text:
\section{Introduction}                                                 %

Generalized parton distributions%
~\cite{Mueller:1998fv,Ji:1996ek,Ji:1996nm,Radyushkin:1996nd,Radyushkin:1996ru}
contain the physics of form factors and parton distributions,
and thereby allow for the study of correlations between transverse position and longitudinal momentum inside hadrons.
In impact-parameter space,
GPDs elegantly describe the transverse structure of fast moving hadrons%
~\cite{Burkardt:2000za,Burkardt:2002hr,Diehl:2002he}.
Intense activity has been generated in this field,
which is largely due to the ability to measure GPDs in deeply virtual Compton scattering,
and resolve the angular momentum content of hadrons.
A number of insightful reviews have appeared on the subject,
see,
for example,
Refs.~\cite{Goeke:2001tz,Diehl:2003ny,Belitsky:2005qn,Boffi:2007yc}.

From a theoretical perspective,
GPDs are rather complicated objects to model.
As with ordinary parton distribution functions,
flexible phenomenological parameterizations would be welcome to aid in their extraction from data.
The large number of constraints imposed on GPDs,
however,
makes such parameterizations challenging to devise.
One such non-trivial constraint required of GPDs is a general bound due to the positivity of the norm on the hadronic light-front Fock space.
These so-called positivity bounds are introduced and discussed in several works%
~\cite{Martin:1997wy,Ji:1998pc,Pire:1998nw,Radyushkin:1998es,Pobylitsa:2001nt,Pobylitsa:2002gw}.

As a simple example of a positivity bound,
consider the mixed coordinate-space density in a quantum mechanical state
$| \psi \rangle$,
which has the form
$\rho(\bm{r}', \bm{r}) = \langle \bm{r}' | \psi \rangle \langle \psi | \bm{r} \rangle$.
The corresponding density is strictly positive semidefinite,
$\rho(\bm{r}) \equiv |\langle \bm{r} | \psi \rangle|^2 \geq 0$.
Accordingly,
the mixed density satisfies the bound
\begin{equation}
|\rho(\bm{r}', \bm{r}) |
\leq
\sqrt{\rho(\bm{r}') \rho(\bm{r})}
,\end{equation}
as a consequence of the Schwarz inequality.
In the case of GPDs,
the underlying parton distribution,
$q(x)$,
is a probability distribution and thereby satisfies the positivity condition
$q(x) \geq 0$.
The GPD is similar in structure to a mixed plus-momentum density in the bound state.
With symmetrical kinematic variables
and for
$x>\xi$,
the incoming parton has momentum fraction
$x_i = (x + \xi) / (1 + \xi)$,
and the outgoing parton has momentum fraction
$x_f = (x- \xi) / (1 - \xi)$.
On account of the Cauchy-Schwarz inequality,
the pion GPD,
which we denote by
$H(x,\xi,t)$,
is bounded by
\begin{equation}
|H(x,\xi,t)|
\leq
\sqrt{  q ( x_f ) q ( x_i )}
,\end{equation}
when
$x > \xi$.
If the GPD is expressed in terms of quark light-front wavefunctions,
this positivity bound is an immediate consequence that arises from the convolution of diagonal Fock-state wavefunctions%
~\cite{Brodsky:2000xy,Diehl:2000xz}.
While not manifestly Lorentz covariant,
the light-front Fock-space expansion makes the positivity bound transparent.
On the other hand,
the large number of constraints on GPDs stemming from Lorentz invariance are best satisfied within Lorentz covariant frameworks,
for which purpose the double distributions (DDs) have been devised%
~\cite{Radyushkin:1997ki,Radyushkin:1998es}.
Such frameworks,
however,
obfuscate the positivity bound.
This situation is addressed in the present work;
and,
we argue that the impulse approximation,
while Lorentz covariant,
is insufficient to describe the higher Fock components self consistently.
As a result,
the positivity bound on GPDs can be violated in the impulse approximation,
and we use the particular model of
Ref.~\cite{Fanelli:2016aqc}
to exemplify this fact.

The calculation of model GPDs in Lorentz covariant frameworks is not entirely new,
however,
the line of investigation pursued in
Ref.~\cite{Fanelli:2016aqc}
represents a physically motivated departure from earlier models.
Such models have largely employed the point-like bound-state vertex arising in the Nambu--Jona-Lasinio model,
a couple examples of which are
Refs.~\cite{Theussl:2002xp,Broniowski:2007si}.
While simple,
the point-like Ansatz provides a solution of the Bethe-Salpeter equation with a contact interaction that includes a binding effect.
As the particular contact interaction cannot be gauged,
the point-like model is complete in the impulse approximation.
The corresponding model GPDs should then satisfy all known constraints,
modulo difficulties arising from the regularization of ultraviolet divergences.
The potential danger of these subtractions on the positivity bound was discussed in
Ref.~\cite{Broniowski:2007si},
where it was found that a particular Pauli-Villars subtraction%
~\cite{Davidson:1994uv}
maintains the positivity bound on GPDs.
As pointed out in
Ref.~\cite{Pobylitsa:2002vw},
one can construct further consistent models of GPDs by summing over these basic contributions evaluated at different constituent masses.
This is the essence of the consistency of the spectral quark model GPDs computed in
Ref.~\cite{Broniowski:2007si};
however,
it must be stressed that,
unlike two-point functions,
GPDs do not possess a spectral representation.
In contrast to these models,
that employed in
Ref.~\cite{Fanelli:2016aqc}
introduces a
\emph{non}
point-like Bethe-Salpeter vertex for the bound state.
This covariant smearing has the salient feature that ultraviolet divergences are cured;
however,
such an Ansatz arises from a non-trivial kernel.
Without knowledge of the underlying dynamics,
one does not know how to gauge the kernel and such contributions must be omitted.
Due to this malady,
the model is incomplete in the impulse approximation.
Consequently the positivity bound cannot be guaranteed;
and,
indeed,
we find that it is (rather severely) violated.%
\footnote{
Beyond writing down flexible parameterizations of GPDs,
there is also interest in computing GPDs using dynamical models.
Considerable interest has been recently generated%
~\cite{Karmanov:2005nv,Carbonell:2008tz,Carbonell:2017kqa}
by the ability to obtain light-front solutions from Bethe-Salpeter wavefunctions by way of the Nakanishi integral representation%
~\cite{Nakanishi:1963zz,Nakanishi:1969ph}.
In light of the present work,
the positivity bound on GPDs provides an essential test of the consistency of form factors and quark distributions obtained in such an approach.
In another direction,
valence quark distributions of pseudoscalar mesons have been obtained from solutions to a model based on truncated Dyson-Schwinger equations%
~\cite{Nguyen:2011jy}.
While incorporating some of the features of QCD,
it is already recognized that the impulse approximation is insufficient to describe GPDs within this approach~\cite{Mezrag:2014jka}.
}

The organization of this work is as follows.
We begin with a short reminder about the definitions of the Lorentz invariant
DDs in
Sec.~\ref{s:DD},
and determine the
DDs for the covariant model of the pion proposed in
Ref.~\cite{Fanelli:2016aqc}.
Technical details in the computation of the DDs are relegated to Appendix~\ref{s:A}.
The DDs are used to compute the pion GPD,
and the positivity bound is shown to be violated,
both in strong and weak forms.
Investigating the cause of this violation leads us to the light-front
Fock-space representation of
GPDs in Sec.~\ref{s:LFWF}.
Here,
an analysis of the pole structure leading to the light-front representation of the GPD is given.
We argue that positivity violation arises from the mismatch between the endpoint behavior of the quark distribution and the crossover value of the GPD.
Appendix~\ref{s:B} provides details about light-front spinors, normalization factors, and other conventions employed.
A brief summary,
which is given in Sec.~\ref{s:summy},
concludes this work.

\section{The Model and its Double Distributions}
\label{s:DD}

While GPDs are not Lorentz invariant objects,
they nonetheless inherit a number of constraints related to the underlying Lorentz covariance of their defining QCD matrix elements.
These constraints
(in particular, the polynomiality of GPD moments)
are elegantly satisfied by employing the DD representation.
The DD for a given model is Lorentz invariant,
and the GPD is obtained by non-covariant integration over a slice in the space where the DD has support%
~\cite{Radyushkin:1997ki,Radyushkin:1998es}.

As our focus is with Lorentz covariant models for GPDs,
we begin with the DD representation.
Pertinent definitions and conventions for pion DDs are reviewed,
followed by the determination of the DDs in a covariant model of the poin.
The positivity bound is then tested in this model,
and found to be violated.

\subsection{Double Distributions}

Matrix elements of twist-two operators with a $t$-channel momentum transfer define moments
which can be summed into the so-called DDs.
Using the symmetric derivative,
which we define by
$\overset{\leftrightarrow}{D} {}^\mu = \frac{1}{2} \left( \overset{\rightarrow}{D} {}^\mu - \overset{\leftarrow}{D} {}^\mu\right)$,
the quark bilinear twist-two operators have the form
\begin{equation}
\mathcal{O}^{\mu \mu_1 \cdots \mu_n}
=
\ol \psi (0) \gamma^{\big\{ \mu} i \overset{\leftrightarrow}{D} {}^{\mu_1} \cdots i \overset{\leftrightarrow}{D} {}^{\mu_n \big\}} \psi(0)
\label{eq:twistO}
,\end{equation}
where the curly brackets denote the complete symmetrization and trace subtraction of the enclosed Lorentz indices.
Matrix elements,
${\mathcal M}^{\mu \mu_1 \cdots \mu_n}$,
of these operators within the pion are defined by
\begin{eqnarray}
{\mathcal M}^{\mu \mu_1 \cdots \mu_n}
\equiv
\Big\langle P'  \Big|
\mathcal{O}^{\mu \mu_1 \cdots \mu_n}
\Big| P \Big\rangle
,\end{eqnarray}
where
$P' = P + \Delta$;
and,
the matrix elements can be parameterized in the form
\begin{eqnarray}
{\mathcal M}^{\mu \mu_1 \cdots \mu_n}
&=&
\sum_{k = 0}^n
\begin{pmatrix} n \\ k \end{pmatrix}
\left( 2 \ol P A_{nk} - \Delta B_{nk} \right)^{\big\{ \mu}
\ol P {}^{\mu_1} \cdots \ol P {}^{\mu_{n-k}}
\notag
\\
&& \phantom{sp} \times
\left(-\frac{\Delta}{2}\right)^{\mu_{n-k+1}}
\cdots
\left(-\frac{\Delta}{2}\right)^{\mu_{n} \big\}}
,\label{eq:DDecomp}
\end{eqnarray}
where the $(nk)$-th moments are Lorentz invariant functions of the $t$-channel momentum transfer,
$A_{nk} = A_{nk}(t)$
and
$B_{nk} = B_{nk}(t)$,
with
$t = \Delta^2$.
The momentum
$\ol P_\mu$
is defined to be the average between the initial and final states,
$\ol P_\mu = \frac{1}{2} ( P' + P)_\mu$.
For
$n = k = 0$,
the matrix element is simply that of the vector current.
Consequently,
we have
$A_{00}(t) = F(t)$,
where
$F(t)$
is the vector form-factor of the pion,
and
$B_{00}(t) = 0$,
due to vector-current conservation.
Time-reversal invariance
restricts the allowed values of
$k$
in the binomial sums.
For the
$A_{nk}(t)$
moments,
$k$ must be even;
while,
for the
$B_{nk}(t)$
moments,
$k$
must be odd.

