text:
\section{Metapopulation framework}
\label{meta_pop}

The metapopulation framework is used to describe the dynamics of systems characterized by well separated but connected units/subpopulations \cite{hanski97-1,tilman97-1,bascompte98-1,hanski04-1,colizza07-03,colizza07-5,colizza07-4,baronchelli2008bosonic}. Within this paradigm very different systems and processes can be described, such as chemical reactions, the evolution of populations, and the spreading of infectious diseases. In general, any spatially distributed set of subpopulations defined by a highly fragmented environment fits this description.

 Modeling such systems as networks is natural \cite{colizza07-03,colizza07-5,colizza07-4,baronchelli2008bosonic}. Nodes are the basics and isolated units, and links allow the movement of particles/individuals. Dynamical processes in metapopulation networks can be described as reaction-diffusion processes \cite{colizza07-4,baronchelli2008bosonic}. While the reaction refers to the dynamics taking place inside each node, the diffusion concerns the movement of individuals between connected nodes (see Figure~\ref{sk}-A for a schematic illustration).
In this section we recall the mathematical formalism needed to tackle these problem for static networks.

\subsection{Reaction}

As mentioned above, we focus on disease/information spreading and contagion processes described using a SIR model \cite{kermac27-1,keeling08-1}. Individuals are divided in three different compartments according to their status, namely Susceptible (healthy, or unaware), Infected (and spreading), and Recovered (cured and no more infective). The evolution of the dynamics is defined by two different transitions. On the one hand,  susceptible individuals in contact with infected ones might become infected. This interaction happens with a rate $\beta$ and can be described as
\begin{equation}
S+I\xrightarrow{\beta} 2I.
\end{equation}
On the other hand, infected people recover from the disease spontaneously, with a rate $\mu$ described as:
\begin{equation}
I\xrightarrow{\mu} R.
\end{equation}
The inverse of this rate defines the characteristic infectious period, i.e. the average time each infected individual spends in the compartment $I$.

The dynamics is determined by the value of these two parameters and by the interaction patterns among individuals. Here, we consider the simple case of homogeneous mixing. The nodes do not have an internal structure, and they all have the same probability of interaction. In particular, whether or not the disease will spread locally depends on the basic reproductive number  $R_0 = \beta/\mu$, describing the average number of secondary cases generated by an infected individual in a fully susceptible population \cite{kermac27-1,keeling08-1}. Diseases characterized by $R_0<1$ die out, i.e.,  the infected individuals are not able to sustain the spreading, while for $R_0 \ge1$ the disease is in general able to take off and spread locally.  However, the finite size of the subpopulations, and the stochastic nature of process, may lead to the extinction of the disease also in the latter case. In particular, the probability that a subpopulation experiences an outbreak give $n$ infected initial individuals is
\begin{equation}
\label{cond1}
P_{outbreak}=1-\frac{1}{R_0^n},
\end{equation}
for all values of $R_0\ge1$ \cite{bailey75-1}.

\subsection{Diffusion}

The diffusion of particles/individuals is a crucial component that drives the entire dynamics of the system. Many different diffusion mechanisms have been proposed with different levels of realism \cite{rvachev85-1,sattenspiel95-1,lloyd96-1,keeling00-1,keeling02-1,colizza07-5,balcan09-1,meloni11-1}. They all translate in the definition of a matrix $d_{ij}$  characterizing the probability that at each time step an individual from $i$ travels/diffuses to the subpopulation $j$. Here we consider a very simple diffusion mechanism with the following properties:
\begin{itemize}
\item at each time step the probability of traveling applies to all individuals in the node independently of their origins. These type of processes are Markovian diffusions.
\item The probability $d_{ij}$ is set to be zero if there is not a link connecting the two subpopulations.
\item Any individual in a node $i$, characterized by $k_i$ neighbors (degree) will have the same probability of reaching any of its neighbors: $d_{ij}=p\Delta t/k_i$ in a time interval $\Delta t$. The diffusion is homogeneous. The quantity $p$ defines the mobility rate of individuals.
\end{itemize}
In these settings, we consider a metapopulation network characterized by $V$ nodes and $N$ individuals. $N_i(t)$ is defined as the number of individuals inside node $i$ at time $t$. We assume that $\sum_i^{V}N_i(t)=N$ for any time $t$ i.e., the total population conserved. A convenient description of such systems is obtained considering degree classes, i.e., by assuming that nodes with the same number of neighbors, or degree, are statistically equivalent.

The average number of individuals in a node of class $k$ is then:
\begin{equation}
N_k=\frac{1}{V_k}\sum_{i|k_i=k}N_i,
\end{equation}
where $V_k$ is the number of nodes of class $k$. The matrix $d_{ij}$ can be generalized for degree classes introducing $d_{kk'}$ as the probability that an individual diffuses from a node of class $k$ to a class $k'$ in an small interval $\Delta t$. Since we are considering homogeneous diffusion, we have $d_{kk'}=p \Delta t/k$.

The variation in the number of individuals in a degree class $k$ in a interval $\Delta t$ can therefore be written by considering the master equation of a random walk on graph \cite{barrat08-1,newman10-1,noh04, baronchelli2010mean}:
\begin{equation}
\label{rand}
d_t N_k(t)= -p \Delta t N_k(t)+k\sum_{k'}N_{k'}(t)d_{k'k}P(k'|k).
\end{equation}
The first term represents the number of people leaving the class $k$. The last term considers the number of individuals arriving the class from all other connected nodes. In particular for uncorrelated networks, in which the probability that a link departing from a node of degree $k$ connects a node of degree $k'$ is independent  of  the destination, the stationary state of Eq.~\ref{rand} is:
\begin{equation}
\label{stationary_simple}
N_k=\frac{k}{\av{k}}\av{N},
\end{equation}
where $\av{N} = N/V$ is the average number of walkers per node. The equilibrium describes the final population size in each degree class. This results is well know  from the theory of dynamical processes on networks \cite{barrat08-1,newman10-1,noh04}. The linear dependence on $k$ remarks the effects of the heterogeneous connectivity patterns on diffusion processes.

\subsection{Invasion threshold}

In metapopulation networks the internal spreading of the disease ($R_0 \ge1$), does not necessarily imply a global spreading \cite{colizza07-03,colizza07-5,colizza07-4,baronchelli2008bosonic}. As schematically shown in Figure~\ref{sk}-B, in the limit $p=0$ the disease is not able to diffuse from one subpopulation to the other, but remains confined to the seeded subpopulations.  The spreading at the metapopulation level depends on the interplay between the time scale of the disease and the time scale of the diffusion. The mobility rate $p$ must be large enough to ensure the diffusion of infected individuals from seeded nodes to others, before the internal dynamics dies out. The minimal required value of the diffusion rate $p^*$ such that for $p>p^*$ the disease is able to spread in multiple nodes affecting a finite fraction of the system, defines the invasion threshold in metapopulation networks (see Figure~\ref{sk}-B).

To identify the critical value $p^*$ for a general uncorrelated metapopulation network, let us consider a SIR epidemics started from a node of general degree $k$ and size $N_k$ characterized by $R_0 \ge 1$. As discussed in the previous section, above threshold the seeded node experiences an outbreak with probability given by Eq.~\ref{cond1}. In this case the number of infected individuals produced during the evolution of the epidemics can be written as $\alpha N_k$, where $\alpha$ depends on the details of the studied disease. In the limit $R_0 \to 1$ for a SIR model, $\alpha$ can be approximated by $\alpha \simeq \frac{2(R_0-1)}{R_0^2}$ \cite{murray2005-1}. In the SIR evolution, each infected individuals stays in the compartment $I$ for an average time $\mu^{-1}$ during which it can travel, and potentially infect other nodes. The diffusion matrix is $d_{kk'}$, so we can write the number of new seeds traveling from a node of class $k$ to a node of class $k'$ as:
\begin{equation}
\label{ll}
\lambda_{kk'}=d_{kk'}\frac{\alpha}{\mu}N_k.
\end{equation}
Let us define $D^{0}_k$ as the number of diseased subpopulation of degree $k$ at generation $0$. These nodes are experiencing an outbreak at the beginning of the process. They are the seeds of the infections. Nodes seeded by one of those in the first generation define the set $D^1_k$ at the following generation and so on. If the initial number of diseased nodes is small, the progression of the disease can be described using a tree-like approximation relating $D^n_k$ with $D^{n-1}_k$ \cite{ball97-1,harris89-1,vazquez06-2}. Following ref. \cite{colizza07-5} we can write:
\begin{equation}
D_k^n=\sum_{k'} D_{k'}^{n-1}(k'-1)(1-R_0^{-\lambda_{k'k}})P(k|k')\left(1-\frac{D_k^{n-1}}{V_k} \right).
\end{equation}
This equation considers that each node of degree $k'$ will seed the infection in $k'-1$ nodes (the total number minus the one from which the node got seeded). The conditional probability $P(k|k')$ measures the probability that each of the $k'$ neighbors subpopulations has degree $k$. The term $1-R_0^{-\lambda_{k'k}}$ considers the probability to observe an outbreak given the number of seeds $\lambda_{k'k}$ arriving from $k'$ to $k$. The last term in the sum describes the fraction of nodes in the degree $k$ still available for seeding. In the limit of $R_0 \sim 1$ and in the early stages of the epidemics we can simply the equation writing:
\begin{equation}
D_k^n=\sum_{k'} D_{k'}^{n-1}(k'-1)\lambda_{k'k}(R_0-1)P(k|k').
\end{equation}
For uncorrelated networks, homogeneous and Markovian diffusion dynamics the critical value of $p$ reads:
\begin{equation}
p^*= \frac{\av{k}^2}{\av{k^2}-\av{k}}\frac{\mu}{(R_0-1)\alpha \av{N}}.
\end{equation}
This result clearly shows the strong impact of the topological properties of the network on the global dynamics \cite{colizza07-03,colizza07-5,colizza07-4}. Indeed, for heavy-tailed networks the ratio $\frac{\av{k}^2}{\av{k^2}-\av{k}}$ is typically small, zero in infinite network size, implying that the heterogeneities of the metapopulation network favors the global spreading of epidemic disease. In this case the critical value of $p$ is much smaller than the respective value for homogeneous  networks.

