text:
\section{Introduction}
Complex network theory has opened the way for exploring many dynamical processes on large-scale systems consisting of individual components connected in a nontrivial topology. One of the most widely studied phenomena occurring on complex networks are spreading processes, with a prominent example attracting widespread attention being the spread of viruses in social or computer networks \cite{ref-3, ref-4, ref-5, ref-6, ref-7, ref-2008}.

There are several approaches being used in the analysis of epidemic spreading. One popular approach is the heterogeneous mean-field (HMF) prescription by coarse-graining nodes within degree classes and relaxing the problem by assuming that all nodes in a degree class have the same dynamical properties \cite{ref-4,ref-5, hmf1, hmf2}. However, it has been shown that HMF can result in different levels of accuracy \cite{hmf-accuracy}.
A more successful approach in determining the outcome of an infection was introduced by Chakrabarti et.al~\cite{ref-8} where the SIS epidemic model was analyzed by using a system of probability equations, which in fact, represents a deterministic non-linear dynamical system (NLDS).
This approach was also used in \cite{Gomez-2010}, where a family of SIS epidemic models is examined, parameterized by the number of stochastic contact trials per unit time, that range from contact processes (where the contagion expands at a certain rate from an infective vertex to one neighbor at a time) to reactive processes (in which an infective individual effectively contacts all its neighbors to expand the epidemics). Using a deterministic model, referred to as the Microscopic Markov-Chain approach (MMCA), which is virtually equivalent to NLDS, the whole phase diagram of the different infection models is constructed and their critical properties are determined. It is worth noting that using different number of stochastic contagion per unit time extends the usability of the model, since this number can surely vary for different real-world problems \cite{bounded-contact}. Recently, a mixed approach using both NLDS and HMF was proposed in \cite{npHMF} which lead to a nonperturbative formulation enhancing the predictive power of the classical HMF approach.
Heterogeneous environments have also been extensively studied. One such is an epidemic model with inhomogeneous infection probabilities on a graph with prescribed degree distribution \cite{ref-2011} where model's dynamics are derived for i.i.d. weights and for weights that are functions of the degrees.

With the help of these theoretical frameworks, the role of network topology in the spreading process has been repeatedly emphasized, yielding the result of a finite threshold for the spreading process in networks with exponentially bounded degree distributions, and a vanishing threshold in infinite uncorrelated networks with a power-law degree distribution. A recent addition to these findings is that for the SIS epidemic model, the vanishing threshold has nothing to do with the scale-free nature of the degree distribution, but is the result of the largest hub being a self-sustainable source for the infection \cite{psv-SIS} (see also \cite{reinfection}). However, the currently established connections are very rough with a topology-related threshold differentiating between two extreme outcomes of the model. With the threshold being satisfied,  there is still a large spectrum for different spreading parameters and the poorly understood role of the network's topology there motivated our work.

In this paper we adopt the approach proposed in \cite{ref-8, Gomez-2010} and study the deterministic epidemic model on graphs, in which the dynamics of individual nodes is described by a discrete-time Markov chain.
In the SIS model, a node can be in one of two states: susceptible (S) or infective (I). Infective nodes can infect other neighbouring nodes, and each node can be randomly cured with probability $\delta$ per unit time. At each time step, an infective node makes a number of trials per unit time to transmit the disease to its neighbours with probability $\beta$. We consider two specific cases: (i) the contact process, which involves a single stochastic contagion per infective node per unit time, and (ii) the reactive process, which involves as many stochastic contagions per unit time as neighbours a node has.
The work in this paper extends that of \cite{ref-8,Gomez-2010}. We derive upper and lower bounds on the probability of a node to be infective, and determine how tight the bounds are around the probability that a node is infective. For both processes the bounds are derived using the $n-$hop neighbourhood of each node. The larger the considered neighbourhood -- the more topological information one uses to determine the bounds, hence the bounds are tighter. We use the difference between the upper and lower bound averaged over all nodes to determine the influence of the network topology on the spreading process and compute numerical results for a real-world e-mail network. For additional clarity, Figure \ref{fig:plotedgraphs} depicts the $1$-hop and $2$-hop neighborhood of a particular node in the Enron e-mail network with degree 10, together with the calculated bounds for its probability of infection derived using only its respective subgraph information.

The outline of the paper is the following. Section \ref{sec:2} gives the definition of the model and recovers known results. The contributions of this paper are contained in sections \ref{sec:3} and \ref{sec:4}. In section \ref{sec:3} the upper and lower bounds on the probability of being infective are derived for the reactive process, and numerical results for the e-mail network are presented. Section \ref{sec:4} gives the bounds for the contact process, along with the corresponding numerical results. Section \ref{sec:conc} concludes the paper and points out future research directions.

\begin{figure}[htbp]
  \begin{center}
   \subfigure[1-hop neighborhood]{
   \label{fig:plotedgraphs-1}
   \includegraphics[scale=0.3]{1-hop-1007.pdf}
  }
   \subfigure[2-hop neighborhood]{
   \label{fig:plotedgraphs-2}
   \includegraphics[scale=0.5]{2-hop-1007.pdf}
  }
  \end{center}
  \caption{1-hop and 2-hop neighborhood for a node extracted from a real-world e-mail network with 33696 nodes. The node (largest in size) has 10 direct neighbors (medium sized). The probability of infection for the given node obtained after simulating a particular configuration of the SIS model was 0.373. \subref{fig:plotedgraphs-1} The 1-hop neighborhood represents a tree with the given node at its center and 10 peripheral nodes. The probability of infection for the node given the 1-hop neighborhood (node's degree) is calculated to be between 0.006 and 0.503. \subref{fig:plotedgraphs-2} The 2-hop neighborhood contains 62 nodes and 92 edges. Peripheral nodes are smallest in size and are two hops away from the central node. The probability of infection for the node given the 2-hop neighborhood topology is calculated to be between 0.297 and 0.416. Note that the difference between the upper and lower bound gets smaller as we use more topology information.}
  \label{fig:plotedgraphs}
\end{figure}

\section{Model definition and analysis}
\label{sec:2}

Consider a closed population of $N$ individuals, connected in a network structure which is represented by a simple, undirected,  unweighted, connected and unipartite graph $G = (V,E)$ with node set $V$ and edge set $E$. The adjacency matrix of the graph is given by $A = [ a_{ij} ]_{N \times N}$, where $a_{ij} = 1$ if node $i$ is connected to node $j$, and $a_{ij} = 0$ otherwise.
Each node can be in one of two possible states: susceptible (S) and infective (I). Susceptible nodes are healthy and can contract the disease upon contact with infective nodes, which spread the disease. After the infectious period of the disease has ended, a node becomes susceptible to the disease once again. The initial set of infective nodes at time 0 is assumed to be non-empty, and all other nodes are assumed to be in state S at time 0.

The state of a node is represented by a status vector, an indicator vector containing a single 1 in the position corresponding to the present state, and 0 in the other $\mathbf{s}_i(t)=[s_i^S(t) \hspace{0.2cm} s_i^{I}(t)]^T,$
for all $i \in \{1, \ldots, N \}$. Let
$
\mathbf{p}_i(t)=[p_i^S(t) \hspace{0.2cm} p_i^{I}(t)]^T
$
be the probability mass function (PMF) of node $i$ at time $t$.
The evolution of SIS is described by the following equations:
\begin{equation}
\begin{array}{lll}
p_i^S(t+1) &=& s_i^S (t) (1 - f_i(t)) + \delta s_i^I(t) \\
p_i^{I}(t+1) &=& s^S_{i}(t) f_i(t) + (1 - \delta) s_i^I(t)
\label{eq:stochastic-SIS}
\end{array}
\end{equation}
and
\begin{equation}
\mathbf{s}_i(t+1) = MultiRealize[\mathbf{p}_i(t+1)],
\label{eq:Multirealize}
\end{equation}
where $MultiRealize[\cdot]$ performs a random realization for the PMF given with $\mathbf{p}_i (t+1)$. In (\ref{eq:stochastic-SIS}) $0 \leq \delta \leq 1$ is the probability of curing and $0 \leq \beta \leq 1$ is the probability of disease transmission from an infective to a susceptible node.

We consider two cases of infection spreading: the contact process and the reactive process. The contact process \cite{contact-1,contact-2,contact-3} is a dynamical process that involves a single stochastic contagion per infective node per unit time, while in the reactive process \cite{reactive-1,reactive-2,reactive-3} there are as many stochastic contagions per unit time as there are neighbours to a node. The distinction between the two processes is reflected in the probability $f_i(t)$ that a susceptible node $i$ receives the infection from any combination of its infective neighbours. The probability $f_i(t)$ has the form:
\begin{equation}
f_i(t) = 1 - \prod_{j=1}^N (1 - \beta r_{ij} s_j^I(t)).
\label{eq:fi-stoc}
\end{equation}
where $r_{ij}$ is a contact probability. Without loss of generality, it
is instructive to think of these probabilities as the transition probabilities of random walkers on the network. The general case is represented by $\lambda_i$ random walkers leaving node $i$ at each time step:
$$
r_{ij} = 1 - \left( 1 - \frac{a_{ij}}{\sum_j a_{ij}}   \right)^{\lambda_i}
$$
The contact process corresponds to a model dynamics of one contact per unit time, $\lambda_i = 1$, $\forall i$, thus $r_{ij} = a_{ij}/\sum_j a_{ij}$.
In the reactive process all neighbors are contacted, which corresponds, in this description, to set the limit $\lambda_i \to \infty$, $\forall i$,  resulting on $r_{ij} = a_{ij}$.

Though exact and realistic, the system of equations (\ref{eq:stochastic-SIS}) is not suitable for the analytical study of the system dynamics, since the new statuses are obtained as a result of a decision process, transforming a continuous variable into a discrete one. That is why, in the further text, we will complement the status dependent system, with a set of adequate probability equations. This approach was introduced by Chakrabarti et.al~\cite{ref-8}, who analyzed the  infection in the network using a system of probability equations, referred to as the Non-Linear Dynamical System (NLDS) model. Adopting their approach to the SIS process (\ref{eq:stochastic-SIS}), we obtain the following set of difference equations for the probabilities of states S and I:
\begin{equation}
\begin{array}{lll}
p_i^S(t+1) &=& p_i^S (t) (1 - f_i(t)) + \delta p_i^I(t) \\
p_i^{I}(t+1) &=& p^S_{i}(t) f_i(t) + (1 - \delta) p_i^I(t)
\label{eq:det-SIS}
\end{array}
\end{equation}
where $f_i(t)$ is now
\begin{equation}
f_i(t) = 1 - \prod_{j=1}^N (1 - \beta r_{ij} p_j^I(t)).
\label{eq:fi-det}
\end{equation}
Note that (\ref{eq:det-SIS}) is a deterministic equation.

