text:
\section{introduction}
The structure of vacuum of Quantum Chromodynamics (QCD) is one of the most important subject in hadronic physics and has been intensively studied for decades. In particular, it is impossible to understand the phase structure of QCD and the hadron spectrum without good understanding of the QCD vacuum.
For example, it has been well known that the spontaneous chiral symmetry breaking (S$\chi$SB) of the QCD vacuum plays the crucial role in the QCD phenomenology in the low energy regime.
The most important consequence of S$\chi$SB is the existence of the massless modes generated
via the Nambu-Goldstone mechanism identified as the pseudo-scalar (PS) mesons in the hadron spectrum.
Furthermore their masses can be explained by the small but finite current quark masses $m_{u,d}\sim5$ MeV which break the chiral symmetry explicitly. The kaons are heavier than the pions because that the $\mathrm{SU}(3)$ flavor symmetry is explicitly broken by the much heavier strange quark mass $m_s\sim135$ MeV. S$\chi$SB also explains the absence of the mass degeneracy between the parity partners such as $N(940,\frac{1}{2}^{+})$ and $N(1535,\frac{1}{2}^{-})$ which is a consequence of the chiral symmetry of QCD Hamiltonian. Moreover one can construct the chiral effective Lagrangian to calculate the interactions between hadrons in the low energy regime.

Although most of the mass spectrum of the light PS mesons can be understood by the spontaneous and explicit chiral symmetry breaking, the large mass splitting between the $\eta$ and $\eta'$ mesons in the flavor $\mathrm{U}(3)$ nonet had remained a puzzle. Even including the current quark masses effect, the mass of  $\eta'$ should satisfy $m_{\eta'}\le \sqrt{3}m_{\pi}$, if $\mathrm{U_A}(1)$ is spontaneously broken~\cite{Weinberg:1975ui}. This puzzle was later resolved by the $\mathrm{U_A}(1)$ anomaly~\cite{Weinberg:1975ui}, namely $\mathrm{U_A}(1)$ symmetry is already broken at quantum level. 'tHooft first suggested that the {\it instanton} breaks the $\mathrm{U_A}(1)$ symmetry explicitly~\cite{'tHooft:1976up} and constructed a dilute instanton gas model which is a semi-classic approximation of the topological charge distribution of Yang-Mills theory to explain $\mathrm{U_A}(1)$ problem. However the approximation itself breakdowns in the infrared regime such that it cannot provide the estimation of the $\eta'$ mass. The strength of this anomaly is characterized by the topological susceptibility $\chi_t$ defined by the following two-point correlation at zero-momentum transfer:
\begin{equation}
\label{eq:TS}
\chi_t\equiv\lim_{V\to\infty}\frac{\langle Q^2_t\rangle}{V}
=\int_x\,\langle 0|T\left(Q_t(x)Q_t(0)\right)|0\rangle,
\end{equation}
where $Q_t(x)$ indicates the topological charge density operator and $V$ stands for the four-dimensional volume in Euclidean space. 'tHooft first suggested that the {\it instanton} breaks the $\mathrm{U_A}(1)$ symmetry explicitly~\cite{'tHooft:1976up} and constructed a dilute instanton gas model which is a semi-classic approximation of the topological charge distribution of Yang-Mills theory to explain $\mathrm{U_A}(1)$ problem. However the approximation itself breakdowns in the infrared regime such that he cannot provide the estimate of the $\eta'$ mass. On the other hand, the first estimation of $\eta'$ mass was given by the Witten-Veneziano formula in the pure Yang-Mills (YM) QCD in the large $N_c$ limit. It is derived from the Ward identity of the flavor singlet chiral current~\cite{Veneziano:1979ec,Witten:1979vv}:
\begin{equation}
\label{eq:CHPT}
\chi_t=\frac{F^2_\pi}{2N_f}\left(m^2_\eta+m^2_{\eta'}-2m^2_K\right).
\end{equation}
Empirically, using Eq.~(\ref{eq:CHPT}) by plugging in the physical masses of the PS mesons one has $\chi_t\approx(175\pm5\,\mathrm{MeV})^4$~\cite{Veneziano:1979ec}. This value has been confirmed by the lattice simulation~\cite{Alles:1996nm}. Furthermore, the dilute gas model of 'tHooft and Witten-Veneziano approach differ from each other in the ratio $\langle Q^4_t\rangle/\langle Q^2_t\rangle$ and the numerical result seems to prefer the latter.~\cite{Ce:2014sfa}. Since the topological susceptibility $\chi_t$ plays such an important role in QCD, naturally there have been many theoretical approaches to compute $\chi_t$ including many lattice QCD (LQCD) simulations~\cite{DelDebbio:2004ns,AliKhan:1999zi,AliKhan:1999zp,Hart:2000wr,Hart:2000gh,Bali:2001gk,Bernard:2012fw,Chiu:2008jq,Aoki:2000kp}, effective QCD-like models~\cite{Fukushima:2001hr,Xia:2013caa,Cheng:1998vj,Dorokhov:2004pw}, QCD sum rule~\cite{Grunberg:1984pa}, $\chi_t$ at finite temperature~\cite{Jiang:2015xqz,Alles:1996nm,Borsanyi:2015cka}, AdS/QCD approach~\cite{Katz:2007tf}, and so on.

In the present work, we employ the nonlocal chiral quark model (NL$\chi$QM) to compute $\chi_t$.
The present model is based on the liquid instanton QCD-vacuum configuration. After the bosonization, the effective partition function of the instanton model becomes a partition function with quarks ($q$) and pseudo-scalar (PS) mesons ($\phi$) with the nonlocal interactions between them. Therefore it is called the nonlocal chiral quark model (NL$\chi$QM,). To identify the topological charge operator $Q_t(x)$ within NL$\chi$QM, we need calculate the four divergence of the flavor singlet current derived by the infinitesimal $\mathrm{U_A}(1)$ rotation of the partition function. From it one can figure out the topological charge operator.

We also consider the small but finite difference $(\Delta)$ between the numbers of the instantons $(N_{+})$ and the anti-instantons $(N_{-})$ in order to derive the appropriate expression of $\chi_t$ in the chiral limit. By computing the two-point correlation defined in Eq.~(\ref{eq:TS}) by using $Q_t(x)$ of our own model, we obtain basically three distinctive contributions for $\chi_t$ for the leading order (LO) in the $1/N_c$ expansion:
1) The contribution with the dynamical quarks $\chi^q_t$, which contains the quark loops and the PS-meson propagator.
2) That consists of the PS-meson propagator without the quark loops $\chi^\phi_t$.
3) A constant contribution from the $\Delta$ effect, i.e. $\chi^\Delta_t$, which survives only in the chiral limit $m_q\sim0$ where $m_q$ stands for the current quark mass with its flavor $q=(u,d,s)$. Furthermore, we verify that NL$\chi$QM reproduces the Witten-Veneziano and Leutwyler-Smilga formulae analytically.

After fixing the average (anti)instanton size $\bar{\rho}=1/3$ fm and inter-(anti)instanton distance $\bar{R}=1$ fm, we generate all the physical quantities needed for computing $\chi_t$ self-consistently in NL$\chi$QM. Our values of the masses and weak decay constants of the PS mesons are in a good agreement with the experimental values. Our numerical value of $\chi_{t}=(165.57\,\mathrm{MeV})^4$ whereas $\chi^\mathrm{QL}_t=(194.30\,\mathrm{MeV})^4$ in the quenched limit. In other words, we find that the inclusion of the dynamical quarks reduces $\chi_t$ by $(10\sim20)\%$ in NL$\chi$QM. It is consistent with the LQCD data~\cite{Bali:2001gk}. Our result is also comparable with other theoretical results and the empirical value $\chi_{t}=(175\pm5\,\mathrm{MeV})^4$.

The present work is organized as follows: In Section II, we briefly introduce our theoretical framework including the details of NL$\chi$QM and the derivation of the expression of $\chi_t$ within NL$\chi$QM. Our numerical results and related discussions are given in Section III. The last Section is devoted to the conclusion and future perspective.
 \section{Theoretical framework}
The local topological charge density operator $Q_t(x)$ of QCD is defined by~\footnote{In literatures, the topological charge is given by $Q_t$, and its density operator by $q_t(x)$. However, in the present work, we will make use of $Q_t(x)$ as the density operator.}
\begin{equation}
\label{eq:TC}
Q_t(x)\equiv \frac{1}{32\pi^2}G^a_{\mu\nu}(x)\tilde{G}^a_{\mu\nu}(x),\,\,\,\,
\tilde{G}^a_{\mu\nu}(x)=\frac{1}{2}\epsilon_{\mu\nu\sigma\rho}G^a_{\sigma\rho}(x).
\end{equation}
Here, $G^a_{\mu\nu}$ and $\tilde{G}^a_{\mu\nu}$ denote the gluon field-strength tensor and its dual one, respectively.
Note that the strong coupling $g_s$ is implicitly included in $G^a_{\mu\nu}$ in Eq.~(\ref{eq:TC}). The topological charge of QCD can be obtained by integrating $(Q_t(x))^2$ over the volume.
A non-zero topological charge implies that the tunneling occurs between the QCD vacua related to each other by the homotopy of the SU(3) color-gauge symmetry. It is worth mentioning that the {\it instanton} is one of the semi-classical solutions to explain this novel QCD phenomenon~\cite{'tHooft:1976up}. Moreover, a non-zero topological charge also indicates that the flavor-singlet axial current of QCD is not conserved because of the $\mathrm{U_A}(1)$ anomaly. Thus, the instanton can explain the $\mathrm{U_A}(1)$ symmetry breaking explicitly~\cite{Diakonov:1995qy}. In QCD with the vacuum angle $\theta\to0$, the four divergence for the $\mathrm{U_A}(1)$ current reads in Euclidean space:
\begin{equation}
\label{eq:CSC}
\partial^\mu J^\mathrm{singlet}_{5\mu}(x)=2N_fQ_t(x)+2\sum_{q=u,d,s}m_qq^\dagger(x)\gamma_5 q(x),
\end{equation}
where $q(x)$ and $m_q$ denote the field and the current mass for a quark. $N_f$ is the number of the flavors of quarks.
To obtain $Q_t(x)$ from an effective model of QCD, one can apply Eq.~(\ref{eq:CSC}) to obtain $\partial^\mu J^\mathrm{singlet}_{5\mu}(x)$ by differentiating the effective Lagrangian of the model with respect to the infinitesimal rotation parameter $\epsilon$ as in $q\to\left(1+i\gamma_5\frac{\epsilon}{2}\right)q$:
\begin{equation}
\label{eq:DL}
\frac{\partial(\delta\mathcal{L}_\mathrm{eff})}{\partial\epsilon}
\equiv \partial^\mu J^\mathrm{singlet}_{5\mu}.
\end{equation}
Comparing Eq.~(\ref{eq:CSC}) with Eq.~(\ref{eq:DL}), one is able to obtain the expression of $Q_t(x)$ and compute the topological susceptibility.
\begin{figure}[t]
\includegraphics[width=14cm]{FIG0.pdf}
\caption{The leading-order diagrams of the topological susceptibility $\chi_t$ in NL$\chi$QM in the large $N_c$ limit. The solid and dash line indicates the quark and pseudo-scalar meson, whereas the solid ($\blacksquare$) and blank ($\square$) squares represent the vertices in $\mathcal{O}(1/\sqrt{N_c})$ and $\mathcal{O}(\sqrt{N_c})$, respectively, and the solid circle ($\bullet$) stands for the vertex in $\mathcal{O}(1)$.}
\label{FIG0}
\end{figure}

In this article, we use the partition function derived from the dilute liquid-instanton QCD-vacuum model (LIM)~\cite{Diakonov:1997sj,Diakonov:1995qy,Diakonov:2002fq} in Euclidean space:
\begin{eqnarray}
\label{eq:EZ}
\mathcal{Z}_\mathrm{eff}[q,q^\dagger]&=&\int\frac{d\lambda_\pm}{2\pi}\int Dq Dq^\dagger
\exp\left[
\int_x\sum_{q}q^\dagger(i\rlap{/}{\partial}+m_q)q+\sum_{a=\pm}\left[\lambda_a Y^a_{N_f}(\bar{\rho})+N_a\left(\ln\frac{N_a}{\lambda_a V \mathrm{\Lambda}^{N_f}}\right)\right]\right],
\cr
Y^a_{N_f}(\bar{\rho})&=&\frac{1}{N^{N_f}_c}\int_x \,
\mathrm{det}_f\left[iJ^a_{qq'}(x,\bar{\rho})\right]=
\int_x\,\mathrm{det}_f\left[\frac{i}{N_c}J^a_{qq'}(x,\bar{\rho})\right],
\cr
J^a_{qq'}(x,\bar{\rho})&=&\int_k\int_pe^{i(k-p)\cdot x}F(k)F(p)\left[q^\dagger(k)\frac{1+a\gamma_5}{2}q'(p)\right]_{N_f\times N_f}.
\end{eqnarray}
Here, we assign $\int\frac{d^4k}{(2\pi)^4}$ with $\int_k$ for brevity, while $[\cdots]_{N_f\times N_f}$ and $\mathrm{det}_f$ denote the $(N_f\times N_f)$ quark-flavor matrix and the determinant over the flavor indices. $\hat{m}_q$ indicates the current-quark mass matrix. In the case of $N_f=3$ one has
$\mathrm{diag}(m_u,m_d,m_s)$. The parameter $a$ indicates the instanton ($+$) and anti-instanton ($-$) contributions. Thus, $N_a$ and $\lambda_a$ denote the number of (anti)instantons and the Lagrange multiplier, respectively. $V$ stands for the four-dimensional volume in Euclidean space, whereas $\mathrm{\Lambda}$ for an argument to make the logarithm dimensionless.

