text:
\section{Introduction}

Dicke superradiance, i.e., the enhanced spontaneous emission in space and time of atoms in highly entangled symmetric Dicke states, has been extensively studied over the last 60 years
\cite{Dicke(1954),Eberly(1971),Manassah(1973),AGARWAL(1974),Haroche(1982),Scully(2006),Scully(2007),
Scully(2009)Super,Kaiser(2012),Kaiser(2013),
Cirac(2011),
Rohlsberger(2010),
Wiegner(2011)PRA,Oppel(2014),Wiegner(2015),Bhatti(2016)}.
In contrast, its cryptic twin, subradiance, has been much less investigated, mainly due to its higher degree of complexity and increased demands for experimental verification, even though considerable progress has been made recently. Since the first indirect observation
\cite{Pavolini(1985)}, the main focus
has been on studying subradiance of two two-level atoms \cite{DeVoe(1996), Hettich(2002), Barnes(2005), Julienne(2012),McGuyer(2015)}. This configuration
is most transparent, less fragile \cite{Woggon(2005)}, and, moreover, can be prepared in both parities, a fully symmetric as well as a fully antisymmetric state, where the latter decouples entirely from the vacuum field for small atom separations \cite{AGARWAL(1974),Haroche(1982)}. For more than two two-level atoms the subradiant Dicke states are merely non-symmetric \cite{Dicke(1954)}; the corresponding states have been recently used to form a unimodular basis \cite{Vetter(2016), Jen(2016)}. Various theoretical investigations have discussed the preparation \cite{Maser(2009),Ammon(2012),Bienaime(2012),Genes(2015),Tang(2015),Scully(2015),Mirza(2016),Durand(2016),Damanet(2016),Bettles(2016), Ganesh(2016), Jen(2017),Hebenstreit(2017),Guerin(2017)} as well as the subradiant emission characteristics of non-symmetric Dicke states for larger atomic ensembles, either using a semiclassical theory \cite{Bienaime(2012), Durand(2016),Damanet(2016), Bettles(2016), Ganesh(2016), Jen(2017), Hebenstreit(2017),Guerin(2017)} or within a full quantum mechanical treatment \cite{Tang(2015),Scully(2015),Mirza(2016),Wiegner(2011)PRA}.
Very recently, the first experimental observation of
retarded subradiant spontaneous decay for more than two emitters has been reported \cite{Guerin(2016)}.

Most theoretical studies of subradiant systems have investigated the temporal aspects of subradiance,
only few have have been devoted to its particular spatial emission properties
\cite{Wiegner(2011)PRA,Tang(2015), Durand(2016)}. Yet, in correspondence to their superradiant counterparts,
distant sources prepared in fully antisymmetric or non-symmetric Dicke states display pronounced directional emission profiles, e.g., exhibiting a strong suppression of spontaneous radiation in particular directions \cite{Wiegner(2011)PRA}.

In this letter, we study the spatial emission characteristics of
light sources arranged in totally antisymmetric states, thereby investigating what we call \textit{directional Dicke subradiance}.
We start to analyze the conditions for achieving totally antisymmetric Dicke states for $N \geq 2$  multi-level atoms or multi-photon sources and
explore the specific spatial emission profiles of emitters prepared in such states.
We next discuss the possibilities to observe subradiant directional emission behavior of classical sources.
In particular, we show that the same multi-photon interferences and thus the same subradiant suppression of incoherent radiation derived for quantum emitters can be obtained with thermal light sources (TLS),
if projected into particular correlated states via photon detection.
Finally, we present measurements of directional Dicke subradiance for up to five TLS.