Since $p_i^S(t) + p_i^I(t) = 1$ for all $i$ and all $t$, we rewrite (\ref{eq:det-SIS}) using $x_i = p_i^I$:
\begin{equation}
x_i(t+1) = (1 - x_i(t))f_i(t) + (1-\delta) x_i(t).
\label{eq:xi-SIS}
\end{equation}
Equation (\ref{eq:xi-SIS}) represents a nonlinear dynamical system $F : [0,1]^N \to [0,1]^N$.  The system (\ref{eq:xi-SIS}) has two fixed points: the origin $x_i = 0, \forall i \in \{1, \ldots, N \}$ and let $x_i^*(G)$ be the fixed point of (\ref{eq:xi-SIS}) different from the origin for the graph $G$.
We will write only $x^*_i$ instead of $x^*_i(G)$ when it is clear which graph $G$ is considered in the context. At the stationary state:
\begin{equation}
\delta x^*_i = (1 - x^*_i) \left[ 1 - \prod_{j=1}^N (1 - \beta r_{ij} x^*_j)  \right].
\label{eq:xi-stat}
\end{equation}

The origin $x_i = 0, \forall i \in \{1, \ldots, N \}$ is a fixed point of the system. Using the Jacobian matrix of the system (\ref{eq:xi-SIS}) evaluated at the origin:
$$
DF|_{(x_i = 0)} = (1 - \delta) I + \beta R,
$$
where $R=[r_{ij}]_{N \times N}$, one finds the well-known result~\cite{ref-8,Gomez-2010} that the origin is stable when
\begin{equation}
\frac{\beta}{\delta} < \frac{1}{\lambda_{1,R} },
\label{eq:stability-cond}
\end{equation}
where $\lambda_{1,R}$ is the largest eigenvalue of the matrix $R$. Whenever the infection to cure ratio $\beta / \delta$ is greater than the network threshold $1 / \lambda_{1,R}$ the disease will reach an endemic state in the network. For a contact process $\lambda_{1,R}=1$, since $R$ is a row stochastic matrix, while for a reactive process $\lambda_{1,R} = \lambda_{1,A}$.
Moreover, when $\beta \neq 0$, $\delta \neq 0$, and $\delta \neq 1$,
the ergodicity of the Markov chains describing the SIS dynamics of each node is guaranteed and therefore (\ref{eq:det-SIS}) has a unique globally stable fixed point. Therefore, there exists a critical value of $\beta$, $\beta_{c}=\delta/\lambda_{1,R}$, such that the origin is a globally asymptotically stable fixed point of (\ref{eq:xi-SIS}) if $\beta < \beta_{c}$, and $x_i^*$ for all $i$ is a globally asymptotically stable fixed point of (\ref{eq:xi-SIS}) when $\beta > \beta_{c}$.

\section{Reactive process}
\label{sec:3}

\subsection{Upper bounds on the probability of being infective}

In this section we consider a family $\Phi$ of all possible simple and connected graphs with at least two nodes (we exclude from this family the empty graph and the graph with a single node and no links) and SIS reactive processes on this family for which the stationary solution (\ref{eq:xi-stat}), different from the origin, is an asymptotically stable fixed point of (\ref{eq:xi-SIS}). For the reactive process,  since $r_{ij}=a_{ij}$, we rewrite (\ref{eq:xi-stat}) as:
\begin{equation}
\label{eq:xi-reactive}
x_i^* = \frac{\left[ 1 - \prod_{j=1}^N (1 - \beta a_{ij} x_j^*)  \right]}{\left[ 1 - \prod_{j=1}^N (1 - \beta a_{ij} x_j^*)  \right] + \delta}
\end{equation}

Our first observation which acted as a building block for deriving the bounds for contact and reactive processes was that the stationary probability of infection of the reactive model (\ref{eq:xi-reactive}) for all nodes $i$, is bounded by
\begin{equation}
\label{eq:bound-reactive}
x_i^* < \frac{1}{1+\delta} \equiv u_i^0.
\end{equation}
This is formally stated in lemma \ref{lemma-main} in Appendix \ref{app-reactive}.

Note that the bound (\ref{eq:bound-reactive}) is independent of the specific network topology. Its right-hand side corresponds to the stationary solution (\ref{eq:xi-reactive}) for an infinitely large full-mesh graph.
Bound (\ref{eq:bound-reactive}) is rough and uses no information about the topology. A better bound can be obtained if one considers the degree of node $i$; in this case, we have:
\begin{equation}
\label{eq:bound-reactive-1}
x_i^* < \frac{1 - \left [ 1 - \frac{\beta}{1 + \delta} \right ]^{k_i}}{1 - \left [ 1 - \frac{\beta}{1 + \delta} \right ]^{k_i}+\delta} \equiv u_i^1 < u_i^0
\end{equation}
where $k_i$ is the degree of node $i$.
In general, one can find progressively better bounds for $x_i^*$ by using more information on the graph topology. In fact, let
\begin{equation} \label{eq:rec-for-u}
 u_i^n  =  \frac{1 - \prod_{j=1}^N (1 - \beta a_{ij} u_j^{n-1})}{1 - \prod_{j=1}^N (1 - \beta a_{ij} u_j^{n-1}) + \delta}
\end{equation}
where
\begin{equation*}
u_i^0 = 1/(1+\delta).
\end{equation*}
Then $x_i^*$ is bounded by
\begin{equation}
\label{eq:bound-reactive-all}
x_i^* < \ldots < u_i^{n} < \ldots < u_i^1 < u_i^0
\end{equation}
for all $i$. For a formal definition and proof see theorem \ref{theorem-reactive-all} in Appendix \ref{app-reactive}.

Using the similar arguments as in the proof of the theorem (\ref{theorem-reactive-all}), it can be shown that $\lim_{n\to \infty} u_i^n = x_i^*$ for all $i$. In this paper we are interested only for small $n$. A similar theorem to the theorem (\ref{theorem-reactive-all}) can also be proved for lower bounds but only for those SIS processes for which $\beta > \delta$. The obvious lower bound is $x_i^*>0$, but replacing 0 in a recurrent relation similar to the one in (\ref{eq:rec-for-u}) will produce only 0s.
Appendix \ref{app-reactive} contains the theorem (\ref{theorem-reactive-all-1}) for lower bounds of $x_i^*$:
\begin{equation}
\label{eq:bound-reactive-all-2}
L_i^0 \leq L_i^1 \leq \ldots \leq L_i^{n} < \ldots \leq  x_i^*
\end{equation}
for all $i$, which is analogous to theorem (\ref{theorem-reactive-all}), and the bounds $L_i^n$ are defined as
\begin{equation*}
L_i^n  =  \frac{1 - \prod_{j=1}^N (1 - \beta a_{ij} L_j^{n-1})}{1 - \prod_{j=1}^N (1 - \beta a_{ij} L_j^{n-1}) + \delta}
\end{equation*}
where
\begin{equation*}
L_i^0 = 1 - \delta/\beta.
\end{equation*}
Note that the left-hand side of (\ref{eq:bound-reactive-all-2}) is defined only for $\beta>\delta$, since $x_i^*>0$. This property comes from (\ref{eq:stability-cond}) since the graph associated with $L_i^0=x_{min}^*$ is a path graph of size $2$ with $\lambda_{1,G}=1$. $L_i^n$ for all $n$ are also going to be defined only for $\beta > \delta$, since the a priori assumption is that the peripheral nodes have no probability of being infected. In order to obtain bounds for $\beta<\delta$, we take a different approach described in the following subsection.

\subsection{Lower bounds on the probability of being infective}

In the previous section we have derived upper bounds which are valid for all $\beta$ and $\delta$ and lower bounds valid only for the SIS processes for which $\beta > \delta$. Since this is a restriction, in this section we find lower bounds valid for all $\beta$ and $\delta$ by observing that if $G'=(V',E')$ is a subgraph of $G=(V,E)$, with $x_i^{*}$ and $x_i^{*'}$ being the stationary solution of (\ref{eq:xi-reactive}) for the graph $G$ and $G'$ respectively for an arbitrary node $i \in V\cap V'$, then $x_i^{*'} < x_i^{*}$. In other words, as we remove edges (and nodes) from a graph, the probability of infection will decrease for each (remained) node. This is stated formally in lemma \ref{lemma-reactive-lower} in Appendix \ref{app-reactive}.
Using this interesting property, we can derive lower bound for an arbitrary node by simply obtaining (numerically) the stationary solution of (\ref{eq:xi-reactive}) for the 1-hop neighborhood starting at node $i$. Then $x_i^{*'}$ is a lower bound for $x_i^{*}$:
\begin{equation}
 \label{eq:bound-reactive-lower}
 l_i^1 \equiv x_i^{*'}\leq x_i^*
\end{equation}
where
\begin{equation}
 x_i^{*'} = \frac{1 - \left[ 1 - \frac{\beta^2 x_i^{*'}}{\beta x_i^{*'} + \delta} \right]^{k_i}}{1 - \left[ 1 - \frac{\beta^2 x_i^{*'}}{\beta x_i^{*'} + \delta} \right]^{k_i} + \delta}
\end{equation}
is the stationary solution of (\ref{eq:xi-reactive}) for the hub (central node) of a star graph $G'$ with $k_i+1$ nodes, $k_i$ being the degree of node $i$.

Note that bound (\ref{eq:bound-reactive-lower}) unlike bound (\ref{eq:bound-reactive}) uses 1-hop topology information (the degree of the node) a priori, thus avoiding the problem when $\beta<\delta$. Consequently, one can find progressively better lower bounds for node $i$ by solving (\ref{eq:xi-reactive}) for different subgraphs of $G$.

To show this, we now define a class of subgraphs called a $p$-hop neighborhood.
Let $i$ be an arbitrary node of the graph $G=(V,E)$, $i \in V$, and let $n_i = \max_{x} l(i,x)$ where $l(i,j)$ is the length of the shortest path between nodes $i$ and $j$. Let $V_i^0=\{ i \}$. We define a subgraph $G_i^p= (V_i^p, E_i^p)$ of $G=(V,E)$ as follows:
\begin{eqnarray*}
V_i^p &=& \{ x | x\in V, 0\leq l(i,x) \leq p \} \\
E_i^p &=& \{ (x,y)| (x,y) \in E, x\in V_i^p, y\in V_i^{p-1} \},
\end{eqnarray*}
where $p=1, \ldots, n_i + 1$. We say that $G_i^p$ is a $p$-hop neighborhood of node $i\in V$. (see Figure \ref{fig:subgraphs}).
For example, $G_i^1=(\{i\}\cup V_i ,E_i)$, where $E_i$ is the set of edges adjacent to node $i$, and $V_i$ is the set of all neighbors of $i$. In fact, $G_i^1$ is a star graph with $k_i$ leaves and root $i$. Note that $G_i^{n_i + 1}$ is the entire graph $G$ and that the first triangle can occur in $G_i^2$ but not in $G_i^1$.

\begin{figure}
\centering
\includegraphics[scale = 0.45]{fig2.pdf}
\caption{b) and c) $1$-hop and $2$-hop neighborhood of the gray node extracted from the graph in a)}
\label{fig:subgraphs}
\end{figure}
Finally, if $l_i^p$ is the probability of infection of node $i$ given its $p$-hop neighborhood, by theorem \ref{theorem-reactive-lower-all} proven in Appendix \ref{app-reactive}, the probability of infection $x_i^*$ given the entire graph $G$ is bounded by
\begin{equation}
 \label{eq:bound-reactive-lower-all}
l_i^1 < l_i^2 < \ldots < l_i^{n_i+1} = x_i^*
\end{equation}
where $n_i+1$ is such that $E_i^{n_i + 1}=E$, i.e. the $n_i + 1$-hop neighborhood of node $i$ contains the entire graph $G$.