\begin{figure}
\begin{center}
 \includegraphics  [width=0.4\textwidth] {fig1.eps}
\caption{(Color Online) Schematic representation of a metapopulation system and its global threshold. In panel A) we show, on the left, the diffusion process on the macroscopic level. Red (gray) nodes represent subpopulations experiencing a local outbreak. White nodes represent subpopulation not yet reached by the disease. Nodes with red (gray) center and white outer layer instead represent subpopulation that have been seeded by diseased population through the thick links connecting them. On the right we show the microscopic diffusion process. Each subpopulation contains individuals divided in three compartment according to their disease status. White are susceptible (white), red (light gray) infectious and dark gray recovered. The arrows represent the flows of migration coupling the internal dynamics. In panel B) we show the critical value of the mobility rate $p^*$. Below this point just a infinitesimal fraction of subpopulations is affected by the disease. For values equal or larger than the critical point the system reach a regime in which a finite fraction of
subpopulations  is  affected by the spreading.  }
\label{sk}
\end{center}
\end{figure}

\section{Activity driven models}
\label{act}

In the following, we adopt the activity driven modeling of time varying networks, which represents a natural framework to study dynamical processes that evolve at the same time scale of the change of the networks \cite{perra12-1}. Each node is characterized by an activity potential $x$,  describing its propensity to establish links.
Formally, $x$ is defined as the number of
interactions that a node performs in a characteristic time window of
given length $\Delta t$, divided by the total number of interactions
made by all nodes during the same time window.
The distribution $F(x)$ defines the probability that randomly chosen node $i$ has activity
potential $x$, and the latter is bounded in the interval
$\epsilon \le x_i \le1$.
In the model, $N$ disconnected nodes are initially considered. To each one of them is assigned the activity/firing rate $a_i = \eta x_i$, defining the probability per
unit time to create new contacts or interactions with other
individuals. The rescaling factor $\eta$ is defined such that the average number of active nodes per unit time in the system is $\eta \av{x}N$. In this setting, the generative process is defined
according to the following rules:
\begin{itemize}
\item At each discrete time step $t$ the network $G_t$ starts with $N$
  disconnected vertices;
\item With probability $a_i \Delta t$ each vertex $i$ becomes active
  and generates $m$ links that are connected to $m$ other randomly
  selected vertices. Non-active nodes can still receive connections
  from other active vertices;
\item At the next time step $t + \Delta t$, all the edges in the
  network $G_t$ are deleted.
 \end{itemize}
Thus, all interactions have a constant duration $\tau_G = \Delta t$, and nodes do
not have memory of any previous time steps. \\
If not specified otherwise, we will consider power-law distributions of activity potential i.e. $F(x)=Ax^{-\gamma}$ that reproduce behavior similar to what is observed in real data \cite{perra12-1}. At each time step the network is a simple random graph with low average connectivity. The
accumulation of connections that we observe by measuring activity
on increasingly larger time slices $T$ generates a skewed $P_T(k)$
degree distribution with a broad variability.
Heterogeneities and nodes with a large number of connections (hubs) is
due to the wide variation of activity rates in the system and the
associated highly active agents. In activity driven models, the
creation of hubs results from the presence of nodes with high activity
rate, which are more willing to repeatedly engage in interactions.\\
The model allows for a simple analytical treatment \cite{perra12-1}. The average degree per unit time of a node $i$ characterized by an activity rate $a_i$ will be:
\begin{equation}
\av{k_i}_t= m a_i + m\av{a}.
\end{equation}
The first contribution is due to the $m$ links generated by the node when active. The second contribution is due to the links that reach node $i$ coming from other active nodes. At each time step the average degree per unit time in the network will be
\begin{equation}
\av{k}_t=2m\av{a}.
\end{equation}
While a snapshot of the instantaneous network would show a set of
stars, the integrated network, defined as the union of all the instantaneous networks at
previous times, is not sparse. It is possible to show that the degree distribution
$P_T(k)$ of the integrated network at time $T$ takes the form:
\begin{equation}
P_T(k)\sim \frac{1}{T m \eta}F\left[ \frac{k}{T m \eta}\right],
\end{equation}
in the limit of small $k/N$ and $k/T$ \cite{perra12-1}. Hence,
the integrated degree distribution has the same function form of the activity potential. Fixing an opportune distribution for $F(x)$, the model reproduces the connectivity distribution observed in the data, and considers explicitly the dynamical evolution of its structure.

\section{Metapopulation models with dynamical coupling patterns}
\label{meta_pop_act}

In the next sections we present an extension of the framework and results obtained in static metapopulation networks, to systems characterized by time-varying topologies. We provide a first modeling approach for the study of relevant phenomena as the epidemic spreading in systems of farmed animals~\cite{Bajardi:2011}, or more in general any type of reaction-diffusion process characterized by a timescale comparable to the one describing the change in the topology of the metapopulation system.

In particular, we consider $V$ nodes and $N$ individuals in a metapopulation network. Each node is characterized by an activity potential $x$ extracted from a distribution $F(x)$. At each time step, individuals interact locally according to a SIR dynamics and move in or out a connected node by following a homogeneous and Markovian diffusion with rate $p$.

 Interestingly, due to the effects of time varying coupling patterns~\cite{perra12-2}, we find expressions that are completely different from the ones observed in the static cases.

\subsection{Diffusion}

The diffusion mechanism has the same properties described in the previous sections, but now occurs on time-varying connections. At each time step $t$, each active node creates $m$ random links with randomly selected vertices, while inactive nodes can be selected by active ones. A networks $G_t$ is created and individuals can diffuse following its links with rate $p$. A convenient representation of such system is obtained considering activity classes. Considering the activity rate $a=\eta x$, the average number of population $N_a$ in nodes of activity class $a$ at time $t$ are:
\begin{equation}
N_a(t)= \frac{1}{V_a}\sum_{i| a_i=a}N_i(t),
\end{equation}
where $V_a$ is the number of nodes in activity class $a$. The variation of the number of individuals in each class of activity in an interval  $\Delta t $ is given by:
\begin{eqnarray}
\label{eq_prl_tot}
d_t N_a(t)&=&-ap \Delta tN_a(t)+a p m \Delta t \av{N}- \nonumber \\
&-&  p m \av{a } \Delta t N_a(t)+ \nonumber \\
&+&p \Delta t \int d a' a'  N_{a'}(t) F(a')
\end{eqnarray}
 The first two terms are contributions due to the activity of
the nodes in class $a$, while the final two terms represent the contribution to
inactive nodes due to the activity of the nodes in all the other
classes. In particular, the first term considers that active nodes will let a fraction $p\Delta t$ move in others nodes. The second term considers that active nodes will connected with $m$ others subpopulations getting a fraction $p\Delta t$ of their individuals. The third term takes into account that active nodes might connected with nodes in class $a$ getting a fraction $p\Delta t$ of their individuals. The last term considers the number of individuals arriving in nodes of class $a$ once these are selected by other active nodes.

 As discussed in more details in ref \cite{perra12-2}, the stationary state of the process is defined by the
infinite time limit $\lim_{t\to\infty}\dot{N}_a\left(t\right)=0$ leading to:
\begin{equation}
\label{beauty}
N_a=\frac{am\langle N\rangle+\phi_1}{a+m\langle a\rangle},
\end{equation}
 where the constant term $\phi_1=\int da aF(a)N_a$ is the average number of individuals potentially moving out from active nodes per
unit time. In order to better understand the physical meaning of this quantity let us consider Eq.~\ref{eq_prl_tot}. This can be rewritten as:
\begin{equation}
d_t N_a(t)= -F_{out,a}(t)+F_{in,a}(t),
\end{equation}
where the two quantities represent the out and in flows (negative and positive terms in Eq.~\ref{eq_prl_tot}) from nodes in the activity class $a$. Since the number of individuals in the system is conserved, summing over all activity classes, we can write:
\begin{eqnarray}
 d_t \int  da N_a(t) VF(a)&=&- \int  da \;\ F_{out,a}(t)VF(a)+ \nonumber\\
 &+& \int  da \;\ F_{in,a}(t)VF(a)=0.
\end{eqnarray}
The two total contributions must be equal with opposite signs. Let us focus on the negative term. The integral over all the classes gives the total number of individuals moving out of any node in the system:
\begin{eqnarray}
F_{out}(t) &=& \int da \;\ F_{out,a}(t) V F(a) \nonumber \\
&=&Vp\Delta t \int da \;\ N_a(t) (a+ m \langle a \rangle ) F(a),
\end{eqnarray}
We can then write:
\begin{eqnarray}
F_{out}(t)&=& V p \Delta t\int da \;\ N_a(t) a F(a)+\\ \nonumber
&+& V p \Delta t m\int da \;\ N_a(t) F(a) \langle a \rangle,
\end{eqnarray}
so that:
\begin{equation}
F_{out}(t)=V p  \Delta t\phi_1 + mVp \Delta t \langle a \rangle \langle W \rangle.
\end{equation}
The first term defines the number of individuals moving out from active nodes in the system. The quantity $\phi_1$ is defined as average number of people potentially moving out of active nodes per unit time. It becomes the actual average in the limit $p=1$. The second term defines the number of individuals moving out from not active nodes that have been selected by active ones.

The stationary state found in Eq.~\ref{beauty} differs substantially from the ones found in static ones  (Eq.~\ref{stationary_simple}), where the number of individuals in each node of degree $k$ is a linear function of the degree. This is not the case in time-varying networks, in fact. The difference is due to the effects of the dynamical connectivity patterns that play a crucial role in the characterization of the stationary state. In particular, in activity driven networks there is a saturation effect for large values of activities. Nodes with high activity have on average $k\sim m$ connections at each time step, and henceforth a limited capacity of collecting individuals \cite{perra12-2}.

\begin{figure}
\begin{center}
 \includegraphics  [width=0.35\textwidth] {fig2.eps}
\caption{(Color Online) Schematic representation of the macroscopic dynamics in time-varying metapopulation networks. In the first time step, $T=1$, just the subpopulation $i$ is diseased (red/gray node). It is the source of the infection. By chance it becomes active and creates $m=1$ random links. Through this connection, thick line, some infected individuals to move to the subpopulation $j$ that will starts to experience the disease at the next time step. Next, for $T=2$, three others nodes are active. All the selected nodes are not diseased so no infected individuals diffuse. At the time step, $T=3$, node $i$ is active again infecting another node. The process is repeated for all the other time steps,  driven by the activity of the each node. }
\label{sk_activity}
\end{center}
\end{figure}

\subsection{Invasion Threshold}

To better illustrate the results, we focus our attention first on the case $m=1$, where each active node creates $1$ random link with other subpopulations. We then tackle the case of a general value of $m$.

