text:
\section{Introduction}
\label{Introduction}
Combinatorial Optimization Problems (COPs) are present in a broad range of real-world applications, such as logistics, manufacturing or biology \cite{paschos2014applications}. Due to the \textit{NP-hard} nature of most of the COPs, finding the optimal solution to medium/large sized problems is intractable \cite{garey1979computers}.
As a result, in the last few decades, heuristic methods have been established as an alternative to approximate \textit{hard} optimization problems in a reasonable amount of time. Despite being widely used, a major drawback of such methods is the need to exhaustively evaluate a large amount of candidate solutions.

In the last decade, the rapid development of Deep Learning (DL) has enabled the creation of neural network-based models that can substantially decrease the computational effort in optimization. Two main frameworks can be distinguished: \textit{constructive methods} and \textit{improvement methods}. The former class generates a unique solution incrementally by iteratively adding an item to a partial solution until it is completed. Conversely, improvement methods take a candidate solution and suggest a modification to improve it. In fact, the improvement process can be repeated iteratively, using the modified solution as the new input of the model. These methods can potentially reduce the extensive search only focusing on trajectories leading to optimal solutions.

In this paper we focus on improvement methods and propose a Neural Improvement (NI) model for graph-based combinatorial problems. This model encodes a given solution by means of edge features and proposes a modification on the pairwise precedence of some items, with the aim of obtaining a better candidate.
To illustrate its usage, we apply the model to solve the Preference Ranking Problem (PRP), an NP-hard problem that tries to find an optimum pairwise consensus in a set of items.

In particular, this paper makes the following contributions:
\begin{itemize}
    \item Presents a Reinforcement Learning formulation for a Neural Improvement model parameterized by Graph Neural Networks and Attention Mechanisms.
    \item Introduces a novel encoding-decoding process which considers as input both the stationary instance information and a candidate solution to be improved by means of the graph-edges.
    \item Conducts an exhaustive analysis on the \textit{short-term} (one improvement step) and \textit{long-term} (multiple improvement steps) inference capabilities of the Neural Improvement model for the PRP. Moreover, we develop a Neural Hill Climbing based on the presented model and compare its performance to conventional procedures.
    \item We demonstrate the applicability of the model by using it as the building block of two advanced Hill climbing methods: Tabu Search and Iterated Local Search.

\end{itemize}

\section{Related Work}
\label{related_work}

Neural Networks (NN) have been used since the decade of the 80s to solve COPs in the form of Hopfield Networks \cite{hopfield82}. However, as seen in recent surveys \cite{bengio2021machine, mazyavkina2021reinforcement}, the growth in the computation power and the development of advanced architectures in the last decade has enabled more efficient applications that are getting closer to state-of-the-art algorithms. As mentioned previously, NN-based optimization methods can be divided into two main groups according to their strategy.

\paragraph{Neural Constructive Methods} Most of the DL-based works develop policies to learn a constructive heuristic. These methods start from an empty solution and iteratively add an item to the solution until a certain stopping criterion is met. One of the earliest works in the \textit{Neural Combinatorial Optimization} paradigm, Bello \textit{et al.} \cite{bello2016neural} used a Pointer Network model \cite{vinyals2015pointer} to parameterize a policy that constructs a solution, item by item, for the Travelling Salesman Problem (TSP). Motivated by the results in \cite{bello2016neural}, and mainly focusing on the TSP, DL practitioners have successfully implemented different architectures such as Graph Neural Networks \cite{cappart2021combinatorial, joshi2020learning} or Transformers \cite{kool2018attention, kwon2020pomo}.

As previously seen in the Operations Research literature, the solutions obtained by these proposals are not competitive with state-of-the-art methods \cite{garmendia2022neural}. In fact, since the performance of these models is still far from optimality (mostly in large size instances), they are usually enhanced with supplementary algorithms that augment the solution diversity at the cost of increasing the computational time. A common practice is to use active search \cite{bello2016neural}, where rewards obtained from the evaluation instances are used to fine-tune the parameters of a model. An alternative is to use sampling \cite{bello2016neural, kool2018attention} or beam search \cite{vinyals2015pointer} to further explore the neighborhood of the solution proposed by the model.

\paragraph{Neural Improvement Methods} Improvement methods, also known as trajectory methods,
are initialized with a given solution, and iteratively propose a (set of) modification(s) to improve it until the solution cannot be further improved. Neural Improvement (NI) methods utilize the learned policy to navigate intelligently across the different neighborhoods.

To that end, the architectures used for constructive methods have been reused for implementing improvement methods. Chen \textit{et al.} \cite{chen2019learning} use LSTMs to parameterize two models: a model outputs a score or probability to each region of the solution to be rewritten, while a second model selects the rule that modifies that region. Lu \textit{et al.} \cite{lu2019learning} use the Transformer model to select a local operator among a pool of operators to solve the capacitated vehicle routing problem (VRP). Finally, Wu \textit{et al.} \cite{wu2021learning} use a similar architecture to train a policy that selects the node-pair to apply a local operator, e.g., 2-opt.

Improvement methods not only incorporate the stationary instance data, but also need to consider the present solution. In fact, the difficulty of encoding the solution information into a latent space to be understandable to the model is a major challenge for most of the combinatorial problems.

In routing problems there are various ways of representing solutions. Each node (or city) can maintain a set of features that indicate the relative position in the current solution, such as the location and distance to the previously and subsequently visited nodes \cite{lu2019learning}. However, this technique does not consider the whole solution as one, instead it only contemplates consecutive pairs of nodes in the solution. A common alternative when using the transformer architecture is to incorporate Positional Encodings (PE), which capture the sequence of the visited cities in a given solution \cite{kool2018attention}. Recently, Ma \textit{et al.} \cite{ma2021learning} propose a \textit{cyclic PE} that captures the circularity and symmetry of the routing problem, making it more suitable in representing solutions than the conventional PE.

However, in some graph problems, the edges can provide useful information that it is not contained in the nodes, namely, the relative information among nodes. Moreover, in some problems the essential information is codified in edges, and thus, prior methods that focus on node embeddings \cite{lu2019learning, ma2021learning} are not capable of properly encoding the relative information.
In the following section, we will present the optimization problem that illustrates the need to develop neural models that consider edge features.

\section{Preference Ranking Problem}
\label{preliminaries}

Ranking items based on preferences or opinions is, in general, a straightforward task if the number of alternatives to rank is relatively small. Nevertheless, as the number of alternatives/items increases, it becomes harder to get full rankings that are consistent with the pairwise item-preferences. Think of ranking 50 players in a tournament using their paired comparisons from the best performing player to the worst. Obtaining the ranking that agrees with most of the pairwise comparisons is not trivial. This task is known as the Preference Ranking Problem (PRP) \cite{heckel2018approximate}. Formally, given a preference matrix $B=[b_{ij}]_{N \times N}$ where entries of the matrix $b_{ij}$ represent the preference of item $i$ against item $j$, the aim is to find the simultaneous permutation of rows and columns of $B$ so that the sum of entries in the upper-triangle of the matrix is maximized (see Eq. \ref{eq:lop_of}).

\begin{figure}
    \centering
    \includegraphics[width=0.7\textwidth]{draft_prp.png}
    \caption{Example of a PRP instance of size $N=5$. \textbf{a}) A preference matrix of size $N=5$ ordered as the identity permutation $\mathbf{\omega}_e = ($1 2 3 4 5$)$. Entries of the matrix contributing to the objective function are highlighted in grey, the sum of the entries in the upper diagonal gives the objective value, which is 51. For this instance, the optimal solution is given by the permutation $\mathbf{\omega}_{opt} =  ($4 1 2 5 3$)$ with an objective value of 60. \textbf{b}) Equivalent complete graph with edge weights; only the edges of the first node are shown for clarity. \textbf{c}) Identity permutation represented as the solution graph.}
    \label{fig:prp}
\end{figure}

\begin{multicols}{2}
Note that row $i$ describes the preference vector of item $i$ over the rest of $N-1$ items, while column $i$ denotes the preference of the rest of the items over item $i$. Thus, in order to maximize the upper triangle of the matrix, preferred items must precede in the ranking (see Fig.\ref{fig:prp} a).

\begin{equation}
\label{eq:lop_of}
f(\mathbf{\omega}) = \sum_{i=1}^{N-1} \sum_{j=i+1}^{N} b_{\mathbf{\omega}(i) \mathbf{\omega}(j)}
\end{equation}
\end{multicols}
Alternatively, the problem can be formulated as a complete bidirected graph where nodes represent the set of items to be ranked and the weighted edges denote the preference between items. A pair of nodes $i$ and $j$ has two connecting edges $(i,j)$ and $(j,i)$, with weights $b_{ij}$ and $b_{ji}$ that form the previously mentioned preference matrix $B$. A solution (permutation) to the PRP can be also represented as an acyclic tournament on the graph, where the node (item) ranked first has only outgoing edges, the second in the ranking has 1 incoming edge and the rest are outgoing, and so on until the last ranked node, which only has incoming edges (see Fig.\ref{fig:prp} b and c).

\paragraph{Applications} Ranking from pairwise comparisons is a ubiquitous problem in modern Machine Learning research. It has attracted the attention of the community due to its applicability in various research areas, including but not being limited to: machine translation \cite{tromble2009learning}, economics \cite{leontief1986input}, corruption perception \cite{achatz2006corruption} or any other task requiring a ranking of items, such as sport tournaments, web search, resource allocation and cybersecurity \cite{anderson2019rankability, cameron2021linear, shah2013case}.

