text:
\section{Introduction}
In recent years, enormous studies on cooperative control for multi-UAV system are overwhelming. Among them, multi-UAV formation tracking control is a common and fundamental problem, and the formation scale has changed from a few UAV groups previously to large-scale formations nowadays. With the exponential growth of formation scale, the system performance is more rigorously required. Hence, researchers proposed optimal control that optimize system performance and formation cost to reduce the system burden.

Optimal control is an effective strategy to balance the system performance and computational consumption.
For discrete-time systems, the optimal control can be achieved by solving the Bellman equation \cite{c1,c2,c3,c4}. However, since the analytic solution of the Bellman nonlinear equation is difficult to be derived directly, all studies above consider the linear systems. In order to approximate optimal controllers for nonlinear systems, reinforcement learning (RL) has been introduced in \cite{c5,c6,c7,c8,c81,c82}, where the actor-critic neural network (NN) is the commonly used RL architecture. The critic NN gives feedback to optimize the actions by evaluating the system performance index, while the actor NN issues optimized control commands to improve the system behaviors.
\begin{figure}[!htbp]
	\centering
	\includegraphics[width=\columnwidth]{Fig0.png}
	\caption{Hundreds of virtual UAVs and four physical UAVs in a large-scale mixed reality experimental platform to realize a UAV formation light show. \label{Fig0}}
	\vspace{-2em}
\end{figure}

In recent years, RL architectures have been widely used in optimal cooperative control. In \cite{c9}, a learning-based adaptive dynamic programming algorithm is used to solve the formation tracking problem for multi-UAV systems with model uncertainty in obstacle environments. In \cite{c10}, for the multi-agent tracking control with actuator faults, an adaptive optimal fault-tolerant  tracking controller is designed by combining the RL algorithm and the backstepping method. In \cite{c11}, a model-free optimal fault-tolerant containment controller using RL method is proposed to solve the containment problem for MASs with time-varying actuator faults. However, the studies above consider the time-triggered mechanism, which will continuously or periodically update the controller and NNs. This will inevitably cause a huge computational consumption when the formation size is large.

This study introduces the event-triggered mechanism where the UAV updates the controller and actor NN only when the specific condition is triggered, which allows the UAV system (UAS) to update control commands on demand, aperiodically rather than continuously and indiscriminately. At the same time, it means that the event-triggered mechanism can effectively reduce the system computational burden compared to time-triggered cases. For the RL-based optimal cooperative problems, a number of studies have introduced the event-triggered mechanism as an improvement, whether for continuous-time systems \cite{c12,c13,c14,c14_1,c14_2,c14_3} and discrete-time systems \cite{c15,c16,c17,c17_1,c17_2,c17_3}. However, these studies only implemente numerical simulations without verifying the algorithm effectiveness for engineering applications.

In order to verify the effectiveness of the proposed algorithm, a large-scale mixed reality experimental platform is established in this study. A large-scale UAV light show is realized using a limited number of physical UAVs and hundreds of virtual UAVs (Fig. \ref{Fig0}). In view of the main limitations of large-scale formation show, such as high requirement for experimental field, expensive experimental equipment, and poor safety factor, the established experimental platform has the advantages of low experimental cost and high safety factor. And the experimental results show that this platform only requires one room and four UAVs to achieve the desired effect of hundreds of UAVs in the large airspace.

This paper proposes an event-triggered optimal formation tracking controller for discrete-time large-scale UASs, and an online actor-critic NN structure is established to implement the control. The main contributions of this study include:
\begin{enumerate}
	\item Considering the main difficulties involved in the decision and control layers for large-scale switching formations, an algorithm framework integrating optimal formation assignment and optimal control is established.

	\item The event-triggered online actor-critic NN is proposed to approximate the local performance index and learn controller. Compared with \cite{c5,c6,c7,c8,c81,c82,c9,c10,c11}, actor NN weights and controller only update at triggering instants.

	\item This study highlights the engineering application of the proposed algorithm, establishes a mixed reality experimental platform for large-scale UAV formation, and verifies the proposed algorithm on this platform.

\end{enumerate}
\begin{figure*}[!pt
	\centering
	\includegraphics[width=\linewidth,scale=1.00]{Fig1.png}
	\caption{The algorithm overview of this study. To solve the large-scale UAV switching formation tracking problem, for the decision layer, the Hungarian algorithm is used to solve the goal formation assignment problem. For the control layer, the event-triggered mechanism and the RL-based Bellman equation are used to optimize the computational efficiency and the control performance of the system, respectively.}
	\label{Fig1}
	\vspace{-0.5em}
\end{figure*}
\iffalse
\subsection{Organization}
This paper is organized as follows. In Section \ref{sec2}, an algorithm overview proposed in this study is presented. In Section \ref{sec3}, the basic theory and problem description are listed. In Section \ref{sec4}, the online actor-critic NNs are proposed to implement the designed event-triggered optimal controller. In Section \ref{sec5}, the mixed reality experimental platform is established and the experimental results are analyzed. And this study is concluded in Section \ref{sec6}.
\fi
\section{Algorithm Overview}\label{sec2}
 As shown in Fig. \ref{Fig1}, an algorithm framework is designed to solve the large-scale UAV optimal formation tracking problem. And the algorithms for optimal assignment and optimal control are summarized in Algorithm \ref{alg:1} and Algorithm \ref{alg:2}.
\begin{algorithm}[!hb]
	\caption{Decision Layer - Optimal Assignment}
	\label{alg:1}

	{\bf Input:} 1) Initial position set $\vec{\mathbf{G}}$; 2) Expected formation is $\vec{\mathbf{S}}$; \\ \hspace*{0.43in}3) UAV number $N$.

	{\bf Output:} 1) Target position set $\vec{\mathbf{F}}$; 2) Optimal assignment
	\\ \hspace*{0.48in} list $\chi^*$; 3) Desired switching trajectory $h(k)$.
	\begin{algorithmic}[1]
		\State [$\vec{\mathbf{F}}$, $\chi^*$, $h(k)$]=Optimal\_Assignment($\vec{\mathbf{G}}$, $\vec{\mathbf{S}}$, $N$).
	\end{algorithmic}
\end{algorithm}
\begin{algorithm}[!ht]
	\caption{Control Layer - Optimal Control}
	\label{alg:2}

	{\bf Input:} 1) Desired trajectory $h(k)$ 2) Real-time states $x(k)$.

	{\bf Output:} 1) Optimized controller $u(k)$; 2) Triggering instants\\ \hspace*{0.48in}  sequence $\{k_l^i\}_{l\in\mathbb{Z}^+}$.

	\begin{algorithmic}[1]
		\State Initialize the actor-critic NN;
		\State Calculate triggering condition $f_i(k)$ with $h_i(k)$ and $x_i(k)$;
		\If{$f_i(k)>0$}
		\State Using actor NN to learn the controller $u_i(k)$;
		\State Calculate and update the actor NN;
		\State The corresponding instant $k$ is recorded in $\{k_l^i\}_{l\in\mathbb{Z}^+}$.
		\Else
		\State $u_i(k+1)=u_i(k)$;
		\State The actor NN remains the same as before.
		\EndIf
		\State Calculate and update the critic NN;
		\State Approximate the system performance index.
	\end{algorithmic}
\end{algorithm}

\section{Preliminaries} \label{sec3}

\subsection{Graph Theory}
For a large-scale UAS with a virtual leader and $N$ followers, the communication network can be described as a graph $\mathcal{G}=\{\mathcal{A},\mathcal{E},\mathcal{W}\}$, where $\mathcal{A}=\{a_1,\dots,a_N\}$ denotes the node set, $\mathcal{E}$ is the edge set and $e_{ij}=(a_i,a_j)\in\mathcal{E}$, and $\mathcal{W}$ is the adjacency matrix with elements $w_{ij}$, for $e_{ij}\in\mathcal{E},~i\neq j$, $w_{ij}=1$, otherwise $w_{ij}=0$. Define $N_i$ as the neighbor set of UAV $a_i$. Then, the in-degree matrix $\mathcal{D}=\mathrm{diag}_{i\in[1,N]}\{\sum_{j\in N_i}w_{ij}\}$. Laplacian matrix is $L=\mathcal{D}-\mathcal{W}$. Further, a diagonal matrix $B=\mathrm{diag}_{i\in[1,N]}\{b_i\}$ describes the communication between followers and the virtual leader. Assume that the leader can communicate with at least one follower, and there exists a spanning tree with the leader as the root in the directed group $\hat{\mathcal{G}}=\{\hat{\mathcal{A}},\hat{\mathcal{E}}\}$ with $\hat{\mathcal{A}}=\{a_0,\dots,a_N\}$ and $\hat{\mathcal{E}}\in\hat{\mathcal{A}}\times\hat{\mathcal{A}}$.
\begin{assumption}
	The graph $\mathcal{G}$ is connected and the directed graph $\hat{\mathcal{G}}$ contains a spanning tree.
\end{assumption}

\subsection{Radial Basis Function (RBF) NNs}
An unknown nonlinear function $\zeta(\varOmega)$ can be approximated by a RBF NN,	$\zeta(\varOmega)=W^{*\mathrm{T}}\psi(\varOmega)$, where $W^*\in\mathbb{R}^s$ is a weight vector, $\psi(\varOmega)\in\mathbb{R}^s$ is a basis function vector with $\psi(\varOmega)=\left[\psi_1(\varOmega),\dots,\psi_s(\varOmega)\right]^\mathrm{T}$, and $s\in\mathbb{Z^+}$ represents the number of NN nodes in the hidden layer. In this paper, $\psi_i(\varOmega)$ is chosen as the Gaussian Basis Function
\begin{equation}
	\psi_i(\varOmega)=\exp\left(-(\varOmega-\nu_i)^\mathrm{T}(\varOmega-\nu_i)/2\iota_i^2 \right),~i=1,\dots,s.
\end{equation}
where $\nu_i$ is the center of the Gaussian kernel function and $\iota_i$ is the width parameter of the function. For the approximation of the RBF NN, it is always possible to find an ideal weight $W^*=\arg_{\min W}\{\sup_{\varOmega}||\zeta(\varOmega)-W^\mathrm{T}\psi(\varOmega)||\}$. As a result, the unknown function $\zeta(\varOmega)$ can be written as
\begin{equation}
	\zeta(\varOmega)=W^{*\mathrm{T}}\psi(\varOmega)+\sigma(\varOmega).
\end{equation}
where $\sigma(\varOmega)$ is the approximation error with $|\sigma(\varOmega)|\leq\sigma_T$, and $\sigma_T$ is a constant.

\subsection{Problem Description}
Consider a large-scale UAS with $N$ followers and a virtual leader, each UAV $a_i$ $(i\in\{0,\dots,N\})$ is modeled as:
\begin{equation}\label{multi-UAV system}
	\begin{cases}
		p_i(k+1)=p_i(k)+v_i(k)T\\
		v_i(k+1)=v_i(k)+u_i(k)T+f_i(p_i(k),v_i(k)).
	\end{cases}
\end{equation}
where $p_i(k)\in\mathbb{R}^m$ and $v_i(k)\in\mathbb{R}^m$ are the position and velocity of the UAV $a_i$, $u_i(k)\in\mathbb{R}^m$ is the control input with $m$ the movement dimension of UAV, and $f_i(\cdot)$ is the unknown bounded nonlinear function. For the virtual leader $a_0$, $u_0(k)$ is known and $f_0(\cdot)=0$.

