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

The pion, being both a Nambu-Goldstone boson and the lightest bound state in quantum chromodynamics (QCD), highlights the challenges in creating consistent theoretical and phenomenological frameworks to describe its partonic structure.  The shape of the pion valence parton distribution functions (PDFs) extracted from experimental data~\cite{Badier:1983mj,Betev:1985pf,Conway:1989fs,Chekanov:2002pf,Aaron:2010ab} in different analyses~\cite{Owens:1984zj,Aurenche:1989sx,Sutton:1991ay,Gluck:1991ey,Wijesooriya:2005ir,Aicher:2010cb,Barry:2018ort} are in sharp contrast among themselves and with perturbative QCD (pQCD)-based frameworks~\cite{Farrar:1979aw,Berger:1979du} at large longitudinal momentum fractions $x$. Central to the disparity is whether the pion PDF has a softer (harder) $(1-x)^2$ $[(1-x)]$ fall-off as $x\to 1$
- various model calculations~\cite{Shigetani:1993dx,Davidson:1994uv,Hecht:2000xa,Chen:2016sno,deTeramond:2018ecg,Bednar:2018mtf,Ding:2019lwe} exemplify this contrast.

The limited available phase space for partonic interactions at large $x$ localizes quantum fluctuations such that large-$x$ dynamics is constrained by confinement, in effect increasing parton correlations as $x\to1$. As the quark distribution at large $x$ is sensitive to nonperturbative quark-gluon dressing, a description of its behavior will also elucidate our understanding of the generation of mass in QCD through dynamical chiral symmetry breaking. Unraveling the complexities of the valence and sea quark contents of the pion is spearheaded by several upcoming experiments - Jefferson Lab tagged deep-inelastic scattering  experiments~\cite{Jlab}, Drell-Yan  measurements at the COMPASS experiment~\cite{Denisov:2018unj} and, also the future Electron-Ion Collider (EIC) facility~\cite{Aguilar:2019teb}. A first-principles lattice QCD (LQCD) determination of the pion valence PDF $q^\pi_{\rm v}(x)$ with controlled statistical and systematic uncertainties is particularly well timed and solicits a synergy of increasing importance between experimental and theoretical efforts.

PDFs are not direct physical observables, such as cross sections, due to the QCD color confinement.
Experimental extraction of $x$-dependent parton physics relies on
the QCD factorization theorem~\cite{Collins:1989gx} and considerable advancements in global analyses~\cite{Harland-Lang:2014zoa,Dulat:2015mca,Ball:2017nwa,Alekhin:2017kpj,Ethier:2017zbq} of experimental data.
LQCD cannot calculate PDFs directly due to its Euclidean space formulation.   QCD factorization can, however, connect $x$-dependent parton physics to a class of hadron matrix elements  ``lattice cross sections" (LCSs) -  that are calculable in LQCD and factorizable with perturbative matching.
Several LQCD methods~\cite{Liu:1993cv,Braun:2007wv,Horsley:2012pz,Ji:2013dva,Ma:2014jla,Radyushkin:2017cyf,Ma:2017pxb} have
been proposed and developed to probe the light-cone structure of hadrons.
These approaches have led to significant achievements in recent years, especially in determinations of flavor non-singlet distributions~\cite{Chambers:2017dov,Orginos:2017kos,Alexandrou:2018pbm,Bali:2018spj,Bali:2019ecy,Lin:2018qky,Sufian:2019bol,Izubuchi:2019lyk,Liang:2019frk,Joo:2019jct}.  A proper quantification and mitigation of systematic errors and numerical artifacts present in these calculations and related theoretical challenges still require further insight and development (for a recent review, see~\cite{Cichy:2018mum}).

In this paper,
we present
an extraction of the $q^\pi_{\rm v}(x)$
from LCSs - LQCD - calculated pion
matrix elements of two local, spacelike-separated and gauge-invariant currents~\cite{Ma:2014jla,Ma:2017pxb}.
These Lorentz covariant matrix elements of two currents spatially separated by a quark propagator are computable on a Euclidean lattice and have a well-defined continuum limit as the lattice spacing $a\to 0$.
Calculations on four distinct lattice ensembles allows for estimation of systematic errors from finite lattice spacing, volume, and unphysical pion mass extrapolations.
 From  parity and time-reversal invariance, this vector-axial (VA) current combination is antisymmetric and directly proportional to the $q^\pi_{\rm v}(x)$ with a perturbatively calculable coefficient function that matches this position space LCS to the $q^\pi_{\rm v}(x)$ in momentum space~\cite{Sufian:2019bol}.   With both leading order (LO) and next-to-leading order (NLO) matching coefficients, we extract $q^\pi_{\rm v}(x)$  from the LQCD-calculated pion matrix elements and find that it is remarkably consistent with the same distribution extracted from experimental data  over the entire range of $x$.  We also find that our calculated NLO coefficient function,
 matching what is calculated in LQCD in position space to PDFs in momentum space,
 is very stable without the large logarithms
 that are often seen in the perturbatively calculated hard coefficients in momentum space.

 The rest of this paper is organized as follows.  In Sec.~\ref{sec:2}, we first define the pion matrix elements that we calculate in LQCD, and introduce the factorization formalism to match the matrix elements in position space to the PDFs in momentum space.  We then present our perturbative calculation,  and  provide results for the NLO matching coefficients.  We demonstrate the effect of NLO matching coefficient and its perturbative stability in the factorized contribution to the pion matrix elements in position space in Sec.~\ref{sec:3}.  In Sec.~\ref{sec:4}, we explore the stability of the  continuum  limit of  the LQCD-calculated pion matrix elements, and present the numerical extraction of $q^\pi_{\rm v}(x)$.  We then present a discussion of our results in Sec.~\ref{sec:5}, and finally, give our conclusions and outlook in Sec.~\ref{sec:6}.