The DDs are generating functions for the moments of twist-two operators.
Written in terms of the moments,
we can define two\footnote{
As it stands,
there is freedom in the decomposition of moments,
Eq.~\eqref{eq:DDecomp},
which ultimately implies that the DDs
$F({\beta},{\alpha},t)$
and
$G({\beta},{\alpha},t)$
are not unique.
This redundancy is akin to gauge freedom%
~\cite{Teryaev:2001qm},
and a minimal gauge is one in which there is only an
$F$-type DD,
and what is called the
$D$-term%
~\cite{Polyakov:1999gs},
which reduces the $G$-type DD to a
$\delta({\beta})$
contribution.
There is a way, furthermore,
to write these two contributions as the projection of a single function,
see
Ref.~\cite{Belitsky:2000vk}.
Nonetheless,
we use two DDs for computational ease,
and note that the more minimal descriptions can be straightforwardly obtained therefrom.
}
DDs
$F({\beta},{\alpha},t)$
and
$G({\beta},{\alpha},t)$
as
\begin{eqnarray}
A_{nk}(t)
&=&
\int_0^\beta d{\beta}
\int_{-1 + {\beta}}^{+1 - {\beta}}
d{\alpha}
\,
{\beta}^{n-k} {\alpha}^{k}
\,
F({\beta}, {\alpha}, t),
\notag \\
B_{nk}(t)
&=&
\int_0^\beta d{\beta}
\int_{-1 + {\beta}}^{+1 - {\beta}}
d{\alpha}
\,
{\beta}^{n-k} {\alpha}^{k}
\,
G({\beta}, {\alpha}, t)
\label{eq:FG}
,\end{eqnarray}
which satisfy the
${\alpha}$-symmetry properties
$F({\beta}, {\alpha}, t) = F({\beta}, -{\alpha}, t)$
and
$G({\beta}, {\alpha}, t) =  - G({\beta}, -{\alpha}, t)$.
These properties express the consequences of time-reversal invariance.
Throughout,
we consider
$\beta >0$
for the quark distribution in the pion.

Using a vector $z_\mu$ that is light-like,
$z^2 = 0$,
and such that
$z_\mu = \frac{\lambda}{\sqrt{2}}  (1, 0, 0, 1)$,
we can sum the moments into the matrix element of the quark bilocal operator%
\footnote{
With QCD gauge interactions,
one needs to assume the light-cone gauge,
$z \cdot A = 0$,
to arrive at Eq.~\eqref{eq:bilocal0},
otherwise a gauge link proportional to
$z \cdot U \left(-\frac{z}{2},\frac{z}{2} \right)$
will appear in the bilocal operator in order to maintain gauge invariance.
}
\begin{eqnarray}
\mathcal{O}(z)
&=&
\ol \psi \left(- \frac{z}{2} \right) \rlap\slash  z \, \psi \left( \frac{z}{2} \right)
\notag \\
&=&
\sum_{n=0}^\infty
\frac{(-i)^n}{n!}
z_\mu z_{\mu_1} \cdots z_{\mu_n} \mathcal{O}^{\mu \mu_1 \cdots \mu_n}
\label{eq:bilocal0}
,\end{eqnarray}
which,
on account of
Eq.~\eqref{eq:DDecomp},
can be written in terms of the generating functions in the form
\begin{eqnarray}
\Big\langle  P' \Big|
\mathcal{O}(z)
\Big| P \Big\rangle
=
\int_0^1 d{\beta} \int_{-1 + {\beta}}^{+1 - {\beta}} d{\alpha}
\,
e^{ - i \left( {\beta} \ol P - {\alpha} \frac{\Delta}{2} \right) \cdot z}
\notag\\
\times
\Big[
2 \ol P \cdot z
\,
F({\beta}, {\alpha}, t)
-
\Delta \cdot z
\,
G({\beta}, {\alpha}, t)
\Big]
.\qquad
\end{eqnarray}
The pion GPD is defined from the Fourier transform of this light-cone correlation of quark fields.
Writing the skewness variable as
\begin{equation}
\xi = - \frac{1}{2} \Delta \cdot z  / \, \ol P \cdot z
,\end{equation}
we have the conventional definition of the
GPD as an off-forward matrix element of the bilocal operator
\begin{equation}
H(x, \xi, t)
\equiv
\int \frac{d\lambda}{4 \pi}
e^{ i x \ol P \cdot z}
\Big\langle P' \Big|
\mathcal{O}(z)
\Big| P  \Big\rangle
\label{eq:bilocal}
.\end{equation}
Expressing the GPD in terms of its underlying Lorentz invariant DDs,
we have the relation
\begin{eqnarray}
H(x,\xi,t)
&=&
\int_0^1 d{\beta} \int_{-1 + {\beta}}^{+1 - {\beta}} d {\alpha}
\, \delta( x - {\beta} - \xi {\alpha})
\notag \\
&& \phantom{space} \times \Big[ F({\beta}, {\alpha}, t) + \xi \, G({\beta}, {\alpha}, t) \Big]
\label{eq:GPDD}
.\end{eqnarray}

All constraints on the GPDs associated with Lorentz invariance are built into the DD representation that appears in
Eq.~\eqref{eq:GPDD}.
For example,
notice that the
$n$-th moment of the GPD with respect to $x$
\begin{eqnarray}
\int_0^1 dx \, x^n H(x, \xi, t)
&=&
\int_0^1 d{\beta} \int_{-1 + {\beta}}^{+1 - {\beta}} d{\alpha}  \, ({\beta} + \xi {\alpha})^n
\notag \\
&&  \times \Big[ F({\beta}, {\alpha}, t) + \xi \, G({\beta}, {\alpha}, t) \Big]
, \quad \end{eqnarray}
is at most an $n$-th [$(n+1)$-st] degree polynomial in
$\xi$,
for
$n$ even [odd].
The zeroth moment,
which must be
$\xi$
independent,
produces the so-called GPD sum rule for the form factor
\begin{equation}
\int_0^1 dx \, H(x, \xi, t)
=
F(t)
,\end{equation}
having used
$B_{00}(t) = 0$.
Finally,
the quark distribution function,
which we denote by
$q(x)$,
is contained in the forward limit,
$\Delta_\mu = 0$,
of the GPD
\begin{equation}
q(x)
=
H(x,0,0)
=
\int_{-1 + x}^{+1 - x} d{\alpha}
\,
F(x,{\alpha},0)
\label{eq:q}
.\end{equation}
Notice that contributions from
$G({\beta},{\alpha},t)$
to both the form factor and quark distribution vanish due to time-reversal invariance.
In this way,
GPDs naturally contain additional information unconstrained by their zeroth moment and forward limit.%
\footnote{
It was pointed out in
Ref.~\cite{Tiburzi:2004qr}
that the ambiguity inherent in defining DDs can be used in reverse to reduce the entirety of the
$F$-type DD to a contribution proportional to
$\delta({\alpha})$.
In this representation,
all of the skewness dependence of the GPD arises from the
$G$-type DD,
specifically in the form
$
H(x, \xi,t) = F(x,0,t) + \xi \int_0^1 d{\beta} \int_{-1 + {\beta}}^{+1 - {\beta}} d{\alpha} \, \delta ( x - \beta - \xi {\alpha}) \, \tilde{G}({\beta},{\alpha},t)
$.
The only constraint on the skewness dependence is through the time-reversal condition,
$\tilde{G}({\beta},{\alpha},t) = - \tilde{G}({\beta},-{\alpha},t)$;
and,
of course,
the positivity bound.
}
Consequently,
the positivity bound provides essential guidance for constructing consistent models for GPDs.

\subsection{The Model \& Violation of the Positivity Bound}

The model of the pion proposed in
Ref.~\cite{Fanelli:2016aqc},
employs an Ansatz for the covariant Bethe-Salpeter wavefunction.
It is written in the form
\begin{equation}
\Psi(k,P)
=
S(k) i \gamma_5 \Gamma(k,P) S(k-P)
\label{eq:model}
,\end{equation}
where
$S(k)$
denotes the constituent quark propagator,
which is assumed to have the free-particle form
\begin{equation}
S(k) = \frac{i}{\rlap \slash k - m + i {\varepsilon}}
,\end{equation}
and
$\Gamma(k,P)$
is the Bethe-Salpeter vertex.
Within this particular model,
the latter is taken as
\begin{equation}
\Gamma(k,P)
\equiv
{\mathcal N} \,
[k^2 - m_R^2 + i {\varepsilon}]^{-1}
[(k-P)^2 - m_R^2 + i {\varepsilon}]^{-1}
\label{eq:BSvertex}
,\end{equation}
where
${\mathcal N}$
is a normalization factor.
The covariant vertext is symmetric under the interchange of quark momentum,
${\Gamma}(P-k,P) = {\Gamma}(k,P)$,
as one expects for isospin symmetric valence quarks.
The mass
$m_R$
is a model parameter,
which additionally serves as a built-in regulator for ultraviolet divergences.%
\footnote{
Notice that because this is an ingredient of the model,
one does not attempt to take the limit
$m_R \to \infty$
to produce regularization independent results.
The covariant smearing of the ultraviolet behavior of the vertex is assumed to be due to the physical structure of the bound state.
}
Previous covariant models,
see,
for example,
Ref.~\cite{Frederico:1992ye},
have adopted a point-like vertex between the quarks and pion.
While there is a binding effect in such Nambu--Jona-Lasinio type models,
the point-like bound-state vertex is an approximation that the model of Ref.~\cite{Fanelli:2016aqc} seeks to remedy.
Notice that beyond
$\gamma_5$,
there are additional structures that can contribute to the Bethe-Salpeter vertex,
but these have been dropped in the interest of simplicity.

\begin{figure}
\resizebox{0.6\linewidth}{!}{
\includegraphics{impulse_triangle.pdf}
}
\caption{
Required Feynman diagram for bound-state matrix elements of twist-two operators computed within the impulse approximation.
Pions are depicted by double lines, with the bound-state vertices labelled by
$\Gamma$.
Quarks are depicted by directed lines, with insertion of the quark bilocal operator appearing in
Eq.~\eqref{eq:twistO}
shown by a cross.}
\label{f:triangle}
\end{figure}

The DDs,
and in turn the GPDs,
can be computed from matrix elements of the twist-two operators,
Eq.~\eqref{eq:DDecomp}.
Because the model employs an Ansatz for the Bethe-Salpeter vertex,
the DDs are computed within the impulse approximation.
The triangle diagram formed from the insertion of the twist-two operators is shown in Fig.~\ref{f:triangle}.
Using the Bethe-Salpeter wavefunction,
these matrix elements are given by
\begin{eqnarray}
{\mathcal M}^{\mu \mu_1 \cdots \mu_n}
&=&
\int_k
\,
\text{Tr} \Big[ \Psi(k,P) S^{-1}(k-P) \ol \Psi(k', P') \gamma^{\big\{ \mu} \Big]
\notag \\
&&
\times
(k + {\Delta} / 2)^{\mu_1} \cdots (k + {\Delta} / 2)^{\mu_n \big\}}
\label{eq:mel}
,\end{eqnarray}
where the shorthand
$\int_k$
indicates the Minkowski four-momentum integration,
$\int_k = \int d^4k / (2 \pi)^4$.
The primed variables are defined to be boosted by the momentum transfer
${\Delta}$,
so that
$k' = k + {\Delta}$
for the struck quark,
along with
$P' = P + {\Delta}$
for the final-state pion.
With a real-valued normalization factor,
${\mathcal N} \in \mathbb{R}$,
the conjugate Bethe-Salpeter wavefunction is given by
\begin{equation}
\ol \Psi (k',P')
=
S(k'-P') i  \gamma_5 \Gamma(k',P') S(k')
.\end{equation}
Notice the equality of the momentum differences for the spectator quark,
$k'-P' = k-P$.