Then, for each follower UAV $a_i$, the position tracking error $\xi_{pi}\in\mathbb{R}^m$ and velocity tracking error $\xi_{vi}\in\mathbb{R}^m$ are defined as
\begin{equation}
	\begin{cases}
		\xi_{pi}(k)=p_i(k)-p_0(k)-\eta_{pi}(k)\\
		\xi_{vi}(k)=v_i(k)-v_0(k)-\eta_{vi}(k).
	\end{cases}
\end{equation}
where $\eta_i(k)=[\eta_{pi}^\mathrm{T}(k),\eta_{vi}^\mathrm{T}(k)]^\mathrm{T}\in\mathbb{R}^{2m}$ is the desired state difference between the leader $a_0$ and the follower $a_i$. Then, define the disagreement error for UAV $a_i$ as
\begin{equation}\label{FTE}
	\begin{cases}
		\begin{aligned}
			\varepsilon_{pi}(k)&=\sum_{j\in N_i}w_{ij}(\xi_{pi}(k)-\xi_{pj}(k))+b_i\xi_{pi}(k)\\
			\varepsilon_{vi}(k)&=\sum_{j\in N_i}w_{ij}(\xi_{vi}(k)-\xi_{vj}(k))+b_i\xi_{vi}(k).
		\end{aligned}
	\end{cases}
\end{equation}
Let $\varepsilon(k)=[\varepsilon_1^\mathrm{T}(k),\dots,\varepsilon_N^\mathrm{T}(k)]^\mathrm{T}$ with $\varepsilon_i(k)=[\varepsilon_{pi}^\mathrm{T}(k),\varepsilon_{vi}^\mathrm{T}(k)]^\mathrm{T}$.
\iffalse
and the disagreement error dynamics is written as
\begin{equation}\label{error dynamics}
	\begin{cases}
		\begin{aligned}
			\varepsilon_{pi}(k+1)&=\varepsilon_{pi}(k)+\varepsilon_{vi}(k)T\\
			\varepsilon_{vi}(k+1)&=\varepsilon_{vi}(k)+\gamma_i(u_i(k)T+f_i)\\
			&~~~-\left\lbrace \sum_{j\in N_i}w_{ij}(u_j(k)T+f_j)+b_iu_0(k)T\right\rbrace
		\end{aligned}
	\end{cases}
\end{equation}
where $\gamma_i=\sum_{j\in N_i}w_{ij}+b_i$. Let $\varepsilon(k)=[\varepsilon_1^\mathrm{T}(k),\dots,\varepsilon_N^\mathrm{T}(k)]^\mathrm{T}$ with $\varepsilon_i(k)=[\varepsilon_{pi}^\mathrm{T}(k),\varepsilon_{vi}^\mathrm{T}(k)]^\mathrm{T}$.
\fi
Define the local performance index function (PIF) as
\begin{equation}\label{PIF}
	V_i(\varepsilon_i(k),u_i(k))=\sum_{l-k}^{\infty}\beta^{l-k}R_i(\varepsilon_i(k),u_i(\varepsilon_i)),
\end{equation}
where $R_i(\varepsilon_i(k),u_i(\varepsilon_i))=\varepsilon_i^\mathrm{T}(k)\varepsilon_i(k)+u_i^\mathrm{T}(\varepsilon_i)u_i(\varepsilon_i)$ is the utility function

\iffalse
Then, the optimal formation tracking controller is defined as
\begin{equation}
	u^*_i=\arg\min_{u_i(\varepsilon_i)}\{R_i(\varepsilon_i(k),u_i(\varepsilon_i))+\beta V^*_i(\varepsilon_i(k+1))\}
\end{equation}

\begin{definition}
	The formation tracking error for the system is $\xi(k)=[\xi_{1}^\mathrm{T}(k),\dots,\xi_{N}^\mathrm{T}(k)]^\mathrm{T}$ with $\xi_{i}(k)=[\xi_{pi}^\mathrm{T}(k),\xi_{vi}^\mathrm{T}(k)]^\mathrm{T}$. If for any follower UAV $a_i$ $(i\in\{1,\dots,N\})$, $\lim_{t\rightarrow\infty}||\xi_{i}(k)||=0$, the desired formation tracking control is achieved.
\end{definition}
\fi

\section{Optimal Assignment and Optimal Control}\label{sec4}
In this section, the algorithm overview shown in Fig. \ref{Fig1} is expanded and detailed separately in three parts: optimal formation assignment, event-triggered optimal controller design, and online actor-critic NNs implementation.
\begin{figure}[!ht]
	\centering
	\includegraphics[width=\columnwidth]{Fig3.png}
	\caption{Two examples of switching formations, with the expected formation shape on the left and the assignments and generated trajectories on the right. \label{Fig7}}
	 \vspace{-2em}
\end{figure}
\subsection{Optimal Assignment for Switching Formations}
For a system with $N$ UAVs of radius $r$, suppose its initial position set is $\vec{\mathbf{G}}=\{\vec{\mathbf{g}}_i^\mathrm{T}\}\in\mathbb{R}^{N\times m}$, the expected formation is $\vec{\mathbf{S}}=\{\vec{\mathbf{s}}_j^\mathrm{T}\}\in\mathbb{R}^{N\times m}$, and the target position set is $\vec{\mathbf{F}}=\{\vec{\mathbf{f}}_j^\mathrm{T}\}\in\mathbb{R}^{N\times m}$ with $\vec{\mathbf{f}}_j=\rho\vec{\mathbf{s}}_j+\vec{d}$, where $\rho\in\mathbb{R}^+$ is the scale factor and $\vec{d}$ is the translation vector. The pseudo-cost assignment algorithm proposed in \cite{c18} is introduced to enable UAVs to reach the target positions simultaneously without collision.

The cost matrix is set as $\mathcal{C}_{ij}=||\vec{\mathbf{g}}_i-\vec{\mathbf{f}}_j||_2^2$, which can be reduced to a pseudo-cost matrix $\kappa=-\vec{\mathbf{G}}_i\vec{\mathbf{S}}_j^\mathrm{T}$ with a series of derivations. Using the Hungarian-LSAP (H-LSAP) algorithm, the optimal assignment list $\chi^*\in\mathbb{Z}^N$ and the minimum cost matrix $\kappa^*\in\mathbb{R}^{N\times N}$ can be calculated
\begin{equation}
	(\chi^*,\kappa^*)=\text{H-LSAP}(\kappa).
\end{equation}
The optimal scale factor $\rho^*$ and translation vector $\vec{d}^*$ are given in \cite{c18}.
Assuming that the maximum allowable velocity during UAV formation switching process is $v_{\max}$, then the formation switching duration is defined as $t_s=\max_{i\in[1,N]}\dfrac{||\vec{\mathbf{g}}_i-\vec{\mathbf{f}}_{\chi(i)}||_2}{v_{\max}}$, where $\chi(i)$ is the position index assigned to UAV $a_i$. Then, the desired switching trajectory for UAV $a_i$ is written as
\begin{equation}
	h_i(k)=\vec{\mathbf{g}}_i+\dfrac{\vec{\mathbf{f}}_{\chi(i)}-\vec{\mathbf{g}}_i}{t_s}kT,\qquad k\in[0,\dfrac{t_s}{T}].
\end{equation}
And the collision avoidance conditions of UAVs are noted $||\vec{\mathbf{g}}_i-\vec{\mathbf{g}}_j||_2\geq2\sqrt{2}r$ and $||\vec{\mathbf{s}}_i-\vec{\mathbf{s}}_j||_2\geq2\sqrt{2}r$.
\subsection{Event-Triggered Optimal Controller Design}

Define the triggering instants sequence for the UAV $a_i$ as $\{k_l^i\}_{l\in\mathbb{Z}^+}$, which is determined by the following condition,
\begin{equation}\label{triggering condition}
	f_i(k)=||e_l^i(k)||^2-\dfrac{(1-2\kappa^2)}{2\kappa^2}||\varepsilon_i(k)||^2,
\end{equation}
where $\kappa\in(\dfrac{1}{2},\dfrac{\sqrt{2}}{2})$, $\varepsilon_i(k)$ is the current disagreement error and the controller $u_i(k)$ only updates at the triggering instant $k_l^i=\inf\{k>k_{l-1}^i,f_i(k)>0\}$, that is, $\hat{u}_i(k)=u_i(\varepsilon_i(k_l^i))$, where $\varepsilon_i(k_l^i)$ is the triggering error. The zero-order holder (ZOH) is used until next triggering instant occurs, one has
\begin{equation}
	u_i(k)=\hat{u}_i(k)=u_i(k_l^i),\quad k\in[k_l^i,k_l^{i+1}).
\end{equation}
\iffalse
And the event-triggered Bellman equation is defined as
\begin{equation}\label{ET Bellman}
	V_i^*(\varepsilon_i(k))=\min_{u_i(k)}\{R_i(\varepsilon_i(k),u_i(k_l^i))+\beta V_i^*(\varepsilon_i(k+1))\}.
\end{equation}
The event-triggered optimal controller is derived as
\begin{equation}\label{event-triggered controller update}
	u_i^*(k)=\arg\min_{u_i(k_l^i)}\{R_i(\varepsilon_i(k),u_i(k_l^i))+\beta V_i^*(\varepsilon_i(k+1))\}.
\end{equation}
\fi
\begin{lemma}\cite{c16}\label{assumption3}
	There exists a positive constant $\kappa$ satisfying the inequality as follows,
	\begin{equation}
		||\varepsilon_i(k+1)||=||g_i(\varepsilon_i(k),u_i(k_l^i))||\leq\kappa||\varepsilon_i(k)||+\kappa||e_l^i(k)||
	\end{equation}
	where the disagreement error $e_l^i(k)=\varepsilon_i(k_l^i)-\varepsilon_i(k),~k\in[k_l^i,k_l^{i+1})$.
And when the event is triggered, $e_l^i(k)=0$.
\end{lemma}
\begin{theorem}
	Considering the large-scale UAS $(\ref{multi-UAV system})$ following the Assumption \ref{assumption3} and the triggering condition (\ref{triggering condition}), the disagreement error is asymptotically stable and formation tracking control for the large-scale UAS $(\ref{multi-UAV system})$ is achieved.
\end{theorem}
\begin{proof}
	$\mathbf{(a)}$ For $\forall k\in[k_{l}^i,k_{l+1}^i)$, the controller $u_i(k)$ remains a constant, $u_i(k)=u_i(k+1)$. Design the Lyapunov function
	\begin{equation}
		\mathcal{V}_{ei}(k)=\varepsilon_i^\mathrm{T}(k)\varepsilon_i(k)+u_i^\mathrm{T}(k)u_i(k).
	\end{equation}

	With the Lemma $\ref{assumption3}$ and the triggering condition $(\ref{triggering condition})$, $\Delta\mathcal{V}_{ei}(k)=\mathcal{V}_{ei}(k+1)-\mathcal{V}_{ei}(k)$ can be derived as
	\begin{equation}
		\begin{aligned}
			\Delta\mathcal{V}_{ei}(k

			&\leq 2\kappa^2||\varepsilon_i(k)||^2+2\kappa^2||e_l^i(k)||^2-||\varepsilon_i(k)||^2\leq 0.
		\end{aligned}
	\end{equation}

	$\mathbf{(b)}$ For $k\in\{k_l^i\}_{l\in\mathbb{Z}^+}$, the controller $u_i(k)$ will be updated, and the Lyapunov function is designed as
	\begin{equation}
		\mathcal{V}_{ei}(k)=\beta^kV_{i}(\varepsilon_i(k)).
	\end{equation}
	Then, the first difference of the $\mathcal{V}_{ei}$ is
	\begin{equation}\label{V_ei}
		\begin{aligned}
			\Delta \mathcal{V}_{ei

			&=-\beta^kR_i(\varepsilon_i(k),u_i(k_l^i))\leq0.
		\end{aligned}
	\end{equation}
	Overall, for $\forall k$, the disagreement error can converge asymptotically, which means that event-triggered formation tracking control is achieved.
\end{proof}
\subsection{Implementation with Online Actor-Critic NNs}
The optimal controller $u_i^*(k)$ is the unique solution of $(\ref{PIF})$, and $u_i^*(k)$ can be derived by the equation $\partial V_i(\varepsilon_i(k))/\partial u_i(k)=0$,
\iffalse
\begin{equation}\label{partial V}
	\dfrac{\partial R_i(\varepsilon_i(k),u_i(k))}{\partial u_i(k)}+\beta\dfrac{\partial V_i(\varepsilon_i(k+1))}{\partial \varepsilon_i(k+1)}\dfrac{\partial\varepsilon_i(k+1)}{\partial u_i(k)}=0.
\end{equation}
Expanding the Eqn. $(\ref{partial V})$, one has $\beta\gamma_i T\dfrac{\partial V_i(\varepsilon_{vi}(k+1))}{\partial \varepsilon_{vi}(k+1)}+2u_i(k)=0$.

