text:
\section{Introduction}
Black hole X-ray binaries (BHXRBs) consist of a stellar-mass black hole (BH) fed by material supplied from a companion star. The accretion flow close to the central BH is quite hot and the radiation is likely to emit in the X-ray regime. Usually, BHXRBs are likely to be transient and undergo changes in ``states'' like quiescence and outbursts. There are mainly four types of spectral states from hard state (HS) to soft state (SS) through intermediate states (see Remillard \& McClintock 2006). Low hard state(LHS) is when hot Comptonized emission dominates over the cold thermal emission while in the high soft state(HSS) thermal emission is the dominant one. For intermediate states, namely hard intermediate (HIMS) and soft intermediate (SIMS), both non-thermal, as well as thermal components are significant. The fourth type of state is the anomalous state or ultra-luminous state (ULS) which is similar to SIMS but at higher luminosity and variability (Belloni 2010 and references therein). \\

The X-ray emissions from BHXRBs are likely to show temporal features like quasi-periodic oscillations (QPOs), varying from a few mHz to few tens of kHz range. QPOs usually become noticeable when the Fourier transform of the light curve is taken and the power density spectrum is produced. QPOs in BHXRBs are classified into two domains: low-frequency QPOs (LFQPOs) and high-frequency QPOs (HFQPOs) with centroid frequency $\le$ 30 Hz and $\ge$ 60 Hz respectively (Belloni 2010 and references therein). Further, there are three types of LFQPOs in BHXRBs, namely, type- A, B, and C (Casella et al. 2005). Type-A is the least common while type-C is the most common among observed LFQPOs. Although type-C LFQPOs are present in all possible spectral states, usually seen by end of LHS and HIMS with frequency $\nu$ in the range of few mHz and 10 Hz (Motta et al. 2012).

The physical origin of LFQPOs in general and type-C, in particular, have been an active area of research. Some works propose different kinds of instabilities due to magneto-acoustic waves (Titarchuk et al. 1998; Cabanac et al. 2010), spiral density waves (Varniere \& Tagger 2002; Varniere et al. 2012), etc. While others consider general relativistic effects like Lense-Thirring precession (Stella \& Vietri 1999; Ingram et al. 2009). Even though several models are available which can explain the observed QPOs, they do not explain the observed states in a way that connects with the QPOs. A comprehensive explanation must physically connect the timing and spectral properties.
Moreover, Marcel \& Neilsen (2021) recently pointed out that the most popular precessing inner flow model (Ingram et al. 2009) does not take into account realistic accretion flow properties, rather considers a specific structure of solid-body for precession, which is unlikely to be responsible for producing Type-C LFQPOs around BHXRBs. Therefore, it is suggestive and worth considering models which can explain both properties together.

Accretion onto the BH is necessarily transonic and multiple sonic points can exist. In such a scenario, standing shocks are likely to form depending on the choice of the flow parameters. The post-shock region formed by low angular momentum sub-Keplerian flow is likely to have all required properties of a corona around BH (Chakrabarti 1989; Chakrabarti \& Titarchuk 1995, hereafter CT95). The accretion flow with two components: sub-Keplerian halo and Keplerian disc can successfully address the spectral as well as temporal properties of BH (CT95, Chakrabarti et al. 2015, Debnath et al. 2014). According to this model, the shock, which occurs at the coronal boundary layer, connects both spectral and temporal properties by changing its size, strength along with changes in mass accretion rates and by its oscillation due to the presence of cooling (Molteni et al. 1996, Garain et al. 2014). The physical origin of LFQPOs can be due to the resonance condition when the timescale of cooling due to Comptonisation matches with the timescale of infall in the coronal region. In this model, the post-shock corona region acts as base of the outflows (Chakrabarti 1999; Singh \& Chakrabarti 2011).

It is likely that BHs are spinning in nature (McClintock et al. 2014 for a review) and can determine the nature of standing shocks: whether form closer or farther from the BH and its strength. It is also possible that BH properties like its mass and spin can be inferred from QPO properties in observations (Zhang et al. 1997; Cui et al. 1998). In this work, we decipher the physical origin of LFQPOs, especially commonly observed type-C, and address all available QPO frequencies for a large number of BHXRBs samples observed by Rossi X-ray Timing Explorer (RXTE) (Motta et al. 2015). The mass and the spin parameters for the individual sources are taken from the literature. Our goal in this study is to apply the well-known shock oscillation model to fit and explain the origin of observed LFQPOs and further establish that Compton cooling can be sufficient to explain them. Such a study has not been performed before to the best of our knowledge.

The paper is organized in the following way: in the next section, we present the governing equations and methodology to evaluate QPO frequencies. In \S 3, we discuss results explaining observed Type-C LFQPOs (hereafter, QPOs) in BHXRBs.
Finally, in \S 4, we briefly summarize our results and conclude.

\section{Governing equations and methodology}

Matter accreting onto a black hole forms a disc-like structure. In our present solution, we consider a thin, axisymmetric, low angular momentum and adiabatic flow around a rotating BH, where the flow is in vertical equilibrium. The fluid equations are time-independent for inviscid accretion flows. We have integrated the flow from the inner sonic point to the outer sonic point. In order to have a shock, the flow must be supersonic when passing through the inner sonic point, i.e. transonic (see Chakrabarti 1989, hereafter C89). The complete solution of the stationary model requires the dimensionless equations of the energy, the angular momentum, and the mass conservation supplied by the transonic conditions at the critical points and the Rankine-Hugoniot conditions at the shock. Presently, however, we have considered dissipation at the post-shock region. The sonic point conditions and shock location are derived following the similar procedures presented in C89.
The BH mass, flow velocity, and length scales are in units of $M_\odot$, the velocity of light c and $r_g=GM_{\rm BH}/c^2$ respectively for the rest of the paper.
Here, we put the model equations in absence of turbulence similar to those presented in Mondal (2020) for the sake of completeness. Similar sets of equations and analysis procedure can also be seen in Das et al. (2010).
The dimensionless energy conservation equation of the flow in pseudo-Kerr (PK) geometry can be written as (C89),

\begin{equation}
\varepsilon=\frac{v^2}{2}+\frac{1}{\gamma-1}{a_s}^2+\Phi_{\rm PK},
\end{equation}
where $\gamma$, $v$ and $a_s$ are the adiabatic index, the radial velocity of the flow,
and the adiabatic sound speed defined by $\sqrt{\gamma P/\rho}$. Here $P$ is the isotropic pressure and $\rho$
is the gas density. We consider the value of $\gamma=4/3$, constant throughout the flow.
The PK potential ($\Phi_{\rm PK}$), introduced by Chakrabati \& Mondal (2006),
is given by,
\begin{equation}
\Phi_{\rm PK}=-\frac{B+\sqrt{B^2-4AC}}{2A},
\end{equation}
where,

\begin{equation}
A=\frac{\alpha^2 l^2}{2r^2sin^2\theta},
\end{equation}

\begin{equation}
B=\frac{\alpha^2 \omega l}{sin^2\theta}+\frac{2al}{r^3sin\theta}-1,
\end{equation}
and
\begin{equation}
C=1-\frac{1}{r-r_0}+\frac{2a\omega}{rsin\theta}+\frac{\alpha^2 \omega^2 r^2}{2sin^2\theta}.
\end{equation}

Here, r, $\theta$, $l$, and $a$ are the radial distance in
spherical coordinate, disc inclination angle, the specific angular momentum, and the spin parameter defined by specific spin angular momentum of a rotating BH. Here,
$r_0=0.04+0.97a+0.085a^2$, and $\alpha^2=(r^2+a^2-2r)/(r^2+a^2+2a^2/r)$,
is the redshift factor. The above potential can mimic the general relativistic considerations up to a spin parameter ($a$) $\leq0.8$.\\

As the matter comes closer to the BH, centrifugal force increases rapidly by $\sim l^2/r^3$, produces a centrifugal
barrier close to the BH, and balances with the gravitational attraction.
Accreting matter piles up behind this layer and ends up forming a shock. For our purposes, we will use the Rankine-Hugoniot shock
conditions (Landau \& Lifshitz 1959) to find the location of the shock.
The conservation of energy at the shock in presence of dissipation (cooling) is given by,
\begin{equation}
\varepsilon_{+}=\varepsilon_{-} - \Delta \varepsilon,
\end{equation}
where $\Delta \varepsilon$ is the cooling due to thermal Comptonisation.
\begin{table*}
\centering
\caption{Scaling parameters and fits statistics for \autoref{fig:CoolingVsQPO}  \label{table:FitStat}}
\begin{tabular}{lcccccr}
\hline
Candidates        &$f_{\rm 0}$ & TS &p-value &$\alpha$ & TS &p-value \\
\hline
MAXI~J1543-564    &$0.017\pm0.001$&24.82&1.4e$-$4&$0.49\pm0.05$&10.32&0.002  \\
MAXI~J1836-194    &$0.014\pm0.001$&23.29&1.7e$-$4&$0.72\pm0.06$&11.34&0.002 \\
H~1743-322        &$0.04\pm0.01$&5.17&0.001&$0.46\pm0.09$&5.2&0.001 \\
GRO~J1655-40      &$0.010\pm0.001$&6.0&1.9e$-$5&$0.18\pm0.029$&6.0&1.9e$-$5 \\
\hline
\end{tabular}
\end{table*}

