text:
\section{Introduction}

\label{Introduction}

Since December 2019, a virus named SARS-CoV-2 has been affecting the entire world drastically until this day.
As of November 1, 2021, the virus had infected 246,594,191 people, including UK Prime Minister Boris Johnson and US President Donald Trump.
Although the epidemic in some countries has been brought under control, the epidemic in most parts of the world is still ongoing.
Nowadays (November 2021), the vaccination rate of COVID-19 vaccines is increasing, but there are still hundreds of thousands of new cases per day.

The number of studies based on the epidemic analysis has considerably grown since the start of the COVID-19 epidemic.
Some are about the characteristics of COVID-19. Although most of the attributes of SARS-CoV-2 cannot be obtained by epidemic analysis, the epidemiological characteristics of COVID-19 can be estimated. Most of the works~\cite{wu2020nowcasting, hao2020reconstruction, cao2020incorporating, deressa2020modeling} focus on the study of the basic reproduction number $R_0$ of COVID-19, which can reflect the propagation ability of SARS-CoV-2, while other works analyze the characteristics of COVID-19 such as the generation interval (cases doubling time)~\cite{guan2020clinical, ali2020serial}, the duration~\cite{walsh2020duration} and the infectiousness~\cite{article}.
Others are about the trend forecast of COVID-19. By combining real data with the model, these works aim to predict the development of COVID-19. Since the beginning of the COVID-19 outbreak, it has been a hot topic. The most common method to predict the number of future infections is to fit real-time data, such as propagation models~\cite{ghamizi2020data, ren2020derivation} and Bayes~\cite{gaglione2020adaptive, de2020epidemiological}. Due to the global characteristics of the epidemic, many focus on combining population mobility data with the propagation model~\cite{2020Understanding, jia2020population, huang2020understanding}.

SIR~\cite{newman10} is a widely used model, and its related models have been well studied in the literature.
Apart from the combination of the population mobility, there are additional aspects that are studied: The SEAIRD model allows for further division of the population~\cite{liu2020towards, nino2019two}; environmental parameters are added to the models~\cite{zhang2017forecasting, Bherwani2020}; and machine learning algorithms are used~\cite{zhang2020predicting, achterberg2020comparing}.

It is worth noting that the significance of prevention has also become the subject of many studies, including reducing population mobility~\cite{jia2020population}, lockdown of the city~\cite{tian2020investigation}, keeping social distance~\cite{du2020effects}, and vaccination~\cite{2021Vaccine,2021Time}.
Based on the development of the epidemic situation before and after prevention, the role of prevention is analyzed.
Almost all the results affirm the role of prevention and point out that the epidemic would worsen more seriously without it.

The above works have studied various aspects of on COVID-19 pandemic, but rare work takes the effect of adaptive changes of prevention measures over time on the epidemic development into account.
During the COVID-19 pandemic, many regions gradually adopt adaptive prevention strategies to try to balance epidemic prevention and economic growth. Different regions often employ different prevention strategies, which may bring new phenomenon that does not exist in the traditional epidemic models.
We propose two extensions to the widely used SIR model, considering adaptive changes in prevention strategies based on the current infection severity and the population mobility between multiple regions.
We show the plateau phenomenon for the first time to address both the theoretical and the empirical perspectives.
We verify from the real-world data that the plateau phenomenon does exist in many regions of the world in the current COVID-19 development, indicating that this is an important phenomenon to study.

This work provides new insights into the development trend of COVID-19 and its prevention in cities.
The development of the epidemic not only has ups and downs but also can have a plateau period of steady development.
Under the adaptive prevention strategies of the city, we may be able to control the epidemic at a low cost and achieve long-term coexistence with the virus.
This is a new option for outbreaks that would not fade away in a short period of time.

\section{Results}
To make it easier to understand our results, we summarize the symbols used in this paper, as shown in Table~\ref{tab:symbol}.
We show our findings below from three aspects: simulation, the real world, and theory.

\begin{table*}[t]
    \setlength{\abovecaptionskip}{2mm}
	\centering
    \caption{A brief explanation of symbols.}
	\small

	\label{tab:symbol}
	\setlength{\tabcolsep}{2mm}
	\begin{threeparttable}
		\begin{tabular}{l|c|c|c}
			\toprule
			\textbf{symbol} &  \textbf{explanation}  &  \textbf{symbol} &  \textbf{explanation} \\
			\midrule
			 S &   the number of susceptible people  &   I  &   the number of infected people \\
			\midrule
			 R &   the number of recovered people  &   N  &   total number of people \\
			\midrule
			 $\beta$ & infection rate  &  $\gamma$  &   recovery rate \\
			 \midrule
			 $r$ & the number of contacts; prevention parameter  &  t  &   day \\
			 \midrule
			 $\theta$ & prevention threshold  &  k  &   reaction speed \\
			 \midrule
			 $[r_L, r_H]$ & the range of changing prevention parameter  &  $[p_L, p_H]$  &   the range of changing proportion of floating population \\
			 \midrule
			 $r_0$ & initial prevention parameter  &  $p_0$  &   initial proportion of floating population \\
			 \midrule
			 $\tilde{r}_t$ & effective prevention parameter  &  $I_0$  &   the initial number of infected people \\
			 \midrule
			 IC & initial condition of the city $(N, \frac{I_0}{N})$  &  EE  &   external environment \\
			\bottomrule
		\end{tabular}
	\end{threeparttable}

\end{table*}

\subsection{Simulation Results}
\label{simulationexperiment}

Based on the epidemic model with the prevention parameter we proposed, we take the COVID-19 as an example to simulate the epidemic development in a single city and in multiple cities, which use one day as the time unit.

\subsubsection{Prevention Strategy}
\label{sec:ps}

During the epidemic, different cities or regions may have different strategies and measures to deal with infectious diseases.
For example, during the COVID-19 outbreak, some regions imposed mandatory mask wearings while some did not, many enforce social distancing,
	but at different scales, such as limited the size of the gathering of no more than 50 or 100 people, closing schools, or restricting
	travels to and from high-risk regions.
All these restrictions can be reflected in two parameter changes within our model.

First is the prevention parameter $r_i$ for each city $i$.
Different social distancing measures essentially all reduce the number of people any individual would meet in a time unit, which is
	modeled by $r_i$.
Thus we use $r_i$ to model the prevention measures, with lower $r_i$ meaning a high level of prevention measures and high $r_i$ meaning
	a low level of prevention measures.
Another parameter affected by the prevention measure is the fraction of
	the floating population $p_i$ --- the proportion of the floating population in the urban population.
A higher prevention level decreases the fraction of the floating population, while a lower prevention level increases the fraction of the floating population.

Most cities or regions also dynamically adapt their prevention measures based on the current infection data --- when the new infection cases
	rise, the prevention measures intensify, and when the number of new cases drops, the prevention measures are relaxed.
We model this scenario by setting a prevention threshold and dynamically changing the prevention parameter $r_i$ and
	the fraction of the floating population $p_i$
	based on whether the current infection cases are below or above the prevention threshold.
Technically, we have three main factors for deciding and changing the prevention measures:

\begin{itemize}
\item
{\bf Prevention threshold}, which sets a limit on the number of new infections within a time period.
New infections only include new cases caused by intra-city infections, excluding imported cases brought outside the city.
When the new number of infected people each day for 14 consecutive days is lower than the prevention threshold, it shows that the epidemic situation is getting under control, and the prevention level begins to decline ($r$ increases).
When the number of newly infected people on any given day is higher than the prevention threshold, it shows that the epidemic may worsen again, and the prevention level begins to rise ($r$ decreases).

\item
{\bf The range of changing prevention parameters}, which gives the range of changes
	of each prevention parameter $r_i$ and the fraction of floating population parameter $p_i$.
	When the prevention measure intensifies, the values are changed to $r_{L}$ and $p_{L}$ respectively, and when the prevention
	measure relaxes, the values are changed to $r_{H}$ and $p_{H}$.

\item
{\bf The reaction speed}, which measured by the number of days $k$ to complete the change.
In the real world, the change of prevention measures never happens instantaneously.
So we use $k$ to model the number of days needed to change $r_{L}$ to $r_{H}$ and $p_{L}$ to $p_{H}$, or in the reverse order.
We use $r_{t+1}=r_{t} \cdot (\frac{r_{H}}{r_{L}})^{\frac{(-1)^{s}}{k}}$ and $p_{t+1}=p_{t} \cdot (\frac{p_{H}}{p_{L}})^{\frac{(-1)^{s}}{k}}$ to represent daily changes in $r$ and $p$.
When $s=0$, it means to relax the prevention.
When $s=1$, it means to strengthen prevention.
$r$ and $p$ are always within the range of the prevention strategy.

\end{itemize}

In general, prevention strategies can be divided into two cases.
The case that the prevention parameter remains unchanged: the parameters of prevention parameter $r$ and the proportion of floating population $p$ are fixed values, and there is no prevention threshold and reaction speed.
This corresponds to the classical infectious disease model, and we refer to it as a model with a {\em constant prevention strategy}.
The case corresponds to the adaptive changes in prevention parameter that we commonly see during the COVID-19 pandemic:
	the full strategy is characterized by the prevention threshold $\theta$, the $r$-range $[r_{L},r_{H}]$, the
	$p$-range $[p_{L},p_{H}]$, and the reaction speed $k$, and we refer to such ones as models with an {\em adaptive prevention strategy}.

\begin{figure*}[t]

	\small
	\centering
	\subfloat[\scriptsize  Single city with constant strategy ]{\label{singlecitywithoutstrategy}\includegraphics[width=0.48\textwidth]{./image/singlecity1.eps}}
	\subfloat[\scriptsize  Single city with adaptive strategy ]{\label{singlecitywithstrategy}\includegraphics[width=0.48\textwidth]{./image/singlecity2.eps}}

	\subfloat[\scriptsize Multiple cities with constant strategies ]{\label{multiplecitieswithoutstrategy}\includegraphics[width=0.48\textwidth]{./image/multi-city1.eps}}
	\subfloat[\scriptsize  Multiple cities with mixed strategies ]{\label{multiplecitieswithstrategy}\includegraphics[width=0.48\textwidth]{./image/multi-city2.eps}}
	\caption{Infectious disease model with constant or adaptive prevention strategies.}
	\label{plateau}

