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 \begin{document}

 \begin{titlepage}

 \begin{flushright}
 arXiv:0802.4122
 \end{flushright}

 \vspace{5mm}

 \begin{center}

 {\Large \bf Growth Index of DGP Model and Current Growth Rate Data}

 \vspace{10mm}

 {\large Hao~Wei$^{\,}$\footnote{\,email address:
 haowei@mail.tsinghua.edu.cn}}

 \vspace{2mm}
 {\em Department of Physics and Tsinghua Center for Astrophysics,\\
 Tsinghua University, Beijing 100084, China}

 \end{center}

 \vspace{5mm}
 \begin{abstract}
Recently, some efforts focus on differentiating dark energy and
 modified gravity with the growth function $\delta(z)$. In the
 literature, it is useful to parameterize the growth rate
 $f\equiv d\ln\delta/d\ln a=\Omega_m^\gamma$ with the growth
 index $\gamma$. In this note, we consider the general DGP model
 with any $\Omega_k$. We confront the growth index of DGP model
 with currently available growth rate data and find that the DGP
 model is still consistent with it. This implies that more and
 better growth rate data are required to distinguish between
 dark energy and modified gravity.\\

 \noindent PACS numbers: 04.50.-h, 98.80.Es, 98.65.Dx
 \end{abstract}

 \end{titlepage}

 \newpage

 \setcounter{page}{2}

\section{Introduction}\label{sec1}
The current accelerated expansion of our
 universe~\cite{r1,r2,r3,r4,r5,r6,r7,r8,r9,r49} has been one of the
 most active fields in modern cosmology. There are very strong
 model-independent evidences~\cite{r10} (see also e.g.~\cite{r11})
 for the accelerated expansion. Many cosmological models have been
 proposed to interpret this mysterious phenomenon, see
 e.g.~\cite{r1} for comprehensive reviews.

In the flood of various cosmological models, one of the most
 important tasks is to discriminate between them. Recently,
 some efforts have been made. For instance, it is important to
 determine that the dark energy is cosmological constant or
 dynamical dark energy~\cite{r1}. Caldwell and Linder proposed
 a so-called $w-w^\prime$ analysis in~\cite{r12} to discriminate
 dark energy models, and then was extended in~\cite{r13,r14}.
 A recent review on $w-w^\prime$ analysis can be found
 in~\cite{r15}. Another tool to discriminate models is the
 statefinder diagnostic proposed by Starobinsky~{\it et al.}
 in~\cite{r16}. For a comprehensive list of relevant works on
 $w-w^\prime$ analysis and statefinder diagnostic, one can see
 e.g.~\cite{r17} and references therein.

Recently, some efforts to discriminate models focus on
 differentiating dark energy and modified gravity with the growth
 function $\delta(z)\equiv\delta\rho_m/\rho_m$ of the linear matter
 density contrast as a function of redshift $z$. By now, most of
 cosmological observations merely probe the expansion history of
 our universe~\cite{r1,r2,r3,r4,r5,r6,r7,r8,r9,r49}. As well-known,
 it is very easy to build models which share a same cosmic expansion
 history by means of reconstruction between models. Therefore, to
 distinguish various models, some independent and complementary
 probes are required. Recently, it is argued that the measurement
 of growth function $\delta(z)$ might be competent, see
 e.g.~\cite{r18,r19,r20,r21,r22,r23,r24,r25,r26,r27,r28,r29,r30,r31,r38}.
 If two models, especially dark energy and modified gravity models,
 share a same cosmic expansion history, they might have
 {\em different} growth history. Thus, they could be distinguished
 from each other.

One of the leading modified gravity models is the so-called
 Dvali-Gabadadze-Porrati~(DGP) braneworld model~\cite{r32,r33},
 which altering the Einstein-Hilbert action by a term arising from
 large extra dimensions. For a list of references on DGP model, see
 e.g.~\cite{r29,r34} and references therein. The first approach to
 study the growth function $\delta(z)$ of DGP model is numerical
 solution, see e.g.~\cite{r25,r27,r35}. The second approach is
 to parameterize the growth rate $f\equiv d\ln\delta/d\ln a$, where
 $a=(1+z)^{-1}$ is the scale factor of our universe.

For many years, it has been known that a good approximation to
 the growth rate $f$, within Einstein gravity, is given by
 \be{eq1}
 f\equiv\frac{d\ln\delta}{d\ln a}=\Omega_m^\gamma,
 \end{equation}
 where $\gamma$ is the growth index, whereas $\Omega_m$ is the
 fractional energy density of matter. In the very beginning,
 Eq.~(\ref{eq1}) was introduced in~\cite{r36,r37}. There, $f$ was
 defined purely in terms of the present value, using the present
 matter density, not valid for arbitrary redshift. Also, it was
 not until~\cite{r21} that it was applied to anything beyond
 matter, curvature, and a cosmological constant. Finally, not
 until~\cite{r28} was it applied to gravity other than general
 relativity, and then in~\cite{r19} generalized to modified
 gravity, varying equation of state, and an integral relation for
 growth. This parameterized approach has been tested in some works
 recently, see e.g.~\cite{r18,r19,r20,r22,r28,r29,r30,r31,r38}.
 The theoretical value of $\gamma$ for $\Lambda$CDM model is
 $6/11\simeq 0.545$~\cite{r18,r19} whereas $\gamma\simeq 0.55$ for
 other parameterized dark energy models~\cite{r19}. The theoretical
 growth index of flat DGP model (whose $\Omega_k=0$ exactly) is
 $\gamma=11/16=0.6875$~\cite{r18} (In fact, $\gamma=11/16$ is
 a high redshift asymptotic value. $\gamma=0.68$ is favored for the
 fit to the whole growth history to the present, while another
 approximation is given in Eq.~(27) of~\cite{r18} for any redshift,
 with $\gamma=7/11$ in the asymptotic future). Therefore,
 it is possible to distinguish the dark energy model (including
 $\Lambda$CDM model) from the flat DGP model.

In this note, we consider the general DGP model with any $\Omega_k$.
 We confront the growth index of DGP model with currently available
 growth rate data and find that the DGP model is still consistent
 with it. On the other hand, it is shown that the $\Lambda$CDM
 model is also consistent with current growth rate data~\cite{r31}.
 This implies that more and better growth rate data are required to
 distinguish between dark energy and modified gravity models.

\section{Growth index of DGP model}\label{sec2}
In the DGP model, the Friedmann equation is modified
 as~\cite{r33} (see also e.g.~\cite{r28,r29,r39})
 \be{eq2}
 H^2+\frac{k}{a^2}-\frac{1}{r_c}\sqrt{H^2+\frac{k}{a^2}}
 =\frac{8\pi G}{3}\rho_m,
 \end{equation}
 where $H\equiv\dot{a}/a$ is the Hubble parameter; a dot denotes the
 derivative with respect to cosmic time $t$; the constant $r_c$ is
 the crossover scale; spatial curvature $k=0$, $k>0$ and $k<0$ for
 flat, closed and open universe, respectively. Here, we only consider
 the self-accelerating branch. It is easy to rewrite Eq.~(\ref{eq2})
 as an equivalent form~\cite{r33} (see also e.g.~\cite{r40})
 \be{eq3}
 H^2+\frac{k}{a^2}=\frac{8\pi G}{3}\left(\sqrt{\rho_m+\rho_{r_c}}
 +\sqrt{\rho_{r_c}}\right)^2,
 \end{equation}
 where $\rho_{r_c}\equiv 3/(32\pi G r_c^2)$. One can alternatively
 recast Eq.~(\ref{eq2}) as the ``standard'' form
 \be{eq4}
 H^2+\frac{k}{a^2}=\frac{8\pi G}{3}\left(\rho_m+\rho_{de}\right),
 \end{equation}
 where
 \be{eq5}
 \rho_{de}=\frac{3}{8\pi Gr_c}\sqrt{H^2+\frac{k}{a^2}}
 =2\sqrt{\rho_{r_c}}\left(\sqrt{\rho_m+\rho_{r_c}}
 +\sqrt{\rho_{r_c}}\right),
 \end{equation}
 in which we have used Eq.~(\ref{eq3}) in the last equality. Here,
 $\rho_{de}$ can be regarded as an {\em effective} ``dark energy''
 component, which compiles the contributions to the Friedmann
 equation from the extra dimensions~\cite{r28,r29}. From
 Eq.~(\ref{eq4}), we have
 \be{eq6}
 1-\Omega_k=\Omega_m+\Omega_{de},
 \end{equation}
 where $\Omega_k\equiv -k/(a^2H^2)$, and
 $\Omega_i\equiv (8\pi G\rho_i)/(3H^2)$ for $i=m$ and $de$. From
 Eqs.~(\ref{eq5}), (\ref{eq6}) and the energy conservation equation
 $\dot{\rho}_{de}+3H(\rho_{de}+p_{de})=0$, we find that the
 {\em effective} equation-of-state parameter~(EoS) for the
 {\em effective} ``dark energy'' component
 $w_{de}\equiv p_{de}/\rho_{de}$ is given by
 \be{eq7}
 w_{de}=\frac{-1+\Omega_k}{1+\Omega_m-\Omega_k}.
 \end{equation}
 For the flat DGP model whose $\Omega_k=0$ exactly, we get
 $w_{de}=-(1+\Omega_m)^{-1}$, which agrees with the one
 of~\cite{r28,r29}. From Eq.~(\ref{eq3}), it is easy to see that
 \be{eq8}
 E^2(z)\equiv\left(\frac{H}{H_0}\right)^2=
 \left[\sqrt{\Omega_{m0}(1+z)^3+\Omega_{r_c}}
 +\sqrt{\Omega_{r_c}}\right]^2+\Omega_{k0}(1+z)^2,
 \end{equation}
 where we have used $\rho_m=\rho_{m0}a^{-3}$; the subscript ``0''
 indicates the present value of the corresponding quantity;
 $\Omega_{r_c}\equiv (8\pi G\rho_{r_c})/(3H_0^2)=1/(4H_0^2 r_c^2)$.
 From Eq.~(\ref{eq8}), we have
 \be{eq9}
 1=\left[\sqrt{\Omega_{m0}+\Omega_{r_c}}
 +\sqrt{\Omega_{r_c}}\right]^2+\Omega_{k0}.
 \end{equation}
 Therefore, only two of $\Omega_{m0}$, $\Omega_{r_c}$ and
 $\Omega_{k0}$ are independent model parameters. For the flat DGP
 model whose $\Omega_{k0}=0$ exactly, Eq.~(\ref{eq9}) becomes
 $\Omega_{m0}=1-2\sqrt{\Omega_{r_c}}$.