In deriving Eq.~(\ref{eq:EZ}), we have assumed the instanton distribution function to be a $\delta$ function, $\delta(\rho-\bar{\rho})$. Here $\rho$ stands for the (anti)instanton size and $\bar{\rho}$ their average value. $F(k)$ stands for the Fourier transform of the instanton zero-mode solution. It plays the role of UV regulator, i.e. form factor (FF) and its explicit form will be given in the next Section.
Furthermore, we assume that $N_+\approx N_{-}\approx N/2=(N_++N_-)/2$ and $\lambda_{+}\approx \lambda_{-}=\lambda$. However, we will consider the small number difference between the instanton and anti-instanton $\Delta=|N_+-N_-|\ll N$ later to interpret the correct behaviour of $\chi_t$ in the chiral limit. Note that the determinant-type interaction, i.e. $2N_f$ 't Hooft interaction is derived directly from the instanton configuration. It gives the explicit $\mathrm{U_A}(1)$ symmetry breaking.

In order to obtain $Q_t(x)$ from Eq.~(\ref{eq:EZ}), we perform the infinitesimal chiral rotation as shown in Eq.~(\ref{eq:DL}) which results in $\mathcal{Z}_\mathrm{eff}\to\mathcal{Z}'_\mathrm{eff}$:
\begin{eqnarray}
\label{eq:EFFPART}
\mathcal{Z}'_\mathrm{eff}[q,q^\dagger]&=&\int\frac{d\lambda_\pm}{2\pi}\int Dq Dq^\dagger
\exp\left[
\int_x\sum_{q}q^\dagger(i\rlap{/}{\partial}+im_q-2\epsilon\gamma_5m_q)q
+\sum_{a=\pm}\left[\lambda_a Y'^a_{N_f}(\bar{\rho})+N_a\left(\ln\frac{N_a}{\lambda_a V \mathrm{\Lambda}^{N_f}}\right)\right]\right],
\cr
Y'^a_{N_f}(\bar{\rho})&=&
(1+2aiN_f\epsilon)\int_x\,\mathrm{det}_{N_f}\left[\frac{i}{N_c}J^a_{qq'}(x,\bar{\rho})\right].
\end{eqnarray}
Note that there are additional terms proportional to $\epsilon$ which break the $\mathrm{U_A}(1)$ symmetry. If we put $F(k)=1$ then perform the Fourier transform of the quark fields, it is easy to find that those additional terms in Eq. (\ref{eq:EFFPART}) coincide with the NJL model result of Eq.~(13) in Ref.~\cite{Fukushima:2001hr}. There they tried to include the {\it ring} diagrams in addition to the leading contributions in $\mathcal{O}(N_c)$
in the large $N_c$ limit in terms of the mean-field approach. Those ring diagrams were identified as the PS-meson propagators.
Here we will not follow their strategy. Instead, we prefer to apply the technique of bosonization to
convert the partition function in Eq.~(\ref{eq:EFFPART}) into the one with quarks and
the auxiliary meson fields $\mathcal{M}$ in the large $N_c$ limit~\cite{Diakonov:1997sj}.

The first step is to employ the following identity for the bosonization:
\begin{equation}
\label{eq:B}
\exp\left(\lambda_{\pm}\mathrm{det}_f\left[\frac{i}{N_c}J^\pm_{qq'}\right] \right)=\int D\mathcal{M}_{\pm}\exp\left\{
i\mathrm{tr}_f\left[\mathcal{M}^{qq'}_\pm J^\pm_{qq'}\right]
-(N_f-1)\left(\frac{1}{\lambda_{\pm}}\mathrm{det}_f[\mathcal{M}^{qq'}_\pm N_c] \right)^{\frac{1}{N_f-1}}\right\},
\end{equation}
where $\mathrm{tr}_f$ stands for the trace over the flavor indices.
$\mathcal{M}_{\pm}$ stands for the left-handed $(+)$ and right-handed $(-)$ nonlinear auxiliary fields. Since, in the bosonized partition function, the interactions between the quarks and mesons are nonlocal, and the chiral symmetry is broken dynamically, therefore it is dubbed the nonlocal chiral-quark model (NL$\chi$QM). After performing the bosonization, the rotated effective partition function in Eq.~(\ref{eq:EFFPART}) becomes
\begin{eqnarray}
\label{eq:EFFPART1}
&&\mathcal{Z}'_\mathrm{eff}[q^\dagger,q,\mathcal{M}_{\pm}]=
\int\frac{d\lambda_\pm}{2\pi}\int Dq Dq^\dagger D\mathcal{M}_\pm
\exp\Bigg\{
\int_x\sum_qq^\dagger(i\rlap{/}{\partial}+i\hat{m})q
+\sum_{a=\pm}N_a\left(\ln\frac{N_a}{\lambda_a V \mathrm{\Lambda}^{N_f}}\right)
\cr
&+&\sum_{a=\pm}\int_x\Bigg[i\mathrm{tr}_f[\mathcal{M}^{qq'}_a J^a_{qq'}]
-(N_f-1)\left(\frac{1}{\lambda_a}\mathrm{det}_f[\mathcal{M}^{qq'}_a N_c]
 \right)^{\frac{1}{N_f-1}}
\Bigg]
\cr
&+&\epsilon\left[2i\int_x\sum_qq^\dagger(i\gamma_5m_q)q+ 2iN_f\sum_{a=\pm}a \int_x\,\Bigg[i\mathrm{tr}_f[\mathcal{M}^{qq'}_a J^a_{qq'}]-(N_f-1)\left(\frac{1}{\lambda_a}\mathrm{det}_f[\mathcal{M}^{qq'}_a N_c] \right)^{\frac{1}{N_f-1}}
\Bigg]\right]\Bigg\}.
\end{eqnarray}

Focusing on the deviations by the infinitesimal rotation in $\epsilon[\cdots]$ and comparing them with Eq.~(\ref{eq:CSC}),
one can define the local topological charge density operator from NL$\chi$QM:
\begin{equation}
\label{eq:TCO}
Q_t[q_f,q^\dagger_f,\mathcal{M}_{\pm}]= \sum_{a=\pm}a \int_x\,
\left[\mathrm{tr}_{f}[\mathcal{M}^{qq'}_a J^a_{qq'}]+i(N_f-1)\left(\frac{N_c^{N_f}}{\lambda_a}\mathrm{det}_{f}\left[\mathcal{M}^{qq'}_a\right] \right)^{\frac{1}{N_f-1}}
\right].
\end{equation}
Following Refs.~\cite{Diakonov:1997sj,Halperin:1998gx} we parameterize the auxiliary meson field $\mathcal{M}^{qq'}_a$.
\begin{equation}
\label{eq:PSP}
\mathcal{M}^{qq'}_\pm\to\sigma_0(1\pm\delta)(U_\pm)_{qq'}=\sigma_0(1\pm\delta)(e^{\pm i\Phi})_{qq'}.
\end{equation}
Here $\sigma_0$ stands for VEV of the flavor-singlet scalar meson, and plays the role to provide the quarks with their
constituent quark masses. In other words, one has the constituent quark mass $M_0=\sigma_0$.
Furthermore we have $M_q=M_0+m_q$ since the quark mass is the sum of the current quark mass and the constituent quark mass.
To determine the value of $\sigma_0$, one minimize the effective action with respect to $\lambda$. By this way, one obtains
\begin{equation}
\label{eq:NOV}
\frac{N}{V}=4N_c\int_k\frac{M^2_0(k)}{k^2+M^2_0(k)},\,\,\,\,M_0(k)=\sigma_0 F^2(k),\,\,\,\,
\lambda=\frac{N}{2V}\left(\frac{2\sigma_0 V N_{c}}{N}\right)^{N_f}.
\end{equation}

We also introduced a new parameter $\delta$ in ~Eq.~(\ref{eq:PSP}) defined as follows~\cite{Diakonov:1995qy}:
\begin{equation}
\label{eq:DELTA}
\delta=\frac{2\pi^2\bar{\rho}^2\Delta}{VN_c}\left(\sum_q\frac{1}{m_qM_q}\right)
=\frac{\Delta}{V}\left(\sum_q\frac{1}{m_q\Sigma_q}\right)
=Q^\mathrm{YM}_t\left(\sum_q\frac{1}{m_q\Sigma_q}\right).
\end{equation}
where $\Delta=|N_+-N_-|\ll N$ is the small difference between the numbers of instantons and anti-instantons.
$Q^\mathrm{YM}_t=\frac{\Delta}{V}$ is the topological charge operator in pure Yang-Millers theory.
Note that $\delta$ is a quantity of $\mathcal{O}(1/N_{c})$.
$\Sigma_q$ denotes the quark condensate for the flavor $q$  which is related with $M_q$ by the following relation:
\begin{equation}
\Sigma_q=M_q\left(\frac{N_c}{2\pi^2\bar{\rho}^2}\right).
\end{equation}
Furthermore, $U_\pm$ can be understood as the $N_f\times N_f$ nonlinear PS-meson field.
Since we are interested in the contributions from the iso-singlet PS mesons for the $\mathrm{U_A}(1)$ anomaly,
we pick up only $\eta$ and $\eta'$ from the flavor $\mathrm{U}(3)$ nonet.
The explicit form of $\Phi$ is given by
\begin{equation}
\label{eq:PHI}
\Phi\equiv\sqrt{2}\,\mathrm{diag}\left(
\frac{1}{\sqrt{N_f}}\frac{\eta'}{F_{\eta'}}+\frac{1}{\sqrt{6}}\frac{\eta}{F_\eta},\,\,
\frac{1}{\sqrt{N_f}}\frac{\eta'}{F_{\eta'}}+\frac{1}{\sqrt{6}}\frac{\eta}{F_\eta},\,\,
\frac{1}{\sqrt{N_f}}\frac{\eta'}{F_{\eta'}}-\frac{2}{\sqrt{6}}\frac{\eta}{F_\eta}
\right)=\mathrm{diag}\left(\Phi_{uu},\Phi_{dd},\Phi_{ss}\right).
\end{equation}
With the representation of Eq.~(\ref{eq:PHI}) where the pion weak-decay constant is normalized in $F_\pi\approx93$ MeV~\cite{Halperin:1998gx}.

