray}
By defining the two constants $\mu_B$ and $\mu_F$, as in the following,
\begin{eqnarray}
\lambda^{+}=e^{\beta\mu_B}\nonumber \\
-\lambda^{-}=e^{\beta\mu_F}
\end{eqnarray}
and multiplying $J^{+}$ by $\lambda^{+}$ and $J^{-}$ by $-\lambda^{-}$ we get the following self-consistent equation, fixing the ``chemical potentials" $\mu_B$ and $\mu_F$,
\begin{eqnarray}
I_B=\int d\epsilon g(\epsilon)\frac{1}{e^{\beta(\epsilon-\mu_B)}-1}=G_{B},\nonumber \\
I_F=\int d\epsilon g(\epsilon)\frac{1}{e^{\beta(\epsilon-\mu_F)}+1}=G_{F},
\label{selfq}
\end{eqnarray}
with  $G_B$ and $G_F$ independent on the energy distribution and only function of the inverse temperature $\beta$ and the two ``chemical potentials" $\mu_B$ and $\mu_F$. In fact we have,
\begin{eqnarray}
{\bf G}&=&\left(\begin{array}{c}G_B\nonumber\\ G_F\end{array}\right)=\left(\begin{array}{c}\frac{(c_1u_2^{-}-c_2u_1^{-})}{u_2^{-}-u_1^{-}} \lambda_+\nonumber\\ \frac{(c_1u_2^{+}-c_2u_1^{+})}{u_1^{+}-u_2^{+}}\lambda_-\\\end{array}\right).
\end{eqnarray}
From the self-consistent Eq. $(\ref{selfq})$ the two constants $\mu_B$ and $\mu_F$ can be interpreted as `chemical potentials" of coupled Bose and Fermi gases and fully determine the evolution of the supersymmetric multiplex network, as long as the equations can be satisfied.
Only the left hand side of the Eqs. $(\ref{selfq})$  depends on the energy distribution $g(\epsilon)$ while the right hand side does not depend on it. Moreover the quantities   $G_B$ and $G_F$  depend on both the chemical potential $\mu_B$ and $\mu_F$ and can be explicitly expressed as
\begin{eqnarray}
G_B&=&e^{\beta\mu_B}\frac{(2-\alpha)e^{-\beta\mu_B}+\alpha e^{-\beta\mu_F}+(1-2\alpha)\sqrt{\Lambda}}{\alpha e^{-\beta\mu_B}+(2-\alpha)e^{-\beta\mu_F}+(1-2\alpha)\sqrt{\Lambda}}\times\nonumber\\
&&\times\frac{(1-\alpha)^2+\alpha^2}{2\alpha}\left[-e^{-\beta\mu_B}+e^{-\beta\mu_F}+\sqrt{\Lambda}\right],\nonumber\\
G_B&=&e^{\beta\mu_F}\frac{-\alpha e^{-\beta\mu_B}+(2-\alpha) e^{-\beta\mu_F}+(1-2\alpha)\sqrt{\Lambda}}{-(2-\alpha) e^{-\beta\mu_B}+\alpha e^{-\beta\mu_F}+(1-2\alpha)\sqrt{\Lambda}}\times\nonumber\\
&&\times\frac{(1-\alpha)^2+\alpha^2}{2\alpha}\left[-e^{-\beta\mu_B}+e^{-\beta\mu_F}+\sqrt{\Lambda}\right],\nonumber
\end{eqnarray}
where $\Lambda$ is given by
\begin{eqnarray}
\hspace*{-5mm}\Lambda=\left(e^{-\beta\mu_B}-e^{-\beta\mu_F}\right)^2+\frac{4\alpha^2}{[(1-\alpha)^2+\alpha^2]}e^{-\beta(\mu_B+\mu_F)}.
\end{eqnarray}
The self-consistent Eqs. $(\ref{selfq})$ that fix the chemical potential $\mu_B$ and $\mu_F$ fully determine the mean-field solution of this model.
In the supersymmetric multiplex network, nevertheless there can be two phenomena that implies a breakdown of this solution.
On one side we can observe a condensation of the links in correspondence of the regime of high values of $\beta$ where the Eqs.$(\ref{selfq})$ do not have a solution. This phenomenon will be discussed more in depth in the next section. On the other side, it is possible to observe in the model stochastic effects that are not captured by the mean-field solution.
\section{Structural properties of the supersymmetric multiplex network}
\label{sim}
The mean-field solution of the model well capture the main characteristics of the supersymmetric multiplex as long as $\alpha$ is not too large.
In fact we found very good agreement of the mean-field theory with the simulation results as long as $\alpha$ is lower than $0.5$.
For higher values of $\alpha$ in the second layer the rewiring process has a higher rate of the process of addition of new links and therefore non-trivial stochastic effects set in that are not captured by the mean-field solution.
For this reason, here we focus on the regime $\alpha<0.5$, where we find very good agreement between the theory and the simulations results.
We will describe the structural properties of the supersymmetric multiplex networks, covering the degree distribution of the networks in the two layers, different types of correlations  typical of multiplex networks, and we will describe the phenomenology related to the supersymmetric multiplex condensation transition in which one node acquires a finite fraction of all the links in both layers.
\subsection{ Degree distribution}
The degree distribution in the network is scale-free in both layers, as predicted by the mean-field solution.
In fact if we consider the dynamical Eq. ($\ref{k1}$) for the degree $k^{[1]}_i$ and the degree $k^{[2]}_i$ and we take only the leading term in the limit $t\gg 1$ we found
\begin{eqnarray}
k^{[1]}_i\simeq d^+u_1^{+}\left(\frac{t}{t_i}\right)^{e^{-\beta(\epsilon-\mu_B)}},\nonumber \\
k^{[2]}_i\simeq d^+u_2^{+}\left(\frac{t}{t_i}\right)^{e^{-\beta(\epsilon-\mu_B)}}.
\label{k12}
\end{eqnarray}
Therefore, using the same mean-field arguments that are used to show that growing complex networks with preferential attachment are scale-free \cite{BA,Bose}, we can approximate the degree distributions $P^{[1]}(k)$ and $P^{[2]}(k)$ in the two layers as
\begin{eqnarray}
P^{[1]}(k)\propto\int d\epsilon g(\epsilon) e^{\beta(\epsilon-\mu_B)}\left(\frac{d^+u_1^+}{k}\right)^{e^{\beta (\epsilon-\mu_B)}}\frac{1}{k},\nonumber \\
P^{[2]}(k)\propto\int d\epsilon g(\epsilon) e^{\beta(\epsilon-\mu_B)}\left(\frac{d^+u_2^+}{k}\right)^{e^{\beta (\epsilon-\mu_B)}}\frac{1}{k}.
\end{eqnarray}
These expression reveals that the degree distributions in the two layers can be seen as a convolution of power-law networks with exponents $\gamma(\epsilon)=e^{\beta (\epsilon-\mu_B)+1}>2$.
In Figure $\ref{fig_dd}$ we show the degree distribution of the two layers for $g(\epsilon)=(\theta+1)\epsilon^{\theta}$ and $\theta=0.5$ for different values of $\beta=0.,1,5$.
The mean-field theory valid as long as the supersymmetric multiplex is not condensed, is in very good agreement with the simulation results.
\begin{figure}
\begin{center}
\centerline{\includegraphics[width=3in]{Pk.eps}    }
\end{center}
\caption{The degree distributions $P^{[1]}(k)$ and $P^{[2]}(k)$ in the two layers of the supersymmetric network. The data is shown for  networks of $N=10^4$ nodes with energy distribution $g(\epsilon)=(1+\theta)\epsilon^{\theta}$ and $\theta=0.5$,  $\alpha=0.3$, $\beta=0,1,5$. The curves are averaged over $100$ multiplex networks realizations.The lines indicate the mean-field expectation for $\beta=0$ and $\beta=1$ and are in very good agreement with the simulation results.  The degree distribution for  $\beta=5$  is a typical degree distribution below the condensation transition where very big hubs emerge in the network. }
\label{fig_dd}
\end{figure}