In general, a totally antisymmetric state of $N$ sources is defined by
\begin{equation}
\ket{A_{N}} = \frac{1}{\sqrt{N!}} \sum_{\mathcal{P}} \text{sgn}(\mathcal{P}) \ket{n_{\mathcal{P}_1},n_{\mathcal{P}_2},\ldots,n_{\mathcal{P}_N}} \ ,
\label{eq:AntiState}
\end{equation}
where $\ket{n_{l}}$ describes the state of source $l$, $l = 1, \ldots, N$, and $\sum_\mathcal{P}$ represents the sum over all permutations of the sources, with $\text{sgn}(\mathcal{P})$ the sign of the permutation.
According to Eq.~(\ref{eq:AntiState}), in order to realize a totally antisymmetric state, all sources have to be prepared in distinct states, i.e., $n_{i}\neq n_{j}$, for $i\neq j$, otherwise the state vanishes.
In particular, in the case of two-level atoms,
a fully antisymmetric state only exists for $N=2$ particles.
Thus constructing totally antisymmetric states for $N>2$ emitters requires internal level schemes with at least $N$ distinguishable states, e.g., an excited state $\ket{e}$ and $N-1$ distinguishable  ground states $\ket{g_{\tilde{l}}}$, $\tilde{l}=1,\hdots,N-1$ \cite{Hebenstreit(2017)}.
We call this kind of source \textit{multi-level single photon emitter} (MSPE).
To construct a totally antisymmetric state for $N$ MSPE we
choose
$n_{1}=e,\, n_{2}=g_{1}, n_{3}=g_{2}, \ldots,\, n_{N}=g_{N-1}$ .

To determine the spatial emission characteristics of such a state we assume without loss of generality the simple source arrangement shown in Fig.~\ref{fig:setup}, where $N$ MSPE are located equidistantly with separation $d$ along the x-axis at positions $\vec{R}_{l} = l \, d \, \vec{e}_x$,  $l=1,\ldots , N$.
The intensity recorded at position $\vec{r}_{1}$ is defined by
\begin{equation}
	I(\vec{r}_{1}) = G^{(1)}_{\rho}(\vec{r}_{1}) = \left< E^{(-)}(\vec{r}_{1}) E^{(+)}(\vec{r}_{1}) \right>_{\rho} \ ,
\label{eq:DefIntensity}
\end{equation}
where $\rho$ is the density matrix of the $N$ MSPE and the (dimensionless) positive frequency part of the electric field operator in the far field of the sources is given by \cite{Wiegner(2015)}
\begin{equation}
\begin{aligned}
	\left[ E^{(-)}(\vec{r}_1) \right]^\dagger = E^{(+)}(\vec{r}_1) \propto \sum_{l=1}^{N} e^{-i\,l\, \delta_{1}} \;\hat{S}_{-}^{(l)} \; .
\end{aligned}
\label{eq:DefE1}
\end{equation}
In Eq.~(\ref{eq:DefE1}), $\delta_1=
- k \, d \,  \sin(\theta_{1})$ corresponds to the relative phase of a photon emitted by source $l$ and recorded by a detector at $\vec{r}_{1}$ with respect to a photon emitted at the origin (see Fig.~\ref{fig:setup}), and $\hat{S}_{-}^{(l)}=\frac{1}{\sqrt{N-1}}\sum_{\tilde{l}=1}^{N-1}\hat{s}_{-}^{(l,\tilde{l})}$ is the sum over all atomic lowering operators $\hat{s}_{-}^{(l,\tilde{l})} = \ket{g_{\tilde{l}}}_{l}\!\bra{e}$, $\tilde{l} = 1, \ldots, N-1$, deexciting the $l$th MSPE from its upper state $\ket{e}_{l}$ to the ground state $\ket{g_{\tilde{l}}}_{l}$.

For $N$ MSPE in the antisymmetric state $\ket{A_{N}}$ with one excitation, i.e., with $\sum_{l=1}^{N}\braket{ \hat{S}^{(l)}_{+} \hat{S}^{(l)}_{-}}_{\ket{A_{N}}}= 1$, the intensity as a function of $\delta_{1}$  calculates
to
\begin{align}
\label{eq:intensity}
	&I_{\ket{A_{N}}}\left(\delta_{1}\right) = \bra{A_{N}} E^{(-)}(\vec{r}_{1}) E^{(+)}(\vec{r}_{1}) \ket{A_{N}} \nonumber \\[1mm]
	&=  \sum_{l=1}^{N} \left< \hat{S}^{(l)}_{+} \hat{S}^{(l)}_{-} \right>_{\ket{A_{N}}} + \sum_{\substack{ l_{1}, l_{2} = 1 \\ l_{1} \neq l_{2}}}^{N} e^{i\, \delta_{1} (l_{1}-l_{2})} \left< \hat{S}^{(l_{1})}_{+} \hat{S}^{(l_{2})}_{-} \right>_{\ket{A_{N}}}  \nonumber \\