\subsection{Numerical results}

In the previous section we have proved that
$$
l_i^p \leq x_i^* < u_i^n
$$
for $i=1, \ldots N$, $p=1, \ldots n_i+1$, and $n=1,2, \ldots $. Note that only when $p=n_i+1$,  $l_i^p = x_i^*$; otherwise $l_i^p < x_i^*$.
The bounds $l_i^1$ and $u_i^1$ are obtained by considering only (first) neighbors of $i$. The bound $u_i^1$ depends on the degree of the node $i$, that is, the information contained in the 1-hop neighborhood of $G$ extracted by starting at node $i$, while for the bound $l_i^1$ one computes the SIS model on the subgraph $G_i^1$, which is the subgraph of neighbors of $i$.
In a similar fashion, the bounds $l_i^2$ and $u_i^2$ are obtained by considering second neighbors of $i$ (neighbors of the first neighbors).
The bound $u_i^2$ can be computed by using $u_j^1$ for all neighbors $j$ of $i$.  Thus, $u_i^2$ reflects the topology of 2-hop neighborhood of $G$ extracted by starting at node $i$. Finally, for $n=n_i +1$, since $G_i^{n_i + 1}$ is the entire graph $G$, $u_i^{n_i+1}$ takes into account the topology of the whole network.
Therefore, it makes sense to calculate the difference $d_i^p = u_i^p - l_i^p$, when $n=p$, and for small values of $p$.
In this way, one could, at least numerically, answer one of the basic questions in mathematical epidemiology for any graph: what is the influence of the graph topology on disease spreading, or more precisely, on the probability that given node will be infected?

Lower bounds are derived as stationary solution of the SIS process for the corresponding subgraphs. On the other hand, upper bounds are found by back-propagation using the equation (\ref{eq:rec-for-u}). As a consequence,  when $p=n_i+1$, $l_i^{n_i+1} =x_i^*$ while $u_i^{n_i+1} > x_i^*$ and thus $d_i^{n_i+1} > 0$.
In fact, see remark 3.3, only when $\lim_{n \to \infty} \left(  u_i^n \right) - l_i^{n_i+1}   = 0$.

In this section we study the Enron e-mail network obtained from \cite{jure-networkdata}, running (\ref{eq:xi-SIS}) on the network. The Enron e-mail network has 33696 nodes and 361622 edges with $\lambda_{1,A} = 118.4177$, and $\beta_{c} =  0.004222$ when
$\delta=0.5$ for the reactive process. We study the upper and lower bounds of the expected density of infection $\rho = \sum_i x_i^* / N$ calculated as
\begin{eqnarray*}
  \hat{\rho_p} = \sum_{i=1}^N \frac{u_i^p}{N} \\
  \breve{\rho_p} = \sum_{i=1}^N \frac{l_i^p}{N} \\
\end{eqnarray*}
for different values of $p$, as well as the average difference $\Delta \rho_p$ between the upper and lower bound for all nodes,
$$
\Delta \rho_p = \sum_{i=1}^N \frac{d_i^p}{N}.
$$
We also calculate $d_i^p$ for 3 nodes: the node with minimum degree, the node with maximum degree, and a node with average degree. To have a better idea of how much local information is being used, Table \ref{table:avgsize} depicts the size of a $p$-hop neighborhood for the Enron e-mail network, $\left| E^p \right|$ , as measured by the number of edges in the corresponding subgraph averaged over all nodes $i$, as well as its fraction of the total number of edges in the network.

\begin{table}[htbp]
\caption{Average size of $p$-hop neighborhood for the Enron e-mail network. $\left| E^p \right|$ is an average of $\left| E_i^p \right|$ over all nodes $i$ and $\left| E \right|$ is the total number of edges in the network.}
\label{table:avgsize} \centering
\begin{ruledtabular}
\begin{tabular}{ccc}
$p$ & $\left| E^p \right|$ & $\left| E^p \right| / \left| E \right|$  \\ \toprule[0.1em]
1 & 10 & 0.0003 \\
2 & 1538 & 0.004 \\
3 & 45067 & 0.125 \\
4 & 207496 & 0.574 \\
\end{tabular}
\end{ruledtabular}
\end{table}

\begin{figure}[htbp]
\centering
\includegraphics[scale = 0.47]{reactive.pdf}
\caption{The density of infective nodes in the Enron e-mail network as the transmission parameter $\beta$ is varied, and $\delta = 0.5$, obtained by simulating (\ref{eq:xi-reactive}) on the network until the model stabilizes, along with the upper and lower bounds, $\hat{\rho_p}$ and $\breve{\rho_p}$, on $\rho$ using  1-hop and 2-hop topology information.}
\label{fig:reactive}
\end{figure}

Figures \ref{fig:reactive} and \ref{fig:gap-reactive} summarize our results.
As depicted in Figure \ref{fig:reactive}, the bounds are surprisingly tight even when only 2-hop topology information is being used. More precisely, we obtain a very good estimate for the infection density $\rho$ by summing over node-level estimates which are using only $0.4\%$ of the network topology on average (see Table \ref{table:avgsize}). The upper bound $\hat{\rho_1}$ is also surprisingly tight given that it only uses the node's degrees while having no information for the edges in the network.

Figure \ref{fig:gap-reactive} shows that the average difference $\Delta \rho_p$ between the bounds decreases as one considers 1-hop, 2-hop, and 3-hop topology information, as expected since the bounds around the stationary infection density $\rho = \sum_i x_i^* / N$ become tighter. Also the spreading becomes less topology dependent as the disease transmission parameter $\beta$ increases.
When $\beta$ is close to $\beta_c$, $x_i^*$ and consequently $\rho$, are close to zero as well. Therefore, as $\beta$ approaches $\beta_c$, it is expected that the value of $x_i^*$ is influenced by the whole network.
For the Enron network, as indicated in Figure \ref{fig:gap-reactive}, the average difference between the bounds calculated from 3-hop neighborhood is close to zero, $\Delta \rho_3 \leq 0.012$ for all $\beta$. Additionally, when $\beta > 0.4$, topology of only 2-hops away is relevant for the spreading process, $\Delta \rho_2 \leq 0.01$. The bounds calculated using only 1-hop topology, i.e. the nodes' degrees are wide apart for all values of $\beta$ for the particular network, indicating that the specific degrees are highly influential in the spreading process.

In this light, we examine the difference $d_i^p$ between the bounds for three randomly chosen nodes with particular degree: one with minimum degree, one with average degree, and one with maximum degree. Note that results vary greatly for the three types of nodes. The difference $d_i^p$ is smallest for the node with minimum degree reaching a maximum of 0.028 for all $\beta$ given only 2-hop topology information (0.4\% of the entire network topology on average). It is also worth noting that the lower bound is very close to the actual result, with the difference being due to the upper bound requiring more information to converge.
Interestingly, while the gap for the node with maximum degree quickly decreases with the increase of $\beta$, it can be large for specific values of $\beta$. In contrast to the minimum degree case, for the node with maximum degree, the difference is due to the lower bound not having converged, while the upper bound is quite tight. Another interesting result for the node with maximum degree is that as $\beta$ gets greater than 0.04, knowing only the neighbors of the node's neighbors suffices for predicting the outcome of the infection.
For the node with average degree, we observe two interesting results. Firstly, the difference $d_i^p$ exists for a relatively wide span of $\beta$ (as in the minimum degree case). The other result is that for some specific values of $\beta$, $d_i^p$ can be relatively large (as in the maximum degree case). However, the difference $d_i^p$ is smaller than 0.03 for all values of $\beta$ given the 3-hop topology information which constitutes approximately 12.5\% of the total network topology on average.

Finally, for all nodes, the bounds on the probability of being infective are tighter as $\beta \to 1$, and looser as $\beta \to \beta_c$. The conclusion from this is that as $\beta \to \beta_c$, network topology plays a bigger role in the dynamics of the spreading process.

\begin{figure*}[htbp]
\centering
\includegraphics[scale = 0.5]{gap-reactive.pdf}
\caption{The average difference $\Delta \rho_p$ between the upper and lower bound (top left) and the difference between the upper and lower bounds that use 2-hop, 3-hop and 4-hop topology information for a node $i$ in the Enron e-mail network that has minimum (bottom left), average (top right) and maximum degree (bottom right) as the transmission parameter $\beta$ is varied and $\delta = 0.5$.}
\label{fig:gap-reactive}
\end{figure*}

\section{Contact process}
\label{sec:4}

\subsection{Bounds on the probability of being infective}

For the contact process, since $r_{ij}=\frac{a_{ij}}{\sum_k{a_{ik}}}$, we rewrite (\ref{eq:xi-stat}) as:
\begin{equation}
\label{eq:xi-contact}
x_i^* = \frac{\left[ 1 - \prod_{j=1}^N (1 - \beta \frac{a_{ij}x_j^*}{\sum_k a_{ik}})  \right]}{\left[ 1 - \prod_{j=1}^N (1 - \beta \frac{a_{ij}x_j^*}{\sum_k a_{ik}})  \right] + \delta}
\end{equation}

From lemma \ref{lemma-contact} and \ref{lemma-contact2} (see Appendix \ref{app-contact}) we have the following bounds for the stationary solution of (\ref{eq:xi-contact})
\begin{equation}
\label{eq:bound-contact}
l_i^0 \equiv \frac{1 - e^{-\beta x_i^*}}{1 - e^{-\beta x_i^*} + \delta} < x_i^* \leq 1 - \frac{\delta}{\beta} \equiv u_i^0
\end{equation}
Note that the bound (\ref{eq:bound-contact}) is independent of the specific network topology. Its left-hand and right-hand side correspond to the stationary solution of (\ref{eq:xi-contact}) for an infinitely large full-mesh graph and a path graph of size 2 respectively.

Similarly to the reactive process, better bounds can be obtained if we use a node's degree:
\begin{eqnarray}
\label{eq:bound-contact-1}
l_i^1 & \equiv & \frac{1 - \left [ 1 - \beta x_p \right ]^{k_i}}{1 - \left [ 1 - \beta x_p \right ]^{k_i}+\delta} < x_i^* \leq \nonumber \\
 & \leq & \frac{1 - \left [ 1 - \beta + \delta \right ]^{k_i}}{1 - \left [ 1 - \beta + \delta \right ]^{k_i}+\delta} \equiv u_i^1
\end{eqnarray}
where $k_i$ is the degree of node $i$ and $x_p$ is the solution of the equation:
\begin{equation*}
x=\frac{1 - e^{-\beta x}}{1 - e^{-\beta x} + \delta}
\end{equation*}
More generally, by using $n$-hop neighborhoods, the stationary solution of (\ref{eq:xi-contact}) for an arbitrary node $i$, $x_i^*$, is bounded by,
\begin{equation}
\label{eq:bound-contact-all}
l_i^0 < l_i^1 < \ldots < l_i^n  <  x_i^* \leq u_i^n \leq \ldots \leq u_i^1 \leq u_i^0
\end{equation}
where
\begin{eqnarray*}
 l_i^n  =  \frac{1 - \prod_{j=1}^N (1 - \beta r_{ij} l_j^{n-1})}{1 - \prod_{j=1}^N (1 - \beta r_{ij} l_j^{n-1}) + \delta} \mbox{ and } \\
 u_i^n  =  \frac{1 - \prod_{j=1}^N (1 - \beta r_{ij} u_j^{n-1})}{1 - \prod_{j=1}^N (1 - \beta r_{ij} u_j^{n-1}) + \delta}
\end{eqnarray*}
and
\begin{equation*}
l_i^0 = \frac{1 - e^{-\beta x_i^*}}{1 - e^{-\beta x_i^*} + \delta} \mbox{ and } u_i^0 = 1 - \frac{\delta}{\beta}
\end{equation*}
For a formal definition and proof see theorem \ref{theorem-contact-all} in Appendix \ref{app-contact}. Note that here, unlike in the reactive process, the problem with $u_i^0 = 1 - \delta/\beta$ when $\delta>\beta$ is avoided since $\beta_c > \delta$.
\subsection{Numerical results}

Again, it makes sense to calculate the difference $d_i^n = u_i^n - l_i^n$ between the upper and lower bound derived by using n-hop topology information for node $i$ to determine the dependence of the contact process on the specific network topology.

