text:
\section{Introduction}
The propagation of ideas and innovations has
led to political, cultural and economic  changes. Social
scientists found that ideas tend to flow along social links, in a similar manner that an epidemic infects a population~ \cite{delre2010will,difOfInov}. Understanding how information propagates in online social network (OSN) platforms has significant real-world impact, from the political stability of states to marketing. Significant efforts have been invested in predicting various properties of information cascades, such as size \cite{lerman2010information}, temporal growth \cite{li2017deepcas}, and virality \cite{cheng14}.

Researchers mainly studied transient-copy propagation protocols (a term coined in \cite{ChengKLLSSA18}), where content is simply replicated in a network, like a re-tweet (contrasted with nomination cascades for example, such as the famous ALS ice water bucket challenge).

It is tempting to think that information propagates in OSNs according to epidemiological models such as Bass \cite{bass1969new} or SIR \cite{kermack1927contribution}. However several ``cautionary tales" were told by various researchers regarding the validity of this image. For example, one important assumption in epidemiological models is that all newly infected individuals arise from the susceptible set (neighbors of infectious people). However, mass media marketing efforts rely on a "broadcast" mechanism, where a large number of individuals can receive the information directly from the same source, which need not be their neighbor. Indeed, \cite{cha2009measurement} who studied information cascades in Flickr, found that out of 10 million total favorite markings, 47\%  were propagated not through the social links, but via other broadcasting mechanisms that Flickr employs. Also \cite{galuba2010outtweeting} found that  33\% of the retweets in their dataset credit users that the retweeters do not follow.

Furthermore, unlike the epidemiological picture of a disease spreading in waves, it was observed  that most cascades are extremely shallow and wide. For example, \cite{goel2016structural} found that the average size of the diffusion trees in Twitter is 1.3, and that the vast majority contain only 1 node. This phenomenon is also observed in other platforms such as Digg and Flickr \cite{cha2009measurement,lerman2010information,bakshy11,goel12}, email forwarding \cite{WU2004327} and recommendation chains \cite{DynamicsOfViral}

The majority of works focus on macro prediction tasks such as predicting the depth of a cascade, its size, or estimating other macro properties such as the transmission rate. Micro-level prediction tasks, such as whether a tweet $t$ will be retweeted or not, received considerably less attention. Even when microscopic properties were computed, like the probability that user $u$ will transmit information to $v$, it was used to derive macroscopic properties such as cascade size, and not for prediction in the standard machine-learning setting (train-test on a specific database of events). In \cite{galuba2010outtweeting}, two model-based algorithms for the task of url retweet prediction were proposed, based on the At-Least-One and Linear-Threshold schemes, and tested for a set of 100 popular URLs, whether they will be retweeted in the following time interval or not. In \cite{petrovic2011rt}, machine learning was used for the task of predicting for a stream of tweets which will get retweeted.

We study a different setting, which is user-centric and not post-centric. Given a user $u \in V$, $V$ is some fixed set of users, and a time interval $[t_0,t_0 + \Delta T]$, the task is to predict whether user $u$ is going to react (retweet, reply, or mention) to an existing post by some user $v \in V$ (which $u$ doesn't necessarily follow). The input to the prediction algorithm is a snapshot of the activity of all users in $V$ at time $[t_0-\Delta T,t_0]$, namely a binary vector indicating whether each user was active or not. The user-centric task coincides with the post-centric task if all users react to at most one post. This is indeed the case for most users in our datasets, as Figure \ref{fig:act_hist} demonstrates.

In this work we address some fundamental questions regarding the nature in which information propagates in OSNs: (1) Can we perform the prediction task without any other features besides the time series of the users' postings (in particular, no linguistic features) (2) Is there an algorithm which performs this task, but is model-agnostic? namely, it does not rely on epidemiological models, and (3) Does the algorithm need to know the social links (which user follows/mentions which user)? Or can the algorithm implicitly learn this information from the snapshot it is given as input?

{\bf Our Contribution.}
We answer these questions, providing new insights into the way information propagates in online social media platforms. We design several prediction algorithms, each using a different approach, including a neural network (NN) based algorithm, $TWCRN$, which does not use the adjacency matrix of $V$. We evaluate our approach on four datasets, spanning a total of 77M tweets, which we collected from Twitter in 2020, following four different major events in that year. Our algorithm  $TWCRN$ performed the prediction task with an average F1 score of 0.86 over all datasets, which were highly imbalanced (on average, only 10\% of users in a time slice of width $\Delta T=12h$ reacted to some post).

We were able to verify that indeed $TWCRN$ implicitly learns information about the social links using a permutation test, where we randomly permuted the input to the NN at train time, contaminating social links information. The algorithm performed very poorly in this setting.

We further designed a very intuitive algorithm, which for every user $u \in V$ learns the conditional probability that $u$ will re-share something in this time interval given $u$'s activity in the previous time interval (ignoring information about all other users). Intuitively, we are learning the ``trends" of $u$, is he a lazy-twitter (taking breaks between tweets) or a chain-tweeter. The performance of this algorithm was extremely competitive to $TWCRN$ (with respect to simplicity and running time), with an average  F1-score of 0.78.

Thus we arrive at {\bf two new insights}. The first is that a relatively accurate prediction at the user's level can be obtained by simply learning the user's habits, regardless of the social links. The second is that a higher accuracy can be achieved by integrating information about social links, but, this information need not be served explicitly, but rather the algorithm can learn the relevant links by itself.

From a technical point of view, we are able to train a rich algorithm with many parameters, $TWCRN$, on a large set of users, $10^4$. Previous work either trained a simple model (perceptron) on a large set \cite{petrovic2011rt}, or a rich algorithm (Linear Threshold with many parameters) but trained on a small dataset (of size 100). To overcome the computational challenge we wrap the NN with an encoder-decoder pair, to reduce dimensionality.

As far as we know, we are the first to use neural networks to perform such a prediction task, with such a success rate. The F1-score achieved in \cite{petrovic2011rt}, using many more features, and the passive-aggressive algorithm of \cite{PA} was 0.46, albeit for a somewhat different problem and setting. Neural networks were used very recently for the first time to predict macro properties of cascades (cascade structure), \cite{CascadesLSTM,li2017deepcas}, or to predict the influence of a given user based on activity features \cite{qiu2018deepinf}.

Our final contribution is to make all datasets openly available to the community, along with the Python code that we wrote for all algorithms.

\section{Related Work}
Users' influence in OSNs and the diffusion processes that stand behind  information propagation in them  were extensively studied in the past years. The works we survey here are by no means a concise review of the huge body of work available on this topic.

One line of work tries to maximize the size of the cascade by picking a good set of influential users that will be the starting seed. In \cite{matsubara2012rise}, the authors tried to predict users' influence by construction of differential equations extended from the Susceptible-Infected model. In \cite{tang2009relational}, the authors incorporated user-specific topic distribution and network structure, and in \cite{kempe2003maximizing, chen2010scalable} by means of a greedy algorithm. In \cite{feng2014influence}, the authors introduce the idea of novelty decay into the Independent Cascade model from \cite{albert2002statistical}.

Another line of work is focused on understanding information diffusion as they unfold, without manipulating the seed. These works typically suggest a generative model that underpins the information cascade and then check how the model fits either simulation or real-world datasets.
Examples include \cite{zhao2015seismic, mishra2016feature} where a self-exciting point process is used to develop a statistical model to predict cascade size; cascades in heterogeneous scale-free networks were studied in \cite{moreno2002epidemic}  under the SIS and SIR model;
a cascade generating function was developed in \cite{Lerman11digg} to compute macroscopic properties of cascades, such as their size, spread, diameter, number of paths, and average path length. In \cite{li2017deepcas} an end-to-end deep learning approach was designed to predict the future size of cascades, without using any hand-crafted features or generative model assumptions.

The third line of work does not deal with prediction but rather with descriptive analysis, providing insights to the distribution of cascade size, depth, width and adoption rate (as time progresses) \cite{cha2009measurement,lerman2010information,ver2011stops,goel2016structural}.

Fewer works tried to predict microscopic post-level or user-level events. In \cite{galuba2010outtweeting}, the task was to predict whether a popular URL that was retweeted several times, will be retweeted in the following time window. The method was again model-based, upgrading the Linear Threshold (LT) and At-Least-One (ALO) models with additional features to achieve better prediction (F1 score of nearly 0.7). In \cite{petrovic2011rt} machine learning was used to predict retweets of an original tweet, albeit with a rather low F1 score (0.46). Our work continues this line of work but differs in two main aspects: we do not have any model-based assumptions as in \cite{galuba2010outtweeting}, and therefore we don't use any hand-crafted features (like the virality of the topic, number of followers, etc.), that were used also in \cite{petrovic2011rt}. Furthermore, our approach does not require an explicit description of the social links.

\section{Methodology} \label{methodology}
Previous studies on user influence in social networks in general, and Twitter specifically \cite{galuba2010outtweeting, petrovic2011rt}, point out that the main predictor of users' activity is the users he follows (i.e., his friends).

We consider three models where the information about the user's  neighbors is taken into account to various degrees. In the first model, \emph{Tweet Prior Network} ($TWPN$) we completely ignore the user's social links and only consider its past activity, see Figure \ref{fig:tw_prior_net}. Our second model, the \emph{Tweet Mask Network} ($TWMN$), is a neural network that takes into account the user's social links and ignores non-adjacent users, Figure \ref{fig:tw_mask_net}. Finally, we train a fully-connected convolutional model, Tweet Convolutional Residual Network ($TWCRN$),  that considers all the activity of all the users in the network and not only the social links, Figure \ref{fig:tw_conv_res_net}.

The input to each NN is the same, a vector $\tau_i \in \{0,1\}^{|V|}$, which for every user $u \in V$ specifies whether he was active at time interval $[t_i-\Delta T,t_i]$ or not. The output vector, $\tilde{\tau}_{i+1} \in {\mathbb{R}}^{|V|}$ is the prediction for every user whether he is going to react to some post at time interval $[t_i,t_i+\Delta T]$ or not.

\subsection{Models definition}
\label{models}
\paragraph{Tweet Prior Network ($TWPN$)}
\label{tw_prior_net}
The architecture of this model is just two layers, input and output, as shown in Figure~\ref{fig:tw_prior_net}. All output nodes in the network use the $\tanh(w_u x_u)$ activation function, where $w_u$ is the weight of user's $u$ single edge, and $x_u$, the input, is the entry in $\tau_i$ corresponding to $u$.

\begin{figure}
    \centering
    \includegraphics[width=0.30\textwidth]{tw_prior_net}
    \caption{TWeet Prior Network ($TWPN$) schematic representation. The vector $\tau_i$ is the activity vector in the time window $[t_i - \Delta T, t_i]$, and $\tilde{\tau}_{i+1}$ is the predicted activity in time window $[t_i, t_i+ \Delta T]$.}
    \label{fig:tw_prior_net}
\end{figure}

\begin{figure}
    \centering
    \includegraphics[width=0.5\textwidth]{tw_mat_net}
    \caption{TWeet Mask Network ($TWMN$) schematic representation. The vector $\tau_i$ is the activity vector in the time window $[t_i - \Delta T, t_i]$, and $\tilde{\tau}_{i+1}$ is the predicted activity in time window $[t_i, t_i+ \Delta T]$.}
    \label{fig:tw_mask_net}
\end{figure}

\paragraph{MLE}
\label{mle_paragraph}
This model is a simpler variant of the $TWPN$ model where for every user $u \in V$,  the conditional probabilities are learned:
\begin{equation}
    p^{a,b}_{u}=Pr\left[I_u^{0} = a \, \big|\, I_u^{-1}= b\right],
    \label{eqn:mle}
\end{equation}

where, $I_u^{0}$ is the activity indicator of user $u$ at the predicted interval,  $I_u^{-1}$ in the activity indicator in the preceding time interval, and $a,b \in \{0,1\}$. The probabilities  $p^{a,b}_{u}$ are estimated solely on the data of user $u$ in the preceding time intervals, using the Maximum Likelihood Estimator, MLE (counting and averaging).