\section{Calculation of Next-to-leading order perturbative kernel}
\label{sec:2}

Following our previous work~\cite{Sufian:2019bol}, we consider the following antisymmetrized matrix element in a hadron $h$
\begin{eqnarray} \label{eq:matelem}\label{eq:1}
\sigma^{\left[h\right],\mu\nu}_{VA}(\xi,p)&=\xi^4 Z_{V} Z_{A} \bra{h(p)}T\{[\overline{\psi}\gamma^\mu\psi](\xi)\nonumber \\
      &[\overline{\psi}\gamma^\nu\gamma^5\psi](0)\}\ket{h(p)}+ V\leftrightarrow A,
\end{eqnarray}
where $\sigma^{\left[h\right],\mu\nu}_{VA}$ depends covariantly on the hadron momentum $p$ and spatial separation $\xi$ between the currents; $Z_{V,A}$ are the renormalization constants of the local currents determined in~\cite{Yoon:2016jzj} for the ensembles used in this calculation. A Lorentz decomposition of Eq.~\eqref{eq:matelem} yields  two scalar functions
$T_{i=1,2}^{\left[h\right]}(\omega,\xi^2,p^2)$  where
${\omega}=-p\cdot\xi$ is the Ioffe time of the process~\cite{Ioffe:1969kf},
 $T^{\left[h\right]}_{i}({\omega},\xi^2,p^2)=-T^{\left[h\right]}_{i}(-{\omega},\xi^2,p^2)$ from parity and time-reversal invariance, and $T^{\left[h\right]}_2$ is power suppressed.
For sufficiently small separations,
$T_{1}^{\left[h\right]}$, which can be isolated by choosing $\mu=1$ and $\nu=2$, can be factorized~\cite{Ma:2017pxb}
\begin{eqnarray} \label{eq:sig}
 T^{\left[h\right]}_{1}({\omega},\xi^2,p^2) &=& \sum_{q}\int_0^1dx\,  K(x{\omega},\xi^2,x^2p^2,\mu^2)\nonumber \\
&&\times f_{q_{\rm v}/h}(x,\mu^2) + \mathcal{O}(\xi^2\Lambda_{\rm QCD}^2),
\end{eqnarray}
where $f_{q_{{\rm v}/h}}(x,\mu^2)\equiv f_{q/h}(x,\mu^2)-f_{\overline{q}/h}(x,\mu^2)$ are valence PDFs, $\mu^2$ is the factorization scale, and the $K$ is perturbative matching coefficient with $K(x{\omega},\xi^2,x^2p^2,\mu^2)=-K(-x{\omega},\xi^2,x^2p^2,\mu^2)$.  Since  $K$ depends on $\xi$, conventional techniques used to calculate matching coefficients in momentum space cannot be applied directly~\cite{NLOcalc}.
To perturbatively calculate  $K(x{\omega},\xi^2,0,\mu^2)$ with an on-shell struck parton, $k^2=x^2p^2=0$, we
 could either calculate the matching coefficient directly in position space or
introduce a ``momentum space" matching coefficient with a ``$D$-dimensional" Fourier transform
\begin{eqnarray} \label{eq:sigmom}
&&\widetilde{T}_{1}^{\left[h\right]}(\widetilde{{\omega}},q^2) \equiv \int \frac{d^D\xi}{\xi^4} \, e^{iq\cdot\xi}\, T_{1}^{\left[h\right]}({\omega},\xi^2,0)\nonumber \\
&=& \int_0^1 dx\widetilde{K}(x\widetilde{{\omega}},q^2,\mu^2)f_{q_{{\rm v}/h}} (x,\mu^2)+\mathcal{O}(\Lambda_{\rm QCD}^2/q^2),
\end{eqnarray}
where
$D=4-2\epsilon$ and
$\widetilde{{\omega}}=\frac{2p\cdot q}{-q^2-i0^+}$.
With the perturbatively calculated $\widetilde{K}$, we can obtain $K$ as
\begin{eqnarray}\label{eq:Km}
K(x {\omega},\xi^2,0,\mu^2)= \xi^4 \int \frac{d^Dq}{(2\pi)^D} e^{-iq\cdot \xi} \widetilde{K}(x\widetilde{{\omega}},q^2,\mu^2)\,.
\end{eqnarray}
To calculate $\widetilde{K}$, we  consider the matrix element of  an on-shell  quark state $q$ in Eq.~\eqref{eq:sigmom}, expand both sides in powers of the strong coupling $\alpha_s$,
and keep up to NLO,
\begin{subequations}\label{eq:matchM}
\begin{eqnarray}
\widetilde{T}_{1}^{\left[q\right](0)}(\widetilde{\omega},q^2)=&\int_{0}^1 dx\, \widetilde{K}^{(0)}(x\widetilde{\omega},q^2,\mu^2) f^{(0)}_{q_{\rm v}/q}(x,\mu^2),\nonumber \\
\\
\widetilde{T}_{1}^{\left[q\right](1)}(\widetilde{\omega},q^2)=&\int_{0}^1 dx\, \widetilde{K}^{(1)}(x\widetilde{\omega},q^2,\mu^2) f^{(0)}_{q_{\rm v}/q}(x,\mu^2)\nonumber \\
&\hspace{-0.3cm}+\int_{0}^1 dx\,\widetilde{K}^{(0)}(x\widetilde{\omega},q^2,\mu^2) f^{(1)}_{q_{\rm v}/q}(x,\mu^2)\nonumber \\.
\end{eqnarray}
\end{subequations}
With the well-known $\overline{\text{MS}}$ perturbative PDFs,
\begin{subequations}\label{eq:fexp}
\begin{align}
f^{(0)}_{q_{\rm v}/q}(x,\mu^2)&=\delta(1-x),\\
f^{(1)}_{q_{\rm v}/q}(x,\mu^2)&= -\frac{1}{\epsilon} \frac{(4\pi)^\epsilon}{\Gamma(1-\epsilon)} \frac{\alpha_s}{2\pi} C_F\left(\frac{1 + x^2}{1 - x}\right)_+ ,
\end{align}
\end{subequations}
$\widetilde{K}^{(0)}$ and $\widetilde{K}^{(1)}$ are
determined by $\widetilde{T}_{1}^{[q](0)}$ and $\widetilde{T}_{1}^{[q](1)}$ using Eqs.~\eqref{eq:matchM} and \eqref{eq:fexp}.
The $\widetilde{T}_{1}^{[q](0)}$ and $\widetilde{T}_{1}^{[q](1)}$ are obtained by calculating the two-current (VA) correlator up to $\mathcal{O}(\alpha_s)$ in $D$ dimension.
Due to Ward-Takahashi identities for vector and  axial-vector currents, UV divergences cancel out within one-loop diagrams and we do not need perturbative renormalization, which means $Z_V=Z_A=1$ in the perturbative calculation. One can also verify that  perturbative collinear divergences from $\widetilde{T}_{1}^{[q](1)}$ cancel exactly with $f^{(1)}_{q_{\rm v}/q}$ in Eq.~\eqref{eq:matchM}, resulting in finite $\widetilde{K}^{(0)}$ and $\widetilde{K}^{(1)}$, and thus up to $\mathcal{O}(\alpha_s)$
\begin{align}
&\widetilde{K}(\widetilde{\omega},q^2,\mu^2) =  \bigg\{\frac{1}{1+\widetilde{\omega}}+\frac{\alpha_s C_F}{4\pi } \nonumber \\
&\times\bigg[ \left(\frac{2+2\widetilde{\omega}^2}{\widetilde{\omega}+\widetilde{\omega}^2}\ln(1+\widetilde{\omega})+\frac{3\widetilde{\omega}}{1-\widetilde{\omega}^2}\right) \ln\left(\frac{\mu^2}{-q^2-i0^+}\right) \nonumber \\
& +\frac{5\widetilde{\omega}}{1-\widetilde{\omega}^2} +\frac{2-2\widetilde{\omega}-\widetilde{\omega}^2}{\widetilde{\omega}+\widetilde{\omega}^2}\ln(1+\widetilde{\omega})  \nonumber \\
&-\frac{1+\widetilde{\omega}^2}{\widetilde{\omega}+\widetilde{\omega}^2}\ln^2(1+\widetilde{\omega}) \bigg] \bigg\} - (\widetilde{\omega} \to -\widetilde{\omega}).
\end{align}
By performing a Fourier transform, we obtain
\begin{eqnarray} \label{eq:FFK}
&&K({\omega},\xi^2,\mu^2)= \frac{1}{\pi^2\omega} [ K^{(0)}({\omega})+\frac{\alpha_s C_{\rm F}}{2\pi}\nonumber \\
&& \{K^{(1,0)}({\omega})+ K^{(1,1)}({\omega}) \ln (-\xi^2\mu^2 e^{2\gamma_E}/4)\}],
\end{eqnarray}
with
\begin{eqnarray} \label{eq:LO}
 K^{(0)}({\omega}) = {\omega} \cos{\omega} ,
 \end{eqnarray}
  %
 \begin{eqnarray}\label{eq:NLO}
K^{(1,0)}({\omega}) &=& \omega \int_0^1 dy \cos(y\omega) \bigg[\frac{1}{2}\delta(1-y) \nonumber \\
&&-\left(\frac{2\ln(1-y)}{1-y}-\frac{y^2-3y+1}{1-y}\right)_+\bigg]\nonumber \\
 K^{(1,1)}({\omega}) &=& -{\omega} \int_0^1 dy \cos(y{\omega}) \bigg(\frac{1+y^2}{1-y}\bigg)_+ \, ,
\end{eqnarray}
where the leading order kernel $K^{(0)}({\omega})$ in Eq.~\eqref{eq:LO} is the same as the result in~\cite{Sufian:2019bol}.
After the integration over $y$, the NLO matching coefficient $K(\omega,\xi^2,\mu^2)$ is very stable and without large logarithms in $\omega$ in the  region  where the lattice QCD data points are available.
Like the typical perturbatively calculated matching coefficients in momentum space, the NLO matching kernels $K^{(1,0)}({\omega})$ and $K^{(1,1)}({\omega})$, {\it before the Fourier transform of $y$ into  position space,} have terms with the standard ``+"  prescription  in Eq.~\eqref{eq:NLO}.  The existence of these ``+" prescription  terms is a natural result of perturbative cancellation of infrared (IR)  divergences between the real and virtual contributions (or Feynman diagrams), and these terms have large logarithmic corrections at the point of the IR cancellation~\cite{Sterman:1986aj,Catani:1989ne}.  When these terms are directly convoluted with PDFs in momentum space to derive cross sections, a resummation of such large logarithmic perturbative corrections from the area of IR cancellation is needed to improve the perturbative stability of factorized cross sections so as to be better compared with experimental data near the kinematic threshold~\cite{Aicher:2010cb,Shimizu:2005fp}.   On the other hand, the  QCD factorization proved for the LCSs~\cite{Ma:2017pxb} matches directly the hadron matrix elements calculated in position space to the PDFs in the momentum space, and is valid when the spatial  separation $\xi$ of two currents is sufficiently small $\xi^2\ll 1/\Lambda_{\rm QCD}^2$.
It is this matching of matrix elements in position space to the PDFs in momentum space that helps reduce the perturbative sensitivity to the IR cancelation  that takes  place at a single point in phase space.  As demonstrated in Ref.~\cite{Ma:2017pxb}, the position space matching coefficient $K({\omega},\xi^2,\mu^2)$ is perturbatively analytic for all values of ${\omega}$ except ${\omega}\to \infty$.  Technically, the Fourier transform over $y$ in Eq.~\eqref{eq:NLO}
gives no $\log({\omega})$ terms to the $K({\omega},\xi^2,\mu^2)$  kernel when ${\omega}$ is in a perturbatively relevant region, and  thus reduces the logarithmic perturbative sensitivity from the terms with the ``+''  prescription.
With a small  spatial separation between two currents required by the QCD factorization and the limited values of hadron momentum, the relevant $\omega$ is never too large in a practical lattice QCD calculation.

A convergence test of this NLO kernel is demonstrated in Sec.~\ref{sec:3}.
We highlight
that a large
hadron momentum $p$ alone does not automatically guarantee QCD factorization of the hadron matrix element in Eq.~\eqref{eq:1} into the PDFs -   and the perturbative kernel, and
contributions from the large $\xi$ region could invalidate the perturbative factorization~\cite{Ma:2017pxb,Sufian:2019bol}.
It is the smallness of the spatial separation that defines the short-distance probe to see the particle nature of the partons inside a hadron and provides a required hard scale for the QCD factorization.  Although not directly related to this calculation, the need to prove QCD factorization in momentum space is not new and is well known for the transverse momentum $k_T$ part of the transverse momentum dependent (TMD) factorization.   The factorization formalism was proved in its conjugated position $b_T$ space, not in the momentum $k_T$ space~\cite{Collins:1984kg}, and the perturbative matching coefficients, as well as the evolution kernels, are calculated in position space and valid only for small $b_T$.
The perturbative calculation method introduced in this paper can be used not only for the current-current operators, but also for operators defining quasi-PDFs~\cite{Ji:2013dva} and reduced pseudo-ITDs~\cite{Radyushkin:2017cyf} whose factorization to the PDFs are also valid for the region where the spatial separation between two active parton fields is small and much less than $1/\Lambda_{\rm QCD}^2$. More importantly, our method is not restricted to NLO, but can be applied to any perturbative order~\cite{Li:2020xml}.  The main subtlety of the method lies in the Fourier transformation, which must be done in $D$ dimensions as indicated in Eq.~\eqref{eq:Km}.

\section{Effect of the next-to-leading order kernel on the Ioffe-time distribution}
\label{sec:3}

 To demonstrate the effect of the NLO kernel on the Ioffe-time distribution (ITD), we  select  $\alpha_s=0.303$ at $\mu=2$ GeV and $-\xi^2\mu^2=1$  and  compare in Fig.~\ref{fig:KITD2} the $K^{(0)}({\omega})/{\omega}$ and $K^{(1)}({\omega})/{\omega}$ effects for ${\omega} \neq 0$. The NLO corrections are tiny at small ${\omega}$ and increase very slowly towards large $\omega$; this can be partially understood from the ratio between $K^{(0)}$ and $K^{(1)}$ around ${\omega}=0$:
		\begin{align}
		\frac{K^{(1)}}{K^{(0)}}=\frac{\alpha_s}{3\pi}+\mathcal{O}({\omega}^2)\approx 0.03+O({\omega}^2).
		\end{align}

	\begin{figure}[htp]
		\begin{center}

			\includegraphics[width=3.45in, height=2.35in]{Kcomparison-band.pdf}
			\caption{\label{fig:KITD2}
				A comparison between $K^{(0)}({\omega})/{\omega}$ and  $K^{(1)}({\omega})/{\omega}$ for $\alpha_s(\mu=2\text{ GeV})=0.303$ and $-\xi^2\mu^2=1$. The uncertainty in $K^{(1)}({\omega})/{\omega}$ is obtained by a 10\% variation in $\alpha_s$.}
		\end{center}
	\end{figure}

 It is important to note that as an asymptotic series, the relative size of $K^{(1)}/K^{(0)}$ as a function of ${\omega}$ actually diverges as ${\omega}\to\infty$, but, only a small range of ${\omega}$ is relevant for the convolution with PDFs in Eq.~(\ref{eq:1}).  What is important is the size of their convolutions with the PDFs in the relevant Ioffe-time window of the lattice QCD data while keeping  $\xi$ small.  Therefore, it is also useful to demonstrate the effect  the NLO kernels could have with various model PDFs in the Ioffe-time space. The convolutions
\begin{equation}
    K^{(1,i)} \otimes q (\omega) =  \int dx \frac{1}{x \omega} K^{(1,i)}(x\omega) q(x)
\end{equation}
with $i=0,1$ for a few PDFs are shown in Figs.~\ref{fig:K10q} and~\ref{fig:K11q}, respectively. Each of the convolutions have similar features. These convolutions represent the difference between the LCS and the ITD, applying the appropriate factors proportional to $\alpha_s$ and $\ln(-\xi^2\mu^2 e^{2\gamma_E}/4) $. The convolutions all rise to a peak around $\omega\sim 4.0$ and begin to decay to 0. The NLO effects are most significant at the highest Ioffe-time range available to our calculations but the corrections will be smaller for large Ioffe times. These convolutions demonstrate a reassuring feature of the position space matching. These convolutions are at the largest $O(1)$ which means the NLO term will be $O(\alpha_s)$ for the entire region of Ioffe time. These convolutions can be compared with those for matching the reduced pseudo-ITD to the PDF in~\cite{Joo:2019jct}.