If the interaction strengths among the instantons and anti-instantons are the same then
the vacuum expectation value (VEV)of the pure Yang-Millers topological charge density operator $Q^\mathrm{YM}_t$ satisfies the following relation:
\begin{equation}
\label{eq:YMQ}
\int_x\langle (Q^\mathrm{YM}_t)^2\rangle\equiv\chi^\mathrm{YM}_t=\frac{N}{V}.
\end{equation}
As noted above, in the instanton configuration, this quantity relates to the instanton number density $N/V$ and can be defined as the topological susceptibility of the pure YM action $\chi^\mathrm{YM}_t.$~\cite{Diakonov:1997sj}.
Performing the trace and determinant over the flavor indices in Eq.~(\ref{eq:TCO}) with the following identities:
\begin{eqnarray}
\label{eq:ID}
\frac{1+\gamma_5}{2}\exp[i\Phi]\pm\frac{1-\gamma_5}{2}\exp[-i\Phi]
&=&(\gamma_5)^{\frac{1\mp1}{2}}\exp[i\gamma_5\Phi],
\cr
\left(\mathrm{det}_{f}\left[e^{i\Phi}\right] \right)^{\frac{1}{N_f-1}}\pm\left(\mathrm{det}_{f}\left[e^{-i\Phi}\right]\right)^{\frac{1}{N_f-1}}&=&\exp\left[\frac{i\mathrm{tr}_f\Phi}{N_f-1}\right]\pm\exp\left[\frac{-i\mathrm{tr}_f\Phi}{N_f-1}\right]=
2\left(
\begin{array}{c}
\cos\\i\sin
\end{array}
\right)i\sin\left[\frac{\sqrt{2N_f}\eta'}{F_{\eta'}(N_f-1)}\right],
\end{eqnarray}
we finally arrive at a rather concise expression for $Q_t(x)$:
\begin{eqnarray}
\label{eq:TCO1}
Q_t(x)&=&\int_k\int_pe^{i(k-p)\cdot x}
\sqrt{M_q(k)M_q(p)}\sum_{q}q^\dagger(k)
\left(\gamma_5+\delta I_{4\times4} \right)\exp[i\gamma_5\Phi_{qq}]q(p)
\cr&-&2(N_f-1)\left(\frac{\sqrt[3]{M_uM_dM_s}N_c}{\lambda^{1/N_f}}\right)^{\frac{N_f}{N_f-1}}
\left(\sin\left[\frac{\sqrt{2N_f}\eta'(x)}{F_{\eta'}(N_f-1)}\right]
-i\delta\cos\left[\frac{\sqrt{2N_f}\eta'(x)}{F_{\eta'}(N_f-1)}\right]\right)
\cr
&=&\int_k\int_pe^{i(k-p)\cdot x}
\sqrt{M_q(k)M_q(p)}\sum_{q}q^\dagger(k)\gamma_5(1+i\gamma_5\Phi_{qq})q(p)
-\chi^\mathrm{YM}_t\left(\frac{\sqrt{2N_f}\eta'(x)}{F_{\eta'}}-i(N_f-1)\delta\right)+\cdots
\end{eqnarray}
where we set $M_q(k)\equiv M_qF(k)$.
From the first line to the second of  Eq.~(\ref{eq:TCO1}), we have used the small-field approximation: $\eta'/F_{\eta'}\ll1$.

Taking Eqs.~(\ref{eq:TS}) and (\ref{eq:TCO1}) into account, the leading order diagrams $\sim\mathcal{O}(N_c)$ for the topological susceptibility $\chi_t$ in NL$\chi$QM are shown in Fig.~\ref{FIG0}. The solid and dash line indicates the quark and PS meson, whereas the solid ($\blacksquare$) and blank ($\square$) squares represent the vertices in $\mathcal{O}(1/\sqrt{N_c})$ and $\mathcal{O}(\sqrt{N_c})$, respectively, and the solid circle ($\bullet$) stands for the vertex in $\mathcal{O}(1)$. After straightforward calculations of the diagrams in according to $Q_t(x)$ in Eq.~(\ref{eq:TCO1}), the explicit expressions of each contributions for $\chi_t$ are given as follows:
\begin{eqnarray}
\label{eq:TST}
\chi_t&=&\left(\chi^a_t+\chi^b_t+\chi^c_t\right)_{q}+\chi^\phi_t+\chi^\Delta_t
=\chi^q_t+\chi^\phi_t+\chi^\Delta_t,
\cr
\chi^a_t&=&2L+L_s,\,\,\,\,
\chi^{b}_t=-\frac{2}{3}\left[\frac{(2L+L_s)^2}{F^2_{\eta'}m_{\eta'}^2}+\frac{2(L-L_s)^2}{F^2_{\eta}m_{\eta}^2}\right],\,\,\,\,
\chi^{c}_t=-4\left[\chi^\mathrm{YM}_t\frac{(2L+L_s)}{F^2_{\eta'}m_{\eta'}^2}\right],
\cr
\chi^\phi_t&=&\left(\chi^\mathrm{YM}_t\right)^2\frac{2N_f}{F^2_{\eta'}m^2_{\eta'}},
\,\,\,\,
\chi^\Delta_t=\delta^2(N_f-1)^2\left(\chi^\mathrm{YM}_t\right)^2
=\left(\chi^\mathrm{YM}_t\right)^3(N_f-1)^2\left(\sum_q\frac{1}{m_q\Sigma_q}\right)^2,
\end{eqnarray}
with the following definitions:
\begin{equation}
\label{eq:LFUNC}
L_{q}\equiv4N_c\int_k\frac{M^2_q(k)}{k^2+M^2_q(k)},\,\,\,L\equiv L_u=L_d,\,\,\,\,
L_0=4N_c\int_k\frac{M^2_0(k)}{k^2+M^2_0(k)}=\frac{N}{V}=\chi^\mathrm{YM}_t.
\end{equation}
Note that $\chi^\Delta_t$ survives only in the chiral limit $m_q\sim0$ because that $\delta\ll1$.

It is interesting to examine our result of Eq.~(18) in the quenched limit (QL) and the chiral limit.
We know that in the quenched limit $\chi^\mathrm{YM}_t\approx\chi^\mathrm{QL}_t$ and $\chi^q_t=0$, since the quark loop contributions are all suppressed in the quenched limit.
Moreover $\chi^\Delta_t$ is also suppressed in the large $N_{c}$ limit, according to $\delta\sim \mathcal{O}(1/N_{c})$. Hence, we can write the followings:
\begin{equation}
\label{eq:QL}
\chi^\mathrm{QL}_t=\left(\chi^\mathrm{YM}_t\right)^2
\frac{2N_f}{F^2_{\eta'}m^2_{\eta'}}\approx\left(\chi^\mathrm{QL}_t\right)^2
\frac{2N_f}{F^2_{\eta'}m^2_{\eta'}}\Rightarrow
\chi^\mathrm{QL}_t\approx\frac{F^2_{\eta'}m^2_{\eta'}}{2N_f}.
\end{equation}
Obviously, as shown in Eq.~(\ref{eq:QL}), we can obtain the Witten-Veneziano formula for the topological susceptibility in the quenched limit~\cite{Diakonov:1995qy}.

As for the chiral limit, we choose the conditions that $\chi^\mathrm{YM}_t\approx \chi^\mathrm{\chi L}_t$ and $\chi^q_t\ll\chi^\mathrm{\chi L}_t$, since $\chi^\Delta_t$ dominates in this limit $m_q\sim0$:
\begin{equation}
\label{eq:CL}
\chi^\mathrm{\chi L}_t=
\left(\chi^\mathrm{YM}_t\right)^3(N_f-1)^2\left(\sum_q\frac{1}{m_q\Sigma_q}\right)^2
\approx
\left(\chi^\mathrm{\chi L}_t\right)^3N_f^2\left(\sum_q\frac{1}{m_q\Sigma_q}\right)^2
\Rightarrow
\chi^\mathrm{\chi L}_t\approx\frac{1}{N_f}\left(\sum_q\frac{1}{m_q\Sigma_q}\right)^{-1},
\end{equation}
which is nothing but the Leutwyler-Smilga formula for the topological susceptibility in the chiral limit~\cite{Leutwyler:1992yt,DiGiacomo:1997wf}. Thus, as for $\chi_t$ with the physical current quark masses, i.e. physical limit (PL) with the conditions that $m_q>0$ and $N_f=3$, we can write
\begin{equation}
\label{eq:PL}
\chi^\mathrm{PL}_t=\chi^q_t+\chi^\phi_t.
\end{equation}
In the following Section, we represent the numerical result of the topological susceptibility $\chi_t=\chi^\mathrm{PL}_t$.

\section{Numerical results and discussions}
In this Section, we present our numerical results and the relevant discussions. The first task is to determine the value of the quark mass: $M_q=M_0+m_q$. It is the sum of the current quark mass $m_q$ and the constituent quark mass $M_0$ coming from S$\chi$SB. The value of $M_0$ can be determined in the chiral limit in LIM using the self-consistent (gap) equation Eq.~(\ref{eq:NOV}). By comparing Eq.~(\ref{eq:NOV}) with Eq.~(\ref{eq:LFUNC}), we identify that $N/V=L_0$ with $m_q=0$.
The form factor $F(k)$ comes from the Fourier transform of the quark zero-mode solution in the instanton vacuum. It consists of the combination of modified Bessel functions~\cite{Diakonov:2002fq}:
\begin{equation}
\label{eq:FF}
F(k)=2t\left[I_0(t)K_1(t)-I_1(t)K_0(t)-\frac{I_1(t)K_1(t)}{t}\right]_{t=\frac{|k|\bar{\rho}}{2}}.
\end{equation}
Here we choose the {\it standard} values for the LIM parameters: The (anti)instanton number density $N/V=1/\bar{R}^4=(1\,\mathrm{fm})^{-4}\approx(197\,\mathrm{MeV})^4$ and the average (anti)instanton size $1/\bar{\rho}=(1/3\,\mathrm{fm})^{-1}\approx591$ MeV~\cite{Diakonov:2002fq}. $M_0$ is found to be $341$ MeV
in according to the self-consistent equation in Eq.~(\ref{eq:NOV}).

The weak decay constants of $\eta$ and $\eta'$ mesons, $F_\eta$ and $F_{\eta'}$
are also needed in the computation of $\chi_t$ as shown in Eq.~(\ref{eq:TST}).
Their analytical expressions derived from the axial-vector current conservation read as~\cite{Nam:2007gf}:
\begin{equation}
\label{eq:FPI}
F^2_{q\bar{q}}=4N_c\int_k\frac{M^2_{q\bar{q}}(k)-\frac{k}{2}M_{q\bar{q}}(k)\frac{\partial M_{q\bar{q}}(k)}{\partial k}+\frac{k^2}{4}\left[\frac{\partial M_{q\bar{q}}(k)}{\partial k}\right]^2}{[k^2+M^2_{q\bar{q}}(k)]^2},\,\,\,\,M_{q\bar{q}}(k)\equiv\frac{M_q(k)+M_{\bar{q}}(k)}{2}
=\frac{(M_{q}+M_{\bar{q}})}{2}F^2(k).
\end{equation}
Here, $F_{q\bar{q}}$ stands for the weak-decay constant for a pseudo-scalar meson consisting of $q$ and $\bar{q}$. For instance, we have $(q,\bar{q})=(u,\bar{d})$ for $F_{\pi^+}$.  First, we compute $F_\pi$ and $F_K$ to check the validity of the model. Choosing $M_{u\bar{d}}=(M_u+M_{\bar{d}})/2\equiv M=346$ MeV for the pion and $M_{u\bar{s}}=(M+M_{\bar{s}})/2=(346+476)/2=411$ MeV for the kaon, we have that
\begin{eqnarray}
\label{eq:WDC}
\mathrm{NL}\chi\mathrm{QM}&:&F_\pi=91.01\,\mathrm{MeV},\,\,\,\,F_K=100.08\,\mathrm{MeV},
\cr
\mathrm{Empirical\,\,value}&:&F_\pi=93\,\mathrm{MeV},\hspace{0.6cm}F_K=108\,\mathrm{MeV},
\end{eqnarray}
where we have used $m_{u,d}\equiv m=5$ MeV and $m_s=135$ MeV.
Similarly, one obtains $F_{u\bar{u}}=F_{d\bar{d}}=91.01$ MeV and $F_{s\bar{s}}=108.28$ MeV in according to Eq.~(\ref{eq:FPI}).
Furthermore, the empirical value of $F_\eta$ is $(91.9\pm0.07)$ MeV from the PDG value~\cite{Agashe:2014kda}.
Hence we have
\begin{eqnarray}
\label{eq:WDC!}
\mathrm{NL}\chi\mathrm{QM}&:&F_{\eta}=96.77\,\mathrm{MeV},\,\,\,\,F_{\eta'}=102.53\,\mathrm{MeV}.
\cr
\mathrm{Empirical\,\,value}&:&F_{\eta}=(91.9\pm0.07)\,\mathrm{MeV}\,\,\,(F_{\eta'}=F_{\eta}\,\,\mathrm{for}\,\,N_c\to\infty).
\end{eqnarray}

The singlet and octet contributions of $F_{\eta}$ and $F_{\eta'}$ were investigated
by using the $\mathrm{U_A}(1)$ PCAC
in Ref.~\cite{Shore:2006mm}
Their results are $(F_{0\eta},F_{8\eta})=(22.8\pm5.7,98.4\pm1.4)$ MeV and $(F_{0\eta'},F_{8\eta'})=(104.2\pm4.0,-36.1\pm1.2)$ MeV.
Moreover, AdS/QCD calculation gives $(F_{0\eta},F_{8\eta})=(17.0,103.0)$ MeV and $(F_{0\eta'},F_{8\eta'})=(129.0,-35.1)$ MeV~\cite{Katz:2007tf}.
We list various estimations for $(F_{\eta},F_{\eta'})$ in Table~\ref{TABLE1}.
\begin{table}[h]
\begin{tabular}{|c||c|c|c|c|}
\hline
&NL$\chi$QM&$\mathrm{U_A}(1)$ PCAP~\cite{Shore:2006mm}&AdS/QCD~\cite{Katz:2007tf}&PDG~\cite{Agashe:2014kda}\\
\hline
$F_{\eta}$&$96.77$&$(22.8\pm5.7,98.4\pm1.4)$&$(17.0,103.0)$&$91.9\pm0.07$\\
\hline
$F_{\eta'}$&$102.53$&$(104.2\pm4.0,-36.1\pm1.2)$&$(129.0,-35.1)$&$-$\\
\hline
\end{tabular}
\caption{The values for $F_{\eta}$ and $F_{\eta'}$ [MeV]. As for Refs.~\cite{Shore:2006mm,Katz:2007tf}, we represent them in the form of $(F_{0h},F_{8h})$, where $h=(\eta,\eta')$.}
\label{TABLE1}
\end{table}
Our value of $F_{\eta'}$ is close to the values of $F_{0\eta'}$ of other calculations and
our value of $F_{\eta}$ is close to the values of $F_{8\eta}$ of other calculations.
Since we know that $F_{\eta'}\sim F_{0\eta'}$ and  $F_{\eta}\sim F_{8\eta}$, i.e. the mixing angle between $\eta$ and $\eta'$ is expected to be large,
such that we will use our values of $F_{\eta}$ and $F_{\eta'}$ to compute $\chi_t$ within NL$\chi$QM.