For the estimation of $\Delta \varepsilon$, we follow the steps below: (i) we consider the cooling from Mondal et al. (2017) for four BH candidates namely, MAXI~J1543-564, MAXI~J1836-194, H1743-322, and GRO J1655-40. The details of the cooling estimation method can be seen in Mondal et al. (2015).
The $\Delta \varepsilon$ used has been estimated using the X-ray spectra observed by RXTE/PCA in the range 2.5-25 keV. It is the area under the curve in the luminosity-energy plot, therefore, uncertainty in its estimation is also on the same order as in luminosity estimation, (ii) cooling is introduced in our hydrodynamic code which solves stationary, conservation equations of inviscid fluid in 1.5 dimension, namely the height is taken into account for the low angular momentum radial flow and the sound speeds before ($a_-$) and after ($a_+$) the shock location are found, (iii) considering energy dissipation across the shock in a radiatively-inefficient flow, the energy loss mostly can occur through thermal Comptonization and is proportional to the temperature (and hence the sound speed) difference in the pre-shock and post-shock regions, $\Delta \varepsilon=f_c n (a_+^2-a_-^2)$ presented in Das et al. (2010); Singh \& Chakrabarti (2011), we estimate the $f_c$ values corresponding to each observed QPO frequency, here, n is the polytropic index of the flow, is written as $1/(\gamma-1)$, (iv) thereafter the $f_c$ profile is fitted as a function of $\nu_{\rm QPO}$ with a power-law function ($f_0 \nu_{\rm QPO}^{-\alpha}$). In \autoref{table:FitStat} we summarize the power-law fitted parameters and their error bars. We also tabulate the fit statistics, both t-statistics and p-value obtained from the fits for all four sources, (v) we find that the function $f_c=0.02\nu_{\rm QPO}^{-0.6}$ fits the observed $f_c$ profile for all four sources within 50\% upper and lower limit of the best fitted power-law curve (green solid line in \autoref{fig:CoolingVsQPO}).

The current cooling is estimated from the thermal spectra of the sources, which might change if the non-thermal component and some other cooling mechanisms are taken into account. The four sources cover the full range of black hole masses in BHXRBs. Furthermore, the QPO frequencies observed for these four sources cover the range of the QPOs observed in all BHXRBs. The functional behavior proposed for fc is not necessarily universal, as it might require further study considering a larger population of black holes, including intermediate-mass and supermassive black holes. However, we anticipate that, as the current profile addresses both the mass of the low mass black hole range and QPO frequency range, it can fit those properties of all other BHXRBs.

It should be noted that the 50\% upper and lower bounds are chosen not from the statistical point of view, rather from observational findings. It has been verified in Chakrabarti et al. (2015) that once the resonance condition satisfies (cooling timescale $\sim$ infall timescale), it gets locked for a couple of  days or weeks and the QPOs can be observed when the resonance condition varies 50\% above and below 1. We apply that finding in our current study, (vi) for all sources presented in this paper we use the fitted function in (v), (vii) for all possible sets of $\varepsilon$ and $l$, flow generates shocks, which gives QPO frequency and the solution keeps searching a suitable location of the shock, which can generate the observed frequency. We repeat the above steps for all BHs considered here.
Here, ``-'' and ``+'' signs stand for pre- and post-  shock quantities.
The mass conservation equation at the shock is given by,
\begin{equation}
\dot{M_{+}}=\dot{M_{-}}.
\end{equation}
The pressure balance condition is given by,
\begin{equation}
W_{+} +\Sigma_{+} v_{+}^2 = W_{-} + \Sigma_{-} v_{-}^2.
\end{equation}

where W, $\Sigma$, and $v$ are the vertically integrated pressure, density and radial velocity of the flow.
After solving a few steps, one can get the pre-and post-shock Mach number relation (C89) at the shock, as below:
\begin{equation}
C_{\rm shk}=\frac{[2+M_+^2(3\gamma-1)]^2}{M_+^2[2+(\gamma-1)M_+^2]}=\frac{[M_-^2(3\gamma-1)+2]^2}{M_-^2[2+(\gamma-1)M_{-}^2-\zeta]},
\end{equation}
where, $\zeta=\frac{2 \Delta \varepsilon (\gamma-1)}{a_{s-}^2}$. Due to piling up of the matter in post-shock flow, it becomes more turbulent, thus the shock invariant quantity indeed modifies if one takes into account the effect of turbulent pressure, which also modifies the QPO frequency significantly (Mondal 2020).

From Eq.~9, the pre-and post-shock Mach number can be written as,
\begin{equation}
        M_{\mp}^2=\frac{-Y\pm\sqrt{Y^2-4XZ}}{2X},
\end{equation}
where, $X=(3\gamma-1)^2-C_{\rm shk}(\gamma-1)$, $Y=4(3\gamma-1)-2C_{\rm shk}-\frac{2\Delta \varepsilon(\gamma-1) C_{\rm shk}}{a_{s-}^2}$, $Z=4$,
in terms of mach invariant quantity, $C_{\rm shk}$ at the shock. Here, $M_{\mp}$ is the Mach number of the pre-and post-shock flow.
We follow the same mathematical procedure and solution technique as discussed in C89 to find the shock location ($X_s$ in $r_g$ unit). It is to be noted that for studying accretion dynamics around black hole unlike particle dynamics (wherein one can choose a location in an ad-hoc manner and no information is available for the correct treatment of inner and outer boundary conditions), it is required that we consider at least two free parameters, $\varepsilon$ and $l$,  which not only determine $X_{s}$ but also the global flow solution containing multiple critical points and all necessary variables like density, pressure, and velocity along the flow.
As we consider that the QPOs can be originated due to the oscillation of the shock and the frequency is
found to be related to the infall time ($t_{\rm infall}$) $\sim$
$X_s/v_+$ $\sim$ $R X_s/v_-$ and $\nu_{\rm QPO}=1/t_{\rm infall} = \nu_0 v_-/R X_s$ (Molteni et al. 1996; Chakrabarti et al. 2005), where $\nu_0$ is $c/r_g$.
Later it was verified by numerical simulation (Garain et al. 2014) and also from observation (Chakrabarti et al. 2015).

\section{Results}

\begin{table*}
\centering
\caption{OBSERVED AND THEORETICAL PARAMETERS USED FOR ESTIMATING THEORETICAL LFQPOs.  \label{table:results}}
\begin{tabular}{lccccr}
\hline
Candidates        &$M_{\rm BH}$ &$a$ &$\varepsilon$ &$l$&Refs. \\
\hline
4U~1543-47        &9.4    &0.55   &1.0001-1.0025 &3.036-3.058&S06, M09  \\
GRO~J1655-40      &6.0    &0.5    &1.0001-1.0007 &3.110-3.338&S03, AK01 \\
MAXI~J1535-571    &8.9    &0.67   &1.0001-1.0002 &2.984-3.062&S19, X18 \\
Swift~J1753.5     &5.5    &0.75   &1.0001 &2.896-2.942&N14, D17, R09 \\
XTE~J1550-564     &9.1    &0.34   &1.0001-1.0017 &3.298-3.534&O11, M14 \\
XTE~J1650-500     &7.3    &0.8    &1.0001-1.0009 &2.814-2.832&SS08  \\
XTE~J1817-330     &6.0    &0.22   &1.0001 &3.42-3.426&S07, F17 \\
XTE~J1859+226     &6.5    &0.4    &1.0001-1.0015 &3.248-3.394&C11, F17  \\
\hline
H~1743-322        &11.2   &0.4    &1.0001 &3.27-3.38&M17, TK18 \\
XTE~J1752-233     &10     &0.52   &1.0001  &3.136-3.202&C20, R11 \\
\hline
\end{tabular}
\\
\noindent{Refs: S06-Shafee et al. 2006, M09-Miller et al. 2009, S03-Shahbaz et al. 2003, AK01- Abramowicz \& Kluzniak 2001, S19- Shang et al. 2019, X18- Xu et al. 2018, N14- Nuestroev et al. 2014, D17- Debnath et al. 2017, R09- Reis et al. 2009, O11- Orosz et al. 2011, M14- Motta et al. 2014, SS08- Slany \& Stuchlik 2008, S07- Sala et al. 2007, F17-Franchini et al. 2017, C11-Corral-Santana et al. 2011, M17- Molla et al. 2017, TK18- Tursunov \& Kolos 2018, C20- Chatterjee et al. 2020, R11- Reis et al. 2011.}
\end{table*}