\begin{figure}[htp]
		\begin{center}

			\includegraphics[width=3.45in, height=2.35in]{K10qc.pdf}
			\caption{\label{fig:K10q}
				The convolution of the $K^{(1,0)}$ kernel with model PDFs.}
		\end{center}
	\end{figure}

\begin{figure}[htp]
		\begin{center}

			\includegraphics[width=3.45in, height=2.35in]{K11qc.pdf}
			\caption{\label{fig:K11q}
				The convolution of the $K^{(1,1)}$ kernel with model PDFs.}
		\end{center}
	\end{figure}

\section{Numerical Results \& Extraction of the $q^\pi_{\rm v}(x)$}
\label{sec:4}
\begin{table}
  \begin{center}
    \setlength\abovecaptionskip{-1pt}
    \setlength{\belowcaptionskip}{-10pt}
    \begin{ruledtabular}
      \begin{tabular}{ccccc}
      ID  & $a$ (fm)  &$m_\pi$ (MeV)  & $L^3\times N_t$ & $N_{\rm cfg}$\\
      \hline
      $a127m413$ & $0.127(2)$ & 413({4}) & $24^3\times 64$ & 2124 \\
      \hline
      $a127m413L$ & $0.127(2)$ & 413({5}) & $32^3\times 96$ & 490 \\
      \hline
      $a94m358$ & $0.094(1)$ & 358({3}) & $32^3\times 64$ & 417 \\
      \hline
      $a94m278$ & $0.094(1)$ & 278(4) & $32^3\times 64$ & 503 \\
      \end{tabular}
    \end{ruledtabular}
    \caption{ \label{tab:lat} Parameters for each gauge ensemble used in this work: lattice spacing, pion mass, spatial and temporal sizes, and number of configurations used.}
  \end{center}
\end{table}
\addtolength{\textfloatsep}{-0.3in}

 The LQCD calculation of  the pion matrix element in Eq.~(\ref{eq:1})
is carried out on four different 2+1 flavor QCD ensembles (listed in Table~\ref{tab:lat}) using the isotropic-clover fermion action generated by the JLab/W\&M Collaboration~\cite{lattices}.
 We refer  to~\cite{Sufian:2019bol} for details about the implementation of a modified sequential source technique, and a combination of Jacobi and momentum smearing to obtain matrix elements for a given momentum $p$ and spatial separation $\xi$ between the currents. In this calculation of the forward matrix elements, the pion source-sink separation $T$ is systematically increased, while holding fixed the current insertion time $t=T/2$, ensuring identical excited-state contamination from both source and sink sides. To extract the desired matrix elements, we assume the following forms of two- and four-point correlation functions:
\begin{eqnarray}
C_{2pt}(T) &=& A\, e^{-m_0 T}\nonumber \\
C_{4pt}(T) &=& e^{-m_0 T} (B+D\, e^{-\Delta m T}),
\end{eqnarray}
and perform simultaneous correlated fits to the two- and four-point functions. We verify that the value of the ground-state energy $m_0$ obtained from this simultaneous fit is consistent with that obtained from $C_{2pt}(T)$ alone and also agrees with the energy-momentum dispersion relation.

In Fig.~\ref{fig:matelemes}, we present fit results of the ratio $C_{4pt}(T)/e^{-m_0 T}$ on the ensembles $a94m278$ and $a94m358$ for momenta  in the range $p\in\lbrace0.41-1.65\rbrace$ GeV and current separation $\xi=3a$, both $p$ and $\xi$ in along the $z$ direction, to demonstrate how reliably we can extract the asymptotic value of $B$, and hence the ITD from $B/A$. The numerical challenges manifest in this formalism are reflected in the signal-to-noise ratio ($S/N$) of the largest momentum $p=1.65$ GeV relative to that of the smallest $p=0.41$ GeV; the former is nearly 3 times smaller. Despite this, we can fit these data up to at least $T=14(\sim1.32\text{ fm})$ even for the largest momentum $p=1.65$ GeV on the lightest pion mass $m_\pi=278$ MeV ensemble. In all the fits, we use the time window such that $S/N \geq 1$.   The Wilson clover fermion action explicitly connects adjacent lattice sites, introducing spurious contact terms in the $\xi=a$ matrix element signals. These data are consequently neglected from our analysis.
\begin{figure}[htp]
\begin{center}
\includegraphics[width=3.4in, height=4.6in]{MatElems.pdf}
\caption{\label{fig:matelemes}
Removal of the leading ground-state time dependence exposes the desired matrix elements in the large $T$ limit, shown here for ensembles $a94m278$ (above) and $a94m358$ (below) for current separations $\xi = 3a$. High momenta data rescaled for $S/N$ comparison. }
\end{center}
\end{figure}
\addtolength{\textfloatsep}{-0.10in}

The matrix elements computed across the four gauge ensembles are shown in Fig.~\ref{fig:ITD}. We only include $\lvert\xi\rvert\le 0.56$ fm in our analysis so that $\xi$ is sufficiently smaller than $\Lambda_{\rm QCD}^{-1}$, thereby ensuring the validity of the short-distance factorization and minimizing higher-twist contributions from large $\xi$.
\begin{figure}[htp]
\begin{center}
\includegraphics[width=3.45in, height=2.35in]{ITD_sys.pdf}
\caption{\label{fig:ITD}
Simultaneous fit to the antisymmetric VA current matrix elements on four different ensembles. The blue band  indicates the ITD in the physical limit. The outer cyan band shows the combined statistical and systematic uncertainties of fit~\eqref{zfit} added in quadrature.}
\end{center}
\end{figure}
Exploiting the analyticity of the LCS $T^{\pi}_{1}({\omega},\xi^2)= \sigma^{12}_{\rm VA}({\omega},\xi^2)$ in ${\omega}$ and denoting $\sigma^{12}_{\rm VA}({\omega},\xi^2)\equiv \sigma_{\rm VA}({\omega},\xi^2)$ in the rest of the article and figures, we obtain the functionally unknown ITD using a flexible $z$-expansion fit~\cite{Boyd:1994tt,Bourrely:2008za} supplemented with chiral, continuum, finite volume~\cite{Briceno:2018lfj} and higher-twist corrections:
\begin{eqnarray} \label{zfit}
\sigma_{\rm VA}({\omega},\xi^2) &=& \sum_{k=0}^{k_{\rm max}=4} \lambda_k \tau^k +b_1 (m_\pi-m_{\pi,{\rm physical}})+b_2 a \nonumber \\
&+& b_3 \xi^2 + b_4 a^2p^2 + b_5 e^{-m_\pi(L-\xi)}\, ,
\end{eqnarray}
\begin{eqnarray}
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{\rm where} \quad \tau = \frac{\sqrt{{\omega}_{\rm cut}+{\omega}}-\sqrt{{\omega}_{\rm cut}}}{\sqrt{{\omega}_{\rm cut}+{\omega}}+\sqrt{{\omega}_{\rm cut}}}
\end{eqnarray}
and $m_{\pi,{\rm physical}} \simeq 0.14$ GeV is the physical pion mass. Higher-order terms $\left(k_{\rm max}>4\right)$ have no statistical significance and are not considered.

  The correction terms of  Eq.~\eqref{zfit} are selected based on each being the dominant   contribution of its type. We consider  now different possible correction terms in  the fit   to Eq.~\eqref{zfit}, such as $a^2$, $m^2_\pi$,  $Le^{-m_\pi(L-\xi)}$, $\sqrt{L}e^{-m_\pi(L-\xi)}$. These corrections are presented in Table~\ref{tab:systematics}. The second column indicates the value of the fitted coefficient of the correction terms and the $\lambda_k$ columns indicate the effect of these corrections on the $z$-expansion fit parameters used to obtain the physical limit $\sigma_{\rm VA}(\omega)$ distribution. We note that for all additionally considered corrections,  the effect is indeed observed to be less than the original corrections of Eq.~\eqref{zfit} and the determination of $q^\pi_{\rm v}(x)$ remains unaffected.
\begin{table*}[htp]
  \centering

  \begin{tabular}{|c|c|c|c|c|c|c|c|}
  \hline
    Correction term  & Fit coefficient & $\lambda_0$   &$\lambda_1$  &  $\lambda_2$ & $\lambda_3$ & $\lambda_4$ & $\chi^2/{\rm d.o.f.}$\\
    \hhline{|=|=|=|=|=|=|=|=|}
    $a^2$ & $-0.049(34)$ &  $0.0104(3)$ & $-0.006(3)$ & $-0.028(9)$ & $-0.901(391)$ & $0.124(135)$ & 1.26 \\
    \hline
    $(m_\pi^2-m^2_{\pi,{\rm physical}})$ & $0.15(12)$ & $0.0104(3)$ & $-0.006(3)$ & $-0.029(10)$ & $-0.926(388)$ & $0.118(132)$ & $1.18$\\
    \hline
    $Le^{-m_\pi(L-\xi)}$ & $0.007(3)$ & $0.0104(3)$ & $-0.006(3)$ & $-0.028(10)$ & $-0.915(402)$ & $0.121(136)$  & 1.22\\
    \hline
    $\sqrt{L}e^{-m_\pi(L-\xi)}$ & $0.026(14)$ & $0.0104(3)$ & $-0.006(3)$ & $-0.029(10)$ & $-0.914(403)$ & $0.121(136)$ & 1.21 \\
    \hhline{|=|=|=|=|=|=|=|=|}
  \end{tabular}
  \caption{Fit parameters of different correction terms in fit Eq.~\eqref{zfit} for the investigation of systematic uncertainties in $\sigma_{\rm VA}(\omega)$.}
  \label{tab:systematics}
\end{table*}

In addition, as seen in Fig.~\ref{fig:ITD} the effects of other possible correction terms such as $m^2_\pi$, $a^2$, $L e^{-m_\pi(L-\xi)}$, $\sqrt{L} e^{-m_\pi(L-\xi)}$ are observed to be very mild. We choose ${\omega}_{\rm cut}=1.0$ as used in~\cite{Joo:2019bzr}; other choices of ${\omega}_{\rm cut}$ were observed to have no effect on the final band in the physical limit and vanishing higher-twist $\mathcal{O}(\xi^2)$  contributions. The blue band in Fig.~\ref{fig:ITD} shows such $\sigma_{\rm VA}({\omega})$ distribution after $b_i$ corrections in Eq.~\eqref{zfit} are subtracted, and where the error band is determined from the $\lambda_k$ covariances. The fit yields
 \begin{eqnarray}
 &&\lambda_0=0.104(3), \, \lambda_1=-0.006(3), \, \lambda_2=-0.029(9), \nonumber \\
 && \lambda_3=-0.907(404),\, \lambda_4=0.124(136),   \nonumber \\
 && b_1=0.174(96), \, b_2=-0.083(43), \, b_3=-0.0004(7),   \nonumber \\
 && b_4=0.007(8), \, b_5=0.102(51)
 \end{eqnarray}
  with $\chi^2/{\rm d.o.f}=1.20$.  As can be seen in Fig.~\ref{fig:ITD}, there appears to be completely negligible $\xi$ effects either higher twist or DGLAP~\cite{Gribov:1972ri,Altarelli:1977zs,Dokshitzer:1977sg}. Therefore, we will assign the $\xi=2 \times 0.094$ fm, the shortest $\xi$ used in this study in the factorization formula~\eqref{eq:FFK} while matching the position space LCS to $q^\pi_{\rm v}(x)$ distribution.  With the physical $\sigma_{\rm VA}({\omega})$ distribution in hand, we can immediately extract the physical $q^\pi_{\rm v}(x)$ with no further extrapolations.
\begin{figure}[htp]
\begin{center}
\setlength\abovecaptionskip{-2pt}
\setlength\belowcaptionskip{-6pt}
\includegraphics[width=3.45in, height=2.5in]{XlatxPDF.pdf}
\caption{\label{fig:xPDF}
The  pion  valence  quark distribution  obtained  from fitting the convolution of $q^\pi_{\rm v}(x)$ and the NLO perturbative kernel~\eqref{eq:FFK} to the determined $\sigma_{\rm VA}({\omega})$ distribution in the fit Eq.~\eqref{zfit}. Fits 1 and 2 label the 2- and 3-parameter functional forms in Eq.~\eqref{eq:qxform}.  }
\end{center}
\end{figure}

