text:
\section{Introduction}
A large amount of interesting data and the practical challenges associated with them are defined in the setting where entities have attributes as well as information about mutual relationships.
Traditional classification models have been extended to capture such relational information through graphs~\cite{hamilton2020graph}, where each node has individual attributes and the edges of the graph capture the relationships among the nodes. A variety of applications characterized by this type of graph-structured data include works in the areas of social analysis~\cite{backstrom2011supervised}, recommendation systems~\cite{YHCEHL18}, computer vision~\cite{Monti_2017_CVPR}, study of the properties of chemical compounds~\cite{gilmer:quantum, scarselli:gnn}, statistical physics~\cite{bapst2020unveiling,battaglia:graphnets}, and financial forensics~\cite{zhang2017hidden,weber2019anti}.

The most popular learning models for relational data use graph convolutions~\cite{kipf:gcn}, where the idea is to aggregate the attributes of the set of neighbours of a node instead of only utilizing its own attributes.
Despite several empirical studies of various GCN-type models~\cite{CLB19, ma2022:is-homophily} that demonstrate that graph convolutions can improve the performance of traditional classification methods, such as a multi-layer perceptron (MLP), there has been limited progress in the theoretical understanding of the benefits of graph convolutions in multi-layer networks in terms of improving node classification tasks.

\paragraph{Related work.}
The capacity of a graph convolution for one-layer networks is studied in~\cite{pmlr-v139-baranwal21a}, along with its out-of-distribution (OoD) generalization potential. A more recent work~\cite{wu2022towards} formulates the node-level OoD problem, and develops a learning method that facilitates GNNs to leverage invariance principles for prediction. In \cite{gasteiger2019combining}, the authors utilize a propagation scheme based on personalized PageRank to construct a model that outperforms several GCN-like methods for semi-supervised classification. Through their algorithm, APPNP, they show that placing power iterations at the last layer of an MLP achieves state of the art performance. Our results align with this observation.

There exists a large amount of theoretical work on unsupervised learning for random graph models where node features are absent and only relational information is available \cite{decelle2011asymptotic,massoulie2014community,mossel2018proof,mossel2015consistency,abbe2015community,abbe2015exact,bordenave2015non,deshpande2015asymptotic,montanari2016semidefinite,banks2016information,abbe2018proof,Li:2019:optimizing,Kloumann:2017:block,gaudio2022exact}. For a comprehensive survey, see \cite{Abbe2018,moore2017csphysics}.
For data models which have node features coupled with relational information, several works have studied the semi-supervised node classification problem, see, for example, \cite{scarselli:gnn,CZY2011,GVB2012,DV2012,GFRT13,YML13,HYL17,JLLHZ19,pmlr-v97-mehta19a,chien2022node,yan:2021:two-sides}. These papers provide good empirical insights into the merits of graph structure in the data. We complement these studies with theoretical results that explain the effects of graph convolutions in a multi-layer network.

In \cite{DSM18,Lu:2020:contextual}, the authors explore the fundamental thresholds for the classification of a substantial fraction of the nodes with linear sample complexity and large but finite degree. Another relatively recent work \cite{Hou2020Measuring} proposes two graph smoothness metrics for measuring the benefits of graphical information, along with a new attention-based framework. In \cite{Fountoulakis2022GraphAR}, the authors provide a theoretical study of the graph attention mechanism (GAT) and identify the regimes where the attention mechanism is (or is not) beneficial to node-classification tasks. Our study focuses on convolutions instead of attention-based mechanisms.

To the best of our knowledge, this area of research still lacks theoretical guarantees that explain when and why graphical data, and in particular, graph convolutions, can boost traditional multi-layer networks to perform better on node-classification tasks. To this end, we study the effects of graph convolutions in deeper layers of a multi-layer network. For node classification tasks, we also study whether one can avoid using additional layers in the network design for the sole purpose of gathering information from neighbours that are farther away, by comparing the benefits of placing all convolutions in a single layer versus placing them in different layers.

\paragraph{Our contributions.}
We study the performance of multi-layer networks for the task of binary node classification on a data model where node features are sampled from a Gaussian mixture, and relational information is sampled from a symmetric two-block stochastic block model\footnote{Our analyses generalize to non-symmetric SBMs with more than two blocks. However, we focus on the binary symmetric case for the sake of simplicity in the presentation of our ideas.} (see \cref{data-model} for details). The node features are modelled after XOR data with two classes, and therefore, has four distinct components, two for each class. Our choice of the data model is inspired from the fact that it is non-linearly separable. Hence, a single layer network fails to classify the data from this model. Similar data models based on the contextual stochastic block model (CSBM) have been used extensively in the literature, see, for example, \cite{DSM18,BVR17,chien2021adaptive,chien2022node,pmlr-v139-baranwal21a}.
We now summarize our main contributions below, which are discussed further in \cref{results}.
\begin{enumerate}
    \item We show that when node features are accompanied by a graph, a single graph convolution enables a multi-layer network to classify the nodes in a wider regime as compared to methods that do not utilize the graph, improving the threshold for the distance between the means of the features by a factor of at least $1/\sqrt[4]{\mathds{E}{\rm deg}}$.
    Furthermore, assuming a slightly denser graph, we show
    that with two graph convolutions, a multi-layer network can classify the data in an even wider regime, improving the threshold up to a factor of at least $1/\sqrt[4]{n}$, where $n$ is the number of nodes in the graph.
    \item We show that for multi-layer networks equipped with graph convolutions, the classification capacity is determined by the number of graph convolutions rather than the number of layers in the network. In particular, we study the gains obtained by placing graph convolutions in a layer, and compare the benefits of placing all convolutions in a single layer versus placing them in different combinations across different layers. We find that the performance is mutually similar for all combinations with the same number of graph convolutions.
    \item We verify our theoretical results through extensive experiments on both synthetic and real-world data, showing trends about the performance of graph convolutions in various combinations across multiple layers of a network, and in different regimes of interest.
\end{enumerate}

The rest of our paper is organized as follows: In \cref{prelims}, we provide a detailed description of the data model and the network architecture that is central to our study, followed by our analytical results in \cref{results}. Finally, \cref{experiments} presents extensive experiments that illustrate our results.

\section{Preliminaries}\label{prelims}
\subsection{Description of the data model}
\label{data-model}
Let $n,d$ be positive integers, where $n$ denotes the number of data points (sample size) and $d$ denotes the dimension of the features. Define the Bernoulli random variables $\varepsilon_1,\ldots,\varepsilon_n\sim \mathrm{Ber}(\nicefrac{1}{2})$ and $\eta_1,\ldots,\eta_n\sim \mathrm{Ber}(\nicefrac{1}{2})$. Further, define two classes $C_b = \{i\in [n]\mid \varepsilon_i=b\}$ for $b\in\{0,1\}$.

Let $\bm{\mu}$ and $\bm{\nu}$ be fixed vectors in $\mathds{R}^d$, such that $\norm{\bm{\mu}}_2 = \norm{\bm{\nu}}_2$ and $\inner{\bm{\mu},\bm{\nu}}=0$.\footnote{We take $\bm{\mu}$ and $\bm{\nu}$ to be orthogonal and of the same magnitude for keeping the calculations relatively simpler, while clearly depicting the main ideas behind our results.} Denote by $\mathbf{X}\in \mathds{R}^{n\times d}$ the data matrix where each row-vector $\mathbf{X}_i\in \mathds{R}^{d}$ is an independent Gaussian random vector according to $\mathbf{X}_i\sim \mathcal{N}((2\eta_i - 1)((1-\varepsilon_i)\bm{\mu} + \varepsilon_i\bm{\nu}), \sigma^2)$. We use the notation $\mathbf{X}\sim \text{XOR-GMM}(n,d,\bm{\mu},\bm{\nu},\sigma^2)$ to refer to data sampled from this model.

Let us now define the model with graphical information. In this case, in addition to the features $\mathbf{X}$ described above, we have a graph with the adjacency matrix, $\mathbf{A} = (a_{ij})_{i,j\in [n]}$, that corresponds to an undirected graph including self-loops, and is sampled from a standard symmetric two-block stochastic block model with parameters $p$ and $q$, where $p$ is the intra-block and $q$ is the inter-block edge probability with $p>q$.
The SBM$(n,p,q)$ is then coupled with the $\text{XOR-GMM}(n,d,\bm{\mu},\bm{\nu},\sigma^2)$ in the way that $a_{ij}\sim \mathrm{Ber}(p)$ if $\varepsilon_i=\varepsilon_j$ and $a_{ij}\sim \mathrm{Ber}(q)$ if $\varepsilon_i\neq \varepsilon_j$\footnote{Our results trivially extend to non-symmetric models with different $p$'s and $q$'s for different blocks in the SBM. However, for simplicity, we focus on the symmetric case.}. For data $(\mathbf{A}, \mathbf{X}) = (\{a_{ij}\}_{i,j\in[n]}, \{\mathbf{X}_i\}_{i\in n})$ sampled from this model, we say $(\mathbf{A},\mathbf{X})\sim \text{XOR-CSBM}(n,d,\bm{\mu},\bm{\nu},\sigma^2,p,q)$.

We will denote by $\mathbf{D}$ the diagonal degree matrix of the graph with adjacency matrix $\mathbf{A}$, and thus, $\mathbf{deg}(i) = \mathbf{D}_{ii}=\sum_{j=1}^na_{ij}$ denotes the degree of node $i$. We will use $N_i = \{j\in[n]\mid a_{ij}=1\}$ to denote the set of neighbours of a node $i$. We will also use the notation $i\sim j$ or $i\nsim j$ throughout the paper to signify, respectively, that $i$ and $j$ are in the same class, or in different classes.

