text:
\section{Introduction}

\textit{Self-organizing networks} (SON) are expected to improve the efficiency of cellular coverage tuning to meet target service performance metrics\cite{6963801}.  Industry standards  \cite{3gpp32500} refer to the category of SON which performs automatic handling of network faults as \textit{self-healing}.  Management of network faults is one of the functional areas defined in an industry framework \cite{fcaps} known as FCAPS: fault, configuration, accounting, performance, and security.  Fault management detects faults and corrects them.  Wireless network faults can be corrected through parameter adjustments which optimize the network performance.  This enables it  to carry the traffic it has been dimensioned for with high reliability and end-user \textit{quality of experience} (QoE).  However, this is also a perpetual and costly task.

We use deep \textit{reinforcement learning} (RL) where the SON learns fault management with no human supervision.    Our proposed addition of deep RL to the SON is shown in Fig.~\ref{fig:overall}.   SON aided with the deep RL-based algorithm monitors the performance data of an outdoor cellular network and analyzes it to derive proper parameter corrective steps and implements them.  For this purpose, we model a cellular cluster of base stations in an outdoor environment with mobile devices scattered in the vicinity with the focus on the downlink.  We refer to any of these mobile devices as a \textit{user equipment} (UE).  We chose the \textit{signal to interference and noise ratio} (SINR) and throughput as measures of cellular capacity.  We focus on the \textit{fourth generation of wireless communications} or \textit{Long Term Evolution} (4G LTE) and its variants since the system-level simulator \cite{VLS-2016} supports them.  The results can be applied to any similar \textit{orthogonal frequency-division multiplexing} (OFDM) including the \textit{fifth generation of wireless communications new radio} (5G NR) where SON has a highly anticipated role \cite{6963801}.

\begin{figure}[!t]
\centering
\begin{tikzpicture}[style=thick,scale=0.8]

\node [rectangle, draw, rounded corners,
         text width=6em, text centered, minimum height=0.5em] at (4,1) (bs1) {\smaller Base Station 1};

\node [rectangle, draw, rounded corners,
         text width=6em, text centered, minimum height=0.5em] at (4,-3.5) (bs3) {\smaller Base Station $n$};
\node at (4,-2.4) {$\vdots$};

\path [draw, latex-latex] (bs1.335) -- node {} (bs3.25);
\path [draw, latex-latex] (bs1.205) -- node {} (bs3.155)

\node [rectangle, draw, rounded corners,
         text width=6em, text centered, minimum height=0.5em,fill=white] at (4,-1.5) (bs2) {\smaller Base Station 2};

\node [rectangle, draw, rounded corners,
            text width=10em, text centered, below of=bs1,fill=gray!30] (fm) {\small Deep Q-learning SON}

\node [rectangle, draw,  minimum width=1, minimum height=2em] at (7.5,2) (ant1) {};
\node [rectangle, draw,  minimum width=1, minimum height=2em] at (7.5,-0.5) (ant2) {};
\node [rectangle, draw,  minimum width=1, minimum height=2em] at (7.5,-2.5) (ant3) {};

\node [rectangle, draw, rounded corners,
    text width=3em, text centered, minimum height=1em, left of=fm, xshift=-3cm](init) {\small $\bm{\varphi}_\text{fault}[t]$};

\node[text width=1cm] at (8.5,0.75) {\smaller \centering Outdoor \\ Antennas};

\path [draw, latex-latex] (init.0)  -- node [near start] {} (fm.180);

\draw  (bs1.0) -| node [below right of = ant1, text width=0.5 cm] {} (ant1.270);
\draw  (bs2.0) -| node [below right of = ant2, text width=0.5 cm] {} (ant2.270);
\draw  (bs3.0) -| node [below right of = ant3, text width=0.5 cm] {} (ant3.270);
\end{tikzpicture}%
\vspace*{-0.1in}
\caption{The Deep $Q$-learning self-organizing network (SON) module interacting with several outdoor base stations.}
\label{fig:overall}
\end{figure}

The first deep RL framework to learn control policies using reinforcement learning was introduced in \cite{mnih2013playing}.  This framework outperformed human experts.     The authors in \cite{7393587} used $Q$-learning as part of their SON implementation for mobile load balancing and mobility optimization for cell reselection and handovers.  They used cells with single antennas.  We on the other hand use \textit{multiple-input multiple-output} (MIMO) in our transceivers---a fundamental setup for present and futuristic network deployments.

Deep learning in mobile and wireless networking with interference alignment was studied in \cite{HeZYZYLZ17}. Relaxed \textit{channel state information} (CSI) assumptions were made in the study where the CSI transition matrix was identical across all users.  We do not make this assumption since we focus on upper layers in the wireless stack.  A two-dimensional convolutional neural network was used in simulations, which imposes unfounded spatially invariant relationships between learning features, or local connection patterns \cite{726791}.  We avoid this in our design of our deep neural network.  The authors in \cite{faris} provided a means to improve the handover execution success rate using supervised machine learning but did not use reinforcement learning which has the ability to learn from previous actions.  In \cite{KHATIB20157549}, a method was proposed to extract the knowledge base from solved fault troubleshooting cases using data mining and supervised learning techniques using fuzzy logic.  Expert opinion was used to define performance measurements and target values.  We on the other hand use RL to derive a policy to map actions to be taken by the self-healing functionality in response to select common number of faults in the network.
The method in \cite{Dean2012} showed that deep RL can be run in a distributed fashion.

Our main contributions are as follows:
\begin{itemize}
\item Introduce a deep RL-based fault handling algorithm which self-organizing networks can implement in a polynomial runtime.
\item Show that this fault management method can improve the radio link performance in a realistic outdoor network setup.
\end{itemize}

\section{System Model}\label{sec:sys_mod}
The system comprises a wireless network of a macro base station operating in the sub-6 GHz frequency range with a single tier of surrounding macro base stations, and a machine learning algorithm using deep RL which could  reside in the serving base station or at a central location.

\subsection{Network}\label{sec:network}
The network is an outdoor cellular cluster using frequency division duplex and multiple access with one tier of neighboring cells each with a hexagonal geometry and an inter-site distance of length $L$.  All of these cells are neighbors to one another.  The UEs are equipped with one antenna each and are allowed to perform handovers between cells.   The cells have multiple antennas each.  Any UE is served by a serving cell $c$, which is a member of the set of cells $\mathcal{C}$.  In this network, there are $q\vert\mathcal{C}\vert$ UEs, where $q$ is the number of UEs per cell.

This cellular network can be in a normal operational state or undergo several issues or faults.  The set of faults are $\mathcal{N} = \{\nu_i\}_{i = 0}^{\vert\mathcal{N}\vert-1}$.  We choose a few common faults which can be resolved by SON and set their rate of occurrence as in Table~\ref{table:network_actions}.

\begin{table*}[!t]
\setlength\doublerulesep{0.5pt}
\caption{Network Faults $\mathcal{N}$}
\label{table:network_actions}
\centering
\begin{threeparttable}
\begin{tabular}{c|lc || c|lc}
\hhline{======}
Action $\nu$ & Definition & Rate & Action $\nu$  & Definition & Rate\\
\hline
 0 & Cluster is normal. & $p_0$  & 5 & Feeder fault alarm cleared.\tnote{\textdagger} &$p_5$\\
1 & Changed antenna azimuth clockwise (e.g., due to wind). & $p_1$  &  6 & Neighboring cell is up again.\tnote{\textdagger} &$p_6$\\

 2 & Neighboring cell is down. &$p_2$ &  7 & Transmit diversity is normal.\tnote{\textdagger} &$p_7$\\
 3 & Transmit diversity failed. &$p_3$ &  8 & Reset antenna azimuth.\tnote{\textdagger} & $p_8$ \\
 4 & Feeder fault alarm (3 dB loss of signal). & $p_4$ & & \\
 \hhline{======}
\end{tabular}
\begin{tablenotes}\footnotesize
\item[\textdagger] These actions cannot happen if their respective alarm did not happen first.
\end{tablenotes}
\end{threeparttable}
\end{table*}