\paragraph{Tweet Mask Network ($TWMN$)}
This neural network extends $TWPN$ by taking into account the information at the user's neighbors as well. The architecture is a  fully connected 2-layer Feed-Forward Neural Network (FFNN) \cite{fine2006feedforward} (i.e., input layer fully connected to the output layer). Again, all output nodes use the $\tanh(\cdot)$ activation function. While the network is fully connected, for each output node $u$ we mask (hence the name) the non-adjacent input nodes.

For each user $u$, the output is given by $\tanh( \sum_{v \in N(u)} w_{v,u} x_v)$, where $x_v$ is the entry in $\tau_i$ corresponding to $v$. The weights $w_{v,u}$ between the user $u$ and the ones he follows $v \in N(u)$ can be interpreted as the influences, which the NN learns by itself.

\begin{figure*}
    \centering
    \includegraphics[width=0.7\textwidth]{tw_conv_res_net}
    \caption{TW ConvResNet ($TWCRN$) schematic representation, where $\tau_i$ is the activity vector in the time window $[t_i - \Delta T, t_i]$, $\tilde{\tau}_{i+1}$ is the predicted activity in time window $[t_i, t_i+ \Delta T]$. \textbf{(a)}  the Encoder part of the Auto Encoder (AE) network with $K$ layers  \cite{hinton2006reducing}, which is responsible for compressing the original activity vector. \textbf{(b)} the inflation step, which receives a 1D vector and transforms it into a 2D matrix by copying it row-wise. \textbf{(c)}  the ConvResNet with $L=18$ or $L=34$ layers, as described in \cite{he2016deep}. \textbf{(d)} the Decoder network, which constitutes the second part of the AE network, with M layers, which is responsible for the final de-compression of the prediction vector.}
    \label{fig:tw_conv_res_net}
\end{figure*}

\paragraph{Tweet Convolutional Residual Network ($TWCRN$)}
This model takes into account all possible connections between users, no restricted to the follower (or mention) social links.
The model consists of four parts as shown in Figure~\ref{fig:tw_conv_res_net}, as follows:

\vspace{1mm}

\noindent{\textbf{Encoder}} - A standard encoder, as described in \cite{hinton2006reducing}, which maps an activity vector of dimension $D$ (in our case $D=10^4$) to dimension $100 = d << D$. Each layer down samples the dimension of the input by a factor of 2 until the output size is $d=100$. The point of this layer is to reduce the computational effort of training the main part, ConvResNet, by reducing dimensionality.

\vspace{1mm}

\noindent{\textbf{Inflater}} - a simple procedure  which receives a vector of size $d$, and transforms it into a $d \times d$ matrix by copying it row-wise. This step is necessary because ConvResNet \cite{he2016deep} is used for images.

\vspace{1mm}

\noindent{\textbf{ConvResNet}} - We study separately two architectures, $\times 18$ and $\times 34$, presented in \cite{he2016deep} (the number represents the number of layers in the neural network)  which were developed for image processing tasks. This is the core of the prediction mechanism. The ConvResNet architecture enables extremely deep neural networks (more than 150 layers deep) to be successfully trained by a standard stochastic gradient descent with backpropagation, overcoming the problem of performance degradation present in very deep neural networks.

\vspace{1mm}

\noindent{\textbf{Decoder}} - Following \cite{hinton2006reducing}, the decoder maps the compressed vector (of dimension $d=100$) to its original dimension $D$. It does that by up-sampling the input vector by factor of 2, until the output size reaches the original input dimension $D$.

\subsection{Training and testing the models}\label{sec:train_test}
A cascade progresses in time, as well as in space (the nodes). In this paper, we focus on the time-aspect, and we partition the timeline along which the data was collected into equal-sized slices of $\Delta T=12$ hours each. For each pair of consecutive time periods $i,i+1$ we define two vectors $\tau_i,\tau_{i+1}$ as mentioned already above: $\tau_i$ is an indicator of  all activity types and $\tau_{i+1}$ only of reaction activity.

The prediction task is, given the vector $\tau_i$, predict the reaction vector $\tau_{i+1}$.

We train each model in the same manner, taking time period $i=1,\ldots,K$ as the train, and testing on time periods $i=K+1, \ldots N$,  where $N$ is the total number of time slices, and $K = \lfloor 0.9 \cdot N \rfloor$. We further split the train into train and validation, resulting in a 70-20-10 data split rule. To avoid over-fitting, we stopped the training if the loss on the validation set did not improve for 50 epochs.

We used the ADAM optimizer \cite{kingma2014adam} with default settings for all three networks, $TWPN$, $TWMN$, and $TWCRN$ (the components of the $TWCRN$ model were trained separately). We chose the Mean Squared Error (MSE) for the loss function. To enrich the gradient flow in the training step, instead of binary vectors $\tau_i$ we used a technique in which each 1 was replaced with a sample from a normally distributed random variable $N(1, 0.01)$, and 0 with a sample from $N(-1, 0.01)$.

To find the conditional probabilities of the MLE model, $p^{a,b}_u$ in Eq.~\eqref{eqn:mle}, we counted for user $u$, the fraction of times that each combination $a,b$ appeared in the pairs $\tau_i,\tau_{i+1}$, for $i=1,\ldots,K$.

At the test step, we fed each model with $\tau_i$, for $i=K+1, \ldots N$, to receive the predicted vector $\tilde{\tau}_{i+1}$. Each entry in $\tilde{\tau}_{i+1}$ (either the output of tanh or of the decoder, depending on the model) is set to 1, if positive, and 0 if negative. The MLE probabilities were rounded to 0 or 1.
This vector is then compared with the real $\tau_{i+1}$ to compute precision, recall, and F1 score.

\section{Data}
\label{data}
We collected four datasets from Twitter, using the \emph{Tweepy} API. Each data set concerns a different major event at that time: \emph{Volcano} (the eruption of the Taal volcano in the Philippines on January 12, 2020), \emph{Kobe} (the death of Kobe Bryant in a helicopter crash on January 26, 2020), \emph{Princess} (the stepping down of the Duke and Duchess of the British royal family in January 2020) and \emph{Beirut} (the explosion in Beirut on August 4, 2020). Table \ref{tab:data} describes the keywords that were used and the size of each dataset, and Table \ref{tab:post_types} shows the breakdown according to different types of posts.

\begin{table*}
    \centering
    \begin{tabular}{l|l|l}
    \textbf{Name} & \textbf{Keyword} & \textbf{Posts}\\
    \hline
    Volcano & taal, volcano, philippines & 17,994,283\\
    Kobe & kobe, bryant & 24,562,000\\
    Princess & meghan, markle, harry, prince, princess & 22,353,429\\
    Beirut & beirut, lebanon, explosion & 14,106,557\\
    Unfiltered & - & 56,338,915\\
    \end{tabular}
    \caption{Description of the five datasets that we collected. The first four were collected during different "viral" events, which took place during the year 2020, and were filtered to include only tweets which were related to those events. The fifth dataset is an unfiltered tweet stream which was recorded during the 8/2021.}
    \label{tab:data}
\end{table*}

There are several possible ways of posting and interacting on Twitter. The simplest post is a \emph{tweet}, i.e., a post that the user writes himself and is not related to any other post. Tweets appear on the home timeline of the sender, and on the home timelines of all his followers, but Twitter's time-line algorithm keeps changing frequently. Features like ``in case you forgot" break the synchronous time-line structure, and suggestions of tweets from users one does not follow break the social link structure.

There are three possible reactions to a tweet: \emph{mention} is a post that contains the "\emph{@username}" syntax in the body of the text, \emph{reply} is a direct response to another tweet and a \emph{re-tweet}, which is a propagation of someone else's tweet (re-tweet can be done also in an automatic manner using the 1-click option). All three reactions will be visible on the home timeline of the reacting user and on the timeline feed of all his followers.

The next key component in the data pre-processing was to recover the social links between the users. We can infer two types of graphs. The first is the {\em mention graph}, in which a link exists between user $u$ and $v$ if $u$ reacted to $v$'s post (but $u$ need not follow $v$). Another graph, the {\em followers graph}, is the one recovered using Twitter's API where a link between $u$ and $v$ exists if user $u$ follows $v$. Note that there need not be an inclusion relationship between the two sets of links, but the way our dataset was collected (using the mention graph), entails that the followers graph is a subgraph of the mention graph.

We recovered both social networks, and as we shall see, the accuracy of the classification task differs according to which network we use. Let us note that querying Twitter's API is computationally more expensive as Twitter limits the number of requests. Therefore it is interesting to know what's the gain, if any, when using the more costly-obtained information of the Twitter followers graph.

\begin{table*}
    \centering
    \begin{tabular}{l|l|l|l|l|l}
    \textbf{Name} & \textbf{PO} & \textbf{TW} & \textbf{RT} & \textbf{MT}\\
    \hline
        Volcano & 17,994,283 & 3,400,415 & 11,810,708 & 2,783,160 \\
        Kobe & 24,562,000 & 2,962,387 & 20,768,520 & 831,093 \\
        Princess & 22,353,429 & 4,694,745 & 15,457,234 & 2,201,450 \\
        Beirut & 14,106,557 & 1,951,752 & 11,418,457 & 736,348 \\
        Unfiltered & 56,338,915 & 35,728,226 & 813,013 & 19,797,676 \\
    \end{tabular}
    \caption{Breakdown of the post types for each data set, where \textbf{PO} is a general post (i.e., tweet, re-tweet or mention), \textbf{TW} is the initial tweet, \textbf{RT} is a re-tweet using the "\emph{RT @username}" syntax, or by clicking the dedicated button and \textbf{MT} is a mention.}
    \label{tab:post_types}
\end{table*}

\begin{figure}
    \centering
    \includegraphics[width=0.5\textwidth]{princess_act_hist_tw_log.png}
    \includegraphics[width=0.5\textwidth]{princess_act_hist_crwl.png}
    \caption{Histogram of the average activity of users in a single time slice of $\Delta T = 12h$ for the Princess dataset. Top: statistics for the mention graph dataset. Bottom: statistics for the followers graph dataset. Evidently, most users tweet or re-share only one post per time slice.}
    \label{fig:act_hist}
\end{figure}

As customary in many works, users that have low activity are filtered out from the dataset. We created two sets, $A$, the active users, users who post at least $a$ posts (either tweet or re-share of some sort), and $P$, the popular users, users that were reacted to at least $p$ times. We chose $a$ and $p$ so that the number of users in the dataset is roughly 10,000 (due to the constraint of memory resources).