Then, the optimal controller $u_i^*(k)$ is solved as
\fi
\begin{equation}\label{optimal_controller}
	u_i^*(k)=-\dfrac{\beta\gamma_iT}{2}\dfrac{\partial V_i^*(\varepsilon_{vi}(k+1))}{\partial \varepsilon_{vi}(k+1)}.
\end{equation}
Let $\dfrac{\partial V_i^*(\varepsilon_{vi}(k+1))}{\partial \varepsilon_{vi}(k+1)}=\dfrac{2\alpha_p\varepsilon_{pi}(k)}{\beta\gamma_iT}+\dfrac{2\alpha_v\varepsilon_{vi}(k)}{\beta\gamma_iT}+\dfrac{V_i^0(\varepsilon_i)}{\beta\gamma_iT}$, where the constants $\alpha_p>0$, $\alpha_v>0$, and $V_i^0(\varepsilon_i)=-2\alpha_p\varepsilon_{pi}(k)\\-2\alpha_v\varepsilon_{vi}(k)+\beta\gamma_iT\dfrac{\partial V_i^*(\varepsilon_{vi}(k+1))}{\partial \varepsilon_{vi}(k+1)}$. Then one has
\begin{equation}\label{controller_split}
	u_i^*(k)=-\alpha\varepsilon_{i}(k)-\dfrac{V_i^0(\varepsilon_i)}{2},
\end{equation}
where $\alpha=[\alpha_p,\alpha_v]\otimes I_m$. And in order to implement the approximation of the optimal controller and the optimized PIF, actor-critic NNs are introduced.
\begin{figure}[!ht]
	\centering
	\includegraphics[width=\columnwidth]{Fig4.png}
	\caption{A framework for implementation with event-triggered online actor-critic NNs for formation tracking control. \label{Fig8}}
	\vspace{-2em}
\end{figure}
\subsubsection{Critic NN Design}
The critic NN, which is utilized to approximate the the optimized PIF,
\iffalse
\begin{equation}\label{critic NN}
	\begin{aligned}
		\dfrac{\partial V_i^*(\varepsilon_{vi}(k+1))}{\partial\varepsilon_{vi}(k+1)}&=\dfrac{2\alpha\varepsilon_{i}(k)}{\beta\gamma_iT}+\dfrac{1}{\beta\gamma_iT}(W_{ci}^{*\mathrm{T}}(k)\psi_i(\varepsilon_i)+\epsilon_{ci,k}),
	\end{aligned}
\end{equation}
where $W_{i}^*\in\mathbb{R}^{s\times m}$ is the ideal weight of the critic NN with  $s$ neurons, $\psi_i(\varepsilon_i)\in\mathbb{R}^{s}$ is the basis function, and $\epsilon_{ci,k}\in\mathbb{R}^m$ is the approximation error. Since $W_{ci}^*\in\mathbb{R}^{s\times m}$ is unknown at the initial moment, the Eqn. $(\ref{critic NN})$ can be written as
\fi
\begin{equation}\label{PIF NN}
	\begin{aligned}
		\dfrac{\partial \hat{V}_i(\varepsilon_{vi}(k+1))}{\partial\varepsilon_{vi}(k+1)}&=\dfrac{2\alpha\varepsilon_{i}(k)}{\beta\gamma_iT}+\dfrac{1}{\beta\gamma_iT}\hat{W}_{ci}^\mathrm{T}(k)\psi_i(\varepsilon_i),
	\end{aligned}
\end{equation}
where $\hat{W}_{ci}\in\mathbb{R}^{s\times m}$ is the estimation of $W_{i}^{*}$, which is trained by the critic NN update law
\begin{equation}\label{critic_NN_update}
	\begin{aligned}
		\hat{W}_{ci}(k+1)&=\hat{W}_{ci}(k)-\mu_{ci}T\psi_i(\varepsilon_i)\psi_i^\mathrm{T}(\varepsilon_i)\hat{W}_{ci}(k),
	\end{aligned}
\end{equation}
where $\mu_{ci}$ is the constant gain for the critic NN.
\subsubsection{Actor NN Design}The actor NN, which is utilized to approximate the formation tracking controller $(\ref{controller_split})$,
\iffalse
\begin{equation}\label{actor NN}
	\begin{aligned}
		u_i^*(k)=-\alpha\varepsilon_{i}(k)-\dfrac{1}{2}(W_{ai}^{*\mathrm{T}}(k)\psi_i(\varepsilon_i)+\epsilon_{ai,k}),
	\end{aligned}
\end{equation}
where
$\epsilon_{ai,k}\in\mathbb{R}^m$ is the approximation error,
and the Eqn. $(\ref{actor NN})$ can be written as
\fi
\begin{equation}\label{controller NN}
	u_i^*(k)=\begin{cases}
		-\alpha\varepsilon_{i}(k)-\dfrac{1}{2}\hat{W}_{ai}^{\mathrm{T}}(k)\psi_i(\varepsilon_i(k)),~ k\in\{k_l^i\}_{l\in\mathbb{Z}^+},\\
		u_i^*(k_l^i),\qquad\qquad\qquad\qquad\quad~ k\in[k_l^i,k_{l+1}^i).
	\end{cases}
\end{equation}
where $\hat{W}_{ai}\in\mathbb{R}^{s\times m}$ is the estimation of $W_{ai}^{*}$, which is trained by the actor NN update law
\iffalse
Substituting the Eqn. $(\ref{controller NN})$ into the Bellman equation $(\ref{ET Bellman})$,
\begin{equation}
	\begin{aligned}
		V_i^*(\varepsilon_i)&=\min_{\hat{W}_{ai}(k)}\left\lbrace||\varepsilon_i(k)||^2+||-\alpha\varepsilon_{i}(k)-\dfrac{1}{2}\hat{W}_{ai}^{\mathrm{T}}(k)\psi_i(\varepsilon_i)||^2\right.\\
		&\left.~~~+V_i^*(\varepsilon_i(k+1))\right\rbrace .
	\end{aligned}
\end{equation}

In order to calculate the weight $\hat{W}_{ai}$ that optimizes $V^*$, the equation $\partial V_i/\partial \hat{W}_{ai}=0$ is solved with the Eqn. $(\ref{PIF NN})$,
\begin{equation}\label{dV/dWa}
	\begin{aligned}
		\dfrac{\partial V_i}{\partial \hat{W}_{ai}

		&=\dfrac{1}{2}\psi_i(\varepsilon_i)\psi_i^\mathrm{T}(\varepsilon_i)\left\lbrace\hat{W}_{ai}(k)-\hat{W}_{ci}(k) \right\rbrace=0.
	\end{aligned}
\end{equation}
To calculate the weight update law for the actor NN, a quadratic function equivalent to the Eqn. $(\ref{dV/dWa})$ is defined as,
\begin{equation}
	\begin{aligned}
		\mathcal{C}(k)&=\dfrac{1}{2}\mathrm{Tr}\left\lbrace \left( \hat{W}_{ai}(k)-\hat{W}_{ci}(k)\right)^\mathrm{T}\psi_i(\varepsilon_i)\psi_i^\mathrm{T}(\varepsilon_i)\right.\\
		&\left.~~~\times\left( \hat{W}_{ai}(k)-\hat{W}_{ci}(k)\right)\right\rbrace,
	\end{aligned}
\end{equation}
where the operator $\mathrm{Tr}(\cdot)$ satisfies $\mathrm{Tr}(ab^\mathrm{T})=a^\mathrm{T}b=b^\mathrm{T}a$, with two vectors $a$ and $b$. Then, the following weight update law can be derived using the gradient descent method,
\fi
\begin{equation}\label{ET_update_law}
	\hat{W}_{ai}(k+1)=\begin{cases}
		\hat{W}_{ai}(k)-\mu_{ai}T\psi_i(\varepsilon_i)\psi_i^\mathrm{T}(\varepsilon_i)\\
		\quad\times\left(  \hat{W}_{ai}(k)-\hat{W}_{ci}(k)\right),~ k\in\{k_l^i\}_{l\in\mathbb{Z}^+},\\
		\hat{W}_{ai}(k),\qquad\quad\qquad\qquad k\in[k_l^i,k_{l+1}^i).
	\end{cases}
\end{equation}
where $\mu_{ai}$ is the constant gain for actor NN.
\iffalse
\begin{remark}
	In \cite{}, both actor NN and critic NN update the weights continuously or periodically, which can be computationally intensive for complex NNs and consume lots of computing resources. Whereas, on the contrary, from the equation $(\ref{ET_update_law})$ proposed in this paper, the actor NN weight $\hat{W}_{ai}$ is updated only at the triggering instants, which consumes lower computational resources during the flight.
\end{remark}
\fi
\begin{definition}
	A system is said to be ultimatelly uniformly bounded (UUB) if there exist positive constants $\delta$ and $\varrho$, $\forall$$x(k_0)<\delta$, $\exists$$T(\varrho,\delta)\geq0$ such that
	\begin{equation*}
		\forall k>k_0+T, \qquad||x(k)||<\varrho.
	\end{equation*}
\end{definition}
\begin{theorem}\label{theorem2}
	For any UAV $a_i$ in the large-scale UAS $(\ref{multi-UAV system})$ with bounded initial states, the optimized event-triggered formation tracking controller $(\ref{controller NN})$ is utilized, where the iterative update laws of the actor-critic NNs are  $(\ref{critic_NN_update})$ and $(\ref{ET_update_law})$, and the constant gains involved satisfy the conditions,
	\begin{equation}\label{conditions}
		\mu_{ci}>\mu_{ai}>0,\quad 0<T<\dfrac{\mu_{ci}-\mu_{ai}}{\mu_{ci}^2\lambda_{\max}^{\psi_i\psi_i^\mathrm{T}}},
	\end{equation}
	where $\lambda_{\max}^{\psi_i\psi_i^\mathrm{T}}$ is the maximum eigenvalues of $\psi_i(k)\psi_i^\mathrm{T}(k)$. Then, the disagreement error $\varepsilon_i(k)$, and the estimation errors $\tilde{W}_{ai}(k)$, $\tilde{W}_{ci}(k)$ of the actor-critic NN weights are UUB, where $\tilde{W}_{ai}(k)=\hat{W}_{ai}(k)-W_{ai}^*$ and $\tilde{W}_{ci}(k)=\hat{W}_{ci}(k)-W_{ci}^*$.
\end{theorem}
\begin{figure*}[hb
	\vspace{-0.5em}
	\centering
	\includegraphics[width=\linewidth,scale=1.00]{Fig2.png}
	\caption{Mixed reality experimental platform framework. To implement the large-scale UAV switching formation control, several physical UAV nodes and large-scale virtual UAV nodes are used to achieve mixed reality interactions.
	\label{Fig2}
\end{figure*}
\begin{proof}
	The stability analysis process will be divided into two parts according to the trigger instants $k\in\{k_l^i\}_{l\in\mathbb{Z}^+}$ and the trigger instant intervals $k\in[k_l^i,k_{l+1}^i)$.