\section{Method}
\label{method}
\paragraph{Reinforcement Learning: Markov Decision Process}
The idea of solving the PRP iteratively with a NI model can be formulated as a Markov Decision Process (MDP), where a policy $\pi$ is responsible for selecting an action $a$ at each step $t$ based on a given state $s_t$ of the problem. The main entities of the MDP in this work can be described as:

\begin{itemize}[leftmargin=0.3in]
    \item \textbf{State.} A state $s_t$ represents the information of the environment at step $t$. In this case, the state gathers data from two information sources: (1) stationary data, which the PRP instance to be solved, and (2) dynamic data, that is, a candidate solution $\omega$ to the problem at step $t$.
    \item \textbf{Action.} At every step, the learnt policy selects an action $a_t$, which involves a pair of items that, according to the policy, are incorrectly ranked. Once selected, an operator is applied that alters the precedences of one, both or more items\footnote{The terms \textit{preference} and \textit{precedence} are interchangeably used throughout the paper as the preference between two items is translated to have a precedent position in the solution $\omega$.}.
    \item \textbf{Reward.} The transition between states $s_t$ and $s_{t+1}$ is derived from an local operator applied in a pair of items given by $a_t$. The reward function represents the improvement of the solution quality across states. Different function designs can be used, as will be explained in Section \ref{learning}.

\end{itemize}

\subsection{NI Model}
We will parameterize the policy $\pi$ as a NN model with trainable parameters $\theta$. Fig. \ref{fig:architecture} presents the general architecture of the model, composed of two sub-models: an encoder and a decoder.

\begin{figure}
    \centering
    \includegraphics[width=0.75\textwidth]{architecture.png}
    \caption{Architecture of the NI model.}
    \label{fig:architecture}
\end{figure}

\paragraph{Encoder}
Given a graph instance of size $N$ that represents a PRP, there are $N \times N$ edges or node pairs, and each edge $(i,j)$ represents the precedence of node $i$ with respect to node $j$. Note that only $N \times (N-1)$ edges need to be considered since edge $(i,i)$ does not provide any useful information. As previously noted, the policy considers both instance information (stationary) and a candidate solution at time step $t$ (dynamic). For this purpose, we will use a bi-dimensional feature vector $\mathbf{x}_{ij} \in \mathbb{R}^{2}$ for each edge $(i,j)$. The first dimension in $\mathbf{x}_{ij}$ denotes the element $b_{ij}$ of the preference matrix when node $i$ precedes node $j$ in the solution, and it is set to zero otherwise. Similarly, the second dimension denotes the element $b_{ji}$ of the preference matrix when node $j$ precedes node $i$ in the solution, and it is set to zero otherwise.

Conversely, nodes do not reflect any problem-specific information. In fact, following a similar strategy to that proposed by Kwon \textit{et al.} \cite{kwon2021matrix}, we select to use vectors of ones as node features $\mathbf{n} \in \mathbb{R}^{N}$. Even though all nodes are initiated with the same value, these features will help to spread edge features across the graph in the encoding: node $i$ will gather information from edges $ik$ and $ki$ where $k: \{1, ..., N\}$.

Node and edge features will be linearly projected to produce \textit{d}-dimensional node $\mathbf{h}_{i}$ and edge $\mathbf{e}_{ij}$ embeddings
\begin{equation}
\label{eq:node_embeddings}
\mathbf{h}_{i} = n_{i} * V_h + U_h
\end{equation}
\begin{equation}
\label{eq:edge_embeddings}
\mathbf{e}_{ij} = \mathbf{x}_{ij}^T * V_e + U_e
\end{equation}
where $V_e$ $\in \mathbb{R}^{2 \times d}$ and $V_h$, $U_e$ and $U_h$ $\in \mathbb{R}^{1 \times d}$ are learnable parameters.

The encoding process consists of $L$ Graph Neural Network (GNN) layers (defined by the superscript $l$) that perform a sequential message passing between nodes and their connecting edges (see left part of Fig. \ref{fig:architecture}). Eqs. \ref{eq:node} and \ref{eq:edge} define the message passing in each layer, where $W_1^l$, $W_2^l$, $W_3^l$, $W_4^l$ and $W_5^l$ $\in \mathbb{R}^{d \times d}$ are learnable parameters, $BN$ denotes the batch normalization layer, $\sigma$ is the sigmoid function and $\odot$ is the Hadamard product.

\begin{equation}
\label{eq:node}
  \mathbf{h}_{i}^{l+1} = \mathbf{h}_{i}^{l} + ReLU\left(BN\left(W_1^l \mathbf{h}_i^l + \sum_{j=1}^N (\sigma(\mathbf{e}^l_{ij}) \odot W_2^l \mathbf{h}_j^l)\right)\right)
\end{equation}
\begin{equation}
\label{eq:edge}
  \mathbf{e}_{ij}^{l+1} = \mathbf{e}_{ij}^{l} + ReLU\left(BN\left(W_3^l \mathbf{e}_{ij}^l + W_4^l \mathbf{h}_{i}^l + W_5^l \mathbf{h}_{j}^l\right)\right)
\end{equation}

The output of the encoder, which is fed to the decoder, consists of the edge embeddings of the last layer $\mathbf{e}_{ij}^L$, plus the graph embedding \(\mathbf{e}_G = \frac{1}{N^2} \sum_{i=1}^{N} \sum_{j=1}^{N} \mathbf{e}_{ij}^L\), which is an aggregation of the edge embeddings.

\paragraph{Decoder}
Graph embeddings are projected to form the query (\(Q= W_g \mathbf{e}_G\)) of a multi-head attention mechanism (MHA) \cite{vaswani2017attention}. The MHA mechanism measures the compatibility of the query with each one of the keys or edge embeddings (\(K = V =\mathbf{e}_{ij}\)). The output is a context vector \(\mathbf{e}_c = \mathrm{MHA}(Q, K, V)\) that is again refined in a second attention layer to produce the logits $\mathbf{u_{ij}}$;
\begin{equation}
 \label{eq:logits}
 \mathbf{u_{ij}} = \left\{
       \begin{array}{ll}
	 C \cdot \mathrm{tanh} \left( \frac{(W_Q \mathbf{e}^c)^T \cdot (W_K \mathbf{e}_{ij}^L)}{\sqrt{d}} \right)      & \mathrm{if\ } i \neq j\;\;  \\
	 - \infty & \mathrm{otherwise} \\
       \end{array}
     \right.
\end{equation}
where the $\mathrm{tanh}$ function is used to maintain the logits within $[-C, C]$ ($C=10$). The logits are then normalized using the \textit{Softmax} function to produce a matrix $\mathbf{p} \in \mathbb{R}^{N \times N}$ which gives the probability of modifying the precedence between items $i$ and $j$. The model will be set to sample from the probability matrix during training and to select the action with maximum probability during inference.

\subsection{Learning}
\label{learning}
\paragraph{Loss Function} The improvement policy will be learned using the REINFORCE algorithm \cite{williams1992simple}. Given a state $s_t = (\mathbf{B}, \mathbf{\omega}_t)$ which includes an instance and a candidate solution at step $t$, the model gives a probability distribution $p_\theta (a_t|s_t)$ of all the possible pairwise preferences to be modified. After performing an operation $O(\mathbf{\omega}_t|a_t) = \mathbf{\omega}_{t+1}$ with the selected pair, a new solution $\mathbf{\omega}_{t+1}$ is obtained. The training is performed minimizing the loss function
\begin{equation}
\label{eq:loss}
 \mathcal{L}(\theta | s) = \mathbb{E}_{p_\theta (s, \mathbf{\omega}_t)} [-R_t \log p_\theta (s, \mathbf{\omega}_t)]
\end{equation}
by gradient descent, where $R_t = \sum\limits_{i=0}^{T-1} \gamma^{i}(r_i - r_{i-1})$ corresponds to the sum of cumulative rewards $r_i$ with a decay factor $\gamma$ in an episode of length $T$ (see Appendix A for further details).

In order to obtain $r$, different Reward Functions (RF) can be found in the literature. Lu \textit{et al.} \cite{lu2019learning} use a reward function (RF1) that takes the objective value of the initial solution as the baseline and, for each subsequent action, the reward at step $t$ is defined as the difference between $f(\mathbf{\omega}_t)$ and the baseline. The drawback of this function is that rewards may get larger and larger and even bad moves far from the baseline can be defined as positive rewards.

Alternatively, the most common approach in recent works \cite{wu2021learning, ma2021learning}, is to define the reward (RF2) as $r_t = \max [f(\mathbf{\omega}_{t+1}), f(\mathbf{\omega}^*)] - f(\mathbf{\omega}^*)$, where $f(\mathbf{\omega}^*)$ is the objective value of the best solution found until time $t$. Note that this alternative yields only non-negative rewards, and all the actions that do not improve the solution receive an equal reward $r_t = 0$. In our case, we use a simple but effective reward function (RF3) $r_t = f(\mathbf{\omega}_{t+1}) - f(\mathbf{\omega}_t)$ which defines the reward as the improvement of the objective value between steps $t$ and $t+1$, and also considers negative values. RF3 reward function yields a faster convergence with less variability as can be seen in the comparison of the mentioned reward functions depicted in Fig. \ref{wrap-fig:1} (more details in Appendix B.1).

\begin{wrapfigure}{r}{5.5cm}
\includegraphics[width=5.5cm]{reward_analysis.png}
\caption{Training curves using different reward functions.}
\label{wrap-fig:1}
\end{wrapfigure}
\paragraph{Automated Curriculum Learning} Curriculum Learning consists of training the models in a controlled manner, where the difficulty of the samples is manually increased throughout the process \cite{bengio2009curriculum}. In this case, the difficulty can be defined as the percentage of moves that worsen the objective value with respect to all the possible moves.

We do not make use of a manual curriculum learning strategy, where the difficulty of the inputs fed to the model is manually increased, as it is done by Ma \textit{et al.} \cite{ma2021learning}.
Instead, we iteratively fed the previously modified solution to the model without any step limit, and finalize the epoch once the model gets stuck in local optima. This enables an automated curriculum learning that does not require any additional hyperparameter.
However, learning is performed with a batch of instances and not all of them reach a local optima in the same number of steps. Thus, we save the best average reward obtained by the model, and we consider the algorithm to be stuck when it does not improve the best average reward for $K_{max} = 5$ iterations.

\paragraph{Operator} The model is flexible, allowing the practitioner to define the operator that best fits the problem, we will use the \textit{insert} operator\footnote{Given an edge $(i,j)$, denoting the items in positions $i$ and $j$ in the solution, the insert operator consists of removing the item at the position $i$ and placing it at position $j$.}, as it yields good results for the PRP \cite{laguna1999intensification}. See Appendix A.1 for further details on the operator.

