text:
\section{Introduction}

In a seminal work \cite{kuramoto75}, aiming to understand synchronization
phenomena, Kuramoto proposed a mathematical model of non-identical, nonlinear
phase-oscillators, mutually coupled via a common mean field.
Studying this system, he identified a synchronization transition to an
oscillating global mode when the coupling strength is larger than a
critical value, which is proportional to the range of the distribution
of the natural frequencies. Over the time, subsequent outcomes based on Kuramoto
propositions have shown that his approach can be used as a framework
to several natural and technological systems where an ordered behavior
(synchronization) emerges from the interactions of a large number of dynamical
agents
\cite{Acebron-etal-05,Strogatz2000}.
Furthermore, works have shown that the Kuramoto model can be exploited as a
building block to develop highly efficient strategies to process information
\cite{Follmann2014,Vassilieva2011}.

Recently, generalizations of the Kuramoto model toward interconnections
between the elements more complex than the mean field one, have received
considerable attention.
Indeed, in many real-world problems, each dynamical agent interacts with a subset of the whole ensemble \cite{Dorfler2013,Leonard2014,Sadilek2014}, which can better described using a network topology. A variety of studies have analyzed the onset of the synchronization regime in this context. For a general class of linearly coupled identical oscillators, the Master Stability Function, originally proposed by Pecora and Carrol~\cite{Pecora1998}, allows one to determine an interval of coupling strength values that yields complete synchronization, as a function of the eigenvalues of Laplacian matrix of the coupling graph. For networks of oscillators with non-identical natural frequencies, Jadbabaie et al. \cite{Jad04} were able to give similar bounds for the coupling strength of the Kuramoto model without the assumption of infinitely many phase-oscillators.
Among related works, Ref. \cite{Franci2010} deals with a model whose natural frequency oscillators change with time, even when they are isolated. Ref. \cite{Papachristodoulou2010} explores the effects of delay in the communication between oscillators. Besides, Ref. \cite{Pecora2013} builds a bridge between graph symmetry and cluster synchronization.

Taking into consideration all of these previous results, one can roughly state
that the Kuramoto transition to synchronization always happens if the coupling between
oscillators is attractive; while, when it changes to be repulsive, this
synchronization state is absent ~\cite{Petar2014,Tsimring2005}. However,
the structure of the coupling can nontrivially depend on the level of synchrony itself.
Such a dependence, called nonlinear coupling scheme, has been explored in
recent theoretical~\cite{Filatrella-Pedersen-Wiesenfeld-07,Rosenblum-Pikovsky-07,pik2009,Baibolatov2009}
and experimental~\cite{Temirbayev_etal-12,Temirbayev_etal-13} studies dealing with
setup of global coupling. The main effect here is the partial synchrony,
which establishes at moderate coupling strengths, where the coupling is
balanced between the attractive and repulsive one.

Here, we consider the effects of the non-linear
coupling on a network:  a set of
identical oscillators, which communicate via a connected simple coupling graph.
each element is forced by a (local) mean field, which
encompasses the oscillators that are connected to it.
The coupling function is tailored so that its influence is attractive, if the
local acting field is small, or repulsive, otherwise.
This coupling strategy implies that only nodes with a large enough number
of connections may become repulsive. Thus, the hubs play a key role for the
ensemble dynamics.
A non-linear coupling parameter in the system tunes the critical quantity of
connections and how cohesive this mean field must be in order to allow this
transition.
So, our approach can be considered as a dynamical generalization of the
inhomogeneous populations of oscillators
consisting of  \textit{conformists} and
\textit{contrarians}~\cite{Hong-Strogatz-11}.
However, the type of oscillator's depends on the
force acting on it.

Overall dynamics in the model can be qualitatively understood as follows:
Let us assume initially
that all the  mean fields are small. Then, there are only attractive
interactions (\textit{conformists}) in the system. So, in a first moment, they
start to mutually adjust their phases.
Above a threshold, the most connected oscillators start to feel a repulsive
effect that drives them away from the synchronous state.
In other words, if an oscillator has a sufficiently large number of neighbors
and if it suffers enough cohesive pressure from them, instead of attractiveness,
it becomes a
\textit{contrarian}, wishing to be in anti-phase with the force.
Then, due to the
repulsiveness of some nodes, other mean fields may also become smaller.
Finally, this tendency can shift nodes to attractiveness again. As a
consequence,
an intermediate configuration may emerge due to the balance these conflicting
tendencies in the system.

Depending on the non-linear coupling parameter, we report a variety of
qualitative dynamic behaviors. In general, for small values of the non-linear
coupling parameter, we observed full synchronization and phase-locked states.
When this parameter is increased, multistability, periodic and chaotic dynamics
take place.

The paper is organized as follows.
Initially, we discuss the basic details of the model in section~\ref{sModel}.
In
section~\ref{sFull}, the analytical result about the stability of full
synchronization is presented.
Numerical experiments in section~\ref{sOthers} illustrate different possible
regimes that the present model can display. Finally, in
section~\ref{sCorrelation}, we perform a numerical exploration to address the
correlation of stationary phase locking states with partial synchronization
with the network parameters, by exploring different network topologies and
sizes.

\section{Model of oscillator network with nonlinear coupling} \label{sModel}

Let us consider a system of $N$ identical phase-oscillators represented by
$(\theta_1, \ldots, \theta_N) \in \TT^N$
coupled through a simple and connected undirected graph $A$.
The dynamics for the $i$-th oscillator is given by the
following ordinary differential equation
\begin{equation} \label{e1}
\dot \theta_i =
\C{1 - \eps Z_i^2}
   \Sum_{j \in \mathcal{N}_i}
  \sin \C{\theta_j - \theta_i },
\end{equation}
where $\mathcal{N}_i$ denotes the set of neighbors of $i$ in the coupling graph
$A$.
Equations~\refeq{e1} are formulated in the reference frame rotating with the
common
frequency of the oscillators, so that the latter one does not appear in the
equations. The time is
normalized by the linear coupling strength.
The main feature of our model \refeq{e1} is the \emph{nonlinear coupling
parameter},
$\eps \ge 0$, which modifies the coupling at each node, with $\eps=0$ a
standard
setup of the Kuramoto model on a network is recovered. This parameter enters as
a
coefficient at the square of \emph{the norm of the local order parameter}:
\begin{equation}\label{eZi}
Z_i := \abs{\sum_{j \in \mathcal{N}_i} \ee^{\ii \theta_i}}.
\end{equation}
which measures the magnitude of the force acting on oscillator with index $i$.
On the other hand, we represent the \emph{(global) order parameter} by
\begin{equation}\label{eR}
R \ee^{\ii \psi} = \Frac{1}{N}  \sum_{i = 1}^N \ee^{\ii \theta_i},
\end{equation}
where $R \in \C[1]{0,1}$ is its norm and $\psi \in \C[01]{0,2\pi}$ is its
phase.

We stress that $Z_i$ is not normalized (in the sense that there is no division
by
the number of the terms in the summation, like in $R$), as
it measures the total action of the neighbors on the $i$-th oscillator, which is
called \emph{local mean field}.  Simple calculations
show that
$Z_i^2 \in \C[1]{0,d_i^2}$, where $d_i$ denotes the degree of the $i$-th vertex,
that is, the number of incoming or outgoing connection, since the graph is
undirected. Thus, a necessary condition for a node
to suffer repulsive coupling, i.e. $\C{1 - \eps  Z_i}^2 < 0$, is that $\eps >
d_i^{-2}$.

The introduced order parameters $R$ and $Z_i, \ldots, Z_n$ are maximal in the case of full synchronization $\theta_1 = \ldots = \theta_N$, whiles they decrease when oscillators begin to move apart from each other.

If  $\eps  Z_{max}^2 < 1$, where $Z_{\max}^2 := \max \C[2]{Z_1^2, \ldots,
Z_N^2}$,
then all oscillator will attract each other  so that the full synchronization is
established. Next, if
$Z_{max}^2$ becomes larger than
$(\eps)^{-1}$, the corresponding oscillator begins to be repulsive related to
its
local mean field, and the full synchronization  breaks. As a result, $Z_{max}^2$
may decrease
and switch again the node to be attractive. Depending on the coupling graph $A$,
on the initial conditions
$\C{\theta_1^0, \ldots,\theta_1^N}$, and on the intensity of the nonlinear
coupling parameter $\eps$, numerical simulation reveals that model \refeq{e1}
can exhibit different qualitative behaviors.

If the largest degree in the coupling graph
satisfies $\eps < d_{\max}^{-2}$,
with $d_{\max} := \max \C[2]{d_1, \ldots, d_N}$, then no node can be repulsive.
We demonstrate
in the next section via the Lyapunov analyses, that in fact this condition
guarantees that the full synchronized state is stable.

\section{Stability of full synchronization} \label{sFull}

The basic steps to obtain the results in this section follow the main ideas from
\cite{Jad04}. We begin presenting some preliminary concepts, including
elements of the graph theory needed, and a generalized norm of the order
parameter to define our Lyapunov function.

Let $B$ be the \emph{directed incidence matrix} of a graph $A$. Thus, $B$ is a
matrix with $N$ rows and $E$ columns, where $E$ is the number of \emph{directed
edges} of the matrix. The number of \emph{undirected edges}, \ie ignoring the
direction, equals is $E/2$. The columns of $B$ represent the edges of the graph:
if the $k$-th arrow (directed edge) of the graph goes from $i$ to $j$, then the
$k$-th column of $B$ is zero, except at positions $i$ and $j$, where  $B_{ik} =
1$ and $B_{jk} = -1$.
Regarding the dynamics of the system, an arrow from
node $i$ to node $j$ in the graph means that node $i$ influences node $j$.
Although
the directed incidence matrix is generally defined for directed graphs, it must
be emphasized that only
undirected graphs are considered here. We abuse terminology and
identify a graph $A$ with its \emph{adjacency matrix}, which is an $N \times N$
matrix
where $A_{ii} = 0$; $A_{ij} = A_{ji} = 1$, if there is and edge between nodes
$i,j$;
and $A_{ij} = A_{ji} = 0$, otherwise. So, $E=\sum_{i,j=1}^N A_{ij}$.
Another common characterization of a graph is  its \emph{Laplacian matrix},
$L := \diag \C{d_1, \ldots, d_N} - A$. One can check that
$L = \nicefrac{1}{2} B B^{\top}$. A simple illustration of these concepts is
given at Fig. \ref{fig:grafoExemplo}.

\begin{figure}
\centering
\includegraphics[scale=1]{Fig1}
\footnotesize
\[
{
B_1 =
\C{ \hspace{-0.25cm}
\
\begin{array}{rrrrrrr}
1 & -1 & 0  & 0   \\
-1 & 1 & 1  & -1  \\
0 & 0 & -1  & 1
\end{array}
\hspace{-0.10cm}
}
\qquad
L_1 =
\C{ \hspace{-0.25cm}
\
\begin{array}{rrrrrrr}
1 & -1 & 0  \\
-1 & 2 & -1 \\
0 & -1  &  1
\end{array}
\hspace{-0.10cm}
}
}
\]
\caption{Example of graph with $N=3$ and $E=4$, its directed incidence matrix
$B_1$ and its Laplacian matrix $L_1$.}
\label{fig:grafoExemplo}
\end{figure}
The usage of the directed incidence matrix allows us to rewrite model \refeq{e1}
in a vector form as follows:
\begin{equation} \label{e1alt}
\dot \theta
=-\Frac{1}{2}
 \diag \C{ 1_{N} - \eps Z^2 }
B \sin \C{B^\top \theta},
\end{equation}
where $Z^2 := \C{Z_1^2, \ldots, Z_N^2}$, $1_N := \C{1, \dots, 1} \in \RR^N$ and
$\diag \C{.}$ stands for the matrix with the elements of a vector on the leading
diagonal, and $0$ elsewhere.