\subsection{Reinforcement Learning}\label{sec:reinf_learning}

\begin{figure}[!t]
\centering
\begin{tikzpicture}[thick,scale=0.6, every node/.style={scale=0.6},   cnode/.style={draw=black,fill=#1,minimum width=3mm,circle},
]

 \node at (3,-4) {$\vdots$};
  \node at (6,-4) {$\vdots$};
    \foreach \x in {1,...,4}
    {

      \pgfmathparse{\x== 3 ? "\vdots" : "s_\x"}
             \pgfmathparse{\x== 4? "s_m" : "\pgfmathresult"}
        \node[cnode=gray!20,label=180:${\pgfmathresult}$] (x-\x) at (0,{-\x-int(\x/5)-0.5}) {};

        \pgfmathparse{\x<4 ? \x : "H"}
        \node[cnode=gray,label=90:$\theta_{1,\pgfmathresult}$] (x2-\x) at (3,{-\x-int(\x/4)}) {};
        \node[cnode=gray,label=90:$\theta_{2,\pgfmathresult}$] (p-\x) at (6,{-\x-int(\x/4)}) {};

    }

	\draw[rounded corners=10pt] (-1,-1) rectangle ++(2,-4) node[below] at (0, -5) {States $\mathcal{S}$};
	\draw[dashed, rounded corners=10pt] (2,0) rectangle ++(5,-6) node[below] at (4.5,-6) {Hidden layers};
	\draw[rounded corners=10pt] (8,-0.5) rectangle ++(2,-5) node[below] at (9.1,-5.5) {Actions $\mathcal{A}$};

	\foreach \x in {1,...,5}
	{
      	\pgfmathparse{\x== 4 ? "\vdots" : "a_\x"}
	\pgfmathparse{\x== 5? "a_n" : "\pgfmathresult"}
        	\node[draw=black,circle,label=0:${\pgfmathresult}$] (s-\x) at (9,{-\x-int(\x/6)+0 }) {};
	}

    \foreach \x in {1,...,4}
    {   \foreach \y in {1,...,5}
        {   \draw (p-\x) -- (s-\y);
        }
    }

    \foreach \x in {1,...,4}
    {   \foreach \y in {1,...,4}
        {  \pgfmathparse{\x<4 ? \x : "H"}
	        \draw (x2-\x) -- (p-\y) ;
        }
    }

    \foreach \x in {1,...,4}
    {   \foreach \y in {1,...,4}
        {  \draw (x-\x) -- (x2-\y);
        }
    }
\end{tikzpicture}
\caption{Structure of the neural network used for the DQN implementation with two hidden layers each of dimension $H$.  $\vert\mathcal{S}\vert = m, \vert\mathcal{A}\vert = n$.}
\label{fig:dnn}
\end{figure}

\begin{figure}[!t]
\centering
\begin{adjustwidth}{0.7cm}{0cm}
\begin{tikzpicture}[node distance = 5em, auto, thick, scale=0.9, font=\scriptsize]]
    \node [rectangle, draw,
    text width=8em, text centered, rounded corners, minimum height=1em,fill=gray!30] (Agent) {Self-Healing Agent};
    \node [rectangle, draw,
    text width=8em, text centered, rounded corners, minimum height=1em, below of=Agent] (Environment) {Radio Environment};

     \path [draw, -latex] (Agent.0) --++ (2em,0em) |- node [text width=5em,near start]{FM Action\\ $a\in\mathcal{A}$} (Environment.0);
     \path [draw, -latex] (Environment.180) --++ (-2em,0em) |- node [text width=5em, xshift=-0.3cm,yshift=-1.3cm] {New state\\ $s^\prime\in\mathcal{S}$} (Agent.180);
     \path [draw, -latex] (Environment.north) --++ (0em,0em) -- node [right] {Reward $r_{s,a}$} (Agent.south);
\end{tikzpicture}
\end{adjustwidth}
\caption{Reinforcement learning elements.  FM stands for fault management.}
\label{fig:reinf}
\end{figure}

We use $Q$-learning with a deep neural network  as in \cite{mnih2013playing}.  This deep neural network is known as the \textit{deep $Q$-network} (DQN) and is shown in Fig.~\ref{fig:dnn}.  We use DQN with experience replay and formulate the SON fault management as a deep RL problem as in Algorithm~\ref{alg:the_fm_alg}.  The framing of the reinforcement learning problem is shown in Fig.~\ref{fig:reinf}.

To formulate this problem as a reinforcement learning problem, we define a \textit{Markov decision process} (MDP) with transition probabilities $p(\cdot)$ as in Fig.~\ref{fig:markov_volte}.  The set of actions carried out by the self-healing agent are $\mathcal{A} = \{a_i\}_{i = 0}^{n-1}$ and the set of network states are $\mathcal{S} = \{s_i\}_{i = 0}^{m-1}$.  These are shown in Table~\ref{table:simulated_son_actions}.    A state $s$ is \textit{terminal} if it is the final state or if the objective has been met.  We define the reward as:
\begin{equation}
r_{s,a}[t] \triangleq \begin{cases}
	r_1, & \; 0 < \vert{\bm\varphi}_\text{fault}[t - 1]\vert < \vert{\bm\varphi}_\text{fault}[t]\vert  \\
	      r_2, & \;  \vert{\bm\varphi}_\text{fault}[t]\vert = \vert{\bm\varphi}_\text{fault}[t-1] \vert  \\
      r_3, &\;  \vert{\bm\varphi}_\text{fault}[t] \vert< \vert{\bm\varphi}_\text{fault}[t-1]\vert  \\
r_4, & \;  \vert{\bm\varphi}_\text{fault}[t]\vert = 0  \, \text{(i.e., objective is met)}
   \end{cases}
   \label{eq:rewards}
\end{equation}
where $\vert\varphi_\text{fault}[t]\vert$ is the number of bits that are set to logic-1 in the fault register at a given TTI $t$. The fault register $\varphi_\text{fault}[t]$ is a register of $u$ boolean entries, where the $i$-th entry in the register corresponds to the fault with identifier $i$ triggered in this cluster.  It is initialized to all logic-0 and set whenever a fault $i$ happens in the network and unset only when all similar faults are cleared.  These faults are shown in Table~\ref{table:network_actions}.

With a network having $\vert\mathcal{C}\vert$ cells, $n$ alarm-clearing actions, and $m$ states, the number of elements in a table required is in $\mathcal{O}(mn \vert\mathcal{C}\vert)$.  In networks with thousands of cells and alarms, the tabular $Q$-learning method to keep track of the state-action values in a table does not scale due to this multiplicative nature.

\begin{figure}[!t]
\centering
\usetikzlibrary{automata,positioning}
    \begin{tikzpicture}[->,>=stealth',scale=0.7, every node/.style={scale=0.7,node distance=1.8cm}]

        \node[initial,state] (s0) {$s_0$};
        \node[state, right=of s0] (s1) {$s_1$};
        \node[state, right=of s1] (s2) {$s_2$};
        \node[accepting,state, right=of s2] (e0) {*};

        \draw[every loop]
(s0) edge [loop above] node {$p(a_0\vert s_0)$} (s0)
(s1) edge[bend right, auto=right] node {$p(a \in \mathcal{S}\vert s_1)$} (s2)
(s1) edge[loop above] node {$p(\nu\in\mathcal{N} \vert s_1)$} (s1)
(s2) edge[loop above] node {$p(a \in\mathcal{A}\vert s_2)$} (s2)
(s2) edge[bend right, auto=right] node {$p(\nu\in\mathcal{N}\vert s_2)$} (s1)
(s2) edge[right, auto=right] node {terminal} (e0)
(s0) edge[right, auto=right] node {$p(\nu\in\mathcal{N} \vert s_0)$} (s1)
	    ;
    \end{tikzpicture}
    \caption{Markov decision process used in the formulation of the SON fault handling algorithm.}
    \label{fig:markov_volte}
\end{figure}

The \textit{episode} $z\colon z \in \{0,1,\ldots,\zeta\}$ is a period of time for an agent-environment interaction to take place. During an episode, the deep RL agent gathers \textit{experience} from a finite number of episodes where each episode has a duration of $\tau$ \textit{transmit time intervals} (TTIs).  This agent stores the experience $e[t]$  defined as $(s, a, r_{s,a}, s^\prime)$   in  a dataset called the \textit{replay memory} $\mathcal{D}$ \cite{mnih2013playing}.

