text:
\section{Introduction} \label{sec:1_intro}

Phasor Measurement Units (PMUs) allow high-resolution insight into power systems dynamics through precise time-synchronized measurements \cite{PMU_OG}. In recent years, electric utilities have made great strides towards deploying PMUs in their networks and utilizing the reported measurements for wide-area situational awareness \cite{PMU_US}. Phasor measurements are used in both online (state estimation, remedial action schemes) and offline (model validation, contingency analysis, post-event diagnosis) applications \cite{onlinePMU},{\cite{jones2013synchrophasor}}, \cite{model_validation}. As shown in fig. \ref{fig:pmu}, to reach the point-of-use from the point-of-measurement, PMU data flows through various communication channels and intermediate data concentrators. Hence, the data is susceptible to channel congestion or component malfunction issues which lead to degraded information quality \cite{NASPI_data_quality}. Reliable measurements are critical to developing robust control and monitoring algorithms for the power grid, making fast and accurate data recovery critical as well.

Traditional model-based recovery methods are sensitive to the underlying model accuracy, and may need the knowledge of real-time network topology. \cmb{ Oftentimes, such methods assume the knowledge of transmission line parameters, and are adversely affected by inaccurate information \cite{Shi_lineparameters}. Another class of model-based methods use linear state estimation (LSE) for PMU data conditioning \cite{jones2013synchrophasor,LSE_WECC}. LSE-based data recovery is contingent on breaker status information and any error or latency in reporting may deteriorate performance \cite{WECC_thorp}.}  On the other hand, measurements from PMUs within a network exhibit spatial and temporal correlation that can be utilized to estimate missing samples without explicit knowledge of the power system model. Several recent papers have addressed model-agnostic PMU data recovery \cite{ tensor, tensor2, kalman, GEIRI, svd, PSCC_algo, MWang_Hankel}. Some of the proposed methods target imputation of data blocks \cite{GEIRI,tensor,tensor2}, while others are aimed at step-ahead prediction \cite{kalman, svd, PSCC_algo, MWang_Hankel}. Further, these recovery approaches broadly employ strategies based on - a) filtering \cite{kalman},  b) low rank matrix completion \cite{PSCC_algo,svd,GEIRI,MWang_Hankel}, or c) low rank tensor completion \cite{tensor,tensor2}.

\begin{figure}
    \centering
    \includegraphics[width=\columnwidth]{figures/pmu_schematic.pdf}
    \caption{PMU data flow from point-of-measurement to point-of-use}
    \label{fig:pmu}
    \vspace{-0.25in}
\end{figure}

In \cite{kalman}, the authors propose a kalman filter-based missing data estimation algorithm that predicts the value of an incoming sample using the last three measurements. The accuracy of this method deteriorates when more than three consecutive entries are missing. Moreover, as the algorithm processes one PMU channel at a time, information from other channels or nearby PMUs cannot be leveraged to reconstruct segments of consecutive missing data.
Matrix (tensor) estimation methods propose to  stack correlated PMU measurement channels together to construct matrices (tensors), whose low-rank property can be exploited to recover corrupt data. Tensor estimation methods are more computationally expensive, limiting their potential for real-time use. Methods to speed up tensor estimation have been explored in \cite{tensor,tensor2}.

In the matrix estimation (ME) area, various strategies have been put forth for stacking measurement channels. In \cite{GEIRI}, the channels are stacked rowwise, and an iterative alternating direction method of multipliers is used to fill missing measurements. In \cite{svd}, the channels are stacked columnwise, and the spatial correlation among PMUs is used to recover missing entries using singular value thresholding. Another variation that uses the temporal correlation among channels is shown in \cite{PSCC_algo}.  Since these methods process multiple PMU channels together, they are able to accurately recover missing data sequences on one channel using information from other devices. On the other hand, data prediction accuracy is severely affected by high noise content in any one channel. An online recovery method exploiting the low-rank property of the Hankel matrix constructed by overlapping segments of PMU data has been proposed in \cite{MWang_Hankel}. As columns in a Hankel matrix overlap, this approach faces the following drawbacks- a) repeated entries greatly increase the size of the Hankel matrix, thereby increasing computation burden, b) noise in the matrix elements are highly correlated, c) noisy entries are repeated multiple times affecting recovery accuracy.

To overcome the limitations discussed above, this paper proposes a novel technique for PMU data recovery. A sequence of PMU measurements is first transformed into a \textit{Page matrix} \cite{Page_OG}, and then recovered using a variation of the truncated singular value thresholding algorithm \cite{chatterjeeUSVT2015}. As the matrix columns consist of non-overlapping data segments, they are smaller in size than Hankel matrices and the problem of highly correlated noise in matrix entries is avoided. An optimal hard threshold is used for singular values; thus the matrix rank does not need to be explicitly estimated at every step, resulting in significant computational savings for online prediction. Two variations of the algorithm are proposed, a) an offline imputation method for archived PMU data, and b) an online one-step ahead prediction method. Performance of the Page matrix method is compared to the Hankel matrix method using the same estimation technique. Extensive numerical tests show that both methods have similar recovery accuracy, and the Page matrix method is computationally much faster.

The proposed algorithms can be applied to both univariate and multivariate time-series (both single-channel and multi-channel cases). Although using measurements from multiple PMUs translates to higher accuracy in data recovery, some use cases might warrant processing single channels. For instance, researchers may have access to limited PMU data due to their sensitive nature. Moreover, computation may be sped up by parallelly processing single measurement channels. This may be useful in cases where the streaming synchrophasor data is of superior quality, and significant data drops are not expected.

Contributions of this work may be summarized as follows. \textit{First}, we propose a model-agnostic method for recovering PMU measurements from noisy signals with data drops. The proposed methodology is fast, scalable, easy to implement, and poses minimal memory requirements, making it well-suited for real-time use.  \textit{Second}, the methodology is extended into two algorithms - a) an offline method intended for recovering archived data, and b) an online method for predicting the next measurement, aimed at real-time applications. \textit{Third}, through extensive numerical experiments on simulated and real data, effectiveness of the algorithms is verified. It is shown that the original measurement signals can be reconstructed with high accuracy even in the presence of additive noise and simultaneous data erasures across multiple channels.

The remaining paper is organized as follows. Section \ref{sec:2_a Prelim} describes the missing data recovery problem. Section \ref{sec:2_b algorithms} succinctly presents the online and offline recovery algorithms, and section \ref{sec: 3_experiments} illustrates their performance. Section \ref{sec:4_conclusion} concludes the paper and outlines future research directions.

\section{Problem Set-up}\label{sec:2_a Prelim}
\vspace{-0.1in}
In this section, we establish the mathematical set-up for the PMU data recovery problem and show how it relates to low-rank ME.
Standard mathematical notations are followed. Calligraphic symbols represent sets, lower case bold letters represent column vectors, and upper case bold letters denote matrices. All zero and all one vectors and matrices of appropriate size are denoted by $\mathbf{0}$ and $\mathbf{1}$ respectively.

\subsection{PMU Data Recovery Using Matrix Estimation}
\vspace{-0.02in}
Simply stated, PMUs are sensors deployed at different points of a power network to measure electrical quantities like voltage and current magnitudes, angles, frequency and rate of change of frequency. Measurements are time-synchronized and typically reported at 30 or 60 frames per second (fps). Due to the physical laws that govern power flow, measurements recorded by a PMU and its neighbors are correlated. Moreover, data within a channel is correlated in time. These spatial and temporal correlations may hence be utilized to recover missing and corrupt measurements.

Formally, the data recovery problem can be posed as follows. Consider a discrete-time setting with time instants indexed by $t\in\mathds{Z^+}$. Let us say that for each $t\in[1,2,\dots T]$, PMU $i$ records a measurement vector $\boldsymbol{x}_{i}(t)$ of length $c$, where $c$ is the number of measurement channels. Measurements may contain observation noise, and it is assumed that $\mathds{E}[\boldsymbol{x}_i(t)]=\boldsymbol{f}_i(t)$, where $\boldsymbol{f}_i(t)$ are the true values of system states. Although the underlying mean signal $\boldsymbol{f}_i(t)$ is strongly correlated in time, it is assumed that the per-step noise are independent mean-zero random variables with time-varying variance. Given some $\boldx_i(t)$, data recovery algorithms may be designed to address two goals: a) \textit{imputation} (estimate $\boldsymbol{f}_i(t)$ for $t\in[1,2,\dots T]$), and b) \textit{prediction} (estimate $\boldsymbol{f}_i(T+1)$).

Time-series data recovery is a well-studied problem that appears in different domains like econometrics, geosciences and healthcare.
Classical methods for time-series imputation and prediction have employed approaches such as hidden Markov and state-space models \cite{TSA_book}. Different deep neural networks (NN) have also been used \cite{TS_GAN,TS_RNN}. Recent work has shown that low-rank matrix estimation methods can provide simple, effective and computationally efficient means for time-series recovery \cite{TS_matrix,mssa}. This class of methods eliminates the training data requirement of NN models, and hence provide a generalized framework suitable for quick deployment.

The objective of ME is to recover a parameter matrix $\mathbf{M}$ from a partially observed signal matrix $\mathbf{X}$ with corrupt entries, where $\mathds{E}(\mathbf{X})=\mathbf{M}$. A detailed picture of the state-of-the-art is available from \cite{LMRC2,LMRC_review} and references therein. A key observation from ME literature is that matrix $\mathbf{M}$ can be reconstructed from partial and noisy observations by considering a low-rank approximation of the observed matrix. ME algorithms are fairly model-agnostic in terms of the structure of $\mathbf{M}$ and the distribution of $\mathbf{X}$ given $\mathbf{M}$. Therefore, PMU measurements can be transformed into matrices and recovered by applying ME methods to the transformed matrix. Truncated singular value decomposition (SVD) based matrix estimation methods are popularly used \cite{chatterjeeUSVT2015}.

\subsection{Matrix Transformation}\label{subsec:page}
\vspace{-0.02in}

Several methods have been proposed to transform time-series signals into matrices. A naive method involves simply stacking signals together \cite{svd,GEIRI,PSCC_algo}. Although empirically this approach has shown reasonable effectiveness, it cannot be used if very few measurement channels are available. Of course, this is not a pressing concern for a transmission network with many PMUs. But in some cases, it may be necessary to work with a limited number of measurement signals. For instance, researchers outside electric utilities may only have access to limited PMU data. Moreover, it may be desirable to process data from blocks of few PMUs in a parallel manner to speed up computation during real-time application.

\begin{figure}
    \centering
    \includegraphics[width=0.9\columnwidth]{figures/matrixify.pdf}
    \caption{Page and Hankel matrix construction from PMU measurements}
    \label{fig:matrixify}
    \vspace{-0.25in}
\end{figure}

An alternative approach described in \cite{MWang_Hankel} uses the Hankel matrix transformation. Overlapping segments of PMU data are placed side by side to form a Hankel matrix. That such matrices are approximately low-rank has been empirically verified in \cite{MWang_Hankel}. As the Hankel matrices contain repeated entries, they are large in size and noisy elements appear multiple times. Repetition of noisy entries may reduce data recovery accuracy and the large matrix size increases computation burden.