\subsection{Multilayer degree correlations}
In the multiplex networks one relevant correlation is between the degrees of the replica nodes.
In particular in a duplex  it is interesting to investigate if a hub in a network is also typically a hub in the other network or if it is typically a low degree node.
In the supersymmetric multiplex network model, we observe that for  $\alpha<0.5$, these correlations are positive.
In fact  in the mean-field solution, approximating the degrees  $k^{[1]}_i$ and $k^{[2]}_i$   for $t\to \infty$ as in Eq.~$(\ref{k12})$, we have
\begin{eqnarray}
k^{[2]}_i=\frac{u_2^{+}}{u_1^{+}}k^{[1]}_i,
\label{k2k1c}
\end{eqnarray}
i.e. the degree of layer 2 is positively and linearly correlated with the degree in layer 1.
In order to compare this mean-field expectations with the simulation results, we measure from the simulations results the average degree in layer 2 conditioned on the degree in layer 1, i.e. $\Avg{k^{[2]}|k^{[1]}}$.
This quantity characterizes the degree correlation in the multiplex network and is defined as
\begin{eqnarray}
\Avg{k^{[2]}|k^{[1]}}=\sum_{k^{[2]}}k^{[2]}P(k^{[2]}|k^{[1]}),
\end{eqnarray}
where $P(k^{[2]}|k^{[1]})$ is the conditional distribution of having a node of degree $k^{[2]}$ in layer 2 given that it has degree $k^{[1]}$ in layer 1.
Since in the mean-field approximation the degrees of  nodes are deterministic variables, the mean-field expectation for   $\Avg{k^{[2]}|k^{[1]}}$ is given by Eq~$(\ref{k2k1c})$.
In Figure $\ref{fig_avgk}$ we display   $\Avg{k^{[2]}|k^{[1]}}$ showing that is  an increasing function of $k^{[1]}$ indicating that the degrees of the same node  in the two layer of the supersymmetric multiplex are positively correlated as long as $\alpha<0.5$. Moreover, the conditional average  $\Avg{k^{[2]}|k^{[1]}}$ is well approximated by the mean-field expectation given by Eq.~$(\ref{k2k1c})$.
\begin{figure}
\begin{center}
\centerline{\includegraphics[width=3.3in]{Avgk.eps}    }
\end{center}
\caption{The average degree in layer 2 conditioned on the degree in layer 1,  $\Avg{k^{[2]}|k^{[1]}}$ is shown and compared with the mean-field theoretical expectations finding very good agreement.  The data is shown for  networks of $N=10^4$ nodes, energy distribution $g(\epsilon)=(1+\theta)\epsilon^{\theta}$ with $\theta=0.5$,  $\alpha=0.3$ and $\beta=0,1,5$. The curves are averaged over $100$ multiplex networks realizations.}
\label{fig_avgk}
\end{figure}
\subsection{ Bose-Einstein condensation in the supersymmetric multiplex network}
The Bianconi-Barab\'asi model \cite{Bose} describing a growing scale-free networks that can mapped to a Bose-Einstein gas, displays the Bose-Einstein condensation in complex networks. This condensation transition is a structural phase transition occurring in the network when the mapped Bose gas is in the the Bose-Einstein condensation  phase. Below this phase transition, in the network, one node grabs a finite fraction of the links and non trivial non-equilibrium process determine the network evolution.

A similar phenomenon occurs also in the supersymmetric multiplex model, where  the condensation occurs simultaneously on the two replicas of the same node. In this model the condensation phase transition occurs at $\beta=\beta_c$ for which $\mu_B=0$. Therefore the equations determining the condensation phase transition are
\begin{eqnarray}
\left\{\begin{array}{l}I_B=\int d\epsilon g(\epsilon)\frac{1}{e^{\beta_c \epsilon}-1}=G^{B},\nonumber \\
I_F=\int d\epsilon g(\epsilon)\frac{1}{e^{\beta_c(\epsilon-\mu_F)}+1}=G^{F},\nonumber \\
\mu_B=0.\end{array}\right.
\end{eqnarray}
Below this phase transition a single node grabs a finite fraction of all the links in both layers.
This condensation can possibly occur at low enough temperatures $T=1/\beta$ only if the integral $I_B(\mu_B=0)$ converges. Therefore, as in the classical Bose-Einstein condensation a necessary condition for this condensation to occur is that $g(\epsilon)\to 0$ as $\epsilon\to 0$.

Since the condensation occurs in the same node in the two layers, we observe that below the condensation transition the two layers develop another type of correlation. In fact we observe that the total overlap of the links in the two layers becomes significant below the condensation transition. The total overlap ${\cal O}^{[1,2]}$ of the links between two layers (in this case layer 1 and layer 2)\cite{PRE,Note} is defined as
\begin{eqnarray}
{\cal O}^{[1,2]}=\sum_{i<j}a_{ij}^{[1]}a_{ij}^{[2]},
\end{eqnarray}
where $a_{ij}^{[1]}$ and $a_{ij}^{[2]}$ are the matrix elements of the adjacency matrix of layer 1 and layer 2 respectively.
In Figure~$\ref{fig_cond}$ we plot the fraction of the links linked to the most connected node in layer 1 and in layer 2. The absence of finite size effects below the condensation phase transition shows that in the supersymmetric multiplex there is one node that grabs a finite fraction of all the links. Moreover, in Figure~$\ref{fig_cond}$ we plot also  the total overlap ${\cal O}^{[1,2]}$of the links, showing that below the condensation transition the total overlap becomes significant.
\begin{figure}
\begin{center}
\centerline{\includegraphics[width=4.1in]{cond3.eps}    }
\end{center}
\caption{The fraction of links $k^{[1]}_{max}/(mN)$ and $k^{[2]}_{max}/(mN)$ linked to the most connected node in layer 1 and in layer 2 are shown together with the total overlap of the links ${\cal O}^{[1,2]}$ versus $T=1/\beta$.The data is shown for  networks of $N=10^3,10^4,10^5$ nodes with  energy distribution $g(\epsilon)=(1+\theta)\epsilon^{\theta}$ and $\theta=0.5$,   $\alpha=0.3$. The curves are averaged over $100$ multiplex networks realizations for $N=10^3$ and $N=10^4$, and over $30$ multiplex network realization for $N=10^5$.}
\label{fig_cond}
\end{figure}
\section{ Entropy rate of the supersymmetric multiplex network}
Given the initial condition, the supersymmetric multiplex evolution up to time $t$ is fully determined by the sequence of symbols $X=\{ \sigma_l^{[1]},i^{[1]}_l,\sigma^{[2]}_l,i_l^{[2]}\}_{l=1,2,\ldots mt}$.
Therefore, similarly to what happens for growing network models \cite{Entropyrate}, it is possible to define an entropy rate of the growing supersymmetric multiplex network.
This entropy rate $H(X)$ can be useful for example if aim at compressing the network, as we could aim at extending  the Shannon's noiseless coding  theorem \cite{Quantuminformation}  to  the sequence $X=\{ \sigma_l^{[1]},i^{[1]}_l,\sigma^{[2]}_l,i_l^{[2]}\}_{l=1,2,\ldots mt}$ encoding the full network evolution.
The entropy rate of the supersymmetric multiplex network model when in the supersymmetric multiplex we have already observed $l-1$ network changes,  is given by
\begin{eqnarray}
H(X)&=&-\sum_{{\bf x}_l}P({\bf x}_l|\{{\bf x}_{\ell}\}_{\ell=1,\ldots, l-1})\nonumber \\
&&\times\log P({\bf x}_l|\{{\bf x}_{\ell}\}_{\ell=1,\ldots, l-1}),
\label{er}
\end{eqnarray}
where ${\bf x}_l=\{ \sigma_l^{[1]},i^{[1]}_l,\sigma^{[2]}_l,i_l^{[2]}\}$.
We note here that the entropy rate of the supersymmetric multiplex, as the entropy rate of growing networks has a very characteristic feature, i.e. contains a leading term of order of $\log (t)$. Therefore it does not converge in the thermodynamic limit $t\to \infty$.
This is due to the fact that the attachment probability in these networks are non-local.
This occurs also in the growth of other networks \cite{Entropyrate} such as random trees, where each new node is attached to a random node of the network with probability $1/t$, where $t$ is the number of  nodes in the network.
In fact it is easy to see that also for this basic, non-local model we have
\begin{eqnarray}
H(X)=\log (t).
\end{eqnarray}