\begin{figure}
\resizebox{\linewidth}{!}{
\includegraphics{pdf.pdf}
}
\caption{
Quark distribution function in the pion.
Using the model Bethe-Salpeter vertex in
Eq.~\eqref{eq:BSvertex},
the normalized quark distribution function,
$q(x)$,
is obtained using
Eq.~\eqref{eq:q},
and plotted as a function of
$x$
(solid curve).
Additionally shown
(dashed curve)
is the quark distribution function obtained from the two-body light-front wavefunction,
Eq.~\eqref{eq:LFWF}.
The effect of higher Fock-state contributions in this model reduces the average
$x$,
however,
higher Fock states only account for
$16 \%$
of the probability distribution.
}\label{f:pdf}
\end{figure}

Determination of the DDs from the above equation is rather technical,
however,
the procedure outlined in
Refs.~\cite{Tiburzi:2002tq,Tiburzi:2004mh}
can be adapted to the present model.
We provide the essential details leading to the extraction of
$F({\beta},{\alpha},t)$
and
$G({\beta},{\alpha},t)$
from
Eq.~\eqref{eq:mel}
in Appendix~\ref{s:A}.
From these DDs,
we obtain the pion GPD via
Eq.~\eqref{eq:GPDD}.
To evaluate the GPD,
we require model parameters.
In Ref.~\cite{Fanelli:2016aqc},
central values for the model parameters are adopted:
$m = 0.220 \, \texttt{GeV}$
and
$m_R = 1.192 \, \texttt{GeV}$.
These values reproduce the pion decay constant determined within the model,
and give a good description of the experimentally measured vector form factor of the pion.
Once the model parameters are fixed,
the normalization factor
${\mathcal N}^2$
follows from the value of the vector form factor at vanishing momentum transfer,
$F(t=0) = 1$;
or,
equivalently from normalizing the quark distribution,
$\int dx \, q(x) = 1$.
The model's quark distribution is shown in Fig.~\ref{f:pdf}.
This quark distribution is contrasted with that obtained from the two-body light-front wavefunction,
which will be determined below in
Sec.~\ref{s:LFWF}.
One attributes the differences as due to higher Fock components introduced by the covariant Ansatz for the Bethe-Salpeter vertex.

\begin{figure}
\resizebox{\linewidth}{!}{
\includegraphics{rplot.pdf}
}
\resizebox{\linewidth}{!}{
\includegraphics{crplot.pdf}
}
\caption{
Investigation of the positivity bounds required on the GPD within the model.
The top panel shows the ratio
$R(x,\xi)$
in
Eq.~\eqref{eq:R1},
which tests the strongest bound.
This bound is tested using the listed values of
$\xi$,
with the dashed vertical lines showing the corresponding starting points,
where
$x = \xi$.
The bottom panel shows the ratio
${\mathcal R}(x,\xi)$ appearing in Eq.~\eqref{eq:R2}.
This ratio tests the weaker positivity bound.
For
$x> \xi$,
both ratios are required to be less than unity.
}
\label{f:positivity}
\end{figure}

To test the self-consistency of the model,
we investigate the positivity bound,
which arises from the positivity of the norm on Fock space.
The strongest bound arises at vanishing momentum transfer.%
\footnote{
At
$t=0$,
the consideration of nonzero skewness,
$\xi \neq 0$,
places one in an unphysical regime,
which
technically requires analytic continuation.
In terms of the Lorentz invariant DDs,
this analytic continuation is trivially carried out by evaluating
Eq.~\eqref{eq:GPDD}
at
$t = 0$.
In the light-front wavefunction overlap representation,
one first performs the integration over the transverse momentum,
which produces functions of
$\bm{\Delta}_\perp^2$,
and then evaluates at the point
$\bm{\Delta}_\perp^2 = - 4 \xi^2 M^2$.
We have checked that the two procedures produce identical results.
Additionally in the \emph{physical} regime,
with
$t < 0$
and
$0 < \xi < \left(1 - \frac{4 M^2}{t}\right)^{-1/2}$,
violation of the positivity bound is qualitatively quite similar to what is shown in Fig.~\ref{f:positivity}.
}
To this end,
we form the ratio
\begin{eqnarray}
R(x,\xi)
\equiv
\frac{|H(x,\xi,0)|}{
\sqrt{  q ( x_f ) q( x_i)}
}
\leq 1
\label{eq:R1}
,\end{eqnarray}
which is bounded by unity from above for
$x>\xi$.
The momentum fractions carried by the struck quark before and after interacting with the current are given by
\begin{equation}
x_i = \frac{x+\xi}{1+\xi},
\quad
\text{and}
\quad
x_f = \frac{x-\xi}{1-\xi}
.\end{equation}
Investigation of this ratio as a function of
$x$
is shown in Fig.~\ref{f:positivity}
using a few values for the skewness parameter
$\xi$.
The model of
Ref.~\cite{Fanelli:2016aqc}
violates the positivity bound in a window
$\xi < x < x_m(\xi)$,
encompassing the majority of
$x$
values.
The turn-over point,
$x_m(\xi) \sim 0.95$,
depends mildly on
$\xi$
as can be discerned from the figure.
In the narrow end-point region,
$x_m(\xi) < x < 1$,
the bound is satisfied,
however,
this region shrinks to zero as the skewness approaches zero.
Notice that as
$\xi \to 0$,
the positivity bound must be saturated according to the limiting behavior of the GPD in
Eq.~\eqref{eq:q};
however,
the approach is from above rather than below.
This is exactly the opposite behavior required by the positivity of the norm on Fock space.
Saturation of the bound is investigated in
Fig.~\ref{f:saturate}.

\begin{figure}
\resizebox{\linewidth}{!}{
\includegraphics{lim.pdf}
}
\caption{
Saturation of the (strong) positivity bound in the limit
$\xi \to 0$.
The ratio
$R(x,\xi)$
appearing in
Eq.~\eqref{eq:R1}
is plotted as a function of
$x$
for the skewness
$\xi = 0.001$,
for which the value
$x = \xi$
is indicated by the dashed vertical line.
Notice the considerable reduction in the range plotted compared to that in
Fig.~\ref{f:positivity}.
Violation of the bound appears linked with the two limits:
$x \to \xi$
and
$\xi \to 0$.
}
\label{f:saturate}
\end{figure}

Due to violation of the positivity bound in
Eq.~\eqref{eq:R1},
we investigate the severity of violation by considering a weaker bound.
Weaker than the bound involving the geometric mean of quark distributions,
there is a positivity bound required due to the inequality between geometric and arithmetic means
\begin{equation}
\sqrt{ q (x_f)  q(x_i)}
\leq
\frac{
q(x_f)
+
q(x_i)
}{2}
.\end{equation}
Hence,
we consider an additional ratio to test the weaker bound
\begin{equation}
{\mathcal R} (x,\xi)
=
\frac{|H(x,\xi,0)|}{
\frac{1}{2}
\left[
q(x_f)
+
q(x_i)
\right]
}
\leq 1
\label{eq:R2}
.\end{equation}
This ratio is shown in
Fig.~\ref{f:positivity}
for the same values of
$\xi$.
Violation of the weaker bound qualitatively follows the same trend as seen in violation of the stronger bound.
The violation is less severe,
but that is precisely what is expected of a weaker bound.

Despite the fully covariant nature of the model,
the positivity bounds required of the GPD are violated.
This points to the model not being self consistent.
Without knowledge of the dynamics giving rise to the Bethe-Salpeter vertex function,
it is not at all obvious how to consistently couple the quark bilocal operator to the dynamics.
Investigation of the light-front representation for the GPD provides considerable intuition about the shortcomings of the model;
and,
it is to this representation that we now turn.

\section{Light-Front Wavefunction Analysis}
\label{s:LFWF}

\subsection{Two-Body Analysis}

The two-body wavefunction for the pion is obtained by the overlap of the
Bethe-Salpeter wavefunction onto on-shell quark and antiquark spinors.
Subsequent integration over the minus-component of momentum produces the restriction to the plane
$x^+ = 0$,
and the light-front wavefunction reads,
see, e.g.~\cite{Liu:1992dg},
\begin{eqnarray}
\psi^{(2)}_{\lambda \lambda'}
(x, \bm{k}_\perp)
&=&
\int \frac{dk^-}{2\pi}
\frac{\ol u_\lambda(k^+,\bm{k}_\perp)}{\sqrt{k^+}}
\gamma^+ \Psi(k,P) \gamma^+
\notag \\
&& \phantom{space}
\times
\frac{v_{\lambda'}(P^+ - k^+,-\bm{k}_\perp)}{\sqrt{P^+ - k^+}}
\label{eq:LFWF2}
,\end{eqnarray}
where we have taken
$\bm{P}_\perp = \bm{0}$
for simplicity.
In the wavefunction,
the variable
$x$
is the plus-momentum fraction of the quark relative to that of the pion,
$x = k^+ / P^+$.
Because the transverse boosts generate a kinematic subgroup of the Poincar\'e group,
the boosted wavefunction,
$\bm{P}_\perp \neq \bm{0}$,
can be obtained by the simple replacement
$\bm{k}_\perp \to \bm{k}_\perp - x \bm{P}_\perp$,
which is the relative transverse momentum.

Using the Bethe-Salpeter wavefunction in Eq.~\eqref{eq:model},
the two-body (valence) light-front wavefunction can be obtained.
For manipulations involving the light-front spinors,
consult Appendix~\ref{s:B}.
Treating the factor of
$\theta[x(1-x)]$
implicitly,
we arrive at the wavefunction
\begin{eqnarray}
\psi^{(2)}_{\lambda \lambda'} (x,\bm{k}_\perp)
&=&
{\mathcal N} \,
\frac{
k_{-\lambda} \delta_{\lambda,\lambda'} - \lambda m \,\delta_{\lambda, - \lambda'}
}
{m_R^2 - m^2}
\notag \\
&&
\times
\Big[
\varphi(x,\bm{k}_\perp; m, m, m_R)
\notag \\
&&
\phantom{s}
-
\varphi(x,\bm{k}_\perp; m_R, m, m_R)
\Big]
,\label{eq:LFWF}
\end{eqnarray}
which has been written with the help of the helicity independent amplitude
\begin{eqnarray}
\varphi(x,\bm{k}_\perp; m_a, m_b, m_c)
&=&
D_W(x,\bm{k}_\perp ; m_a, m_b)
\notag \\
&& \phantom{sp}
\times
\frac{D_W(x,\bm{k}_\perp ; m_a, m_c)}{x^2 (1-x)}
.\quad
\end{eqnarray}
This amplitude has been expressed in terms of the propagator for the Weinberg equation%
~\cite{Weinberg:1966jm}
\begin{equation}
D_W(x,\bm{k}_\perp ; m_a, m_b )
=
\frac{1}{
M^2 - \frac{\bm{k}_\perp^2 + x m_a^2 + (1-x) m_b^2}{x(1-x)}
}
,\end{equation}
in the unequal mass case.
At this stage,
the first mass argument of the amplitude
$\varphi$
is redundant,
however,
the dependence on three different masses will be utilized below in computing the GPD.
The light-front helicity structure of the wavefunction in Eq.~\eqref{eq:LFWF} has both opposite helicity,
$\delta_{\lambda, - \lambda'}$
and same helicity,
$\delta_{\lambda, \lambda'}$
contributions.
The latter are accompanied by a unit of quark orbital angular momentum to preserve the spin of the pion.
This is reflected by the factor of transverse momentum,
$k_{\lambda} = k_1 + i \lambda k_2$,
appearing in the numerator of the wavefunction.
Such contributions are symmetric under the interchange of the mass parameters,
$m \leftrightarrow m_R$.
The contributions from opposite helicity states are not symmetric under this interchange.