Figures \ref{fig:contact} and \ref{fig:gap-contact} show the numerical results. As in the reactive process, we study the upper bound $\hat{\rho_p}$ and lower bound $\breve{\rho_p}$ on $\rho$, as well as the average difference between the upper and lower bounds $\Delta \rho_p$. We also study $d_i^p$ for 3 nodes: the node with minimum degree, a node with average degree, and the node with maximum degree. Note that $\beta_c = 0.5$ when $\delta = 0.5$.

In general, the contact process is less dependent on the network topology than the reactive process, as the largest value of $\Delta \rho_1$ is an order of magnitude less than the corresponding value for the reactive process. The more topology information is included in the calculation of the bounds, the difference between them decreases. Also, the probabilities that each of the 3 examined nodes is infective are equally dependent on the network topology, since $d_i^n$ for $n = 1,2,3$ are similarly valued. Contrary to the reactive process, the bounds on the probability of being infective are tighter as $\beta \to \beta_c$ (see Figure \ref{fig:contact}). In the Appendix \ref{app-limit}, we show that when $\beta$ is close to $\beta_{c}= \delta$, the probabilities of being infective have an analytical solution in closed form, they are no longer topology dependent, and are functions only of the spreading process parameters $\beta$ and $\delta$.

\begin{figure}[htbp]
\centering
\includegraphics[scale = 0.45]{contact.pdf}
\caption{The expected infection density $\rho$ in the endemic state for the Enron e-mail network for the contact process as $\beta$ is varied, and $\delta=0.5$. The bounds on $\rho$ calculated with no topology information $\hat{\rho_0}$, $\breve{\rho_0}$, 1-hop topology information $\hat{\rho_1}$, $\breve{\rho_1}$, and 2-hop topology information $\hat{\rho_2}$, $\breve{\rho_2}$ are depicted as well.}
\label{fig:contact}
\end{figure}

\begin{figure*}[htbp]
\centering
\includegraphics[scale = 0.4]{gap-contact.pdf}
\caption{The average difference $\Delta \rho_n$ between the upper and lower bound (top left) and the difference between the upper and lower bounds that use 0-hop, 1-hop, 2-hop and 3-hop topology information for a node $i$ in the Enron e-mail network that has minimum (bottom left), average (top right) and maximum degree (bottom right) as the transmission parameter $\beta$ is varied and $\delta = 0.5$.}
\label{fig:gap-contact}
\end{figure*}

\section{Conclusions}
\label{sec:conc}

In this paper we have derived the upper and lower bounds on the probability that a node is infective for the SIS model of infection spreading on networks, where the behavior of a node is modeled with a discrete-time Markov chain SIS model. We have considered the reactive and the contact process as two cases of the spreading process. For both processes we use the difference between upper and lower bounds on microscopic level to assess the dependence of the spreading processes on network topology. Numerical results are given on the Enron e-mail network. For both processes, the bounds are progressively better as one considers a larger $n-$hop neighborhood of a node. For the reactive process, both bounds on the probability that a node is infective are tighter as $\beta \to 1$ and their difference is largest for nodes with average degree. Conversely, the bounds on the probability that a node is infective for the contact process are tighter as $\beta \to \beta_c$.

One  of the main implications of the paper is that if $\beta$ is larger than its critical value (when $\beta$ is close to $\beta_c$ the probability of a node to be infective is anyway close to zero), one can estimate the probability of being infective using only local information (considering only $n-$hop local topology, for small $n$), without knowing the whole network. Consequently, from this local information one can also estimate the density of being infective on the whole network, as well as assess the extend to which the topology affects the outcome of the infection on macroscopic level.

The results of this paper are easily extendable to other ergodic models (such as SIRS, for example) and are related to all types of spreading (idea, failure, rumor) \cite{rumor-model, GoffmanNewill, infoblogspace}, regardless on the type of the spread agent. How these results can be extended to SIR model by considering SIRS model and taking one of its parameters to approach zero (or one) so that SIRS model in this limit approaches SIR model is a question for further research.

redpajama_set_name: RedPajamaArXiv


There's a lot of visual legerdemain on display in Opera Atelier's production of The Magic Flute, which opened Saturday night at the Elgin Theatre, but due to a certain earthbound quality to much of the music making, it's difficult to call the whole experience the sort of enchanted evening one was expecting.
Director Marshall Pynkoski has staged this work many times before, most recently in an acclaimed 2006 mounting that featured some of the current cast, but magic — especially of the Mozartian variety — is an elusive will o' the wisp and this production doesn't ultimately capture its essence.
Things start off very promisingly, with Gerard Gauci's exquisitely painted set proving to be the pop-up book of everyone's dreams, complete with a sublime dragon.
Colin Ainsworth establishes once again, from his very first notes, that vocal purity is the best attribute a tenor can possess. Add perfect leading man looks and a wonderful sense of bewildered charm and you have the quintessential Tamino.
The three attendant ladies of the Queen of the Night who magically float into view are also deft performers: Carla Huhtanen, Cassandra Warner and Laura Pudwell provided the sweetest of sounds with the tartest of commentary in a vintage bit of Pynkoski's staging.
All seemed set for fair sailing, but there were problems on the horizon. Although he has been much admired in the past, I found Olivier LaQuerre not quite comically endearing enough for my taste as Papageno, a role that can admittedly wear out its whimsical welcome rather quickly.
And while there isn't really anything to fault vocally in Laura Albino's by-the-book rendition of Pamina, our endangered heroine, there's a certain flat-footedness to her performance that robs our story of one of its major tent posts: a lady worth going through hell to redeem.
Things sink down a bit further when we finally get into the domain of the evil sorcerer, Sarastro. Admittedly, this is where Emanuel Schikaneder's libretto gets a bit much, combining elements of Moorish villainy, Freemason rituals and Viennese comedy, not always to the best effect.
A seemingly endless dance sequence involving saffron-robed men of Middle Eastern appearance waving wheat sheaves brought to mind the cast of Homeland performing a musical number from Oklahoma!, which is really not the right idea at all.
And the evil slave, Monostatos — admittedly a hard role to play without falling into racial stereotyping — is given a simply dull reading, both dramatically and vocally, by Aaron Ferguson.
Probably the biggest musical disappointment of the evening was the Sarastro of Joao Fernandes, whose imposing physical presence was undercut by a vocal performance lacking in power as well as clarity.
With a weakish villain and a lacklustre heroine, we couldn't really get all that involved with the story, despite Ainsworth's best efforts as our hero.
There was, however, a wonderful wake-up call given the production by Ambur Braid as the Queen of the Night. She eschewed the diva-esque posturing that many women adopt for the role and gave us instead a ravishing creature of glacially cold evil, which made the sharply carved icicle notes she dispensed during her signature Act II aria seem all the more appropriate.
The fact that Ainsworth, Braid and some of their colleagues were capable of reaching the high bar that Mozart has set for them means that Pynkoski knows where a great production of The Magic Flute ought to go.
But with less than inspired vocal support further down the line and a solid, but surprisingly unentrancing reading of the score by David Fallis and the Tafelmusik Baroque Orchestra, it's no wonder that the show's intense visual beauty actually proved cloying by the final curtain.
Everyone admits that the libretto of The Magic Flute is an earthbound affair, just fine for the suburban Viennese theatre, where it debuted in 1791. But the music, written by Mozart in the final year of his life, is something truly glorious that has endured the centuries.
Opera Atelier usually strikes a superb balance between sight and sound, which is one of its unique strengths. This time around, however, things are lovely to look at, as always, but not so magical to hear.


We were recently asked to extend the Code Analysis rules for Visual Studio. Here is an example I prepared for a demo which I have to show how an organization can add their own custom rules to FxCop. The assembly can then be deployed to your developers and can also be deployed to your Visual Studio Team Foundation Build server so your rules can be checked during any server builds you are doing.
The following example class simply scans the code to enforce a naming convention and provide a warning (or error) to the developer that it is not compliant with your companies coding standards. This makes the manual code review more efficient. If you are looking for a tool to do Code Reviews with your developers I would recommend you check out Team Foundation Sidekicks 2008 by Attrice Corporation.
I created a new empty Windows Class Library project in Visual Studio 2008 named RuleTest.
I added the following references: FxCopCommon, FxCopSdk and Microsoft.Cci. These are located in the following directory: C:\Program Files (x86)\Microsoft Visual Studio 9.0\Team Tools\Static Analysis Tools\FxCop. NOTE: On a 32-bit system the "Program Files" directory is simply named "Program Files", I built this sample on Vista x64 so my "Program Files" directory for Visual Studio is located under "Program Files (x86)".
When you compile your Class Library and get your assembly you must place it in the following directory so Visual Studio will use it. NOTE: You will have to close Visual Studio to get it to load your new rule.
Then you can right click your project and select "Run Code Analysis"
The code for this custom rule demo is posted here on my SkyDrive.


I have a white prayer shawl with Shivas on it. I wear it while meditating and in satsang. This is the shakti. The perfect shakti to create the balance when sometimes Kali Ma is the only one who can hold my hand while I'm doing the WORK. The quality is amazing and you won't find one like this anywhere except for Ma's India.
The shawl is lovely. It's a great design and the material is very nice. I am very pleased with my purchase.


