text:
\section{Introduction}
Quantum chromodynamics (QCD) is regarded as the underlying theory of the nuclear strong interactions, and so hadron physics. Even though its Lagrangian is apparently simple, high-level complexity phenomena take place, such as quark-gluon confinement and the emergence of hadron masses (EHM)~\cite{Roberts:2020hiw}. The Dyson-Schwinger equations (DSE) formalism has proven to be a very robust approach to QCD in the continuum~\cite{Roberts:1994dr,Fischer:2018sdj}, capable of taming its non-perturbative character. Supplemented by the bound-state Bethe-Salpeter (BS) and Faddeev equations~\cite{Faddeev:1961cu,Salpeter:1951sz}, the DSE formalism becomes an ideal platform for the calculation of hadron masses and several structural properties; see, for example Refs.~\cite{Eichmann:2016yit,Cui:2020tdf,Arrington:2021biu,Qin:2019hgk}. The derivation of QCD's DSEs do not require any assumptions on the running coupling, therefore, both perturbative and non-perturbative facets of the strong interactions can be addressed within this formalism. At the same time, the DSE approach is not restricted to a certain domain of current quark masses~\cite{Hilger:2014nma,Raya:2019dnh,Qin:2019hgk,Chen:2020ecu}. Moreover, hadron observables can be traced down to fundamental pieces, namely propagators and vertices, hence maintaining a clear connection to QCD's fundamental degrees of freedom, quarks and gluons~\cite{Raya:2015gva,Chang:2013nia,Chen:2020wuq,Qin:2020rad}. The structure of the DSEs is such that any $n$-point Green function is related to at least one higher order function, therefore yielding an infinite set of coupled integral equations~\cite{Roberts:1994dr}. In order to arrive at a tractable problem, a sensible truncation is needed; thus, systematicity and symmetry principles become imperative~\cite{Binosi:2016rxz,Munczek:1994zz, Bender:1996bb}. Historically, Ward-Green-Takahashi identities (WGTI)~\cite{Ward:1950xp,Green:1953te,Takahashi:1957xn} have been crucial in symmetry-preserving studies of hadron properties. Such relations ensure, among other things, current-conservation and the appearance of Goldstones modes in connection with dynamical chiral symmetry breaking (DCSB)~\cite{Munczek:1994zz, Bender:1996bb}. Furthermore, WGTI impose relationships between propagators and vertices, as well as constraints between the kernels of the one-body and two-body problems~\cite{Chang:2009zb,Qin:2020jig}. Nevertheless, the mathematical form of the one-body and two-body kernels (quark self energy and BS equation kernels), which satisfy such consistency relations, is not always unique~\cite{Chang:2020iut}. Taking advantage of this fact, we
derive a \emph{modified} version of the so called rainbow-ladder (RL) truncation. Subsequently, within a contact interaction (CI) model, we analyze its impact on the structure of the quark-photon vertex (QPV) and $\rho$ meson properties, as derived from their corresponding Bethe-Salpeter equations. More precisely, we shall expose how, in addition to the $\rho$ meson pole in the timelike axis, the structure of the QPV develops an anomalous magnetic moment (AMM) term. It is known that DCSB generates an anomalous chromonagnetic moment for dressed light-quarks, which is large at infrared momenta and generates an electromagnetic moment with commensurate size but opposite sign~\cite{Chang:2010hb,Bashir:2011dp}. Thus, it is a highly desirable feature for the QPV, exhibited quite transparently in our present approach. Its impact on the structural properties of hadrons is put in manifest when studying electromagnetic form factors (EFF): while the elastic EFF of spin-0 mesons is unaltered by the AMM piece, the latter displays from mild to notorious impact on EFF involving spin-1 mesons (and baryons as well)~\cite{Wilson:2011aa,Raya:2018ioy,Raya:2021}.

The manuscript is organized as follows: Section II introduces aspects of constructing symmetry-preserving truncations of quark DSE and meson BS equation, based upon vector and axial-vector WGTIs. In Section III, we present the CI model within the RL truncation and its modified version (MRL). The mass spectrum of light-mesons $\{\pi$, $\rho\}$ is included to compare and contrast. Section IV focuses on the derivation and structure of the QPV. Subsequent sections capitalize on $\rho$ meson structural properties: EFFs of the $\rho$ meson are discussed on Section V, while its valence-quark distribution amplitudes (PDAs) are derived in Section VI. Conclusions and final remarks are presented in Section VII.

\section{Symmetry-preserving truncations}
Within the DSE approach, the properties of valence quark/antiquark bound-states are encoded within solutions of its BS equation. Mesons appear as poles in the corresponding inhomogeneous BS equation~\cite{Qin:2020jig, Chang:2009zb}, which takes the form~\cite{Chang:2009zb,Qin:2020jig}:
\begin{equation}
\label{eq:BSEGen}
    \Gamma_{H}(p;P)=\tilde{\gamma}_H+\int_{q} K^{(2)}(q,p;P)\chi_{H}(q;P)\;,
\end{equation}
where $\chi_{H}(q;P)=S(q_+)\Gamma_{H}(q;P)S(q_-)$ denotes the BS wavefunction, such that: $\Gamma_{H}(q;P)$ corresponds to the BS amplitude of a meson $H$, whose specific structure in terms of Dirac matrices depends on its quantum numbers; $S(q^{\pm})$ represent the quark and antiquark propagators. The two particle irreducible quark/antiquark scattering kernel is denoted by $K^{(2)}(q,p;P)$; and $\tilde{\gamma}_H$, as the BS amplitude, is defined by a specific combination of Dirac matrices that specify the $J^{PC}$ channel ($\tilde{\gamma}_H= \gamma_\mu$ for the vector vertex and $\tilde{\gamma}_H=\gamma_5 \gamma_\mu$ for the axial-vector vertex). Herein, we use the notation $\int_{q}$ to refer to four dimensional Euclidean integral, regularized in a Poincar\'e covariant manner. Finally, the kinematics is defined as follows: $P$ is the total momentum of the quark/antiquark system; $q_+=q+\eta P$ and $q_-=q-(1-\eta)P$, with $\eta\in[0,1]$ defining the relative momentum (in a Poincar\'e covariant framework, no single observable depends on $\eta$).  The fully-dressed quark propagator obeys a DSE of the form:
\begin{equation}
\label{eq:quarkPropGen}
    S^{-1}(p)=[S^{(0)}(p)]^{-1}+\int_{q} K^{(1)}(q,p)S(q)\;,
\end{equation}
where $S^{(0)}(p)=[i \gamma \cdot p+m^{\text{bm}}]^{-1}$ corresponds to the bare quark propagator, with a Lagrangian current quark mass $m^{\text{bm}}$, and $K^{(1)}(q,p)$ the one-body kernel. The above equation is often referred to as gap equation. In both Eqs.~(\ref{eq:BSEGen}, \ref{eq:quarkPropGen}), and throughout the rest of the manuscript, we supress all remormalization constants, as well as color and flavor indices, for notational convenience.

As has been pointed out in the Introduction, a practical way to construct and relate $K^{(1)}$ and $K^{(2)}$, relies upon WGTIs. The chiral limit vector and axial vector WGTIs take the form:
\begin{eqnarray}\label{eq:vWGTI}
i P_{\mu}\Gamma_{\mu}(k;P)&=&S^{-1}(k_{+})-S^{-1}(k_{-})\;.\\
\label{eq:avWGTI}
P_{\mu}\Gamma_{5\mu}(k;P)&=&S^{-1}(k_{+})i\gamma_{5}+i\gamma_{5}S^{-1}(k_{-})\;,
\end{eqnarray}
where $\Gamma_{\mu}$ and $\Gamma_{5\mu}$ are the vector and axial-vector vertices. Now consider the gap equation in QCD~\cite{Roberts:1994dr}:
\begin{equation}
\label{eq:quarkPropQCD}
    S^{-1}(p)=[S^{(0)}(p)]^{-1}+\frac{4}{3}g^2 \int_{q} D_{\mu\nu}(p-q) \gamma_\mu S(q) \Gamma_\nu(p,q)\;,
\end{equation}
where $g$ is the Lagrangian coupling constant; $D_{\mu\nu}$ and $\Gamma_\nu$ are the fully-dressed gluon propagator and quark-gluon vertex (QGV), respectively. Thus we can identify
\begin{equation}
\label{eq:K1}
    K^{(1)}(q,p)=\frac{4}{3} g^2 D_{\mu\nu}(p-q)\gamma_\mu \otimes \Gamma_\nu(q,p)\;.
\end{equation}
If we restrain ourselves to the tree-level QGV $\Gamma_\nu \to \gamma_\nu$, hence neglecting all the rich structure that the fully-dressed vertex might have~\cite{Albino:2018ncl,Sultan:2018qpx,Bashir:2011dp}, and replace the gluon propagator by an effective one, $D_{\mu\nu} \to D_{\mu\nu}^{\text{eff}}$, to compensate the missing pieces in $\Gamma_\nu$~\cite{Qin:2011dd,Maris:1999nt}, the one-body kernel becomes
\begin{equation}
\label{eq:K1RL}
    K^{(1)}(q,p)=\frac{4}{3}g^2 D_{\mu\nu}^{\text{eff}}(p-q)\gamma_\mu \otimes \gamma_\nu\;.
\end{equation}
The two-body kernel $K^{(2)}$ can be obtained by combining Eqs.~(\ref{eq:BSEGen}-\ref{eq:avWGTI}) and Eq.~\eqref{eq:K1RL}, which yields
\begin{eqnarray}
\label{eq:vecIdWG}
\int_{q}K^{(2)}(q,p;P)[S(q_+)-S(q_-)]= \hspace{2cm}&\\ \nonumber
-g^2\frac{4}{3}\int_{q} D_{\mu\nu}^{\text{eff}}(p-q)\gamma_\mu[S(q_+)-S(q_-)]\gamma_\nu \;,& \\
\label{eq:axIdWG}
\int_{q}K^{(2)}(q,p;P)[S(q_+)\gamma_5+\gamma_5S(q_-)]=\hspace{2cm}& \\ \nonumber
-g^2\frac{4}{3}\int_{q} D_{\mu\nu}^{\text{eff}}(p-q)\gamma_\mu[S(q_+)\gamma_5+\gamma_5 S(q_-)]\gamma_\nu \;.&
\end{eqnarray}
Then the simplest choice that satisfies the vector and axial-vector WGTIs symmetry constraints is
\begin{equation}
\label{eq:defRL}
    K^{(2)}(q,p;P)=-\frac{4}{3}g^2 D_{\mu\nu}^{\text{eff}}(p-q)\gamma_\mu \otimes \gamma_\nu=-K^{(1)}(q,p;P)\;.
\end{equation}
Such kernels define the RL truncation: $K^{(1)}$ refers to the `\emph{rainbow}' part, while $K^{(2)}$ corresponds to the `\emph{ladder}' piece. Notably, this simple choice is sufficient to ensure the appearance of pions as Goldstone bosons of DCSB~\cite{Munczek:1994zz,Bender:1996bb}, while also being a sensible approximation to compute its structural properties~\cite{Ding:2019lwe, Raya:2015gva, Chang:2013nia}.