Table~\ref{table:results} summarizes properties of BHXRBs, namely mass ($M_{\rm BH}$) and spin ($a$), which exhibit QPOs in RXTE observations and the best possible flow parameters (in columns 4 and 5) in our theoretical solution which can address the physical origin of QPOs. It can be noticed that even a narrow range of specific energy ($\varepsilon$) and specific angular momentum ($l$) can successfully explain QPOs in general. Since we do not have $\varepsilon$ and $l$ beforehand apart from QPO frequency from observation, we solve the flow equations for all possible values of those two basic quantities that can produce shock, thus the QPOs. Therefore it is likely to have degeneracy in the solution as we are exploring the whole parameter space. Furthermore, QPOs are observed for a couple of days to weeks, for some sources it can be months, therefore by that time flow can change its topology due to the presence of mass outflow from the disc surface, which can carry both energy and angular momentum from the flow (Blandford \& Begelman 1999). This implies that for a given source it is not expected to have the same $\varepsilon$ and $l$ throughout the QPO observation period. Therefore the degeneracy in the solution we are getting has physical implications both in accretion onto BHs and the origin of QPOs. However, this degeneracy is higher in the case of LFQPOs as the area of shock formation is larger and the QPO frequencies are less sensitive to the spin of the BH.
Fig.~\ref{fig:CoolingVsQPO} shows the variation of cooling factor $f_{c}$ with QPO frequency $\nu_{\rm QPO}$ for some typical BHXRBs: MAXI J1543-564, MAXI J1836-194, H1743-322, and GR0J1655-40. These BHXRBs cover the possible range of $M_{\rm BH}$ and $a$. For the given value of observed  $\nu_{\rm QPO}$, typical values of $f_{c}$ were estimated using the methodology described in the previous section. Based on Fig.~\ref{fig:CoolingVsQPO}, a functional dependence of $f_{c}$ on $\nu_{\rm QPO}$ can be written as $f_{c} \propto 0.02 \nu_{\rm QPO}^{-0.6}$. It can be seen from four different cases that the fitting relation can be safely applied for $\nu_{\rm QPO} \ge 0.5$~Hz. This indicates that the amount of cooling in the post-shock region determines the QPO properties. The higher the cooling, the lower is the QPO frequency. Such functional relation can be verified in the case of other BHXRBs as well and a general trend is established. As the cooling is estimated from integrating the Comptonisation part of the spectrum and the $f_c$ is estimated using the same cooling and pre-and post-shock sound speeds solving hydrodynamic equations, it can make a bridge between theory and observation in finding QPOs. Such attempt has not been done before in other theoretical studies.\\

\begin{figure*}
\centering{
\includegraphics[width=0.75\linewidth]{Figures/all_fcool_qpo_R1-2.eps}}
\caption{Functional dependence of cooling factor, $f_{c}$, on QPO frequency,$\nu_{\rm QPO}$, for BHXRBs. Black points represent observational data points, the green solid lines are fitted power-law function, the grey shaded region includes the 50\% range of theoretically fitted (green) values followed by the satisfaction of resonance condition. The red dotted curve shows the generalized function used in this paper to estimate QPO frequencies for other BHs.
\label{fig:CoolingVsQPO}}
\end{figure*}

\begin{figure*}
\centering{
\hspace{-1.2cm}
\includegraphics[width=0.37\linewidth]{Figures/xs-qpo-4u1543.eps}
\hspace{-0.6cm}
\includegraphics[width=0.37\linewidth]{Figures/xs-qpo-GRO1655.eps}
\hspace{-0.6cm}
\includegraphics[width=0.37\linewidth]{Figures/xs-qpo-MAXI1535.eps}\\
\hspace{-1.2cm}
\includegraphics[width=0.37\linewidth]{Figures/xs-qpo-Swift1753.eps}
\hspace{-0.6cm}
\includegraphics[width=0.37\linewidth]{Figures/xs-qpo-XTE1550.eps}
\hspace{-0.6cm}
\includegraphics[width=0.37\linewidth]{Figures/xs-qpo-XTE1650.eps}\\
\hspace{-1.2cm}
\includegraphics[width=0.37\linewidth]{Figures/xs-qpo-XTE1817.eps}
\hspace{-0.6cm}
\includegraphics[width=0.37\linewidth]{Figures/xs-qpo-XTE1859.eps}
}
\caption{QPO frequency, $\nu_{\rm QPO}$, evolution with shock location, $X_{s}$, for all BHXRBs with $M_{\rm BH}$ $< 10 M_\odot$. The solid red dots show the observed frequencies from Motta et al. (2015) and empty squares show the theoretically estimated frequencies. \label{fig:qpoVsXsMless10} Different empty squares are associated with the range of values of both $\varepsilon$ and $l$ as shown in table~\ref{table:results}}
\end{figure*}

The variation of $\nu_{\rm QPO}$ with $X_{s}$ for all BHXRBs with $M_{\rm BH}$ $< 10 M_\odot$ is shown in Fig.~\ref{fig:qpoVsXsMless10}. Using the range of values for parameters, $\varepsilon$ , $l$, $M_{\rm BH}$, and $a$, mentioned in table~\ref{table:results} for each BHXRB, we could successfully explain the observational data points (solid red dots) using our theoretical solutions (empty black squares).
It can be concluded that to have higher values of $\nu_{\rm QPO}$, the shock needs to form closer to the BH and the corona region should be more compact (see Appendix \ref{App:hfqpos}). Similarly, Fig.~\ref{fig:qpoVsXsMGe10} shows results for a few BHXRBs with $M_{\rm BH}$ $\ge 10 M_\odot$. The theoretical estimate following the methodology in the previous section and using parameters mentioned in table~\ref{table:results}, the origin of observed values of $\nu_{\rm QPO}$. For all possible values of $M_{\rm BH}$, corona size seems to be of similar size to produce same $\nu_{\rm QPO}$. For the lowest value of $\nu_{\rm QPO}$ around 1 Hz, the dissipative standing shocks form at several hundreds of $r_{g}$ while for the highest value like around a few tens Hz the shock should be located at some tens of $r_{g}$. The general trend of the evolution of QPOs with shock location can be related to the spectral states change. As the state changes from a hard to soft through intermediate, the shock is located far away from the BH and moves inward, and the QPOs frequency gradually increases. Some sporadic QPOs are observed in intermediate states. These features have been observed for other BHXRBs that can be explained using hardness intensity diagram (Belloni 2010; Katoch et al. 2021; Alabarta et al. 2021; Shui et al. 2021 and references therein) or from mass accretion rates ratio diagram (Mondal et al. 2014).\\

\begin{figure*}
\centering{
\includegraphics[width=0.5\linewidth]{Figures/xs-qpo-H1743.eps}
\hspace{-0.5cm}
\includegraphics[width=0.5\linewidth]{Figures/xs-qpo-xte1752.eps}}
\caption{Same as \autoref{fig:qpoVsXsMless10}, but for candidates with $M_{\rm BH}$ $\ge 10 M_\odot$. \label{fig:qpoVsXsMGe10}}
\end{figure*}

\begin{figure}
\centering{
\includegraphics[width=1.1\linewidth]{Figures/spin-qpo.eps}}
\caption{Dependence of QPO frequency, $\nu_{\rm QPO}$, on the BH spin, $a$. Different curves correspond to a fixed value of $l$. The other flow parameters are set fixed at $\varepsilon=1.0001$, $M_{\rm BH}=10 M_\odot$, and $\Delta \varepsilon=4\times10^{-5}$. \label{fig:SpinVsQPO}}
\end{figure}

\begin{figure}
\centering{
\includegraphics[width=1.1\linewidth]{Figures/ang-qpo.eps}}
\caption{Variation of QPO frequency, $\nu_{\rm QPO}$, with specific angular momentum of the flow, $l$. Different curves correspond to a fixed value of $a$. The other flow parameters are set fixed at $\varepsilon=1.0001$, $M_{\rm BH}=10 M_\odot$, and $\Delta \varepsilon=4\times10^{-5}$. \label{fig:AngVsQPO}}
\end{figure}

Fig.~\ref{fig:SpinVsQPO} shows the theoretical estimate of $\nu_{\rm QPO}$ versus BH spin, $a$, for different values of $l$. Some parameters like $\varepsilon$, $\Delta\varepsilon$ and $M_{\rm BH}$ have been assigned particular values like $1.0001$, $4\times10^{-5}$ and $10 M_{\odot}$ respectively. The peak values of $\nu_{\rm QPO}$ are found to be the largest for highest $a$ and lowest $l$. For particular $a$, $\nu_{\rm QPO}$ increases with the decrease in $l$ while it decreases with an increase in $a$ for particular $l$. The dependence of $\nu_{\rm QPO}$ on $l$ for particular values of $a$ are shown in Fig.~\ref{fig:AngVsQPO}. The behaviour of $\nu_{\rm QPO}$ in Fig.~\ref{fig:AngVsQPO} follows the same trend as in Fig.~\ref{fig:SpinVsQPO}. The reason behind the above dependencies is as follows: higher spin parameter pushes the shock location away from the BH and hence decreases the infall velocity of the flow ($v_-$), so based on the equation of $t_{\rm infall}$, it increases thus decreases  $\nu_{\rm QPO}$. Similar behaviour is observed in $l$ v/s $\nu_{\rm QPO}$ variation.