In Einstein gravity, the growth function $\delta(z)$ at scales much
 smaller than the Hubble radius obeys the following differential
 equation~\cite{r18,r19,r20,r21,r31,r40}
 \be{eq10}
 \ddot{\delta}+2H\dot{\delta}=4\pi G\rho_m\delta.
 \end{equation}
 In modified gravity, Eq.~(\ref{eq10}) has been modified
 to~\cite{r27,r28,r29,r40}
 \be{eq11}
 \ddot{\delta}+2H\dot{\delta}=4\pi G_{\rm eff\,}\rho_m\delta,
 \end{equation}
 where $G_{\rm eff}$ is the effective local gravitational
 ``constant'' measured by Cavendish-type experiment, which is
 time-dependent. In general, $G_{\rm eff}$ can be written as
 \be{eq12}
 G_{\rm eff}=G\left(1+\frac{1}{3\beta}\right),
 \end{equation}
 where $\beta$ is determined once we specify the modified
 gravity theory. In the DGP gravity, $\beta$ is given
 by~\cite{r27,r29,r39,r40}
 \be{eq13}
 \beta=1-2r_cH\left(1+\frac{\dot{H}}{3H^2}\right).
 \end{equation}
 By using Eq.~(\ref{eq3}), $\beta$ can be written as~\cite{r40}
 \be{eq14}
 1+\frac{1}{3\beta}=\frac{4\Omega_m^2-4\left(1-\Omega_k\right)^2
 +\alpha} {3\Omega_m^2-3\left(1-\Omega_k\right)^2+\alpha}\,,
 \end{equation}
 where
 \be{eq15}
 \alpha\equiv 2\sqrt{1-\Omega_k}\left(3-4\Omega_k+2\Omega_m\Omega_k
 +\Omega_k^2\right).
 \end{equation}
 For the flat DGP model whose $\Omega_k=0$ exactly, we get
 $\beta=-(1+\Omega_m^2)/(1-\Omega_m^2)$, which agrees with the
 one of~\cite{r28,r29}. Following~\cite{r21,r31}, we rewrite
 Eq.~(\ref{eq11}) as
 \be{eq16}
 \left(\ln\delta\right)^{\prime\prime}
 +\left(\ln\delta\right)^{\prime 2}
 +\left(2+\frac{H^\prime}{H}\right)\left(\ln\delta\right)^{\prime}
 =\frac{3}{2}\left(1+\frac{1}{3\beta}\right)\Omega_m,
 \end{equation}
 where a prime denotes the derivative with respect to $\ln a$.
 By using Eqs.~(\ref{eq4}), (\ref{eq6}) and the energy conservation
 equation $\dot{\rho}_{de}+3H(1+w_{de})\rho_{de}=0$, we find that
 \be{eq17}
 \frac{H^\prime}{H}=\frac{\dot{H}}{H^2}=-\frac{3}{2}
 +\frac{\Omega_k}{2}-\frac{3}{2}w_{de}\left(1-\Omega_k
 -\Omega_m\right),
 \end{equation}
 where $w_{de}$ is given in Eq.~(\ref{eq7}). Substituting
 Eq.~(\ref{eq17}) into Eq.~(\ref{eq16}), we obtain
 \be{eq18}
 \left(\ln\delta\right)^{\prime\prime}
 +\left(\ln\delta\right)^{\prime 2}
 +\left(\ln\delta\right)^{\prime}\left[\frac{1}{2}\left(1+
 \Omega_k\right)-\frac{3}{2}w_{de}\left(1-\Omega_k
 -\Omega_m\right)\right]
 =\frac{3}{2}\left(1+\frac{1}{3\beta}\right)\Omega_m,
 \end{equation}
 In fact, the growth rate
 $f\equiv d\ln\delta/d\ln a=\left(\ln\delta\right)^{\prime}$. By
 using the definition of $\Omega_m$, the energy conservation
 equation $\dot{\rho}_m+3H\rho_m=0$ and Eq.~(\ref{eq17}), we have
 \be{eq19}
 \Omega_m^\prime=\Omega_m\left[3w_{de}\left(1-\Omega_k
 -\Omega_m\right)-\Omega_k\right].
 \end{equation}
 Therefore, we find that
 \be{eq20}
 \left(\ln\delta\right)^{\prime\prime}=f^\prime=
 \Omega_m\left[3w_{de}\left(1-\Omega_k-\Omega_m\right)
 -\Omega_k\right]\frac{d\,f}{d\,\Omega_m}.
 \end{equation}
 So, Eq.~(\ref{eq18}) becomes
 \be{eq21}
 \Omega_m\left[3w_{de}\left(1-\Omega_k-\Omega_m\right)
 -\Omega_k\right]\frac{d\,f}{d\,\Omega_m}+f^2
 +f\left[\frac{1}{2}\left(1+
 \Omega_k\right)-\frac{3}{2}w_{de}\left(1-\Omega_k
 -\Omega_m\right)\right]
 =\frac{3}{2}\left(1+\frac{1}{3\beta}\right)\Omega_m,
 \end{equation}
 where $w_{de}$ and $\beta$ are given in Eqs.~(\ref{eq7})
 and~(\ref{eq14}), respectively. Substituting Eq.~(\ref{eq1}) into
 Eq.~(\ref{eq21}) and expanding around $\Omega_m=1$ (good
 approximation especially at $z\, \lower .75ex \hbox{$\sim$} \llap{\raise .27ex \hbox{$>$}} \,1$), after some tedious
 algebra, we finally arrive at
 \be{eq22}
 10\gamma\left(\Omega_m-1\right)-\Omega_k\left(1-2\gamma\right)
 +3\left(1-2\gamma\right)\left(1-\Omega_m\right)
 =6\left(\Omega_m-1\right)+\Omega_m\left[\left(\Omega_m
 -1\right)\left(\Omega_m+1\right)+2\Omega_k\right],
 \end{equation}
 where we have ignored the higher order terms of small quantities
 $1-\Omega_m$ and $\Omega_k$. Noting that Eq.~(\ref{eq6}), namely
 $1-\Omega_m=\Omega_k+\Omega_{de}$,
 we consider three cases for Eq.~(\ref{eq22}).

 \begin{description}
  \item[Case~(I)]
  $\Omega_k=0$ exactly or
  $\Omega_k\ll\Omega_{de}=1-\Omega_m\ll 1$.\\
  In this case, throwing out the terms of $\Omega_k$ in
  Eq.~(\ref{eq22}), then eliminating $\left(\Omega_m-1\right)$ in
  both sides, and using $\Omega_m\to 1$ finally, we have
  $\gamma=11/16$. Obviously, it agrees with the known one of the
  flat DGP model~\cite{r18}.

  \item[Case~(II)]
  $\Omega_{de}\ll\Omega_k=1-\Omega_m\ll 1$.\\
  In this case, eliminating $\left(\Omega_m-1\right)=-\Omega_k$ in
  both sides of Eq.~(\ref{eq22}) and then using $\Omega_m\to 1$,
  we have $\gamma=4/7$. In fact, it coincides with the curvature
  solution found firstly in~\cite{r51} and could be considered as
  a special case of the results in~\cite{r21,r18}  with $w=-1/3$.

  \item[Case~(III)]
  $\Omega_k\sim\Omega_{de}\sim 1-\Omega_m\ll 1$.\\
  In this case, $\Omega_k$, $\Omega_{de}$ and $1-\Omega_m$ are
  at the same order. Noting that $1-\Omega_m=\Omega_k+\Omega_{de}$,
  for convenience, we parameterize
  $\Omega_k=m\left(1-\Omega_m\right)$, where $0<m<1$. It is worth
  noting that generally $m$ is time-dependent and one considers
  only an instantaneous value of $m$. Substituting into
  Eq.~(\ref{eq22}), then eliminating $\left(\Omega_m-1\right)$
  in both sides, and using $\Omega_m\to 1$ finally, we have
  \be{eq23}
  \gamma=\frac{11-3m}{16-2m}.
  \end{equation}
  Obviously, when $m\to 0$ and $1$, $\gamma\to 11/16$ and
  $4/7$, respectively.
 \end{description}

\noindent For the flat DGP model whose $\Omega_k=0$ always, the
 only theoretical growth index is given by $11/16$. For the DGP
 models whose $\Omega_k\not=0$, the situations are different.
 Noting that $\Omega_m\propto (1+z)^3$, $\Omega_k\propto (1+z)^2$
 and $\Omega_{de}\propto (1+z)^{3(1+w_{de})}$ with $w_{de}<-1/3$
 to accelerate the expansion of our universe, $\Omega_k$ increases
 faster than $\Omega_{de}$ when $z$ increases. So, for high $z$,
 $\Omega_{de}\ll\Omega_k=1-\Omega_m\ll 1$ eventually. Thus, we have
 $\gamma=4/7$ eventually, regardless of the value of $\Omega_{k0}$.
 However, if $\Omega_{k0}$ deviates from $0$ very small, it is still
 possible that $\Omega_k\ll\Omega_{de}=1-\Omega_m\ll 1$ at high $z$,
 where $\gamma=11/16$; eventually $\gamma=4/7$ at higher $z$. On the
 other hand, if $\Omega_{k0}$ deviates from $0$ not so small, the
 only theoretical growth index is given by $4/7$.