	$\mathbf{(a)}$ For $\forall k\in[k_l^i,k_{l+1}^i)$, the triggering condition $f_i(k)\leq0$ is satisfied, then design the Lyapunov function as follows,
	\begin{equation}
		\begin{aligned}
			\mathcal{V}(k
			&=\sum_{i=1}^{N}\varepsilon_i^\mathrm{T}(k)\varepsilon_i(k)+\dfrac{1}{2}\sum_{i=1}^{N}\mathrm{Tr}\left\lbrace\tilde{W}_{ai}^\mathrm{T}(k) \tilde{W}_{ai}(k)\right\rbrace\\ &~~~+\dfrac{1}{2}\sum_{i=1}^{N}\mathrm{Tr}\left\lbrace\tilde{W}_{ci}^\mathrm{T}(k) \tilde{W}_{ci}(k)\right\rbrace>0.
		\end{aligned}
	\end{equation}
\iffalse
	The first difference of $\mathcal{V}_e(k)$ is
	\begin{equation}\label{term1}
		\begin{aligned}
			\Delta\mathcal{V}_e(k

			&\leq \sum_{i=1}^N\left\lbrace 2\kappa^2||\varepsilon_i(k)||^2+2\kappa^2||e_l^i(k)||^2-||\varepsilon_i(k)||^2 \right\rbrace\leq0
		\end{aligned}
	\end{equation}

	For the first difference of $\mathcal{V}_{la}(k)$ is
	\begin{equation}\label{term2}
		\begin{aligned}
			\Delta\mathcal{V}_{la}(k

			&\leq-\sum_{i=1}^N\dfrac{\mu_{ai}T}{2}\left\lbrace \mathrm{Tr}\left( \tilde{W}_{ai}^\mathrm{T}(k)\psi_i\psi_i^\mathrm{T}\tilde{W}_{ai}(k)\right)\right.\\
			&\left.-\mathrm{Tr}\left( \hat{W}_{ci}^\mathrm{T}(k)\psi_i\psi_i^\mathrm{T}\hat{W}_{ci}(k)\right)-\mathrm{Tr}\left( \tilde{W}_{ci}^{\mathrm{T}}(k)\psi_i\psi_i^\mathrm{T}\tilde{W}_{ci}(k)\right)\right\rbrace,
		\end{aligned}
	\end{equation}
	For the first difference of $\mathcal{V}_{lc}(k)$ is
	\begin{equation}\label{term3}
		\begin{aligned}
			\Delta\mathcal{V}_{lc}(k

			&\leq-\sum_{i=1}^N\dfrac{\mu_{ci}T}{2}\left\lbrace \mathrm{Tr}\left( \tilde{W}_{ci}^\mathrm{T}(k)\psi_i\psi_i^\mathrm{T}\tilde{W}_{ci}(k) \right) \right.\\
			&~~~+(1-\mu_{ci}T\lambda_{\max}^{\psi_i\psi_i^\mathrm{T}})\mathrm{Tr}\left(\hat{W}_{ci}^\mathrm{T}(k)\psi_i\psi_i^\mathrm{T}\hat{W}_{ci}(k) \right)\\
			&~~~\left.-\mathrm{Tr}\left( {W}_{ci}^{*\mathrm{T}}\psi_i\psi_i^\mathrm{T}{W}_{ci}^*\right)\right\rbrace.
		\end{aligned}
	\end{equation}

	The following inequalities are used in simplification,
	\begin{equation}
		\begin{aligned}
			\mathrm{Tr}\left(\tilde{W}_{ai}^\mathrm{T}(k)\psi_i\psi_i^\mathrm{T}\tilde{W}_{ci}(k)\right)&\leq\dfrac{1}{2}\left\lbrace \mathrm{Tr}\left(\tilde{W}_{ai}^\mathrm{T}(k)\psi_i\psi_i^\mathrm{T}\tilde{W}_{ai}(k)\right)\right.\\
			&\left.~~~+\mathrm{Tr}\left(\tilde{W}_{ci}^\mathrm{T}(k)\psi_i\psi_i^\mathrm{T}\tilde{W}_{ci}(k)\right)\right\rbrace.
		\end{aligned}
	\end{equation}
	\begin{equation}\label{tildeW_hatW}
		\begin{aligned}
			\mathrm{Tr}\left(\tilde{W}_{ci}^\mathrm{T}\psi_i\psi_i^\mathrm{T}\hat{W}_{ci}(k) \right)&=\dfrac{1}{2}\left\lbrace \mathrm{Tr}\left(\tilde{W}_{ci}^\mathrm{T}(k)\psi_i\psi_i^\mathrm{T}\tilde{W}_{ci}(k)\right)\right.\\
			&\left.~~~+\mathrm{Tr}\left(\hat{W}_{ci}^\mathrm{T}(k)\psi_i\psi_i^\mathrm{T}\hat{W}_{ci}(k)\right)\right.\\
			&\left.~~~-\mathrm{Tr}\left(W_i^{*\mathrm{T}}\psi_i\psi_i^\mathrm{T}W_i^{*}\right)\right\rbrace .
		\end{aligned}
	\end{equation}
\fi
	For the first difference of $\mathcal{V}(k)$,
	\begin{equation}
		\begin{aligned}
			\Delta\mathcal{V}(k)&\leq-\sum_{i=1}^N\dfrac{\mu_{ai}T}{2}\mathrm{Tr}\left(\tilde{W}_{ai}^\mathrm{T}(k)\psi_i\psi_i^\mathrm{T}\tilde{W}_{ai}(k)\right)\\
			&~~~-\sum_{i=1}^N\dfrac{(\mu_{ci}-\mu_{ai})T}{2}\mathrm{Tr}\left(\tilde{W}_{ci}^\mathrm{T}(k)\psi_i\psi_i^\mathrm{T}\tilde{W}_{ci}(k)\right)\\
			&~~~+\sum_{i=1}^N\dfrac{\mu_{ci}T}{2}\mathrm{Tr}\left(W_{ci}^*\psi_i\psi_i^\mathrm{T}{W}_{ci}^*\right),
		\end{aligned}
	\end{equation}
	where $\sum_{i=1}^N\dfrac{\mu_{ci}T}{2}\mathrm{Tr}\left(W_{ci}^*\psi_i\psi_i^\mathrm{T}W_{ci}^*\right)\leq\tau$, $\tau>0$. and $\varsigma=\min_{i\in[1,N]}\left\lbrace\mu_{ai}T\lambda_{\max}^{\psi_i\psi_i^\mathrm{T}},(\mu_{ci}-\mu_{ai})T\lambda_{\max}^{\psi_i\psi_i^\mathrm{T}}\right\rbrace$. Then, one has $\Delta\mathcal{V}(k

			\leq-\varsigma\mathcal{V}_l(k)+\tau$.

	Then, with $k$ iterations, one has
	\begin{equation}
		\begin{aligned}
			\mathcal{V}(k)&\leq(1-\varsigma)^k\mathcal{V}_l(0)+\dfrac{\tau}{\varsigma}\left(1-(1-\varsigma)^k\right)\\
			&~~~-\mathcal{V}_l(0)+\sum_{i=1}^{N}\varepsilon_i^\mathrm{T}(0)\varepsilon_i(0).
		\end{aligned}
	\end{equation}

	$\mathbf{(b)}$ For $\forall k\in\{k_l^i\}_{l\in\mathbb{Z}^+}$, the controller $u_i^*(k_l^i)$ is updated, then design the Lyapunov function as follows,
	\begin{equation}
		\begin{aligned}
			\mathcal{V}'(k
			&=\sum_{i=1}^N\beta^kV_i(\varepsilon_i(k))+\dfrac{1}{2}\sum_{i=1}^{N}\mathrm{Tr}\left\lbrace\tilde{W}_{ai}^\mathrm{T}(k) \tilde{W}_{ai}(k)\right\rbrace\\ &~~~+\dfrac{1}{2}\sum_{i=1}^{N}\mathrm{Tr}\left\lbrace\tilde{W}_{ci}^\mathrm{T}(k) \tilde{W}_{ci}(k)\right\rbrace>0.
		\end{aligned}
	\end{equation}
	Similarly to the previous case, $\mathcal{V}'(k)$ is bounded.

	For both cases, the disagreement error $\varepsilon(k)$ of the system and all the estimation errors $\tilde{W}_{ai}(k)$, $\tilde{W}_{ci}(k)$ are UUB.
\end{proof}

\iffalse
\begin{table}[h]
\caption{An Example of a Table}
\label{table_example}
\begin{center}
\begin{tabular}{|c||c|}
\hline
One & Two\\
\hline
Three & Four\\
\hline
\end{tabular}
\end{center}
\end{table}
\fi

\section{Mixed Reality Experiment}\label{sec5}
In this section, a mixed reality experimental platform is constructed to verify the proposed optimal assignment and optimal control algorithms for large-scale UAV formation.
\subsection{Mixed Reality Experimental Platform}
In order to verify the effectiveness of the algorithm, the mixed reality large-scale UAV experimental platform shown in Fig. \ref{Fig2} is established, including a real experimental scenario and a virtual experimental scenario. The real scenario contains only several physical UAV nodes limited by the experimental site, and their state information is obtained by the motion capture system -- OptiTrack, and transmitted to the formation controller via a router. In contrast, the virtual scenario can contain hundreds of virtual UAV nodes, whose dynamics model is designed as a second-order model. The formation controller uses the obtained state information of all nodes to calculate the control input of each node and send it back to each node for formation control. And to visualize the formation effect, the state information of physical nodes is also sent to the virtual scene for real-time display.

In this experiment, 4 physical UAVs and 116 virtual UAVs, a total of 120 UAVs, are used to achieve a large-scale formation. The Laplacian matrix used in the system is
\begin{equation*}
	\setlength{\arraycolsep}{1.2pt}
	\renewcommand{\arraystretch}{1.6}
	L=\left[
	\begin{array}{cccccccc}
		4&-1&-1&0&\cdots&0&-1&-1\\
		-1&4&-1&-1&0&\cdots&0&-1\\
		-1&-1&4&-1&-1&0&\cdots&0\\
		\cdots&\ddots&\ddots&\ddots&\ddots&\ddots&\cdots&\cdots\\

		-1&-1&0&\cdots&0&-1&-1&4
	\end{array}
	\right]\in\mathbb{R}^{120\times 120}.
\end{equation*}
The diagonal matrix $B=\mathrm{diag}(\mathrm{mod}(N,2))$. And the other parameters are listed in Table \ref{table_1}
\begin{table}[!h]\footnotesize
	\renewcommand{\arraystretch}{1.2}
	\caption{Experimental setup}
	\vspace*{10pt}
	\centering
	\label{table_1}

	\begin{tabular}{l l l}
		\hline\hline
		Parameter & Value & Description  \\[0.3ex] \hline
		s & Optitrack &  RBF NN nodes \\
		$\iota_i$ & 1 &Gaussian Basis Function width\\
		$\nu_i$& [-3,3] & Gaussian Basis Function center. \\
		$\hat{W}_{ai}(0)$ & $\{0.3\}_{60\times2}$ & Initial actor NN weights \\
		$\hat{W}_{ai}(0)$ & $\{0.3\}_{60\times2}$ & Initial critic NN weights\\
		$\mu_{ai}$ & 6 & Actor NN gain\\
		$\mu_{ci}$ & 8 & Critic NN gain\\
		$\alpha$ & $[6,4]$ & Parameter in controller $u(k)$\\
		$T$ &$0.01$ & Sampling period\\ [0.8ex]
		\hline\hline
	\end{tabular}
\vspace{-1.5em}
\end{table}

\subsection{Results Analysis}
As shown in Fig. \ref{Fig3}, the large-scale UAS successfully generates collision-free optimal formation switching trajectories between multiple formations using the optimal assignment algorithm. With the optimized formation tracking controller $(\ref{controller NN})$, the large-scale mixed reality UAV nodes can follow the generated expected trajectories and the formation tracking error $\xi(k)$ is bounded as shown in Fig. \ref{Fig4}. With the event-triggered mechanism, the controller update frequency per UAV is significantly reduced. As shown in Fig. \ref{Fig5}, the event-triggered algorithm can reduce the update frequency to 27\% of the time-triggered algorithm, which updates the controller continuously or periodically. And the triggering instants sequence for UAVs $1-30$ in the last $1000$ iterations is also illustrated, where the triggering instants for each UAV are aperiodically and on-demand. Fig. \ref{Fig6} illustrates that the actor and critic NN weights are UUB. And the optimal formation tracking control problem is solved.
\begin{figure}[!htbp]

	\subfigure[Cross-shaped mixed reality large-scale formation]{
		\includegraphics[width=0.95\columnwidth]{formation2.png}
	}
	\subfigure[Circular mixed reality large-scale formation]{
		\includegraphics[width=0.95\columnwidth]{formation3.png}
	}
\vspace{1em}
	\caption{The large-scale UAV switching formations in the experiment. \label{Fig3}}
	\vspace{-1.5em}
\end{figure}
\subsection{Summary}
The mixed reality platform built in this study combines the strong engineering applicability of physical experimental platforms with the high flexibility and low cost of virtual simulation platforms. On the one hand, compared with the fully virtual simulations, it can more accurately verify the effectiness of the proposed algorithm for practical UAV dynamics and real-world experimental scenes. On the other hand, compared with the fully physical experiments, the platform has significant advantages in experimental cost and field requirements, which can achieve a heavyweight UAV formation show with lightweight experimental equipment.