Many modern moisture meters use digital displays and have a wide variety of special features meant to make them more versatile as moisture testing tools. However, not every user needs or favors digital moisture meters. Some users prefer an analog moisture meter design that emphasizes simplicity and reliability over fancy features.
One example of a high-end analog pin moisture meter that both amateurs and professionals enjoy using is Delmhorst's own BD-10 moisture testing device.
The bright and clear analog display on the BD-10 is designed to be incredibly easy to read, and the pin moisture meter is easy to use—simply push the pins into the material to be tested and push the button. The needle on the analog display will move to indicate the moisture content of the material being tested.
Delmhorst's BD-10 moisture meter is calibrated for a wood moisture reading scale for use with flooring, wood studs, and other hardwood materials. For all other building materials, the BD-10 has a secondary reference moisture reading scale. While the wood reading scale is able to provide quantitative measurements of moisture in wood, the reference scale provides qualitative moisture measurements. This reference moisture reading scale is typically used to get quick pass/fail moisture content assessments in non-wood materials.
Because the meter is an analog type with a simple button-press operation, it's incredibly easy to learn. This makes it ideal both for amateur users and for pros who need a simple moisture testing device for their employees to use while they get used to testing moisture content.
Any moisture testing device, no matter how rugged, will eventually slip out of calibration. It's important to have a means of testing pin moisture meter accuracy on a moment's notice. In most cases, this requires a secondary device such as a moisture content standard (MCS). However, in the case of the BD-10 pin moisture meter, the device has a built-in calibration check.
All you have to do to verify moisture meter accuracy for Delmhorst's BD-10 meter is push a button. The meter takes care of the rest. If the moisture meter is accurate, the needle should fall somewhere within the green band on the analog display.
As with all of Delmhorst's pin moisture meters, the BD-10 is designed from the ground up to be lightweight enough to not be a burden on a user's tool belt, but rugged enough to stand up to the tough conditions that may be found on the jobsite. This helps to ensure the BD-10 can provide years of reliable use.
This moisture testing device weighs a mere 10 ounces, and features easy-to-replace pins at the top—making it easy to keep the meter operating in top condition.
Like all of Delmhorst's pin moisture meter models, the BD-10 features a universal probe socket design that allows users to attach any Delmhorst moisture meter electrode to it. This greatly enhances the utility of the BD-10 pin moisture meter because the specialty electrodes can allow it to be used for testing different building materials in areas that would be hard to reach reliably with the standard pins at the top of the meter.
For example, the 26-ES electrode can get deep into insulation to test it safely or it can punch through a wall with its insulated pins to test the fiberglass (or other insulating material) behind it.
All of the above makes the BD-10 a great moisture testing device for both DIY enthusiasts and for professionals alike. If you need a reliable and accurate moisture testing solution, reach out to the experts at Delmhorst today!


text:
Sports & Gaming
How to Deal with Failure
Lesson time 12:05 min
While Lewis has won more races than anyone in F1 history, he has learned valuable lessons from losses along the way. Learn how to deal with adversity and failure, and how to use those experiences to help you improve and get stronger.
Students give MasterClass an average rating of 4.7 out of 5 stars
Topics include: Why Failure Is Necessary Confront Your Challenges Set Yourself Impossible Goals Evolve Your Relationship With Failure Review Mistakes to Improve Preparation
Share Lesson
Teaches a Winning Mindset
World racing champion Lewis Hamilton teaches you how to prepare your mind, body, and spirit for victory in your own life.
1. Meet Your Instructor
2. Ignite Your Passion
3. The Power of Influences & Inspiration
4. At One with the Machine
5. How to Deal with Failure
6. How to Build Trust and Promote Teamwork
7. How to Exercise Self Discipline
8. Optimize Your Body for Performance
9. Mental Preparation
10. The Power of Diverse Interests
11. Influence the World Beyond Your Own
12. Pave the Path for Others
[MUSIC PLAYING] LEWIS HAMILTON: My first race, I remember I was practicing, I was going into this first corner, and this young kid hit me from behind. And I went off into the wall, crashed into these big tires, hit my head on the steering wheel. Nose was bleeding, car was busted. I remember my dad, like, running. And I remember him arriving just terrified. Are you okay, are you okay? And I was like, can you fix the car for the race? That's all I was concerned with, because I still wanted to race, and we had a race to win. And the next day, we won a race after my first race. I kind of never looked back from then. [MUSIC PLAYING] I have a very close relationship with failure. And the reason for it is I've failed more times than I can remember. But the lessons that I've learned through those failures have ultimately ended up with me having success. It's character building. It's where I hone in on my strengths or where I build strength. It's those difficult times where you think, am I not good enough? Should I stop? Now, I've made sometimes the same mistake multiple times. But that's okay. Because eventually, through trial and error, I don't make those mistakes anymore. Failure-- in my opinion, failure is 100% necessary for greatness. To achieve greatness, to have that success, you've got to fail as many times as possible. So don't shy away from it. And don't take it as a negative. Every single successful person who's achieved great things, whether it's climbing Mount Everest, whether it's getting to a top of a company, whether it's being the best athlete possible, they've all failed more times than they'll be able to remember. But through those lessons that they've learnt through those failures, that's how they've become great. No one's been great from the get go and then just being great. That's-- except for Superman, because he was just born great. So just know that that is a part of the journey. And whatever failures you have are only going to make you stronger. [MUSIC PLAYING] When I first got to cars, I was progressing from go-karts to cars. It's a big, big step, really exciting, because it was the first time I would have a car that looks like a Formula One car. And if the step goes right, I might be on my way to getting to Formula One. This is what all the other greats have been through this process. So this is the way. And as soon as I got there, I was crashing all the time-- crashing, finishing far down the grid. I wasn't winning the races, couldn't keep up with the other guys, because every time I tried to eke out more performance, I would crash. So it was really hard to get to the limit. My confidence was really shot. There was a moment where we-- me and my dad, we arrived home. We were sat in front of the garage in the car. And we didn't get out for 5-10 minutes. And in that moment, I thought my career was over. We were both like, maybe, maybe you're just not b...
As the winningest Formula 1 driver in the history of the sport, Lewis Hamilton knows what it takes to come out on top. Now, he's teaching you how to achieve greatness in your own life. Whether you already know your goals or are still trying to figure them out, you'll learn how to face your fears, turn negatives into positives, and continuously challenge yourself in order to find—and reach—your true potential.
Featured Masterclass Instructor
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redpajama_set_name: RedPajamaCommonCrawl


text:
Stephen Hicks Wins Prize for Smart Glasses
Award Clinical Neurology
Stephen Hicks, Research Fellow in Neuroscience and Visual Prosthetics, has won the 2014 SET for BRITAIN Gold Award and Engineering Medal
Andrew Smith, MP for Oxford East, with Dr Stephen Hicks at the exhibition
SET for BRITAIN is a series of poster competitions and exhibitions run by the Parliamentary and Scientific Committee in the House of Commons. Its main purpose is to encourage, support and promote Britain's early-career research scientists. This year's exhibition and reception took place in the House of Commons Terrace Marquee on 17 March 2014 during National Science and Engineering Week.
The judges considered 120 posters in the five fields of Biomedical Science, Chemistry, Engineering, Mathematics, and Physics. They awarded the prizes based on the very best research work and results by an early-stage or early-career researcher together with their ability to communicate their work to a lay audience.
Dr Hicks is based in the OcuLab research group in the Nuffield Department of Clinical Neurosciences and also works closely with the Department of Engineering. His work, primarily funded by the National Institute for Health Research, aims to improve functional vision for people with severely impaired sight.
Over 300,000 people in the UK are registered as blind. Stephen Hicks and colleagues are developing a pair of smart-glasses to help people use their remaining vision to see and avoid obstacles and enjoy increased independence. Using computer vision and electronic components usually found in mobile phones, the researchers are building and testing concepts which they intend to use to construct an affordable pair of glasses. The smart-glasses comprise a camera to sense the environment and a digital display to show an enhanced view.
The latest prototype glasses use a depth camera which measures the distance to nearby objects, a little like radar. The researchers have developed algorithms that build, process and update 3D models of the local environment in essentially real time. Nearby objects are shown as bright regions of light and distant objects or clear paths are shown as dark. The floor plane is detected in order to emphasise trip hazards and steps.
The lenses are Organic Light Emitting Diodes that show an enhanced image to the wearer while appearing transparent to everyone else. This allows the eyes to be seen, which is important for social interaction.
User testing has shown that the glasses currently in development are already helping registered blind people to have a better ability to detect potential obstacles in their environment.
This SET for BRITAIN Gold Award and Engineering Medal comes on top of the Royal Society Brian Mercer Award for Innovation won by Stephen Hicks in 2013.
Download Stephen Hicks' SET for BRITAIN 2014 poster 'Smart glasses to help the blind to see'.
You can find more information about this research at the Oxford Smart Specs Research Group website.
Testing epilepsy drug on people with Alzheimer's disease
Timothy Behrens recognised in prestigious Blavatnik Awards for Young Scientists
Parkinson's research group receive data sharing award
Angela Vincent honoured for excellence in epilepsy research
Ground-breaking study for Huntington's disease under way
Sarosh Irani wins Graham Bull Prize
NDCN staff win teaching awards
Oxford is joint top recruiter to drug-resitant epilepsy study
Advances made in understanding how eye movements are affected by medication in Parkinson's
Prize for work on gene therapy for retinal diseases


Turn your Tripp Trapp into a stand-alone high chair with the Stokke Tray. Perfect for quick feedings or crowded tables, the Scandinavian designed Stokke Tray's clean lines compliment the Tripp Trapp for a unique, stunning seat. Suitable for 6 months to 3 years. Note: The Stokke Tray is not designed to hold the child in the chair. We recommend you always use the Tripp Trapp harness when your child is seated in the chair.


The PT1322 is a highly efficiency, current mode control step-up DC/DC converter with an integrated 120mΩ RDS(ON) N-channel MOSFET. The fixed 1MHz switching frequency and internal compensation circuitry reduce external component count and save the PCB space. The built-in internal soft-start circuitry minimizes the inrush current at start-up. The PT1322 is available in SOT23-6 package.


Storage costs can soon mount up if your running a large file hosting site. To limit this as much as possible, YetiShare will only ever store 1 copy of each file.
Duplicate files are not stored, so the same file will only ever be kept in storage once. Unique download urls are still generated on each upload for stats, privacy etc.
Deleting a file removes the download url, not the original file, if there's more than 1 in the system. Deleting the last download url of a file will remove the original.
Logging of md5 file hashes on upload. Optionally show these to your users to validate file contents.
File servers can be chained to store files until full. See the file servers page for more information.


Samsung has announced that its 2019 lifestyle TVs will be on display at CES 2019.
The Frame and Serif TVs both offer QLED displays and a range of smart features, said the company.
"The traditional TV was only focused on technical features, such as picture quality and performance, but now TVs are also a lifestyle platform that blends in consumers' daily life," said Samsung.
"This year's models are enhanced lifestyle TVs that deliver a TV experience like nothing before."
Samsung's 2019 Frame TV displays digital pieces of artwork when the TV is not in use, imitating a painting frame, and also features a Luminance Sensor to adjust on-screen colours based on ambient brightness.
This is on top of a new QLED panel in the device, along with Samsung's digital assistant Bixby.
The new Serif TV is also focused on looking more like a work of art than a normal TV, and combines this with Samsung's latest QLED technology.


