text:
Living La Vida Locals
Mayon Volcano's History Has a Story to Tell
by Renzo Salao
You heard about it from your classes back in grade school.
Mt. Mayon, the perfectly cone-shaped wonder of a volcano in Bicol, is one of the Philippines' greatest attractions. But what you can see and read from the pages of your textbooks couldn't do justice to one of the most interesting volcanoes in the world.
Here are some fascinating stories about Mayon you probably missed out on:
The 'Beautiful' Folklore
Mt. Mayon is situated in the Bicol Region, particulary in Legazpi, Albay. The volcano is referred to in those parts as "Bulkang Magayon" which literally translates to "beautiful volcano". They say that the name of Mayon comes from an ancient regional folktale about a princess named Daragang Magayon.
The princess, whose name means "beautiful maiden" in Bikolano, was part of a Mayon-sized love triangle between two opposing warriors. The battle pitted the love of her life against his archrival, with the two laying siege on the grounds where the volcano now stands. Magayon ran towards her lover upon seeing him wounded in the clash. Both of them were eventually surrounded by the enemy, and so she stabbed herself in the heart while her lover died in her arms. The story goes that they were buried on that exact spot, and as time went on, the land had risen to form what is now Mayon Volcano. It is believed that the spirit of the princess rests within the volcano, while the clouds that engulf it belong to her beloved. In remembrance of this tale, the region of Albay celebrates the Daragang Magayon Festival every year.
Looks That Can Kill
Mt. Mayon may be the best example for the saying that looks can be deceiving. The volcano still makes headlines every so often, for reasons other than its grandeur. While Mayon is renowed for its beauty, the volcano has had its fair share of deadly eruptions throughout history. It has erupted 52 times in the past half millenium, dating back to the first recorded one way back in 1616, chronicled by Dutch explorer Joris van Spilbergen. For comparison, the famed mount Vesuvius has also recorded over fifty eruptions, but has only done so a handful of times within the past hundred years, the last one being all the way back in 1944.
Earlier this year, Mayon was in the news for renewed activity once more. It was the 4th time in the past ten years, solidifying Mayon's status as the Philippines' most active volcano and one of the deadliest in the world.
The Year without Summer
The most destructive eruption in Mayon's recorded history occurred in 1814, more than two hundred years ago. The eruption overwhelmed and destroyed dozens of villages within its surrounding area with an outpouring of hot gas and volcanic lava. The beautifully cultivated slopes of Mayon were buried beneath a steaming sheet of sand and ash.
The eruption was so strong that it contributed to what they called the 1816 "Year without a Summer", along with the explosion of Mount Tambora in Indonesia in 1815. The amount of ash within the atmosphere due to volcanic activity blocked out the sunlight, leaving the world in a perpetual winter for an entire year.
The Tragedy of Cagsawa Ruins
The most tragic casualty in Mayon's explosive history would have to be Cagsawa church. During the major eruption in 1814, residents of the town of Cagsawa were made to evacuate. The priest of the local church ordered the bells to be rung in order to warn the townsfolk of the impending disaster. However, due to the abrupt nature of the eruption, hundreds were forced to take refuge within the closed doors of the convent. The lava stream and accompanying ash proved to be too much and engulfed the church where it stood.
The site remains as one of the most picturesque vantage points of Mayon today. The blackened ruins of the church tower stand tall to this day, serving as a reminder for both the beauty and calamity that surrounds it.
Mayon As We Know It
Today, the area that surrounds the volcano is considered the Mayon Volcano Natural Park and remains a protected sanctuary to preserve its pristine conditions. Despite the obvious dangers, the nearby vicinity of Mayon Volcano is still inhabited by thousands of people and visited by thousands more. The fertile soil and bountiful harvests keep locals happy, while tourists from all over still flock to the mountain to climb its slopes and take in its views.
Mayon serves as one of the most popular tourist attractions in the country and offers a challenging trek for adventurous hikers. The climb usually takes 3-4 days and features a 40-degree ascent on lose volcanic cinder as you approach the summit. The history that surrounds Mayon makes the trip that much more meaningful.
Thinking of planning a trip to take in the scenery yourself? Check out our Bicol page here to score some great deals when you visit.
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About Renzo
Renzo spends most of his time trying to enjoy his two great loves: Food and Sports. A fresh new restaurant or a quick pick-up game of hoops will get him out of the house. He's an avid fan of the Washington Wizards, and hopes to be able to buy the team someday. But for now, he's currently in law school, trying to make his dreams come true.
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text:
\section{Introduction}
The traffic in mobile Internet is growing at a breathtaking rate due to the extreme popularity of mobile devices (e.g., smartphones and sensors). Analysis shows that there will be 80 billions of devices connected to Internet by 2025, resulting in a tenfold traffic growth compared with 2016 \cite{R1}. The availability of enormous mobile data and recent breakthroughs in \emph{artificial intelligence} (AI) motivate researchers to develop AI technologies at the network edge. Such technologies are collectively called edge AI and represent a latest trend in machine learning. {\bf Edge machine learning} concerns training of edge-AI models and is the theme of this paper \cite{R2,R3,R4A}. The migration of learning from central clouds towards the edge allows edge servers to have fast access to big data generated by edge devices in real time for fast training of AI models. In return, downloading the trained models to the devices provisions them intelligence to respond to real-time events. Presently, edge learning is the R\&D focus of leading Internet and telecommunication companies (e.g., Microsoft and Qualcomm) as they strive to apply AI to support \emph{Internet-of-Tings} (IoT) applications ranging from auto-pilot to healthcare.

Research on edge learning is cross-disciplinary as it merges two areas: computer science and wireless communication. They concern two key aspects of edge learning, namely \emph{fast data processing} and \emph{fast data acquisition} from edge devices (smartphones and sensors), respectively. The two aspects cannot be decoupled as their performances are interwound under a common goal of fast learning. While computing speeds are growing rapidly, wireless data acquisition suffers from scarcity of radio resources and hostility of wireless channels, resulting in a bottleneck for fast edge learning \cite{R4,R5}. In particular, edge learning typically requires uploading enormous data generated by a large number of edge devices. One example is the training of  Tesla's AI model for auto-driving using sensing data uploaded by millions of Tesla vehicles on the road. Given the conflict between large-scale data and scarce radio resources, wireless data acquisition can potentially cause excessive communication latency \cite{R6,R7,R8}. Therefore, suppressing communication latency poses a grand challenge for data acquisition in edge learning and calls for innovations on \emph{radio resource management} (RRM).

Attempts to tackle this challenge has led to the emergence of a new class of RRM techniques to enable intelligent data acquisition for edge learning. They are based on the principle that radio resources are allocated to edge devices not only based on channel states (as in the conventional approach \cite{R9}) but also considering how important their data is for learning. This gives the name \emph{importance-aware RRM}. Conventional designs target radio access and thus focus on data rates \cite{R10} or \emph{Quality-of-Service} (QoS) \cite{R11}. In contrast, importance-aware RRM targeting edge learning will attempt to improve learning performance (i.e., learning speed and accuracy). The new objective calls for a new design approach integrating tools from machine learning and wireless communication. The aim of this article is to provide an overview of the area of importance-aware RRM by introducing the background, the new deign principles, and the research opportunities as well as recent advancements in different directions.

\section{Background}
\subsection{Wireless Communication and Machine Learning}
Recent years have witnessed growing cross-disciplinary research merging wireless communication and machine learning. One research focus is to apply AI to improve the efficiency, robustness, and adaptivity of a communication system. Research in this vein forms the area of AI-assisted  wireless communication (AI-comm) where communication is the goal and learning is a tool. The emerging area of edge learning is fundamentally different where learning is the goal and wireless communication is the tool. Their differences in system operations are illustrated in Fig. \ref{fig:1}. AI-comm is introduced and compared with edge learning as follows.

\begin{figure*}[h]
\begin{center}
{\includegraphics[width=12cm]{fig1.pdf}}\\
\caption{Comparison between (a) AI-comm system and (b) edge learning system.}
\vspace{-10pt}
\label{fig:1}
\end{center}
\end{figure*}

\subsubsection{AI-assisted Wireless Communication (AI-comm)}
Traditional communication systems are based on a highly modular architecture divided into numerous functional blocks such as encoder/decoder and channel estimator. The resultant decomposed design not only compromises system performance but also results in high overhead and the lack of flexibility. Furthermore, existing system designs tend to assume oversimplified channel models. Consequently, theoretical performance is difficult to be fully materialized in practice. AI-comm research represents an attempt to overcome the above weaknesses by designing more integrated and versatile systems leveraging the power of AI \cite{R12,R13,R14,R15,R16}. In \cite{R12,R13}, researchers proposed novel schemes integrating channel estimation and data detection by applying sparse Bayesian learning. The innovation makes it possible to simultaneously recover a channel matrix and transmit symbols from the received signal with less channel-training overhead. Real channels are complex and frequently have no known models. To overcome the difficulty, researchers proposed in \cite{R14,R15} that deep learning can be applied to fit auto-encoders to a blackbox enclosing the channel and encoders/decoders. The deployment of such auto-encoders at transceivers provides a system adaptivity to an unknown propagation environment. Most recently, there have been breakthroughs in using recurrent-neural-network to construct a new class of error-correction codes \cite{R16}. They were shown to outperform even the state-of-the-art codes.