\subsection{Network architecture}\label{network-arch}
Our analysis focuses on MLP architectures with $\mathrm{ReLU}$ activations. In particular, for a network with $L$ layers, we define the following:
\begin{align*}
    &\mathbf{H}^{(0)} = \mathbf{X},\\
    &\begin{rcases}
        f^{(l)}(\mathbf{X}) = (\mathbf{D}^{-1}\mathbf{A})^{k_l}\mathbf{H}^{(l-1)}\mathbf{W}^{(l)} + \mathbf{b}^{(l)}\\
        \mathbf{H}^{(l)} = \mathrm{ReLU}(f^{(l)}(\mathbf{X}))
    \end{rcases} \text{ for } l\in [L],\\
    &\mathbf{\hat{y}} = \varphi(f^{(L)}(\mathbf{X})).
\end{align*}
Here, $\mathbf{X}\in \mathds{R}^{n\times d}$ is the given data, which is an input for the first layer and $\varphi(x)={\rm sigmoid}(x) = \frac{1}{1 + e^{-x}}$, applied element-wise.
The final output of the network is represented by $\mathbf{\hat{y}} = \{\hat{y}_i\}_{i\in[n]}$. Note that $\mathbf{D}^{-1}\mathbf{A}$ is the normalized adjacency matrix\footnote{Our results rely on degree concentration for each node, hence, they readily generalize to other normalization methods like $\mathbf{D}^{-\frac12}\mathbf{A}\mathbf{D}^{-\frac12}$.} and $k_l$ denotes the number of graph convolutions placed in layer $l$. In particular, for a simple MLP with no graphical information, we have $\mathbf{A} = \mathbf{I}_n$.

We will denote by $\theta$, the set of all weights and biases, $(\mathbf{W}^{(l)}, \mathbf{b}^{(l)})_{l\in [L]}$, which are the learnable parameters of the network. For a dataset $(\mathbf{X},\mathbf{y})$, we denote the binary cross-entropy loss obtained by a multi-layer network with parameters $\theta$ by $\ell_{\theta}(\mathbf{A}, \mathbf{X}) = -\frac{1}{n}\sum_{i\in[n]}y_i\log(\hat{y}_i) + (1-y_i)\log(1-\hat{y}_i)$,
and the optimization problem is formulated as
\begin{align}
    \mathrm{OPT}(\mathbf{A}, \mathbf{X})=\min_{\theta \in \mathcal{C}} ~ \ell_{\theta}(\mathbf{A}, \mathbf{X}),\label{eq:OPT}
\end{align}
where $\mathcal{C}$ denotes a suitable constraint set for $\theta$. For our analyses, we take the constraint set $\mathcal{C}$ to impose the condition $\norm{\mathbf{W}^{(1)}}_2\le R$ and $\norm{\mathbf{W}^{(l)}}_2 \le 1$ for all $1<l\le L$, i.e., the weight parameters of all layers $l>1$ are normalized, while for $l=1$, the norm is bounded by some fixed value $R$. This is necessary because without the constraint, the value of the loss function can go arbitrarily close to $0$. Furthermore, the parameter $R$ helps us concisely provide bounds for the loss in our theorems for various regimes by bounding the Lipschitz constant of the learned function. In the rest of our paper, we use $\ell_{\theta}(\mathbf{X})$ to denote $\ell_{\theta}(\mathbf{I}_n, \mathbf{X})$, which is the loss in the absence of graphical information.

\section{Results}\label{results}
We now describe our theoretical contributions, followed by a discussion and a proof sketch.

\subsection{Setting up the baseline}
Before stating our main result about the benefits and performance of graph convolutions, we set up a comparative baseline in the setting where graphical information is absent. In the following theorem, we completely characterize the classification threshold for the $\text{XOR-GMM}$ data model in terms of the distance between the means of the mixture model and the number of data points $n$. Let $\Phi(\cdot)$ denote the cumulative distribution function of a standard Gaussian, and $\Phi_{\rm c}(\cdot) = 1 - \Phi(\cdot)$.
\begin{theorem}\label{thm:threshold-without-graph}
    Let $\mathbf{X}\in\mathds{R}^{n\times d}\sim \text{XOR-GMM}(n,d,\bm{\mu},\bm{\nu},\sigma^2)$.
    Then we have the following:
    \begin{enumerate}
        \item Assume that $\|\bm{\mu}-\bm{\nu}\|_2\le K\sigma$ and let $h(\mathbf{x}):\mathds{R}^d\to\{0,1\}$ be any binary classifier. Then for any $K>0$ and any $\epsilon\in(0, 1)$, at least a fraction $2\Phi_{\rm c}\bpar{\nicefrac{K}{2}}^2 - O(n^{-\epsilon/2})$ of all data points are misclassified by $h$ with probability at least $1 - \exp(-2n^{1-\epsilon})$.
        \item For any $\epsilon>0$, if the distance between the means is $\norm{\bm{\mu}-\bm{\nu}}_2=\Omega(\sigma(\log n)^{\frac12+\epsilon})$, then for any $c>0$, with probability at least $1-O(n^{-c})$, there exist a two-layer and a three-layer network that perfectly classify the data, and obtains a cross-entropy loss given by
        \[
        \ell_{\theta}(\mathbf{X}) = C\exp\bpar{-\frac{R}{\sqrt2}\|\bm{\mu}-\bm{\nu}\|_2\bpar{1\pm \sqrt{c}/(\log n)^{\epsilon}}},
        \]
        where $C\in [\nicefrac12, 1]$ is an absolute constant and $R$ is the optimality constraint from \cref{eq:OPT}.
    \end{enumerate}
\end{theorem}
Part one of \cref{thm:threshold-without-graph} shows that if the means of the features of the two classes are at most $O(\sigma)$ apart then with overwhelming probability, there is a constant fraction of points that are misclassified. Note that the fraction of misclassified points is $2\Phi_{\rm c}(\nicefrac K2)^2$, which approaches $0$ as $K\to\infty$ and approaches $\nicefrac12$ as $K\to 0$, signifying that if the means are very far apart then we successfully classify all data points, while if they coincide then we misclassify roughly half of all data points. Furthermore, note that if $K=c\sqrt{\log n}$ for some constant $c\in[0, 1)$, then the total number of points misclassified is $2n\Phi_{\rm c}(K)^2\asymp \frac{n}{K^2}e^{-K^2} \asymp \frac{n^{1-c^2}}{\log n} = \Omega(1)$.
Thus, intuitively, $K\asymp \sqrt{\log n}$ is the threshold beyond which learning methods are expected to perfectly classify the data. This is formalized in part two of the theorem, which supplements the misclassification result by showing that if the means are roughly $\omega(\sigma\sqrt{\log n})$ apart then the data is classifiable with overwhelming probability.

\subsection{Improvement through graph convolutions}
We now state the results that explain the effects of graph convolutions in multi-layer networks with the architecture described in \cref{network-arch}. We characterize the improvement in the classification threshold in terms of the distance between the means of the node features.

\begin{theorem}\label{thm:gc-improvement}
Let $(\mathbf{A},\mathbf{X})\sim \text{XOR-CSBM}(n,d,\bm{\mu},\bm{\nu},\sigma^2,p,q)$. Then there exist a two-layer network and a three-layer network with the following properties:
\begin{itemize}
    \item If the intra-class and inter-class edge probabilities are $p, q = \Omega(\frac{\log^2 n}{n})$, and the distance between the means is $\norm{\bm{\mu}-\bm{\nu}}_2=\Omega\bpar{\frac{\sigma\sqrt{\log n}}{\sqrt[4]{n(p+q)}}}$, then for any $c>0$, with probability at least $1-O(n^{-c})$, the networks equipped with a graph convolution in the second or the third layer perfectly classify the data, and obtain the following loss:
    \[
    \ell_{\theta}(\mathbf{A}, \mathbf{X}) = C'\exp\bpar{-\frac{CR\|\bm{\mu}-\bm{\nu}\|_2^2}{\sigma}\bpar{\frac{p-q}{p+q}}(1\pm \sqrt{\nicefrac{c}{\log n}})},
    \]
    where $C>0$ and $C'\in[\nicefrac12, 1]$ are constants and $R$ is the constraint from \cref{eq:OPT}.
    \item If $p, q = \Omega(\frac{\log n}{\sqrt{n}})$ and $\norm{\bm{\mu}-\bm{\nu}}_2=\Omega\bpar{\frac{\sigma\sqrt{\log n}}{\sqrt[4]{n}}}$, then for any $c>0$, with probability at least $1-O(n^{-c})$, the networks with any combination of two graph convolutions in the second and/or the third layers perfectly classify the data, and obtain the following loss:
    \[
        \ell_{\theta}(\mathbf{A}, \mathbf{X}) = C'\exp\bpar{-\frac{CR\|\bm{\mu}-\bm{\nu}\|_2^2}{\sigma}\bpar{\frac{p-q}{p+q}}^2(1\pm \sqrt{\nicefrac{c}{\log n}})},
    \]
    where $C>0$ and $C'\in[\nicefrac12, 1]$ are constants and $R$ is the constraint from \cref{eq:OPT}.
\end{itemize}
\end{theorem}

Part one of \cref{thm:gc-improvement} shows that under the assumption that $p,q=\Omega(\nicefrac{\log^2 n}{n})$, a single graph convolution improves the classification threshold by a factor of at least $\nicefrac{1}{\sqrt[4]{n(p+q)}}$ as compared to the case without the graph (see part two of \cref{thm:threshold-without-graph}). Part two then shows that with a slightly stronger assumption on the graph density, we observe further improvement in the threshold up to a factor of at least $\nicefrac{1}{\sqrt[4]{n}}$. Note that although the regime of graph density is different for part two of the theorem, the result itself is an improvement. In particular, if $p,q = \Omega(\nicefrac{\log n}{\sqrt{n}})$ then part one of the theorem states that one graph convolution achieves an improvement of at least $\nicefrac{1}{\sqrt[8]{n}}$, while part two states that two convolutions improve it to at least $\nicefrac{1}{\sqrt[4]{n}}$. However, we also emphasize that in the regime where the graph is dense, i.e., when $p,q=\Omega_n(1)$, two graph convolutions do not have a significant advantage over one convolution. Our experiments in \cref{experiments:synthetic} demonstrate this effect.
\begin{figure}[H]
    \centering
    \begin{subfigure}[b]{0.45\textwidth}
        \includegraphics[width=\linewidth]{img/intuition/orig_data}
        \caption{Original node features at the first layer.}
        \label{fig:intuition-orig-data}
    \end{subfigure}
    \begin{subfigure}[b]{0.47\textwidth}
        \includegraphics[width=\linewidth]{img/intuition/conv_1}
        \caption{Feature representation after GC at the first layer.}
        \label{fig:intuition-conv-1}
    \end{subfigure}

    \begin{subfigure}[b]{0.45\textwidth}
        \includegraphics[width=\linewidth]{img/intuition/transformed_data}
        \caption{Feature representation at the last layer.}
        \label{fig:intuition-transformed-data}
    \end{subfigure}
    \begin{subfigure}[b]{0.47\textwidth}
        \includegraphics[width=\linewidth]{img/intuition/conv_2}
        \caption{Feature representation after GC at the last layer.}
        \label{fig:intuition-conv-2}
    \end{subfigure}

    \caption{Placement of a graph convolution (GC) in the first layer versus the last layer for data sampled from the $\text{XOR-CSBM}$. For this figure we used $1000$ nodes in each class and a randomly sampled stochastic block-model graph with $p=0.8$ and $q=0.2$.}
    \label{fig:intuition}
\end{figure}

An artifact of the $\text{XOR-CSBM}$ data model is that a graph convolution in the first layer severely hurts the classification accuracy. Hence, for \cref{thm:gc-improvement}, our analysis only considers networks with no graph convolution in the first layer, i.e., $k_1 = 0$. This effect is visualized in \cref{fig:intuition}, and is attributed to the averaging of data points in the same class but different components of the mixture that have means with opposite signs.
We defer the reader to \cref{gc-first-layer} for a more formal argument, and to \cref{additional-experiments-synthetic} for experiments that demonstrate this phenomenon.
As $n$ (the sample size) grows, the difference between the averages of node features over the two classes diminishes (see \cref{fig:intuition-orig-data,fig:intuition-conv-1}). In other words, the means of the two classes collapse to the same point for large $n$. However, in the last layer, since the input consists of transformed data points that are linearly separable, a graph convolution helps with the classification task (see \cref{fig:intuition-transformed-data,fig:intuition-conv-2}).