\subsection{Applications of the Neural Improvement model}
\label{applications}
\paragraph{Neural Hill Climber}
The Hill Climbing heuristic (HC) is a procedure that continuously tries to improve a given solution performing local changes and looking for better candidate solutions in the neighborhood. Examples of conventional HC procedures include, among others, \textit{Best First Hill Climbing} (BFHC), that selects the first candidate (neighbor) that improves the present solution; \textit{Steepest-Ascent Hill Climbing} (SAHC), which selects the best candidate solution from the whole neighborhood; and \textit{Stochastic Hill Climbing} (SHC), that randomly picks one solution from the neighborhood.

We propose the Neural Hill Climber (NHC), which iteratively gives the pair of items with maximum probability of being modified. Once the local operator is performed in the given pair, the new solution is again fed to the model. In general, HC heuristics do not allow the objective value to decrease. Thus, when the action given by the model does not improve the solution, we sort the probability vector and select the first action that improves it.
Eventually, just as conventional HC procedures, the neural method will get stuck in a local optima where an improving move cannot be found. In this case, an alternative is to restart the procedure departing from another random candidate solution.

\paragraph{Advanced Hill Climbers}
Beyond the HC, the NI model can be used as the core of numerous methods to create intelligently guided algorithms. One of the many examples is the Tabu Search (TS) \cite{glover1993user}, which enhances the performance of the HC method allowing worsening moves whenever a local optima is reached. Instead of restarting the solution, a move in the neighborhood is made with the goal of finding a better optima. In order to avoid getting trapped in cycles, TS maintains a tabu memory of previously visited states to prevent visiting them again. Another algorithm is the Iterated Local Search (ILS). Once the search gets stuck in a local optima, instead of restarting the algorithm with a new random solution as in standard HC algorithms, ILS perturbs the best solution found so far and the search is resumed in this new solution. The perturbation level is dynamically changed based on the total budget left (number of evaluations or time).

We use the NI model to guide the local moves of a Neural Tabu Search (NTS) and a Neural Iterated Local Search (NILS) and analyse their performance together with NHC, comparing them to conventional alternatives in the following section\footnote{Note that standard designs of ILS and TS have been followed from basic literature, and it is not the aim to reach state-of-the-art results, but to illustrate the easy application of the proposed model, and its immediate beneficial impact.}.

\section{Experiments}
\label{experiments}

In this section, we present a thorough experimentation of the proposed NI model. First, we perform experiments to analyse its short-term performance (\textit{one-step}) and, then, we evaluate the long-term (\textit{multi-step}) capabilities of the model implemented in the different algorithms: NHC, NTS and NILS.

\paragraph{Setup} For the experiments we follow a common practice, training the model using randomly generated instances, where gradients are averaged from a batch of 64 instances. We train two models using instances of two sizes: $N=20$ and $N=40$\footnote{Even though we use instances of the same size to train each model, note that due to the element-wise operations performed in the encoder, it is possible to combine instances of different size.}. We use small model sizes due to reduced computational resources. In fact, we prove the generalization capability of these models to infer larger instances than those used for training. If not mentioned differently, the model trained with instances of size ($N=20$) will be used. See Appendix A.2 for more details on the hyperparameters.

We have implemented the algorithms using \textit{Python 3.8}. Neural models have been trained in an \textit{Nvidia RTX 2070} GPU, while methods that do not need a GPU are run on a cluster of 55 nodes, each one equipped with two \textit{Intel Xeon X5650} CPUs and 64GB of memory. See the supplementary material for the code implementation.

\subsection{NI Model Performance Analysis}

\paragraph{One-step} Short-term analysis focuses on the capability of the NI model to provide a solution that outperforms the present one. In terms of neighborhood, we would expect NI to be able to identify the best or almost some of the best neighbors. Fig. \ref{fig:rew_hist} sorts the rewards of all the possible operations obtained in 9 subsequent optimization steps, while the reward obtained by the model is highlighted by a vertical line. The model is capable of reaching more difficult situations over time, which can be noted by the left shift of the distribution. In fact, the lack of improvement moves in the last step (bottom-right corner) forces the model to select a negatively rewarded move.

Moreover, if we were to take all the possible actions and sort them based on the obtained improvement performing each particular action, we could rank the model selection. Fig.\ref{fig:rank_hist} shows an histogram of selected-action rankings among all the possibilities\footnote{To compose the figure we randomly generated 1000 different instances with random initial solutions. Then, all the possible actions were sorted based on the improvement reward and the rank of the action selected by the model was saved.}. Considering that only $(N-1)^2$ insert operations are valid, on average, the action that the model takes is ranked between the $98^{th}$ and $99^{th}$ percentile ($5^{th}$ out of $361$ for $N=20$, $13^{rd}$ out of $2401$ for $N=50$ and $31^{st}$ out of $9801$ for $N=100$). More details can be found in Appendix B.2.

\begin{figure}
     \centering
     \begin{subfigure}[b]{0.32\textwidth}
         \centering
         \includegraphics[width=\textwidth]{reward_hist_trajectory1_2.png}
         \caption{}
         \label{fig:rew_hist}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.32\textwidth}
         \centering
         \includegraphics[width=\textwidth]{rank_hist.png}
         \caption{}
         \label{fig:rank_hist}
     \end{subfigure}
     \hfill
     \begin{subfigure}[b]{0.32\textwidth}
         \centering
         \includegraphics[width=\textwidth]{heatmap_def.png}
         \caption{}
         \label{fig:mo_heatmap}
     \end{subfigure}
        \caption{(a) Histograms of the improvement of the objective value performing all the possible insert operations in a random solution for 9 subsequent optimization steps. The reward of the action selected by the model is highlighted with a vertical line. (b) The second histogram shows the ranking of the action selected by the model among all the possible actions on 1000 different instances. (c) Pareto analysis regarding the gap percentage to optimum value and the total number of objective value evaluations.}
        \label{fig:short-term}
\end{figure}

\paragraph{Multi-step}
\label{long_term_exp}
The NI model learns to consistently improve the solution even in difficult situations. However, we still need to analyse its performance as the building block of a HC algorithm. For that purpose, we implement a \textbf{NHC} guided by the NI model trained with instances of size 20 as described in Section \ref{method}. We compare NHC to conventional HC procedures: \textbf{BFHC} and \textbf{SAHC}. The multi-step performance assessment will be performed considering a bi-objective problem: (1) obtain a high quality solution and (2) reach this solution with the minimum number of solution evaluations. For this experiment, we run the algorithms until they get stuck in a local optima. Fig. \ref{fig:mo_heatmap} illustrates the pareto analysis of the mentioned problem. NHC performs slightly better in terms of solution quality when compared to conventional hill climbing procedures. NHC, SAHC and BFHC obtain an average gap of 0.276\%, 0.277\% and 0.286\% respectively. Regarding the number of solution evaluations, NHC is the cheapest among all three procedures evaluating on average 355 solutions. BFHC explores 1261 solutions, and SAHC 5729, being the most expensive procedure since it needs to evaluate all the possible actions (entire neighborhood) before performing the move. All the solutions in the pareto front belong to NHC.

\begin{wrapfigure}{r}{5.5cm}
\includegraphics[width=5cm]{performance_20.png}
\caption{Gap to optimum value during an execution of a PRP of size 20.}
\label{wrap-fig:2}
\end{wrapfigure}
\paragraph{Performance} The second experiment examines HC algorithms explained in Section \ref{applications}. The performance of the methods is measured for differently sized instances with three different maximum number of evaluations: N, 10N and 100N, where N is the size of the instance to be solved. In addition to the previously mentioned methods, we incorporate: an additional HC procedure, the Stochastic Hill Climbing (\textbf{SHC}), that randomly picks a candidate from the neighborhood; a NHC trained using instances of size 40 (\textbf{NHC-40}); a conventional Tabu Search algorithm with an underlying Best-First strategy (\textbf{BFTS}); and finally, the Neural Tabu Search\textbf{(NTS)} algorithm. The performance is measured by means of the average gap percentage to the optimum value, given by the state-of-the-art metaheuristic \cite{lugo2021diversity}. For each size, we use 1280 different, randomly generated instances.

As shown in Table \ref{tab:performance}, among the conventional HC methods, BFHC is the best performing one. SAHC suffers from its exhaustive search procedure and SHC performs poorly due to the lack of an improving strategy in its search. \textbf{The NHC model is capable of finding better solutions than BFHC}. Regarding NHC models, note that they perform better in those instance-sizes used for training. Fig. \ref{wrap-fig:2} shows the fluctuation of the quality of the obtained solutions over different optimization steps. NHC is capable of quickly (few evaluations) reducing the gap compared to BFHC and SAHC. See Appendix B.3 for results with time limits. Regarding the NTS, apart from reducing the gap with respect to the conventional method for all the sizes, it is able of outperforming HC methods in some conditions.