We make further test in NL$\chi$QM by computing the quark condensate, $\Sigma_q\equiv i\langle q^\dagger q\rangle$. Note that $\Sigma_q$ also appears in the LS formula for $\chi_t$ in Eq.~(\ref{eq:CL}). Within NL$\chi$QM, the chiral condensate is given by~\cite{Nam:2007gf}:
\begin{equation}
\label{eq:QC}
\Sigma_q=4N_c\int_k\left[\frac{M_q(k)}{k^2+M^2_q(k)}-\frac{m_q(k)}{k^2+m^2_q(k)}\right].
\end{equation}
Here, we set $m_q(k)=m_q F^2(k)$ to tame the UV divergence. As for $q=(u\sim d,s)$, we have the following values in NL$\chi$QM:
\begin{equation}
\label{eq:QCV}
\Sigma_{u,d}\equiv \Sigma=(251.31\,\mathrm{MeV})^3,
\,\,\,\,\,\,\,\,
\Sigma_s=(242.93\,\mathrm{MeV})^3.
\end{equation}
The ratio of those values $R=\Sigma/\Sigma_s$ is about $0.91$ locating inside other empirical and theoretical estimations $(0.75\sim1.05)$~\cite{Nam:2006ng}. The PS-meson masses can be expressed by the combination of the quark condensate, current quark mass, and pion weak decay constant via $\chi$PT in the large $N_c$ limit as follows~\cite{Evans:1996kf}:
\begin{equation}
\label{eq:GOR}
m^2_\pi =\frac{2m\Sigma}{F^2_\pi},\,\,\,\,
m^2_K =\frac{m\Sigma+m_s\Sigma_s}{F^2_\pi},\,\,\,\,
m^2_\eta=\frac{2}{3}\frac{(m\Sigma+2m_s\Sigma_s)}{ F^2_\pi}.
\end{equation}
Using the numerical values of the condensates and weak-decay constants within the present model as shown above, we obtain the followings:
\begin{eqnarray}
\label{eq:MASS}
\mathrm{NL}\chi\mathrm{QM}&:&
m_\pi=138.43\,\mathrm{MeV},\,\,\,
m_K=493.16\,\mathrm{MeV},\,\,\,
m_\eta=563.82\,\mathrm{MeV},\,\,\,
m_{\eta'}=954.76\,\mathrm{MeV},
\cr
\mathrm{Experiment}&:&
m_\pi=138.04\,\mathrm{MeV},\,\,\,
m_K=495.67\,\mathrm{MeV},\,\,\,
m_\eta=547.86\,\mathrm{MeV},\,\,\,
m_{\eta'}=957.78\,\mathrm{MeV}.
\end{eqnarray}
Note that the value of $m_{\eta'}$ is determined by equating Eqs.~(\ref{eq:CHPT}) and (\ref{eq:TST}).
From Eq.~(\ref{eq:TST}) the value of $\chi_{t}$ depends on the value of $m_{\eta'}$, however, the values of $\chi_t$ and
$m_{\eta'}$ is also related by  Eqs.~(\ref{eq:CHPT}) such that we can determine $m_{\eta'}$ in NL$\chi$QM. It is worth mentioning that various quantities, such as the PS-meson mass, the weak decay constant, and the quark condensate, are all reproduced well within the model with only two free parameters ($\bar{\rho}$ and $\bar{R}$). All the relevant parameters and inputs of our numerical calculation of the topological susceptibility are summarized in Table~\ref{TABLE2}.
\begin{table}[h]
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
$1/\bar{\rho}$
&$\sqrt[4]{N/V}$
&$\hspace{0.4cm}M_0\hspace{0.4cm}$
&$m_{u,d}\equiv m$
&$\hspace{0.4cm}m_s\hspace{0.4cm}$
&$M_{u,d}\equiv M$
&$\hspace{0.4cm}M_s\hspace{0.4cm}$
&$\hspace{0.4cm}m_\eta\hspace{0.4cm}$
&$\hspace{0.4cm}m_{\eta'}\hspace{0.4cm}$
&$\hspace{0.4cm}F_\eta\hspace{0.4cm}$
&$\hspace{0.4cm}F_{\eta'}\hspace{0.4cm}$\\
\hline
$591$&$197$&$341$&$5$&$135$&$346$
&$476$&$563.82$&$954.76$&$96.77$&$102.53$\\
\hline
\end{tabular}
\caption{Model parameters and theoretical inputs [MeV] in the present calculations.}
\label{TABLE2}
\end{table}

Using Eq.~(\ref{eq:TST}) and all the parameters discussed above, we present our main results for the full, Witten-Veneziano (WV), and Leutwyler-Smilga (LS) formulae with physical input values as follows:
\begin{equation}
\label{eq:FTS}
\chi_{t}=(165.57\,\mathrm{MeV})^4,
\,\,\,\,\chi^\mathrm{WV}_t=(194.30\,\mathrm{MeV})^4,
\,\,\,\,\chi^\mathrm{LS}_t=(162.54\,\mathrm{MeV})^4.
\end{equation}
$\chi^\mathrm{WV}_t=\chi^\mathrm{QL}_t$ since the WV formula is derived in the large $N_{c}$ limit and the dynamical quark contribution is neglected. Although we are able to make our values of $\chi_t$ to be closer to the empirical one by adjusting the free parameters, we prefer to not to do so since it does not tell much for relevant physics. Our estimation is about $10\%$ smaller than the empirical value $\chi_t=(175\pm5\,\mathrm{MeV})^4$. Furthermore, we observe that $\chi_{t}<\chi^\mathrm{QL}_t$ in general in according to Eq.~(\ref{eq:FTS}). It means that the dynamical quark contributions reduce the topological susceptibility by $(10\sim20)\,\%$ within NL$\chi$QM.

Finally, we would like to make comparison between our results and other theoretical estimations on $\chi_t$. In Ref.~\cite{Fukushima:2001hr},  $\chi_t$
was computed by using the NJL model with the standard parameter sets with the additional ring diagrams contribution in terms of the mean-field approach.
They found that $\chi_t=(166\,\mathrm{MeV})^4$ with $m_\eta=487$ MeV. This value is very close to our full and LS values.
Furthermore, this result can be improved by taking into account that the standard parameter set for determining $m_{\eta'}$ is not suitable
for computing $\chi_t$ due to the lack of confinement in the NJL model.

There are many lattice computations of the topological susceptibility, and it is interesting to compare those results with ours.
The LQCD simulation of the CP-PACS collaboration~\cite{AliKhan:1999zi,AliKhan:1999zp} gives $m_\eta\approx863$ MeV
and $\chi_t=(178(9)\,\mathrm{MeV})^4$
in the continuum limit.
This simulation is the two-flavor full QCD configuration with the improved actions, i.e. a tree-level Symanzik-improved and the RG improved Iwasaki actions.
The UKQCD collaboration performed the LQCD simulations, in which the color $\mathrm{SU}(3)$ Wilson-gauge action is coupled to clover improved Wilson fermions. They computed $\chi_t$ in $N_f=2$~\cite{Hart:2000wr,Hart:2000gh}, and obtained $\chi_t=(177\,\mathrm{MeV})^4$.
Those results are substantially larger than ours, however, it may relate to the fact that their dynamical quarks are only two flavors.

The LQCD simulation by the SESAM and T$\chi$L collaborations with two flavors of dynamical Wilson fermions have also been carried out. They gave $\chi_t\approx(183\,\mathrm{MeV})^4$ for a certain lattice set, whereas $\chi^\mathrm{QL}_t\approx(199\,\mathrm{MeV})^4$ for the quenched case~\cite{Bali:2001gk}. Note that the hierarchy between the full and the quenched results is similar to our observation $\chi_{t}<\chi^\mathrm{QL}_t$. In Ref.~\cite{Grunberg:1984pa}, using the QCD sum rue (QCDSR) with the help of the flavor $\mathrm{SU}(2)$ LQCD data for the gluon condensate, it gave $\chi_t\approx(180\,\mathrm{MeV})^4$ employing the renormalization scale $\Lambda_{\overline{\mathrm{MS}}}=175$ MeV.  In Ref.~\cite{Chiu:2008jq}, via LQCD simulation using $(2+1)$-flavors of domain-wall fermions, the authors estimate $\chi_t=(153\sim187\,\mathrm{MeV})^4$, depending on the quark mass. The comparison between our result and the other theoretical estimations are listed in Table~\ref{TABLE4}.

\begin{table}[h]
\begin{tabular}{|c||c|c|c|c|c|c|c|c|c|}
\hline
&NL$\chi$QM&NJL~\cite{Fukushima:2001hr}&LQCD~\cite{DelDebbio:2004ns}&LQCD~\cite{Hart:2000wr,Hart:2000gh}&LQCD~\cite{Bali:2001gk}&LQCD~\cite{Aoki:2000kp}&LQCD~\cite{AliKhan:1999zi,AliKhan:1999zp}&LQCD~\cite{Chiu:2008jq}&QCDSR~\cite{Grunberg:1984pa}\\
\hline
$\sqrt[4]{\chi_t}$&$165.57\,(194.30_\mathrm{QL})$&$166$&$191\pm5$&$177$
&$183\,(199_\mathrm{QL})$&$174$&$178(9)$&$153\sim187$&$180$\\
\hline
\end{tabular}
\caption{Topological susceptibility $\sqrt[4]{\chi_t}$ [MeV] from various theoretical estimations.}
\label{TABLE4}
\end{table}

From all the comparisons, our main results are comparable to the $N_f=2$ and $(2+1)$ LQCD data, showing some deviations. As expected, approaches based on QCD, such as the NJL model and QCDSR, provide similar values to ours with below $10\%$ differences.

\section{Conclusion and outlooks}
We have studied the QCD topological susceptibility $\chi_t$ by employing the nonlocal chiral quark model (NL$\chi$QM). This model is based on the liquid-instanton model of the QCD-vacuum configuration. Various nonperturbative quantities, such as the PS-meson masses, the weak decay constants, and the quark condensates, are well reproduced within this model with only two free parameters ($\bar{\rho}$ and $\bar{R}$) in principle. We then derived a concise expression of the topological charge-density operator from NL$\chi$QM with the determinant manifesting the $\mathrm{U_A}(1)$ anomaly. The value of $\chi_t$ was computed by using the correlation functions of the topological-charge density operator.