\subsubsection{Case $m=1$}

Let us consider a SIR epidemic process started from a single node,  see Figure~\ref{sk_activity} for a schematic representation.
We define $D_a^n$ as the number of diseased nodes in the activity class $a$ and generation $n$. As seen in the previous sections, when the number of diseased subpopulations is small, it is possible and convenient to adopt a tree-like approximation relating $D_a^n$ with $D_a^{n-1}$. At each time step each node might be infected by other seeded subpopulations if:
\begin{itemize}
\item  The node is active and connects with a seeded subpopulation that successfully infects it.

Given $\lambda_{a'a}$ seeds arriving from a nodes in the class $a'$ to the nodes of class $a$, the destination will experience an outbreak with probability $1-R_0^{-\lambda_{a'a}}$.
\item The node is not active but is selected by an active and seeded subpopulation that seeds it.
\end{itemize}
Hence, there are two different contributions:

\begin{eqnarray}
\label{eq_m1}
D_a^n &=& a \Delta t V_a\sum_{a'}D_{a'}^{n-1}\left( 1-R_0^{-\lambda_{a'a}} \right)\left( 1-\frac{D_{a}^{n-1}}{V_a}\right)\frac{1}{V}+ \nonumber \\
&+&  V_a\sum_{a'}a' \Delta t D_{a'}^{n-1}\left( 1-R_0^{-\lambda_{a'a}} \right)\left( 1-\frac{D_{a}^{n-1}}{V_a}\right)\frac{1}{V}. \nonumber \\
\end{eqnarray}

\noindent The value $\lambda_{a'a}$ represent the average number of seeds arriving from a node of class $a'$ to a node of class $a$. In analogy with Eq.~\ref{ll} we can write:

\begin{equation}
\lambda_{a'a}=d_{a'a}\frac{\alpha}{\mu}N_{a'} \sim p \Delta t \frac{\alpha}{\mu}N_{a'}.
\end{equation}

\noindent  Indeed, for $m=1$ the degree per unit time of nodes that can infect or can be infected is $1+\av{a}$. They have at least one connection, plus a contribution given by the average value of activity of all the other nodes. For power-law distributions of activity $\av{a}\sim \mathcal{O}(\epsilon)\ll1$, and we can approximate the degree to $1$.

We make further approximations and simplification by setting without losing generality $\Delta t=1$, and by considering (i) that for values of $R_0$ close to one $( 1-R_0^{-\lambda_{a'a}}) \sim \lambda_{a'a}(R_0-1)$, and (ii) that in the early stages of the spread the large majority of nodes are not seeded so that $( 1-\frac{D_{a}^{n-1}}{V_a})\sim 1$. We can write:
\begin{eqnarray}
\label{eq_m1_2}
D_a^n &=& a F(a)\Omega \sum_{a'}D_{a'}^{n-1}N_{a'}+ \nonumber \\
&+& F(a)\Omega\sum_{a'}a'D_{a'}^{n-1}N_{a'}, \nonumber \\
\end{eqnarray}
where $\Omega=p(R_0-1)\frac{\alpha}{\mu}$. In general, it is not easy to solve directly this equation. In order to find a close form we therefore introduce a set quantities:
\begin{eqnarray}
\theta^n &=& \sum_a D_a^n N_a\nonumber \\
\xi^n &=& \sum_a a D_a^n N_a  \nonumber \\
\phi_h &=& \sum_a a^{h}F(a)N_a, \;\ h=1,2 \nonumber \\
\end{eqnarray}
By multiplying both sides of  Eq.~(\ref{eq_m1_2}) by $N_a$ and summing, we obtain
\begin{equation}
\label{eq22}
\theta^n =\phi_1 \Omega \theta^{n-1}+\Omega \av{N} \xi^{n-1}
\end{equation}
On the other hand, by multiplying both sides of  Eq.~(\ref{eq_m1_2}) by $aN_a$ and summing, we obtain
\begin{equation}
\label{eq33}
\xi^n=\phi_2\Omega\theta^{n-1}+\Omega \phi_1\xi^{n-1}
\end{equation}

In the continuous time limit, we can write Eqs.~(\ref{eq22}) and~(\ref{eq33}) in a differential form:
\begin{eqnarray}
 \partial_{n} \theta &=&(\phi_1\Omega-1)\theta^{n-1}+\Omega \av{N}\xi^{n-1}\\
\partial_{n} \xi &=&\phi_2\Omega\theta^{n-1}+(\phi_1\Omega-1)\xi^{n-1}
\end{eqnarray}

The Jacobian matrix of this set of linear differential equations takes the form
\[ J= \left( \begin{array}{cc}
\phi_1\Omega-1 & \Omega \av{N}  \\
\phi_2\Omega & \phi_1\Omega-1  \\ \end{array} \right)
\]
and has eigenvalues
\begin{equation}
\Lambda_{(1,2)} = \phi_1\Omega-1 \pm \Omega \sqrt{\phi_2 \av{N}}
\end{equation}
The epidemic threshold is obtained by requiring the largest eigenvalues to be larger than $0$, which leads to the condition for the global outbreak:
\begin{equation}
\Omega(\phi_1+\sqrt{\phi_2 \av{N}} >1
\end{equation}

\noindent we can write the threshold condition on the mobility rate

\begin{equation}
\label{thre_1}
p^* = \frac{\mu }{(R_0-1)\alpha}\frac{1}{\phi_1+\sqrt{\phi_2 \av{N}}}.
\end{equation}

This equation is the central result of our analysis, and it is worth highlighting some aspects of it. First, the invasion threshold is not function of the time-integrated network representation. It depends on two functions $\phi_1$ and $\phi_2$. As shown in details before, the first quantity is the average number of individuals potentially moving out from active nodes. The second quantity is an higher order function of less clear physical interpretation. Second, both quantities act together in lowering the value of the threshold, meaning that not only the amount of mobility observed in the network is responsible for an easier outbreak of the contagion process, but also its heterogeneity act in the same way. Finally, Eq.~(\ref{thre_1}) shows that a thorough consideration of the time-varying nature of the network is crucial not to introduce biases in the description of the processes, also in metapopulation systems.

We test the analytical prediction of Eq.~(\ref{thre_1}) by extensive analytical simulations. Considering $V=10^5$, $m=1$, $F(a)=Aa^{-2.2}$, $\epsilon=10^{-3}$, $\mu=10^{-2}$ and $R_0=1.1$ we evaluated the number of diseased subpopulation as a function of $p$.  Figure~\ref{fig3}-A confirms that the analytical value perfectly matches the simulations.
It also shows that at large values of $p$ the number of diseased subpopulations reaches a maximum, and decreases afterwards. This is in an interesting behavior due to the particular choice of $m=1$ in the activity driven model. When $p$ is large, a connected node loses all of its individuals immediately. Thus, at each time step very active nodes give to a single, and with high probability less active, node all the seeds, which then reside for a longer time on the new node. This turns out to limit strongly the number of possible new seeded subpopulations that can be generated. In Figure~\ref{fig3}-B we show the number of diseased subpopulation as a function of $p$, and $R_0$. We fixed  $V=10^4$, $m=1$, $F(a)=Aa^{-2.2}$, $\epsilon=10^{-3}$, and $\mu=10^{-2}$. The plot clearly show the validity of the analytical formulation for a wide range of reproductive numbers.

\begin{figure}
\begin{center}
 \includegraphics  [width=0.4\textwidth] {fig3.eps}
\caption{(Color Online) In panel A) we show the number of diseased nodes in a metapopulation network, $D_\infty$, as a function of mobility rate $p$. We consider $V=10^5$ subpopulations, $\av{N}=10^3$ individuals per subpopulation, $m=1$, $\epsilon=10^{-3}$ and $\eta=1$. We select a power-law distribution of activity potential $F(x) \sim x^{-\gamma}$ with $\gamma=2.2$. We then consider $\mu =10^{-2}$, and $R_0=1.1$. The triangle represents the analytical prediction of the invasion threshold according to Eq.~\ref{thre_1}. In panel B) we show the phase space of a SIR process. Considering  $V=10^4$ subpopulations, $\av{N}=10^3$ individuals per subpopulation, $m=1$, $\epsilon=10^{-3}$ and $\eta=1$. We select a power-law distribution of activity potential $F(x) \sim x^{-\gamma}$ with $\gamma=2.2$. The 3D surface represents the value of the final number of diseased nodes in the metapopulation system as a function of the local threshold $R_0$ and of the diffusion rate $p$. The red  (light gray) curve defines the global diffusion threshold $p_
c$ for each $R_0$. Each plot is made averaging $10^2$ independent simulations. Each one of them started with $1$\% of random seeds.}
\label{fig3}
\end{center}
\end{figure}

\subsubsection{General case, $m>1$}

The general case of an arbitrary number of links established by active nodes can be derived following the same approach described before. The only difference is the expression of $\lambda_{a'a}$ that for active nodes now becomes:
\begin{equation}
\lambda_{a'a}\sim \frac{p}{m}\frac{\alpha}{\mu}N_a',
\end{equation}
where we have neglected the contribution to the degree given by other active nodes.
The value of $\lambda_{a'a}$ for inactive nodes, that are selected by active ones, is the same as in the $m=1$. Thus, the process is now asymmetric. Active and passively selected nodes have in general a different degree and a different capacity to accumulate individuals. Eq~(\ref{eq_m1_2}) becomes:
\begin{eqnarray}
\label{eq_m1_3}
D_a^n &=& a F(a)m \Omega \sum_{a'}D_{a'}^{n-1}N_{a'}+ \nonumber \\
&+& F(a)\Omega\sum_{a'}a'D_{a'}^{n-1}N_{a'}. \nonumber \\
\end{eqnarray}
Following the same steps and introducing the same quantities we get a the threshold:
\begin{equation}
\label{thre_2}
p^* = \frac{\mu }{(R_0-1)\alpha}\frac{2}{(m+1)\phi_1+\sqrt{4m\overline{N}\phi_2+(m-1)^2\phi_1^2 }}.
\end{equation}

Remarkably, while this result reduces to the previous one, Eq.~(\ref{thre_1}), when $m=1$, the functional form is now different for a general value of $m$. This is due to the possibility of active nodes to release individuals to more than one single subpopulation, which interestingly does not translate in a simple shift of $p^*$. However, also in this case the critical value is a function of the number of individuals moving due to active and selected nodes, and of its heterogeneity, which again act together in determining a smaller threshold.