Finally, it is worth noting that the above results are obtained as
 high redshift asymptotic values, rather than values for the whole
 growth history or the asymptotic future. On the other hand, the
 general solution of $\gamma$ is obtained in~\cite{r18} for the
 flat DGP model. We refer to~\cite{r18} for details on this.

\section{Confronting with current growth rate data}\label{sec3}
The most useful currently available growth rate data involve the
 redshift distortion parameter $\beta_L$~\cite{r41} observed through
 the anisotropic pattern of galactic redshifts on cluster
 scales~\cite{r42} (see also~\cite{r31}). The parameter $\beta_L$
 is related to the growth rate $f$ as~\cite{r31}
 \be{eq24}
 \beta_L=\frac{f}{b},
 \end{equation}
 where $b$ is the bias factor. We present the currently available
 data for $\beta_L$ and $b$ at various redshifts in Table~\ref{tab1},
 along with the inferred growth rates. This is an extended version
 of the dataset used in Ref.~\cite{r31}, and contains a new data
 point at $z=0.77$~\cite{r45}. Hereafter, we call the five data
 points except the one at $z=0.77$ as dataset ``Fobs'' and call
 all the six data points as dataset ``Fobsext''.

About the currently available growth rate data, it is worth noting
 that there is considerable variation in analysis of different
 references and hence there is no accomplished consensus in fact.
 On the other hand, many of these results are not of the growth
 rate in isolation but fold in other large scale structure
 information. Besides, in Table~\ref{tab1}, some of the quoted
 values include the other datasets in the analysis, e.g. \cite{r46}
 includes \cite{r43} to derive their value of $\beta_L$. So, one
 should use these data with caution.

Using the growth rate data in Table~\ref{tab1}, we can perform
 a $\chi^2$ analysis to find the growth index $\gamma$ and
 check its consistency with the theoretical values. As well-known,
 the corresponding $\chi^2$ reads
 \be{eq25}
 \chi^2({\bf p},\gamma)=\sum\limits_i\left[\frac{f_{obs}(z_i)-
 f_{th}(z_i;{\bf p},\gamma)}{\sigma_{f_{obs}}}\right]^2,
 \end{equation}
 where $f_{obs}$ and its corresponding $1\sigma$ uncertainty
 $\sigma_{f_{obs}}$ are given in Table~\ref{tab1}; $\bf p$ denotes
 the model parameters; $f_{th}(z_i;{\bf p},\gamma)$ can be obtained
 from Eq.~(\ref{eq1}), in which $\Omega_m$ can be rewritten as
 a more convenient form
 \be{eq26}
 \Omega_m(z)=\frac{\Omega_{m0}(1+z)^3}{E^2(z)},
 \end{equation}
 and $E(z)$ can be found in Eq.~(\ref{eq8}).

 \begin{table}[tbp]
 \begin{center}
 \begin{tabular}{ccccc} \hline\hline
 $z$ & $\beta_L$ & $b$ & $f_{obs}$ & Reference\\ \hline
 $0.15$ & $0.49\pm 0.09$ & $1.04\pm 0.11$
 & $0.51\pm 0.11$ & \cite{r43}\\
 $0.35$ & $0.31\pm 0.04$ & $2.25\pm 0.08$
 & $0.70\pm 0.18$ & \cite{r7}\\
 $0.55$ & $0.45\pm 0.05$ & $1.66\pm 0.35$
 & $0.75\pm 0.18$ & \cite{r44}\\
 $0.77$ & $0.70\pm 0.26$ & $1.3\pm 0.1$
 & $0.91\pm 0.36$ & \cite{r45}\\
 $1.4$ & $0.60^{+0.14}_{-0.11}$ & $1.5\pm 0.20$
 & $0.90\pm 0.24$ & \cite{r46}\\
 $3.0$ & {\bf ---} & {\bf ---} & $1.46\pm 0.29$ & \cite{r47}\\
 \hline\hline
 \end{tabular}
 \end{center}
 \caption{\label{tab1} The currently available data for $\beta_L$
 and $b$ at various redshifts, along with the inferred growth
 rates. Notice that Ref.~\cite{r47} only reports the growth rate
 and not the $\beta_L$ and $b$ parameters, since the growth rate
 was obtained directly from the change of power spectrum
 $Ly-\alpha$ forest data in SDSS at various redshift slices. This
 is an extended version of the dataset used in Ref.~\cite{r31},
 and contains a new data point at $z=0.77$~\cite{r45}.}
 \end{table}

It is worth noting that the references in Table~\ref{tab1} have
 assumed flat $\Lambda$CDM (with $\Omega_{m0,\Lambda}=0.30$ for the
 five data points except the one at $z=0.77$, and with
 $\Omega_{m0,\Lambda}=0.25$ for the data point at $z=0.77$) when
 converting redshifts to distances for the power spectra and
 therefore their use to test models different from $\Lambda$CDM
 might be unreliable, as stressed in~\cite{r31}. However, we can get
 around this problem in a new way. As mentioned above, the key is
 the redshift-distance relation. If the DGP model and $\Lambda$CDM
 model share the same redshift-distance relation, these growth rate
 data can also be used in the DGP model. To this end, we should
 properly select the model parameters of DGP model in order to
 reproduce the same redshift-distance relation of $\Lambda$CDM
 model. There is a simple and efficient method. As well-known
 in any textbook, the comoving distance is given by
 \be{eq27}
 r(z)\equiv\frac{1}{H_0\sqrt{\left|\Omega_k\right|}}\,
 F\left(\sqrt{\left|\Omega_k\right|}\int_0^z
 \frac{d\tilde{z}}{E(\tilde{z})}\right),
 \end{equation}
 where the function $F(x)=x$, $\sin x$ and $\sinh x$ for
 $\Omega_k=0$, $\Omega_k<0$ and $\Omega_k>0$, respectively.
 For convenience, we use the dimensionless comoving distance
 $H_0r(z)$ instead. It is easy to get the $H_0r(z)$ line for the
 flat $\Lambda$CDM model with $\Omega_{m0,\Lambda}=0.30$. Then, we
 discretize it into many points in a redshift range (for instance,
 $0\leq z\leq 4$, which covers the range of current growth data),
 and manually assign a relative ``error'' (say, $0.5\%$) to these
 discrete points. So, we have many {\em fake} ``data points'' in
 hand. Then, we fit the DGP model to these {\em fake} ``data
 points'' and find out the ``best fit'' parameters. Obviously,
 the DGP model with these ``best fit'' parameters will share the
 same redshift-distance relation with the flat $\Lambda$CDM model.
 Hence, the growth rate data in Table~\ref{tab1} can also be used
 for the corresponding DGP model. Finally, there is a minor remark
 on the procedure mentioned above. In fact, it holds only for the
 low redshift quantities considered here. Comparison of the
 distances to CMB last scattering ($z\sim 1100$) will show large
 differences between these matching models. Fortunately, the
 redshift of current growth data is less than $4$ and the procedure
 mentioned above works well.

 \begin{center}
 \begin{figure}[htbp]
 \centering
 \includegraphics[width=0.98\textwidth]{repflat.eps}
 \caption{\label{fig1} The $H_0r(z)$ of flat DGP model with the
 corresponding ``best fit'' parameters (red dashed line) and flat
 $\Lambda$CDM model with $\Omega_{m0,\Lambda}=0.30$ (black solid
 line) are shown in left panel. The right panel shows the relative
 departure between these two $H_0r(z)$ lines.}
 \end{figure}
 \end{center}

We consider the flat DGP model whose $\Omega_{k0}=0$ exactly
 at first. Following above method, we find that the ``best fit''
 parameter of flat DGP model is $\Omega_{r_c}=0.1519$ (the
 corresponding $\Omega_{m0}=0.2204$). In Fig.~\ref{fig1}, we show
 the $H_0r(z)$ of the corresponding flat DGP model along with the
 one of flat $\Lambda$CDM model with $\Omega_{m0,\Lambda}=0.30$.
 The largest relative departure between these two $H_0r(z)$ lines
 in range $0\leq z\leq 4$ is less than $1.5\%$. Similarly, we
 consider the general DGP model with any $\Omega_{k0}$ and find
 that the ``best fit'' parameters of DGP model are
 $\Omega_{m0}=0.2217$ and $\Omega_{r_c}=0.1734$ (the corresponding
 $\Omega_{k0}=-0.0921$). In Fig.~\ref{fig2}, we show the $H_0r(z)$
 of the corresponding DGP model along with the one of flat
 $\Lambda$CDM model with $\Omega_{m0,\Lambda}=0.30$. Obviously,
 these two $H_0r(z)$ lines are degenerate in fact. The largest
 relative departure between the $H_0r(z)$ of DGP model with the
 corresponding ``best fit'' parameters and flat $\Lambda$CDM model
 with $\Omega_{m0,\Lambda}=0.30$ in range $0\leq z\leq 4$ is less
 than $0.19\%$ surprisingly. The DGP model with corresponding
 ``best fit'' parameters excellently reproduces the same
 redshift-distance relation of the flat $\Lambda$CDM model with
 $\Omega_{m0,\Lambda}=0.30$. So, the growth rate data in
 Table~\ref{tab1} can also be used for the corresponding DGP model.
 It is worth noting that all the above ``best fit'' parameters are
 consistent with the constraints of~\cite{r29,r48,r39} (see also
 e.g.~\cite{r34,r50}) and therefore they are also observationally
 acceptable.

 \begin{center}
 \begin{figure}[htbp]
 \centering
 \includegraphics[width=0.98\textwidth]{repgen.eps}
 \caption{\label{fig2} The same as in Fig.~\ref{fig1},
 except for the DGP model with $\Omega_{k0}\not=0$.}
 \end{figure}
 \end{center}

Here, we fit the growth index $\gamma$ of these ``reproduced'' DGP
 models to the growth rate data in Table~\ref{tab1}. For the case
 of flat DGP model whose $\Omega_{k0}=0$ exactly, setting
 $\Omega_{m0}$ and $\Omega_{r_c}$ as the corresponding ``best fit''
 values and minimizing $\chi^2$ with respect to $\gamma$, we find
 that for dataset Fobs,
 $\gamma=0.438^{+0.126}_{-0.111}$ with $1\sigma$ uncertainty, or
 $\gamma=0.438^{+0.272}_{-0.209}$ with $2\sigma$ uncertainty; for
 dataset Fobsext, $\gamma=0.429^{+0.123}_{-0.108}$ with $1\sigma$
 uncertainty, or $\gamma=0.429^{+0.264}_{-0.205}$ with $2\sigma$
 uncertainty. Obviously, the only theoretical growth index
 $\gamma=11/16=0.6875$ is consistent with these results at
 $2\sigma$ uncertainty.