\section{Summary and conclusions}
In this paper we address the physical origin of type-C LFQPOs in almost all BHXRBs observed from RXTE data. The oscillation of standing shock caused by the resonance condition due to matching of cooling and infall timescales can successfully explain the scenario. This scenario can also explain the spectral states. It is in this two-fold ability of its explanation that we see its power. At the onset of the outburst, the Keplerian disc just starts forming far from the BH, when only the hot sub-Keplerian flow dominates and the spectrum becomes harder, as the disc proceeds inward, more soft photons intercept hot electrons in the corona, therefore cooling increases and corona shrinks. When the cooling is significant enough to destruct the corona completely, the disc becomes fully Keplerian, which is the SS or can be high SS. In between these HS and SS, when the cooling timescale matches with the compressional heating timescale $-$ the resonance condition is fulfilled, the QPO appears (Molteni et al. 1996, Garain et al. 2014). Applying the above theory to large samples, our main results are as follows:\\

(1) There is a power-law dependence of cooling factor in the post-shock region on the QPO frequency which is possibly generic in nature, requires further study.

(2) The thermal Comptonisation cooling leads to compact corona forming close to the BH and a smaller standing shock location causes the higher value of QPO frequency. So the standing shock location is correlated with the QPO frequency.

(3) The QPOs due to oscillation of the standing shocks are likely to be weakly dependent on BH masses and spins as the shock forms far from the BH.

(4) Only two free parameters of the accretion flow like specific angular momentum and specific energy are sufficient to explain the QPO frequencies in all given BHXRBs.

In the present work, for mathematical simplicity pseudo-Kerr potential has been invoked to describe the BH space-time however a full general-relativistic study has been left for future work and will be reported elsewhere. The estimation of cooling energy from the power-law spectral component for all sources in Table~\ref{table:results} is beyond the scope of this paper. We aim to estimate the above cooling and verify our present claim of $f_c$ in follow-up work.

\section*{Acknowledgments}
CBS  is  supported  by  the  National  Natural  Science  Foundation  of China under grant No. 12073021. SM acknowledges Ramanujan Fellowship grant (\#RJF/2020/000113) for this research.

\section*{Data Availability}
Data information may not be applicable for this article. No new data has been analysed, as it is mostly a theory-based article. The numerically created data that support the findings of this study are available from the corresponding authors, upon reasonable request.

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CBS Drops Teasers of Prince Harry and Meghan Markle's Candid Conversation with Oprah [VIDEO]
*CBS has revealed a teaser of the two-hour "Oprah with Meghan and Harry: A CBS Primetime Special" set to air on Sunday, March 7. The network said Winfrey spoke with the Duchess of Sussex in "a wide-ranging interview covering everything from stepping into life as a royal, marriage, motherhood (and) philanthropic work, to how she is handling life under intense public pressure."
In two promos that aired Sunday, Meghan doesn't speak, but Harry recalled how his mother Princess Diana was stalked and harassed by British media, in the same way they treat his wife.
"My biggest fear is history repeating itself," he tells Winfrey. "It has been unbelievably tough for the two of us, but at least we have each other."
READ MORE: Prince Harry's 'Carpool Karaoke': He Swears, Raps, FaceTimes Meghan, Says UK Media Was Destroying His 'Mental Health' (Watch)
Oprah's interview with Meghan Markle and Prince Harry is about to be the TV event of the year pic.twitter.com/GcQWDpqjYJ
— Gibson Johns (@gibsonoma) March 1, 2021
Harry also explained that his mother had to find her way alone after divorcing Prince Charles.
"I'm just really relieved and happy to be sitting here talking to you with my wife by my side because I can't begin to imagine what it must have been like for her going through this process by herself all those years ago," he said, adding, "because it's been unbelievably tough for the two of us. But at least we have each other."
The highly anticipated interview hints at some "shocking" revelations … including, per TMZ, a suggestion Meghan's been "silenced" by Queen Elizabeth and the Palace.
A look at Meghan Markle and Prince Harry's interview with Oprah. I AM READY🍿!!! pic.twitter.com/TzMtGQPxiY
— TV Fanatic👑⚜ (@TvKhaleesi) March 1, 2021
Days after Harry and Megan's Oprah interview was announced, Buckingham Palace issued a statement stating that "they will not be returning as working members of the Royal Family."
"The Duke and Duchess of Sussex have confirmed to Her Majesty The Queen that they will not be returning as working members of The Royal Family," the statement said.
"Following conversations with The Duke, The Queen has written confirming that in stepping away from the work of The Royal Family it is not possible to continue with the responsibilities and duties that come with a life of public service," the statement continued. "While all are saddened by their decision, The Duke and Duchess remain much loved members of the family."
The 90-minute special with Oprah will air on CBS on Sunday, March 7 at 8 EST/PST.
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redpajama_set_name: RedPajamaCommonCrawl


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Q: Maximization of Output based on Input What I want to do is find the values for $X = $ { $x_j$ } that will produce the maximum $y$.
I'm currently trying to maximize my output $y$, based on my inputs $X$.
Say there are inputs, $X = $ { $x_1 , x_2 , x_3 \cdots , x_j $ }. Each example has all the features in $X$, and a $y$ value - ie one example is $ ( X_i, y_i) $
What I want to do is find the values for $X = $ { $x_j$ } that will produce the maximum $y$.
One (shitty) idea is create a neural network with $j$ input nodes in the first layer and have one single output node. Train the NN, which would let me predict the output $y$ based on $X$ which isn't helpful for my example. So I would then generate a bunch of randomized values for $X$ and find the value that outputs the largest $y$ which is obviously super inefficient.
Another (shitty) idea is to train the NN like above, but this time use some sort of Reinforcement learning to optimize the inputs. I don't know much about RL, but it seems to be unnecessary and not helpful in this situation because the training examples are varied which means the $y$ value wouldn't be optimized? (I don't know much about this specifically.)
Is there a specific model or algorithm that would let me find the maximum $y$ based on my $X$ values?
This question is pretty similar to this but here they don't actually give a specific model to follow.
NEW EDIT : As requested by @whuber a more clear explanation of the context. I am conducting an experiment that has many parameters I am able to vary. I can then develop a large(ish) dataset with each of the parameters/features somehow affecting my final output $y$. The inputs are my features/parameters  $X =$ {$x_j$} and each example of $(X_i, y_i)$ contains a variation on the features called $X_i$ where $i$ is the number of training examples and $j$ is the number of features comprised in $X$. - I have no idea what the relationship between $X$ and $y$ so I don't know what $f$ maps from $X \mapsto y$
I want to know what I changes I can do to my parameters ($X =$ {$x_j$} ) in my experiment in order to maximize my output ($y$).

A: OP has answered this question by stating

I think I have found what I was looking for.
I can approximate my $ y = f(x_1, x_2, x_3, x_4, x_5, x_6) = g(x_1, x_2, x_3, x_4, x_5, x_6) + \varepsilon $ using an Artificial Neural Net, then from there using a genetic algorithm to optimize the output.

but I don't think that this is a good solution.
Using a neural network inherently introduces lots of hard problems: selecting how many neurons in what configuration, an initialization method, an activation function, an optimizer, a learning rate, regularization strategies (L1, L2, dropout, mixup, max norm...) -- to succeed, all of these things must be chosen to be "just right" for whatever problem you're trying to solve. Then the genetic algorithm step adds more complexity, and more tuning, on top of that.
If you generalize from using a neural network to any function approximation method, you are employing a surrogate surface, which you denote as $g$, and performing the optimization over that surface. There's no particular need to use a neural network. A popular method to use in place of a neural network is a Gaussian process. See: Jones et al (1998), "Efficient Global Optimization of Expensive Black-Box Functions."
One desirable attribute that you would want your surrogate surface interpolates well between your data points, neither changing values too quickly or too slowly. A well-studied category of surrogate surfaces for this type of problem is the Gaussian process; these methods are usually characterized in terms of a length-scale parameter which exactly controls the behavior between data points. In this sense, there is essentially only one "knob," the length-scale, that you have to fiddle with.
Once you're satisfied that you have a "good" surrogate surface, you can directly optimize it. The values $g$ and their gradients are easily computed and cheap to evaluate, so you can quite readily use multi-start optimization, or really any global optimization method, to find optima on the surface.