\section{ The entanglement entropies of the layers  of the supersymmetric multiplex network }
In order to evaluate the complexity of a single layer, recently new attention has been devoted to quantum information measures \cite{Vonneuman,Garnerone,Jesus2}. Already  the von Neumann entropy \cite{Vonneuman} of single networks has been extended to multilayer networks in Ref. \cite{Math}.
Here we propose to consider the entanglement entropies of the layers of the supersymmetric multiplex network as a generalization of the quantum entropy proposed in   <ref. \cite{Garnerone}.
Following \cite{Garnerone} here we  perform a  mapping between the layers of the supersymmetric multiplex   network with $M=2$ and two  bipartite quantum states.
In particular we will consider the states $\ket{A^{[1]}},\ket{A^{[2]}} \in {\cal H}_{a} \otimes {\cal H}_b$ with ${\cal H}_a \simeq {\cal H}_b \simeq \mathbb{C}^N$, given by
\begin{eqnarray}
\ket{A^{[1]}}&=&\frac{1}{\parallel A^{[1]}\parallel}_F\sum_{i,j} e^{-\beta \epsilon_i/2} a^{[1]}_{ij}\ket{i}\ket{j}\nonumber\\
\ket{A^{[2]}}&=&\frac{1}{\parallel A^{[2]}\parallel}_F\sum_{i,j} e^{-\beta \epsilon_i/2} a^{[2]}_{ij}\ket{i}\ket{j}
\end{eqnarray}
where ${\bf a^{[1]}}$ is the adjacency matrix of the first layer of the supersymmetric multiplex network,  ${\bf a^{[2]}}$ is the adjacency matrix of the second layer of the supersymmetric multiplex network. Moreover,  $\parallel A\parallel=\sqrt{\mbox{Tr}{\bf A}^{\dag}{\bf A}}$ denotes the Frobenious norm of the matrix ${\bf A}$ and the matrix elements $(i,j)$ of the matrices ${\bf A^{[1]}}$ and ${\bf A^{[2]}}$ are given respectively by $A^{[1]}_{ij}=e^{-\beta\epsilon_i/2}a^{[1]}_{ij}$ and $A^{[2]}_{ij}=e^{-\beta\epsilon_i/2}a^{[2]}_{ij}$.
Using the terminology of \cite{Garnerone} we will refer to $\ket{A^{[1]}}$ and $\ket{A^{[2]}}$ as pure network states.