\subsection{Placement of graph convolutions}
We observe that the improvements in the classification capability of a multi-layer network depends on the number of convolutions, and does not depend on where the convolutions are placed. In particular, for the $\text{XOR-CSBM}$ data model, putting the same number of convolutions among the second and/or the third layer in any combination achieves mutually similar improvements in the classification task.
\begin{corollary}[Informal]\label{cor:placement}
Consider the data model
$\text{XOR-CSBM}(n,d,\bm{\mu},\bm{\nu},\sigma^2,p,q)$ and the network architecture from \cref{network-arch}.
\begin{itemize}
    \item Assume that $p, q = \Omega(\nicefrac{\log^2 n}{n})$, and consider the three-layer network characterized by part one of \cref{thm:gc-improvement}, with one graph convolution. For this network, placing the graph convolution in the second layer ($k_2=1,k_3=0$) obtains the same results as placing it in the third layer ($k_2=0,k_3=1$).
    \item Assume that $p, q = \Omega(\nicefrac{\log n}{\sqrt{n}})$, and consider the three-layer network characterized by part two of \cref{thm:gc-improvement}, with two graph convolutions. For this network, placing both convolutions in the second layer ($k_2=2,k_3=0$) or both of them in the third layer ($k_2=0,k_3=2$) obtains the same results as placing one convolution in the second layer and one in the third layer ($k_2=1,k_3=1$).
\end{itemize}
\end{corollary}

\cref{cor:placement} is immediate from the proof of \cref{thm:gc-improvement} (see \cref{one-gc,two-gcs}).
In \cref{experiments}, we also show extensive experiments on both synthetic and real data that demonstrate this result.

\subsection{Proof sketch}
In this section, we provide an overview of the key ideas and intuition behind our proof technique for the results. For comprehensive proofs, see \cref{proofs}.

For part one of \cref{thm:threshold-without-graph}, we utilize the assumption on the distribution of the data. Since the underlying distribution of the mixture model is known, we can find the (Bayes) optimal classifier\footnote{A Bayes classifier makes the most probable prediction for a data point. Formally, such a classifier is of the form $h^*(\boldsymbol{x})=\argmax_{b\in\{0,1\}}\Pr{y=b\mid\boldsymbol{x}}$.}, $h^*(\mathbf{x})$, for the $\text{XOR-GMM}$, which takes the form $h^*(\mathbf{x}) = \mathds{1}(|\inner{\mathbf{x},\bm{\nu}}| - |\inner{\mathbf{x},\bm{\mu}}|)$, where $\mathds{1}(\cdot)$ is the indicator function. We then compute a lower bound on the probability that $h^*$ fails to classify one data point from this model, followed by a concentration argument that computes a lower bound on the fraction of points that $h^*$ fails to classify with overwhelming probability. Consequently, a negative result for the Bayes optimal classifier implies a negative result for all classifiers.

For part two of \cref{thm:threshold-without-graph}, we design a two-layer and a three-layer network that realize the (Bayes) optimal classifier. We then use a concentration argument to show that in the regime where the distance between the means is large enough, the function representing our two-layer or three-layer network roughly evaluates to a quantity that has a positive sign for one class and a negative sign for the other class. Furthermore, the output of the function scales with the distance between the means. Thus, with a suitable assumption on the magnitude of the distance between the means, the output of the networks has the correct signs with overwhelming probability. Following this argument, we show that the cross-entropy loss obtained by the networks can be made arbitrarily small by controlling the optimization constraint $R$ (see \cref{eq:OPT}), implying successful classification.

For \cref{thm:gc-improvement}, the main idea is to show that for the (Bayes) optimal networks designed for \cref{thm:threshold-without-graph}, placing graph convolutions in the second or the third layer reduces the effective variance of the functions representing the network. This stems from the fact that for the data model we consider, multi-layer networks with $\mathrm{ReLU}$ activations are Lipschitz functions of Gaussian random variables, and placing graph convolutions in a layer reduces the Lipschitz constant. First, we compute the precise reduction in the variance of the data characterized by $K>0$ graph convolutions (see \cref{lem:var-redn}). Then for part one of the theorem where we perform one graph convolution, we use the assumption on the graph density to conclude that the degrees of each node concentrate strongly. This helps us characterize the variance, and hence, the Lipschitz constant, which further helps us bound the output of the multi-layer networks. Part two of the theorem studies the placement of two graph convolutions using a similar argument. In this case, the variance (and thus, the Lipschitz constant) depends on the number of common neighbours of a pair of nodes rather than the degree of a node.

\section{Experiments}\label{experiments}
In this section we provide empirical evidence that supports our claims in \cref{results}. We begin by analyzing the synthetic data models $\text{XOR-GMM}$ and $\text{XOR-CSBM}$ that are crucial to our theoretical results, followed by a similar analysis on multiple real-world datasets tailored for node classification tasks. We show a comparison of the test accuracy obtained by various learning methods in different regimes, along with a display of how the performance changes with the properties of the underlying graph, i.e., with the intra-class and inter-class edge probabilities $p$ and $q$.

For both synthetic and real-world data, the performance of the networks does not change significantly with the choice of the placement of graph convolutions. In particular, placing all convolutions in the last layer achieves a similar performance as any other placement for the same number of convolutions. This observation aligns with the results in \cite{gasteiger2019combining}.

\subsection{Synthetic data}\label{experiments:synthetic}
In this section, we empirically show the landscape of the accuracy achieved for various multi-layer networks with up to three layers and up to two graph convolutions.
In \cref{fig:synthetic}, we show that as claimed in \cref{thm:gc-improvement}, a single graph convolution reduces the classification threshold by a factor of $\nicefrac{1}{\sqrt[4]{\mathds{E}\,\mathbf{deg}}}$ and two graph convolutions reduce the threshold by a factor of $\nicefrac{1}{\sqrt[4]{n}}$, where $\mathds{E}\,\mathbf{deg} = \frac{n}{2}(p+q)$.
\begin{figure}[!ht]
    \centering
    \begin{subfigure}[b]{0.49\textwidth}
        \includegraphics[width=\linewidth]{img/synthetic/test_accuracy_p=0.2_q=0.02_2_layers}
        \caption{Two-layer networks with $(p,q)=(0.2,0.02)$.}
        \label{fig:synthetic-sparse-2layers}
    \end{subfigure}
    \begin{subfigure}[b]{0.49\textwidth}
        \includegraphics[width=\linewidth]{img/synthetic/test_accuracy_p=0.2_q=0.02_3_layers}
        \caption{Three-layer networks with $(p,q)=(0.2,0.02)$.}
        \label{fig:synthetic-sparse-3layers}
    \end{subfigure}
    \begin{subfigure}[b]{0.49\textwidth}
        \includegraphics[width=\linewidth]{img/synthetic/test_accuracy_p=0.5_q=0.1_2_layers}
        \caption{Two-layer networks with $(p,q)=(0.5,0.1)$.}
        \label{fig:synthetic-dense-2layers}
    \end{subfigure}
    \begin{subfigure}[b]{0.49\textwidth}
        \includegraphics[width=\linewidth]{img/synthetic/test_accuracy_p=0.5_q=0.1_3_layers}
        \caption{Three-layer networks with $(p,q)=(0.5,0.1)$.}
        \label{fig:synthetic-dense-3layers}
    \end{subfigure}
    \caption{Averaged test accuracy (over $50$ trials) for various networks with and without graph convolutions on the $\text{XOR-CSBM}$ data model with $n=400,d=4$ and $\sigma^2=\nicefrac{1}{d}$. The x-axis denotes the ratio $K = \norm{\bm{\mu}-\bm{\nu}}_2/\sigma$ on a logarithmic scale. The vertical lines indicate the classification thresholds mentioned in part two of \cref{thm:threshold-without-graph} (red), and in \cref{thm:gc-improvement} (violet and pink).}
    \label{fig:synthetic}
\end{figure}

We observe that the placement of graph convolutions does not matter as long as it is not in the first layer. \cref{fig:synthetic-sparse-2layers,fig:synthetic-sparse-3layers} show that the performance is mutually similar for all networks that have one graph convolution placed in the second or the third layer, and for all networks that have two graph convolutions placed in any combination among the second and the third layers.
In \cref{fig:synthetic-dense-2layers,fig:synthetic-dense-3layers}, we observe that two graph convolutions do not obtain a significant advantage over one graph convolution in the setting where $p$ and $q$ are large, i.e., when the graph is dense. We observed similar results for various other values of $p$ and $q$ (see \cref{additional-experiments-synthetic} for some more plots).

Furthermore, we verify that if a graph convolution is placed in the first layer of a network, then it is difficult to learn a classifier for the $\text{XOR-CSBM}$ data model. In this case, test accuracy is low even for the regime where the distance between the means is quite large. The corresponding metrics are presented in \cref{additional-experiments-synthetic}.