We next define the estimated function $Q^*(s,a)$, which is the expected discounted reward when starting in state $s$ and selecting an action $a$  as \cite{mnih2013playing}:

\begin{equation}
    \label{eq:bellman_deep}
    Q^*(s,a) \triangleq \mathbb{E}_{s^\prime} \left [ r_{s,a} + \gamma \max_{a^\prime} Q^*(s^\prime,a^\prime) \,\bigg\vert\, s, a \right ]
\end{equation}

If we define a DQN with its weights at time $t$ as ${\bm\theta}_t$, then (\ref{eq:bellman_deep}) can be approximated as $Q(s,a;{\bm\theta}_t) \approx Q^*(s,a)$ as $t\to \infty$.  This DQN is trained through minimizing the \textit{mean squared error} (MSE) convex loss function
\begin{equation}
    \label{eq:loss}
    L_t({\bm\theta}_t) \triangleq \mathbb{E}_{s,a} \left [(y_t - Q(s,a;{\bm\theta}_t))^2 \right ]
\end{equation}
where $y_t$ is an estimate obtained from the DQN using its weights at time $t-1$ as:
\begin{equation}
    \label{eq:yest}
    y_t \triangleq \mathbb{E}_{s^\prime} \left [ r_{s,a} + \gamma \max_{a^\prime} Q(s^\prime,a^\prime;{\bm\theta}_{t-1}) \,\bigg\vert\, s, a \right ].
\end{equation}
The weights ${\bm\theta}$ are updated after every iteration in time using a method of the stochastic gradient descent algorithm (SGD) called ``adaptive moments'' \cite{KingmaB14}.  We also use the \textit{rectified linear unit} (ReLU) $x\mapsto \max(0,x)$ as the activation function of each node in the DQN.  This deep learning process repeats for all the episodes $z$.

\begin{table*}[!t]
\setlength\doublerulesep{0.5pt}
\caption{SON Fault Management Algorithm -- Simulated Actions $\mathcal{A}$ and States $\mathcal{S}$}
\label{table:simulated_son_actions}
\vspace*{-.1in}
\centering
\begin{tabular}{ clcl }
\hhline{====}
Action $a$ & Definition & State $s$ & Definition \\
\hline
0 & No actions issued. & 0 & No actions issued (a transient state). \\
1 & Faulty neighbor cell is up again. & 1 & Number of active alarms has increased. \\
2 & Serving cell transmit diversity enabled.  & 2 & Number of active alarms has decreased. \\
3 & Serving cell losses recovered.  \\
4 & Serving cell azimuth set to default value.\\
\hhline{====}
\end{tabular}
\end{table*}

During an episode $z$, the deep RL agent tries to maximize the total value of the discounted rewards it receives in response to its action.  It uses a near-greedy action selection rule.  This is because with large number of episodes $\zeta$, every actions will have been sampled enough for the state-action value function to converge \cite{Sutton}. The near-greedy action selection rule of choice is the $\epsilon$-greedy strategy for learning. In this strategy, $\epsilon$ is the \textit{exploration rate} and serves to select a random action $a\in\mathcal{A}$ with a probability $\epsilon\colon 0 < \epsilon < 1 $, known as exploration, or selects an action from the replay memory $\mathcal{D}$, which is also known as exploitation, with a probability $1-\epsilon$. The exploration rate decays in every episode until it reaches the minimum exploration rate $\epsilon_\text{min}$.

\renewcommand{\thefootnote}{\fnsymbol{footnote}}

\section{Fault Handling Algorithms}\label{sec:algorithm}

\subsection{Random}
The faults are cleared from a random sample of active faults.  We choose the discrete uniform random distribution for the healing of the faults in the network since the discrete uniform distribution maximizes the discrete entropy \cite{Cover}.  This is a non-trivial lower bound of performance compared to taking no action.

\subsection{First-In, First-Out}
In this approach, the SON takes fault handling actions  immediately in the next TTI in the order these faults happen.

\subsection{Proposed}
Our proposed deep RL-based algorithm  is shown in Algorithm~\ref{alg:the_fm_alg}. Unlike FIFO, this algorithm can handle faults regardless of the order they happen due to the $\epsilon$-greedy learning strategy.

\begin{algorithm}[!t]
 \small
  \caption{\small SON Fault Management}
  \label{alg:the_fm_alg}
 \DontPrintSemicolon
  \KwIn{The set of fault handling actions $\mathcal{A}$ in a network $\mathcal{C}$.}
  \KwOut{Optimal fault handling commands given during a frame $z$, which has a duration of $\tau$.}
  Define the fault management states $\mathcal{S}$, the exploration rate $\epsilon$, the decay rate $d$, the discount factor $\gamma$, and minimum exploration rate $\epsilon_\text{min}$.\;
  Initialize time, states, actions, fault handling register, and replay memory $\mathcal{D}$.\;
  \Repeat {$\vert\bm{\varphi}_\text{fault}[t]\vert = 0$ {\rm or} $t \ge\tau$} {
  $t := t  + 1$\;
  $\epsilon := \max(\epsilon\cdot d, \epsilon_\text{min})$ \;
    Sample $r \sim \text{Uniform}(0,1)$\;
  \eIf {$r \le \epsilon$} {
  Select an action $a \in \mathcal{A}$ at random.\;
  } {
  Select an action $a = \arg\max_{a^\prime} Q(s,a^\prime;\bm{\theta}_t)$. \;
  }
  Perform action $a$ to resolve alarm and update $\bm{\varphi}_\text{fault}[t]$.\;
  Obtain reward $r_{s,a}$ from (\ref{eq:rewards}).\;
  Observe next state $s^\prime$.\;
Store experience $e[t] \triangleq (s, a, r_{s,a}, s^\prime)$ in $\mathcal{D}$.\;
Sample from $\mathcal{D}$ for experience $e_j\triangleq (s_j, a_j, r_j, s_{j+1})$.\;
\eIf {$s_{j+1}$ {\rm is terminal}} {
Set $y_j:= r_j$
} {
Set $y_j := r_j + \gamma\max_{a^\prime} Q(s_{j+1}, a^\prime; \bm{\theta}_t)$
}
 Perform SGD on $(y_j - Q(s_j, a_j; \bm{\theta}_t))^2$\;
  $s := s^\prime$\;
}
  Proceed to the next LTE-A frame $z+1$.\;
 \end{algorithm}

We next compute the time complexities of these various fault handling algorithms:
\begin{itemize}
\item For the random algorithm, an action is randomly sampled from a list of actions, therefore it has a time complexity in $\mathcal{O}(1)$ per iteration or $\mathcal{O}(\tau)$ total.
\item The First-In First-Out (FIFO) fault-handling algorithm reviews the alarm register every TTI and therefore has a time complexity in $\mathcal{O}(\max(u, \vert\mathcal{C}\vert))$ per iteration or $\mathcal{O}(\tau \max(u, \vert\mathcal{C}\vert))$ total.
\item For our proposed algorithm, the time complexity of the for DQN backpropagation algorithm is at least in $\mathcal{O}(k(\bm{\theta})\tau\zeta \vert\mathcal{C}\vert\vert\mathcal{A}\vert)$ \cite{scikit-learn}, where $k(\bm{\theta})$ is a function of the depth and number of the hidden layers $\bm{\theta}$.
\end{itemize}

Although our proposed algorithm has the highest time complexity cost, the complexity is not dependent on the number of UEs being served, and therefore it is scalable in the number of UEs served in a cluster. Furthermore, while the random algorithm can be trivially distributed across multiple cells independently and require a space complexity in $\mathcal{O}(\vert\mathcal{A}\vert)$, the distributed implementation is less scalable for the FIFO model since it requires $\vert\mathcal{C}\vert(\vert\mathcal{C}\vert - 1)/ 2$ links to communicate about faults and fault management leaving us with a message passing complexity in $\mathcal{O}(\vert\mathcal{C}\vert^2)$.  Our proposed algorithm can be run in a distributed fashion owed to its deep learning component \cite{Dean2012} and centralized collection point at the SON leaving us with message passing complexity in $\mathcal{O}(\vert\mathcal{C}\vert)$.  We refer to the source code \cite{mycode} for further implementation details.