In order to  characterize the complexity of the layers we propose to evaluate the entanglement entropy of the pure network states  $\ket{A^{[1]}}$ and $\ket{A^{[2]}}$. Therefore we define the
reduced density matrices $\rho^{[1]},\rho^{[2]}$ given by
\begin{eqnarray}
\rho^{[1]}&=&\mbox{Tr}_b \ket{A^{[1]}}\bra{A^{[1]}}, \nonumber \\
\rho^{[2]}&=&\mbox{Tr}_b \ket{A^{[2]}}\bra{A^{[2]}}
\end{eqnarray}
and we calculate the entanglement entropy $S^{[1]}$ and $S^{[2]}$  given by
\begin{eqnarray}
S^{[1]}&=&-\mbox{Tr}_a \rho^{[1]}\log \rho^{[1]},\nonumber \\
S^{[2]}&=&-\mbox{Tr}_a \rho^{[2]}\log \rho^{[2]}.
\end{eqnarray}
Using the explicit expression for the reduced density matrices in terms of the degree of the nodes in the different layers $\rho^{[1]}$ and $\rho^{[2]}$, i.e.
\begin{eqnarray}
\rho^{[1]}&=&\sum_i \frac{e^{-\beta \epsilon_i}k_i^{[1]}}{\sum_j e^{-\beta \epsilon_j}k_j^{[1]}}\ket{i}\bra{i}\nonumber \\
\rho^{[2]}&=&\sum_i \frac{e^{-\beta \epsilon_i}k_i^{[2]}}{\sum_j e^{-\beta \epsilon_j}k_j^{[2]}}\ket{i}\bra{i}
\end{eqnarray}
we found that the entropies $S^{[1]}$ and $S^{[2]}$ are given by
\begin{eqnarray}
S^{[1]}&=&-\sum_i \frac{e^{-\beta \epsilon_i}k_i^{[1]}}{\sum_j e^{-\beta \epsilon_j}k_j^{[1]}}\log\left( \frac{e^{-\beta \epsilon_i}k_i^{[1]}}{\sum_j e^{-\beta \epsilon_j}k_j^{[1]}}\right),\nonumber \\
S^{[2]}&=&-\sum_i \frac{e^{-\beta \epsilon_i}k_i^{[2]}}{\sum_j e^{-\beta \epsilon_j}k_j^{[2]}}\log\left( \frac{e^{-\beta \epsilon_i}k_i^{[2]}}{\sum_j e^{-\beta \epsilon_j}k_j^{[2]}}\right).
\end{eqnarray}
Moreover, in the asymptotic limit $t\gg 1$ we can evaluate the entropy using the asymptotic relations given by Eqs.~$(\ref{asymptotics})$.
We found that
\begin{eqnarray}
E^{[1]}-TS^{[1]}+T\log (mc_1t)=F^{[1]}\nonumber \\
E^{[2]}-TS^{[2]}+T\log (mc_2t)=F^{[2]}
\end{eqnarray}
where
\begin{eqnarray}
E^{[\nu]}&=&\avg{\epsilon}_{\nu}\nonumber \\
F^{[\nu]}&=&-T\avg{\log k^{[\nu]}}_{\nu}
\end{eqnarray}
with $\nu=1,2$ and
\begin{eqnarray}
\Avg{f}_{\nu}=\sum_i  \frac{e^{-\beta \epsilon_i}k_i^{[\nu]}}{\sum_j e^{-\beta \epsilon_j}k_j^{[\nu]}} f_i
\end{eqnarray}
Finally by using the mean-field solution of the model we can evaluate the energies $E^{[1]},E^{[2]}$, and the free energies $F^{[1]},F^{[2]}$, as long as the supersymmetric multiplex is not in the condensed phase and $\alpha<0.5$.
If we define $E_B$ and $E_F$ respectively as the average energies calculated over the Bose and Fermi distributions with ``chemical potentials" $\mu_B$ and $\mu_F$, i.e.
\begin{eqnarray}
E_B=\int d\epsilon g(\epsilon)
\frac{\epsilon}{e^{\beta(\epsilon-\mu_B)}-1}\nonumber \\
E_F=\int d\epsilon g(\epsilon)
\frac{\epsilon}{e^{\beta(\epsilon-\mu_F)}+1}
\end{eqnarray} we have, in the mean-field approximation,
\begin{eqnarray}
\left(\begin{array}{c}E^{[1]}\nonumber \\E^{[2]}\end{array}\right)={\bf V}\left(\begin{array}{c}E_B\nonumber \\E_F\end{array}\right).
\end{eqnarray}
with
\begin{eqnarray}
{\bf V}&=&\left(\begin{array}{cc}\frac{1}{mc_1}d^{+}u_1^{+}\lambda^{+}& -\frac{1}{mc_1}d^{-}u_1^{-}\lambda^{-}\nonumber \\ \frac{1}{m c_2}d^{+}u_2^{+}\lambda^{+}& -\frac{1}{mc_2}d^{-}u_2^{-}\lambda^{-} \end{array}\right).
\end{eqnarray}
Similarly also   the ``free energies" $F^{[1]}$ and $F^{[2]}$ can be estimated using the mean-field solution of the model.
\section{Relation between the entanglement entropies of the supersymmetric multiplex and its entropy rate}
We note here a surprising result. In fact the entanglement entropies $S^{[1]}$ and $S^{[2]}$ have a immediate classical meaning because they can be linked to the entropy rate of the network evolution.
In fact, by calculating explicitly the entropy rate of the supersymmetric multiplex, defined in Eq. $(\ref{er})$, we get
\begin{eqnarray}
H(X)=S^{[1]}+S^{[2]}+2h(\alpha)
\end{eqnarray}
where  $h(\alpha)$ is given by
\begin{equation}
h(\alpha)=-\alpha\log (\alpha)-(1-\alpha)\log (1-\alpha).
\end{equation}
Therefore, the entanglement entropies  of the supersymmetric multiplex network  are related to the entropy rate of the supersymmetric multiplex,  which is described by a classical  non-equilibrium process.
The relation between the entropy rate $H(X)$ and the entanglement entropies $S^{[1]}$ and $S^{[2]}$ remains valid for every value of $\alpha\in[0,1)$ and also below the condensation phase transition. Nevertheless, the scaling of the entanglement entropies with the system size changes below the condensation phase transition.

\section{ Conclusions}
In conclusion here we have  investigated the properties of the supersymmetric multiplex network model in which nodes have intrinsic fitness and the evolution describes both the addition of new links according to the generalized preferential attachment, and rewring of the links.
The resulting multiplex network has scale-free layers and develops interesting degree-degree correlations.
The supersymmetric multiplex model  can be fully characterized by coupled quantum Bose-Einstein and Fermi-Dirac statistics.
In fact the dynamic rules of the supersymmetric multiplex networks evolution exploit the symmetries of the multilayer structure and, as a consequence of this, the multiplex network evolution is not determined exclusively by the Bose-Einstein statistics or by the Fermi-Dirac statistics, but is determined by  Bose-Einstein and Fermi-Dirac statistics with  coupled ``chemical potentials" $\mu_B$ and $\mu_F$.
The resulting supersymmetric multiplex network  can undergo a Bose-Einstein condensation of the links in which one node acquires a finite fraction of the links in all the layers, and simultaneously every pair of layers develops a significant overlap of the links.
Moreover, an interesting relation  has been shown to exists between the entanglement entropies of the layers in the supersymmetric multiplex network, measuring the complexity of these layers with quantum information theory tools, and the entropy rate of the classical supersymmetric multiplex network.
In conclusion, in this work the evolution of supersymmetric multiplex networks with fitness of the nodes is characterized. The   complexity of the supersymmetric multiplex networks, and its underlying symmetries have been shown to be related to quantum statistics. In fact  in multilayer networks there are additional symmetries  that are not present in undirected single networks. These symmetries   allow for an evolution determined simultaneously by Bose-Einstein and Fermi-Dirac statistics. Moreover, interesting results relate the complexity of these structures measured by quantum information theory tools and their non equilibrium classical dynamics determined by their entropy rate.

redpajama_set_name: RedPajamaArXiv


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The three-seater Metro couch by Softline creates a modern and permanently timeless ambience with its angular shapes. The special something: if needed, the Metro sofa bed can be turned into a comfortable single and double bed in just a few steps. The depth of the seat is normally 68 cm, while there is space of 135 cm x 200 cm for lying when it is folded out.
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2) environmental justice work with Native American Tribes on the Klamath River.
Both of these areas of scholarship have been nationally recognized through the award of research grants, speaking invitations, and coverage of research by high profile media outlets including the Washington Post, National Geographic, British Broadcasting System, and National Public Radio. Her book Living in Denial: Climate Change, Emotions and Everyday Life came out with MIT Press in the Spring of 2011. Norgaard is the recipient of the Pacific Sociological Association's Distinguished Practice Award for 2005.


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Release is thrilled to be starting some new partnership work, working with some Brighton-based Charities supporting homeless and vulnerably housed people in the area.
Release will be delivering some 1-2-1 counselling for service-users based at Justlife, Stopover, and Safehaven Mother & Baby.
- Justlife Brighton works specifically with single homeless people who are living in vulnerable situations.
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text:
When patients are subjected to investigations or interventions without consent under provisions of provincial legislation, prescribers are required to clearly indicate the scope of enforced care, when it starts and stops, how patients' rights have been communicated and how and when the enforcement is reviewed.
Connect Care supports are similar for Mental Health Act (MHA) and Public Health Act (PHA) requirements:
If a patient is deemed (by the required number and type of providers) to be both non-compliant and compellable for a defined set of interventions, an order is placed in the chart to activate this status.
Mental Health Act - "Flag Patient as Certified (Mental Health Act)"
Public Health Act - "Flag Patient as Certified (Public Health Act)"
The order composer includes direction that relevant legislated forms must be completed and that the patient must be informed that they are being detained and why.
Links are provided within the order composer to relevant forms (which can be completed online) and communication letter templates.
Other links remind the provider about requirements for compliance with the applicable Act.
The Public Health Act has requirements related to timelines for examining a patient (see the "External Guides and Forms" section below for more details).
Patient resources are identified that can be provided to the patient and/or designated decision-makers.
Completed forms should be saved as PDF files or scanned and attached to the patient's chart using Media Manager.
External Guides and Forms
Mental Health Act (compelled treatment)
Forms: Mental Health Act
Public Health Act (compelled investigation, treatment, isolation)
Persons detained under section 39 of the Public Health Act must be examined within 24 hours of arrival at the facility.
Persons isolated under section 44 of the Public Health Act shall be re-examined by a physician at least once every 7 days to determine whether the person may be released from the order.
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The order contains links to the relevant forms, which are maintained by the Government of Alberta.
Forms: PHA - Medical Officer of Health
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Support: Certification Orders