\section{Conclusion}\label{sec6}
For the large-scale switching formation tracking problem, this study introduced the optimal formation assignment algorithm and proposed an optimal controller, which broken the main technical limits in decision and control layers of large-scale UASs. Further, compared with the time-triggered controller, the designed event-triggered algorithm reduced the update rate for controller and actor NN to 27\%. More notably, this paper integrated the strong engineering applicability of practical experiments and high flexibility of virtual platforms to practically achieve large-scale switching formation. However, this study ignored the spatial constraints within the practical scene and the dynamics accuracy of the virtual UAV. In future work, autonomous obstacle avoidance in large-scale switching formation will be realized, and the virtual UAV dynamics will be improved in more detail.

\begin{figure}[!htbp]
		\vspace{-1em}
	\centering
	\includegraphics[width=\columnwidth]{formation_error.pdf}
	\vspace{1em}
	\caption{The norm of formation tracking error $||\xi(k)||$. The moments when the tips appear in the curve are the switch from one formation to another. \label{Fig4}}
\end{figure}
\begin{figure}[!htbp]
		\vspace{-1em}
	\centering
	\includegraphics[width=\columnwidth]{trigger_times.pdf}
	\vspace{1em}
	\caption{The triggering instants sequence
		and the mean triggers for the event-triggered mechanism compared to the time-triggered mechanism.
		\label{Fig5}}
\end{figure}
\begin{figure}[!htbp]
		\vspace{-1em}
	\centering
	\includegraphics[width=\columnwidth]{NN_weight.pdf}
	\vspace{1em}
	\caption{Actor-critic NN weight norm for all UAVs, where the solid lines represent the physical UAVs and the dotted lines represent the virtual UAVs. \label{Fig6}}
\end{figure}

\addtolength{\textheight}{-8cm}

redpajama_set_name: RedPajamaArXiv


text:
Q: .Net Core 2.2 XML Serialization/Deserialization I am unable to serialize/deserialize XML in .Net Core 2.2.
I am receiving the following exception: System.TypeLoadException: 'Could not load type 'System.ServiceModel.Dispatcher.XPathMessageFilter' from assembly 'System.ServiceModel, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089'.'
I have Googled, of course, to no avail thus far.
I have added the System.ServiceModel.Primitives NuGet package but the XPathMessageFilter type isn't contained in that package. Has anyone had success with this issue?

A: You should use System.Xml Namespace for serializing/de-serializing and navigating XML documents in dotnet core.
System.ServiceModel Namespace works with dotnet framework.

redpajama_set_name: RedPajamaStackExchange


text:
Q: PHP: compare two strings for existence of 2 same words in both of them I need to create a function that will return true or false based on comparison results.
I have two strings:
$one = 'sample product - White - Large'; // White is separate key, and large is separate too
$two = 'White Large';

Do you know any quick way for doing that task? Exploding two strings might not be safe as some strings instead of White will have: Blue - Black - Large. So I'm looking for existence of Blue - Black.
Another example of my data is:
$one = 'sample product - White - Blue - Large';  // White - Blue is separate key, Large is separate too.

If someone have any ideas on how to do it, I would really appreciate it.
Thanks,
eloleon

A: I'd go for a strategy like that:

*

*explode the strings into arrays by whitespaces (using regexes)

*use array_intersect() to find matches


text:
Q: A longer dash like the line from rightarrow without an arrow tip I want to use arrows to talk about edges in graphs. For example I write $\to \to$ to represent two adjacent directed edges.
An undirected edge followed by a directed edge would be represented by  something like $- \to$, but this looks bad, because the line $-$ is shorter than $\to$.
How do you make $-$ longer? Line drawing commands like rule or \tikz\draw do not look right, because they make a rectangle with sharp corners unlike the rounded corners of \to. (or perhaps making $\to$ shorter is the better way?)

A: Here's a solution:
\documentclass{article}

\usepackage{mathtools}
\newcommand{\mathdash}{\relbar\mkern-9mu\relbar}

\begin{document}

     \[ \begin{array}{l}
     A - B \\A \rightarrow B \\
     A \mathdash B\\
     \end{array} \]%

\end{document}


CA Technologies has integrated its Release Automation solution with JFrog's Artifactory binary repository management system, the two companies announced. The move was motivated by CA customer demand for a repository offering high availability (HA), said David Cramer, vice president of CA's Application Delivery Product Management group.
"Our customers are delivering new applications and making changes to existing applications at a scale that was unimaginable just a few years ago," Cramer said in a statement. "The tools used in developing, testing and deploying these applications are mission critical and must be available at all times. By working together with leading companies like JFrog, we can help our customers implement continuous delivery at very high scale and win in the application economy."
CA Release Automation is an enterprise-class continuous delivery solution for automating and standardizing application deployments. It's designed to automate complex, multi-tier release deployments via orchestration and promotion of apps from development through production.
Artifactory, JFrog's flagship product, was one of the first cloud-based binary repository managers. It integrates with the open-source Jenkins continuous integration (CI) server, Atlassian's Bamboo CI, JetBrains' TeamCity build and CI server, the Gradle and Apache Maven project automation tools, and the NuGet package manager for .NET, among others. It is the only binary repository to offer HA, the company says.
"The binary repository is really the heart of the software delivery pipeline," Adam Frankl, JFrog's VP of marketing, told ADTmag, "which is why we've invested so heavily in HA. We're seeing a major change in the enterprise that's driven by DevOps, so if your binary repository goes down, not only does your development work stop, but also potentially your operations team stops. And minutes of downtime are a huge expense."
Binary repositories are also rapidly emerging as a critical part of the industry response to the new challenges of polyglot programming, explained 451 Research analyst Jay Lyman. This "best-tool-for-the-job" trend involves a much greater variety of application components (languages, frameworks, databases, messaging, Web servers, and so on) and infrastructures (bare metal servers, traditional datacenters, virtual environments, public, private and hybrid clouds, containers, and so on), he said.
"Organizations need to be able to empower their developers and lines of business to take advantage of polyglot programming," Lyman told ADTmag in an e-mail, which may mean a certain language on the back end for performance, scalability, or other reasons, and another framework on the front end for presentation or UI advantages. A big part of being able to support the greater variety of application components and infrastructure scenarios is proactive binary repository management that offers visibility into applications, dependencies, and process."


Auto insurance Jonesboro AR. Look for the BEST Deals on Car Insurance Quotes HERE!
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"Her mind was as sharp as ever"
Jane Kim (seated on floor at right), a computer scientist in New York City, recently brought her daughters (also on floor) to Korea to meet her 99-year-old grandma (seated at right on couch). She lives near Seoul with Jane's aunt (on couch at left); Jane's mother (on couch in center) was visiting from Chicago. Photo by Tom Foran.
Would her grandma remember her?
Jane Kim, 41, wasn't sure. It had been 23 years since she'd last visited her in Korea, and she was nearly 100 years old.
Jane's parents had met in medical school in Korea in the late 1960s and, in the early 1970s, had been recruited to practice in the midwestern United States, where, at the time, there weren't enough doctors. They settled in Milwaukee, and by 1977 they had Jane and two other kids.
That year, Jane's maternal grandmother flew over from Seoul to meet her and her siblings and help out with them a little. When she saw how badly she was needed, she decided to stay a whole year, even though she only had a short-term tourist visa. The U.S. government barred her from ever coming back.
So, for the rest of her childhood, Jane saw her grandma only occasionally, when she and her family made short visits to Korea.
Jane went to college and graduate school, built a career, married, and had two daughters. And last year, she decided it was time they met their great-grandmother, who now splits her time between a nursing home and her youngest daughter's apartment.