\subsection{Real-world data}\label{experiments:real-world}
For real-world data, we test our results on three graph benchmarks: \emph{CORA}, \emph{CiteSeer}, and \emph{Pubmed} citation network datasets \cite{sen2008collective}. We observe the following trends: First, we find that as claimed in \cref{thm:gc-improvement}, methods that utilize graphical information in the data perform remarkably better than a traditional MLP that does not use relational information.
Second, all networks with one graph convolution in any layer (red and blue) achieve a mutually similar performance, and all networks with two graph convolutions in any combination of placement (green and yellow) achieve a mutually similar performance. This demonstrates a result similar to \cref{cor:placement} for real-world data, showing that the location of the graph convolutions does not significantly affect the accuracy.
Finally, networks with two graph convolutions perform better than networks with one graph convolution.
\begin{figure}[!htb]
    \centering
    \begin{subfigure}[b]{\textwidth}
        \includegraphics[width=\linewidth]{img/real/custom-gcnconv/Cora_test_acc_epochmax_max}
        \caption{Accuracy of various learning models on the CORA dataset.}
        \label{fig:cora-max-max}
    \end{subfigure}
    \begin{subfigure}[b]{\textwidth}
        \includegraphics[width=\linewidth]{img/real/custom-gcnconv/Pubmed_test_acc_epochmax_max}
        \caption{Accuracy of various learning models on the Pubmed dataset.}
        \label{fig:pubmed-max-max}
    \end{subfigure}
    \begin{subfigure}[b]{\textwidth}
        \includegraphics[width=\linewidth]{img/real/custom-gcnconv/CiteSeer_test_acc_epochmax_max}
        \caption{Accuracy of various learning models on the CiteSeer dataset.}
        \label{fig:citeseer-max-max}
    \end{subfigure}
    \caption{Maximum accuracy (percentage) over $50$ trials for various networks. A network with $k$ layers and $j_1,\ldots,j_k$ convolutions in each of the layers is represented by the label $k$L-$j_1\ldots j_k$.}
    \label{fig:real-data-accuracy-max}
\end{figure}

In \cref{fig:real-data-accuracy-max}, we present for all networks, the maximum accuracy over $50$ trials, where each trial corresponds to a random initialization of the networks. For $2$-layer networks, the hidden layer has width $16$, and for $3$-layer networks, both hidden layers have width $16$. We use a dropout probability of $0.5$ and a weight decay of $10^{-5}$ while training.

For this study, we attribute minor changes in the accuracy to hyperparameter tuning and algorithmic tweaks such as dropouts and weight decay. This helps us clearly observe the important difference in the accuracy of networks with one graph convolution versus two graph convolutions. For example, in \cref{fig:cora-max-max}, we note that there are differences among the accuracy of the networks with one graph convolution (red and blue). However, these differences are minor compared to the difference between the accuracy of networks with one convolution (red and blue) and networks with two convolutions (green and yellow). We also show the averaged accuracy in \cref{additional-experiments-real}.
Note that the accuracy slightly differs from well-known results in the literature due to implementation differences. In particular, the GCN implementation in \cite{kipf:gcn} uses $\tilde{\mathbf{A}} = \mathbf{D}^{-\frac12}\mathbf{A}\mathbf{D}^{-\frac12}$ as the normalized adjacency matrix, however, we use $\tilde{\mathbf{A}}=\mathbf{D}^{-1}\mathbf{A}$.\footnote{Our proofs rely on degree concentration, and thus, generalize to the other type of normalization as well.} In \cref{additional-experiments-real}, we also show empirical results for the normalization $\tilde{\mathbf{A}} = \mathbf{D}^{-\frac12}\mathbf{A}\mathbf{D}^{-\frac12}$, that match with already known results in the literature.

\section{Conclusion and future work}\label{future-work}
We study the fundamental limits of the capacity of graph convolutions in deeper layers of a multi-layer network for the $\text{XOR-CSBM}$ data model, and provide theoretical guarantees for their performance in different regimes of the distance between the means. Through our experiments on both synthetic and real-world data, we show that the number of convolutions is a more significant factor for determining the performance of a network, rather than the number of layers in the network.

Furthermore, we show that placing graph convolutions in any combination achieves mutually similar performance enhancements for the same number of convolutions. Additionally, we observe that multiple graph convolutions are advantageous only when the underlying graph is relatively sparse. Intuitively, this is because in a dense graph, a single convolution can gather information from a large number of nodes, while in a sparser graph, more convolutions are needed to gather information from a larger number of nodes.

Our analyses for the effects of graph convolutions are limited to a positive result for node classification tasks, and thus, we only provide a minimum guarantee for improvement in the classification threshold in terms of the distance between the means of the node features. To fully understand the limitations of graph convolutions, a complementary negative result (similar to part one of \cref{thm:threshold-without-graph}) for data models with relational information is required, showing the maximum improvement that graph convolutions can realize in a multi-layer network. This problem is hard due to two reasons: First, there does not exist a concrete notion of an \emph{optimal} classifier for data models which have node features coupled with relational information. Second, a graph convolution transforms an iid set of features into a highly correlated set of features, making it difficult to apply classical high-dimensional concentration arguments.

Another limitation of our work is that we study only node classification problems. A possible future work is an extension of our results to other learning problems, such as link prediction.

\section*{Acknowledgements}
K. Fountoulakis would like to acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC). Cette recherche a \'et\'e financ\'ee par le Conseil de recherches en sciences naturelles et en g\'enie du Canada (CRSNG), [RGPIN-2019-04067, DGECR-2019-00147].

A. Jagannath acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC). Cette recherche a \'et\'e financ\'ee par le Conseil de recherches en sciences naturelles et en g\'enie du Canada (CRSNG),  [RGPIN-2020-04597, DGECR-2020-00199].