\paragraph{Broadcasticity.}
Another parameter that is of interest is the depth of the cascade. As noted, most cascades are shallow. Various measures were used to compute depth, including the Wiener index in \cite{goel2016structural}, the average distance between all pairs of nodes in a diffusion tree. We suggest a much simpler criterion, which does not require the laborious task of computing the diffusion tree. We call it the {\em broadcasticity} measure, and it measures how much the diffusion resembles a broadcast rather than a diffusion. It's computed using the Jaccard index of the two sets $A$ and $P$:

\begin{equation}
    B = 1 - J(A, P) = 1 - \frac{|A \cap P|}{|A \cup P|}
    \label{eqn:broadcastisity}
\end{equation}

High broadcasticity means that $A$ and $P$ are almost disjoint, namely users either tweet or react, but very few do both. This is exactly the case of a shallow 1-hop diffusion. If a diffusion on the other hand is deep and wide   (like an epidemic spreading in the population), then many users belong to both $A$ and $P$, and the broadcasticity is low. Note that a shallow diffusion with few long paths still attains large broadcastisity

Table \ref{tab:data_broadcastisity} describes the various features of each dataset with respect to $A$, $P$ and the broadcastisity.
\begin{table*}
    \centering
    \begin{tabular}{l|l|l|l|l|l|l|l}
    \textbf{Name} & \textbf{$a$} & \textbf{$|A|$} & \textbf{$p$} & \textbf{$|P|$} & \textbf{$Posts$} & \textbf{\#slices}  & $B$ \\
    \hline
        Volcano & 103 & 3,189 & 207 & 7,757 & 2,710,915 & 108 & 0.97  \\
        Kobe & 167 & 4,674 & 167 & 4,835 & 1,380,543 & 87 & 0.98 \\
        Princess & 234  & 5,151 & 234 & 7,866 & 2,710,915 & 87 & 0.92 \\
        Beirut & 105 & 3,830 & 210 & 5,778 & 960,228 & 117 & 0.93 \\
        Unfiltered & 100 & 3,943 & 201 & 5,238 & 721,301 & 28 & 0.99 \\
    \end{tabular}
    \caption{Datasets are filtered to remove low-activity users. The set $A$ of active users that (re-) share at least $a$ posts (over the entire time period), and popular users $P$ whose tweets were re-shared at least $p$ times. The number of time slices $\tau_i$ is given in column 7, and the broadcastiscity in the last column.}
    \label{tab:data_broadcastisity}
\end{table*}

\begin{table*}
    \centering
    \begin{tabular}{l|c|c|c|c|c|c}
    \textbf{Name} & \multicolumn{3}{c|}{\textbf{Network Crawl}} & \multicolumn{3}{c}{\textbf{Tweet Log}}\\
    \hline
        & N & $E_c[L]$ & $E[L]$ & N & $E_c[L]$ & $E[L]$ \\
        \cline{2-7}
        Volcano & 8,990 & 3.953 & \color{green}{2.943} & 10,440 & 4.019 & \color{red}{4.648} \\
        Kobe & 8,339 & 3.921 & \color{green}{2.368} & 9,225 & 3.965 & \color{green}{2.593} \\
        Princess & 9,793 & 3.991 & \color{green}{2.869} & 11,891 & 4.075 & \color{green}{3.579} \\
        Beirut & 7,943 & 3.9 & \color{green}{2.498} & 8,876 & 3.948 & \color{green}{3.103} \\
        Unfiltered & 7,208 & 3.86 & \color{red}{6.23} & 7,363 & 3.87 & \color{red}{6.23} \\
    \end{tabular}
    \caption{Mean shortest path ($E[L]$) between any two randomly chosen nodes in the social networks. The $E_c[L] = log(N)$, where $N$ is the number of \textbf{valid} users in the social networks, and $E_c[L]$ is the critical mean shortest path (i.e., the network should satisfy the condition $E[L] \leq E_c[L]$, to be considered a small world (\textbf{SW}) network). \color{green}{Green} - the criterion is satisfied, \color{red}{red} - the criterion is not satisfied.}
    \label{tab:mean_shortest_path}
\end{table*}

\section{The Experiment}
Recall the classification task described in Section \ref{sec:train_test}. Given a vector $\tau_{i} \in \{0,1\}^{|V|}$, in which the $j^{th}$ entry is 1 if user $j$ tweeted in time window $i$, our goal is to predict the vector $\tau_{i+1}$, in which the $j^{th}$ entry is 1 if user $j$ reacted to some post in time interval $i+1$.
\subsection{Other baselines}\label{sec:baseline}
We benchmarked our model against four other popular models. The first two are  random guess models $RND_{p=0.5}$ and $RND_{p=\pi}$ which predict $\tau_{i+1}[j]$ using a fair random coin flip, or the fraction of users that were active in the previous time window, $\pi$.
The two last models are variations of the SI model, At-Least-One ($ALO$) and Linear-Threshold ($LT$). We follow the $LT$ and $ALO$ models that were  developed in  \cite{galuba2010outtweeting} as we found them the most general. The intuition of both is that if the neighbors of the user  were active in the preceding time window, it may stir the user's decision to become active himself in the next time window. Each algorithm takes a different try at estimating the probability that user $u$ will become active in the next time window; \cite{galuba2010outtweeting} use the following expression for $LT$:
\begin{equation}
    p_{u}^{LT} = A\Big(\alpha_{v_1,u},\ldots,\alpha_{v_k,u}, \beta_{u}, \gamma\Big)T\Big(\mu_{u}, \sigma_{u}^2, t_{u}^{post}\Big)
    \label{eq:p_LT}
\end{equation}
The $\alpha_{v_i,u} \in [0, 1]$ are the influence of a neighbor of $u$, $v_i$, on $u$. The $\beta_{u} \in [0, 1]$ is a prior probability of user $u$ to become active, $\gamma \in [0, 1]$ is the virality of the topic that is being discussed. $A(\cdot)$ is an \textbf{a-}temporal component, i.e., the probability that the user will respond to some post due to the influence that was exerted on him from his social circle. Concretely, this component is given by

 \begin{equation*}
        A(\cdot) = \sigma_{a, b}\bigg(\gamma\Big(\beta_{u} + \sum_{v:v \rightarrow u}\gamma\alpha_{v,u}p_{u}\Big)\bigg),
    \end{equation*}

where $\sigma_{a, b}(x) = \frac{1}{1+e^{-a(b-x)}}$ is a sigmoid function.

The second component of  Eq.~\ref{eq:p_LT}, $T(\cdot)$, is a temporal component of the predicted activity probability, and it represents an empirical observation regarding the time that passes from a moment when any user in the social network initiates a new post until the first of his followers responds to it ($\mu_{u}$ and $\sigma_{u}^2$ are the mean and SD of the latter). This component is unique for each social network, and is given by

\begin{equation*}
    T\Big(\mu_{u}, \sigma_{u}^2, t_{u}^{post}\Big) = \frac{1}{2}erfc\Big(-\frac{ln(t_{u_i}^{post})-\mu_{u}}{\sigma_{u}\sqrt{2}}\Big)
    \label{eqn:temp}
\end{equation*}

The parameter $t_{u_i}^{post}$ represents the time of post's initiation relative to the start of the time window, and $erfc(x) = 1 - \frac{2}{\sqrt{\pi}}\int_{0}^{x} e^{-t^2}dt$, is a complementary Gauss error function.\\
For $ALO$ the following is used in \cite{galuba2010outtweeting}:
    \begin{equation}
       p_u^{ALO}= 1 - \Big(1-\gamma\beta_{u}\Big)\prod_{v:v \rightarrow u}\Big(1-\gamma\alpha_{v,u}p_{u}\Big)
        \label{eq:p_ALO}
    \end{equation}

In both cases, we followed the rule in \cite{galuba2010outtweeting}, where a user is predicted to react if $p_u>0.5$

\subsection{Training the baseline models}
The base-line models were trained similarly to our models, using 90\% of the time intervals for train and 10\% for test.
Table \ref{fig:act_hist} shows the total number of time intervals per dataset.

$RND_{p=0.5}$ and $RND_{p=\pi}$ have no tunable parameters.
The parameters of $ALO$ and $LT$ were set as follows. Optimization was performed with Python's \texttt{Hyperopt} library, with the F1 score as the function to maximize. This library uses the
Tree of Parzen Estimators hyper-parameter optimization algorithm from \cite{bergstra2011algorithms}. The parameter $\gamma$, topic virality, was set to 1, since all tweets come from the same topic. Also the temporal part $T(\cdot)$ was set to 1, since we are not interested in the event that a tweet $t$ is re-shared sometime in the future, but whether user $u$ re-shared some content in a very limited time interval. Due to the computational constrains, the optimization was performed only on the prior vector of the $p_u$'s. The dataset in \cite{galuba2010outtweeting} included 100 URLs for which retweeting was predicted, ours include 10,000 events, and the number of $\alpha_{u,v}$'s is even larger. Therefore, the influence matrix $\alpha_{u,v}$ was supplied from the output of the $TWMN$ model, where the weight of the edge in the NN that connects $v$ and $u$ may be thought of as the influence of $v$ on $u$.

\begin{table*}
    \centering
    \begin{tabular}{l|l|l|l|l}
    \textbf{Model} & \textbf{CPU} & \textbf{RAM} & \textbf{Accelerator} & \textbf{Run Time}\\
    \hline
    $RND_{p=0.5}$ &  $CPU_{low}$ & 32 GB & None & $31.75\pm1.48[s]$\\
    $RND_{p=prop}$ &  $CPU_{low}$ & 32 GB & None & $30.00\pm1.22[s]$\\
    $MLE$ &  $CPU_{low}$ & 32 GB & None & $28.38\pm1.41[s]$\\
    \hline
    $ALO$ &  $CPU_{high}$ & 16 GB & None & $1.45\pm0.38[H]$\\
    $LT$ &  $CPU_{high}$ & 16 GB & None & $1.29\pm0.31[H]$\\
    \hline
    $TWMN_{SHUF}$ &  $CPU_{high}$ & 16 GB & GPU & $1.18\pm0.75[H]$\\
    $TWMN_{all 1}$ &  $CPU_{high}$ & 16 GB & GPU & $54.35\pm22[m]$\\
    $TWMN$ &  $CPU_{high}$ & 16 GB & GPU & $1.12\pm72[H]$\\
    \hline
    $TWPN$ &  $CPU_{high}$ & 16 GB & GPU & $1.29\pm54[H]$\\
    \hline
    $TWCRN_{x18}^{SHUF}$ &  $CPU_{high}$ & 16 GB & GPU & $1.1\pm0.28[H]$\\
    $TWCRN_{x18}$ &  $CPU_{high}$ & 16 GB & GPU & $54\pm11.5[m]$\\
    \hline
    $TWCRN_{x34}^{SHUF}$ & $CPU_{high}$ & 16 GB & GPU & $1.23\pm0.32[H]$\\
    $TWCRN_{x34}$ & $CPU_{high}$ & 16 GB & GPU & $1 \pm 0.23[H]$\\