The limitations of Hankel matrices may be overcome by using Page matrices \cite{TS_matrix, mssa}. A Page matrix is constructed from observation vector $\boldx(t)$ by placing contiguous segments of size $L>1$ side by side as non-overlapping columns of the resultant matrix \cite{Page_OG}. A schematic description of the matrix transformation process is shown in fig. \ref{fig:matrixify}.
It can be seen that when a time-series of the same length is transformed, the Hankel matrix is much larger than the corresponding Page matrix. The low-rank property of Page matrices has also been examined in \cite{TS_matrix}. It is established that, in expectation, for a large class of processes, the generated Page matrix is either exactly or approximately low-rank. These proceeses include linear recurrent functions (LRF) described by $f(t)=\sum_{g=1}^G \alpha_g f(t-g)$, for some $G\geq1$. That power systems quantities such as bus voltages, line currents and frequency follow LRF has been previously concluded in literature. For example, it is posited that steady state power systems measurements at any instant are a linear combination of the last three measurements \cite{PMU_AR}. This result has also been used to deisgn the kalman filter-based data prediction and smoothing algorithm in \cite{kalman}.

The LRF nature of PMU measurements also helps in formulating a prediction algorithm. Once the low-rank approximation of the transformed Page matrix is obtained via some ME technique, the last row of this matrix can be expressed as a linear combination of the other rows. Therefore, future values can be forecast by applying linear regression to the approximate Page matrix.

\subsection{Optimal Singular Value Thresholding (OSVT)} \label{subsec:OSVT}

Various techniques exist for low-rank ME \cite{LMRC_review,LMRC2}. In the proposed model-agnostic recovery framework, no information about the rank of the Page matrices is available beforehand. Hence, a variation of the truncated SVD method that does not need matrix rank information has been used in this paper \cite{chatterjeeUSVT2015}. The optimal singular value threshold is chosen based on findings reported in \cite{optimal_singular_value}. The main steps in the estimation algorithm are detailed next in algorithm \ref{algo:OSVT}. It is assumed that missing data points in the observation matrix are preliminarily filled in by the last available observation.

\begin{algorithm}
\caption{Optimal Singular Value Thresholding (OSVT)}\label{algo:OSVT}
\begin{algorithmic}[1]
\State \textbf{Scaling: } Entries of the observation matrix $\mathbf{X}$ are scaled to lie in the interval -1 to 1. Let the scaled observation matrix be called ${\mathbf{Y}}$ with individual entries $y_{i,j}$. Mathematically, ${y}_{i,j} = ({x}_{i,j}-0.5(a+b))/0.5(b-a)$, where $a$ and $b$ are the minimum and maximum entries of $\mathbf{X}$ respectively.
\State \textbf{Singular value decomposition: } Let ${\mathbf{Y}}=\sum_{i=1}^m \sigma_i\boldsymbol{u}_i\boldsymbol{v}_i^T$ be the singular value decomposition of ${\mathbf{Y}}$. The singular values are given by $\sigma_i$; and $\boldsymbol{u}_i$ and $\boldsymbol{v}_i$ are the corresponding left and right singular vectors respectively.
\State \textbf{Singular value thresholding: } Choose a set $S$ of \textit{thresholded} singular values such that : $S:= \{\sigma_i>\sigma_{th}\}$, where the optimality threshold $\sigma_{th}$ is given by:
\[\sigma_{th} = \sqrt{2(\zeta+1)+\frac{8\zeta}{(\zeta+1)+\sqrt{\zeta^2+14\zeta+1}}}\]
Here, $\zeta = m/n$, where ${\mathbf{Y}}$ is a $m\times n$ matrix. Moreover, $m\leq n$. In the case that $m>n$, the estimation algorithm must be applied to $\mathbf{X}^T$ to obtain an estimate of $\mathbf{M}^T$.
\State \textbf{Low rank approximation: } The low rank approximation of matrix $\mathbf{Y}$ is given by $\mathbf{\hat{Y}}=\sum_{\sigma_i\in S} \sigma_i \boldsymbol{u}_i \boldsymbol{v}_i^T$. The final estimation $\hat{\mathbf{M}}$ of the parameter matrix is obtained by scaling back the values of $\hat{\mathbf{Y}}$ to the interval $[a,b]$.
\end{algorithmic}
\end{algorithm}

The hard singular value threshold proposed in \cite{optimal_singular_value} is optimal in an asymptotic sense. It is postulated that for large low-rank matrices, when a data singular value $\sigma_i$ is too small, the corresponding singular vectors $\boldsymbol{u}_i$ and $\boldsymbol{v}_i$ are very noisy and the component $\sigma_i \boldsymbol{u}_i \boldsymbol{v}_i^T$ should not be used in approximating matrix $\hat{\mathbf{Y}}$ from $\mathbf{Y}$. The cutoff for singular values is determined to be $\sigma_{th}$ as described in algorithm 1. The alternative method used in literature for estimating matrix rank involves- a) selecting a threshold for rank approximation error, and b) choosing the lowest rank for which the approximate matrix does not violate the predetermined error threshold. The choice of the approximation error threshold is somewhat arbitrary and has been empirically decided in works like \cite{MWang_Hankel}. Using a hard threshold eliminates the need for repeated calculations of rank approximation error at every step, thereby significantly improving computation speed. It is further shown in \cite{optimal_singular_value} that the optimally tuned thresholding method outperforms (in terms of mean squared error) classical truncated SVD when signal noise content is low to moderate; and the methods perform roughly similarly when noise content is high.

\subsection{Multivariate Time-Series Recovery} \label{subsec:stacked_page}
\vspace{-0.02in}
\begin{figure}
\vspace{-0.06in}
    \centering
    \includegraphics[width=0.89\columnwidth]{figures/stacked_matrix.pdf}
    \caption{Stacked Page matrix for multivariate data recovery}
    \label{fig:stacked_matrix}
    \vspace{-0.25in}
\end{figure}

As mentioned before, PMU measurements in a network are correlated, and hence information from different PMUs can be utilized to recover degraded data. Readings from multiple PMU channels can be transformed into a `stacked' Page matrix by concatenating individual Page matrices columnwise, as shown in fig. \ref{fig:stacked_matrix}. The low-rank property of stacked Page matrices for a large class of processes including LRF has been verified in \cite{mssa}.
Let $N$ be the total number of PMU measurement channels available. The data recovery process can now be summarized with the following steps: a) transform observation vectors $\boldsymbol{x}_i(t), i\in[1,2,\dots, N], t\in[1,2,\dots,T]$ to Page matrices $\mathbf{P}_i, i\in[1,2,\dots,N]$, each with dimension $L\times T/L$, by placing non-overlapping contiguous data segments of length $L>1$ (an algorithmic hyperparameter) side-by-side as columns; b) concatenate the individual Page matrices columnwise to form a stacked Page matrix $\mathbf{X}$ of dimension $L\times (NT/L)$; c) perform OSVT (algorithm 1) on matrix $\mathbf{X}$ to obtain a denoised estimate $\hat{\mathbf{X}}$; d) learn a forecasting model that expresses the last row of $\hat{\mathbf{X}}$ as a linear combination of its remaining rows. The in-sample imputation and prediction error for this method scales as $1/\sqrt{NT}$ \cite{mssa}

\section{Data Recovery Algorithms} \label{sec:2_b algorithms}
\vspace{-0.06in}
This section shows how the individual pieces described in the previous section are put together for recovering degraded PMU data. The algorithms can be applied to both single-channel and multi-channel data using suitable Page matrices.

\subsection{Offline Data Imputation}
\vspace{-0.02in}
Let us consider the problem of denoising already recorded PMU measurements and imputing missing readings. Assume $n$ number of PMUs, each with $c$ measurement channels. Then the total number of data channels available is $N=n\times c$.
{The observations are partitioned into say $k$ windows of length $T$ each. Note here that for the imputation task, hours of data can be processed at once. Thus, $T$ can be quite large. It is assumed here that $T$ is perfectly divisible by the value of $L$ chosen.}
The sequential steps to be performed for offline data imputation are listed in algorithm 2.

\begin{algorithm}[h!]
\caption{Offline PMU data imputation}\label{algo:offline}
\begin{algorithmic}[1]
\State{\textbf{Initialization:} Set $T\leftarrow$ window length, $N\leftarrow$ number of PMU channels, $k\leftarrow$ number of data windows.}
\State {\textbf{For} $j = 1:k$, \textbf{do}}
\State \hspace{8pt} {\textbf{Matrix transformation:} Construct a stacked Page matrix using data from $N$ PMU channels in the $j^{th}$ measurement window with $T$ observations, as described in section \ref{subsec:stacked_page}.}
\State\hspace{8pt} {\textbf{Low-rank matrix estimation:} Obtain a low-rank approximation of the stacked Page matrix $\hat{\mathbf{X}}$ using the OSVT method outlined in algorithm \ref{algo:OSVT}.}
\State\hspace{8pt}{\textbf{Recover estimated measurements:} Reshape matrix $\hat{\mathbf{X}}$ to recover the estimated measurements.}
\State {\textbf{End for}}
\end{algorithmic}
\end{algorithm}

\subsection{Online Data Prediction}
\vspace{-0.02in}
The online forecast problem pertains to predicting the signal value $\boldsymbol{f}(T+1)$ given past observations $\boldsymbol{x}(t), t\in[1,2,\dots,T]$. This is analaogous to performing regression with noisy data. The online forecasting algorithm proposed in this paper- \textit{first}, denoises and imputes past observations (algorithm \ref{algo:offline}), and \textit{second}, uses linear regression to learn the relationship between the last row and remaining rows of the imputed observation matrix. Next, the learned regression parameters are used to predict the next sample from a Page matrix shifted by one sample. Of course, the first data window of length $T$ needs to be filled before next-step prediction can proceed. The forecast procedure is described with better clarity in algorithm \ref{algo:online}.

\begin{figure} [t!]
    \centering
    \includegraphics[width=0.8\columnwidth]{figures/regression.png}
    \caption{Visual description of matrices $\mathbf{G},\mathbf{H}, \mathbf{G'}$ and $\mathbf{H'}$ for a Page matrix using data from a single channel}
    \label{fig:reg}
     \vspace{-0.1in}
\end{figure}

\begin{algorithm}[h!]
\caption{Online PMU data prediction}\label{algo:online}
\begin{algorithmic}[1]
\State {\textbf{Initialization:} Set $T \leftarrow$ window length, $N \leftarrow$ total number of PMU channels, $j\leftarrow 0$}.
\State {\textbf{While} PMU data streams are available, \textbf{do}:}
\State \hspace{8pt} {\textbf{Matrix formation:} Convert measurement vectors $\boldsymbol{x_i}(t+j)$, $i\in[1,2,\dots N]$, $t\in[1,2,\dots T]$ to a stacked Page matrix $\mathbf{X_{T+j}}$, say. }

\State \hspace{8pt} \textcolor{black}{\textbf{Matrix imputation:}
Using algorithm \ref{algo:offline}, denoise and impute $\mathbf{X_{T+j}}$ to obtain ${\mathbf{\hat{X}_{T+j}}}$. }

\State \hspace{8pt} {\textbf{Learn the linear forecast model:} Partition matrix $\mathbf{\hat{X}_{T+j}}$ into two parts $\mathbf{G}$ and $\mathbf{H}$ such that $\mathbf{G}$ comprises of the first $L-1$ rows in $\mathbf{\hat{X}_{T+j}}$ and $\mathbf{H}$ contains the last. Linear regression here pertains to estimating the parameter vector {$\boldsymbol{\beta_j}$} for which $\mathbf{H}=\mathbf{G}{\boldsymbol{\beta_j}}+\boldsymbol{\epsilon}$ in the least squares sense. }

\State \hspace{8pt} {\textbf{Forecast the one-step-ahead data:} Construct matrix $\mathbf{G'}$ with the last $L-1$ rows of $\mathbf{\hat{X}_{T+j}}$. Estimate $\mathbf{H'}$ from $\mathbf{G'}$ as $\mathbf{H'}=\mathbf{G'}\boldsymbol{\beta_j}$ using the value of $\boldsymbol{\beta_j}$ learnt in step 5.
For the univariate prediction case, the last entry of $\mathbf{H'}$ is the prediction of the next measurement $x(T+j+1)$. For the multivariate case, pertinent entries from $\mathbf{H'}$ need to be extracted. For clarity, a visual description of the matrices $\mathbf{G},\mathbf{H}, \mathbf{G'}$ and $\mathbf{H'}$ is provided in fig. \ref{fig:reg}}.