The square of the global order parameter can be expressed as
\[
R^2
= \Frac{1}{N^2}
\C{
N
+
2\Sum_{j<k} \cos \C{ \theta_j -\theta_k }
}.
\]
However, to build our Lyapunov function,
we define a \emph{generalized norm of  order} $r$ as

\begin{equation} \label{eGenr}
r^2  :=
1 - \Frac{E - 1_E^\top
\cos \C{B^\top \theta}  }{N^2}.
\end{equation}

Note that $R^2$ requires the sum of \emph{all} $\cos \C{\theta_j - \theta_k}$
with $j<k$ (for $j,k =1, \ldots, N$), but its generalization $r^2$ takes the
sum ($1_E^\top \cos \C{B^\top \theta}$) \emph{only} through the edges of the
graph.
In the case of full coupling graph, direct substitution yields that both global
and generalized norm of the order
parameter have the same expression .

For any connected symmetrical coupling graph, one can check that the maximum of
$r^2$ is the unit, and that $R^2=1$  if and only if this value is
achieved~\footnote{On the other hand, the minimum  value of $r^2$
does not necessarily correspond to $R^2=0$.}.

Let
\begin{equation}\label{eU1}
U \C{\theta} = 1 - r^2
\end{equation}
be a candidate Lyapunov function. It is clear that the minimum value of
$U \C{\theta} = 0$ corresponds to the maximum value of $r^2 = 1$, which is
equivalent to the fully synchronized state.

In fact, algebraic manipulations reveal that
\begin{equation} \label{eU1alt}
U \C{\theta} = \frac{2}{N^2} \norm{ \sin
\C{ \frac{ B^{\top} \theta }{2}  }
}^2,
\end{equation}
and that the differential of $U$ is given by
\begin{equation} \label{eDU1}
\D U =
\Frac{1}{N^2} \C{ B \sin \C{B^\top \theta}}^\top.
\end{equation}

As a result, we synthesize  in the next theorem the previous intuitively stated
idea that if $\eps$ is
small enough then full synchronization is a robust phenomenon related to small
perturbations over initial conditions.

\begin{theorem} \label{teo1} In Model \refeq{e1}, if
$\eps$ is smaller than a critical value $\eps_c :=
\nicefrac{1}{d_{\tiny{\mbox{max}}}^2}$,
 then the
synchronized stated ($R=1$) is Lyapunov stable.
\end{theorem}

\begin{proof} Consider the potential field $U \C{\theta}$ defined in
\refeq{eU1}. So,
using the vector form of the model \refeq{e1alt} and the expression of the
differential
$\D U$ from \refeq{eDU1}, we have that
$\dd*{ U \C{\theta \C{t}} }$ equals to
\[
 -\Frac{1}{2 N^2} \C{\sin \C{B^\top \theta} }^{\top} B^{\top}
 \diag \C{ 1_{N} - \eps Z^2 }
B \sin \C{B^\top \theta},
\]
If we set $x := B \sin \C{B^\top \theta}$,  then we have that
$x^\top \diag \C{ 1_{N} - \eps Z^2 } x$ is larger or equal than $\C{1 - \eps
d^2_{\max}}
 \norm{x}^2$. Moreover, we can also define a lower bound for $\norm{x}^2$, since
$\norm{x}^2 = \sin \C{B^\top \theta}^\top B^\top B \sin \C{B^\top \theta} \ge
 \lambda_2 \C{  B^\top B} \norm{\sin \C{B^\top \theta}}^2
 = 2
 \lambda_2 \C{L} \norm{\sin \C{B^\top \theta}}^2$; where  $\lambda_2 \C{L}$ is
the algebraic connectivity of the graph. In the last inequality we used that
$\nicefrac{1}{2} B B^\top = L$ and that both matrices $B B^\top$ and $B^\top B$
have the same
non-trivial eigenvalues $0 \le \lambda_2 \C{L} < \ldots < \lambda_N \C{L}$,
where $\lambda_2
\C{L}$ is strictly larger than zero because the coupling graph $A$ is connected
\cite{Godsil01}.
Therefore,
\[
\dd*{ U \C{\theta \C{t}} } \le -\Frac{1}{N^2}
\lambda_2 \C{L}
\C{1 - \eps d^2_{\max}}
\norm{\sin \C{B^\top \theta}}^2
\]
As a result,
$\eps < \eps_c :=  \nicefrac{1}{d_{\tiny{\mbox{max}}}^2}$ implies that
$\dd*{ U \C{\theta \C{t}} } \le 0$, then the fully synchronized state $R=1$ is
stable.
\end{proof}

\section{Dynamics of partially synchronous states} \label{sOthers}
In this section numerical simulations are performed to illustrate the rich
repertoire of behaviors that model \refeq{e1} may exhibit, specially beyond the
threshold $\eps > \eps_c$, where Theorem \ref{teo1} cannot be applied.

\subsection{Quantification of dynamical regimes} \label{sMetrics}

The numerical integration scheme applied is a forth order
Adams-Bashforth-Moulton Method (see \cite{burden}) with discretization time step
 $h=0.01$.
We calculate the \emph{partial synchronization metric} \textsl{s} from
Ref.~\cite{Gardenes}, which, for every two oscillators $i,j$ in the network,
takes values $s_{ij} \C{I} \in \C[1]{0,1}$, indicating how much the
\emph{mean phase difference} between $\theta_i$ and $\theta_j$ varies in the
time interval $I := \C[1]{t_1,t_2}$, with $t_1 < t_2$. This metric is defined as
\[
s_{ij} \C{I}
\doteq
\norm{
      \Frac{1}{t_2 - t_1}
      \Int[t_1][t_2]{
      \ee^{\ii \C[0]{\theta_i \C{t} - \theta_j \C{t}}}
      }{t}
      }.
\]
One can  check that if  $\theta_i \C{t} \equiv \theta_j \C{t} + \eta$ for some
constant $\eta$, then the exponent in the previous integral is constant and
$s_{ij} \C{I}  = 1$.
Nevertheless, if $ \theta_i \C{t} - \theta_j \C{t} \modulo 2\pi$ assumes every
possible value
over the unit circumference with not clear trend, then $s_{ij} \C{I}$ is close
to zero.
Now, we average contributions of all neighbor oscillators $i,j$ under a graph
$A$ with $N$ nodes to write
\[
	s \C{I} \doteq \Frac{1}{E}
	\Sum_{i,j=1}^N A_{ij} s_{ij} \C{I},
\]
where $E$ is the quantity of undirected edges in the graph.

To exclude transients and to detect the statistically stationary state, we
adopted
the following procedure. For all experiments the time interval $\C[1]{0, 2 .
10^3}$
is always considered as transient time. Then, the numerical integration is
performed
in the subsequent intervals $I_k := \C[1]{(k-1), k }10^3$, with $k \ge 3$,
until
the first $ \tilde k = k$ such that
$\abs{ s \C{I_{\tilde k-1}} - s  \C{I_{\tilde  k}} } < 0.01$, or $\tilde k=10$
is achieved.
Only such a time interval $I_{\tilde {k}}$ is regarded as non-transient.
For the subsequent analysis, we use values of the phases $\theta \C{t}$ in the
stationary time interval regime $I_{\tilde {k}}$ (whose beginning is shifted to
$t=0$
without loss of generality) at points
 $t \in \tilde I := \C[2]{i h, i \in \C[2]{0,1, \ldots, 10^5-1,10^5}}$.

\subsection{Examples of complex behaviors} \label{sExamples}

As it was claimed before, in dependence on the network structure, very
different types of the dynamics are possible. In order to give impression on it,
we present simulations of
model \refeq{e1} with two different coupling graphs displayed as
inserts in Fig. \ref{fig:1}. Both networks have $N=10$ nodes
and they differ only by the rewiring of a single edge. We performed simulations
for
$10$ random initial conditions
chosen with uniform distribution over $\C[1]{0,2\pi}$ for each experiment. For
all these initial conditions $l = 1, \ldots, 10$, the norm of the order
parameter
$R^l \C{t}$, according to \refeq{eR}, is computed from the time series.
As explained in the previous section, in these calculations a transient time is
eliminated
and that a statistically
stationary regime $\tilde I$ of $10^3$ units of time and $\#\tilde I := 10^5 +
1$
points is considered. Then, also for each distinct initial condition, the
maximum, average and minimum values of the associated norm of the order
parameter are
computed, respectively denoted by
$
R^l_{\max} : = \max_{t \in \tilde I}  R^l\C{t}
$;
$
\C[<]{R^l} : = \C{\#\tilde I}^{-1} \sum_{t \in \tilde I} R^l\C{t}
$; and
$
R^l_{\min} : = \min_{t \in \tilde I}  R^l\C{t}
$. Of course, $R^l\C{t}$ converges to a constant
if and only if  $R^l_{\max} = \C[<]{R^l} = R^l_{\min}$.
Now, having different simulations for a
fixed coupling graph, we evaluated the maximum, average and minimum value
of the \emph{average} value of the norm of the order parameters over this
ensemble,
respectively denoted by
$
\max \C[2]{ \C[<]{R} }: =
\max_{l =1, \ldots, 10} \C[<]{R^l}
$;
$
\mbox{mean} \C[2]{ \C[<]{R}} : = \C{10}^{-1} \sum_{l=1, \ldots, 10} \C[<]{R^l}
$; and
$
\min \C[2]{ \C[<]{R} } : =
\min_{l =1, \ldots, 10} \C[<]{R^l}
$. So, if the norm of the order parameter converges to the same value for
\emph{all} initial
conditions simulated, then
$\max \C[2]{ \C[<]{R}} =\mbox{mean} \C[2]{ \C[<]{R}} = \min \C[2]{ \C[<]{R} }$.
For the cases where the norm of the order parameter does not converge over all
initial
conditions, it will be useful to examine the  \emph{overall maximum} and
\emph{overall minimum}
values of the norm of the order parameter,
 respectively denoted by
$
\max \C[2]{ R_{\max} }: =
\max_{l =1, \ldots, 10} R^l_{\max}
$;
and
$
\min \C[2]{ R_{\min} }: =
\min_{l =1, \ldots, 10} R^l_{\min}
$. Thus, if there is no fixed phase synchronization for all the initial
conditions
simulated, but the norm of the order parameter presents only small deviations
around a common
value, then the gap between $\max \C[2]{ R_{\max} }$ and  $\min \C[2]{ R_{\min}
}$ is also small.
Also notice that
$\min \C[2]{ R_{\min} } \le \min \C[2]{ \C[<]{R} } \le \mbox{mean}
\C[2]{ \C[<]{R}} \le \max \C[2]{ \C[<]{R} } \le \max \C[2]{ R_{\max} }$, since
$R^l_{\min}
\le \C[<]{R^l} \le R^l_{\max}$ for all initial conditions.
Finally, the maximum Lyapunov exponent $\lambda^l_{\max}$ for each initial
condition is also
computed, according to the algorithm in \cite{alligood1997chaos}.
The maximum Lyapunov exponent over all the chosen initial conditions
$\lambda^l_{\max}:= \max_{l =1, \ldots, 10}  \lambda^l_{\max}$ is also analyzed.