We test the analytical prediction of Eq.~(\ref{thre_2}) by extensive analytical simulations. Considering $V=10^5$, $m=3$, $F(a)=Aa^{-2.2}$, $\epsilon=10^{-3}$, $\mu=10^{-2}$ and $R_0=1.1$ we evaluated the number of diseased subpopulation as a function of $p$. As show in Figure~\ref{fig4}-A the analytical value perfectly matches the simulations.
For values of $m>1$ the behavior observed for large $p$ and $m=1$  disappears as expected. In Figure~\ref{fig4}-B we show the number of diseased subpopulation as function of $p$, and $R_0$. We consider $V=10^4$, $m=3$, $F(a)=Aa^{-2.2}$, $\epsilon=10^{-3}$, and $\mu=10^{-2}$. Also in this case the plot confirms the analytical prediction for the mobility threshold.

\begin{figure}
\begin{center}
 \includegraphics  [width=0.4\textwidth] {fig4.eps}
\caption{(Color Online) In panel A) we show the number of diseased nodes in a metapopulation network, $D_\infty$, as a function of mobility rate $p$. We consider $V=10^5$ subpopulations, $\av{N}=10^3$ individuals per subpopulation, $m=3$, $\epsilon=10^{-3}$ and $\eta=1$. We select a power-law distribution of activity potential $F(x) \sim x^{-\gamma}$ with $\gamma=2.2$. We then consider $\mu =10^{-2}$ and $R_0=1.1$. The triangle represents the analytical prediction of the invasion threshold according to Eq.~\ref{thre_2}. In panel B) we show the phase space of a SIR process. Considering  $V=10^4$ subpopulations, $\av{N}=10^3$ individuals per subpopulation, $m=3$, $\epsilon=10^{-3}$ and $\eta=1$. We select a power-law distribution of activity potential $F(x) \sim x^{-\gamma}$ with $\gamma=2.2$. The 3D surface represents the value of the final number of diseased nodes in the metapopulation system as a function of the local threshold $R_0$ and of the diffusion rate $p$. The red (light gray) curve defines the global diffusion threshold $p_
c$ for each $R_0$. Each one of them started with $1$\% of random seeds.}
\label{fig4}
\end{center}
\end{figure}

In order to measure more directly the effects induced by time-varying couplings, we compare the behavior of the fraction of diseased subpopulations, $D_\infty $, for activity driven networks integrated over $T$ time steps with the explicit dynamic counterpart we consider so far. In the integrated networks links are accumulated over time, and the spreading process is run in the resulting static graph i.e. $\mathcal{G}_{int}=\cup_{t=0}^{t=T}\mathcal{G}_t$. As show in Figure~\ref{both} when the explicit dynamics of the connections among subpopulation is neglected and integrated over time the critical value of the mobility threshold is orders of magnitudes smaller. This plot clear show the biases that might be introduced by time integrating representations of the system and the importance of considering dynamical coupling patterns for processes that evolve with comparable timescales. These results nicely generalize to metapopulation systems the findings obtained in networks constituted by the interactions of
single individuals~\cite{perra12-1,perra12-2}.

\begin{figure}
\begin{center}
 \includegraphics  [width=0.4\textwidth] {fig5.eps}
\caption{(Color Online) The plot shows the number of diseased nodes in a metapopulation network, $D_\infty$, as a function of mobility rate $p$ on activity driven networks (dots) and corresponding integrated, static, ones (squares). The integration has been performed considering $50$ time steps. We fix $V=10^4$ subpopulations, $\av{N}=10^3$ individuals per subpopulation, $m=3$, $\epsilon=10^{-3}$ and $\eta=1$. We select a power-law distribution of activity potential $F(x) \sim x^{-\gamma}$ with $\gamma=2.2$. We then consider $\mu =10^{-2}$ and $R_0=1.1$. Each plot is made averaging $10^2$ independent simulations. Each one of them started with $1$\% of random seeds.}
\label{both}
\end{center}
\end{figure}

\section{Conclusions}
\label{conclu}

In this paper we have analyzed reaction-diffusion processes in metapopulation networks characterized by time varying coupling patterns, described in the activity driven framework. We have focused on the spreading and contagion processes of diseases and information, modeled through a SIR model. Here, the reaction dynamics inside each node is described considering a homogeneous mixing approach, where each pair of individuals has the same probability of interact, while the diffusion of individuals between connected nodes is Markovian. In this setting, we have characterized analytically the conditions for a global spreading as a function of the process parameters and the time varying couplings. Noteworthily, they are strikingly different from the static case, and turn out to be a function of the average number of individuals potentially moving out from active nodes, that in the early phases of the process spread the diseases to the selected target nodes. These findings not only provide the first analytical
insight into time varying metapopulation processes, but clearly point out that dynamical couplings affect spreading phenomena also in reaction-diffusion processes, and that important biases might be introduced by neglecting them.

Recent analysis have shown that real time-varying networks are characterized by strong dynamical correlations and memory~\cite{holme11-1}. These complex properties are difficult to describe analytically, and in this paper we have provided a first description of reaction-diffusion processes in the simpler setting of a Markovian, memoryless, time-varying metapopulation networks with no dynamical correlations. Furthermore, we have considered Markovian and homogenous random walks. Different mobility rules, as well as a full consideration of the dynamical properties of real-world networks, might introduce non-trivial effects on the global dynamics as observed for static metapopulation networks~\cite{colizza07-5}. All these features are definitely important and call for future extensions of the present framework.
\section{Acknowledgments}

The authors are grateful to Alessandro Vespignani for helpful discussions, insights, and comments. The authors thank also an anonymous referee for helpful suggestions that helped improving the manuscript.

redpajama_set_name: RedPajamaArXiv


text:
Merck Manual Professional Version
2018 © Merck Sharp & Dohme Corp., A Subsidiary of Merck & Co., Inc.
Justin L. Kaplan MD; Robert S. Porter MD
Internal Medicine, Diagnosis, Family Practice, Point of Care, Public Health
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redpajama_set_name: RedPajamaCommonCrawl


I participated in the 2017 World Goldpanning Championships in Moffat Scotland. Moffat is a small town, but it is beautiful and has many tourists.
The championships were held at the athletic park after the nation's parade. I am grateful for the fact that the BGA(British Goldpanning Association) has managed the championships wonderfully with such a small staff.
I am a beginner in the world competition for the second time. I should have practiced panning before going to Scotland, but I was busy with work. For this reason I was defeated in the second round.
I attempted gold prospecting in the natural river before and after the championships. I paid a mining fee at the Museum of Lead Mining near Moffat and went to a nearby river.
When I was looking for a place suitable for gold digging, I saw many gold diggers because it was the summer vacation period.
Although I searched all over the place, I couldn't find any bedrock. A gentleman from London showed me the location of the bedrock. The depth to the bedrock was 50 to 100 cm. I only got fine gold in a few hours of work.
In the evening, I was attacked by the well-known Scottish midges. I brought mosquito coils from Japan and the effect was small. I wanted to have a spray-type insecticide, but I gave up because I can't take it on an airplane.
Scottish landscape is wonderful and could have been enjoyed without midges and rain.
"The Dark Sky Town" is good joke?


text:
History of the West Park
Cleveland, Cuyahoga County, Ohio
Go to Main Page
Almost West Park
A section about places of interest that are not technically in the West Park area but are of interest.
11601 Lorain Avenue
by Gary Swilik
(Photo c1960. Provided by Gary Swilik) Photo by Charles Chaney, April 2005
Click here to see it at Google Maps
The Lyric theater seems almost forgotten today. The larger and better-known Riverside and Variety theaters seem to get most of the attention when it comes time to reminisce about double-feature matinees at the local movie house. Yet the Lyric, if my memory serves me, was quite impressive with a classic lobby including at least one elegant chandelier. You hear less about it only because it closed a lot longer ago and.....until now.......a photo of the place hasn't been seen in years!
To be accurate, the Lyric wasn't located in West Park but about a block east of the old city line (West 117th Street) at 11601 Lorain Avenue. But its bright neon marquee was visible from well inside the old city limits and drew a large West Park audience for many years. In fact, if you looked east down Lorain Avenue the brightly flashing marquees of the Variety and Lyric Theaters, only two blocks apart, lit up the night and gave the impression of a small theater district.
The Lyric, like the old West Park theater and the Riverside, is yet another theater associated with Max Lefkowich and Abraham Polster. They bought the property the Lyric stood on from the Senate Theater Company in April of 1926. Old city directories indicate the Lyric was already built and operating as a "moving picture theater" but we can't be absolutely certain the new owners didn't provide new construction.
In fact, Lefkowich and Polster already owned yet another theater, The Tivoli, located between the Variety and the Lyric at 11625 Lorain. But that's another story.
Lefkowich and Polster owned the Lyric until June of 1946, when they sold the property, but the Lyric continued under different ownership for many years finally closing in the early 60's. The last show ran on Saturday, July 21st, 1962. A double-feature of THE BIG COUNTRY, with Gregory Peck, and THUNDER ROAD, with Robert Mitchum. Of course, back then no theater ever ran less than two films!
The Lyric still stands and now houses a worthy organization entitled AACCESS - OHIO, an acronym for the Arab American Community Center for Economic and Social Services, a community-based, nonprofit, human service organization. The exterior of the building appears to be in fine shape and includes what looks to be part of the original Lyric Marquee.
The author is indebted to Ron Chucksa, 1959 John Marshall High School grad, who shared valuable research essential to the preparation of this article.
See entry at Cinema Treasures for the Lyric Theater
The Linndale Roundhouse
The Linndale Roundhouse and train station complex, on West Park's southeast border, was once a very important part of railroad operations in the Cleveland area. Many West Park baby boomers had fathers, uncles, and older brothers who made their living there...
----Gary Swilik
For more information click The Linndale Roundhouse
Memphis Drive-In Theatre
10543 Memphis Avenue
We lost an old friend in 2006 when the Memphis Drive-In Theatre closed forever. Constructed in 1954, the 1000 car facility eventually had three screens showing double-features. In its later years it was the site of a flea market swap meet on Wednesdays, Saturdays, and Sundays
The screen and snack bar building were demolished in early 2007.
See entry at Cinema Treasures for the Memphis Triple Drive-In Theatre
Robert Hall Clothes
Built c1953. Thousands of West Park baby boomers got their first suit here. Remember the Robert Hall's catchy commercial jingle that we all used to go around singing:
"Values go up, up, up, And prices go down, down, down,
Robert Hall this season Will show you the reason:
Low overhead, Low overhead."
"Robert Hall Commercial"
When the values go up, up, up...
and the prices go down, down down...
[Robert Hall Clothing Stores]
music by Leon Mitchell;
words by Charles A. Gaston;
Original version (c) 1946;
Copyright by Charles A. Gaston & Leon Mitchell;
(c) Feb. 28, 1957; EU 467 561.
Go to memories & comments
Email The West Park History website
Updated 5 July 2014