\end{figure*}

Figure~\ref{plateau} shows the development of the epidemic in a single city and multiple cities with constant or adaptive
	prevention strategies.
The y-axis is the value of $I$ for a particular day, which is the number of current existing infected individuals that can still transmit
	the disease (note that it is not the number of newly infected cases on that day).
As a convention, for a constant prevention strategy that does not change $r$, e.g. $r$ is always $6$, we denote it as $r=6$ in the
figure legend; for an adaptive prevention strategy,
	if we initially set a prevention strategy to be at a certain level, and then it will change
	in the range $[r_L, r_H]$ when the newly infected case per day drops below the threshold, we denote it as $r_0=6$ and
	$r_L,r_H$ to the appropriate values in the legend.
The fraction of floating population $p$ and the corresponding $p_0$ and $p_L, p_H$ are treated in the same manner.
The initial conditions of cities are all $IC = (200000,0.5\%)$, while the external environment is $IC = (100000,0.01\%)$.
\begin{itemize}
\item
Figure~\ref{singlecitywithoutstrategy}: In the single-city model with a constant prevention strategy, the change curve of the number of existing infections is smooth.
The number of infections either continues to decline ($r \le 8$), or rises first and then falls ($r>8$).
\item
Figure~\ref{singlecitywithstrategy}: In the single-city model with an adaptive prevention strategy, the change curve of the number of existing infections is no longer smooth.
Compared to the single-city model with a constant prevention strategy (Figure~\ref{singlecitywithoutstrategy}), it has a distinctive feature ---
	a long period in which the number of existing infected people remains more or less the same, with small fluctuations.
We refer to such a flat period as a \textbf{plateau}, and it is the main phenomenon we are going to study in this paper.
\item
Figure~\ref{multiplecitieswithoutstrategy}: This is the case in three cities that have constant prevention strategies.
In the multi-city model, it can be found that the urban epidemic situation affects each other under the influence of population mobility.
The number of infections in city C should have risen to a higher level ($I>5000$), but instead, it begins to decline earlier under the influence of other cities.
On the contrary, there has been an increase in the number of infections in the external environment EE which should have been declining ($r=6$).
There is no plateau phenomenon in this case.
\item
Figure~\ref{multiplecitieswithstrategy}: In this case, two of the cities (B and C) adopt adaptive prevention strategies, and one city (A) as well
	as the external environment use a constant prevention strategy.
The phenomenon of horizontal fluctuation in the number of existing infections, i.e. the plateau, appears again.
More interestingly, the plateau appears in every city,  has occurred in every city and the environment, even if some cities and the environment
	adopt a constant prevention strategy.
\end{itemize}

\subsubsection{Plateau}
We can see that the adoption of adaptive prevention strategies is strongly correlated to the
	emergence of the plateau.
When there is no adaptive prevention strategy deployed, we do not see the plateau phenomenon(Figure~\ref{singlecitywithoutstrategy} and Figure~\ref{multiplecitieswithoutstrategy}).
However, the adoption of adaptive strategies itself is not sufficient to guarantee the appearance of the plateau, which can be
	seen in the blue curve in Figure~\ref{singlecitywithstrategy}.
Moreover, in the multi-city situation, even if some city does not adopt an adaptive prevention strategy, it still exhibit a plateau
	(city A in Figure~\ref{multiplecitieswithstrategy}), seemingly under the influence of other cities with adaptive prevention strategies.
Thus, the actual condition of the emergence of plateau needs to be further analyzed.

\begin{figure*}[t]

	\small
	\centering
	\subfloat[\scriptsize ]{\label{threshold}\includegraphics[width=0.33\textwidth]{./image/factor1.eps}}
	\subfloat[\scriptsize ]{\label{changingrange}\includegraphics[width=0.33\textwidth]{./image/factor2.eps}}
	\subfloat[\scriptsize ]{\label{changerate}\includegraphics[width=0.33\textwidth]{./image/factor3.eps}}

	\caption{The influence of indicators on the plateau.}
	\label{strategyinfluence}

\end{figure*}

\subsubsection{The Effect of Prevention Strategies}

We use the single-city model for this test to make the effect of prevention strategies more direct, as shown in Figure~\ref{strategyinfluence}:
\begin{itemize}
    \item \textbf{Prevention threshold $\theta$.}
    As shown in Figure~\ref{threshold}, when there is a plateau in the development of the epidemic, it can be found that the prevention threshold $\theta$ is positively correlated with the height of the plateau. The greater the prevention threshold, the higher the plateau.

    \item \textbf{The range of changing the prevention parameter $[r_L,r_H]$.}
    As shown in Figure~\ref{changingrange}, when there is a plateau in the development of the epidemic, different $[r_L,r_H]$ will not change the height of the plateau.
    However, $[r_L,r_H]$ will determine whether the plateau occurs.
    When $r_0=4, r_L=4, r_H=8$, the plateau does not occur, and the number of existing infections continues is declining.
    When $r_0=9, r_L=9, r_H=15$, the number of existing infections will rise at first and then decrease, but there will still be a plateau after.
    A closer look at the blue line and the purple line, the size of the changing range is related to the amplitude.
    The greater the range of change, the greater the amplitude.

    \item \textbf{The reaction speed $k$.}
    Figure~\ref{changerate} shows that $k$ affects the fluctuation amplitude of the plateau. The smaller the $k$, the greater the fluctuation of the number of existing infections during the plateau.
\end{itemize}

Through our simulations, we can see that the emergence of the plateau is related to the range of changing the prevention parameter $[r_L,r_H]$, and the height of the plateau is positively correlated with prevention threshold $\theta$. It shows that the integration of prevention strategies, especially the adaptive ones, would change the dynamics of the epidemic that is not covered by the traditional epidemic models.

\begin{figure*}[t]

	\small
	\centering
	\subfloat[\scriptsize  ]{\label{multiplecitiesplateau}\includegraphics[width=0.33\textwidth]{./image/p-multi1.eps}}
	\subfloat[\scriptsize
	]{\label{onecitywithplateau}\includegraphics[width=0.33\textwidth]{./image/p-multi2.eps}}
	\subfloat[\scriptsize ]{\label{noplateau}\includegraphics[width=0.33\textwidth]{./image/p-multi3.eps}}

	\caption{The plateau phenomenon under the multi-city model.}
	\label{multistrategyinfluence}

\end{figure*}

As shown in Figure~\ref{multistrategyinfluence}, it is found that the plateau also exists in the multi-city model:
\begin{itemize}
    \item \textbf{Changes in the plateau of cities.} In the multi-city model, if all cities have the same $IC$ and adopt adaptive prevention strategies, they will all appear to plateau.
    The plateau of cities A, B and C end differently. City A is the earliest, and city C is the latest.
    However, when $I$ of city A drops to the same as city B, it will synchronize with city B and enter the plateau, as shown in Figure~\ref{multiplecitiesplateau}.
    When the plateau of city B (and A) ends, it will be synchronized with city C.
    The emergence of the synchronization phenomenon is due to the same prevention intensity among cities and the balance of the flow of infected people.
    \item \textbf{Cities with constant prevention strategies could also appear to plateau in the multi-city model.} In Figure~\ref{onecitywithplateau}, both city A and city C adopt a constant prevention strategy, in which the number of infections in city A should rise at first and then decline, and the number of infections in city C should be declining all the time.    However, under the influence of population mobility by city B, all cities have appeared plateau. Thus it can be seen that the emergence of the plateau in the multi-city model is also related to population mobility.
    \item \textbf{The cities that would have appeared to plateau did not appear that in the multi-city model.} As shown in Figure~\ref{noplateau}, city B is supposed to have a plateau, while city A and C, one will go down, the other will go up. However, all three cities are in decline. City A has been rising for some time, but obviously falling back ahead of time. This further highlights the impact of population mobility in the multi-city model.
\end{itemize}

The above experimental results show that quite an interesting plateau phenomenon emerges even in the multi-city model with complex epidemic dynamics within cities and population mobility dynamics across cities.
In particular, the results strongly indicate that all cities are interdependent in terms of epidemic development --- their plateau phenomenon co-occur, and even a city that would not have a plateau by itself would appear to plateau under the influence of other cities with adaptive strategies.
This suggests that in battling the COVID-19 pandemic, one should not look only at the local prevention strategies, but also need to take into account other regions' strategies and population mobility, and perhaps some global coordination would be more effective.

\subsection{Empirical Results}
\label{sec:realworld}

In fact, the plateau phenomenon also appears in the real world epidemic, in particular in the current COVID-19 pandemic.
We collect the epidemic data as of October 25, 2021, from data source DXY\footnote{https://ncov.dxy.cn/}, which collected data from the World Health Organization (WHO), and China National Health Commission.
We have carried on the plateau fitting to the data of 213 countries (through the coefficient of determination) and found that 77 countries have obvious plateau phenomenon in more than one month~\footnote{https://github.com/Complex-data/COVID-19\_Data}. This is double the 35 countries we counted before (October 2020).
The coefficient of determination $D^2$ is calculated as follows:

\begin{align*}
D^2 & = 1- \frac{\sum_{i=1}^{n}(y_i-Y_i)^2}{\sum_{i=1}^{n}(Y_i-\overline{Y})^2},
\end{align*}
where $y_i$ is the number of existing infections of simulation, $Y_i$ is the number of existing infections of real data, and $\overline{Y}$ is the average number of existing infections of real data. $D^2 \in (-\infty, 1]$, the closer the value of $D^2$ is to $1$, the better the degree of the fitting.

Among other countries, 113 of them are still suffering worsening situations or are facing a new rising of the epidemics, while 22 countries are or have subsided.

\begin{figure*}[!tpb]
	\centering

	\subfloat[\scriptsize Poland ($D^2=0.9074$)]{\includegraphics[width=0.48\textwidth]{./image/Poland.eps}}
	\subfloat[\scriptsize Philippines ($D^2=0.9315$)]{\includegraphics[width=0.48\textwidth]{./image/Philippines.eps}}

	\subfloat[\scriptsize Portugal ($D^2=0.9244$)]{\includegraphics[width=0.48\textwidth]{./image/Portugal.eps}}
	\subfloat[\scriptsize Libya ($D^2=0.9713$)]{\includegraphics[width=0.48\textwidth]{./image/Libya.eps}}
	\caption{\small Examples of countries that have a clear plateau phenomenon.
        The number of existing infections is calculated by the confirmed cases, minus the sum of recovery cases and death cases.
	}
	\vspace{-0.025in}
	\label{realworlddata}

\end{figure*}

Figure~\ref{realworlddata} shows 4 countries that have experienced plateaus, including Poland, the Philippines, Portugal, and Libya:

\begin{itemize}
    \item Poland, with a population of 38 million, had 16,478 existing infections at the beginning of October 2020. The number of existing infections had risen for 50 days, reaching 440,000. Then, possibly under the prevention of the local government, the number of existing infections dropped to about 230,000 and entered a brief plateau. However, in March 2021, the number of existing infections in Poland rose again to 400,000. It was quickly brought under control in April and entered a three-month plateau in June with 150,000 existing infections. In October, the number of existing infections in Poland showed another upward trend.
    \item The Philippines, with a population of 102 million, had been on a plateau from November 2020 to March 2021, and the number of existing infections remains at around 30,000. After that, the epidemic had rebounded, with the number of existing infections reaching as high as 190,000 in early April 2021. Under a period of prevention, the number of existing infections in the Philippines dropped to 50,000 and entered a new plateau (May-July). In August 2021, the epidemic in the Philippines rebounded again, and the number of existing infections rebounded to 180000 before being brought back under control in late September. The Philippines may enter a plateau again after that.
    \item Portugal, with a population of 10.35 million, had about 180,000 existing infections in February 2021. It was possible that under the adaptive prevention of the local government, the number of existing infections had been controlled at 20,000 to 30,000 since April, entering a three-month plateau. In July, the epidemic in Portugal intensified again. Fortunately, when the number of existing infections rose to 54,000, it was soon brought under control. Until October, the decline in the number of existing infections in Portugal slowed down and may once again enter a new plateau.
    \item Libya, with a population of 6.87 million, had 28,000 existing infections at the end of December 2020. The number of existing infections had been declining until it reached a plateau in April 2021 and remained at around 10,000. The plateau lasted three months and the outbreak broke out again in July. The number of existing infections in Libya rose to 80,000 in August and it would rise further in October. But if the Libyan government takes appropriate prevention, the epidemic will enter a new plateau and keep the number of existing infections around 80,000 without rising.
\end{itemize}

These data clearly support the existence of the plateau phenomenon in the real world, which means it is important for us to study in more detail the plateau phenomenon. Although it may be difficult to pinpoint the exact reasons that cause the plateau phenomenon for each country, from our simulation result observations, we believe that the plateau phenomenon in these countries is likely related to the adaptive prevention strategies adopted by the countries.