It is worth pointing out that the solution to Eqs.~(\ref{eq:vecIdWG}-\ref{eq:axIdWG}) is not unique. In fact, given the rainbow approximation for the one body problem, it is possible to derive a fully consistent symmetry-preserving two body kernel that extends beyond the RL truncation, as it is discussed in Ref.~\cite{Chang:2020iut,Ding:2018xwy}. In addition to the ladder part, other terms of the form
\begin{equation}
    K^{(2)}(q,p;P)=\tilde{D}^j(q,p) \tilde{\Gamma}_{j}(q,p)\otimes \tilde{\Gamma}_{j}(q,p) F^j(q,p)\;,
\end{equation}
can be added to the two-body kernel~\cite{Dai:1990ap}. Herein, $F^j$ are Lorentz invariant scalar functions, $\tilde{\Gamma}_{j}$ are different combinations of Dirac matrices, and $\tilde{D}^j$ are tensor structures that might be needed to contract Lorentz indices. The particular choices $\tilde{\Gamma}_{j}(q,p) = \{ \mathbb{I},\;\gamma_5,\;i/\sqrt{6}\sigma_{\mu\nu}\}$ and $\tilde{D}^j(p,q)F^j(p,q)  \to \xi \tilde{D}$, the latter being reduced to a simple constant, preserve the consistency constraints and so Eqs.~(\ref{eq:vecIdWG}-\ref{eq:axIdWG}). Thus, the inhomogeneous BS equation becomes
\begin{eqnarray}\nonumber
    \Gamma_{H}(q;P)&=&\tilde{\gamma}_H-\frac{4}{3}g^2\int_{q} D_{\mu\nu}^{\text{eff}}(p-q)\gamma_\mu \chi_H(q;P) \gamma_\nu\\
    &+& \xi \tilde{D} \int_{q}  \tilde{\Gamma}_{j} \chi_H(q;P)\tilde{\Gamma}_{j}\;.
\label{eq:inBSEERL}
\end{eqnarray}
The product $\xi \tilde{D}$ sets the strength of the non-ladder (NL) term. In the next section we shall discuss about the truncation herein derived, Eq.~\eqref{eq:inBSEERL}, within a vector-vector symmetry-preserving contact interaction (CI) model of QCD~\cite{GutierrezGuerrero:2010md, Roberts:2010rn,Wilson:2011aa}.

 \medskip
\section{Contact Interaction model}
Let us recall the quark gap equation in the RL truncation:
\begin{eqnarray}
\label{eq:quarkGapRL}
    S^{-1}(p)=[S^{(0)}(p)]^{-1}+\frac{4}{3}\int_{q} g^2 D_{\mu\nu}^{\text{eff}}(p-q) \gamma_\mu S(q) \gamma_\nu\;.\hspace{0.3cm}
\end{eqnarray}
Clearly, the quark DSE decouples from the QGV and gluon DSEs. The only remaining ingredient is $D_{\mu\nu}^{\text{eff}}(p-q)$, the effective gluon propagator. This piece is supposed to compensate for all the missing pieces in the QGV~\cite{Maris:1999nt,Qin:2011dd}, often requiring an artificial enhancement in the infrared~\cite{Sultan:2018qpx}. Thus we appeal to the illustrative CI model introduced in Refs.~\cite{GutierrezGuerrero:2010md, Roberts:2010rn},
\begin{equation}
    \label{eq:gluonprop}
    g^2D_{\mu\nu}^{\text{eff}}(p-q) \to \frac{1}{m_G^2}\delta_{\mu\nu}\;,
\end{equation}
where $m_G = 0.132$ GeV is an infrared mass scale. Besides preserving the relevant symmetries, the CI model typically yields semialgebraic expressions and captures the non-perturbative traits of QCD~\cite{GutierrezGuerrero:2010md, Roberts:2010rn,Wilson:2011aa}. In addition, the CI model produces sensible results for the hadron mass spectrum~\cite{Yin:2021uom, Gutierrez-Guerrero:2019uwa,Yin:2019bxe,Chen:2012qr}, including tetraquarks~\cite{Bedolla:2019zwg}, while also providing crucial benchmarks for many hadron structural properties~\cite{Wilson:2011aa,Raya:2018ioy,Raya:2017ggu,Bedolla:2016yxq, Segovia:2015hra, Segovia:2014aza}. The following sections are dedicated to illustrate some of the implications of the gluon model Ansatz from Eq.~\eqref{eq:gluonprop}, in the RL and MRL truncations.

\subsection{Contact Interaction in RL truncation}
In the CI model, the DSE for the quark propagator adopts the form
\begin{equation}
\label{eq:quarkPropCI}
    S^{-1}(p)=[S^{(0)}(p)]^{-1}+\frac{4}{3 m_G^2} \int_{q}  \gamma_\mu S(q) \gamma_\mu\;,
\end{equation}
while the homogeneous meson BS equation is written as
\begin{equation}
\label{eq:mesonBSECI}
    \Gamma_H(p;P)=-\frac{4}{3 m_G^2} \int_{q}  \gamma_\mu \chi_H(q;P) \gamma_\mu\;.
\end{equation}
A general solution of Eq.~\eqref{eq:quarkPropCI} is $S^{-1}(p)=i\gamma\cdot p + M$, which exhibits a momentum independent mass function, $M$. The gap equation becomes
\begin{equation}
M=m+\frac{M}{3\pi^2 m_{G}^{2}}\int_{0}^{\infty}ds\frac{s}{s+M}\;,
\end{equation}
which requires a regularization procedure. Following standard literature,~\cite{GutierrezGuerrero:2010md}, we perform a proper time regularization~\footnote{A substraction scheme is also possible, as illustrated in Ref.~\cite{Serna:2017nlr}.}:
\begin{equation}
\frac{1}{s+M^2}=\int_{0}^{\infty}d\tau e^{-\tau (s+M^2)}\rightarrow\int_{\tau_{\text{UV}}^2}^{\tau_{\text{IR}}^2}d\tau e^{-\tau (s+M^2)}.
\end{equation}
The mass scale $\Lambda_{\text{IR}}:=1/\tau_{\text{IR}} = 0.24$ GeV guarantees confinement by ensuring the absence of quark production thresholds, while $\Lambda_{\text{UV}}:=1/\tau_{\text{UV}}=0.905$ GeV represents an ultraviolet cut-off, setting the scale of all dimensioned quantities because the theory is non renormalizable. Therefore, the mass function can be obtained by solving
\begin{eqnarray}
M&=&m+\frac{M}{3\pi^2 m_{G}^{2}}\mathit{C}^{iu}(M^2)\;,\\
\frac{\mathit{C}^{iu}(M^2)}{M^2}&=&\Gamma(-1,M^2\tau_{\text{UV}}^2)-\Gamma(-1,M^2\tau_{\text{IR}}^2)\;,
\end{eqnarray}
where $\Gamma(a,z)$ is the incomplete Gamma function.

Concerning the meson BS equation in the CI, Eq.~\eqref{eq:mesonBSECI},  it is clear that a dependence on the relative momentum is forbidden by the interaction. Then, the pseudoscalar and vector meson BS amplitudes adopt the form
\begin{eqnarray}
\label{eq:BSApi}
\Gamma_{0^-}(P) &=& \gamma_5 \left[ i E_{0^-}(P) + \frac{\gamma \cdot P}{M} F_{0^-}(P) \right]\;,\\
\label{eq:BSArho}
\Gamma^{1^-}_{\mu}(P)&=&\gamma_{\mu}^{T}E_{1^-}(P)+\frac{1}{M}\sigma_{\mu\nu}P_{\nu}F_{1^-}(P)\;,
\end{eqnarray}
where $\gamma_{\mu}^{T}=\gamma_{\mu}-\frac{ \gamma \cdot P \;
 }{P^{2}} \, P_{\mu}$. In a RL treatment of the CI, $F_{1^-}(P) = 0$ (an analogous result holds for the axial-vector meson). Appealing to the WGTIs from Eqs.~(\ref{eq:vWGTI}, \ref{eq:avWGTI}), and contracting with $P_\mu$, one arrives at the chiral limit identities ($P^2=0=-m_H^2$):
\begin{eqnarray}\nonumber
M&=&\frac{8M}{3m_{G}^{2}}\int_{q}\left[\frac{1}{q^2+M^2}+\frac{1}{(q-P)^2+M^2}\right]\;,\\
0&=&\int_{q}\left[\frac{P\cdot q}{q^2+M^2}-\frac{P\cdot(q-P)}{(q-P)^2+M^2}\right],
\end{eqnarray}
which must be satisfied even after regularization, therefore imposing
\begin{eqnarray}
\label{eq:CIvecID1}
M&=&\frac{16M}{3m_{G}^{2}}\int_{q}\frac{1}{q^2+M^2}\\
\label{eq:CIaxID1}
0&=&\int_{q}\frac{\frac{q^2}{2}+M^2}{(q^2+M^2)^2}.
\end{eqnarray}
Notice that Eq.~\eqref{eq:CIvecID1} is merely the chiral-limit gap equation, whereas Eq.~\eqref{eq:CIaxID1} entails that the axial-vector WGTI is satisfied if, and only if, the model is regularized so as to ensure there are no quadratic or logarithmic divergences~\cite{Roberts:2010rn}.

\subsection{Contact Interaction in Modified RL}
Let us now consider the BS equation in the MRL truncation, Eq.~\eqref{eq:inBSEERL}. Supplemented by the effective gluon in the CI model, Eq.~\eqref{eq:gluonprop}, and setting $\tilde{D}=4/3m_G^2$, the modified homogeneous BS equation becomes
\begin{eqnarray}
\label{eq:CIinMRL}
\Gamma_H(P)=-\frac{4}{3m_{G}^{2}}\int_{q}\left[\gamma_{\mu}\chi_H(P)\gamma_{\mu} - \xi \tilde{\Gamma}_{j}\chi_H(P)\tilde{\Gamma}_{j}\right],\hspace{0.6cm}
\end{eqnarray}
where we have made evident the momentum-independent nature of the BS amplitude and quark mass function. Recalling that $\tilde{\Gamma}_{j} = \{ \mathbb{I},\;\gamma_5,\;i/\sqrt{6}\sigma_{\mu\nu}\}$ and performing Fierz transformatioon, it can be shown that the NL term, the one proportional to $\xi$, can be rewritten as $\frac{1}{3}\sigma_{\alpha\beta}\text{tr}_{D}[\sigma_{\alpha\beta}\chi_{H}(P)]$ and does not contribute in the case of pseudoscalar mesons; it impacts, however, the vector meson case. Particularly, the $F_{1^-}(P)$ BS amplitude in Eq.~\eqref{eq:BSArho} is no longer zero. This is a crucial difference with respect to the well known CI-RL truncation, which is clearly recovered in the limit case $\xi = 0$.