Lastly, we have run a Neural Iterated Local Search (\textbf{NILS}) for 100000 evaluations. In N=100, NILS obtained an average gap of $0.36\%$ while the ILS method achieved a gap of $0.43\%$ (further results in Appendix B.4).

\begin{table}[t]
  \footnotesize
  \caption{Comparison of improvement methods. Average gap \% to the best known value for different maximum number of solution evaluations (E). Best results among the HC procedures are highlighted in bold while the best results among TS are underlined. The overall best result has an star.}
  \label{tab:performance}%

\makebox[\textwidth][c]{
    \begin{tabular}{lrrrrrrrrr}
\toprule
       & \multicolumn{3}{c}{N=20} & \multicolumn{3}{c}{N=50}& \multicolumn{3}{c}{N=100} \\
\cmidrule(lr){2-4}\cmidrule(lr){5-7}\cmidrule(lr){8-10}
Method & E20  & E200 & E2000  & E50  & E500 & E5000 & E100  & E1000 & E10000 \\ \midrule

BFHC  & 10.37\% & 2.44\% & 0.28\%     & 8.42\%  & 2.84\%  & 0.68\%      & 6.74\% & 2.63\% & 0.81\%\\
SAHC  & 14.42\% & 13.00\% & 5.81\%     & 11.36\% & 10.95\% & 10.02\%     & 8.93\% & 8.77\% & 8.68\%\\
SHC   & 13.30\% & 10.21\% & 8.07\%     & 10.60\% & 9.32\%  & 8.42\%      & 8.50\% & 7.86\% & 7.36\%\\
NHC-20 & \textbf{1.75}\%* & \textbf{0.79}\%* & \textbf{0.16}\%*    & 2.87\%  & 1.51\%  & 0.66\%      & 3.42\% & 1.82\% & 0.80\%\\
NHC-40 & 1.98\% & 0.83\% & 0.17\%    & \textbf{2.25}\%*  & \textbf{1.24}\%*  & \textbf{0.65}\%      & \textbf{3.03}\%* & \textbf{1.67}\% & \textbf{0.79}\%\\
[1ex]

BFTS &  10.82\% & 2.45\% & 0.32\%      & 8.46\% & 2.87\% & 0.68\%      & 6.76\% & 2.64\% & 0.82\%\\
NTS &  \underline{2.71\%} & \underline{0.92\%}  & \underline{0.31\%}       & \underline{2.52\%}  & \underline{1.25\%}  & \underline{0.55\%}*       & \underline{3.12\%} & \underline{1.66\%}* & \underline{0.75\%}*\\

\bottomrule
\end{tabular}%
}
\end{table}%

\subsection{Real-World Case: NBA Historical Ranking}
Here, we use our model in a real-world application. Specifically, we use the historical data of the NBA from the 2004 season until 2020 with the aim of ranking all the NBA teams based on their historical performance\footnote{Used API documentation is available at \url{https://github.com/swar/nba_api}}. The preference matrix $B$ is formed by the pairwise comparisons between 30 NBA teams such that the preference of team A against team B is defined as the sum of matches that team A have won against team B. In total, 25,697 matches are considered. The entries of the instance matrix are normalized between $0-1$. The NHC model is able to give the solution that maximizes the objective value without any restart in a few seconds. The optimal objective value for the normalized matrix is 219.58, the ranking of the teams is shown in the Appendix B.5.

Note that using different conditions to define the preference matrix may change the ranking, i.e., using points for and against instead of won matches. In fact, a team that wins most of the matches with a small advantage would be ranked poorly when only considering difference of points.

\section{Conclusion and Future Work}
\label{conclusion}
This paper proposes a Neural Improvement model that employs an edge-based encoding and decoding framework. This model combines the benefits of steepest ascent and best first, being able to provide a solution (almost) as good as that provided by SA, and as fast (or even faster) than BF. This has major implications for most of the state-of-the-art metaheuristics, which could use NI models instead of neighborhood-based, conventional, procedures.

From the conducted experiments, we have observed that the output of our model tends to be categorical, i.e., the model is usually certain of its selection (even if it is not the optimal). This drastically reduces the diversity of the solutions,  since the model completes similar trajectories across different executions. This and other aspects require a more sound analysis, and thus we plan to investigate the following strategies: (1) Using a supplementary NN model that detects the most visited solutions, and transfers this information to the main model in order to avoid visiting solutions with similar features repeatedly; (2) Using a population of models that collaborate (or compete) for optimizing a given instance.

Regarding the operators used, in this case, the insert operators was chosen with literature support, however, it is not clear if any operation can be accurately learned by the NI model. This is another aspect that requires further research.
Finally, we believe that obtaining the state-of-the-art using neural improvement heuristics will be feasible in the future, but still considerable effort needs to be devoted to the correct implementation of complex neural networks in C++ code.

redpajama_set_name: RedPajamaArXiv


I know the path. It is straight and narrow. It is like the edge of a sword.
I rejoice to walk on it. I weep when I slip. Though, therefore, from my weakness I fail a thousand times, I will not lose faith, but hope that I shall see the Light when the flesh has been brought under perfect subjection, as some day it must.
I am but a seeker after Truth. I claim to have found a way to it. I claim to be making a ceaseless effort to find it. But I admit that I have not yet found it.
To find Truth completely is to realize oneself and one"s destiny, i.e., to become perfect. I am painfully conscious of my imperfections, and therein lies all the strength I posses, because it is a rare thing for a man to know his own limitations.
I have no secret methods. I know no diplomacy save that of truth. I have no weapon but non-violence. I may be unconsciously led astray for a while, but not for all time. My life has been an open book. I have no secrets and I encourage no secrets.
I claim to have no infallible guidance or inspiration. So far as my experience goes, the claim to infallibility on the part of a human being would be untenable, seeing that inspiration too can come only to one who is free from the action of opposites, and it will be difficult to judge on a given occasion whether the claim to freedom from pairs of opposites is justified. The claim to infallibility would thus always be a most dangerous claim to make.
experience of the world is available to us and would be for all time to come.
It is true that I have often been let down. Many have deceived me and many have been found wanting. But I do not repent of my association with them. For I know how to non-co-operate, as I know how to co-operate.
The most practical, the most dignified way of going on in the world is to take people at their word, when you have no positive reason to the contrary.


White Giant Calla Lily. This incredible Calla Lily is absolutely awesome and will reach 7' with good moisture and fertility. We know it is at least zone 7b for cold hardiness. It is hard to describe its majesty when in full flower with its giant white funnels which will also make excellent cut flowers. It has repeat bloomed for us all summer, but the spring rush is the best. In colder climes, one can use it as a large container plant and when it gets below the mid to low 20's, move it into the garage or just bring it into the house until spring. If given enough light, it will flower inside through the winter. This is a great perennial for wet areas, and the more sun the better the flower production. One of our dear customers, Mrs. Overton, had Calla Lilies growing in her garden here. This really shocked me, as I thought that they were more tropical in nature, until one of our clients mentioned that she used them in containers on her patio and the pots were left out all winter. This finally convinced me.


"Dirty Laundry" is a song recorded by American recording artist Kelly Rowland, for her fourth studio album, Talk a Good Game (). Co-written and produced. Dirty Laundry Lyrics: Let's do this dirty laundry, this dirty laundry / Let's do this dirty laundry, this dirty laundry / When you're soaked in tears for years, it never airs. Kelly Rowland has revealed how her former Destiny's Child bandmates, Beyoncé and Beyoncé reacts to Kelly Rowland's Dirty Laundry song.
While Kelly Rowland dropped some pretty shocking revelations about Beyoncé and an abusive relationship on "Dirty Laundry," it appears as if. Kelly Rowland and The-Dream talk about Kelly's emotional song, "Dirty Laundry," off her upcoming "Talk A Good Game" album. Kelly Rowland is airing out all her dirty laundry today. After letting the world know she liked her kisses down low on the first track from her.
Dirty Laundry by Kelly Rowland song meaning, lyric interpretation, video and chart position. After spending the first minute of "Dirty Laundry" revealing how she struggled with the solo success of former Destiny's Child groupmate. The previous night, Kelly Rowland broke down during her performance of 'Dirty Laundry' and had the entire crowd damn near in tears, as she sung about her.


Jorkens Practises Medicine and Magic · ss Best Broadcast Stories, ed. Hilton Brown, Faber & Faber 1944; read over BBC radio, August 16, 1940.
Voyages Through Time and Space (illustrated).
Bound with The Ship That Sailed the Time Stream.
Also in pb (Penguin 1983).


text:
Crateús är en kommun i Brasilien.   Den ligger i delstaten Ceará, i den östra delen av landet,  km nordost om huvudstaden Brasília. Antalet invånare är .

Följande samhällen finns i Crateús:

 Crateús

I övrigt finns följande i Crateús:

 Morro da Pendênica (ett berg)
 Morro Pelado (en kulle)
 Serra Serrinha (ett berg)
 Serrote dos Pastos Bons (en kulle)
 Serrote Pelado (en kulle)

Omgivningarna runt Crateús är huvudsakligen savann. Runt Crateús är det glesbefolkat, med  invånare per kvadratkilometer.  Savannklimat råder i trakten. Årsmedeltemperaturen i trakten är  °C. Den varmaste månaden är oktober, då medeltemperaturen är  °C, och den kallaste är april, med  °C. Genomsnittlig årsnederbörd är  millimeter. Den regnigaste månaden är april, med i genomsnitt  mm nederbörd, och den torraste är augusti, med  mm nederbörd.

Källor

Externa länkar

Indelningar i Ceará

redpajama_set_name: RedPajamaWikipedia


OK, so hopefully you're on board with the notion that social media marketing has changed business, that the popularity of social networking sites has changed customer relationships, so that companies can no longer promote their wares in the same way that they did a few years ago.
You get that the customer is now in control, and that by the time they contact you they've already done their homework. You understand that your marketing department, your sales team – in fact your entire organization – needs to realign itself to fit the expectations of an increasingly more-demanding, more fickle customer base.
So you've read a few books, subscribed to a few blogs, maybe even forked-out your hard-earned cash to attend a social media marketing conference or three.
You get back to work, itching to put into practice all that you've heard, with your head full of "customer engagement" this, and "remarkable content" that. You start a company blog, set-up a couple of social media accounts, and start "listening", start "engaging" and start contributing to the "conversation". You've well and truly drunk every drop of the Inbound Marketing KoolAid.
What went wrong? Simple: you were lied to.
Similarly, as in the days of the Wild West, there are plenty of snake oil salespeople who are more than willing to share their ' social media wisdom' with you – for a shekel or two.
But what if I'm not sick? Sure, social media marketing might be just what the doctor ordered for many organizations. However, what many so-called "Marketing 2.0 Experts" fail to acknowledge is that, right here and right now, there are certain companies in certain industries that are doing just fine thank you very much – without any of this newfangled social media stuff. If your new and existing customer base AREN'T on Facebook/Twitter/GooglePlus/Whatever, and DON'T want you in their email Inbox, then there's nothing broke that needs fixing.
Yeah, good luck with that. Ten will get you five that the majority of people in your company aren't going to play ball.
Changing existing corporate culture is the single biggest hurdle a marketer will face in trying to create a more social media-centric organization. Change isn't going to happen unless everyone – from CEO downwards – is on board and convinced of the merits.
Another sweeping generalization. At the end of the day, the most appropriate method of reaching a particular customer base is totally dependent upon that customer base – is has nothing to do with your own wishes and preferences. That's not to say that traditional marketing can't learn from (and even integrate with) some of the new Marketing tools. It's just an acknowledgement that some people still prefer to have a printed mailer in their hand rather than be forced to scan a QR code, for example.
More than that, many of the concepts of "traditional" marketing remain valid today. Just because the packet's been updated doesn't mean the ingredients have changed.
Don't hold your breath. Sure, having good content is certainly very important. But unless you're out there pointing your customers to it, you're going to be disappointed. Customers didn't fall over themselves to find you before. They're not going to suddenly start now.
Blogging is dead. Email is dead. Twitter is dead. Google Plus is launched and five minutes later everyone says that Facebook is dead. Or maybe it's Google Plus that's dead.
Could it be that, perhaps, none of these things are dead, and that you're just not using them as effectively as you could be? Perhaps the approach for Google Plus, for example, isn't the same as for Twitter? (hint: it's not).
I'm sure that you can come up with many more examples of such snake oil pitches and, if you've been bitten by any of them, then I feel for you.
Inbound marketing techniques and social media marketing channels are, without doubt, an extremely powerful and flexible tools. But that's all they are: tools. The fundamental principles of commerce, of marketing and of sales haven't changed. They've simply had to evolve as customers themselves have evolved.
I read this article on the KEXINO website and thought it might be something for you. The article is called There Are Lies, Damn Lies – And Social Media Marketing and can be found at https://kexino.com/marketing/there-are-lies-damn-lies-and-marketing/.