The two-body light-front wavefunction is not symmetric under the interchange of quark and antiquark,
i.e.~$x \leftrightarrow 1 - x$.
The wavefunction vanishes linearly at both endpoints,
$x = 0$
and
$x =1$.
The vanishing at
$x = 0$
is particularly interesting because it arises from an exact cancellation between the two terms appearing in
Eq.~\eqref{eq:LFWF}.
The quark distribution obtained from the two-body light-front wavefunction takes the simple quantum mechanical form
\begin{equation}
q^{(2)}(x)
=
\sum_{\lambda, \lambda'}
\int \frac{d \bm{k}_\perp}{2 (2\pi)^3}
\left| \psi^{(2)}_{\lambda \lambda'} (x, \bm{k}_\perp) \right|^2
\label{eq:q2}
,\end{equation}
and is plotted in Fig.~\ref{f:pdf}.
The absolute normalization is closely examined in Appendix~\ref{s:B}.
Qualitatively this two-body quark distribution is similar to the full quark distribution function obtained in the model.
The full distribution has a smaller value of
$\langle x \rangle$,
for example,
which is consistent with expectations from higher Fock components.
The difference is not very appreciable:
$\langle x \rangle = 0.47$
in the full model,
while
$\langle x \rangle^{(2)} = 0.50$
within the two-body sector.
The
$x \leftrightarrow 1-x$
asymmetry is practically negligible for the two-body quark distribution,
which is a fortunate circumstance on physical grounds.
Integrating the two-body quark distribution over
$x$,
we find that the two-body Fock state
accounts for
$84 \%$
of the quark distribution.

From the two-body wavefunction,
one can obtain the GPD only in a limited kinematic regime.
In the region
$x > \xi$,
we have
\begin{eqnarray}
H^{(2)}(x, \xi, t)
&=&
\sum_{\lambda, \lambda'}
\int \frac{d \bm{k}_\perp}{2 (2\pi)^3}
\psi^{(2)}_{\lambda \lambda'} \left(x_i, \bm{k}_\perp \right)
\psi^{(2)*}_{\lambda \lambda'} \left(x_f, \bm{k}'_\perp  \right)
,\notag \\
\end{eqnarray}
where the boosted transverse momentum is given by
\begin{equation}
\bm{k}'_\perp = \bm{k}_\perp + \left( 1 - \frac{x_i + x_f}{2} \right) \bm{\Delta}_\perp
.\end{equation}
Due to the convolution of the initial- and final-state wavefunctions,
the two-body GPD self consistently satisfies the positivity bound.
The tradeoff is that the two-body approximation violates Lorentz invariance
(for example,
the sum-rule for the form factor does not hold).
Additionally when
$x < \xi$,
higher Fock components are necessarily required for non-vanishing contributions to the GPD.

\subsection{Complete Light-Front Analysis}

One similarity between the two-body and higher Fock-state contributions is that they both vanish at
$x = 0$.
While this is required of the former,
the latter are generally non-vanishing at $x=0$.
Elaboration on this point is made in
Refs.~\cite{Antonuccio:1997tw,Tiburzi:2002sx}.
The vanishing of this model's quark distribution at
$x = 0$
leads us to the culprit of positivity violation.
To demonstrate this,
we turn to the light-front representation of the model's GPD.

Complementary to the representation in terms of DDs,
the GPD can be evaluated directly from the bilocal matrix element in
Eq.~\eqref{eq:bilocal}
computed within the model.
This alternative expression for the GPD is
\begin{eqnarray}
H(x,\xi,t)
&=&
\frac{1}{2 \ol P {}^+}
\int_k
\delta \left( x + \xi - \frac{k^+ }{\ol P {}^+} \right)
\,
\text{Tr} \Big[ \Psi(k,P)
\notag \\
&& \phantom{spa} \times
 S^{-1}(k-P) \ol \Psi(k', P') \gamma^{+} \Big]
\label{eq:LCGPD}
.\end{eqnarray}
Results for the quark distribution and GPD obtained from
Eq.~\eqref{eq:LCGPD}
agree numerically with those determined from DDs.
Our investigation of the violation of the positivity bound leads us to consider the GPD at the crossover point,
$x = \xi$.
We show in the form of an integral that the GPD is nonvanishing at the crossover,
$H(\xi, \xi, t) \neq 0$,
using light-front integration.%
\footnote{
Given that the quark distribution vanishes at the endpoint,
$x=0$,
it is already numerically evident from
Figs.~\ref{f:positivity} and \ref{f:saturate}
that the GPD does not vanish at the crossover.}
This result can also be established analytically from the DDs,
however,
the light-front integration offers a more intuitive
picture,
not to mention the ability to display using more compact expressions.

To obtain the GPD,
we integrate the expression in Eq.~\eqref{eq:LCGPD} over
$k^-$.
The integral is performed by the residue theorem,
and different residues are required depending on the value of
$k^+$.
A particularly illustrative discussion of the contour integration for light-front and instant-form dynamics can be found in
Ref.~\cite{Sawicki:1991sr}.
We restrict our attention to the region
$x > \xi$,
for which residues at the spectator poles are required.
There are two such poles:
one for the spectator quark,
and one for the spectator regulator particle having mass
$m_R$.
Due to the Ansatz in
Eq.~\eqref{eq:BSvertex},
the spectator propagator for the regulator is squared in the bilocal current matrix element.
For ease in evaluating and displaying the results,
we use the standard trick to rewrite the square of a propagator in terms of a derivative of the propagator,
namely
\begin{equation}
\frac{1}{\left[(P-k)^2 - m_R^2\right]^2}
=
\frac{\partial}{\partial m_A^2}
\frac{1}{(P-k)^2 - m_A^2}
\Bigg|_{m_A = m_R}
.\end{equation}
A different mass,
$m_A$,
is required for this intermediate step because
$m_R$
appears elsewhere in the expression for the GPD.
Carrying out the light-front integration,
we arrive at the result
\begin{eqnarray}
\theta(x - \xi)
H(x,\xi,t)
=
{\mathcal N}^2
\int \frac{d \bm{k}_\perp}{2 (2 \pi)^3}
\frac{\partial}{\partial m_A^2}
\frac{{\mathcal H}_m - {\mathcal H}_A}
{m^2 - m_A^2}
\Bigg|_{m_A = m_R}
\notag \\
\label{eq:LFGPD}
\end{eqnarray}
where
${\mathcal H}_m$
and
${\mathcal H}_A$
denote contributions to the integrand that arise from taking the residue at the spectator quark pole
and spectator regulator pole,
respectively.
The former is given by
\begin{eqnarray}
{\mathcal H}_m
&=&
2 \left( \bm{k}_\perp \cdot \bm{k}'_\perp + m^2 \right)
\notag \\
&&
\times
\varphi(x_i, \bm{k}_\perp; m, m_R, m)
\,
\varphi(x_f, \bm{k}'_\perp; m, m_R, m)
, \quad\end{eqnarray}
while the latter takes the form
\begin{eqnarray}
{\mathcal H}_A
&=&
2 \left( \bm{k}_\perp \cdot \bm{k}'_\perp + \frac{1-x^2}{1-\xi^2} m^2 + x_i \, x_f \, m_A^2 \right)
\notag \\
&&
\times
\varphi(x_i, \bm{k}_\perp; m_A, m, m_R)
\,
\varphi(x_f, \bm{k}'_\perp; m_A, m, m_R)
.\notag \\
\end{eqnarray}

Using Eq.~\eqref{eq:LFGPD},
we derive the crossover behavior by taking the limit
$x \to \xi$
from above.
To this end,
it is useful to note the finite limit
\begin{equation}
\lim_{x \to 0}
\varphi(x, \bm{k}_\perp; m_a, m_b, m_c)
=
\frac{1}{(\bm{k}_\perp^2 + m_b^2) (\bm{k}_\perp^2 + m_c^2)}
\label{eq:lemma}
,\end{equation}
which is independent of the mass
$m_a$.
As a consequence,
we have the non-vanishing result
\begin{widetext}
\begin{eqnarray}
H(\xi, \xi, t)
&=&
{\mathcal N}^2
\int \frac{d \bm{k}_\perp}{(2 \pi)^3}
\frac{\bm{k}_\perp \cdot \bm{k}^{(0)}_\perp + m^2 }
{\left[\left(\bm{k}^{(0)}_\perp\right)^2 + m^2\right]
\left[ \left(\bm{k}^{(0)}_\perp\right)^2 + m_R^2\right]}
\,
\frac{\partial}{\partial m_A^2}
\frac{\varphi(x_0, \bm{k}_\perp; m, m_R, m)
 - \varphi(x_0, \bm{k}_\perp; m_A, m, m_R)
}{m^2 - m_A^2}
\Big|_{m_A = m_R},
\notag \\
\label{eq:cross}
\end{eqnarray}
\end{widetext}
where we have defined the crossover values
\begin{eqnarray}
x_0
&=&
x_i(x = \xi )
=
\frac{2 \xi}{1 + \xi}
,\end{eqnarray}
for the initial quark's momentum fraction,
and
\begin{eqnarray}
\bm{k}_\perp^{(0)}
&=&
\bm{k}_\perp + \frac{1}{1 + \xi} \bm{\Delta_\perp}
,\end{eqnarray}
for the relative transverse momentum of the final-state quark.
Finally,
taking the limit
$\xi \to 0$
results in
\begin{equation}
\lim_{\xi \to 0}
H(\xi, \xi, t)
=
0
,\end{equation}
which can be easily demonstrated upon noting that
$x_0 \to 0$
in this limit,
then subsequently applying
Eq.~\eqref{eq:lemma} to the expression for the GPD at the crossover,
Eq.~\eqref{eq:cross}
\footnote{
One can generalize these findings in the following way.
Adopting a more general
(but asymmetric)
Ansatz for the Bethe-Salpeter amplitude having the form
\begin{equation}
\Gamma(k,P)
=
{\mathcal N} \,
[k^2 - m_R^2 + i {\varepsilon}]^{-1}[(P-k)^2 - m_R^2 + i {\varepsilon}]^{-\nu / 2}
,\notag \end{equation}
for
$\nu = 1$, $2$, $\cdots$,
it is straightforward to show using light-front integration that the corresponding crossover value of the GPD,
$H(\xi, \xi, t)$,
is non-vanishing,
but vanishes in the limit of vanishing skewness,
$\xi \to 0$.
Thus models of this type will violate the positivity bound in an analogous way to the
$\nu = 2$
model detailed above.
The model with
$\nu =0$,
by contrast,
satisfies the positivity bound,
and was considered previously in
Refs.~\cite{Tiburzi:2002tq,Tiburzi:2004mh}.
This particular case is best viewed as smearing the bilocal current rather than the bound-state vertex,
see Ref.~\cite{Bakker:2000pk}.
}

\begin{figure}
\resizebox{\linewidth}{!}{
\includegraphics{cross.pdf}
}
\caption{
Value of the GPD at the crossover point,
$x = \xi$,
plotted as a function of
$\xi$.
For simplicity,
we determine the value using
$t = 0$.
The vanishing
$\xi \to 0$
limit of the crossover value,
implies vanishing of the quark distribution function at the endpoint,
$x = 0$.
The non-vanishing value of
$H(\xi, \xi, t)$
for
$\xi \neq 0$,
then leads to (infinite) violation of the positivity bound in Eq.~\eqref{eq:R1}.
Close inspection shows that
$H(\xi, \xi, t) \propto \xi^2$,
for
$\xi \ll 1$.
}
\label{f:cross}
\end{figure}