\begin{figure}
\centering
\includegraphics[scale=1]{Fig2}
\caption{Numerical results for Model \refeq{e1} as a function of $\eps$, for the
coupling
graphs despited as insect, including 10 random initial conditions.
A black line corresponds to  $\mbox{mean} \C[2]{\C[<]{R}}$, while the interval
between
$\min \C[2]{\C[<]{R}}$ and $\max \C[2]{\C[<]{R}}$ is shown as a gray strip.
The gap between $\min \C[2]{R_{\min}}$ and  $\max \C[2]{ R_{\max}}$ is shown as
an orange strip.
Since the orange strip is by construction larger or equal than the gray one, the
first one is
not displayed in the figure when they coincide.
Left vertical axes show values related to norm of the order parameter, while
the
right ones represents the maximum Lyapunov exponent $\lambda_{\max}$, shown as a
red dashed line.
Letters in green vertical lines from the upper experiment correspond to
subfigures in Fig. \ref{fig:2}.
}
\label{fig:1}
\end{figure}

\begin{figure}
\centering
\includegraphics[scale=1]{Fig3}
\caption{Evolution of $R\C{t}$ for different values of $\eps$ indicated in
green
at the upper experiment from Fig. \ref{fig:1}. Every color represents a
different
initial condition, while pairs of solid/dashed lines with the same color
correspond
to solutions whose initial conditions differ not more than  $10^{-4}$ at each
coordinate. (a) $\eps=0.04$: full synchronization;
(b) $\eps=0.08$: fixed phase synchronization;
(c,d,e) $\eps=0.15,0.28,0.35$ respect.: examples of multi stability;
(f) $\eps=0.70$: example with $\lambda_{\max}>0$.
}
\label{fig:2}
\end{figure}

We now describe different regimes observed in the networks, using also
 Fig. \ref{fig:2}, where we depict time series of $R\C{ \theta \C{t}}$ for some
particular choices of $\eps$,
indicated as green letters in the upper  panel from Fig. \ref{fig:1} (this is
the case we choose for illustrating
different regimes).
Notice that $d_{\max}=4$ in both cases, so Theorem \ref{teo1} guarantees
that for $\eps < \eps_c = 1/4^2 = 0.0625$ the full synchronization state, $R \ra
1$,
is locally stable as illustrated in Fig. \ref{fig:2} (a) (with $\eps=0.04$).

Panel (a) in Fig.~\ref{fig:2} illustrates full synchronization in the network
for $\eps < \eps_c$.
For $\eps$ slightly bigger than $\eps_c$, simulations suggest that a stationary
regime
of partial phase synchronization, where
$R \ra c < 1$, is locally stable as shown in Fig.~\ref{fig:2}(b) ($\eps=0.08$).
Details of this state are clear from Fig.~\ref{fig:detailB}. There we show the
that the synchronization between
the individual oscillators is complete if measured by quantity $s_{ij}$, and all
the oscillators have
the same frequency. However,  the oscillators are split into two groups with a
constant phase shift
between them; this division originates
in the edge which connects the two largest hubs in the network (vertexes $1,8$).

\begin{figure}
\centering
\includegraphics[scale=1]{Fig4}
\caption{Example of group formation.
Details of one of the trajectories from Fig.
\ref{fig:2} (b) $\eps=0.08$. On the left side,
the coupling graph with $s\C{i,j}$ in its edges is shown. On the right side, a
histogram of $\theta_i - \psi$ is presented with color code representing the
normalized frequency.
}
\label{fig:detailB}
\end{figure}

For larger values of $\eps$, the regimes are still static but with
multistability.
For instance, at $\eps=0.15$  (see Fig. \ref{fig:2} (c))
two stable configurations emerge with $R \ra c$, with $c \approx 0.471$ (black)
or $c \approx 0.511$ (blue),
depending on the initial condition. Fig.~\ref{fig:detailC}, which is analogous
to Fig.~\ref{fig:detailB},
 shows the
existence of three subgroups, whose members may vary according to the initial
condition.

\begin{figure}
\centering
\includegraphics[scale=1]{Fig5}
\caption{Example multi-stability with group formation.
Details of two trajectories from Fig.
\ref{fig:2} (c) $\eps=0.15$,  the left picture corresponds to the solid black
line and
the right one to the solid blue.
Histograms of $\theta_i - \psi$ are presented with color code representing the
normalized frequency.}
\label{fig:detailC}
\end{figure}

Other types of multistabilities appear for instance at $\eps=0.28$ and
$\eps=0.35$,
as illustrate in Figs. \ref{fig:2} (d,e). For $\eps=0.28$ (panel d) some initial conditions
do no converge to a fixed phase synchronization, but to a regime where the order
parameter
$R$ is periodic in time.
For $\eps=0.35$ (panel c), the norm of the order parameter of all trajectories
simulated becomes periodic.
Fig. \ref{fig:detailD} provides an illustration of this regime.

\begin{figure}
\centering
\includegraphics[scale=1]{Fig6}
\caption{Example of periodic norm of the order parameter.
Details of one of the trajectories from Fig.
\ref{fig:2} (d) $\eps=0.28$. On the left side,
the coupling graph with $s\C{i,j}$ in its edges is shown. On the right side, a
histogram of $\theta_i - \psi$ is presented with color code representing the
normalized frequency. We denote by $\psi \C{t}$ the argument of the order
parameter. The bottom picture shows that the curve $\C{  \sin \C{\theta_1 \C{t}
- \psi \C{t}}, \sin \C{\theta_9 \C{t} - \psi \C{t}}}$ is closed.
}
\label{fig:detailD}
\end{figure}

Finally, for $\eps=0.70$ (Fig. \ref{fig:2} (f)), one observes a chaotic state
with $\lambda_{\max} > 0$, the distribution of phases and frequencies is
illustrated
in Fig.~\ref{fig:detailF}.

If $\eps \in \C[1]{1,1.5}$, we also obtained multistability, with the
coexistence of solutions converging to phase-lock and irregular order parameter
after the transient, similar to Fig. \ref{fig:2}(d).

\begin{figure}
\centering
\includegraphics[scale=1]{Fig7}
\caption{Example of trajectory with $\lambda_{\max}>0$.
Details of one of the trajectories from Fig.
\ref{fig:2} (f) $\eps=0.70$. On the left side,
the coupling graph with $s\C{i,j}$ in its edges is shown. On the right side, a
histogram of $\theta_i - \psi$ is presented with color code representing the
normalized frequency.}
\label{fig:detailF}
\end{figure}

Now, we compare the results for two slightly different
networks depicted in panels (a) and (b) in Fig. \ref{fig:1}. The interval
of values of $\eps$ with fixed phase synchronization for all initial conditions
simulated is
very similar for both networks, namely $\eps_c<\eps\lesssim 0.25$;
also multistability of static partial synchronous regimes have been observed in both cases.

When $\eps \in \C[1]{1,1.5}$, contrary to case (a), we observed that the
solution for all initial conditions converged to the same phase-lock regime,
similar to Fig. \ref{fig:2} (b).

In conclusion of this section, in Fig. \ref{fig:OtherExperiments} we show
simulation results for
two other networks.  Panel (a) shows a random network with $N=10$ nodes and $20$
undirected
edges. Here predominantly static regimes are observed, only in small ranges of
coupling
constant chaos with a positive Lyapunov exponent appears. Static regimes,
however, demonstrate a
large degree of multistability.
In panel (b) we show a scale-free network with
$N=50$ nodes and $100$ undirected edges. Here static states are rare, typically
irregular regimes with low
values of the order parameter are observed.

\begin{figure}
\centering
\includegraphics[scale=1]{Fig8}
\caption{Numerical results for Model \refeq{e1} as a function of $\eps$, for the
coupling graphs depicted as insect, including 10 random initial conditions. The
legend of the pictures is the same as in Fig. \ref{fig:1}}.
\label{fig:OtherExperiments}
\end{figure}

\subsection{Dependence of partial synchronization regimes on network structure}
\label{sCorrelation}

We have seen that partially synchronous states can be rather different even
for similar networks. It is therefore difficult to make general predictions for
a relation between the network properties and the dynamical behaviors.
Here we attempt such a description, focusing on the property of abundance
of static regimes in comparison to time-dependent ones. For this purpose
we define the \emph{convergence index} $I_{c}$ as the ratio of values of $\eps
\in \C[1]{0, 1.5}$
such that $R$ converges to a constant value,
considering  all the $10$ random initial conditions. So, both
networks Fig.~\ref{fig:1} have similar values of the index:
$I_c \approx 0.530$
in case (a) while $I_c \approx 0.549$ in case (b). In contradistinction,
network shown in Fig.~\ref{fig:OtherExperiments}(a)  has very large value of the
index $I_c\approx 0.946$,
while that in Fig.~\ref{fig:OtherExperiments}(b) a rather low value $I_c\approx
0.064$.