\section{Performance Metrics}\label{sec:benchmarks}
We evaluate the downlink SINR with power allocation using the waterfilling algorithm at the transmitter and the zero-forcing equalization at the receiver as in \cite{VLS-2016}.
We also use the average downlink cell throughput and the downlink user throughput, which is derived from its empirical cumulative distribution function (CDF) as follows: peak (95\%), average, and edge (5\%) \cite{link}.
\begin{table}[!t]
\centering
\caption{Machine Learning Parameters}
\label{table:ml_parameters}
\setlength\doublerulesep{0.5pt}
\vspace*{-0.1in}
\begin{tabular}{ lr }
\hhline{==}
Parameter & Value \\
\hline
Neural network hidden layer width $H$ & $24$ \\
Loss function $L_t({\bm\theta}_t)$ & mean squared error \\
Optimizer &  \cite{KingmaB14} \\
Number of episodes $\zeta$ & 50  \\
Discount factor $\gamma$ & 0.950 \\
Exploration rate $\epsilon$ & 1.000\\
Exploration rate decay $d$ &  0.91 \\
Minimum exploration rate $\epsilon_\text{min}$ & 0.010\\
One episode duration $\tau$ & 20 TTIs \\
Number of states & 3 \\
Number of actions & 5 \\
\hhline{==}
\end{tabular}
\end{table}

\section{Simulation Results}\label{sec:results}

\begin{table*}[!t]
\setlength\doublerulesep{0.5pt}
\caption{Radio Environment Parameters}
\label{table:parameters}
\centering
\begin{threeparttable}
\vspace*{-0.2in}
\begin{tabular}{ lrlr}
\hhline{====}
Parameter & Value & Parameter & Value\\
 \hline
Bandwidth  & 10 MHz & Downlink center frequency & 2100 MHz \\
LTE cyclic prefix & Normal & Cellular geometry & Hexagonal \\
Inter-site distance &  200m & Scheduling algorithm & Proportional Fair \\
Number of cells in the network & 21 & Propagation model & COST231 \\
Propagation environment & Urban & Number of concurrently active UEs per cell $q$\tnote{\textdagger}  & $ \{10  ,50\}$ \\
BS  antenna model\tnote{\textdagger}  & 3gpp 36.942 & BS maximum transmit power & 46 dBm \\
BS antenna height & 25 m & BS antenna electrical tilt & 4$^\circ$ \\
BS MIMO configuration (\# Tx, \# Rx antennas) & $(4,2)$ & Noise power density & -174 dBm/Hz \\
UE average movement speed & 3 km/h   & UE height & 1.5 m \\
Shadow fading margin standard deviation & 8 dB& BS number of sectors per site & 3 \\
\hhline{====}
\end{tabular}
\begin{tablenotes}\footnotesize
\item[\textdagger]  BS is short for \textit{base station} and UE is short for \textit{user equipment}.
\end{tablenotes}
\end{threeparttable}
\end{table*}

\begin{table*}[!t]
\setlength\doublerulesep{0.5pt}
\caption{Throughput performance per algorithm for different number of users per cell}
\label{table:dl_ue_throughput}
\vspace*{-0.1in}
\centering
\begin{tabular}{ p{0.1\textwidth}ccc|ccc|ccc || ccc}
 & \multicolumn{9}{c}{User Equipment (UE) Throughput [Mbps]}  & \multicolumn{3}{c}{Cell Throughput [Mbps]} \\
 \cline{2-13}
  & \multicolumn{3}{c}{Random\tnote{\textdagger}} & \multicolumn{3}{c}{FIFO} & \multicolumn{3}{c}{Proposed} & Random & FIFO & Proposed  \\
\cline{2-13}
UEs per cell & Peak &  Average & Edge  & Peak & Average & Edge  & Peak & Average & Edge & \multicolumn{3}{c}{Average}\\
\hline
$q = 10$ & 3.48 & 1.78 & 0.53 & {3.52} & {1.79} & {0.54} & \textbf{3.55} & \textbf{1.84} & \textbf{0.58} & 17.77 &  17.95 & \textbf{18.37} \\
$q = 50$ & 0.68 & 0.38 & 0.13 & 0.68 & 0.38 & 0.13  & 0.68 & 0.38 & 0.13 & 18.81 & 18.96 & \textbf{18.97}  \\
\hhline{=============}
\end{tabular}
\end{table*}

We use the Vienna LTE-A Downlink System Level Simulator to simulate the outdoor network in Fig.~\ref{fig:network} with reproducibility  \cite{VLS-2016}. The choice between \mbox{LTE-A} or 5G in the sub-6 GHz range is driven by the OFDM numerology scaling factor.  We implement Algorithm~\ref{alg:the_fm_alg} using both MATLAB and Python \cite{mycode}.  The parameters used in our simulation are summarized in~\mbox{Tables}~\ref{table:ml_parameters}~and~\ref{table:parameters}.   Each episode has a duration of $\tau=50$ TTIs.  In LTE-A or 5G, the duration of 1 TTI is equal to 1 ms.   We set the rate of occurrences of faults in Table~\ref{table:network_actions} as $p_0 = 5/9, p_1 = p_2 = p_3 =p_4 = 1/9$.  This way we give all faults an equally likely chance of occurrence which is the worst case.  For the rewards in (\ref{eq:rewards}), we set $r_1 = -1, r_2 = 0, r_3 = 1, r_4 = 5$.

In Fig.~\ref{fig:sinrcdf}, we show the average downlink SINR distribution for all three algorithms for $q=10$.  While the FIFO algorithm performs incrementally better than the random algorithm, our proposed algorithm has a slightly higher downlink SINR overall and a significantly higher SINR gain in the range from 2 to 7 dB.  The random algorithm leads to the worst performance due to the poor handling of faults. For our proposed algorithm, we show the results after $\zeta= 50$ episodes, which is after a total of $\tau\zeta =1$ second.

The quantitative results of our simulation are shown in Table~\ref{table:dl_ue_throughput}. We observe that when the cell serves a low number of users (i.e., low cell load), our proposed algorithm outperforms the random algorithm as a lower bound and outperforms the FIFO algorithm. However, as the cell serves more UEs ($q=50$), the performance of all algorithms becomes similar since the cellular resources are near depleted (i.e., a bottleneck) at highload and therefore clearing alarms does not lead to significant improvements.

\begin{figure}[!t]
\centering
\scalebox{0.36}{\input{figures/network.tikz}}
\vspace*{-.1in}
\caption{The simulated outdoor network.}
\label{fig:network}
\end{figure}

\begin{figure}[!t]
\centering
\scalebox{0.36}{\input{figures/sinr.tikz}}
\vspace*{-0.1in}
\caption{The average downlink SINR empirical CDF as measured by the user equipment (UEs) for all three algorithms ($q = 10$).}\label{fig:sinrcdf}
\end{figure}

\section{Conclusion}\label{sec:conclusions}

In this paper, we attempted to find an optimal solution policy for a RL based fault management algorithm in an outdoor realistic cellular environment.  We motivated the need for deep RL in resolving  faults in similar cellular environments.
The use of deep RL allows the distributed implementation of the fault handling algorithm, which is useful when the cluster size is large.
Our proposed solution works by allowing RL to learn how to improve the DL SINR through exploration and exploitation of various alarm corrective actions.
The simulations showed that the deep RL-based method, which we proposed, can improve the performance of the cellular network measured by the downlink SINR and downlink throughputs.
Therefore, the proposed deep RL-based automated cellular network tuning framework is useful in maintaining the end-user QoE in a network with impairments and faults.