A plot of the
$\xi$-dependence of the GPD at the crossover is shown in Fig.~\ref{f:cross},
and confirms its non-vanishing value,
as well as the vanishing forward limit.
These two features are directly at odds with the positivity of the norm on the light-front Fock space.
The vanishing of the crossover's forward limit confirms that the model's quark distribution function vanishes at
$x = 0$,
as we have numerically shown above.
In terms of the general light-front wavefunction representation,
we have schematically
\begin{equation}
q(x = 0)
=
H(0,0,0)
=
\sum_n
\Big| \psi^{(n)} (x = 0, \cdots) \Big|^2
=0
.\end{equation}
We write the $n$-body Fock component of the bound state as
$\psi^{(n)}$,
and only indicate the active quark's momentum fraction
$x$,
which is at the endpoint,
$x = 0$.
Due to positivity of the norm,
the vanishing quark distribution at the endpoint implies that
\begin{equation}
\psi^{(n)} (x = 0, \cdots) = 0,
\quad
\forall n
\label{eq:end}
.\end{equation}
Approaching the crossover from above,
the GPD at the crossover has an expansion in terms of diagonal Fock-component overlaps,
which schematically takes the form
\begin{eqnarray}
H(\xi,\xi,t)
=
\sum_n
\psi^{(n)}( x_i, \cdots)
\psi^{* (n)} (x_f = 0, \cdots )
.\end{eqnarray}
Given the endpoint behavior of the wavefunctions deduced from the norm,
Eq.~\eqref{eq:end},
we should very likely have
$H(\xi, \xi, t) = 0$
for self consistency,
which is in contradiction with
Eq.~\eqref{eq:cross}.%
\footnote{
Mathematically speaking,
it is possible that the crossover value,
as the sum of infinitely many vanishing contributions,
need not itself vanish.
If this scenario is realized,
however,
the positivity bound in
Eq.~\eqref{eq:R1}
will nevertheless be violated.
}
This contradiction is precisely the source of the observed (infinite) violation of the positivity bound in
Eq.~\eqref{eq:R1}
at
$x = \xi$.
Away from the crossover,
violation then persists until the relatively large value of
$x = x_m(\xi)$,
as discussed above.

\section{Summary}
\label{s:summy}

We investigate GPDs in the quark model for the pion proposed in
Ref.~\cite{Fanelli:2016aqc}.
A feature of this model is the covariant smearing of the Bethe-Salpeter vertex,
which was put forward in order to provide realistic bound-state structure beyond the point-like approximation.
The covariant nature of the model,
moreover,
guarantees that all constraints associated with Lorentz invariance of the underlying matrix element are automatically satisfied.
This fact enables us in
Sec.~\ref{s:DD}
to derive the DDs for the model,
see
Eq.~\eqref{eq:FandG}.
The GPD obtained from the DDs is then scrutinized using the ratios in
Eqs.~\eqref{eq:R1} and \eqref{eq:R2}.
Positivity of the norm on the light-front Fock space requires both of these ratios to be less than unity,
with the former bound stronger than the latter.
Both bounds,
however,
are violated for nearly all values of
$x > \xi$.
This is shown in
Fig.~\ref{f:positivity}.
Such violation,
moreover,
is tied to a mismatch between the endpoint behavior of the quark distribution and the crossover value of the GPD,
see Eq.~\eqref{eq:cross}.
As the former vanishes and the latter is non-vanishing,
the mismatch leads to an infinite violation of the positivity bound.

The
GPDs encompass physics of both quark distributions and form factors.
We have shown that fully covariant models,
which can be tuned to reproduce the experimentally measured quark distributions and form factors,
need not give a good description of GPDs.
In fact,
the behavior of the model's GPD at the crossover is inconsistent with its quark distribution.
While the model is defined at a low scale,
QCD radiation will drive the model's quark distribution at the endpoint away from zero as the renormalization scale is raised.
The positivity bounds,
however,
are stable with respect to evolution.
Thus,
the defect in the model at a low scale will persist at higher scales.
The value of the GPD at the crossover,
moreover,
directly enters the imaginary part of the deeply virtual Compton scattering amplitude.
This imaginary part then appears in the cross section through interference terms with Bethe-Heitler processes,
which enable GPDs to be accessed experimentally.
The model therefore fails to describe GPDs at the most phenomenologically relevant point.
The mismatch in endpoint and crossover behavior requires proper treatment of higher Fock states in order to resolve.
Such treatment requires one to go beyond the impulse approximation.
While theoretically challenging,
consistent modeling of GPDs presents an essential test in the phenomenological description of hadron structure.
Passing this test will help enable great insight into the nature of bound states in QCD.

\begin{acknowledgments}

This work was supported in part by the U.S.~National Science Foundation, under Grant No.~PHY15-15738.
BCT would like to thank G.~A.~Miller for numerous insights in studying GPDs.

\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


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text:
De Waterslootse Poort was een stadspoort aan de westelijke zijde van de Nederlandse stad Delft. De poort wordt voor het eerst genoemd in de tweede helft van de 15e eeuw in een Keurboek van de stad. De poort werd over het kanaal de Watersloot gebouwd, waaraan ze haar officiële naam dankt, en scheidde de Binnenwatersloot van de Buitenwatersloot.

De poort is ook bekend geweest onder andere namen, die refereerden aan de plaats of streek in de richting waarvan de poort was opgebouwd, zoals Westlandse of Maaslandse Poort.

Zoals de meeste andere poorten, heeft deze poort ook de naam van een heilige gedragen: St. Joris. Die naam kwam waarschijnlijk uit de tijd voor de Hervorming, toen jaarlijks vanuit het dorpje De Lier een processie werd gehouden van de St. Joris kerk aldaar, naar de Waterslootse Poort. Na enig ceremonie werd de poort geopend, waarna de processie zich vervolgde langs de Binnenwatersloot, over de Haverbrug en terug de poort uit.

Metamorfose

Net als de meeste andere poorten van Delft, heeft deze poort enkele metamorfoses ondergaan. Er zijn maar weinig voorstellingen bekend van de poort die dateren van voordat ze haar laatste uiterlijk kreeg. Op een kaart van Jacob van Deventer uit 1557 is nog te zien hoe de Waterslootse Poort eruit heeft gezien voordat ze flink veranderde tussen 1573 en 1593. De kaart werd gemaakt in opdracht van de Spaanse koning Filips II, om zo de verdedigingswerken van de Hollandse steden in kaart te krijgen, mocht het tot een belegering komen. Op die kaart is te zien dat de poort een eenvoudige verbinding had uit de stad en over het stadskanaal naar de overzijde. De poort zelf bestond uit het poortgebouw, met twee ronde torens aan beide zijde, waarvan de spitse daken duidelijk boven de poort zelf uitstaken. Het lijkt erop dat de Waterslootse Poort een grotere en minder elegante versie van de Oostpoort was.

Over de periode in de tweede helft van de 16e eeuw is meer bekend over het uiterlijk van de poort. Zo kreeg de poort omstreeks 1593 haar definitieve uiterlijk, waarbij het oorspronkelijke ontwerp flink was gewijzigd. Daarvoor, in 1573, ondergingen de verdedigingswerken van de Waterslootse Poort al een modernisering. Dat had alles te maken met de komst van Willem van Oranje naar de stad Delft, waar hij bescherming zocht tegen de Spanjaarden achter de Delftse verdedigingswerken. Om die verdediging te versterken werden onder meer de stadspoorten van Delft gemoderniseerd volgens de laatste militaire inzichten.

De stadsgracht werd flink verbreed voor de poort. Midden in de verbreding werd een bolwerk aangelegd: een soort ommuurd eiland, wat de poort een machtig en imposant uiterlijk gaf. Vanaf die tijd kon men niet eenvoudig meer het stadskanaal overbruggen. Komend vanaf de Binnenwatersloot, liep men eerst de imposante Waterslootse Poort zelf door. De poort werd door een stenen brug verbonden met het bolwerk. Aan beide zijden van die brug was een muur opgetrokken, waarin schietgaten waren aangebracht. De brug leidde naar een kleine voorpoort, die toegang tot het bolwerk gaf. Vanaf het bolwerk kon de andere zijde van het kanaal worden bereikt, over een ophaalbrug. Op een kaart uit 1649 is te zien dat ook deze ophaalbrug bewaakt werd door een bescheiden poorthuis.

De poort zelf had ook veranderingen ondergaan. Zo waren het niet langer twee lange torens, met spitse daken, die de poort flankeerden, maar waren het grote ronde torens geworden, die ieder nog breder dan de poort zelf waren. Zij waren iets hoger dan de poort zelf, maar alleen vanwege de balustrade die erbovenop was gebouwd. In de balustrade waren weer schietgaten aangebracht, waardoor een klein geweer naar buiten kon schieten. Boven de torens en de poort was het Delflandse Hof gebouwd. Een flink gebouw, waar de rechtbank of "Vierschaer" van Delfland zitting had. Daar werd recht gesproken over de landen die tot het toenmalige Delfland hoorden. Het gebouw bevatte drie schoorstenen, die boven het blauwe, leistenen dak uitkwamen. De poort werd tevens gebruikt als gevangenis: een populaire bestemming voor stadspoorten.

Afbraak
Op 26 juni 1846 werd in de gemeenteraad meegedeeld dat de nieuwe brug voor de Waterslootse poort ten behoeve van de spoorwegen was voltooid en dat de Waterslootse poort eigenlijk in de weg stond. In 1847 werd het gebouw dan ook voor 3000 gulden verkocht om gesloopt te worden. In hetzelfde jaar viel het doek voor de Waterslootse Poort en werd zij afgebroken.

Poort in Delft
Voormalig bouwwerk in Delft

redpajama_set_name: RedPajamaWikipedia


Under the guise of paying tribute to Vietnam veterans, songwriters Dave Gibson, Roger Kirby and Carl Conge have joined the chorus of unwarranted criticism ... of the Vietnam War, if not in the history of the U.S. military, as being commonplace enough to represent the image of the typical Vietnam veteran.
"On behalf of the Silver Creek DAR Chapter, allow me to be the first to say, "Welcome home, Vietnam War veterans,'" Lola DeGroff said. Pontoon Beach Mayor Mike Pagano read a proclamation proclaiming March 29 Thank a Vietnam Veteran Day and recognizing the service of Vietnam War veterans.
"On behalf of the Silver Creek DAR Chapter," said Lola DeGroff, "allow me to be the first to say, 'Welcome Home Vietnam War veterans.'" Pontoon Beach Mayor Mike Pagano read a proclamation proclaiming March 29 "Thank a Vietnam Veteran Day" and recognizing the service of Vietnam War veterans.
A truck carrying the replica of the Vietnam Veterans Memorial, in Washington D.C., is escorted through San Dimas on its way to Lone Hill Middle School in .... "I'm a Vietnam veteran, and I thought it would be great for all of our citizens, especially the ones that can't make it to Washington, to see it," he said.
... Helping Veterans, presents Jeannie Drayton and her son, Jimel, with a certificate honoring Jimmy Drayton, a Vietnam War veteran who died in 2006. ... Ten other Vietnam veterans received certificates, commemorative pins, special coins and bumper stickers as part of their long-delayed welcome home.
The Vietnam War Veterans Recognition Act, signed into public law last year, designates March 29 as National Vietnam War Veterans Day. The U.S. flag is ... He is president of Vietnam Veterans of America Chapter 154 headquartered at the Veterans Support Center, 18025 15 Mile Road, Clinton Township.
... of other veterans got their "Thank you's" Thursday as Sen. Joe Donnelly honored veterans, in celebration of the recently named Natioanl Vietnam Veterans Day. Donnelly was the coauthor of a bipartisan bill, signed by President Donald Trump last March, that named March 29 Vietnam War Veterans Day.