redpajama_set_name: RedPajamaCommonCrawl


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Fund raiser video for plastic surgeons volunteering their services to benefit kids in third world countries.
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A ServSafe course for Food Safety Managers will be offered at St. Albert the Great on a Wednesday of each month, from 9am-5pm. Please visit picfoodsafety calendar site for dates. The test will be the same day at the conclusion of the course. If you pass the course, you will receive a certificate that is required for Church food handling, for example potlucks/meals, and for working in many food service establishments. If you do not pass the course, you can retake the test at later time.
Note: It is required by Michigan Law that at least one person who is certified needs to be present at events that have food served.
The cost is $150.00 for non-profits (please contact PIC Food Safety for non-profit pricing), but typically your parish or the committee that sponsors you will pay some or all of the cost. If you cannot make the course on August 24th, you will have more choices, because the course will be offered on a monthly basis at St. Albert the Great Parish.
If you obtain or already have this certificate, you will need to take a 2 hour class on food allergens, cost is $12 for non-profits, that is now required in the state of Michigan for 2017.


Riccard displayed an entire arsenal of moves as she scored — and rebounded — at will. She also collected 18 rebounds. Her points and rebounds are both OVAC Championship records.
However, the Red Devils were unable to capitalize on several chances. Beaver Local trimmed the deficit to six at the final stop by limiting St. C. to eight points and one field goal.
Beaver Local took its first lead of the game with 5:16 to go when Riley Britt drilled a 3-pointer, which came during a St. C. scoreless stretch that eventually reached three and a half minutes before Macy Malin converted a free throw.
Rileigh Simpson buried a 3-pointer for the Devils and Malin split a pair at the line to bring the Red Devils within one at 48-47.
St. Clairsville actually thought it had sent the game to overtime when Cassidy Stephens buried a shot from top of the key just before the final buzzer. However, the official quickly ruled it was a 2-pointer.
St. Clairsville was led by Keri Klinkoski's 18 points. She also had seven rebounds. Simpson and Malin went for 13 and 12 points, respectively.


text:
Why postman Keith should've written for the reader
Postman Keith's under a lot of pressure. He and his staff are expected to deliver more mail but with less resources and staff at my local Royal Mail delivery office in Leeds.
These things are important to Keith but not to frustrated customers who turn up wanting their parcels from 8.00AM as it says on their missed delivery cards.
Keith tried to preempt his customers' frustration by writing this helpful notice:
Keith's helpful notice
Buried somewhere beneath the passive voice and convoluted language is a message. I interpreted it to be this:
Collect your mail here after 10.00AM. This is a temporary change by Royal Mail and we're sorry your delivery card was wrong.
Why is this new copy better?
Firstly it gets to the point more quickly because the most critical information is right at the start. Even if you read no further than the first sentence, you're still told what you need to know.
Secondly, it's empathetic to the reader's frustration and takes clear responsibility for the problem. You could argue the reader deserves more explanation but these technicalities are best described by polite staff. That's instead of nebulous references to 'automation' and 'national agreements'.
Not only is my copywriting simple and clearer than before, it's better because it's written for the reader and tackles two important priorities for them:
Their needs: "How do I get my mail?"
Their feelings: "I'm frustrated because my delivery card is wrong."
Poor Keith fell into a common trap
I expect Keith and his Royal Mail colleagues face legitimate pressures and have valid concerns, it's just that an instructional notice for customers isn't the best place to air them.
Keith's error was to write for himself in terms he understands but not readers. He also hid meaning beneath jargon to avoid the difficult issue of responsibility and let his priorities dictate the content not the readers'.
To get your message across successfully always write for your readers about what matters to them.
If all else fails, buy some Tippex.
Larner	on March 13, 2013 at 11:06 am
Nice post, Chris – couldn't agree more. I would also add that the notice is pretty worthless unless it's bobbed through the letterboxes of the households in the catchment area; catch 'em before they set off and avoid further disappointment.
In this context, it's a little like the 'road closed' signs you get at the end of a mile-long stretch that really could have done with a diversion sign at the earliest possible junction.
Chris Kenworthy	on March 13, 2013 at 11:10 am
Thanks Larner. You're right – there's probably another post to explore consistent communication across different mediums.


The team, led by John Elefteriades, M.D., chief of cardiac surgery, studied 212 patients who had undergone TAA repair in the period from 1997 to 2009. They found that those with TAA were nine times more likely than those in the general population to have intracranial (brain) aneurysms at the same time.
Location also played a role in the increased risk; if the aneurysm was in the descending aorta, the risk of having a concurrent ICA was nearly five-fold greater than in patients with TAA in the ascending aorta.
Hypertension also increased the prevalence of both kinds of aneurysms—thoracic and brain — at the same time. Nearly 12% of patients with hypertension had both TAA and ICA, as opposed to less than 2% of those with normal blood pressure. Smoking also increased the risk.
Brain hemorrhage after an ICA rupture has been associated with high death rates. Forty percent of patients die within one month, and 30 percent of the survivors have persistent neurologic problems. In contrast, the rate of adverse outcomes after treatment of unruptured ICAs is as low as 1%.
Other researchers are Gregory A. Kuzmik, B.A., Marina Feldman, M.D., Maryann Tranquilli, R.N., and Michele Johnson, M.D., of Yale School of Medicine, and John A. Rizzo, Ph.D., of Stonybrook University School of Medicine.
The research was supported by a National Institutes of Health, National Heart, Lung and Blood Institute Medical Student Research Fellowship.


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Download 2730 – Spider-Man 3 (G) GBA Rom
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text:
Die Kannenbäckerstraße ist eine Ferienstraße im Westerwald und im Kannenbäckerland. Sie wurde 1978 eröffnet, hat eine Länge von 35 km und führt über verschiedene rheinland-pfälzische Landesstraßen. Zum Teil führt diese Straße durch den Naturpark Nassau.

Verlauf
Die Kannenbäckerstraße beginnt in Neuhäusel mit der von der Bundesstraße 49 abzweigenden Kreisstraße 114 und mündet beim Vallerauer Hof in die Landesstraße 310. Dieser folgend durchquert sie Hillscheid und erreicht die Stadt Höhr-Grenzhausen. Der Landesstraße 307 nach Osten folgend erreicht die Kannenbäckerstraße Hilgert, die Stadt Ransbach-Baumbach und Mogendorf. Im weiteren Verlauf über die Landesstraße 313 berührt die Kannenbäckerstraße Siershahn und durchquert die Stadt Wirges. In östlicher Richtung folgt sie der Landesstraße 300, durchquert Moschheim und endet in der Ortsgemeinde Boden an der Bundesstraße 255. Von Neuhäusel bis Höhr-Grenzhausen ist der Verlauf der Kannenbäckerstraße identisch mit dem Verlauf der Deutschen Limes-Straße.