The BS equation can be recast into an eigenvalue equation by finding proper projectors that decouple $E_{1^-}$ and $F_{1^-}$ in Eq.~\eqref{eq:BSArho}, such that Eq.~\eqref{eq:CIinMRL} yields
\begin{equation}\label{kerneln}
\begin{aligned}
\left[\begin{array}{c}E_{1^{-}}(P)\\F_{1^{-}}(P)\end{array}\right]=\frac{1}{3\pi^2m_G^2}\left[\begin{array}{cc}K_{EE}^{1^{-}}&K_{EF}^{1^{-}}\\K_{FE}^{1^{-}}&K_{FF}^{1^{-}}\end{array}\right]\left[\begin{array}{c}E_{1^{-}}(P)\\F_{1^{-}}(P)\end{array}\right],
\end{aligned}
\end{equation}
where the integration kernels, $K_{ij}:=3\pi^2m_G^2 \mathcal{K}_{ij}$, are written as
\begin{eqnarray}
\mathcal{K}_{EE}^{1^-}=-P^{2}\tilde{I}(P^2)\;&,&\;\mathcal{K}_{EF}^{1^-}=-\frac{P^2}{2}I(P^2)\;,\\
\mathcal{K}_{FE}^{1^-}=\eta_\xi I(P^2)\;&,&\;\mathcal{K}_{FF}^{1^-}=\eta_\xi \left(I(P^2)-\frac{P^2}{M^2}\tilde{I}(P^2) \right),\hspace{0.5cm}
\end{eqnarray}
 the integrals:
\begin{eqnarray}
&&I(Q^2):=\frac{1}{3\pi^2m_G^2}\int_{0}^{1}d\alpha\bar{\mathcal{C}}_{1}^{\text{iu}}(\omega(M^2,\alpha,Q^2))\;,\\
&&\tilde{I}(Q^2):=\frac{1}{3\pi^2m_G^2}\int_{0}^{1}d\alpha\alpha(1-\alpha)\bar{\mathcal{C}}_{1}^{\text{iu}}(\omega(M^2,\alpha,Q^2)\;,\hspace{0.5cm}
\end{eqnarray}
the argument $\omega(M^{2},\alpha,P^{2}):=M^2+\alpha(1-\alpha)P^2$ and, finally,
\begin{eqnarray}
\nonumber
&&\eta_\xi := \frac{2M^2\xi}{3}\;,\;\bar{\mathcal{C}}_{1}^{\text{iu}}(\omega):=-\frac{d}{d\omega}\mathcal{C}^{\text{iu}}(\omega)\;.
\end{eqnarray}
Physical solutions of Eq.~\eqref{kerneln} are only valid for discrete values of $P^2 = -m_H^2$. The smallest $P^2$ that satisfies the eivengalue equation yields the ground-state meson mass. To produce other physical observables, the BS amplitudes must be canonically normalized, according to the condition
\begin{eqnarray}
1=2N_{c}\frac{d}{dP^{2}}\frac{1}{3}\text{tr}_{D}\int_{q}\Gamma_{\mu}(-K)S(q)\Gamma_{\mu}(K)S(q-P)|_{K=P}\;.\hspace{0.5cm}
\end{eqnarray}
Computing the vector meson decay constant, and its tensor counter part, is straighforward from the expressions
\begin{eqnarray}
f_{v}m_{v}&=&\frac{N_{c}}{3}\int_{q}\text{tr}_{D}\gamma_{\mu}S(q)\Gamma_{\mu}S(q-P)\;,\\
f_v^\perp m_v^2&=& \frac{N_{c}}{3} \int_q \sigma_{\mu\nu} P_\nu S(q)\Gamma_{\mu}S(q-P)\;.
\end{eqnarray}
The masses and decay constants of $\pi$ and $\rho$ mesons are collected in Table~\ref{tab:masscball}, in both RL and MRL truncations. The parameter $\xi=0.6$ has been tuned to produce $m_\rho = 0.770$ GeV, as compared with $m_\rho = 0.929$ GeV, obtained in the CI-RL; on the other hand, the leptonic decay constant is quite similar in both truncations, practically independent of $\xi$. Canonically normalized BS amplitudes the $\rho$ meson are listed in Table~\ref{tab:masscball} as well. As already suggested, the static properties of pseudoscalar and axial vector mesons remain unchanged, since the NL term in the BS kernel does not contribute in such channels; we follow standard literature, \emph{e.g.}~\cite{Roberts:2010rn,Roberts:2011wy}, to compute the static properties of pion.
\begin{table}[ht!]
\caption{\label{tab:masscball} CI model results in the RL and MRL truncations. The model parameters: $m_{G}=0.132\;\text{GeV}$, $\Lambda_{\text{UV}}=0.905\;\text{GeV}$, $\Lambda_{\text{IR}}=0.240\;\text{GeV}$ and $\xi=0.6$. The current quark mass is set to $m=m_{u/d} = 7$ MeV, which yields $M = 0.368$ GeV. }
\begin{tabular}{c|cc|ccc|cc}
\hline
 &$m_{\pi}$  & $f_{\pi}$   &$m_{\rho}$ &$f_{\rho}$ & $f_{\rho}^\perp$ & $E_\rho$ & $F_\rho$\\
\hline
CI-RL  & 0.140 & 0.101&  0.929& 0.129 & 0.133 & 1.531 & -\\
CI-MRL & 0.140 & 0.101&  0.770& 0.125 & 0.134 & 1.230 & 0.503 \\
\hline
\end{tabular}
\end{table}

\section{Quark-Photon vertex in Modified RL}
The quark-photon vertex in the CI-MRL satisfies  the inhomogeneous BS equation
\begin{eqnarray}\label{qfv}
\Gamma_\mu^\gamma(Q)=\gamma_\mu&&-\frac{4}{3m_G^2}\int_q \gamma_\alpha S(q)\Gamma_\mu(Q)S(q-Q)\gamma_\alpha\nonumber\\
&&+\frac{4\xi}{3m_G^2}\int_q \tilde{\Gamma}_j S(q)\Gamma_\mu(Q)S(q-Q)\tilde{\Gamma}_j
\end{eqnarray}
A general solution of Eq.~\eqref{qfv} admits a decomposition in terms of 3 tensor structures, namely:
\begin{eqnarray}
\Gamma_\mu^\gamma(Q)=V_1(Q^2)\gamma_\mu^L+V_2(Q^2)\gamma_\mu^T+V_3(Q^2)\gamma_\mu^A\;,&&\nonumber \\
\gamma_\mu^L=\gamma_\mu-\gamma_\mu^T\;,\gamma_\mu^T=\gamma_\mu-\frac{\slashed{Q}Q_\mu}{Q^2}\;,\gamma_\mu^A=\frac{\sigma_{\mu\nu}Q_\nu}{M}\;.&&\label{eq:qfvstructure}
\end{eqnarray}
This simplicity is due to the momentum independent nature of the CI model. By solving Eq.~$(\ref{qfv})$, plainly one obtains that the longitudinal piece is simply
\begin{equation}
 V_1(Q^2):=P_L(Q^2)=1\;,
\end{equation}
while the transverse dressing functions are expressed as
\begin{eqnarray}
&&V_2(Q^2)=\left[P_T^{-1}(Q^2)+\eta_\xi\frac{Q^2}{2}\frac{I^2(Q^2)}{1-\eta_\xi \bar{I}(Q^2)}\right]^{-1}\;,\\
&& \label{eq:qfv38} V_3(Q^2)= \frac{\eta_\xi I(Q^2)}{P_T^{-1}(Q^2)\left[1-\eta_\xi \bar{I}(Q^2)\right]+\eta_\xi \frac{Q^2}{2} I^2(Q^2) }\;,\hspace{0.5cm}
\end{eqnarray}
\text where $P_T(Q^2):=[1+Q^2\tilde{I}(Q^2)]^{-1}$, and
\begin{eqnarray}
\bar{I}(Q^2)&&:=I(Q^2)-\frac{Q^2}{M^2}\tilde{I}(Q^2) \;.
\end{eqnarray}
The  $V_2(Q^2)$ dressing function produces a timelike vector meson pole at $Q^2 = -m_\rho^2$, while $V_3(Q^2)$ can be regarded as a profile function for the anomalous magnetic moment term (AMM), $\gamma_\mu^A$.  Notably, in the $Q^2 \to 0$ limit, the fully dressed QPV becomes
\begin{equation}
    \Gamma_\mu^\gamma(Q) \overset{Q^2\to 0}{=} \gamma_\mu + \frac{\sigma_{\mu\nu}Q_\nu}{2M} \left(\frac{2\eta_\xi I(0)}{1-\eta_\xi I(0)} \right)\;,
\end{equation}
such that, with the parameters listed in Table~\ref{tab:masscball}, one gets
\begin{equation}
\label{eq:zetaMRL}
    \zeta_{\text{MRL}}:=\left(\frac{2\eta_\xi I(0)}{1-\eta_\xi I(0)} \right) \approx 0.19.
\end{equation}

The automatic incorporation of the AMM piece to the QPV, via inhomogeneous BS equation, is a desirable feature of the MRL truncation. The CI model plainly exposes it. This characteristic is not present in the RL approximation~\cite{Chang:2010hb}, and so in the CI-RL case; the latter corresponding to the case $\xi = 0$, which implies $V_2(Q^2) = P_T(Q^2)$ and $V_3(Q^2) = 0$~\cite{Roberts:2010rn, Roberts:2011wy}. Within the CI-RL approach, the AMM term is typically added by hand, such that the behavior of $V_3(Q^2)$ is modeled according to the exponential Ansatz~\cite{Wilson:2011aa,Raya:2018ioy,Raya:2021}:
\begin{equation}
\label{eq:AMMRL}
    V_3^\text{CI-RL}(Q^2) :=\frac{\zeta_{\text{CI-RL}}}{2}\text{exp}[-Q^2/(4 M^2)]\;,
\end{equation}
where $\zeta_{\text{RL}} \in [0,\;0.5]$ is a strength parameter, fully compatible with $\zeta_{\text{MRL}} \approx 0.19$. Thus, when dealing with the CI-RL truncation, we modify the QPV to account for the AMM, such that
\begin{equation}
\label{eq:EnhanceQPV}
    \Gamma_\mu^{\gamma} \overset{\text{RL}}{:=} \gamma_\mu^L + \gamma_\mu^T P_T(Q^2) + \gamma_A  V_3^\text{CI-RL}(Q^2)\;.
\end{equation}
The vertex dressing $V_2(Q^2)$ is compared with its CI-RL counterpart, $P_T(Q^2)$, in the upper panel of Fig.~\ref{fig:vertexdress}. The presence of the vector meson pole at $Q^2 = -m_\rho^2$ is a natural artifact of the RL truncation when obtaining the QPV through its corresponding BS equation~\cite{Maris:2002mz,Eichmann:2019bqf,MiramontesLopez:2021oul,Xu:2021mju}. It is then expected that electromagnetic form factors, in the vicinity of $Q^2 = 0$, be affected by the $\rho$ pole (for instance, it influences the associated charge radius)~\cite{Maris:1999bh}; but the effects should be otherwise immaterial at large space-like momenta~\cite{Maris:1999bh,Raya:2015gva}. The $Q^2$ profiles of the AMM dressing functions, in both truncations, are displayed in the lower panel of Fig.~\ref{fig:vertexdress}. It is clear that $V_3(Q^2)$ enhances the strength of the QPV in the low $Q^2$ domain, and its contribution vanishes as $Q^2$ grows; the CI-MRL case is power-law suppresed, in contrast with the Gaussian Ansatz in Eq.~\eqref{eq:AMMRL}. In any case, the enhancement-damping patterns manifest in electromagnetic form factors involving spin-1 mesons, but are strictly ruled out in elastic form factors of spin-0 mesons~\cite{Wilson:2011aa,Raya:2018ioy,Raya:2021}.