123 m² property with terrace located in a new development with communal areas with garden and pool, as well as beautiful views of the golf course and mountains, for sale in an exclusive location a few metres from the beach.
Green 12 is a new development that includes 40 homes distributed between 2 buildings built with the best quality materials, with garage and storage rooms. It has excellent communal areas with a garden and pool available to residents.
This 123 m² property consists of 2 bedrooms with wardrobes, 2 complete bathrooms, a kitchen and a living-dining room. It also enjoys a large 68 m² terrace with access from the living room and the master bedroom. In addition, it includes an air conditioning system divided into different zones.
Ideal for anyone who wants to live on the front line of the golf course and a few metres from the beach, and with a guaranteed return of 5%.


text:
Soben Chairman Takes Non-Executive Director Role
Soben Chairman, Paul Moultrie, will scale back his involvement in the business to take a Non-Executive Director role on the Soben board.
Paul Moultrie joined Soben in 2016 bringing more than 30 years' experience in the construction industry, and has played a key part in developing the business to where it is today.
Commenting on the decision, he said; "Half way through last year I reduced my time involvement in Soben to around two days per week. The next part of the plan was to step back a little bit more to a Non-Executive position, where I will be supporting the Board one day per month. I'll be there to offer strategic business advice and to be a sounding board for the Directors. That plan is now in place.
"This new arrangement will allow me to concentrate on my other passions of golf and golf fitness as well as spending more time with my family."
Soben Founder & Group CEO, Scott Smyth said; "I have known Paul for almost 30 years since we worked together in private practice. Paul has been a tremendous asset to the business over the last four years and immense support to me personally."
"I wish Paul the best with his new endeavours and I look forward to continuing our working relationship as he fulfils his Non-Exec role."
Paul will continue to work closely with Scott, and with Andrew Gallagher, who was promoted to the position of UK & Europe Managing Director earlier this year.
Since lockdown, Soben has implemented robust working from home arrangements and is operating business as usual. Despite a marked reduction in the volume of construction tenders coming to market, the team's specialist experience in high tech manufacturing, data centres, renewable energy and infrastructure is expected to shield it from any wider economic downturn.

redpajama_set_name: RedPajamaCommonCrawl


My two year old daughter was diagnosed with type�1 diabetes 10 months ago. Over the last three months, she has been saying her "tummy hurts". Sometimes it is before she eats, sometimes after. There doesn't seem to be a pattern that I can find. Is this common? What can I do to help her feel better? She doesn't necessarily slow down in activity during these times. Sometimes she is a little fussy. Could it possibly be that she is getting too much sugar-free juice?
It is very difficult to tell what can be causing these symptoms, as children without diabetes or any other condition often complain of tummy aches (my five year old daughter is a typical example!). I am assuming you have ruled out the possibility of these symptoms being due to hypos. These are extremely difficult to pick up in children under five as they cannot tell you what is wrong. If the pains are happening frequently, you should have her checked out by your daughter's paediatrician.


text:
Rebecca's Story
REBECCA'S STORY: SMALLHOLDING
Rebecca was a former Captain with the Army Royal Logistics Corps but left the military in July 2015. Now based in York and serving as a Reservist, She was keen to explore opportunities available in the land-based sector with organizations who were looking to recruit Reservists. Rebecca had a number of transferable skills and qualifications in the adventure training sector. However, she did not want to build a career in this sector, she wanted to gain ideas about what she could do in the future.
She attended a Rural Week in May 2016 in which she quickly identified smallholdings as an area she would enjoy and could build a career in. Her rural background, love of working with animals and being outdoors, and the idea of being self-sustained, pulled her towards running a smallholding, which would allow her to experience all four of her joys.
The Former Army Captain has decided that running her own smallholding in the future is something she would like to do. HighGround are running a smallholding course later in 2016 and Rebecca has expressed interest in attending to find out more about how this could be possible.


Nick Finck is one of the leading voices in the field of User Experience (UX). While some seem to think User Experience is only related to website and software design, Nick takes it beyond that to include any interaction between you and whatever business or product you are using.
A veteran on the Internet, Nick published and ran one of the first and most definitive online magazines, called Digital Web Magazine. Though new content is no longer added, hundreds of pages worth of wisdom remain available – and in demand.
And Nick is not just some geek stuck in an office somewhere. He travels extensively, attending conferences and giving talks about what he does and why it's important. Which is exactly what I asked him first, when we sat down to talk.
AP: What is user experience, why is it important and why does it matter to you?
NF: The user experience matters to me because it is a shift in how we do business. Prior to the stockmarket businesses was about appeasing management, once the stockmarket came around businesses was about investors. Now with the user experience being a major factor, businesses are starting to return their focus back to the customer. The voice of the customer is now superseding the voice of management and investors, which I deeply feel is the right way to do business.
User Experience is not so much a role or a job title as it is a philosophy. It focuses on things such as usefulness, value, creditability, desirability, findability, usability, and accessibility. Many professionals practice user experience by focusing on these aspects within the work they do, be it interaction design, information architecture, web design, content strategy and more.
It is important because it is no longer good enough just to offer a product or service. User experience has becoming the differentiating factor in what makes a product or service successful or a failure. Some of the more successful examples have been the Zappos, Virgin Air, Nike+, Logitech Harmony, Netflix, and of course Apple. Of course you don't need to be a multi-million dollar corporation in order invest in user experience and see good results.
AP: What is your personal philosophy on balancing structure, content and design?
NF: While I spend a lot of my work focused on the structural aspects of projects and the strategy, I feel that it is crucial to strike a balance between design and structure, however in most cases content still remains king. If Amazon didn't have books, they would be nowhere today. If Flickr didn't have photos, they would be nowhere. If Google didn't have indices of web pages and news they would be nowhere today. That said, content does rely on design and structure to be successful.
It really depends on what kind of thing we are talking about here. For example the balance of design and content is going to be quite a bit different for The New York Times than it is for MOMA. There is no one set rule for the right balance here, there is only what works for the needs of what you are designing and building. To discover those needs you need to do the research, which often means interviewing users, and crunching numbers through web analytics.
AP: You often give presentations and share your expertise with peers and even competitors. What do you get out of being part of a community?
NF: I have always felt that you will only be as successful in life as the size of your heart. I have been able to get to where I am at in my career thanks to the kind contributions of time, effort, and wisdom of my peers, colleagues, and mentors. Being involved in the community on such a level has allowed me to give back so others can advance in their careers much like I have. I try to give back every day as much as I can because I am grateful to have learned from some of the best and brightest people in this industry out of the pure kindness of their hearts.
So if I was rewarded anything for my efforts, it was the reward of watching a junior level web professional move into upper management, watching someone get accepted to a prestigious design college, watching someone land a job in the US related to what they love doing and secured a visa for doing it, watching someone totally unskilled at a particular craft become the known thought leader on that subject. All these things I had a direct impact on and I am happy to have done so.
AP: You once wrote 'The heart is as important to the mentoring process as the brain is.' How do you apply this in your own life?
NF: It's true. While your brain can allow you to build knowledge and wisdom, it is your heart that allows you to build compassion and empathy. The brain alone enable you to advance your career and make smart business decisions, but you may find that will lead you down a career path you are not interested in. Following your heart allows you to seek out what you are truly passionate about, what wakes you up in the morning and what keeps you going. Its a personal question you need to ask yourself; Would you rather be greatly successful and hate the work you do or would you rather make a modest income and love what you are doing? If you choose the latter the work will find you, if you choose the prior you will struggle every day to win over the work.
It's taken me years to really understand this about life. I have had a lot of ups and downs, a lot of failures and with them lessons learned. I wouldn't change a thing about that. Each experience builds on itself and you grow as person through it. Every day is a new day, and every day I try to be more true to what I am passionate about than the day before. Life is too short to worry about what went wrong or why, know where you want to be and set down that path with passion and understanding.
AP: Professionally, what is the greatest challenge you've overcome and how did you do it?
NF: I would have to say that the greatest challenge I have had in my career is to know and accept what I am good and doing and what I am not so good at doing. Understanding your limits at a particular craft is always an eye opener. For me it was understanding that there are people out there who do some things better than I, and perhaps more passionate about doing that kind of work than I. Instead of looking at this as competition, I look at this as an opportunity to course-correct myself in pursuing what I am really good at doing and passionate about. There were a series of failures connected with this change and things I had to let go of, but over time I was able to do it and now I feel I am finally on the right path.
One example is learning that as much as I wanted to be a visual web designer there are far more skilled and formally trained people out there who simply do better work than I could. Its not to say that if I set my mind to it I couldn't it done, but it really helped me understand there is a difference between wanting to do something and being passionate about doing something. My passion was elsewhere within the world of user experience, not so much in visual design though the two are related to some degree. Coming to that realization helped me set a career path for myself and set milestones for how I intended to get there.
For more about Nick Finck visit his business site, Blue Flavor, or his personal site and weblog. You can also find Nick on Twitter and explore the archives of Digital Web Magazine.
This quote really hit home; and is something I've started thinking about.