redpajama_set_name: RedPajamaArXiv


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text:
Preparing for 2020: News Organizations Ramp Up for an Election Cycle Certain to be Dynamic, Fast-Paced and Combative
Gretchen A. Peck July 1, 2019
In the wake of the 2016 presidential election, the press received some rather harsh criticism about its national coverage. Type in "press failures of 2016," and Google will unkindly deliver a long list of critical analysis about the media and how it handled the Trump vs. Clinton battle for the White House.
Disillusioned voters blamed the press for a failure to present Trump as a viable nominee, let alone as their likely future president. Some declared that journalists missed the story of the Trump voter entirely.
That type of criticism—that the press had missed the Trump story—wasn't entirely fair, according to Peter Wallsten, senior politics editor at the Washington Post.
"If you look back at the Post's coverage, we saw Trump as an interesting and important story from the beginning, and we had reports out across the country," he said. "But I think if there was a mistake across the media, it was that people made assumptions. I'm not saying that it is a mistake that the Post made, but I do think there were assumptions about whether Trump could win or not. To the extent that it was a phenomenon of 2016, we are reminding our reporters that an important part of our philosophy for covering politics is to not make assumptions and to not be predictive in our coverage."
The press has also been lambasted for burying the ledes and focusing too often on personality and the outrages du jour rather than on the candidates, their policy positions and the direct impact on the lives of the American people.
Asked how the reporters and editors at the Washington Post plan to strike a balance between personality and policy in its 2020 coverage, Wallsten said, "We see personality as an important aspect of political coverage. The stories do very well. Also, those stories can tell you a lot about the candidates and their character and what kind of president they would be.
"For instance," Wallsten continued, "we had a piece that we published on Cory Booker and his relationship with an Orthodox Rabbi. It's a fantastic story, and in some ways, that's a personality story, but you learn so much about Cory Booker and the kind of person he is when you read that story. Those sorts of stories can engage readers—and readers who aren't necessarily interested in the political story."
Covering policy is essential, too, Wallsten said. "You have to write about policy in an engaging way. A story that illustrates how we want to take on policy is a piece (we did) about Elizabeth Warren. We took a deep dive on her idea of a 'wealth tax,' and how that was the center of all her policy proposals. We added up the cost of all of her policy proposals, and then looked at whether it was realistic that a wealth tax could pay for it. It was a deeply substantive story—also, very readable…Campaigns are a contest of ideas, in addition to being a contest of personalities, and we see both as crucial for our coverage."
For some news businesses, collaborations have been born out of necessity—the need to "do more with less." For others, collaborative journalism makes sense logistically and for the benefit of the content.
Julie Pace is the Washington Bureau Chief for the Associated Press (AP). Over the course of her career, she's covered four presidential elections, and now leads a team of political reporters and editors who are based all across the country.
Julie Pace
"One of the things that was a real priority for me this cycle was to ensure that our political team wasn't just based in Washington and New York," she said.
The AP's greatest strength, she said, is that it has talented political reporters in every state. For 2020 coverage, Pace's goal was to integrate all of those reporters, to encourage greater collaboration and communication, and operate as a single national political team.
The AP's 2020 team will be guided by what Pace referred to as three pillars: "You want to cover the ins and outs of the campaign operation and the candidates themselves—how they're strategizing and how they're positioning themselves. You want to aggressively cover their policy rollouts—what they're saying about what they'd do as president. And then the third piece of it—and I think this is equally important—is that you want to cover the voters."
Based in Des Moines, Iowa, Annah Backstrom Aschbrenner is the USA Today Network's 2020 campaign editor. She'll be directing a team comprised of reporters from all across the country, working in tandem to fully cover the 2020 campaigns and election. As the campaigns kicked off, reporters were assigned to each of the candidate's campaigns, and in the cases where a candidate has some local or regional context (Amy Klobachar and Minnesota, for example), local reporters will greatly contribute to coverage as well.
"We're approaching this from all angles, to make sure that we're utilizing the resources we have all over the country—ideally, getting a better perspective and painting a more accurate picture of the thoughts of the country," Backstrom Aschbrenner said. "I think the USA Today Network has a unique opportunity because of the scope of the network. We have large papers in Iowa, in Wisconsin, in Michigan and Ohio, and several papers in Pennsylvania, and those are states that will be in ultra-focus in 2020. I feel like we have a little bit of a leg up when it comes to coverage. We're not visiting these communities; we live in them."
At USA Today Network's newspapers and across its 2020 coverage team, trust and accuracy are part of every conversation, Backstrom Aschbrenner said.
"After 2016, there has been some lack of trust in the media, and all of us are cognizant of that and take the responsibility very seriously. We are educating an electorate," she said. "We're not just covering the churn-and-burn of the day; we are trying to arm people with the information they need to cast an educated vote."
Fresh Perspectives
In speaking with editors and reporters covering 2020, another trend emerged. There is a sense that it's not enough to simply not repeat past perceived mistakes; they've got to be proactive and innovative in how they'll cover campaigns and the election.
"We've built the biggest campaign team that the Washington Post has ever fielded," Wallsten said. The reporters tasked with 2020 election coverage are members of distinctive teams, yet there will be overlap and collaboration among them. For example, the Post has a core campaign team, with approximately a dozen reporters and three editors.
"We're particularly excited about this group, because it's a mix of campaign veterans and other reporters who have never covered politics and bring a valuable fresh perspective," Wallsten said.
The newspaper's Congressional and White House reporters will also provide 2020 coverage and context. There's also the muscle of the investigative team, which Wallsten said has "embarked on a vigorous vetting of all the candidates and their backgrounds, their records and their policies." They've also added a seven-day-a-week politics breaking-news team and a new campaign newsletter.
Post reporters will be tasked with covering candidates and particular campaigns, but Wallsten noted that flexibility in how reporters are assigned will allow the news team to "change it up as the dynamics require." Though some candidates may garner more attention than others by virtue of those dynamics, the edict at the Post is to cover even the race's lesser-known ones.
"We recently had a big story on Andrew Yang and the phenomenon around him. We have another story that's going to run on the front page about Marianne Williamson and her campaign," Wallsten said. "We're not intimidated by the big field. We actually relish the big field. It makes for an engaging, lively campaign—that gives us a lot to write about."
Kristin Roberts, McClatchy's vice president of news, joined the company in the wake of her work heading up 2016 presidential coverage for Politico. Leading up to the 2018 midterm elections, Roberts transformed how the news organization would newly cover campaigns and public policy. Under her leadership, McClatchy launched The Influencer Series, a four-state program that surveyed more than 200 community leaders across political ideologies, economic circumstances and professions. The series unfolded over the course of six months, and it allowed McClatchy reporters to deeply explore policies important to the publisher's audiences.
Kristin Roberts
"By the time we got to the end of 2018, we had delivered a body of journalism that was directly relevant," Roberts said. "The response to that was so strong that we're going to be building out that model for 2020."
What the initiative revealed was that readers wanted two different things pre- and post-election.
"The political media, generally, gave them a lot about the candidates themselves—about their personalities and what they were saying, about what they were tweeting, about the intrigue inside their campaigns," Roberts said. "We know that our audience in 2016 wanted that because it was a traffic bonanza. We know it was being consumed. But what our readers and viewers were telling us after the election was: 'This wasn't serious. We needed a serious conversation around policy.'"
The dialogue between McClatchy's political reporters/editors and readers/voters continues. The Influencer Series does too, under a fresh rebranding as the Priorities Project. Live events are also fundamental to the project. In November 2019, McClatchy will host another such event, which will mimic the previous one held last November.
"We brought together 50 influential leaders (to Florida). We split them into working groups, which were each tasked with a set of recommendations for the state legislature on the policy problem that our audience had identified as among the most pressing this year," Roberts said. "It was an extraordinary experience because we set up working groups that included people who would never work together in any other setting. We had people on the guns panel who came from completely opposite ends of the spectrum on gun-control issues, on school safety issues. And they were able to come up with a set of agreed principles and suggest solutions for state lawmakers to pursue. We did that for multiple topics. That turned into a white paper, and then, we printed it up and hand-delivered it to every member of the state legislature in Tallahassee. It was a mind-blowing experience, where we were able to demonstrate not only the convening power of McClatchy and the Miami Herald, but our ability to bring together a group of people who would be at odds with one another, and come up with a constructive solution."
Though McClatchy's titles may not have the deep pockets of major market national and international newspapers, it can leverage the collective power of all of its political reporters, across the company and really connect the dots for readers between policy considerations, and how those choices will impact their lives at the local level.
"Over the course of the last 2.5 years, the leadership of the company and the leadership of all the newsrooms have worked very hard to make those 30 news organizations into one organization," Roberts said. "The product of that is an ability to leverage the strength of the political reporters in 30 news organizations."
(Left to right) Washington Post publisher Fred Ryan, executive editor Marty Baron and national security editor Peter Finn look on as senior politics editor Peter Wallsten speaks during the Pulitzer Prize announcements in April 2018. (Photo by Matt McClain/Washington Post)
Waging War on Disinformation
Just recently, an altered video of Speaker of the House Nancy Pelosi was making the rounds on social media, designed to mislead viewers/voters about her physical and mental wellbeing.
At the Washington Post, "a fair amount" of time is spent detecting, correcting and rooting out disinformation.
"(Disinformation) is a big new development that we're dealing with," Wallsten said. One of the reporters on the 2020 campaign team will even be partly focused on disinformation.
"We're not just talking about foreign interference," he continued. "We're talking about all sorts of information that can spread quickly on social media-and at times is spread by candidates, politicians, and even the president. We need to be prepared. We have a fact-checking operation here that is fully engaged in that and has really set the standard for calling out politicians when they speak untruths.
"The fact-checker is going to be a big part of coverage this cycle. Not only do we want to call out the disinformation, we also need to be prepared to deal with it when it comes to us over the course of our reporting. There is, no doubt, going to be efforts to try to get us to publish inaccurate information, and we have to be ready for that. Part of that is being absolutely rigorous in the vetting of information and sources."
McClatchy's Roberts largely sees fact-checking as a journalism "niche" that sprang forth from the 2016 election aftermath. Third-party fact-checking organizations continue to help voters sort fact from fiction, and Roberts noted that they're partnering with tech companies like Google and Facebook to combat the glut of digital disinformation.
At the Associated Press, at least two reporters will be tasked with fact-checking and reporting on the origins of 2020-related disinformation.
"We're putting actual sources behind it," Pace said. "We recognize that it's not something that we can just ask our political reporters to do, even though they need to be on guard for it. We have to put people on this project. It's that crucial to our coverage of the election."
Election security, as a subtopic, will be part of the AP's reporting mission, too.
"We know, for sure, that there will be other attempts to meddle and interfere in the election. The challenge for us is that there will be probably be different players besides just Russia," Pace said. "There will probably be different techniques beyond what we learned about in 2016. How do we stay ahead of the curve? How can we make sure we're in a place where we are understanding what is happening and are able to inform the public about what is happening?"
She continued, "One of the challenges is also trying to understand the real impact on the election. In 2016, we now know—because of the intelligence community and Bob Mueller has put it plainly—Russians interfered with the election. They did so to try to help Trump win. But what we don't know is what the impact of that was. We don't know if Trump won because of this effort. We don't. But we have to try to figure out the impact, and that's really a complex reporting endeavor…A lot of groups don't have an incentive to talk about this, but we have to be really aggressive on that front in this cycle."
Advising the Press
Campaign and election seasons are sprawling, and the trail leading to Nov. 3, 2020 will be long, bumpy and hazardous for the press.
Already with several female candidates in contention for the Democratic nomination, there may be evidence to suggest that women candidates aren't getting as fair a shake in the media as their male counterparts, according to an ongoing study being conducted by Storybench, which (at press time) had analyzed the full text of 1,397 articles.
Polling is also potentially hazardous for the press—not necessarily reporting on polls, but rather, allowing polls to sway coverage decisions.
Roberts said, "Avoid national polling and making all coverage decisions based on national polling. I have been warning reporters and editors alike for years about their over-reliance on polling to make their decisions about campaign coverage. National polling and state polling are weak. In fact, state polling is weaker than national polling. Relying on them is going to serve media organizations poorly and the public poorly in turn."
Wallsten explained some of the edicts in place at the Washington Post as its journalists journey toward 2020: "Keep our eyes open, and be ready for everything, and to not be predictive in our coverage, but to capture the dynamics as they are, as they're happening—to keep our eyes and our minds open to every and any possibility.
"I think that's been a signature aspect of our coverage for many recent elections," he continued. "It is part of why we've been able to often capture dynamics earlier than others. And it also explains the fact that we're covering the whole field, and we see everyone and every new dynamic as a way to sort of use the election to write about what's happening in America."
Tags: Associated Press, Feature, McClatchy, USA Today Network, Washington Post
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One thought on "Preparing for 2020: News Organizations Ramp Up for an Election Cycle Certain to be Dynamic, Fast-Paced and Combative"
Dr. Dane S. Claussen
Actually, the US mainstream news media have received harsh criticism after every presidential election in my lifetime, and it's generally been well deserved. After every election, a bunch of graybeards sit around and conclude "we'll do better next time," and four years later, the coverage is just as bad or worse.