\begin{figure}[t!]
\includegraphics[width=8.6cm]{V2vertex.pdf}\\
\includegraphics[width=8.6cm]{V3vertex.pdf}
\caption{\textit{Quark-photon vertex dressing functions} as obtained from Eqs.~(\ref{eq:qfvstructure}-\ref{eq:qfv38}). The upper panel displays the dressing function $V_2$, associated with the $\rho$ meson pole. Vertical grid lines indicate the location of the poles, $Q^2 = -m_\rho^2$, such that $m_\rho = 0.929$ GeV in CI-RL and $m_\rho = 0.770$ GeV in CI-MRL. Notably,  $V_2(Q^2)=P_T(Q^2)$ in the CI-RL case. The lower panel depicts the dressing of the AMM piece of the QPV. Strictly speaking, the CI-RL case implies $V_3(Q^2) = 0$; therefore, the Gaussian Ansatz from Eq.~\eqref{eq:AMMRL} and Refs.~\cite{Wilson:2011aa,Raya:2018ioy,Raya:2021} is displayed instead ($\zeta_{\text{CI-RL}}=\zeta_{\text{CI-MRL}}=0.19$). \label{fig:vertexdress}}
\end{figure}

Finally, it is worth noticing that the QPV defined through Eqs.~(\ref{eq:qfvstructure}, \ref{eq:qfv38}) exhibits the correct asymptotic limit, \emph{i.e.} $\Gamma_\mu^\gamma (Q) \to \gamma_\mu$ as $Q^2 \to \infty$; therefore exposing that a dressed quark becomes pointlike for a large-$Q^2$ probe~\cite{Bermudez:2017bpx}. In the next section, we study the $\rho$ meson elastic EFF, capitalizing on how it is affected by the anomalous magnetic moment.

\medskip
\section{Electromagnetic form factors}
The coupling of a photon to a $1^-$ meson is characterized by three elastic form factors, such that the $\gamma\rho$ vertex can be expressed as~\cite{Roberts:2011wy}:
\begin{eqnarray}
\label{eq:lambdavertex1}
\Lambda_{\lambda,\mu\nu}(K,Q)&=&\sum_{j=1}^3 T^{(j)}_{\lambda,\mu\nu}(K,Q) F_j(Q^2) \;\\\label{eq:lambdavertex2}
T^{(1)}_{\lambda,\mu\nu}(K,Q)&=&2K_\lambda P_{\mu\alpha}^T(p_i)P_{\alpha\nu}^T(p_f)\;,\\ \nonumber
T^{(2)}_{\lambda,\mu\nu}(K,Q)&=&\left[Q_\mu-p_{\mu}^i\frac{Q^2}{2m_\rho^2}\right]P_{\lambda\nu}^T(p_f) \nonumber \\
&-&\left[Q_\nu+p_{\nu}^f\frac{Q^2}{2m_\rho^2}\right]P_{\lambda\mu}^T(p_i)\;,\\ \nonumber
T^{(3)}_{\lambda,\mu\nu}(K,Q)&=&\frac{K_\lambda}{m_\rho^2}\left[Q_\mu-p_{\mu}^i\frac{Q^2}{2m_\rho^2}\right]\left[Q_\nu+p_{\nu}^f\frac{Q^2}{2m_\rho^2}\right]\;.
\end{eqnarray}
The kinematic variables are defined as follows: $p^i = K-Q/2$  and $p^f = K+Q/2$ denote the incoming and outgoing meson momenta, respectively, and $Q$ is the photon momentum; the on-shell conditions, $p_i^2=p_f^2=-m_\rho^2$, impose $K\cdot Q=0$, $K^2=-m_\rho^2-Q^2/4$; and, as explained elsewhere~\cite{Roberts:2011wy}, a symmetry-preserving treatment demands the WGTIs:
\begin{eqnarray*}
p_\mu^i \Lambda_{\lambda,\mu\nu} = p_\nu^f \Lambda_{\lambda,\mu\nu} = Q_\lambda \Lambda_{\lambda,\mu\nu}=0\;.
\end{eqnarray*}
In the impulse approximation~\cite{Roberts:1994hh}, meson EFFs are completely described in terms of quark propagators, BS amplitudes and the QPV. Particularly, the elastic form factor of the $\rho$ meson reads
\begin{eqnarray}
\label{eq:impulse}
\Lambda_{\lambda,\mu\nu}(Q^2)&&=2 N_c\ \text{tr}\int_q \left[\Gamma_\nu^\rho(-p_f)S(q+p_f)\right.\nonumber\\
&&\left.\times i\Gamma_\lambda^\gamma(Q)S(q+p_i)\Gamma_\mu^\rho(p_i)S(q)\right]\;,
\end{eqnarray}
where $\Gamma_\mu^\rho$ is the BS amplitude and $\Gamma_\lambda^\gamma(Q)$ is the QPV. Form factors are obtained from Eqs.~(\ref{eq:lambdavertex1}, \ref{eq:lambdavertex2}, \ref{eq:impulse}), choosing appropriate projectors that decouple them from $\Lambda_{\lambda,\mu\nu}$. The particular expressions for $F_i(Q^2)$ are shown explicitly in Appendix A. It turns out convenient to relate the form factors $F_j(Q^2)$ with the electric, magnetic and quadrupole form factors, respectively
\begin{eqnarray}
&&G_E(Q^2)=F_1(Q^2)+\frac{2}{3}\frac{Q^2}{4M_\rho^2}G_Q(Q^2)\;,\\
\nonumber &&G_M(Q^2)=-F_2(Q^2)\;,\\
\nonumber&&G_Q(Q^2)=F_1(Q^2)+F_2(Q^2)+F_3(Q^2)\left[1+\frac{Q^2}{4M_\rho^2}\right]\;.
\end{eqnarray}
Naturally, the $Q^2 \to 0$ limit defines the charge, magnetic and quadrupole moments:
\begin{eqnarray}
&&G_E(Q^2\to 0)=1\;,\\
&&G_M(Q^2\to 0)=\mu_\rho \;,\nonumber \\
&&G_Q(Q^2\to 0)=\mathcal{Q}_\rho\;. \nonumber
\end{eqnarray}

\begin{figure}[t!]
\includegraphics[width=8.6cm]{Rho_FFs.pdf}
\caption{$\rho$ \textit{meson form factors}. From top to bottom: $G_M$, $G_E$, $G_Q$. Solid thick lines are the results obtained in the CI-MRL truncation, whereas the dotted lines are their analogous in the CI-RL approach~\cite{Roberts:2011wy}.\label{fig:FFs}}
\end{figure}

The computed form factors are depicted in Fig.~\ref{fig:FFs}. The electric form factor $G_E$ exhibits a zero and remains negative thereafter. For the CI-MRL truncation, the zero is located at $Q^2 \approx 1.96$ GeV$^2$, while the CI-RL exhibits a zero at $Q^2 \approx 5$ GeV$^2$. This zero crossing was also observed in the DSE-BS approach from Ref.~\cite{Xu:2019ilh}. The magnetic form factor $G_M$, which turns out to be positive definite and monotonically decreasing, is quite similar in both truncations on the domain shown. The largest difference is  appreciated at low $Q^2$. This can be attributed to the lack of AMM term in the QPV for the CI-RL truncation, which enhances the value of $G_M$ in a vicinity of $Q^2 = 0$, without altering the large-$Q^2$ behavior. In Fig.~\ref{fig:zoomGM} we observe that, if the AMM piece is included in the CI-RL description, by using the vertex Ansatz from Eqs.~(\ref{eq:AMMRL}, \ref{eq:EnhanceQPV}), magnetic form factors become even more similar. The effects on $G_E$ and $G_Q$ are immaterial and not shown. The quadrupole form factor $G_Q$ is negative and decreases in magnitude as $Q^2$ increases; CI-MRL and CI-RL truncations produce results with notorious different magnitudes.

\begin{figure}[t!]
\includegraphics[width=8.6cm]{GMzoom.pdf}
\caption{$\rho$ \textit{meson magnetic form factor}. Solid thick line corresponds to the CI-MRL result. For the CI-RL case, we have employed the QPV Ansatz from Eqs.~(\ref{eq:AMMRL}, \ref{eq:EnhanceQPV}). With the strength parameter set to $\zeta_{\text{CI-RL}}=\zeta_{\text{CI-MRL}}=0.19$ in such case, the resemblance to the CI-MRL result is striking.  \label{fig:zoomGM}}
\end{figure}

Some static properties that can be read from the form factors are collected in Table 2, namely charge, magnetic and quadrupole moments. For completeness, we have also included the corresponding radii, as defined from
\begin{equation}
    \textless r_i^2 \textgreater= -6 \frac{1}{G_i(0)} \frac{d G_i(Q^2)}{dQ^2}\Bigg|_{Q^2=0}\;.
\end{equation}

As can be inferred from Table 2, the MRL truncation produces results which are closer to those obtained from using sophisticated gluon models~\cite{Xu:2019ilh,Xu:2021mju} and lattice QCD~\cite{Owen:2015gva}, whereas the CI-RL gives results closer to the structureless meson limit. As explained before, the QPV Ansatz from Eqs.~(\ref{eq:AMMRL}, \ref{eq:EnhanceQPV}) makes the CI-RL magnetic form factor $G_M(Q^2)$ more similar to the CI-MRL case, and therefore the static properties derived from there.