\subsubsection{AI-Comm vs. Edge Learning}
The main differences between AI-Comm and edge learning are elaborated as follows.
\begin{itemize}
\item {\bf Goal: communication vs. learning:} Typical AI-comm and edge-learning systems are compared in Fig. \ref{fig:1}. The goal of the former is communication, namely transportation of generic data from one place to another over the air. Rate maximization and reliability are the main design criteria. In contrast, the goal of an edge-learning system is learning, namely training of an AI model using distributed data. The main design criteria are learning speed and accuracy. Reliability may not be critical. For instance, for federated edge learning (see Section 2.2.2), perturbing stochastic gradients with noise can help avoid model overfitting or its being trapped at a local minimum \cite{R17,R18}.

\item {\bf Passive vs. active learning:} For AI-Comm, the learning of an AI model (e.g., auto-encoder) is decoupled from communication and based on a given historical dataset from past  measurement. The learning process is \emph{passive} in the sense of lacking proactive data selection. In contrast, as elaborated in the next section, a key operation in edge learning is \emph{active data acquisition}, namely selecting and transmitting important data to accelerate the learning process, which is a main theme of this work and discussed in the next section. In other words, the edge-learning process is \emph{active} and integrated with communication.

\end{itemize}

\subsection{Communication-Efficient Edge Learning}
Distributed learning refers to machine learning at a server using data distributed at remote devices. Edge learning is a specific scenario of distributed learning with an air interface between server and devices. In traditional distributed learning studied mostly by computer scientists, communication channels are modelled coarsely as ``bit pipes" [4, 5]. Edge-learning research advances the area by the deployment of advanced communication techniques (e.g., RRM) for efficient data acquisition. There exist two paradigms for edge learning. In one paradigm called \emph{centralized edge learning} [see Fig. \ref{fig:1}(b)], learning is performed only at the server and training data is directly acquired from edge devices by wireless transmission \cite{R3}. To preserve user privacy, the other paradigm, called \emph{federated edge learning} (see Fig. \ref{fig:2}), avoids data uploading by distributing learning at both servers and edge devices, which is coordinated using wireless links \cite{R4,R19,R20}. Specifically, devices transmit to the server their updates on local AI models that are \emph{averaged} (see Fig. \ref{fig:2}) and then applied to update the global model. In view of high dimensionality in data/updates, the approach of importance-aware RRM has the key feature of \emph{active data/update acquisition} for communication-efficient edge learning. Its basic principle is to adopt notions of \emph{data importance} from the existing literature of machine learning for RRM. The notions are introduced separately for the two mentioned paradigms as follows.

\begin{figure*}[h]
\begin{center}
{\includegraphics[width=12cm]{fig2.pdf}}\\
\caption{Federate edge learning system.}
\vspace{-10pt}
\label{fig:2}
\end{center}
\end{figure*}

\subsubsection{Centralized Edge Learning}
Consider distributed learning by direct data acquisition. To improve communication efficiency, it is natural to acquire only data samples that are ``important" for learning. Two data-importance metrics from the area of active learning are \emph{data uncertainty} and \emph{data diversity} \cite{R21}. Data classification is an important topic in machine learning that has a wide-range of applications ranging from computer vision to information retrieval. Targeting classification, active learning largely concerns the selection of data samples from a large unlabelled dataset for manual labelling and then training a classifier model. From the perspective of a single data sample, its informativeness for learning can be quantified by data (classification) uncertainty, referring to how confident it can be correctly classified using the real-time model \cite{R22}. On the other hand, when considering a batch of samples, the total informativeness depends not only on uncertainty of individual samples but also on their diversity, referring to non-overlapping information \cite{R23}.

Existing work on active learning by computer scientists focuses on data selection where communication is irrelevant. On the other hand, for importance-aware RRM research, communication engineers adopt the importance metrics from the area of active learning, namely data uncertainty and diversity, to design importance-aware RMM for \emph{active data acquisition} in edge learning.

\subsubsection{Federated Edge Learning}
There exist two schemes for federated learning featuring different types of update by edge devices. For one scheme, the edge devices transmit to the server their local models whose average replaces the global model. The other scheme is based the method of \emph{stochastic-gradient descent} (SGD), where devices transmit local gradient vectors and their average is applied to update the global model using SGD. For either scheme, the learning procedure iterates between 1) the broadcast of the global model by the server for updating local models and 2) transmission by edge devices for updating the global model. The iteration continues until the global model converges. Each iteration is called a \emph{communication round}. For federated learning, the concern of communication overhead has also motivated researchers to develop algorithms for selecting only a subset of devices with important updates for transmission. The theme is called \emph{active (model) update acquisition}. There exist two importance metrics corresponding to the two mentioned schemes. One is \emph{model variance} which indicates the divergence of a particular local model to the average of all local models. The other is \emph{gradient divergence} that reflects the level of changes on the current gradient update w.r.t. the previous one. Using these metrics to schedule updating devices, a number of so called ``lazily updating" algorithms have been designed for communication-efficient federated learning \cite{R24, R25}. Another approach for reducing communication overhead is to compress gradient vectors by exploiting their sparsity in significant elements \cite{R26, R27}.

Importance-aware RRM in the context of federated edge learning builds on the mentioned update-importance metrics. Thereby, data importance analytics provides a new dimension for improving the communication efficiency and coping with the negative effect of wireless propagation on learning performance.

\subsubsection{Radio Resource Management}
Radio resources, primarily referring to time, frequency and space, create signalling dimensions, which are used in cellular systems to provide radio access to mobile users \cite{R10, R28}. Dividing and sharing of each type of resource among users have resulted in a set of multi-access schemes including \emph{time-division multi-access} (TDMA) \cite{R29}, \emph{orthogonal frequency-division multi-access} (OFDMA) \cite{R30, R31}, \emph{space-division multi-access} (SDMA) \cite{R32}, and \emph{code-division multi-access} (CDMA) \cite{R33}. Building on these schemes, RRM is a broad area covering topics including admission control, scheduling, link adaptation, and interference coordination \cite{R34}. In this project, we consider two key topics in RRM, retransmission and scheduling, for their importance in practical systems e.g., \emph{long-term evolution} (LTE).

{\bf Retransmission} is a simple method for ensuring communication reliability in the presence of fading \cite{R6}. Its principle is to repeat the transmission of a data packet until it can be correctly decoded at a receiver. Thus, a retransmission technique essentially performs dynamic time allocation to transmission of different packets under the reliability constraint. Among different variations, a particular retransmission technique of our interest is called Hybrid \emph{automatic repeat request} (ARQ) implemented in LTE systems. Its key feature is to combine different transmitted versions of the same packet by \emph{maximal-ratio combining} (MRC) so as to incrementally enhance its receive \emph{signal-to-noise ratio} (SNR).

Focusing on radio access, traditional scheduling algorithms attempt to balance two goals. One is to allocate radio resources to meet different users' QoS requirements, namely their desired data rates and latency requirements \cite{R35}. The other goal is to maximize the spectral efficiency. Scheduling driven by this goal attempts to exploit \emph{multiuser diversity}, referring to independent fading in different users' channels \cite{R36}. However, this causes biased resource allocation in favor of users with best channels and being unfair to others. Practical algorithms usually attempt to balance two goals by maximizing spectral efficiency while observing some fairness constraints. Examples include proportionally fair scheduling \cite{R37} or max-min fair scheduling \cite{R38}.

One can see that traditional RRM designs targeting radio-access networks are mainly driven by spectral efficiency and reliability. On the other hand, importance-aware RRM targeting edge-learning systems has learning performance as the main concern as illustrated in Fig. \ref{fig:3}. This motivates the consideration of data importance in the design, yielding new techniques such as importance-aware retransmission and scheduling as introduced in the sequel.

\begin{figure*}[h]
\begin{center}
{\includegraphics[width=15cm]{fig3.pdf}}\\
\vspace{-5pt}
\caption{An edge learning system.}
\vspace{-25pt}
\label{fig:3}
\end{center}
\end{figure*}

While conventional RRM targets radio access, the new class of importance-aware RRM techniques share the following principle (also see Fig. \ref{fig:3}).
\begin{framed}
\noindent{\bf Principle 1} (Principle of importance-aware RRM for edge learning). In an edge-learning system, radio resources should be allocated to edge devices for transmissions based on the \emph{importance levels} of their local data and their \emph{channel states}.
\end{framed}

Thereby, data importance analytics provides a new dimension for improving the communication efficiency and coping with the negative effect of wireless propagation on learning performance. Such an approach has been adopted in practice such as Google's implementation of federated learning systems. In the following sections, we shall discuss specific research directions of importance-aware RRM for centralized edge learning and federated edge learning, as summarized in Table 1.

\begin{figure*}[h]
\begin{center}
{\includegraphics[width=17cm]{Importance-AwareRRM.pdf}}\\
\end{center}
\end{figure*}

\section{Importance-Aware Retransmission}
\subsection{Principle and Opportunities}
Importance-aware retransmission are new retransmission protocols for active data acquisition in centralized edge learning systems. Designing the optimal retransmission policies need address two issues:
\begin{itemize}
\item The {\bf importance distribution} over data samples are non-uniform. The distribution affects the optimal time allocation for transmitting individual samples.