redpajama_set_name: RedPajamaCommonCrawl


As well as copyright itself there are a number of other 'rights' or classes of copyright such as: public domain, orphan works, crown copyright and database rights. There are also associated terms such as 'third party rights' and 'copyright free' that need some explanation.
Third party rights are those owned by a copyright owner who is not the creator of the work; the illustrations in a book or the images on a webpage are often third party materials. In a history textbook the illustrations, archive photographs, letters and maps that are used are often third party images.
The second question is, "Does the permission to use them cover how you intend to use them?" The school may have a licence to use images from a subscription service but that may not cover, for instance, publishing them through a website, or a vle.
Because someone else has permission to use an image on a website or in a slideshow from, say a gallery or museum, their permission to publish doesn't automatically transfer to you; you will need to go to the gallery or museum yourself and ask for your own permission to use them.
Acknowledging the source of third party materials fully is one way of making the position clear and helping others identify the source.
When works have passed out of copyright there are said to be in the public domain, or PD, and they can be freely copied, adapted and distributed. There are many good reasons – maintaining provence, acknowledging sources, avoiding plagiarism, encouraging sharing and letting others find the original – for continuing to use acknowledgements even if the work is in the public domain.There are a number of major digital resources on the WWW that are comprised of digitised materials that are in the public domain, such as the pioneering Project Gutenberg. Creative Commons has a PD classification.
'Orphan works' are those where the creator or copyright owner is not known or cannot be contacted. If the owner can't be contacted then the work cannot be be used and an impasse is reached. Orphan works include a huge amount of historical material in libraries, museums and archives which cannot be made opening accessible to the public.
The issue of orphan works is an on-going and a solution may be found in the future.
"No Known Restrictions" is a term used to indicate that the material being published - often old photographs or documents - has no known copyrights associated with them. This claim should be made only after due process of trying to trace the owner and if published used in conjunction with a Take Down Noitice. For more about this topic see Module 4.
This is a term often used as an expressesion hope rather than accurately describing a particular class of 'copyrights'. By free is meant either - or perhaps both - no charge and/or no copyright restrictions for the purposes you have in mind. There's plenty of material available which is free in both these senses but which has copyrights, moral rights and other rights in law such as rights of privacy or personality, in place.
In the UK 'Crown Copyright' describes material which is produced by employees of the Crown in the course of their duties. 'Crown Copyright' includes legislation, government codes of practice, Ordnance Survey mapping, government reports, official press releases, government forms and many public records. 'Parliamentary Copyright' applies to materials such as Hansard the record of the Houses of Commons and Lords, Parliamentary Bills and to government white and green papers. Therefore, most material originated by ministers and civil servants is protected by Crown Copyright. Crown copyright is for 50 years except for materials which has not been published when it is 125 years. Guidance about Crown Copyright is from the Office of Public Sector Information (OPSI) at http://www.opsi.gov.uk/advice/crown-copyright/index.htm which says that "extracts of up to 250 words from official sources may be re-used without the need to apply for a licence." Some Crown Copyright materials have the copyright waived and are placed into the Public Domain.
Performance rights apply to literary, musical and dramatic works and give the performers - actors or musicians - rights to sell or licence their contribution for reproduction, distribution, rental and lending of a work they have appeared in. Performance rights last for 50 years, work world-wide and form the basis of an important income stream for many performers.
A freelance or amateur photographer has full copyright of the work they produce. When 'moral rights' were introduced in the UK by the Copyright Act of 1988, the right for creators and authors to be acknowledged gave photographers a lever to have their work acknowledged even if they were in the employ of a company or newsagency. Moral Rights have to be 'asserted' or agreed before work is done. Photographs in old newspapers, magazines and books often have no acknowledgements making it difficult to trace if permissions for re-use are being sought.
There is another 'moral right' in regard to photography - the right of a client who has commissioned a photograph on a private basis - wedding, private party, family group, studio portrait, etc - the photographer and/or publisher needs their explicit permission to make use of the photographs.
In the UK it is generally OK to photograph in public places - with some restrictions including 'harassment' and ALWAYS with a dose of common sense; as there is no right to privacy in public places as a rule - public toilets being an obvious example. However, the UK Human Rights Act does provide that people have a right to privacy in their own homes - therefore, you can't, for instance, photograph people in the privacy of their house or back garden without permission. The term 'public place' is open to interpretation so, some public-seeming places may, in fact be private - e.g. shopping centres pedestrian ways.
Laws about the uses of photography and video differ in different countries - and even in different states or regions of a particular country. Take care!
As with everything else - you have to apply 'rights' to particular situations and balance your rights with those of other people who may be involved. 'Common sense' plays a large part in the practice of taking photography and video.


MalaMala Rattrays Camp is located within the MalaMala Game Reserve. This private reserve lies strategically sandwiched between the Kruger National Park and the Sabi Sand Wildtuin. The unfenced borders between MalaMala and the Kruger National Park on one side, and the Sabi Sand Wildtuin on the other allow animals to migrate unhindered to the perennial Sand River which flows north to south through MalaMala for 20 kilometers (13 miles). This well preserved wilderness is a "honey-pot" to the most sought-after wildlife species, as well as a host of smaller creatures. MalaMala is part of a conservation gene pool that covers 5.5 million acres of land in the heart of the South African Lowveld. The reserve supports a variety of habitat types; dense riverine forest, acacia-combretum bushveld, open grassland and rocky outcrops, each sustaining different plant and animal species. Drives are varied and full, with a different view around each corner. Due to the rich ecosystem, sightings of the Big Five in the MalaMala Game Reserve reach astronomical proportions. In the 17 years that MalaMala has been providing a luxury safari experience, each of the Big Five have been viewed daily while on game drives at least 96% of the time. The epitome of regal colonial safari style, MalaMala Rattrays Camp bears the style of crystal and leather, with beautiful furnishings that are a treat to the connoisseur of the finer things in life, captured over generations on a land that remains as old as time. Rattray's includes 8 luxury khayas (the Zulu for "home") for a maximum of 16 guests in camp. Each khaya functions as an inclusive home, complete with hand-selected furnishings, lavish "his" and "hers" bathrooms, secluded outdoor shower, private verandah with grand river views and private heated plunge pool, 24-hour temperature control air-conditioning, heating and overhead fans, hairdryer, direct dial telephones, mini-bar, safe and tea & coffee making facilities. Optional amenities include satellite television, laptop computer with wireless internet connectivity and DVD player. Morning and afternoon game drives are included in the accommodation cost.


text:
Home » OPINION » Columns » TODD SMITH: Band-Aid, Amazon, Google top brand index
TODD SMITH: Band-Aid, Amazon, Google top brand index
Posted by: For the MBJ in Columns, MBJ FEATURE, NEWS, OPINION 08/10/2017
Band-Aid, Amazon and Google are the strongest brands according to the latest YouGov 2017 BrandIndex. Craftsman and Dawn rounded out the Top 5.
Johnson & Johnson fell out of the Top 10 this year, from number 6 to number 11. Quaker replaced it in the Top 10.
The Top 20 Brands With Best Ad Awareness chart reveals that this year, 19 of the Top 20 brands with the highest ad awareness scores were down by statistically significant margins compared to last year—with the exception being Sprint.
To calculate advertising awareness, respondents were asked,
"Which of the following brands have you seen an advertisement for in the past two weeks?"
Brands that made the biggest awareness gains since last year include Uber, Blue Apron, Trivago, Dollar Shave Club, Lyft, Hulu, Nintendo, Mattress Firm, Stella Artois, and Sprint.
A big drop by Apple (was 18, now 22) and Dish Network (was 12, now 32) took both brands out of the list this year.
Two new brands entered the ad awareness Top 20 this year: Sprint (11) and Pizza Hut (21).
Brandchannel interviewed YouGov BrandIndex's CEO Ted Marzilli, to discuss the Top 10 brands and the risers in the ad awareness category.
1. What is unique and consistent amongst this year's Top 10 brands that puts them in this category?
Innovation and usefulness are rewarded by consumers. None of the companies on this list could ever be considered "complacent." It's a high, difficult bar to reach, and a lot of luck and serendipity are involved. But there is no question about the payoff when those two elements come together.
2. To what do you attribute Walmart's being the biggest gainer in the past year?
By nature, Walmart is a fighter and it doesn't intend to let Amazon run away with the online trophy so easily. Its brand health improved considerably once it bought ecommerce superstore Jet.com for $3.3 billion, instantly putting it in a much more competitive position with Amazon. It overhauled its grocery departments and debuted its own mobile payment app, all likely contributing to its move up.
3. With Uber rising to the top spot in terms of ad health, have recent headlines—albeit critical ones—lifted Uber's brand awareness?
Uber may have had its issues this year, but its name has become as ubiquitous as Coca-Cola for ride sharing. The best brands still advertise even when hitting rough spots. See Toyota and their massive recalls and Congressional appearances of 2010—it never stopped advertising its product.
YouGov BrandIndex tracks the perception of more than 1,500 major brands daily, interviewing 4,800 people every week day from a representative sample of the U.S. population, totaling more than 1.5 million interviews per year.
The primary ranking uses YouGov BrandIndex's flagship INDEX score as measurement of brand health and averages six sub-scores: General Impression, Quality, Value, Satisfaction, Reputation, and Willingness to Recommend.
Find out more about the healthiest and most visible brands at the BrandIndex.com.
Facebook Fights Fake News
Facebook has launched "Related Articles" that appear below news links to stories lots of people are posting about on Facebook, or that are suspected to be false news and have been externally fact checked by Facebook's partners. Appearing before someone reads, Related Articles will surface links to additional reporting on the same topic to provide different viewpoints, and to truthfulness reports from the fact checkers.
If users see drastically different angles when they compare a story to its Related Articles, they might deem it suspicious and skip it, be less likely to believe or share it, or could click through the Related Articles and make up their own mind. That could reduce the spread and impact of false news without Facebook itself having to be the honesty police. Related Articles could also balance out some of the radical invective that can subtly polarize the populace.
Pre-click Related Articles have rolled out in the U.S., Germany, France, and the Netherlands. These countries were chosen to get the rollout first because Facebook has established fact-checking partnerships there. "We don't want to be and are not the arbiters of the truth. The fact checkers can give the signal of whether a story is true or false," said Facebook News Feed integrity product manager Tessa Lyons.
Meanwhile, Facebook's machine learning algorithm has improved its accuracy and speed, so the social network will now send more potential hoaxes to fact checkers.
Facebook has shown Related Articles after people click links since at least 2014. Even then it was getting flack for dispensing fake news. In April Facebook tested the new pre-click version as part of its multi-prong attack on fake news following criticism that misinformation influenced the 2016 U.S. presidential election. That includes downranking hoaxes and click bait, reducing referral traffic to ad-filled spam sites to cut off their funding, and promoting local journalism and news literacy.
Most directly, it partnered with Snopes, AP, PolitiFact and others external agencies so it can add warning labels to stories externally vetted as false.
Golden Mic | Rick Cleveland, Sports Legend
The Spin Cycle grew up reading the pearls of wisdom from legendary sports writer Rick Cleveland. My lifelong love of sports – especially football – was fueled in large part from his magic and passion that made the words come alive on the sports pages of history.
It's only fitting that Cleveland has been inducted into the Mississippi Sports Hall of Fame. There's no one more deserving of this enshrinement!
He is the head coach of sports writers across the state and throughout the Southeast, and can write with the best of them. Cleveland has been the draft writer of Mississippi sports for more than four decades. He launched his career as a freelancer for the Hattiesburg American, then spent years at The Clarion-Ledger – and now writes for Mississippi Today, while also penning a syndicated column.
Cleveland is former director of the Mississippi Sports Hall of Fame. The establishment of the hall had a lot to do with a column he wrote 20 years ago about the need for a sacred place to recognize the legends of Mississippi sports history. In writing about the legends, in bringing their feats to life in living color, Cleveland himself has become a legend, and for that he wins the Golden Mic!
Each week, The Spin Cycle will bestow a Golden Mic Award to the person, group or company in the court of public opinion that best exemplifies the tenets of solid PR, marketing and advertising – and those who don't. Stay tuned – and step-up to the mic! And remember … Amplify Your Brand!
Todd Smith is president and chief communications officer of Deane, Smith & Partners, a full-service branding, PR, marketing and advertising firm with offices in Jackson. The firm — based in Nashville, Tenn. — is also affiliated with Mad Genius. Contact him at todd@deanesmithpartners.com, and follow him @spinsurgeon.
… we'd like to ask for your support. More people are reading the Mississippi Business Journal than ever before, but advertising revenues for all conventional media are falling fast. Unlike many, we do not use a pay wall, because we want to continue providing Mississippi's most comprehensive business news each and every day. But that takes time, money and hard work. We do it because it is important to us … and equally important to you, if you value the flow of trustworthy news and information which have always kept America strong and free for more than 200 years.
If those who read our content will help fund it, we can continue to bring you the very best in news and information. Please consider joining us as a valued member, or if you prefer, make a one-time contribution.
band-aid Business Coca-Cola Google jet.com Mississippi NEWS Uber Walmart	2017-08-10
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text:
Europe,Financial,News 1 Highspeed,Britain
Atkins secures preliminary design contract for Britain
HS2, the company overseeing the project to build a high-speed line between London, Birmingham and northern England, has awarded Atkins a £13.3m contract to prepare preliminary designs for the County South section of the line which will run 91km through the counties of Buckinghamshire, Oxfordshire and Northamptonshire.
The contract encompasses civil and structural design services and includes the design work for the Colne Valley Viaduct, the twin-bore tunnels under the Chilterns, and a range of new green tunnels that are designed to blend in with the natural surroundings.
"We have to very aware of how we minimise the impact the construction and operation of the line could have on the communities through the which it will travel," says Mr David Tonkin, CEO of Atkins UK.
Work will start immediately and will be completed to coincide with the HS2 hybrid bill to Parliament by the end of 2013.
Categories: Europe, Financial, News
Tags: 1 Highspeed, Britain