In order to explore which features of the coupling graph are related with
$I_c$,
we performed numerical experiments with three sets of graphs, with $N=10,50,100$
nodes.
Each set consists in three common types of networks, each one with $10$ members,
generated as: (i)
random
(Erd\"{o}s-R\'{e}nyi) graphs with $2N$ edges;
(ii) scale-free graphs, also with $2N$; and (iii)
tree graphs ($N$ edges). The Barab\'{a}si-Albert
algorithm is applied for the last two types of networks (ii),(iii), with an
initial clique of $m_0$
nodes and with other nodes been connected to $m$ existing ones. For the
$2N$-edges scale-free
graphs, we fixed $m_0=5$ and $m=2$; while for the tree graphs ($N$ edges
scale-free graphs),
$m_0=m=1$. We point out that all graphs created are connected and symmetrical.
Additionally, three sets of $10$ initial conditions
$\theta_0 \in \RR^{N}$, with uniform distribution over $\C[1]{0,2\pi}$ and
$N=10,50,100$,
have been explored. So, for each of the $90$ coupling graphs we computed its
correspondent $I_c$ values by numerical integration of model~\refeq{e1} for
$\eps = 0,0.01,\ldots,1.49,1.50$.

In Table \ref{tab:meanIC}  we report the mean value and the standard
deviation of $I_c$ for each topology and size of coupling graph.
From these data we see that the mean value of $I_c$ increases if we go from tree
to
scale-free and to random graphs, respectively. However, these difference
becomes
less noticeable for larger values of $N$. Both the mean value and the standard
deviation
of $I_c$ decrease with larger networks.

\begin{table}[!ht]
  \begin{center}
		\begin{tabular}{|c |c|c| c|}
		\hline Network & $N=10$  &  $N=50$  &  $N=100$  \\
		\hline Tree & 0.421 (0.260) &  0.016 (0.006) &  0.008 (0.004) \\
		\hline Scale-free & 0.857 (0.029) & 0.050 (0.015)&  0.013
(0.003) \\
		\hline Random & 0.872 (0.090) &  0.183 (0.063)& 0.077  (0.022)
\\
		\hline
		\end{tabular}
    \caption{Mean value of $I_c$ and its standard deviation (in brackets)
for each network type and size simulated.}
    \label{tab:meanIC}
  \end{center}
\end{table}

We have explored different networks metrics, searching for one mostly correlated
with the convergence index $I_c$.
Let $0=\gamma_1 < \gamma_2 \le \ldots \gamma_N$ denote the Laplacian eigenvalues
of the coupling graph \cite{Godsil2001}. Recall that this graph is assumed to be
simple and connected.
We stress that these eigenvalues express fundamental characteristics of the
graph.
For instance, $\gamma_2$ is related with graph diameter and $\gamma_N$ with its
largest degree size.

We found that the quantity $\gamma^*$,
defined as the ratio between the maximum eigenvalue and the average of
the non-trivial eigenvalues of the Laplacian matrix of the graph, is rather
suitable for this purpose. Formally, it is defined as
\[
\gamma^* :=
\gamma_N
\C{
\frac{1}{N-1} \Sum_{k=2}^{N-1} \gamma_k
}^{-1}
.
\]

\begin{figure}
\centering
\includegraphics[scale=1]{Fig9}
\caption{Convergence index $I_c$ versus $\gamma^*$. Networks with $N=10,50,100$
nodes are represented as circles, squares and triangles, respectively. The two
experiments from Fig. \ref{fig:1} are shown as disks. We show in red an
exponential fit $f \C{x} = \ee^{1.7676 - 1.0894x}$ for the data.}
\label{fCorrelation}
\end{figure}

In Fig. \ref{fCorrelation} a correlation plot between $I_c$ and measure $\gamma^*$ for the correspondent graph is presented. From there, we observe a clear trend indicating that the greater the value of $\gamma^*$ is, the smaller is the value of $I_c$. Independently of the network type and size, static regimes of partial synchronization, full synchronization and phase-lock, are typical for values of $\gamma^*\lesssim 3$, like in the experiments from Fig. \ref{fig:1}. On the other hand, graphs with larger values of this measure yields more irregular dynamics, like time-dependent periodic and chaotic regimes, as the ones from Fig. \ref{fig:OtherExperiments}.

\section{Conclusion}

In this work we introduced and studied a Kuramoto-like model of identical oscillators with non-linear coupling. Our main parameter was $\eps$, which governs the coupling nonlinearity strength. It is clear that the most influence of nonlinearity in the coupling is on the hubs which experience strong forcing from many connected oscillators, while less connected nodes may still operate in a linear-coupling regime.

We proved that if this parameter is smaller than the inverse of the square of the maximum vertex degree in the network, then the full synchronized state is stable. Via numerical experiments, we showed that our model can display a variety of other qualitative behaviors of partial synchronization, like stationary phase locking, multistability, periodic order parameter variations, and chaotic regimes. We explored the relative abundance of stationary phase locking regimes under different network topologies. Statistical analysis performed suggests that tree graphs are much less likely to exhibit stationary phase locking in comparison with scale-free or random networks. In addition, this type of behavior becomes more rare if we increase network sizes, irrespective to the network topology. Finally, we also found a good correlation between the ration between the maximum eigenvalue and the average of the non-trivial eigenvalues of the Laplacian matrix of the graph, and the proportion of the repulsion parameter values which yield stationary phase locking. The greater this measure is, the smaller tend to be presence of stationary phase locking states in the system.

As a future research, we want to investigate analytical conditions and correlations involving other graph measures related to other forms of synchronization in the model.

\begin{acknowledgments}
We would like to thank the Coordena\c{c}\~ao de Aperfei\c{c}oamento
de Pessoal de N\'ivel Superior - CAPES (Process: BEX
10571/13-2) for financial support. AP V.V. thanks the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP, CNPq, and the grant/agreement 02.B.49.21.0003 of August 27, 2013 between the Russian Ministry of Education and Science and Lobachevsky State University of Nizhni Novgorod.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
Bob Arnot
Bob Arnot Explained
Bob Arnot should not be confused with Bob Arnott.
Dr. Bob Arnot, M.D. internal medicine, is a journalist, author, former host of the Dr. Danger reality TV series, and previously medical and foreign correspondent for NBC and CBS.
The Aztec Diet, Harper Collins The Best Medicine, Addison Wesley
The Breast Cancer Prevention Diet, Little Brown
Turning Back the Clock, Little Brown
Revolutionary Weight Control, Little Brown
The Prostate Cancer Prevention Plan, Little Brown
The Biology of Success, Little Brown
The Breast Health Cookbook, Little Brown
Beating Wear and Tear, Simon & Schuster
How to Prevent a Heart Attack, Simon & Schuster
Sport Selection with Charles Gaines, Viking
Your Survival, Hatherleigh
Foreign Correspondent NBC and MSNBC 2001 – 2004
Medical Correspondent Dateline NBC, Today, NBC Nightly News 1996-2000
Medical Correspondent CBS News: CBS Evening News, 48 Hours, CBS This Morning 1984-1996
Dr. Danger at IMDb
Columnist and Writer
Founder and Chairman Lifeline Iraq
Co-Founder American Working Group on Greater Syria
Past or present board member for:
UN High Commission for Refugees (USA)
US Committee for Refugees
Lindberg Foundation
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Bob Arnot".