We find that such an effective model gives correct expressions for the Witten-Veneziano (WV) and Leutwyler-Smilga (LS) formulae for $\chi_t$. Moreover, The {\it ring} diagrams appearing in the generic NJL model in terms of the mean-field approach, are naturally emerged as the PS-meson propagations in NL$\chi$QM. Furthermore, we obtain  $\chi_{t}=(165.57\,\mathrm{MeV})^4$, $\chi^\mathrm{WV}_t=(194.30\,\mathrm{MeV})^4$, and $\chi^\mathrm{LS}_t=(162.54\,\mathrm{MeV})^4$, which are comparable with the other theoretical estimations. Note that, phenomenologically, it is $\chi_{t}=(175\pm5\,\mathrm{MeV})^4$. We also figure out that there is a tendency that $\chi_{t}<\chi^\mathrm{QL}_t$, showing the $(10\sim20)\,\%$ decrease with the dynamical-quark contributions in comparison to the QL cases. A similar tendency is also found in a full-LQCD simulation.

We note that topological susceptibility  $\chi_t$ is deeply related to the axion potential as a function of temperature ($T$)~\cite{Borsanyi:2015cka}. Moreover, $\chi_t$ reveals rich information on the QCD phase diagram as an order parameter of $\mathrm{U_A}(1)$ symmetry and its relation with
S$\chi$SB is also studied~\cite{Jiang:2015xqz}. As already explored in our previous works~\cite{Nam:2011vn,Nam:2013fpa}, the present model has provided successful descriptions for various QCD properties at finite $T$ as well as quark chemical potential $\mu_q$. It is based on the instanton QCD-vacuum configuration which is responsible for the nontrivial mechanisms of S$\chi$SB and its (partial) restoration. Hence, we expect that the careful studies on $\chi_t$ in medium within the current theoretical framework will shed light on understanding of the strongly-interacting systems at finite $T$ and/or $\mu_q$. Related works are under progress and will appear elsewhere.
\section*{Acknowledgements}
S.~i.~N. is grateful to the hospitality for his stay at National Taiwan University (NTU), where the present work was performed partially, with the financial supports from NSC102-2112-M-033-005-MY3 from Ministry of Science and Technology (MOST) of Taiwan. His work is also in part supported by the NRF grant funded by MEST (Center for Korean J-PARC Users, Grant No. NRF-2013K1A3A7A06056592). He also appreciates the fruitful discussions with K.~H.~Woo.
C.~W.~K. is supported by NSC102-2112-M-033-005-MY3 from Ministry of Science and Technology (MOST) of Taiwan.

redpajama_set_name: RedPajamaArXiv


text:
Dusit Thani Laguna | Mercurio Design Lab S.r.l. | World Design Awards 2021
Mercurio Design Lab S.r.l.: Winner of World Design Awards 2021. Dusit Thani Laguna, formerly known as Laguna National Golf and Country Club—one of the prominent golf and country clubs in Singapore since its inauguration in 1993—is a premier urban golf resort integrated with a five-star luxury hotel. A renowned golf destination that hosts international tournaments and major championships, the state-of-the-art union of a world-class golf club and a Dusit-Thani branded hotel introduces a new set of social and recreational privileges for golf members and hotel patrons.
The property features an American-designed course regarded as more than normally difficult with no less than four lakes, undulations which often make the course resembles a green moonscape, and clusters of sculpted sand bunkers lying in wait for even the most experienced golfer. It was this charged image that inspired Mercurio Design Lab's design for the hotel and existing clubhouse.
Inspired by the gentle undulation of the golf course, the sleek, curvilinear form of Dusit Thani Laguna soars over a six-story hotel and three-story redesigned clubhouse. It thrusts up out of the landscape itself, sweeping up from the ground to create a shelter for the hotel before surging on to cover the existing clubhouse, splaying out in the middle to provide an entrance canopy on one side and the frame for the all-day dining room and ballroom/ banquet room on the other. The roof which makes the architecture does not just enclose the structure but becomes the body.
The swooping image—an overarching roof and a shared glazed facade— although ostensibly edgy, blends smoothly with the scenery. The awkward marriage and the discrepancy in heights of the two functions are disguised by a single and unified roof, shaped to complement the surging landscape of the resort. The architecture then appears less violent to the natural surrounding as it looks like it is one with the golf course.
From the golf course, the left side of the building houses the hotel with standard rooms and a group of penthouses with private terraces. On the same side lies a gorgeous pool that spans the entire length of the hotel. At the right side of the building is the clubhouse, where players can relax after a round of golf. The center area holds the golf club lobby, the all-day dining, and the ballroom and acts as a central volume. It kind of separates the two, the hotel and clubhouse, but also serves as a link emphasizing Dusit Thani Laguna as the perfect space for sports and recreation, catering to golfers and leisure-seekers alike.
In the context of design, there was not much technical difficulty in accomplishing the project, except for the roof's unusual form that becomes the main challenge. After extensive technology research, the roofing, built of cementitious fiberboards and a marine-grade membrane, displays a seamless surface with no visible joints. The structure then stands formidably with sleekness, seen from the outside to the inside, presenting a unique aesthetic character that commands anyone's utmost attention. An optimal visual effect is achieved both from afar and from a closer look from whatever angle it is viewed and takes a life of its own, encompassing the club and hotel functions under one dominant, exciting sculptural form, complementing the gorgeous natural scenery.
Overall, the project faced some roadblocks during construction, but as it now stands beautiful on the golf course as one of the most remarkable buildings in Singapore is well worth the effort.
Mercurio Design Lab S.r.l.
Dusit Thani Laguna
Massimo Mercurio
Hospitality Built
Kimberly Liu
©Mercurio Design Lab S.r.l.
Mercurio Design Lab S.r.l. (MDL) is an award-winning Italian design studio that creates avant-garde concepts inspired by the vibrancy of Asia. The team is composed of passionate architects, engineers, designers and artists who integrate art with technology in their design process, while respecting the three fundamental criteria: the functional, the aesthetic and the social.
With an Italian spirit and rich cultural heritage that originated in Rome for more than 50 years, MDL creates new milestones and commit with great passion to bring ideas and solutions into the fields of Architecture, Interior Design and Industrial Design.
Fengxian Kindergarten Of Shanghai | ANTAO | World Design Awards 2021
GROW | Studio Roosegaarde | World Design Awards 2021

redpajama_set_name: RedPajamaCommonCrawl


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In fact, the report, titled "Country Reports on Terrorism 2016", complains, of late, US investigators have had "limited success in coordinating the seizure of illicit proceeds with Indian counterparts", which was not the case in the past.
"The degree of training and expertise in financial investigations involving transnational crime or terrorism-affiliated groups varied widely among the federal, state, and local levels and depended on the financial resources and individual policies of various jurisdictions", the report says.


text:
Q: How XSLT Templates Rules are applied Let's say I have following XML:
XML
<bookstore>
<book category="cooking">
    <title lang="en">Everyday Italian</title>
    <author>Giada De Laurentiis</author>
    <year>2005</year>
    <price>30.00</price>
</book>
<book category="children">
    <title lang="en">Harry Potter</title>
    <author>J K. Rowling</author>
    <year>2005</year>
    <price>29.99</price>
</book>
<book category="web">
    <title lang="en">XQuery Kick Start</title>
    <author>James McGovern</author>
    <author>Per Bothner</author>
    <author>Kurt Cagle</author>
    <author>James Linn</author>
    <author>Vaidyanathan Nagarajan</author>
    <year>2003</year>
    <price>49.99</price>
</book>
<book category="web" cover="paperback">
    <title lang="en">Learning XML</title>
    <author>Erik T. Ray</author>
    <year>2003</year>
    <price>39.95</price>
</book>

and following XSLT:
XSLT
    <?xml version="1.0" encoding="utf-8"?>
<xsl:stylesheet version="2.0"
                xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
                xmlns:fo="http://www.w3.org/1999/XSL/Format"
                xmlns:xs="http://www.w3.org/2001/XMLSchema"
                xmlns:fn="http://www.w3.org/2005/xpath-functions"
                xmlns:msxsl="urn:schemas-microsoft-com:xslt"
                exclude-result-prefixes="fo xs fn msxsl">

  <xsl:output method="xml" indent="yes" />

  <xsl:template match="/">
    <xsl:element name="rootnode">
      <xsl:choose>
        <xsl:when test="//bookstore/book[year!=2005]">
          <xsl:message select="'book exists'" />
          <xsl:apply-templates></xsl:apply-templates>
        </xsl:when>
      </xsl:choose>
    </xsl:element>
  </xsl:template>

  <xsl:template match="book[year!=2005]">
    <xsl:element name="not2005">
      <xsl:copy-of select="." />
    </xsl:element>
    <!--<xsl:apply-templates select="@* | node()" />-->
  </xsl:template>
</xsl:stylesheet>

Once transformed xml looks like this:
Result
<?xml version="1.0" encoding="UTF-8"?>
<rootnode>Everyday ItalianGiada De Laurentiis200530.00Harry PotterJ K. Rowling200529.99<not2005>
        <book category="web">
            <title lang="en">XQuery Kick Start</title>
            <author>James McGovern</author>
            <author>Per Bothner</author>
            <author>Kurt Cagle</author>
            <author>James Linn</author>
            <author>Vaidyanathan Nagarajan</author>
            <year>2003</year>
            <price>49.99</price>
        </book>
    </not2005>
    <not2005>
        <book category="web" cover="paperback">
            <title lang="en">Learning XML</title>
            <author>Erik T. Ray</author>
            <year>2003</year>
            <price>39.95</price>
        </book>
    </not2005>
</rootnode>

instead of what I'm expecting:
Expected result
<?xml version="1.0" encoding="UTF-8"?>
<rootnode>
    <not2005>
        <book category="web">
            <title lang="en">XQuery Kick Start</title>
            <author>James McGovern</author>
            <author>Per Bothner</author>
            <author>Kurt Cagle</author>
            <author>James Linn</author>
            <author>Vaidyanathan Nagarajan</author>
            <year>2003</year>
            <price>49.99</price>
        </book>
    </not2005>
    <not2005>
        <book category="web" cover="paperback">
            <title lang="en">Learning XML</title>
            <author>Erik T. Ray</author>
            <year>2003</year>
            <price>39.95</price>
        </book>
    </not2005>
</rootnode>

Why following is transformed/picked up?

Everyday ItalianGiada De Laurentiis200530.00Harry PotterJ K.
  Rowling200529.99

and also curious why my xsl:message is not popping up as well?
<xsl:message select="'book exists'" />

Any article pointers explaining fundamental concept that I'm obviously missing would be appreciated...

A: Change
  <xsl:choose>
    <xsl:when test="//bookstore/book[year!=2005]">
      <xsl:message select="'book exists'" />
      <xsl:apply-templates></xsl:apply-templates>
    </xsl:when>
  </xsl:choose>

to
<xsl:apply-templates select="bookstore/book[year != 2005]"/>

Your current code only works as you rely on built-in templates https://www.w3.org/TR/xslt20/#built-in-rule but they have the effect of outputting any text nodes of elements you don't explicitly match.

redpajama_set_name: RedPajamaStackExchange


For many visitors, the Tuscan countryside becomes their treasured memory – green hills, silvery olive groves, pastoral views punctuated by cypress trees, villas, vineyards and church spires on the hill. The Chianti region between Siena and Florence is famous for the delicious wines and products that are coaxed from its soil, almost all of them from small properties sustainably farmed. Today is your day to savor, swirl, taste, laugh, explore and relax. Visit two charming medieval villages where tourists are few but pleasures are many. Stop in one of the most famous wineries in Chianti and taste a selection of wines accompanied by local products.


Locally based Nationwide Real Estate Investment Biz Seeking Sharp Mind! We are looking for a responsible person with Sales Experience to become a Team Member of our fast growing Nationwide Real Estate Investing Business.
Could you email me the info please?
I have 4 Duplexes. 100% occupied. Would you be interested?
I would like to be on your buyers list.


Bug Fabric, an online fabric shop based in Redmond, Washington, was born of a love for fabric and quilting. We pride ourselves in offering an outstanding selection of high quality fabrics to accommodate your sewing, quilting and home decor needs. We strive to maintain an updated site, as well as an inventory of the most recent fabrics the market has to offer.
I'm a busy wife and mother, as well as being Bug Fabric's head buyer, bookkeeper, internet guru and advertiser, I so appreciate the ladies on my passionate staff...they work hard to make sure your orders are processed with care and shipped in a timely and efficient manner. What can I say? We have a great team of women here at Bug Fabric!
One of our goals is to provide you with competitively priced fabrics, without sacrificing quality. We strive to ship orders promptly so you can start working on your next project as soon as possible. We go the extra mile to provide you with exceptional customer service and hope you'll return and shop with us often.


Congratulations to all lodge charity stewards, fund raisers and brethren of Staffordshire.
and presented a cheque for that amount to the President of the Grand Charity R.W.Bro.Richard Hone QC.
Approximately 500 members and their guests attended the dinner and witnessed the occasion. Photographs of the event are available to view and download by following the link below.