    \end{tabular}
    \caption{Hardware specs with corresponding mean run times, where $CPU_{low}$ is Intel i7-8550U @ 1.80GHz, $CPU_{high}$ is Intel Xeon @ 2.00GHz and GPU is Tesla P100-PCIE-16GB, [H], [m] and [s] stands for "Hours", "minutes" and "seconds" respectively. }
    \label{tab:hardware_runtimes}
\end{table*}

\begin{landscape}
\begin{table*}
  \centering
  \resizebox{\columnwidth}{!}{\begin{tabular}{|l||*{15}{c|}}
    \hline

    \textbf{Metric} &
    \textbf{P} & \textbf{$F_1$} & \textbf{R} &
    \textbf{P} & \textbf{$F_1$} & \textbf{R} &
    \textbf{P} & \textbf{$F_1$} & \textbf{R} &
    \textbf{P} & \textbf{$F_1$} & \textbf{R} &
    \textbf{P} & \textbf{$F_1$} & \textbf{R} \\
    \hline\hline
    $RND_{p=0.5}$ &
    \mathval{0.19} & \mathval{0.28} & \mathval{0.5} &
    \mathval{0.29} & \mathval{0.34} & \mathval{0.5} &
    \mathval{0.34} & \mathval{0.4} & \mathval{0.5} &
    \mathval{0.17} & \mathval{0.23} & \mathval{0.5} &
    \mathval{0.33} & \mathval{0.4} & \mathval{0.5}\\
    \hline
    $RND_{p=\pi}$ &
    \mathval{0.19} & \mathval{0.21} & \mathval{0.24} &
    \mathval{0.29} & \mathval{0.29} & \mathval{0.34} &
    \mathval{0.34} & \mathval{0.38} & \mathval{0.43} &
    \mathval{0.17} & \mathval{0.18} & \mathval{0.22} &
    \stdcell{0.63}{0.02} & \stdcell{0.64}{0.01} & \stdcell{0.64}{0.01} \\
    \hline
    $MLE$ &
    \mathval{0.42} & \mathval{0.42} & \mathval{0.46} &
    \stdcell{0.31}{0.02} & \stdcell{0.38}{0.02} & $0.56$ &
    \stdcell{0.58}{0.02} & \mathval{0.6} & \mathval{0.68} &
    \mathval{0.22} & \mathval{0.29} & \mathval{0.44} &
    \stdcell{0.63}{0.01} & \stdcell{0.63}{0.01} & \stdcell{0.64}{0.01} \\
    \hline\hline
    $ALO$ &
    \stdcell{0.18}{0.02} & \stdcell{0.26}{0.03} & $0.52$ &
    \stdcell{0.18}{0.06} & \stdcell{0.26}{0.07} & $0.51$ &
    \stdcell{0.31}{0.03} & \stdcell{0.38}{0.04} & $0.53$ &
    \stdcell{0.09}{0.02} & \stdcell{0.15}{0.03} & \stdcell{0.51}{0.02} &
    \mathval{0.4} & \mathval{0.54} & \mathval{0.83}\\
    \hline
    $LT$ &
    \stdcell{0.18}{0.03} & \stdcell{0.26}{0.04} & \mathval{0.52} &
    \stdcell{0.17}{0.04} & \stdcell{0.24}{0.05} & \mathval{0.5} &
    \stdcell{0.31}{0.05} & \stdcell{0.37}{0.06} & \stdcell{0.53}{0.01} &
    \stdcell{0.11}{0.03} & \stdcell{0.17}{0.05} & \stdcell{0.53}{0.01} &
    \mathval{0.17} & \mathval{0.17} & \mathval{0.17} \\
    \hline\hline
    $TWMN_{all 1}$ &
    \mathval{0.49} & \mathval{0.45} & \mathval{0.49} &
    \stdcell{0.31}{0.02} & \stdcell{0.38}{0.01} & \mathval{0.59} &
    \stdcell{0.57}{0.01} & \stdcell{0.57}{0.01} & \mathval{0.66} &
    \mathval{0.21} & \mathval{0.29} & \mathval{0.53} &
    $0.39$ & \stdcell{0.46}{0.02} & \stdcell{0.56}{0.02} \\
    \hline
    $TWMN$ &
    \mathval{0.47} & \mathval{0.48} & \best{0.52} &
    \stdcell{0.32}{0.02} & \stdcell{0.44}{0.02} & \best{0.83} &
    \stdcell{0.6}{0.03} & \stdcell{0.63}{0.03} & \stdcell{0.75}{0.01} &
    \mathval{0.26} & \mathval{0.32} & \mathval{0.46} &
    \mathval{0.64} & \mathval{0.64} & \mathval{0.65} \\
    \hline\hline
    $TWPN$ &
    \mathval{0.51} & \mathval{0.49} & \mathval{0.5} &
    \stdcell{0.33}{0.01} & \stdcell{0.45}{0.01} & $0.8$ &
    \mathval{0.63} & \mathval{0.66} & \best{0.78} &
    \best{0.327} & $0.36$ & $0.45$ &
    \mathval{0.68} & \mathval{0.68} & \mathval{0.68} \\
    \hline\hline
    $TWCRN_{x18}^{SHUF}$ &
    \mathval{0.23} & \mathval{0.2} & \mathval{0.18} &
    \mathval{0.22} & \mathval{0.3} & \stdcell{0.48}{0.02} &
    \mathval{0.41} & \mathval{0.42} & \stdcell{0.43}{0.01} &
    \mathval{0.15} & \mathval{0.19} & \stdcell{0.25}{0.02} &
    \mathval{0.59} & \mathval{0.58} & \mathval{0.58} \\
    \hline
    $TWCRN_{x18}$ &
    \stdcell{0.54}{0.02} & \stdcell{0.51}{0.01} & $0.49$ &
    \best{0.38} & \beststdcell{0.5}{0.02} & \stdcell{0.75}{0.07} &
    \mathval{0.7} & \mathval{0.73} & \mathval{0.77} &
    \stdcell{0.32}{0.02} & \beststdcell{0.42}{0.02} & \beststdcell{0.62}{0.02} &
    \mathval{0.837} & \best{0.836} & \best{0.835} \\
    \hline\hline
    $TWCRN_{x34}^{SHUF}$ &
    \mathval{0.23} & \mathval{0.2} & \mathval{0.18} &
    \mathval{0.21} & \stdcell{0.28}{0.02} & \stdcell{0.45}{0.03} &
    \mathval{0.41} & \mathval{0.42} & \mathval{0.44} &
    \mathval{0.15} & \mathval{0.19} & \stdcell{0.25}{0.02} &
    \stdcell{0.59}{0.01} & \stdcell{0.58}{0.01} & \stdcell{0.58}{0.01} \\
    \hline
    $TWCRN_{x34}$ &
    \beststdcell{0.55}{0.01} & \best{0.52} & \stdcell{0.49}{0.01} &
    \mathval{0.36} & \stdcell{0.49}{0.01} & \stdcell{0.79}{0.03} &
    \best{0.71} & \best{0.74} & \stdcell{0.777}{0.01} &
    \stdcell{0.32}{0.02} & \stdcell{0.419}{0.01} & \stdcell{0.61}{0.04} &
    \beststdcell{0.838}{0.01} & \stdcell{0.835}{0.01} & \stdcell{0.832}{0.02} \\
    \hline\hline
  \end{tabular}}
  \label{tab:mt_graph_res}
  \caption{Summary of a 5-fold validation results on the test set for the datasets acquired through the mention graph technique, i.e., each cell is the average of five train-test executions ((most of the mean values were rounded up to the second decimal point, unless a higher precision was needed to decide on the best value, and standard deviations smaller then $0.01$ are omitted). The best values for each metric are represented by the \textcolor{green}{green} color.}
\end{table*}
\end{landscape}