\item {\bf Quality-vs-quantity tradeoff.} Increasing the average number of retransmission can improve quality of the acquired dataset but reduce its size (quantity) due to a finite budget, giving rise to the said tradeoff. Though both quality and quantity of the training dataset are important for accurate learning, they need be balanced given a limited transmission budget (time slots).
\end{itemize}

By addressing these issues, there are several promising research opportunities that warrant future investigation.
\begin{itemize}
\item[1)] {\bf Uncertainty-aware ARQ:} The technique aims at optimizing the said quality-and-quantity tradeoff by controlling the retransmission of each data sample based on its uncertainty and effective SNR (after MRC). The key design step is the mathematical derivation of the tradeoff between the effective SNR and data uncertainty under a constraint on learning accuracy. The uncertainty can be measured using either entropy or distance to classification boundary. A key design challenge is to derive a tractable measure of learning accuracy. In the subsequent design example, the measure therein is derived based on ensuring a high likelihood that the received data sample agrees with its label, regulating the effect of channel noise on learning. Building on the derived SNR-uncertainty tradeoff, a retransmission policy can be then designed to enable intelligent data acquisition for accelerating AI-model convergence.

\item[2)] {\bf Batch-mode ARQ exploiting local data diversity:}  This direction targets the scenario of batch-mode training where data is acquired in batches (in e.g., a broadband or MIMO system) and the AI-model is updated using batch data (instead of single samples as in the preceding sub-task). Consider data pre-selection at an edge device where a batch is selected from the local dataset for transmission. Besides uncertainty, it is important to consider the diversity of the samples within the same batch as discussed earlier. Both metrics can be integrated in a single measure called Fisher information matrix \cite{R39}. Then {\bf uncertainty-and-diversity aware ARQ} can be designed by mathematically deriving a tradeoff between effective SNR and Fisher information.  Building on the result, it is possible to design practical retransmission policies for centralized edge learning.

\item[3)] {\bf Importance-aware ARQ exploiting global data diversity:} Importance-aware retransmission can be also designed to account for global data diversity. Specifically, data to be acquired (single sample or a batch) should be informative w.r.t. to the global dataset at the edge server. In particular, for classification, it is highly desirable to obtain new data guiding a classifier model to explore a new dimension with high discriminant gain but insufficient existing data. Based on this principle, policies on making retransmission decisions can be designed to account for global diversity of received data samples, which can be evaluated at the server using the global dataset and classifier model. This requires modification of the mentioned Fisher information matrix and then can leverage a similar design approach as described in the last bullet.

\item[4)] {\bf Extension to federated edge learning:} The preceding techniques designed for active data acquisition can be extended to the paradigm of federated edge learning. The designing principles are similar while specific techniques need be redesigned due to the changes on the learning approach and importance metrics (to model variance and gradient divergence).
\end{itemize}

\subsection{Example Design of Importance-Aware ARQ}
Based on the recent work in \cite{R40}, a design example of importance-aware ARQ is introduced as follows.

\noindent{\bf System model:} Consider the edge learning system with retransmission as shown in Fig. \ref{fig:3}. There are multiple edge devices and an edge server, each equipped with a single antenna. The labelled dataset distributed over devices is transmitted to the server to train a classifier model. The server and the devices are connected by two separate channels: a low-rate noiseless label channel and a high-rate data channel with noise and fading. Upon receiving a data sample, the edge server makes a binary decision on whether to request a retransmission to improve the sample quality or a new sample from the scheduled device. The decision is communicated to the device by transmitting either a positive ACK or a negative ACK. Upon receiving a request from the server, each device transmits either the previous sample or a new sample randomly picked from its buffer. During each symbol block, the active device sends the data using linear analog modulation that is found recently to be an efficient method for multimedia transmission \cite{R41}. To reduce the overhead of broadcasting a large-size model to edge devices, the model can be compressed by pruning the model parameters with small values \cite{R40}. Unlike inference, the use of model for importance evaluation can tolerate aggressive compression without incurring significant performance degradation.

To exploit the time-diversity gain provided by retransmitting, multiple noisy observations of the same data sample are combined coherently using the MRC to maximize the receive SNR. The objective of designing the retransmission protocol is to minimize the duration of wireless data acquisition, thereby reducing radio-resource consumption and accelerating learning.

\noindent{\bf Learning model:} The supervised training of a classifier model at the server is considered. A coarse model at the server is refined progressively in the process of data acquisition plus training. A classical \emph{support vector machine} (SVM) classifier is considered in this example design as shown in Fig. \ref{fig:3}, which seeks an optimal hyperplane as a decision boundary by maximizing its margin to data points, i.e., the minimum distance from the hyperplane to each data point \cite{R42}. The points defining the margin, namely support vectors, directly determine the decision boundary (see Fig. \ref{fig:3}). The importance of a data sample for learning is measured by its uncertainty to the classifier. Since a SVM classifier makes less confident inference on a data sample which is located near the decision boundary, the uncertainty of a data sample can be suitably measured by the inverse of its distance to the boundary.

Since a noisy received data sample may mislead the model training if the predicted label differs from the ground truth received without noise, a pair of transmitted and received data samples should be forced to lie at the same side (ground-truth) of the decision boundary in the classifier model so that the predicted labels are identical. This event is called noisy data alignment and its probability is referred to as the {\bf data-alignment probability} \emph{as illustrated in Fig. \ref{fig:4}}. From the distance-based uncertainty definition for SVM, the data samples with higher uncertainty are closer to the boundary and thus more vulnerable to noise corruption.

\begin{figure}[h]
\begin{center}
{\includegraphics[width=8.5cm]{fig4.pdf}}\\
\caption{Illustration of noisy data alignment and data-alignment probability.}
\vspace{-20pt}
\label{fig:4}
\end{center}
\end{figure}

\noindent{\bf Importance-aware ARQ design for binary classification:} The ARQ protocol is designed to bias channel-use allocation towards providing better protection for more important (nearer to the SVM classification boundary) data samples against channel noise. To provide a guarantee on model accuracy, the design satisfies a constraint on the data-alignment probability defined early. This leads to a varying receive-SNR constraint on a data sample based on its importance level. The importance-aware ARQ protocol is a threshold based control policy with a SNR threshold adapted to data importance given as below.
\begin{framed}
\noindent{\bf Protocol 1} (Importance-aware ARQ for binary SVM classification). Consider the acquisition of a data sample ${\bf x}$ from a scheduled edge device. The edge server repeatedly requests the device to retransmit ${\bf x}$  until the effective receive SNR satisfies
\begin{equation}\label{eq:1}
{\rm SNR} > \min ( \theta_{0} \; \mathcal{U}_{\sf d}(\bf x), \theta_{\rm SNR}),
\end{equation}
where $\theta_0$ represents the data-alignment probability, $ \mathcal{U}_{\sf d}(\bf x)$ represents the distance-based uncertainty, and $\theta_{\rm SNR}$ is a given maximum SNR.
\end{framed}
It can be observed from \eqref{eq:1} that the SNR threshold  is  proportional  to  the  distance-based uncertainty of the data sample. One can see in Fig. \ref{fig:4} that a sample near the decision boundary has a higher level of uncertainty (importance) but is more vulnerable to noise corruption. Thus, it requires a higher receive SNR and hence more retransmissions to achieve the required data-alignment probability. This is aligned with the result in \eqref{eq:1}.