Home › More News › 2/3/17 ~ New Employment Opportunity!
2/3/17 ~ New Employment Opportunity!
The Wakulla County Board of County Commissioners is seeking qualified applicants for a Planner position in the Planning and Zoning Division. This is a full-time professional position, which involves technical review of planning and zoning applications; including variances, site plans, rezoning requests, land use amendments, subdivision requests and other land development proposals. This position also assists in the administration of the Comprehensive Plan and the Land Development Code by providing technical planning information to the public, Wakulla County Board of County Commissioners and the Planning Commission. Special projects will be assigned to this position as warranted by the Director of Planning and Community Development.
The successful applicant will be knowledgeable in one or more areas related to urban planning such as: comprehensive planning, zoning, infrastructure (storm water, transportation, etc.), or environmental issues.
Minimum qualifications include 18 years of age, high school graduate, a Bachelor's Degree (B.A.) in Urban Planning, Geography or related field and/or 3 years of applicable experience, or an equivalent combination of education and experience.
Strong written and verbal communication skills are required; familiarity with plans review, G.I.S. and/or transportation planning is a plus.
To apply, send a Wakulla County application to: Human Resources, P.O. Box 1263, Crawfordville, Florida 32326. County applications are available at: www.mywakulla.com or at the County Administrator's Office, 3093 Crawfordville Highway, Crawfordville, Florida 32327. Previous applicants are still being considered and need not re-apply. Drug screening is required. Veteran's Preference will be given to qualified applicants. Wakulla County is an Affirmative Action/Equal Opportunity Employer. Salary will be based upon qualifications and experience. Closing date for this position is Friday, February 24, 2017.


text:
300 Troops Moved to California From Arizona, Texas to Help Protect Border
by: Associated Press, Mary Beth McDade
Posted: Nov 26, 2018 / 03:04 PM PST / Updated: Nov 26, 2018 / 10:55 PM PST
The military says about 300 troops who had been deployed in south Texas and Arizona as part of a border security mission have been moved to California for similar work.
In a statement Monday, U.S. Northern Command says the 300 include military police and engineering and logistics troops. They were moved to California over the past several days.
The total number of active-duty troops now involved in the border mission, which began in late October, has dropped to about 5,600, according to Northern Command. Last Wednesday, Defense Secretary Jim Mattis said the number was 5,764, and officials had previously said it was between 5,800 and 5,900.
The military's role is limited largely to erecting barriers along the U.S.-Mexico border and providing transportation and logistical support to Customs and Border Protection.
Trademark and Copyright 2021 The Associated Press. All rights reserved.
by Erika Martin / Jan 15, 2021
Dozens more partiers were arrested as sheriff's officials busted three underground events in central Los Angeles Thursday night, deputies say.
The operation by the L.A. County Sheriff's Department's Super-Spreader Task Force targeted two locations in downtown L.A. and a third venue in Mid-City, where officials say a total of 137 people were arrested.
Nation/world / 1 hour ago


SING HALLELUJAH FOR THE ALL NEW PRODUCTION OF SISTER ACT STARRING ALEXANDRA BURKE!
This all new production of SISTER ACT is directed and choreographed by Craig Revel Horwood with musical supervision and arrangements by Sarah Travis. Set and costume design is by Matthew Wright, with lighting design by Richard G Jones and sound design by Richard Brooker.
Come and see the habits hit the road again and why this fabulous family friendly show has been seen by more than 6 million people worldwide.
Alexandra Burke singing Fabulous Baby!


Mesothelioma is a "despicable disease", but there is an opportunity to "fight it head-on". That was the message from the Institute of Occupational Safety and Health (IOSH) at the launch of the latest phase of its No Time to Lose campaign.
The event was held on 9 April at BMA House in London. On the same day an IOSH-organised 'thunderclap' – a social media tool used to spread messages to as wide an audience as possible – was sent out from 295 social media accounts, reaching an audience of nearly half-a-million.
At the seminar, stakeholders and industry professionals heard how IOSH plans to raise awareness of the risks of exposure to asbestos – the most deadly carcinogen – in workplaces.
Every year, well over 100,000 people die across the globe from an asbestos-related disease; yet an estimated 125 million are still exposed at work annually. In the UK alone, the annual death toll from asbestos-related diseases caused by workplace exposure stands at about 5,000. The most common of those diseases is mesothelioma.
Liz Darlison, director of services at the charity Mesothelioma UK, described No Time to Lose as a "wonderful campaign" and urged delegates to take action. She said: "Mesothelioma is the most despicable cancer you can imagine being diagnosed with. It's a death sentence.
Liz highlighted the fact that 20 tradesmen die in the UK every week from asbestos-related diseases.
Colette Willoughby, the principal examiner for asbestos at the British Occupational Hygiene Society (BOHS), said asbestos is an issue for everyone – adding that tens of millions of tons of the mineral still remains in UK buildings. In fact, an estimated half a million UK buildings still contain asbestos, despite its use being banned in 1999.


text:
Season's musings
Whether you be a news junkie, a media-savvy person, a Joe Blow or a Johnny-come-lately, you must have been bingeing on the recent uplifting news of the nomination of Claude Gay, the daughter of a Haitian immigrant, to the post of Harvard President. From very reliable sources, her father is an engineer and an alumnus of St Martial and a cousin of hers, Roxane Gay, is a writer and op-ed contributor to the NY Times. Indeed, it is a big deal since it reeks of trailblazing cachet: first African American (man or woman) and second woman ever for this prestigious post. Such event in its implication resembles the famous milestone in November 2008 when the son of an African immigrant broke a most singular glass ceiling to become a resident of 1600 Pennsylvania Ave.
Within the past few years, we have had our pick of pride-generating stories. Barely a few weeks ago, Rice University held a festive-cum-great pomp celebration of a Haitian-born engineer as a first African American President, Réginald Desroches. The Lone Star state was the last to enact the emancipation edict of Abe Lincoln and that gave rise to the present-day Juneteenth celebration. For the longest time, Rice University had the reputation of an institution with hidebound traditions. Therefore, it was a remarkable break with its past to have picked such an individual. Prior to that a few years ago, it was the turn of Reynold Verret at Xavier University. As luck would have it, Réginald Desroches's brother, Pascal Desroches, was recently elevated as CFO at AT&T. Of course, we have a seat at the table in the upper echelon of medical academic centers at NYU, Yale and University of Miami with François, Désir and Ford, respectively.
All of this sounds like soothing music to our ears, lately victims of cacophonous sounds of bleak news from our homeland. The contrast couldn't be starker. As if the dark side of the above fairy tales exists for the stated purpose of spoiling our joy. The same outlets that make us binge also provide gory details about some very unpleasant developments back home. We have become unwitting witnesses, enfolded in unfolding events over which we hold little influence that carry life-altering consequences for us.
This conundrum comes straight out of Machiavelli's road map of malfeasance, or Dante's version of modern-day Inferno. One would be hard-pressed to find a more appropriate term to describe the mayhem taking place. This places our birthplace in the most unpleasant casting of a play about kindred spirits relishing the chaos à la Somaliland. The practical effect on our psyche is that we become ensconced in a position of receiving a gift coin with faces holding opposite vectors: awe and shock. Like the awe of such paramount achievements being belittled by the repulsive shock felt at the sight of hooligans burning or ransacking schools, of all places, with impunity. Or one can see the tale of two different societal outcomes based on reverence of a yardstick of scholarship. One rewards it and another is busy to eschew it and put it asunder. Education reverence encourages the systematic building of temples for its dissemination, nurture and preservation.
When education of the populace resides in a very distant second tier position, erection of temples follows a half-hearted, scattershot pattern. Such higgledy-piggledy arrangement eventually allows replacement of hallowed temples in a hollowing-out process by rubbles. Hence knowledge dissemination becomes stymied, and instead of measuring up to international yardsticks, the reign of free fall begins. Imagine if a society capable of birthing such amazing minds were instead using its resources in the business of nurturing such temples. One would end up with success stories like South Korea in a matter of a few generations!
If this above zeitgeist were not bad enough, we have to contend with a cruel, cynical observation that "we are smart enough to shine at the most competitive level overseas but dumb enough to always allow the incompetent and corrupted members of our lot to handle the helm of our nation." As always, this begs the question, "How come?" A simple question with a very complicated answer, if one could be found to begin with. "How come" has now acquired the status of a holy grail search. It also forces us to reckon with an anomaly that has lasted far too long. The brain drain that leaves the field parched, threadbare, creates a void filled by the less capable and establishes a vicious cycle that feeds on itself.
The acceleration of the drain of the underclass speaks volume for the wretched conditions. For the longest time they were willing to face the dangers of rickety boats bracing unfriendly high seas turbulence to land ashore in South Florida as "boat people." US Coast Guards vigilance and constant repatriation of loaded boats has changed the venue. Desperation nowadays makes folks go on the treacherous trek on foot of long distances from South America to reach a promised land without missing a beat. I once visited a batey when AMHE held its only congress in the Dominican Republic. I was floored when many of our compatriots repeated verbatim, "No matter how bad things are in the DR, they are even worse back home."
"How come" needs to be asked by each of us because we should be able to say, "Let's put an end to this nonsense and let's start taking care of this sick patient called our motherland."
As a terrible year is in the throes of its last leg and another one is announcing its arrival to bring some shimmy and its own sashay, we can only hope that better days are ahead and reason will prevail over madness, enlightenment will call dibs over backwardness and finally that light will fray a path bereft of and simply allergic to darkness.
I wish each and every one of you Merry Christmas and Happy New Year and may your health be better.


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Could Mistletoe Give the Kiss of Death to Cancer?
30-Nov-2012 9:00 AM EST, by University of Adelaide
The University of Adelaide.
Health Sciences student Zahra Lotfollahi with a sample of mistletoe extract at the University of Adelaide's Waite Campus.
A sample of the mistletoe extract Fraxini, which has shown the most promise in early laboratory tests at the University of Adelaide.
Newswise — Mistletoe has become an important symbol of Christmas but it also has the potential to play a vital role as an alternative therapy for sufferers of colon cancer.
At the University of Adelaide in Australia, scientists are interested in how the extract of mistletoe could either assist chemotherapy or act as an alternative to chemotherapy as a treatment for colon cancer.
Colon cancer is the second greatest cause of cancer death in the Western world. Mistletoe extract is already authorized for use by sufferers of colon cancer in Europe, but not in some countries such as Australia and the United States due to a lack of scientific testing.
For her Honours research project recently completed at the University of Adelaide, Health Sciences student Zahra Lotfollahi compared the effectiveness of three different types of mistletoe extract and chemotherapy on colon cancer cells. She also compared the impact of mistletoe extract and chemotherapy on healthy intestinal cells.
In her laboratory studies, she found that one of the mistletoe extracts - from a species known as Fraxini (which grows on ash trees) - was highly effective against colon cancer cells in cell culture and was gentler on healthy intestinal cells compared with chemotherapy.
Significantly, Fraxini extract was found to be more potent against cancer cells than the chemotherapy drug.
"This is an important result because we know that chemotherapy is effective at killing healthy cells as well as cancer cells. This can result in severe side effects for the patient, such as oral mucositis (ulcers in the mouth) and hair loss," Ms Lotfollahi says.
"Our laboratory studies have shown Fraxini mistletoe extract by itself to be highly effective at reducing the viability of colon cancer cells. At certain concentrations, Fraxini also increased the potency of chemotherapy against the cancer cells.
"Of the three extracts tested, and compared with chemotherapy, Fraxini was the only one that showed a reduced impact on healthy intestinal cells. This might mean that Fraxini is a potential candidate for increased toxicity against cancer, while also reducing potential side effects. However, more laboratory testing is needed to further validate this work," Ms Lotfollahi says.
"Mistletoe extract has been considered a viable alternative therapy overseas for many years, but it's important for us to understand the science behind it," says one of Ms Lotfollahi's supervisors, the University of Adelaide's Professor Gordon Howarth, a Cancer Council Senior Research Fellow.
"Although mistletoe grown on the ash tree was the most effective of the three extracts tested, there is a possibility that mistletoe grown on other, as yet untested, trees or plants could be even more effective.
"This is just the first important step in what we hope will lead to further research, and eventually clinical trials, of mistletoe extract in Australia," Professor Howarth says.
Credit: The University of Adelaide.
Caption: Health Sciences student Zahra Lotfollahi with a sample of mistletoe extract at the University of Adelaide's Waite Campus.
Caption: A sample of the mistletoe extract Fraxini, which has shown the most promise in early laboratory tests at the University of Adelaide.


text:
Carriera
Ottenuta la cittadinanza azera, nel 2016 debutta con la selezione caucasica. Negli europei del 2018 segna tre reti nella vittoria per 5-3 contro la Francia. Il 16 gennaio 2022 viene incluso nella lista definitiva dei convocati dell' per il campionato europeo 2022.