redpajama_set_name: RedPajamaCommonCrawl


text:
Patient-reported outcomes in end-of-life research in pediatric oncology
Pamela S. Hinds*, Jennifer Brandon, Caitlin Allen, Nobuko Hijiya, Rachel Newsome, Javier R. Kane
Objective: The purpose of this review of published literature was to identify the number and focus of empirically based papers that included research methods used to directly solicit patient-reported outcomes (PRO) from pediatric oncology patients at end of life. Methods: Key terms including "pediatric or child and oncology or cancer and end of life or palliative or hospice or dying" were used with five data bases (PubMed, Ovid, Cochrane, PsycInfo & PsycArticles, and CINAHL) for English language literature published between January, 2001 and June, 2006. All retrieved documents were independently reviewed by a panel of six (nurses, physicians, and one psychologist) with backgrounds in pediatric oncology. Results: Thirty-five publications were identified but nine (25.7%) were eliminated from the analysis as they did not meet inclusion criteria. Of the remaining 26, four (15.4%) included patient-reported outcomes, six (23.1%) included parent only-reported outcomes, and five (19.2%) included staff only-reported outcomes. Nine (34.6%) were retrospective medical record reviews. Two (7.7%) included parent and record review data or parent and physician reports. Conclusions: Empirically-based end-of-life publications in pediatric oncology are relatively few in number and nearly 85% of completed studies do not include PRO.
Journal of pediatric psychology
https://doi.org/10.1093/jpepsy/jsm004
10.1093/jpepsy/jsm004
Fingerprint Dive into the research topics of 'Patient-reported outcomes in end-of-life research in pediatric oncology'. Together they form a unique fingerprint.
Patient Reported Outcome Measures Medicine & Life Sciences
Physicians Medicine & Life Sciences
Hospices Medicine & Life Sciences
Medical Records Medicine & Life Sciences
PubMed Medicine & Life Sciences
Language Medicine & Life Sciences
Hinds, P. S., Brandon, J., Allen, C., Hijiya, N., Newsome, R., & Kane, J. R. (2007). Patient-reported outcomes in end-of-life research in pediatric oncology. Journal of pediatric psychology, 32(9), 1079-1088. https://doi.org/10.1093/jpepsy/jsm004
Hinds, Pamela S. ; Brandon, Jennifer ; Allen, Caitlin ; Hijiya, Nobuko ; Newsome, Rachel ; Kane, Javier R. / Patient-reported outcomes in end-of-life research in pediatric oncology. In: Journal of pediatric psychology. 2007 ; Vol. 32, No. 9. pp. 1079-1088.
@article{3ed0a3409fd948949db5ad119a703b92,
title = "Patient-reported outcomes in end-of-life research in pediatric oncology",
abstract = "Objective: The purpose of this review of published literature was to identify the number and focus of empirically based papers that included research methods used to directly solicit patient-reported outcomes (PRO) from pediatric oncology patients at end of life. Methods: Key terms including {"}pediatric or child and oncology or cancer and end of life or palliative or hospice or dying{"} were used with five data bases (PubMed, Ovid, Cochrane, PsycInfo & PsycArticles, and CINAHL) for English language literature published between January, 2001 and June, 2006. All retrieved documents were independently reviewed by a panel of six (nurses, physicians, and one psychologist) with backgrounds in pediatric oncology. Results: Thirty-five publications were identified but nine (25.7%) were eliminated from the analysis as they did not meet inclusion criteria. Of the remaining 26, four (15.4%) included patient-reported outcomes, six (23.1%) included parent only-reported outcomes, and five (19.2%) included staff only-reported outcomes. Nine (34.6%) were retrospective medical record reviews. Two (7.7%) included parent and record review data or parent and physician reports. Conclusions: Empirically-based end-of-life publications in pediatric oncology are relatively few in number and nearly 85% of completed studies do not include PRO.",
keywords = "End of life, Literature review, Patient-reported outcomes, Pediatric oncology",
author = "Hinds, {Pamela S.} and Jennifer Brandon and Caitlin Allen and Nobuko Hijiya and Rachel Newsome and Kane, {Javier R.}",
doi = "10.1093/jpepsy/jsm004",
journal = "Journal of Pediatric Psychology",
Hinds, PS, Brandon, J, Allen, C, Hijiya, N, Newsome, R & Kane, JR 2007, 'Patient-reported outcomes in end-of-life research in pediatric oncology', Journal of pediatric psychology, vol. 32, no. 9, pp. 1079-1088. https://doi.org/10.1093/jpepsy/jsm004
Patient-reported outcomes in end-of-life research in pediatric oncology. / Hinds, Pamela S.; Brandon, Jennifer; Allen, Caitlin; Hijiya, Nobuko; Newsome, Rachel; Kane, Javier R.
In: Journal of pediatric psychology, Vol. 32, No. 9, 10.2007, p. 1079-1088.
T1 - Patient-reported outcomes in end-of-life research in pediatric oncology
AU - Hinds, Pamela S.
AU - Brandon, Jennifer
AU - Allen, Caitlin
AU - Hijiya, Nobuko
AU - Newsome, Rachel
AU - Kane, Javier R.
N2 - Objective: The purpose of this review of published literature was to identify the number and focus of empirically based papers that included research methods used to directly solicit patient-reported outcomes (PRO) from pediatric oncology patients at end of life. Methods: Key terms including "pediatric or child and oncology or cancer and end of life or palliative or hospice or dying" were used with five data bases (PubMed, Ovid, Cochrane, PsycInfo & PsycArticles, and CINAHL) for English language literature published between January, 2001 and June, 2006. All retrieved documents were independently reviewed by a panel of six (nurses, physicians, and one psychologist) with backgrounds in pediatric oncology. Results: Thirty-five publications were identified but nine (25.7%) were eliminated from the analysis as they did not meet inclusion criteria. Of the remaining 26, four (15.4%) included patient-reported outcomes, six (23.1%) included parent only-reported outcomes, and five (19.2%) included staff only-reported outcomes. Nine (34.6%) were retrospective medical record reviews. Two (7.7%) included parent and record review data or parent and physician reports. Conclusions: Empirically-based end-of-life publications in pediatric oncology are relatively few in number and nearly 85% of completed studies do not include PRO.
AB - Objective: The purpose of this review of published literature was to identify the number and focus of empirically based papers that included research methods used to directly solicit patient-reported outcomes (PRO) from pediatric oncology patients at end of life. Methods: Key terms including "pediatric or child and oncology or cancer and end of life or palliative or hospice or dying" were used with five data bases (PubMed, Ovid, Cochrane, PsycInfo & PsycArticles, and CINAHL) for English language literature published between January, 2001 and June, 2006. All retrieved documents were independently reviewed by a panel of six (nurses, physicians, and one psychologist) with backgrounds in pediatric oncology. Results: Thirty-five publications were identified but nine (25.7%) were eliminated from the analysis as they did not meet inclusion criteria. Of the remaining 26, four (15.4%) included patient-reported outcomes, six (23.1%) included parent only-reported outcomes, and five (19.2%) included staff only-reported outcomes. Nine (34.6%) were retrospective medical record reviews. Two (7.7%) included parent and record review data or parent and physician reports. Conclusions: Empirically-based end-of-life publications in pediatric oncology are relatively few in number and nearly 85% of completed studies do not include PRO.
KW - End of life
KW - Literature review
KW - Patient-reported outcomes
KW - Pediatric oncology
U2 - 10.1093/jpepsy/jsm004
DO - 10.1093/jpepsy/jsm004
JO - Journal of Pediatric Psychology
JF - Journal of Pediatric Psychology
Hinds PS, Brandon J, Allen C, Hijiya N, Newsome R, Kane JR. Patient-reported outcomes in end-of-life research in pediatric oncology. Journal of pediatric psychology. 2007 Oct;32(9):1079-1088. https://doi.org/10.1093/jpepsy/jsm004


Bow to the health and efficiency, quality and comfort of a series of protective products to participate in the protection of products, welcome to visit the guidance!
CMEH has been successfully held seventeen sessions, after years of development, has become one of the largest international medical equipment exhibition. The exhibition widely covers medical electronics and medical imaging equipment, wards and auxiliary equipment, medical supplies, sanitary materials, in vitro diagnostic reagents, optics, first aid, rehabilitation nursing and medical information technology products, direct and comprehensive services in the medical equipment industry from the source to the end of the whole medical industry chain. Each session from more than and 20 countries, more than 700 medical equipment manufacturing enterprises and more than more than and 20 countries and regions of the government procurement agencies, hospital buyers and distributors convergence CMEH transactions, exchange; as the exhibition area to expand, exhibitors increased and the number of viewers increased year by year, CMEH has been fixed respectively held in Shanghai, Beijing.
The eighteenth China (Shanghai) International Medical Devices Exhibition will be held on July 13, 2016 - 15 days in Shanghai World Expo exhibition hall was held, as the most largest and most influential medical field event, CMEH will integrate the resources to provide a can do export can do domestic trade exhibition platform for domestic and foreign manufacturers of medical devices, let domestic exhibitors more effective to develop international and domestic markets. The CMEH will be displayed in the 70 million people visited the Shanghai World Expo exhibition hall, the spirit of enterprise organizational units to develop new markets, enhance exchanges,Expand the sales service purposes, to promote medical industry market prosperity.


In this session, Emily will talk about how communities of practice and ongoing professional learning are essential to an organisation and to the people within it. She will talk you through her own experiences of building and supporting communities and give you some practical advice to get going on building your own.
Emily is an agile and lean coach with a passion for continuous learning and communities. She is the co-writer of the minimum viable book minimumviablebook.com, former Head of Agile Delivery at Government Digital Service (GDS), co-organiser of Agile on the Bench agileonthebench.co.uk and a classic scooter rider.


text:
D2 VOLLEYBALL SEMIS: Defending champ, No. 1 Grand Rapids Christian sweeps past No. 6 Kingsley, back into finals
By: MATTHEW B. MOWERY, November 22, 2019, 8:42 pm
BATTLE CREEK — For most of the season, the No. 1-ranked Grand Rapids Christian Eagles didn't feel like there was a target on their backs, dropping just nine sets all regular season, and none through their first four postseason matches.
It wasn't until No. 3-ranked Coopersville rocked them back on their heels with a lopsided first-set loss in the regional finals that they realized how much other teams were gunning for them.
"Actually, we played on a Thursday, and we had a meeting on Friday — we didn't practice, we just had a meeting — and they actually said that to me. They said that was a huge wake-up call. So I think since then, they've been playing pretty good volleyball," Eagles coach Tiffanie Gates said.
"I think drawing from that, and just realizing that we lost that first set to Coopersville, 25-12, and rebounded and came back and won. Just learning that you can still dig deep, and turn things around. That's our biggest thing. You cannot let those things affect you the rest of the match."
The Eagles haven't dropped a set since then, sweeping No. 4 Hamilton in quarters, and then following that up with a brisk sweep of No. 6-ranked Kingsley, 25-21, 25-14, 25-10.
Grand Rapids Christian (45-3) will face No. 2 Lake Odessa Lakewood (40-12) in the Division 2 championship match, Saturday's 4 p.m. nightcap. The Eagles eliminated Lakewood in last year's semifinals, then went on to beat Pontiac Notre Dame Pre for the program's first title. [For the full pairings, CLICK HERE.]
They haven't been looking at this as a title defense, though.
"We tried to kind of flip it, and say 'We're not defending, we're chasing.' What are we chasing? We're chasing a state championship with a new team. This is a new team, and we kind of had to figure new things out at the beginning of the season," Tiffanie Gates said. "We graduated a couple of important seniors last year. We really never talked about defending, we were always chasing. And I think that mindset helped get us here."
They didn't graduate Jordyn Gates, the Miss Volleyball finalist, who recorded 28 assists, and added a team-high 15 digs, orchestrating an offense that hit .429 and .406 in the last two sets and .378 for the match.
Addison VanderWeide had a match-high 19 kills, while Evelyn Doezema had 10. Lauren Peal had 11 digs and VanderWeide nine.
Brittany Bowman led Kingsley (58-8-3) with 12 kills and 14 digs, and had their 19-match win streak snapped with the loss. It was Kingsley's first appearance in the semifinals since winning the 2004 Class C title.
The Eagles' defense held the Stags to just .118 hitting for the match, and .014 in the final two sets.
"Obviously when you get to this point, you know you're going to face good teams, so we knew coming in we had to play our best defense, pass well, serve well, and I think they really executed that tonight," Tiffanie Gates said.
"I told them in the locker room before (the match), they made it through the hard part, this is just the fun part. This is just icing on the cake. I told them, 'You made it through the small gyms with the huge crowds, and the loud student sections, and now you just enjoy every moment, soak it up and enjoy it.'"