text:
Martin Rees, Baron Rees of Ludlow (ur. 23 czerwca 1942 w Yorku) – brytyjski naukowiec: astronom, kosmolog i popularyzator tych dziedzin, związany z Uniwersytetem w Cambridge i przewodniczący (dziekan, ang. Master) tamtejszego Trinity College (2004–2012). Astronom królewski Wielkiej Brytanii od 1995 roku, jako 15. na tym stanowisku, a także 60. prezes Towarzystwa Królewskiego w Londynie (ang. Royal Society, 2005–2010).

Rees to laureat licznych nagród, w tym Nagrody Templetona (2011) oraz prestiżowych nagród w astronomii i fizyce, ustępujących statusem głównie Nagrodzie Nobla jak Złoty Medal Królewskiego Towarzystwa Astronomicznego (ang. Royal Astronomical Society, 1987), Nagroda Crafoorda (2005), Medal Isaaca Newtona (2012) i Medal Diraca od ICTP (2013).

Jako astrofizyk przysłużył się potwierdzeniu Wielkiego Wybuchu przez badania kwazarów. Popularyzował wiedzę o Kosmosie i futurologię przez książki, publiczne wykłady i wywiady.

Życiorys
Studiował w Trinity College na Uniwersytecie w Cambridge, gdzie w 1967 roku uzyskał stopień doktora pod kierownictwem Denisa Sciamy. Po stażach podoktorskich wyjechał do Stanów Zjednoczonych, wykładał na University of Sussex oraz macierzystej uczelni, gdzie kierował Instytutem Astronomii.

Prowadził badania nad pochodzeniem mikrofalowego promieniowania tła, tworzeniem galaktyk, zajmował się także kwazarami, gdzie jego badania rozkładu kwazarów były ostatecznym dowodem na brak zastosowania teorii stanu stacjonarnego. Martin Rees wyraził opinię, że szukane inteligencji pozaziemskich (program Search for Extraterrestrial Intelligence) jest opłacalne, nawet jeśli szansa na sukces jest mała.

Jest członkiem Royal Society, a w latach 2005-2010 sprawował funkcję prezesa tego towarzystwa. W 1995 objął stanowisko Astronoma Królewskiego Wielkiej Brytanii. W latach 2004–2012 był przewodniczącym (dziekanem, ang. Master) Trinity College w Cambridge. Zasiadł w radach British Museum i Muzeum Nauki w Londynie. W dniu 6 września 2005 otrzymał tytuł barona (Baron Rees of Ludlow, hrabstwo Shropshire) i miejsce w Izbie Lordów jako par dożywotni.

Wyróżnienia

Planetoida (4587) Rees została nazwana jego imieniem.

Publikacje
Rees to autor ponad 500 artykułów naukowych i kilku książek popularnonaukowych, w tym:
 1999:
 1999: Ta siła fatalna. Czarne dziury we Wszechświecie, wraz z M. Begelmanem, Prószyński i S-ka, .
 2000: Tylko sześć liczb, Grupa Wydawnicza KAW, .
 2006: Nasz kosmiczny dom, Prószyński i S-ka, .

Przypisy

Linki zewnętrzne

 Strona internetowa Martina Reesa

Astronomowie królewscy
Brytyjscy kosmolodzy
Brytyjscy popularyzatorzy fizyki
Brytyjscy popularyzatorzy astronomii
Wykładowcy Uniwersytetu w Cambridge

Prezesi Royal Society
Parowie dożywotni
Odznaczeni Orderem Zasługi (Wielka Brytania)
Laureaci Nagrody Templetona
Laureaci Nagrody Crafoorda – astronomia
Laureaci Złotego Medalu Królewskiego Towarzystwa Astronomicznego
Laureaci Dannie Heineman Prize for Astrophysics
Laureaci Medalu Karla Schwarzschilda
Laureaci Medalu Bruce
Laureaci Petrie Prize Lecture
Laureaci Medalu Isaaca Newtona
Laureaci Medalu Diraca ICTP
Laureaci Albert Einstein World Award of Science
Laureaci Henry Norris Russell Lectureship

Urodzeni w 1942
Ludzie urodzeni w Yorku
Absolwenci Trinity College (Cambridge)

redpajama_set_name: RedPajamaWikipedia


text:
Urns, Pendants & Headstones
Stephen Sondheim's Pivotal Relationship with Oscar Hammerstein
Posted on December 2, 2021 by Martin Oaks under Community, Cremation, Hello world, Memorial, Resources
Stephen Sondheim, who died recently at the age of 91, grew up in a highly dysfunctional home. The man who was to become the central figure in the American Theater for six decades was raised in an atmosphere of material privilege laced with significant emotional turmoil.
Sondheim's father, Herbert, was a clothing manufacturer and his mother, nicknamed Foxy, was a designer. Their marriage was toxic: the neurotic Foxy loved her husband, but Herbert was married to his career. Sondheim later guessed that it was a marriage of convenience on his father's part because "he needed a designer."
The family lived in New York's venerable San Remo apartments on Central Park West, where Sondheim said he was an "institutional child. I was brought up by a cook, a nanny or boarding school or camp…it was an environment that supplied you with everything except meaningful human contact. I had no sense of family at all."
When he was ten, Sondheim's parents divorced, much to Foxy's chagrin. She was saddled with raising a child she did not want. (Years later, in a note composed on the eve of her open heart surgery, she wrote to Sondheim: "The only regret I have in life is giving you birth.") Serious pathology.
The divorce settlement provided Foxy enough funds to purchase a home near Doylestown, Pennsylvania, in the heart of pastoral Bucks County. It was four miles from Highland Farm, the home of Broadway lyricist supreme Oscar Hammerstein (Showboat, Oklahoma, and Carousel) and his wife Dorothy.
In March of 1942, when Sondheim, age 12, began regularly visiting the Hammerstein home, he discovered what "family" was — he developed a relationship with Oscar, the man who became his surrogate father and inspiration for creative composition.
Initially, Sondheim's connection was with Jamie Hammerstein; the boys were only a year apart and both loved competitive games. Soon, however, Sondheim became a full-fledged member of the household. "I infiltrated the family," he chuckled.
Oscar, who had lost his parents at an early age, related to Sondheim's plight — it was a natural mentoring relationship. It was also the luckiest break in Sondheim's life to that point.
"Unexpected significant moments," Sondheim wrote later, "which happen entirely by chance, keep life surprising and sometimes change its direction permanently." Moving to Bucks County "led to my meeting Oscar and finding a channel into the work I was meant to do."
Sondheim always pointed out that it was Hammerstein's force of personality that figured into his eventual vocation– "I was always interested in imitating Oscar. If he had been an archeologist, I would have become an archeologist."
Since Hammerstein was the foremost Broadway lyricist of the time, Sondheim gravitated in that direction. In 1946, he and two friends composed a sprawling, three-act, twenty-song, fifty-cast-member musical, By George — it chronicled campus life at George School, the nearby college preparatory academy all three attended.
Sondheim had lofty expectations when he gave the material to Hammerstein for review: he asked for a professional opinion, not one based on personal ties. Hammerstein did just that. "It's the worst thing I've ever read," he told a crestfallen Sondheim. "I didn't say it doesn't show talent. But it's just terrible. If you want to know why it's terrible, I'll tell you."
The two poured over the libretto for hours, line by line. "It was a step-by-step guide to everything I needed to know," Sondheim reported. "I have never forgotten a word he said."
About that tutorial, Sondheim told The Paris Review: "I probably learned more about writing songs that afternoon than I learned the rest of my life. He taught me how to structure a song, what a character was, what a scene was; he taught me how to tell a story, how not to tell a story…from then on, until the day he died, I showed him everything I wrote."
The personal and professional bond between the pair continued until Hammerstein passed away at 65 in August of 1960.
At his final birthday party, Hammerstein gave photos of himself to the assembled family, which included Sondheim. In an awkward moment, Sondheim asked Hammerstein to sign the picture — "it was like asking your father for an autograph," Sondheim said.
Hammerstein hesitated and then inscribed it, "smiling the whole while, like the cat who ate the cream," Sondheim remembered. It read, "For Stevie, my friend and teacher."
The teacher reference came from a lyric Hammerstein wrote for The King and I — "By your pupils you'll be taught."
A few years ago, Sondheim was asked what he would say to Hammerstein if the two had one more chance to talk. In hushed tones, Sondheim replied, "I would ask him, are you proud of me?"
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Motorcycle customization comes in many forms because most people do something to personalize their bike to make it their own, and at Bob's Used Motorcycle Parts is where you can find the parts to get it done.
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Have you got selected in a public sector bank in the latest IBPS recruitment?Then there are service bond agreements that need to be understood that include certain rules related to probation, minimum service period & amount to pay.With candidates getting ready to join their allotted bank, we have collected those details for you in advance to prepare them early..
Public sector banks to increase their business and compete with private sector banks have started opening new branches across the nation.To stop employees from moving out frequently, there are service bonds in govt banks too.
For the year 2016-17, IBPS had recently announced allotments for 12600 PO jobs, 24,600 clerk jobs & 4300 Specialist officer jobs.
If you are new to bank jobs, then the following question will come up in your mind sooner or later.
What is a Bond & what will happen if I break it?
A service bond is an agreement that candidates will have to sign at the time of joining agreeing to serve the bank for a minimum period (2 or 3 years).
Incase they quit or resign before the specified duration, that individual has to pay the pre-specified amount.This is also called Indemnity bond.
Note:Only those selected for PO (officer – scale I) & SO (Specialist officer) are required to sign service bonds.It is not required for clerk posts.
So for the first time ever we present a list containing details about the service bond conditions in public banks..
Data in the above tabulation were collected from recruitment notices issued by corresponding banking organizations.It is possible for them to modify these requirements while recruiting for current or future vacancies.
There could be some who might not understand certain sections in the list.For their benefit, answers for commonly asked questions pertaining to bond agreements in public sector banks can be found below.
Is there any format for bond agreement?
The bank to which you are allotted will provide you with a format.
The below image is of an indemnity bond format.Once the joining dates are announced, you can download this document from the bank`s website.
Should I pay the bond amount in advance?
Not required.The specified value should be paid to the bank only if you resign from service before completing the minimum service period.
We hope this compilation from BankExamsIndia.com will help you in comparing the joining conditions for all the public sector banks in India.
In case you have questions related to the service bonds, ask it through the form below.
Thnk u very much.. Keep updating us.