	&= \frac{N}{N-1} \left[ 1 - \frac{1}{N^2} \frac{\sin\left(\frac{N\delta_{1}}{2}\right)^{2}}{\sin\left(\frac{\delta_{1}}{2}\right)^{2}} \right]  \, ,
\end{align}
where in Eq.~(\ref{eq:intensity}) we exploited the fact that all interference terms contribute with equal weight, i.e., $\braket{\hat{S}^{(l_{1})}_{+} \hat{S}^{(l_{2})}_{-}}_{\ket{A_{N}}}=-1/[N(N-1)]$, for $l_{1} \neq l_{2}$. Note that this equality is also expressed in the cross-correlation coefficient \cite{Agarwal(2014)}, which is identical for all source pairs $l_{1} \neq l_{2}$
\begin{equation}
\label{eq:correlationsAnti}
\frac{\braket{\hat{S}^{(l_{1})}_{+} \hat{S}^{(l_{2})}_{-}}_{\ket{A_{N}}}}{\sqrt{\braket{\hat{S}^{(l_{1})}_{+} \hat{S}^{(l_{1})}_{-}}_{\ket{A_{N}}}\braket{\hat{S}^{(l_{2})}_{+} \hat{S}^{(l_{2})}_{-}}_{\ket{A_{N}}}}}=-\frac{1}{N-1} \ .
\end{equation}
\begin{figure}[b]
\centering
\includegraphics[width=0.7\columnwidth]{Figure1_Subradiance}
\caption{Setup considered for the oberservation of directional Dicke subradiance: $N$ light sources are aligned along the x-axis equidistantly at positions $\vec{R}_{l}$, $l=1,\hdots,N$, with separation $d\gg \lambda$. In the far field of the sources, $N$ detectors measure the $N$th-order correlation function at positions $\vec{r}_{j}$, $j=1,\hdots,N$.
}
\label{fig:setup}
\end{figure}

Eq.~(\ref{eq:intensity}) displays an intensity profile marked by pronounced dips of vanishing radiation, analogous to the inverted intensity profile  of a coherently illuminated  grating with $N$ slits. Note that pronounced peaks in the intensity characterized by a grating function are  well known for
$N$ two-level atoms in \textit{symmetric} Dicke states, arranged in the same manner as in Fig.~\ref{fig:setup} \cite{Wiegner(2011)PRA}. Such \textit{superradiant} emission profiles can further be observed when recording higher-order intensity correlation functions for both,  $N$ uncorrelated fully excited two-level atoms \cite{Oppel(2014),Wiegner(2015)} and $N$ uncorrelated classical light sources \cite{Oppel(2014),Bhatti(2016)}. Yet, in contrast to the sharp peaks of \textit{increased} intensity  in the case of superradiant emission, the inverted grating function of Eq.~(\ref{eq:intensity}) reveals highly focused dips of \textit{reduced} intensity, i.e., directional Dicke subradiance. Equally to its superradiant counterpart
\cite{Wiegner(2011)PRA,Oppel(2014),Wiegner(2015),Bhatti(2016)}, the subradiant intensity profile of Eq.~(\ref{eq:intensity}) for $N$ MSPE in the antisymmetric state $\ket{A_{N}}$ with one excitation displays a visibility of  $\mathcal{V}=1$, with the minima located at $\delta_{1} = 2 m \pi$, $m \in \mathbb{Z}$, having an angular width of $\delta\theta_{1} \approx 2\pi / (N k d)$.
Note that these properties describe distinctive features of superradiance \cite{Wiegner(2011)PRA,Oppel(2014),Wiegner(2015),Bhatti(2016)} but can also be used, as in our case, to characterize the particular
attributes of Dicke subradiance.

A further option to construct totally antisymmetric states $\ket{A_N}$ and observe the corresponding subradiant behavior is to make use of multi-photon sources (MPS). Hereby, each source $l$ emits a discrete number of photons $n_{l}$,
assumed to be different from the other sources, i.e., $n_{i}\neq n_{j}$, for $i\neq j$.
This could be realized, e.g., by combining $n_{l}$ single photon emitters for each source $l$.
Again considering the source arrangement of Fig.~\ref{fig:setup}, the (dimensionless) positive frequency part of the electric field operator in the far field of the sources
reads \cite{Bhatti(2016)}
\begin{equation}
\begin{aligned}
	\left[ E^{(-)}(\vec{r}_1) \right]^\dagger = E^{(+)}(\vec{r}_1) \propto \sum_{l=1}^{N} e^{-i\,l\, \delta_{1}} \;\hat{a}_{l} ,
\label{eq:DefE2}
\end{aligned}
\end{equation}
where $\hat{a}_{l}$ denotes the annihilation operator of a photon emitted from the $l$th MPS.
Choosing $n_{1}=0, n_{2}=1, \ldots, n_{N}=N-1$
yields again the intensity profile of Eq.~(\ref{eq:intensity}), i.e., a distribution following a negative grating function and displaying directional Dicke subradiance, yet with a different global prefactor of $N^{2}/2$
\cite{AdditionalInformation}.