\State \hspace{8pt} {\textbf{Update:} Set $j\leftarrow j+1$}
\State {\textbf{End while}}
\vspace{-2pt}
\end{algorithmic}
\end{algorithm}

\begin{figure*}[h!]
\centering
    \begin{minipage}[t]{0.32\textwidth}
    \centering
    \vspace{0pt}
    \includegraphics[width=0.9\columnwidth]{figures/V_mag.png}
    \caption{PMU measurements: Positive sequence voltage magnitude}
    \label{fig:PMU_V}
    \end{minipage}%
    \begin{minipage}[t]{0.32\textwidth}
    \centering
    \vspace{0pt}
    \includegraphics[width=0.9\columnwidth]{figures/V_ang.png}
    \caption{PMU measurements: Positive sequence voltage angle (unwrapped)}
    \label{fig:PMU_A}
    \end{minipage}%
    \begin{minipage}[t]{0.32\textwidth}
    \centering
    \vspace{0pt}
     \includegraphics[width=0.9\columnwidth]{figures/F.png}
    \caption{PMU measurements: Frequency}
    \label{fig:PMU_F}
    \end{minipage}%
    \vspace{-0.2in}
\end{figure*}

\subsection{Choice of Hyperparameters}

{Selecting \textit{good} hyperparameters is essential for achieving high-accuracy data recovery while minimizing computation time. For the data recovery algorithms proposed in this work, two main hyperparameters need to be chosen- a) $L$ or the number of rows in the Page matrix, and b) $T$ or length of data window. }

{$\bullet$\textit{ Choice of $L$}: Empirically, it was observed that choosing a $L$ value in the 5-10 range yielded good results for both the online prediction and offline imputation tasks. Keeping the parameter $L$ small enables capturing the short-term temporal patterns in PMU data. However, for very noisy data, increasing $L$ can help in obtaining smoother estimates.}

{$\bullet$ \textit{Choice of $T$}: The in-sample imputation and prediction error for the multivariate data recovery method scales as $1/\sqrt{NT}$.
Therefore, the longer the data window, the better the prediction accuracy. On the other hand, choosing a long data window increases computation time. As computation time is not a prime concern for offline data imputation, a fairly long window can be chosen. In the numerical results section of this paper, data imputation with $T=54000$ (30 minutes of data) has been demonstrated .}

{Computation time is of greater concern when it comes to online prediction, as every prediction step requires a matrix estimation and linear regression operation. Hence, choosing a shorter time window is beneficial. However, the window length $T$ should be selected carefully. If $T$ is too small, prediction accuracy will be impacted by measurement noise. If $T$ is too large, the data window may contain obsolete modes thereby degrading prediction accuracy. It was empirically observed that a data window of about $\sim$ 30-45 samples yielded good performance without unduly increasing prediction time.}

{\subsection{Scalability} The size of the Page matrix will also be determined by the number of PMU channels available. In a real system with hundreds of field PMUs, computation may be sped up by dividing the PMUs into groups with similar modal signatures and processing the groups in parallel. Grouping together PMUs geographically close to each other will also enhance visibility into `local' dynamics which might have been obscured by aggregating signals over a wide-area grid. Some strategies for grouping PMU signals to ensure low-rankness of the measurement window have been presented in literature \cite{PMU_grouping}. }

During a disturbance, the system deviates from its predicted behavior, and the low-rank property of the stacked Page matrix may not hold true. Therefore, at the onset of a disturbance, online predictions may vary greatly from observed measurements. The difference between the actual observations and algorithm predictions decreases gradually.

\section{Numerical Results} \label{sec: 3_experiments}
\vspace{-0.06in}
This section describes the numerical tests performed to validate the performance of the proposed imputation and prediction methodologies. The first set of tests are performed on simulated data, artificially distorted by the injection of additive noise and random data drop. The next set of tests considers real noisy PMU measurements recorded by a U.S. utility. in this case, the \textit{true values} of the measurements are unknown, but visual inspection reveals that reasonable values are predicted for swathes of missing data. All computations are performed on a PC with 16 GB RAM and 2.6 GHz Intel core i7-9750HF processor.

\subsection{Simulated Measurements Dataset}
\vspace{-0.04in}
Numerical tests were performed on 86.6 seconds of measurements from PMUs installed at ten generator bus terminals of the IEEE 39-bus transmission model\cite{dataport}.  Quasi-steady state operations and three-phase faults were recorded using RTDS power systems simulator and GTNETx2 based PMUs at 60 fps reporting rate. During the length of the simulation, quasi steady-state conditions were simulated by modulating the mechanical torque of generator $G_1$ every 200 ms by a random perturbation within $\pm 1\%$ of the nominal value. The data also shows three disturbances. At 18.33 seconds, a self-clearing three-phase fault is followed by tripping of the faulted line, leading to a topology change. At 55.67 seconds, the tripped line is reconnected, restoring the initial network topology. At 78.13 seconds, another three-phase self-clearing three-phase fault takes place.

In this study, three measurement channels from each PMU were used - positive sequence voltage magnitude, positive sequence voltage angle and frequency. Data from all ten PMUs are shown in figures \ref{fig:PMU_V}, \ref{fig:PMU_A} and \ref{fig:PMU_F}. PMUs are referred to by the generator terminal they are installed at. For example, the PMU at generator $G_1$ terminal is called PMU $G_1$. Voltage angle at PMU $G_1$ is considered as the reference angle.

Simulated measurements have been used for evaluating the data recovery algorithms as the `\textit{ground truth}' data is available for comparison. On the other hand, in real PMU measurements, some readings may already be missing or corrupt, and there is no way of \textit{exactly knowing} what those measurements should have been. Further, as this simulation records network topology changes, we can investigate if varying topologies affect recovery accuracy.

\subsection{Data transformation}
\vspace{-0.05in}
The PMU measurements are scaled before being transformed into the stacked Page matrix described in section \ref{subsec:stacked_page}. The scaling process used in this paper is described below:\\
$\bullet$ \textit{Voltage magnitude}: Measurements were transformed into the per unit (p.u.) system.\\
$\bullet$ \textit{Voltage angle}: The reference voltage angle is subtracted from individual channel data. In the dataset used, angle readings were already unwrapped. For unwrapping angles in real-time, the strategy outlined in \cite{unwrap_angle} may be followed.\\
$\bullet$ \textit{Frequency}: Frequency measurements were scaled as follows: $f_{scaled} = (f_{measured}-60)\times 10 $.

The scaling method described above empirically showed good results; however other approaches may also be used.

\subsection{Error Metric}\vspace{-0.04in}
Mean absolute percentage error (MAPE) has been used as the error metric to evaluate the accuracy of the proposed algorithms. Mathematically, MAPE for a time-series of length $n$ maybe expressed as:
\begin{align*}
    MAPE = \frac{1}{n}\sum_{t=1}^n \bigg| \frac{A_t-\hat{A_t}}{A_t} \bigg|
\end{align*}
Here, $A_t$ is the actual time-series value and $\hat{A_t}$ is the corresponding prediction. As it intuitively conveys relative error, MAPE is widely used in regression problems and model evaluation tasks.

\begin{figure}
    \centering
    \includegraphics[width=0.8\columnwidth]{figures/MAPE_offline_drop.png}
    \caption{Error in $G_2$ PMU channels with simultaneous data drop in all PMU channels (median over 20 runs)}
    \label{fig:MAPE_drop}
    \includegraphics[width=0.8\columnwidth]{figures/MAPE_offline_noise.png}
    \caption{Error in $G_2$ PMU channels with zero-mean additive noise on all $G_2$ PMU channels (median over 20 runs)}
    \label{fig:MAPE_noise}
    \vspace{-0.2in}
\end{figure}

\subsection{Offline Data Imputation}\label{subsec:offline_data_impu}

\begin{figure*}
    \centering
    \begin{minipage}[t]{0.33\textwidth}
    \subfloat[Positive sequence voltage magnitude]{\includegraphics[width=\textwidth]{figures/Vmag_recovered.png}}\\\vspace{-0.1in}
    \end{minipage}%
    \begin{minipage}[t]{0.33\textwidth}
    \centering
    \subfloat[Positive Sequence voltage angle (referenced)]{\includegraphics[width=\columnwidth]{figures/Vang_recovered.png}}\\\vspace{-0.1in}
    \end{minipage}%
    \begin{minipage}[t]{0.33\textwidth}
    \centering
    \subfloat[Frequency]{\includegraphics[width=\columnwidth]{figures/F_recovered.png}}
    \end{minipage}%
    \vspace{0.04in}
    \caption{Imputed measurements with 50\% simultaneous missing data and 2\% additive noise on all $G_2$ PMU channels }
    \label{fig:imputed_G2}

    \begin{minipage}[t]{0.33\textwidth}
    \centering
    \subfloat[Positive sequence voltage magnitude]{\includegraphics[width=\columnwidth]{figures/Vmag_recovered_online.png}}\\
    \end{minipage}%
    \begin{minipage}[t]{0.33\textwidth}
    \centering
    \subfloat[Positive Sequence voltage angle (referenced)]{\includegraphics[width=\columnwidth]{figures/Vang_recovered_online.png}}\\
    \end{minipage}%
    \begin{minipage}[t]{0.33\textwidth}
    \subfloat[Frequency]{\includegraphics[width=\columnwidth]{figures/F_recovered_online.png}}
    \end{minipage}
    \vspace{0.04in}
    \caption{Predicted measurements with 50\% simultaneous missing data and 2\% additive noise on all $G_2$ PMU channels }
    \label{fig:predicted_G2}
    \vspace{-0.2in}
\end{figure*}

As communication channel congestion may impact all PMU channels, data erasures may be correlated. To capture the efficacy of the proposed imputation method under realistic data degradation conditions, the following modes were checked:

$\bullet$ \textit{Data drop}: Simultaneous data drops on all PMU channels in the network were considered. A fraction of timestamps (determined by the chosen data drop rate) were randomly selected and corresponding measurements were dropped from all PMU channels. As the data drop rate is increased, the chance of missing consecutive data segments also increases. Error on all channels of PMU $G_2$ as the data drop rate is varied is shown in fig. \ref{fig:MAPE_drop}. These are median values of observations over 20 runs. It is evident that the measurements can be reconstructed with acceptable accuracy. Time taken for imputation did not vary significantly with data drop rate and median time taken over 100 runs was 0.0184 seconds. In the interest of brevity, only results for PMU $G_2$ has been included in this paper, but similar results were obtained for other PMU channels as well.