Note

Collegamenti esterni

redpajama_set_name: RedPajamaWikipedia


Band to Join, Vocalist, Vocalist - Baritone, Vocalist - Tenor, Vocalist - Soprano, Rhythm Guitar, Lead Guitar, Acoustic Guitar, Bass Guitar, Drums, Trumpet, Keyboard, Piano, Background Singer, Fiddle, Dobro, Vocalist - Alto, Steel guitar, Harp.
Lots of artist out there that have influenced me, but the one that stands out as far as inspiring me to play is my dad.
Gibson EB bass Markbass amp and lots of PA stuff, too much to mention.


text:
Q: Undefined local variable or method `conn' for main:Object (NameError) on Dashing start I am trying to setup a Dashing dashboard for some monitoring. The data to be used to populate the dashboards widgets will be coming from an Oracle database. Dashing has been installed and the test dashboards are working fine but when I created my own job to populate a widget with data from the Oracle instance dashing fails to start, the following error is displayed

/home/{home}/dashboard/jobs/new.rb:25:in `<top (required)>': undefined local variable or method `conn' for main:Object (NameError)
    from /usr/local/lib/ruby/gems/2.0.0/gems/backports-3.6.8/lib/backports/std_lib.rb:9:in `require'
    from /usr/local/lib/ruby/gems/2.0.0/gems/backports-3.6.8/lib/backports/std_lib.rb:9:in `require_with_backports'
    from /usr/local/lib/ruby/gems/2.0.0/gems/dashing-1.3.7/lib/dashing/app.rb:171:in `block in require_glob'
    from /usr/local/lib/ruby/gems/2.0.0/gems/dashing-1.3.7/lib/dashing/app.rb:170:in `each'
    from /usr/local/lib/ruby/gems/2.0.0/gems/dashing-1.3.7/lib/dashing/app.rb:170:in `require_glob'
    from /usr/local/lib/ruby/gems/2.0.0/gems/dashing-1.3.7/lib/dashing/app.rb:181:in `<top (required)>'
    from /usr/local/lib/ruby/gems/2.0.0/gems/dashing-1.3.7/lib/dashing.rb:3:in `require'
    from /usr/local/lib/ruby/gems/2.0.0/gems/dashing-1.3.7/lib/dashing.rb:3:in `<top (required)>'
    from config.ru:1:in `require'
    from config.ru:1:in `block in '
    from /usr/local/lib/ruby/gems/2.0.0/gems/rack-1.5.5/lib/rack/builder.rb:55:in `instance_eval'
    from /usr/local/lib/ruby/gems/2.0.0/gems/rack-1.5.5/lib/rack/builder.rb:55:in `initialize'
    from config.ru:1:in `new'
    from config.ru:1:in `'
    from /usr/local/lib/ruby/gems/2.0.0/gems/thin-1.6.4/lib/rack/adapter/loader.rb:33:in `eval'
    from /usr/local/lib/ruby/gems/2.0.0/gems/thin-1.6.4/lib/rack/adapter/loader.rb:33:in `load'
    from /usr/local/lib/ruby/gems/2.0.0/gems/thin-1.6.4/lib/thin/controllers/controller.rb:182:in `load_rackup_config'
    from /usr/local/lib/ruby/gems/2.0.0/gems/thin-1.6.4/lib/thin/controllers/controller.rb:72:in `start'
    from /usr/local/lib/ruby/gems/2.0.0/gems/thin-1.6.4/lib/thin/runner.rb:200:in `run_command'
    from /usr/local/lib/ruby/gems/2.0.0/gems/thin-1.6.4/lib/thin/runner.rb:156:in `run!'
    from /usr/local/lib/ruby/gems/2.0.0/gems/thin-1.6.4/bin/thin:6:in `<top (required)>'
    from /usr/local/bin/thin:23:in `load'
    from /usr/local/bin/thin:23:in `'

The ruby code (new.rb) being run is

require 'rubygems'
require 'oci8'

# :first_in sets how long it takes before the job is first run. In this case, it is run immediately
SCHEDULER.every '15m', :first_in => 0 do |job|

tnsname = '(DESCRIPTION = (ADDRESS = (PROTOCOL = TCP)(HOST = {ORACLE_SERVER})(PORT = 1521)) (CONNECT_DATA = (SID = {SID})))'

conn = OCI8.new('{USER}', '{PASS}', tnsname)

last_value = rowitem

cursor = conn.parse("SELECT count(status) AS status_count FROM generation WHERE billcycle is NULL AND status = '13'")
cursor.define(1, Integer)
cursor.exec()
rowitem = []

while r = cursor.fetch()
        rowitem = r
end

send_event('new', { current: rowitem, last: last_value } )
cursor.close()
end
conn.logoff

Commenting out the SCHEDULER & send_event lines allows the script to be run manually and results are returned as expected.
This is my 1st time using Ruby so excuse any obvious mistakes but if anyone can help getting this to work I will be grateful.

A: The error message tells you everything you need to know: The conn variable is not defined, on line 25:
SCHEDULER.every '15m', :first_in => 0 do |job|
  # ...

  conn = OCI8.new('{USER}', '{PASS}', tnsname)

  # ...
end

conn.logoff

You defined conn inside the scope of the block, then tried to access it from outside. That is not how variables work - you cannot access them from outside of where they are defined.
A trivial fix is to move the logoff method call up inside the block:
SCHEDULER.every '15m', :first_in => 0 do |job|
  # ...

  conn = OCI8.new('{USER}', '{PASS}', tnsname)

  # ...

  conn.logoff
end

redpajama_set_name: RedPajamaStackExchange


text:
This Is How Teens' Digital Behavior Is Changing
Read more: http://www.businessinsider.com/teens-digital-behavior-changes-2014-10#ixzz3G9N09AUE
Retail can be a parallel for public library branches so these data might be interesting for some strategists:
"Compared to last year, a greater percentage of teens boys say they prefer to shop online than in stores.
Meanwhile, teen girls seem to be reverting back to stores to do their shopping. "
"Teen girls are leaving Amazon and eBay in favor of content-heavy commerce sites like Net-A-Porter and Pinterest. Teen boys, however, are still shopping on Amazon in droves. eBay is losing both boy and girl shoppers."
"Other retail brands also gained more teen girl shoppers, including Forever 21, Victoria's Secret, and Brandy Melville, while Urban Outfitters and Nordstrom faltered among this demographic."
"With the exception of Nike, many top male-oriented retail brands are failing to attract teenage boys online. Rather, boys seem to prefer the convenience of one-stop shopping on sites like Amazon. "
More data on the decline of DVD in this target demographic:
"Teens are going online to download or stream movies like never before. This has come at the expense of movie rental stores and DVD-by-mail services. "
"There is still a lot of room for the movie-streaming trend to grow. Nearly seven in every ten teens say they plan to rent movies from Netflix over the next five years. "
"Gaming is still a popular source of entertainment for teens, and they are playing about as many physical pre-owned games as they did a year ago. Among those who do buy pre-owned games, more than 40% of teens say they get them from GameStop. Still, the retailer is expecting Netflix-level disruption in the video game industry. GameStop recently announced the closure of 120 of its brick-and-mortar stores, in favor of establishing a larger online business where customers can buy pre-owned games and consoles, as well as download digital games. "
Facebook is not sufficient as a social media strategy for teen engagement for public libraries.
"Instagram has increased its lead over Facebook as the most popular social network among teens. Three in every four teens say they use the photo- and video-sharing app, compared to less than half who say they use Facebook. This suggests that teens are leaving Facebook, Twitter, and other traditional social networks for more visual-oriented sharing apps.
Although Snapchat was not an option for teens to select as a social network that they use, 4% of respondents still wrote it in on the survey that they use it. This means the actual number of teens using Snapchat is much higher."
Yep, Doh! Teens are mobile.
"Teen iPhone ownership and interest continues to soar.
About 66% of teens currently own an iPhone.
73% say they want an iPhone for their next smartphone.
Teen were also asked about Apple's recently announced iWatch device. A considerable 16% of teen respondents said they would be interested in the iWatch if it was priced at $350. "
"GoPro is quickly becoming a popular gift item for teens. One percent of teens say the camera device will be on their holiday wish list this year, compared to two years ago when it was virtually unmentioned.
However, most teens likely view GoPro cameras as a device that can be shared amongst their family. Seventeen percent of teens say their family already owns a GoPro device, compared to less than 10% last year. "
Read more: http://www.businessinsider.com/teens-digital-behavior-changes-2014-10#ixzz3G9NENPiS
Comments Off on This Is How Teens' Digital Behavior Is Changing


← Curve Balls. Worry. Thanksgiving.
In an attempt to lure you into looking at some earlier slices of life in the desert, I am going to reprint the page called The Beginning. I would ask that when you finish reading these brief paragraphs, you click on the link below, and leave comments for me at the bottom of my first blog post. Have you ever felt like a misfit in church?
Welcome to my blog, When the River Won't Flow.
I started writing this blog in 2014 after we had moved to the Sonoran Desert of Arizona and I thought I was missing water. Living in the desert was new to me: I had grown up in the midwest and had lived much of my adult life in South Carolina. Everything in those places was green, and water was plentiful. This scruffy desert stuff was new.
But I discovered that I wasn't missing water in the usual sense. What I was missing was a church home where my husband and I could feast on the words of scripture and the body and blood of Our Lord. Try as we might, we were unable to solve this problem. But as so often happens in life, prayers were answered, and something we could not have predicted happened. A church found us.
This entry was posted in Church and tagged Desert, Liturgy, Music, Prayer, Waiting, Worship. Bookmark the permalink.