Note that when computing the $N$th-order intensity correlation function $G^{(N)}_{N\, TLS}(\delta_{1},\hdots, \delta_{N})$ of a light field produced by $N$ TLS,
similar multi-photon interference terms appear as those occuring in the derivation of $I_{\ket{A_{N}}}\left(\delta_{1}\right)$ for $N$ MPS \cite{AdditionalInformation}. This indicates how directional subradiant behavior can be observed also with classical light sources, i.e., by exploiting correlations produced among TLS when recording a specific number of photons at particular positions \cite{Oppel(2014),Bhatti(2016)}.

To corroborate this argument we consider again the source arrangement of Fig.~\ref{fig:setup}, where this time

$N$ detectors are placed at positions $\vec{r}_j$, $j=1, \ldots , N$, in the far field of $N$ TLS. The density matrix $\rho_{N\, TLS}$ of the field  generated by the $N$ TLS can be written in the number-state representation in the form \cite{Oppel(2014),Bhatti(2016)}
\begin{equation}
	\rho_{N\, TLS} = \bigotimes_{l=1}^{N} \sum_{n_{l}=0}^{\infty} P_{TLS}(n_{l}) \ket{n_{l}}\bra{n_{l}} \ ,
\label{eq:rho_TLS}
\end{equation}
where $P_{TLS}(n_{l})$ denotes the (Bose-Einstein) distribution of source $l$, and

we assume equal mean photon numbers for all sources, i.e., $\bar{n} = \bar{n}_{l} = \braket{\hat{a}_{l}^{\dagger}\hat{a}_{l}}_{\rho}$, $l=1,\hdots, N$.

The $N$th-order intensity correlation function for $N$ light sources is defined by \cite{Glauber(1963)Quantum}
\begin{equation}
\begin{aligned}
	G^{(N)}_{N}(\vec{r}_{1},\hdots, \vec{r}_{N}) = \left<: \prod_{j=1}^{N} E^{(-)}(\vec{r}_{j}) E^{(+)}(\vec{r}_{j}) : \right>_{\rho_{N}} ,
\label{eq:DefGN}
\end{aligned}
\end{equation}
where $\left< : F :\right>_{\rho_{N}}$ represents the (normally ordered) quantum mechanical expectation value of the operator $F$ for a field in the state $\rho_{N}$.

To observe directional Dicke subradiance
via measurements of $G^{(N)}_{N}(\vec{r}_{1},\hdots, \vec{r}_{N})$ we suppose that $N-1$ detectors are placed at the fixed \textit{subradiant positions} (SP)
\begin{equation}
\delta_{j}=2 \pi \frac{(j-1)}{N} \ \ , \ \  j=2,\hdots ,N \ .
\label{eq:AntiPos}
\end{equation}
These positions are identical to the arguments of the $N$th roots of unity and therefore fulfill the identity
\begin{equation}
\label{eq:mthroots}
	\sum_{j=2}^{N}e^{i\delta_{j}n}=\begin{cases} \ \ -1 \ \ &, n\neq\{0\} \ , \ \text{mod}(N)\\(N\!-\!1)  \ &, n=\{0\} \ , \ \text{mod}(N) \, . \end{cases}
\end{equation}

Since we assume $N$ statistically independent TLS, we can make use of the Gaussian moment theorem to write Eq.~(\ref{eq:DefGN}) also in the form
\begin{equation}
\label{eq:GNTLS}
	G^{(N)}_{N\, TLS}(\delta_{1},\hdots, \delta_{N}) = \sum_{\mathcal{P}}\prod_{j=1}^{N} \left< E^{(-)}(\delta_{j}) E^{(+)}(\delta_{\mathcal{P}_{j}}) \right>  ,
\end{equation}
where now $\sum_{\mathcal{P}}$ refers to the sum over all permutations
of the $N$ detectors, and

the first moment is given by [cf. Eq.~(\ref{eq:DefE2})]
\begin{equation}
\begin{aligned}
	\left< E^{(-)}(\delta_{j_1}) E^{(+)}(\delta_{j_2}) \right> =  \bar{n} \sum_{l=1}^{N} e^{i l (\delta_{j_{1}}-\delta_{j_{2}})} \ ,
\label{eq:crosscorr}
\end{aligned}
\end{equation}
where the label $\rho_{N\,TLS}$ of the expectation value has been dropped for simplicity.