 The extraction of $q^\pi_{\rm v}(x)$ is achieved  by  numerically evaluating the convolution of the NLO kernel equation~\eqref{eq:FFK} and the following phenomenologically motivated functional forms of the PDF:
\begin{eqnarray} \label{eq:qxform}
q^\pi_{\rm v}(x) = \frac{x^\alpha(1-x)^\beta(1+\gamma x)}{B(\alpha+1,\beta+1)+ \gamma B (\alpha+2,\beta+1)}
\end{eqnarray}
using the library ROOT~\cite{ROOT}. The high correlation of the sampled $\sigma_{VA}(\omega)$ data guarantees that increasing the sampling density or varying the number of derived pseudodata samples will have no impact on the $q^\pi_{\rm v}(x)$ fit parameters.

 The parameters in the PDF parametrization equation~\eqref{eq:qxform} are determined by fitting the convolution of the model PDF and the NLO perturbative kernel to $\sigma_{\rm V A}(\omega)$ in a manner similar to Ref.~\cite{Joo:2019bzr}, where the Ioffe-time zero point is fixed in this calculation by the LO$+$NLO perturbative kernel.  The isolation of $\sigma_{VA}(\omega)$ is a multistep process, and begins by performing a correlated fit of lattice data from all four ensembles according to Eq.~\eqref{zfit}. This yields $\sigma_{\rm V A}(\omega,\xi^2)$ plus corrections. Removing the $b_i$ corrections from the obtained $\sigma_{\rm VA}(\omega,\xi^2)$ distribution, we obtain the blue band indicated by $\sigma_{\rm V A}(\omega)$ - now in the physical limit.  The covariance matrix of the $\lambda_k$ coefficients from the correlated $z$-expansion fit provides an error estimate of the $\sigma_{\rm VA}(\omega)$ physical distribution. We choose 30 correlated data points from the continuum band of $\sigma_{V A}(\omega)$, equally spaced in the Ioffe-time interval $\omega\in [0-4.71]$; a number in accordance with the 20 data points available from the $a94m278$ and $a94m358$ lattice ensembles. Using the mean and covariance matrix of these data points, we create 200  Gaussian distributed pseudodata samples with appropriate correlations and perform the following numerical fit
\begin{eqnarray} \label{eq:numfit}
\sigma_{V A}(\omega) = \int_0^1 dx\, K^{\rm LO + NLO}(x,\omega)\, q^\pi_{\rm v} (x)
\end{eqnarray}
to obtain $q^\pi_{\rm v} (x)$. As these discrete values resulting from the fit in Eq.~\eqref{zfit} are highly correlated, the addition of more discrete data points from the fitted $\sigma_{\rm VA}(\omega)$ distribution  does not improve the outcome of the $q^\pi_{\rm v} (x)$ fit parameters. We confirmed this by increasing the number of $\sigma_{\rm VA}(\omega)$ sampling points to 100. A similar result is obtained if one chooses 20 sampling points or less, as was done in our previous work (Ref.~\cite{Sufian:2019bol}). One can also see that increasing or decreasing the number of pseudodata samples from 200 will  not have any impact on the $q^\pi_{\rm v} (x)$ fit parameters, again due to the $\sigma_{\rm V A}(\omega)$ data correlations. What is required to improve the $q^\pi_{\rm v} (x)$ fit parameters is a larger range of Ioffe time.  In the above fit, we have used the constraints $\alpha \leq 0$ and $\beta \leq 4$.

For the above fit, we use $\alpha_s=0.303$ at the initial scale $\mu_0=2\text{ GeV}$~\cite{Buckley:2014ana}. Systematic uncertainties in each PDF parameter set are estimated by a 10\% variation in $\alpha_s$ as in ~\cite{Joo:2019bzr}. The 2-parameter fit, by fixing $\gamma=0$ in Eq.~\eqref{eq:qxform}, yields
\begin{eqnarray} \label{eq:2params}
\alpha = -0.17(7)_{\rm stat}(2)_{\rm sys}, \quad \beta = 1.24(22)_{\rm stat}(7)_{\rm sys}
\end{eqnarray}
with $\chi^2/{\rm d.o.f}=1.41$. Stated uncertainties are statistical (systematic) first (second). In a 3-parameter fit, with an unconstrained $\gamma$, we obtain
\begin{eqnarray} \label{eq:3params}
\alpha&=&-0.22(11)_{\rm stat}(3)_{\rm sys}, \, \beta = 2.12(56)_{\rm stat}(14)_{\rm sys},\nonumber \\
  \gamma &=& 4.28(1.73)_{\rm stat}(25)_{\rm sys}
\end{eqnarray}
with $\chi^2/{\rm d.o.f} \approx 1.29$.  The present calculation has achieved a better statistical precision in the $\beta$ value compared to the previous LCS determination~\cite{Sufian:2019bol} where it was found in a 3-parameter fit $\beta=1.93(68)$. Inclusion of an additional $\rho\sqrt{x}$-term in~\eqref{eq:qxform} was found to be consistent with zero. Commensurate $\chi^2/{\rm d.o.f}$ between fits~\eqref{eq:2params} and~\eqref{eq:3params} limits the selection of one fit over another based solely on the goodness of the fit. These fits are shown in Fig.~\ref{fig:xPDF}. We elected not to extrapolate our ITD obtained from our $z$-expansion fit beyond the largest Ioffe time ${\omega}=4.71$ when determining the PDF. It has been shown~\cite{Karpie:2019eiq} when using sophisticated inversion methods  that the large-$x$ behavior is well reproduced even with the limited range in Ioffe time.

\section{Discussion}
\label{sec:5}

As shown in Fig.~\ref{fig:ITDrecons}, extrapolating the central value of the $\sigma_{\rm VA}({\omega})$ distribution from the $z$-expansion fit (blue) and the associated 2- (red) and 3-parameter (cyan) fits reveals that precise LQCD data at large ${\omega}$ are required to distinguish between different large-$x$ behaviors of $q^\pi_{\rm v}(x)$.
\begin{figure}[htp]
\begin{center}
\includegraphics[width=3.45in, height=2.45in]{ITDfit-2.pdf}
\caption{\label{fig:ITDrecons}A comparison of the reconstructed $\sigma_{\rm VA}({\omega})$ distribution using Eq.~\eqref{eq:numfit} for $4.0<{\omega}<5.0$ from the PDF fits and that obtained from~\eqref{zfit}. Fits 1 and 2 label the 2- and 3-parameter functional forms in Eq.~\eqref{eq:qxform}.  }
\end{center}
\end{figure}
We validate our PDF fitting procedure by reconstructing the $\sigma_{\rm VA}(\omega)$ distribution by convolving the NLO kernel with the PDFs obtained from the pseudodata samples. The $\sigma_{\rm VA}({\omega})$ distribution reconstructed from the 2-parameter fit underestimates the uncertainty of the distribution in the physical limit by about 8\%-12\% for ${\omega} >4$, and starts to deviate from the blue band as ${\omega}$ increases. This observation together with the smaller $\chi^2/\text{d.o.f}$ favors the $q^\pi_{\rm v}(x)$ extracted using the 3-parameter fit~\eqref{eq:3params}. For a fixed $\alpha$, one can show that the ITD falls off faster for a smaller $\beta$ as a function of ${\omega}$ compared to that for a larger $\beta$ in a 2 or 3 or more parameter PDF functional form. Therefore, precise data at higher Ioffe time $({\omega} \sim 8-10)$ will provide
a better
discrimination between different $\beta$ values in a future LCS calculation.

While PDFs can minimally be described by the $x^\alpha (1-x)^\beta$ functional form, encompassing the Regge theory~\cite{Regge:1959mz} and pQCD based power counting rules~\cite{Brodsky:1973kr}, modern global analyses~\cite{Harland-Lang:2014zoa,Dulat:2015mca,Ball:2017nwa,Ball:2017nwa} inform our decision to allow for an interpolating function between these small-$x$ and large-$x$ regions and thus a better and less biased description of PDFs. In particular, the fit~\eqref{eq:3params} includes the possibility of $\gamma=0$ and is more flexible.

For a comparison with global fits of $q^\pi_{\rm v}(x)$, we evolve our extracted PDF sets to a scale of $\mu^2=27$ GeV$^2$, from an initial scale $\mu_0=2$ GeV shown in Figure~\ref{fig:xPDF}, large enough for the validity of factorization. Fig.~\ref{fig:evolPDF} shows a comparison with the PDF extraction using LO factorization of the E615 data~\cite{Conway:1989fs}, which shows a $(1-x)$ large-$x$ behavior, and the analysis~\cite{Aicher:2010cb} where the next-to-leading-logarithmic threshold soft-gluon resummation effects~\cite{Sterman:1986aj,Catani:1989ne} are included in the calculation of the Drell-Yan cross section, which shows a softer $(1-x)^2$ falloff.   A comparison between the pion PDFs obtained from previous lattice calculations using the LCS~\cite{Sufian:2019bol}, quasi-PDFs~\cite{Izubuchi:2019lyk,Chen:2018fwa}, and pseudo-PDFs~\cite{Joo:2019bzr} methods can be found in~\cite{Joo:2019bzr}.
\begin{figure}[htp]
\begin{center}
\setlength\abovecaptionskip{-2pt}
\setlength\belowcaptionskip{-2pt}
\includegraphics[width=3.45in, height=2.45in]{evoXPDF-2.pdf}
\caption{\label{fig:evolPDF}
Comparison of pion $xq^\pi_{\rm v}(x)$ distribution obtained from this calculation with the $xq^\pi_{\rm v}(x)$ distributions extracted from the experimental Drell-Yan cross sections. The blue data points are from LO analysis~\cite{Conway:1989fs} and  the ``ASV-rescaled" black data points compiled from~\cite{Chang:2014lva} are the E615 rescaled data according to analysis~\cite{Aicher:2010cb}.  }
\end{center}
\end{figure}

We need QCD factorization and perturbatively calculated matching coefficients to enable us to extract the PDFs since they are neither direct physical observables, nor directly calculable in lattice QCD.   However, QCD factorization is an approximation, and power corrections to the factorization formalism are likely more important when the observable, such as  the Drell-Yan cross section, or  the LQCD-calculated hadron matrix element, is pushed to the edge of phase space where $x\to 1$.  On the other hand, we can get some information on  the $x\to 1$ behavior of PDFs from the convolution of the factorized formalism,  by measuring  the physical cross sections or  calculating the  hadron matrix elements in LQCD not too close to the edge of phase space. However, the garnered  information on $x\sim 1$  will be mild  since the contribution from this region is much smaller than that from  the smaller $x$ regions.  This is exactly the reason why PDFs extracted from world data in QCD global analyses have a large uncertainty as $x\to 1$.  Although it might be difficult to pin down the exact ``power of $(1-x)$'' of  the pion  PDFs, the extraction of PDFs from future improved LQCD calculations of good hadron matrix elements,  the LCSs that are calculable in LQCD and factorizable to PDFs,  might help improve the accuracy of determining this ``power'', since the matching coefficients for LCSs in position space are more perturbatively stable at larger $x$ than the momentum-space matching coefficients for experimentally measured cross sections.