These Banana Oatmeal Cookies are the perfect, healthy, portable breakfast for busy mornings. No refined sugar! Also a gluten free and Paleo friendly recipe.
About 300 days a year, Keith and I have plain yogurt and some kind of fruit like cherries or blueberries for breakfast. I guess you could call that a rut. Honestly I don't mind keeping breakfast simple and rarely tire of our routine. But then I see a recipe like Faith's Healthy Fig and Pecan Breakfast Cookies and start craving something new. Something like cookies for breakfast.
A trio of overripe bananas were just the motivation I needed and these Banana Oatmeal Cookies came along as a happy interlude from our routine.
You might remember my Almond Flour Muffins? (These cookies are a riff on that recipe: plus oats, minus carrots.) When I made those muffins, I remember thinking that a nut flour base for baked goods would certainly result in a texture reminiscent of a hockey puck. Instead, the muffins were light and tender. The same is true of these cookies.
These Banana Oatmeal Cookies are perfect for a busy morning when you need a portable breakfast or if you're just ready for a change in routine.
In a large bowl, whisk together hazelnut flour, baking soda, salt and cinnamon. Stir in oats, coconut and walnuts until evenly distributed.
Add dates, bananas, vinegar, and coconut oil to the bowl of a food processor and process until smooth. Add eggs and process just until combined.
Pour date mixture over hazelnut flour mixture and stir until combined and no pockets of dry ingredients remain.
Scoop batter out in scant 1/4-cupfuls and place on prepared baking sheet about 2-inches apart. Flatten batter balls to 1/2-inch thick disks with the bottom of a glass or mug.
Bake for 15 to 18 minutes or cookie tops are set. Transfer to a wire rack to cool. Enjoy warm or cold.
So yummy! Thanks for the recipe! This is a keeper, my batter happened to be a bit wet, so I added 1/4 cup of coco powder and I added chopped dried mixed berries-so yummy!!
Hi, Allison! I'm so glad they turned out – love your additions too.
I added stevia and a handful of chocolate chips so the kids will be more willing to eat them! They turned out great. Wonderful recipe, thank you!
This sounds amazing! I've never baked with hazelnut flour! Do you make your own?
It's such a great flour – I use Bob's Red Mill brand. But I should try making my own!!
I was so impressed to see absolutely no sugar in these, Marissa. Like you, I'm stuck in a bit of a breakfast rut, but for me it's oatmeal. Loving the idea of repurposing my morning oatmeal into these healthy cookies. Never had cookies for breakfast before (well, OK then, I probably have! At least I've never 'officially' had them!).
haha, I may have had a chocolate chip cookie or two in my life before 8am. 😉 Thanks, Helen.
We always seem to have overripe bananas leftover so I'll earmark this recipe for those times. They look perfect to slip into Mr NQN's lunch too!
Yes, definitely good for an afternoon snack as well as breakfast!
Me likes cookies and one or two with some coffee, count me in Marissa. I Pinned this as the ingredient list (hazelnut flour, vinegar) intrigues. Happy Friday!
Cookies for breakfast? Sign me up! I love the flavors and bananas to keep things wonderfully moist! And I'm Dorothy, I'm not a big fan of raisins in my cookies, but I do love dates! Gotta make these this weekend!
What, no raisins? 🙂 I'm with you though on the dates…so gooey good.
Hi Marissa! I've never been much of a breakfast person, but if these cookies were in the kitchen I sure could be! I love the flavor combination you have here, especially the dates! I'm not a fan of raisins so whenever a recipe calls for them I substitute dates.
I'd love to make you a batch! And that's a great idea, Dorothy- somehow that substitute never occurred to me, but it makes a lot of sense.


That is true, but the riders failed to produce a state champion in individual play the last 3 years for the boys season. Isn't that worth something to talk about for a change?
It would be interesting to see if RR would have a 15? state winning streak if the post season was played out doors instead of indoors. I feel that RR is overall more of a finesse team instead of a 'grinder' team. They tend to need the conditions to be just right, if not, their shots are just not quite as sharp. When it is windy out, they do not look overpowering or untouchable.
Now don't get me wrong, RR has had and has a good team- but there have been other good teams that have come close to beating RR.
As for RR not having an individual state champion the last three years, I'm not convinced that is a huge deal. Each team in the state (for the most part) has at least one good, quality player. Plus the East part of the state has been so deep the past few years- I mean, the East went 7-1 in the first round at state for singles individuals.


Every day new viruses, trojans, worms, spyware and malware are unleashed in the computing world. Not all computer viruses behave the same way, and neither should all virus removal. At QCS we use our knowledge of virus removal tactics to do far more than what you could do at home by scanning with anti-virus programs. This offers you a much more comprehensive result, as well as minimizing potential damage to your system and your files.
We understand that losing files to a virus can make your life miserable. QCS technicians focus on a step-by-step procedure to remove the infection while preserving your data and software to get your computer back up and running quickly. We NEVER recommend a wipe-and-reinstall unless it's the last resort.
At QCS peace of mind for our customers is our number one concern. If you want proper and secure installation of home security equipment to make sure that it is efficient and effective don't hesitate to call QCS for any and all home security needs. Backing up all your devices is the best way to achieve peace of mind with all your electronic files. Never worry about losing anything important! Call QCS and have our technicians set up a back up for your device today! That way you will never have to wonder if your files are safe. Have QCS foolproof your home today!
Your computer restarts on its own.
Your computer does not run normal.
You get pop up ads to purchase bogus software to remove the virus.


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Grammy Award winning Songwriter , Producer and Talent Development specialist JODI MARR has written and produced multi language, multi genre hits for worldwide acts ,winning awards and accolades around the globe. She won her first GRAMMY in 2003 in the Latin market for her number one single "DE VERDAD" from the Rock Album of that year "SOY" by ALEJANDRA GUZMAN, followed by hits for RICKY MARTIN , JENNIFER LOPEZ, LUIS FONSI ,PAULINA RUBIO ,EDNITA NAZARIO and others. She is a founding board member of the LATIN SONGWRITERS HALL OF FAME, and served for several years as a Governor of the RECORDING ACADEMY. ( Grammys/ NARAS)
In 2006 Jodi developed then unknown 19-year-old London based university student named MIKA, who was signed by Universal Music Group global chairman Lucian Grainge and legendary star maker Tommy Mottola . MARR wrote several singles on Mika's debut album "Life In Cartoon Motion", and was credited as associate producer. The album went on to sell over 10 million copies worldwide, achieving gold or platinum sales in 32 markets. in 2009 She wrote and produced the breakthrough single " NEW YORK" for THE VOICE UK's star judge artist PALOMA FAITH, which charted in the top twenty for over a year in the UK. She has penned several well known film and tv themes and features such as the theme to 2010's " KICK ASS" movie with LADY GAGA producer RED ONE and MIKA,and features on COUGARTOWN, DESPERATE HOUSEWIVES, GREYS ANATOMY, THE WIRE and other Prime Time staples.
In 2014 Jodi started an artist development and publishing venture with a UK partner,. She is creative Director of ABFAB ARTISTS with offices in Miami, London and Nashville. She has consulted for both AMERICAN IDOL and the X FACTOR including helping with the original casting for FIFTH HARMONY and worked as a vocal producer on both shows.
Some of her most notable work includes:MIKA's "Grace Kelly", Ricky Martin's "Jaleo", Paloma Faith "New York", Kristin Chenoweth "Fathers and Daughters", CAROLE KING's A CHRISTMAS CAROLE album ( two songs) and Alejandra Guzman "De Verdad'.
As a producer, writer and performer, Jodi has been awarded several Gold and Platinum records, and received over 30 Grammy certifications, plus nominations and awards in the UK such as the coveted IVOR NOVELLO , BRIT awards and others.
MARR is currently living and working between NASHVILLE and LONDON, teaching as an adjunct professor at Nashville's esteemed BELMONT UNIVERSITY's CURB COLLEGE OF MUSIC SONGWRITING program and working on new projects for 2018

redpajama_set_name: RedPajamaCommonCrawl


The title, Smile, of this new watercolor painting from visual artist @K_DougDE pretty much sums up what this piece is about. With so much going on in the world right now, a simple smile can be the big difference in one person's day.
Douglas, Keara. Smile. 2015. Acrylic. 14×11 inches.
I painted Smile back in 2015. This was my very first watercolor painting, which is not my normal paint medium of choice. I wanted to try something new, well not really new for me. I've painted with watercolor paints before and often use watercolor in my #DEMusicBlocks, it's just not a preferred paint of choice for me. I guess you could say this painting is out of the norm for me. The particular brand of watercolors I used for this piece are from the Artist Loft collection from Micheal's Arts and Crafts. For me, watercolor paints always seem to be cheaper than acrylic and oil paints for some reason, so I was happy about this purchase. I didn't want to invest too much into the paint itself since I don't use this type often. My surface of choice for this piece is Cheap Joe's Art Stuff prime canvas panel. Even though these are already pre-primed, I always prime again with Liquitex Matte Primer.


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Team effort at Warner Robins saves millions of dollars in Air Force managed F-15 parts
RICHMOND, Va. – A DLA team is helping the Air Force solve an ongoing maintenance challenge involving high-demand specialized parts.
AF Year in Photos
This year's photos feature Airmen from around the globe involved in activities supporting expeditionary operations and defending America. This annual feature showcases the men and women of the Air Force.
Retired F-15 aircraft play role in Air Force readiness
Each year many F-15 aircraft come to Robins Air Force Base, Georgia, to go through a Planned/Scheduled Depot Level Maintenance process to receive upgrades and repairs to sustain them for the rigors of flight. But what if the aircraft can no longer be repaired?
F-15 EPAWSS Program Begins Low-Rate Initial Production Installations on F-15E Aircraft
The U.S. Air Force F-15 Eagle Passive/Active Warning and Survivability System (F-15 EPAWSS) program achieved a major milestone on July 19, 2022, when Boeing began installing the Electronic Warfare (EW) system on operational F-15E aircraft at its San Antonio facility.
U.S. Air Force celebrates 50 years of F-15 flight
Past and present members of the F-15 Program Office, retired F-15 pilots, representatives from The Boeing Co., and senior Air Force leaders gathered in a hangar at Wright-Patterson Air Force Base on July 28, to celebrate, share stories and mark the fiftieth anniversary of the F-15's first flight.
Air Force executes first in-flight Next Generation Aircrew Protection test in F-15E Strike Eagle
The Air Force Research Laboratory's 711th Human Performance Wing and the 28th Test and Evaluation Squadron executed an in-flight vapor purge test in a F-15E Strike Eagle, Aug. 16-19, 2022.
Testing the Eagle II
The 96th Test Wing's F-15EX on a test mission in the local area.
F-15EX completes first flight
The first F-15EX completed its initial flight in St. Louis Feb. 2. The fighter jet took off and landed from St. Louis Lambert International Airport, Missouri.