A: I think I have found what I was looking for.
I can approximate my $ y = f(x_1, x_2, x_3, x_4, x_5, x_6) = g(x_1, x_2, x_3, x_4, x_5, x_6) + \varepsilon $ using an Artificial Neural Net, then from there using a genetic algorithm to optimize the output.

redpajama_set_name: RedPajamaStackExchange


In the early days of metal clay, there were new inventions, experiments and tools almost all the time. Naturally, things have slowed down. I'm watching with interest what's happening with the Silhouette, a computer controlled cutting machine.
One of the ways to use the Silhouette is is make a stencil and use that with your clay, but inventive metal clay artists took it a step further and began to cut metal clay directly with the Silhouette!
The first artist I heard of doing this was Wanare Tanner, who uses it to make custom, fancy bezels. I've posted before about her book on the subject. She also sells pre-cut bezels and Silhouette files.
Another metal clayer doing wonderful things with the Silhouette is Paula Long of http://wearthemusic.co She has an instructional video.
The official Silhouette blog also has great tutorials, you access that from inside the Silhouette Studio software.
What about you? Have any favorite work being done in metal clay using a computer controlled cutter? A favorite blog to learn how to use the Silhouette? The comments are always open, thanks!


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Teheranno (alternativamente Teheran-ro, cuja tradução é "Rua Teerã") é uma rua localizada no distrito de Gangnam em Seul, Coreia do Sul. Ela inicia na estação Gangnam, no Yeoksam-dong e passa pelo Samseong-dong. É coloquialmente conhecida como "Teheran Valley" devido o número de empresas do segmento de internet que operam ali, incluindo o Yahoo!, e as rivais coreanas Daum e Naver. As também concorrentes Samsung e Hynix também possuem escritórios nessa região. Várias companhias coreanas e internacionais de negócios e finanças, incluindo a POSCO, o Standard Chartered e o Citibank, também mantêm escritórios aqui. Alguns dos mais altos arranha-céus da Coreia e imóveis mais caros estão localizados em Teheranno. O Governo Metropolitano de Seul estima que mais da metade do capital de risco da Coreia, algo em torno de 200.000.000.000 wons (aproximadamente $200.000.000), estão investidos no Teheran Valley.

Teheranno é uma seção de 3,5 km da Korean Highway 90, e corre para o leste, da estação Gangnam à estação Samseong e ao complexo COEX/KWTC. As estações Yeoksam e Seolleung também localizam-se ao longo da Teheranno. Todas as estações fazem parte da linha 2 do Metrô de Seul.

Nome
Em 1976, o Governo Metropolitano de Seul sugeriu que a cidade de Seul e Teerã, no Irã, trocassem o nome das ruas por ocasião da visita à Coreia do prefeito de Teerã. No ano seguinte, a rua anteriormente denominada Samneungno foi renomeada para Teheranno, que corria através de uma área relativamente pouco desenvolvida, que foi anexada à Seul em 1963. Nos anos seguintes, o distrito de Gangnam experimentou um crescimento fenomenal e ondas de construção que continuam até hoje, com Teheranno se tornando uma das ruas mais movimentadas da Coreia do Sul. Em Teerã, existe a Seul Street, que passa ao norte da cidade, próximo ao distrito de Evin.

Galeria de imagens

Ruas e avenidas de Seul
Gangnam-gu
Parques tecnológicos da Coreia do Sul

redpajama_set_name: RedPajamaWikipedia


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Home / Lodging / Cabin Rentals
Our cabins are located close to three different trails (Pocahontas, Indian Ridge, and Pinnacle Creek trails) and are handbuilt from the ground up, including the custom made furniture and beds. Each guest is guaranteed a comfortable stay in the best-looking lodging around.
ROOM STYLE
Our cabins are handbuilt from the ground up including the custom made furniture beds. Each cabin features an open, rustic lodging feel that comfortably accommodates those looking to get away from the hustle and bustle of everyday life. Our rooms are furnished with all of the essentials, including a coffee pot, microwave, mini-fridge, charcoal grill, bedding, bath towels, and toilet paper. We're open year-round, so each cabin comes equipped with heating and air conditioning so you can visit anytime you're ready to get away. We have quick access to three trails on the Hatfield-McCoy Trail System, including Pinnacle Creek, Pocahontas, Indian Ridge trails.
Our cabins are outfitted with one bedroom, one kitchenette, and one bath each. If you have questions or need specific accommodations, please contact us here us or call us directly at 304-920-2073.
HATFIELD-MCCOY TRAILS
Whether you are a hardened veteran rider or you're just wanting to have a relaxing ride deep in the woods, our cabins are located close to three amazing trails. Indian Ridge Trail offers a wide variety of terrain and levels of difficulty. Along the way of this system, you'll find access to ATV-friendly towns such as Northfork and Keystone, WV. Pinnacle Creek Trail has immediate connections to Mullens and Pineville, WV. Both of these rural towns are ATV-friendly and feature amenities and great views! Connecting to the Pinnacle Creek and Indian Ridge, the head of the Pocahontas Trail is near the historic town of Bramwell, which features fuel and dining options including the Corner Shop. The Corner shop is known for its homemade ice cream, hand-patted burgers, and soda fountain.
GREEN DATES: Available for booking
RED DATES: Not available for booking
We offer relaxing getaways from the normal day-to-day, immersing our guests in a deep-woods experience. Our cabins, and much of their furniture, are hand-built and provide the necessary amenities you'll need when you're not on the trails.
Quick Trail Access
Proximity to Stores
Family Board-Games
Hand-Built Furniture
Bathroom & Kitchen Sinks
Private Restroom/Shower
7001 Black Oak Road
Rock, West Virginia 24747
Fused With Passion In Appalachia • Website Created By Starry Eyes Media
Fused With Passion In Appalachia
Website Created By Starry Eyes Media


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From: El Cerrito, CA, USA
Creedence Clearwater Revival (CCR for short) hailed from the San Francisco area and, unlike most Bay Area rock bands of the 60s, played more straight forward rock and roll than their psychedelic neighbors like the Jefferson Airplane and Grateful Dead. The group was influenced by the swampy blues that came out of southern Louisiana in the late 1950s and early-mid 1960s. CCR cultivated a Louisiana connection through its choice of song and album titles, such as 'Born On The Bayou'/Bayou Country, as well as through the southern "good ol' boy" image projected by its members. The band consisted of brothers John (lead vocals, lead guitar, harmonica, piano) and Tom Fogerty (rhythm guitar, piano, backing vocals), along with Stu Cook (bass guitar, backing vocals) and Doug Clifford (drums, percussion, backing vocals).
Originally known as the Golliwogs, they were signed to the Fantasy record label in 1964 and released seven singles throughout the next 3½ years under that moniker. Heavily influenced by the British Invasion, their music during this period resulted in little to no commercial success. In 1967, the band, somewhat frustrated with their efforts to date, made the decision to reinvent themseves based on the rapid evolution of the music scene that was swirling all around them. They coined themselves Creedence Clearwater Revival after a friend of a friend of Tom Fogerty's, Credence Nuball. "Clearwater" initially originated from a beer commercial, but also reflected on the environmental movement of the time. "Revival" came from the fact that the band had already been playing together for quite some time and was ready for a positive change.
In June, 1968, they released their first single, 'Suzie Q' (a blues tune originally penned by Dale Hawkins in 1956), which was broken up into two parts to fit on the record. The A-side is what most people are familiar with and still gets played on the radio to this day, but the lesser known B-side is quite psychedelic and evolves into a hypnotic vibe/song all of its own. That same month they issued their first self-titled LP, which also includes the full version of 'Suzie Q' and another great track titled 'Porterville'.
At the beginning of 1969, the band really took off, starting with the release of their third single ('Proud Mary' b/w 'Born On The Bayou'), which hit #2 on the U.S. charts and a second LP (Bayou Country), which peaked at #7. A third LP titled Green River was then issued in the summer of 1969. This album includes the hit singles 'Green River' and 'Bad Moon Rising', and also reached #7 on the charts. At around this time, the band appeared at Woodstock, but their presence there is still somewhat unknown due to the fact that they played at around 3:00AM and also their record label didn't allow the release of any of the set to be put in the Woodstock movie or on the soundtrack. The fall of 1969 saw the release of yet another successful single ('Down On The Corner' b/w 'Fortunate Son') and LP (Willy And The Poor Boys). This album peaked at #3 on the charts and includes both sides of the 45 as well as another group favorite, the Leadbelly penned 'The Midnight Special'. All in all, they churned out a staggering four singles and three albums within the year 1969.
1970 continued to bring great fortune to CCR with the release of their fifth LP (Cosmo's Factory) in the summer of that year. This album includes a slew of classics ('Travelin' Band', 'Up Around The Bend', 'Lookin' Out My Back Door', 'Who'll Stop The Rain', 'Run Through The Jungle') and is considered by many to be their best, hitting #1 in both the U.S. and U.K. When The Beatles broke up in the winter of 1970, CCR became the most successful rock and roll band in the world, despite never landing a #1 single on either side of the Atlantic. At the tail end of 1970, the group issued a fan book titled Inside Creedence, hosted a TV special and released a sixth LP titled Pendulum. This album includes the classic 'Have You Ever Seen The Rain' and the awesome balad 'It's Just A Thought'.
By 1971, things began to come apart when Tom Fogerty had a falling out with his brother John over control of the band, which prompted him to abruptly split the scene. In 1972, the remaining threesome released a final LP titled Mardi Gras, which flopped horribly and, after a final tour of Europe, they decided to finally call it quits in October of that year.
All in all, CCR is considered by many to have been one of the most successful U.S. rock and roll bands of all time. Their truly classic music fueled a generation and is still highly regarded and played often on the radio to this day.
Artist photo by Baron Wolman.
Original LP/EP Label: Fantasy 8382
Released: June, 1968
(Original 45 Label: Fantasy 616, A&B - June, 1968)
Bayou Country
Born On The Bayou
(Original 45 Label: Fantasy 619, B - January, 1969)
Proud Mary
(Original 45 Label: Fantasy 619, A - January, 1969)
Released: August, 1969
(Original 45 Label: Fantasy 622, A - April, 1969)
(Original 45 Label: Fantasy 625, A - July, 1969)
(Original 45 Label: Fantasy 622, B - April, 1969)
Willy And The Poor Boys
Down On The Corner
(Original 45 Label: Fantasy 634, A - October, 1969)
(Original 45 Label: Fantasy 634, B - October, 1969)
The Midnight Special
Cosmo's Factory
Released: July, 1970
Lookin' Out My Back Door
Run Through The Jungle
Up Around The Bend
Who'll Stop The Rain
Have You Ever Seen The Rain?
Hey Tonight
It's Just A Thought
Released: April, 1972
Someday Never Comes
(Original 45 Label: Fantasy 676, A - March, 1972)