\ifCLASSOPTIONcaptionsoff
  \newpage
\fi


I just saw a commercial for a new TV series on ABC called Last Resort. The show might be interesting, but I fell in love with the song, Nothing But the Water by Grace Potter and the Nocturnals. I literally shushed my Mom and ran to a computer to find out what it was.
I just saw her perform that live last night in Indy! She sounded amazing.
What a beautiful song. I love Grace's voice and will be going to find this music in iTunes right away!!! Thanks for sharing.


As a parent, all you want for your child struggling with obsessive-compulsive disorder (OCD) or related anxiety disorders, is hope. The specific fears, thoughts and anxieties of these disorders are difficult for both your child and your family.
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As with all of our OCD and anxiety care, your son or daughter will find our core therapy is a mix of cognitive behavioral therapy (CBT) with an emphasis on exposure and response prevention (ERP). Through ERP, our team works with your child to develop hierarchies for gradual, but increasing, exposure to what drives their obsessions and compulsions. Studies continue to demonstrate the effectiveness of this approach, as do outcome studies conducted by Rogers.
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Your child will stay busy, but they do have time for breaks and personal activity. You and your family may visit your child on the weekends and participate in therapeutic passes. Treatment can also include community outings and guest speakers.
The personal involvement of Rogers' full-time, board-certified child and adolescent psychiatrists and clinical psychologists is one reason why the Rogers Adolescent Center for OCD and Anxiety is one of the nation's best resources helping teens with OCD and related anxiety disorders get their lives back. But that dedication extends to all members of the team who will engage your son or daughter in gaining essential skills to address their unique, and often complex, needs.
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Pet Rescue Saga Level 1104 | Pre-views, level help, tips and videos for ALL Facebook King levels!
Pet Rescue Saga Level 1104 with tips and tricks by the helpful Pet Rescue Saga Help Group Admins and awesome Members.
This video walkthrough for Pet Rescue Saga Level 1104 will give you some cheat peaks for solving Level 1104 by yourself, use the pause function to stop the video if it goes to fast.
TIPS FOR PET RESCUE SAGA LEVEL 1104: Remove a vine blocks using the bombs in the middle and you will move 2 pets and the bottom. Once you charge the Rocket use it on the last pet on the right side. To get the pets down at the bottom use a bomb again to remove a vine blocks from the bottom.


This pattern is quick to make. It might be a bit difficult for a beginner but if you have mastered RAW, it will be easy. The yellow beads are 8mm wooden rondelle beads but glass rondelle beads would also work.


text:
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Much as I love Shakespeare's Richard III, I also love to see Richard portrayed more positively. Philippa Gregory's latest in her "Cousin's War" series, The Kingmaker's Daughter (2012) , takes up the end of the Wars of the Roses from the point of view of Anne Neville, the woman who is "in this humor wooed/in this humor won" in the Shakespeare's notorious seduction scene.
I think this is the first of Gregory's works that I've read, and I was quite favorably impressed. I am not a particular scholar of the era, but I know the basics, and her research seems sound to me. She includes a five-page bibliography of resources in case anyone feels like checking her work. Everything I casually checked was accurate or accepted as possible.
Anne's story, unfortunately, is a fairly depressing one: married at fourteen to the ill-fated Prince Edward, son of Henry VI and Margaret of Anjou; widowed at fifteen; imprisoned; married to Richard; one surviving child; two years as queen to the embattled Richard, during which reign their son dies; then dying herself at twenty-eight only a few months before Richard is killed by the future Henry VII. All this I knew before. But Gregory manages to bring alive not only Anne herself but the members of her family whose history I'd never thought much about: Richard Neville, a.k.a. the Kingmaker, 16th Earl of Warwick, whose machinations and shifting loyalties drove much of the latter part of the Wars of the Roses; Anne Beauchamp, her mother, a great heiress in her own right; and her older sister Isabel, married to Richard's older brother George, Duke of Clarence, famously said to have been drowned in a butt of malmsey.
Anne's tale opens during Warwick's first split with his Yorkist allies, when the new king Edward IV marries the widowed Elizabeth Woodville Grey, embarrassing Warwick, who had been negotiating for a marriage with a French princess. The numerous members of the Woodville and Grey families rapidly take Warwick's place as Edward's confidants and advisors, derailing his plans to marry Isabel and Anne to their cousins, the king's brothers, George and Richard. A failed rebellion against the Woodville influence rapidly turns to a plot to depose Edward on trumped-up grounds of illegitimacy in favor of George, now married hastily to Isabel. "Cousin's War" doesn't begin to describe this mess of shifting allegiances. Not only is this brother against brother, but the mother of all the York brothers, Cecilly, Warwick's aunt, is secretly scheming against her older son in favor of her younger. I hadn't absorbed exactly how shifty George was before, or how much reason Richard would have later had to mistrust him, given his record.
The scheme to put George and Isabel on the throne is quickly abandoned in favor of a complete shift in loyalty, the formerly Yorkist Warwick now making common cause with the Lancastrians in the person of the cold and clever Margaret of Anjou and her son by Henry Vi, another Edward, to whom the teenaged Anne is quickly married. Not a single one of these people are likeable: Isabel is a whiny schemer, George (Clarence) a traitor to his brother, Warwick and his wife a power-hungry pair of manipulators, Margaret of Anjou a brutal ice queen, and Prince Edward an abusive jerk who treats Anne like dirt. The obedient Anne is hopelessly lost in these shifting alliances. Her loyalty is to her family and the father she believes loves her, and she confusedly tries to adopt whatever factional role is called for. It takes the Anne rather longer than it should to realize that she is really nothing but a pawn.
Richard, however, comes across fairly well in the early part of the book: a courtly knight, entirely loyal to his brother and genuinely fond of Anne. His supposed deformity is nowhere in evidence. And after Anne's father and husband are killed, her mother and mother-in-law are imprisoned, and her sister's allegiance shifted firmly back to the Yorkists, Anne is completely isolated. At that point she finally tries to make some choices of her own, though still shadowed by her father's passionate wish that she or her sister should become queen and put Neville blood on the throne of England in the next generation. And then she is reunited with Richard. It's hard to believe that at this point, married then widowed and remarried, she is still only sixteen.
After a relatively happy decade of marriage to Richard, despite some indications that he is perhaps not quite as perfect a knight as she wishes, and the birth of their son (yet another Edward), Edward IV dies, and Richard is drawn directly into conflict with the Woodville faction over the control of the young princes. As depicted in Shakespeare, this does not end well, though Anne's death before the end of the reign means we never reach the final defeat of the Yorkists.
It's an impressive tale, despite its sadness, and I enjoyed how Gregory takes up the tale of the women who are usually given short shrift by history. Isabel's harrowing experience of childbirth aboard a ship, the legal trickery that gives the two sisters their mother's lands while she is still alive, and the cruel choices facing the women involved in this level of politics are brought vividly to life. I did raise my eyebrows a bit at the credence given to the Woodville women's supposed powers of witchcraft, but Gregory never quite steps over the line; all the supposed acts of witchcraft could simply be bad luck, bad weather, or outright delusion.
While it is frustrating that Anne is definitely one of the pawns rather than one of the power-players, and her passivity can be maddening, this is still a worthwhile read that adds another dimension to my understanding of the Wars of the Roses. I'd recommend it to anyone interested in this era of history.
Read for yourself:
Posted at 11:23 PM in Books/Reading | Permalink

redpajama_set_name: RedPajamaCommonCrawl


Loc-Line 3/4" Male NPT Valve for 3/4" ID System, pack of 10.
Regulate coolant or air flow to your work area. 1/4 turn of handle opens or closes the valve. Light-weight and compact. Body and stem material is acetal copolymer. Stem seals are nitrile (Buna N).
61516 Loc-Line 3/4" Male NPT Valve for 3/4" ID System, pack of 2.