In the case that detector $\delta_{1}$ is not involved in the sum, i.e., for $j_{1/2}=2,\hdots , N$, Eq.~(\ref{eq:crosscorr}) simplifies to [cf. Eq.~(\ref{eq:mthroots})]
\begin{align}
\label{eq:crosscorr2}
	& \left< E^{(-)}(\delta_{j_1}) E^{(+)}(\delta_{j_2}) \right>  =  \bar{n} \left[ 1 + \sum_{l=2}^{N} e^{i \delta_{l} (j_1 - j_{2})} \right] \nonumber \\
	 & =\begin{cases} \ \ 0 \ \ &, (j_1 - j_{2}) \neq\{0\} \ , \ \text{mod}(N) \\ N  \bar{n}  \ &, (j_1 - j_{2}) =\{0\} \ , \ \text{mod}(N) \, , \end{cases}
\end{align}
which means that all cross-correlation terms of any two fixed detectors $j_1 \neq j_{2}$ vanish.
Eq.~(\ref{eq:GNTLS}) thus reduces to
\begin{equation}
\begin{aligned}

	&G^{(N)}_{N\, TLS}(\delta_{1},\text{SP}) =  \prod_{j=1}^{N}  \left< E^{(-)}(\delta_{j}) E^{(+)}(\delta_{j}) \right> \\
		&+ \sum_{k =2}^{N} \left| \left< E^{(-)}(\delta_{1}) E^{(+)}(\delta_{k}) \right> \right|^{2}	\prod_{\stackrel{j=2}{j\neq k }}^{N}\left< E^{(-)}(\delta_{j}) E^{(+)}(\delta_{j}) \right>  \, ,
\label{eq:GNTLS22}
\end{aligned}
\end{equation}
where the interference term
is given by [cf. Eq.~(\ref{eq:mthroots})]
\begin{align}
\label{eq:interference}
	& \sum_{k =2}^{N} \left| \left< E^{(-)}(\delta_{1}) E^{(+)}(\delta_{k}) \right> \right|^{2} = \sum_{k =2}^{N} \left|  \bar{n} \sum_{l=1}^{N} e^{i l (\delta_{1}-\delta_{k})} \right|^{2} \nonumber \\

	& = \bar{n}^{2}\, (N-1) \sum_{l_{1},l_{2}=1}^{N} e^{i\delta_{1}(l_{1}-l_{2})} - \bar{n}^{2} \sum_{ \substack{l_{1},l_{2} = 1\\ l_{1}\neq l_{2}}}^{N} e^{i\delta_{1}(l_{1}-l_{2})} \nonumber \\
	& = \bar{n}^{2} N^{2} \left[ 1 - \frac{1}{N^2} \frac{\sin\left(\frac{N\delta_{1}}{2}\right)^{2}}{\sin\left(\frac{\delta_{1}}{2}\right)^{2}} \right] \, .
\end{align}
The normalized $N$th-order intensity correlation function
finally reads
\begin{equation}
\begin{aligned}

	g^{(N)}_{N\, TLS} (\delta_{1},\text{SP})  = 2 - \frac{1}{N^{2}} \frac{\sin\left(\frac{N\delta_{1}}{2}\right)^{2}}{\sin\left(\frac{\delta_{1}}{2}\right)^{2}} \ ,
\label{eq:gNfinal}
\end{aligned}
\end{equation}
displaying an inverted grating function identical to the one obtained for quantum sources in Eq.~(\ref{eq:intensity}), i.e., a subradiant intensity distribution $I_{\ket{A_{N}}}\left(\delta_{1}\right)$ produced by MSPE and MPS in the totally antisymmetric state $\ket{A_{N}}$.
Note that due to the different constant term the visibility of the classical subradiant pattern
of Eq.~(\ref{eq:gNfinal}) equals $\mathcal{V}_{TLS}=1/3$, independently of the number of sources $N$.