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Q: Paradoxical CORS error: Either no 'Access-Control-Allow-Origin' present OR 'Access-Control-Allow-Origin' header contains multiple values I'm currently working with NGINX and Node.
In my NGINX configuration I'm adding the allow-origin header as follows, before passing it off to an authorization port that contains my Node app:
location /auth {
    add_header Access-Control-Allow-Origin *;
    proxy_pass http://watchdog:3000;
}

In my Node middleware I'm also setting the headers to accept any origin:
app.use((req, res, next) => {
    res.setHeader('Access-Control-Allow-Origin', '*');
    next();
}

When I do this, my Chrome rightfully complains that I'm setting the header twice:
The 'Access-Control-Allow-Origin' header contains multiple values '*, *', but only one is allowed.

Clearly setting the header both in NGINX and in Node is redundant.
However, what's fascinating (and frustrating) is that when I remove the Node middleware while leaving in the NGINX header, I get the following Chrome console error:
No 'Access-Control-Allow-Origin' header is present on the requested resource.

So basically the error claims that either 1) the header is set too many times, or 2) the header is not set at all.

A: The error disappeared when I attempted the third possibility: only set the header in Node, and not in NGINX.
To summarize, here are my findings:

*

*Setting the header in NGINX and Node did not work

*Setting the header in NGINX only did not work

*Setting the header in Node only worked
That said, I'm still lost as to why this was the solution. Why did setting the header only in NGINX do absolutely nothing? Perhaps because of the way NGINX handles the proxy_pass?
Any theories / explanations would be much appreciated.


In November, industrial production grew 3.5% over the same month in the previous year, according to the latest data released by the National Statistical Institute (INDEC). The reading came in below the 4.4% year-on-year growth observed in October. November's print marked the seventh consecutive month of growth in industrial output, following 15 consecutive contractions.
The monthly reading reflected higher output in fewer than half of all components of the index. The basic metallurgic industry expanded 15.7% annually, and output in non-metallic mineral products rose 11.4% in year-on-year terms. The all-important food industry declined 1.6% in the surveyed period, and production of chemical products and substances dipped 3.5%.
The accumulated average annual variation in industrial production over the January–November period was 1.9%, just above the 1.8% reading observed in the January–October period.
Panelists participating in the LatinFocus Consensus Forecast expect industrial production to expand 1.9% in 2018, which is up 0.2 percentage points from last month's forecast. For 2019, the panel expects industrial output to rise 2.4%.


text:
Dodgers will give Will Smith 'a good…
Dodgers will give Will Smith 'a good runway' as the primary catcher
Dodgers manager Dave Roberts said he expects to give Will Smith, pictured, "the lion's share" of playing time at catcher the rest of the season with veteran Russell Martin "in there a couple times a week is kind of what I see." (AP Photo/Mark J. Terrill)
PUBLISHED: July 26, 2019 at 5:24 p.m. | UPDATED: July 26, 2019 at 5:25 p.m.
WASHINGTON, D.C. — As far back as spring training, the Dodgers expected Will Smith to arrive in the major leagues this season and start significant games at catcher for them at some point.
That time is now.
Smith was promoted from Triple-A Oklahoma City on Friday for the third time this season. He is expected to stay this time and serve as the Dodgers' primary catcher, likely for the rest of the season and potentially in a postseason run.
"Seeing him on a big-league field and seeing the way he conducted his at-bats, handled the pitching staff, following gameplans – even in big spots against good pitching how he handled himself, staying in the strike zone and what he did at the Triple-A level … he's performed, really. Big time," Dodgers manager Dave Roberts said. "So he's checked every box. Now you've got to go out there and give him a little bit of runway."
Smith's defensive skills have always been highly-rated. But he has had a breakout year offensively, hitting .269 with a .986 OPS and 20 home runs in 61 games with the OKC Dodgers. In nine games at the major-league level over his first two promotions, he hit .269 with a .999 OPS and three home runs – two walk-offs to win games.
Roberts said he expects to give Smith "a good runway" with "the lion's share" of playing time with veteran Russell Martin "in there a couple times a week is kind of what I see."
The window opened for Smith's ascension with the continued collapse of Austin Barnes' offensive game (and some recent defensive miscues as well). Barnes hit .289 with an .895 OPS in 2017, giving the Dodgers hope that he would develop into a two-way player and every-day catcher.
Since then, however, Barnes has hit .200 with a .618 OPS in 471 plate appearances. He had just seven hits in his last 60 at-bats before being demoted to Triple-A this week.
"Very difficult discussion with Austin," said Roberts, who gave Barnes the news along with Dodgers president of baseball operations Andrew Friedman. "It's more about just trying to get him on track offensively. I think just to get him back in a good place mentally and mechanically. He's a major-league player. He helps us in so many ways – in the clubhouse, behind the plate. But we see him as an offensive player as well. Just to get him out of this hot box (the pressure of the big leagues) will be best for him and it will help us as well.
"For any decision we made, you also have to have a solution. To have Will playing the way he's playing, so consistently on both sides of the baseball, just made a difficult decision a little bit easier."
STRIPLING START
Right-hander Ross Stripling said he is still bothered by neck stiffness, leaving his next scheduled start (Tuesday in Colorado) questionable.
Stripling played catch on flat ground on Friday afternoon and said he still felt the discomfort in the right side of his neck.
"If you think about pitching, that whipping action there at the end," Stripling said. "It's not so much pain, but I think I'm protecting it."
Roberts said Stripling is expected to make that start in Colorado "right now" but he would have to throw a bullpen session Saturday or Sunday to test the neck and prove his readiness to pitch. Right-hander Jaime Schultz traveled to Washington with the team in case a roster move needs to be made.
FREESE OUT
Tyler White was officially added to the roster Friday after being acquired in a trade with the Houston Astros. David Freese was returned to the Injured List with a persistent hamstring problem in his left leg. Freese spent more than two weeks on the IL before the All-Star break due to the same problem.
"It's just something we can't get over," Roberts said. "He's doing everything he can to stay on the field. We're just not getting the best version of him as far as his health."
White will replace Freese as a right-handed bat off the bench and occasional first baseman.
After batting .276 with 12 home runs and an .888 OPS last season, White slumped to a .225 batting average, .650 OPS and just three home runs in 71 games with the Astros this year.
"Just kind of a grind so far," White said. "I don't want to blame it on anything in particular. It's just been tough for me to gain any momentum this year. I've had some good weeks. It's just been tough to put together a good month.
"I'm excited to have some new scenery and join a new team."
Kiké Hernandez had an MRI on his left hand after leaving Wednesday's game with an injury. The results had not been reviewed by the team's medical staff before Friday's game, but Roberts said he expected Hernandez to be available to play defense only.
Dodgers (LHP Clayton Kershaw, 8-2, 2.84 ERA) at Nationals (TBA), Saturday, 1:05 p.m., SportsNet LA (where available), 570 AM