text:
Segment Y in the press
Uber's tricky vision aims to tempt Indians from car ownership
Financial Times, 26 Aug '15
» India's manufacturing sector benefits from China's challenges
» Uber's tricky vision aims to tempt Indians from car ownership
» Mahindra to buy controlling stake in Peugeot scooter unit
» Luxury carmakers hindered by Indian potholes
» Global car groups to rev up India exports
» Nissan considers introduction of electric cars in Thailand
» Japan disaster affects Indian car production
» Indian auto boom gets bubbly
» India doesn't need green cars: Environment minister
» Superbike sales rise as Harley Davidson enters India
» Micra marks Ghosn's bid to make up for lost time
» Foreign luxury cars: Picking up speed in India
» Maruti Suzuki plans to drive into MUV segment
» In India, 'green cars' look like a hard sell
» Ford makes push to boost Asian presence
» Harley-Davidson plots India sales drive
» Harley-Davidson set to finally ride into India
» Superbike sales speed up in slowing economy
» 25 years later, second small car revolution
» India's car makers see glut
» PSA again exploring India opportunities
» Tough Times for the Tata Nano
» Can small really be beautiful?
» India cranks out small cars for export
» Will Tata's great car gamble backfire?
» Can Tata rev up Jaguar?
» Tata unveils world's cheapest car
» Automakers come knocking
» Coming soon, the $5000 car
» India's automotive plastics use to rise
» China readying new taxes on gas guzzlers
» New cars for under $5000
» At the Beijing Auto Show, signs of a behemoth to come
» Chinese automaker plans assembly line in Malaysia
» Chinese firm plans car plant in Malaysia
Uber likes to make bold predictions - as perhaps befits a six-year-old company with a valuation of more than US$ 50 billion. Travis Kalanick, co-founder and chief executive, says his ride-hailing service can become sufficiently ubiquitous in the west not only to kill-off old-fashioned taxis, but even to tempt some hardcore motorists to stop driving altogether.
In emerging markets, the company makes an even more eye-catching claim. Mumbai's battered old red buses are carrying adverts bearing the slogan: "The freedom to own a car, without ever buying one". These imply that Uber could become so widespread that millions of people might decide never to get behind the wheel at all.
At first, this sounds absurd. Some transport experts do claim that countries such as the US and the UK have reached a stage dubbed "peak car", whereby total vehicles use is starting to dip. But Indian car ownership remains tiny, at about 2%, according to research companies. This is far lower than in developed markets, where more than half of people tend to be drivers, as well as countries such as China.
Consequently, almost everyone agrees this level will rise dramatically. Analysts predict 4% of Indians will have cars by 2020. This in turn explains why General Motors unveiled plans to sink another US$ 1 billion into its loss making Indian operation last month, joining a host of global automakers gearing up for a future boom in car sales.
Yet Uber recently unveiled plans to invest US$ 1 billion into India, as well. This was partly to keep pace with Ola, its larger Bangalore-based rival. However, the splurge was also underpinned by a long-term bet, which Mr Kalanick outlined in a recent speech.
He argued that pollution and congestion leave cities in India and China facing an "existential" crisis. "We're offering a real alternative to a world that looks like a parking lot and moves like a traffic jam,' he said.
Tempting people away from cars is tricky. Vehicle ownership remains a powerful status symbol in emerging markets. That said it is not always a pleasant experience. Interest rates are high, making vehicle financing expensive. India's roads are bumpy and hectic. Parking is a nightmare. There is a reason why so many wealthy Indians employ drivers.
Uber's hopes of becoming chauffeur to the country's rising middle classes therefore rest on building a service that is both more convenient and cheaper than driving. It has a long way to go. Even in big cities like Mumbai or Bangalore, its service can be patchy, with much longer wait times than in New York or London.
Fixing that is mostly a question of supply. Uber has 150,000 drivers in India, but the idea that it could come close to 1 million over the next few years is not outlandish.
Ola predicts it will cross the million mark by 2017. The fact that only 2.4 million cars were sold in India last year gives a sense of the scale of the two companies' ambitions. This big potential increase in Uber's driver network was behind last week's tie-up with Tata, India's largest business group.
Tata invested US$ 100 million in the US Company. In exchange, it hopes its motoring and finance arm will provide vehicles, financing and insurance to all those first-time cabbies.
Different types of services can also help. In San Francisco, Uber offers a cheap carpool option, in which multiple riders hop in and out of the same vehicle. A comparable service is some way off in India, but could eventually find favour in a country where customers are thrifty, and shared taxis are already relatively common.
Take all of this together, and the idea that taxi aggregators might prise some of India's coming generation away from car ownership does not seem quite so ridiculous.
"Young Indian people living in big cities used to buy a small car," said Paul Blokland, of Segment Y Automotive Intelligence, an India-based research group. "But now they might well decide to save that money, given it is expensive, and they can't find anywhere to park it anyway."
This does not mean Uber's path will be easy, particularly given India's treacherous regulatory environment. But if even a small portion of future car buyers decide to rely on cabs, it could help car ownership levels settle well below the levels typically seen in mature industrial economies. And if Uber wins even a portion of this business, it will go a good way to justifying its US$ 50 billion valuation too.