For most countries, especially those where the COVID-19 epidemic is still worsening, if proper adaptive prevention strategies are enforced, we could expect that they will also enter the plateau in the future. Thus, understanding the plateau phenomenon would be useful for most countries that are suffering from the COVID-19 epidemic.

\subsection{Theoretical Results}
In the simulation study, we find that epidemic development might enter a plateau period after the SIR model is integrated with an adaptive prevention strategy. The results suggest some simple relationships such as the emergence of the plateau is related to the changing range of prevention parameter $[r_L,r_H]$, and the height of the plateau is positively correlated with the prevention threshold $\theta$. In this section, we will analyze theoretically the conditions of the emergence and the ending of the plateau as well as the properties of the plateau. Our analysis focus on the single-city model, while the multi-city model involves much more complicated dynamics due to the mobile populations between the cities.

\subsubsection{Effective Prevention Strategy and the Ideal Model}
As suggested from the simulation study, the plateau is related to the adaptive prevention strategy, but it is also the case that not every prevention strategy would generate plateau  (See Figure~\ref{changingrange}). We infer that this is related to the effective prevention parameter $\tilde{r}_t$, as defined in Supplementary Section A.
The effective prevention parameter $\tilde{r}_t$ is the value of prevention parameter $r$ when the effective reproduction number $R_t=1$.
Intuitively, when $R_t=1$, the number of infections an infected individual makes before recovered is exactly $1$, meaning that the number of existing infected cases would remain the same.
Thus, $\tilde{r}_t$ is the corresponding prevention parameter that would maintain the infection cases the same.
Note that in general the effective prevention parameter $\tilde{r}_t$ is different from the actual value of the prevention parameter $r$ used: the former is the would-be value to keep the infection cases the same while the latter is the actual value of the prevention strategy used at each day. This is also the reason we use different notations to distinguish the two. The effective prevention parameter $\tilde{r}_t$ has the following simple but important property:
\begin{lemma} \label{lem:monotoner}
	The effective prevention parameter $\tilde{r}_t$ is monotonically increasing with time $t$.
\end{lemma}
\begin{proof}
	$\tilde{r}_t$ is defined as the value of $r$ when $R_t=1$, we have
	\begin{align}
	\label{effectivereproductionnumber}
    R_t &= \frac{r\beta}{\gamma} \cdot \frac{S}{N}\\
	\label{eq:effectiveprevention}
	\tilde{r}_t &= \frac{N \cdot \gamma}{S \cdot \beta}.
	\end{align}
	Since the number of susceptible people $S$ is monotonically decreasing with time $t$ while other parameters $N,\beta,\gamma$ stay constant, we have  that $\tilde{r}_t$ is monotonically increasing.
\end{proof}

In the model, we have several aspects that try to reflect the real-world scenario, such as
	the 14 day grace period before relaxing the prevention parameter, and
	the changing of the strategies taking some time governed by parameter $k$.
To emphasize the essence of the model, for the theoretical analysis, we consider the following simplified {\em ideal} single-city model, which is consistent with the principle of full model .
In the ideal model, once the daily new cases drop to the prevention threshold $\theta$, we immediately adjust the prevention strategy
	$r$ such that we keep the daily new cases to be exactly $\theta$, as long as we have $r\le r_H$.
Moreover, we assume that the city starts with a significant number of infected cases and under intense prevention control,
	and thus the prevention strategy is relaxed when the infection cases drop below the prevention threshold.
Technically we require that the initial infection number $I_0$ satisfies $I_0 \cdot \gamma > \theta$, that is, the number of daily recovered people initially is $I_0 \cdot \gamma$ and it is more than $\theta$. This corresponds to the real-world scenario where the prevention strategies are only employed after the epidemic outbreak already begins, and the adaptive strategies are designed to maintain the infection cases at a low level after the initial infection peak already occurs. Note that the above description on the ideal model only applies to the adaptive prevention strategy. The constant prevention strategy remains the same in the ideal model. We will also use the simulation results from the full model to validate the accuracy of the prediction from the ideal model.

\subsubsection{The Emergence and the Ending of Plateau}

We first investigate the conditions for the presence or the absence of the plateau, in the single-city model.
Let $t_\theta$ be the time when the number of daily recovered people drops to $\theta$, i.e. $I\gamma = \theta$.
We assume that initially $I_0 \gamma > \theta$, and under intense prevention control, thus $I$ will eventually drop to $\theta$.
With Lemma~\ref{lem:monotoner}, we can derive the following result connecting the effective prevention parameter with the plateau phenomenon.
\begin{theorem}
	\label{condition}
	In the ideal single-city model with an adaptive prevention strategy, at any time $t$, if the effective prevention parameter at this time $\tilde{r}_t \ge r_H$, then there will be no plateau after time $t$. On the other hand, if $\tilde{r}_{t_\theta} < r_H$, then plateau will start at $t_\theta$.
\end{theorem}
\begin{proof}{(Sketch)}
When $\tilde{r}_t \ge r_H$, we know that for any time $t'>t$, $\tilde{r}_{t'} > \tilde{r}_t$ according to Lemma~\ref{lem:monotoner}.
This means that for all time $t'>t$, the actual prevention parameter $r$ as the property that $r \le r_H < \tilde{r}_{t'}$.
Since $\tilde{r}_{t'}$ corresponds to the effective reproduction number
	$R_{t'} = 1$, this implies that $R_{t'} < 1$ by Equation~\eqref{effectivereproductionnumber}, which in turn implies that
	for all time $t' > t$, the number of new infections any infected people would generate is less than $1$, and the epidemic will keep receding.

Now suppose that $\tilde{r}_{t_\theta} < r_H$.
According to the definition of $\tilde{r}_{t_\theta}$, $I \gamma = \theta$ at time $t_\theta$.
The ideal mode can be adjusted to $r=\tilde{r}_{t_\theta}$ at which the daily infection number balances with the daily recovery number $I \gamma$.
It can always keep the prevention parameter $r$ as $\tilde{r}_t$ until it increases to $r_H$.
During this period, the daily infection and daily recover balance each other, i.e. the plateau.
\end{proof}

The above theorem shows that the relationship of the effective prevention parameter $\tilde{r}_t$ and the upper bound of the prevention parameter range $r_H$ directly
	determine the presence of the plateau.
Note that for a constant prevention strategy with a fixed value $r$, it is clear that it has no plateau because it is essentially the
	same as the standard SIR model.
Therefore, we can obtain the following conclusion on the emergence and the ending of the plateau.
\begin{corollary}[Condition for the emergence of the plateau]
	\label{cor:emergenceplateau}
	In the ideal single-city model, the condition that the plateau will emerge is that we use an adaptive prevention strategy and
	$\tilde{r}_{t_\theta} < r_H$.
\end{corollary}
\begin{corollary}[Condition for the ending of the plateau]
	\label{cor:endplateau}
	In the ideal single-city model, given that plateau appears at time $t$, it will end at time $t'>t$ when $\tilde{r}_{t'} \ge r_H$.
\end{corollary}
Corollary~\ref{cor:emergenceplateau} states that plateau will appear when the effective prevention parameter is still less than $r_H$ and the daily recovery number hit the prevention threshold, while Corollary~\ref{cor:endplateau} states that the plateau will end once the effective prevent intensity reaches $r_H$.
We defer the discussion on the actual calculation of the condition $\tilde{r}_{t_\theta} < r_H$ to Section~\ref{sec:length} when we study the length of the plateau.

We use simulation results shown in Figure~\ref{Ircomparison} to validate these conditions in our actual model.
Figure~\ref{Istate} shows the epidemic development under two adaptive prevention strategies.
The first strategy, shown in the blue curve, has a clear plateau period.
In Figure~\ref{rstate}, we show the corresponding changes of the effective prevention parameter and the actual prevention parameter.
For the blue curve, Figure~\ref{rstate} shows the corresponding changes in the actual prevention parameter $r$, which fluctuates between $r_L=6$ and $r_H=10$ for a period of time.
During this period, the yellow curve, corresponding to the effective prevention parameter $\tilde{r}_{t,1}$ of the first strategy increases gradually from $8$ to $10$.
Since $\theta=40$ and $\gamma=0.12$, when y-axis $I$ in Figure~\ref{Istate} is $40/0.12 \approx 333$,
	the corresponding effective prevention parameter is around $8$, which is less than $r_H=10$, consistent with Corollary~\ref{cor:emergenceplateau} that the plateau would appear.
When $\tilde{r}_{t,1}$ increases to $10 = r_H$, we can see that the plateau ends in the corresponding blue curve on the left.
For the second strategy, the red curve in Figure~\ref{Istate} without plateau.
The actual prevention parameter $r$ keeps at the level $r_H=8$ in this case (the red curve in Figure~\ref{rstate}), while the effective
	prevention parameter $\tilde{r}_{t,2}$ starts at $8$ and increases slowly above $8$ (the purple curve in Figure~\ref{rstate}).
This is also consistent with Corollary~\ref{cor:emergenceplateau}, meaning that when $\tilde{r}_{t_\theta} \ge r_H=8$, there will be no plateau in this case.