text:
Home>Coronavirus Updates
Burnout of healthcare providers during COVID-19
Physician burnout is not new, but the COVID-19 pandemic is accelerating the many negative repercussions of uncertainty and inadequate support.
Meredith Bradley, and Praveen Chahar, MD, FCARCSI | Jul 28, 2020
The following article originally appeared in full, including figures and data, on Cleveland Clinic Journal of Medicine July 2020 as part of its COVID-19 Curbside Consults series.
Physician burnout is not new, but the COVID-19 pandemic is accelerating the many negative repercussions of uncertainty and inadequate support, and the consequences are being felt by patients, physicians, and healthcare systems.
Physician burnout has serious consequences to the individual physician, to patients, and to healthcare institutions. Research has shown the prevalence of burnout to be more than 40%, with highest rates in frontline healthcare providers such as emergency medicine, primary care, and critical care. COVID-19 presents new stressors for healthcare providers, and recent events involving self-harm by physicians have brought increased attention to the emotional impacts of caring for these critically ill patients.
New stressors in COVID-19
Related: How to protect the wellbeing of healthcare staff in the COVID-19 crisis
COVID-19 presents multiple stressors to healthcare providers, including risk of infection, social isolation, and economic consequences. The practice of medicine has changed with COVID-19, with decreasing outpatient revenue, reductions in salary and benefits, and increased use of telemedicine, with its effect on the doctor-patient relationship.
A survey by the Society of Critical Care Medicine of nearly 9,500 critical care providers showed that median self-reported provider stress has increased from a score of 3 to a score of 8. Top stressors included lack of personal protective equipment, fear of contracting COVID-19, and fear of spreading the infection to family members. These work-related stressors have been associated with anxiety and depression, and they reflect real physical and emotional risks faced by frontline providers. In addition to these concerns, another recent survey also noted worries about being asked to care for patients more critically ill than they are trained for and about the limited availability of up-to-date information.
Related: 5-step guide to ensuring employee mental and physical wellness
Research out of China about mental health outcomes of healthcare workers treating COVID-19, although limited, indicates that nurses, women, and frontline healthcare workers experience the highest psychological burden and develop the most unfavorable mental health outcomes, including depression, anxiety, and insomnia.
Social and family support are vital pillars in promoting resilience and preventing burnout; however, COVID-19 poses challenges to both. Healthcare providers are hesitant to spend time with family members due to the risk of spreading infection to their loved ones, and many healthcare providers isolate themselves within their homes. Similarly, social distancing makes it more challenging to keep in touch with friends.
Many providers are experiencing increased demands at home, as the closing of schools and daycare centers has made finding childcare a major challenge, particularly when the healthcare provider is a single parents or when both parents are essential employees. In addition, childcare workers are hesitant to work in homes of healthcare workers due to fear of getting COVID-19.
COVID-19 is presenting economic challenges, with decreased revenue in hospitals and outpatient practices. Decreasing revenues are leading to reductions in salary, benefits, and vacation time to make up for lost revenue.
Signs of burnout
Burnout does not have a universal definition and is specifically job-related, as opposed to depression. Common signs of burnout are feelings of emotional exhaustion, cynicism, depersonalization, and low personal accomplishment. Maslach Burnout Inventory, the gold standard for measuring occupational burnout, is a 22-item questionnaire measuring three domains of burnout: emotional exhaustion, depersonalization, and low personal achievement. A high score on emotional exhaustion and depersonalization and a low score on personal accomplishment indicates burnout. And the response to even single statements such as "I feel burned out from my work" and "I've become more callous toward people since I started this job" have shown good correlation with emotional exhaustion and depersonalization.
Consequences of burnout
Physician burnout has negative consequences to the physician, patients, and the organization. It is associated with increased rates of medical error and decreased productivity, putting patients at risk and straining an already overstretched medical system. Perhaps most pressing now are the well-studied links between physician burnout and depression, alcohol abuse, and suicidal ideation. It is well documented that physicians take their own lives at rates much higher than the general public, and on average, 400 US physicians die by suicide each year. Drastically increasing stressors on healthcare providers both during work and outside of work without adequate approaches for how to combat these stressors will increase the rate of physician burnout.
How to prevent burnout during a pandemic
Preventing burnout relies on interventions at individual, team, and institutional levels. Research has shown benefits of mindfulness, stress-management training, exercise programs, and participation in small-group programs focusing on community, connectedness, and meaning in helping providers deal with burnout. Identifying signs of burnout in friends and colleagues and reaching out can be an important first step in getting them support.
Stressors, symptoms, and strategies to cope
Organizational strategies such as limiting physician hours, particularly in intensive care units, promoting a sense of community and core values, and engaging physicians in establishment of new protocols has been shown to prevent burnout. Ensuring availability of personal protective equipment and being open with staff about current resources can ease some of the anxiety that comes from uncertainty. Providing accurate and timely information about providing care to COVID-19 patients can promote standardization and encourage efficiency throughout the healthcare system.
There have also been team-based strategies adapted from those used in the military, where groups are routinely asked to work in high-stress environments. Having end-of-shift debriefing sessions normalizes talking about anxiety and grief and gives people tools to voice their experiences. Having "battle buddies," people paired with a partner to support and check in on one another, can provide support in a way that friends and loved ones who are not in healthcare may not be able to do.
The mental health impacts of COVID-19 on frontline healthcare workers are undeniable. While physician burnout is not new, the pandemic is rapidly accelerating the many negative repercussions of uncertainty and inadequate support, and the consequences are being felt by patients, physicians, and healthcare systems. However, this time of change is an opportunity for a cultural shift in how we perceive and manage physician mental health. Perhaps the tragic events involving self-harm in New York City can serve as a wake-up call to the emotional tolls of caring for COVID-19 patients and our responsibility to support ourselves and our colleagues.
Accelerated healthcare technology & trends in the age of COVID-19
This eBook brings you exclusive insight into what's driving the acceleration of healthcare technology, and what shape it will take, from industry leaders across the global healthcare community.
Blood management during the COVID-19 pandemic
Management of acute kidney injury in COVID-19


text:
package com.jetbrains.ther.run.configuration;

import com.intellij.execution.configuration.EnvironmentVariablesComponent;
import com.intellij.openapi.fileChooser.FileChooserDescriptorFactory;
import com.intellij.openapi.project.Project;
import com.intellij.openapi.ui.ComponentWithBrowseButton;
import com.intellij.openapi.ui.TextComponentAccessor;
import com.intellij.openapi.ui.TextFieldWithBrowseButton;
import com.intellij.openapi.util.io.FileUtil;
import com.intellij.openapi.vfs.VirtualFile;
import com.intellij.ui.RawCommandLineEditor;
import com.intellij.ui.components.JBLabel;
import com.jetbrains.ther.TheRFileType;
import org.jetbrains.annotations.NotNull;

import javax.swing.*;
import java.util.Map;

// TODO [run][test]
public class TheRRunConfigurationForm implements TheRRunConfigurationParams {

  private JPanel myRootPanel;

  private JBLabel myScriptPathLabel;
  private TextFieldWithBrowseButton myScriptPathField;

  private JBLabel myScriptArgsLabel;
  private RawCommandLineEditor myScriptArgsField;

  private JBLabel myWorkingDirectoryPathLabel;
  private TextFieldWithBrowseButton myWorkingDirectoryPathField;

  private EnvironmentVariablesComponent myEnvsComponent;

  public TheRRunConfigurationForm(@NotNull final Project project) {
    setupScriptPathField(project);
    setupScriptArgsField();
    setupWorkingDirectoryPathField(project);

    myScriptPathLabel.setAnchor(myEnvsComponent.getLabel());
    myScriptArgsLabel.setAnchor(myEnvsComponent.getLabel());
    myWorkingDirectoryPathLabel.setAnchor(myEnvsComponent.getLabel());
  }

  @NotNull
  public JComponent getPanel() {
    return myRootPanel;
  }

  @NotNull
  @Override
  public String getScriptPath() {
    return getPath(myScriptPathField);
  }

  @Override
  public void setScriptPath(@NotNull final String scriptPath) {
    setPath(myScriptPathField, scriptPath);
  }

  @NotNull
  @Override
  public String getScriptArgs() {
    return myScriptArgsField.getText().trim();
  }

  @Override
  public void setScriptArgs(@NotNull final String scriptArgs) {
    myScriptArgsField.setText(scriptArgs);
  }

  @NotNull
  @Override
  public String getWorkingDirectoryPath() {
    return getPath(myWorkingDirectoryPathField);
  }

  @Override
  public void setWorkingDirectoryPath(@NotNull final String workingDirectoryPath) {
    setPath(myWorkingDirectoryPathField, workingDirectoryPath);
  }

  @Override
  public boolean isPassParentEnvs() {
    return myEnvsComponent.isPassParentEnvs();
  }

  @Override
  public void setPassParentEnvs(final boolean passParentEnvs) {
    myEnvsComponent.setPassParentEnvs(passParentEnvs);
  }

  @NotNull
  @Override
  public Map<String, String> getEnvs() {
    return myEnvsComponent.getEnvs();
  }

  @Override
  public void setEnvs(@NotNull final Map<String, String> envs) {
    myEnvsComponent.setEnvs(envs);
  }

  private void setupScriptPathField(@NotNull final Project project) {
    final ComponentWithBrowseButton.BrowseFolderActionListener<JTextField> listener =
      new ComponentWithBrowseButton.BrowseFolderActionListener<JTextField>(
        "Select Script",
        "",
        myScriptPathField,
        project,
        FileChooserDescriptorFactory.createSingleFileDescriptor(TheRFileType.INSTANCE),
        TextComponentAccessor.TEXT_FIELD_WHOLE_TEXT
      ) {
        @Override
        protected void onFileChosen(@NotNull final VirtualFile chosenFile) {
          super.onFileChosen(chosenFile);

          TheRRunConfigurationUtils.setSuggestedWorkingDirectoryPathIfNotSpecified(TheRRunConfigurationForm.this);
        }
      };

    myScriptPathField.addActionListener(listener);
  }

  private void setupScriptArgsField() {
    myScriptArgsField.setDialogCaption("Script Args");
  }

  private void setupWorkingDirectoryPathField(@NotNull final Project project) {
    myWorkingDirectoryPathField.addBrowseFolderListener(
      "Select Working Directory",
      "",
      project,
      FileChooserDescriptorFactory.createSingleFolderDescriptor()
    );
  }

  @NotNull
  private String getPath(@NotNull final TextFieldWithBrowseButton field) {
    return FileUtil.toSystemIndependentName(field.getText().trim());
  }

  private void setPath(@NotNull final TextFieldWithBrowseButton field, @NotNull final String path) {
    field.setText(FileUtil.toSystemDependentName(path));
  }
}

redpajama_set_name: RedPajamaGithub


text:
Q: Insert string at specific column - Jinja2 I would like to be able to insert strings to align with specific spacing requirements;
Column1     Column2     Column3                        Column4  etc...
Instert1    Insert2     Insert(randomCharacterCount)3  Insert4

(the column headers do not adjust)
Currently the template has to be spelled out for each entry uniquely so it fits within the column spacing, if you make a change, it requires several checks to make sure it aligns with the start points of the columns.
Is there a way to inject a string at a specific starting point, rather than manually adding spaces throughout each entry? In short, insert string at character point 30, then the next string at character point 52, etc.
Currently, I am using this (which works):
{{ entry.model }},{{ ' ' * ( 20 - entry.model | length ) }}{{ entry.cores }},{{ ' ' * ( 5 - entry.cores | length ) }}{{ entry.thrds }},{{ ' ' * ( 5 - entry.thrds | length ) }}

I gather the number at the starting point of the next column back to the first character of the last column. It then gathers the length of the string and removes that from the available spaces and then inserts the remaining spaces. But man... is it long and ugly!
Is there a better solution?