waiting for the bus for two hours at 2am enjoying every bit of our time sitting along a walkway in Alabang. Kit and i were enjoying the company of Lawstude while Manny was busy with his big red backpack. pass 3am we decided to take the bus to Turbina in Laguna and from there we took the bus to Lucena. even though we were stranded for two hours, we were quite confident with our schedule since the schedule was a bit lax. upon arriving in the city of Lucena, which is Quezon province's capital city, we took a mini bus going to the town of Mauban. just few minutes upon boarding, the bus immediately left the grand terminal. for shortly an hour, we arrived at this little congested coastal town of Mauban. we were there 3hours earlier for the first boat trip to Cagbalete island. so we took some time to take some pictures and dropped by some shops to have our breakfast. people were quite curious as the four of us wore dark shirts which lead our tricycle driver to think that we were a rock band who will be traveling to Cagbalete for a show. since it was a weekend, most of the people in this town took time walking along the driveway near the docksite. some were fishing, kids were playing, while traders were busy in preparing their goods. we boarded this medium-sized public motor boat which little by little were filled with goods. sacks of cement, sacks of rice, big boxes and even ice blocks. a number of people started to board and lucky enough, along with us is the owner of the resort where we plan to stay in the island. so we had a good chat with them. trip was a little rough but it was expected as the sea which we were to cross is connected to the Pacific ocean. the people infront of the boat got wet because of the splash created by the waves. an hour later, we had a view of the Sabang port, which was the main docking port of the island of Cagbalete. small but crowded wooden houses occupies a large part of the coast but the beach was really beautiful. one can be tempted to just jump off the boat and enjoy the beach. the boat cannot dock directly along the beach because it was low tide. so a small flat-surfaced boat has to transport us to the shoreline. sand was so fine on this side of the island but most of the houses though, gives a contrast to the beautiful beach. one has to cross the island to see a more secluded beach that this island takes pride on. that's on the next post. note: there are only two trips from Mauban to Cagbalete island. 10:00am and 4:00pm.
That is so beautiful! I would love to go there.
what a preview! i couldn't wait to see the photos of the other side of the island. mukha kayong rockers?:D buti di nagpa-autograph!
fabulous new blog banner! perfect for summer.
hehe... yan nga yung island na sinasabiko... hahaha..
sayang, im so busy that i couldn't find time to travel around the city!!!
"to think that we were a rock band who will be traveling to Cagbalete for a show" --->why not diba? baka nakalibre pa kayo ng accomodation ala rocker style =D.
oh now the adventure begins. is this your first time here? i can't wait.
natawa talaga ko don sa mga tga mauban na napagkamalan tayo na combo.
kaya ipinanganak na ang "the comboboys" lol. iniisip ko pa nga kung ipopost ko ang mala eraserheads nating photoshoot sa cagbalete eh. ang saya talaga doon.
wohoo!! galing ng adventure nyo... can't wait to see more about this trip!
>hi joy, wait till you see the other side.
>hi luna, im sure you'll love the other side. nagulat nga kami. pero ok na rin dahil nagkaroon tuloy kami ng pangalan.
>hi reena, wait till you see the other side.
>hi faery, thanks! more photos coming.
>hi chyng, dami pang parating.
>hi carver, it's not that nice yet. wait till you see the other side of the island.
>gillboard, ito na pala yon. ganda ang kabila nito.
>hi ailee, sayang. nagkita man lang sana tayo. dami pa namang mapupuntahan sa quezon.
>theonoski, hahaha... yung tricycle driver lang naman ang nag akala. gusto to na nga sana talaga naming tumugtog doon.
>hi photo cache, yes. it was our fisrt time there. this place was recommended by allan.
>oman, patawa nga talaga yon kasi hindi pa natin kaagad naintindihan nung sinabi niyang combo.
astig nga yung mga album photo shoot natin.
>hi shionge, wait till you see the other side. thanks for dropping.
>nash, magaling talaga yon. buti naman at nakausap mo na siya. sama ka namin one time.
Hmm looks like you and your group has the "rockstar swag". Naks!
Looking forward to more photos of the island. I prefer these kind of beaches than sell-out places like Boracay... we used to go beach/island hunting din kase when I used to live in Negros.
I like the new banner btw!
Natawa ako dun sa napagkamalan kayong rock band members. May long hair ba kayong kasama bukod sa dark colors ang sinot nyo? I only heard about lucena. Hindi ko alam kung ano ang maii-offer ng lucena city. Hindi siya wellknown, narinig ko lang kasi.
Daddy says this is very far from my house. It is beautiful. Nice.
ang sarap talaga mag-travel.. keep exploring dong!
Very beautiful island. The sky is so blue so does the sea. Love the scenery. I like to travel but hate the waking up so early to catch the transport or plane.
donG...how beatifull the picture was,can't even imagine if i was there..beatifull!!!
wow!! sana wag kang magsawa dyan sa mga ginagawa mo kuya dong ah!! ang ganda kasi talaga!! ang ganda ng town at yung way papunta sa beach!! ^__^ great escape!!
hmmm...the boat actually looks scary. wala bang RORO type of boat?
gusto ko sumakay ng banka. kaso sobrang pranig ako eh. haha.
swerte ng mga taong nakatira malapit sa beach, lalo na pag ganito kaganda.
dami ko sana itatanong, pero sige, hintayin ko na lang next posts.
i miss the sea and the beaches back home. I promised myself that if i get through this stage of my life... i'll give myself a vacation back home!
thanks for sharing your adventures DonG!
>hi rayts, ganda talaga dun. sana makapunta ka rin.
>garando, wala nga akong ibang maisip kung bakit nya kaming pinaghinalang na rock band. naka dark colored shirts lang naman kami.
matutuwa ka nga sa cagbalete kung yon ang hanap mo.
>redlan, oo nga. natawa talaga kami. wala namang long hair. ako din nakadaan na ako dito pero hindi ko pa masyadong na explore ang lucena or quezon in general.
>benghui. it definitely is far but im sure malaysia has its own beautiful beaches too.
>hi nyl, lalo na pag summer. salamat!
>hi alicesg, so you're just not the type who enjoy the backpacking style. you're more of a lesiure travel type of person.
>baboon, thanks! im glad you like the format. yes it's a beautiful island but wait till you see the other side. if you're afraid of the waves, this will not be the place for you as it is connected to the pacific ocean.
>hi cyndirellaz, maraming salamat. as long as im traveling im blogging. abangan mo ang kabilang side ng beach.
>luke, we definitely had fun.
>hi reena, kulit mo ulit. hehehe... walang roro papunta doon. medyo delikado nga tong mga ganito lalo na pag maalon.
>pao, mahihirapan ka nga doon pag maalon.
>hi lalaine, marami pang padating. salamat sa pag abang.
>mavs, salamat. medyo simple na nga ito kasi marami ka pang makikitang magandang kuha.
>hi ellesig, swerte pag kalamado ang dagat pero tingin ko delikado pag may bagyo.
tanong ka lang. dami pa din namang pictures na padating.
>hi teacher vic, salamat. white sand nga sa bandang yon kaya sarap maligo. salamat s pag abang.
>hi em, you definitely deserve a break and our country will be the best place. enjoy your weekend.
>hi jeanny, medyo mahina na nga to may mga mas madlas pa.
These are amazing shots. I love your adventures and the encounters you have. That last shot makes me feel good. The anchor will hold.
astig! mukhang masaya ang adventure no ni lawstude ah!
Mukhang masaya din to ah.
ui..napagkamalan kayong rock band?? astig ah..hahaha..
post nyo yung mala eraserheads nyong pics...aabangan namin yun.
Hahaha, it's funny that those tricycle drivers thought that you guys are rockers who would be performing somewhere! Now isn't that kind of stereotypical, hahaha!
It's also interesting to note that the houses seems.. pataas in your view. They are all cramped up!
Great adventure! superb photos and what more can I say... Hale to you!
pretty palayan. i miss my province. i am just new in blogs. hello.
Looks like you had lots of fun in Quezon province!
All 4 men wearing black tee? Maybe they thought you're the band KISS? lol!
Another fine outing from Mr. Dong!
Wonderful views. Like a lot the beach!
There are really so many other beautiful places to go to in this country of ours, and many of them are well-kept secrets. I do plan to visit all the nice places here in Pinas and your blog is really, really helpful.
The last picture is framed well! Galing!
how much ang entrance fee?
were did you stay in cagbalete and pagbilao? how many days do we need to visit the places in quezon that you've been to?
we were planning on exploring quezon po kasi.
we stayed at villa cleofas bait ng may ari. sa pagbilao hindi kami nag overnight.
I was a Maubanin and live in Cagbalete for 1 year as grade 5 student. It was tagalog town but majority are Visayan taking advantage of the fishes. Gosh i miss this barangay. It has been 20 years that i have not visited this place again.


text:
Soixante, soixante-deux est une chanson d'Eddy Mitchell, écrite sur une musique de Pierre Papadiamandis et parue en 1987, sur l'album Mitchell.

Histoire
Avec Soixante, soixante-deux, Eddy Mitchell rappelle que le début des années 1960, n'a pas seulement été pour les jeunes gens de sa génération l'avènement du rock 'n' roll, les filles et les surprises-parties, mais que ces « années d'insouciance », étaient aussi celles de  la mobilisation des appelés du contingent pour la Guerre d'Algérie, les affrontements entre OAS et FLN...

[...] Y a pas que le sable qui sent chaud, Y a surtout le grain de ta peau
M'apprendre à tuer, Quand j'veux t'aimer, Et rester ici
Tous dans l'même bateau, J'préfère les Naufrageurs
L'Algérie c'est beau, Oui mais vue du Sacré-Cœur

Soixante, soixante-deux, Quelque part ça m'fait peur
Soixante, soixante-deux, Y avait pas que des rockers
Terrorisme et O.A.S., Infos d'époque, R.A.S
La vérité sur ces années est encore tabou [...]

(texte Claude Moine)

Autour de la chanson

Le vers « Tous dans l'même bateau, J'préfère les Naufrageurs  », est une allusion au film de Cecil B. DeMille Les Naufrageurs des mers du sud.

Eddy Mitchell, en 1977, avec la chanson Et la voix d'Elvis, aborde/effleure déjà cette période.

En 1994, le chanteur consacre un roman autobiographique à cette époque P'tit Claude.

Discographie

 1987 : album Barclay Mitchell.

Discographie live :

1990 :
 Eddy Mitchell au Casino de Paris.
 45 tours Polidor 865 382-7 : Soixante, soixante-deux, Manque de toi (titres extraits de l'album live).
 1997 : Mr Eddy à Bercy 97

Notes et références

Liens internes
 Liste des chansons interprétées par Eddy Mitchell
 Liste des chansons composées par Pierre Papadiamandis pour Eddy Mitchell

Chanson interprétée par Eddy Mitchell
Chanson composée par Pierre Papadiamandis
Chanson de 1987

redpajama_set_name: RedPajamaWikipedia


text:
ISSA Los Angeles Announces Women in Security Panelists for Annual Security Summit
Stephanie Douglas, Pamela Fusco, and Andrea Hoy to Speak on Cybersecurity Panel at ISSA LA's 8th Annual Summit
ISSA LA Summit 8
Los Angeles, CA (PRWEB) May 12, 2016
The Los Angeles Chapter of the Information Systems Security Information (ISSA-LA) is pleased to announce Stephanie Douglas, Pamela Fusco, and Andrea Hoy as distinguished panelists for the Women in Security session to be held during its 8th Annual Information Security Summit set to take place Friday, May 20th at the Universal City Hilton in Universal City, California.
"Incorporated here in the heart of Southern California, the ISSA Los Angeles Chapter was the first and founding chapter of the internationally-recognized cyber professional's organization ISSA," said Andrea Hoy, President, ISSA International Board of Directors. "This year, as was done in previous years, one of the most well-attended sessions is returning; the Women in Security Panel. What I like about this session is that I always see the largest diversity in the audience—be it age range, years in the workforce, or even gender—all participating with questions that are affecting them today."
This open, honest discussion, scheduled for 1:30pm on Friday the 20th, will dig in to these critical topics:
Our panelist's entry into the Information / Cyber Profession
How the industry and profession has changed over the past two decades, (What were the tipping points?)
How we have changed with the cyber evolution, both professionally and personally
What can we expect in the next 5-10 years and "WHY"
Highlight milestones, challenges, discoveries ("When to pull the plug or plunge forward")
Cultivate interest for those desiring to expand their horizons in the cyber arena, where to go and how to get there ("When you love the work you do, but feel alone")
"The panelists are always willing to share openly about their experiences and how they overcame some of the challenges they faced in their careers," Hoy added. "The topics covered have always ignited conversation around how we sustain and grow our cyber professionals for the future. While women are said to only account for 10% of today's Information Security professionals (ISC2's Global Information Security Workforce Study), the need for improvement over the past 3-5 years—in spite of what we hear—needs continued improvement."
More details about the Women in Security panel can be found at http://sched.co/6Bur.
Additionally, Cynthia Marcotte Stamer will moderate a panel discussion entitled Telemedicine & Other Remote Healthcare Privacy, Security & Quality, with panelists Nora Belcher, Elle Ross, and Marcy Zwelling-Aamot. This distinguished panel will share and discuss key challenges and insights on strategies for designing and using telemedicine and other mobile and remote care technologies and practices to deliver or support the delivery of effective telemedicine and other remote health care services while managing healthcare privacy, security and quality and delivering financially viable, quality healthcare in accordance with medical legal and ethical standards. Learn more by visiting http://sched.co/6AqD.
As a bonus, we have another special guest joining the group during the opening reception at Saddle Ranch Chop House (http://sched.co/5azW) on Thursday evening as we wrap up the training and kick off the Summit. Joining us is Meredith O'Connor, a teen pop star and anti-bullying icon whose radio hit songs are loved by millions, and concerts have sold out around the world. O'Connor is an advocate and role model for overcoming adversity, and for women in technology.
"In this day and age, no matter what industry, online security is key for protecting yourself. I always encourage fans, young women, even teens my age all over the world to get educated in this growing, and influential field," said O'Connor.
For those of you that can join us earlier in the day on Thursday, the Applying Threat Intelligence to Improve Security Awareness Programs session with Araceli Treu Gomes is one that mustn't be missed. More details about this free training session for summit attendees can be found at http://sched.co/6T01.
We would also like to invite creative, talented women to show us how cybersecurity challenges are done—physical security, web, reversing, and forensics—by participating in our annual Capture the Flag event. More details about this technical challenge can be found at http://sched.co/6StK.
Finally, if DevOps is your thing, we would encourage attendees to meet industry expert Chenxi Wang as she discusses containers and security during her session entitled Rethink Systems Security with Containers. More details about this session can be found at http://sched.co/5blM.
Since ISSA-LA is all about the community, registration for the event is open to anyone interested in learning more about information security. The Information Security Summit is part of ISSA-LA's important community outreach program.
"Whether you are new to the field, a longstanding practitioner, or just someone who is tired of hearing about it in the news and wants to understand cybersecurity and privacy better, please join us in growing women in security for the cybersecurity future of our profession," added Hoy.
There's so much to do and the sessions are filling up fast. In fact, some training sessions are already sold out. So, don't delay. Register today at https://summit.issala.org/register.
For more information on ISSA-LA Summit 8 and for registration details, please visit http://summit.issala.org/.
About Information Systems Security Association (ISSA):
The Information Systems Security Association is a not-for-profit, international organization of information security professionals and practitioners. It provides educational forums, publications and peer interaction opportunities that enhance the knowledge, skill and professional growth of its members. The primary goal of ISSA is to promote management practices that will ensure availability, integrity and confidentiality of information resources.For more information or to register, please visit: http://www.issa-la.org. Join the movement today!
Sean Martin, CISSP
ISSA Los Angeles Summit
@issala
ISSA Los Angeles