Quellen
 Kannenbäckerstraße beim Landesamt für Vermessung und Geobasisinformation Rheinland-Pfalz
 Landschaftsinformationssystem Rheinland-Pfalz: Karte zum Streckenverlauf der Kannenbäckerstraße
 Kannenbäckerstraße beim Wanderatlas Deutschland

Ferienstraße in Rheinland-Pfalz
Verkehr (Rheinland)
Verkehrsbauwerk im Westerwaldkreis

redpajama_set_name: RedPajamaWikipedia


According to this report, the Global Wearable Electronics market is expected to grow from $13.25 billion in 2017 to reach $98.24 billion by 2026 with a CAGR of 24.9%. Rising proliferation of smart glasses, increasing average life expectancy, increasing demand of consumers towards communication, networking, positioning and recognition technologies are some of the key factors fueling the market growth. However, factors such as lack of design features, higher power usage of wearable devices, high initial investment and users concerns regarding data privacy are restraining the market growth.
Wearable electronics are accessories with advanced electronic technologies. Wearable devices are worn on the body, which enable wireless networking and mobile computing. These devices enable end-users to integrate computer in their daily activity and use technology to take advantage of advanced features and characteristics. Wearable electronics devices comprise product such as smart goggles, finger worn scanners, wrist wears for instance wrist bands and electronics watches, foot wears namely fitness and sport shoes and athletic shoes, and others products such as neck-wear and head bands.
Some of the key players in Wearable Electronics market include Xiaomi Technology Co. Ltd., Texas Instruments, Inc., Sony Corp, Samsung Electronics Co. Ltd., Qualcomm, Inc., Pebble Technology Corp., Nike, Inc., LG Electronics Inc., Jawbone Inc., Google, Inc., Garmin Ltd., Fitbit, Inc., AT & T Inc., Apple, Inc. and Adidas Ag.
11.1 Xiaomi Technology Co. Ltd.
11.4 Samsung Electronics Co. Ltd.
11.13 AT & T Inc.


text:
In 24 hours, an implicated conductor is gone
Message from Michigan:
Michigan Opera Theatre announced today that its Principal Conductor Stephen Lord has resigned from the company, effective immediately. MOT accepted the resignation following public allegations of Lord's past behavior, which do not align with the Company's values and standards.
Stephen has had a long and successful relationship with Michigan Opera Theatre, and we appreciate his artistic leadership, especially in his last three years as Principal Conductor," said MOT President and CEO Wayne S. Brown.
MOT's 2019-20 season begins in Oct. 12 at the Detroit Opera House.
Opera Theatre of St Louis has also severed ties with Lord.
UPDATE: Lord denies harrassment.
Luigi Nonono says:
This is outrageous. Their only concern should be with current and future behavior. They have no right to punish people for their pasts. Why would anyone want to enter a career in such a self-righteous, puritanical atmosphere? I am disgusted. No one is perfect, least of all, artists. Artists have traditionally had license to misbehave. No one understands what goes into making art of any kind. Shocking things could be utterly necessary. Like wild animals, approach with caution. Such things cannot change.
Jules R says:
What a disgusting comment. You clearly have no conception of what art means or what it means to be an artist. You're just looking for an excuse for people in power to harm and abuse others. Shame on you.
If this guy had a 9-5 er, he'd have been fired long ago. An employer does not need guilt determined by a jury to fire someone. If that were the case, very few would ever lose a job. Welcome to the real world.
Musiclover says:
O, Lord….
John Rook says:
What is not aligned with MOT's standards, his behaviour or the allegations? Because at this stage, it's only the latter.
Maybe he's guilty, but let's have trial by jury, not by Twitter.
The allegations are backed up by texts, emails, Grindr messages, etc. It isn't twitter outrage that fueled this. It's decades of using power to sexually harass young musicians. This isn't even news–it was an open secret, as the original article clearly stated.
Saxon Broken says:
It is an "internal disciplinary matter" not something for the criminal courts. If the employer feels there are grounds for dismissal, they won't usually publish the evidence but treat the hearing as confidential.
Concordia says:
How the mighty have fallen!
The View from America says:
Poof! Just like that.
Sue Sonata Form says:
Arthur Miller wrote about stuff like this; it was called "The Crucible". Nothing has changed. Recommended reading for the under 40s.
I can personally confirm the allegations are true–I have seen the text messages, Grindr messages, and have close friends he propositioned–one of whom was 15 years old at the time.
Wasn't it Trump who used the "witch hunt" allegory…? Interesting.
christopher storey says:
My comment on this being a flagrant breach of natural justice has been suppressed. Why ?
norman lebrecht says:
Nobody gets suppressed round here for telling the truth.
Apologies … my comment was on the ENO similar thread


The definition given this word by its inventor, the nineteenth-century Italian criminologist Cesare Lombroso was "semi-insane". He believed that criminality was inherited and that a criminal was born with physical defects identifying him as a degenerate human being, an atavism. He created mattoid from the Italian matto, insane, plus the ending -oid for some likeness or resemblance (from Greek eidos, form). He used it for what psychiatrists call "borderline dwellers", those who exist on the margins between reason and madness — in everyday speech we might call them cranks, eccentrics, or misfits.
Last modified: 21 January 2006.


This carbon offsetting proposal could nearly double emissions from the airline industry.
It sounds like a fine riddle: what can grow exponentially but still remain the same size? A new global deal on climate emissions from aviation promises just that: "carbon neutral growth" from an industry that is the world's fastest growing source of greenhouse gases.
When diplomats meet in Montreal this week for the triennial Assembly of the International Civil Aviation Organization (ICAO), the results are likely to be prosaic: a delay in cutting emissions until 2021, at which time a voluntary scheme would be introduced that allows airlines to continue polluting by paying others to clean up for them. The controversial "carbon offsetting'"scheme at the heart of this proposal is likely to involve counting reductions in greenhouse gas emissions twice, posing a significant new threat to hopes of avoiding dangerous climate change.
Read the full article on New Internationalist's website.
Oscar Reyes is an associate fellow for the Institute for Policy Studies.