text:
Litigation notes
Contract disputes Privilege Enforcement post-Brexit Jackson reforms
Final report published today in Lord Justice Jackson's year-long costs review
This post is part of the following categories:
Class actions, Costs, Disclosure, Evidence, Funding, Part 36 offers, Pre-action
The final report in Lord Justice Jackson's civil litigation costs review was published this morning. The report presents the Judge's findings and supporting evidence following his year-long review. It will now be for the Ministry of Justice to consider the report and accept or reject the various recommendations.
A full copy of the report, running to some 500 pages, is available on the Judiciary website. We will be holding a seminar on 11 February at which we will highlight the key issues from the report, followed by a panel discussion with Herbert Smith partners and distinguished external speakers including Lord Justice Jackson.
The report makes a large number of recommendations in wide-ranging areas. The most important points affecting major commercial litigation include the following:
Conditional fee agreements (CFAs) / after the event (ATE) insurance: CFA success fees and ATE insurance premiums should cease to be recoverable from the opposing party.
Cost shifting: Full costs shifting (i.e. the "loser pays" rule) should remain for commercial litigation, but qualified one-way cost shifting should be introduced for personal injury and defamation claims.
Collective actions: There should be full costs shifting as a default position (save in personal injury collective actions) but the court could order that a different costs regime should operate in appropriate cases.
Contingency fees: Contingency fees (where the lawyer is remunerated by way of a share in the client's damages) should be permitted, subject to a requirement for independent advice, but the losing party should pay costs on a conventional basis.
Third party funding: Third party funding should be supported, subject to limitations on the funders' ability to withdraw funding in ongoing litigation and appropriate capital adequacy requirements.
Disclosure: There should be a "menu" of disclosure options available for large commercial and similar claims.
Witness statements and expert reports: There should be case management measures to control the content or length of statements, together with costs sanctions for breach, but otherwise no major changes are needed.
Part 36 offers: Where a claimant obtains a more favourable result than its own Part 36 offer, the claimant's damages should be increased by 10% (possibly scaled down for higher value claims). Further, the broad interpretation of whether a judgment is "more advantageous" than a defendant's Part 36 offer (as introduced by BAA v Carver) should be reversed.
Case management: Cases should, where possible, be assigned to a judge who has relevant expertise and remain with that judge for the life of the case.
Costs management: Judges should have a discretion to adopt costs management procedures where beneficial for a particular case. However, no case has yet been made out for costs management in the Commercial Court.
Alternative Dispute Resolution (ADR): ADR should be encouraged, including through better education for practitioners and the public, but should not be compulsory.
Pre-action protocols: The general practice direction on pre-action conduct should be substantially repealed and replaced by an obligation to conduct appropriate pre-action correspondence and exchange of information, with costs sanctions to curb unreasonable behaviour.
Lord Justice Jackson was appointed by the then Master of the Rolls, Sir Anthony Clarke, to lead this fundamental review of the rules and principles governing the costs of civil litigation. His objective was to make recommendations "in order to promote access to justice at proportionate cost".
Lord Justice Jackson's review commenced in January 2009. On 8 May he published an interim report identifying numerous issues and options for consultation. Our e-bulletin sent out the same day summarised the key points on which views were sought (see post).
There followed a three-month consultation in which the Judge received over 300 separate written submissions running to several thousand pages and also conducted a series of public seminars and events. The last four months of 2009 were spent preparing the final report.
THE REPORT IN MORE DETAIL
Conditional fee agreements (CFAs) / after the event (ATE) insurance:
Lord Justice Jackson recommends that CFA success fees and ATE insurance premiums should cease to be recoverable from the opposing party in litigation. Parties would still be entitled to enter into such arrangements in order to fund their litigation, but they would have to bear the additional costs of doing so (for a claimant, this might be out of any damages awarded).
The Judge identifies a number of flaws with the current regime of recoverable success fees and ATE premiums, including the following:
It is open to all litigants, "whether rich or poor and whether human or corporate", and therefore is not restricted to those who merit financial support with their litigation.
The party with the benefit of the arrangement generally has little or no interest in the level of costs being incurred in its name, and therefore exerts little or no control over those costs.
It places an excessive costs burden on opposing parties, whose costs liability may become grossly disproportionate if they contest the case to trial (possibly quite reasonably) and lose.
The Judge says that if his recommendation to end recoverability is implemented, there should be:
A move to qualified one-way costs shifting (where the claimant is awarded costs if successful but does not have to pay the defendant's costs if it loses, unless the parties' conduct or financial resources merit a different order) for certain categories of litigation, including personal injury and defamation claims, to protect against the risk of adverse costs orders. Such a measure would however have no place in the context of commercial, construction or similar litigation.
Measures to assist personal injury and other claimants in meeting success fees, including a 10% increase in the level of general damages for pain, suffering and loss of amenity, as well as for nuisance, defamation and any other tort which causes suffering to individuals.
Enhancement to the regime for claimants' Part 36 offers (see below).
If his main recommendation is rejected, and therefore success fees / ATE premiums remain recoverable, the Judge recommends various control measures. For example, the success fee / ATE premium should be irrecoverable if liability is admitted within the protocol period, and a cap on the level of ATE premiums (at 50% of damages) should be introduced. Also, where the ATE insurer is entitled to avoid the policy (e.g. for non-disclosure), it should be required to pay out to the opponent but would then have a right of recovery against the insured.
We support the abolition of recoverable success fees and ATE premiums in commercial cases. There is no obvious reason why defendants should be liable for the additional costs of claimants choosing to litigate on a risk free basis – potentially resulting in the defendant paying a multiple of the claimant's reasonable costs. In some cases, recoverability may interfere with a defendant's access to justice in that the defendant feels undue pressure to settle for more than a case is worth.
We also welcome the Judge's recognition that, if recoverability is abolished, there are no special rules needed for commercial claims to insulate the parties in respect of CFA success fees or adverse costs orders. Where a commercial party wishes to fund its litigation via a CFA with a success fee, or to obtain insurance against adverse costs liability, it can do so at its own expense.
Cost shifting:
As noted above, Lord Justice Jackson recommends that full cost shifting should remain for commercial, construction or similar litigation, but that qualified one-way cost shifting should be introduced for certain other categories of litigation, including personal injury and defamation claims.
He recommends that there should be further consultation to determine which categories of litigant should benefit from one-way costs shifting, including whether it should be introduced for any categories of professional negligence litigation. He expresses the view that this may be difficult to justify outside clinical negligence, as most of those who employ solicitors, accountants, architects, etc could afford to take out before-the-event insurance (also known as legal expenses insurance) to cover their potential liability for legal costs if they chose to do so.
We agree with the Judge's recommendation that full cost shifting should remain for major commercial litigation. This is an important safeguard for both claimants and defendants, allowing claimants with meritorious claims to recover their reasonable legal spend in addition to damages and protecting defendants from unmeritorious claims.
Collective actions:
The report recommends that, as a default position, there should be full costs shifting in collective actions (save in personal injury collective actions, where qualified one-way costs shifting would be the default). However, the court would be able to direct at the certification stage that a different costs regime should operate.
The Judge notes that the arguments advanced during the costs review ranged between two principal positions: (i) no costs shifting, or one-way costs shifting, to promote access to justice for claimants who would otherwise be deterred by fear of adverse costs liability; and (ii) full costs shifting to deter frivolous claims.
In the research we carried out on the views of large corporates and institutions relating to class action reform, clients were unanimous in their view that the cost shifting rules must be retained as a protection against weak claims.
The Judge sees his proposal as a middle way, providing for the discipline of full costs shifting in "many (perhaps most) cases", but allowing the court flexibility where a different regime would be appropriate after considering the nature of the case, the funding arrangements and the resources of the parties.
He draws support for this recommendation from the proposal of the GC100 Group, referred to in the report, that costs shifting should remain the norm in group actions, but there should be a "reasonable amount of judicial discretion to order that costs should lie where they fall, or be capped, in appropriate, exceptional circumstances" for example where there is "genuine concern as to access to justice, unconscionable behaviour by the defendant, or overwhelming merits".
The Judge specifically comments that where a claim is weak or lacking in merit, the court would no doubt insist that two way costs shifting should prevail.
Contingency fees:
The report recommends that both solicitors and counsel should be permitted to enter into contingency fee agreements with their clients (where the lawyer is remunerated by way of a share in the client's damages). However, a losing defendant would only have to pay costs on a conventional basis: so far as the contingency fee exceeded what would be chargeable under a normal fee agreement, this would be borne by the client.
The solicitor and client would have to agree at the outset how any liability for the defendant's costs would be met. If the solicitor agreed to take on this risk, it should be reflected in the solicitor's percentage share of the damages. Similarly, disbursements could be payable by the client or funded by the solicitors as part of the contingency arrangement, in which case this risk should also be reflected in the percentage payable on success.
The Judge comments that it is desirable that as many funding methods as possible should be available to litigants, particularly if success fees and ATE insurance premiums become irrecoverable (as he has recommended). Further, he sees particular force in the freedom of contract argument: if the client wishes to enter into a contingency fee agreement with its lawyer, it should be free to do so.
However he recommends, as a safeguard, that contingency fee agreements should not be valid unless countersigned by an independent solicitor who certifies that he or she has advised the client about its terms.
He also recommends that contingency fees should be subject to regulation along the lines of the proposals the Ministry of Justice has put forward in respect of contingency fees in tribunal proceedings (which are currently permitted). Specifically, the regulations should:
Introduce a requirement that clear and transparent advice and information be provided on costs, other expenses and other methods of funding available.
Provide a maximum percentage of the damages that can be recovered in fees. (The Judge does not comment on what the maximum should be, save for personal injury claims where he recommends a cap of 25% of the claimant's damages excluding damages referable to future costs or losses.)
Control the use of unfair terms and conditions (for example regulating clauses that penalise claimants where they wish to transfer the case to another lawyer or where they refuse advice to settle a claim).
Contingency fees elicit a wide range of responses, as the Judge observes, but clearly their availability would increase the options available at a time when commercial clients are demanding more creative billing solutions from their lawyers.
Third party funding:
Lord Justice Jackson expresses the view that third party funding (where a third party funds a claim in return for, usually, a share of the proceeds) is beneficial and should be supported. It promotes access to justice and does not impose additional financial burdens on opposing parties. He notes that third party funding is likely to become even more important as a means of funding litigation if success fees under CFAs become irrecoverable.
The Judge considers whether third party funders should be regulated or should subscribe to a voluntary code. He concludes that a voluntary code would be sufficient, but that the question of full regulation by the FSA should be re-visited if and when the third party funding market expands.
The Judge notes that a draft voluntary code has been developed by the Third Party Litigation Funders Association in conjunction with the Civil Justice Council. He does not comment on the detail of the code, save to say that:
The code should not permit a funder to withdraw from a case unless there are "proper grounds", though the Judge does not expand on what those grounds might include. He clearly does not support the current practice in which funders can reserve the right to withdraw at any time subject to paying accrued obligations.
There need to be effective capital adequacy requirements for funders in order to protect claimants, bearing in mind that that the litigation being funded may last for a number of years.
The Judge also recommends that third party funders should be potentially liable for the full amount of adverse costs, subject to the judge's discretion. Their liability to the defendant should not (as at present) be restricted to the amount of funding they had provided to the claimant.
The Judge recommends a "menu" of disclosure options for large commercial claims and other claims where the costs of standard disclosure are likely to be disproportionate to the sums in issue or the value of the rights in issue. (Large personal injury and clinical negligence cases will however be specifically excluded as, the Judge notes, standard disclosure usually works satisfactorily in those cases).
Under the proposal, the court will select the order which is most appropriate to the case and standard disclosure will no longer be the starting point. A draft rule encapsulating the menu option was prepared by a disclosure working group (which included Herbert Smith partners Ted Greeno and Gary Milner-Moore) and subsequently revised by the Judge following various consultation meetings. He sets it out in full in the report and recommends that it is taken as the starting point for a new CPR rule, but comments that it cannot be finalised until the new e-disclosure practice direction has itself been finalised (it is due to be brought into effect in April).
The options in the "menu" range from dispensing with disclosure at one end of the spectrum to full scale Peruvian Guano (the train of enquiry test) at the other. Lord Justice Jackson specifically says that it is important in his view that the train of enquiry test be included as one of the options, as this level of disclosure is sometimes appropriate in fraud cases.