\begin{landscape}
\begin{table*}
  \centering
  \resizebox{\columnwidth}{!}{\begin{tabular}{|l||*{15}{c|}}
    \hline
    \backslashbox{\textbf{Model}}{\textbf{Data Set}} & \multicolumn{3}{c|}{\textbf{Volcano}} &
    \multicolumn{3}{c|}{\textbf{Kobe}} &
    \multicolumn{3}{c|}{\textbf{Princess}} &
    \multicolumn{3}{c|}{\textbf{Beirut}} &
    \multicolumn{3}{c|}{\textbf{Unfiltered}} \\
    \hline
    \textbf{Metric} &
    \textbf{P} & \textbf{$F_1$} & \textbf{R} &
    \textbf{P} & \textbf{$F_1$} & \textbf{R} &
    \textbf{P} & \textbf{$F_1$} & \textbf{R} &
    \textbf{P} & \textbf{$F_1$} & \textbf{R} &
    \textbf{P} & \textbf{$F_1$} & \textbf{R} \\
    \hline\hline
    $RND_{p=0.5}$ &
    \mathval{0.1} & \mathval{0.16} & \mathval{0.5} &
    \mathval{0.1} & \mathval{0.17} & \mathval{0.5} &
    \mathval{0.11} & \mathval{0.18} & \mathval{0.5} &
    \mathval{0.09} & \mathval{0.15} & \mathval{0.5} &
    \mathval{0.31} & \mathval{0.39} & \mathval{0.5} \\
    \hline
    $RND_{p=\pi}$ &
    \mathval{0.1} & \mathval{0.1} & \mathval{0.1} &
    \mathval{0.1} & \mathval{0.1} & \mathval{0.11} &
    \mathval{0.11} & \mathval{0.12} & \mathval{0.12} &
    \mathval{0.09} & \mathval{0.09} & \mathval{0.1} &
    \mathval{0.32} & \mathval{0.4} & \mathval{0.55} \\
    \hline
    $MLE$ &
    \mathval{0.8} & \mathval{0.81} & \mathval{0.86} &
    \stdcell{0.73}{0.03} & \stdcell{0.78}{0.02} & \mathval{0.88} &
    \mathval{0.88} & \mathval{0.89} & \mathval{0.97} &
    \stdcell{0.59}{0.01} & \mathval{0.65} & \mathval{0.79} &
    \mathval{0.63} & \mathval{0.64} & \mathval{0.64}\\ \hline\hline
    $ALO$ &
    \mathval{0.09} & \stdcell{0.16}{0.01} & \mathval{0.51} &
    \mathval{0.08} & \stdcell{0.14}{0.03} & \stdcell{0.5}{0.01} &
    \stdcell{0.11}{0.1} & \stdcell{0.18}{0.02} & \stdcell{0.53}{0.02} &
    \stdcell{0.07}{0.01} & \stdcell{0.12}{0.02} & \stdcell{0.54}{0.01} &
    \mathval{0.32} & \mathval{0.47} & \mathval{0.87} \\
    \hline
    $LT$ &
    \stdcell{0.1}{0.01} & \stdcell{0.17}{0.02} & \mathval{0.56} &
    \stdcell{0.09}{0.02} & \stdcell{0.15}{0.03} & \mathval{0.56} &
    \stdcell{0.12}{0.01} & \stdcell{0.19}{0.02} & \mathval{0.55} &
    \stdcell{0.07}{0.01} & \stdcell{0.12}{0.02} & \stdcell{0.56}{0.01} &
    \mathval{0.31} & \mathval{0.2} & \mathval{0.15} \\
    \hline\hline
    $TWMN_{all 1}$ &
    \mathval{0.81} & \mathval{0.81} & \mathval{0.85} &
    \stdcell{0.74}{0.02} & \stdcell{0.8}{0.01} & \mathval{0.93} &
    \mathval{0.86} & \mathval{0.86} & \mathval{0.97} &
    \stdcell{0.6}{0.02} & \stdcell{0.66}{0.17} & \mathval{0.79} &
    \stdcell{0.37}{0.03} & \stdcell{0.44}{0.02} & \stdcell{0.55}{0.01} \\
    \hline
    $TWMN$ &
    \mathval{0.8} & \mathval{0.86} & \mathval{0.97} &
    \stdcell{0.74}{0.02} & \stdcell{0.83}{0.02} & \best{0.997} &
    \mathval{0.86} & \mathval{0.87} & \mathval{0.99} &
    \mathval{0.56} & \mathval{0.69} & \mathval{0.96} &
    \mathval{0.47} & \mathval{0.54} & \mathval{0.62} \\
    \hline\hline
    $TWPN$ &
    \mathval{0.8} & \mathval{0.86} & \mathval{0.97} &
    \stdcell{0.73}{0.03} & \stdcell{0.82}{0.02} & \mathval{0.98} &
    \mathval{0.86} & \mathval{0.87} & \mathval{0.99} &
    \stdcell{0.58}{0.02} &  \stdcell{0.71}{0.02} & \mathval{0.96} &
    \mathval{0.69} & \mathval{0.68} & \mathval{0.68} \\
    \hline\hline
    $TWCRN_{x18}^{SHUF}$ &
    \mathval{0.09} & \mathval{0.01} & \mathval{0.1} &
    \mathval{0.09} & \stdcell{0.1}{0.01} & \stdcell{0.12}{0.01} &
    \mathval{0.1} & \mathval{0.1} & \mathval{0.1} &
    \mathval{0.08} & \stdcell{0.09}{0.01} &  \stdcell{0.12}{0.01} &
    \mathval{0.56} & \stdcell{0.55}{0.01} & \mathval{0.55} \\
    \hline
    $TWCRN_{x18}$ &
    \best{0.892} & \mathval{0.927} & \mathval{0.966} &
    \best{0.785} & \best{0.877} & \mathval{0.995} &
    \best{0.975} & \mathval{0.9832} & \mathval{0.992} & \beststdcell{0.71}{0.01} &
    \best{0.82} & \mathval{0.97} & \best{0.842} & \best{0.83} & \best{0.82} \\
    \hline\hline
    $TWCRN_{x34}^{SHUF}$ &
    \mathval{0.11} & \mathval{0.11} & \mathval{0.12} &
    \mathval{0.1} & \mathval{0.11} & \mathval{0.12} &
    \mathval{0.11} & \mathval{0.11} & \mathval{0.11} &
    \mathval{0.1} & \stdcell{0.1}{0.01} & \stdcell{0.12}{0.01} &
    \mathval{0.56} & \mathval{0.56} & \mathval{0.551} \\
    \hline
    $TWCRN_{x34}$ &
    \mathval{0.891} & \best{0.929} & \best{0.97} &
    \mathval{0.78} & \mathval{0.876} & \mathval{0.996} &
    \mathval{0.974} & \best{0.9833} & \best{0.993} &
    \stdcell{0.68}{0.02} & \stdcell{0.8}{0.01} & \beststdcell{0.977}{0.01} &
    \mathval{0.84} & \mathval{0.827} & \stdcell{0.81}{0.01} \\
    \hline\hline
  \end{tabular}}
  \label{tab:crwl_graph_res}
  \caption{Summary of results on the test set for the datasets acquired through the follower graph technique, i.e., each cell is the average of five train-test executions (most of the mean values were rounded up to the second decimal point, unless a higher precision was needed to decide on the best value, and standard deviations smaller then $0.01$ are omitted). The best values for each metric are represented by the \textcolor{green}{green} color.}
\end{table*}
\end{landscape}

\subsection{Results}
We turn to describe the results of evaluating both the algorithms described in Section \ref{methodology} and the baseline algorithms, Section \ref{sec:baseline}, on the data that we collected, Section \ref{data}.

Our raw dataset spans the mention graph. Namely, the social links are derived from users re-sharing posts of other users. We further removed low-activity users from the dataset, remaining with roughly $10^4$ users as described in Table \ref{tab:data_broadcastisity}. In our experiments, we ran the algorithms also on the followers graph dataset, which we obtained from the mention graph dataset by removing users which no one follows or they follow no one, by querying Twitter's API.

\vspace{1mm}

To assess the impact of using the adjacency matrix $A$ on the performance of $TWMN$ we trained a second variant, $TWMN_{all-1}$, in which the masking is removed, namely the NN becomes fully connected (the same as replacing $A$ with the all one matrix).

The convolutional network $TWCRN$ does not receive explicitly the social links. To understand whether it implicitly learns them or not, we performed the following permutation test, which resulted in a model we call $TWCRN_{SHUF}$. At train time, the input vectors $\tau_i$ that are fed into the model are randomly shuffled, anew for every $i$, while the labels of the result vectors $\tau_{i+1}$ were kept without change.

Table \ref{tab:hardware_runtimes} describes the hardware and the running time it took to train each model. The Table \ref{tab:crwl_graph_res} describes the results for the mention graph dataset, while the Table \ref{tab:mt_graph_res}: describes the results for the followers graph dataset. Since the training of the algorithms contains random choices, we repeated each execution five times. The standard deviations in both tables are over these five executions.

Note that our dataset is imbalanced. There are more zeros than ones in each $\tau_i$. The average density of $\tau_i$ is given by the  precision of the $RND_{p=0.5}$ algorithm.

\vspace{1mm}

We summarize our main findings that we read from Tables Table \ref{tab:mt_graph_res} and \ref{tab:crwl_graph_res}:

\begin{itemize}
    \item Our first observation is that the results obtained from the followers graph dataset are significantly better for all four datasets, with F1 score nearly twice as good in three out of the four (for the leading method). This means that the signal embedded in the followers graph is stronger than the one embedded in the mention graph. Trying to understand why, we ran Botometer \cite{botOrNot} on the users that were removed from the mention graph, and found that their bot score was on average much lower than the remaining users (e.g. for the Princess dataset, the score was 0.97 vs 1.62, out of 5).

    \item The best results, across all datasets, were achieved by $TWCRN$ (both for the follower graph and the mention graph) with an average F1 score of 0.86. This NN does not take into account the social links, at least not explicitly (perhaps the NN learns them implicitly). This network is also completely agnostic to epidemiological models. A clue to that $TWCRN$ learns the network structure in some implicit way lies in the fact that $TWCRN_{SHUF}$ fails miserably in all datasets.
    As we've mentioned in the introduction, many works have pointed out that information spreads  differently in social networks than epidemics spread in the population. Thus, it may be that  $TWCRN$ is able to learn this more complicated model of infection, which eludes simple human intuition.

    \item Having said that, we see that the simple $MLE$ algorithm performs surprisingly well on all datasets, achieving an average F1 score of 0.78 on the followers graph dataset. The $MLE$ follows a very simple intuition - it learns the user's ``trends", whether the user takes a break between tweets, or is a chain-twitter. Note that the $MLE$ algorithm completely ignores the social links.

    \item $TWMN$ is the only of our algorithms that takes into account the social links. Indeed it outperforms $MLE$, with an average F1 score of 0.81, but its performance is just slightly better than $TWMN_{all-1}$ (at an average F1 score of 0.8), where again the social links are not explicitly served. Hence we may conclude that the NN is able to learn by itself the important social links, and does not need it as an explicit input.

    \item $TWPN$ performs better than the MLE, and the same as $TWMN$, at an average F1 score of 0.81. The intuition behind $TWPN$ is similar to  $MLE$, with the difference that $TWPN$ is basically learning a logistic regression per user rather than estimating the probabilities by averaging (although the tanh function is used and not the logit).

    \item The two baseline models $ALO$ and $LT$ perform poorly, slightly improving over the random guess. There are several ways to explain these poor results. This may be attributed to the way we have constructed the classification task, which may not be suitable for such models.
    Another possibility is that the influence weights $\alpha_{u,v}$ that are used in Eq.~\eqref{eq:p_ALO} and \eqref{eq:p_LT}, which we derived from the weights of $TWPN$, were not a good choice.
\end{itemize}

\section{Discussion}
In this work we checked two premises, the first is whether one can develop a prediction model which is completely agnostic to the motivation of information cascades as viewed from an epidemiological standpoint. If yes, then how much does the social link structure is a vital input to that prediction algorithm, or, can it be learned implicitly. We answered both questions positively, showing that a high F1 score is obtainable with a neural network that does not receive the social link structure explicitly, but does make use of it (as the random shuffle test shows). We also show that a slightly lower F1 score can be obtained by two simple algorithms, $MLE$ and $TWPN$, that completely ignore the social links. The role of the social links in predicting user activity should be further studied in future work, in other OSNs, and in other settings.

If we take out the Beirut dataset, which was our smallest dataset, then we discover that the ranking of F1 scores is inverse to the ranking of broadcasticity score, Princess is leading with highest F1 score and lowest broadcasticity, and Kobe vice-a-versa.

We found that the results are significantly better in followers graph dataset, obtained by removing users that interact only with users that are not in their followers or friends list. Our first guess that these users are bots turned out false, and we leave this point as well for future work.

Finally, let us discuss the limitations of our approach. Our prediction was done for datasets that were collected around a single topic. We have not checked how well this method performs for a database that is not topic oriented. Our prediction task is time-constrained, namely, the input to the prediction algorithm is the activity in the last 12h, and prediction is made for the following 12h. While we played with these time slices and note a minor effect on the results, we did not try other configurations such as training for a week and predicting for the next day. We did not evaluate our models on platforms other than Twitter. Nevertheless, we expect them to generalize well on any platform which provides the same mechanisms for communication and social interaction since we did not use any domain-specific features such as linguistic features or other meta-data features.