The Michigan Federation of Music Clubs.
Promote the appreciation and understanding of the value of music in the home, the community, the nation, and the world.
We are an organization of music enthusiasts; professional artists and educators; collegiate chapters; student and junior performers; and composers.


The Country Living Spring Fair is at the Business Design Centre, Islington, London N1 from 20-24 March.
This popular fair attracts visitors from across London and the Home Counties and further afield with exhibitors from throughout the UK. Exhibitors are generally unique and unusual small businesses presenting artisan products, wherever possible representing the best of British design and creativity. In addition to the home and fashion accessories, there are theatres and workshops that focus on art and craft, features on interior design and expert advice about nature and country pursuits. Visit www.countrylivingfair.com for more information.
Popular Patchwork and The Country Living Spring Fair have three pairs of tickets to giveaway – a pair of tickets is worth £32. Just enter online to be with a chance to win.


text:
Ольвійська хора  — являла собою сільськогосподарську околицю Ольвії, і структурно була частиною неї.
Від часу заснування Ольвії в 647—646 р. до н. е. поступово навколо Ольвії сформується її хора. Виникла досить велика кількість маленьких сільських поселень, які спеціалізувалися на полюванні, землеробстві, рибальстві, тваринництві, на ремеслі. Культура і побут в цих поселеннях не відрізнялися від культури і побуту ольвіополітів, оскільки це були такі ж переселенці з міст Греції, що і жителі Ольвії. Враховуючи сільськогосподарську спрямованість економіки, Ольвія, як і багато інших грецьких колоній, мала сільськогосподарську округу що називалася хора, поселення якої були розмішені достатньо вузькою смугою, до 5–7 км, по узбережжю Березанського і Буго-Дніпровського лиманів.

Динаміка освоєння регіону мала таку історію на початку VI ст. до н.е. на Кінбурнському півострові, на лівому березі одного із рукавів Дніпровської дельти засновується Ягорлицьке ремісниче поселення. Іноді його помилково включають до ольвійської хори, але насправді воно було сезонним торжищем і ремісничим осередоком, де працювали вихідці з фракійського регіону, Середнього Подніпров'я, Північного Кавказу і навіть з віддалених східних територій. Про це свідчить дуже широкий типологічний спектр мідних та бронзових предметів, які виготовлялись в майстернях Ягорлицького поселення.

До середини VI ст. до н.е. освоюється і лівий берег Березанського лиману, в наступні десятиліття античні поселення з'являються на правому березі Буго-Дніпровського лиману. У другій половині цього століття ланцюжок античних поселень досягає широти сучасного Миколаєва і в цей же час освоюється лівий берег Бузького лиману. Ці поселення мали вигляд невеликих хуторків землянкової забудови, в яких мешкала одна родина з 5–7 чоловік.

Кінець VI — перша чверть V ст. — час стабільного існування поселень Ольвійської хори, але вже в кінці першої третини V ст. до н.е. населення сконцентровано в Ольвії і на Березані, а сільська округа скорочується до розмірів невеликого приміського району. На межі V–IV ст. до н.е. починається заснування нових сільськогосподарських поселень, але це вже урбанізовані селища з кам'яним будівництвом на місцях колишніх архаїчних поселень, або нові. Вони проіснували до останньої третини IV ст., тобто до облоги Ольвії військами Зопіріона.

Говорячи про населення хори архаїчної доби, більшість якого становили греки, треба відзначити свідчення Геродота, про калліпідів або елліно-скіфів, що, як з'ясовано завдяки останнім дослідженням, мешкали в районі Аджигольської балки. Це були варвари, які вели осілий спосіб життя і зазнали сильного культурного впливу з боку еллінів, але продовжували займатись, переважно, відгінним скотарством, в той час, коли на решті поселень греки займались землеробством.

Наступний етап в історії хори — остання третина IV — перша чверть III ст. до н.е. Її територія досягла максимальних розмірів — це було результатом економічного піднесення ольвійської держави. З'являються поселення на нових місцях — у верхів'ях Березанського і на правому березі Дніпровського лиманів, на Кінбурнській косі. На півночі, як і в архаїчний час, межі хори сягали широти сучасного Миколаєва. Змінюється і тип поселень, збільшується їхня площа, відтоді вони являли собою окремі садиби з товстими стінами, що було викликано вимогами безпеки поселень. З другої чверті III ст. до н.е. територія ольвійської хори контролюється місцевими племенами. Останнім часом уточнена дата загибелі хори Ольвії  - близько  215  р. до н. е. (а не 250 р. до н. е.).  Під натиском скіро-галатських племен в цей час разом із нижньобузькими гинуть гетські поселення на правому березі Дністра і на лівому березі Дніпра. Ольвійська хора після 215 р. до н. е. обмежена лише тільки територією лівого берега Бузького лиману. Події військово-політичної та економічної кризи в середині ІІ ст. до н.е. завершуються розгромом Ольвії в середині І ст. до н.е. царем гетів Берібістою. Ольвіополіти протягом цілого століття займались землеробством виключно поблизу міських стін, принаймні ніяких слідів сільських поселень того періоду біля Ольвії наразі не виявлено.

В І ст. до н.е. — І ст. н.е. сільськогосподарське освоєння  регіону почалось спочатку. Серйозна загроза від сарматських племен примусила Ольвію посилювати свою обороноздатність, тому поселення Ольвійської хори тоді складали єдину систему укріплених пунктів-фортець, розташованих у зоні прямого бачення одна від одної. Не дивлячись на певні проблеми, Ольвія і її хора в цей час переживає певне піднесення. Значних військових зіткнень тут не відбувалось, але, разом із перебуванням в Ольвії римського гарнізону, в урочищі Дідова Хата виявлено римський тимчасовий табір.

В середині ІІ століття простежується певна дестабілізація життя Ольвійської хори, що було викликано нападами тавро-скіфів на територію Ольвійської хори. На більшості приольвійських укріплень дослідженнями зафіксовано сліди пожеж. Але римські підрозділи, надіслані Антонієм Пієм на допомогу ольвіополітам захистили Ольвію і життя в хорі знову стабілізується. У другій половині ІІ — на початку ІІІ ст. життя городищ досягає найвищого розквіту і на території ольвійської держави з'являються неукріплені поселення черняхівського типу. Але з середини ІІІ ст. починається занепад економіки, пов'язаний із просуванням готських племен. Врешті в цей період Ольвія і сільські поселення її хори припиняють своє існування.

У 2018 р. під час розкопок поселення Ольвійської хори, біля села Дніпровське Білозерського району Херсонської області, вперше виявила тут святилище (теменос)

Див. також
 Хора
 Скелька

Посилання

Ольвія

redpajama_set_name: RedPajamaWikipedia


Unemployment in the Netherlands will grow again this year, but much more slowly than in previous years, according to the labour market forecast from Dutch social security agency UWV.
While economic figures show that the Dutch economy is improving, the labour market is not yet benefiting from the recovery.
The UWV forecasts that 66.000 jobs will disappear in 2014: a large number, but much smaller than the 143.000 jobs that were lost in 2013. Last year's figure, a record high for unemployment numbers, was due in part to tens of thousands of job losses in the government and healthcare sectors.
The continued job losses in 2014 will be partly offset, however, by a further increase in the numbers of self-employed people. The UWV expects that there will be 32.000 more self-employed workers in 2014, following on from the larger increase of 54.000 in 2013.
The only areas of clear employment growth are in temporary employment bureaus, freelancers and wholesale trade.
Rob Witjes, head of labour market information for UWV, said that because the crisis has lasted so long, it may take even longer for the labour market to recover, as employers are cautious about taking on new staff.
An economic improvement of 0,5 per cent is fragile, he said, and most companies are still in a "reset" phase, examining how they can operate more intelligently, rather than expand their staff. "Digitisation continues and everything is focused on cost control," Witjes said.
One example of this is industry, which despite benefiting from the upturn in world trade, will still shed 8.000 jobs this year due to investments in labour-saving techniques, undertaken in order to remain competitive with other countries.
Another is the construction sector, which while it is expected to recover slightly due in part to lower house prices and mortgage rates in the Netherlands, will only seen a slow-down in job losses.
The sharp contraction in public sector employment continues in 2014, as half of the total 66.000 jobs expected to go are in government.
The large losses in the healthcare sector last year will continue this year, thanks to new legislation on funding long-term healthcare that will cut jobs in elderly and home care.
UWV did have some good news, however: there are still opportunities this year in the labour market. The slight revival in the economy meant that the numbers of jobs increased by 80.000 to a total of nearly 700.000.
While that number is far below the record one million jobs before the crisis, it does mean that there will definitely be more movement in the labour market this year, which makes 2014 a good time to start at least looking for a new job in the Netherlands, just in case.


NEW YORK, July 9 (Reuters) - My kids got a great report from the dentist at their last checkup. From the receptionist? Not so much.
When I went to make an appointment for their next cleaning in six months, she shocked me by saying I owed nearly $3,000 in charges dating back to 2014.
"We have a payment plan," she said, trying to be helpful.
I needed information instead, and immediately concluded that plunking down my credit card was the wrong way to go.
Old medical bills plague many Americans, harming their credit scores and holding them hostage to collection agencies. They make up more than half of all collections items noted on credit reports, said Chi Chi Wu, an attorney with the National Consumer Law Center.
Contact the insurance company first to make sure the charges are legit. Ask for a supervisor to escalate your case.
If that fails, ask your employer's human resources department to step in. If that is not an option, search for independent medical billing advocates near you or nationwide services like CoPatient.com. Some charge flat fees, but most work on contingency for a percentage of the amount they save you.
Sunni Patterson, co-founder of Medical Bill & Claim Resolution, an nationwide advocacy company based in Illinois, said it sometimes works best when one of her advocates is on a three-way call with the patient and the insurance company.
In my case, the dentist had no record of being paid for a slew of cavity fillings in 2014. As is pretty standard, I had signed an agreement that I was legally responsible for those bills.
When I tried to negotiate with the dentist's office, it would not budge on the balance due.
But I kept calling back to talk to billing to keep the dialogue going.
"Providers are a bit more sensitive to not losing you as a customer and maintaining their reputations," said Wu.
And they can negotiate if they want to, said Adria Gross, chief executive of MedWise Insurance Advocacy, based in Monroe, New York. She has negotiated medical bills down from $1 million. One bill of $257,000 ended up being only $7,000 by the end.
What works best is evidence. I spent a couple of hours on the phone with Aetna, and they found receipts that showed the dentist had cashed checks for a large part of the balance. Negotiating leverage achieved.
One way to combat this: Check your credit report every year, which is free (www.annualcreditreport.com), said Greg McBride, chief financial analyst for Bankrate.com.
The stakes can be high - even a paid collection stays on your credit report for up to seven years, although it will have a diminished effect on your credit score over time.
A new law prevents medical debt from landing on your credit report for 180 days, giving you time to sort it out. New credit score models do not even count medical collections, said McBride, but they are not yet in wide use.
To dispute an old bill in collection, pursue multiple avenues at once, said Gerri Detweiler, education director for Nav.com.
First file a dispute with the three main credit bureaus - TransUnion, Equifax and Experian. Next, go to the collections agent. If you can work out a payment, ask the agent to recall the notice (and get this in writing) before you pay so that it is wiped from your credit history.
"Technically, their agreements say no pay-for-removal deals, but it is worth making part of the conversation," said Detweiler.
Finally, go to the government to lodge a complaint - either your state's attorney general or insurance commissioner, or to the federal Consumer Finance Protection Bureau (www.consumerfinance.gov/complaint/).