\begin{table}[ht!]
\caption{\label{tab:static} $\rho$ \textit{meson static properties}, as obtained from its elastic electromagnetic form factors. The CI-RL results match those from Ref.~\cite{Roberts:2011wy}. In our current framework, it corresponds to the $\xi = 0$ limit of the CI-MRL truncation. For comparison, we have included novel DSE results from~\cite{Xu:2019ilh}. Additionally, Lattice QCD~\cite{Owen:2015gva} predicts $\mu_\rho = 2.21(8)$ and $r_E = 0.82(4)$ fm, and the structureless meson limit dictates $\mu_\rho = 2$ and $\mathcal{Q}_\rho = -1$.}
\begin{tabular}{c|ccc}
\hline
 &  \;CI-MRL\; & \;CI-RL\; & \;DSE\; \\
\hline
$r_E$/fm & 0.692 & 0.561 & 0.72 \\
$r_M$/fm & 0.603 & 0.515 & 0.69 \\
$r_{\mathcal{Q}}$/fm & 0.612 & 0.512 & - \\
\hline
$r_E m_\rho$ & 2.706 & 2.644 & 2.76 \\
$r_M m_\rho$ & 2.359 & 2.430 & 2.63 \\
$r_{\mathcal{Q}} m_\rho$ & 2.394 & 2.414 & - \\
\hline
$\mu_\rho$ & 2.500 & 2.110 & 2.01 \\
$\mathcal{Q}$ & -0.327 & -0.850 & -0.36 \\
\hline
\end{tabular}
\end{table}

\section{Distribution amplitudes}
To scrutinize a little further into the structure of the $\rho$ meson, and the effects of BS kernel truncation, we now examine the so called valence-quark distribution amplitudes. Particularly, let us consider two leading-twist distributions amplitudes of the $\rho$ meson: $\phi_\parallel(x)$ and $\phi_\perp(x)$. Intuitively, those describe the light-front momentum carried by the quark in a longitudinally or transversely polarised $\rho$,~\cite{Ball:1996tb}. In terms of quark propagators and BS amplitudes, the distributions can be written as~\cite{Gao:2014bca}:
\begin{eqnarray}
\nonumber
n\cdot P f_\rho  \phi_\parallel(x) && = m_{\rho} N_c \text{tr} \int_q \delta_n^x(q^+) \gamma \cdot n \; n_\nu \chi_\nu^\rho(q;P) \;, \\ \label{eq:PDAsdef}
f_\rho^{\perp} \phi_\perp(x) && = -\frac{1}{2} N_c \text{tr} \int_q \delta_n^x(q^+) n_{\mu}\sigma_{\mu\alpha} \mathcal{O}_{\alpha\nu}^{\perp} \chi_\nu^\rho(q;P)\;,
\end{eqnarray}
where $\delta_n^x(q^+):=\delta(n \cdot q^+ - x n \cdot P)$ and $\mathcal{O}_{\alpha\nu}^{\perp}=\delta_{\alpha\nu}+n_{\alpha}\bar{n}_{\nu}+\bar{n}_{\alpha}n_{\nu}$, and $n$ is a light-like four-vector such that $n^2 = 0$, $n\cdot P = -m_\rho$; $\bar{n}$ is a conjugate light-like four-vector, $\bar{n}^{2}=0$, $n\cdot \bar{n}=-1$; and, with the above definitions, $\int_0^1 dx \phi_\parallel(x) = \int_0^1 dx \phi_\perp(x) = 1$.

The PDAs can be obtained from their corresponding Mellin moments, $\textless x^m \textgreater = \int_0^1 dx x^m \phi(x)$.
After evaluating the Dirac trace, a series of algebraic manipulations involving Feynman parametrization, supplemented by the uniqueness of Mellin moments, enable us to identify
\begin{eqnarray}\nonumber
\phi_\parallel(x) &&=\frac{1}{f_{\rho}} \frac{N_c}{4\pi^2}m_\rho \Large[ 2x(1-x) E_\rho + F_\rho \Large]\;\bar{\mathcal{C}}_{1}^{\text{iu}}(\omega(M^2,x,-m_\rho^2))\;,\\
\phi_\perp(x) &&=\frac{1}{f_\rho^{\perp}} \frac{N_c}{4\pi^2}M  \left[ E_\rho + \left( 1+\frac{m_\rho^2}{M^2}x(1-x)\right)F_\rho \right] \nonumber \\
&& \times \;\bar{\mathcal{C}}_{1}^{\text{iu}}(\omega(M^2,x,-m_\rho^2))\;.\label{eq:PDAs}
\end{eqnarray}

\begin{figure}[t!]
\includegraphics[width=8.6cm]{PDA_MRL.pdf}
\caption{$\rho$ \textit{meson PDAs}. Computed distributions, Eq.~\eqref{eq:PDAs}, in the CI-MRL truncation.\label{fig:PDA MRL}}
\end{figure}

The obtained PDAs are displayed in Fig.~\ref{fig:PDA MRL}. Both distributions manifest symmetry under the exchange $1 \leftrightarrow 1-x$, which is expected in the isospin symmetric limit $m_u = m_d$. The parallel distribution, $\phi_\parallel$, is more compressed with respect to its perpendicular counterpart, an expect pattern from sophisticated momentum-dependent interactions~\cite{Gao:2014bca}. It is evident that the derived PDAs do not vanish at the endpoints, in contradiction with QCD prescriptions~\cite{Gao:2014bca,Ball:1996tb,Lepage:1980fj}. The same occurs for the pion leading-twist PDA in the CI model, for which $\phi_\pi(x) = 1$ in the chiral limit~\cite{Roberts:2010rn}. Nonetheless, it is quite interesting that, in the absence of the $F_\rho$ BS amplitude (the CI-RL case), the distribution $\phi_\parallel$ actually exhibits soft endpoint behavior. This is well understood from Eqs.~\eqref{eq:PDAs} and drawn in Fig.~\ref{fig:PDA comp}.

\begin{figure}[t!]
\includegraphics[width=8.6cm]{PDA_para.pdf}\\
\includegraphics[width=8.6cm]{PDA_perp.pdf}
\caption{$\rho$ \textit{meson PDAs}. Computed distributions, Eq.~\eqref{eq:PDAs}, in the CI-RL and CI-MRL truncations. Notably, $\phi_\parallel(x)$ in the CI-RL exhibits soft endpoint behavior.\label{fig:PDA comp}}
\end{figure}

\section{Conclusions}
Starting from the leading-order symmetry-preserving RL truncation for the two-body problem, we have illustrated how, although the vector and axial vector WGTIs provide necessary consistency conditions to construct the interrelated one body and two body kernels, these turn out insufficient to determine the kernels in an unambigous manner~\cite{Chang:2020iut}. Particularly, we construct a two-body kernel completely consistent with the aforementioned WGTIs that includes NL terms. The MRL truncation lets unaltered the pseudoscalar and axial vector meson properties, but yields some implications in the vector channel. This can be well illustrated by employing the CI model described in Section III. Among other things, we have seen how solutions of the QPV BS equations using the MRL kernel, automatically generate an anomalous magnetic moment term in the vertex structure. This is in addition to the vector meson pole at $Q^2=-m_\rho^2$, which is an artifact of the RL truncation~\cite{MiramontesLopez:2021oul}.  In the presence of DCSB, a dressed light-quark possesses a large anomalous electromagnetic moment~\cite{Chang:2010hb,Bashir:2011dp}. Therefore, the automatic incorporation of such term is an important outcome of the constructed two-body kernel in MRL truncation. Immediate consequences are naturally noted in the $\rho$ meson properties. For instance, although the produced decay constants are practically invariant under the effects of the NL pieces we have introduced in the BS kernel, the experimental mass of the $\rho$ can be faithfully obtained within the CI-MRL, in contrast with the CI-RL approach which produces a larger value~\cite{Roberts:2011wy}. In some way, the NL term of the two-body kernel mimicks the effects of the pion cloud effects, which correct the inflated masses produced when they are not considered~\cite{Eichmann:2008ef};
whether or not our kernel is actually related to pion cloud effects is currently under investigation. On another note, whereas the CI-RL truncation yields static properties (as derived from the corresponding EFF) closer to the structureless meson limit, CI-MRL results are more compatible with those obtained from more sophisticated approaches~\cite{Xu:2019ilh,Owen:2015gva}. Focusing on the magnetic form factor, we have reinforced the importance of the AMM for a good description of vector mesons. Finally, we have derived the $\rho$ meson $\phi_\parallel(x)$ and $\phi_\perp(x)$ distribution amplitudes. The necessity of employing a regularization scheme, and subsequently cut-offs, to deal with the CI model, makes the PDAs not vanishing at the endpoints. This is also observed in the pion case: the chiral limit pseudoscalar yields $\phi_\pi(x) =1$~\cite{Roberts:2010rn}. Interestingly, in the absence of the $F_\rho$ piece of the Bethe-Salpeter amplitude (the CI-RL case), the distribution $\phi_\parallel(x)$ actually vanishes at the endpoints. Although it is an expected behavior from QCD grounds,~\cite{Gao:2014bca}, it seems rather incompatible with the pion result and the CI framework in general. Having exposed some impacts of the two-body kernel on the QPV structure and $\rho$ meson properties, via masses and decay constants, electromagnetic form factors and distribution amplitudes, the question on its implications on the distribution functions remains unanswered. This is an aspect of the $\rho$ meson structural properties that will be addressed elsewhere. A similar study for the open flavor case, in particular the Kaon sector, will be conducted as well.

\begin{acknowledgments}
The authors acknowledge valuable comments from José Rodríguez-Quintero.
\end{acknowledgments}

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Allgreen properties finally made a name in the en bloc hot market. It has acquired Crystal Tower for S$180.65 million, translate to S$1,840 psf ppr which is quite bullish bid by analysts for this freehold property.
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Federal Premium Shooters Hancock and Connor Crowned World Champions
Vista Outdoor Pressroom - September 20, 2018
Federal Premium Ammunition sponsored shooter and world champion, Caitlin Connor.
Federal Premium Ammunition sponsored shooters and brand ambassadors, Vincent Hancock and Caitlin Connor, each won gold medals and were crowned world champions at the International Shooting Sport Federation (ISSF) World Championship in Changwon, South Korea, held August 31 to September 15, 2018.
The two-time Olympic gold medalist Hancock picked up his fourth World Championship title in Men's Skeet to close the World Championships. Hancock marched through the rainy qualification rounds without a miss over 125 targets and only missed once in the final to secure his place in the record books. Hancock becomes the first person ever to win four World titles in Men's Skeet and is also now one of three men in the Shotgun discipline to earn four world titles in his career.
Along with the gold, Hancock also secured an Olympic Men's Skeet quota for the United States. A quota is essentially a country's ticket to participate in a specific event in the 2020 Olympic Games in Tokyo, Japan. In Shooting competition at the Olympic Games, a country can earn up to two quotas in each event – but that doesn't guarantee a specific athlete to compete in the Games, just that his/her country has a spot to do so.
In her final, Caitlin Connor didn't miss until the 35th target and finished with a score of 57. Olympic shooting legend Kim Rhode won silver and Amber English took the bronze, marking the first U.S. sweep ever in women's skeet.
"The final was very exciting," said Connor. "I was a little nervous at first, but then I got into the groove and had fun shooting with my teammates. It feels really good to have had three U.S. flags up there. I was glad it was us three. It was a great day for USA."
This win was Connor's first international gold medal. She won silver in 2015 and six other World Cup silver medals across her career. Coming into the competition, Rhode was ranked No. 1 in the world, Connor third and English fourth. In addition to the podium sweep, the United States claimed the maximum number of two Olympic Games quotas available in Women's Skeet.
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The joke about pictures comes courtesy of O'Reilly himself. As media outlets have exposed over the past couple of weeks, O'Reilly has told tall tales of his exploits of his pre-Fox News days as a foreign TV correspondent. He has said he saw awful things take place in Northern Ireland and El Salvador, for instance. When pressed on what he'd witnessed, O'Reilly has said that he actually saw those awful things in pictures he'd seen. That claim has birthed many Internet jokes. (Disclosure: This O'Reilly fact-checking movement started with an article from Mother Jones, the employer of the Erik Wemple Blog's wife).
Wrong, according to a strange strain of thought in the media-crit industry. In an appearance on Fox News just days after the O'Reilly critique surged, the Baltimore Sun's David Zurawik distinguished the controversy from the Brian Williams scandal, saying, "Bill O'Reilly is the most popular person on cable news TV, but it's a nighttime show that has a very different agenda and no one, in cable TV — CNN, MSNBC, Fox — says these are journalistic entities, so there's a difference right there." Might want to check that statement with the cable nets, Z.
Of course, there's no incompatibility between "an opinion guy" and a "journalist." The opinion sections of media outlets each day carry the work of journalists. But the sentiments of Zurawik and Costello and many others have served to ease the pressure on O'Reilly and Fox News as they try to make this very big problem go away.