\printbibliography

redpajama_set_name: RedPajamaArXiv


The dedication in Ann Miller's new book, "Hatch Guide for Upper Midwest Streams," is not unusual in its expressed gratitude to her husband, Ken Ankli, and their three daughters: Aura, Abbey and Aiden.
Authors often thank those close to them for putting up with their shenanigans during the time it took to write the book.
What's unusual, though, is Miller thanking them "for lovingly putting up with escaped bugs in the house." That, and her expressed appreciation for them coping with her 3½-year obsession, which led to constructing small, running streams in the garage so she could observe and photograph the life stages of the insects she was writing about.
"My project started off largely in the garage, but I had a photo studio in the house, and the darn things kept flying away," said Miller, an aquatic biologist by training and an avid fly angler. "I had them in a sealed-up room, but when a size-18 sulphur (a tiny, yellow fly) gets away, they are pretty hard to find.
Miller, of Stevensville, is the president of the Fly Girls of Michigan Inc., a Federation of Fly Fishers chapter dedicated to introducing women to the pleasures of fly fishing. She began fly fishing 25 years ago. It's common to find her on a stream somewhere, fly rod in hand, challenged to solve the puzzle of what big trout or steelhead are eating.
Miller hopes her book will help others solve the puzzle, too.
"If you can solve the puzzle, you can catch more fish," Miller said. "People assume that all the bugs are in all rivers. They are not, just as there are not grouse or ducks in every woods or marsh.
Miller said her research blew away a widely held belief that gray drakes, the big flies that emerge between May and July, live in gravelly, fast water.
Miller's book, published by Frank Amato Publications in Portland, Ore., is a handy and well-crafted piece, small enough to fit in a boat bag, but rich in detailed information and loaded with 120 terrific color close-ups of the flies typically eaten by upper Midwest trout and the artificial flies that imitate them.
Miller's prose is terse and informative. She explains where each insect lives, how it behaves and when and how to fish the corresponding fly. Fly tiers will appreciate the tying recipes she provides, while anglers should be aided by a handy emergence chart in the back that suggests when to look for the bug.
"Insects are the heart of fly fishing," Miller said. "I know there are people who throw streamers (flies that imitate small fish) and you can catch really big trout that way. We know that brown trout cruise and eat smaller trout at night, but that doesn't mean they don't eat big mayflies. They do — along with crayfish and mice.
"But if you look at the history of fly fishing going back to England, that was a time when you could only fish with dry flies and fish only upstream. Fishing a fish underwater was considered bait.
Look for Miller's book at local Midwest fly shops, on Amazon.com or write her at annrmiller@aol.com.
To find Miller, check the nearest trout steam with a hatch.
This entry was posted in Uncategorized and tagged Ann Miller, Artificial Fly, Field Guide, Fly Fishing, Fly Hatches, Trout. Bookmark the permalink.


Today, the Pigeon Mafia had a special visitor. A Collared Dove joined them on the ground as they were tucking into some seed. I have no idea where it came from, but it seemed quite at home with the flock of Ferals. I thought that was rather unusual, but since I don't see many CD's, I might be wrong.
Hopefully this was the first of many visits and maybe there will be a pair next time?
Nice to see another successful release.
The CDs I get in the garden (only 2 or 3 and only as occasional visitors) are content to eat in the company of ferals and woodpigeons but I wouldn't say they really socialise with them.
The CD that visited the garden was not Charlene. She went to the rescue centre in Wallington. This was a random passer-by.
We have quite a few CD's around us but I've never seen them around the pigeons before. I hope it finds a mate for you.
Nice for you got get the CD as a visitor Paul. This year we have around 10 that come about. They are very nice looking birds.
That is one brave C Dove MC. Usually I find they keep their distance from the Ferals who are that much bigger. Hope you get to see more in your garden as they are smashing birds.


Play Noun with a group of your favorite people!
- If they figure it out within one minute, then team 1 gets a point. Otherwise, no points are awarded.
Each Noun word pack has 100 words in it. The first pack is free, so give it a try!


Thank you for your interest in Dosko. We look forward to serving you!
You will be notified when the account has been created.
GNE is excited to partner with your company in the near future.
Weight 330 lbs. 2,310 lbs. 2,880 lbs.
Flywheel 3/4" Thick x 16" Dia. 3/4" Thick x 22" Dia.
Weight 390 lbs. 930 lbs.
Chipper Hopper Size 14" x 14" x 24" Deep 18" x 22"
Chipper Feed Opening 3" x 3" 4" x 5"
Mulcher Hopper Size 20" x 20" 20" x 20"
Mulcher Feed Opening 8" x 8" 8" x 8"
Log Capacity 25" L x 16" Dia. 25" L x 16" Dia.
Cylinder 25" L x 4" Dia. 24" L x 5" Dia.
Weight 607 lbs. 725 lbs.


text:
Q: Choosing best security option for WCF We have a project that contains a WCF Service and a few clients that connect to it. Some of them are PCs using NetTcp to connect to the service. Few others run on Windows Mobile Devices(Compact Framework), using BasicHttp to connect.
We can't use Windows Authentication, because different PCs use different Windows accounts.
How can we secure the service to only allow valid PCs and Mobile devices to use it and deny other devices?

A: I believe the best security you could enable would be SSL over HTTP and a standard authentication scheme via a username and password.  For a really great inclusive review of the various security aspects of WCF check out the Codeplex site:  http://www.codeplex.com/WCFSecurity
Specifically this page:  http://www.codeplex.com/WCFSecurityGuide

redpajama_set_name: RedPajamaStackExchange


The idea began in the summer of 1974. Because of the increasing demand for electricity and limited availability of wholesale power, the Board of Municipal Utilities directed its immediate attention toward long range power supply planning. The results of engineering and economic studies undertaken by Phelps, Hogland and Phillips Engineering Company indicated that construction of a coal-fired steam-electric station of a size sufficient to meet the Board's projected long-term electric requirements would result in the lowest cost power supply, providing that surplus power could be sold until full utilization was needed.
On September 21, 1977 the City of Sikeston authorized Phelps, Hogland and Phillips to proceed on final engineering for the project. The idea had become a reality. The Sikeston Power Station Project was a one-unit, 235 megawatt coal-fired steam electric generating station located approximately one mile west of the center of Sikeston on a 622 acre site. Phelps, Hogland and Phillips was the Project Manager and Burns & McDonnell Engineering performed the duties of design engineering, preparation of plans and specifications, contract analysis and evaluation and other related services. The total principal amount of bonds that were sold was $240,000,000.00. The first issue was closed in March, 1978 for $90,000,000.00 and the second issue for $150,000,000.00 was closed in February, 1979. Groundbreaking for the project took place on March 25, 1978. Initial energy was produced on June 30, 1981 and commercial operation was achieved on August 27, 1981.
Power generated by the Station's steam turbine flows to a nearby substation owned by the Southwest Power administration. From there it flows into the main power grid that serves the entire Midwest. Sikeston 's power needs are also met by one of the circuits from the SWPA substation and through five BMU substations around the city. The power needs of the City of Sikeston account for roughly one-third of the generating capacity of the 235 megawatt Sikeston Power Station.


Tripod censer with peonies, Kangxi yuzhi (1662-1722), on show at the Royal Academy in November, above, and below, pair of paper screens, Kano School, 18th century, at Gregg Baker Oriental Ar t So much hot air has reverberated around the rise of the Asian art market in New York in recent years that even collec- tors might be forgiven for presuming that London has had its day. Moreover, it looked as though the huge London-based Asian art trade was ceding the city's tradi- tional pre-eminence without so much as a whimper.
It all began with the auction houses. Ever since Sotheby's Julian Thompson first pio- neered Western-style auctions in Hong Kong in the early Seventies, it seems that both Sotheby's and Christie's chose to Carved ceiling panel wood and polychrome, Gujarat, 17th century, at Maharukh Desai develop first the Far Eastern and then the New York market at the expense of Lon- don. Then, three years ago, the hugely suc- cessful International Asian Art Fair was launched alongside Asia Week in the New York salerooms, and London provided almost half the exhibitors. Even Giuseppe Eskenazi, one of the world's most respect- ed Oriental art dealers, anglophile and champion of the London market, appeared to turn renegade. For the last two years he has staged spectacular exhibitions in a rent- ed space on the Upper East Side, dismayed by the lack of opposition to proposed fur- ther harmonisation of taxes within the EU, taxes which threaten the very existence of an important art market anywhere in the Union.
Behind the scenes, though, the Asian art trade in London began to rally. It was felt by Eskenazi and others that what happened to London would depend on them. Next month, they orchestrate what the dealer Michael Goedhuis describes as a tough rearguard action. Over 40 of the city's lead- ing dealers join forces with the four big auction houses, leading museums and the wider academic community to stage 'Asian Art in London' (10-21 November). This impressive series of museum and dealer exhibitions, auctions, seminars, lectures, recitals and receptions is intended to remind the world of the unrivalled exper- tise, and range and depth of material on offer, both on the market and in London's exceptional museum collections, some cele- brated, others little known. There will be enough going on in London to tempt even the busiest of enthusiasts or collectors.
Expertise, as this initiative recognises, is the heart and life-blood of a sound art mar- ket. In Britain, it has evolved around some of the greatest institutional collections in the West, collections enriched by genera- tions of connoisseurs, and out of London's long-held position as the clearing house of world art. Both traditions continue to flourish in London as nowhere else in Europe. New York, in contrast, offers a wealth of Asian art collectors but relatively few scholars, a handful of world-class Asian art dealers and just two intense, glamorous weeks of commercial activity a year.
Jingoistic though it sounds, no other cap- ital in the world could lay on such a feast as this. At dealers Speelman, for instance, is a show of Buddhist Sculpture and Works of Art; at Sydney Moss, Japanese Paintings of the Edo Period. John Eskenazi presents Gandhara Art from the lst-4th Century. The Textile Gallery is showing at Colnaghi Tex- tile Art from the Silk Road, 200 BC to AD 1600. Spink offers a collection of Chinese blue and white; Sam Fogg examples of manuscripts and printing; Danart, gold jew- ellery from South East Asia. And so it goes on, with each of the participating dealers presenting a show (for a guidebook with details of all events, telephone 0171-293 6444).
It was the organisers' aim to encourage people into the galleries rather than bring the dealers under a single roof, and in order to facilitate gallery-hopping, three late-night openings have been arranged in London's main Asian art-dealing neigh- bourhoods. On the 16th, it is Mayfair, on the 17th, St James's. The following day, the spotlight moves to Kensington Church Street and environs. Don't miss, too, the inaugural show of Chinese Ming and Qing period furniture at Hong Kong dealer Grace Wu Bruce's new Mayfair gallery (12A Balfour Mews), perhaps the biggest recent vote of confidence in the London art market.
The auction houses are playing their part, as sponsors of exhibitions, seminars and lec- tures, and as salerooms fielding strong sales. Christie's ices the cake of its regular November auctions with its first-ever sale devoted to the art of the Ming Dynasty, plus 'Asian Art for the Country House', and a private American collection of Japanese kakiemon porcelain. It sponsors China- Mania at Kensington Palace State Apart- ments, a reconstruction of William and Mary's famed porcelain gallery. Sotheby's Institute is host to a three-day symposium on the export of Chinese porcelain around the world, with contributions from distin- guished international experts.
The centrepiece of the proceedings, how- ever, is a loan exhibition at the Royal Academy of arguably the finest collection of Chinese Imperial ceramics in private hands (reputably finer than many a public collection, too). Never before exhibited or published, the Au Bak Ling Collection, formed by a self-educated Hong Kong edu- cational publisher, is a coup for the organ- isers, spanning 600 years or so of production but concentrating on the glorious porcelains made for the Ming and Qing emperors. It comes under the auspices of Asia House, a body aiming to forge closer cultural and business links between Britain and Asia.
Lovers of Chinese porcelain will also have an opportunity to enjoy the world- class collections of London University's Percival David Foundation. It presents Rare Marks on Chinese Porcelain, and a two-day seminar examining its holdings. The Percival David deserves a wider repu- tation, so too does the university's relative- ly new Brunei Gallery at SOAS. Its current temporary show is Treasures from Kuwait: the Al Sabah Collection of Islamic Art.
If anyone is left on their feet by the 20th, they can dip into their pockets for the high- profile black-tie gala dinner promised at the V&A (Queen Noor of Jordan as guest of honour, David Tang the after-dinner speaker), in aid of Great Ormond Street Hospital's Centre for International Child Health. Part of the point of the event is to remind collectors that London is a safe, civilised and genial place to be.