To reach higher visibilities for classical sources one could increase the number of fixed detectors, e.g., using multiples $\alpha$ of complete sets of $N-1$ detectors placed at the SP, i.e., $\alpha(N-1)$, $\alpha \in \mathbb{N}_{+}$. In this case we obtain
\cite{AdditionalInformation}
\begin{equation}
\begin{aligned}
	 g^{(1+\alpha(N-1))}_{N\, TLS} (\delta_{1},\alpha\! \times\! \text{SP})  \sim  1 + \alpha - \frac{\alpha}{N^{2}} \frac{\sin\left(\frac{N\delta_{1}}{2}\right)^{2}}{\sin\left(\frac{\delta_{1}}{2}\right)^{2}}  ,
\label{eq:gNafinal}
\end{aligned}
\end{equation}
where in the limit $\alpha\gg 1$ the visibility $\mathcal{V}_{TLS}^{(\alpha)}=\alpha/(\alpha+2)$ approaches unity, as in the case of quantum sources.

\begin{figure}[b]
	\centering
		\includegraphics[width=1.0\columnwidth]{Figure2_Subradiance}
	\caption{
(Color online) Experimental  setup  to  measure $g^{(N)}_{N\, TLS}$ with $N$ pseudothermal light sources. M: mirror, L: lens.	For details see text and Ref.~\cite{Oppel(2014)}.}
	\label{fig:Experiment}
\end{figure}

Note that recently
an isomorphism between $G^{(m)}_{\rho_{N}}$ and $G^{(1)}_{\tilde{\rho}_{N}^{(m-1)}}$, $m \in \mathbb{N}_{+}$, was identified for a light field $\rho_{N}$ produced by $N$ sources \cite{Wiegner(2015),Bhatti(2016)}, i.e.,
\begin{equation}
	G^{(m)}_{\rho_{N}}(\delta_1, \hdots,\delta_m) = G_{\tilde{\rho}_{N}^{(m-1)}}^{(1)}(\delta_{1})\, G_{\rho_{N}}^{(m-1)}(\delta_{2},\hdots,\delta_{m})  ,
\label{eq:Gm_rho_G1}
\end{equation}
where $\tilde{\rho}_{N}^{(m-1)}$ describes the state of the field after $m-1$ photons have been recorded at positions $\delta_{2},\hdots, \delta_{m}$. In the case of $N$ TLS and $\alpha(N-1)$ detectors placed at the SP the projected state $\tilde{\rho}_{N\, TLS}^{(\alpha(N-1))}$ reads
\begin{equation}
\label{eq:thermal_state_matrice}
\tilde{\rho}_{N\, TLS}^{(\alpha(N-1))}\!= \frac{ \left[\prod_{j=2}^{N} E^{(+)}(\delta_{j}) \right]^{\alpha}\!\! \rho_{N\, TLS}   \left[\prod_{j=2}^{N} E^{(-)}(\delta_{j}) \right]^{\alpha} }{G_{\rho_{N\, TLS}}^{(\alpha(N-1))}(\alpha\!\times\!\text{SP})} ,
\end{equation}
with $\text{Tr}[\tilde{\rho}_{N\, TLS}^{(\alpha(N-1))}] = 1$. The state $\tilde{\rho}_{N\, TLS}^{(\alpha(N-1))}$ is not of diagonal form, where the nondiagonal terms describe the correlations between the TLS induced by the detection of $\alpha(N-1)$ photons at the SP.
The corresponding cross-correlation coefficient
is given by \cite{AdditionalInformation}

\begin{equation}
\label{eq:correlationsTLS}
	\frac{\left< \hat{a}^{\dagger}_{l_{1}} \hat{a}_{l_{2}} \right>_{\tilde{\rho}_{N\, TLS}^{(\alpha(N-1))}}}{\sqrt{\left< \hat{a}^{\dagger}_{l_{1}} \hat{a}_{l_{1}} \right>_{\tilde{\rho}_{N\, TLS}^{(\alpha(N-1))}}\left< \hat{a}^{\dagger}_{l_{2}} \hat{a}_{l_{2}} \right>_{\tilde{\rho}_{N\, TLS}^{(\alpha(N-1))}}}} = - \frac{\alpha}{N+N\alpha-\alpha} \, ,
\end{equation}
demonstrating that the cross correlations
are identical for any two sources $l_{1}\neq l_{2}$.
In particular,
for
$\alpha \gg N$, Eq.~(\ref{eq:correlationsTLS}) becomes identical to Eq.~(\ref{eq:correlationsAnti}), displaying the correlations between any two of $N$ multi-level atoms prepared in the totally antisymmetric state ${\ket{A_{N}}}$.