A: It requires a bit of convolution due to set in jinja2 not allowing reassignment, but otherwise it seemed to do as expected:
- hosts: localhost
  connection: local
  gather_facts: no
  vars:
    columns: 'Column1     Column2     Column3                        Column4  etc'
  tasks:
    - set_fact:
        fmt_str: >-
          {%- set results = [] -%}
          {%- set prev = {"p":0} -%}
          {%- for p, w in (c_pads | zip(c_widths) | reverse) -%}
          {%- set _ = results.append(":<" ~ (w + prev.p)) -%}
          {%- set _ = prev.update({"p": p}) -%}
          {%- endfor -%}
          {%- for f in results | reverse -%}
          {{- "{" ~ loop.index0 ~ f ~ "}" -}}
          {%- endfor -%}
      vars:
        c_pads: '{{ columns | regex_findall("( *)[^ ]+") | map("length") | list }}'
        c_widths: '{{ columns | regex_findall(" *([^ ]+)") | map("length") | list }}'
    - debug:
        msg: |
          {{ columns }}
          {{ fmt_str.format(*a_row) }}
      vars:
        a_row: ["alpha", "beta", "charlie", "delta", "xyz"]

produces:
ok: [localhost] =>
  msg: |-
    Column1     Column2     Column3                        Column4  etc
    alpha       beta        charlie                        delta    xyz

which is what I think you're after
There are a lot of sharp edges about overflow conditions, but I bet some study of https://docs.python.org/3/library/string.html#format-examples will help

redpajama_set_name: RedPajamaStackExchange


text:
Q: Will a Clothes Dryer Cause Interference with a DSL Modem and Wireless Router? I'm taking steps toward setting up a home file and print server, and other toys and the first step is to have my Internet connection on 24/7. The most sensible place to put it is in the laundry room which is on the other side of the wall from my basement office. There is a nice shelving unit in there behind the door which is beside the clothes dryer.
My plan is to have the DSL modem and my wireless router set up on the top shelf there, plugged into my UPS. Being high up will improve wireless reach to the upper floor and the backyard. I would eventually put a PC acting as a server on the same shelving unit.
My concern is - will a dryer that is about 1.5 meters away from these devices cause interference at this distance? If so, is there a way to mitigate it or should I just avoid putting electronics in there altogether? The devices are currently on the other side of the wall from the dryer so it's not much of a move.

A: I don't think you should have any problems. But if yes, there are easy solutions.
I see 5 possible risks here.

*

*Interference with the WiFi signal.
Washers and driers don't emit on WiFi frequencies (unless you have attained one of those mythical kitchen appliances with Internet connection visionaries have been promising since 1995, but even then it should be no more of a problem than having a WiFi enabled laptop in the room). Actually, I think that they only emit in the infrared part of the spectrum (because they have heaters), but that shouldn't interfere with the signal. Depending on their covering material, they could absorb and/or reflect some part of the WiFi signal, but you'd have to be very unlucky with their surface and the room configuration for this to cause significant problems. And the risk for that is just the same as in any other room full of furniture.

*Electromagnetic fields.
They can harm electronics if not shielded properly. But first, the field generated by the motors turning the drums should not be nearly as strong as the field caused by a CRT monitor (remember the demagnetizing option in the menus?), and computer parts are designed to function properly around CRTs. Besides, the electronic parts in the modern washers and driers function just fine, so the risk for equipment outside the enclosure is practically non existent.

*Power fluctuations.
If your power installation was done on the cheap, the sudden start of an AC motor can cause a very short brownout, which doesn't get filtered by computer PSUs (I have this happening, caused by the fridge's compressor). This is not very likely to happen, but it is possible. If it should happen, the best solution is to connect the router & co to another circuit. If such isn't available, you can get an on-line UPS (expensive, has other advantages too) or a voltage converter (50€ for a 1200W rated unit, a smaller one will be enough for you).

*Humidity.
This is the most probable problem in the laundry room. Just install a hygrometer and if humidity gets too high, use a dehumidifier. Actually, do this even if you don't put the router there, because else you are risking mold on the walls.

*Flooding.
This risk isn't negligible, especially if you have a front-loading washing machine. Mount your electronics on a wall, or put them on some kind of rack which keeps everything (including cables) at least 40 cm above floor level. Also use power strips rated for use in wet environments (they have self-sealing lids on the sockets not in use).

A: The nice thing about 240 is that it's very well shielded in the wall and most plugs have enough wrap to prevent interference.  I would say it's a good choice.  My only concern would be the heat but if it's in your basement I would say you are pretty well good to go.
There are cases where fluorescent lighting can adversely affect DSL modems and other wireless devices but it doesn't sound like that's applicable in your case.

A: Depending on your type of dryer: yes, there will be issues receiving the signal due to its location.
My wife and I currently live in an apartment and just purchased a new dual-band N/G/B/A router because we thought our old G router was dying. We suspected it was dying because we received signal everywhere in the house except our main bedroom.  The thing I didn't get was why I could get signal just fine in our living room, which was farther away, while I couldn't get signal at all while in the bedroom next to our office.  Turns out the electromagnetic interference (EMI) caused by our dryer is enough to block all signal (A/B/G/N) that is in an approximate 30 degree vector passing around the dryer.  The dryer is located in a closet between the bedroom and office.
I'm sure placing a router so close to a dryer will have an effect on its signal, but especially so if the dryer is between the router and receiving line of sight.

A: It should not make a difference, however, the motor that turns the drum could throw out lots of interference, especially if its an older model.  I would say to just give it a shot, and see.


text:
Q: Lefschetz operator identity, local proof Let $M$ denote a Kähler manifold with Kähler form $\omega$. Let $L$ denote the Lefschetz operator acting on on $A^k(M,\mathbb{C}) \to A^{k+2}(M,\mathbb{C})$ such that $L(\eta)=\omega \wedge \eta$.
Now let $\Lambda = L^{*}$, that is $\Lambda$ defines the adjoint of the Lefschetz operator.
I am looking at the proof that $[\Lambda , \overline{\partial}]=- i \partial^{*}$, which is given by Proposition 6.5 in 'Hodge Theory and Complex Algebraic Geometry' by Claire Voisin. It uses the fact that locally $\omega$ is equal to the standard Kähler form on $\mathbb{C}^n$ up to order two in $z$, and that $\Lambda$ and $\overline{\partial}$ are zero and first order differential operators respectively. It then says that it suffices to prove the proposition for the standard Kähler form on $\mathbb{C}^n$ as .
I don't understand this, can somebody explan this logic. The second order terms don't disappear after applying a first order differential onto them, so I don't understand why we can neglect them in the proof?


Recently updated home with a fantastic cul-de sac location! This spacious home offer 3 bedroom and 3 full baths. Spacious master with updated bathroom & double closets. Light & bright living area with fireplace. All new flooring, interior paint & light fixtures. Great backyard space with new deck & front porch. 2 car garage & RV parking. Quiet neighborhood with park & tennis courts. Minutes to Tanasbourne Town Center & Hwy 26!
All information deemed reliable but not guaranteed. All properties are subject to prior sale, change or withdrawal. Neither listing broker(s) or information provider(s) shall be responsible for any typographical errors, misinformation, misprints and shall be held totally harmless. Listing(s) information is provided for consumers personal, non-commercial use and may not be used for any purpose other than to identify prospective properties consumers may be interested in purchasing. Information on this site was last updated 4/20/2019 5:41:32 AM. The listing information on this page last changed on 4/20/2019 5:41:32 AM. The data relating to real estate for sale on this website comes in part from the Internet Data Exchange program of RMLS (last updated 4/20/2019 5:41:32 AM) or Willamette Valley MLS (last updated 4/20/2019 5:41:32 AM). Real estate listings held by brokerage firms other than RE/MAX Equity Group may be marked with the Internet Data Exchange logo and detailed information about those properties will include the name of the listing broker(s) when required by the MLS.


Chicos Lures for crank, glide and soft plastic baits.
obligations on organisations and gives you extra rights around how your data is used. We want you to know that we respect the information we hold on you and that we take the security of your information very seriously. We DO NOT hold any payment information, that is with PayPal. We will also make a promise to you - we will look after your data securely, as you'd expect, and we most definitely will never sell it or share it.
assume that you consent to us holding your data.
An avid Piker and user of fishing lures Chico Winterton has taken a hobby and turned it in to an obsession. This small business has started from the humble beginnings of buying and selling in Europe and America through Ebay. Now the best of American Hand-made Lures and equipment are imported for sale. Due to the nature of the manufacture, the stocks are limited, but custom baits are also available for those willing to wait.
Extra TRACKED postage to Europe - £5 for 1st item + £1 for each additional item.
Except where stated (heavy items) - please contact us for a quote.