text:
Q: Clone Ubuntu on USB to a larger USB stick? I have an old, unbranded 2GB USB with 10.10 that is running a Samba server connected to a RAID array (basically a makeshift NAS.) As most people do, I started running out of space with the various servers and packages I needed to install over the years. I purchased a 16GB USB drive (one of those SanDisk micro ones) to upgrade it, but I'm not sure how I should go about cloning the old 2GB disk to the new 16GB. I am doing this from my MacBook Pro. For reference, my diskutil list is...
/dev/disk0 (MacBook Pro)
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *500.1 GB   disk0
   1:                        EFI                         209.7 MB   disk0s1
   2:                  Apple_HFS Mac OS X                499.2 GB   disk0s2
   3:                 Apple_Boot Recovery HD             650.0 MB   disk0s3
/dev/disk1 (upgrade USB)
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:     FDisk_partition_scheme                        *16.0 GB    disk1
   1:             Windows_FAT_32 NO NAME                 16.0 GB    disk1s1
/dev/disk2 (old USB)
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:     FDisk_partition_scheme                        *2.1 GB     disk2
   1:                      Linux                         254.8 MB   disk2s1
   2:                  Linux_LVM                         1.9 GB     disk2s5

Using this answer as well as the Ubuntu USB instructions for OS X, my initial thought was to...

*

*Unmount both disks.

*dd if=/dev/disk2 of=/dev/disk1

*Repartition the 16GB to utilize the entire disk.

However, it feels like it just shouldn't be that easy, and I'm worried I might mess something up on the upgrade USB. Is this the correct course of action, or am I missing something important?
Thanks!

A: the dd command sounds right for the job.
In any case even if it doesn't work for some reason it won't mess up anything on your old usb stick since it is just reading from it and writing to the other one.
However to speed things up I'd advise you to use the bs flag and set it to 512k so your command should look like
dd if=/dev/disk2 of=/dev/disk1 bs=512k

this sets the read/write blocksize to 512kb instead of the default 512 bytes


What if Dark Angel was to return, but not the entire cast could return. Whom should take whose place?
I thought of my cast for all of 5 seconds, so the list's a bit half assed.
Because her face is somewhat similar to Jessica, and she's also a tomboy, like Max.
Looks a bit similar to Michael Weatherly. His accent would be a bit of a problem, but I bet he could learn.
Dunno, I just think that he could make a good Lydecker.
A wise old scientist with a stick it to the man attitude? Is anyone else even remotely suitable?
Do you know an actor that could replace someone from the current cast, and maybe even suite the role better than one of the current actors, then post it here.
interesting, but no... to british and like i don't know how to explain it, not to neerdy.
sean bean, and denis hopper look to old for their role.... . at the limit, sean bean for lydecker... .
for max, i can't imagine somebody else that JA, and for another characters too... . I think it must be the same actors, and it's difficult for me to play the game, imagining somebody else to their roles... .
clean the guy up?? you mean to shave him ?
nicer? lydecker doesn't need to look very nice, no ?
yes, original cast members are essential but thats the problem with another tv series, many actors have went to movies so going back to tv will be a step down for them so thats why we need to aim for a movie. That way we'll have a bigger budget and for some of the actors its a step up!!
Feels like we've lost focus on the topic.
This is about which actors we'd like to see replacing whom. Not whether it's likely we'll see a new season or whom caused the show to get shot down.