text:
2012 Electoral College Wrap Up, Part 1
This is the first part in a two part look at how FHQ's weighted average stacked up in examining the 2012 electoral college. We'll first take a global look at FHQ in the context of the other models out there. Part two will take a micro view of the FHQ model in relation to the electoral college results.
Now that we are nearly a week removed from the re-election of President Obama, FHQ thought it would circle back around and take a look back at how we did in examining the state of play within the electoral college. The answer is not too bad. What was 49 out of 51 correct state-level projections based on our simple weighted average in 2008 morphed into a perfect 51 out of 51 score in 2012.
FHQ was not alone. Drew Linzer (Emory) at Votamatic and Simon Jackman (Stanford) blogging for the Huffington Post and Sam Wang (Princeton) at the Princeton Election Consortium all were either right on or in Wang's case cautiously calling a tie in Florida. [And truth be told, Florida was a tie, but one that consistently -- around FHQ anyway -- ever so slightly favored the president. Again, we're talking about a decreasing fraction of a point as election day approached.] Oh, and Nate Silver of FiveThirtyEight fame pegged it at 332-206, too. This was a great thing for the so-called "quants".
Despite that, there are a couple of notes that are floating around out there and are worth mentioning.
1) FHQ won't take any victory laps because of this.1 Don't get me wrong. It is nice to be a dart and not, say, the board itself, but this actually has very little to do with what FHQ was doing under the hood -- or what any of the above folks were doing, for that matter. If we were all making sausage, then FHQ and the others were merely turning the crank on our various sausage making apparati. The filling -- the polls -- was what really nailed the election projection on the state level.2 Drew first published his model in June. FHQ followed in July. The polls, even through our different lenses. told the story then. 332-206. Over the course of the summer and into the fall, that changed very little. For FHQ, Florida got as close as 0.04 points in favor of the president, but then took a turn back toward Obama. That was it. The Sunshine state was always the only state that ever truly threatened to jump what FHQ calls the partisan line into the Romney group of states. The polls were not only right on the money, but they were overall, pretty consistent. Jim Campbell's argument/observation that the September polls are a better predictor of November election outcomes came to pass. What we got in October was just noise before state-level polling reverted or began reverting to those post-convention, pre-October numbers.
As FHQ asked throughout October, were we witnessing a movement toward Romney in the polls or the typical sort of narrowing (Campbell 2008) that tends to mark the late campaign polls. The latter may not have been the true answer but it was closer than simply talking about Romney's momentum. Tom Holbrook's (1996) equilibrium theory of candidate support through the polls seems to have been the correct lens through which to view the dynamics of the race as election day drew nearer.
Score this one for the polls, then.
2) But where does that leave the models? After all, the sausage maker has some utility, too. Well, FHQ's natural inclination is to piggyback on the above point and state the obvious. The polls were right on and you didn't really need a statistical model -- complex or otherwise -- to accurately project the electoral college. In true self-deprecating fashion (Bear with me. I'll get there.) -- something FHQ is good at -- our little ol' weighted average was accurate enough to get all but two states right in 2008 and every last one in 2012. Again, it was the polls. In fact, if you removed the weighting and took the raw average of all the publicly available polls released on and before election day in all of 2012 you would come up with the same thing: 332-206. As I told Drew over the summer in a brief Twitter exchange, my hope was at that point just after the conventions that the race would tighten up so that we could, in fact, get a true measure of the utility of the more complex statistical models projecting the electoral college. As it stood then -- and how it ended up even with some narrowing -- there was a lot of overlap between the Bayesian models and the more pedestrian averages.
Mind you, I'm not saying that there is no place for these models. Boy, is there. I'm with John Sides on this one: The more models we have, the better off we all are on this sort of thing. Rather, my point is to suggest that the simple averages are a decent baseline. As November 6 approached and the FHQ numbers did not budge in the face of changing information following the Denver debate, I began to think of the FHQ weighted average like the Gary Jacobson measure of congressional candidate quality. Now sure, there have been herculean efforts littering the political science literature to construct multi-point indices of candidate quality, but they don't often perform all that better than Jacobson's simple test. "Has challenger/candidate X held elective office?" That simple, binary variable explains most of the variation in the levels of success that various candidates -- whether challenging an incumbent or vying for an open seat -- have enjoyed across a great number of elections. The multi-point indices only slightly improve the explanatory power.
Now, lord knows, I'm not trying to draw definitive comparisons between the work here at FHQ and Jacobson's oft-cited body of work. Are there parallels? Yes, and I'll leave it at that. Sometimes the best models are the simplest ones. Parsimony counts and to some extent that is what FHQ provides with these electoral college analyses. And again, the reason I was hoping that the polls would tighten as we got closer to election day was to demonstrate just exactly how much better the more complex models were. My expectation was that there would be a noticeable difference between the two. But there wasn't; not in terms of projecting which states would go to which candidates. By other measures, the more complex models wiped the floor with FHQ (as, admittedly, they should have).3
The tie that binds all of these models -- if you really want to call the pre-algebra that FHQ does a model -- is a reliance on polling. And that raises a different question as we shift from reviewing 2012 to looking at 2016 and beyond. The quants "won" this one. But it was not without a wide-ranging -- and fruitful, I think -- discussion about the accuracy of polling. The one question that will continue to be worth asking is whether the seemingly perpetually dropping rates of response to public opinion polls continue to drop and what impact that will have. If that continues, then there would almost certainly have to be a tipping point where phone-based polls begin to more consistently miss the mark. The good news moving forward is that the online polls -- whether YouGov, or Google Consumer Surveys or Angus-Reid -- performed quite well in 2012; offering a ray of hope for something beyond phone polls in a time when cell phones are hard to reach and landlines are disappearing.
Still, we are now at a point where pollsters are talking about the "art of polling" as a means of differentiating from other pollsters instead of the overarching science of polling. That has implications. If all pollsters guess wrong about the underlying demographics of the electorate, all the polls are wrong. Of course, the incentive structure is such that pollsters want to find something of a niche that not only separates them from the competition to some extent but helps them crack the code of the true demographic breakdown of the electorate. [Then they can all herd at the end.]
The bottom line remains: these projections are only as good as the polling that serves as the sausage filling. If garbage goes in, then garbage is more likely to come out. On the other hand, if the polling is accurate, then so too are the projections.
1 I won't take any victory laps, but I will extend to all of those who have been both loyal and happenstance readers alike a very sincere thank you for spending some or all of election season with us. And yeah, that stretches back to late 2010. Thank you.
2 This is something Harry Enten of the Guardian mentioned via Twitter on Saturday and AAOPR more or less confirmed today.
3 One factor that should be noted here that may separate FHQ from the more involved models is polling variability. 2008 was witness to a great deal of polling variability. The margins in that open seat presidential election jumped around quite a bit more than in 2012 when an incumbent was involved. 2016, in some respects is shaping up as a repeat of 2008. That is even more true if both Hillary Clinton and Joe Biden pass on runs for the Democratic nomination. Both races would be -- at least from our vantage point here three years out -- wide open and influence the polling that is conducted across firms and across states. Yet, even with that unique situation, FHQ lagged just one correctly predicted state -- North Carolina -- behind FiveThirtyEight.
Invisible Primary, 2016
2012 Election Night Live Blog
Posted by Josh Putnam at 1:30 PM
Labels: 2012 presidential election, electoral college, electoral college projections, Mitt Romney, Obama, state polls
The 1988 Electoral College Spectrum
2 + 2 = -15: Double-Dipping on the Ames Straw Poll
The Death of the Ames Straw Poll?
What to Watch for Election Night
The Electoral College Map (11/6/12): Election Day
Live by the 3, Die by the 3 (...and other thoughts...