Results for the extreme scenario where readings from all PMUs are missing are shown here. For \textit{less extreme} cases, i.e. when data from only some of the PMU channels are missing, higher accuracy in signal reconstruction may be expected.

$\bullet$ \textit{Additive noise}:
{Noise in PMU measurements may arise due to errors in calibration, instrumentation and quantization. Existing studies suggest that the zero-mean gaussian distribution is a suitable model to characterize this noise. The signal-to-noise ratio (SNR) for real transmission-level PMUs is estimated to be around $\sim$45 dB, while for distribution-level PMUs the SNR is estimated to be lower \cite{PMU_noise}. Similar noise was injected into PMU $G_2$ channels for the numeric tests in this work. }

Zero-mean gaussian noise was added to all PMU $G_2$ channels. The standard deviation of the noise distribution on each channel was given by a percentage of the median of true steady-state data (let us call this percentage the \textit{noise rate}). Data recovery error with varying noise rates is shown in fig. \ref{fig:MAPE_noise}. Median computation time over 100 runs was 0.0192 seconds.

For both the cases above, the number of rows in the stacked Page matrix was 10. Fig. \ref{fig:imputed_G2} shows both the corrupt and imputed data when 2\% noise was added to the PMU $G_2$ channels and 50\% of the readings were missing. It can be seen that the PMU signals are reconstructed with reasonable accuracy even when consecutive data segments are missing. Further, the data recovery accuracy is robust to topology changes in the power network.

\begin{figure*}
    \centering
    \includegraphics[width=0.8\textwidth]{figures/online_missing.png}
    \caption{Prediction error in $G_2$ PMU channels with simultaneous missing data on all $G_2$ PMU channels (median over 20 runs)}
    \label{fig:pred_missing}
    \includegraphics[width=0.8\textwidth]{figures/online_noise.png}
    \caption{Prediction error in $G_2$ PMU channels with additive noise on all $G_2$ PMU channels (median over 20 runs)}
    \label{fig:pred_noise}
    \vspace{-0.1in}
\end{figure*}

\subsection{Online Data Prediction}
Similar numerical tests were conducted with the same PMU dataset for assessing online data prediction accuracy. Performance of the stacked Page-matrix based prediction algorithm has been compared with the Hankel-matrix based prediction method put forth in \cite{MWang_Hankel}. For better comparison, the same ME technique is used for both algorithms.

$\bullet$ \textit{Prediction error}: Figures \ref{fig:pred_missing} and \ref{fig:pred_noise} show the prediction error for different data drop rates (simultaneous) and additive noise on all $G_2$ PMU channels. The results are median observations over 20 runs. Data drops and noise were introduced in the data in the same manner as discussed in section \ref{subsec:offline_data_impu}. It is observed that the prediction error of the Page matrix method is similar to/slightly better than the Hankel matrix based method. The corrupt and reconstructed signals when 50\% data drop and 2\% noise is added to all $G_2$ PMU channels is shown in fig. \ref{fig:predicted_G2}. In the experiments, number of rows used was 5, and window length considered was 25.

$\bullet$ \textit{Prediction time}: One-step ahead predictions have multiple applications. Missing samples can be filled in with predicted values. Similarly, irregularities in data may be detected looking at how far  measurements stray from their predictions. Now, for any real-time algorithm implementation, computation time is of prime concern. U.S. electric utilities typically use PMUs with reporting rates of 30 or 60 fps. For these PMUs, the time intervals between two consecutive samples is 0.0333 or 0.0167 seconds. Therefore, in order to predict a sample before it arrives at the control center, the prediction time must be much lower.

Our numeric tests showed that the prediction time for the proposed Page matrix algorithm was $\sim$0.001 seconds. In comparison, time taken by the Hankel matrix based method was $\sim$0.003 seconds. All times are median values recorded over 100 runs. The prediction times did not vary significantly with varying rates of data drop or noise. Thus, we see that the method proposed in this paper is much faster than the Hankel-matrix based method, and provides similar/slightly better accuracy.

{$\bullet$ \textit{Window length of Hankel matrix:} The preceding set of experiments showed that the proposed Page matrix-based data recovery method provided accuracy levels similar to the Hankel matrix-based method, while speeding up computations. The computational savings are largely due to the smaller size of the Page matrix for the same measurement window. A natural question arises here: how would using a shorter time window for the Hankel matrix method affect data recovery accuracy? It is expected that predictions obtained using a smaller number of observations will be noisy and less accurate. This notion is experimentally verified in this work.}
\begin{figure*}
\centering
\includegraphics[width=\textwidth]{figures/3methods_missing.png}
\caption{\cmb{Prediction error in $G_2$ PMU channels with simultaneous missing data on all $G_2$ PMU channels (median over 20 runs)}}
\label{fig:Hankel_long_short}
\vspace{-0.15in}
\end{figure*}

{Figure \ref{fig:Hankel_long_short} shows how the recovery accuracy varies when data is dropped simultaneously from all channels of PMU $G_2$ using the same methodology as section \ref{subsec:offline_data_impu}. Three matrix transformations were checked, a) Page matrix (dimensions $5\times 6$), b) Hankel matrix with longer window (dimensions $5\times 26$), and c) Hankel matrix with shorter window (dimensions $5\times 6$). For the first two cases, measurement window length used for predicting the next sample is $T=30$, while for the third case it becomes $T=10$. As the Page matrix and Hankel matrix with shorter window have the same dimensions, time taken to predict the next sample using these matrices is almost the same. However, as evident from figure \ref{fig:Hankel_long_short}, the Page matrix method yields higher recovery accuracy. When using a Hankel matrix with longer window, the prediction accuracy improves, but computation time increases as well.}

\begin{figure}
    \centering
    \includegraphics[width=\columnwidth]{figures/ranks.png}
    \caption{Matrix rank for different data windows}
    \label{fig:ranks}
    \vspace{-0.2in}
\end{figure}

$\bullet$ \textit{Verifying the low rank-property}: The low rank properties of both the stacked Page and Hankel matrices were checked for all the data windows, as shown in fig. \ref{fig:ranks}. It can be seen that both the Page and Hankel matrices are generally low-rank, and the matrix ranks increase at the beginning of events. During the first event, the Hankel matrix becomes full-rank, and the low-rank property does not hold.

\subsection{Real PMU measurements dataset} \vspace{-0.05in}
Next, we check how well the proposed algorithms perform with real PMU data from an anonymized U.S. electric utility. The data corresponds to 30 minutes of measurements (54000 samples) from four PMUs of the utility, each of which reports three channels- positive sequence voltage magnitude, positive sequence voltage angle, and frequency. PMU reporting rate is 30 fps. The voltage angle of PMU4 is considered as reference, since it has the least amount of missing entries. Voltage angles have been unwrapped using the algorithm from \cite{unwrap_angle}.

The recorded measurements were quite noisy, and had large patches of missing data. The percentage of missing entries, and maximum length of consecutive missing data segments in each channel is shown in fig. \ref{fig:dom data quality}. It can be seen that the PMU channels have data missing in the $\sim$20-40\% range. Maximum length of missing data segments is $\sim$100. The noisy and intermittent PMU measurements are shown in fig. \ref{fig:domPMU}, and the imputed measurements are shown in fig. \ref{fig:cleandom}. Since there is no way to know what the actual measurements should have been, objectively evaluating the imputation algorithm is not possible. However, visual inspection shows that the proposed algorithm is able to impute the measurements very well. Median computation time to impute 54000 measurement samples over 20 runs was 0.109 seconds.

{Figure \ref{fig:cleandomHankel} shows the imputed measurements when using the Hankel matrix method (in algorithm 2, measurements are transformed into a stacked Hankel matrix in place of a Page matrix). Visually, it appears that the Hankel method does not provide better estimates than the Page method. Moreover, time taken for imputation using the Hankel method was $\sim 1.74$ seconds, much higher than the Page method.}

{Further, additional $2\%$ noise was injected into the channels of PMU1 and recovered using the proposed offline imputation method using Page matrix. The noisy and imputed data is shown in figure \ref{fig:domPMUnoisy}. It can be inferred that the proposed imputation method is able to recover data from real noisy PMU archives.}

\begin{figure}
    \centering
    \includegraphics[width=\columnwidth]{figures/data_quality.png}
    \caption{Data quality in the real PMU dataset}
    \label{fig:dom data quality}
    \vspace{-0.2in}
\end{figure}

\begin{figure*}
\centering
\includegraphics[width=\textwidth]{figures/domPMU.png}
\caption{Thirty minutes of measurements from four PMUs in an anonymized U.S. electric utility. Data is reported at 30 fps. The vertical lines show data drops.}
\label{fig:domPMU}
\includegraphics[width=\textwidth]{figures/cleanPMU.png}
\caption{Imputed PMU data using Page matrix}
\label{fig:cleandom}
\includegraphics[width=\textwidth]{figures/domPMUHankel.png}
\caption{\cmb{Imputed PMU data using Hankel matrix}}
\label{fig:cleandomHankel}
\vspace{-0.1in}
\end{figure*}

\begin{figure*}
\centering
\includegraphics[width=\textwidth]{figures/dom_noisy.png}
\caption{\cmb{Imputed readings for PMU1 after additional noise is injected into its channels}}
\label{fig:domPMUnoisy}
\vspace{-0.08in}
\end{figure*}

\section{Conclusion} \label{sec:4_conclusion}

In this work, a simple model-agnostic data recovery method based on low-rank matrix approximation has been proposed for improving the quality of phasor measurements with additive noise and data drop. The method is applicable for both single and multiple measurement channels; and can deal with simultaneous and consecutive data drop on all channels. Two variations  of  the  recovery  algorithm  are  shown-  a)  an  offline  block-processing method   for   imputing   past   measurements,   and   b)   an   online method for predicting future measurements. The performance of the proposed algorithms have been illustrated through extensive numeric experiments on simulated measurements on the IEEE 39-bus test system. It is seen that the proposed methodology has high accuracy, has low memory requirement and is computationally faster than other methods in literature. The performance of the algorithm is independent of the underlying system model, topology changes, and measurement noise distribution. Tests on real PMU data validate the performance of the data recovery strategy put forth in this work. The fast computation speed and ease of implementation make the algorithms developed in this work suitable for quick deployment.

redpajama_set_name: RedPajamaArXiv


The core project is the main Falcon system. It contains the Falcon engine, the basic command line tools (as the compiler/interpreter) and the RTL module.
It is commonly released together with the "Feathers" module, so this project never releases project-specific packages.


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text:
Q: Hint oracle to use indexes on the subquery -- Oracle SQl I have a query as follows
select *
from
( select id,sum(amt) amt from table_t group by id
) t inner join table_v v on (v.id = t.id)
order by t.amt desc;

table_t has no index and has 738,000 rows and table_v has an index on id and has 158,000 rows.
The query currently fetches the results in 10 seconds.
The explain query plan shows a full table scan.. How can I improve the performance here ?
If I add an index on id for table_t will it help. Because I am using it in a subquery ?