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You are currently browsing the tag archive for the 'bonhoefferblog' tag.
Dietrich Bonhoeffer (1906-45) was a German theologian and pastor who spoke out against the Nazi regime during World War II. His resistance against Hitler's regime culminated with him being hung in a concentration camp at Flossenbürg.
Today, Bonhoeffer's works are loved by many. His writing, despite time, is still youthful, enlightening, and inspirational.
So, check out Mark 8:31–38 because it's the passage Bonhoeffer discusses in the following excerpt. Then… read and be encouraged!
The call to discipleship is connected here with the proclamation of Jesus' suffering. Jesus Christ has to suffer and be rejected. God's promise requires this, so that scripture may be fulfilled. Suffering and being rejected is not the same. Even in his suffering, Jesus could have been the celebrated Christ. Indeed, the entire compassion and admiration of the world could focus on the suffering. Looked upon as something tragic, the suffering could in itself convey its own value, its own honor, and dignity. But Jesus is the Christ who was rejected in his suffering. Rejection removed all dignity and honor from his suffering.
It had to be dishonorable suffering.
Suffering and rejection express in summary form the cross of Jesus. Death on the cross means to suffer and die as one rejected and cast out. It was by divine necessity that Jesus had to suffer and be rejected. Any attempt to hinder what is necessary is satanic. Even, or especially, if such an attempt comes from the circle of disciples because it intends to prevent Christ from being Christ.
The fact that it is Peter, the rock of the church, who makes himself guilty doing this just after he has confessed Jesus to be the Christ and has been commissioned by Christ, shows that from its very beginning the church has taken offense at the suffering Christ. It does not want that kind of Lord, and as Christ's church, it does not want to be forced to accept the law of suffering from its Lord. Peter's objection is his aversion to submitting himself to suffering. That is a way for Satan to enter the church.
Satan is trying to pull the church away from the cross of its Lord.
So Jesus has to make it clear and unmistakable to his disciples that the need to suffer now applies to them, too. Just as Christ is only Christ as one who suffers and is rejected, so a disciple is a disciple only in suffering and being rejected, thereby participating in crucifixion. Discipleship as allegiance to the person of Jesus Christ places the follower under the law of Christ, that is, under the cross.
Eighty years ago, as war clouds gathered over Europe, the 33-year-old Christian theologian Dietrich Bonhoeffer, then a faculty member at Union Theological Seminary in Manhattan, returned to his native Germany after a short stay in the United States.
At the time, Bonhoeffer believed his church's response to Hitler and Nazism was marked by weakness and cowardice. He saw his country consumed by a monstrous cancer that had devoured nations and had already murdered many hundreds of people on its way to murdering millions.
It was a fateful and ultimately lethal decision. Six years later, on April 9, 1945, a month before the end of World War II in Europe, the Nazis executed Bonhoeffer for his opposition to the regime.
Before coming to New York, Bonhoeffer had already been banned by the Gestapo, and in the six years after his final return to Germany, he became the dominant figure of the Protestant resistance. Although more than seven decades have passed since he was hanged for his anti-Nazi "crimes," there are today numerous articles, books, dramas, poems, operas, songs and films about the young Lutheran pastor who has been called a Protestant saint.
Earlier, Bonhoeffer had battled the infamous "Deutsche Christen" or "German Christian" movement, which critics derisively called the "Brown Church," because many of its leaders dressed in brown storm troopers' uniforms. Its bishops proudly wore swastikas on their ecclesiastical robes and publicly offered the infamous stiff-armed Nazi salute.


text:
Aaspere est un village de la commune de Haljala du comté de Viru-Ouest en Estonie.
Au , il compte 268 habitants.

Notes et références

Liens internes
 Route nationale 1

Aaspere


Discover the naturally stunning Tierra del Fuego, an archipelago located at South America's southernmost tip, on this epic four-night cruise. Starting in Punta Arenas and ending in Ushuaia, you'll cruise through some truly breath-taking sights, including soaring glaciers and beautiful wildlife.
The outer edge of the world awaits you on this adventurous eight-night journey along the same waterways which inspired Charles Darwin. This spectacular itinerary retraces much of the route the renowned British naturalist took through the Fuegian Archipelago in the 1830's, a voyage that inspired him to write the Origins of the Species and formulate the theory of evolution.


text:
Published on Civil Service World (https://www.civilserviceworld.com)
Home > Defiant NHS chief rejects government's health service funding claims
Defiant NHS chief rejects government's health service funding claims
Written by Seb Whale on 12 January 2017 in News
Comments from NHS England chief executive prompt former Treasury permanent secretary Nick Macpherson to warn of a "bottomless pit" on health service funding
The head of NHS England has publicly contradicted Theresa May's claim that the government is providing the health service with more funding than it requires.
Stevens argued it would be "stretching it" to say the NHS has received more cash than it asked for and said hospitals are facing "substantial pressures".
The NHS chief also suggested ministers were misleading the public over claims that extra money had been earmarked for the health service.
Department of Health accused of "underhand attempt" to mask financial woes [1]
Spending Review: NHS chief Simon Stevens warns over funding [2]
Doctors and purses: lifting the lid on the relationship between the Treasury and the Department of Health [3]
His comments, to the Public Accounts Committee, came after it was reported that May's aides believe he has been insufficiently enthusiastic and responsive amid the mounting crisis on NHS wards.
The prime minister on Sunday claimed the government has met and exceeded demands for funding outlined in NHS England's five-year forward view.
But Stevens said that the health service would have received £10bn in pledged funding by 2020, but spread across six years, rather than five as claimed by the Conservatives.
Mr Stevens said: "I don't think that's the same as saying we're getting more than we asked for over five years, because it was a five-year forward view not a six-year forward view.
"And over and above that, we obviously had a Spending Review negotiation in the meantime and that has set the NHS budget for the next three years...
"Like probably every part of the public service we got less than we asked for in that process. So I think it would be stretching it to say the NHS has got more than it asked for."
When pressed by committee chair Meg Hillier whether there is a "clear gap" between what the NHS is taking in versus what it needs, he replied: "There are clearly very substantial pressures, and I don't think it helps anybody to try and pretend that there aren't.
"But that's not a new phenomenon to some extent. It is a phenomenon that is intensifying."
He added: "I do believe there are some very genuine choices to be made across the NHS and there is a circle to be squared. I think that's right."
Reacting to Stevens' appearance, former Treasury permanent secretary Sir Nick Macpherson – who was in post at the finance ministry during the 2015 Spending Review negotiations – said Stevens was a "good guy" but "should not determine health spending".
Macpherson tweeted: "NHS bottomless pit. Money should be linked to reform."
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[2] http://www.civilserviceworld.com/articles/news/spending-review-nhs-chief-simon-stevens-warns-over-funding
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[7] https://www.civilserviceworld.com/tags/operational-delivery
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[9] https://www.civilserviceworld.com/categories/government-and-politics
[10] https://www.civilserviceworld.com/categories/health-and-social-care
[11] http://www.politicshome.com


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European French Oak 7 1/2" x 1/2"


This weekend sees the start of the 2013 Rugby Championship tournament. With Australia boasting a new coach still smarting from their Lions series defeat, New Zealand for some reason still leaning heavily on older, out-of-form players, South Africa frantically calling in reinforcements from Japan and elsewhere, and Argentina recovering from a summer pasting by England, it looks to be a very open and intriguing tournament.
But let's face it, the rugby is of secondary importance here – what really matters, as we all know, is who's wearing the best shirt. Obviously. So, let's take a look at what the Southern Hemisphere titans will be covering their modesty with this time out.
The clear favourites and current champions of everything in the international rugby stakes will shock the world by wearing a black shirt with white bits on it this year. We know, we can barely contain our excitement either. You have to feel for Adidas' kit designers, as there's really very little you can do with an All Black jersey – they might as well give it to the work experience lad, yknow?
That said, there are some subtle differences from the 2011/12 shirt that we've noticed – the slighty odd 'half-white' collar they wore last time out now goes all the way around the neckline, and looks much better for it, and in this image at least, the famous silver fern actually looks a bit more silver than it has done before – it's traditionally been white, but we like it. Quite why they've made the fern and the Adidas logo silver and left the AIG logo white is a matter for the suits to discuss, but there's no doubt it looks weird. And while we're at it – New Zealand, you've got a shirt sponsort now, deal with it. By making the AIG logo tiny and too far up the chest, you're not 'preserving the sanctity of the All Black jersey' – you're just making it look like the shirt sponsor has been hurriedly pressed onto the jersey by the lad down the local sports supply shop.
You're probably all familiar with this shirt already after the Lions tour, but let's take a moment to appreciate what is a very fine bit of rugby shirt design. We're not the biggest fans of Kooga here at Rugby Shirt Watch, their shirts tend to have all the class and restraint of a 90s shell suit, but you have to hand it to them for what they've done with the Wallaby shirt. Last year's effort was handsome and understated, if a little dull, but this one keeps things class, but adds a bit of modern design flair with that green collar/shoulder stripe motif – and it works. If this is what happens when the designers at Kooga spend a bit of time thinking about making a great rugby shirt, we really wish they'd do it more.
It's more of the same from Canterbury and South Africa, although let's face it, there's not a lot wrong with what the New Zealand firm have done with the Springbok shirt in recent years. We like the toning down of the colour palette – all you need on a South Africa shirt if green and gold, and the use of subtle contrast piping and ribbing on the body of the shirt stops it from looking too plain – the new collar design is pretty decent too.
As an aside, while it might not make an appearance at all, we really hope that the Springboks' new alternate kit gets a run-out away to the All Blacks – lime green and white, how smart is that?!
The team that turned the Tri-Nations into the Rugby Championship celebrated their entrance to the top table of international rugby with a new kit supplier in Nike, and an abandonment of the traditional horizontal blue and white hoops,for a more angled affair. As you can see, there's not much to choose between this year and last year's efforts, with one unfortunate addition – yup, those really are 'puma spots' up the sides of the shirt. We're sure Nike would tell us that they're designed to enhance grip on the ball, or some such nonsense, but honestly, they just look like the shirt has some kind of awful skin condition… Argentina unveiled a rather different post-Championship kit last year, that was bold and daring, but in a much more enjoyable way – Nike should have carried on down that road and left the animal-based gimmicks to less reputable suppliers.