This presentation is going to focus on the use of course books, materials and teaching aids. There are many materials that we can bring to our classroom that will help with the teaching of our lessons and these include, though they're not limited to, things such as the wipe board, similar to the one that we're using here, various types of visual aids, created or bought worksheets, the use of cassettes CDs and DVDs and the use of video and in these classroom materials, we can also include things such as dictionaries and course books, various types of resource books that we'll have a look at and other materials such as photo copiers, computers, OHPs. So what we'd like to do is just to take a general look at some of the issues relating to each of these types of materials.
This Unit gives emphasis on the Past Tense and its structure and usage. Out of the three tenses, the past tense while it varies according to its structure, it is the most easier tense that is easier to pin point what specific structure does the sentence has by just looking at its usage. While it is important to stress out to the learners the difference of the structures, it is also important to take time to expose the learners to different past simple form of words especially the words or verbs that has irregular past simple form.


New research from iSuppli suggests PC shipments will rise 11.2 per cent year-on-year, while laptops based on solid state memory will attract significant sales by 2009, analysts say.
Analysts at iSuppli have increased predictions for PC sales in 2007, citing stronger-than-anticipated demand for laptops.
iSuppli now predicts global PC shipments will rise to 264 million units in 2007, up 11.2 per cent from 239 million in 2006. The previous forecast envisioned 10.7 per cent growth for the year.
"Notebook PC shipments rose to 21.8 million units in the first quarter of 2007, up 23 per cent from 17.7 million in the first quarter of 2006," said Matthew Wilkins, principal analyst, compute platforms, for iSuppli.
iSuppli expects notebooks to account for almost 40 per cent of total 2007 PC market shipments.
The analysts also issued revised forecasts for the use of flash memory drives as a replacement for hard drives in laptops, predicting that flash-equipped portables would account for 12 per cent of the market by the end of 2009.
They also expect 35 per cent of notebooks will be equipped with Hybrid Hard Drives (HHD) (flash combined with hard drives) by the end of 2009.
Chander added: "The penetration of HHDs in notebooks will rise more quickly in the near term than for solid state drives, given that HDD vendors are increasing both the capacity and areal density of their notebooks in 2007 and beyond. Furthermore, HHDs cost less to produce and offer a level of data integrity that can only be delivered by tried-and-true HDD technology.
Intel's Robson - also known as Turbo Memory - is also expected to take off in 2007. The combination of SSDs, HHDs, Turbo Memory and other solutions will propel flash memory's penetration of notebook data storage to nearly 60 per cent by the fourth quarter of 2009, iSuppli predicts.


Age Range: > 3 years old.
This is super. I have 4 grandchildren ages 3-7 and they can't leave it alone. So much creativity is coming out of this toy purchase, and they are playing well together and collaborating to build complex structures and vehicles. I predict we will have to have more sets.


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FIRE > Newsdesk > Top Story > Princeton must clarify it won't investigate Joshua Katz for opinion piece
(EQRoy / Shutterstock.com)
Princeton must clarify it won't investigate Joshua Katz for opinion piece
by Alex Morey
Princeton classics professor Joshua Katz faces not just criticism for a controversial op-ed he wrote — but formal calls for the Ivy League university to punish him for it. Troublingly, while Princeton makes strong promises of free speech and academic freedom, the university's public statements on the matter have suggested it may indeed be investigating or planning to punish Katz.
To reassure faculty that they can express their views without fear of retribution, Princeton must immediately clarify that Katz's views are wholly protected by institutional policy, and will not expose him to punishment.
'A Declaration of Independence'
Katz has been harshly criticized for a July 8 piece that ran in Quillette, titled "A Declaration of Independence by a Princeton Professor." The op-ed was a response to a July 4 open "Faculty Letter" signed by several hundred Princeton faculty members, staff, and students, demanding Princeton take certain steps to respond to racial injustice on campus.
FIRE criticized a number of the letter's demands as illiberal, in one instance illegal, and a threat to free speech and academic freedom.
Katz's response in Quillette identified similar problems and discussed some of the letter's proposals he supported, and others he disagreed with.
One of the most controversial assertions has been Katz's criticism of the Faculty Letter's demand for acknowledgement of, and an apology to, a former student group. In his discussion of the issue, Katz hyperbolically referred to Princeton's Black Justice League as "a small local terrorist organization":
The Black Justice League, which was active on campus from 2014 until 2016, was a small local terrorist organization that made life miserable for the many (including the many black students) who did not agree with its members' demands. Recently I watched an "Instagram Live" of one of its alumni leaders, who—emboldened by recent events and egged on by over 200 supporters who were baying for blood—presided over what was effectively a Struggle Session against one of his former classmates. It was one of the most evil things I have ever witnessed, and I do not say this lightly.
Princeton 'will be looking into the matter further.'
Princeton President Christopher Eisgruber criticized Katz's description of the Black Justice League in a statement to The Daily Princetonian, suggesting the statement was outside the bounds of what "free speech permits":
While free speech permits students and faculty to make arguments that are bold, provocative, or even offensive, we all have an obligation to exercise that right responsibly[.] Joshua Katz has failed to do so, and I object personally and strongly to his false description of a Princeton student group as a 'local terrorist organization.' By ignoring the critical distinction between lawful protest and unlawful violence, Dr. Katz has unfairly disparaged members of the Black Justice League, students who protested and spoke about controversial topics but neither threatened nor committed any violent acts.
The Daily Princetonian also reported a separate statement from Princeton spokesperson Ben Chang, pledging that the university's administration "will be looking into the matter further." The same article reported that a "number of recent alumni and students took to Twitter to call for the University to take action against Katz."
So @Princeton professor Joshua Katz just wrote a piece calling Black student organizers terrorists…
grounds for dismissal of faculty include "conduct shown to substantially impair performance of the full range of his or her responsibilities as a member of the Faculty"
— micah herskind #8toabolition (@MicahHerskind) July 10, 2020
I'd love for @Princeton to explain how Joshua Katz can possibly remain in good standing as a teacher after writing something this incendiary and menacing about students at his own institution pic.twitter.com/ImCwmJyUKO
— isi litke (@isilitke) July 11, 2020
.@Princeton Changing the name of the School is a start, but you're not done. We want structural change, not just symbolic measures. In his "Declaration of Independence" letter, Professor Joshua Katz has demonstrated cause for his dismissal from the Faculty. (1/2)
— #BLACKLIVESMATTER (@voltairebud) July 11, 2020
FIRE is not aware of any action that has yet been taken. However, Princeton's suggestion alone that such action might be forthcoming has serious — and chilling — implications.
Freedom of speech does not mean freedom from criticism or social consequences. Katz's article has sparked intense debate, and weathering criticism is part of that debate. Likewise, administrators can also criticize student or faculty speech, but should be careful not to convey the message that their criticism may be followed by punitive action.
It is not clear whether Princeton means to suggest it will formally investigate, but the statement that the university is "looking into" Katz's extramural speech certainly commingles criticism with the university's authority. That's a problem not just for Professor Katz, but for any faculty member or student wishing to express their views on campus without fear of institutional censorship.
Princeton must immediately clarify that Katz's protected expression will not be punished.
Schools: Princeton University


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Chute Management
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.. automodule:: paradrop.backend.chute_api
.. autoflask:: paradrop.backend.chute_api:ChuteApi.routes

redpajama_set_name: RedPajamaGithub


Getting ready for a night out, or winding down from the dance floor-- this sweatshirt keeps you toasty warm.
This reversible sweatshirt is made with super-soft drapey fabric and features bold graphic lettering on both sides. It has a crew neckline and ribbed banding details on the neckline, cuffs & hem.


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Welcome! Are you looking for unique wall art, home decor or gifts? My fine art photography is perfect for you. You will find prints, metal prints or canvas for your walls, bookshelves, mantle or office. One of a kind decorative pillows for your living room or bedroom. Don't see exactly what you are looking for? Feel free to contact me about a custom order!
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Being the leading specialist engineering company in our field, Lee Warren is a fantastic place to work. With plans for continual year on year growth, we are always looking for great people to join us.
If after reading our core values you truly believe your values are aligned with ours, and you feel excited about joining Lee Warren, let's keep talking.
Our current vacancies are listed below, however, even if an appropriate vacancy isn't listed, we would still like to hear from you, and would ask you to submit your current CV below (Expression of Interest).
Before submitting your CV please review our privacy notice. By submitting your CV you agree and accept these terms.
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Responsible for the day to day commercial management of a number of projects in order to ensure the success of the project, including maximising profit.
Apply best practice and continuous improvement in the commercial support to the Contracts Manager and Project Team.
Pursue own professional development and provide support and guidance to promote the development of other commercial staff.
Demonstrate a high level of commercial and technical knowledge and work as part of the Project Team.
Identify risks and put into place strategies to manage and minimise risks.
Efficient procurement of approved Sub-Contractors and services in accordance with Lee Warren policies and procedures.
Conduct all duties to comply with the Lee Warren Health and Safety and Environmental Policies.
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Establish and maintain Lee Warren commercial processes and procedures on projects.
Identify, manage and reduce unnecessary costs and inefficient activities.
Maximise cash flow through timely preparation of Variations and submission of Valuations, Applications for Payment and Invoices and ensure payments are received in accordance with Contract conditions.
Manage the prompt preparation and settlement of Final Accounts including Variations and Claims.
Produce accurate forecasts and budgets for use on Evo-M and by the Project Team, ensure that projects meet agreed budgets and targets.
Prepare and present accurate and timely Cost and Value Reconciliation Reports (CVR's).
Through an understanding of contractual, commercial, insurance and legal processes relating to contracts, ensure Lee Warren's position is protected.
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Chris Sawyer | Friday, April 04, 2014 If you mention 'Dinner For One' to most Brits, they are unlikely to know what you are talking about unless they happen to have spent some time in a German-speaking country or perhaps in Scandinavia or Eastern Europe where the film is also popular.
Last Friday a German student of ours at OISE Oxford brought up the topic of 'Dinner For One' during our weekly students' lunch. Initially I wondered whether he was asking our opinion on eating out alone but after a few moments a vague memory of this black and white short film came to mind.
The reason for this is that despite being originally written by a British author and the dialogue being entirely in English, 'Dinner For One' has not been aired on British TV for over 30 years and as such is not the New Years Eve staple here that it has come to be in other countries.
Also known as 'The 90th Birthday', or by its corresponding German title, 'Der 90. Geburtstag', 'Dinner for One' is a two-hander comedy sketch written by British author Lauri Wylie for the theatre in the 1920s. German television station Norddeutscher Rundfunk (NDR) later recorded an 18 minute-long performance of the piece in 1963 which went on to become one of the most frequently repeated TV programmes of all time. It has become somewhat of an institution in Germany with as much as half of the population tuning in to watch it every New Years Eve.
The film features a 90-year old upper-class Englishwoman, Miss Sophie, who is enjoying a celebratory birthday meal with 4 imaginary (presumably deceased) friends, following "the same procedure as every year" (the film's catchphrase). Meanwhile the butler serving the meal takes it upon himself to keep up the charade, consuming the 4 friends' drinks as they toast Miss Sophie's birthday and becoming increasingly drunk with every course. The main source of hilarity is a tiger-skin rug with a large head which the butler trips over each time he goes to fetch the next course.
Now, I don't mean to be a party pooper but from a British point of view, I can't say I'm convinced that this is the best we have to offer by means of comedy. In fact I find its popularity rather mystifying. But don't take my word for it, see for yourself by clicking the image below!