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The eighth word of verse (30:22) is divided into 3 morphological segments. A conjunction, noun and possessive pronoun. The prefixed conjunction wa is usually translated as "and". The noun is masculine plural and is in the genitive case (مجرور). The noun's triliteral root is lām wāw nūn (ل و ن). The attached possessive pronoun is second person masculine plural.


text:
Jazzlet
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Commented on Decision Fatigue
Greg @155 I'd argue they aren't even feminists, they happily work with the most odious of America's christian right wing who in all other respects are about as anti-feminist as you can get. Personally I like the description Feminism Approriating...
@ 90 I say "London" heavy because the Guardian hasn't been known as the "Manchester Guardian" since 1959, they started printing in London in 1961, and moved the editorial staff there in 1964. Although the Guardian still has an office...
The Guardan staff are split in their attitudes to transgender people, one or two of them are good, a few are OK, but significant number are truly awful. They're the best of the London heavies in general, but you should...
Commented on Omicron
What all of you optimists except Charlie seem to be forgetting is that long COVID affects 15-80%* of all cases even the mildest. There is already evidence that having had beta or delta COVID doesn't protect you from having omicron,...
Commented on Lessons learned: writing really long fiction
WaveyDavey I find the JD Robb books to be mostly a fun fairly light read, they are not classical romances in that the main protagonist does not change from book to book, although we do see other romances develop over...
Commented on Ever Young?
I am 56 and was going to say, like several others have, that losing both parents did it for me, but I had to go off and do some household adulting which gave me time to ponder the question for...
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Howard NYC commented on Decision Fatigue
there's "carpet bombing" and then there's "precision bombing" for varying definitions of "precision"... smart(er) bombs which are more likely to hit the desired target... a sniper's bullet patiently awaiting a specific head in the crowd to be in clear line of sight... knowing which wire to cut to wreck a U235/U238 purification facility... what all those have in common? intel the better the intel the less effort to succeed at hurting the enemy and with lowered 'collateral damage' what the US learnt from the Israelis has been patience and accuracy and assembling vast mappings of interconnections to locate weakest links......
Troutwaxer commented on Decision Fatigue
It's also a matter of record that dictators don't like talented military officers. They're the ones who have the necessary strategic and tactical capabilities to overthrow the dictator, so they're frequently killed by their own side, because the dictator remaining in power is more important than winning a war of aggression....
context = Russia Stalin having become infamous for 300 (350?) seniormost officers executed during WW2 including during darkest days after Hitler reneged on their quasi-alliance... but there's a difference between execution due to paranoia of a dictator and higher than expected fatality rates on the battlefield a plausible scenario that NATO could have quietly circulated was 'grinding down' of RUS to ensure it is unable to be a threat for a full decade after end of RUS-UKR war another all too plausible scenario being internal strife amongst Kremlin inner circle has been leading towards deciding whomever is to be Putin's...
Pigeon commented on Decision Fatigue
Which would you expect a USSR type to be more likely to describe as a tragedy - victory in the Great Patriotic War, or defeat in economic war 45-odd years later?...
Mike Collins commented on Decision Fatigue
That quote of Putin is cherry picked. I just heard on Radio 4 what came before "For the millions of Russians stranded outside their Motherland .."...
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Hilary Duff gives fans a glimpse at her bikini body on getaway with son Luca
March 16, 2015 - 11:13 GMT hellomagazine.com Hilary Duff showed off the hard-earned results from her regular gym visits on Sunday. The 27-year-old, who is currently enjoying an exotic holiday
Hilary Duff revealed the hard-earned results from her regular gym visits on Sunday. The 27-year-old, who is currently enjoying an exotic holiday, proudly showed off her toned physique with a revealing Instagram picture.
"Hey #moms #westillgotit #loveyourbod", she captioned the picture, which showed her smiling in front of a mirror in a black bandeau bikini.
CLICK ON PHOTOS TO ENLARGE
Hilary Duff showed off her bikini body on Instagram
The actress is on holiday with her close friends and two-year-old son Luca, who she also shared an adorable picture of on Sunday. The black and white snap shows her giving the youngster a kiss while she carries him on the beach.
"Never knew love before…" she wrote.
Hilary Duff is on holiday with her son Luca Comrie
Hilary also gave fans another glimpse at her bikini body with a poolside picture, telling her 2.9million followers, "Isn't terrible here…"
The Youngers star appears to be enjoying her beach break, which comes just weeks after she reportedly filed for divorce from her husband Mike Comrie.
The actress recently filed for divorce from her husband Mike Comrie
According to TMZ, Hilary listed the couple's separation date as January 2013, and is seeking sole custody of their son Luca Cruz Comrie, who turns three on Friday.
Hilary recently opened up about the split and said it has changed her view on whether people are meant to be together forever. Speaking to Cosmopolitan US, she said: "Mike and I were very in love when we met. We both really wanted to get married. I'd been working since the age of 11 or 12, so making that choice at a young age seemed right for me. Maybe it wasn't, but we spent the majority of our time together really happy.
She continued: "I don't want to sound bitter because I'm definitely not, but I don't know if people are meant to be together forever. Things happen over a long relationship that you can't always fight."
More about hilary duff
Hilary Duff 'so proud' to share first trailer for How I Met Your Father with Kim Cattrall
Stars and royals who have tested positive for the coronavirus or say they've likely had it
Hilary Duff shares incredible and long-awaited news with fans
Celebrity birthdays: Hilary Duff turns 27
Haylie Duff pregnant: read her sweet baby announcement
Pregnant Haylie Duff puts her wedding plans on hold
Hilary Duff reportedly files for divorce from Mike Comrie
Hilary Duff's son and Lisa Osbourne's daughter reunite for ice-cream date: see cute photos
Haylie Duff: inside her fun flower-filled baby shower


Are these temperature transmitters not the perfect match for your application?
This range of temperature transmitters are available as either head transmitters (TMT187/188) or as rail mounted devices (TMT127/128). The TMT187/188 head transmitters can be installed in the form B sensor head and have a fixed measurement range as well as a 4 to 20 mA analog output.
The TMT127/187 RTD temperature transmitter is a two-wire transmitter with an analog output and a three- or four-wire resistance thermometer input.
The TMT128/188 TC temperature transmitter is a two-wire transmitter with an analog output and thermocouple input.
More measuring ranges and sensor types on request!


Mobile Components : Introduction of Mobile Communication, Introduction to Mobile Phones, Cellular Mobile Telephone Service, Service Information of Mobile Phone (Base Band Module, Base Band), Identification of different IC's, Supply Voltage Regulation, Powering UP & Down the Phone, Receiver, Transmitter, Headset, Detection, Memory, SRAM, EEPROM, FLASH, Display Circuit/Monitor, Comparison with computer, Batteries and charger, SIM Card, Network Section (PFO, FDK, Antenna, Antenna Switch), Chip Level and BGA training, GSM Codes, Block Diagram of different phones, Ball IC Practice, How to fix the Ball IC, Checking of PCB Prints, Introduction of different categories of mobile phones, SMD Rework Station, Practice on Working Phones, Parts Replacing & Checking.
Trouble Shooting : Fault finding Procedure, SIM Card Faults, Network Problem, Charging and Battery Problems, Power ON/OFF Problems, General Faults, Display Problems, Software Problems, Keyboard Problems, Motherboard Tracing & Trouble shooting.
Mobile Software & Trouble Shooting : Use of Logo Manager, Identification of Dongle Switch and interface Cable, Indentify how to connect different type of interface cable with different mobiles, Unlock, Flashing, Blue tooth, Loading Games, Video clip, Blacklisting software, Remote Software, UFS3.
Copyright © 2018 OCSM. All Rights Reserved.