We support the introduction of the "menu" approach for large cases. This has the benefit of ensuring that the court and the parties focus at an early stage on the extent of the disclosure required, which is often key to controlling the costs of the disclosure exercise. It also allows the court the flexibility to set the appropriate level of disclosure in any particular case.
Lord Justice Jackson suggested in his preliminary report that disclosure assessors might be appointed in document heavy cases to assist the judge. Views were divided on this during the subsequent consultation. He quotes for example from the client survey Herbert Smith carried out for the purposes of our submissions to him where 59% were in favour.
The Judge does not in his final report recommend any formal rule change to provide for disclosure assessors but comments that it would be possible for parties to agree in any given case, subject to the approval of the court, to engage a disclosure assessor. If this takes place on a voluntary basis and proves to be effective in saving costs then consideration could be given to providing for this as an option in the rules.
Lord Justice Jackson also recommends that solicitors, barristers and judges alike be given appropriate training on how to conduct e-disclosure efficiently. He has already had meetings with the Judicial Studies Board, the Law Society and Bar Standards Board concerning this.
Witness statements and expert reports:
Lord Justice Jackson considers that witness statements can be unnecessarily lengthy, for example where a statement contains extensive argument (which is inadmissible in any event) or repeats / refers to documents without adding to what they say. He puts forward two proposals for "curbing litigants' over-enthusiasm for prolixity".
The first is case management – the court hearing argument at an early case management conference (CMC) about what matters need to be proved and then giving specific directions relating to witness statements, including possibly limiting their length. We do not consider that this proposal is likely to be effective. As the Judge himself comments, any CMC which goes into a case in this level of detail will be an expensive event and he does not recommend it as a matter of routine. He suggests that it be adopted in those cases where it would be cost effective, in particular in cases were the parties are proposing to spend excessive and disproportionate sums on the preparation of witness statements. We doubt it will generally be possible in advance to identify such cases. The Judge suggests it will be apparent from the costs estimates lodged which will indicate what sum will be spent on witness statements, but the problem usually emerges much later, once statements are served and the costs have already been incurred.
The second proposal is to apply costs sanctions against parties responsible for producing prolix or irrelevant statements. Whilst we agree with this we do not believe it is likely to provide much of a deterrent in practice.
The Judge discusses in the body of his report the potential usefulness of supplementary oral evidence and differing judicial approaches to allowing such evidence. He concludes that no rule change is required but that court guides might indicate an intention to use existing powers more actively. We agree this would be helpful. However, the starting point will remain that to be sure of evidence being admitted at trial, it needs to have been dealt with in the witness statement.
With regard to expert reports, there is power in the CPR to make an order limiting the recoverability of experts' fees and expenses from the opposing party, but it is seldom exercised in practice. Lord Justice Jackson recommends that CPR Part 35 be amended to require that a party seeking permission to adduce expert evidence provide an estimate of the costs of that evidence to the court. This might encourage judges to make more use of their powers in appropriate cases. He also recommends that judges be more willing to impose costs sanctions where prolix or irrelevant expert evidence has led to wastage of costs.
"Hot tubbing" (or as it is more formally known, concurrent expert evidence) met with a mixed response in the consultation period. The Judge suggests it should be piloted in cases where the experts, the lawyers and the judge consent. If the results are positive, consideration should be given to amending CPR Part 35 for appropriate cases.
Part 36 offers:
In a recommendation foreshadowed in his preliminary report, Lord Justice Jackson suggests that the effect of the decision in Carver v BAA plc [2008] EWCA Civ 412, [2009] 1 WLR 113 should be reversed. In the Carver case the claimant beat the defendant's Part 36 offer but only by a very small margin. The court held that it could not be said that the final outcome was "more advantageous" than accepting the offer made. The Judge comments that Carver introduces an unwelcome degree of uncertainty and tends to depress the level of settlements. We agree that this decision is unhelpful and should be reversed.
A new proposal in the final report is that where a defendant rejects a claimant's offer but fails to do better at trial, the claimant's damages should, unless there are good reasons not to, be enhanced by 10%. In the case of higher value claims however, say over £500,0000, the Judge notes that there may be a case for scaling down the uplift. With regard to non-monetary claims it is suggested that the judge should make a broad assessment of the value of any non-monetary relief awarded.
The reasons behind this proposal are to make a more level playing field as between claimants and defendants and to encourage settlement. In CFA cases, Lord Justice Jackson also suggests that the claimant's enhanced recovery, where a well-judged offer has been made, will compensate for his need to pay the success fee out of damages.
Case management:
The Judge makes a number of suggestions here but the key points in the context of commercial litigation are:
Cases should be assigned wherever possible to judges who have relevant expertise and so far as possible a case should remain with the same judge.
Case management conferences and pre-trial reviews should only take place where they will be used as occasions for effective case management and the judge should have proper time for pre-reading.
There is to be greater concentration on compliance with court orders and the entire timetable for the action, including the trial date or trial window, is to be drawn up as early as is practicable.
Two lords justices should be designated for issues concerning the interpretation or application of the CPR, and at least one of them should sit on any such appeals so far as possible in order to promote consistency. Until 2006 Lord Justice Brooke was usually a member of the court in any case where interpretation of the CPR arose but there has been no such judge since that time.
The Court of Appeal should support first instance judges who make robust but fair case management decisions.
We agree with these recommendations, in particular relating to judicial assignment and proper pre-reading time. We have consistently commented that we are in favour of case management but that it has to be informed case management. This requires a judge with the relevant expertise, sufficiently familiar with the issues, to make informed decisions.
Costs management:
Costs management entails the parties preparing and exchanging litigation budgets and the court approving such budgets. The budgets are far more detailed than the estimates currently required to be filed. There are two pilots of costs budgeting currently underway, a voluntary pilot in the Birmingham Mercantile Court and TCC (from 1 June 2009 until 31 May 2010) and a compulsory pilot in defamation proceedings in London and Manchester for 12 months commencing 1 October 2009.
The main arguments against costs management are that it generates additional costs and makes additional demands upon the limited resources of the court. Lord Justice Jackson believes however that it will save more costs than it generates and that costs management goes hand in hand with case management.
The Judge favours a gradualist approach. Training should be provided to lawyers and judges on costs management. Rules on how it would apply should be drafted, but not until the summer of 2010 once feedback from the pilots is available. Those rules will set out a standard costs management procedure which judges would have a discretion to adopt if they see fit, whether of their own motion or upon application by one of the parties. The rules would incorporate the concept of proportionality as well as reasonableness. At a later stage the question of making costs management mandatory in certain categories of litigation or certain courts should be re-considered in the light of experience.
The Judge accepts, however, that no case has been yet made out for introducing costs management into the Commercial Court.
He comments that when the rules for costs management are being drafted, it will also be necessary to amend the rules in respect of costs capping as although they are separate concepts there must be harmony between both sets of rules. In particular, in his view, the requirement for exceptional circumstances before the court will make a costs capping order (in 23A1 of the Practice Direction to Part 44) will have to be removed.
Alternative Dispute Resolution (ADR):
Lord Justice Jackson does not recommend any rule changes in relation to ADR. Instead he emphasises the need to better educate practitioners and the public about ADR. He recommends that an authoritative ADR handbook of equivalent status to the annual publications on civil procedure be prepared by a neutral body (ideally the Civil Justice Council). This would give details of all reputable mediation providers, although no formal accreditation scheme is recommended. The handbook should be used as the standard text for training and educating judges and lawyers. In tandem, a simple and clear brochure should be prepared to better educate the public and small businesses about ADR.
We endorse the call for further education, whilst recognising that ADR processes are flexible and developing and should not be curtailed. Accordingly, in our opinion, any handbook should not constitute a blueprint that limits the flexibility of ADR processes.
The Judge emphasises his view that, despite its many benefits, parties should never be compelled to mediate. We agree with this approach. In the commercial context the parties are well able to determine whether a mediation should take place and at what stage. Nonetheless the judiciary continue to have an important role to play in promoting mediation in appropriate cases, both within and even more importantly outside the commercial context, where litigants have less experience of ADR and may need guidance.
Pre-action protocols:
Lord Justice Jackson recommends that the existing 10 pre-action protocols for specific types of litigation be retained, subject to amendments in some cases, as by and large they perform a useful function. On the other hand he concludes, rightly in our view, that the general practice direction on pre-action conduct (which applies to all litigation unless a specific pre-action protocol applies) should be substantially repealed. He points out that it often leads to delays and to pre-action costs being incurred unnecessarily, particularly in large commercial claims, because of its "one size fits all" approach.
Instead there would simply be an obligation for there to be appropriate pre-action correspondence and exchange of information, with costs sanctions used to curb unreasonable behaviour. For example, a claimant who began proceedings without giving the defendant appropriate notice and an opportunity to respond would be at risk as to costs.
We welcome these recommendations. As the Judge observes, during the consultation exercise before the general protocol was introduced, the majority of consultees were opposed to it and both court users and the judiciary continue to believe it serves no useful purpose.
Class actions, Costs, Disclosure, Evidence, Funding, Part 36 offers, Pre-action Jackson reforms
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text:
UK signals it will suspend extradition treaty with Hong Kong
Foreign Secretary Dominic Raab is expected to make the announcement on the Hong Kong treaty when he addresses Parliament on Monday. The move is likely to stop short of sanctioning Chinese officials
Britain will on Monday announce plans to suspend or revoke its extradition treaty with Hong Kong, but will stop short of sanctioning Chinese officials, the South China Morning Post has learned.
The move will further exacerbate London's diplomatic stand-off with Beijing, as US Secretary of State Mike Pompeo begins his London visit to hammer out an Anglo-American strategy on China with Prime Minister Boris Johnson.
Foreign Secretary Dominic Raab is expected to make the announcement on the Hong Kong treaty when he addresses Parliament on Monday, after weeks of lobbying from lawmakers to suspend a legal instrument they fear could be used by Hong Kong for political persecution in future.
The Post was briefed about Raab's move by a source with knowledge of his thinking after the foreign secretary signalled that an imminent change to the extradition treaty could be under way.
"On Hong Kong, I'm going to go to the House of Commons tomorrow to make a further statement on the work we've been doing with our partners in government," Raab told Sky News.
"I've said that we'd review a whole range of other considerations," Raab said. "One of the things that we reviewed is our extradition arrangements, and I will be updating the House on the conclusion of that review, along with other things that we've been looking at, tomorrow."
Hong Kong student activist Nathan Law Kwun-chung, who has recently fled to London, said on Twitter, that the move would receive support in Parliament.
"Talked to many members of the parliament on this issue, and got very strong support on the idea of suspending the extradition treaty with Hong Kong," Law tweeted, adding: "Change is happening."
Talked to many members of the parliament on this issue, and got very strong support on the idea of suspending the extradition treaty with Hong Kong.
Change is happening.#HongKong https://t.co/88euAp3mgY
— Nathan Law 羅冠聰 😷 (@nathanlawkc) July 19, 2020
Iain Duncan Smith, ex-leader of the Conservative Party and co-founder of the Inter-Parliamentary Alliance on China, said: "If tomorrow the UK Foreign Secretary Dominic Raab decides to suspend the extradition treaty … this is the right thing to do in response to the Chinese government crackdown on people in Hong Kong."
But sources say Raab is unlikely to sanction any Chinese or Hong Kong officials, a step that China has repeatedly warned Britain not to take.
"If UK government goes that far to impose sanctions on any individual in China, China will certainly make a resolute response to it," Chinese ambassador to the UK, Liu Xiaoming, told BBC on Sunday.
"You've seen what happens in the United States, they sanction Chinese officials, we sanction their senators, their officials - I do not want to see this tit-for-tat happen in … China-UK relations," Liu added.
China's imposition of national security laws has been followed by rapidly worsening relations between Beijing and London. The UK has already agreed to let up to 3 million Hongkongers with British National (Overseas) passports to relocate there, with a path to British citizenship, citing Beijing's violation of the Sino-British Joint Declaration.
The UK will become the latest Five Eyes member to cut off fugitive-transfer arrangements with its former colony in the wake of Beijing's imposition of the new national security law.
Canada and Australia have suspended their treaties with Hong Kong, citing fear of political persecution. The US was preparing a similar move last week, while New Zealand was reassessing the legal instrument as part of a "deliberate, considered review" of its relations with Hong Kong.
According to the Mutual Legal Assistance in Criminal Matters (United Kingdom) Order, enacted in 2002, either Hong Kong or the UK may terminate the agreement at any time by giving notice to the other.
In that event, the agreement will cease to have effect on receipt of that notice. Requests for help which have been received before termination would still be processed in accordance with the terms of this agreement as if it was still in force.
The UK will also become the first European country to make the move, as the European Union has also been debating whether to nullify the extradition treaties between Hong Kong and Belgium, Czech Republic, Denmark, Finland, France, Germany, Ireland, Italy, the Netherlands, Poland, Portugal, Spain and Sweden.
#Boris Johnson
A fool isn't someone who is wrong, a fool is someone who is afraid of being wrong.