There are practically hundreds of hospitality business indicators that you can use ideal now. These indicators are normally identified as the hotel administration KPI. When you have an successful KPI set for your hotel business, this eliminates the guesswork when it will come to controlling the hotel business. What this does is that it checks the performance of your business by means of the numbers or the figures so that the professionals will be in a position to use the information in telling what is definitely gong on within just the hotel. Prior to you get close to and investigation about the hotel administration KPI, you ought to know the big difference amongst that and the hotel KRIs. These two are frequently as opposed to each other but they are fairly varied. The hotel KRIs do not emphasis on the excellent facet of the performance of the corporation alternatively, you will get information about how dangerous your hotel routines are. Possessing explained that, they are also really beneficial when it will come to monitoring the health of your business.
Now, when wanting for the finest hotel administration KPI for your business, you ought to not only emphasis on the full organization due to the fact it would be really hard to do so. You will need to have to divide the KPIs into distinctive groups or classifications so that it will be much easier for you to retain observe of them. Among the the varieties of KPIs that you can benefit from are the KPIs for reception or entrance desk effectiveness, housekeeping, kitchen, gross sales, restaurant, keep, servicing and paying for amid others.
A lot of motels these days provide housekeeping solutions for their consumers. If the hotel that you are controlling supplies this sort of to your company, it is vital that you retain observe of its performance. This is due to the fact several consumers are meticulous when it will come to the cleanliness of their surroundings primarily their rooms. They are on a vacation so they be expecting them selves to be pampered and not to be liable for the task of cleansing their rooms. You can evaluate the effectiveness of your housekeeping solutions by means of KPIs this sort of as the amount of obtainable staff customers for cleansing, the responses of shoppers based mostly upon the housekeeping solutions they have acquired and the total volume of time demanded for cleansing amid others.
Of training course, you can not deny the simple fact that it is vital for you to know how well your business is responding when it will come to the gross sales department. Hard cash movement is really considerable primarily in this form of business. Your hospitality business indicators may possibly differ listed here in accordance to the distinctive gross sales initiatives that you set out. For occasion, if you have a web page, you can verify the amount or the share of inquiries that have turned into gross sales. You can also use KPIs that will convey to you about the amount of gross sales per head on your restaurant or your bar. You can also evaluate the gross financial gain on gross sales, the stock turnover, the carrying charge of the stock and the stock worth.
Apart from the financials and the purchaser gross sales, it is vital that you are well informed of how your staff members are accomplishing. Constantly guarantee that you have a set of excellent hotel administration KPI that will aid you in monitoring the behavior, the professionalism and the demeanor of your staff.


In the RV I knew where everything was....I spend a lot of time looking for a can of what not, or the gadget someone has stashed in a new drawer. I, also, have a lot of willing helpers to put away groceries....but I want to be able to quickly FIND things....and so Stacia and I spent a day with the label maker.
I need to finish the cupboards and move on to the pantry. I ran out of energy!


text:
Q: create recursive power of 2 '*' in python In pyschools, I am stuck in the power of 2 recursive function

    >>> createStars(0)      # 2 to power of 0 = 1
    '*'
    >>> createStars(1)      # 2 to power of 1 = 2
    '**'
    >>> createStars(2)      # 2 to power of 2 = 4
    '****'
    >>> createStars(3)      # 2 to power of 3 = 8
    '********'

What I am trying to do is as following:

def createStars(x):
    if x == 0:
        return '*'
    else:
        return '*' * x + createStars(x-1)

However, this seems to be a summation of 'x' not power of 2.
Meaning, this will break when the x is higher than 2
I know how to do the power of 2 recursively but no idea where to change to make createStars() work.

def power(x, n):
    if n == 0:
        return 1
    else:
        return x * power(x, n-1)

PS. I know it is easy to use non-recursive method to solve it.
    But would like to seek advice how to do it in recursive way.
Thanks.

A: def createStars(x):
    if x == 0:
        return '*'
    else:
        return createStars(x-1) * 2

(Each step back in the recursion doubles the number of stars in the output string).

A: You're very close!
I would suggest comparing the two pieces of code you gave us. (I'm going to rename it a bit to make the analogy more clear):
def createStars(n):
    if n == 0:
        return '*'
    else:
        return '*' * n + createStars(n-1)

def power(x, n):
    if n == 0:
        return 1
    else:
        return x * power(x, n-1)

They have almost exactly the same structure. In particular, the last line of each has a slightly different structure.
In the (working) power, you multiply the result for n-1 by x. So, when computing the power(2, 6), you increase power(2, 5) by 2. (i.e. you multiply 32 by 2 to get 64).
In the (not working) createStars, you're not multiplying the result for the n-1 case by anything; you're just adding stuff to the start of it. What if you change it to make the structures match?
Also, you should check what the result is for createStars(1).


We would like to belive that at least some of the amazing pictures we find on the internet haven't been photoshopped. It would be nice to know the lighting, colors or shapes are there for real, and the world is naturally beautiful. Have you ever had this feeling that seeing something with your own eyes leaves you a little bit disapointed? We've been spoiled by a phony perfection around us, not noticing that flaws are actually the best part.
These pictures were believed to be legit just to prove they're a Photoshop creation.
Next story Figure Skaters And Their Faces!


text:
Intel Breaks Ground on Two Ohio Chip Manufacturing Sites
Sept. 9, 2022 — Today, President Joe Biden joins Intel, Ohio Gov. Mike DeWine and other federal, state and local officials to celebrate breaking ground in the Silicon Heartland on two of the world's most advanced chipmaking facilities. As part of Intel's commitment to develop a skilled talent pipeline for its two new leading-edge chip fabs, Intel also announced the first phase of funding for its Ohio Semiconductor Education and Research Program. During this first phase, Intel is providing $17.7 million for eight proposals from leading institutions and collaborators in Ohio to develop semiconductor-focused education and workforce programs.
"Today marks a pivotal moment in the journey to build a more geographically balanced and resilient semiconductor supply chain. The establishment of the Silicon Heartland is testament to the power of government incentives to unlock private investment, create thousands of high-paying jobs, and benefit U.S. economic and national security. We would not be here today without the support of leaders in the administration, Congress and the state of Ohio, who share a vision to help restore the United States to its rightful place as a leader in advanced chipmaking," said Pat Gelsinger, Intel CEO.
Why It's Important: Semiconductors are the brains behind the technology that powers our digital age. These chips are critical to the foundations of the U.S. economy, national security and technology leadership. Investing to revitalize the U.S. chipmaking ecosystem will bring a broad range of economic benefits, while helping to restore balance, dependability and resilience to the global semiconductor supply chain.
In Ohio, Intel's more than $20 billion planned investment in a new semiconductor manufacturing site to produce leading-edge chips is expected to generate 7,000 construction jobs and 3,000 long-term positions in manufacturing and engineering. In addition to providing capacity for Intel's next-generation products, the company expects these new factories to support growing demand for the company's new foundry business, Intel Foundry Services (IFS).
How Intel Supports U.S. Research and Development (R&D) and Manufacturing: Intel's investment in Ohio builds on the company's announcement in Arizona to build two new fabs and its expansion in New Mexico to add advanced packaging capabilities. When combined with Intel's silicon R&D capabilities, this new site in Licking County, Ohio, will expand the company's U.S. "lab-to-fab" pipeline.
Intel also recently celebrated the grand opening of the latest expansion of its leading-edge developmental factory in Oregon, where engineers advance Moore's Law by creating new transistor architectures, wafer processes and packaging technologies that underpin the company's product roadmap. That investment represents the next phase of Intel's commitment to driving U.S. leadership in semiconductor research and development.
About Intel's Commitment to Education: Intel's Ohio Semiconductor Education and Research Program will fund collaborative proposals led by the University of Cincinnati, Central State University, Columbus State Community College, Kent State University, Lorain County Community College, Ohio University and two from The Ohio State University. Altogether, these eight proposals involve more than 80 institutions of higher education across Ohio. The eight leading institutions will receive $17.7 million in funding over three years as part of Intel's $50 million commitment to Ohio higher education institutions over the next decade.
This collaborative program will enable higher education institutions to address semiconductor manufacturing workforce shortages and technical challenges, and to innovate and develop new capabilities with an emphasis on chipmaking. Intel expects this first iteration of the program to produce nearly 9,000 graduates for the industry and provide more than 2,300 scholarships over a three-year period, fostering a diverse homegrown talent pipeline.
Semiconductors are the brains behind the technology that powers our digital age. These chips are critical to the foundations of the U.S. economy, national security and technology leadership. Investing to revitalize the U.S. chipmaking ecosystem will bring a broad range of economic benefits, while helping to restore balance, dependability and resilience to the global semiconductor supply chain.
How Intel Supports U.S. Research and Development (R&D) and Manufacturing
Intel's investment in Ohio builds on the company's announcement in Arizona to build two new fabs and its expansion in New Mexico to add advanced packaging capabilities. When combined with Intel's silicon R&D capabilities, this new site in Licking County, Ohio, will expand the company's U.S. "lab-to-fab" pipeline.
About Intel's Commitment to Education
Intel's Ohio Semiconductor Education and Research Program will fund collaborative proposals led by the University of Cincinnati, Central State University, Columbus State Community College, Kent State University, Lorain County Community College, Ohio University and two from The Ohio State University. Altogether, these eight proposals involve more than 80 institutions of higher education across Ohio. The eight leading institutions will receive $17.7 million in funding over three years as part of Intel's $50 million commitment to Ohio higher education institutions over the next decade.
More Context
Intel is committed to expanding digital readiness to reach 30 million people in 30,000 institutions in 30 countries. This education and workforce program is one more step forward in Intel's 2030 Goals and the company's dedication to using tech as a force for good, underscoring its aim to make technology fully inclusive and to expand digital readiness worldwide.
This week, the U.S. National Science Foundation and Intel launched the first phase of the $100 million national collaboration over the next 10 years to conduct research and to expand and diversify the workforce.
In March, Intel launched the semiconductor manufacturing Quick Start program at Mesa Community College in Arizona. Quick Start is an accelerated two-week program that prepares students for rewarding careers as semiconductor technicians with hands-on learning from experienced Intel employees as instructors.
This year, Intel expanded its AI for Workforce program in which Intel collaborates with community colleges to address workforce readiness skills through instruction in artificial intelligence. Currently there are 70 schools in 32 states participating in the AI Incubator Network, and in July, Intel and others awarded $600,000 to 15 community colleges to build their AI labs.
About Intel
Intel (Nasdaq: INTC) is an industry leader, creating world-changing technology that enables global progress and enriches lives. Inspired by Moore's Law, we continuously work to advance the design and manufacturing of semiconductors to help address our customers' greatest challenges. By embedding intelligence in the cloud, network, edge and every kind of computing device, we unleash the potential of data to transform business and society for the better. To learn more about Intel's innovations, go to newsroom.intel.com and intel.com.
Source: Intel


In a finale called "The Choice," Homeland avoided making its toughest one. But Carrie also had a decision to make, and chose well.
A major storyline ends mundanely, for once without any shocker twist. But can Homeland find its way out of its own narrative labyrinth?
In which Homeland gets its pulse racing dangerously fast, but still shows it can deliver the character scenes that set it apart from other spy thrillers.
The hunt for a mole was a staple of Homeland's predecessor 24. "Two Hats" put that storyline front and center—but ended up taking it in a very different direction.
Brody finds himself spirited away under surprising circumstances. But man, could he use a vacation.
Each subplot in "The Clearing" is about a relationship whose partners have private motivations—whether they want something from the other, or just want to escape.
The overarching theme of the episode was that, while there may be a new balance of power among the characters, there may not be enough trust for it to work.
Carrie and the CIA break Brody down to remake him, and in the process, Homeland makes itself into potentially quite a different, and exciting, series.
Homeland's season two has not been stingy with the forward motion and plot developments, and last night, it dropped a game-changer.
SPOILER ALERT: Before you read this post, get yourself a glass of white wine—just a glass of white wine!—and watch last night's Homeland.
SPOILER ALERT: Before you read this post, turn on your classified satellite-video link and watch last night's Homeland.
SPOILER ALERT: Before you read this post, heat up some vegetable lasagna and watch last night's second season premiere of Homeland.


Laune Rangers Under 16s made it two wins from two in the Mid Kerry Competition with an away victory in Beaufort on Sunday morning.
There were a number of players missing on both sides but it didn't affect the Rangers style of play as they went on to score 6 goals on the day. The first came directly from a free kick as Dáire Cleary put the ball to the top corner of the net from 25 yards out. He went on to score another goal and was joined on the goals list by his brother Seán (an U14 player), Mark O'Connor, and Shane Doona (2).
The defence were solid in the first half as they conceded a solitary point, while they didn't allow much more in the second half as Beaufort tagged a further 1-4. Cormac Doyle made some key blocks and a great interception to snuff out another Beaufort attack, while Rory O'Connor (another U14) also came into the side and certainly didn't weaken it.
Laune Rangers will host Cromane/Glenbeigh/Glencar in the third Round of fixtures. The game will take place on Saturday 19th November at 2:30pm in JP O'Sullivan Park.
Laune Rangers: Jack Evans, Cormac Doyle, Conor Murphy, Oisin Daly, Rory O'Connor, Sean Arthurs, James Hurley (0-1), Kevin Fitzpatrick (0-1f), David Mangan (0-1), Ronan O'Shea (0-1), Dáire Cleary (2-5, 1-3f), Eoin Clifford, Mark O'Connor (1-2), Shane Doona (2-1), Sean Cleary (1-1). Subs: Peadar Foley, Ronan Fitzpatrick.