For the case of DGP model with $\Omega_{k0}\not=0$, setting
 $\Omega_{m0}$, $\Omega_{r_c}$ and $\Omega_{k0}$ as the
 corresponding ``best fit'' values and minimizing $\chi^2$ with
 respect to $\gamma$, we find that for dataset Fobs,
 $\gamma=0.465^{+0.134}_{-0.117}$ with $1\sigma$ uncertainty, or
 $\gamma=0.465^{+0.290}_{-0.221}$ with $2\sigma$ uncertainty; for
 dataset Fobsext, $\gamma=0.457^{+0.131}_{-0.115}$ with $1\sigma$
 uncertainty, or $\gamma=0.457^{+0.282}_{-0.217}$ with $2\sigma$
 uncertainty. Obviously, the theoretical growth index
 $\gamma=11/16=0.6875$ is consistent with these results at
 $2\sigma$ uncertainty, whereas the other theoretical growth index
 $\gamma=4/7\simeq 0.5714$ is consistent with these results at
 $1\sigma$ uncertainty.

\section{Concluding remarks}\label{sec4}
In summary, we consider the growth index of general DGP model with
 any $\Omega_k$ in this note. We confront the growth index of DGP
 model with current growth rate data and find that the DGP model
 is still consistent with it. On the other hand, it is shown that
 the $\Lambda$CDM model is also consistent with current growth rate
 data~\cite{r31}. This implies that more and better growth rate
 data are required to distinguish between dark energy and modified
 gravity models.

Some remarks are in order. Firstly, it is worth noting that the
 references in Table~\ref{tab1} have assumed flat $\Lambda$CDM
 (with $\Omega_{m0,\Lambda}=0.30$ for the five data points except
 the one at $z=0.77$, and with $\Omega_{m0,\Lambda}=0.25$ for the
 data point at $z=0.77$) when converting redshifts to distances
 for the power spectra and therefore their use to test models
 different from $\Lambda$CDM might be unreliable, as stressed
 in~\cite{r31}. Although we can get around this problem by means
 of reproducing the same redshift-distance relation between
 the DGP model and $\Lambda$CDM model, the really complete solution
 to this problem lies on the reanalyzing the power spectra with the
 proper redshift-distance relation in the corresponding modified
 gravity. Secondly, in fact, we fixed $\Omega_{m0}$ while fitting
 for $\gamma$ in section~\ref{sec3}. This is required to ensure
 the validity of matching procedure of finding an equivalent DGP
 model. We admit that this weakens our conclusion. It is desirable
 to find a new method to improve the validity of matching
 procedure in the future works. Thirdly, one may use other
 parameterizations to the growth rate $f$, such as
 $f=\Omega_m^\gamma(1+\eta)$~\cite{r30}, or $f=\Omega_m^\gamma$
 with $\gamma=\gamma_0+\gamma_0^\prime z$~\cite{r38}. However, the
 additional parameters $\eta$ and $\gamma_0^\prime$ are found to
 be negligible in fact~\cite{r30,r31,r38}. On the other hand, since
 currently available growth rate data points are so few and have
 large errors, it is difficult to tightly constrain these
 additional parameters. Fourthly, although as shown in~\cite{r23}
 that non-trivial dark energy clustering or interaction between
 dark energy and dark matter might bring some troubles,
 we consider that combining the probes of expansion history and
 growth history is still promising to distinguish the dark energy
 and modified gravity. Of course, new idea to distinguish dark
 energy and modified gravity is still desirable.

\section*{Acknowledgments}
We thank the anonymous referee for expert comments and quite useful
 suggestions, which help us to improve this work. We are
 grateful to Professor Shuang~Nan~Zhang and Professor Rong-Gen~Cai
 for helpful discussions. We also thank Minzi~Feng,
 as well as Hong-Sheng~Zhang, Nan~Liang, Rong-Jia~Yang, Wei-Ke~Xiao,
 Pu-Xun~Wu, Jian~Wang, Lin~Lin and Yuan~Liu, for kind
 help and discussions. The initial part of this work was completed
 during the period of Chinese New Year 2008, with an impressive
 disaster of snowstorm and cold rain in southern China. We
 acknowledge partial funding support from China Postdoctoral Science
 Foundation, and by the Ministry of Education of China, Directional
 Research Project of the Chinese Academy of Sciences under project
 No.~KJCX2-YW-T03, and by the National Natural Science Foundation
 of China under project No.~10521001.

redpajama_set_name: RedPajamaArXiv


Video game audio solution provider Audiokinetic has released Wwise 2009.3, the latest version of its award-winning audio pipeline solution, including a number of notable new enhancements.
Audiokinetic and McDSP had announced a technological partnership a few months ago, and the ML1 and FutzBox plug-ins are the first results of this collaboration.
The Montreal-based company, whose tool is used by companies such as High Voltage and Frontier Developments, also gave a sneak-peek of its roadmap for Wwise for 2010, and revealed that new features will include a convolution reverb.


text:
Facebook Hot Desk
We just deleted over a third of our Facebook page Like base!
Should you be doing the same? Possibly. But why, you ask?
Back in the old days (2010), the only thing any business with a Facebook page thought about was Likes. How many Likes do we have? How many Likes can I get $100? How quickly can I get another 1,000 Likes?
Growing your social community was critically important. The more Likes your Facebook business page had, the more people would see your content, and hopefully engage with it. The more people engaged, the more people beyond that initial group were also exposed to your posts. This is the basic concept of organic reach. Well, that just proves that you need lots of Likers right? Wrong!
Page Likes and Organic Reach
We remember when we first started posting on Business Pages, organic reach was sitting at approximately 16%, this dropped to 6% in 2014. 2016 saw it sitting at 3% and today? Well today its below 1%, yes BELOW 1%.
If the audience that is exposed to your post interacts with it in some way, Facebook thinks "wow, this must be good content" and will feed your post out to a little more of your audience. But what if the 1 person that saw that post was a "bought" Like or someone who only liked your page because of that "Like our page to go into the draw to win an iPad" competition you ran last year? Well, they probably won't interact with the post, ergo, the post reach is stunted by the algorithm and your content doesn't get out there, even if it's the best, most amazing content your business has produced! With the continued tweaks to the newsfeed algorithm, users who Like your page might never actually see your content organically.
But there is an even more important reason why the quality of Likes is more important than the quantity… and that's audience purity.
What is Audience Purity and why does it matter?
With the organic reach of Facebook sitting as low as it is, businesses are being forced to turn to paid advertising to get their message or content out there. In order to do this you need to create an audience to send your content out to. The most obvious of these: your current Like base. Of course! But what if more than half of them are "Zombie Likes". And by Zombies I don't mean the walking dead (or maybe I do?), I mean non genuine followers. People who are not actively wanting to know more about your business. You are about to spend money pushing your wares to people who don't want to know. Money that could be spend reaching people who do!
And let's not forget the most powerful audience tool that we have right at our fingertips, the Lookalike Audience. When you create a lookalike audience, Facebook looks for users with the same demographic and interests etc as your existing audience. You then pay to advertise to them. Before creating a lookalike audience with your Like base, you need to ask yourself' "What kind of audience am I pulling into my funnel?" This is also true of lookalike audiences from old email lists, event databases etc. The more diluted these audiences are to start, the less robust your lookalike audience is going to be. And that means one thing: your ads are going to be doomed to produce little, or what it does produce is at high cost!
But what about Social Proofing?
At the most basic level, 'social proof' refers to the basis that people are (sadly) sheep and follow the flock. People allow their purchase decisions to be influenced by the demonstrated actions of others. To put it another way, when people see other people buying or endorsing a product, they will want it too – ergo a purchase validator.
By now you know that Facebooks is removing Like counts from posts. Their reason? "To emphasise the quality of content users share and take away the popularity aspect, which has associated mental-health implications for teens." Great, I'm happy to see that vanity metric vanish. But what does this mean for your posts? Even though the Likes can't be seen, it's still very important your content is engaging (in particular getting people to comment or share). Remember the organic engagement formula? The more people engage, the more people will be shown your content. And it has an effect on the cost of your ads. Yes, the more "social proof" your ads have, the less it costs you to get the post out to your audience.
Our Decision
Coming back to us, in our case, we've been around since 2011. Recently we ran a series of posts through the ad account specifically targeting our Facebook Like base and found the quality of return to be poor. Why? The business we were in 2011 is unrecognisable to the one we are now and the original Likers from 8 years ago are not necessarily relevant to our audience target market today.
So, what does this mean? We could be wasting our money and poisoning our marketing funnel! Why? Quite simply, we could be advertising to an audience (both our original and lookalike) that are irrelevant and not interested in our services. This means our top of funnel is polluted which filters all the way down, our social proofing is poor and the cost of advertising is much higher than it should be.
An interesting little side fact: According to one study, only 1% of users who Like a brand on Facebook will actually visit that brand's Facebook Page.
The moral of the story: the number of Likes your page has isn't important…. The quality of the Likes is important.
Time to revisit your audience and possibly rethink your Like count?
Facebook to limit number of ads Pages can run simultaneously
Facebook Unveils New Logo
Agency Transparency
Facebook Campaign Budget Optimisation Not Yet Mandatory
Why You Should Use A Specialist Agency
The Facebook Link Shim
The Facebook Sales Funnel
A Basic Guide To The Facebook Pixel
The Dunbar Effect
© 2019 ALL RIGHTS RESERVED. BLUE FLAME SOCIAL MEDIA | ABN 70 850 926 405
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redpajama_set_name: RedPajamaCommonCrawl