A: If you have an index on (id,amt) you would minimise the work in the group by/summation process (as it could read the index). If both columns are nullable then you may need to add a "where id is not null" so it will use the index. [That's implied by the later join on id, but may not get inferred by the optimizer.]
Next step would be to use a materialized view for the summation, maybe with an index on (amt,id) (which it could use to avoid the sort). But that is refreshed either at a commit or on request or at scheduled intervals. It doesn't help if you need to do this query as part of a transaction.
Both the index and the materialized view would add work to inserts/updates/deletes on the table but save work in this query.

redpajama_set_name: RedPajamaStackExchange


text:
D. R. Smith (David R.)
Sawflies (Hymenoptera: Symphyta) in a juniper-oak-grassland habitat in southern Arizona.
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A new species of Xiphydria Latreille (Hymenoptera: Xiphydriidae) reared from river birch, Betula nigra L., in North America.
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A new species of Diprion (Hymenoptera: Diprionidae) damaging Pinus spp. in Korea.
S. Cho (Soowon)
J. Han
The Nearctic sawflies of the genus Hemitaxonus Ashmead (Hymenoptera: Tenthredinidae).
Taxonomic changes in the Tenthredinidae (Hymenoptera, Symphyta).
Extended distribution for Pristiphora abbreviata (Hartig) (Hymenoptera: Thenthredinidae).
Two sawflies new to North America (Hymenoptera: Tenthredinidae).
New synonymy in Pleroneura Konow (Hymenoptera: Xyelidae).
A review of the subfamily Heterarthrinae in North America (Hymenoptera: Tenthredinidae).
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The genus Susana Rohwere and Middleton (Hymenoptera: Tenthredinidae).
The genus Craterocercus Rohwer (Hymenoptera: Tenthredinidae).
Symphyta of the West Indies, including those collected during the Bredin-Archbold-Smithsonian biological survey of Dominica (Hymenoptera).
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A new species of Strongylogaster (Hymenoptera: Tenthredinidae) from North America.
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First food plant record for Lagideus Konow (Hymenoptera: Pergidae), a new species feeding on Fuchsia and Ludwigia (Onagraceae) in Argentina.
S. G. Bado
Review of the eastern United States species of the leaf-folding sawflies of the genus Phyllocolpa Benson (Hymenoptera: Tenthredinidae).
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Rhadinoceraea n. sp. (Hymenoptera: Tenthredinidae) from West Virginia, a second species on Zigadenus (Liliaceae).
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Filacus, a new genus for four species of sawflies previously placed in Macrophya or Zaschizonyx (Hymenoptera: Tenthredinidae).
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Food plants and life histories of sawflies of the families Tenthredinidae and Pergidae (Hymenoptera) in Costa Rica, with descriptions of four new species.
A new Rhadinoceraea (Hymenoptera: Tenthredinidae) feeding on Zigadenus (Liliaceae) from southeastern United States.
W. McDearman
Review of southeastern Asian sawfly genus Eusunoxa Enslin (Hymenoptera: Tenthredinidae).
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A new species of Conaspidia Konow (Hymenoptera: Tenthredinidae) from India and review of the Indian species.
A new genus and species of Allantinae (Hymenoptera: Tenthredinidae) from southeastern United States.
T. L. Schiefer
The stem-boring sawfly genus Cephus Latreille (Hymenoptera: Cephidae) in Japan.
A new Janus (Hymenoptera: Cephidae) from Quercus, and a key to North American species.
J. D. Solomon
Rediscovery of the perreyiine genus Barilochia Malaise (Hymenoptera: Pergidae) in South America.
A new species of Sericoceros Konow (Hymenoptera: Argidae) damaging billetana trees, Triplaris caracasana Cham. (Polygonaceae) in Paraguay.
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New synonymy and combinations in sawflies (Hymenoptera: Symphata).
New sawflies of the genera Dielocerus Curtis and Themos Norton from South America (Hymenoptera: Argidae).
Sawflies of the tribe Pseudodineurini in North America (Hymenoptera: Tenthredinidae).
Sawflies of the Holarctic genus Patycampus Schiodte (Hymenoptera: Tenthredinidae).
Liliacina diversipes (Kirby) (Hymenoptera: Tenthredinidae), a sawfly genus and species new to the United States.
Urocerus sah (Mocsary) (Hymenoptera: Siricidae) new to North America and key to North American species of Urocerus.
Review of the sawfly genus Lagium (Hymenoptera: Tenthredinidae).
The sawfly genus Nematinus in North America (Hymenoptera: Tenthredinidae).
Flight records for twenty-eight species of Macrophya Dahlbom (Hymenoptera: Tenthredinidae) in Virginia, and an unusual specimen of E. epinota (Say).
New records for Eriotremex (Hymenoptera: Siricidae) from southeast Asia and New Guinea.
Studies on the leaf-mining sawflies of the tribe Fenusini in Asia (Hymenoptera: Tenthredinidae).
Nepionema, a nematine sawfly genus new to North America, and an unusual new species of Nematus (Hymenoptera: Tenthredinidae).
The larva of Lagium atroviolaceum (Norton) (Hymenoptera: Tenthredinidae).
Seasonal flight activity of Vanhornia eucnemidarum Crawford (Hymenoptera: Vanhorniidae) in the mid-Atlantic states.
Two new species of Gilpinia (Hymenoptera: Diprionidae) feeding on Pinus kesiya in Thailand.
The first record of Nematus Panzer from South America: a new species from Argentina (Hymenoptera: Tenthredinidae).
The Rohwer sawfly types (Hymenoptera: Symphyta) in the University of Nebraska State Museum.
Xiphydria prolongata (Geoffroy) (Hymenoptera: Xiphydriidae) adventive in North America.
Symphyta (Hymenoptera) of Sri Lanka.
Collections of Stephanidae (Hymenoptera) in the Mid-Atlantic States including an Eastern record for Schlettererius cinctipes (Cresson).
North American sawflies described by Klug and Konow (Hymenoptera: Symphyta).
Dr. Marion Russell Smith, a bibliography.
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Conifer sawflies, Diprionidae: key to North American genera, checklist of world species, and new species from Mexico (Hymenoptera).+
Aulacidae (Hymenoptera) in the Mid-Atlantic states, with a key to species of eastern North America.
The sawfly genus Periclista in Korea and Taiwan (Hymenoptera: Tenthredinidae).
Nearctic species of the genus Ptenus Kirby (Hymenoptera: Argidae).
Sawflies of the genus Croesus Leach in North America (Hymenoptera: Tenthredinidae).
Nearctic sawflies. III. Heterarthrinae: adults and larvae (Hymenoptera: Tenthredinidae).
Checklist of the Pergidae (Hymenoptera: Symphyta) of the Western Hemisphere, with a new genus and two new species.
Nearctic sawflies. I. Blennocampinae: adults and larvae (Hymenoptera: Tenthredinidae).
Nearctic sawflies. II. Selandriinae: adults (Hymenoptera: Tenthredinidae).
Key to genera of Nearctic Argidae (Hymenoptera) with revisions of the genera Atomacera Say and Sterictiphora Billberg.
A new Nearctic Xyela causing galls on Pinus spp. (Hymenoptera: Xyelidae).
Nearctic sawflies of the genera Neoptilia Ashmead, Schizocerella Forsius, Aprosthema Konow, and Sphacophilus Provancher (Hymenoptera: Argidae).
A new Gilpinia from China (Hymenoptera: Diprionidae).
The South American sawfly genus Acidiophora Konow (Hymenoptera: Tenthredinidae).
The sawfly tribe Lycaotini in South America (Hymenoptera: Tenthredinidae).
Suborder Symphyta.
Nearctic sawflies. IV. Allantinae: adults and larvae (Hymenoptera: Tenthredinidae).
A new pine sawfly from Thailand (Hymenoptera: Diprionidae).
Notes on sawflies (Hymenoptera: Symphyta) with two new species and a key to North America Loderus.
Symphyta (Hymenoptera: Pergidae, Argidae, Tenthredinidae) collected at the Reserva Ecológica do IBGE, Brasília, DF.
List of the Symphyta (Hymenoptera) of Israel, with description of four new species.
The berry and rose stem-borers of the genus Hartigia in North America (Hymenoptera: Cephidae).
A new species of Anoplonyx (Hymenoptera: Tenthredinidae) feeding on larch in northern Japan.
A new Profenusa (Hymenoptera: Tenthredinidae) from red oak, with keys to the adults and known larvae of the Nearctic species.
A synopsis of the sawflies (Hymenoptera, Symphyta) of America south of the United States: Argidae.
A new species of Janus Stephens (Hymenoptera: Cephidae) from Indonesia.
Rediscovery of Corynophilus pumilus (Klug), and a new genus and two new species of Symphyta from South America (Hymenoptera, Pergidae & Xiphydriidae).
A new species of Janus (Hymenoptera: Cephidae) from Indonesia.
A synopsis of the sawflies (Hymenoptera: Symphyta) of America south of the United States: Tenthredinidae (Allantinae).
The Nematus "magus group" (Hymenoptera: Tenthredinidae) in North America.
A new sawfly (Hymenoptera: Pergidae) feeding on guava, Psidium guajava L. (Myrtaceae), in Costa Rica.
Review of the genus Acordulecera Say (Hymenoptera: Pergidae) of the West Indies, and the first records of Symphyta from Montserrat and St. Kitts.
A new sawfly genus from India for the "forgoten" Periclista bumasta Konow, 1907 (Hymenoptera: Tenthredinidae).
Review of the cypress and juniper sawflies of the genus Susana Rohwer and Middleton (Hymenoptera: Tenthredinidae).
The abbotii and erythrogaster groups of Nematus Panzer (Hymenoptera: Tenthredinidae) in North America.
The xiphydriid woodwasps of North America (Hymenoptera: Xiphydriidae).
Identification of the Acordulecera "potato" sawflies of Peru and Bolivia, with descriptions of these and related species from South America (Hymenoptera: Pergidae).
Pergidae (Hymenoptera) from New Guinea and Australia in the Bishop Museum.
A new species of the leafmining sawfly genus Metallus (Hymenoptera: Tenthredinidae) from eastern North America.
A synopsis of the sawflies (Hymenoptera: Symphyta) of America south of the United States: introduction, Xyelidae, Pamphiliidae, Cimbicidae, Diprionidae, Xiphydriidae, Siricidae, Orussidae, Cephidae.
The sawfly genus Arge (Hymenoptera: Argidae) in the Western Hemisphere.
A new Xyela (Hymenoptera: Xyelidae) from western United States.
A new species of Xiphydriidae (Hymenoptera) from Chile.
A synopsis of the sawflies (Hymenoptera: Symphyta) of America south of the United States: Tenthredinidae (Nematinae, Heterarthrinae, Tenthredininae).
A new species of Derecyrta Smith (Hymenoptera: Xiphydriidae) from Colombia and Ecuador.
Two new fern-feeding sawflies of the genus Aneugmenus Hartig (Hymenoptera: Tenthredinidae) from South America.
Xiphydriidae of the Philippines, insular Malaysia, Indonesia, Papua New Guinea, New Caledonia, and Fiji (Hymenoptera).
New species of Argidae and Pergidae (Hymenoptera) from Central America.
Superfamily Formicoidea.
A new genus and species of Allantinae (Hymenoptera: Tenthredinidae) from Brazil.
Review of the Gasteruptiidae (Hymenoptera) of eastern North America.
The genera Macroxyela Kirby and Megaxyela Ashmead (Hymenoptera: Xyelidae) in North America.
Sawflies (Hymenoptera: Symphyta) in urban environments in the Washington, D.C. area.
Recognition of two species in the pine feeding "Neodiprion fulviceps complex" (Hymenoptera: Diprionidae) of western United States.
M. R. Wagner (Michael R.)
Review of the sawfly genus Eriocampidea (Hymenoptera: Tenthredinidae).
J. H. Lawton (John H.)
Notes on the systematics and natural history of Dielocerus fasciatus (Enderlein) and key to species of the genus (Hymenoptera: Argidae).
J. Adis
Two new species of ants of the genera Tapinoma Foerster and Paratrechina Motschoulsky from Puerto Rico (Hymenoptera: Formicidae).
R. J. Lavigne (Robert J.)
A new trigonalid wasp (Hymenoptera: Trigonalidae) from eastern North America.
I. C. Stocks (Ian C.)
A new species of Heterarthrus Stephens (Hymenoptera, Tenthredinidae) leafmining Salix spp. in Japan.
A fossil Siricidae (Hymenoptera) from Argentina.
P. Fidalgo
Review of the Australian subfamily Pteryperginae (Hymenoptera: Symphyta: Pergidae).
J. Macdonald
The sawfly genus Kambaitina Malaise (Hymenoptera: Tenthredinidae) in India.
V. Vasu
The genus-group names of Symphyta (Hymenoptera) and their type species.
M. Abe (Masaki)
Pamphilius middlekauffi Shinohara and Smith, new species, for "Pamphilius ocreatus" of authors (Hymenoptera: Pamphiliidae).
Description and life histiry of a new species of Nematus on Robinia hispida in New York.
D. C. Darling (D. Christopher)
Revision of the 'ophrynopine' genera Argentophrynopus gen. n., Guiglia Benson, Kulcania Benson, Ophrella Middlekauff, Ophrynon Middlekauff, Ophrynopus Konow, and Sitrocorsia Konow (Hymenoptera: Orussidae).
L. Vilhelmsen (Lars)
The Australian species of the subfamily Pergulinae, with descriptions of two new Pergula Morice species (Hymenoptera: Symphyta: Pergidae).
Records of Cephidae (Hymenoptera) from China and southeastern Asia with two new species of Janus Stephens.
F.-S. Huang
Revision of the southeastern Asian sawfly genus Busarbia Cameron (Hymenoptera: Tenthredinidae).
An annotated systematic world catalogue of the Pergidae (Hymenoptera).
Description and life history of a new species of Nematus (Hymenoptera: Tenthredinidae) on Robinia hispida (Fabaceae) in New York.
Two new species, larval descriptions, and life history notes on some Panamanian sawflies (Hymenoptera: Argidae, Tenthredinidae).
L. S. Kimsey (Lynn S.)
Review of the southeastern Asian sawfly genus Anapeptamena Konow (Hymenoptera: Tenthredinidae).
T. P. Saini
Selandriinae, a subfamily of Tenthredinidae new to Australia, and a review of other Australian Tenthredinidae (Hymenoptera: Symphyta).
Four new sawflies from eastern North America, three species of Tenthredo and one of Dolerus (Hymenoptera: Tenthredinidae).
H. Goulet (Henri)
Revision of the genus Indostegia Malaise (Hymenoptera: Tenthredinidae) in India.
Catalog of Hymenoptera in America north of Mexico. Volume 3. Indexes.
K. V. Krombein (Karl Vorse)
P. D. Hurd (Paul D.)
New Tab Download
Checklist of the sawflies (Hymenoptera: Symphyta) of India.
S. M. Blank (Stefan M.)
Review of the genus Eutomostethus Enslin (Hymenoptera, Tenthredinidae, Blennocampinae) from India, with new species and a key to species.