He caught 54 passes for 917 yards, a 17.0 average, and 13 touchdowns in 11 games (eight starts) last season despite dealing with a high ankle sprain during the second half of the season. Jennings sat out the Mountaineers' bowl game to rest his ankle and prepare for the draft.
Jennings returned punts his first two seasons, producing a modest 3.2 average on 34 returns. He also returned kickoffs his first two seasons, averaging 20.7 yards on seven returns.
Walterfootball.com rates Jennings as the 12th best receiver in the draft and a potential third- to fifth-round pick.
▪ The Dolphins are showing interest in Boston College guard Chris Lindstrom, whom ESPN"s Mel Kiper has going 21st to Seattle.
The Dolphins have met with him three times and sent three team officials (including offensive line coach Pat Flaherty) to work him out privately in the Boston area on March 18, the night before his Pro Day, according to a source.
Zierlein said: "Lindstrom is one of the most athletic interior lineman in the 2019 draft with a rare ability to match movement quickness with anyone across from him. His quickness can place him in position to make blocks on both the first and second levels and he has an impressive ability to cover lateral space and protect his gaps as a pass blocker. Lindstrom is scrappy at the point of attack but lacks the length, mass and strength some teams will want. His final destination could be as a guard/center in a zone scheme where he can become a long-time starter.
▪ NFL Network draft analyst Charles Davis, who's also Fox's No. 2 NFL game analyst, said from what he's hearing, he doesn't expect the Dolphins to take a quarterback at No . 13.
The Dolphins believe they can find their quarterback of the future in the 2020 draft but have been open-minded to drafting one in 2019 if the right one emerges.


text:
Cardi B performs in bathrobe after wardrobe malfunction
2019 Bonnaroo Music and Arts Festival – Day 4
Cardi B declared the show much go on as she performed in a bathrobe after suffering a wardrobe malfunction during a live show.
The rapper had taken to the stage in a long sleeved, multi-coloured sequinned body suit for the start of her set at the Bonnaroo music and arts festival in Tennessee, but had to resort to a white bathrobe after the skin tight ensemble split.
According to The Tennessean newspaper, she told the crowd: "I just wanna let y'all know that my outfit rip.
Cardi B in her original outfit (Amy Harris/Invision/AP)
"We gonna keep it moving, baby. We gonna keep it sexy. I don't know how in this f***ing robe, but we gonna do it!"
The performance comes after she cancelled and postponed a string of shows while recovering from cosmetic surgery.
Last week, she tweeted she has been working out consistently because she does not want to go under the knife again.
In May, the rapper was due to headline the 92Q Spring Bling Festival in Baltimore, Maryland but the event was pushed back to September 8.
She also cancelled an appearance in El Paso, Texas.


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