CORAL GABLES, Fla., Nov. 1, 2018 /PRNewswire/ -- MasTec, Inc. (NYSE: MTZ) today announced better than expected third quarter financial results and increased 2018 annual guidance.
Third quarter 2018 revenue was $1.98 billion, compared with $1.96 billion for the same period last year. GAAP net income was $120.5 million, or $1.52 per diluted share, compared to $64.2 million, or $0.77 per diluted share, in the third quarter of 2017, a 97% increase. GAAP results exceeded the Company's previously announced diluted earnings per share expectation by $0.29, inclusive of a $0.23 per diluted share benefit related to the impact of re-measurement of the Company's U.S. deferred income tax balances because of the Tax Cuts and Jobs Act.
Third quarter 2018 adjusted net income and adjusted diluted earnings per share, both non-GAAP measures, were $105.2 million, or $1.33 per adjusted diluted share, compared to $68.0 million, or $0.82 per adjusted diluted share, in the third quarter of 2017, a 62% increase. Adjusted diluted earnings per share exceeded the Company's previously announced third quarter 2018 expectation by $0.07.
Third quarter adjusted EBITDA, also a non-GAAP measure, was $226.3 million, compared with $179.6 million in the third quarter of 2017, a 26% increase. Third quarter adjusted EBITDA margin rate of 11.4% increased 220 basis points compared to last year's period. Third quarter adjusted EBITDA also exceeded the Company's previously announced 2018 third quarter guidance expectation by approximately $6 million.
During the third quarter, the Company successfully finalized contractual resolution related to a recently completed large Oil & Gas long-haul pipeline construction project. Cash collections related to this resolution were received subsequent to quarter end.
The Company also announced record 18-month backlog as of September 30, 2018 of $7.8 billion, a $114 million sequential increase when compared to second quarter 2018, and a $2.8 billion increase, or 56%, compared to the third quarter of 2017.
Adjusted net income, adjusted diluted earnings per share and adjusted EBITDA, which are all non-GAAP measures, exclude certain items which are detailed and reconciled to the most comparable GAAP-reported measures in the attached Supplemental Disclosures and Reconciliation of Non-GAAP Disclosures.
Jose Mas, MasTec's Chief Executive Officer, commented, "We had a great quarter despite regulatory and hurricane flooding disruptions on selected projects. We are proud to report record results and increase our annual guidance expectation. Importantly, our record backlog level across multiple segments continues to give us strong visibility for continued growth in 2019 and beyond. Our continued confidence in the future is evidenced by our 2018 share repurchase activity, with 1.6 million shares repurchased during the third quarter, and 4.3 million shares repurchased on a year-to-date basis. Additionally, our board approved an additional $150 million share repurchase authorization in September 2018."
George Pita, MasTec's Executive Vice President and Chief Financial Officer noted, "We successfully completed contractual resolution on a recently completed large Oil & Gas pipeline project, as expected and previously communicated. This resolution yielded a significant October cash inflow to MasTec. Since quarter end, we have received over $700 million in cash inflows from this and other large Oil & Gas projects, significantly reducing our leverage and increasing our liquidity since the end of the third quarter. This strong October cash inflow allows us to further increase our record annual 2018 cash flow from operations projection, now expected to exceed $550 million. Excluding any fourth quarter share repurchase or acquisition activity, we expect to reduce our year-end net debt level to $1.1-$1.2 billion, compared to approximately $1.7 billion as of the end of the third quarter. In any event, our balance sheet remains in excellent shape, providing us ample liquidity to finance any opportunities to generate additional value for our shareholders, including share repurchases or strategic acquisitions."
Based on the information available today, the Company is providing initial fourth quarter guidance, and increasing full year 2018 guidance expectations. The Company currently estimates full year 2018 revenue of approximately $6.9 billion. Full year 2018 GAAP net income and diluted earnings per share are expected to approximate $308 million and $3.85, respectively. Regarding full year 2018 expectations for non-GAAP measures, adjusted EBITDA is expected to approximate $719 million or 10.4% of revenue and adjusted diluted earnings per share is expected to be $3.76, a 29% increase over 2017.
For the fourth quarter of 2018, based on updated project schedules for large Oil & Gas project activity, the Company expects revenue of approximately $1.9 billion. Fourth quarter 2018 GAAP net income is expected to approximate $80 million with GAAP diluted earnings per share expected to approximate $1.02. Fourth quarter 2018 adjusted EBITDA, a non-GAAP measure, is expected to approximate $194 million with adjusted diluted earnings per share, a non-GAAP measure, expected to approximate $1.05.
Management will hold a conference call to discuss these results on Friday, November 2, 2018 at 9:00 a.m. Eastern time. The call-in number for the conference call is (323) 994-2082 or (888) 204-4368 and the replay number is (719) 457-0820, with a pass code of 5168578. The replay will run for 30 days. Additionally, the call will be broadcast live over the Internet and can be accessed and replayed through the investor relations section of the Company's website at www.mastec.com.
Net income attributable to MasTec, Inc.
(a) Represents the tax effect of the adjusted items that are subject to tax, including the tax effects of non-cash stock-based compensation expense. Tax effects are determined based on the tax treatment of the related items, the incremental statutory tax rate of the jurisdictions pertaining to each adjustment, and taking into consideration their effect on pre-tax income.
Ended December 31, 2018 Est.
Guidance for the Year Ended December 31, 2018 Est.
The tables may contain slight summation differences due to rounding.
MasTec, Inc. is a leading infrastructure construction company operating mainly throughout North America across a range of industries. The Company's primary activities include the engineering, building, installation, maintenance and upgrade of communications, energy and utility infrastructure, such as: wireless, wireline/fiber, satellite communications and customer fulfillment activities; petroleum and natural gas pipeline infrastructure; electrical utility transmission and distribution; power generation; and industrial infrastructure. MasTec's customers are primarily in these industries. The Company's corporate website is located at www.mastec.com. The Company's website should be considered as a recognized channel of distribution, and the Company may periodically post important, or supplemental, information regarding contracts, awards or other related news on the Events & Presentations page in the Investors section therein.