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What is PHP, and why does your server's version of PHP matter?
PHP is the primary language WordPress is built upon and the more efficiently it allows your server to interact with your readers' browser, the better their experience. Advancements in technology bring down costs. Streamlined PHP 7 means more money for you, because you build more quickly with fewer costs.
For starters: How Do I Know Which Version of PHP I'm using?
If you use the Give plugin, we've made it staggeringly easy to determine which version of PHP you are using. Navigate to Donations → Tools → System Info (tab) and scroll down to the "Webserver configuration" section. There you'll see which version of PHP you are using.
Imagine I handed you a hammer and 17 nails and told you to build a shed out of a pile of wood. It's possible, right? You'll just need to be creative.
Now, imagine I gave you the same assignment with the same pile of wood, but I gave you 57 nails, a nail gun, 15 galvanized lag bolts with nuts, washers, and 13 pieces of steel angle-iron with pre-drilled holes. Sitting on top of the pile of wood is now a hydraulic air wrench and a drill. The job just got a lot easier, right?
Advances in technology bring down production costs. This principle carries across many fields, from assembly lines for automobiles to large agricultural machinery designed to harvest crops more efficiently.
The same thing has happened for web technology with the benefit of a much higher rate of advancement. Advances which took the automobile assembly line many years to streamline because they are changing physical products take web developers a matter of months to change the digital landscape.
PHP is the programming language underscoring WordPress. Without going too terribly far into geek-speak to explain it, simply thinking of it as a language telling computers what to do is helpful.
Languages can be modified, adapted over time for efficiency. The very word "blog" is an example of language adapting to be more efficient: a portmanteau of "web log" which itself is a phrase that makes vastly more efficient the explanation of the process of digital publishing.
A more efficient language is a better language, because you can communicate the same thing in less time.
Version 5.2 of PHP shipped in January of 2011. It was a phenomenally stable release of PHP which served to advance technology and stabilize not only WordPress, but the many other platforms which relied upon it.
Coincidental with the release of PHP 5.2 was a surge in the number of websites in the world, from just over 200,000,000 websites at the end of 2010, the number more than tripled by the end of 2012, to almost 700,000,000 according to Internet Live Stats.
That confluence of maturing web infrastructure and the release of a stable PHP release meant that every web host on the scene quickly began supporting it. Web commerce was still very much a wild west. The same web hosts that began providing "one click" WordPress installs were now burying PHP version update responsibility in their terms and conditions — passing the buck to the site owner.
So, how long does a release last?
Each release branch of PHP is fully supported for two years from its initial stable release. During this period, bugs and security issues that have been reported are fixed and are released in regular point releases. After this two year period of active support, each branch is then supported for an additional year for critical security issues only. Releases during this period are made on an as-needed basis: there may be multiple point releases, or none, depending on the number of reports. Once the three years of support are completed, the branch reaches its end of life and is no longer supported. A table of end of life branches is available.
Have you seen the perfect storm brewing yet?
A technology that goes completely stale after three years, installed on web hosts where the onus for updating that technology is placed on users who have neither the understanding of why nor the skills how to update it.
That brings us to 2016, where some web hosts are still chugging along with PHP 5.2 running on their servers. To be clear and fair: lots of hosts have stepped up and updated their users to more recent versions, and they did make it clear in the terms and conditions whose job is was to update it, in the first place.
Since then, 5.3, 5.4, 5.5, and 5.6 were released. Finally, just this year, PHP 7 was released. To use our analogy from above, this release was the nail gun and galvanized bolts for the web operation.
Besides the "it's no longer supported" argument, are there other reasons to update to PHP 7?
Yes: that brings us back to the pile of wood that is your WordPress site.
Benchmarks are not infallible guides, but early tests are showing that PHP 7 is significantly faster than even it's most recent older sibling. Fast is good. If you are accepting donations on your WordPress website, fast is the difference between a donation, and no donation.
Fast also means more efficient use of server resources. That means the ability to welcome more concurrent visitors which means, again, more money.
Advancements in technology bring down costs. Streamlined PHP 7 means more money for you, because you can build a better shed, which lasts longer, and you can build it more quickly, which costs less, too.
We could go into all of the specific highly geeky enhancements of PHP 7, but that is better handled here.
Learn about PHP and stay informed.
The simple decision to pay attention. Be aware of which version of PHP you are running, and update to PHP 7 with the help of your web host. This could mean dozens of saved man-hours of support for your staff, a better experience for potential donors, and thousands of dollars in donations. When someone hands you a power drill, you might as well plug it in and build a better shed.
Many Give users (myself included) have migrated over to PHP 7.1 or 7.2 and can say, from experience, that Give works great over here! Contact your webhost today to get guidance on switching to a free version of PHP.


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Sensationnel keyword En ligne. Sunglasses. Having the ideal summer wedding? Candies and chocolates might not be the best wedding favor to depart for guests in the hot summer sun. Sunglasses are a great quirk to save your guests pleasurable and to remind them of your special daylight for years to come. A plus? Frames come in a variety of styles and can be personalized in consequently many ways. You are limited lonesome by your imagination! behind tote bags, sunglasses can after that be personalized professionally by many wedding and party vendors.
S'mores Kits. absolute for weddings in late summer or to the lead fall, individual s'mores kits are out of the ordinary creative every second to more normal wedding favors. These can be as basic or as decadent as you prefer, and as a result they can take effect for any budget. all you need are some graham crackers, marshmallows, chocolate bars and cute craft supplies to create these adorable and unforgettable gifts for your guests.
Candy in Personalized Wrappers. A bit more upon the received side, personalized candy wrappers and candy seem to be mainstays behind it comes to wedding favors. From those oft-present Jordan almonds to the more highly developed chocolate bars, this is unusual easy and reasonable showing off to grow a personal be adjacent to to your wedding. Why mess taking into account a classic? choose your candy and pick out those personalized candy wrappers. It's a great way to make an proclaim on wedding guests bearing in mind a sweet-tooth, and it then makes for a well-appreciated shower or bachelorette party gift.
Hangover Rescue Kits. Hangover rescue kits or "cures" are a must-have if your guests will be drinking. From a personalized bottle of water, to a hangover remedy-packed kit, you can create this wedding favor as easy or as puzzling as you like. As subsequently the additional do-it-yourself ideas, this concept is gymnastic and budget friendly. Hangover rescue kits after that create good bachelor and bachelorette party favors!
Sachets. You probably already know that sachets are little bags of perfumed flowers or aromatic herbs that people typically place in drawers or closets to create the vent odor pleasant. What you might not know is that these herb and flower-filled pouches create creative wedding favors as well. As following sunglasses or totes, these progressive wedding party favors can either be bought or made at home.


ARTICLE I: Name: The name of the organization shall be the Association for Public Interest Law at the University of New Mexico School of Law (APIL at UNM Law).
Raise and allocate funds in order to provide grant recipients with an opportunity to gain practical experience in public interest law.
Assist public interest governmental or non-governmental non-profit agencies to achieve their goals by encouraging and enabling students to undertake unpaid summer internships.
Educate students about career opportunities in public interest law and legal services. Create a community where students can demonstrate their individual and communal support of public interest law.
ARTICLE III: Membership: All UNM School of Law students are eligible to become members of APIL at UNM. They may become members by demonstrating an interest in the group, and participating in APIL at UNM activities. Voting rights are limited to members who pay $5.00 yearly dues each spring of the school year.
ARTICLE IV: Executive Council: The affairs of APIL at UNM shall be managed by its Executive Council. Executive Council action shall be by a majority. In circumstances where not all of the members of the Executive Council are present, a 2/3 quorum is necessary.
Members-The Executive Council shall be comprised of the duly elected officers of APIL at UNM and any additional members elected to the Council. Additional members shall be comprised of one student from each year. Other than the First-year member, the members of the Council shall be elected by all the membership in the spring. The First-year member shall be elected in the first official APIL at UNM meeting for the academic year. There shall be an election for one student-at-large in the event there is an even number of members on the Executive Council. The member-at-large shall be elected by the voting membership at the second official meeting of APIL at UNM for the academic year.
Term-Executive Council members shall serve from the spring of the academic year they were elected to the following spring, with the exception of the First Year member and the student-at-large who shall serve from the time of their election to the next election.
Removal-Any member of the Executive Council may be removed from office by an affirmative vote of of the Executive Council.
Vacancies-Any vacancy of a member of the Executive Council shall be filled by a majority vote of the membership. A member elected to fill a vacancy shall be elected for the unexpired term of his/her predecessor.
Committees-The Executive Council may from time to time, form such committees or subcommittees, to perform any duties specified by the Executive Council, provided that any decision requiring the expenditure of Grant Funds must be approved by a majority of the Executive Council before the expenditure is authorized.
ARTICLE V: Officers: The officers of APIL at UNM shall be a President, a Vice-President, a Treasurer, and a Secretary. All of these positions may be held by one or more persons as to be determined by the membership.
Election-Officers shall be elected by the membership. Elections shall be held in the spring semester by a majority vote of the membership at a meeting with written notice of the meeting.
Term-Officers shall serve from the spring of the academic year they were elected to the following spring.
Removal-Any Officer may be removed by an affirmative vote of of the Executive Council.
Vacancies-Any vacancy of any office shall be filled by a majority vote of the Executive Council. Any Officer elected to fill a vacancy shall be elected for the unexpired term of his/her predecessor in office.
President-The President shall be the principle Executive Officer of APIL at UNM. Subject to the direction and control of the Executive Council. He/She shall be in charge of the business and affairs of the Organization; shall see that the resolutions and the directives of the Executive Council are carried into effect; and in general shall discharge all duties incident to the Office of the President.
Vice-President-The Vice-President shall assist the President in the discharge of his/her duties as the President may direct, and shall perform such other duties as from time to time may be assigned to him/her by the President or by the Executive Council. In the absence of the President or in the event of his/her inability or refusal to act, the Vice-President shall perform the duties of the President and when doing so shall have the powers of and be subject to all restrictions upon the President.
Treasurer-The Treasurer shall be the principle accounting and financial office of the organization. He/She shall have charge of and be responsible for the maintenance of adequate books of account for the Organization; and be responsible for the receipt of funds and the disbursement of the funds. The Treasurer shall perform all duties incident to the Office of Treasurer and such other duties as from time to time may be assigned to him/her by the President or by the Executive Council.
Secretary-The Secretary shall record the minutes of the meetings of the general membership and the Executive Council, and see that notices are posted for meetings of the membership and the Executive Council.
ARTICLE VI: APIL Public Interest Fellowship.
Awards of Grants-The Executive Council shall disburse fellowship grants to support legal work in the public interest by funding University of New Mexico School of Law students in public not-for-profit law agencies and legal services projects. Grants shall be awarded and payments made directly to the recipient in a manner to be determined by the Executive Council.
Form of Grant Applications-The Executive Council may prescribe the form of the grant application and the types, amount and detailed information to be furnished by grant applicants.
Participation in APIL at UNM during the school year. Participation includes a minimum five-hour commitment in the fall semester and a minimum five-hour commitment in the spring semester for a total of ten hours at any APIL at UNM sponsored event.
A firm commitment of employment at a public interest law job for the summer. This requirement may be met by working a number of hours per week as determined by the Executive Council. The applicant must work under the supervision of an attorney licensed to practice law.
A letter from an employer verifying that a firm offer has been extended in accordance with the specified hours as determined by the Executive Council in Article VI (C) (2).
Note: Federal law prohibits APIL at UNM from funding Federal judicial externships.
Any grant recipient may be asked to serve in the grant selection committee the following year.
The nature of the supervision received.
Note: These reports shall be retained by the Secretary and shall be made available for public view.
The selection committee shall consider, but are not limited to the following factors in determining grant awards: Present and future commitment to public interest work, and presentation of the student's application (including the interview). The Committee will also consider the quality of supervision and training provided by the organization. While all factors are important, personal commitment to public interest law will be accorded the greatest weight. In the course of the interview, applicants may be asked to further explain their financial status. This information will assist the Committee in determining how to best allocate funds.
No grant shall be given the purpose of which is contrary to the purpose of APIL at the UNM, as set out in Article II.
The Executive Council has sole power for development of the grant application form, administration of grant applications, and conducting the election for a Selection Committee, which shall interview the applicants and recommend grant awards in the manner prescribed by the Executive Council in compliance with the Constitution.
The Selection Committee shall consist of a combination of Executive Council members and past grant recipients.
The Administration shall disperse all grant awards as determined by APIL at UNM.
This Committee will participate in the Student Bar Association (SBA) public interest fellowship in accordance with the rules established by the SBA public interest fellowship committee bylaws.
ARTICLE VII: Amendments to the Constitution. Such action may be taken at a meeting of the membership with written notice of the purpose of the meeting. All amendments must receive an affirmative vote of 2/3 of the Executive Board and 2/3 of the membership present.