\begin{figure}[t]
	\centering
	\vspace{-0.4cm}
	\subfloat[\scriptsize The change curve of I]{\includegraphics[width=0.48\textwidth]{./image/Istate0.eps}\label{Istate}}
	\subfloat[\scriptsize The change curve of r]{\includegraphics[width=0.48\textwidth]{./image/rstate0.eps}\label{rstate}}
	\caption{The relationship between the plateau and the prevention parameter. $\tilde{r}_{t,1}$ expressed the changes in the effective prevention parameter of the first prevention strategy, while $\tilde{r}_{t,2}$ stands for the second prevention strategy.
	}
	\label{Ircomparison}
	\vspace{-0.4cm}
\end{figure}

\subsubsection{The Height of the Plateau}

Although the number of infected people in the plateau has small fluctuations, it is basically maintained at a same value.
We call the value around which the number of existing infections fluctuates is the height of the plateau, and denote it as $I_P$.
In the ideal model, the height of the plateau $I_P$ is when the number of existing infected people does not change, that is, when the
	effective reproduction number $R_t=1$.
Using the relations we derived before, we can obtain the following result on $I_P$.
\begin{theorem} \label{thm:height}
In the ideal single-city model, the height of the plateau is given as follows:
\begin{equation*}
 I_{P}=\frac{\theta}{\gamma},
\end{equation*}
where $\theta$ is the prevention threshold and $\gamma$ is the recovery rate.
\end{theorem}
\begin{proof}
In the plateau we have $R_t=1$, and the newly infected people per day is exactly equal to the prevention threshold $\theta$ (in the ideal model).
According to the SIR model, the newly infected people per day is $\frac{r \beta IS}{N}$ (excluding the number of recovered people).
Thus in the plateau,
\begin{align}
\theta&=\frac{r\beta I_P S}{N}. \label{eq:theta-di}
\end{align}
From Equation~\eqref{effectivereproductionnumber}, we know that $\frac{r\beta S}{N} = \gamma$.
Plugging it into Equation\eqref{eq:theta-di}, we have $I_P = \theta / \gamma$.
\end{proof}

Theorem~\ref{thm:height} directly shows that the height of the plateau has positive linear relationship with the prevention threshold $\theta$, and it is not
	related to the other parameters such as the range of prevention strategy $[r_L, r_H]$ or the speed of prevention $k$.
This result is consistent with our simulation study findings.
In particular, comparing with Figure~\ref{threshold},
	when we plug in $\theta = 10, 20, 40, 80$ with $\gamma = 0.12$, we obtain the theoretical heights as
	$I_P = 83, 167, 333, 667$, while the experimental averages we obtain the simulation results
	are $77,154,308,622$ respectively, indicating that the theoretical
	results match with the simulation results reasonably well.
The reason that the simulation results are consistently lower than the theoretical predictions is because in our actual model, we have an
	asymmetric strategy adjustment: we need 14 consecutive days of new cases dropping below $\theta$ to relax the prevention, while we only need
	one day of new cases rising above $\theta$ to strengthen the prevention.
This asymmetric control push the actual height lower than our theoretical prediction from the ideal model.

\subsubsection{The Length of the Plateau}
\label{sec:length}

After obtaining the height of the plateau, we can further calculate the length of the plateau by the Area Method.
We denote the length of the plateau, i.e. the time period from when the plateau begins to the plateau ends, as $T$.
It is clear that $T \cdot I_P$ is the area covered of the plateau.
We just need to calculate the area underlying the plateau to get $T$.
The result is given in the following theorem.

\begin{theorem} \label{thm:length}
In the ideal single-city model, assuming that the number of new infections falls to $\theta$ is the beginning of the plateau, the length of the plateau is given as follows:
\begin{equation}
 T=\frac{S_B - S_E}{\theta}, \label{eq:length}
\end{equation}
where $S_E$ is the number of susceptible people when the plateau ends, and $S_E=\frac{\gamma N}{\beta r_H}$; $S_B$ is the number of susceptible people when the plateau begins, and it is the solution of the following equality:
\begin{align}
S=(S_0+I_0)- I_P +\frac{N\gamma}{r_0\beta}\ln{\frac{S}{S_0}}, \label{eq:I-S}
\end{align}
where $S_0, I_0$ are the number of initial susceptible and infected people, and $r_0$ is the initial prevention parameter in the range $[r_L, r_H]$.
\end{theorem}

\begin{proof}{(Sketch)}
In the curve with $I$ as y-axis and time as x-axis, the area under curve (AUC)  by time $t$ is the cumulative existing infected people
	 by time $t$.
On average, each infected individual takes $1/\gamma$ time to recover, so each infected individual is counted $1/\gamma$ times.
Therefore, the AUC by time $t$ is the total number of once infected people multiplied by $1/\gamma$, which is $(I+R) /\gamma$.
Since $S+I+R = N$, so we have the AUC by time $t$ is $(N-S)/\gamma$.
Let $t_B, t_E$ be the time when the plateau begins and ends, and correspondingly $S_B$ and $S_E$ are the numbers of susceptible people
	at time $t_B$ and $t_E$ respectively.
Then we have the AUC between $t_B$ and $t_E$ is $(N-S_E)/\gamma - (N-S_B)/\gamma = (S_B - S_E) / \gamma$.
Since the height of the plateau is $\theta/\gamma$ by Theorem~\ref{thm:height}, we know the length of the plateau
	$T = \frac{(S_B - S_E) / \gamma}{\theta/\gamma} = \frac{S_B - S_E}{\theta}$.
Thus Equation\eqref{eq:length} holds.

We now show how to derive $S_B$ and $S_E$.
First, for $S_E$, we know from Corollary~\ref{cor:endplateau} that when the plateau ends, $\tilde{r}_{t_E} = r_H$, and by the definition
	of $\tilde{r}_{t_E}$, we know $R_{t_E} = 1$.
 Plugging these values into Equation~\eqref{effectivereproductionnumber}, we obtain that $S_E = \frac{\gamma N}{\beta r_H}$.

To derive the result for $S_B$, we rely on the equation below connecting $I$ and $S$ in the SIR model~\cite{Zhen2004}:
\begin{align*}
I=(S_0+I_0)-S+\frac{N\gamma}{r\beta}\ln{\frac{S}{S_0}},
\end{align*}
Before the plateau appears, the prevention parameter $r$ is fixed to a value $r_0$.
When the plateau appears, $I$ is equal to $I_P$.
Thus, when plugging $I=I_P$ and $r=r_0$ into the above equation, we obtain Equation\eqref{eq:I-S}, and $S_B$ is the solution of this equation.

\end{proof}

Note that $S_B$ derived from Equation~\eqref{eq:I-S} can be used to test condition $\tilde{r}_{t_\theta} < r_H$ in
	Corollary~\ref{cor:emergenceplateau}:  $\tilde{r}_{t_\theta} = \frac{N \cdot \gamma}{S_B \cdot \beta} $ according to Equation\eqref{eq:effectiveprevention}.

We now validate Theorem~\ref{thm:length} with the experimental results.
We compare our theoretical prediction on the plateau length with the experimental results from Figure~\ref{threshold},
	with the initial condition $IC = (200000,0.5\%)$ and parameters $r_0=6, r_L=6, r_H=10, k=5$, $\theta$ from $10$ to $80$.
Table~\ref{tab:height} summarizes the comparison result.
We can see that the theoretical and experimental results match reasonably well.
Moreover, the estimation error is mainly from the error in the estimation of the height --- if we replace the theoretical heights with
	the experimental heights, we get much closer estimates of $3920, 1984, 1002, 509$ respectively, which means our theoretical AUC prediction
	is quite accurate.

\begin{table*}[t]
    \setlength{\abovecaptionskip}{2mm}
	\centering
    \caption{\small The experimental and theoretical heights and lengths of the plateau for settings in Figure~\ref{threshold}.}
	\small

	\label{tab:height}
	\setlength{\tabcolsep}{10mm}
	\begin{threeparttable}
		\begin{tabular}{l|c|c|c|c}
			\toprule
			\small $\theta$ &  \small 10  &  \small 20  &  \small 40 &  \small 80  \\
			\midrule
			I (experimental)        & 77 & 154 & 308 & 622 \\
			\midrule
			I (theoretical)        & 83 & 167 & 333 & 667 \\
			\midrule
			days (experimental)        & 3,929 & 1,975 & 1,002 & 514 \\
			\midrule
			days (theoretical)        & 3,637 & 1,830 & 927 & 475 \\
			\bottomrule
		\end{tabular}
	\end{threeparttable}

\end{table*}

\section{Conclusion and Discussion}
In this paper, we study an epidemic development phenomenon: plateau. This phenomenon is formed under the change of prevention strength of adaptive prevention strategies.  In the traditional infectious disease model, it is difficult to find the existence of the plateau.  We investigate empirically from both simulations and real-world data on the plateau phenomenon, in both single-city model and multi-city model, and further provide theoretical analysis in the single-city model. In the two years since the outbreak of COVID-19, we found more and more countries have entered a plateau. It is difficult to achieve a complete regression of the epidemic in a short term. It may be a better solution to control the epidemic through adaptive prevention strategies. In the single-city model, we obtain a number of results on the emergence and the characteristics of the plateau phenomenon. Our results in the multi-city model suggest that all regions are interconnected and local prevention strategies would have effects on other regions as well. The plateau phenomenon well explains the persistence of the current COVID-19 epidemic and provides a new solution for countries still suffering from the epidemic.

There could be some future work along this direction. On the empirical side, one could investigate in more detail the real-world plateau phenomenon and their correlations with specific prevention strategies used. On the theoretical side, the multi-city model is much more challenging due to the complicated population mobility dynamics. It would be very important and beneficial to obtain some insightful results in the multi-city model. We hope that our findings could help the understanding of the COVID-19 pandemic (and other epidemics as well) in connection with different prevention strategies, and assist policymakers in predicting the effect of their prevention strategies. At present, our findings are being applied to the epidemic prevention work in Shenzhen.

\section{Materials and Methods}
\subsection{Experimental Hypothesis}
We base the choice of our parameters on the research that has been made on the COVID-19.

A person stays infected by COVID-19 for 8.4 days on average \cite{wu2020nowcasting}. The recovery rate is thus
defined as $\gamma= 1/8.4 = 0.12$.
For the infection rate $\beta=0.015$, we use the most common indicator in the epidemic research, the reproduction number $R$ to calculate, as shown in Supplementary Section A in detail.

We used the epidemic data provided by the Information Center of Shenzhen Public Security Bureau to better estimate the number of contacts --- prevention parameter $r$.
We estimate the number of contacts among people $r=24$ under normal conditions.
With the assistance of the Information Center of Shenzhen Public Security Bureau, the population mobility ratio $p$ is estimated according
to the population mobility data of Shenzhen in 2019 and 2020.
During the outbreak of COVID-19 in 2020, Shenzhen implemented strict restrictions on population mobility, and the proportion of population mobility was around $5\%$.
In the same period in 2019, the proportion of people moving fluctuated between $10\%$ and $20\%$.
In this paper, it is assumed that the proportion of population mobility under normal conditions is $p=20\%$.