text:
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Georgia Tech Professor Leads Multi-Institution Team in Combatting Hospital Acquired Infections
Fri, 06/26/2020
Researchers from Georgia Tech, University of Virginia, and the University of Iowa have teamed up to prevent, control, and intervene against hospital acquired infection (HAI) outbreaks.
Detection and control of HAIs, such as Clostridioides difficile infection (CDI), is a fundamental public health problem and a resource intensive challenge for hospitals. And with the spread of Covid-19 on the rise, the need to combat HAI outbreaks is more critical than ever.
Despite the huge importance for hospitals, and the interest from both clinical and epidemiological researchers, these problems remain poorly understood and all too common. According to the Centers for Disease Control and Prevention (CDC), one in thirty-one hospital patients in the United States are infected with at least one HAI on any given day. HAIs are particularly challenging because of the high cost of patient treatment and disinfection of hospital facilities, as well as penalties against hospitals if HAIs occur.
In an effort to combat the rate of HAIs, the cross-institute group of researchers, led by Georgia Tech School of Computational Science and Engineering (CSE) Associate Professor B. Aditya Prakash, are creating a holistic approach to better understanding, preventing, and treating HAI outbreaks by developing a network-based framework to improve hospital infection control.
Equipped with a $1.2 million grant from the National Science Foundation (NSF), this three-year project aims to create a countermeasure toolkit to aid infectious disease experts.
"This will simultaneously improve care for current patients, make work safer for healthcare workers, and help prevent the incursion of Covid-19 into hospitals," said Prakash.
"Our research brings together researchers from different backgrounds - data scientists, epidemiologists, hospital infection control experts and clinicians - in order to adopt a very interdisciplinary methodology. Through this, we aim to develop a new network-based approach that improves hospital infection control using data driven models and data science algorithms."
Given that each hospital is unique, the focus of the project is to design fundamental strategies and provide guidance for hospital infection control decision makers to determine what exact policies are best for each individual location.
Currently, there is limited data on HAI outbreaks, and the dynamics of HAI spread are more complex than other diseases due to several compounding factors. In response to these issues, the team says it is seeking a paradigm shift and will pursue a holistic view for this problem. The team will do so by modeling the disease spread using high dimensional clinical and mobility network data of healthcare workers and patients.
This type of data includes onsite surveys, RFID-type sensors, manual check-ins, anonymized electronic medical records, and more, to determine which areas are at higher risk for contagion exposure, who is most likely to come into contact with that area and with each other, and who may get eventually infected.
This research will use a unique fine-grained, large-scale dataset of operations from the University of Iowa Hospitals and Clinics collected over 10 years, supplemented with data collected from other hospitals. Results will be validated with the help of domain experts including epidemiologists and clinicians involved in hospital infection control.
These varying datasets will be combined to build a complete picture of disease transmission pathways to help hospitals quickly detect, understand, and control future HAI spread. To accomplish this, researchers will focus on multiple aspects of the infection control cycle: developing better surveillance techniques, more informed and carefully designed interventions, and more accurate exposure risk assessment tools.
"Building a comprehensive framework is very challenging because it is dependent on the layout of the hospital, the personnel, and how they all interact, in addition to the transmission characteristics of the disease itself. So, there are many combinations, which is why we need nimble models that can ingest heterogeneous dynamic data, leverage global information, and yet be useful at an individual level," said Prakash.
To overcome these issues, researchers created a new class of two-mode cascade models to use throughout this project. This particular class has very different dynamics than current standard models used in heterogenous data analysis and has not been previously studied in data mining.
"These are difficult problems on networks, and we will invent rigorous and scalable methods using tools from data science, machine learning, and combinatorial optimization," said Prakash.
The team expects their research will lead to novel computational methods `and algorithms, in addition to guiding the next stage of advances in infectious disease practice.
Core Research Areas:
Data Engineering and Science
Kristen Perez
kristen.perez@cc.gatech.edu
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text:
Exmouth Journal > News
East Budleigh shop nominated for awards
Published: 9:08 AM September 28, 2009
Updated: 10:43 PM November 6, 2020
STAFF at the East Budleigh Community Shop are celebrating after the store was nominated for a national award – known as the rural Oscars. Based near the village hall, in High Street, the shop has been named in the list of nominees for the fifth annual
STAFF at the East Budleigh Community Shop are celebrating after the store was nominated for a national award - known as the rural Oscars.
Based near the village hall, in High Street, the shop has been named in the list of nominees for the fifth annual Countryside Alliance Awards.
The awards, voted for by the public, focus on community togetherness, the efforts people go to in developing the wellbeing of their village and promoting rural life.
John Tresidder, who works as a volunteer at the shop, said: "The fact we have been nominated is recognition for all the good work it has done for the area.
"It really has made an impact. The shop is nearly a year old and we're thriving."
John said it would be nice to win because there had been a lot of work undertaken to set up the shop and to run it.
He added: "It would be great also for the volunteers who help out here and the manager.
"It is a friendly shop. All the stock is as local as we can get it - meat, veg, eggs - everything sourced from quite nearby.
"We are a focus of the community. People sit outside, chat and have a coffee."
Juliette Field, a customer from Exmouth, said: "The shop offers a nice place to sit if you happen to be walking by and want to stop off for a drink and something to eat.
"I'm not surprised it has been nominated for the awards - it is a wonderful, cute little place."
The categories for the Countryside Alliance Awards include local food, village shop/post office, enterprise, traditional business and rural hero of 2009.
For more information about the awards, visit the following website address at: www.countryside-alliance.org.uk


our site analysis and client interview was due on friday. that meant a whole week of sleepless nights. but in the end we have to redo it. just when i thought i would be able to enjoy the weekends!!! so i had to scrap my plans of going home on friday. had to instead, be in kaed up to 4 am. thank god some people have cars and i didn't have to walk all the way back. i was also out of clean clothes then, and my dinner consisted of roti sweetie. on the way home today the car exploded. yup. thank god we were at the gas station at the time. actually i was sitting in the front passenger seat and moi papitos was filling the tires (why does it say tyres is spelled wrong?)when i hear this boom! i thought one of the tires exploded but it was actually the radiator.
are they sick of me?