\section{Conclusion and Outlook}
\label{sec:6}

In this  paper we have presented the first LCS calculation of $q^\pi_{\rm v}(x)$ that incorporates results on four gauge ensembles, among these the lightest pion mass used in any lattice QCD calculation to access  $q^\pi_{\rm v}(x)$, as well as the first derivation of NLO matching coefficients from position space directly to momentum space.
The $q^\pi_{\rm v}(x)$ extracted from our LQCD calculation is remarkably consistent with that extracted from experimental data.   Given  that the NLO matching coefficient $K$ is very stable  and without large threshold logarithms  that are often seen in momentum space matching coefficients, our approach, plus future gauge ensembles with smaller lattice spacings, has the unique potential to provide a better determination of the ``power of $(1-x)$" of the $q^\pi_{\rm v}(x)$ distribution as $x\to 1$.

Central to this endeavor are  calculations in the near future with finer lattice spacings.
With a simpler nonperturbative UV renormalization, different choices of current combinations, and the nontrivial hadron-independent and stable NLO matching coefficients, the LCS  formalism  with two-current correlators is well equipped  to unravel the enigmatic structure of the pion and other hadrons, especially those that are difficult, if not impossible, to study experimentally,  complementary to other approaches, such as  the quasi- and pseudo-PDFs approaches.
\\

\section*{ACKNOWLEDGMENTS}
We thank Carl  Carlson, Martha Constantinou, Luka Leskovec, Tianbo Liu, Wayne Morris, Anatoly Radyushkin, Nobuo Sato, and Jian-Hui Zhang who provided insights and expertise that greatly assisted this research.

This work is supported by Jefferson
Science Associates, LLC under U.S. DOE Contract No. \#DE-AC05-06OR23177 within the framework of the TMD Collaboration.
We acknowledge the facilities of the USQCD Collaboration
used for this research in part, which are funded by the Office of Science of the U.S. Department
of Energy. This material is based in part upon work supported by a grant from the Southeastern Universities Research Association (SURA) under an appropriation from the Commonwealth of Virginia. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1548562~\cite{xsede},  and the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for providing HPC resources on {\tt Frontera} that have contributed to the results in this paper.  This work was performed in part using computing facilities at William and Mary which were provided by contributions from the National Science Foundation (MRI grant PHY-1626177), the Commonwealth of Virginia Equipment Trust Fund and the Office of Naval Research. In addition, this work used resources at (National Energy Research Scientific Computing Center) NERSC, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. \#DE-AC02-05CH11231, as well as resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. \#DE-AC05-00OR22725 (ALCC Project No. \#NPH134).  The configurations used in this work were generated under INCITE. The software codes
{\tt Chroma}~\cite{Edwards:2004sx}, {\tt QUDA}~\cite{Clark:2009wm,Babich:2010mu} and {\tt QPhiX}~\cite{QPhiX2} were used.
The authors acknowledge support from the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Nuclear Physics, Scientific Discovery through Advanced Computing (SciDAC) program.
Also acknowledged is support from the U.S. Department of Energy Exascale Computing Project. C.E. is supported in part by the U.S. Department of Energy under Contract No. DE-FG02-04ER41302 and a Department of Energy Office of Science Graduate Student Research fellowship, through the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists, Office of Science Graduate Student Research (SCGSR) program. Y. M. is supported in part by the National Natural Science Foundation of China under Grants No. 11875071 and No. 11975029. K.O. acknowledges support in part  by the U.S. Department of Energy through Grant Number DE- FG02-04ER41302, by STFC consolidated Grant No. ST/P000681/1.

\providecommand{\href}[2]{#2}
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redpajama_set_name: RedPajamaArXiv


You are not an accident child. You are a person of destiny. There are gifts and talents in you just waiting to be released. You have potential that you have not tapped into yet. You are a child of the Most High God!!! I want to encourage you to expand your vision and pursue bigger dreams. Stay in faith. Live with expectancy. Know that any moment YOUR SUDDENLY could happen! You will meet someone who has exactly what you need. You could inherit land and gain your inheritance. Suddenly you could get an idea that will lead to promotion. Miracles Happen when you stay connected to the Holy Spirit.


WASHINGTON ― President Barack Obama on Wednesday commuted the sentences of 214 federal prisoners who were incarcerated on drug charges. The White House said the announcement meant Obama had commuted 562 sentences, more than the past nine presidents combined.
Of that group, 67 had been given life sentences, meaning that up until Wednesday they were living behind bars believing they would die there.
As part of the Obama administration's clemency initiative, the president had shortened the sentences of dozens of individuals in 2016, including in March and in June. The White House said the 214 number was the highest number of commutations announced in a single day since at least 1900, according toBuzzfeed News. Obama has now commuted more sentences than any presidentsince Calvin Coolidge.
Deputy Attorney General Sally Q. Yates said the announcement was "yet another step in the administration's efforts to restore proportionality to unnecessarily long drug sentences," and that the president had already doubled the number of commutations granted in all of 2015.
"But we are not done yet, and we expect that many more men and women will be given a second chance through the Clemency Initiative," Yates said.
The Clemency Project, an outside initiative that helps screen federal prisoners applying for a presidential commutation and submits applications to the Justice Department's Office of the Pardon Attorney, represented 118 of the applicants who had their sentences commuted on Wednesday. Many of the individuals granted clemency on Wednesday are now scheduled for release in December 2016, and others will gain their freedom in August 2018. Additional individuals granted clemency on Wednesday had lengthy sentences shortened, but will not be getting out for many years. An individual sentenced to life in prison in 2009 for intending to distribute thousands of kilograms of marijuana, for example, had his sentence reduced to 30 years.
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Jason Hernandez, whose life sentence was commuted in 2013, told HuffPost that he'd been worried he'd find out a family member had died when he was summoned to the warden's office. Instead, he was told the good news.
But Hernandez had expected the moment to be more joyful. He had imagined jumping, hollering, dancing and singing. In reality, his heart raced. He had trouble breathing. Guilt sank in.
When they're released, former prisoners have to adjust to a world that looks very different from the one they left.
Stephanie George, who was sentenced to life in prison in a drug case, said she was so confused by Facebook that she set up five different accounts, not realizing that she was creating an entirely new page each time and not just signing in. Norman Brown, whose life sentence was commuted last summer,joked that he was used to cellphones "as big as computers" when he was first arrested.
Reynolds Wintersmith, who was sentenced to life in prison on a crack charge when he was still a teenager, said he was amazed to see how many people were staring at their smartphones on the street. "You know how much you missing?" he asked.


text:
What is the point of discussing something conceptually (Criticism)
by Cody Miller , Music of the Spheres - Never Forgot, Tuesday, August 07, 2018, 10:00 (343 days ago) @ kidtsunami
edited by Cody Miller, Tuesday, August 07, 2018, 10:05
I want to try and explain the complexities of software engineering, but it's honestly REALLY hard to tell people how complex some problems are for very little fixes or how easy some fixes have been for what seemed like very complex problems. You honestly never know.
This is probably true. But from the perspective of the player, they don't really care when something is broken. Simple or complex to fix, the result is still the same on their end. The player is paying money for the game, and there are other games out there that are competition.
That's fine, but we're specifically talking about the instances where someone says it's an "EASY" fix... don't change the goal posts.
Like you guys are doing? I was talking about an easy fix CONCEPTUALLY to the system. Not implementation.
Conceptually it's not that hard to edit a movie...
Because you start with the conception! That informs how you actually go about cutting the film. If that foundation is bad, it doesn't matter what you do because it won't be effective.
Michael Bay generally executes on what he intends. But what he intends is stupid.
Likewise designing an inventory management with this shortcoming is stupid. Even if it was hard to implement.
It's honestly hard to explain software development. - MacAddictXIV, 2018-08-06, 06:50
SAS == SAAS - also complexity explained - Blackt1g3r, 2018-08-06, 07:25
SAS == SAAS - also complexity explained - MacAddictXIV, 2018-08-06, 07:58
It's honestly hard to explain software development. - slycrel, 2018-08-06, 13:40
Priorities. - MacAddictXIV, 2018-08-07, 09:48
It's honestly hard to explain software development. - Cody Miller, 2018-08-06, 13:52
It's honestly hard to explain software development. - Blackt1g3r, 2018-08-06, 14:32
It's honestly hard to explain software development. - kidtsunami, 2018-08-07, 08:10
What is the point of discussing something conceptually - kidtsunami, 2018-08-07, 09:31
What is the point of discussing something conceptually - Cody Miller, 2018-08-07, 10:00
What is the point of discussing something conceptually - Harmanimus, 2018-08-07, 10:04
What is the point of discussing something conceptually - Malagate, 2018-08-07, 12:03
What is the point of discussing something conceptually - MacAddictXIV, 2018-08-08, 06:48
Scrolling lists suck. - cheapLEY, 2018-08-07, 14:09
Scrolling lists suck. - Cody Miller, 2018-08-07, 14:14
Scrolling lists suck. - Harmanimus, 2018-08-07, 14:39
Lol! - cheapLEY, 2018-08-07, 15:26
Lol! - Cody Miller, 2018-08-07, 18:13
Lol! - Malagate, 2018-08-08, 08:24
Lol! - breitzen, 2018-08-08, 08:55
It just keeps getting... - Malagate, 2018-08-08, 09:11
Just FYI, it took me maybe 0.1 seconds to find it. - Harmanimus, 2018-08-08, 09:14
Lol! - Claude Errera, 2018-08-08, 09:15
Lol! - Harmanimus, 2018-08-08, 11:29
Lol! - MacAddictXIV, 2018-08-08, 12:30
Lol! - Tails, 2018-08-08, 13:49
+1 - breitzen, 2018-08-08, 13:57
Questing UI - MacAddictXIV, 2018-08-08, 12:31

redpajama_set_name: RedPajamaCommonCrawl


WASHINGTON — (ENEWSPF)–February 28, 2017. On Saturday, Feb. 25th more than 30,000 supporters attended over 150 events in 120 congressional districts across the country in support of the Affordable Care Act. Our Revolution called the turnout "an inspiring display of resistance and a warning to Republicans" who threaten the law.
The turnout reflects shifting attitudes towards the ACA. Support has reached an all-time high, with a recent Pew Research survey showing that 54% of the American people support the landmark health care law.
Our Revolution partnered with OFA, PCCC, PDA, Healthcare Now, DFA, NNU, American Family Voices, WFP, Bold Alliance, Alliance for Retired Americans, and MoveOn to educate and mobilize supporters of the ACA and a move towards a Medicare for All system.