text:
History of the Va'a
(Source: Wikipedia)
Va'a have been traveling the Pacific Ocean for more than 4,000 years. In around 2,000 BC a wave of seafaring people emerged from Asia and ventured out into the Eastern Pacific Ocean, for the first time in Human history. The earliest va'a are thought to have originated at this time and we now know that ancient Polynesians and their ancestors settled the most remote islands of the Pacific in single and double hull va'a. These canoes were often sailing vessels and could be much larger than today's racing V6. When the first Europeans arrived in Polynesia, sailing va'as of up to 30 meters in length were recorded, designed for long ocean passages.
Va'a were originally developed by the Austronesian speaking peoples of the islands of Southeast Asia for sea travel, and were used to transport these peoples both eastward to Polynesia and New Zealand and westward across the Indian Ocean as far as Madagascar during the Austronesian migration period. Even today, it is mostly among the Austronesian groups (Malay, Micronesian, Melanesian and Polynesian peoples) that va'a are used.
Va'a for fishing are also used among certain non-Austronesian groups, like the Sinhala in Sri Lanka, where they are known as oruwa, as well as among some people groups in the Andaman and Nicobar Islands.
When Magellan's ships first encountered the Chamorros of the Mariana Islands in 1521, Antonio Pigafetta recorded that the Chamorros' sailboats far surpassed Magellan's in speed and maneuverability.
The Polynesian Voyaging Society has two double hull sailing va'a, Hōkūle'a and Hawai'iloa, and sails them between various islands in the Pacific using traditional Polynesian navigation methods without instruments.
The technology has persisted into the modern age. Va'a can be quite large fishing or transport vessels, and in the Philippines, outrigger canoes (called bangka, parao or balanghai) are often fitted with petrol engines. The links between seafaring and outrigger canoes in the Philippines extend through to political life, in which the smallest political unit in the country still called Barangay after the historical Balanghai outrigger proas used in the original migrations of the first Austronesian peoples across the archipelago and beyond.
History of modern Va'a Sport
Records show that from the beginning there were Va'a races, mostly between fishermen, families and small Polynesian and Melanesian villages. Later, teams from different islands were competing against each other and today, paddlers from all over the world come together to race in Va'a.
The modern Va'a sport was developed in Tahiti and Hawaii. At the beginning of the 19th Century, Va'a races in the lagoon already played an important role during the traditional cultural "Heiva" festival in Tahiti. At the turn of the 20th Century, organized va'a races emerged in Hawaii, where clubs like Hui Nalu and the Outrigger Canoe Club that were founded at that time still thrive today.
In particular from Tahiti and Hawaii, the modern va'a sport spread around most of the Polynesian, Micronesian and Melanesian Islands, but also moved to Australia, USA, Canada, South America and Asia…and finally to Europe.


text:
Q: How to convert Gtk.Image to base64 I have a Gtk.Image object and I want to convert it's data to a base64 encoded string (for use with imgur). How would I achieve that?

A: Has to run it through a gdk.pixbuf, but this seems the easiest:
import cStringIO
import base64

pixBuf = gtkImage.get_pixbuf()

fH = cStringIO.StringIO()
pixBuf.save_to_callback(fH.write, "png")
encodedBuffer = base64.b64encode(fH.getvalue()) #base64 encoded png

redpajama_set_name: RedPajamaStackExchange


text:
Q: Angular6: Mat-tree-node selection/click event implementation I am using Angular Material Tree Control with dynamic data.
Here is the link of complete example:
example is here
It works as mentioned in example. Now i want to enable each node click event and send the (angular expression) bound data in my typescript function.
Can anyone guide me ?
I tried different codes but tree node couldn't be enabled for clicking.
See html :
    <mat-tree [dataSource]="dataSource" [treeControl]="treeControl">
  <mat-tree-node *matTreeNodeDef="let node" matTreeNodePadding>
    <button mat-icon-button disabled ></button>
    {{node.item}}
  </mat-tree-node>
  <mat-tree-node *matTreeNodeDef="let node; when: hasChild" matTreeNodePadding>
    <button mat-icon-button  (click)="applyFilter($event)"
            [attr.aria-label]="'toggle ' + node.filename" matTreeNodeToggle>
      <mat-icon class="mat-icon-rtl-mirror">
        {{treeControl.isExpanded(node) ? 'expand_more' : 'chevron_right'}}
      </mat-icon>
    </button>
    {{node.item}}
    <mat-progress-bar *ngIf="node.isLoading"
                      mode="indeterminate"
                      class="example-tree-progress-bar"></mat-progress-bar>
  </mat-tree-node>
</mat-tree>

I tried this source but still unable to fix it. I tried with stack overflow solutions but it couldn't solve my issue yet.
 ngAfterViewChecked() {
    this.treeNodes.forEach((reference) => {
      if (!this.hasListener.includes(reference.nativeElement)) {
        console.log('* tick');

        this.renderer.listen(reference.nativeElement, 'click', () => {
          this.updateHighlight(reference);
        });
        this.renderer.listen(reference.nativeElement.children.item(0), 'click', () => {
          this.updateHighlight(reference);
        });

        this.hasListener = this.hasListener.concat([reference.nativeElement]);
      }
    });

    this.hasListener = this.hasListener.filter((element) => document.contains(element));
    console.log('*', this.hasListener.length);
  }

A: You could wrap your {{node.item}} in a mat-button and bind to the click event from there to pass the node element to your component method.
<mat-tree-node *matTreeNodeDef="let node" matTreeNodePadding>
    <button mat-button (click)="logNode(node)">
      {{node.item}}
    </button>
</mat-tree-node>

Then in your component
 logNode(node){
    console.log(node)
  }


Left side seal between the Blazer body side and the single wall removable top. 'Single Wall' tops bolt from the top down into the bed. 'Double Wall' tops bolt from the bed up into the top.
Left side refers to the Drivers side of the vehicle.


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text:
Q: Handling Data Annotation Validation with Custom ValidationResult I have a custom ValidationAttribute like this :

public class ReceiverRegion : ValidationAttribute
    {
        private RegionService regionService;
        private CityService cityService;

        public ReceiverRegion() : base("Incorrect region code")
        {
            this.regionService = new RegionService();
            this.cityService = new CityService();
        }

        protected override ValidationResult IsValid(object value, ValidationContext validationContext)
        {
            int regionId = Convert.ToInt32(value);
            int plate = Convert.ToInt32((validationContext.ObjectInstance as CorporateOrderItem).ReceiverCity);

            int productGroupId = Convert.ToInt32(validationContext.Items["productGroup"].ToString());

            if (!CheckReceiverRegionExistence(regionId, plate, productGroupId))
            {
                IEnumerable regions = this.regionService.GetList(cityService.GetByPlate(plate).PKCityId);

                return new CorporateOrderValidationResult(base.ErrorMessage, regions.Select(r=>r.Name));
            }
            return CorporateOrderValidationResult.Success;
        }

        private bool CheckReceiverRegionExistence(int plate, int regionId, int productGroup)
        {
            return !(regionService.GetByCityAndRegionIdForProductGroup(plate, regionId, productGroup) == null);
        }
    }

But as you can see in IsValid method, I'm trying to return a custom object which inherits from ValidationResult. My problem is, I can't access the extra members of my CorporateOrderValidationResult instance since IsValid returns the base ValidationResult type. Below is the code where I call validate and get a collection of ValidationResult as return value.

List results = new List();
bool isValid = Validator.TryValidateObject(instance, context, results, true);

I tried to cast results object to List<CorporateOrderValidationResult>, but no matter what I try(for instance --> item as CorporateOrderValidationResult or results.OfType<CorporateOrderValidationResult>() or (CorporateOrderValidationResult)item) I either get InvalidCastException or null value. Is there a possible way to convert this list of result to a list of my custom result class? Thanks...