Next, the learning performance of the proposed importance-aware ARQ is evaluated by experiments on handwritten-digit recognition using the well-known MNIST dataset. The dataset consists of 10 categories ranging from digit ``0" to ``9" with a total of 60,000 labeled training data samples. In the experiments, two relatively less differentiable classes of ``3" and ``5" letters are chosen for binary classification using SVM. The maximum transmission budget is set to be 4,000 (channel uses). Two baseline protocols are considered. One is without retransmission (maximizing the size of acquired data) and another is the conventional channel-aware ARQ (in e.g., LTE), where the retransmission decisions depend merely on the channel states.

\begin{figure*}[h]
\begin{center}
{\includegraphics[width=13cm]{fig5.pdf}}\\
\vspace{-10pt}
\caption{Learning performance for a binary SVM classifier trained with wirelessly acquired data.}
\vspace{-25pt}
\label{fig:5}
\end{center}
\end{figure*}

 As illustrated in Fig. \ref{fig:5}(a), the performance of the protocol without retransmission degrades dramatically when the number of received samples is sufficiently large as they are too noisy. This emphasizes the need of retransmission. On the other hand, the importance-aware ARQ outperforms the channel-aware ARQ throughout the whole training duration. This confirms the performance gain due to taking into account of data importance in radio resource allocation for data acquisition. The underlying reason for the performance improvement of importance-aware ARQ is further illustrated by plotting the distribution of average numbers of retransmissions over a range of sample uncertainty (inversely proportional to sample distance to the decision boundary) in Fig. \ref{fig:5}(b). It can be observed that the channel-aware ARQ has close-to-uniform distribution since the SNR is independent on the sample uncertainty. In contrast, the retransmission for importance-aware ARQ is concentrated in the high uncertainty region. This is aligned with the importance-aware design principle.

The extension of the design to convolutional neural network models can be found in \cite{R40} where significant performance gain of importance-aware design is also observed.

\noindent{\bf Importance-aware ARQ  design for multi-class classification:} In this section, the importance-aware ARQ developed for binary classification is extended for multi-class classification.  By using the one-versus-one implementation \cite{R43}, a $C$-class SVM classifier can be decomposed into $L = C(C-1)/2$ binary component classifiers, each is trained by the data samples of the two concerned classes. The corresponding output of each input sample ${\bf x}$ is a $L$-dimension vector recording the $L$ scores, denoted by $\bold{s} = [s_1(\bold{x}),s_2(\bold{x}), \cdots, s_L(\bold{x})]$. A reference coding matrix $\bold{M} \in \mathbb{R}^{C \times L}$ is built to map the output ${\bf s}$  to the class indexes. By comparing the Hamming distances between ${\bf s}$ and each row in ${\bf M}$, the predicted class index $\hat{\bf c}$ is the row index with the smallest distance. Consequently, the single-threshold policy for importance-aware ARQ is extended to a multi-threshold policy given as below.
\begin{framed}
\noindent{\bf Protocol 2} (Importance-aware ARQ for multi-class SVM classification). For training a $C$-class SVM classifier, the edge server repeatedly requests the device to retransmit ${\bf x}$ until the effective receive SNR satisfies
\begin{equation}
\rm{SNR} > \min (\theta_{0}/|s_\ell(\bold{x})|^2, \theta_{\rm{SNR}}),~ \forall \ell \in \{\ell| m_{\hat{c}\ell} \neq 0\},
\end{equation}
where $m_{\hat{c}\ell}$ represents the element in the $\hat{c}$-th row and the $\ell$-th column of ${\bf M}$, $|s_\ell(\bold{x})|^2$ represents the distance-based uncertainty of the $\ell$-th binary component classifier.
\end{framed}

As in the binary SVM case, experimental results show that the importance-aware ARQ  consistently outperforms the two conventional schemes, namely the channel-aware ARQ scheme and the non-retransmission scheme.

\section{Importance-Aware Scheduling for Centralized Edge Learning}
\subsection{Principle and Opportunities}
While retransmission focuses on RRM in time, scheduling is another dimension to explore for importance-aware RRM in a multiuser edge-learning system. There exist two types of multiuser diversity in such a system. One is the independent fading in multiuser channels, called \emph{multi-user channel diversity}. The other is the heterogeneous importance levels across multiuser datasets, called \emph{multi-user data diversity}. Conventional scheduling in wireless networks exploits only the former. However, in edge learning system, it is desirable to jointly exploit both types of diversity so as to maximize the communication efficiency. However, doing so leads to two potentially conflicting goals: one is to schedule devices with the best channels to maximize the data-transmission reliability and the other is to select devices with most informative data. Since both goals are important for learning, they need to be balanced. This sets the following objective of designing \emph{importance-aware scheduling}.
\begin{framed}
\noindent{\bf Principle 2} (Principle of importance-aware  scheduling for centralized  edge learning). Targeting active wireless data acquisition for centralized learning, the importance-aware scheduling should simultaneously exploit the {\bf multi-user channel-and-data diversity} to improve edge-learning performance.
\end{framed}

Based on the above principle, we can envision the rise of many interesting research opportunities with some described as follows.
\begin{itemize}
\item[1)] {\bf Joint channel-and-uncertainty scheduling:} A key step of designing the scheduling algorithm is to derive a \emph{data-importance indicator} (DII) as a function of both data uncertainty and reliability (measured by e.g., channel state) as shown in Fig. \ref{fig:6}. For instance, an indicator can be the uncertainty of a data sample (evaluated using the real-time model under training) under a constraint on the data-alignment probability defined in the preceding section for providing a guarantee on learning performance. Then maximizing the DII can be applied as a criterion for scheduling to ensure both the data's reliability and usefulness for learning.

\begin{figure}[h]
\begin{center}
{\includegraphics[width=8.5cm]{fig6.pdf}}\\
\caption{The computation of data-importance indicator at an edge device.}
\vspace{-10pt}
\label{fig:6}
\end{center}
\end{figure}

\item[2)] {\bf Batch-mode scheduling exploiting multiuser data diversity:} Consider a broadband system with OFDMA or a MIMO system with SDMA, multiple devices can be scheduled for simultaneous transmission and thereby distributed data samples can be acquired in batches. This allows more efficient training of the AI model in the batch mode. For retransmission in the preceding section, it is desirable to ensure data diversity in each batch besides uncertainty of individual samples. The current scenario is more complex as it concerns multiuser data diversity instead of local diversity at a single device in the retransmission scenario. Correspondingly, a sophisticated DII function for the current scenario need be derived to account for data diversity, uncertainty, and reliability. The function can build on the mentioned Fisher information matrix as an integrated measure of data uncertainty and diversity. Subsequently, by developing a suitable signalling procedure, the derived DII can be applied to scheduling for edge learning in the batch mode.

\item[3)] {\bf Scheduling exploiting global data diversity:} The scheduling algorithms can be further designed to ensure global data diversity introduced earlier. This requires redesigning the DII function to account for both multiuser diversity and global diversity.
\end{itemize}

In the sequel, an example design is discussed for importance-aware scheduling for centralized edge learning systems.

\subsection{Example Design of Importance-Aware Scheduling}
\noindent{\bf System model:} Consider a multiuser edge learning system with one server and $K$ devices, as shown in Fig. \ref{fig:7}. Each device is equipped with a local buffer storing $N$ data samples.  To train a classifier model at the server, the devices time share the wireless channel to upload the training data samples to the server. In each sample block, there are three steps for selecting a device to upload one data sample. First, the edge server broadcasts the current global model to all devices. Second, the data importance is evaluated at each device, measured by the DII and denoted as $I_k$ for the $k$-th device. Finally, the device with largest DII is selected for data uploading. As in the preceding section, analog modulation is adopted for data transmission. The received data sample at the server is distorted by channel fading and noise. The distortion depends on the SNR, which can be calculated at both the server and devices, all of which have perfect CSI.

\begin{figure}[h]
\begin{center}
{\includegraphics[width=9cm]{fig7.pdf}}\\
\caption{An edge learning system with importance-aware scheduling.}
\vspace{-20pt}
\label{fig:7}
\end{center}
\end{figure}

\noindent{\bf Learning model:} As in the preceding section, binary soft-margin SVM model is considered. Prior to wireless data acquisition, the server has a coarse initial classifier that can be used for data-importance evaluation at the beginning and will be refined progressively in the training process. The importance of a noisy received data sample can be measured using its \emph{expected uncertainty}. Based the distance-based uncertainty measure introduced in the preceding section, the expected uncertainty is translated to the expected distance between the data sample and the current decision boundary of the classifier model.

\begin{figure}[h]
\begin{center}
{\includegraphics[width=8.5cm]{fig8.pdf}}\\
\caption{Effect of channel fading and noise on DII with unlabelled-data.}
\vspace{-15pt}
\label{fig:8}
\end{center}
\end{figure}

\noindent{\bf Importance-aware scheduling:} Targeting the scenario where labelling is costly, the data samples in the devices are assumed to be unlabelled. And the label is generated for the selected data after transmission to the server by recruiting a labeller. To design the scheduling scheme, the effect of channel fading and noise on the expected received data samples at the server is first analyzed, as illustrated in Fig. \ref{fig:8}, where ${\rm SNR}_k$ and ${\bf x}_{k,n}$ are the SNR and the $n$-th data sample of the $k$-th device, and $d({\bf x}_{k,n})$ is the distance between ${\bf x}_{k,n}$ and the decision boundary, respectively. The DII of the selected data sample in the $k$-th device, refers to the sample with the maximum expected uncertainty among the local data. In \cite{R44}, the DII is shown to have the following expression
\begin{equation}\label{eq:3}
I_k= -\frac{1}{{\rm SNR}_k}+\max_{n\in\mathcal{N}_k} {\mathcal{U}_{\sf d}\left({\bf x}_{k,n}\right)},
\end{equation}
where $\mathcal{N}_k=\{1,2,\cdots,N\}$ represents the sample index set, and $\mathcal{U}_{\sf d}\left(\cdot\right)$ is a distance-based uncertainty measure. One can observe that in the derived DII, both data uncertainty (the last term) and the channel quality (the SNR term) are in a simple addition form. The DII being a monotone increasing function of SNR is due to the fact that the channel fading and noise tend to degrade the importance of data samples by making their distances to the decision boundary more likely to be larger than smaller (see Fig. \ref{fig:8}). In other words, channel distortion harms the learning performance which is aligned with our intuition.