text:
Leisure | Work | School | Film History | Web sites
Special Presentation: Work | School | Leisure
Aron, Cindy S. Working at Play: A History of Vacations in the United States. New York: Oxford University Press, 1999.
Braden, Donna R. Leisure and Entertainment in America. Dearborn, Mich.: Henry Ford Museum & Greenfield Village, 1988.
Butsch, Richard, ed. For Fun and Profit: The Transformation of Leisure into Consumption. Philadelphia: Temple University Press, 1990.
Grover, Kathryn, ed. Hard at Play: Leisure in America, 1840-1940. Amherst: University of Massachusetts Press, 1992.
Nasaw, David. Going Out: The Rise and Fall of Public Amusements. New York: BasicBooks, 1993.
Swanson, Richard A., and Betty Spears. History of Sport and Physical Education in the United States. Madison, Wisc.: WCB Brown & Benchmark, 1995.
American Social History Project. Who Built America?: Working People and the Nation's Economy, Politics, Culture, and Society. Vol. 2: From the Gilded Age to the Present. New York: Pantheon Books, 1992.
Amott, Teresa, and Julie Matthaei. Race, Gender, and Work: A Multi-Cultural Economic History of Women in the United States. Boston: South End Press, 1996.
Claypool, Jane. The Worker in America. New York: Franklin Watts, 1985. [juvenile literature]
Cullinan, Gerald. The United States Postal Service. New York: Praeger Publishers, 1968.
Davis, Madison. A History of the Washington City Post-Office from 1795 to 1903. Lancaster, Pa.: New Era Printing Company, 1903.
Diner, Steven J. A Very Different Age: Americans of the Progressive Era. New York: Hill and Wang, 1998.
Dubofsky, Melvyn. Industrialism and the American Worker, 1865-1920. Wheeling, Ill.: Harlan Davidson, Inc., 1996.
Kessler-Harris, Alice. Out to Work: A History of Wage-Earning Women in the United States. New York: Oxford University Press, 1982.
Bullough, William A. Cities and Schools in the Gilded Age: The Evolution of an Urban Institution. Port Washington, N.Y.: Kennikat Press, 1974.
Church, Robert L. Education in the United States: An Interpretive History. New York: The Free Press, 1976.
DeJong, David H. Promises of the Past: A History of Indian Education in the United States. Golden, Colo.: North American Press, 1993.
Nasaw, David. Schooled to Order: A Social History of Public Schooling in the United States. New York: Oxford University Press, 1979.
Film History:
American Mutoscope & Biograph Company. Picture Catalogue. New York: n.p., 1902.
Horwitz, Rita, and Harriet Harrison, preparers. The George Kleine Collection of Early Motion Pictures in the Library of Congress: A Catalog. Washington, D.C.: Library of Congress, 1980.
Loughney, Patrick G. "A Descriptive Analysis of The Library of Congress Paper Print Collection and Related Copyright Materials." Ph.D. diss., The George Washington University, 1988.
Musser, Charles. Edison Motion Pictures, 1890-1900: An Annotated Filmography. Washington, D.C.: Smithsonian Press, 1997.
Musser, Charles, ed. Motion Picture Catalogs by American Producers and Distributors 1894-1908, a Microfilm Edition. Frederick, Md.: University Publications of America, 1984.
Niver, Kemp R., comp. Biograph Bulletins, 1896-1908. Los Angeles: Locare Research Group, 1971.
Niver, Kemp R. Early Motion Pictures: The Paper Print Collection in the Library of Congress. Washington, D.C.: Library of Congress, 1985.
Related American Memory Web Sites:
The American Variety Stage: Vaudeville and Popular Entertainment, 1870-1920
Inside an American Factory: The Westinghouse Works, 1904
The Last Days of a President: McKinley and the Pan-American Exposition
Inventing Entertainment: Early Motion Pictures and Sound Recordings of the Edison Companies
Return to America at Work, America at Leisure Home Page


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GT-Protocol Blog HOW MUCH WILL 1000 POLYGON (Matic) TOKENS BE WORTH BY 2025 – Polygon Matic Cyptocurrency
HOW MUCH WILL 1000 POLYGON (Matic) TOKENS BE WORTH BY 2025 – Polygon Matic Cyptocurrency
How much will 1,000 Polygon tokens be worth by 2025? The Polygon has already increased in popularity this year, and just recently it reached a new all-time high. Polygon is an Ethereum token that powers the Polygon network. It offers faster transactions on the Ethereum blockchain and tackles one of the major problems that prevent the widespread adoption of blockchains and cryptos. That problem has to do with scalability. The network wants to be the de-facto platform on which developers will deploy and run decentralized applications in a secure and decentralized manner. Macro reached an all-time high on May 18, 2021, when it hit $2.68. It then traded at $1.49. How high will it go in the short and long term?
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Polygon is important!
Polygon is one of the top 20 cryptos in the market, and I'll be discussing an interesting projection into the future of the coin if you didn't know by now. Polygon heavily relies on the Ethereum network. It is Ethereum native and committed to the Ethereum roadmap. Therefore, it seeks to solve some of the main issues associated with Ethereum. The Ethereum network limitations include high gas fees, low transaction rates, and poor user experience. Polygon is trying to build a multi-layer ecosystem of Blockchains compatible with the Ethereum Blockchain. As a result, the Polygon network will make different Blockchains not only interoperable but also easily scalable. Sandeep Nail, Jayanti Kanani, and Anurag Arjun are the software engineers that founded Polygon in 2017. The project began as the MATIC network but then changed its name to Polygon in February 2021 to extend its global scope. MATIC is still its ticker symbol and the name of its native coin. The MATIC coin is used to power several aspects of the Polygon network. Polygon is a notable player in various crypto sectors such as dApps, NFTs, and the decentralized autonomous organization (DAO). So, Polygon is one of the most promising cryptocurrency projects that have a high chance of growth in the future.
Polygon network's structure
Polygon architecture has four layers: the Ethereum layer, the Security layer, the Polygon network layer, and the Execution layer. This structure can speed up transaction rates on particular Blockchains without jeopardizing security or user experience. If the first two layers, i.e., the Ethereum and security layers, are optional but the other two layers are mandatory, then the Polygon network is quite flexible and allows the inclusion or exclusion of optional layers depending on the project's current status and goals. Apps built using the Polygon network are usually faster and more scalable than those developed using the Ethereum network. It needs It has to be said that Polygon has enjoyed the attention of investors and crypto enthusiasts because of its effort to speed up transactions on Ethereum and make Ethereum easy to use.
Furthermore, some of the most popular apps that migrated to the Polygon network are Aave, SushiSwap, Beefy Finance, Polymarket, and Curve Finance. Let's not also forget that the network has attracted interest from high-profile investors like Mark Cuban, who recently announced his support for the network. Therefore, with increasing demand and investor interest in the network in the future, the Polygon coin value will increase in the crypto market.
Polygon SDK
It is a flexible, modular framework which contributes to creating numerous types of applications with the use of plasma side chains designed to facilitate off-chain transactions, making them fast and cost-effective for the blockchain. The MATIC network built an environment that enabled the cheaper, easier, and faster launch of decentralized applications to market. The attractiveness of the MATIC solution was backed by high gas fees on Ethereum and increased demand for the development of dApps. Polygon has created a layer 2 network for developing Ethereum compatible and interoperable Blockchain networks. Its modular framework enables builders to create sovereign blockchains with customizable functionality. The platform can boast scalable consensus algorithms, modular security as a service features, and a bespoke web assembly execution environment. This means Polygon is capable of creating enterprise-ready blockchain networks and delivering cost-efficient and almost instantaneous transactions.
Polygon's Layer-2 Solution
When I talk about blockchain scaling solutions, they are usually subdivided into two levels. Layer 1 and Layer 2 solutions. Layer 1 refers to scaling functions within the blockchain itself using novel consensus algorithms and increasing block limits. Layer 2 scaling solutions refer to off-chain solutions; they remove elements of computational power from the main blockchain before being executed on side chains. This helps to increase throughput on the main chain layer. Two solutions, including Polygon, have been gaining popularity lately and are considered critical to the mass adoption of cryptocurrencies.
Before I talk about Polygon price analysis, I need to mention that there are risks if you invest in this project. Why? Because it has a unique setup, such as the following. The underlying technology mainly depends on Ethereum's limited speed and scalability. When Ethereum finally moves to f2 and solves its scalability and speed issues, the need for the Polygon network will become less necessary. Therefore, Polygon has to verify its usability in the future. There are other competitors, like polka dot and cosmos. If Polygon doesn't move fast and create better solutions, it might be less popular. The Polygon is 100% focused on the Ethereum network. Polygon solutions won't be relevant if another blockchain such as Cardano eventually knocks Ethereum down. Polygon has a long way to go. It isn't yet clear how the technology will evolve, and there is still a lot to be done. Finally, consider market volatility. It's unavoidable.
MATIC Price History
With that said, let's take a look at the coin price history. The MATIC network began its crypto adventure on April 29th, 2019 at $0.004. The MATIC network began its crypto adventure. Token began to climb again and again. The price hit $0.03 by the end of May 2021 with some fluctuations and decreased further by the beginning of June to $0.01. The token remained constant until the end of July at a price of $0.02.
It is interesting to note that at the start of August 2021, MATIC fell by $0.01 and remained at the same price level with small adjustments until November. By the beginning of December 2021, MATIC effectively reached $0.04, gaining investor interest. By mid-December the token was severely decreased to $0.01 MATIC and traded at $0.014 at the end of 2019 and the start of January 2020. The token continued to trade at $0.014. The price thereafter began to vary and by February reached $0.02. The coin dropped dramatic ally by mid-march to $0.006 owing to the COVID-19 epidemic while the crypto market plummeted. Furthermore, towards the end of May, the price began to rebound and resist at $0.025.
In addition, during mid-August 2021, the token reached $0.031 and settled around $0.012 in early November. MATIC was exchanged at $0.017 at the end of December 2020. The token prices smashed a new coinage in 2021, ranging from $0.94 to $2.1 and showing the highest recovery rate of all crypto, including Bitcoin or Ethereum heavy weights. MATIC has endured and maintained its trend, which is part of why many traders think Polygon will have a strong future.
Experts Opinion on Polygon
Capital.com is one of the intriguing forecasts, and they predicted that MATIC would trade over $5 in late 2025 and would transact over $12 in late 2030. By their estimation, according to trading beasts, at the end of 2021, Polygon s' projected maximum price will be about $1.8. They also predicted that the coin would reach at least $2.33 by the end of 2022. The digital coin prices are more optimistic. MATIC would trade at a median price of $1.66 by the end of 2023 and may hit $3.47 by the end of 2025. But Gov. Capital thinks Matic has a brighter future than this. They predict that the coin will trade at about $5.22 in 2026. Wallet investors' predictions aren't too far off. They think MATIC will reach $1.941 dollars by 2021 and reach $14 by the end of 2025.
My MATIC Price Prediction
Polygon began 2021 at $0.0018. The price also began to climb to improve the protocol. The community might cooperate with certain other projects and start-ups because MATIC has unique qualities such as scalability and safety that may increase. Ethereum's user base and the price can increase with future measures to cure congestion on Ethereum. Therefore, I predict that new investor switches and market trends for MATIC might lead to achieving new milestones. The cryptocurrency can therefore touch $6.6 by the end of the year, based on.
Price Prediction for 2025
Because the crypto market is so volatile, Polygons' market cap has fluctuated significantly. It sits at just over $9 billion, but at its all-time high, the coin was over $14 dollars in market cap. This puts it in the top 20 cryptocurrencies by market cap. Of course, Polygon is not the only coin that is looking to bridge the gap between the Ethereum blockchain and other applications. In 2025, Stargate and Polkadot have the same mission too. Macroeconomics could hit a new high by breaking its previous price records. I also believe it will be among the top ten cryptocurrencies by then. Several inbound developments and partnerships might lead to its growth as well. We still don't know the extent to which Ethereum 2.0 would change the current setup, but if the Polygon network can further work on transactions per second, which might eventually help Ethereum holders, it could cause the token's price to surge at $68.2, but macroeconomics might crash if the bears go on pulling the prices down because of a possible market crash or any external controversies against Ethereum. As a result, MATIC prices may fall by $30.3 over the next four years. MATIC could be seen trading at $11.7 with its improved scalability and Layer 2 blockchain's long-term success.
1000 MATIC in 2025
1,000 MATIC at my predicted price of $68.2 would cost $68,200 at my predicted price. That's close to a 7,000% increase in profit with today's price. Polygon seems to be a good investment, and it has an innovative team behind it.
Furthermore, many giant projects, investors, and cloud miner centers support the network. The Polygon network is doing its best to ensure that the asset not only remains competitive but shines above the rest as well. In other words, as more people start to realize the potential of Polygon technology, its price will gradually rise over the years. Don't forget that you should only invest what you can afford to lose.
[This article is a transcription of a video made by Crypto Diary]
[Original video: https://youtu.be/kIKR0FiRrS8]