\subsection{Epidemic Model with Prevention Strategies}
We incorporate the constantly changing prevention measures as well as the population mobility between regions into the SIR model.
For the COVID-19 with a latent period, we do not choose the SEIR model, because using the SIR model in the process of studying the prevention strategy can simplify the analysis process, and is no different from the SEIR model.

To incorporate the prevention strategies and their dynamic changes into the model, we add a prevention parameter $r$, which represents the number of people that individuals will contact per unit of time.
Cities dynamically adapt their prevention measures based on the current infection data --- when the new infection cases
	exceed expectations the prevention measures intensify, and when the number of new cases drops, the prevention measures are relaxed.
We model this scenario by setting a prevention threshold and dynamically changing the prevention parameter $r_i$ and
	the fraction of the floating population $p_i$
	based on whether the current infection cases are below or above the prevention threshold.
Technically, we have three main factors for deciding and changing the prevention measures: prevention threshold, the range of changing prevention parameter, and the reaction speed.
Based on the variability of parameters, it is divided into constant prevention strategy and adaptive prevention strategy.

We extend the single-city model to multiple cities that $\beta$ and $\gamma$ are the same across cities since they model the intrinsic characteristics of the virus.
The prevention strategies are different across cities, modeling different prevention measures taken among the cities.
In order to ensure the dynamic balance of population mobility in multiple cities, we put forward a reasonable rule of population mobility and combine it with the external environment $EE$, so that population mobility can be added to the model.
Model details and code can be found in Supplementary Section B.

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


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text:
<?php
namespace TYPO3\CMS\Backend\Form\FormDataProvider;

use TYPO3\CMS\Backend\Form\FormDataCompiler;
use TYPO3\CMS\Backend\Form\FormDataGroup\TcaInputPlaceholderRecord;
use TYPO3\CMS\Backend\Form\FormDataProviderInterface;
use TYPO3\CMS\Backend\Utility\BackendUtility;
use TYPO3\CMS\Core\Utility\GeneralUtility;
use TYPO3\CMS\Core\Utility\StringUtility;
use TYPO3\CMS\Lang\LanguageService;

/**
 * Resolve placeholders for fields of type input or text. The placeholder value
 * in the processedTca section of the result will be replaced with the resolved
 * value.
 */
class TcaInputPlaceholders implements FormDataProviderInterface
{
    /**
     * Resolve placeholders for input/text fields. Placeholders that are simple
     * strings will be returned unmodified. Placeholders beginning with __row are
     * being resolved, possibly traversing multiple tables.
     *
     * @param array $result
     * @return array
     */
    public function addData(array $result)
    {
        foreach ($result['processedTca']['columns'] as $fieldName => $fieldConfig) {
            // Placeholders are only valid for input and text type fields
            if (
                ($fieldConfig['config']['type'] !== 'input' && $fieldConfig['config']['type'] !== 'text')
                || !isset($fieldConfig['config']['placeholder'])
            ) {
                continue;
            }

            // Resolve __row|field type placeholders
            if (StringUtility::beginsWith($fieldConfig['config']['placeholder'], '__row|')) {
                // split field names into array and remove the __row indicator
                $fieldNameArray = array_slice(
                    GeneralUtility::trimExplode('|', $fieldConfig['config']['placeholder'], true),
                    1
                );
                $result['processedTca']['columns'][$fieldName]['config']['placeholder'] = $this->getPlaceholderValue($fieldNameArray, $result);
            }

            // Resolve placeholders from language files
            if (StringUtility::beginsWith($fieldConfig['config']['placeholder'], 'LLL:')) {
                $result['processedTca']['columns'][$fieldName]['config']['placeholder'] = $this->getLanguageService()->sl($fieldConfig['config']['placeholder']);
            }

            // Remove empty placeholders
            if (empty($result['processedTca']['columns'][$fieldName]['config']['placeholder'])) {
                unset($result['processedTca']['columns'][$fieldName]['config']['placeholder']);
            }
        }

        return $result;
    }

    /**
     * Recursively resolve the placeholder value. A placeholder string with a
     * syntax of __row|field1|field2|field3 will be recursively resolved to a
     * final value.
     *
     * @param array $fieldNameArray
     * @param array $result
     * @param int $recursionLevel
     * @return string
     */
    protected function getPlaceholderValue($fieldNameArray, $result, $recursionLevel = 0)
    {
        if ($recursionLevel > 99) {
            // This should not happen, treat as misconfiguration
            return '';
        }

        $fieldName = array_shift($fieldNameArray);
        $fieldConfig = $result['processedTca']['columns'][$fieldName]['config'];

        // Skip if a defined field was actually not present in the database row
        // Using array_key_exists here, since NULL values are valid as well.
        if (!array_key_exists($fieldName, $result['databaseRow'])) {
            return '';
        }

        $value = $result['databaseRow'][$fieldName];

        switch ($fieldConfig['type']) {
            case 'select':
                // The FormDataProviders already resolved the select items to an array of uids,
                // filter out empty values that occur when no related record has been selected.
                $possibleUids = array_filter($value);
                $foreignTableName = $fieldConfig['foreign_table'];
                break;
            case 'group':
                $possibleUids = $this->getRelatedGroupFieldUids($fieldConfig, $value);
                $foreignTableName = $this->getAllowedTableForGroupField($fieldConfig);
                break;
            case 'inline':
                $possibleUids = array_filter(GeneralUtility::trimExplode(',', $value, true));
                $foreignTableName = $fieldConfig['foreign_table'];
                break;
            default:
                $possibleUids = [];
                $foreignTableName = '';
        }

        if (!empty($possibleUids) && !empty($fieldNameArray)) {
            $relatedFormData = $this->getRelatedFormData($foreignTableName, $possibleUids[0], $fieldNameArray[0]);
            $value = $this->getPlaceholderValue($fieldNameArray, $relatedFormData, $recursionLevel + 1);
        }

        if ($recursionLevel === 0 && is_array($value)) {
            $value = implode(', ', $value);
        }
        return (string)$value;
    }

    /**
     * Compile a formdata result set based on the tablename and record uid.
     *
     * @param string $tableName Name of the table for which to compile formdata
     * @param int $uid UID of the record for which to compile the formdata
     * @param string $columnToProcess The column that is required from the record
     * @return array The compiled formdata
     */
    protected function getRelatedFormData($tableName, $uid, $columnToProcess)
    {
        $fakeDataInput = [
            'command' => 'edit',
            'vanillaUid' => (int)$uid,
            'tableName' => $tableName,
            'inlineCompileExistingChildren' => false,
            'columnsToProcess' => [$columnToProcess],
        ];
        /** @var TcaInputPlaceholderRecord $formDataGroup */
        $formDataGroup = GeneralUtility::makeInstance(TcaInputPlaceholderRecord::class);
        /** @var FormDataCompiler $formDataCompiler */
        $formDataCompiler = GeneralUtility::makeInstance(FormDataCompiler::class, $formDataGroup);
        $compilerResult = $formDataCompiler->compile($fakeDataInput);
        return $compilerResult;
    }

    /**
     * Return uids of related records for group type fields. Uids consisting of
     * multiple parts like [table]_[uid]|[title] will be reduced to integers and
     * validated against the allowed table. Uids without a table prefix are
     * accepted in any case.
     *
     * @param array $fieldConfig TCA "config" section for the group type field.
     * @param string $value A comma separated list of records
     * @return array
     */
    protected function getRelatedGroupFieldUids(array $fieldConfig, $value)
    {
        $relatedUids = [];
        $allowedTable = $this->getAllowedTableForGroupField($fieldConfig);

        // Skip if it's not a database relation with a resolvable foreign table
        if (($fieldConfig['internal_type'] !== 'db') || ($allowedTable === false)) {
            return $relatedUids;
        }

        $values = GeneralUtility::trimExplode(',', $value, true);
        foreach ($values as $groupValue) {
            list($foreignIdentifier, $_) = GeneralUtility::trimExplode('|', $groupValue);
            list($recordForeignTable, $foreignUid) = BackendUtility::splitTable_Uid($foreignIdentifier);
            // skip records that do not match the allowed table
            if (!empty($recordForeignTable) && ($recordForeignTable !== $allowedTable)) {
                continue;
            }
            $relatedUids[] = $foreignUid;
        }

        return $relatedUids;
    }

    /**
     * Will read the "allowed" value from the given field configuration
     * and returns FALSE if none or more than one has been defined.
     * Otherwise the name of the allowed table will be returned.
     *
     * @param array $fieldConfig TCA "config" section for the group type field.
     * @return bool|string
     */
    protected function getAllowedTableForGroupField(array $fieldConfig)
    {
        $allowedTable = false;

        $allowedTables = GeneralUtility::trimExplode(',', $fieldConfig['allowed'], true);
        if (count($allowedTables) === 1) {
            $allowedTable = $allowedTables[0];
        }

        return $allowedTable;
    }

    /**
     * @return LanguageService
     */
    protected function getLanguageService()
    {
        return $GLOBALS['LANG'];
    }
}

redpajama_set_name: RedPajamaGithub


Background of the Camisa Trademark.
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text:
package Dancer::Hook;
#ABSTRACT: Class to manipulate hooks with Dancer

use strict;
use warnings;
use Carp;

use base 'Dancer::Object';

__PACKAGE__->attributes(qw/name code properties/);

use Dancer::Factory::Hook;
use Dancer::Hook::Properties;
use Dancer::Exception qw(:all);

sub new {
    my ($class, @args) = @_;

    my $self = bless {}, $class;

    if (!scalar @args) {
        raise core_hook => "one name and a coderef are required";
    }

    my $hook_name = shift @args;

    # XXX at the moment, we have a filer position named "before_template".
    # this one is renamed "before_template_render", so we need to alias it.
    # maybe we need to deprecate 'before_template' to enforce the use
    # of 'hook before_template_render => sub {}' ?
    $hook_name = 'before_template_render' if $hook_name eq 'before_template';

    $self->name($hook_name);

    my ( $properties, $code );
    if ( scalar @args == 1 ) {
        $properties = Dancer::Hook::Properties->new();
        $code       = shift @args;
    }
    elsif ( scalar @args == 2 ) {
        my $prop = shift @args;
        $properties = Dancer::Hook::Properties->new(%$prop);
        $code       = shift @args;
    }
    else {
        raise core_hook => "something's wrong with parameters passed to Hook constructor";
    }
    ref $code eq 'CODE'
      or raise core_hook => "the code argument passed to hook construction was not a CodeRef. Value was : '$code'";

    my $compiled_filter = sub {
        my @arguments = @_;
        return if Dancer::SharedData->response->halted;

        my $app = Dancer::App->current();
        return unless $properties->should_run_this_app($app->name);

        Dancer::Logger::core( "entering " . $hook_name . " hook" );

        $code->(@arguments);

    };

    $self->properties($properties);
    $self->code($compiled_filter);

    Dancer::Factory::Hook->instance->register_hook($self);
    return $self;
}

1;

=head1 DESCRIPTION

Manipulate hooks with Dancer

=head1 SYNOPSIS

  # inside a plugin
  use Dancer::Hook;
  Dancer::Hook->register_hooks_name(qw/before_auth after_auth/);

=head1 METHODS

=head2 register_hook ($hook_name, [$properties], $code)

    hook 'before', {apps => ['main']}, sub {...};

    hook 'before' => sub {...};

Attaches a hook at some point, with a possible list of properties.