text:
Archive for army
ALOHA FROM HELL By Richard Kadrey – Reviewed
Posted in Reviews, Uncategorized with tags action, aloha from hell, anti-hero, army, assassin, betrayal, book, book three, books, brutal, building an army, capture the imagination, characters, Clive Barker, creates, crime, darkly brilliant, death, demented genius, demon fighter, demon killer, destroy earth, destroy heaven, destroy hell, drama, drips reality, entertaining, entertainment, epic, excitement, exciting, faith, fantasy, fiction, Fighting, god, gods, great adventures, heaven, hell, hellions, hero, horror, horror novel, joe lansdale, kadrey, LA, la underworld, lies, literature, los angeles, lucifer, magazine, magic, magician, monster fighter, monster hunter, morpheus tales, murder, Neil Gaiman, nemesis, novel, novels, pages, plot, plots, private detective, read, reading, reality, religion, review, reviewed, reviewer, reviews, richard kadrey, sandman slim, sandman slim series, series, slim, Stephen King, story, sub-rosa, third book, thriller, world, write, writer, writers, writing, you must read on September 6, 2013 by stanleyriiks
I hate Richard Kadrey. I hate his books. I hate Sandman Slim, one of the greatest anti-heroes to ever be captured on the page.
Kadrey writes books I wish I'd written. He had created a world and characters that I can only dream of creating. He has plots that make me want to read the whole book in one sitting because I want to find out what happens so bad. But also I want to read slowly, to savour every sentence, and respect every line because there is such a wit and darkness in these pages.
This is the third book in the amazing Sandman Slim series, featuring Slim who is a magician returned from hell after turning monster fighter and demon killer. He lives in an LA underworld ruled by Sub Rosa (old magical) families and factions. And finds himself involved as a bodyguard to Lucifer, a private-detective and monster hunter. Slim is my hero. The dude rocks my world, and I wish, I so wish, that he was mine. We would have such great adventure together. But what am I saying? We do have such great adventures together, but that bugger Kadrey creates them! I don't want to share, I want Slim all to myself.
The third book in the series see Slim having to head down to Hell as his nemesis is having success building an army of hellions and plans to head up to Heaven to destroy it, and then destroy the rest of the world. Of course, there's excommunicated priests, demons and gods, magic, fighting, betrayal, lies, and all manner of excitement to get in the way of things moving along smoothly.
Slim narrates with a unique voice that entertains with a brisk pace and style that you will find hard to match. The closest comparable voice stylistically would be Joe Lansdale's East Texas drawl. But Kadrey goes further, where most are afraid to go. He seems unafraid to deal with difficult and controversial issues such as religion and faith, all the while having a wicked sense of humour, and one hellish, fetid darkness that sucks the reader in.
Like the very best fantasists, Clive Barker and Neil Gaiman at the top of their game, Kadrey creates a magnificent world that drips reality, characters that ooze personality, and plots that truly capture the imagination.
The third book in the series continues on the success of the previous two books. You must read the Sandman Slim novels. You MUST read one of them.
I hate Richard Kadrey, I want to be Richard Kadrey. I love Sandman Slim. I look forward to most adventures together.
Darkly brilliant.
Demented genius.
CONTROL POINT By Myke Cole – Reviewed
Posted in Reviews with tags action, action-packed, army, army officer, biloxi blues, bioloxi blues, book, books, brutal, buried, characters, coming of age, contractor, control point, control power, crime, dangerous, dead, death, entertaining, epic, excitement, exciting, fantasy, fiction, fire demons, goblin, goblin-like, half killed, harry potter, hell of a time, horror, horror novel, juxtaposed, killed, latent, latent episode, law, little fantasy, magazine, magic, magical powers, magically powers, manipulation, military, military story, morpheus tales, murder, myke cole, new power, newness, novel, novels, oscar britton, pages, plot, prohibited, read, reading, review, reviewed, reviewer, reviews, science fiction, SF, shot, sorcerer, speed, Stephen King, story, stripes, teenagers, thriller, too dangerous, tough challenges, weapons, write, writer, writers, writing on April 10, 2013 by stanleyriiks
Oscar Britton is an army officer, and when he and his team are called to deal with a prohibited latent, they have a hell of a time. A latent is a person who develops magical powers. Certain magical powers are prohibited as too dangerous. One of Britton's men is half killed by fire demons, and two teenage latents are shot dead, a school is burned, and Oscar has an argument with a sorcerer.
A few hours later Oscar has a latent episode, finding himself on the other side of the law. Knowing he has a prohibited magical power (opening wormhole-like gates) he goes on the run.
What follows is actually even more exciting and action packed than the beginning. As Oscar is "recruited" as a contractor for the army, and must face the tough challenges of learning to control his power on the front-line of a war with goblin-like creatures.
This doesn't really have a slew of original ideas, but it's put together very well, creating that newness and excitement. The military and magic are juxtaposed, and Oscar and his team work together to discover their powers and use them for good, despite the military's view of them as weapons.
The book is a cross between Harry Potter and Stripes, or Biloxi Blues. The unique mix of military and magic makes this book. There is a little too much concentration on Oscar's struggle to deal with his new power and his manipulation by the military, but that serves its own purpose and works within the context of the story. A kind of coming-of-age tale, using all the best bits of a military story, but a little fantasy thrown in for good measure. You can't help but love little Marty, the goblin. There is plenty of action to speed things along.
Intelligent, exciting, pulse-racing and action packed. Full-on magical military mayhem.
FLU By Wayne Simmons – Reviewed
Posted in Uncategorized with tags action, army, balfast, book, books, brian keene, brutal, characters, civilian, crown prince, dangerous, dead world, dead-fucks, demons, disease, disgusting, edge, efficient, fantasy, fever, fiction, flu, guilt, heroes, horror, horror novel, humans, issues, non-dead, novels, personal demons, police, polish, post-apocalyptic, read, reading, rehash, remero, review, reviewed, reviewer, simmons, smooth, stephen jones, the walking dead, thriller, tough sell, trilogy, troubles, uk, wayne simmons, writer, writing, writing style, xombie king, zombie, ZOMBIE APOCALYPSE, zombie novel, zombit fiction with an edge on April 4, 2011 by stanleyriiks
A few years ago zombie novels were like gold-dust. Now they're ten a penny. Most are bog standard zombie rehashes, offering nothing new. The king of zombie fiction is Brian Keene, whose zombie novels create a sense of undeniable dread and looming, unstoppable danger. So the question is, does Simmons have anything to offer, and can be usurp the king?
Sadly the answer is both yes and no.
Flu is a post-apocalyptic zombie novel, focusing on the further spread of the disease which kills and then brings you back, and the few survivors in Belfast as they try to stay alive as long as possible, seeking out supplies, grouping together with other non-dead humans, and having to deal with the dead-fucks. The story uses sectarian issues and guilt, police, army and civilian survivors in a nice mix, which gives the book its edge.
This isn't The Walking Dead rehashed in Belfast. Although there are clear homages to Romero's trilogy and other zombie movies.
The story has some brutal and some disgusting moments, which help take it beyond the average, but what really put this book ahead of most of the rest is Simmons easy and efficient writing style (polished to within an inch of its life), and his characters, all of which suffer their own personal demons they have to battle along with the zombies. The humans really are the heroes of this novel, a tough sell, but one that works in this case.
The UK is bereft of zombie novels, the only decent one I can remember is the composite novel created by Stephen Jones and loads of others, Zombie Apocalypse, the exceptional London-based zombie novel told ingeniously in a series of documents.
While Flu isn't an inventive as Jones' effort, it still works very well and is a massively satisfying zombie novel that creates a dead world you want to explore further, and leaves enough questions for us to want to read the sequel, Fever, coming in the summer. And Flu definitely shows Simmons' massive potential to become Great Britain's crown prince of zombie fiction.
Not perfect, but a damn good try. Zombie fans will love it, horror fans will love it. Simmons writes like a demon, smooth and dangerous. Zombie fiction with an edge.
THE SKINNER By Neal Asher – Reviewed
Posted in Reviews, Uncategorized with tags action, adolescent, adult, AI, alien, amount, army, asher, back-stoies, body chemistry, book, book review, books, builds nicely, cleverly put together, colonise, detail, dicover more, enough action, entertained, execute, fatal, fauna, fiction, great ideas, hive mind, hoop, horror, ideas, immortal, information, janer, jay hoop, later stages, leeches, massive, mission, monster, neal asher, novel, novels, old crew, overseer, pirates, planet, plot, police, polity, prador, problems, review, reviewed, reviews, sable keech, seas, secret, SF, skinner, solid story, spatterjay, story, strangers, surface, survivor, the skinner, twists and turns, universe, war, war drone, water filled, waves, writer on March 18, 2011 by stanleyriiks
Three strangers meet on the way to the planet's surface. That planet, which has little serviceable surface, is Spatterjay, a mostly water-filled world. And the seas of Spatterjay are filled with all manner of creatures all ready and willing to eat you and anything else that invades their watery home: including the strange leeches, whose bite, if not fatal, will change your body chemistry until you are immortal, or near as damnit.
One of the party of three is Sable Keech, several hundreds of years old, and finally returning to Spatterjay to complete his mission: to find the remaining survivors of Jay Hoop's crew and execute them. They were an ancient gang who sold cored-human slaves to the alien Prador's during the war. Despite the war now being over a Prador adult and adolescent have arrived on the planet in secret with one of Hoop's old crew, intent on causing problems.
Another of the three is Janer, part of a hive mind that may have secret plans to colonize the planet.
Throw into this mix semi-immortal pirates; a monster that skins people alive; the various fauna that occupies most of the planet and is intent on eating everything else; an AI overseer that acts as the planet's police and army; and a War Drone; and you get a massive amount of story, huge back-stories, and a huge amount of information that fortunately doesn't slow down the plot too much.
It takes a little while to get into the book because of the sheer volume of stuff you need to know, but it's so full of great ideas that you can't help but keep reading. The book builds nicely, we have enough action and enough ideas to not only keep you entertained but make you want to discover more. Fortunately Asher's produced not only more Spatterjay novels, but also Polity novels (based on the more organised part of the universe that only make a brief appearance here). Asher's universe is massively detailed and cleverly put together, and the novel is the same. What it lacks in pace to begin with is swiftly made up for in the later stages, and you can forgive this because of the amount of detail expounded.
Full of great ideas, with a good solid story and plenty of twists and turns, this first book of Spatterjay is the ideal entry into this virgin territory, and I have high hopes for the other books in the series, which I will most definitely be seeking out.
DEATH'S HEAD By David Gunn – Reviewed
Posted in Reviews, Uncategorized with tags action-packed, adventures, alien, aliens, amazon, andy remic, army, beasts, book, boy's own adventure in space, cave system, command, Conan, creatures, david gunn, deaths head, deniability, details, druss, fantast fiction, fantasy, fast paced, feros, final battle, general, great fun, grin, grin on your face, gunn, haphazard, insubordination, kell, killing, kind of book, lashed to death, legionnaire, massive alisn beast, mission, murder, novel, organic, pet, plotting, prison, review, reviewed, reviewer, science fiction, SF, sven, telepathy, tool, tougher than shit, treason, trouble, true hero, war, wookie on February 7, 2011 by stanleyriiks
Amazon suggested this book to me because of a previous purchase of one of Andy Remic's books. Andy Remic writes the kind of fast-paced, action-packed SF and fantasy stories that thrill and entertain in equal measure, so I was looking forward to this one.
For once amazon got it pretty much spot on.
Sven is an ex-sergeant Legionnaire who is about to be lashed to death for insubordination, until a group of Ferox (unfriendly Wookie-type creatures) attack the out-post he's stationed at, killing everyone but him. One of the massive alien beasts talks to Sven using telepathy and Sven is taken back to their camp where he lives with them as a kind of pet.
This is the beginning of Sven's adventures.
When the cave system the Ferox live in is attacked and Sven is saved, he becomes a tool of the General, given mission where the army needs deniability. Sven's unique abilities and his tougher than shit attitude not only get him into trouble, but also out of it, as he tackles prison, treason, war and command.
Ok, so Sven's adventures feel very much organic, the plotting for the novel seems to have happened during the writing process and each episode doesn't connect too much with what follows or what came before other than occasional details, but that doesn't matter.
The haphazard plotting makes it feel like a real adventure, and you can't help but enjoy Sven's "fuck you" attitude. This guys got huge balls and isn't afraid to display them for all to see. You want Sven to win, whatever it is he's doing. He's one of those grumpy bastards, like Kell, Conan and Druss, that we're used to seeing in fantasy fiction, but a lot less so in SF. Here we have a true hero, who knows the difference between right and wrong, but does things he own ways, whether it gets him into trouble or not.
So the aliens involved in the final battle all become a bit confused, and you're not sure quite who's fighting who, but who cares!
Sven is what carries the story on, and Gunn gives us a great helping of action to keep things speeding along nicely so we don't get too worried about the details. Great fun, the kind of book that puts a grin on your face. A boy's own adventure in space.
LEGEND By David Gemmell – Reviewed
Posted in Reviews, Uncategorized with tags army, attached, axe, bandit, bank of theives, battle, book, books, characters, coward, cuttthroats, david gemmell, death, defending, drenai novels, dros delnoch, druss, entertaining, epic, fantasy, fiction, force, forces, fortress, heroic, incredible, legend, lost, massive, monks, myth, nadir, novel, protrayed, return of the jedi, review, reviewed, reviewer, reviews, sect, seige, story, Thermopylae, warrior, writer, writers, writing on January 17, 2011 by stanleyriiks
This is the book that started Gemmell's career. The epic battle to protect Dros Delnoch fortress, to stop the invading hordes of the Nadir. It's a fantasy tale of Thermopylae. If the fortress is lost the entire Drenai empire will follow, but the warriors are outnumbered fifty to one and everyone knows it's just a matter of time before the fortress falls. They know this even before the Nadir's massive army arrives.
An ancient warrior, nearly sixty, and aching with fatigue, is called upon to assist. Druss takes his axe and his knowledge, prepared to die to help slow the mighty Nadir forces. He knows it is a lost cause, but he will do everything he can.
A group of monks, a warrior sect, head to the fortress to aid them knowing only death awaits.
A coward helps a woman being attacked in a forest, and suddenly finds himself part of the defending force.
A bandit is called upon, taking his band of thieves and cutthroats to help out.
The massive siege is masterfully portrayed. Gemmel's detailing is spot on. The characters are brilliant and you can't help but will them to win, despite the incredible odds.
His first book set off a career and Gemmel is still recognised as one of the masters of heroic fantasy. This book takes from myth and legend, but history and even has a Return of The Jedi moment for those of you reading carefully.
Action packed, cleverly plotted, and brimming with character and sparkling with genius, Legend is a book that's difficult to put down and easy to enjoy. I think I will be seeking out more of Gemmel's work and working my way through his back catalogue of Drenai novels.
FIREFIGHT By Chris Ryan – Reviewed
Posted in Reviews, Uncategorized with tags adventure, afghanistan, ahmed, army, authenticity, basic, big bad villain, bond, book, brutal murder, bucket load, captain, cardboard, characters, chris ryan, cia, clumpy, crime, drunk, eak, failures, fans, firefight, fleming, hot gadgets, james bond, london, mi5, miltary, mission, mordern, novel, novelist, panache, plots, predictable, purists, regiment, review, reviewed, reviewer, sas, sexy women, sister, small details, style, taliban, terror attack, terrorist, thriller, true hero, urban, will jackson, writing on October 26, 2010 by stanleyriiks
A kind of grown-up boy's own adventure. A gritty, urban, modern James Bond, without the sexy women, the hot gadgets, or Fleming's style. In fact without the panache, without the fast cars, and the big bad villain. Without any of the accessories that make Bond such a great character. So what do we have?
Former SAS Captain Will Jackson is a drunk, having left the regiment two years ago after the brutal murder of his wife and child in a terrorist attack. But Jackson is called in by MI5 for one last mission, to seek out Faisal Ahmed, a former CIA operative who has gone rogue and intends to target London in a massive terror attack. Jackson must put together a crack team to follow the only lead they have, to Afghanistan to attempt to save Ahmed's sister from the Taliban in the hope that she will lead them to him.
Ryan's writing style is basic, and even a little clumpy in areas. His characters are cardboard, his plots are weak and predictable. What he does bring to the table is authenticity, and he does that by the bucket load. Despite the failures of many parts of the book, it still manages to hold up (just), because of the small details that make you think, yes, that's right.
There are better thrillers, there are better books, better characters, better plots, but you won't get authenticity much better than this. For purists and fans only, the bloke is a true hero, but he's not a novelist.

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Proof that a discrete subgroup of $\mathbb(R)^n$ is isomorphic to an integer lattice I have to prove that a discrete subgroup or $\mathbb{R}^n$ is a lattice, which I am doing in a manner similar to the one in this question. However, I am unable to understand the method described there as I haven't seen what indexes and cosets are yet.

I am given an outline, where $G$ is a discrete subgroup, $F$ is the vector space generated by $G$ of basis $\{a_1,...,a_p\}$, and $H$ is the subgroup of $G$ generated by $\{a_1,...,a_p\}$.
Let $P = G \cap\{ \sum\limits_{i=1}^{p}\lambda_i a_i, 0 \leq \lambda_i < 1 \} $. I have so far proven that $P$ is finite and that for every $x\in G$, there exists unique $(y,z)\in H \times P$ such that $x=y+z$.
I now have to prove that there exists $k>0$ such that $kx\in H$, therefore, by writing $kx=y_k+z_k$, there exists $z_k=0$. How do I prove this?

The rest of the proof is limpid, given that it will prove that $G$ is isomorphic to $\mathbb{Z}^p$.

A: I have found the answer, through proving that $z_k$ is not injective. As it takes finitely many values, there exists $(k,n)\in {(\mathbb{N}^*)}^2$ such that $z_k = z_{k+n}$. Thus,
$$kx-y_k=(k+n)x-y_{k+n} \iff nx = y_{k+n}-y_k\in H$$
Therefore, there exists an $n\in\mathbb{N}^*$ such that $nx\in H$.