Based on the DII in \eqref{eq:3}, the scheduling scheme for binary SVM is to select the device with largest DII in each sample block, as described in Scheme 1.
\begin{framed}
\noindent{\bf Scheme 1} (Importance-aware scheduling without label information). Consider the acquisition of a data sample from multiple edge devices in an edge learning system. The edge server schedules device $k^*$ for data transmission if
\begin{equation}
k^*=\arg \max_{k}\;\left\{-\frac{1}{{\rm SNR}_k}+\max_{n\in\mathcal{N}_k} {\mathcal{U}_{\sf d}\left({\bf x}_{k,n}\right)} \right\}.
\end{equation}
\end{framed}
The design can be easily extended to a general classifier by replacing the distance-based uncertainty measure with a general measure. The criterion in Scheme 1 shows that simultaneous exploitation of multi-user data-and-channel diversity is required for learning performance improvement rather than a single type of diversity. Besides, the influence of the wireless transmission, i.e., the transmit SNR, on the scheduling criterion is interesting. When the wireless channels are unreliable, saying the SNR is low, the received data samples at the server are severely corrupted by channel noise and become useless regardless of their uncertainty (importance) before transmission. In this case, only multi-user channel diversity is exploited. When the SNR is large, it is more critical to exploit the data diversity, as there is little distortion of the received data samples.

The extension of Scheme 1 to \emph{convolutional neural network} (CNN) models can be found in \cite{R44} by essentially replacing the uncertain measure with one that fits CNN, e.g., entropy.

\noindent{\bf Performance:} Experiments are carried out to verify the performance gain of the importance-aware scheduling with respect to conventional schemes exploiting only a single type of multiuser diversity. The first benchmarking scheme, namely channel-aware scheduling, only utilizes the multiuser channel diversity and the other, namely data-aware scheduling, only exploits the multiuser data diversity. The experimental settings are as follows. There are $K=10$ edge devices in the system, each of which is equipped with a local buffer with the size $N=10$. The transmission budget $T$ for the binary SVM  learning task is 100 channel uses, each of which is for transmitting a single data sample. Rayleigh fading channels with unit variance are considered with the average transmit SNR=15 dB. The well-known MNIST dataset also used in previous experiments is adopted for training.

The test accuracies of models trained using different schemes are compared in Fig. \ref{fig:9}. One can observe that importance-aware scheduling can achieve signifiant improvement in test accuracy of about 5\% over channel-aware scheduling and of about 8\% over data-aware scheduling. Moreover, the model convergence of the new design is faster too.

\begin{figure}[h]
\begin{center}
{\includegraphics[width=7.5cm]{fig9.pdf}}\\
\caption{Learning performance evaluation for importance-aware scheduling.}
\vspace{-15pt}
\label{fig:9}
\end{center}
\end{figure}

\section{Importance-Aware Scheduling for Federated Edge Learning}
\subsection{Principle and Opportunities}
The previous designs of importance-aware scheduling for centralized edge learning can be extended to the paradigm of federated edge learning. The extension essentially involves changing the data-importance metrics to model variance and gradient divergence that suits federated learning. On the other hand, scheduling designs should also factor in some unique features of federated learning such as the following two.
\begin{itemize}
\item {\bf Update synchronization:} The key operation of averaging local updates (local gradients/models) at the server requires synchronization of updates by edge devices. To be specific, the duration of one communication round is determined by the slowest device in computing and communication. As a result, the learning latency can be excessive when the number of devices are many and they have high heterogeneity in computing capacities, channels, and local dataset sizes.
\item {\bf Communication-computation tradeoff and lazy updating:} Researchers have discovered a \emph{communication-computation tradeoff} that increasing local computation load can be traded for reduced communication overhead \cite{R45}. To be specific, increasing the number of rounds for only updating local models at devices allows the reduction of communication frequency for updating the global models, called ``lazy updating", without incurring significant performance loss.
\end{itemize}

Based on the above discussion, a design principle of importance-aware scheduling for federated edge learning can be proposed as follows.
\begin{framed}
\noindent{\bf Principle 3} (Principle of importance-aware scheduling for federated edge learning).
Targeting active wireless data acquisition for federated learning, the importance-aware scheduling should exploit 1) the {\bf multi-user diversity in channels and local updates (channel-and-data diversity)} and 2) {\bf communication-computation tradeoff} under the constraint of update synchronization to improve edge-learning performance.
\end{framed}

The fundamental changes on the scheduling principle compared with the conventional rate-maximization paradigm introduce many new challenges and give rises to many research opportunities. A few are described as follows.

\begin{itemize}
\item[1)] {\bf RRM for update synchronization:}  Due to the mentioned heterogeneity among edge devices, there exist \emph{``stragglers"} (slow devices) among them that can potentially slow down the learning process. To alleviate the bottleneck, one way is to design scheduling for allocating more bandwidth for transmission by stragglers and less for fast devices \cite{R46}. This to some extent can equalize their total latency (computing plus communication latency) and thereby facilitate update synchronization needed for federated learning. On the other hand, to avoid squandering bandwidth on extremely slow devices, scheduling should exclude slowest devices by applying thresholds on their computing capacities or channel capacities or both. Note that more updating devices lead to faster model convergence (in terms of the number of communication rounds) by exploiting a larger distributed dataset. Hence the said thresholds should balance the two conflicting effects of increasing the number of scheduled devices: 1) reducing the number of communication rounds and 2) increasing the computation-and-communication latency per round. In summary, RRM (e.g., scheduling and bandwidth allocation) can be designed by optimizing the number of scheduled devices based on the tradeoff to reduce the overall learning duration in seconds.

\item[2)] {\bf Solving the dilemma in lazy updating:} There exists a dilemma for lazy updating. Being too lazy in updating of the global AI model will reduce the average number of updating devices in each round and thereby compromise the learning performance. That, however, will reduce the total communication overhead (and hence latency) in each round. This creates a dilemma that will be solved by scheduling design. This requires a quantitative understanding of the dependence of the learning accuracy and latency (in seconds but not the number of communication rounds) on a few factors including the level of updating laziness, channel distortion and latency, number of devices, and the amount of radio resources. The task will require the interplay of communication theory and federated learning theory (e.g., SGD convergence analysis). The results will be applied to improve the previously developed algorithms of importance-aware scheduling to integrate the optimal level of laziness to minimize communication overhead. Thereby, communication latency for federated edge learning can be further reduced.
\end{itemize}

\subsection{Sketch of Two Example Designs}
There exist few results on importance-aware scheduling for federated edge learning that integrate RRM and learning. To help readers to better understand earlier discussion, we sketch two example designs with some concrete steps delegated to future investigation.

\subsubsection{Importance-aware scheduling for exploiting multiuser update diversity}  As mentioned, for federated learning, a local gradient with a larger norm or a local model with a larger variation (w.r.t. the global model) tend to contribute more significantly to the global model convergence \cite{R24}. In particular, the global loss function is observed to decrease approximately with the square of the global gradient norm, on which local gradients with larger norms have more influences. This justifies the use of gradient norm or model variation as an importance metric for scheduling. The aim of the scheduling design is to simultaneously exploit multiuser diversity in both channels and the local updates (gradient/model). The scheduling procedure and the open challenge are described as follows.

\begin{itemize}
\item {\bf Step 1 (Global Model Broadcasting):} At the beginning of each communication round, the edge server broadcasts the current global model to all devices.

\item {\bf Step 2 (Local Gradient/Model Calculation):} Based on the received model, each device uses local data to compute an updated local model (or a gradient for updating the model) using the backpropagation algorithm. Subsequently, the gradient norm (or model variation) can be computed.

\item {\bf Step 3 (Importance Indicator Uploading):} Each device reports the scalar importance indicator (gradient norm or model variation) and CSI to the server via some control channel.