text:
Few things in our world stay static for long, and that includes technology. With new innovations and ideas consistently sculpting the ever-fluctuating landscape of modern technology, the possibilities today are greater than ever before. Cloud computing is among the most popular recent shifts in how data is used and stored, opening the door to compelling possibilities that remove the need for in-house servers and computer-specific file and program access.
Seen by many as both the present and future of computing across all avenues, recreational and professional alike, cloud computing offers a wealth of opportunity.
Cloud Computing Explained
The idea of cloud computing sounds a little more ethereal in concept than it actually is: in reality, cloud computing simply refers to the practice of using remote servers to host programs and store data rather than physical, on-site servers. Servers can be managed by an in-house team, much like traditional servers, or can be hosted by a third party that allows individuals or companies to use space as needed.
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While cloud computing was once a choice, some companies are shifting over to an entirely cloud-based model. This trend is now turning cloud computing into an essential step rather than an optional one, leading to a rapid growth in popularity.
The History of Cloud Computing
The idea of the cloud seems fairly modern in its capabilities, a perception that is likely spurred by a relatively recent embrace of this approach to storage and hosting. However, the original concept aligns more closely with the start of modern computing.
Theoriginal framework for what is now cloud computing was first noted over 50 years ago. The idea was proposed by Defense Advanced Research Projects Agency, a division of the U.S. Department of Defense, in 1963. For the price of just $2,000,000, DARPA requested that scientists at MIT create a solution that would allow a computer to be used by multiple people, simultaneously. At this time, computers were a far cry from today's MacBooks and ThinkPads, with large bolts of magnetic tape in use to store data. Despite the unusual nature of the ask, MIT's computer science experts created a way to allow several people to work with the same machine at the same time. The term "virtualization" was coined to describe this process.
Virtualization, despite its early origins, is still an important concept in computing (virtual servers are becoming increasingly popular as well), but not exactly in its original sense. Anyone who has used a virtual private network to connect to work servers from home or a program like GoToMyPC or Remote Desktop Protocol to access a remote desktop has had experience in the current ideation of this concept.
Virtualization pre-dated the internet as well; the groundwork of the internet formally came into being in 1969 with the ARPANET, an abbreviation for Advanced Research Projects Agency Network, as created by J.C.R. Licklider. His original vision included what he called the Intergalactic Computer Network, a concept that, in practice, evolved into what is today the internet. And, while cloud computing and the internet are not one in the same, the internet is a key element of cloud computing; without the internet, cloud computing as it exists today is an impossibility.
The idea of a web-supported server first began to make waves in the 1990s as the Internet crawled into the public eye. This original context referred more to empty space – the "cloud," so to speak – between a service provider and an end user, and the potential this space had in optimizing software and application availability. The tech giant Salesforce was among the first to bring modern cloud computing into reality in 1999, using the internet to deliver products to users rather than through physical items like floppy disks or CD-ROMs.
Amazon is another key player in the debut of cloud computing. In 2006, Amazon launched Amazon Web Services (AWS), a still-popular option for hosting and storage for those who do not want or need their own servers. The original version Google Drive, Google's answer to web-based alternatives to Microsoft Office, launched in 2006 as well. Google began offering hosting services in conjunction with IBM the following year, and NASA's OpenNebula, an open-source network for both hybrid cloud and private clouds, came about in 2008.
Over the last decade, cloud-based options have grown exponentially, with countless companies offering software options, hosting options, and infrastructure options designed to optimize workflow and manage business costs in a way standard server technology can't.
Unsure Which Cloud Model is Right for You? We Can Help.
What Cloud Computing Services Are Available?
Cloud computing, or cloud technology, comes in several different forms: IaaS, PaaS, and SaaS. These three cloud platforms make up the bulk of the cloud service providers, cloud storage, and any other cloud computing services.
Infrastructure as a Service, more commonly known as IaaS, is a form of virtualization in which outside cloud service providers hosts many of the components of a traditional on-site data center, like servers and networking hardware.
For companies that do not want to handle these tasks, do not have the resources or manpower to take on the complexities that come with on-site services, or want to offload these functions in favor of more important priorities, an IaaS platform can be compelling. In many cases, IaaS options can take on far more than simply hosting data and applications; these operations can encompass a wide range of related tasks and services, including network security, data management, billing, system monitoring, and backup and recovery services. This allows for a greater level of automation on the end user side as these routine functions are taken on virtually.
IaaS users receive data and support via a wide area network, most commonly the internet. Once services are available, users can then expand on what is being offered, including downloading new programs, using IaaS servers to create virtual machines, installing operating systems, and creating storage buckets to manage workloads. In general, IaaS frameworks require the use of a third-party provider. The most common employed for this service include public cloud services like Amazon Web Services and Google Cloud Platform, although private clouds are becoming increasingly popular as a business' cloud infrastructure.
Pros and Cons of IaaS
Like other cloud computing services, there are both advantages and disadvantages of which users should be aware. The primary benefit is, of course, convenience and simplicity. There's no complicated back-end maintenance, leaving developers free to focus on more important tasks. These models can also be affordable, with pricing based on a per-use basis or a flat monthly fee without regard for usage needs like most of the cloud computing vendors today.
For some cloud solutions, availability can be a challenge. If a cloud vendor experiences downtime or has tech issues, these generally cannot be remedied on the user's end. It can also be difficult to migrate products and services to other competing platforms as functionality is often tethered to a PaaS infrastructure. Any internal changes may offer challenges in work progress; for example, if a provider stops providing compatibility for a certain software suite or coding language, progress on a development project can effectively cease immediately.
Possibly the most common form of cloud computing, software as a service, or SaaS, allows providers to share software applications over the web. With a hosted application management model, businesses can employ solutions that are available from everywhere across varying devices via network-based access to an individual copy of a software product. While access and data use are specific to each customer, the source code is universal and any changes that are rolled out apply to all users. Service-level agreements with service providers can dictate whether data is stored locally or in a larger public cloud space.
SaaS programs exist in virtually every arena, including email, financial tools, bookkeeping, customer relationship management, billing, and human resources functions. Some businesses choose to use solely cloud-based software while others utilize a blend of traditional and SaaS solutions. Some of the largest players in this space include names like Salesforce, Oracle, Intuit, and SAP, many of which offer integrated suites that can address a large portion of a business' support needs.
Pros and Cons of SaaS
SaaS programs have plenty of advantages for users, the largest of which is most commonly scalability. As revenue, customer relationships, or any other aspect of a business grows, SaaS products can grow, too, allowing for the use of an increasing depth of services and features for the given workloads of SaaS applications. Automatic updates are also advantageous, ensuring all users are up to date and will not encounter compatibility issues. Accessibility is easier with SaaS solutions, as users can often utilize software across multiple devices and operating systems anywhere with internet access. SaaS programs can also rival traditional alternatives cost-wise, with the use of a cloud reducing on-site support requirements.
However, SaaS solutions aren't perfect. Like IaaS and PaaS, users must rely on an outside vendor, which opens the door to vulnerabilities and service interruptions that can't be controlled. Those who store mass amounts of proprietary data in the cloud may also be concerned about security and protection. Further, automatic updates aren't always wanted. Some companies choose not to update their software for varying reasons, and automatic updates may force features that are undesirable or complicate ongoing tasks and workloads.
Platform as a Service, or PaaS, is a cloud model in which hardware tools, most commonly those used for application development and other computing services, are hosted and shared over the internet rather than on on-site servers. This allows developers to work in a web-based space rather than relying on downloaded and installed platforms. Unlike IaaS, PaaS opportunities do not replace a company's entire IT infrastructure but rather offer options in a complementary fashion. These solutions are used in conjunction with existing platforms, infrastructure, and applications that employ additional computing resources for key services. This can provide an optimized environment for large-scale projects without forcing users to worry about the underlying support requirements.
While PaaS options come in numerous forms and for many functions, application development is the primary purpose of most PaaS solutions. PaaS products offer a collaborative environment that can move and grow as needs for development and computing resources change, creating a flexible way to enhance the process of computation and storage infrastructure.
Pros and Cons of PaaS
Like all cloud solutions, availability can be a challenge. If a cloud vendor experiences downtime or has tech issues, these generally cannot be remedied on the user's end. It can also be difficult to migrate products and services to other competing platforms as functionality is often tethered to a PaaS infrastructure. Any internal changes may offer challenges in work progress; for example, if a provider stops providing compatibility for a certain software suite or coding language, progress on a development project can effectively cease immediately.
As indicated, cloud computing can cover numerous different aspects of computing requirements. However, it's also important to note that all clouds aren't made equal. Depending on business and security needs, due diligence on the varying options is an essential part of choosing cloud-based solutions.
Public clouds, as the name implies, are clouds that can be used by members of the public. Most cloud-based solutions operate through public clouds, providing easy access to all kinds of users. Google Docs, for example, functions in a public cloud that all Google account holders are able to access. Documents and data are still kept private and accounts are managed individually, but use of the cloud itself is not. With a public cloud, all storage, infrastructure, hardware, and software are managed by the cloud provider with no real input from users.
Public clouds are often preferred by recreational web users due to their ease of use and lower costs with no need to purchase or provide maintenance. Business users appreciate public clouds for similar reasons, with additional benefits including a large opportunity to scale and reasonably high levels of reliability. However, privacy can be a very real concern for those companies that work with proprietary or confidential data.
Private clouds are the opposite of public clouds: private clouds only exist for the use of one individual organization or operation. Private clouds can be located at an on-site data center or can be hosted by third parties specializing in private servers. When a private cloud is in use, all resources are limited to, and can only be accessed by, permitted members. This form of cloud usage is often preferred by companies that desire higher levels of security, customization, or organization. These are most commonly employed by government bodies, financial institutions, healthcare organizations, and other companies that feel obligated to protect and manage data in a more stringent manner.
Private clouds are more flexible, more functional, and are also extremely scalable. However, they are almost always more expensive and, if they are operated in-house, require a similar level of maintenance and support as traditional physical servers, eliminating any cost savings benefits. Although the costs can be higher, what a business gets for the price is greater. Cloud infrastructure, cloud storage, hardware and software, and any other cloud computing or workloads can be handle by a competent private cloud provider.
For many users, hybrid clouds offer the best of both worlds, providing a way to harness the privacy of a private cloud with the flexibility and ease of use of a public cloud. Others will utilize a mix of onsite infrastructure and a public cloud or private cloud. For example, a business may wish to host sensitive information on a private cloud while other forms of data, particularly high-volume applications, on public cloud platforms. Hybrid clouds also allow for a concept known as cloud bursting in which functions can transfer between clouds when user needs so require. A busy season, like tax season at a financial products company, is an example of this – during the year, the demands of customer access to tax software isn't high, but in March and April, usage surges in a way that could exceed limits of a small or modest private cloud. With the ability to shift some functions into the public cloud, businesses can effectively prevent service interruptions.
Hybrid clouds are frequently viewed as most flexible of cloud computing options and allow for the greatest sense of control while still reducing costs. Use of a hybrid cloud also provides ease of use with minimal onboarding obligations as getting started can be a gradual process split between both clouds. Some businesses get their feet with a hybrid cloud model allowing for an easier cloud adoption since they feel they can get versatility with a multiple cloud set up.
Although hybrid clouds seem like the best of both worlds, they have a number of downsides as well. The primary issue with a hybrid cloud model is performance. When computers and some data is stored locally, but other servers or applications are hosted elsewhere performance can decrease. Another factor to consider is there is additional hardware costs since you will maintain having data onsite. Many companies also have cyber security concerns with their data being split into multiple locations and having to ensure multiple fronts are protected and secure.
Why Is Cloud Computing Important?
In many ways, nothing typifies the state of modern technology like cloud computing. As a deviation from the origins of computer use, many benefits of the cloud promote collaboration, flexibility, and easy access. Web users, both casual and regular, can access just about anything in the cloud, from shared Google Docs to bookkeeping software like QuickBooks. Cloud computing is a demonstration of where technology has been as well as where it's going, representing the best in present business trends.
Cloud Computing for Business
While cloud computing is certainly convenient and appreciated by recreational web users, businesses are far better positioned to take advantage of the benefits of cloud computing. With cloud solutions, businesses of all sizes are able to access applications and development spaces, and manage infrastructure from virtually anywhere, leading to optimization that can't be matched using traditional servers. When using the cloud, employees can check database records on the go, upload receipts to accounting software, generate dashboards with a few clicks, or do whatever else is necessary to keep business moving forward.
Cloud computing also offers scalable opportunities that can allow for growth and change over time, ensuring there are no storage or software constraints as goals are achieved and targets grow. Via a combination of IaaS, SaaS, and PaaS options, businesses can create a cost-effective and customizable approach to a business infrastructure that facilitates fast, efficient, and accessible workspaces.
The Risks of Cloud Computing
Nothing on the internet is completely secure, and that includes services and solutions hosted in the cloud. While all providers work diligently to reduce the risk to users, there are still many ways in which cloud users can find their data compromised, applications at risk, and productivity at a standstill. While different users will have different fears and priorities in ensuring safety in cloud computing, the most serious risks to users include:
The possibility of unauthorized access to user data
Security risks including unscrupulous employees, vendor security, and poor employee training
Compliance and legal risks, particularly for companies operating under more stringent privacy regulations, like GDPR , DFARS, or HIPAA
Availability risks, like scheduled or unscheduled server downtime
As with any technology, companies should carefully evaluate the risks when shifting to a new cloud infrastructure or cloud provider.
Despite the ever-present risks of hacking, viruses, and other ways in which information and access can become compromised, cloud service providers work tirelessly to provide the best possible security to users and clients. While measures differ based on the service in questions, cloud security functions typically employ a multi-faceted approach in order to ensure as many bases are covered as possible. While different operations have varying priorities, the most common security methods include:
Identity Management: A way to ensure only those authorized can access data, many providers use a combination of SSO security or biometric-based ID systems to manage the identity of users. This kind of information is generally encrypted to prevent against hacker and provider employee access.
On-site Security: In addition to protecting access virtually, providers also utilize physical security to safeguard the technology that supports cloud-based servers, like routers, against vandalism and natural resource damage.
Employment Screenings: To ensure just anyone can't come into contact with private or sensitive data, employment screenings are generally rigorous for those involved in the hiring and training of provider employees.
Data Encryption: Data maintained in the cloud is highly encrypted to prevent against unauthorized access, with common methods including cyphertext-policy and key-policy attribute-based encryption, fully homomorphic encryption, and searchable encryption.
Competent service providers also take compliance seriously, working to meet the regulations surrounding legislation like the Sarbanes-Oxley Act and the Health Insurance Portability and Accountability Act (HIPAA).
Disaster recovery is primary focus for cloud providers. As no business can afford to lose data, cloud computing providers go to great lengths to ensure that information can be recovered, even in disaster situations. In this context, disaster recovery includes a backup and restoration strategy in which numerous copies of client data are maintained in several forms so that even an unprecedented event cannot destroy everything.
Data is often backed up in multiple locations and at multiple intervals. For example, a provider may make a daily or even hourly copy of data that is stored for a period of time, like a week, while also creating physical backup copies on a slightly less frequent timeline, like once a month. The details of a particular provider's disaster recovery plan are generally included in service-level agreements, including any kind of compensation should disaster recovery fall short. This should be a key component of due diligence for users considering several options.
The Costs of Cloud Computing
Cloud computing is frequently touted as a cost-effective alternative to more traditional services, offering a scalable resource that can save money, reduce hardware and software needs, optimize performance, and accommodate growth. However, this is hardly a quantifiable description of what companies can expect when transitioning to the cloud.
Despite the fact that the cloud can be a way to save money, the true costs are extremely variable. Some cloud solutions, like Google Drive, are completely free, while others may cost thousands or even millions of dollars to properly implement. Companies that require expansive, enterprise-scale solutions will find themselves facing far steeper costs than a startup striving to get off the ground.
The best way to evaluate costs is to reach out to SaaS, PaaS, and IaaS operations, seek quotes, and perform a comprehensive cost-benefit analysis before moving forward, regarding both costs today and in the future. Many cost-saving opportunities won't happen this year or next year, but instead several years down the road, so consider the ways in which cloud computing can reduce license costs, FTE requirements, and other related charges.
Cloud computing is an important part of the present and the future of modern technology. With impressive opportunities available for both professional and recreational web users alike, it's guaranteed that cloud computing will continue to offer compelling solutions today and for years to come.
The Best IT Platform
If you're looking to make the transition to a cloud platform, like a public cloud, private cloud, hybrid cloud, or are just looking to update your infrastructure, we can help you navigate what is currently available and steer you in the right direction. Looking for a cloud provider or cloud platform can be challenging, especially with so many popular types of cloud like Google Cloud, Microsoft Azure, Rackspace, and Amazon Web Services.
We can help you maneuver through these crowded options and point you in the right direction. We have the most secure private cloud environment in the country that can handle any cloud computing work, but you may not need that and we will be up front and tell you. You may just need some extra cloud storage, more computing power, or frankly different software to handle your company's workloads. We can show you how the benefits of cloud can improve your productivity, mobility, and cyber security.
At Avatara our definition of cloud computing is simple: it is simply a better way to run a business.
Who We Are and How We Operate – Part 2, The Sales Team
What is Infrastructure as a Service (IaaS)?