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Avoiding the Thucydides Trap
Home /Asia, China, China-US, International Relations/Avoiding the Thucydides Trap
Asia,China,China-US,International Relations |
By Sabena Saddiqui
Managing the world's most important geopolitical relationship is not an easy task, especially when US–China ties have a global influence and trickle-down effect to all of their allies. In recent years, the historical Thucydides Trap theory has been used quite often to describe the US–China equation and its risks. Reminding world leaders that war always remains more likely than peace and that it is wise to constantly exercise restraint, this theory retains some relevance.
Reducing China's bilateral trade deficit with the U.S. could still bring relations back on track.
Analysing the background of the Peloponnesian War (431–404 BCE), Thucydides, a historian in the fifth century BCE, concluded that war was unavoidable: 'It was the rise of Athens, and the fear that this instilled in Sparta, that made war inevitable'. Being the dominant power, Sparta had pre-emptively attacked the rising power, Athens, even though it may not have been a real threat. At the end of the day, it was the dominant Sparta that was victorious but it was a long war that lasted almost three decades.
Presenting the 'Thucydides Trap' as one of the greatest mis-judgements of history, Harvard University's Professor Graham Allison was the first to use it in reference to the US and China. Having identified 16 similar cases over the last 500 years, Allison was worried that out of those sixteen scenarios, twelve resulted in war. Highlighting similarities, he commented that 'Thucydides's Trap is the dangerous dynamic that occurs when a rising power threatens to displace a ruling power. That is actually the best lens for understanding what's happening in relations between a rising China and a ruling United States today'.
Identifying five ways to avoid war between the two countries, based on observations regarding the previous experience of the Cold War, Allison stressed that first, war between nuclear powers is 'mutually assured destruction'. Second, leaders must remember that they risk starting a war they cannot win. Third, more space should be created to reduce risks by creating new 'precarious rules of the status quo'. Fourth, the domestic economy is most vital for both powers to maintain peace. And finally, relying on hope is no real strategy.
Alarmingly, one of the prime validations of the Thucydides Trap theory in recent times has been the outbreak of the First World War. Despite Britain and Germany being the two largest global trading partners, similar to the US and China today, they still went to war. In practical terms however, the absence of nuclear weapons at the time likely made starting the war easier. In the case of the Soviet Union and the US, in contrast, the presence of nuclear weapons kept war at bay. However, even though nuclear weapons have made great-power conflict nearly obsolete, the stakes remain high.
Nonetheless, the assumption that war is inevitable is less relevant in this nuclear century. Also, it is not practical to base foreign policy objectives on a theory which is 2,400 years old. Putting things into perspective, the US and China cannot fall into the Thucydides Trap, since many other factors determine their relations in this modern-day scenario. With geo-economics shaping the global power balance and with multiple dynamics at work, it is not a foregone conclusion that a growing power will come into conflict with an established power. Nor is it definite that the balance of power will remain the same. Furthermore, conflict is quite unlikely when both powers are co-dependent to the extent of being dubbed 'Chi-merica' by historian Niall Ferguson and economist Moritz Schularick.
Dividing 'Chimerica' into two virtual economic rather than monetary units, Ferguson and Schularick argue that 'East Chimericans have the renminbi, West Chimericans the dollar. Nevertheless, the scale of the financial transactions between the two halves is comparable with the flows that traditionally have occurred within nation states rather than between them'. Basically, divergences first appeared when Beijing tried to reduce financial risk factors by introducing new foreign exchange policies to stabilise the yuan. However, reducing China's bilateral trade deficit with the US could still bring relations back on track to what they were in 2015, and so balance the developing economic world order.
Recently, Richard Weitz, Director of the Center for Political-Military Analysis at the Hudson Institute, participated in a very positive discussion at the Center for China and Globalization (CCG) in Beijing. Observing that the China–US trade dispute did not represent the beginning of an economic Cold War, the expert stated that the two countries had just 'hit a rough patch'. Removing the commercial conflict of interest could lead to a breakthrough in bilateral relations. Furthermore, notwithstanding the wide range of smaller differences of opinion, remaining engaged and maintaining dialogue is the best way to reduce friction.
Interestingly, the year 2018 marks the fortieth anniversary of the signing of the Joint Communiqué on the Establishment of Diplomatic Relations between China and the United States, thus Sino-American ties are now four decades old and there can be no better time than this to get over their 'rough patch'.
Sabena Siddiqui is a foreign affairs journalist and Sinologist focusing on the Belt and Road Initiative, CPEC and South Asia. She also works as an op-ed writer at China.org.cn, South China Morning Post and Asia Times. Find her on Twitter @sabena_siddiqi. Image Credit: CC Wikimedia Commons.
Informing the public: On China's International Import Expo #CIIE, the British press fails again
The Long Read: A Southeast Asia perspective on climate change and negative emission technologies
TAGS: China U.S. relations Thucydides Trap trade


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Media|NBC Buying Web Service to Stream Phone Video
https://nyti.ms/19co6LQ
NBC Buying Web Service to Stream Phone Video
By Brian Stelter
When a plane crashes or a protest turns violent, television crews speed to the scene. But they typically do not arrive for minutes or even hours, so these days photos and videos by amateurs — what the news industry calls "user-generated content" — fill the void.
Those images, usually found by frantic producers on Twitter and Facebook, represented "the first generation of user-generated content for news," said Vivian Schiller, the chief digital officer for NBC News. The network is betting that the next generation involves live video, streamed straight to its control rooms in New York from the cellphones of witnesses.
On Monday, NBC News, a unit of Comcast's NBCUniversal, will announce its acquisition of Stringwire, an early stage Web service that enables just that. Ms. Schiller imagined using Stringwire for coverage of all-consuming protests like those that occurred in Tahrir Square in Cairo.
"You could get 30 people all feeding video, holding up their smartphones, and then we could look at that," she said in an interview by phone. "We'll be able to publish and broadcast some of them."
Such a vision fits neatly into the future many academics predict. That future has fewer professional news-gatherers but many more unpaid eyes and ears contributing to news coverage.
Stringwire is embryonic. What NBC is really acquiring is Phil Groman, who developed the technology while a graduate student in the Interactive Telecommunications Program at New York University.
A screen shot of the Stringwire dashboard.
Such "acqui-hiring," in which a start-up is bought primarily for its talent, is normally associated with technology companies like Google and Apple, not television networks like NBC. But that is partly the point of Monday's announcement, Ms. Schiller said: to send a message that the network news division wants more entrepreneurs like Mr. Groman.
Mr. Groman, who graduated from N.Y.U. in May, will become a product lead, based at the NBC News Digital Group's office in San Francisco, where he will finish building Stringwire. The service works by tapping into the multitudes of people who send Twitter messages when they witness a news event. Those people will receive a Twitter post that asks them to click a link and point their camera at what they are seeing. Without any special app, the service will start streaming live video to NBC. The video submissions will be vetted just like any other material the network uses, Ms. Schiller said.
"Wherever you see a swarm of eyewitnesses on Twitter, that's the sweet spot for Stringwire," she said, citing the July 6 crash-landing of an Asiana jet in San Francisco. That day, photos from a passenger and a short YouTube video from the terminal were the primary images on television until a local news helicopter arrived.
Ms. Schiller said Stringwire could have also helped coverage of the hunt for the suspects in the Boston Marathon bombing, when the movements of reporters were restricted. Several times during NBC's coverage in April, local residents were interviewed via Skype from neighborhoods that had been cordoned off.
Generally, during news events, "we might have reporters there, but they may not be in the right places," Ms. Schiller said. "They may not have the kind of access that eyewitnesses do."
Clay Shirky, the N.Y.U. professor who introduced Ms. Schiller to Mr. Groman, said that by having reporters reach out to witnesses, "you don't get the Pulitzer Prize-winning shot, but you get real information about life on the ground." He said Mr. Groman's insight was in applying "multiple sources and editorial judgment."
The acquisition is the first by NBC News since its Web joint venture with Microsoft was dissolved last year. Their joint Web site, msnbc.com, has become NBCNews.com. The strategy now involves "building things in-house and placing a lot of bets," Ms. Schiller said.
While Stringwire will initially be used by the news division, she said she thought the service had "great commercial opportunities," suggesting that it could be licensed to others, creating a new source of revenue for NBC.