text:
Sound Recording 101. Where did it Start?
Sound recording and playback are a physical, electrical, mechanical, or electronic re-production and are uttering of sound waves, including recorded voice, musical instruments, spoken word, music, and other sound effects. There are many types of sound recording devices. There are studio compressors, tape machines, record and playback machines, and tape heads. The two basic categories of sound recording technologies are digital recording and analog recording. Digital recording involves the use of computer hardware and software to create and reproduce sound.
The earliest known form of sound recording was the phonograph. It was invented by Samuel Simon in 1843. He created what is now called the "Simonic phonograph," a cylinder-shaped device that could record sound vibrations into a disk. The cylinders were usually made of wood, with a thin layer of oil that preventing the moisture from accumulating inside.
The first commercially available sound recording devices were made by RCA Corporation. Theirault, RCA Victor, RCA Records, and RCA Vibrating Discs were the first versions of this recording machine. Over time, advancements in materials and equipment made it possible for mass production of these first phonographic discs. Today's equipment, however, is designed for the precise reproducibility and high quality sound recording needs of the music industry. There are also compact disks and computers that can read and are played back sound recordings.
Today's technology continues to improve and advance the recording process. Computer-based audio recordings are made digitally using samplers and other computer hardware. One major improvement is the addition of a "lifting system" to the stylus. The lifting system makes it possible to play back the signal at different pitches without using mechanical force. This is very noticeable when listening to or recording fast-moving music such as rock or rap, used commonly in music recording studios. The sudden changes in pitch makes it impossible to match the signal exactly, as it were.
Computer based recordings can also be done using what is called "paraphonic" tracking. This technique requires tracking a signal at more than two frequencies at the same time, and it requires an instrument or headset that can generate a stereo signal. Because the signal generated has more than 2 frequency bands, it is generated at different volumes which can be heard individually or mixed together to make a full stereo mix. Although a bit of a hassle, the ability to do this is a noticeable difference between recording using tape and recording to a computer.
Another way to classify a recording is by its frequency response, which is measured in Hertz (Hz) or kilohertz (kH). The frequency response of a recording will vary greatly depending on the instrument being used and its capabilities. A high pitched voice would have a much different sound wave pattern (higher frequency response) than a synthesizer playing a piano piece with a low B note. Recording is a very important part of technology, as it allows us to preserve memories and pass them on to future generations.
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Getting Started with Product Design
Product design is one of the most vital elements of product development. No matter how… Read More »Getting Started with Product Design
Finding Insurance for your Home
Property insurance offers protection against all potential risks to real property, including fire, theft, storm… Read More »Finding Insurance for your Home


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Q: In Graphviz, how to set only one edge to spline=curve I am trying to draw a lavaan model using Graphviz and am happy in general with how it looks (1st graph), but would like the edge between the two dimensions to be curved but all the others to be straight.
Is it possible to get the edge between dimensions (edge d1 to d2) to curve by specifying graph [layout = neato, overlap = FALSE, outputorder = edgesfirst, splines = curved], as you can see in the second graph, but this makes all of them curved.
Could anyone guide me how to get the desired result?
Here is the code to reproduce the first graph:
grViz("
digraph CFA {
graph [layout = neato, overlap = FALSE, outputorder = edgesfirst]
node [shape = rectangle]
edge [arrowhead = vee]
# Nodes (variables)
m1 [pos = '-5,1.5!', label = 'VAR1']
m2 [pos = '-5,0.5!', label = 'VAR2']
m3 [pos = '-5,-0.5!', label = 'VAR3']
m4 [pos = '-5,-1.5!', label = 'VAR4']
d1 [pos = '-1.5,0!', label = 'Info', shape = ellipse, width=1]
d2 [pos = '1.5,0!', label = 'Support', shape = ellipse, width=1]
m5 [pos = '5,1.5!', label = 'VAR5']
m6 [pos = '5,0.5!', label = 'VAR6']
m7 [pos = '5,-0.5!', label = 'VAR7']
m8 [pos = '5,-1.5!', label = 'VAR8']
# Edges (loadings)
d1->m1 [label = '1']
d1->m2 [label = '0.82']
d1->m3 [label = '1.20']
d1->m4 [label = '0.70']
d2->m5 [label = '1']
d2->m6 [label = '0.89']
d2->m7 [label = '1.08']
d2->m8 [label = '1.15']
# Define Error
m1->m1 [label = '0.34', dir=both, tailport = 'sw', headport = 'nw', arrowhead=curve, arrowtail=curve, style=dashed]
m2->m2 [label = '0.45', dir=both, tailport = 'sw', headport = 'nw', arrowhead=curve, arrowtail=curve, style=dashed]
m3->m3 [label = '0.28', dir=both, tailport = 'sw', headport = 'nw', arrowhead=curve, arrowtail=curve, style=dashed]
m4->m4 [label = '0.98', dir=both, tailport = 'sw', headport = 'nw', arrowhead=curve, arrowtail=curve, style=dashed]
m5->m5 [label = '0.64', dir=both, tailport = 'se', headport = 'ne', arrowhead=curve, arrowtail=curve, style=dashed]
m6->m6 [label = '0.31', dir=both, tailport = 'se', headport = 'ne', arrowhead=curve, arrowtail=curve, style=dashed]
m7->m7 [label = '0.42', dir=both, tailport = 'se', headport = 'ne', arrowhead=curve, arrowtail=curve, style=dashed]
m8->m8 [label = '0.25', dir=both, tailport = 'se', headport = 'ne', arrowhead=curve, arrowtail=curve, style=dashed]
d1->d1 [label = '0.65', dir=both, tailport = 'se', headport = 'ne', arrowhead=curve, arrowtail=curve, style=dashed]
d2->d2 [label = '0.72', dir=both, tailport = 'sw', headport = 'nw', arrowhead=curve, arrowtail=curve, style=dashed]
# Covariance
d1->d2 [label = '0.45', dir = both, arrowhead=vee, arrowtail=vee, splines=curved, tailport = 's', headport = 's']
}
")

And here are the plots:
First CFA plot with all edges straight

Second CFA plot with curved edges

A: One way is to use a dummy node which we will try to curve the edge around (change the height to control the curve)
dummy [pos = '0,0!', height=1.5, label='', color=white]

Then you can set the correlation / curved edge with
d1:s->d2:s [label = '0.45', dir = both]