redpajama_set_name: RedPajamaCommonCrawl


text:
W. B. Yeats: A Life, Volume II: The Arch-Poet 1915-1939
by R. F. Foster
The first volume in Roy Foster's magisterial biography of W.B. Yeats was hailed as "a work of huge significance" (The Atlantic Monthly) and "a... Read more
stupendous historiographical feat" (Irish Sunday Independent). Now, the eagerly awaited second volume explores the complex poetic, political, and personal intricacies of Yeats's dramatic final decades, a period that saw the Easter Rebellion, the founding of the Irish state in 1922, and the production of Yeats's greatest masterpieces. In the conclusion of this first fully authorized biography, Foster brilliantly illuminates the circumstances--the rich internal and external experiences--that shaped the great poetry of Yeats's later years: "The Wild Swans at Coole," "Sailing to Byzantium," "The Tower," "The Circus Animals Desertion," "Under Ben Bulben," and many others. Yeats's pursuit of Irish nationalism and an independent Irish culture, his continued search for supernatural truths through occult experimentation, his extraordinary marriage, a series of tempestuous love affairs, and his lingering obsession with Maud Gonne are all explored here with a nuance and awareness rare in literary biography. Foster gives us the very texture of Yeats's life and thought, revealing the many ways he made poetry out of the "quarrel" with himself and the upheaval around him. But this consummate biography also shows that Yeats was much more than simply a lyric poet and examines in great detail Yeats's non-poetic work--his essays, plays, polemics, and memoirs. The enormous and varied circle of Yeats's friends, lovers, family, collaborators and antagonists inhabit and enrich a personal world of astounding energy, artistic commitment and verve; while the poet himself is shown returning again and again to his governing preoccupations, sex and death. Based on complete and unprecedented access to Yeats's papers and written with extraordinary grace and insight, W.B. Yeats, A Life offers the fullest portrait yet of the private and public life of one of the twentieth century's greatest poets.
Fundamentals of Biochemistry: Life at the Molecular Level
Experiments in Biochemistry: A Hands-on Approach...
The Official Laboratory Research Notebook (100 duplicate...
Publisher: Jones & Bartlett Learning


text:
Nick Jones, Digital producer
Published: January 31, 2019, 10:09 pm
Tags: Recalls, News, Consumer
Publix issues popcorn chicken recall
Publix Super Markets on Thursday issued a voluntary recall for its popcorn chicken, which is commonly sold in the deli at its grocery stores.
Publix said the popcorn chicken was sold in both its hot and refrigerated sections of its stores all across Florida. Some stores in Georgia were also affected.
According to Publix, the product may contain "foreign material."
The products were sold between Jan. 17 - 31. No other chicken products were affected by the recall, Publix said. All of the questionable products were removed from the shelves.
Customers who have purchased the product in question may return the product to any store for a full refund.
Nick Jones
Lifetime Jacksonville resident, journalist and experienced broadcast news producer with a passion for classic and exotic cars.


text:
namespace Merchello.Core.Gateways.Taxation
{
    using Merchello.Core.Models;

    using Umbraco.Core;

    /// <summary>
    /// Defines an invoice taxation strategy base class
    /// </summary>
    public abstract class TaxCalculationStrategyBase : ITaxCalculationStrategy
    {
        /// <summary>
        /// The invoice.
        /// </summary>
        private readonly IInvoice _invoice;

        /// <summary>
        /// The tax address.
        /// </summary>
        private readonly IAddress _taxAddress;

        /// <summary>
        /// Initializes a new instance of the <see cref="TaxCalculationStrategyBase"/> class.
        /// </summary>
        /// <param name="invoice">
        /// The invoice.
        /// </param>
        /// <param name="taxAddress">
        /// The tax address.
        /// </param>
        protected TaxCalculationStrategyBase(IInvoice invoice, IAddress taxAddress)
        {
            Mandate.ParameterNotNull(invoice, "invoice");
            Mandate.ParameterNotNull(taxAddress, "taxAddress");

            _invoice = invoice;
            _taxAddress = taxAddress;
        }

        /// <summary>
        /// Gets the <see cref="IInvoice"/>
        /// </summary>
        protected IInvoice Invoice
        {
            get { return _invoice; }
        }

        /// <summary>
        /// Gets the tax address
        /// </summary>
        protected IAddress TaxAddress
        {
            get { return _taxAddress; }
        }

        /// <summary>
        /// Computes the invoice tax result
        /// </summary>
        /// <returns>
        /// The <see cref="ITaxCalculationResult"/>
        /// </returns>
        public abstract Attempt<ITaxCalculationResult> CalculateTaxesForInvoice();
    }
}

redpajama_set_name: RedPajamaGithub


Samsung will be the main supplier of Apple's upcoming A9 chip that will power the next-generation iPhone, reports South Korean newspaper Maeil Business (via Reuters). The newspaper notes that Samsung will supply around 75% of chips for the next iPhone, and that the processors will be produced at the company's factory in Austin, Texas. Apple's A8 chip Last month, a report from Korea's ET News said that Samsung had begun work on the processor in Texas. Previous reports noted that Samsung and Taiwan Semiconductor Manufacturing Company (TSMC) would be producing the A9 chip, although Samsung was chosen to be the primary supplier in a deal that was said to be worth billions. BusinessKorea reported last month that Apple would be relying more heavily on Samsung for iPhone 6 and Apple Watch components including RAM, NAND flash storage, and batteries. Apple's A9 chip is expected to power the iPhone 6s and presumably the next-generation iPad Air and iPad mini. Apple is also expected to launch a larger-screened iPad Pro at some point this year, although that device has been rumored to utilize Apple's A8X processor.
Apple CEO Tim Cook met with a top Chinese government official in Beijing Wednesday to discuss the security of user data, reports Reuters. The meeting comes after web censorship blog Great Fire claimed earlier this week that hackers worked with Chinese authorities to harvest Apple ID information from Chinese users visiting iCloud.com. Yesterday, Apple issued a statement acknowledging the attacks on its servers and launched a new browser security guide on its website. The guide stressed the importance of digital certificates, asking users to check for any certificate warnings in their browser and ensure that they are connected to iCloud.com versus a malicious third-party website that resembles the service's homepage. China has become an increasingly important market for Apple, as the company now has eleven retail stores in the country and sells the iPhone on all three major wireless carriers. Apple also launched the iPhone 6 and iPhone 6 Plus in China last Friday following a week of successful pre-orders. Note: Due to the political nature of the discussion regarding this topic, the discussion thread is located in our Politics, Religion, Social Issues forum. All forum members and site visitors are welcome to read and follow the thread, but posting is limited to forum members with at least 100 posts.
Apple In Talks to Roll Out HealthKit to Medical Professionals Across U.S.