text:
Houston and Driscoll, an observation about the chaos the Driscoll resignation introduced for the family
http://www.patheos.com/blogs/warrenthrockmorton/2015/06/29/hillsongs-brian-houston-interviewed-mark-and-grace-driscoll-after-all/
http://wp.production.patheos.com/blogs/warrenthrockmorton/files/2015/06/DriscollHillsong.mp4
Those of you who listened to the whole audio may recall that Mark Driscoll said it was a challenge for his kids, because they had spent their whole lives in the church, at Mars Hill. Now they aren't there.
The passivity of the language when Driscoll talks about the social lives of his kids is remarkable. After all, whose decision to resign membership and eldership at Mars Hill put the Driscoll kids in that situation? Mark Driscoll, obviously, and Grace Driscoll, slightly less obviously. When Driscoll has shared stories of exation involving his children it's actually easy to have some sympathy for them simply because when their dad makes the kinds of decisions he's described himself making, and that he made in the way he's described, it WOULD be confusing. By Driscoll's most recent account ...
I never got to say good-bye to the church and the people and so what went public was actually the resignation letter that went to the legal governing board that was in authority over me and so, uh, i uh, I know under the circumstances there wasn't a way to do that that would have been, uh, clean or easy. I don't have any criticism of the board. I think that, for the people, that there wasn't closure and I didn't, we didn't get to say anything.
And we didn't expect to resign. I met with the board. There was a whole list of things that were charged by current and former leaders and there was an internal governance struggle and threats of legal action that it got very complicated. And a lot of it was anonymous through the internet so you don't know who is saying or doing what. And so I invited the board to do a full examination, interview [emphasis added] anybody, anything, and we would submit to whatever verdict that they determined.
... When I think about eight weeks we met Friday and Saturday, October 10 and 11. I remember because the 11th was my birthday and so Grace and I were present with the board and they said: "We see in your history of leadership, less in more recent years but particularly in the past, pride, anger and a domineering leadership style." That would be the exact words they used. "We don't see anything disqualifying. These are areas we want you to grow. We want you to leadership at the
church soon." They wanted to do some clean up internally. "We want you back on January 4 in the pulpit, give you time to heal, things to cool down, and for some changes to be made."
We agreed to that. I sent in a go-forward plan and then we went home to have birthday cake with the kids. I think it was on Monday night. I was in the bedroom. Grace was in the living room. And so we told the board and told the kids, you know, we come back and ["will do"? garbled] preaching and try and love and serve and, and fix what was a struggling church and God had provided a way for us to do that as volunteers. And so I was to come back as a volunteer. [emphasis added]
And then on that Monday night I was in the bedroom, Grace was in the living room and he spoke to me and he spoke to her in a supernatural way that neither of anticipated or expected. Ah, and so Grace walked in and she said, "I feel like the Lord just spoke to me and said what we're supposed to do." and I said "I feel like the Lord spoke to me and said what we're supposed to do." It's not what we wanted; it's not what we agreed to; it's not what we've planned for. And so I asked her, "Well, what did the Lord say to you?" cuz I didn't wanna influence and she said, uh, she said we're [Grace Driscoll speaks but it's low and indistinct, Driscoll pauses a moment and is urged to continue by Houston] "The Lord revealed to me that , you know, a trap has been set, there's, there's no way, chance we can return to leadership" and I didn't know what that meant or what was going on at the time. And I'm, I said, [garbled] "We need to resign". So this is not what we anticipated
and a lot of people've thought, you know, "maybe he's another plan" but we didn't. We didn't know what we were doing.
And Grace fell to the floor and she was just sobbing uncontrollably and I'd never seen my wife like that. She was devastated. So we prayed and slept on it and decided we would make sure we got this right. Talked to pastors, those that we trust and sent in our resignation then on, it would have been Tuesday. ...
As you can see from this narrative what Mark and Grace Driscoll would have told their children, according to Mark Driscoll's most recent narrative, anyway, would have been drastically different from what reality turned out to be Monday, let alone Tuesday. Compare that to this:
https://docs.google.com/document/d/1wYBTnRpPHRb8N1nqtgP2FcHcdnBeMIqCYy2SyQCEWBg/edit
Transcript | Mark Driscoll | Thrive 2015-05-01
It finally came to the point where God released my wife and I from our responsibility to ministry. He spoke to us audibly. It wasn't what we were expecting. It wasn't what we had agreed to. We were both pretty shocked and the announcement was going to come out that week. [emphasis added] And, uh, our server, our e-mail and things apparently were hacked and there was no way to get anything done without it being a public situation. And so the Board, which are good, godly people in authority, which I appreciate -- they released a statement earlier than we were anticipating, so um, but that meant, and I agree with that decision, I'm not critical of it. But that meant that I hadn't told my kids that I had resigned and they were in school, taking test, it was a test week, …. we threw some stuff in a bag and ran to school to grab the kids and within minutes it was on TV, I think it was on CNN.
Since by the new account the resignation letter was drafted, it seems, the very day the resignation was announced, there wouldn't have been time to notify the children of a decision that was taking shape the night before. The Thrive account mentions "things apparently were hacked" but there's never been any evidence anything of the sort occurred. If Mark Driscoll really drafted his resignation letter October 14, 2014 and sent it to the BoAA then it would be natural for the BoAA to disclose that resignation. The only thing that could be "relatively" sure about information within the leadership culture at Mars Hill was that there was informational hemorrhaging at almost every level. Wenatchee The Hatchet could write an entire post about the nature of the informational leaks that happened over the last ... few years ... but that's not interesting at the moment. What is interesting is that at the Thrive performance Mark Driscoll made it seem like the resignation "could" have been released by the Board sooner than expected and that, well, the implication that email or serves were hacked and there was no way for anything to get done without it being public is sidestepping a more obvious point.
When the president of Mars Hill resigned it was the resignation of the highest ranking legal officer in the corporation and it would have to be a matter of public record for state record purposes. It would also be news.
Driscoll told Houston "we never got to say goodbye". That's what the resignation letter already did. It turned out Mark Driscoll resigned from the only church he was eve ra member of, a church he co-founded back in 1995. He resigned after he had, as he told Houston, both initiated an investigation and agreed to submit to the findings of that investigation right up to the point that he heard some voice say "a trap has been set."
Was that voice worth resigning over? Was that voice worth actually or just potentially dismantling the social lives of the Driscoll children over? After all back in 2007 it wasn't unknown that the Driscolls and Petrys visiteded each other. When Munson's shunning edict came down it's not like that didn't establish as policy an ending of social interactions between families.
So if the latest Driscoll account is true (and it does seem to fit the Thrive narrative, more or less) then the Driscoll resignation comes across as impulsive and reactionary; it also comes across as a decision that flatly contradicted what Driscoll said he would agree to comply with. It's not difficult to imagine, as Driscoll said was a concern since the resignation, that there'd be some worry the Driscoll kids might be upset or resentful about their parents decision to bail on the church they helped plant that the kids grew up in.
And as Mark Driscoll used to teach about husbandly/fatherly headship, it means that it's your responsibility even if technically you'd say it wasn't really your fault. Regardless of whether Mark can claim God said " a trap has been set", it was Mark Driscoll who decided to interpret that as "we should quit" rather than to submit to the leadership he said he was going to submit to and see where things led.
Labels: Houston interviews driscolls, resignation
The Evolution of Markulinity: seeds of implosion, ...
The Evolution of Markulinity: combining a blue col...
The Evolution of Markulinity: Driscoll looks back ...
The Evolution of Markulinity: 2000, the eruption o...
The Evolution of Markulinity: The Dude Gospel, the...
The Evolution of Markulinity: Driscoll to Houston ...
Mark Driscoll, the Houston interview, and the "Tes...
so Driscoll said it was revealed to him "a trap ha...
pending series of posts on Mark Driscoll and the T...
Houston and Driscoll, an observation about the cha...


Standard Kia spectra with great miles and. Easy to drive.
There hasn't been much. . . Good on gas. Its a standard like that too. The electronic parts ate wearing out but its 15 years old. It's quiet still engine starts fine. Had a battery for over 7 years in it before changing. Had arm replaced when got it nothing else. . But the usual spark plugs and tires. Oil change be careful of tilted oil pan most Kias have that so they try and say you have a slow leak where as they didn't tighten it on right because it's tilted.
My car is a small car and it makes it easy to get into tighter parking stalls.
It works great. Just a few problems with it. One problem that my car has is the speedometer has stopped working but it is not to bad because I never used it much before plus when driving you only need to follow the speed of other cars. When I drive a night I usually use the waze app to see my speed if there is not another car near me. The acceleration is not the best but it is not bad either I feel like it is better than a Dodge caravans acceleration.
High performing, reliable Ford f250 super duty.
Our Ford f250 super duty extended cab pickup truck is a great vehicle. It has had only minor issues, such as having to fix the steering because it veered to the right and minor maintenance repairs. It has a lot of power being a v8 and really is a great vehicle for a family with dogs and it has been very convenient for hauling things. We love this truck and would not hesitate to purchase another Ford truck in the future, .


text:
Q: Prove that $\| BC\| \leq \| B\|\| C\|$ I have problem with this:
$$\| BC\| \leq \| B\|\| C\|$$
where $\|\cdot\|$ means spectral norm defined as $$\|A\|=\text{max}\lbrace\|Ax\|:x\in\mathbb{C^n, \|x\|=1}\rbrace$$
where the norms on the are according to standard scalar product.
For my homework I had to solve $\|A+B\|\leq\|A\|+\|B\|$ which I managed to do by myself but this second inequality seems to be (at least for me) much harder. Any ideas?

A: Recall (or prove) that $||Ay|| \le ||A|| \ ||y||$ for every $y$.
Then, apply this twice to get,  $$||BCx||  \le   ||B|| \ ||Cx|| \le ||B|| \ ||C|| \ ||x||.$$

redpajama_set_name: RedPajamaStackExchange


With a little DIY or a couple of phone calls many things can be fixed or changed about a home. There are definitely things to be on the lookout for when you buy a home but don't get caught up on the details that don't fit your personality. Most of the time those things can be changed with no problem!
Here's a list of 7 things you don't need to worry about when buying a home.
Paint Colors: Changing the color of paint may be one of the easiest fixes of all. With a little bit of time and creativity it's the easiest way to personalize your house. It's rare that you find a house with your exact style anyway so paint colors are probably going to be on your "to change" list of any house you'd buy.
Wall Paper: Wall paper can be tricky to remove which is why some buyers are hesitant to purchase a home where they'll need to change the wall paper. But again, with a little DIY and elbow grease wall paper doesn't need to be scary. It will be a short term project for a house you'll love for years.
Hardware: The cabinet pulls and door knobs can be easily overlooked for sellers but stand out to buyers as something that makes the house outdated. There really is no simpler fix than replacing these though. And if it's out of your new homeowner budget to replace them all a can of spray paint can make a huge difference in updating the old bronze style!
Appliances: As long as the current appliances in the house work you'll be able to cook your meals. Appliances can be easily replaced as soon as your budget allows. It's never worth letting your dream house pass you by just because the kitchen hasn't been updated to stainless steel.
Flooring: Many sellers will work with you on replacing flooring or making amends for a flooring concession if the flooring truly is in need of replacement or repair. However, if it's just not your style it's an easy update that can be made.
Age: As long as the house has been kept up well and updated throughout the years to meet current codes and standards the actual age of the house shouldn't be too much of an issue. Many old homes can be old just in structure but almost brand new in amenities.
Curb Appeal: It's always nice to pull up to a beautiful home. But if the bushes in the front are overgrown or the lawn isn't perfect the yard probably just needs a little TLC to become the best looking house on the block.


text:
Q: argparse multiple optional arguments I'm writing a script which searches for a regex in one or more input files. If no input file is provided (or there is an "-" instead of a file), it should search in stdin.
Example: myscript.py [-h] [-u | -c | -m] [infile [infile ...]] regex
What I don't understand is - how does it differentiate filename from regex?
Let's say I type in myscript.py file1 file2 regex. How does it know that regex is a regular expression and not another file?
My code is as below:
def init_parser():
  parser = argparse.ArgumentParser(
    description="The script searches one or more named input files for lines\
     containing a match to a regular expression pattern."
  )
  parser.add_argument(
    '-f','--infile', nargs='*', type=argparse.FileType('r'), default='-',
    help='the name of the file(s) to search.'
  )
  parser.add_argument('regex', help='the regular expression.')
  group = parser.add_mutually_exclusive_group()
  group.add_argument(
    '-u', '--underscore', action='store_true',
    help='prints "^" under the matching text.'
  )
  group.add_argument(
    '-c', '--color', action='store_true',
    help='highlights matching text.'
  )
  group.add_argument(
    '-m', '--machine', action='store_true',
    help='generates machine readable output.'
  )

  return parser

Since there are no flags to specify  the regex, the script can't differentiate between files and regex. If I don't specify a file (because I want it to read from stdin) it thinks that my regex is a file and it fails.

A: Assuming you will always have a regex on the commandline, if you put the regex argument first, then infile, this will take the other positional arguments you specify:
parser.add_argument('regex', help='the regular expression.')
parser.add_argument('infile', nargs='*', type=argparse.FileType('r'), help='the name of the file(s) to search.')


A young guy and two old men were shooting hoops at an arcade basketball machine in Taiwan… Guess who got the highest score? Well, it's not who you'd expect!
This clip was filmed in Luchou Distinct, New Taipei City. The old man on the left takes arcade basketball to the next level so casually.
The video went viral due to the unexpected result. Even foreign websites are reporting on it, and sharing it.
The man looks so confident even when he leaves. Have you ever witnessed surprising abilities like this?
Did Ariana Grande Steal Music Video Ideas From a Small Australian Band?


Sessions are always changing. Hubb's API makes it easy to see which sessions have been modified.
This article will go over how to see which changes have occured to Sessions specifically in a designated time frame.
Here's a link to our full documentation on this endpoint.
In the body of the call, you can designate a specific Start Date and End Date. This will be the date range for when changes were made.
This will show all updates to sessions during the time-frame listed above. This includes any updates, deletions, additions, etc. made to sessions during this time.
Still have questions? Need help tweaking this call?
Contact Hubb Support at support@hubb.me for further assistance.