You will also need the graph option splines=true.
Adding these produces

redpajama_set_name: RedPajamaStackExchange


text:
Share this Story: Things are finally looking up for the Islanders
Things are finally looking up for the Islanders
The Islanders have won a league-leading 23 games and former Canadiens goalie Jaroslav Halak has won 18 of those.
Pat Hickey • Montreal Gazette
Anders Lee of the New York Islanders celebrates after a goal against the Tampa Bay Lightning at the Nassau Veterans Memorial Coliseum on Dec. 20, 2014. Photo by Alex Trautwig /Getty Images
UNIONDALE, N.Y.
These are not my father's New York Islanders.
Things are finally looking up for the Islanders Back to video
But they're getting close.
My father was an Islanders season-ticket holder from Day One until his death in 1985. He kept the faith through the pains of expansion and was rewarded when the team won four consecutive Stanley Cups from 1980 to 1983 and was the runner-up to another dynasty, the Edmonton Oilers, in 1984.
There have been a lot of lean years since the glory days for the Islanders.
There have been ownership fiascos. NHL commissioner Gary Bettman once lined up John Spano as the Islanders' owner only to discover later that Spano was a penniless con man. At least four former owners of the Islanders have gone to prison for financial malfeasance not related to the hockey team.
The hockey management hasn't done much better. This is a team that traded away players like Zdeno Chara, Ziggy Palffy, Roberto Luongo and Pat LaFontaine.
Chara went to Ottawa in a deal that included Alexei Yashin, a talented but unpredictable Russian. Mike Milbury gave Yashin a 10-year, $63.9-million contract in 2001, but the Islanders bought him out after six seasons. The final year of that buyout is still counting against the Islanders' salary cap.
Milbury passed over Dany Heatley and Marian Gaborik to make Rick DiPietro the No. 1 overall pick at the 2001 NHL draft and then traded Luongo and Olli Jokinen to Florida to make room for the unproven goaltender. But you can't blame Milbury for the worst contract in the Islanders' history. It was owner Charles Wang who gave DiPietro a 15-year, $67.5-million deal. A series of knee and hip injuries ended DiPietro's career and the Islanders used a compliance buyout in 2003 to take his salary off the cap. But the team will be paying him through 2029.
However, the Islanders' fortunes are changing.
For several years, there have been high hopes because general manager Garth Snow and his staff have done a very good job at the draft. There are 12 homegrown players on the Islanders roster, including the top five scorers — John Tavares, Kyle Okposo, Brock Nelson, Ryan Strome and Frans Nielsen.
Despite the young talent, the Islanders have made the playoffs only twice in eight seasons under Snow's watch. They finished last in the Metropolitan Division last season after their slim playoff chances disappeared completely when Tavares broke his leg at the Olympics.
The one ingredient that has been missing with the Islanders has been a goaltender, and that's a surprise because Snow was a goalie. During Snow's first eight years on the job, the Islanders went through 12 goaltenders. There were some good ones near the end of their careers — Martin Biron, Dwayne Roloson and Evgeni Nabokov — and promising youngster Kevin Poulin, whose best days are ahead of him. There also was a collection of journeyman backups — Peter Manino, Yann Danis, Al Montoya, Wade Dubliewicz, Joey MacDonald, Anders Nilsson, Nathan Lawson and Mikko Koskinen.
This season, the goaltending is vastly improved with former Canadien Jaroslav Halak between the pipes. After bouncing from St. Louis to Buffalo to Washington last season, the veteran Slovak signed a four-year, $18-million deal with the Islanders and has provided the team with some stability.
"We've had some stability in the time I've been here, but we've also had injuries," said Jack Capuano, who is in his fifth year as the Islanders' head coach. "So far, things have been going well for us. Obviously, it starts with the goaltending, and when those guys are playing well you've got a chance to win."
St. Louis dealt Halak to Buffalo at the trade deadline last season and the Sabres immediately flipped him to Washington.
"It was a crazy season for me, being traded two times in such a such a short time," Halak said. "It's part of the business. As a player, you don't want to go through anything like that, but you have to deal with it.
"When I got to Washington, I just wanted to play games and get to the playoffs, (but) it didn't happen," the goalie added. "When I got traded here, there was interest from both sides. They wanted to sign me and I wanted to sign. I'm glad we got it done."
Halak was traded to the Islanders on May 1. He could have waited to test free agency, but recognized the young talent on Long Island and the need for a goaltender.
The Islanders have won a league-leading 23 games and Halak has won 18 of those. He earned a place in the Islanders' record book with 11 consecutive wins, eclipsing the mark of 10 set more than three decades ago by Hall of Famer Billy Smith.
"(The record) feels great, but it's a team effort," Halak said. "Some of the games went to shootouts. Back then, there were no shootouts, it was either regulation or OT. In a shootout, it's always 50-50 and the guys have scored some big goals for me. If the team plays well in front of me, there's a good chance we'll get two points."
While the team's young forwards are learning to win, Snow provided some leadership and defensive help when he added Nick Leddy and Johnny Boychuk to a blue line anchored by Lubomir Visnovsky.
"It's been a long time coming around," Kyle Okposo said. "We've taken some lumps. We wanted to be better and Garth did a good job in the off-season and brought in some key guys and we're learning how to win."
Said Tavares: "It's been frustrating and it's still early in the season, but we seem to be turning things around, particularly at home."
The Islanders have been buoyed by good crowds in their final season at the Coliseum — they move to the Barclay Center in Brooklyn next season — and have a 13-3 record at home after going 13-19-9 at home last season.
Halak took a maintenance day Monday. He noted that it has been five years since the Canadiens traded him to St. Louis for Lars Eller and that facing his former team doesn't have the same significance it did in the past.
"I don't know," Halak said when asked if he would face the Canadiens Monday night.
But it will be a surprise if he doesn't. Halak is 4-0 against Montreal with an 0.98 goals-against average.
phickey@montrealgazette.com
twitter.com/zababes1


Modalizy continues to expand its coverage in Europe, now adding Portugal as the 15th country where its Modalizy Pass Mastercard can be used – for example to use the tram in Lisbon (pictured).
Having been in business barely a year, Modalizy has already earned two awards for its innovative approach. The startup offers a mobility card with a wide range of options, including trains, taxis, public transport, cycle hire, and fuel.
Mobility services can be paid via the Modalizy Pass Mastercard in the three Benelux countries, the four Scandinavian countries, the UK and Ireland, Germany and Switzerland, France, Italy and Spain, and now also Portugal.


Hydrant Flushing will continue on Tuesday, April 9th. The Fire Department will include three crews working from 9:00 am to 4:00 pm. The areas where the hydrant flushing will occur are between South Oakland Avenue and South Emerald Lane at West Freeman Street going north as well as between South Oakland Avenue and South Illinois Avenue at West Chautauqua Street going north as well as between South Wall Street and South Lewis Lane at East Park Street going north. Customers may notice a change in water pressure and possible discoloration. The water is safe to drink. However, if your water is discolored, wait a few hours before doing laundry. If you have water related questions, please call 529-1731.
The Carbondale City Council will hold a public hearing to discuss the City's proposed budget of all funds, including the Carbondale Public Library, for fiscal year ending April 30, 2020. The hearing will be held at the Carbondale Civic Center on April 9, 2019 at 7:00 pm. The proposed budget will be available for public review beginning Monday, March 25, 2019 at the Carbondale Public Library, City Finance Department, and the City Clerk's Office.


Devil Kush was born of an experimental cross between a male Purkle x OG Kush and a specimen of Sir Jack.
Devil Kush Regular Marijuana Seeds by Exotic Seed: Devil Kush was born of an experimental cross between a male Purkle x OG Kush and a specimen of Sir Jack. Of the resulting hybrid, we selected different individuals showing characteristic features of its Kush descent. Its structure is totally columnar, with little branching, thus it is advisable for the SOG-type crop. It produces buds in lumps with a very high amount of resin, suitable for all kinds of extractions. It has a nice physical sedative effect, recommended to go to sleep or to the end of the day or watch a movie. Something to keep in mind when growing Devil Kush is its experimental nature, as we offer it in F2, where we can find a wide range of possibilities and aromas, something that seemed interesting for growers looking for different things and possible parents for home crosses.


Pack your baggage and join this exciting 5 -day safari holiday in Tanzania! During this safari, you will go on extensive game drives in Tarangire National Park, Lake Manyara National Park, Serengeti National Park and Ngorongoro Crater; you will have the opportunity to spot wildlife in their natural habitat and explore the magnificent Tanzanian national parks.
Today after breakfast you will start 4 hours drive with lunch boxes to Serengeti national park, we will break for picnic lunch before get to Serengeti national park, enter to the park for evening game drive before heading to your campsite or lodge at center of Serengeti for dinner and overnight.
Today we have fully day in most beautiful park in the world after breakfast we will start our game drive and late afternoon we will stop for picnic lunch continue with game drive until sunset before back to our campsite / lodge for diner and overnight.
Today after breakfast we will do game on route while driving heading to Ngorongoro crater often referred to as wonder of world. You will do a game drive break for picnic lunch and late evening ascend from crater and drive to your campsite/ Lodge in Karatu for dinner and overnight.
Today after breakfast we will drive you to Lake Manyara national park for game drive, After noon you will break for picnic lunch, after lunch game drive will continue until mid day where we will exit from the park and drive back to your hotel in Arusha/Moshi for dinner and over night.
Lake Manyara national park is one of the UNESCO World Heritage site. Set in the grasslands, Savannahs, Woods, Mountain scenery and hot springs. This park is home of Flamingoes, Elephants, Lions, Buffaloes, Leopard, Hippo, Gazelle, Baboons, Tree hyrax, and many more.


Tin cans are a really good material that can be easily upcycled. Any cans are good and you no longer have to throw them away and with them your money. Because let's be honest here! when we buy canned products, we pay more for the tin can than the product itself.
With just a few design ideas of your own you can transform these cans into pretty and useful items to decorate and personalize both your home and garden. I like using the cans with a pop up or easy-open lid so there are no rough edges on the cans once I remove the lid so there's no room for injuries.
These tin can flower pots are insanely easy to make you'll want to find more ideas to upcycle all your tin cans in the future! There are many ways you can use tin cans to make flower pots but I think the easiest and fastest is by painting them in the color and design of choice. if you're a good designer you can create some super duper flower pots (unlike yours truly here, who's a total disaster; and I call myself a creative blogger, ha!).