\item {\bf Step 4 (Importance-Aware Scheduling):} By collecting the importance indicators and CSI from all devices, the edge server selects a subset of devices for uploading and allocates radio resources (bandwidth or time) for their transmission. Designing the scheduling policy can be formulated as a joint optimizaiton problem over user selection and bandwidth allocation for the goal of improving learning performance. Some suitable criteria can be maximizing the model test accuracy under a latency constraint or minimizing the training latency under an accuracy guarantee. A tractable solution approach hinges on the derivation of learning performance as a closed-form function of local updates and channel states. This remains largely an {\bf open problem}.

\item {\bf Step 5 (Local Update Transmission):} The scheduled devices then transmit their concrete gradient vectors to the edge server for gradient aggregation and global model updating.
\end{itemize}
The above five steps will be iterated till the global model converges.

\subsubsection{Energy-efficient scheduling for lazy updating:} Computing a local gradient/model update is an energy consuming process as it involves repeated backpropagation over a CNN model typical having millions to billions of parameters. One issue with existing scheduling schemes for federated edge learning is that it requires all devices to perform such computation but only selects a subset for transmission (see e.g., \cite{R46}) ). This is not energy efficient when the number of devices is large. One idea to improve the efficiency is to limit the computation of gradient/model updates to other scheduled devices. Then implementing the idea requires the design of a new scheduling metric. Consider lazy updating discussed earlier. One suitable design is the variation between the current global model and the local model a device transmits a number of rounds ago and stores in its memory, called \emph{model age indicator} (MAI). To be specific, in the $i$-th round, assume that the local model stored in the device $k$ is $\hat{w}_k^{(i)}$ with staleness of $\tau_k^{(i-1)}$  rounds, i.e., $\hat{w}_k^{(i-1)}=w_k^{(i-1-\tau_k^{(i-1)})}$. Given the current global model $w^{(i)}$, the MAI  is given as $\lVert \hat{w}_k-w^{(i)} \rVert$. The key advantage of using the MAI as a scheduling metric is it is unnecessary for a device to perform model uploading, which is complex and energy hungry, unless it is scheduled for uploading. Instead, a device need only perform the less complex computation of the MAI using the stored model and received global model, and then report the MAI to the server. Thereby, the total energy consumption of devices are reduced.

In the context of lazy updating, the motivation of scheduling devices with relative MAI is that their data are infrequently explored in the global model training and thus scheduling them can yield significant model improvements due to data diversity. On the other hand, it is undesirable to keep MAI too small as too aggressive exploitation of multiuser data diversity loses the ``laziness" needed for exploiting multiuser channel diversity.

Based on the above discussion, the procedure for energy efficient lazy updating is as follows.
\begin{itemize}
\item {\bf Step 1 (Global Model Broadcasting):} The server broadcasts the global model to all devices.

\item {\bf Step 2 (MAI Reporting):} Each device computes the MAI using a stored local model and the received global model. Then all devices transmit their MAI to the server.

\item {\bf Step 3 (Scheduling):} Using global MAI and CSI, the server schedules a subset of devices to upload the global model and allocates bandwidth for their transmission. The resource allocation policy can be formulated as an optimization problem for energy efficient  uploading based on their channel conditions and the time for transmission in a round. A tractable solution combines the energy consumption and learning performance as a closed-form function of channel conditions and computation capacities. This remains largely an {\bf open problem}.

\item {\bf  Step 4 (Local Model Updating and Transmission):} The scheduled devices update their local models and transmit them to the server using the allocated spectrums.

\item {\bf Step 5 (Global Update):} The edge server aggregates the gradients and updates the global model.
\end{itemize}
Again, the above steps will be iterated till the global model converges.

\section{Concluding Remarks}
Two 5G missions, namely gigabit access and tactile response (network response time of several milli-seconds), have not yet been fully realized.  On the one hand, the existence of massive number of subscribers and IoT devices congest the network and reduce the average access speeds. On the other hand, the latency of computing (at both devices and base stations), protocols (e.g., admission and routing), and round-trip wireless communication add up to multiply the total response time. The two missions will continue to drive the 6G development. As driven by the availability of massive mobile data, 6G will have a new mission of realizing ubiquitous computing and intelligence to support next-generation AI driven intelligent applications. This mission has resulted in the recent emergence of the new research area, edge AI. However, the full potential of edge computing and learning cannot be unleashed without gigabit access and tactile response. To tackle this challenge, the main approach of edge-AI research is to seamlessly integrate communication and learning theories. Importance-aware RRM represents a main thrust in this area. Advancements in this direction will make significant contributions towards realizing a communication-efficient intelligent network edge. Besides those discussed in the preceding sections, the importance-aware design principle can be also applied to other RRM techniques including spectrum allocation, power control, and multi-antenna transmission such that more bandwidth, power, and spatial degrees-of-freedom can be allocated to the uploading by devices with more important data.

redpajama_set_name: RedPajamaArXiv


WASHINGTON (AFP) - The Federal Reserve acknowledged on Wednesday its computer systems were accessed by hackers but said the incident did not affect the central bank's "critical operations."
The acknowledgement came days after the hacker group known as Anonymous claimed it had posted personal information of some 4,000 bankers, purportedly obtained from the Fed.
"The Federal Reserve System is aware that information was obtained by exploiting a temporary vulnerability in a website vendor product," a Federal Reserve spokesman said in a statement in response to an AFP query.
"The vulnerability was fixed shortly after discovery and is no longer an issue. This incident did not affect critical operations of the Federal Reserve System."
On Monday, an Anonymous-linked Twitter account called Operation Last Resort, claimed in a tweet to have obtained and posted "4k banker d0x via the FED."
The group argues it is taking actions responding to the suicide last month of Aaron Swartz, an Internet freedom advocate who was being prosecuted for illegally downloading millions of academic journal articles he had allegedly planned to distribute for free.
"This tragedy is basis for reform of computer crime laws, and the overzealous prosecutors," the Twitter account states.
The incident comes after the US Department of Energy confirmed it was the target of a cyber attack in January, which stole employee and contractor data.
The news also comes after revelations of high-profile cyber-attacks targeting US news media including The New York Times and The Wall Street Journal said to be originating from China.


text:
Keel laid for first Coast Guards Offshore Patrol Cutter Argus
2020 May 9 13:48
The keel laying ceremony for the US Coast Guard's, first of class, Offshore Patrol Cutter (OPC) ARGUS (WMSM-915), was held on April 28, 2020 at Eastern Shipbuilding Group's Nelson Street facility. The ceremony was performed and recorded without audience to comply with CDC guidelines to combat the spread of COVID-19, the USCG said in its news release.
The keel laying represents the ceremonial start of a ship's life by commemorating the assembly of the initial modular construction units. Historically, to attest that the keel was properly laid and of excellent quality, the shipbuilder would carve their initials into the keel. This practice is commemorated by welding the ship's sponsor's initials into the keel authentication plate.
The ship's sponsor is CAPT Beverly Kelley, USCG (Ret.). CAPT Kelley was the first woman to command a U.S. military vessel as the Commanding Officer of the 95-foot patrol boat, USCGC CAPE NEWAGEN in 1979. Throughout her distinguished career, she became the first woman to command both a medium endurance cutter and a high endurance cutter in USCGC NORTHLAND and USCGC BOUTWELL respectively.
Eastern's President Mr. Joey D'Isernia noted the following: "Eastern Shipbuilding Group is humbled and proud to have been chosen to build this next generation ship for the world's best Coast Guard, and we think today represents a milestone that all those involved in the program can be proud of.
The steel joined here today is unlike any you or I have seen before. This steel has been ravaged by 162 mph winds, generated by the 3rd most powerful hurricane to make landfall in this country's history. This steel has borne witness to a Pandemic that has caused fear and shaken our core.
But through all this, it remains sturdy, it remains resilient, and today it will join with other steel to become stronger, more defined, and more resolute. Today is representative of how we build, and of unwavering resolve in the face of adversity for a Coast Guard and a nation that deserves nothing less."
Joey D'Isernia was accompanied on the podium by CAPT Andrew Meverden, representing the USCG, and Mr. Bradley Remick, the expert welder charged with welding the sponsor's initials onto the ceremonial keel authentication plate.
The OPC is designed to conduct multiple missions in support of the nation's maritime security and border protection. The OPC will provide a capability bridge between the national security cutter, which patrols the open ocean in the most demanding maritime environments, and the fast response cutter, which serves closer to shore. The OPC design includes the capability of carrying an MH-60R or MH-65 helicopter and three operational Over The-Horizon small boats. The vessel is also equipped with a highly sophisticated combat system and C4ISR suite that will enhance capabilities to execute the service's missions.
On September 15, 2016, the U.S. Coast Guard exercised the option for Detail Design on Eastern Shipbuilding Group's OPC contract. Eastern Shipbuilding Group will construct the Offshore Patrol Cutters to replace the Medium Endurance Cutters currently in service. The contract includes the production of up to four vessels.
OPC Characteristics:
•Length: 360 feet
•Beam: 54 feet
•Draft: 17 feet
•Sustained Speed: 22 Plus knots
•Range: 8500 Plus nautical miles
•Endurance: 60 Days