Currently supported properties:

=over 4

=item apps

    an array reference containing apps name

=back

=head2 register_hooks_name

Add a new hook name, so application developers can insert some code at this point.

    package My::Dancer::Plugin;
    Dancer::Hook->instance->register_hooks_name(qw/before_auth after_auth/);

=head2 hook_is_registered

Test if a hook with this name has already been registered.

=head2 execute_hooks

Execute a list of hooks for some position

=head2 get_hooks_for

Returns the list of coderef registered for a given position

=head1 AUTHORS

This module has been written by Alexis Sukrieh and others.

=head1 LICENSE

This module is free software and is published under the same
terms as Perl itself.


text:
Brynja K. Pétursdóttir (* 26. Dezember 1977) ist eine isländische Badmintonspielerin.

Karriere
Brynja Pétursdóttir siegte 1995 erstmals bei den nationalen Titelkämpfen der Junioren in Island. Bei den Erwachsenen gewann sie 1999 ihren ersten Titel. Weitere Titelgewinne folgten 2000 und 2001. 1999 und 2001 nahm sie an den Badminton-Weltmeisterschaften teil.

Sportliche Erfolge

Weblinks

Badmintonspieler (Island)
Isländischer Meister (Badminton)
Isländer
Geboren 1977
Frau

redpajama_set_name: RedPajamaWikipedia


england london waterloo = WAT = Rail/Tube station, subject of a famous song by The Kinks!
Ely Place commemorates a London palace of the Bishops of Ely, the earliest record[s] are from 1286 when the bishop was John de Kirkby. When he died in 1290, he [bequeathed] a messuage and adjoining tenements to his successor. The will refers to the property as in the parish of St Andrew near Holborn. Kirkby's successor was Wm du Luda, who held the see between 1290 and 1298. It is believed that the chapel on the ground left by Kirkby during this time. The garden at Ely was noted for its strawberrys, as recorded in Shakespeare's Richard III, where the Duke of Gloster says, "My Lord of Ely when I was last in Holborn, I saw good strawberries in your garden there, I do beseech you send for some of them." The gardens [of] the bishop sloped down to the River Fleet; and probably Plum Tree Court, Saffron Hill and Vine Street derive [their] name from them. Saffron Hill - once a liberty or area free from jurisdiction of the county sheriffs and magistrates, and the haunt of undesirable characters. It is the background for much of Oliver Twist.
The thoroughfare known as Ely Place is unique in several respects. The gate is closed nightly at 10, and up to 1939 from that hour until 6am one of the three watchmen, on duty in turn, paraded round the cul-de-sac calling out the hours. At one time the weather was also announced. Next to the chapel is St Audrey's House. St Audrey was a popular name for St Etheldreda, who died of a tumour to in the throat caused by the early love of necklaces. At the fair at Ely, necklaces and lace were sold as St Audrey's. From this was derived the word tawdry, "You promised ma a tawdry-lace and a pair of sweet gloves." Winter's Tale.


Brilliant colours combine with sterling silver for this pair of earrings.
Strong, warm colours combine with bright sterling silver for these eye-catching earrings.
The top two beads, a tiny 3mm rondelle and a large 8mm orange/red rondelle are genuine Cubic Zirconia, all other sparkling beauties are genuine Swarovski crystals.
The colours are bright, but in warm shades.
The earrings dangle from sterling ear wires that sport a little heart in front. They will come with clear rubber stoppers to prevent loss.
Total length is 6.5cm, all metal (including the little granulated Bali bead) is solid sterling silver.


The PluginLogger class is a modified Logger that prepends all logging calls with the name of the plugin doing the logging. The API for PluginLogger is exactly the same as Logger.
Definition at line 14 of file PluginLogger.java.
Creates a new PluginLogger that extracts the name from a plugin.
Definition at line 22 of file PluginLogger.java.
References org.bukkit.plugin.Plugin.getDescription(), org.bukkit.Server.getLogger(), org.bukkit.plugin.PluginDescriptionFile.getName(), org.bukkit.plugin.PluginDescriptionFile.getPrefix(), and org.bukkit.plugin.Plugin.getServer().


A real-life pilot introduces kids to the greatest planes that ever flew.
How cool is a supersonic jet that can zip, dip, and zoom through the air? Or a helicopter that hovers as still as a hummingbird? In this 32-page beginning reader, a real-life pilot introduces kids to the greatest planes that ever flew. Enticing photographs and fascinating facts ensure that a child's natural curiosity is both inspired and satisfied. Like each book in this successful series, Planes offers a high-excitement topic from a knowledgeable and trusted source.


Home » Recipes » Desserts » The No-Fail GLUTEN FREE Pie Crust…that's amazingly DELICIOUS!
The No-Fail GLUTEN FREE Pie Crust…that's amazingly DELICIOUS!
Hey guys, it's Robin….and it's great to be back!
Pie crust. Let's talk pie crust.
If you are like me, a lovely flaky pie crust is hard to come by. Pie crust for me is just so high maintenance it seems like Russian Roulette if it comes out or not. It was my mother who made the perfect crust growing up…and had the "touch". Then came in this whole gluten-free thing (more than half of our immediate family has Celiac Disease…and many of our extended family does as well) so making delicious and flaky pie crust had been benched for quite some time. Thirteen years ago (when many of us were diagnosed) gluten free pie crust was something awful and you just ate the filling….and that was it.
Since that time, my mother had to go gluten-free as well and came across a recipe that was something that held it's own…plus it is really hard to ruin.
And another thing — it actually tastes good. As in, those who eat gluten love it and request it as well! Because yep, it's flaky, it's buttery, and it's absolutely DELICIOUS!!
***And one more thing……do my mom a favor and make your edges pretty. Nothing hurts her eyes more than seeing ugly pie crust edges. You'll see her hands down below (when I was with her several months ago), and her world would be a happier place if everyone in the world fluted their pie crust edges. Ha!
Anyway, because of all those requests from both gluten-eaters and NON….. I thought it would be good to share this tasty Gluten Free Pie Crust recipe with you!
First, you'll want to sift all the dry ingredients — the tapioca flour, cornstarch, potato starch (make sure it is starch not flour), rice flour, xanthan gum, salt and sugar. Then cut in the butter and Crisco with a pastry cutter or fork.
Cut the Crisco and butter until it becomes pea sized. Mix thoroughly together all the liquids (egg, vinegar, and ice water) in a separate bowl than add it to the butter mixture and mix well.
It should look like this. Divide it into two balls if you are making large pies or divide into three balls for small pies. Cover with plastic wrap and chill in the refrigerator for at least an hour.
After it has been chilled, roll our your ball between two sheets of plastic wrap.
Roll it out until it is about 1 1/2 – 2 inches larger than your pie plate on all edges.
Flip the dough onto your pie plate and roll the excess edges under until it meets the edge of the pie plate.
Then you can make a pretty edge. Remember my mom's request? Yep, take 2 minutes more and pretty up your crust!
Go ahead and prick the dough with a fork. This is to avoid bubbles and it helps it to keep its' shape.
There you have it. Now it is just waiting for something luscious to fill it to make it a perfect peach, strawberry, lemon meringue, coconut cream, chocolate cream, or whatever pie you want to make it. YUM!
« Shred Your Chicken…in SECONDS!
Thank you for this. Three of us are GF–and one is lactose free. Do you have a recommendation for a butter replacement? Use all Crisco? Thank you!
Oh yes, I would use first use margarine to replace the butter. Then if not, go ahead and use all Crisco/shortening.
What if your one of the people who knows the horrible things crisco & margarine do to our health. What do you recommend then? Is all butter an option?
I would recommend using lard to replace the Crisco/shortening first before using all butter. Butter has a higher percentage of water than shortening and lard is the more similar.
Thanks Robin, I had forgotten about lard. It would be perfect.
Make homemade ghee. I am gluten free, but just recommended to go dairy free by my holistic physician. She said I can alternate ghee for butter. And it's easy to make in a crock pot!
Has anyone tried this recipe without the xanthan gum? It affects me very much like gluten itself.
Have you tried guar gum? Our family can't have xanthum gum because it's corn based. Guar gum works the same way and it's often even cheaper!
Can't wait to try this pie crust! It looks beautiful.
Thanks, Kirsten. You are correct: "Guar gum works the same way," and it is equally indigestible.
Has anybody actually used anything else? Or simply omitted it?
Ca n this be used for baked fruit pies, without pricking the bottom crust and baking it? I'm thinking double crust blueberry and apple pies, and single crust pumpkin, squash and quiche. Thanks!
YES! I forgot to mention that yes you can skip pricking the the bottom fill it with an egg base filling or baked fruit pie filling before baking the crust. I have added that in.
Thanks Robin! I think I will try this with the blueberries and nectarines that are abundant now, and then fall and winter recipes. Could be a new classic recipe!
Ellen, you only prick the crust when a recipe tells you that you need a baked pie crust. If you don't want to prick it then place pie weights or dried beans to prevent the crust bubbling up.
What is crisco? Haven't seen it in the land of Australia.
It's shortening… you can use vegetable fat shortening if you prefer.
This looks amazing Ashley! Ps I have the same rolling pin. ?
What can be used instead of Corn Starch – it has the same affect as gluten. Really need a great recipe – would love to hear your thoughts.
Can you make the pie dough and then referigerate overnight and use the next day with good results?
Could I sub coconut flour for the rice?
It is worth a try.
I can't find potato starch ANYWHERE and got potato flour. Is that going to make the recipe not work? We don't have a lot of options of place to get specialty flours here and that was all Whole Foods had.
Potato Flour is pretty different than potato starch. Sometime they put on the package Potato Starch Flour which can be confusing but ut is potato starch. I would replace it with cornstarch or arrowroot and not use the potato flour.
I get my potato starch, rice flour, tapioca flour at the Asian markets.
Im a bit confused with the baking instructions; are you suppose to blind bake the crust prior to adding the filling (regardless of the type of filling?) or no need to blind bake only for fruit based fillings and blind bake for all others?? Thanks for sharing!
If you are using apples, peaches or cherries or other fruit … don't bake your pie crust prior. Fill and bake. If you are making like a strawberry pie, bake crust first. Hope that helps.
I just wanted to thank you for this awesome recipe!!! I have been gluten free for over 6 years and this is the first pie crust that actually tasted like it should — flaky, buttery and delicious!
Can this be made with a gluten free flour mix instead of adding all the different ones myself? If so what would the cups or weight be?
Has anyone tried making with an egg replacer product or a "flax egg". We are allergic to egg and wheat. Many thanks.
I was wondering the same thing…. we are dairy & egg, soy & gluten free. 2/6 are at least….
This recipe is truly a keeper! It was developed by Betty Hagman and first published in 1990 in her ground-breaking book, The Gluten-free Gourmet.
With the ability to purchase GF flours that are now one for one replacement. I just don't see why you have to buy a bunch of unnecessary ingredients any more. So, our question again is Can this be made with a gluten free flour mix instead of adding all the different ones ourselves? If so what would the cups or weight be PLEASE?
Tried this recipe out and it was absolutely perfect. I make a single crust to top a Turkey Pot Pie and my husband raved about it. First GF crust we have liked. Thanks so very much! Eager to use the remaining half of recipe for another pie or tarts.
Find more great homemade and secret family recipe ideas on House of Ideas.