text:
DXC Technology Delivers Fourth Quarter Growth in Revenue, Earnings per Share, Margins, and Cash Flow
Richard Adamonis
Jonathan Ford
Q4 Earnings per Share was $1.93, including the cumulative impact of certain items of $(0.35) per share, reflecting restructuring costs, transaction, separation and integration-related costs, amortization of acquired intangible assets, pension and OPEB actuarial and settlement gains, and a tax adjustment related to U.S. tax reform
Q4 Non-GAAP Earnings per Share was $2.28
FY18 Earnings per Share was $6.04, including the cumulative impact of certain items of $(1.90)
FY18 Non-GAAP Earnings per Share was $7.94
FY18 Net Cash from Operating Activities was $3,243 million
FY18 Adjusted Free Cash Flow was $2,427 million
TYSONS, Va., May 24, 2018 - DXC Technology (NYSE: DXC) today reported results for the three and twelve months ended March 31, 2018.
"In fiscal 2018, DXC successfully executed on our strategic roadmap, including the integration of CSC and HPE Enterprise Services, achievement of our first-year financial objectives, and a strengthened leadership position in digital transformation," said Mike Lawrie, DXC's chairman, president and CEO. "Revenue in the quarter grew year-over-year and sequentially, and we delivered more than $1.1 billion dollars of in-year savings. We continue to invest in our digital capabilities and strategic partnerships, and we achieved strong growth in digital this year. Looking ahead, we expect to complete the Perspecta transaction next week, and we have positioned DXC Technology to deliver EPS and margin expansion in fiscal 2019."
Financial Highlights - Fourth Quarter Fiscal 2018
Diluted earnings per share was $1.93 in the fourth quarter, including $(0.50) per share of restructuring costs, $(0.33) per share of transaction, separation and integration-related costs, $(0.37) per share of amortization of acquired intangible assets, $0.55 per share of pension and OPEB actuarial and settlement gains, and $0.30 per share of tax adjustment related to U.S. tax reform. This compares with $(1.05) in the year ago period.
Non-GAAP diluted earnings per share was $2.28.
Revenue in the fourth quarter was $6,294 million compared with $1,889 million in the year ago period. Revenue grew 4.3% compared with $6,036 million in the prior year on a pro forma combined company basis.
Income before income taxes was $661 million for the fourth quarter, including $(208) million of restructuring costs, $(124) million of transaction, separation and integration-related costs, $(153) million of amortization of acquired intangibles and $203 million of pension and OPEB actuarial and settlement gains. This compares with $(187) million in the year ago period.
Non-GAAP income before income taxes was $943 million compared with $548 million in the year ago period on a pro forma combined company basis.
Net income was $565 million for the fourth quarter, including $(145) million of restructuring costs, $(97) million of transaction, separation and integration-related costs, $(108) million of amortization of acquired intangibles, $161 million of pension and OPEB actuarial and settlement gains, and $88 million of tax adjustment related to U.S. tax reform. This compares with $(138) million in the prior year period.
Non-GAAP net income was $666 million.
Adjusted EBIT was $1,017 million in the fourth quarter compared with $615 million in the prior year on a pro forma combined company basis. Adjusted EBIT margin was 16.2% compared with 10.2% in the year ago quarter which is presented on a pro forma combined company basis.
Net cash provided by operating activities was $701 million in the fourth quarter, compared with $173 million in the year ago period.
Adjusted free cash flow was $557 million in the fourth quarter.
Financial Highlights - Fiscal 2018
Diluted earnings per share was $6.04 in fiscal 2018, including $(2.06) per share of restructuring costs, $(1.00) per share of transaction, separation and integration-related costs, $(1.37) per share of amortization of acquired intangible assets, $0.60 per share of pension and OPEB actuarial and settlement gains and $1.94 per share of tax adjustment related to U.S. tax reform. This compares with $(0.88) in the year ago period.
Revenue in fiscal 2018 was $24,556 million compared with $7,607 million in the year ago period. Revenue declined (3.3)% compared with $25,394 million in the prior year on a pro forma combined company basis, in line with fiscal 2018 targets.
Income before income taxes was $1,671 million for fiscal 2018, including $(803) million of restructuring costs, $(408) million of transaction, separation and integration-related costs, $(591) million of amortization of acquired intangibles and $220 million of pension and OPEB actuarial and settlement gains. This compares with $(174) million in the year ago period.
Non-GAAP income before income taxes was $3,253 million compared with $2,184 million in the prior year on a pro forma combined company basis.
Net income was $1,782 million for fiscal 2018, including $(597) million of restructuring costs, $(291) million of transaction, separation and integration-related costs, $(398) million of amortization of acquired intangibles, $175 million of pension and OPEB actuarial and settlement gains and $561 million of tax adjustment related to U.S. tax reform. This compares with $(100) million in the prior year period.
Non-GAAP net income was $2,332 million.
Adjusted EBIT was $3,499 million in fiscal 2018 compared with $2,445 million in the prior year on a pro forma combined company basis. Adjusted EBIT margin was 14.2% compared with 9.6% in the prior year which is presented on a pro forma combined company basis.
Net cash provided by operating activities was $3,243 million in fiscal 2018, compared with $978 million in the prior year.
Adjusted free cash flow was $2,427 million in fiscal 2018.
Global Business Services (GBS)
GBS revenue was $2,361 million in the quarter compared to $1,043 million for the prior year. GBS revenues grew 3.3% year-over-year on a pro forma combined company basis, reflecting our clients' continued shift from traditional application services to Enterprise Applications and growth in our Business Process Services businesses. GBS profit margin in the quarter was 19.9%, up from 12.4% in the prior year on a pro forma combined company basis, reflecting ongoing cost actions in the business. New business awards for GBS were $2,038 million in the fourth quarter.
Global Infrastructure Services (GIS)
GIS revenue was $3,223 million in the quarter compared to $846 million for the prior year. GIS revenues grew 3.6% year-over-year on a pro forma combined company basis. The GIS revenue reflects strong growth in our Workplace and Mobility business as well as growth in Cloud and Platform services as clients migrate to hybrid infrastructure environments. GIS profit margin in the quarter was 14.8%, up from 11.4% in the prior year on a pro forma combined company basis, reflecting cost actions and process automation. New business awards for GIS were $2,862 million in the fourth quarter.
United States Public Sector (USPS)
USPS revenue was $710 million in the quarter. USPS revenue grew 11.1% year-over-year on a pro forma combined company basis, reflecting growth in two of our largest contracts. USPS profit margin in the quarter was 17.0%, up from 9.9% in the prior year on a pro forma combined company basis, reflecting ongoing cost actions in the business. New business awards for USPS were $522 million in the fourth quarter.
Returning Capital to Shareholders
During the fourth quarter, DXC Technology returned $123 million to shareholders in the form of common stock dividends and share repurchases.
Earnings Conference Call and Webcast
DXC Technology senior management will host a conference call and webcast today at 5 p.m. EDT. The dial-in number for domestic callers is (800) 289-0438. Callers who reside outside of the United States should dial +1 (323) 794-2423. The passcode for all participants is 6166236. The webcast audio and any presentation slides will be available on DXC Technology's Investor Relations website.
A replay of the conference call will be available from approximately two hours after the conclusion of the call until May 31, 2018. Replay numbers can be found here. The replay passcode is also 6166236.
In an effort to provide investors with supplemental financial information, in addition to the preliminary and unaudited financial information presented on a GAAP and pro forma basis, we have also disclosed in this press release preliminary non-GAAP information including: constant currency, earnings before interest and taxes ("EBIT"), EBIT margin, adjusted EBIT, adjusted EBIT margin, non-GAAP income before income taxes, non-GAAP net income, non-GAAP EPS and adjusted free cash flow. Reconciliations of the preliminary non-GAAP measures to the respective most directly comparable measures calculated on a GAAP or pro forma basis, as well as the rationale for management's use of non-GAAP measures, are included below.
DXC Technology is the world's leading independent, end-to-end IT services company, serving nearly 6,000 private and public-sector clients from a diverse array of industries across 70 countries. The company's technology independence, global talent and extensive partner network deliver transformative digital offerings and solutions that help clients harness the power of innovation to thrive on change. DXC Technology is recognized among the best corporate citizens globally. For more information, visit dxc.technology.
All statements in this press release that do not directly and exclusively relate to historical facts constitute "forward-looking statements." These statements represent current expectations and beliefs, and no assurance can be given that the results described in such statements will be achieved. Such statements are subject to numerous assumptions, risks, uncertainties and other factors that could cause actual results to differ materially from those described in such statements, many of which are outside of our control. For a written description of these factors, see the section titled "Risk Factors" in DXC's Quarterly Reports on Form 10-Q for the quarters ended June 30, 2017, September 30, 2017, December 31, 2017 and any updating information in subsequent SEC filings, including DXC's upcoming Form 10-K for the fiscal year ended March 31, 2018. No assurance can be given that any goal or plan set forth in any forward-looking statement can or will be achieved, and readers are cautioned not to place undue reliance on such statements which speak only as of the date they are made. We do not undertake any obligation to update or release any revisions to any forward-looking statement or to report any events or circumstances after the date of this press release or to reflect the occurrence of unanticipated events except as required by law.
View the charts and complete press release


text:
Celebrity News | Jun 7, 2017
Celebrity News: Buy Kristin Cavallari and Jay Cutler's Chicago Home
Celebrity News: Buy Kristin Cavallari and Jay Cutler's Chicago Home – Former reality star and accessories designer Kristin Cavallari is best known for her gallivanting through Laguna Beach and The Hills, but now it's her Midwest home that's making headlines. Cavallari and her husband, former NFL quarterback Jay Cutler, have listed their mansion in the Chicago suburb of Lake Forest.
Trulia reports that the 7-bedroom, 10-bath home, built in 2013, is currently listed at $4.75 million. The 11,000-square-foot sprawl boasts hardwood flooring, a winding staircase, and a spacious, marble-accented kitchen, plus amenities including an indoor basketball court, a wine cellar, a screening room, and five fireplaces to keep the home warm on those cold Chicago nights. The couple purchased the home in 2014 for $4.25 million.
See also: Celebrity Homes: Get Inspired by Catherine Zeta-Jones Home Office
The change of venue is likely due to Cutler's departure from the Chicago Bears. The former quarterback recently announced his retirement from the sport and his new gig as a contributor on Fox Sports. People reported in April that Cutler, Cavallari, and their three children were set to relocate to Nashville. The move, says Cavallari, was bittersweet, though she's looking forward to planting new roots in a new city.
See also: Celebrity News: Peek African-Inspired Decor of Beyoncé's Baby Shower
"I have to say I'm kind of sad," Cavallari told People. "My mom is in Chicago. I've made a lot of really good friends, so I definitely am sad…[but] knowing that we're going to be there for a very long time, if not forever, is a very exciting thing for me because my life is so hectic and so crazy that having a permanent home base is very comforting to me."
Keep following Celebrity Homes to have the opportunity to be inside celebrity homes and to know the latest celebrity news! Don't forget to leave a comment bellow!
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Source: architecturaldigest.com
Celebrity News | Jul 18, 2016
Celebrity News: Relax Like a Champion at CR7 Hotels
Celebrity News | Apr 13, 2017
Celebrity News: Peter Marino's Jaw-Dropping Hamptons Garden
Celebrity News | May 25, 2017
Now You Can Live at Jennifer Lawrence's NYC Apartment
Inside Celebrity Homes: Tommy Lee House at Calabasas
Celebrity News: Mike Jeffries is Selling Mirror-Covered Mansion
Buy Ben Affleck's Estate on Hampton Island