Have you got a passion for addressing the major issues and challenges facing today's global community? The BA Development Studies programme draws upon the significant expertise of our academic staff. This exciting programme examines key topics in international development, while analysing the roles and impact of a wide variety of regional and international actors. By the time you graduate, you will have cultivated a deep knowledge of the causes of - and responses to - poverty, marginalisation and vulnerability in developing countries and the process of dramatic social, economic and political change.
Why study Development Studies at SOAS?
Find out more about our Development Studies department page.
What does the BA programme look like?
Taster Lecture: Should we give to charity?
**Please note that final year students may not take any introductory level modules, including languages.
Our teaching and learning approach is designed to support and encourage students in their own process of self-learning, and to develop their own ideas, responses and critique of international development practice and policy. We do this through a mixture of lectures, and more student-centred learning approaches (including tutorials and seminars). Teaching combines innovative use of audio-visual materials, practical exercises, group discussions, and guided reading as well as conventional lecturing. Assessment of most modules is through a combination of coursework and written examination.
The introductory and core modules provide the solid disciplinary grounding, whilst options allow students to develop deeper expertise in areas of their own interest. In their final year, students have the opportunity to complete either an Independent Study Project, an extended 10,000 word essay, supervised by one of the Department staff; or an assessed Professional Placement.
As a rough guide, 1 credit equals approximately 10 hours of work. Most of this will be independent study (see Approaches to teaching and learning at SOAS). It will also include class time, which may include lectures, seminars and other classes. Some subjects, such as learning a language, have more class time than others. In the Department of Development Studies, most undergraduate modules have a 2-hour lecture and a 1-hour tutorial every week. A few modules, which are jointly taught with PG students, have a 1-hour lecture and a 1-hour tutorial every week.
The degree structure allows students to develop their understanding of the world, other peoples' ways of life and how society is organised, with specific focus on violence and conflict, the role of aid, refugees and forced migration.
Graduates go on to work in development planning and in government and non-governmental organisations (NGOs). Other career paths include journalism, the civil service, banking and the social and educational services. Others are interested in specialising further through postgraduate studies, not only in Development Studies, but also in Economics, Politics, Social Anthropology, Law, Geography, History and Languages.


1883 Seated Liberty Dime. NGC graded MS-65. CAC Approved.
1884 Seated Liberty Dime. PCGS graded MS-66. CAC Approved.
A frosty, mostly white example that is quite well struck on each side. The brilliant surfaces have a sheet of silver luster that shimmers and sparkles and is uninterrupted by any noticeable abrasions.


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Tag Archives: cyberattack United States
Who is Afraid of Shamoon? How to Wipe a Country Off the Face of the Earth
Suspected Iranian hackers infiltrated critical infrastructure and government computers in the Persian Gulf nation of Bahrain in July-August 2019, raising fears among leaders in the region that Tehran is stepping up its cyberattacks amid growing tensions…Hackers broke into the systems of Bahrain's National Security Agency—the country's main criminal investigative authority—as well as the Ministry of Interior and the first deputy prime minister's office, according to one of the people familiar with the matter.
On July 25, 2019 Bahrain authorities identified intrusions into its Electricity and Water Authority. The hackers shut down several systems in what the authorities believed was a test run of Iran's capability to disrupt the country, the person said. "They had command and control of some of the systems," the person said. The breaches appeared broadly similar to two hacks in 2012 that knocked Qatar's natural-gas firm RasGas offline and wiped data from computer hard drives belonging to Saudi Arabia's Aramco national oil company, a devastating attack that relied on a powerful virus known as Shamoon. Bahrain is the smallest country in the Persian Gulf, but it is strategically important because it's the permanent home of the U.S. Navy's Fifth Fleet and Navy Central Command. It is closely allied with its much larger neighbor, Saudi Arabia, a regional rival of Iran.
The Bahrain authorities haven't definitively attributed the attack to Iran, but they have been provided intelligence by the U.S. and others suggesting Iran is behind it, the people familiar with the matter said…."In the first half of 2019, the Information & eGovernment Authority successfully intercepted over 6 million attacks and over 830,000 malicious emails. The attempted attacks did not result in downtime or disruption of government services,"
Excerpt from High-Level Cyber Intrusions Hit Bahrain Amid Tensions With Iran, WSJ, Aug. 7, 2019
This entry was posted in covert action, cyberwar, War and tagged computer virus, cyber intrusion, cyber spying, cyber weapons, cyber-espionage, cyberattack, cyberattack Iran, cyberattack Saudi Arabia, cyberattack United States, cyberdefense, cybersecurity, cyberspace, cyberwarriors, cyberweapons, duqu virus, Flame virus, Shamoon virus, siemens virus, Stuxnet, Stuxnet Iran nuclear power plants, stuxnet United States, Stuxnet virus, Stuxnet worm on August 13, 2019 by Stoa.
Predators: Tax Avoidance in Luxembourg
Antoine Deltour and Raphaël Halet, two ex-employees of PwC, an accounting firm, and Edouard Perrin, a French journalist, had been tried in Luxembourg for their role in leaking documents that revealed sweetheart tax deals the Grand Duchy had offered to dozens of multinationals. ..The whistle-blowers faced up to ten years behind bars. However, the prosecutor—perhaps sensitive to the strong public and, in some places, political support for them abroad—called for suspended sentences of 18 months. In the end the judge handed Messrs Deltour and Halet suspended sentences of 12 months and nine months, respectively. But a conviction is a conviction; Transparency International, an anti-corruption group, called it "appalling". Mr Perrin, who had published an article that drew on the leaked documents, was acquitted.
The "LuxLeaks" affair has highlighted the role played by certain European Union countries, including Ireland and the Netherlands as well as Luxembourg, in facilitating tax avoidance. Luxembourg is not a typical tax haven levying no or minimal income tax; its statutory rate is 29%. Instead, it is a haven "by administrative practice", argues Omri Marian of the University of California, Irvine, who has studied LuxLeaks in detail. Luxembourg's tax authority in effect sold tax-avoidance services to large firms by rubber-stamping opaque arrangements that helped them to cut their tax bills dramatically in both their countries of residence and their countries of operation.]
Excerpt from Tax avoidance: Grand dodgy, Economist, July 2, 2016
This entry was posted in corruption/Illegal markets, Espionage, geoeconomics, Markets, power elite and tagged cyberattack United States, LuxLeaks, tax avoidance, tax evasion, tax havens on July 19, 2016 by Stoa.