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Watch Blake Shelton Perform "Turnin' Me On" Acoustic
Blake Shelton has released a brand new acoustic performance of his latest single, " Turnin ' Me On."
Blake Shelton Delivers Brand New Single, "Turnin' Me On"
Blake Shelton unveiled his brand new single earlier this week titled "Turnin' Me On."
WATCH: Blake Shelton Visits a Palm Reader With Jimmy Fallon
Blake Shelton seemed more than psyched to visit a palm reader with Jimmy Fallon .
WATCH: Blake Shelton Crushed By Jimmy Fallon Playing 'Name That Song'
Country music icon, TV star, funnyman—there's not a lot Blake Shelton can't do.
WATCH: Blake Shelton Releases Video For "I Lived It"
Country superstar Blake Shelton has just released a new video for his song "I Lived It," which appears on his most recent album Texoma Shore .
Blake Shelton Serenades 'Kimmel' Audience With Two Songs From 'Texoma Shore'
Blake Shelton kicked off 2018 with a spirited two-song performance on Jimmy Kimmel Live on Monday evening (January 8). The country star played two tracks off his latest release, Texoma Shore , which showcased both his sensitive and funny sides. One of the more poignant songs on his new album is a...
Blake Shelton Invites Young Cancer Survivor To Illinois Show
Bake Shelton is set to have a very special guest in attendance when he plays the TaxSlayer Center in Moline, IL, in February. RELATED: Blake Shelton Performs "I'll Name the Dogs" with Jennifer Hudson The country star will host 8-year-old Sammy Hodgett, who three years ago survived a furious bout...
WATCH: Blake Shelton Performs "I'll Name the Dogs" with Jennifer Hudson
Are you #TeamBlake or #TeamJHud? Blake Shelton was joined by Jennifer Hudson on stage during the top eleven eliminations of The Voice November 28. The country superstar and his fellow coach performed his newest single, " I'll Name The Dogs ." The Voice is coming closer to the end of season 13 as...
WATCH: Blake Shelton Reads Mean Tweets About His 'Sexiest Man Alive' Title
Whether you agree or disagree with People for naming Blake Shelton 2017's Sexiest Man Alive, you have to watch him read mean tweets about his new title. The country superstar appeared on The Ellen DeGeneres Show recently to discuss the honor and had to have some fun backstage. The "I'll Name The...
Blake Shelton Named People's Sexiest Man Alive 2017
People has named Blake Shelton 2017's Sexiest Man Alive! What's more exciting for the country superstar than receiving this honor? Well, he now has something in common with his fellow judge on The Voice (and 2013's Sexiest Man Alive), Adam Levine . The 41-year-old tells the magazine that he credits...

redpajama_set_name: RedPajamaCommonCrawl


Exquisite chocolate & liqueur truffles, created in the Belgian style, with soft chocolate truffle centres. Exclusive to The Chocolate Box. Included in the box are: Sparkling Wine Truffle, Tia Maria Truffle, Rum Truffle, Cointreau Truffle, Grand Marnier Truffle, Ganache Truffle, Gianduja (Hazelnut Praline) Truffle, Strawberry Truffle, Honey Truffle, Praline Milk Truffle, Praline Dark Truffle.
14 exquisite chocolates per box.
Sugar, cocoa butter, cocoa mass, milk powder, wheat glucose syrup, water, flavours, alcohol, emulsifier (soy lecithin), hazelnuts, natural flavours, gum acacia, colour (E120, E124, E132). Milk chocolate contains cocoa solids 37% min, milk solids 22%min. Dark chocolate contains cocoa solids 63% min. White chocolate contains cocoa solids 39% min, milk solids 23% min. THIS PRODUCT CONTAINS TREE NUTS, MILK, SOY (LECITHIN) WHEAT (GLUCOSE SYRUP) AND ALCOHOL. MAY CONTAIN TRACES OF OTHER NUTS.


Traditional incandescent lights are familiar, their colours are vary from soft and warm to cool and bright and they are initially less expensive, but can have a large impact on your hydro bill and are less environmentally friendly. This is why most landscape lighting professionals are leaning toward LED lights.
LED lights use less energy and have longer usage and are therefore less costly in the long-run, though may be more expensive up-front.
Solar powered lights are another option as they have no cost other than the initial install and maintenance. The light produced, however, may not be as bright or consistent as incandescent or LED lights, which will affect how the water feature is seen.
When you've decided on which type of lighting best suits your needs, you'll need to remember that the cords and junction boxes need to be hidden somewhere. You'll want to see your gorgeous water feature, not an ugly cord.
Regardless of which type of lighting you choose, remember that the properties of light change when it hits water. Water dissipates light beams, causing them to create different angles by bending the rays of light. It can also create a glare if just angled in the wrong direction.
Because of how light changes when shone at or immersed in water, it's a good idea to do a test-run before installation, especially if your water feature is complex. This is where hiring a professional is a good use of money. The last thing you want to do is to take apart your hard work because a few lights just won't react the way you expected them to.
Also remember that you'll probably need more light, as much as ½ more than anticipated, because of how light dissipates in water, especially depending on the type of material being used and the depth at which the light will be at.
You will need to have your lights maintained a couple of times a year. Don't believe systems that say they are maintenance-free. Lights can become cloudy, plant life will grow around it and water will become murky. Landscaping professionals like Nite Time Décor offer year-round lighting maintenance packages to keep your water features looking amazing, no matter what.


From times to times, our shower pipes get damaged and leaks appear. With the Pattex Repair Express paste, no need to call a plumber, you can make the job done in 3min.
1. Cut the water, clean your pipe and make sure there is no more humidity.
2. Cut a little piece of Repair Express paste 64g with a cutter. For small repairs, we advise you to use Repair Express doses.
3. Mix the paste with your fingers till it gets fully white and takes the shape you want.
4. Apply the paste on the leak of your shower pipe and take care that it is fully covered.


text:
<?php

namespace Energine\forms\components;
use Energine\share\components\Grid, Energine\forms\gears\FormConstructor, Energine\share\gears\QAL, Energine\share\gears\Field, Energine\share\gears\FieldDescription, Energine\share\gears\SimpleBuilder, Energine\share\gears\Data, Energine\share\gears\DataDescription;
/**
 * Form results.
 *
 * @code
class FormResults;
@endcode
 */
class FormResults extends Grid {
    /**
     * Form ID.
     * @var int $formID
     */
    private $formID;

    /**
     * @copydoc Grid::__construct
     */
    public function __construct($name,  array $params = null) {
        parent::__construct($name, $params);
        //Якщо ідентифікатор форми вказаний невірно або не вказаний, то не вивалювати помилку, а красиво показати.
        if (!$this->formID = $this->getParam('form_id'))
            $this->formID = false;
        else
            $this->setTableName(FormConstructor::getDatabase() . '.form_' . $this->formID);

        $this->setOrder(array('pk_id' => QAL::DESC));
    }

    /**
     * @copydoc Grid::defineParams
     */
    protected function defineParams() {
        return array_merge(
            parent::defineParams(),
            array(
                 'form_id' => false
            )
        );
    }

    /**
     * @copydoc Grid::loadDataDescription
     */
    protected function loadDataDescription() {
        $result = parent::loadDataDescription();
        //Якщо у конфігі вказано обмеження на кількість полів, які мають відображатися у Grid'і (states: main, getRawData), то застосувати його.
        //Інакше відобразити всі поля.
        if (in_array($this->getState(), array('main', 'getRawData'))) {
            $numFields = $this->getConfigValue('forms.result_num_fields', 6);
            if (count($result) > $numFields)
                $result = array_splice($result, 0, $numFields);
        }

        return $result;
    }

    /**
     * @copydoc Grid::main
     */
    protected function main() {
        if (!$this->formID)
            $this->returnEmptyRecordset();
        else {
            parent::main();
        }
    }

    /**
     * @copydoc Grid::createDataDescription
     */
    protected function createDataDescription(){
        $result = parent::createDataDescription();
        if(in_array($this->getState(), array('main', 'getRawData') )){
            $result->getFieldDescriptionByName('pk_id')->setType(FieldDescription::FIELD_TYPE_INT);
        }
        return $result;
    }

    /**
     * Return empty recordset.
     */
    private function returnEmptyRecordset() {
        //Тип форми змінюється для того, щоб xslt опрацював помилку не в Grid'і.
        $this->setType(self::COMPONENT_TYPE_FORM_ALTER);
        $this->removeProperty('exttype');

        $f = new Field('error_msg');
        $fd = new FieldDescription('error_msg');
        $fd->setType(FieldDescription::FIELD_TYPE_STRING);
        $fd->setMode(FieldDescription::FIELD_MODE_READ);
        $f->setData($this->translate('ERROR_NO_FORM'), true);

        $d = new Data();
        $dd = new DataDescription();
        $d->addField($f);
        $dd->addFieldDescription($fd);

        $this->setData($d);
        $this->setDataDescription($dd);

        $this->setBuilder(new SimpleBuilder());
    }
}


text:
La sélection de la ville hôte pour les Jeux olympiques et paralympiques 2018, où trois villes sont candidates à l'organisation, Annecy en France, Munich en Allemagne et PyeongChang en Corée du Sud, voit cette mission confiée à la ville coréenne. La décision est prise lors d'un vote ayant eu lieu lors de la  session du Comité international olympique organisée à Durban le .

Villes candidates
 Annecy :
 Munich :
 Pyeongchang :

Selon la procédure du Comité international olympique, les villes intéressées par une candidature à l'organisation des Jeux olympiques d'hiver 2018 avaient jusqu'au  pour déposer leur dossier auprès du CIO et devenir des « villes requérantes ».