\begin{figure}[t]
	\centering
		\includegraphics[width=1.0\columnwidth]{Figure3_Subradiance}
	\caption{(Color online) Experimental results. (a) Average intensity $I_{2 \, TLS} (\delta_{1})$ of $N=2$ TLS demonstrating that the pseudothermal light sources are spatially incoherent in first order. (b)-(e) Measurement of the normalized $N$th order correlation function $g^{(N)}_{N\, TLS} (\delta_{1},\delta_{j}\!=\!2\pi\frac{j-1}{N}; j\!=\!2,\hdots ,N) = \mathrm{G}^{(N)}_{N \, TLS}(\delta_{1},\delta_{j}\!=\!2\pi\frac{j-1}{N}; j\!=\!2,\hdots ,N)/[I_{N \, TLS} (\delta_{1}) \prod_{j = 2}^{N} I_{N \, TLS} (\delta_{j}\!=\!2\pi\frac{j-1}{N})]$ for $N = 2, \ldots, 5$ as a function of the first detector at $\delta_{1}$ (red solid curves). The suppression of incoherently emitted radiation at $\delta_{1} = 0$ after $N - 1$ photons have been recorded at the SP at $\delta_{j}\!=\!2\pi\frac{j-1}{N}$, $j=2,\hdots ,N$, is clearly visible. The theoretical predictions of Eq.~(\ref{eq:gNfinal}) are displayed by the black (dashed) curves.

	}
	\label{fig:Measurement}
\end{figure}

To measure $g^{(N)}_{N\, TLS}$ for $N$ statistically independent TLS we use the pseudothermal light of a coherently illuminated rotating ground glass disk \cite{Estes(71)} (coherence time $\tau_{c}\approx50$ms), impinging on a mask with $N$ identical slits of width $a=25\mu$m and separation $d=200\mu$m (see Fig.~\ref{fig:Experiment}). As coherent light source we utilize a linearly polarized frequency-doubled Nd:YAG laser at $\lambda=532$nm. Working in the high intensity regime we employ a conventional digital camera placed in the far field of the mask to determine $g^{(N)}_{N\, TLS}(\delta_1, \hdots,\delta_N)$,
where we correlate $N-1$ pixels of the camera located at the SP $\sim \delta_{2},\hdots, \delta_{N}$ with one moving pixel $\sim \delta_{1}$ (integration time of the camera
$\tau_{i}\approx 1 \text{ms} \ll \tau_{c}$) \cite{Oppel(2014)}.

The experimental results
for $g^{(N)}_{N\, TLS}(\delta_1, \hdots,\delta_N)$ obtained in this way for $N=2,\hdots,5$ TLS are shown in Fig.~\ref{fig:Measurement}. From the plots the directional Dicke subradiant behavior of the $N$ TLS is clearly visible, with dips of vanishing radiation that are
in excellent agreement in position, depth and width with the theoretical predictions of Eq.~(\ref{eq:gNfinal}). This confirms the theory outlined above stating that a) with distant quantum sources as well as classical TLS in corresponding states
directional subradiance can be observed  [cf. Eqs.~(\ref{eq:intensity}) and (\ref{eq:gNafinal})], and that b) directional subradiance of TLS occurs
due to the similarity between the totally antisymmetric state ${\ket{A_{N}}}$ of $N$ quantum sources and the highly correlated state $\tilde{\rho}_{N\, TLS}^{(\alpha(N-1))}$, obtained from $N$ initially uncorrelated TLS via $\alpha(N-1)$ photon detection events at the SP [cf. Eqs.~(\ref{eq:AntiState}) and (\ref{eq:thermal_state_matrice})], leading to identical cross correlations for $N$ quantum sources and for $N$ TLS in the limit $\alpha\gg N$ [cf. Eqs.~(\ref{eq:correlationsAnti}) and (\ref{eq:correlationsTLS})].