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US tech investing giant Tiger Global leads $14 million Series A round into AI chatbot startup Zowie
Riddhi Kanetkar
Zowie cofounders: Matt Ciolek and Maja Schaefer (CEO).
US investing giant Tiger Global has led a $14 million Series A round into chatbot startup Zowie.
The Polish startup aims to transform customer service queries into sales for ecommerce sites.
It comes as bigger funds increasingly pile money into early-stage startups.
When Maja Schaefer first started raising seed capital for her AI chatbot startup Zowie, she got in touch with a local venture capital firm Inovo.
"We could talk in Polish, it was casual," she told Insider.
But the jump to raising Zowie's Series A round was "much more difficult."
Zowie has just landed $14 million in a deal led by tech investing giant Tiger Global. The startup, which counts the likes of L'Oreal and Avon among its customers, has developed a chatbot for e-commerce sites that aims to transform customer service queries into sales.
The round comes less than six months after closing a $5 million seed round in January. It is also in line with Tiger's move to back more early-stage funds after the New York hedge fund was hit with $17 billion in losses due to the widespread tech sell-off.
Zowie's bot can detect and automate responses to repetitive questions such as status updates on package deliveries in order to reduce the workload on support agents. The startup claims it can also detect buying intent among visitors to a site and connect customers with actual support staff.
"Given the growth of the e-commerce vertical and increased consumer spending globally, Zowie is uniquely positioned to continue reaching more e-commerce customers and expanding the business on a global scale," John Curtius, partner at Tiger Global, said.
The Polish firm integrates with companies such as e-commerce marketplace Shopify and marketing automation platform Klaviyo, and charges businesses for every package of automated interactions that they buy.
The Series A round was also backed by Munich-based VC network 10x Founders — whose founding investors have invested in the likes of delivery giant DeliveryHero and mobility company Tier. Meeting with 10x was a "door opener", as they connected Schaefer with Gradient Ventures, Google's AI investing arm — who also co-invested in Zowie's $5 million seed round in January.
Darian Shirazi, general partner at Gradient Ventures, cited the "incredibly large market for Zowie's solution" as a key factor for investing in the startup. "Every merchant on Shopify, BigCommerce, and every other e-commerce platform is a potential customer for Zowie's products and services," he added.
It was the investors at Gradient that made the connection to Tiger Global.
Zowie will use the newfound capital to bolster its growth in the US, where most of its customer base is located.
"Having US investors is really valuable because we're scaling there, and they help us hire and interview the right people," Schaefer said.
"It's important to be close to the market, and understand cultural differences, buyer perspectives, and the hiring market. I can recommend this to every European founder — if the US market is important, aim to get on board with an American investor."
Startup female founder


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Time Magazine Sold To Tech Couple Benioffs For $190M In Cash | Business Standard News
by business-standard.com posted 2years ago 60 views
Salesforce.com founder Marc Benioff gets a new role - that of a media baron. : Nick Turner & Gerry Smith & Nico Grant | Bloomberg Last Updated at September 17, 2018 22:41 IST Salesforce.com founder Marc Benioff and his wife Lynne agreed to acquire Time magazine from Meredith Corp. for $190 million in cash, joining Jeff Bezos among tech billionaires buying venerable print publications. The move thrusts the brash 53-year-old entrepreneur, who helped lead the shift of software to an on-demand model, into a new role: media baron.


I bet right now you are sitting in study hall and thinking about how in a few short months you will graduate, move out, and be free!
And the freedom will be A-MAZING. Long gone will be the days when you have a midnight (or 11 p.m. on weeknights) curfew. You are probably imagining all the fun you will have between 1 and 5 a.m. Lord knows that's when the best stuff happens! And all of the new guys you will meet. And all of the parties you will go to that the parental units previously ruled out. Just imagining it all is probably making the time move even more slowly.
The reality is, time doesn't move as slowly as you think it does. In the blink of an eye, 10 years will have passed. So hear me out. I have a few things I want you to know.
It's okay to not know who or what you want as an 18-year-old. In fact, it is really the only state of mind you can possibly be in. But while you are exploring and making new and independent decisions, remember that your words and your actions always impact people. And it may be years down the road before you know how deeply you have hurt someone. So take a cue from me, weigh your words heavily. Weigh your actions even more. Some things simply cannot be taken back.
I know you are stubborn, but surprisingly, you love to let others impact how you want to live your life. Stop! Stop doing what other people think "seems like a good idea." News flash: this is usually because it benefits them the most. Figure out the things that you love (you already know what they are, they have never changed!) and do them. Don't let small obstacles stand in your way. I promise you will end up doing them either way, just a few years behind schedule. Save yourself the trouble.
I know… after awhile, it's hard cohabitating with 3-5 other people who all have different opinions about which way the toilet paper goes. And the proper temperature for a household. And how to load the dishwasher. But trust me, they are teaching you a great lesson in the future. And I promise you, as each year passes, it becomes harder and harder to find two hours to even have dinner together! Cherish the days when you see these wonderful people more hours per day than you will per year. Plus, you could probably learn a thing or two from them. You actually don't know everything.
Remember all of the nerdy romance books you used to read as a pre-teen? Well…it's not going to be like that. But guess what? It can be a little bit. Stop settling for options that aren't even close. I know he seems nice. I know he seems like he has good intentions. But deep down, you know that something isn't right. When you get that feeling, it's time to move on. I promise you, you are totally fine on your own. Plus, heads up, you are going to meet someone who would rather die than ever make you cry. Don't give up until it's him.
I know you are assuming you are going to get married at 22. And I know you think that there will be a baby on the way a few years later. Those are really nice thoughts, but they aren't your story. Some of your friends will make this a reality, and when you hold their sweet babies, you may feel like you will never have what they do. And it may sting a little. But guess what? I'm not going to tell you to stop feeling that way. However, you must understand that God's timing is perfect. And no matter how many times you hear this, it won't feel perfect until you are standing where I am. But you will believe it then, and it will be worth it.
I wanted to include that if you would just listen to me (or maybe your mom!) it would make a lot of things easier. But I know you, and I know you prefer to learn things the hard way.
And you know what? That's okay. The hard times will make you stronger. Your bad decisions will make you wiser. And all of those things together will make you overwhelmingly thankful to stand where I am today.