London is the capital of England, and therefore attracts many homebuyers to the city. We help people moving in, out and around London with the legal side of their conveyancing transaction.
Our conveyancing solicitors for London will ensure that you are well versed with accurate property searches if you're buying, and relevant information and checks if you are selling. Capital Conveyancing is experienced with various types of property transactions in London, including sale, purchase, remortgage and transfer of equity. Whether you're buying or selling, a house or a flat, we can help you.
Are you buying or selling property in London?
London is a popular choice for people at many different stages of their lives, whether they are moving out for the first time, starting a family, or looking to settle down.
As London is such a dense city, you need to find a property solicitor who understands the complications that may arise when buying or selling property in the capital. Capital Conveyancing has experience with many types of transactions, and can help to make your dream home or sale a reality.
The Capital Conveyancing team is regulated by the Council of Licensed Conveyancers, and have in depth knowledge of the London boroughs and the particular conveyancing issues that may arise during the process of your sale or purchase.
Why choose Capital Conveyancing for your sale or purchase?
London's geography is as diverse as its residents and the boroughs include many wooded areas, compact urban centres, grand listed buildings and flat greenery. Your conveyancer at Capital Conveyancing will carry out a number of environmental and planning searches to make sure your home is protected from the many aspects of life in the city.
Our conveyancers here at Capital Conveyancing understand the different areas of London in depth, and can tailor your conveyancing transaction, whether you are buying, selling, remortgaging or arranging a property solicitor for your transfer of equity.
What are common conveyancing issues in London?
Our conveyancers will need to perform several property searches in order to properly inform you of any planning or environmental issues specific to the area before you commit to buying a property.
Despite the many beautiful and affluent areas of London, the councils are constantly trying to find extra housing and this could lead to new developments in some areas. To avoid the shock of having a block of flats crop up in your back garden, speak to one of our London conveyancers, who will run the appropriate searches and ensure your new home stays just the way you like it.
Give Capital Conveyancing a call today on 0207 4065880 for an instant quote on conveyancing for the London area. Our team of expert solicitors and conveyancers are waiting to make your dream home a reality, without any hidden catches. We can also help with the legal side of selling your house in any London borough.
The aim of Capital Conveyancing is to make the process of buying or selling property in London easier for everyone, regardless of the type of property or the circumstances.


text:
namespace firebase {
namespace database {
namespace internal {
class Callbacks;
class DataSnapshotInternal;
class DatabaseReferenceInternal;
class QueryInternal;
}  // namespace internal

class Database;
class DatabaseReference;

/// A DataSnapshot instance contains data from a Firebase Database location. Any
/// time you read Database data, you receive the data as a DataSnapshot. These
/// are efficiently-generated and cannot be changed. To modify data,
/// use DatabaseReference::SetValue() or DatabaseReference::RunTransaction().
class DataSnapshot {
 public:
  /// @brief Copy constructor. DataSnapshots are immutable, so they can be
  /// efficiently copied.
  ///
  /// @param[in] snapshot DataSnapshot to copy.
  DataSnapshot(const DataSnapshot& snapshot);

  /// @brief Copy assignment operator. DataSnapshots are immutable, so they can
  /// be efficiently copied.
  ///
  /// @param[in] snapshot DataSnapshot to copy.
  ///
  /// @returns Reference to the destination DataSnapshot.
  DataSnapshot& operator=(const DataSnapshot& snapshot);

#if defined(FIREBASE_USE_MOVE_OPERATORS) || defined(DOXYGEN)
  /// @brief Move constructor. DataSnapshots are immutable, so they can be
  /// efficiently moved.
  ///
  /// @param[in] snapshot DataSnapshot to move into this one.
  DataSnapshot(DataSnapshot&& snapshot);

  /// @brief Move assignment operator. DataSnapshots are immutable, so they can
  /// be efficiently moved.
  ///
  /// @param[in] snapshot DataSnapshot to move into this one.
  ///
  /// @returns Reference to this destination DataSnapshot.
  DataSnapshot& operator=(DataSnapshot&& snapshot);
#endif  // defined(FIREBASE_USE_MOVE_OPERATORS) || defined(DOXYGEN)

  /// Destructor.
  ~DataSnapshot();

  /// @brief Returns true if the data is non-empty.
  bool Exists() const;

  /// @brief Get a DataSnapshot for the location at the specified relative path.
  ///
  /// @param[in] path Path relative to this snapshot's location.
  /// It only needs to be valid during this call.
  ///
  /// @returns A DataSnapshot corresponding to specified child location.
  DataSnapshot Child(const char* path) const;

  /// @brief Get a DataSnapshot for the location at the specified relative path.
  ///
  /// @param[in] path Path relative to this snapshot's location.
  ///
  /// @returns A DataSnapshot corresponding to specified child location.
  DataSnapshot Child(const std::string& path) const;

  /// @brief Get all the immediate children of this location.
  ///
  /// @returns The immediate children of this snapshot.
  std::vector<DataSnapshot> GetChildren() const;

  /// @brief Get the number of children of this location.
  ///
  /// @returns The number of immediate children of this snapshot.
  size_t GetChildrenCount() const;

  /// @brief Does this DataSnapshot have any children at all?
  ///
  /// @returns True if the snapshot has any children, false otherwise.
  bool HasChildren() const;

  /// @brief Get the key name of the source location of this snapshot.
  ///
  /// @note The returned pointer is only guaranteed to be valid while the
  /// DataSnapshot is still in memory.
  ///
  /// @returns Key name of the source location of this snapshot.
  const char* GetKey() const;

  /// @brief Get the key name of the source location of this snapshot.
  ///
  /// @returns Key name of the source location of this snapshot.
  std::string GetKeyString() const;

  /// @brief Get the value of the data contained in this snapshot.
  ///
  /// @returns The value of the data contained in this location.
  Variant GetValue() const;

  /// @brief Get the priority of the data contained in this snapshot.
  ///
  /// @returns The value of this location's Priority relative to its siblings.
  Variant GetPriority() const;

  /// @brief Obtain a DatabaseReference to the source location for this
  /// snapshot.
  ///
  /// @returns A DatabaseReference corresponding to same location as
  /// this snapshot.
  DatabaseReference GetReference() const;

  /// @brief Does this DataSnapshot have data at a particular location?
  ///
  /// @param[in] path Path relative to this snapshot's location.
  /// The pointer only needs to be valid during this call.
  ///
  /// @returns True if the snapshot has data at the specified location, false if
  /// not.
  bool HasChild(const char* path) const;

  /// @brief Does this DataSnapshot have data at a particular location?
  ///
  /// @param[in] path Path relative to this snapshot's location.
  ///
  /// @returns True if the snapshot has data at the specified location, false if
  /// not.
  bool HasChild(const std::string& path) const;

  /// @brief Returns true if this snapshot is valid, false if it is not
  /// valid. An invalid snapshot could be returned by a transaction where an
  /// error has occured.
  ///
  /// @returns true if this snapshot is valid, false if this snapshot is
  /// invalid.
  bool IsValid() const;

 private:
  /// @cond FIREBASE_APP_INTERNAL
  friend class internal::DatabaseReferenceInternal;
  friend class internal::DataSnapshotInternal;
  friend class internal::Callbacks;
  friend class internal::QueryInternal;
  /// @endcond

  DataSnapshot(internal::DataSnapshotInternal* internal);

  internal::DataSnapshotInternal* internal_;
};

}  // namespace database
}  // namespace firebase

#endif  // FIREBASE_DATABASE_CLIENT_CPP_SRC_INCLUDE_FIREBASE_DATABASE_DATA_SNAPSHOT_H_


Unless you are fluent in Bulgarian you won't be able to pronounce its name, but once you've been there you will remain enchanted forever. It's about 100 kilometres from Sofia, in the Sredna Gora, or Central Highlands, range, but it may as well be light years away.
Its well-preserved half-timbered houses evoke the mid-19th Century when its commercial significance provided the upsurge of national consciousness. It was at the centre of the 1876 April Uprising against the Ottoman Turks, a revolt that ended in failure but is considered one of the most courageous stands in modern Bulgarian history. Its importance started to fade after the liberation, and since then the town has been getting increasingly fossilised. Fewer than 3,000 people live in it today, as opposed to about 12,000 in the 19th Century, and tourism is the largest source of revenue.
Now largely a museum town, it provides some interesting insights into the ways of the Revival Period Bulgarians. Curiously, some of them have not changed that much: you are bound to note that some of the most beautiful houses belonged to... tax collectors.


I've often had trouble finding a consolidated list of draft picks for the Padres; in other words, a site where a list of all the players picked is posted. Well you know what? I can fix that. Below are the 2012 Padres selections.


When you delete an email, there is no artificial delay between when you click delete and when that message is actually deleted from StartMail servers. It's practically instant, so there's no need to worry about StartMail retaining anything you don't want to be preserved on the Net anymore.
It will, however, remain on our backup servers for three days. That's the length of time that each backup snapshot is held, and backups are an essential feature for any email service. The backups are buried deep inside private networks, protected by many layers of security.
The backups contain your closed vault, so your password would be required to open it. As a consequence, neither StartMail nor an attacker would be able to access your emails within a backup.
After the three-day period has elapsed, the previous backup is erased forever.


text:
Pyhätunturi - góra położona w gminie Kemijärvi, w prowincji Laponia, w północnej Finlandii. Leży na terenie Parku Narodowego Pyhä-Luosto. Stoki góry poprzecinane są trasami narciarskimi. Często organizowane są tu zawody Pucharu Świata w narciarstwie dowolnym. W 1994 r. zorganizowano tu zawody w biegu na orientację - Jukola.

Bibliografia

Szczyty Finlandii
Fińskie ośrodki narciarskie

redpajama_set_name: RedPajamaWikipedia


Attorney Timothy P. Kottemann, has practiced aggressively in the above mentioned areas of practice for 25+ years. He graduated from Mississippi College School of Law in 1991. Since that time, he has developed an excellent reputation by representing many clients throughout Mississippi and the surrounding areas by taking care of their legal needs.
Every day, Mr. Kottemann, stands committed to maintaining a superior level of legal counsel, integrity, and personal performance, so that his clients' experience is a positive and successful one.
Timothy P. Kottemann, Attorney at Law, brings years of expertise, reputation, and resources to bear in every case. He utilizes cutting edge litigation techniques and strategies to make sure that his client's story is told--the right way. He is aggressive, creative, and tireless in his pursuit of justice in each and every case.


text:
Na baště sv. Jiří je ulice na Hradčanech v Praze vedoucí od Písecké brány na Tychonovu ulici. Nazvána je podle bašty svatého Jiří, součásti Mariánských hradeb. Podobně jako nedaleké ulice Na baště sv. Ludmily a Na baště sv. Tomáše kopíruje tvar bývalého barokního opevnění Pražského hradu postaveného v druhé polovině 16. století a první polovině 17. století. Počátkem 20. století začali hradby bourat a v prostoru uvedených bašt vznikla vilová čtvrť, jedna z nejluxusnějších lokalit v Praze.
V letech 1910 - 1913 tu postavili převážně řadové "kotážové" domy, vily a dvojdomy.

Kolem ulice je park Charlotty G. Masarykové (dříve Park nebo sad u Písecké brány), kulturní památka České republiky od roku 1971.

Budovy, firmy a instituce
 Park Charlotty G. Masarykové - Na baště sv. Jiří
 Univerzitní centrum na Baště - Na baště sv. Jiří 13

Odkazy

Reference

Externí odkazy

Na baště sv. Jiří
Hradčany (Praha 6)
Ulice na Hradčanech
Objekty nazvané podle svatých