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|Runescape Mobile Phone! study focus room education degrees, courses structure, learning courses. Go Now All Education. › Get more: Education. Mobile - The RuneScape Wiki.
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RuneScape 3 MOBILE - TOP 5 THINGS YOU SHOULD DO! Howsit Goin Guys! RuneScape Mobile is a fantacy massively multiplayer online role playing game (MMORPG) developed by Jagex.
Old School RuneScape is Jagex's official term for a previous version of the RuneScape game that was introduced from the August 2007 Archive of RuneScape, a backup of the RuneScape source code as it had been on 10 August 2007.It is also commonly referred to as OSRS or 2007scape.. This version of the game was announced in a news post on 13 February 2013, which was followed by the opening of a ...
After a successful period in early access, RuneScape will be joining the ranks of mobile gaming early this summer with a full release on Android and iOS...
Mobile is an Invention perk that reduces the cooldowns of Surge, Escape, Barge, and Bladed Dive at the cost of no adrenaline gain. It can be created in weapon and armour gizmos.. While activating Surge, Escape, Barge, or Bladed Dive places the player in a combat stance, mobile will not drain the player's divine charges stored in their charge pack unless active combat is initiated; this makes ...
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As such, RuneScape and mobile go together like your Rune armour and that totally unsuspicious dude who says they're going to trim it for you. "RuneScape has always been a clear candidate for bringing...RuneScape mobile's launched went better than expected, except for the part where the servers crashed, that is. Find out about the incident!Mobile is an Invention perk that reduces the cooldowns of Surge, Escape, Barge, and Bladed Dive at the cost of no adrenaline gain. It can be created in weapon and armour gizmos. While activating Surge, Escape, Barge, or Bladed Dive places the player in a combat stance, mobile will not drain the player's divine charges stored in their charge pack unless active combat is initiated; this makes ...The portable deposit box was a fate cards reward from the Sizzling Summer promotional event. This item allows the player to place a deposit box almost anywhere in the game and will last for 1 hour. All unused portable deposit boxes from the original promotion were removed from the game on 1 January 2013 with the update Happy New Year!.. During the September 2014, 2015, 2017, 2018, and 2019 ...RuneScape Mobile is an upcoming mobile client for RuneScape and Old School RuneScape (known as Old School Mobile) announced on 17 July 2017.There will be two separate apps for the games, and the apps will be available for free on iOS and Android. There is currently no scheduled release date for the mobile app for the main version of RuneScape.The app for Old School RuneScape was originally ...
Mobile updates are updates which generally affect the mobile version of the game. Mobile updates are listed in reverse chronological order. For an alphabetical list, see Category:Mobile updates. 5 March - Get into the RuneScape Mobile Android Beta! 28 February - RS3 Mobile Android Beta Cap increase incoming! 18 December - Mobile Dev Blog - Xmas '18 4 July - RS Mobile: May 2018 Playtest ...RuneScape:Twitch - OSRS Wiki - Old School RuneScape Wiki. Schools Details: To keep the Twitch chat meet the Wiki's standard of off-site moderation, Twitch's Automod is active, along with the accounts listed in the table below. Any Old School RuneScape Wiki Administrator may claim chat mod. Additional chat mods may be added as needed in the future. Listen to music from Runescape Mobile Beta. Find the latest tracks, albums, and images from Runescape Mobile Beta.RuneScape's modern mobile version is now available in early access on Android. RuneScape has been around for over eighteen years, starting as a browser-based MMO.RuneScape mobile's launched went better than expected, except for the part where the servers crashed, that is. Find out about the incident!RuneScape mobile's launched went better than expected, except for the part where the servers crashed, that is. Find out about the incident!
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RuneScape Wiki is a FANDOM Games Community. View Mobile Site FandomShop Newsletter Join Fan Lab ...,Mobile RuneScape Wiki Fandom. How. Details: Mobile is an Invention perk that reduces the cooldowns of Surge, Escape, Barge, and Bladed Dive at the cost of no adrenaline gain.RuneScape now features more ways to play, brand new skills and over 200 gripping story-driven quests. Same Gielinor - Incredible graphics. Play RuneScape on Windows, Mac or Linux and experience jaw-dropping visuals, lightning fast performance and an expansive viewing distance - or continue your adventure on the go with upcoming iOS and Android ...RuneScape Mobile is the mobile client for RuneScape announced on 17 July 2017. It was released 17 June 2021 for all iOS and Android users. Prior to this, it was available on Android as Mobile Early Access to all members on 29 October 2018 through the Android Beta program, and on iOS for selected beta testers. RuneScape 3 MOBILE - TOP 5 THINGS YOU SHOULD DO! Howsit Goin Guys! RuneScape Mobile is a fantacy massively multiplayer online role playing game (MMORPG) developed by Jagex.RuneScape Mobile. Play the world's greatest MMORPG on your smartphone. According to forappslovers.com the number of downloads of RuneScape Mobile is 1193274 The version of...
Mobile updates are updates which generally affect the mobile version of the game. Mobile updates are listed in reverse chronological order. For an alphabetical list, see Category:Mobile updates. 5 March - Get into the RuneScape Mobile Android Beta! 28 February - RS3 Mobile Android Beta Cap increase incoming! 18 December - Mobile Dev Blog - Xmas '18 4 July - RS Mobile: May 2018 Playtest ...,Runescape mobile is on it's way to release and in this video I've partnered up with Jagex to cover Runescape mobile had a rough launch, and since then there hasn't been much word of mouth about...Updated REVIEW for RuneScape 3 Mobile! RuneScape 3 MOBILE - TOP 5 THINGS YOU SHOULD DO! Howsit Goin Guys! In this video I go over my TOP 5 Favourite things to ...This article provides players with a list of ways to make money in RuneScape, along with the requirements, estimated profit per hour, and a guide explaining each method in detail. The list is separated into hourly methods, which can be done more or less continuously, and recurring methods, which can be done once every set amount of time.2021. 17 June - RuneScape Mobile Survival Guide. 16 June - RuneScape Mobile Release - Rolling Updates. 16 June - Mobile Launch & Elder God Wars - A Message From Mod Warden. 22 April - RuneScape On Mobile This Summer - A Message From Mod Warden.After a successful period in early access, RuneScape will be joining the ranks of mobile gaming early this summer with a full release on Android and iOS...RuneScape is a Java and C++-based massively multiplayer online role-playing game (MMORPG) operated by British developer Jagex Ltd. With over 9.5 million active free accounts and more than 500 thousand paid member accounts, RuneScape is the second most-played MMORPG in the world, and the most popular free MMORPG in the world for three years in a row. RuneScape offers both free and subscription ...
RuneScape Wiki is a FANDOM Games Community. View Mobile Site FandomShop Newsletter Join Fan Lab ...,F250 for sale illinoisCalculates the adrenaline gained from the Divert basic ability based on the damage the player takes, the player's shield tier, and if the player is under the PvM effect of Natural Instinct. Calculates the average damage for bleed abilities. Calculates the average damage for auto attacks and (most) non-bleed abilities.Old School RuneScape is Jagex's official term for a previous version of the RuneScape game that was introduced from the August 2007 Archive of RuneScape, a backup of the RuneScape source code as it had been on 10 August 2007.It is also commonly referred to as OSRS or 2007scape.. This version of the game was announced in a news post on 13 February 2013, which was followed by the opening of a ...Is it worth to have invigorating4 mobile + impatient 4 devoted 2 on my main sirenic chaps or should they be impatient 4 devoted 2 and enhanced devoted 4 and use the invigorating 4 mobile + impatient 4 devoted 2 on pernix chaps as a switch? See full list on oldschool.runescape.wiki
RuneScape Mobile, a MMORPG mobile game. The biggest feature of RuneScape mobile version is to allow cross-platform games between mobile and PC, and seamless progress synchronization...,Hp compaq 8200 elite boot from usbUpdated REVIEW for RuneScape 3 Mobile! RuneScape 3 MOBILE - TOP 5 THINGS YOU SHOULD DO! Howsit Goin Guys! In this video I go over my TOP 5 Favourite things to ...RuneScape Mobile is an upcoming mobile client for RuneScape and Old School RuneScape (known as Old School Mobile) announced on 17 July 2017.There will be two separate apps for the games, and the apps will be available for free on iOS and Android. There is currently no scheduled release date for the mobile app for the main version of RuneScape.The app for Old School RuneScape was originally ...1. Mobile is an Invention perk that reduces the cooldowns of Surge, Escape, Barge, and Bladed Dive at the cost of no adrenaline gain. It can be created in weapon and armour gizmos . While activating Surge, Escape, Barge, or Bladed Dive places the player in a combat stance, mobile will not drain the player's divine charges stored in their charge pack unless active combat is initiated; this makes mobile extremely beneficial for non-combat skilling where these movement abilities are ideal. Listen to music from Runescape Mobile Beta. Find the latest tracks, albums, and images from Runescape Mobile Beta.RuneScape Mobile is an upcoming mobile client for RuneScape and Old School RuneScape (known as Old School Mobile) announced on 17 July 2017. There will be two separate apps for the games, and the apps will be available for free on iOS and Android. There is currently no scheduled release date for the mobile app for the main version of RuneScape.
As such, RuneScape and mobile go together like your Rune armour and that totally unsuspicious dude who says they're going to trim it for you. "RuneScape has always been a clear candidate for bringing...,Is it worth to have invigorating4 mobile + impatient 4 devoted 2 on my main sirenic chaps or should they be impatient 4 devoted 2 and enhanced devoted 4 and use the invigorating 4 mobile + impatient 4 devoted 2 on pernix chaps as a switch? Mobile RuneScape Wiki Fandom. How. Details: Mobile is an Invention perk that reduces the cooldowns of Surge, Escape, Barge, and Bladed Dive at the cost of no adrenaline gain.Updated REVIEW for RuneScape 3 Mobile! RuneScape 3 MOBILE - TOP 5 THINGS YOU SHOULD DO! Howsit Goin Guys! In this video I go over my TOP 5 Favourite things to ...Welcome to the RuneScape Mobile Members Beta! RuneScape Mobile is a cross-platform game, allowing you to continue your journey from where you left off on PC!Runescape.wiki traffic estimate is about 1,799,758 unique visitors and 14,398,064 pageviews per day. Relying on Google Mobile-Friendly test runescape.wiki isn't optimized for mobile and tablet...RuneScape's modern mobile version is now available in early access on Android. RuneScape has been around for over eighteen years, starting as a browser-based MMO.
RuneScape:Twitch - OSRS Wiki - Old School RuneScape Wiki. Schools Details: To keep the Twitch chat meet the Wiki's standard of off-site moderation, Twitch's Automod is active, along with the accounts listed in the table below. Any Old School RuneScape Wiki Administrator may claim chat mod. Additional chat mods may be added as needed in the future. ,RuneScape, sometimes referred to as RuneScape 3, is a fantasy massively multiplayer online role-playing game (MMORPG) developed and published by Jagex, first released in January 2001. RuneScape was originally a browser game built with the Java programming language, but was largely replaced by a standalone C++-coded client in 2016.The game has had over 200 million accounts created and is ...This article provides players with a list of ways to make money in RuneScape, along with the requirements, estimated profit per hour, and a guide explaining each method in detail. The list is separated into hourly methods, which can be done more or less continuously, and recurring methods, which can be done once every set amount of time.https://runescape.wiki/w/Enchant Enchant spells are a type of magic spells from the standard spellbook used to give certain items magical properties. Enchantment spells always require cosmic runes, and one or more kinds of elemental runes (and sometimes catalytic runes for crossbow bolts.) RuneScape Mobile, a MMORPG mobile game. The biggest feature of RuneScape mobile version is to allow cross-platform games between mobile and PC, and seamless progress synchronization...Old School RuneScape Mobile is an upcoming version of Old School RuneScape for mobile platforms. It was announced on 17 July 2017. It will allow players to play Old School RuneScape for free on their Android and iOS mobile devices. It will work cross-platform with the desktop client, allowing players to play using the same characters. At RuneFest 2017, players had the chance to play Old School ...Is it worth to have invigorating4 mobile + impatient 4 devoted 2 on my main sirenic chaps or should they be impatient 4 devoted 2 and enhanced devoted 4 and use the invigorating 4 mobile + impatient 4 devoted 2 on pernix chaps as a switch? RuneScape Mobile is an upcoming mobile client for RuneScape and Old School RuneScape (known as Old School Mobile) announced on 17 July 2017.There will be two separate apps for the games, and the apps will be available for free on iOS and Android. There is currently no scheduled release date for the mobile app for the main version of RuneScape.The app for Old School RuneScape was originally ...