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Q: the value of $e$ and the method of getting it We define e to be a number which satisfies the following condition
$$\lim _{a \to 0} \frac{e^a-1}{a}=1. $$
How did we arrive to the following from above equation
$$e=\lim _{n \to \infty} \bigg(1+\frac{1}{n}\bigg)^n ? $$
so that we get the value of n

A: The approach you mention is difficult, but possible. I have presented it in my blog post. The main steps are as follows:
1) Define $a^{b}$ (without using any logs or $e$) rigorously for $a > 0$ and any real $b$.
2) Show that $\lim_{a \to 0}\dfrac{x^{a} - 1}{a} = f(x)$ exists for all $x > 0$ and hence defines a function of $x$. This function is denoted by $\log x$ and $e$ is then a number such that $\log e = 1$.
3) With $\log x$ defined above we have the following properties: $\log(xy) = \log x + \log y, \log 1 = 0, \log(1/x) = -\log x, \log(x^{y}) = y\log x$.
4) $\lim_{x \to 0}\dfrac{\log(1 + x)}{x} = 1$
5) Putting $x = 1/n$ in above limit and get $\lim_{n \to \infty}\log\left(1 + \dfrac{1}{n}\right)^{n} = 1$ and noting that $\log e = 1$ we get $\lim_{n \to \infty}\left(1 + \dfrac{1}{n}\right)^{n} = e$.
Proof of 1), 2) and 4) is hard but not too hard.

A: It's easier to start from the first equation and prove that it's the same as the second one.
From
$$L := \lim _{a \to 0} \frac{e^a-1}{a}$$
set $e^a - 1 = t$, so that $a = \ln(1 + t)$:
$$L = \lim_{t \to 0} \frac{t}{\ln(1 + t)} = \lim_{t \to 0} \left(\frac{\ln(1 + t)}{t}\right)^{-1} = \lim_{t \to 0} \left(\ln\left[\left(1 + t\right)^{1/t}\right]\right)^{-1} = \left(\ln\left[\lim_{t \to 0} \left(1 + t\right)^{1/t}\right]\right)^{-1}$$
The last step is legit because both $1/x$ and $\ln x$ are continuous functions.
Now, recalling that $L = 1$ (from your first equation) we have that
$$\begin{align}
\ln\left[\lim_{t \to 0}\left(1 + t\right)^{1/t}\right] &= 1\implies\\
\lim_{t \to 0}\left(1 + t\right)^{1/t} &= e
\end{align}$$
Or, equivalently, with one last change of variable
$$e=\lim _{x \to +\infty} \left(1+\frac1x\right)^x.$$

redpajama_set_name: RedPajamaStackExchange


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Ivory Coast Violence: Testimonies of the Displaced
April 22, 2011 | Doctors Without Borders
In western Ivory Coast, many people who have fled brutal violence do not dare to return home.
Some 28,000 people have taken refugee in a camp while others are living outside in the bush. Doctors Without Borders/Médecins Sans Frontières (MSF) staff are working in the camp and also running mobile clinics to places where displaced people are sheltering.
These testimonials were collected in April, from people displaced by the brutal post-election violence in the region.
Ivory Coast: Elections Turn to War
Peter DiCampo
Peter DiCampo is a documentary photographer whose goal is to contribute his work to a dialogue on international development and perceptions of Africa. He began his career as a Peace Corps Volunteer...
Migrants, Displaced People and Refugees
Ivory Coast: The Aftermath
Conflict and Peace Building


The Himalaya - India's abode of snow!
The fifth contact of Lunar Eclipse!
Tortoise crawling near Ramnagar forest!
The Moon moving out of the Earth's Umbra!
Vanity thy name is sadhu!
Fifth contact, U4, Lunar Eclipse.
Approach to Everest Base Camp!
The largest land mammal - Elephant!
Large Green Barbet nesting in New Delhi!
A day in the life of the Himalaya: Ladakh and Uttarakhand in sunrise mode!
The heavenly state of Sikkim, in India!
Dancing Jalebis in hot oil!
Sparring Goral on the cliffs!
Making Ravana's head for the kill!


The SEND Local Offer brings together information that will be helpful to children and young people with special educational needs and/or disabilities (SEND) and their families.
Bramble Academy supports many children with a wide range of additional and special needs. For some children these needs are ongoing, for others it may be a shorter term interaction.
Some children come to our school with clearly identified needs whilst others may be seeking a better understanding of their difficulties as they grow older.
Our top priority is to ensure that the day to day teaching for our children is right, resulting in happy and confident children who move forwards with their learning and maximise their potential in every way possible. Through close and regular monitoring of progress, both academically and emotionally, and through close communication with parents we are able to target our support in a range of ways individually tailored for each child. This can include additional in-class support, small group support or even one-to-one support.
As well as providing a wide range of help in school we link closely with other outside agencies to provide support for our children and their families. We enjoy close links with the SFSS which include Speech and Language Service, the Communication and interactions team and Educational Psychologists. These services can provide advice and assessment when needed but also the reassurance to parents that school are catering well for our most vulnerable pupils.
If you have any urgent queries, please contact our SENDCo, Barbara Crawshaw, 01623 635 928.


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The Future of Longform Publishing
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Last June, Brookings launched the Brookings Essay, positioning Brookings near the front of the emergence of longform journalism in digital publishing. In the spirit of Brookings's commitment to high-quality, independent research, each Brookings Essay covers major topics of public policy by distinguished authors, including Brookings scholars. The intention of the Brookings Essay is to engage a wider audience in the most pressing policy issues facing the U.S. and the world.
On April 29, Brookings hosted a panel discussion with representatives from some of the foremost leaders in longform publishing to discuss their experiences and plans for longform in the future, and explore the impact of this platform on public policy and public debate. The participants included representatives from ESPN, The New York Times, Slate and The Washington Post.
This event coincided with the publication of the latest Brookings Essay, Stuart Taylor's "The Big Snoop: Life, Liberty, and the Pursuit of Terrorists." Each Brookings Essay can be found at www.brookings.edu/essay.
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text:
FIGHTING-ILLINI
UIS women lose conference opener
MARCIA MARTINEZ
Nearly each time the Missouri S&T Miners tried to pull away from the University of Illinois Springfield Prairie Stars in a women's basketball game Thursday, the Stars answered.
It wasn't until late in the second half that UIS failed to respond and the Miners capitalized. The Stars' first-ever Great Lakes Valley Conference game ended in a 76-57 loss at The Recreation and Athletic Center Thursday.
UIS (2-3 overall, 0-1 in the GLVC) rallied late in the second half, but came up short. Back-to-back baskets by junior Susan Coryell got UIS within 55-47 of the Miners with nine minutes 35 seconds remaining in the second half. The Stars would get no closer than eight points.
UIS missed four straight shots. The Miners rebounded each miss and scored on all four possessions for nine points.
"We went on some runs and did good, but they answered back," Coryell said. We just need to work harder on doing better on defense and blocking them out."
Missouri S&T scored 12 straight points and pulled away for good.
"We allowed them to have easy offensive possessions," UIS coach Marne Fauser said. "We didn't get out and do what we were supposed to do to make it tougher on them. We just allowed them to do what they wanted to do."
Andrea Downs capped the Miners' 12-0 run with a 3-pointer for a 67-47 lead at the 6:36 mark.
"That was an important stretch of the game," Missouri S&T coach Alan Eads said. "We did a good job of rebounding. Our defensive rebounding was a little better that stretch and we were patient in the offense. We shared the basketball and we got good shots. That was the key in that particular stretch."
The Miners (3-1, 1-0) had four players in double figures. Downs and Courtney Kemp led the team with 14 points apiece.
UIS junior forward Paulina Pogorzelski grabbed 12 rebounds and tossed in a game-high 20 points with 16 in the opening half. Sophomore center Erin Glogovsky added 14 points and nine rebounds. Coryell finished with 12 points.
Missouri S&T led from start from finish and was up 40-31 at halftime. The Miners dominated in the second half.
"We had nine offensive rebounds at halftime," Fauser said. "We had nine to finish the game. I was very pleased with our offensive rebounding in the first half.
"We've got to play together as a team and we've got to know that we're there to help each other out. We just didn't do that for 40 minutes."
UIS sophomore guard Kelly Thompson injured her right ankle with five minutes to go in the first half. She didn't return and left the court on crutches. Fauser said her status is day-to-day.
Marcia Martinez can be reached at 788-1547.