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My Sperry amethyst ring is one of a kind and cannot be duplicated. Buy now or contact Katy Beh today.


Magnificent Lodging Space on the South of the Garden.
Soluxe Hotel Guangzhou offers 403 tastefully designed guest rooms and 45 suites with panoramic views of the city skyline or the beautifully landscaped Tianhe Park. All rooms and suites are located from the 28th floor upwards. Each of the deluxe rooms and suites is elegantly decorated with classic contemporary art, sumptuous carpets, soothing earth tone fabrics and sleek furnishings.The boundaries of the rooms dissolve with the expanse of floor-to-ceiling windows and endless views across the city. Stay here to enjoy the splendor in the grass, the glory in the flower, and indulge yourself into the beautiful landscape of Tianhe Park.Designed with your convenience in mind, our ample deluxe rooms offer kinds of recreation and communication technology, including Intelligent Personal Television, Broadband Internet and iPhone/iPod docking station.


Your pool is filled with water, and rain is just water, so rain shouldn't have any effect at all on your pool, other than changing the level, should it? In fact, rain certainly can have an impact on your pool. Rain is acidic, meaning it's pH level is lower than your pool. Your pool should be at a level at about 7.5, because that is the pH level of your eye. This is to protect your eyes from burning. The pH being low is what causes that burning feeling in your eyes when swimming. Since rain has a lower pH than your pool, it can cause a change.
You may have to raise the pH of your pool, depending on the chemistry of your pool and how much rainfall there was. If it is just a light rain, then you may not need to raise it. It might go down, but it will only be temporary and should correct itself on its own. If the chemicals in your pool are generally well balanced, then there should be no problems from a small rainfall. If there's a large rainfall, then you may need to take some action. If your water level goes up more than an inch, then drain the pool a little bit and check the pH level. It should be better at that point. The chlorine will have gotten a bit diluted with the rainfall, and your pH will rise again with the lower concentration of water.
Believe it or not, but rain can actually be good for your pool in some cases. Some chemicals, like calcium and stabilizer, will only lower in your pool if they are diluted. If those chemicals are leveled too high in the water, then a good rainfall can fix up that imbalance quite nicely. You should be careful when you use stabilizer as it can build up over time and cause problems.
It is a surprise to most people when they realize how much chemistry goes into maintaining a pool. Everything must be kept in proper balance, or else you can have problems like burning eyes, or water that's not sanitary. Make sure after every rainfall that your pool's chemistry is kept in balance.
Home Blog What Does Rain Do To Your Pool?


on patrol, they are the best!
I think I've caught a cold.
My friend is a koala.
because her fur is thick.
Originally published in KidVisions, September 2005 and Fandangle Magazine , October 2006.
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text:
San Jose neighbors mistake massive house cat for a wild animal
Updated: 5:49 PM PST Jan 19, 2016
Colleen Pizarev
Spock naps with his friend Fluff Ball.
SOURCE: Colleen Pizarev
Over the past year, strangers have knocked on Colleen Pizarev's door to warn her that a wild animal is in her house.These people are usually walking to the park near Pizarev's home in San Jose, and when they spot her 27-pound Maine Coon named Spock in the window, they mistake the cat for a bobcat or a lynx."They're worried that I'm keeping an illegal wild animal," Pizarev said in an interview. "I'm always like, 'No! Look, he has a tail.'"She added: "In most cases, I've been able to diffuse it."Pizarev is a lover of the Maine Coon breed, among the largest of the domesticated cat breeds. Several years ago, she adopted a rescue through Maine Coon Adoptions in Oakland. When that cat passed away, she adopted a Maine Coon-Abyssinian mix named Fluff Ball. And four years ago, Spock came to her through a breeder. Spock was originally supposed to be a show cat but wasn't able to follow this path when one of his eyes turned a color unacceptable for competition.Spock eats up to a pound of fresh meat a day and measures 46 inches long. Pizarev says his growth has taken off in the past year and she thinks that's why people have recently been knocking on her door.Spock has grown so large that he now takes up half the bed. "He's like having another person in your bed," Pizarev said.He's also knocking stuff over throughout the house."He'll jump on a small table and the table knocks over because of the momentum and weight," Pizarev said. "We have to lock up our table lamps because he knocks them over on the floor. We only bring them out if we're having guests."All of that said, Spock is a gentle giant. "I love this breed because they're very smart," Pizarev said. "They don't bite or scratch. They're extremely affectionate."She added: "He's a lap cat and likes to sit on laps." And that's something a wild animal would never do.
(SF GATE) —
Over the past year, strangers have knocked on Colleen Pizarev's door to warn her that a wild animal is in her house.
These people are usually walking to the park near Pizarev's home in San Jose, and when they spot her 27-pound Maine Coon named Spock in the window, they mistake the cat for a bobcat or a lynx.
"They're worried that I'm keeping an illegal wild animal," Pizarev said in an interview. "I'm always like, 'No! Look, he has a tail.'"
She added: "In most cases, I've been able to diffuse it."
Pizarev is a lover of the Maine Coon breed, among the largest of the domesticated cat breeds. Several years ago, she adopted a rescue through Maine Coon Adoptions in Oakland. When that cat passed away, she adopted a Maine Coon-Abyssinian mix named Fluff Ball. And four years ago, Spock came to her through a breeder. Spock was originally supposed to be a show cat but wasn't able to follow this path when one of his eyes turned a color unacceptable for competition.
Spock eats up to a pound of fresh meat a day and measures 46 inches long. Pizarev says his growth has taken off in the past year and she thinks that's why people have recently been knocking on her door.
Spock has grown so large that he now takes up half the bed. "He's like having another person in your bed," Pizarev said.
He's also knocking stuff over throughout the house.
"He'll jump on a small table and the table knocks over because of the momentum and weight," Pizarev said. "We have to lock up our table lamps because he knocks them over on the floor. We only bring them out if we're having guests."
All of that said, Spock is a gentle giant. "I love this breed because they're very smart," Pizarev said. "They don't bite or scratch. They're extremely affectionate."
She added: "He's a lap cat and likes to sit on laps." And that's something a wild animal would never do.


text:
Home » Events & media » Fourty years of ASIO's unclassified history
Image: ANU Coral Bell School
Fourty years of ASIO's unclassified history
Professor of International Security & Intelligence Studies
From Hot War to Cool Oceans: ANU Wargames at Kioloa
By: Dr Andrew Carr, Program Convenor of the Master of Strategic Studies at the ANU Strategic and Defence Studies Centre.
How popular culture gets Australian spy work wrong
Jakarta pressures Julie Bishop on Papua
Official ASIO history says it was penetrated by foreign spies
Politics podcast: John Blaxland on The Secret Cold War - The Official History of ASIO
The Protest Years: history shows ASIO at its lowest ebb
Dr John Blaxland takes us through 40 years of Australian spy history, from KGB moles in ASIO to political activism in the 60s to the sophistication of espionage.
His book 'The Secret Cold War: The Official History of ASIO, 1975 to 1989' written with Rhys Crawley is the latest volume in a three-part series that explores the role ASIO played in Australia's post-war political and social history.
Dr John Blaxland is an Associate Professor at the Australian National University's Strategic and Defence Studies Centre and a former Director of Joint Intelligence Operations at Headquarters Joint Operations Command.
Watch the full interview Forty years of ASIO's unclassified history on ABC Nightlife.
Tags: John Blaxland, ASIO, Australia, spying, History


This Milano fitted lounge furniture achieves an elegant finish by combining striking Pure White shelving with subtle Imperial Grey back panels. The modern design can also be configured to feature painted drawer fronts as well.
This contemporary lounge collection co-ordinates a selection of shelving units and fitted cabinets, with integrated technology and your choice of bespoke finishing touches.
Bring a contemporary charm to your home with our Milano range. These fitted bookshelves feature a two tone effect, with Imperial Grey back panels that wonderfully complement the Pure White painted finish. The blend of these two on trend tones brings a modern and sophisticated touch to any space.
The soft close drawers have been finished with contemporary, long brushed nickel handles. These work well alongside the clean lines and striking finish of the Milano range. However, we have a wide choice of different handles and knobs, meaning you can find the right design to suit you.
In addition to fitted cabinets and shelves, Strachan can provide matching freestanding furniture that complements the rest of your bespoke suite. This effortlessly modern coffee table seamlessly ties in with the Milano range, giving you a polished and on trend look throughout your room.


text:
First Look at Spider-Man: Across the Spider-Verse (Part One)
Published: Saturday, 04 December 2021 22:24
Miles Morales (Shameik Moore) is back in SPIDER-MAN: ACROSS THE SPIDER-VERSE and this time he's traveling to another parallel universe to help out Gwen Stacy (Hailee Steinfeld and a new team of Spider-People including Spider-Man 2099 voiced by Oscar Isaac who plays the Miguel O'Hara version. The first look reveals this is part one of a two-part film. A new poster also accompanied the first look.
Oscar Issac made a brief appearance as Spider-Man 2099 in the post-credit scene in SPIDER-MAN: INTO THE SPIDER-VERSE and in the new preview they will collide, literally in a new universe.
SPIDER-MAN: ACROSS THE SPIDER-VERSE (Part One) is coming exclusively to movie theaters on October 7, 2022.
Miles Morales returns for the next chapter of the Oscar®-winning Spider-Verse saga, an epic adventure that will transport Brooklyn's full-time, friendly neighborhood Spider-Man across the Multiverse to join forces with Gwen Stacy and a new team of Spider-People to face off with a villain more powerful than anything they have ever encountered.
Joaquim Dos Santos
Kemp Powers
Justin K. Thompson
Screenplay by:
Phil Lord & Christopher Miller and David Callaham
Based on the MARVEL Comic Books
Avi Arad
Amy Pascal
Phil Lord
Christina Steinberg
Shameik Moore


text:
IP still studying options
Published 9:20 am Friday, September 24, 2010
By Charlie Passut
FRANKLIN—Local and company officials say that International Paper Co. could make a decision on what to do with the shuttered paper mill in Franklin by the end of the year.
Lisa Perry, director of the Department of Economic Development in Isle of Wight County, said she had met recently with some of IP's top management.
"They indicated that they are still very involved in the due diligence process with the two consortium prospects for reuse," Perry said Thursday. "And they went so far as to say they anticipate maybe making an announcement by the end of the year."
Perry said the news was encouraging.
"That's the first really tangible evidence we've heard of any announcement to this point," she said. "We were pretty excited to hear that. It means that things are probably going well with respect to the ongoing negotiations and related due diligence on the reuse.
"(IP officials) have been careful to talk to us about updates versus announcements. This was the first time the word 'announcement' has been used. So we're hopeful that things are going well."
Meanwhile, the company projected a more reserved tone.
"There is no real significant update," IP spokeswoman Donna Wadsworth said Wednesday. "We are continuing to research and study the alternatives, and continuing to have conversations with those folks who have made proposals. We anticipate that the studies and next-step decisions regarding the future of the Franklin site could be completed in the fourth quarter of this year."
Wadsworth said the mill remains idle.
"There are still about 30 employees at the Franklin site and they're continuing to primarily focus on site preservation," she said. "Beyond that, (everyone) continues to study and wait for a final decision. It takes a significant amount of time to look at the possibilities, and that's what we're doing. We're sifting through that as carefully as we can."
John Smolak, president and chief executive officer for Franklin-Southampton Economic Development Inc., said he had also had a phone conversation with Wadsworth recently.
"She didn't say there would definitely be an announcement; she said there might be one," Smolak said Thursday. "That was basically all she related. They're obviously doing the work they need to do with the companies that are potentially looking to repurpose the plant. If they have something by the end of the year, that might be announced."
Smolak added that there could be more than two finalists in negotiations with IP.
"There are a minimum of two that are probably still involved," he said. "There could be others. We haven't really been privy to a lot of information beyond the time that they started this whole process."
One of the consortiums still believed to be in negotiations with IP is the Leaf Clean Energy Co., which has ties to former Democratic gubernatorial candidate Terry McAuliffe. In late July, McAuliffe said his group was one of the finalists and predicted that IP would announce a sale of mill facilities in August.
Several renewable energy companies have made unsolicited proposals to IP for possible reuse of the plant, which closed in the spring. One proposal is to convert the mill, which had about 1,100 employees when the mill closure was announced last October, into a biomass energy power plant.
It is believed between 400 and 500 jobs would be created under various proposals to repurpose the IP facilities.
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