By day, Zach is a mild-mannered computer programmer. By night, he naps and browses Reddit and also makes me dinner, which I always appreciate. He doesn't blog much, and when he does it's so short he should probably be using Twitter, which he has at echthroi. What he lacks in verve and volume he makes up for with large volumes of dry humor, random bursts of insight you only realize were insightful three days later, and sheer apathy. When faced with a project that requires the participants to really and truly care about self-improvement, what better person to scoop up than the dude who barely reads and demand he accept your reading challenge?
Renay: Zach! Thank you for joining us for lady fun times in 2012. Since you'll be appearing here throughout the year after I prod or bribe you (with Godiva truffles) into follow-up posts, you should share a little about yourself so Ana and Jodie know what they're getting into accepting this wacky plan of mine. Please tell me your hopes, dreams, and your favorite type of books (which will soon become of Key Importance).
Zachariah: Right, nothing says slow-ball opening question like "What are your lifelong aspirations?!" :D I believe you already have the answer to that one though (you DID mention Godiva chocolate), so moving on to favorite books...I go classic nerd all the way with Sci-Fi and Fantasy. I have a fondness for books with whiz-bang plots and zero character development, but I have been tempted into deeper waters once or twice.
Renay: It's the "once or twice" part that interests me. Sometime mid-2011 I asked you how many books by women you had read. At the time, the answer was zero. Of course, you only had seven books when I posed the question, but looking back, what did you think about only having read men every time you chose a book?
Zachariah: I felt pretty ambivalent about it. One the one hand, it was seven books by four authors; two of them were actually re-reads of some of my favorite books, and another two were direct sequels to something I had just read. So there was more going on with the book choices than the normal pseudo-chaos of book selection. On the other hand, I'm not facing a shortage of known-to-be-awesome books by women in my home bookshelves, so it was interesting to me that I hadn't read at least one female author yet in 2011.
Renay: Yes. Because you live with the co-founder of a blog called Lady Business. You went to the library and checked out more books by dudes instead of reading the books by ladies that you often trip over to enter our living room. Let me be clear: I am not knocking reading books by the dudes, because I like plenty of male writers. In fact, when you ask me to list favorite authors, if I don't slow down and think, I'll have five or six men before I even drop one woman writer: we are all a product of our culture.
Let's go back in time to 2010 (the joy of spreadsheets), where your (individual author) breakdown was eleven men to five women. Even though you read 40 books, you completed The Series of Unfortunate Events (dude) and caught up with The Wheel of Time (OH GOD all of those words). Male authors recurred across your 2010 list (Snicket, Simmons, Jordon, Scalzi, Gaiman, Green) but all female authors only occurred once (Pearson, Priest, L'Engle, Ryan, Marchetta). I suspect what we would find if we went back to 2009, 2008, 2007 and so on (much like I did in my own reading when this was pointed out to me) that men will often surpass women in sheer number on your reading lists, especially in fantasy and science fiction, which are the genres of your choice.
This is not a new debate or a new problem. Ana, Jodie and I documented one such debate last year. Your "ambivalence" is unfortunately not unique to your position.
Zachariah: Were we to go back before 2009 I think my reading lists would have like two books per year, but I agree with the thrust of your suspicion. I'm particularly interested in my apparent propensity for reading series rather than standalone stories, and look forward to finding out how well this is going to carry over as I make the change to primarily female authors in this challenge.
Renay: I tried to think of fantasy and science fiction series by woman off the top of my head and just failed out of that (classy, self) so I'll also be interested to see how many you come across without it just being Bujold, Bujold, oh hey, how about Bujold? given the makeup of our finances and library offerings.
1. Stories by ladies about ladies.
2. Stories by ladies about men.
3. Stories by men about ladies.
4. Stories by men about men.
For this challenge, we agree to read five books by ladies (options #1 and #2). After the fifth book, the sixth book can be from options #3 and #4, if, say, a certain YA author decides to do something outrageous like sign the entire first printing of his book and therefore it comes out early, ten days into this project. We also have the choice of not reading a male author at that point, but if we continue reading women writers, we won't be able to read another book by a man until we've read six additional titles by ladies.
Traditionally published books and sequential art from middle grade to adult count, but fanfiction does not. So, fine, I won't go read the Inception fanfiction I'm behind on to count toward the challenge. Whatever.
There will also be no obfuscating. Books have to go on the list dated when you finish them!
In the end, one of us will have read more books by ladies.
Zachariah: To clarify, if we opt out of reading a male-authored book, then that book is replaced by a female-authored book; it is not "saved" so that we may later read two (or however many) male-authored books in a row. If I have the understanding of this correct, then...challenge accepted!
Zachariah: Thank you! I do hope there won't be any hard feelings once I've won.
I am pretty excited (I don't know that Zach feels excitement about things other than gourmet coffee and naps and days off, so you'll have to ask him) because I know I'm going to get introduced to tons of new authors.
Since all the anthologies you've ever pointed out to me were male-centric, I feel that also might be violating the spirit of the challenge, unless we single out only the stories by women. I'm open to options, though!
I don't see a way to make it fair and easy to track. Anthologies will likely have to wait until 2013! Alas.
Love that we can track your progress (is a stalker). I'm so excited for your new discoveries and to hear about how this goes.
As previously agreed with Zach, some of my January books won't appear there until after the reviews are posted. ;) But after that, active, updated list at all times.
Comics reading is SO hard. In a project I'm doing, compiling reviews of SF/F media and the gender breakdown, I decided to count comic reviews as SF/F reviews and the writers and artists as "authors". The numbers are bleak. It's dudes as far as the eye can see, on the writing and artistic side. There's definitely more work involved if you want to read women-produced content in comics, as far as I can tell.
I read five books this year (I am definitely jealous of your totals) which was pretty balanced, but in my school reading it was almost all men. SIGH, lit theory. However, I also earned a degree, so I am trying to go easy on myself. The final push and now I have tons of time to read ladies. \o/ I am a little nervous; this project will be the first time I've held myself publicly accountable for my reading diversity since 2008 when I tried to talk about the lack of diversity in my reading and was accused of shaming other people and making them feel bad for not trying to improve their own reading diversity (oh gosh thinking about it makes my head hurt). I hope this endeavor goes a little better.
Yep. Thinking most of it is alternative/indie type stuff. I read a bit about the panels at ComiCon with DC and their abysmal men to women ration, and basically wanted to bite the head off the douche on the panel.
To be fair, most of those books were not heavy books at all. And it's not like I've got a school load to get through beside it. This year my resolution is 25, though that might be more challenging, as I have some real bricks waiting for me at home. Your project will turn out to be very interesting though, I'm sure of it. It's funny how keeping track of something and being much more conscious of it can affect the experience. People who guilttrip you for expressing your own experiences can go jump in a lake.
I didn't quite tell the people involved to go jump in a lake, but it was close. Maybe I should have, looking back, it might have saved me some heartache. Oh, diversity, why so controversial among white people?
Before the year is out we'll probably BOTH have read Bujold. DO NOT WORRY, SEV.
If you come across any good new authors in your readings, please post the names!


The Lyngby Toolbox is a Matlab program package for functional neuroimaging analysis. The toolbox contains a number of models: FIR-filter, Lange-Zeger, K-means clustering among others, visualizations and reading of neuroimaging files.
Authors: Finn Årup Nielsen, Peter Toft, Matthew G. Liptrot, Cyril Goutte, Lars Kai Hansen.
Availability: The toolbox is free for non-commercial use.
Finn Årup Nielsen, Matthew G. Liptrot, Lars Kai Hansen, 1997-2002.
The Brede Toolbox is a neuroinformatics toolbox primarily written in Matlab and it contains functions for handling bibliographic structures (such as PubMed/MEDLINE structure), volumes, sets of locations (3D Talairach coordinates), with transformation/analysis functions suchs as HTML and VRML generation, statistical analysis, affine transformations, functional volumes modeling with, e.g., independent component analysis, Corner Cube visualizations, ... It also contains the Brede Database distributed as XML, see also the web-pages for the Brede Database that has visualizations of the data.
Availability: This software is free for non-commercial use.
Finn Årup Nielsen, 1999 june - 2003.
MRIWarp is software for warping of magnetic resonance (MR) brain images: A set of Unix utilities for performing a non-linear registration of PET of fMRI volumes by non-linear alignment of structural MRI images.
A program to make polygons from a volume. Includes filtering, downsampling, isosurfacing, mesh decimation. The isosurfacing is done with the marching cubes algorithm. Has been compiled under Linux, SGI, HP and Sun.
Author: The program was made here in 1995 by Jesper James Jensen.
Finn Årup Nielsen; Peter Toft; 1997 August.
PLAB - short for Parallel Matlab - is a simple interface for parallelizing Matlab computations, either on multiprocessor machines or in an environment of other Unix computers that can be remotely logged on to.
The The Beowulf Job Manager is a combined queueing and load balancing tool designed for a clusters of work stations or servers, e.g. a Linux Beowulf "farm" of computers.
cvs2html is a Perl program to give a nice overview in HTML of the information in a CVS (concurrent version system) archieve. Multidirectory repositories and links to source code are supported.
Availability: Perl code available. A little cvs status program can also be downloaded. cvs2html is included in many Linux distributions.
Finn Årup Nielsen; Peter Toft; 1997.
A package to enable communication from IDL (interactive data language) to Matlab. It consists of a number of IDL functions and a shared library programmed in C. Presently, it only support matrices (2-dimensional structures) with doubles.
Authors: Finn Årup Nielsen and Peter Toft on the initiative of Steven Strother.
Availability: The package is available (IDL and C).
Finn Årup Nielsen fn@imm.dtu.dk, 1997 november.
A C and Java program that should enable an easy link between a VRML world/browser and virtual reality hardware equipment such as head set, magnetic tracker, spaceball and glove.
Availability: The package is in its very early development. Anyone who is interested in the early sparse (messy) implementation should contact Finn.
Recon2D.tar.gz 2D reconstruction, Version 2.0, 1996-10-08.
Recon3D.tar.gz 3D reconstruction, Version 1.0, 1996-10-08.
C-based packages for 2D and 3D and reconstruction of PET images.
Authors: Made by Peter Toft in connection with his PhD Thesis along with Jesper James Jensen and Peter Philipsen.
Availability: The packages come with full source code. We hold the original rights for the program, but you may freely distribute them FOR NON-COMMERCIAL USE ONLY. The Software is protected by the GNU General Public License.


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Wander Lord
Interesting on art, nature, people, history
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Iraq – Arabian Nights
Iraq covers the ancient region of Mesopotamia, land between the Tigris and the Euphrates. It borders Turkey, Iran, Kuwait, Saudi Arabia, Jordan, and Syria. Its area is 437,072 square kilometers. Its official name is Republic of Iraq.
Arabs make up the majority of Iraq's population. Arabic is the country's main language. The Kurds form the next-largest group and they speak Kurdish.
In about 3300 BC the Sumerians created one of the world's first civilizations in Mesopotamia. Muslims from Arabia conquered the area in the AD 600s. Many of the greatest Muslim philosophers, poets, and writers lived in Baghdad, the center of the Muslim world.
In 1258 the Mongols conquered the city. The Ottoman Turks took control in the 1500s. During World War I British troops ended Ottoman rule. In 1932 the country became independent. In 1980 Iran-Iraq war broke out and lasted until 1988. In early 1991 there was the Persian Gulf War between Iraq and Kuwait. In March 2003 U.S. and British forces invaded the country because they were feared that Iraq was making illegal weapons.
Al-Askari Mosque in Samarra
Baghdad is the capital of the country. It lies on the banks of the Tigris River. About 1,200 years ago caliph al-Mansur chose a village called Baghdad for his capital. The city was built within rounded walls and was called the City of Peace or the Round City. The stories in The Arabian Nights tell about the glory of Baghdad during the reign of Harun al-Rashid. Today Baghdad is a center of the art and culture of Islam.
Today Iraq is one of the world's leading oil producers. It also produces oil products, chemicals, construction materials, and processed foods.
The Euphrates is the longest river in the country. The area west and southwest of the Euphrates River is a part of the Syrian Desert.
Iraq has a short coastline on the Persian Gulf between Iran and Kuwait.
Iraq's highest peak, Mount Ebrāhīm (3,600 meters).
Photos from livinternet.ru
Abbasid Palace
Al-Askari mosque
Citadel of Erbil
City of the Dead in Najaf
Coat of arms of Iraq
Excavations of the palace of the Caliphs in Samarra
Flag of Iraq
Gate in the walls of Erbil in northern Iraq
Fortress tower Talisman in Baghdad
Golden Mosque in Baghdad
Great Mosque in Samarra
Imam Ali Mosque
Ishtar Gate in Babylon
Mar Mattai monastery
Market in Baghdad
Mausoleum of Zimurrud Khatun in Baghdad
Muezzin in Baghdad
National Museum of Iraq
Nebuchadnezzar's palace
Nedjef, panorama of the city
Ruins of Babylon
Rabban Hormizd Monastery
Ruins of the ancient city of Khatra
Ruins of the Assyrian city of Ashur with its ziggurat in the background
Ruins of the Sasanid Palace in Ctesiphon
Sanctuary of the Yazidis in Mosul
Shanidar Cave
Sennacherib's castle
Swords of Cadiz
The ancient city of Nineveh
The fortress walls of Najaf
The sacred Shiite city of Najaf is buried in the sand
The walls of the Great Mutawakkil Mosque. The length of the sides of the mosque is 240 and 156 meters.
Treasury of the country
Ziggurat in Nimrud
Ziggurat in Ur
Ziggurat of the moon god Nanna
Jordan – country with ancient history
Interesting Saudi Arabia
Turkey – amazing country
Iran – Modern Persia
Israel – Jewish State
Lebanon – small Middle Eastern country
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