Is it normal to have the conviction that optimism isn't true?
A few people are arguing why I have to see the worst in anything: you gotta be more pessimistic, pessimism is true, optimism, none of it is true. I'm not sure you can call that a conviction but it functions like one, it's an anti-conviction, I have strong non-belief in optimism, however harsh it is it's about the truth, is that normal?
Pessimism and optimism have nothing to do with being true or false. It's how you look at a situation and/or the outcomes of the situation.
Only one of them are not true-false in this paradox you wrote above, pessimism is about the truth, it's not about merely feeling good and simply and clearly, if it's not true it's a lie and I can't accept that. I will accept your answer as to not true and false and leave it at that.
No by definition pessimism is "a tendency to see the worst aspect of things or believe that the worst will happen; a lack of hope or confidence in the future." Being pessimistic just means that you look and focus on the worst outcomes. It has nothing to do with likelihood of the outcomes.
If a situation has two possible outcomes of equal likelihood, one good and one bad, a pessimist will choose to focus on the bad one while an optimist will choose to focus on the good one. Neither is true and neither is a lie, it's just perspective.
True, I'll have to think about that, if it's deliberately false it's a lie, am I the only one who faces reality?, and I believed in that definition for years, call me the pessimist, yes! I can't contradict your answers while you're contradicting me, it's either about waking me up from my delusions, or simply helping me in any other way, am I right, I don't contradict you. However I agree with expecting the bad and not the good, pessimism is difficult, it's not a simple matter of seeing the worst outcome, it's really and I'm not disagreeing, a matter of first seeing things in rose-coloured glasses and taking them off to see the reality, that's what seeing the bad is about, that's the pessimist's opinion of reality, I believe in it therefore it's true, I accept that. If you can't accept something as true, you don't believe it, and what good is being a pessimist when you don't accept it as true? Don't argue, I'm correct, I'm an expert, accept it!
Optimism isn't true or false. It's a way of thinking. You can adopt it or not. I personally don't. You sound like a realistic/skeptical person from this point of view.
What about detachment, how do you feel about detachment?
What's wrong with not being interested in detachment? I tried Buddhism several times (it finally worked when I was in a mental institution) and I'm not interested in it, and any religion that interferes with picky eating, or my fancy clotes or rich lifestyle, am I the only one who thinks that although Buddhism is for everyone, some of us want money?
The glass doesn't have to be half full, or half empty. The glass can just be.
It's neither, I'm not optimist or pessimist with everything I do, I follow many many philosophies (and many many sciences but more philosophies than sciences), with Buddhism the glass just is because it's even for posh people to convert to a different lifestyle, but then it's not my kind of life so I'm neither optimistic nor pessimistic about Buddhism, just dandy about it.
Whatever happened to your love affair with the Amish?
It's still there, only I'm waiting for the book to arrive in the post! Does a person have to do things in the same style just because it was mentioned previously? I was talked into returning to my anti-christian roots. Without argument I was simply told that Christianity is not good and I agreed with it.
Well actually when you think about it, there is only one way it will work out in the end, so guess what, " it will all work out ok."
Really? I thought positive, with optimism and by thinking positive, they're both a paranoid delusional fantasy world of false assurance, making logical fallacies, it's not true! Even if things will work out OK they return back to the normal screwed up going downhill. Therefore I smile in that situation, and don't let misery and suffering afflict my heart. :) Yes for some people it will all work out OK and I'll have a think about it, I half-agree with you.


I want to upgrade my hdd to a 200gb WD. I use the sid5 'build a hdd from scratch'. Everything seems to go fine. All the partitions are made. All the files seemingly in the right place. I reboot, then lock the hdd. It says success.
However when I put it back in my xbox I get the error 21 screen and red/green flashing.
I've tried placing the jumper in master, cs, and jumperless all with he same result.
The original hdd boots up perfectly.
Where am I going wrong? Is there an easier way to build the hdd?
I don't know SID 5 Babylon or what that has to do with building a new HDD.
The usual tool for doing that on the PC is XBHDM and that I can't help with either.
But if you already have a working HDD in the Xbox and you want to put a new 200GB (250GB?) in it then the tool to use is Chimp2618 or more particularly now Chimp261812.
This will clone your existing HDD, partition and lock it correctly.
That YT video is by the guy who actually updated Idotsfan's original to Chimp261812. He's very recently updated it again so it can simply be installed like any other App on the E:\drive. It now boots straight in to the program's main menu and also without having to extract the linuxboot.cfg file to the root of the E:\drive as was necessary before.
Sorry, it was the Xboxhdm that came with SID5.
Thanks for the info, archangle. I'll give chimp a go and see what happens.


Restart on Crash was added by WhiteTiger in Apr 2012 and the latest update was made in Apr 2019. The list of alternatives was updated Apr 2013 There is a history of all activites on Restart on Crash in our Activity Log. It's possible to update the information on Restart on Crash or report it as discontinued, duplicated or spam.
ProcessAlive is a simple tool that automatically restarts selected processes when it detects that they have stopped.
Alternatives to Restart on Crash for Windows, Blackberry, Software as a Service (SaaS), Mac, Linux and more. Filter by license to discover only free or Open Source alternatives. This list contains a total of 5 apps similar to Restart on Crash.
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Los investigadores del Instituto Karolinska de Estocolmo identificaron a un grupo de 64 genes que puede ser usado para predecir la respuesta de cinco aos de los pacientes de cncer de mama a la terapia adyuvante. In San Francisco, harm reduction became an official city policy several months ago; officials are not aware of any other cities that have such a philosophy. Newcomer, who also is an adjunct professor of psychiatry at Washington University. Afdhal et al. enrolled 404 patients who had already failed treatment with peginterferon and ribavirin. The proposed cuts are all about the politics of the NHS and nothing to do with evidence witness the fact that the promised impact assessment has STILL not been published. Also, those treated with XZK were 30 percent less likely to die from a cardiovascular problem and 33 percent less likely to die from any cause. Stork opens by revealing that he loves chiropractic and is, in fact, heading to one as soon as the show is done taping. Most cancer goes away, or never progresses, even with NO medical treatment. This gives us the best evidence yet that in a community with domesticated animals, but before dairying, the infecting strain was actually the human pathogen. Ethan R. Anderson, 21, of Ohio 141, Ironton, was indicted on charges of trafficking in marijuana, possession of marijuana and possession of drugs. The proportion of patients with an abnormal QT interval, defined by the atrisk line on the QT nomogram, was the primary outcome. As part of the bodys immune system, lymph nodes help filter out harmful substances. In these women, increased BMI became associated with both shorter time to cancer recurrence and shortened survival, the researchers said. These cancers may involve the mouth, the tongue, the tonsils, the throat the pharynx, and the nasal passageways.
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text:
Q: Get unique JSON keys with JQ in raw format This is a follow up question on answer to this question:  Get all unique JSON key names with JQ
How to get the unique keys in raw format from this
{"a": 1, "b": 2, "c": 3}
{"a": 4, "b": 5, "d": 6}

The answer to above question is as follows. But this outputs the data in a 'list' like format:
$ jq -n '[inputs | keys[]] | unique' input.json
[
  "a",
  "b",
  "c",
  "d"
]

How to get just the raw values i.e., a,b,c without open close brackets and double quotes? Usually this can be achieved with jq -r but not in this case.
a
b
c
d

A: You can just un-wrap the list generated form unique operation using unique[] and still use the raw output mode -r
jq -nr '[inputs | keys_unsorted[]] | unique[]'

I've also used keys_unsorted over keys to preserve the key ordering.
jqplay demo

redpajama_set_name: RedPajamaStackExchange


This recipe is great! It is easy to do, it saves money and it lasts for months!
Let me warn you... you will get quite a workout in one arm as you stir it. But it is well worth it.
Combine dry ingredients, slowly add water and oil. Cook over medium heat, stirring until stiff. Let cool and knead. Store in zip-lock bag or plastic container, so it won't dry out!
Get out your cookie cutters, toy rolling pin, old plastic lids, mini tractors, bulldozers, hard plastic animals to make foot prints, etc... get creative as to what to make and what toys to use while playing with the play dough.
Your children will be entertained for a good period of time!
This play dough is non-toxic as you can see it is made of all consumable ingredients. It is not very tasty unless you like lots of salt!
Have Fun! Play with your kids during this table time activity.