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These key races will be indicators of how the US House race plays out on election night.
Republicans are strongly favored to take over the US House due to a favorable political environment and the effects of the redistricting process, but there is still considerable uncertainty about how election night will play out – whether the Republicans will win in a landslide, if they narrowly win, or if Democrats defy the odds and retain control of the House.
Here are the races of Dave Wasserman The Cook Political Report suggests watching the polls close on Tuesday for an indication of how the night is going.
VA-02: Elaine Luria vs. Jen Kiggins
Ms. Luria was first elected to Congress in the 2018 Democratic wave, but faces a tough challenge from Republican Jen Kiggins in a district that has become slightly more Republican in the redistricting. Ms. Luria has spent much of her campaign highlighting her pro-democracy work in Congress; if she retains her seat, it could be an indication that Democrats have a chance to retain control of the House or significantly limit their losses.
VA-07: Abigail Spanberger vs. Yesli Vega
Like her colleague Ms. Luria, the moderate Ms. Spanberger was first elected to her seat in suburban Washington, D.C. in the 2018 wave. Her race against Yesli Vega, an ultra-conservative Prince William County commissioner , expected to be competitive: Ms. Spanberger was only narrowly re-elected in 2020, and she is running in a district that is mostly new after redistricting. If Ms. Vega wins, Republicans will likely easily win the House.
VA-10: Jennifer Wexton vs. Hung Cao
Of Virginia's three flagship races, it's the one Democrats feel most confident about. Ms. Wexton, another two-term holder, takes on retired US Navy Captain Hung Cao in a Democratic-leaning district. If Mr. Cao is the winner, it would likely signal the start of a red wave.
IN-01: Frank Mrvan vs. Jennifer-Ruth Green
Indiana's First Congressional District, centered around the majority-black town of Gary, has long been a Democratic stronghold. The seat was held for decades by Pete Visclosky, who retired after the conclusion of the last Congress and was replaced by Mr. Mrvan. Now Mr. Mrvan faces an uphill fight for re-election against Jennifer-Ruth Green, a black and Asian pilot who attacked Mr. Mrvan for serving the interests of "rich white people". If Ms. Green wins, it will likely mean the Republicans are on for a big night.
NH-02: Ann Kuster vs. Robert Burns
Veteran Democratic Rep. Ann Kuster's district covers much of the northern and western part of Granite State. Ms Kuster has been re-elected to that seat by more than 10 points in the past two cycles, but may face a tougher challenge this time around from Republican Robert Burns. It's a seat Democrats would expect to take on a competitive night — the other New Hampshire seat held by Democrat Chris Pappas is expected to be closer.
Other Races to Watch
Several other races will go a long way in determining which party controls the House and to what extent. Three of those few in South Texas, in a state that tends to count its votes quickly, where veterans, conservative Democratic Representatives Henry Cuellar and Vicente Gonzalez are seeking re-election in a blushing region that Democrats in the State believe that the national party has neglected . Michelle Vallejo, a progressive Democrat, is also running for a competitive open seat against Republican Monica De La Cruz.
There are several top Democrats whose seats appear to be in jeopardy, and perhaps no top Democrat is more in jeopardy than Sean Patrick Maloney – the Democratic campaign leader who spent lavishly on his own re-election bid against Republican Michael Lawler.
Mr Maloney, who angered progressive Democrats over the summer when he decided to run in a redesigned district that is currently largely represented by Representative Mondaire Jones, is the campaign committee's second consecutive chairman. Congressman to face a surprisingly tough re-election fight after Rep. Cheri Bustos of Illinois in 2020. Ms. Bustos is retiring at the end of her current term.
By the time polls close on the West Coast, the overall direction of the race will likely become clearer. Republicans are hoping to win seats in the traditionally Democratic territory of Oregon and California, although the final results of the close races in those states are unlikely to be known on election night.
Carragher 'surprised' by FSG announcement but Neville says 'selling Liverpool makes sense'
Once a solace, rain is now ruining Australia's mood
The deadliest crowd crushes of the past decade
Simon Cowell credits his eight-year-old son with saving his life


One Fine Ford: CAL Automotive Creations' 1930 Model A "Afterthought"
You know that one rod that stops you in your tracks?
The one you can't get out of your head no matter how many Deuce Coupes, roadsters and Shoeboxes you see? Well, this amazing Model A by Andy Leach is all that.


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Public Schools in Montgomery, Minnesota
Le Sueur County
There are 5 Public Schools in Montgomery, Minnesota, serving a population of 2,921 people in an area of 3 square miles. There is 1 Public School per 584 people, and 1 Public School per square mile.
In Minnesota, Montgomery is ranked 184th of 1018 cities in Public Schools per capita, and 115th of 1018 cities in Public Schools per square mile.
List of Montgomery Public Schools
Find Montgomery, Minnesota public schools, including charter schools, k-12, elementary, middle, and high schools.
Montgomery Pre K-8 101 2nd Street Northeast Montgomery, MN
Montgomery-Lonsdale Elementary School 700 4th Street Northwest Montgomery, MN
Montgomery-Lonsdale Middle 101 2nd Street Northeast Montgomery, MN
Montgomery-Lonsdale Secondary School 101 2nd Street Northeast Montgomery, MN
Tri-City United High School 700 4th Street Northwest Montgomery, MN
About Montgomery Public Schools
Montgomery Public Schools are tuition-free, publicly funded schools that are legally required to accept and provide an education to all children from Kindergarten age through Grade 12 in Montgomery, MN. Each of the fifty state constitutions includes a requirement for the provision of a Public School system, and each state, including Minnesota, also has a compulsory education law that requires school-age children to attend school.
Montgomery Public School calendars
Montgomery school district
Montgomery Public School Statistics
Find Montgomery Public School Enrollment and Educational Attainment (Age 25+). Data Source: U.S. Census Bureau; American Community Survey, 2018 ACS 5-Year Estimates.
Montgomery Public School Enrollment
Nursery & Preschool Enrollment 7 (35.0%) 530 (83.3%)
Kindergarten Enrollment 50 (100.0%) 281 (90.4%)
Elementary School Enrollment (Grades 1-4) 203 (96.7%) 1,221 (90.0%)
High School Enrollment (Grades 9-12) 142 (100.0%) 1,540 (95.4%)
Montgomery Educational Attainment (Age 25+)
Less than 9th Grade Education 9 (0.5%) 456 (2.4%)
9-12th Grade (No Diploma) 181 (9.6%) 926 (4.8%)
High School Graduate (Including Equivalency) 730 (38.7%) 6,675 (34.9%)
Public Schools near Montgomery
Other Montgomery Offices


Earlier security guards were treated as a luxury but at present, it has become a need. You can find them everywhere to protect schools, banks, businesses, other important places even individuals are keeping them for their and their home's security. To hire and take their services you can contact any local security guards agency or online you can get so many agencies that provide well trained Houston security guards for personal or other security reasons. Private security is one of the increasing services asked by most of the individuals. In that case, you need to contact Houston private security. They will provide the best guards for your protection.
Guards are there to provide us with safety and security all the time. They are proactive while performing their duties.
Guards are properly trained and responsible to perform various duties at the same time. They do their job in shifts whether it is day or night. They keep an eye on CCTV or individuals who are visiting society, banks or business premises.
Hiring a security guard is not a very expensive task. You can avail their services at a nominal rate.
Security guards are very active and quick responsive while performing their duties and perform the entire task which is needed for an individual's safety.
Security guards are qualified and expertise. They are physical, mentally and emotionally trained and well trained to take themselves and others out from the crime and danger.
"It is always better to be safe than sorry" this is true in case of safety and one should never compromise on it. Guards are there for our help and safety till the police arrive and to prevent the criminal activities before it occurs.


Holidays bring joy — and often food anxiety. How to cook, how to serve, and, finally, how much? In an era when we all seem to be on a diet, do you give in and make everything Grandma did?
Today's goal is not to re-create a Norman Rockwell painting, but to make a festive meal you will be happy to serve on Thanksgiving Day. The biggest change: If you don't need to present the whole turkey for carving at the table, cook a turkey breast instead.
If you start with a fresh turkey breast, you don't have to worry about thawing it in time to cook for dinner. It will probably come with directions and a pop-up timer, but here are the basics: A 5-pound to 6-pound turkey breast roasted at 325 °F will cook in about 2 hours. Basting with butter or oil isn't necessary. You'll remove the skin before slicing and serving, because that's where most of the fat is.
The breast will supply about 3 pounds of solid white meat. A 3-ounce serving — about the size of a deck of cards — contains 115 calories, 26 grams protein, less than a gram of fat, 71 mg cholesterol, no carbohydrate or fiber, and 44 mg sodium.
Gravy. A turkey breast won't provide a lot of juice, so add some nonfat chicken broth. To thicken, start with a tablespoon of flour or cornstarch dissolved in a half cup of cold water. Stir it with a whisk. Add chopped mushrooms for a giblet texture.
Vegetables. Instead of adding things to your vegetables, let them be themselves. Steam the beans and use fresh-cut veggies as an appetizer tray, maybe with a little low-fat dip. Plain sweet potatoes — hold the marshmallows, please — add color to your plate.
Dessert. Skip the big pies and do a tray of mini-tarts or petit fours from a bakery or the freezer.
The great plate debate. Consider using 8-inch plates and leaving Grandma's 10-inch china in the cupboard. Smaller plates will help people choose smaller portions without having to think about it.
Fuss less. Cleanup is easier with throwaway foil roasting pans. Aluminum foil makes a perfect cover to keep your turkey breast from over-browning and your outside-the-bird stuffing from drying out.
Plan your menu. Shoot for quality, not quantity. You don't need more food than your family and guests will eat or more leftovers than you can enjoy. As you plan the menu, ask what they'd miss if it weren't there.
Call for help. You can call the USDA Meat and Poultry Hotline toll-free at 888-674-6854 from 10 a.m. to 4 p.m. weekdays except federal holidays and Thanksgiving Day, when it's open from 8 a.m. to 2 p.m. The USDA will answer e-mail questions sent to mphotline.fsis@usda.gov.