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NCMI NEWS
How to play Hearthstone's Battlegrounds mode
11 months ago WPUser
Heathstone's new Battlegrounds mode, which is in early access for Descent of Dragons pre-purchasers now, takes after the autobattler craze started by Dota Auto Chess. All the work is in preparation. The actual fights happen without your input.
I didn't get into any of the Auto Chess spinnoffs, and didn't expect to get into Battlegrounds. But dammit, it hooked me immediately. It's unreasonably satisfying. Something about knowing what's going to happen before it does—a massive resummoning of my minions, maybe—is terribly seductive. And the slow building of power over the course of a game makes me feel like an evil mastermind.
Or a down-on-his-luck peasant. Sometimes, the cards you're dealt just don't cut it. It's also a bit slow in the early rounds, but that hasn't stopped me from wanting to play more.
There's a comprehensive tutorial the first time you launch Battlegrounds, but if you forgot anything or want to know what's going on in streams, here's how it works.
How to get in to the Battlegrounds beta
Right now, the only way to play Battlegrounds is to pre-order the Descent of Dragons expansion. If you attended BlizzCon or bought a Virtual Pass, you also have access. The early access period will last until 12 am PST on November 12. At that point, the open beta begins, and anyone can play.
You can find Battlegrounds by clicking the new 'Modes' button at the main menu.
(Image credit: Blizzard)
How Battlegrounds is structured
Battlegrounds is a competition between eight players. Like in regular Hearthstone, you're trying to defend your hero while dealing damage to the opposing hero—heroes, in this case. The last hero standing wins.
Games alternate between two phases. First, there's a recruit phase in the Tavern where you can purchase minions, play them, use your hero power, and upgrade the selection of minions. After that, you enter combat with another player. Combat is completely automated. If you're able to clear out their minions, your remaining minions help you damage their hero.
Once combat has resolved, you head back to the Tavern for another buy phase. You don't lose minions who died. The only thing that carries over from combat phases into buy phases is your hero's health.
Choosing a hero
Battlegrounds will launch with 24 heroes, but at the start of a match, you only have three to pick from. Your hero power will inform your strategy, so keep it in mind as you plan. So far, I've found that simple permanent buffs are my best bet.
The recruit phase
Rather than mana, your resource in Battlegrounds is gold. You begin with three gold, and get one more gold each round. Gold acts like mana and does not carry over between rounds, so you'll have four gold at the start of the second recruit phrase even if you had gold left over after the first phase. (Which you won't, because there's no reason not to buy a minion during the first phase.)
Minions always cost three gold, no matter how powerful they are. Gold can also be spent to increase the power level of the minions offered in the Tavern, represented by stars. The cost of moving to the next tier decreases each round.
If you recruit three of the same minion, they'll combine into a powerful gold version of that minion and you'll be given a card you can redeem for another free minion a tier higher. If you've buffed one of those three minions, those buffs will carry over to the gold card, so tripling is never a bad thing. (That is, unless your strategy rests on having two of those minions in play for some reason. That hasn't been the case for me yet, and you can always find new, non-gold versions of a tripled minion to play.)
Refreshing the stock of minions available costs one gold, but freezing them in place so they'll be available in the next round costs nothing. If you see a minion you want but can't afford it, smash that freeze button.
You can also use your hero power during this phase, unless it's a passive power, and it'll cost between one and four gold depending on your hero.
Once you've recruited a minion, you can then place it on the board, which doesn't cost anything. A played minion can't be returned to your hand, but you can sell it back for one gold. You can rearrange minions on the board after they've been placed.
The battle phase
During battles, all you have to do is sit back and watch. Your minions will duke it out with one of the other eight players' minions until they're all dead, or one side has won. When you win, your remaining minions will contribute to your hero's attack number—the higher the minion tier, the more attack it adds—and then your hero gets to take a swipe at the opposing hero. You'll continue to fight every remaining player until one is left standing. (This means that occasionally you'll fight a player that's already dead, if there are an odd number left.)
Minions always attack from left to right, so you can set up strategy where a minion on the left side of the board sets up one on the right by sacrificing itself early to trigger an effect.
After the battle phase, you head back to the Tavern for another Recruit phase.
Basic strategy
Winning requires a combination of two tactics. One is to buff your minions to absurd levels. This is possible because, after battles, your minions always return to the state they were in during the last recruit phase. If you use a Battlecry card that increases another card's attack by two, it'll have that buff for the rest of the game. Some cards also have effects that trigger at the beginning and end of a turn, which refers to when you enter the Tavern and when you exit the Tavern. Those are permanent. Near the end of a Battlegrounds game, just about every minion on the board has double digit attack and health numbers.
The second tactic is to set up chain reactions. Each battle phase is a last-minion-standing brawl, and sometimes the other side can be worn down by focusing on summoning and other in-battle effects.
It can be difficult to decide when to sell back a buffed one-star minion to make room for a new five-star minion. Sometimes it's worth doing, but a board full of low-level minions who've been hitting the gym can work, too.
One decision to make early on is which minion types you're going for: Mech, Murloc, Demon, Beast, or a combination, as some powers and cards benefit from variety. What I've found important is knowing when to change plans, ditch one strategy and pick up another. Also pay attention to who you're battling next. If they're at the bottom of the pile, it might be a good round to bump the Tavern tier level up.
We'll have more on Battlegrounds soon. If you're liking it, or not liking it, let us know how you feel in the comments.
Tags: Hearthstone
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Rookie QB gets win against Cam Newton. Well done lad.
Barring disaster, Mark Sanchez will never play an NFL snap ever again.
You know Sanchez is already in Dallas? He's backing up the rookie Prescott untill Romo returns although your point is valid on his career direction!
Siemian could win this job easily. Kubiak has liked him for ages and it's not like Paxton Lynch is Andrew Luck. If he plays the whole season like he did tonight and can iron out a few mistakes, he would be wanted elsewhere if Denver didn't want him.
They've drafted Lynch with the aim of developing into the starter, I think it'll take a lot for Siemian to qin this job long term, as I've said before Denver is my team so I've been following the QB situation here, realistically Trevor Siemians best result here is to get himself the back up job long term or even impress enough that someone else chases him for a starting gig but it'll take something special for them to burn a first round pick to keep Siemian as starter.
RG3 and the Browns are a perfect fit.
Larry Fitzgerald. What a player!
Interesting talk coming out of Dallas that if Prescott plays well enough he may keep the job when Romo comes back, guess they've had enough of the injuries?
Jimmy G converted some big 3rd downs.
A decent snap by the Cardinals and the Patriots lose but Garropolo was pretty good.
Great first weekend so far. I backed Kansas and Oakland all up. Still can't believe I collected on that. How gutsy was the play call to go for 2 and win the game!
Career peak in fantasy this week too. Only way is down unfortunately. I play in a league of 14 with 3 franchise players each, so already 39 players missing from draft. Picked up Sanu, Snead and Demarco Murray this season and all had brilliant games. My franchise gun, AJ Green also killled it, as did Bailey my kicker and Suh dominated in defense. Fat Boy Lacy was ok. Brady my other franchise player obviously out. Stuck with Mariota for 4 weeks who was basically rubbish but threw 2 TDs to Murray. Extremely handy!
Watch them bust next week!!
Playing without Gronk at Arizona on his first career start, I reckon he'd have got the plaudits regardless of if that kick was good or not.
RG3 now on IR, poor kid can't catch a break!
RG3 didn't play well yesterday but Cleveland are a terrible, terrible team with a bad line. He was a punching bag for the second half. Furthermore, they have no ground game to support the pass so without the deep ball, they have nothing. Plus, that Philly DEF is good. I'm not saying RG3 is good, he's not, but it's not entirely his fault.
I hope the Redskins can win but it's the ultimate unknown. A bit like following Richmond in the AFL. I'm hoping the improved secondary can have a flow on effect to the pass rush.
Is Cousins actually any good? Pittsburgh are down a few starters on DEF so opening night at home is not bad way to start for him.
Rams should win. 49ers just aren't good at all.
Brown & Ben. Seriously? What a throw/catch/call.
Cousins poor start to the game has cost Redskins a lead should be 14-7 or 10-7 at worst.
What a frustrating half of football.
Should be level at worst. The last Steeler touchdown could have gone anywhere but Cousins was off on the first few possessions and when you're playing Pittsburgh, that is not a luxury you can afford. He hardly saw a snap in the pre-season but has said he wouldn't be rusty.... hmmm.
The Steeler offense started to move the sticks pretty easily. Ominous.
He just threw a pick, off the back foot, on a 3 man rush.
Speeding up the snap count should not be a priority. Stopping the run would be a start, as would tidying up offside calls and establishing a running game.
Cousins could also start to throw the ball closer to the sticks on third and long; rather than throwing it well short and asking the receivers to make plays.
Oh well... Steelers will be hard to stop this season but Washington looked terrible. Just horrific.
Rams were deplorable, 49ers looked ok. Carlos Hyde is an elite RB that just needs to stay fit, Kerley looks an excellent late pick up, and their D line is still very good.
Everyone knows Big Ben is throwing to Antonio and they still cant stop it. Incredible player.
If the Steelers can stay fit on offense I don't know how easily they can be stopped. I mean it's week 1 but they're so productive. Even a decent defense should be enough to help them win 10-12 games pretty comfortably.
Antonio Brown was the only first choice skill player available on offense. They had TE1/WR2/RB1 all missing and they still put up 35-odd points.
Washington stink so much. Cousins has bet on himself. He better start improving.
The Jets are good. The Bills secondary was hopeless... eventually they had to start defending the pass and that helped Forte who struggled early on. Scoreline flattered the Bills I thought.
They are. Their defense is really good, particularly the front 7.
Fitzpatrick tosses it downfield and Marshall & Decker make some plays. Agreed: fun to watch.
Going to lose fantasy due to opponent having Melvin Ingram. Bloody linebacker on 20 points in a half of football!!


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Patrick Stewart says Picard series is 'a world of Star Trek he never envisioned'
"These guys were breaking those rules again and again and again," says the Jean-Luc Picard actor
By Morgan Jeffery
Thursday, 16th January 2020 at 4:11 pm
Patrick Stewart very nearly turned down the chance to reprise his iconic role of Jean-Luc Picard in a new Star Trek series – but has revealed that it was the creative team's willingness to 'break the rules' of the franchise that convinced him to sign up.
Stewart will play Jean-Luc again in Star Trek: Picard, 18 years after his final big-screen outing as the character in 2002's Nemesis.
"I was all ready with my speech of refusal," he explained last night (15th January) at a screening of the first episode in London's Leicester Square.
"Indeed, I insisted through my representative that I would meet them face-to-face, and tell them why I was going to say, "NO!"– I did my best.
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"And [once] the meeting was over, I asked my agent, 'Would you ask them if they could put on paper the things that they said to me just now. Because I'd like to study them a lot closer.' Because, believe me, the very last thing that I felt I wanted, or needed, was to return to Star Trek.
Star Trek: Picard has already been renewed for season 2
"Well, two days later, 35 pages showed up, and I read them, and… I was hooked. Because what they were writing about was an image of the future of Jean-Luc and the world of Star Trek that I had never envisioned before, and thought could not even be possible under the overriding rule of what Star Trek is, and what it isn't.
"These guys were breaking those rules again and again and again. And, well, that's the kind of stuff that interests me. And with increasing excitement, I signed on."
Alex Kurtzman, executive producer on the Star Trek franchise, agreed that his desire and that of the creative team on Picard was to do something with the series and the character of Jean-Luc that had "not been done before".
"Patrick said, 'I don't want to just do season 8 of The Next Generation. I want it to be the next chapter of this man's life.' Picard is living with regret and loss in a way that is profound. The idea that he has this opportunity in a very unexpected way to right the wrongs he feels he was a part of; he has a second chance to make amends.
Patrick Stewart and Marina Sirtis in Star Trek: Picard
"It's a beautiful story. You almost never get to tell that story from the point of view— Jean-Luc is 92 years old in Starfleet years How many shows allow you to tell the story from the point of view of somebody who's looking back on their life, and giving them one last chance of hope? I think that's what we really wanted to say."
Star Trek: Picard will explore the retired Admiral Picard's life post-Starfleet, as a new arrival in his life takes him on an unexpected journey of discovery. Franchise veterans Jonathan Frakes (Will Riker), Marina Sirtis (Deanna Troi), Brent Spiner (Data) and Jeri Ryan (Seven of Nine) will also reprise their roles, alongside Trek newcomers Alison Pill, Harry Treadaway and Santiago Cabrera.
The series launches Friday 24th January on Amazon Prime Video.
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