Mobile updates are updates which generally affect the mobile version of the game. Mobile updates are listed in reverse chronological order. For an alphabetical list, see Category:Mobile updates. 5 March - Get into the RuneScape Mobile Android Beta! 28 February - RS3 Mobile Android Beta Cap increase incoming! 18 December - Mobile Dev Blog - Xmas '18 4 July - RS Mobile: May 2018 Playtest ...,Old School RuneScape is Jagex's official term for a previous version of the RuneScape game that was introduced from the August 2007 Archive of RuneScape, a backup of the RuneScape source code as it had been on 10 August 2007.It is also commonly referred to as OSRS or 2007scape.. This version of the game was announced in a news post on 13 February 2013, which was followed by the opening of a ...RuneScape Mobile. Play the world's greatest MMORPG on your smartphone. According to forappslovers.com the number of downloads of RuneScape Mobile is 1193274 The version of...RuneScape Mobile is the mobile client for RuneScape announced on 17 July 2017. It was released 17 June 2021 for all iOS and Android users. Prior to this, it was available on Android as Mobile Early Access to all members on 29 October 2018 through the Android Beta program, and on iOS for selected beta testers. Updated REVIEW for RuneScape 3 Mobile! RuneScape 3 MOBILE - TOP 5 THINGS YOU SHOULD DO! Howsit Goin Guys! In this video I go over my TOP 5 Favourite things to ...Mobile is an Invention perk that reduces the cooldowns of Surge, Escape, Barge, and Bladed Dive at the cost of no adrenaline gain. It can be created in weapon and armour gizmos. While activating Surge, Escape, Barge, or Bladed Dive places the player in a combat stance, mobile will not drain the player's divine charges stored in their charge pack unless active combat is initiated; this makes ...Old School RuneScape Mobile is a version of Old School RuneScape for mobile platforms. It was announced on 17 July 2017 and was released on 30 October 2018. It allows players to play Old School RuneScape for free on their Android and iOS mobile devices[1]. It works cross-platform with the desktop client, allowing players to play using the same accounts.[2]Runecrafting is a free-to-play artisan skill released with the launch of RuneScape 2. It allows players to craft runes from rune or pure essence at Runecrafting altars, which can then be used for casting Magic spells. Players can train the skill for runes at the various altars, which can be accessed from mysterious ruins dotted around the map with the respective talisman.Check out our runescape mobile selection for the very best in unique or custom, handmade pieces Well you're in luck, because here they come. There are 3 runescape mobile for sale on Etsy, and...After a successful period in early access, RuneScape will be joining the ranks of mobile gaming early this summer with a full release on Android and iOS...
,Mobile is an Invention perk that reduces the cooldowns of Surge, Escape, Barge, and Bladed Dive at the cost of no adrenaline gain. It can be created in weapon and armour gizmos. While activating Surge, Escape, Barge, or Bladed Dive places the player in a combat stance, mobile will not drain the player's divine charges stored in their charge pack unless active combat is initiated; this makes ...This article provides players with a list of ways to make money in RuneScape, along with the requirements, estimated profit per hour, and a guide explaining each method in detail. The list is separated into hourly methods, which can be done more or less continuously, and recurring methods, which can be done once every set amount of time.https://runescape.wiki/w/Enchant Enchant spells are a type of magic spells from the standard spellbook used to give certain items magical properties. Enchantment spells always require cosmic runes, and one or more kinds of elemental runes (and sometimes catalytic runes for crossbow bolts.) Old School RuneScape Mobile is an upcoming version of Old School RuneScape for mobile platforms. It was announced on 17 July 2017. It will allow players to play Old School RuneScape for free on their Android and iOS mobile devices. It will work cross-platform with the desktop client, allowing players to play using the same characters. At RuneFest 2017, players had the chance to play Old School ...1. Mobile is an Invention perk that reduces the cooldowns of Surge, Escape, Barge, and Bladed Dive at the cost of no adrenaline gain. It can be created in weapon and armour gizmos . While activating Surge, Escape, Barge, or Bladed Dive places the player in a combat stance, mobile will not drain the player's divine charges stored in their charge pack unless active combat is initiated; this makes mobile extremely beneficial for non-combat skilling where these movement abilities are ideal. RuneScape 3 MOBILE - TOP 5 THINGS YOU SHOULD DO! Howsit Goin Guys! RuneScape Mobile is a fantacy massively multiplayer online role playing game (MMORPG) developed by Jagex.After a successful period in early access, RuneScape will be joining the ranks of mobile gaming early this summer with a full release on Android and iOS...For the mobile RuneScape client, see RuneScape Mobile. Mobile Release date 25 January 2016 Gizmo type Weapon, Armour Maximum rank Standard 1 Ancient 1...RuneScape Mobile is the mobile client for RuneScape announced on 17 July 2017. It was released 17 June 2021 for all iOS and Android users. Prior to this, it was available on Android as Mobile Early Access to all members on 29 October 2018 through the Android Beta program, and on iOS for selected beta testers.
Runescape.wiki traffic estimate is about 1,799,758 unique visitors and 14,398,064 pageviews per day. Relying on Google Mobile-Friendly test runescape.wiki isn't optimized for mobile and tablet...,Runecrafting is a free-to-play artisan skill released with the launch of RuneScape 2. It allows players to craft runes from rune or pure essence at Runecrafting altars, which can then be used for casting Magic spells. Players can train the skill for runes at the various altars, which can be accessed from mysterious ruins dotted around the map with the respective talisman.Welcome to the OSRS Wiki! We are the official Old School RuneScape encyclopaedia, written and maintained by the players. Since our start on 14 February 2013, we've been the go-to destination for all things Old School. Welcome to the RuneScape Mobile Members Beta! RuneScape Mobile is a cross-platform game, allowing you to continue your journey from where you left off on PC!Runescape.wiki traffic volume is 1,648,499 unique daily visitors and their 13,187,990 pageviews. Designing your sites to be mobile friendly ensures that all of your web pages perform well on all...2021. 17 June - RuneScape Mobile Survival Guide. 16 June - RuneScape Mobile Release - Rolling Updates. 16 June - Mobile Launch & Elder God Wars - A Message From Mod Warden. 22 April - RuneScape On Mobile This Summer - A Message From Mod Warden.Updated REVIEW for RuneScape 3 Mobile! RuneScape 3 MOBILE - TOP 5 THINGS YOU SHOULD DO! Howsit Goin Guys! In this video I go over my TOP 5 Favourite things to ...Runescape Mobile App Download! rs3 mobile download Looking to download safe free latest software now.RuneScape Mobile is an upcoming mobile client for RuneScape and Old School RuneScape (known as Old School Mobile) announced on 17 July 2017.There will be two separate apps for the games, and the apps will be available for free on iOS and Android. There is currently no scheduled release date for the mobile app for the main version of RuneScape.The app for Old School RuneScape was originally ...RuneScape Mobile, a MMORPG mobile game. The biggest feature of RuneScape mobile version is to allow cross-platform games between mobile and PC, and seamless progress synchronization...
,Old School RuneScape Mobile is an upcoming version of Old School RuneScape for mobile platforms. It was announced on 17 July 2017. It will allow players to play Old School RuneScape for free on their Android and iOS mobile devices. It will work cross-platform with the desktop client, allowing players to play using the same characters. At RuneFest 2017, players had the chance to play Old School ...1. Mobile is an Invention perk that reduces the cooldowns of Surge, Escape, Barge, and Bladed Dive at the cost of no adrenaline gain. It can be created in weapon and armour gizmos . While activating Surge, Escape, Barge, or Bladed Dive places the player in a combat stance, mobile will not drain the player's divine charges stored in their charge pack unless active combat is initiated; this makes mobile extremely beneficial for non-combat skilling where these movement abilities are ideal. RuneScape Mobile is the mobile client for RuneScape announced on 17 July 2017.It was released 17 June 2021 for all iOS and Android users. Prior to this, it was available on Android as Mobile Early Access to all members on 29 October 2018 through the Android Beta program, and on iOS for selected beta testers.. Apple users require at least iOS 14 and Android requires Android 8.0 or later, 2GB ...RuneScape Mobile is the mobile client for RuneScape announced on 17 July 2017. It was released 17 June 2021 for all iOS and Android users. Prior to this, it was available on Android as Mobile Early Access to all members on 29 October 2018 through the Android Beta program, and on iOS for selected beta testers.
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Runecrafting is a free-to-play artisan skill released with the launch of RuneScape 2. It allows players to craft runes from rune or pure essence at Runecrafting altars, which can then be used for casting Magic spells. Players can train the skill for runes at the various altars, which can be accessed from mysterious ruins dotted around the map with the respective talisman.
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Welcome to the OSRS Wiki! We are the official Old School RuneScape encyclopaedia, written and maintained by the players. Since our start on 14 February 2013, we've been the go-to destination for all things Old School.
20 August 2021. Elder God Wars Dungeon: The Nodon Front. Future Updates. 22 July 2021. Battle of The Monolith - Coming Soon. Future Updates. 21 May 2021. RuneScape On Mobile This Summer - A Message From Mod Warden. Mobile.
Welcome to the RuneScape Mobile Members Beta! RuneScape Mobile is a cross-platform game, allowing you to continue your journey from where you left off on PC!
Updated REVIEW for RuneScape 3 Mobile! RuneScape 3 MOBILE - TOP 5 THINGS YOU SHOULD DO! Howsit Goin Guys! In this video I go over my TOP 5 Favourite things to ...
Calculates the adrenaline gained from the Divert basic ability based on the damage the player takes, the player's shield tier, and if the player is under the PvM effect of Natural Instinct. Calculates the average damage for bleed abilities. Calculates the average damage for auto attacks and (most) non-bleed abilities.
Listen to music from Runescape Mobile Beta. Find the latest tracks, albums, and images from Runescape Mobile Beta.
RuneScape Mobile is the mobile client for RuneScape announced on 17 July 2017. It was released 17 June 2021 for all iOS and Android users. Prior to this, it was available on Android as Mobile Early Access to all members on 29 October 2018 through the Android Beta program, and on iOS for selected beta testers.
Old School Runescape Mobile is a mobile version of Old School Runescape, which is a version of Runescape 2 as it was in the year 2007. This means that the graphics are dated, but don't let that...
This article provides players with a list of ways to make money in RuneScape, along with the requirements, estimated profit per hour, and a guide explaining each method in detail. The list is separated into hourly methods, which can be done more or less continuously, and recurring methods, which can be done once every set amount of time.
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RuneScape:Twitch - OSRS Wiki - Old School RuneScape Wiki. Schools Details: To keep the Twitch chat meet the Wiki's standard of off-site moderation, Twitch's Automod is active, along with the accounts listed in the table below. Any Old School RuneScape Wiki Administrator may claim chat mod. Additional chat mods may be added as needed in the future.
RuneScape Mobile. Play the world's greatest MMORPG on your smartphone. According to forappslovers.com the number of downloads of RuneScape Mobile is 1193274 The version of...