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Girls' soccer goes for gold to continue a 20-year legacy
Sophia Wu|December 19, 2016
Originally published on March 24, 2015
Senior mid-fielder Maetal Kogan preps an instep kick during the 2–1 victory against Tamalpais on March 3. Photo by Karina Huft
The varsity girls' soccer team is kicking off the season with a new head coach, a new 3–4–3 formation, and determination to continue their winning streak.
Head coach Gene Vrana is making a few changes to the team this season after being assistant coach for 16 years. Vrana plans to integrate a 3–4–3 formation into the team's practice regimen, with three backs, four mids, and three forwards. The 3–4–3 formation allows for maximum offense and is also easily convertible to defense. "That puts a bit of a challenge on the three backs, but it also sets us up for instant offense, with four midfielders and three forwards," he said. "Learning the rotation to cover for your teammate when she goes up is something that we need to work on."
The 3–4–3 formation allows for maximum offense and is also easily convertible to defense.
This season, the team will also put more emphasis on fundamentals."I want to see the strength of our team be manifested in a very dynamic offense, but also in a defense," Vrana said. "I'm anticipating a combination of success, but most importantly, improvement, over the season."
To achieve this success, the team members will have to ramp up their efforts. "We're definitely being pushed harder this year, and we have a lot more goals this year," sophomore defender Amanda Kallenburg said. "We're taking it more seriously and we're more committed."
Sophomore forward Amelia Streiffer weaves and sweeps past two Tamalpais players. Photo by Karina Huft
Commitment has indeed led to the success of Lowell girls' soccer. The Cardinals defeated the Washington Eagles last season 6–0 in the championship game with an aggressive offense. "I think last season, we developed an attacking approach that involved our defenders in the attack," Vrana said. "The offense was a total team offense. In whatever formation we play, that's really important, so that was effective last year."
The team has been around for almost 21 years and has won the championship title 19 times, losing only twice to the Lincoln Mustangs in 1996 and 1997. This season the Cardinals have been undefeated in the league, and Coach Vrana hopes to continue the team's legacy. "It's difficult when you have a team as strong and as successful as Lowell girls' soccer has been to get them to commit to working even harder to get even better," Vrana said.
Vars girls soccer wins 22nd consecutive AAA championship title with new coach
Vars girls soccer celebrates senior day with a 2-0 win over the Mission Bears
One woman, two jobs: Counselor takes on head coach title
Varsity girls soccer crowned champions
Junior midfielder Iryne Chu dribbles the ball while keeping it away from a Mission Bears defender on March 3 at the AAA Championship game at Washingto...
After win over Eagles, varsity girls soccer completes a perfect season
With eyes on the soccer ball, sophomore defender Shannon Li prepares to kick. Photo by Anita LiuThe varsity girls soccer team ended their last home g...


Nice SHADOW AND ACT post about Carl Franklin despite his attempts, not getting any feature film directing gigs since 2003.
Carl Franklin is one of my favorite directors (read my coverage of him here), and the fact that he can't get films to direct is a loss for everybody, especially film fans like myself.
Look to your house Hollywood! Look to your house!
Remembering Elizabeth Taylor : A life in pictures.
Others will speak on her as both actress and person, I will simply say that if you haven't seen her movies, for whatever reason, give them a try. I think you'll find in her work, regardless of whether or not the specific film speaks to you, a voracious talent who brought that passion to bear on film.
And I think there is much for a new generation to learn, from those oft scathing films and performances that remain of her.
Will always remain of her.
And taking the late, great Paul Newman's example, please reach out to people who matter to you and say how you feel about them now, when they can hear you. When it matters.
Family, friends, influences, inspirations, tell them now.
Through this blog I got to meet and speak to two people, and thank them for their work, who have since passed. I got the chance to say to them, rather than speak in memory of them, and that does make all the difference to both you and them.
Take 2 minutes today and thank someone who matters to you.


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You are here: Home » News » U.S. & World News » Latin American church leaders mark 50 years of 'option for the poor'
Latin American church leaders mark 50 years of 'option for the poor'
Catholic News Service | Cody Weddle | August 23, 2018	| 0 Comments
Pope Francis visits Hogar San Jose children's home in 2017 in Medellin, Colombia. Latin American church leaders will meet in Medellin Aug. 23-26 to commemorate the 50th anniversary of a landmark regional bishops' meeting that took place in the same city in 1968. CNS photo/Paul Haring
Latin American church leaders will meet in Medellin Aug. 23-26 to commemorate the 50th anniversary of a landmark regional bishops' meeting that took place in the same city in 1968.
The event will bring together hundreds of Catholic laypeople and religious from the region to reflect on the landmark bishops' conference that shifted the church's emphasis to the "preferential option for the poor."
"Celebrating 50 years is not just an important event for CELAM (Latin American bishops' council), but for the whole church of Latin America and the Caribbean," said Auxiliary Bishop Juan Espinoza Jimenez, CELAM secretary-general and a member of the central commission charged with planning the event. Other groups involved in the organization are the Confederation of Religious in Latin America and the Caribbean (CLAR), Caritas Latin America and the Archdiocese of Medellin.
Father Rigoberto Perez Garrido, CELAM's executive press secretary, said organizers expect up to 300 people to attend the congress.
"This took months of planning, together with several institutional teams from the various organizations," he said.
Attendees may choose from 22 working groups focused on specific areas of the church's evangelization in the region, including justice, peace and reconciliation; education; youth; the church and the poor; and mediums of social communication. The congress aims to reflect on the 16 documents produced from the original Medellin conference, which dramatically shifted the church's focus in region toward the poor majority.
"It was decided that dialogue must start with all of the poor, and that's why Medellin was so important," said Father Francisco Hernandez Rojas, regional coordinator of Caritas Latin America and the Caribbean, the umbrella organization for the church's charitable agencies in the region. "Medellin led us to connect with that impoverished world and learn how to work in those communities."
For Catholic groups like Caritas, which works directly with the region's poor, the Medellin conference "established a base of ideas" that continues to influence and inspire their work today, Father Hernandez said.
And the church's newfound focus on the poorest and societal inequalities was especially pertinent for Latin America, a region that by some accounts remains the world's most unequal. The decade of the '60s saw rapid, sustained economic growth around the world, but most of the new wealth in Latin America went to the region's elite.
The bishops in Medellin concluded that the church must work with the poor for their liberation from poverty, which "opened the horizon for the region," said Bishop Espinoza.
The official conclusion of the 1968 conference was that the "bishops couldn't remain indifferent given the tremendous social injustices in Latin America, which keeps the majority of our people in painful poverty, in many cases close to human misery."
And to commemorate the historic conference, participants in this congress will use the same philosophy of "see, judge, act," which the bishops used in 1968 for the elaboration of official documents.
Organizers plan to deepen the focus on the poorest in the region and find areas where the 1968 goals have not been met.
"This is a challenge to use the past to go forward, with energy and strength to construct a more promising future," said Father Hernandez.
Each working group will produce a document analyzing the church's progress and challenges going forward in their respective areas, using the 1968 conclusions as a guide. From September through December, the documents and commitments they contain will be reviewed, to be published as part of an official report from the congress.
"We want to reflect in the same way that reflection was used in Medellin. It must be a cultural, familial, societal reflection, using as a reference what happened 50 years ago," said Bishop Espinoza.
Tags: CELAM, Latin American bishops' council, Medellin conference, Option for the poor
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The weather is cold and snowy outside… So here is a bit of winter warmer, an overview from one of my typical working days of a summer in Germany.
7:30 – Monday morning, Wake up time. View out my window is the picturesque city of Konstanz, Germany. Getting dressed is super easy as there is no formal dress code at work- think Google style offices and company culture (we even have beanbags) Right jeans and a t-shirt it is then!
8.20 – Time to leave for work. Ill grab a croissant at one of the many many bakeries in the city centre. Konstanz is situated right on lake Bodensee ( a holiday destination) so the summer bike ride to work along the lake is beautiful. It usually takes me about 20 minutes to bike over the border to Switzerland where the offices are located.
8.40 – I arrive at work. Grab myself a tea and head into the office (the sun is rising over the alps – well that's not a bad view). I head to the office with some of the other interns as well as the rest of the international department.
9.00 – Time for today's first meeting. Where we plan as a team the upcoming content for social media. We prep the upcoming schedule and analyse any new trends etc.
10.00 – I can then begin to create the social media content, interns get A LOT of responsibly for their markets (myself being responsible for the UK) so you get the opportunity to be creative.
12.00 – Lunch time! There are 2 huge kitchens and an outdoor balcony here so today we are having a team BBQ. After which some of us go sunbathe by the lake or play table tennis or pool in the games room.
13.00 – 6.30 Back to work. We have an upcoming campaign running so the afternoon is full of research and meetings for it. I also have some of my regular tasks to complete. Posting on social media, reporting statistics, different CRM tasks. Additionally I am running my own project where I am responsible for optimising a section of the website. It's always busy here and day to day my schedule differs and is filled with a range of different tasks. Creating your own plan, managing your time and prioritising has been an extremely important skill I have had to learn and learn fast.
6.30 onwards. After a very busy day of work, all the interns head down to an outdoor bar by the harbour, where we finish the evening (like most) with a very large maß of beer!
So there is a little glimpse into what a working place abroad can be like (so much more than better whether).
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