Les dossiers ont été étudiés par une commission d'experts qui a remis ses conclusions à la commission exécutive du CIO. Le , la commission exécutive a communiqué à Lausanne la liste des « villes candidates » : Munich, PyeongChang et Annecy. Il apparaît donc que des trois villes requérantes, aucune n'a été éliminée à ce stade du processus de sélection de la ville hôte.

La phase de candidature a démarré à ce stade, et les trois villes candidates ont disposé d'une année pour convaincre les membres du CIO. Elles ont toutes trois remis leur dossier de candidature avant la date limite du .

La commission d'évaluation du CIO était présidée par Gunilla Lindberg. Elle a visité les villes candidates selon le calendrier suivant :
 Annecy : 9 - 12 février ;
 PyeongChang : 16 - 19 février ;
 Munich :  - 4 mars.

La commission d'évaluation a rendu publiquement ses conclusions le 10 mai 2011, affirmant que les trois villes présentent « trois candidatures d'un niveau extrêmement haut ».

Les membres du CIO ont élu la ville hôte des JO d'hiver de 2018 lors de la  organisée à Durban, en Afrique du Sud, le . Sur  du CIO votants, PyeongChang a recueilli , Munich 25 et Annecy 7. La ville coréenne a donc été élue dès le premier tour de vote.

Annecy (France)

La France avait accueilli les Jeux d'hiver pour la dernière fois à Albertville en 1992. Depuis, le pays avait posé trois candidatures à l'organisation des Jeux d'été avec Lille pour 2004 et Paris pour 2008 et 2012.

La ville d'Annecy a été choisie comme la ville requérante française le  contre Nice, Grenoble et Pelvoux, par le Comité national olympique et sportif français (CNOSF). Pelvoux se définit comme une candidature à taille humaine et raisonnable, mais les nombreuses infrastructures à construire et le bénéfice très surévalué en font clairement une ville outsider. Nice profite d'un pôle de glace idéal, mais l'inconvénient est l'écart entre la ville et Isola 2000. Grenoble était l'autre ville favorite et faisait jouer son statut de ville-hôte des Jeux d'hiver en 1968. Des critiques sont néanmoins formulés contre le rapport du comité olympique, qui applique des jugements variables selon les candidatures et qui, à titre de transparence, fut révélé au public, ce qui influença le vote et affaiblit Pelvoux et Nice.

Résultats du vote pour la désignation de la ville candidate française pour les Jeux olympiques d'hiver 2018 par le Comité national olympique et sportif français:

Edgar Grospiron, l'ancien champion français de ski acrobatique est le directeur général de cette candidature jusqu'à sa démission le . Le , Charles Beigbeder est devenu président du comité de la candidature d'Annecy à l'organisation des Jeux olympiques d'hiver de 2018. Annecy possède un budget de  d'euros.

Historique
En 2010, la commission du CIO rend son évaluation : les sites sont trop dispersés. Le plan est remanié. L'alternance des continents n'était pas non plus favorable avec des Jeux d'hiver en 2014 prévus à Sotchi.

Pour la 123 session du CIO à Durban, seul le Premier ministre François Fillon se déplaca, Killy aurait recommandé a Nicolas Sarkozy de ne pas y aller pour éviter d'être associé au fiasco. La presse avait anticipé le peu d'espoirs face à l'archi-favori PyeongChang. Un membre de l'équipe avait prédit, en off, qu'il espérait entre 7 et 15 voix. Annecy ne récolta que 7 voix au tour unique de vote sur 95 votants. L'Équipe déclara que les quelques votants seraient les membres du CIO en sympathie avec la France. Pour 2022, Nice voulut y participer mais la France préféra se concentrer sur les Jeux d'été de 2024, avec succès.

Les causes seraient un budget de candidature faiblard de 30 millions €, la moitié de celui de Munich, le quart de PyeongChang, ainsi qu'une gouvernance ayant changée trois fois et surtout des habitants locaux peu satisfaits. Slate cite également des échecs au niveau de la gouvernance chez les fédérations sportives.

Projet
Les dates proposés étaient du 9 au 25 février 2018 pour les Jeux olympiques et du 9 au 18 mars pour les Jeux paralympiques.

Le budget est de 176 millions $. Le budget du COJO est de 1.42 millards €. Le budget hors-COJO avec les infrastructures hors-sportives sont de 2.5 milliards, à comparer avec les presque 7 milliards € investits annuellement pas l'état pour la région rhône alpe.

Deux pôles étaient prévus, un à Annecy, l'autre à Chamonix, chacun possédant des épreuves de neige et de glisse, un centre de média et un village olympique. Seul le pôle d'Annecy servirait pour les Jeux paralympiques. Le seul site hors des pôles est la piste de glisse de La Plagne.

Ancien projet
Jusquen 2010, le projet était de faire profiter les épreuves à un maximum de stations, les sites étant trop dispersés. Seuls sont affichés les sites ayant changés d'emplacement.

Munich (Allemagne)
L'Allemagne n'a pas accueilli les Jeux d'hiver depuis 1936 et la précédente candidature du pays pour les Jeux hivernaux remonte à 1986 avec Berchtesgaden pour les Jeux de 1992, finalement attribués à Albertville. La candidature de Munich s'appuyait sur la ville de Garmisch-Partenkirchen, hôte des Jeux de 1936, pour les épreuves de neige.

En cas de désignation, Munich, qui avait organisé les Jeux olympiques d'été de 1972, aurait été la première ville à accueillir les Jeux olympiques d'été et d'hiver.

PyeongChang (Corée du Sud)
Ce sera la  de la Corée du Sud, après ses deux échecs successifs de 2010 et 2014. PyeongChang fut jusqu'ici à chaque fois battue sur le fil, par Vancouver d'abord, puis par Sotchi.  .

Villes ayant eu l'intention de se présenter

  Innsbruck
  Sofia
  Santiago
  Harbin et Changchun
  Denver, Reno/Lake Tahoe et Salt Lake City
  Nice, Grenoble et Pelvoux
  Bordjomi
  Almaty
  Bohinj
  Östersund
  Genève
  Bukovel

Un référendum était prévu par le canton de Genève en 2009 pour décider de la poursuite de la candidature de la Suisse pour les Jeux de 2018. Toutes les récentes candidatures suisses ont été des échecs : Sion en 1972, 2002 et 2006, Berne en  2010, Zurich en 2014. Cette candidature est finalement retirée le 8 décembre 2008. Finalement, Genève a décidé de soutenir la candidature de sa voisine française Annecy dans la course à l'organisation des JO 2018.

L'Autriche n'a pas présenté de nouvelle candidature, malgré l'intérêt d'Innsbruck pour être la représentante du pays dans la course à l'investiture. Les échecs successifs d'Innsbruck pour 2002, de Klagenfurt pour 2006 et de Salzbourg pour 2010 et 2014 ont laissé des traces. De plus, Innsbruck a été choisie par le CIO pour organiser les Jeux olympiques de la jeunesse d'hiver 2012.

La Suède est l'un des pays qui a le plus déposé de candidatures pour les Jeux d'hiver, sans jamais avoir été retenu. Dans un passé récent, Göteborg, Åre, Falun et Östersund ont toutes échoué à plusieurs reprises. Le gouvernement suédois a un temps envisagé une candidature de Stockholm pour les Jeux d'hiver de 2014 ou 2018, mais le projet a vite été abandonné. Östersund a été envisagée comme représentante suédoise pour 2018.

La Norvège a finalement renoncé à accueillir les Jeux olympiques, le coût de 2,4 milliards d'euros étant trop élevé et les chances d'attribution à Tromsø jugées trop faibles. Tromsø avait précédemment battu Trondheim et Oslo/Lillehammer pour l'investiture à la candidature norvégienne.

Début janvier 2009, le porte-parole du comité olympique américain annonce qu'il n'y aura aucune candidature américaine pour les JO de 2018, ceci dans le but de préserver les chances de la candidature de Chicago pour les Jeux olympiques d'été de 2016, qui finalement échoueront face à Rio de Janeiro. Salt Lake City, hôte des Jeux de 2002, Denver, désignée pour accueillir les JO d'hiver en 1976 mais qui avait renoncé à les organiser en 1974, et Reno/Lake Tahoe étaient candidates. Au , la candidature de Denver est dépendante du résultat de la candidature de Chicago pour 2016, mais le USOC, après l'échec de Chicago 2016, ne veut pas d'une candidature en 2018.

Harbin et Changchun (candidatures chinoises) ont renoncé à être candidates en octobre 2009, en raison d'une candidature coréenne de Pyeongchang qui est plus aboutie, selon les autorités chinoises.

Vote
Le vote définitif a eu lieu le  à Durban. La ville de PyeongChang a obtenu une majorité absolue dès le .

Notes et références

Voir aussi

Articles connexes
 Jeux olympiques d'hiver de 2018
 Jeux paralympiques d'hiver de 2018

Liens externes
 Pyeongchang 2018
 Candidature d'Annecy :

 Dossier de ville candidate, en 3 volumes, à partir de RERO / Internet Archive : I (présentation), II (sites), III (organisation).

2018
Jeux olympiques d'hiver de 2018
Jeux paralympiques d'hiver de 2018


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Home/Syndicated Posts/South Texas Border Patrol Captures 136 Illegal Aliens
Customs, Border and Immigration NewsIn The NewsSyndicated Posts
South Texas Border Patrol Captures 136 Illegal Aliens
Rich MitchellMarch 8, 2022
EDINBURG, Texas – Rio Grande Valley Sector Border Patrol (RGV) agents arrested 136 migrants unlawfully present in the United States in four separate events across the Rio Grande Valley.
On March 7, Fort Brown Border Patrol Station agents observed a group of 86 migrants walking north from the Rio Grande in Brownsville, Texas. The group included 31 family members and 55 single adults. The majority of the migrants, 75, are from Nicaragua, and the rest are from other Central American countries and Colombia.
Hours earlier, the Rio Grande City Police Department (RGC PD) received information regarding two apartments in Rio Grande City, Texas, being used to harbor migrants. RGV agents alongside RGC PD officers approached both apartments and discovered a total of 12 migrants and one caretaker. Agents determined the migrants are nationals from Mexico, Honduras, and Peru illegally present in the United States. All migrants were arrested by Border Patrol agents and the caretaker, a Mexican national, was turned over to RGC PD.
That same day, RGV agents along with Hidalgo County Constable Precinct 1, discovered five undocumented migrants being harbored inside a Weslaco, Texas, residence. The migrants were identified as citizens from El Salvador and Mexico illegally present in the United States.
On March 8, RGV agents received information of a residence in Sullivan City, Texas, possible harboring migrants. Agents responded to the location and encountered 33 migrants unlawfully present in the United States and transported them to a Border Patrol station. No caretaker was identified.
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