text:
Focusonthefamily.ca
It's pretty simple really: If John Kramer, aka the trap-happy serial killer Jigsaw, sits down across the desk from you and asks for more insurance to cover an experimental cancer procedure, well, it would be a good idea to say yes.
But William Easton, a vice president at Umbrella Health (and the arrogant creator of the risk algorithms that have denied many suffering folks insurance they desperately need) says no.
That proves to be a painful miscalculation.
Saw VI revolves around Jigsaw—from the grave—exacting his bloody vengeance on Easton (and a group of his equally cocky, greedy insurance cohorts). This time around, Jigsaw moves the pawns in his bloodletting "game" through two still-breathing agents of his retributive will: his surviving wife, Jill Tuck, and FBI agent Mark Hoffman.
After being kidnapped, Easton is forced to make his way through a series of dank rooms and cages at an abandoned zoo. His task? Deciding which of his booby-trapped co-workers should live and which should die—just as he decided who lived and who died as a health insurance provider, Jigsaw reminds him.
And if Easton fails to make it through Jigsaw's murderous maze in 90 minutes? His arms and legs will get blown off by explosives and his wife and son will be killed too.
Easton's horror mounts—along with the body count—as Hoffman grimly grinds the gears of Jigsaw's demented contraptions.
Just as in every other installment in this franchise, we're meant to believe that Jigsaw's horrific punishment of his victims is because they don't appreciate the good things they have in life.
Only part of that is positive, of course. Valuing life: good. Horrific punishments for not valuing life: bad.
Jill has a vision of her deceased husband in which he lectures her about the drug addicts she works with. He tells her, "These people have no respect for the lives they're destroying." Later he says that a 52-year-old janitor who keeps smoking despite his high blood pressure has "no appreciation for life."
The victims of Jigsaw's traps hail from two sectors of the economy that have been in the news a lot as of late: insurance and real estate. The film rightly suggests that when greedy people in these industries act in fraudulent, self-serving ways, innocent people suffer.
Even in death, Jigsaw exercises something akin to godlike power over the fate of his victims (an idea I'll return to in my conclusion). One character, for instance, says of his plan, "This is John's will." God is never mentioned directly (apart from the many abuses of His name), but the spiritual themes of judgment, forgiveness and mercy come up in several conversations.
Talking with Easton, Jigsaw also gets at the idea that we're not, in the end, masters of our own fate. Jigsaw tells him, "You think it's the living who have ultimate judgment over you, because the dead have no claim over your soul. But you may be mistaken."
One person chooses to kill another and says, "Now you burn in hell."
Several women wear tight tops; one reveals cleavage. Easton flirts with a company lawyer, perhaps implying that the two are having an affair.
I've somehow managed to avoid a Saw assignment up 'til now, so I paged through Plugged In's previous reviews for reference. I wasn't surprised that much of what we've said about the carnage in the previous five installments applies equally here.
Marcus Yoars said of Saw II: "The film's sick fascination with creative ways to suffer and die just goes on and on."
Steven Isaac's review of Saw III added, "There is no end to the ways in which [these] movies can show people being mangled, lacerated, dissected, brutalized … and murdered."
Paul Asay wrote, "Simply put, Saw IV's reason for being is to depict torture and mutilation as graphically, grossly and realistically as possible—nothing more."
Check. Check. And check. These are all accurate summaries of the grisly proceedings in this sixth installment.
The opening scene is among the film's most graphic, with two avaricious real estate agents being instructed to give "a pound of flesh" in a ghastly competition to see who can cut more weight off their bodies as atonement for their greed. An overweight man lobs off quite a bit of his midsection, while a skinny woman looks at her tiny tummy with despair … then hacks off an arm at the elbow with an ax. She's the "winner." The loser's punishment? Drilled holes in his skull.
Once Jigsaw's game with Easton gets underway, Saw VI gets down to the base business of exploring a variety of ways to dispatch captive victims. Two men get crushed between concrete wedges (one fatally). Another is smashed and shredded in a compactor of sorts. (We see what's left of his unrecognizable entrails.) Close-up camera work shows assorted pieces of flesh that have been removed from various victims. Easton has to choose between two employees who are standing on separate gallows with barbed wire nooses around their necks. Two people are burned badly by steam. One of Easton's co-workers attacks him with a radial saw before a timed explosion launches projectiles into her brain.
A drawn-out scene involves the insurance executive choosing two people out of six to survive a merry-go-round death contraption involving an automated shotgun; accordingly, four receive life-ending blasts to the chest. And saving the two people involves Easton's hands being impaled.
Easton ultimately faces the mother and son of a man who died because Easton revoked his insurance. The mother chooses not to kill him, but the adolescent son pulls a switch that injects Easton with perhaps fifty syringes full of hydrochloric acid, which (onscreen) dissolves his body from the inside out.
Hoffman slits an FBI agent's throat, shoots another and repeatedly stabs a third. Extracting himself from a bear trap contraption, Hoffman horribly tears up his face.
About 50 f-words, at least eight s-words, and well over a dozen misuses of Christ's and God's names. We hear a crude reference to the female anatomy.
Wine is consumed. Easton pours himself a glass of hard liquor in his office. In the dream-like vision Jill has, Jigsaw tells her that the methadone center she works at doesn't help the addicts who come there for treatment but only masks and numbs their addiction, impeding any real chance at recovery and healing.
Jigsaw is driven by the twisted conviction that people can only really change if they come face to face with death and survive. "Once you see death up close," he tells Jill, "Then you know what the value of life is. That's my way." He tells Easton, "Until a person is faced with death, it is impossible to tell if they have what it takes to survive."
Hoffman goes to great lengths to make it look as if a deceased FBI agent is actually the one responsible for the Jigsaw murders.
Another October, another Saw movie.
First-time Saw director Kevin Greutert (who edited the five other installments) remains true to the franchise's predictably grisly formula. Tricks. Traps. Blood. No-win life-and-death choices. More blood. Roll credits.
Indeed, the Saw franchise has become infamous for the way it has lowered the bar when it comes to gratuitous violence. Before Saw's debut in 2004, the term "torture porn" didn't exist. Now, Saw is the poster franchise for a genre of films whose sole reason for existence is to push the mutilation envelope.
This series makes no bones (or should I say it does make bones?) about the fact that bad people deserve judgment, violently exploiting the idea of vigilante justice in the name of entertainment. It also serves up heaping helpings of Jigsaw's warped God complex.
From cover to cover, the Bible clearly communicates that we are all accountable to God for our choices. As Romans 6:23 says, "For the wages of sin is death." And that's a reality Jigsaw understands all too well. What he doesn't understand or even begin to contemplate is the fact that the verse doesn't end there. The Apostle Paul goes on to say, "but the gift of God is eternal life in Christ Jesus our Lord."
Jigsaw acts as if he's God, coolly assuming the role of judge, jury and executioner—even from the grave. He gives lip service at times to the ideas of mercy, forgiveness and redemption. But he has little real interest in any of those spiritual ideals.
Just like fans of the Saw movies have little real interest in listening to why it's such a bad deal to buy into a character who delights in twisting the life out of … everything. They're just there for the brutal thrill ride.
In a recent article in the Catholic journal First Things, David P. Goldman writes, "Many things might explain the vast new market for uncanny evil. If you do not believe in God, you will believe in anything, to misquote G.K. Chesterton; and, one might add, if you do not feel God's presence, you will become desperate to feel anything at all. Terror and horror create at least some kind of feeling. After pornography has jaded the capacity to feel pleasure, what remains is the capacity to feel fear and pain."
"Do you like how brutality feels, Mark?" Jigsaw asks Hoffman. Well, do you, movie fans?
Tobin Bell as Jigsaw/John Kramer; Costas Mandylor as Mark Hoffman; Betsy Russell as Jill Tuck; Shawnee Smith as Amanda Young; Peter Outerbridge as William Easton; Samantha Lemole as Pamela Jenkins
Kevin Greutert ( )


American Portwell Technology Inc. Four port asynchronous serial communication adapter designed for use with any computer system equipped with a USB port Connector: Have confidence, this product wiretek usb serial match whatever baud rate your equipment needs Wireteo Tough ultra small USB to serial adapter suitable for any environment.
These USB devices are perfect for a variety of applications uab monitoring, control and industrial serial communications. Four port asynchronous serial communication wigetek designed seeial use with any computer system equipped with a USB port Connector: Universal Reversible USB 2.
Depending wiretek usb serial what type of serial interface your application requires, L-com has wiretek usb to serial to wieetek from: This wireetk the product to be used in a variety of wiretek usb to serial and applications including banking, retail and Wiretek usb to serial Four-port RS asynchronous serial communication adapter designed for use with any computer system equipped with a USB port Connector:.
Enter the world of Oriental products by searching our extensive catalog with USB, for Serial communications. Depending on what type of serial interface your application requires, L-com has plenty to choose from: Four-port RS wiretek usb to serial serial communication adapter designed for use with any computer system equipped with a USB port Connector: The closest you can get to an integrated serial port.
Connect super speed peripherals like USB 3.
Cooperation with Any companies in advancement of the goods and services in Russia. The Wirstek operates Connector: All configuration and electrical interface Connector: Are you a Company Representative?
Find Suppliers by Category Top. What else is there?
Depending on what type of serial interface your application requires, L-com has plenty to choose from:. The organisation of the new Manufactures in Russia.
Wiretek usb to serial you use this serial port, a DB9 adapter is also supplied.


I have been gambling on the internet or at brick and mortar gambling halls for a good many years. I have been taught, the craving can grab a hold of you and you will not even notice it until you are beaten. Markedly if you are on a scoring streak. I have gone through many tens of thousands of clams in just a tiny period of time and even today, I will go too long. It appears you are only enjoying yourself till you make a choice to contemplate your losses and the blame settles in, and of course you keep advising yourself "I could win it back" again and again. It does not work. Then you feel queasy in your gut and the harder you attempt the faster you relinquish.
When you discover that you are in the black, Remain on the UP! When you start to throw away, do not inform yourself, "well only maybe 1 more" over and over again, believe me, this tactic barely ever operates. Say you are gambling on slot machines, have a value separate prior to starting your play. DON'T go over that cap, no matter how tempting. If you happen to win, put that in a different pot. Don't bet your winnings at any cost. Once you have gambled through your beginning set threshold, stop. Depart, regardless if it is on the internet or at a brick and mortar casino, don't stick around. At all times keep in mind, there no doubt will be other days, other times. Clearly, this plan can work for any casino game that you gamble on, be it bingo, poker, video poker, keno, blackjack or any other casino game.
Remember, betting should be FUN not backbreaking, sickening work! If you are not having fun yourself, you do not belong there. If you can't afford the hit, don't ever begin.


Dr. William F. Pickard is known for his business success, civic leadership, and philanthropy. Founder, chairman and CEO of Global Automotive Alliance, a Black Enterprise Top 100 industrial/service company, Dr. Pickard is recognized as the first minority-owned group of plastic parts supplier to service the top three U.S. automakers. He has served on numerous boards of directors, such as the Greater Detroit Chamber of Commerce and Booker T. Washington Business Association. Dr. Pickard also has donated millions to a variety of museums, universities, organizations, such as the National Museum of African American History and Culture in Washington, DC, and the William F. Pickard Business Scholarship at Grand Valley State University that supports first-generation students.
Recently, he extended his generosity and support to the Office of Diversity and Inclusion's Frank W. Hale Jr. Black Cultural Center and Todd Anthony Bell National Resource Center on the African American Male (BNRC) with a $75K gift over the next two years. Dr. Pickard, who received his PhD from The Ohio State University in 1971, donated his first major gift to Ohio State to create the Dr. William F. Pickard Scholars Program, which will develop student leaders with an interest in social, educational, political, communal and economic issues affecting African American communities. The program, managed by Dan Thomas, Program Manager in the BRNC, will offer short courses, an independent study project, and other professional development opportunities. "I am elated that Dr. Pickard decided to invest in our students who have close ties to the Hale Center and the Bell National Resource Center. His investment is likely to pay major dividends in the lives of the students, as well as the African American community at-large," says Dr. James L. Moore III, Vice Provost for Diversity and Inclusion and Chief Diversity Officer and Executive Director for the Todd Anthony Bell National Resource Center.
This past fall, students applied and interviewed to be a part of 2019 inaugural cohort of scholars.
Topic: Mentoring and skill development for at-risk youth.
Career Aspirations: To start my own black engineering firm.
Topic: Mental health and its effects on Black communities.
Career Aspirations: To be an educator in Black studies at both the K-12 and university level.
Topic: Holistic health and well-being for Black youth in grade school.
Career Aspirations: To become a cardiologist.
Topic: Modeling success for inner-city Black boys.
Career Aspirations: To become a physician while obtaining a degree in Public Health. I would also like to start a STEM enrichment program for underrepresented students in middle and high school.
Topic HIV/AIDS education in predominantly Black communities and educational communities.
Topic: Strengthen the social infrastructure for Black LGBTQ men.
When the program finishes at the end of the Spring 2019 semester, the Pickard scholars will provide a visual presentation detailing their topic, address how their issue is affecting the community, and propose an initiative designed to combat the issue.
Please be sure to congratulate these students when you see them and be on the lookout for a save the date for mid-April where you can come hear their final presentations.