A: I tried to reproduce this behavior, but everything works as expected:
public class TestClass
{
    [TestValidation]
    public string TestProp { get; set; }
}

public class TestValidationAttribute : ValidationAttribute
{
    protected override ValidationResult IsValid(object value, ValidationContext validationContext)
    {
        return new TestResult();
    }
}

public class TestResult : ValidationResult
{
    public TestResult()
        : base("test")
    {
    }
}

Code for validation:
var instance = new TestClass();
var context = new ValidationContext(instance, null, null);
var results = new List<ValidationResult>();
bool isValid = Validator.TryValidateObject(instance, context, results, true);
//Contains one instance of TestResult
var customResults = results.OfType<TestResult>().ToArray();

A: I know this is old question, but first result in Google when you ask for custom ValidationResult class. Example presented by Vyacheslav Volkov works, but why?
I spent few hours today trying to make my code working - the key line is:
public TestResult(): base ("test")
I was not going to use error message at all, I had my own structure for this so I wrote my ctor like this:
public TestResult() : base("") - empty string sent to base class has consequences, that are not mentioned in documentation. TryValidate() method will not insert our object into results collection as it is returned by our version of IsValid(), but will build new one with default error message for this field, like "Field " + fieldName + " is Invalid" and put it instead of the one we want.


text:
Timely Insights for Healthcare Experts
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First Treatment for Post-partum Depression FDA Approved
Tuesday, March 19, the FDA approved Zulresso (brexanolone) injection for intravenous (IV) use to treat post-partum depression (PPD) in adult women. No other drug before now has been approved to specifically treat PPD. Zulresso will be available through Risk Evaluation...
FDA Allows Marketing of Device to Treat Carbon Monoxide Poisoning
The Food and Drug Administration (FDA) has allowed marketing of ClearMate to treat patients suffering from carbon monoxide poisoning in emergency rooms. Malvina Eydelman, M.D., director of the Division of Ophthalmic, and Ear, Nose and Throat Devices in the FDA's...
FDA Approves a New Generic Valsartan to Mitigate Shortages
As of March 12, 2019 the U.S. FDA approved a new generic of Diovan (valsartan) for high blood pressure and heart failure to relieve the shortage from multiple recalls of generic valsartan products from several manufacturers. The approval of the new generic of Diovan...
Increase in Measles 2018 -Feb 2019
Measles, also known as rubeola or "first disease", is a highly contagious viral infection caused by paramyxovirus, causing a prodrome of fever, cough, coryza, and conjunctivitis followed by eruption of maculopapular rash. The CDC states 2 main reasons for the increase...
CDC Report Confirms HIV Prevention has Stalled
CDC published a report today that provides the most recent data on HIV trends in America from 2010 to 2016. The results show a stagnation in the decline of HIV infections, with numbers of HIV Infections leveling off at about 39,000. When taking a deeper dive into the...
Washington Public Officials Investigate Measles Outbreak
Public Officials in Clark County, Washington are investigating a measles outbreak after reports of 34 confirmed cases and nine suspected cases since the first of January. Of the 34 cases, thirty-two have been confirmed to be unimmunized, while four remain unverified....


It's a redeeming day in America when even the most highly organized and well-funded criminals realize how difficult the U.S. legal system is to manipulate.
Neumont University – who has spent the last 2.5 years suing, stalking, and harassing me in an attempt to censor negative student reviews of their school from the web – is one such entity. Unfortunately for Neumont, they apparently forgot that outside of Utah, the reach of their powerful "LDS" Mormon friends is still rather limited.
Neumont: A Big Fish In A Small Pond?
In the case of Neumont – a for-profit technical institute based in Utah that lacks both regional and ABET accreditation – even paying off newspapers like the Salt Lake Tribune and Deseret Times, hiring one of the largest law firms in the western United States, getting two judges on their "SLAPP lawsuit" docket both of whom have a history of colluding with Mormon figures, and threatening their own students and faculty against speaking out… STILL didn't prevent an embarrassing, and costly, courtroom loss.
Of course, the best part of all is that I spent exactly $0 on a legal defense.
On February 9, 2015, I gave Neumont University, LLC until February 19, 2015, to serve defendant Jesse Nickles "by email at jesse@littlebizzy.com and file proof of this service." Doc. 69 at 9. More than a month has passed since this 10-day service deadline ran, and Neumont has not filed proof of service or explained why service of the filing of the notice was not possible. … As Neumont has apparently elected not to avail itself of these extensions of the service deadlines and the ability to serve Nickles by email, I now give Neumont until April 1, 2015, to comply with my prior instructions or have its claims against Nickles dismissed without prejudice and this case closed.
After proceedings dragged on for more than 2 years, Neumont's legal costs had jetted past $100,000 according to court-required disclosures (which Neumont had unsuccessfully attempted to hide from the court), despite claiming initial losses against my web hosting business, Little Bizzy, of only $72,000 (the lost revenue of one student who allegedly decided not to attend Neumont after "reading negative reviews" of the school on CollegeTimes). Due to my financial inability to hire a corporate attorney, the case eventually went into default judgement, at which point Neumont suddenly (and without explanation) changed their lost revenue claims to be over $1 million.
What never ceases to amaze me is how pretty much every single for-profit diploma mill falls into exactly the same pitfalls; specifically, scam schools like Neumont and their president, Edward "Ned" Levine get so carried away running their corrupt little fiefdoms and are so thoroughly cut off from reality that they literally can't see beyond their own minuscule worlds of fraud, threats, and ego-stroking power trips.


The European Union has decided to level up it's policies for data protection concerning it's citizens given the trend towards big data collection of users for marketing & online social connection purposes.
** ALERT 1 ** If you do not serve any citizens of the European Union, then stop reading, because this will not affect you.
However, if you do serve European customers EVEN if your company is not based in the European union this affects you.
** ALERT 2 ** I am not a lawyer! None of what I write should be taken as legal advice and am writing this solely as an interpreter of the GDPR, reading others' articles, and from general understanding of data protection laws. When designing compliant processes you should always consult a lawyer.
Without getting too much into it, GDPR has a few minimum requirements for compliance that you need to follow in order to not get hit with the fine hammer which can nail you with a fine up to $20,000,000.
We're not really sure how the EU will be able to collect that if your company is located in any country outside the EU, but I will say if you receive a notice in the mail, you'll probably want to avoid vacationing in France anytime soon.
Avoiding fines however, is quite easy. Here are the few things you need to implement in order to be compliant.
** Alert 3 ** As a North American company I have focused on the aspects of GDPR which are most likely to affect the "average" North American company. If your company is based in the EU, you should absolutely consult a GDPR specialist or a lawyer when designing and implementing your GDPR compliant processes.
Any user which comes under the purview of GDPR (so anyone in the EU) must have an easily accessible way to send a request to you company that will allow them to request any information you may have on them.This one is a bit trickier and you have a few things to consider.
Obviously the easiest way to do it is place an information request form on your site, but that request form should have a way to identify someone not only by email, as doing it by email only is very insecure.
Should you have a fair amount of information on someone, anyone with an email address can just request a ton of information about someone else without verification of identity.
Thus you should have a way to identify customers on another basis, for example the amount of their last payment, their last billing order ID, or another form of Personally Identifiable Information so that you can quickly verify someone's identity.
Upon request from a user, you are obligated to erase ANY trace of that contact data from your company databases.
There are more exceptions and I highly encourage you to do your own research.
Once you complete the erasure of the contact, you are obligated to notify the contact of the erasure, and notify them of all the other parties that have had access to that person's information, in the case they may want to remove themselves from those parties as well.
Those are the big ones that I discovered. Of course your proximity to the European Union might affect these regulations and you may need to pay attention to others as well.
For those most part, understanding and implementing the above as a small-medium business operating in North America should keep you safe.
To read the GDPR articles for yourself, visit this site where you can browse and search the articles form items that may directly affect your company.
If you use FormLift, you may be wondering if it is GDPR compliant, or at least how you can ensure GDPR compliance with it.
The short answer is mostly. We have plans to make it completely compliant BEFORE the deadline enforcement date of GDPR which is 25 May 2018.
The item that has to be added for compliance is the ability to easily delete contacts from the submissions table, however you can do that VIA the PHPAdmin if need be.
EDIT: 2018/05/05: FormLift is fully GDPR compliant as of version 7.4.0 which was released on May first.
We are also adding a special custom field types to FormLift. The GDPR field which will auto generate a compliant checkbox.
This will not be sent to Infusionsoft, but it doesn't need to. As long as it is present in the form you are fine.
So, simply add this field to your form, and you should be good to go.


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Die Cynodontia (wörtlich "Hundezähner") sind eine Gruppe der Therapsida. Sie weisen innerhalb der Therapsiden die größte Artenvielfalt auf. Sie werden heute von den Säugetieren repräsentiert, alle anderen Untergruppen starben bereits im Mesozoikum aus.

Die ersten Cynodontia erschienen vor ca. 270 Mio. Jahren während des Perms. Fossilien aus dieser Zeit wurden in Südafrika, Sambia, Russland und Westeuropa gefunden. Die Tiere überlebten das Massenaussterben am Ende des Perms und erlebten eine rasche adaptive Radiation in der Trias –, eine Entwicklung, die in der Entstehung der Säugetiere gipfelte. Jene Cynodontia, die keine Säugetiere waren, überlebten wahrscheinlich bis zur Unterkreide, zumindest aber bis in den Mitteljura.

Merkmale
Die Cynodontia teilen eine Reihe von Merkmalen mit den Therocephalia, mit denen sie zusammen das Taxon Eutheriodontia bilden. Ihre Monophylie ist durch insgesamt 27 Synapomorphien, die meisten den Schädel betreffend, gut begründet. Ihre Schädel ähneln denen der Säugetiere, die Schläfenregion ist breit, der Jochbogen lädt weit aus, die Schnauze ist meist niedrig. Von Procynosuchus und seinen Verwandten abgesehen, gibt es bei allen Cynodontia einen sekundären Gaumen, der Atmungs- und Nahrungsweg voneinander trennt. Gaumenfenster gibt es nicht. Das Flügelbein erreicht hinten nicht mehr das Quadratbein. Das Quadratjochbein, das bei den Säugern fehlt, und das Quadratbein, das bei den Säugern zum Amboss, einem der Gehörknöchelchen, geworden ist, sind stark reduziert. Am großen, plattenförmigen Hinterkopf entstehen allmählich die zwei Kopfgelenke der Säugetiere.

Im Unterkiefer ist das Dentale der mit Abstand größte Knochen. Die dahinter liegenden Knochen werden weiter zurückgebildet. Im Unterkiefer folgen auf die Eckzähne 7 bis 13 Backenzähne, die breit und mit zahlreichen Höckern versehen sind. Die Backenzähne sind teilweise schon in Prämolare und Molare unterteilt.