The Venue: Stithians Reservoir, somewhere South West of Redruth, Cornwall. This is a large water about 274 acres in reality, but feels and looks much bigger.
As with many SW waters it is approached with some trepidation by sensible 'up-country' drivers, who have to drive down barely tarmacked cart tracks complete with the unmissable potholes now prevalent in the UK since the reign of Chancellor George Osborne!
This lake is heavily used by sailors and wind surfers, so fishermen in float tubes have to use a degree of caution as to where they fish if they wish to survive the day! Many of the other users are children undertaking water-sports training and are not expert at avoiding small obstacles in their way! Be warned!
The Occasion: The Cornish Open Competition, in conjunction with Snowbee.
The weather: Somewhat mixed. Sunny in the morning with a strong breeze, this was forecast at about 9mph but was obviously higher when on the water. Around 11.30am the wind rose in intensity and produced a noticeable wave action on the water surface. Clouds also started to appear around this time. Just before 1.00pm the heavens opened with a vengeance, producing some extremely heavy rain squalls for much of the rest of the afternoon until just before the finish at 4.00pm - when the rain abated, the wind dropped and the sun reappeared for the weigh-in.
Nature notes: Mainly cormorants and ducks were spotted. A mallard with a large brood of young ducklings was seen.
The fishermen: A small contingent of 'up-country' regulars and a good smattering of Cornish familiar faces from previous years – some of the latter are extremely competent fishermen. For those unfamiliar with the Cornish term 'up-country' this basically means anybody coming from the North or East of the Cornish town of Rrrr-drooth - (Redruth to you and me).
The Leicester pot-hunters were present, as was a failing old gentleman from Oxfordshire. A specimen hunter from Trowbridge, and a Kayaking Dartmoor walker from Devon. The Cornish set included a very competent fisherman who can make a Mercedes car sound absolutely atrociously loud. Drifter, who was in charge before nipping off to see the queen for tea and biscuits, Chris who was apparently in charge of pasty picking, Colin who was renewing his memories of what Cornwall looks like, and some other fellows who can be found floating around on Drift when the weather is good. Fourteen in all.
There were supposed to be others present, but some of them were obviously flummoxed by the necessary cartographic skills required to find the place, and the Mancunians who apparently preferred the comforts of NHS beds to a pleasant day floating around in a gale while submerged up to their waists in cold water.
The fishing: This is a very large water. There was some speculation that the stocking ratio appeared to be about one trout to six acres or so. I'm sure this is not the case but on this day it was quite hard to both find and tempt the trout. Drifter did find a few not far from where they had been stocked by the sailing club. He braved the chance of a quick death by sailing boats, and stubbornly proceeded to hook and lose a few at the net in this area for much of the match. Kevin eventually located a shoal by the entrance to the dam arm and snagged five of them by ripping his lure back quickly through their midst – this tactic hooking enough fish to win the day. I think I caught the first fish of the day, a lively blue, when approaching the buoy line when being blown down to the causeway across the end of the lake. This was a bit of a problem as it was essential to net the trout before it was one side of the buoy line with me the other – which as you may imagine would have been a tad problematic when being driven at speed by the wind. I just managed it as my legs caught the buoy rope. Lucky or what? Ruan later spent the afternoon just the other side of this line catching his three fish to take third place. Colin and Chris spent time admiring Ruan's technique and thinking to themselves that they wished they had some of his special flies. Both were also able to inspect my fins out of water at this point, because I had developed chronic cramp in the thighs – very painful and not to be recommended! It was now that I wished dearly that my motor was on the FT and working. (The trip to Cornwall over the result some of Mr. Osborne's austerity affected roads, had ripped the wire clamp and some wires out of the motor head and I couldn't get it to go before we started – or in fact since! A bigger job for another day when I have a bit more time).
Andre and Gary plus a few of the local lads, had headed South down the reservoir and were by now spread across its width, slightly North of the dam arm entrance, but I never saw a rod bent when I was watching. Gary at least, eventually moved back up by the causeway. I got out and had a bite to eat, and also sort out a couple of knots in my leader before going back on the water. I had already lost a blue or rainbow over the far side of the lake before getting cramp, I now completed the misery by hooking, playing and then losing a brown just as the monsoons started. Time now for me to get out and finish for the day just before 1.00pm. After putting my stuff into the car and having a chat to Colin I decided to spend a short while in the café warming up with a cup of coffee and to watch points from there. The super monsoon now arrived and I was glad to be inside, albeit surrounded by screeching small children and attractive young women. The window glass looked like waterfalls at this point.
At the weigh-in it transpired that Kevin had won the competition with five fish, albeit quite small examples. Andre had some nicer fish to come fourth, and Gary had three respectable examples to place him into second place. Ruan had a bad day and only finished third. Another Cornish stalwart Vaughan finished in ninth so had a dire day by his standards. John had spent the day specialising in catching brown trout so failed miserably to get any championship points. I'm glad he came though!
As for flies and lines: an intermediate line appeared to have taken most fish and a damsel nymph seemed to be the best fly. However, I did hook three fish and am pretty sure that they all came to a black and green montana nymph. I did hear others claim black and green worked for them. It's almost a certainty that Ruan was using a black and green fritzy affair to catch his fish!
The fishing was undoubtedly hard. The fish stock levels are not massively high for the size of water and on this day the fish did appear to be in small groups or singles. The weather undoubtedly affected the catch rate too. 26 browns and blues + 9 browns for a group of 14 generally very competent anglers works out around the rod average for this water, but these guys would generally do better than that.
Asides: Unfortunately, my cover was blown by a Cornishman who instantly recognised me as an England trout team Champion – this greatly amused Andre and Gary. I just stayed quiet and kept my head down! The same guy told Gary that there were big carp in the lake. Gary later said he saw people in white coats walk the gent quietly away!?
Acknowledgements: Many thanks to Dave Williams for his efforts in organising this Championship. Thanks also go to Snowbee for the prizes. Chris and his wife are thanked for collecting and distributing the pasties to the hungry horde. We would also like to thank the staff in the café for coming in early to provide the excellent bacon butties for us.
Well done Tony good report. Gary and I fished the bank opposite to where you caught. We both had plenty of pulls and lost another rainbow each during the afternoon. The fish were definitely not shoaled, you had to work up and down the whole bank. Both of us were on black based flies, I caught on Steve F's Black Diawl Bach and Steve N's Black and Green thing, the fish I lost was on a small Montana. I think Gaz was pretty much the same, he was on an intermediate mine came to the floater.
All in all it was a well organised day and the company was, as always, very pleasant. The girls were 12 miles away on the coast in Porthleven, they had a brief shower at lunchtime and were basking in glorious sunshine all afternoon - Cornwall !!!
Thanks to Drifter for organising, already looking forward to next years event - hopefully on Drift.
An England International !!! Well you kept that quiet for a few years !! I may have to get my rods out and pit myself against the best of the best !!
You will have to update them first Steve we use carbon fibre ones now.
I look forward to that Stevie. Can you remember where you left your rods after all this time?
Mind you, you might have to be quick to join me on the water, I can hardly hold a rod any more! People tell me that retirement from fishing is in the offing!
Let's hope that's still a few years off yet Tony. You will still be coming to the A.G.M.so get building up your fitness and that could add a few years. Best of luck.
Talking of health issues Ivan has been in hospital again, this time a mini stroke ! told him to give up the party lifestyle and grow old a little more gracefully just like me !


text:
Middle School Projects >
Opened September 2016
$61,371,000 Budget
166,000 sq. ft.
1,100 Student Capacity
32 Classrooms + 9 Additional Teaching Spaces
Natural Light & Fresh Air
Abundant natural light and constant fresh outside air to all classrooms
Seismic Reinforcement
Campus Design
Large Venue for School & Community Events
Centrally located gym, commons and courtyard
State of the Art HVAC Systems
Efficient heating & cooling
Building is a Learning Tool
Used as a Swing School
Generate 172 kW-hours
On September 6, 2016, the new middle school building in the Timberland development opened its doors to students. The building was designed by Mahlum Architects and built by Skanska USA.
Between 2016 to 2021, the building served as a "swing school," while three elementaries and one option school were torn down and rebuilt. Vose was the first to occupy the building followed by Hazeldale, William Walker and the Arts & Communication Magnet Academy (ACMA).
The school cost $61-million dollars to build. It's deemed an essential Risk Category IV facility as outlined in the BSD Resilience Plan. The school contains seismic bracing designed to withstand an earthquake as well as a generator with extra fuel capacity, allowing the facility to serve as an emergency shelter in the aftermath of a natural disaster.
The District worked with designers to make the building a learning tool; for example, a steel x-brace was left exposed to allow students to see how the building was built to withstand an earthquake. In addition, hundreds of solar panels were installed on the roof, generating more than 129,000 kWh per year. An interactive solar kiosk, courtesy of the Bonneville Environmental Foundation, uses a secure iPad to display solar data. Also located on the roof, an innovative weather monitoring station allows students to monitor wind speed and direction.
Time Lapse Video of Construction
Architect: mahlum architects
Contractor: skanska usa


Texas SB 2 (Sen. Dan Patrick, author) was passed during the 83rd Legislative Session and goes into effect on 9.1.13. The Turkish Gulen Harmony Charter Schools as well as all other charter schools in Texas will be required to follow the many new SB 2 mandates.
One of the negative aspects about SB 2 is that it takes away the authority over charter schools from the elected members of the Texas State Board of Education and shifts that authority over to the unelected Texas Commissioner of Education who is appointed by the Governor.
Turkish Gulen Harmony Charter Schools and other charters will have to make sure the principal and teachers have attained at least a baccalaureate degree.
A majority of the school board members must be qualified to vote (i.e., U. S. citizens).
The names of school board members must be listed on the school's website.
The Texas Attorney General can sue for fiduciary misapplication of public funds.
The school superintendent's salary must be posted on the school's website.
(2) in a position other than a position described by Subdivision (1) if a school district could employ the person in that position.
Sec. 12.1202. REQUIREMENT FOR MAJORITY OF MEMBERS OF GOVERNING BODY. A majority of the members of the governing body of an open-enrollment charter school or the governing body of a charter holder must be qualified voters.
Sec. 12.1211. NAMES OF MEMBERS OF GOVERNING BODY LISTED ON WEBSITE. An open-enrollment charter school shall list the names of the members of the governing body on the home page of the school's Internet website.
(a) Notwithstanding the applicable provisions of the Business Organizations Code [Texas Non-Profit Corporation Act (Article 1396-1.01 et seq., Vernon's Texas Civil Statutes)] or other law, on request of the commissioner, the attorney general may bring suit against a member of the governing body of an open-enrollment charter school for breach of a fiduciary duty by the member, including misapplication of public funds.
Sec. 12.129. MINIMUM [TEACHER] QUALIFICATIONS FOR PRINCIPALS AND TEACHERS. A person employed as a principal or a teacher by an open-enrollment charter school must hold a baccalaureate degree [high school diploma].
Sec. 12.136. POSTING OF CHIEF EXECUTIVE OFFICER SALARY. An open-enrollment charter school shall post on the school's Internet website the salary of the school's superintendent or, as applicable, of the administrator serving as educational leader and chief executive officer.
Here is the reason that thinking parents should not put their children into the Harmony or Idea Charter Schools.
The RTTT–D grant funds were sent directly from the U. S. Dept. of Ed. to the Harmony/Idea Charters without the purview of the state education agency. These RTTT-D requirements basically mean that Harmony/Idea Charters are compelled to follow the Common Core Standards Initiative (i.e., national standards, national curriculum, national assessments, national teacher evaluation system tied to individual student scores, and national database).
The 83rd Legislative Session passed HB 462 — .
HB 462 became effective on 6.14.13 and bans local public school districts (and the Texas State Board of Education) from utilizing Common Core Standards (CCS) and national CCS assessments.
How are Harmony and Idea Charters (considered to be public schools because they take public dollars) going to live up to the RTTT-D that requires schools to follow the Common Core Standards Initiative (Type #2) while at the same time Harmony and Idea Charters must follow Texas law in HB 462 that bans the Common Core Standards Initiative in Texas public schools? All public schools in Texas, including charters, are mandated to teach the SBOE-adopted curriculum standards (TEKS) which are Type #1. (Type #1 vs. Type #2 — http://educationviews.org/2-types-of-education-philosophies-chart/ ).
How can children effectively learn Type #1 curriculum that emphasizes correct, fact-based answers while at the same time they are learning subjective, opinion-based, project-driven, group-think, Type #2 curriculum that emphasizes the process over right answers and seeks to indoctrinate children into the social justice agenda?
Bottom line: No thinking, caring parent should put his/her children into the Turkish Gulen Harmony Charter Schools or the Idea Schools because the students in those schools will be indoctrinated into the Common Core Standards.
1. Eligible applicants include only individual local educational agencies (LEAs) (as defined in this document) and consortia of LEAs.
3. At least forty percent of participating students across all participating schools (as defined in this document) must be students from low-income families, based on eligibility for free or reduced-price lunch subsidies under the Richard B. Russell National School Lunch Act, or other poverty measures that LEAs use to make awards under section 1113(a) of the ESEA. If an applicant has not identified all participating schools at the time of application, it must provide an assurance that within 100 days of the grant that its participating schools (as defined in this document) will meet this standard.
iv. a LEA school board evaluation (as defined in this document).
ii. The ability to match student level P-12 and higher education data.
c. The LEA has policy and regulatory protections in place that ensure Family Educational Rights and Privacy Act (FERPA) compliant privacy and information protection while enabling access and use by stakeholders.
The Race to the Top District competition (RTT-D) will build on the lessons learned from the State-level competitions and support bold, locally directed improvements in teaching and learning that will directly improve student achievement and teacher effectiveness.
As importantly, they will create opportunities for students to identify and pursue areas of personal passion– all of this occurring in the context of ensuring that each student demonstrates mastery in critical areas identified in college- and career ready standards.
Content standards for kindergarten through 12th grade that build towards college- and career-ready graduation requirements (as defined in this document) by the time of high school graduation. A State's college- and career-ready standards must be either (1) standards that are common to a significant number of States; or (2) standards that are approved by a State network of institutions of higher education, which must certify that students who meet the standards will not need remedial course work at the postsecondary level.