Vollständige Skelette wurden nur wenige gefunden, wahrscheinlich war der Schwanz meist kurz. Stets gibt es vier Kreuzwirbel. Die Gliedmaßen, Schulter- und Beckengürtel sind säugerähnlich, die Anzahl von Zehengliedern, ähnlich wie bei den Reptilien, noch hoch (Phalangenformel 2,3,4,4,3).

Systematik

Arten (Auswahl)
 Traversodontidae
 Gomphodontosuchinae
 Protuberum ,  & , 2009
 Protuberum cabralensis ,  & , 2009

Literatur
 Thomas S. Kemp: The Origin & Evolution of Mammals. Oxford University Press, Oxford 2005. ISBN 0-19-850761-5.
 Oskar Kuhn: Die Säugetierähnlichen Reptilien. A. Ziemsen Verlag, 2003, ISBN 3-89432-797-9.

Weblinks

 Palæos Cynodontia: Overview

Synapsiden
Synapsida

redpajama_set_name: RedPajamaWikipedia


NCERT solutions for class 12 Maths has been written to help students understand all the problems in the textbooks prescribed by NCERT. The class 12 maths NCERT solutions help students solve the exercises given in the textbooks and get good marks in their board exam. Download NCERT solutions for Class 12 Maths PDF format for all chapters English and Hindi Medium for UP Board (Intermediate NCERT), MP Board, Gujrat Board ( onward) as well as CBSE Board updated form. We are planning to upload class 12 R D Sharma, P K Garg, R S Aggarwal book. Let's continue diving deeper into the world of math and master topics from class 12 (NCERT) such as inverse trigonometric functions, matrices and determinants, .
NCERT Solutions for Class 12 Maths includes all the questions provided in NCERT Books for 12th Class Maths Subject. Here all questions are. NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Chapter 2 Inverse Trigonometric Functions Chapter 3 Matrices. Here is a list of all of the math skills students learn in grade 12! These skills are organized into categories, and you can move your mouse over any skill name to .
Free NCERT Solutions for Class 12 Maths in PDF form free download. CBSE books sols Hindi & English medium for for CBSE, MP & UP Board. Unit I: Relations and Functions. 1. Relations and Functions. Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto. NCERT Solutions for Class 12 Maths has been written to help students like you who are appearing for different board exams as well as the JEE.


DAWSON SPRINGS, KY., — Kimble R. Ladd, 82 of Dawson Springs passed away Tuesday, February 12, 2019 at Baptist Health in Madisonville, Kentucky. He was born in Ilsley, KY on March 16, 1936 to the late McKinley Ladd and Lillian Rowe Ladd. He was of the Pentecostal faith and he had worked as a security guard.
He was preceded in death by his sister Valva Berger.
He is survived by his 3 children Beverly Anderson of Smyrna, TN., Alan (Robin) Ladd of Crofton, Tim (Amy) Ladd of Dawson Springs, 2 sisters Glenda Faye St. Vincent of Madisonville, Gail Frasier of Earlington, 1 brother Deon Ladd of Dawson Springs, 7 grandchildren, many great grandchildren, several nieces and nephews.


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Junkyard Gem: 1938 Ford De Luxe Tudor Sedan
Edward Halcomb January 18, 2023
Since most of the historical gems I document in the junkyard (that's right, historical, so those of you who are fixing to blow a brain gasket because you don't consider a certain Junkyard Gem to be as good as your beloved Chevelle SSs or Porsche 911s can calm down now) are found in the big self-service yards with high inventory turnover, I don't write about many vehicles from the 1930s. Oh, sure, I do find such cars now and then — a 1937 Hudson and a 1938 Oldsmobile just this year, for example — but for prewar iron, it's best to head for an old-time family-owned yard that's been in the same spot forever.
Now that the former Martin Supply in Windsor, Colorado, has become a very professional but somewhat sterile seller of mostly late-model inventory, my go-to establishment when I want to give my old film cameras a workout is now Speedway Auto Wrecking, just off I-25 in Dacono. Speedway is only open on Saturday mornings now, but it's worth scheduling your weekend around a visit. There are hundreds, maybe thousands of American cars and trucks from the 1930s through 1970s in this sprawling family-owned yard a half-hour north of Denver.
I found this Ford not too far from the section with all the Chevrolet Vegas and Chevettes (at least a couple of dozen of each) and an easy walk to the 30 or so Corvairs. I was there with my artist friend, Paul Heaston, who sketched a portrait of the Dodge truck you see in the background while I shot photos.
I brought a foursome of American film cameras from the 1910s-1950s period with me, but I haven't developed the film yet. Check in at my photography page later to see the shots.
Judging by the apparent vintage and decayed condition of the tires plus the completely sun-nuked interior, I'm going to guess that this car last moved under its own power when Dwight D. Eisenhower was president.
Ford was notable during the 1930s for selling low-cost cars with eight-cylinder engines. Chevrolets and Plymouths had to get by with straight-sixes in 1938.
And Ford's eight-bangers weren't old-timey straight-eights. This is the 221-cubic-inch (3.6-liter) flathead V8, rated at an impressive 85 horsepower. Chevrolet's six also made 85 horses that year, thanks to its modern overhead-valve design; the Plymouth flathead sixes made either 70 or 82 horsepower in 1938.
You could get the '38 Ford with a smaller-displacement version of the flathead V8, known as the V8-60, but most American Ford buyers went for the 221.
Two trim levels were available for the 1938 Tudor two-door sedan: the upscale De Luxe and the penny-pinching Standard. This being the De Luxe, it has the snazzier grille.
The list price for this car was $665, or about $15,215 in 2022 dollars. That was quite a deal, and the De Luxe Tudor was the second-best-selling version of the 1938 Ford (the Standard Tudor was #1), with better than 100,000 sold.
Plymouth's De Luxe two-door sedan cost $773 that year, or about $16,223 today. Chevrolet's counterpart, the Master De Luxe Coach, listed at $730 ($15,320 now). Chevrolet won the sales battle that year, with close to a half-million cars out the door, but Ford was close behind.
The interior in this one is nonexistent, basically. Perhaps someone will rescue this car, either for a period restoration or a hot rod, but there's no hurry — the elements have already done about all the damage they can do to this car by now.
A new kind of value in the low-priced field!
Automotive HistoryClassicsFordJunkyardJunkyard GemJunkyard Gemssedan
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2023 Ford Bronco Sport recalled over leaking ABS module


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HomeMusicBrown Eyed Girls' Ga-in found guilty, fined for illegal use of narcotic drug propofol
Brown Eyed Girls' Ga-in found guilty, fined for illegal use of narcotic drug propofol
(From left) Brown Eyed Girls' Ga-in, actor Ha Jung-woo and singer Wheesung (Instagram, Korean Film Council)
K-pop girl group Brown Eyed Girls member Son Ga-in was found guilty of illegally using propofol, classified as a narcotic and psychotropic drug in Korea.
The Suwon District Court issued a summary order and imposed a fine of 1 million won ($885) on Ga-in, 33, after she was summarily indicted on charges of violating Korea's Narcotics Control Act earlier this year, according to an exclusive report by Korean news outlet The Fact.
With a summary order, Ga-in's case did not go to trial. According to Korea's Ministry of Justice website, "a summary order is issued to the effect that the defendant is sentenced to a fine or penalty, or to forfeit."
Ga-in was found guilty of administering propofol, a sleep anesthetic, in a place in Gyeonggi Province in South Korea between July and August 2019. Propofol is used for anesthesia in surgeries.
Her crime became known after a plastic surgeon in his 70s was indicted on charges of violating the Narcotics Control Act and Medical Act. The Suwon District Court sentenced the doctor to one year and six months in prison and imposed a fine of 3 million ($2,655).
In June 2020, the doctor sold three boxes of Etomidate injection, an anesthetic drug, to Ga-in at a plastic surgery clinic in Seoul, which he runs, for 1.5 million won ($1,326).
He was also accused of injecting propofol to four people including Ga-in for about a year from August 2019.
Korea's Ministry of Food and Drug Safety issued standards to prevent misuse and abuse of propofol.
Last September, the ministry issued a notice, stating that propofol is a "psychotropic drug used to induce and maintain the general anesthetic state."
"Medical professionals must properly adjust propofol dose based on the patient's weight, always bearing in mind that propofol has a high risk of misuse and abuse. Propofol should not be administered independently without reasons related to surgery, surgical procedures, or medical examinations," the ministry said.
It also "advised that the number of propofol injection for simple surgical procedures does not exceed once every month and that medical professionals check on the patient's propofol usage history before prescribing." Use of propofol in Korea must be reported to authorities.
Propofol intoxication was identified as the cause of death of the King of Pop Michael Jackson in 2009.
In Korea, celebrities were found guilty of propofol misuse and abuse. In March, a court convicted singer-songwriter Wheesung, 39, of abusing propofol and sentenced him to one year in prison suspended for two years.
In May, prosecutors sought a fine of 10 million won ($8,850) against actor Ha Jung-woo for getting 10 injections of propofol at a clinic in Gangnam, Seoul from January to September 2019. He apologized for his actions.
In November 2013, actresses Park Si-yeon, Lee Seung Yeon and Jang Mi-inae were convicted for illegal use of propofol.
Source: Manila Bulletin (https://mb.com.ph/2021/07/01/brown-eyed-girls-ga-in-found-guilty-fined-for-illegal-use-of-narcotic-drug-propofol/?utm_source=rss&utm_medium=rss&utm_campaign=brown-eyed-girls-ga-in-found-guilty-fined-for-illegal-use-of-narcotic-drug-propofol)


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Николай Сенявский () (ок. 1489 — 2 февраля 1569) — один из крупнейших польских магнатов, стражник польный коронный (1531), подкоморий галицкий (1532), староста галицкий и коломийский (1534), каштелян белзский (1537), воевода белзский (1542—1553), польный гетман коронный (1539—1561), воевода русский (1553—1569), гетман великий коронный (1561—1569)

Биография
Старший сын хорунжего галицкого Рафаила из Сенявы (ум. 1518) и Агнешки Гебровской. Принимал участие в военных действиях на юго-восточных границах Великого княжества Литовского. В 1512 году участвовал в битве с крымскими татарами под Лопушным. С 1518 года служил ротмистром при короле Сигизмунде I Старом. С 1522 года участник многочисленных боев с крымскими татарами и молдаванами. В 1530—1537 гг. служил ротмистром конницы на Подолье. Пытаясь прекратить разрушительные татаро-турецкие нападения на украинские земли, организовал ряд военных походов на Крымское ханство, в частности на крепости Очаков и Белгород-Днестровский. Построил для своего проживания Бережанский замок. Николай Сенявский руководил обороной южных польских границ. В 1531 году участвовал в разгроме молдавской армии в битве под Обертыном.

Активно вмешивался в молдавские дела. В 1552 года при поддержке Николая Сенявского молдавский престол занял Александр Лэпушняну, ставший ленником Польши.

Семья
Около 1511 года женился на Катаржине Кола (ум. после 1544), дочери подкомория галицкого и польного гетмана коронного Яна Кола.

Дети
 Иероним Ярош Сенявский (1516—1579) — каштелян каменецкий и воевода русский
 Сенявский, Николай (1520-1584) — польный гетман коронный и каштелян каменецкий
 Анна Сенявская — жена каштеляна краковского Спытка Иордана
 Ян Сенявский (ум. 1583) — судья земский галицкий и каштелян львовский
 Катаржина Сенявская (ум. до 1569) — жена с 1543 г. Анджея Бучацкого Творовского (ум. 1569)
 Рафаил Сенявский (ум. 1592) — каштелян каменецкий (1589)

Сенявские
Родившиеся в 1480-е годы
Гетманы польные коронные
Гетманы великие коронные
Воеводы русские
Каштеляны белзские
Воеводы белзские


I have tried to kept it "light" this year, but at 10 challenges I think perhaps not too "light".
I will be adding the books that we read linked to their reviews into this post, which will be accessible via the tabs at the top of our blog so if you wish to access it again you easily can. And all the badges below link to the challenge host's main post, just in case you would like to join in too!
The Seventh Continent (Antarctica, the sea, the space, a supernatural/paranormal world, history, the future – you name it).
Any book by any author born in a Nordic country (Denmark, Finland, Iceland, Norway and/or Sweden) or a book set in a Nordic country.
Read at least five books by different European authors or books set in different European countries.
2012 Memorable Memoirs Reading Challenge ~ hosted by Betty Boo Chronicles.
For the buttons I created (including this one to the right) see this page.
The Basics and Fill in the Gaps perpetual challenge list.
Which of these challenges will join in?
glad we caught this...we've got you on the participants page now. Thanks for joining the challenge that you made some great buttons for!
I won't make a comment then on the page since you have us included.
I am glad you like the buttons!
Thank you for the welcome Helen, and the interesting challenge.
I found your challenge via JoV's blog.
Thanks for joining the Books in Translation challenge! I hope you enjoy the books you choose. Good luck with your other challenges as well!
For the comment and the challenge. I am looking forward to it since I love translations.
I joined the European Reading Challenge as well and I'm browsing a little through the participant's list. I'm so interested in what everybody is reading for the challenge!
Anyway, I'm curious what books you'll choose so I will come back for more! Happy reading!
Welcome home from Asia and welcome to the book blogosphere!
I promised myself not to over do it this year... but look what I have gone and done. As a new blogger (several years ago) I just could not say no to challenges. Now as a bit more seasoned blogger.... well I have not done much better - 10 challenges is a lot.
We should get quite a few books with a European setting or author this year since we did last year as well. I am hoping for some good ones!
Yep you and are the same. I could not control myself. I was thinking 5 challenges...nope!
Have you seen the blog - A Novel Challenge? It lists tons of challenges going on, which is where I found some of these.
I will be by to check out your challenges soon!
Thanks for signing up for the European Reading Challenge. I look forward to seeing which books you pick!
The Nordic Challenge is a good crossover. I hadn't seen that one before -- thanks for the tip!
I like the Nordic Challenge as well. But I am afraid we may be a bit on our own for that one.
Looking forward to what you and everyone else reads.
To be honest I do not need any more challenges beside the one saying keep your blog alive and improve.
Anyway I hope you will enjoy the challenges.
I agree, and was thinking the same thing but I guess I just could not resist.
All the very best for the challenges in 2012. You can do it!


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Q: Installing Flask on Ubuntu I'm having difficulty installing Flask on my Ubuntu machine. In fact, I tried 2 different Ubuntu computers and neither of them worked.
I followed this tutorial https://pythonprogramming.net/creating-first-flask-web-app/  where all steps are well explained.
The problem is. When I type localhost:5000 or just localhost or 127.0.0.1:5000 I get "Can't connect. Something is broken" you know that sort of message you get when server can't find index.html or index.php
Everything during the installation went okay. The only thing that didn't work well was installing virtual environment. It downloaded okay but when I ran sudo virtualenv xyz I got No such command. But Django & Flask can work without it so it shouldn't be an issue.
Any ideas ?
I deleted those as Flask don't need files to be named index.html.


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Home Canada News Londoners invited to Lighting of the Lights for 1st time since 2019...
Londoners invited to Lighting of the Lights for 1st time since 2019 – London
A well-established tradition continues in Victoria Park on Friday with the Lighting of the Lights and, for the first time since the onset of the COVID-19 pandemic, the public is invited to attend.
The City of London is putting out the invite for all to view the moment the switch is flipped on over 75,000 lights in Victoria Park. The event gets underway at 6:15 p.m. on Friday, Nov. 26, with live entertainment. The countdown to turning on the lights goes at 6:50 p.m.
The lights can then be viewed nightly from 5 p.m. to 11 p.m. until Jan. 1, 2022.
Magic of Lights to make Longwoods Road Conservation Area a winter wonderland
"I hope you'll join me and thousands of other Londoners for the annual lighting of the lights in Victoria Park. It's not only a time-honoured holiday tradition this year, it's proof of how far we've come," Mayor Ed Holder said Thursday.
"You'll remember last year restrictions were such that we could not invite the public. It was all very low key and not at all like most of us were accustomed to. But one year later, despite a more contagious variant, we're able to share in the celebration together and carefully. There are a number of reasons for this, not the least of which is vaccines."
However, the city is asking that attendees maintain physical distance from anyone outside of their household and "wear a mask/face covering when physical distance cannot be maintained."
Heading to Victoria Park for the Lighting of the Lights tonight? There are several options to bike or bus downtown. Many bus routes are a short walk away from Victoria Park.
Find all the details & prepare for your trip: https://t.co/bhPyqrzFjh@Downtown_London @tourism_london pic.twitter.com/s5ULsE6RMu
— City of London (@CityofLdnOnt) November 26, 2021
Among the illuminated conifers are specially decorated and dedicated trees:
Also Read: Gwyneth Paltrow Learns the Word "Snatched" Thanks to Kim Kardashian
Woman charged after falsely posing as nurse in B.C. hospital for a year: police
Freezing rain wreaks havoc on roads in Edmonton region, several fatal collisions Thursday morning
the Angel tree, lit in white, to honour the lives of children who have passed
the tree to commemorate troops overseas, lit in yellow
the tree of Hope, lit in pink for those who've been diagnosed with or have survived breast cancer
the tree of Wishes, lit in blue for the Make-A-Wish foundation
the purple tree to Shine the Light on Woman Abuse
the Remember, Honour, Celebrate tree, lit in red in remembrance of lives lost to HIV/AIDS
the Donor tree, lit in blue and green to represent the Trillium Gift of Life Network
the Carpenter's Union Tree, lit in yellow and blue
The city says the promenade deck at city hall, sometimes used to view the lights from above, will remain closed this year due to the pandemic.
Also in Victoria Park, the Santa House will run this holiday season through appointments will be required to visit. More information can be found on TLC Foundation's website.
Santa and his reindeers have made the trip down to Victoria Park thanks to the help of City staff and @lpsmediaoffice.
Let the holidays begin. pic.twitter.com/EP9mVK8Bo8
The outdoor skating rink at Victoria Park is slated to open Dec. 4, weather-permitting, as will the rink at Storybook Gardens.
Also Read: If you're hoping for some TV drama, this week's debates might deliver - National
The Rotary Rink at Covent Garden Market is expected to open Dec. 10, officials say.
Festival of Markets highlights Downtown London's holiday festivities
The city adds that public washrooms are currently available in Victoria Park from 10 a.m. to 8 p.m. weekdays and from 9 a.m. to 8 p.m. on weekends near the bandshell. Come Dec. 6, those hours will change to 10 a.m. to 10 p.m. daily.
Gender-neutral washrooms are available daily from 7 a.m. to 11 p.m. on Dundas Place at 179 Dundas St., on the south side of the street just east of Richmond Street.
For the rest of the year, the city says those travelling downtown or to the Old East Village by vehicle can enjoy two hours of free parking daily at municipal on-street parking meters and in municipal lots.
Downtown London
holiday tradition
lighting of lights
lighting of the lights
Londoners
Mayor Ed Holder
winter tradition
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From the beginning, J.R. Watkins has been committed to providing high-quality products and excellent customer service. Watkins first introduced the "Trial-Mark Bottle" and America's first money-back guarantee in 1869. Relying on door-to-door sales, Watkins gave customers a risk-free way to try his products by adding a molded "trial mark" to each bottle. Customers who used the natural products and stayed above the mark could get a full refund.