In conclusion we presented a detailed discussion of the spatial aspects of Dicke subradiance, i.e., the intensity profiles observed for the incoherently emitting distant sources prepared in corresponding states.
We examined the conditions to achieve totally antisymmetric states for  multi-level atoms or multi-photon sources and derived analytical expressions for the resulting spatial spontaneous emission patterns. We also showed that directional Dicke subradiance can be observed with incoherently emitting TLS, i.e., by measuring higher order photon correlations projecting the TLS into highly correlated states. The latter is an unexpected outcome as subradiance is considered to be a purely
nonlocal, nonclassical phenomenon displayed by quantum sources \cite{Hebenstreit(2017)}.

\begin{acknowledgments}
The authors thank G. S. Agarwal and S. M\"ahrlein for helpful comments and fruitfull discussions.
The authors gratefully acknowledge funding by the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German Research Foundation (DFG) in the framework of the German excellence initiative. D.B. gratefully acknowledges financial support by the Cusanuswerk, Bisch\"ofliche Studienf\"orderung.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
Amy Gelsthorpe
Order Star Fishing
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I landed a shooting star!
October 11, 2016 October 11, 2016 | amygelsthorpe
I am super excited to announce that I just signed another Children's Book CONTRACT!!!!
For those of you who are bad at math like me…
This means I have signed TWO book contracts in the last two months!
I am so excited to announce that STAR-FISHING will be published in late 2017 to early 2018!
Again, I am thankful for my literary agent Sandy Fuller with Alp Arts without her this would not be possible! Also, to Tannya Derby my publisher at Maclaren-Cochrane Publishing- thank you for another opportunity and for the love you have of my first two books!
Star-Fishing holds a special place in my heart. I chose the name "Billy" in honor of my daddy who passed away almost 9 years ago with pancreatic cancer. Although, he wasn't an avid star gazer and this story is fictional- he taught me how to fish and chase my dreams. He was a hard worker and loved the many accomplishments of his children. I know he would be very proud of me landing my shooting star!
My dedication page:
Star-Fishing summary:
When Billy decides he wants to know what stars are made of, he seeks to catch one of his own. Billy doesn't consider the obstacles that come when one attempts to catch a star… He can only dream about what he'll learn when he catches his star. Mommy plays into Billy's ideas and makes a game out of his Star-Fishing experience, a smart and fun strategy to encourage Billy's imagination… Together they imagine the shooting star visiting exciting places and creatures like Mt. Everest, the North Pole, a hopping kangaroo and more… The outcome is pleasing, sentimental, and unique!
Undoubtedly, Billy isn't the only child who has contemplated such adventures… No doubt children will make up their own shooting star adventures after reading Star-Fishing!
I'm so thankful to God for leading me to fulfill my dreams of becoming a published author! If this were not in His plan and His will it never would have happened!
Looking forward to many more contracts!
< My future illustrator is 9…
New Focus… Decision >
One thought on "I landed a shooting star!"
That's fantastic Amy I can't wait to see them both on the shelves. I loved your first two books for women!
Follow Amy Gelsthorpe on WordPress.com
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redpajama_set_name: RedPajamaCommonCrawl


USTA Colorado provides the Job Listings as a free service to the Colorado tennis community. To list a job opening, please send information to Kurt Desautels.
The listing will run until USTA Colorado is notified to remove it.
Earn extra money officiating events that fit within your busy schedule.
Looking to get out of the heat for the summer? Come work in the mountains! Starting June 1 through Labor Day. Responsibilities: Running Juniors and adult clinics as well as privates and semi privates. There is a monthly maintenance pay so you will also be responsible for making sure the courts are maintained, stocked with supplies and looking good. This job also comes with free housing while you are employed with us. Please send resumes to Meagan Donohue, Fitness Director at The Club at Crested Butte.
Skyline Swim and Tennis Club is seeking a local, seasonal assistant tennis professional with experience working with tennis players of all abilities and levels. Skyline officially opens Memorial Day and closes Labor Day. The club has 400 families and a robust tennis community. Tennis programming runs throughout the entire summer.
Shoulder season work (April-October) is also available.
Tennis professional should feel comfortable teaching large groups, semi private and private lessons.
Compensation is competitive and dependent upon experience and generally between 8k-15k.
If you are interested please email the tennis director, Andrew Green.
The city of Aurora is seeking highly motivated and talented individuals for a career in the Recreation Division. The Recreation Specialist manages the day to day operation of the youth and adult tennis programs and leading varied sports programs for the Recreation Division while ensuring quality customer service.
This position reports to the Director of Tennis and is generally full time April through August, and limited part time the rest of the year. Looking for someone with experience running both Junior and Adult programming. Certification and experience in 10 and Under tennis and Cardio tennis a plus.
BSTC is a members-only facility located in the heart of Broomfield, Colorado which offers a tennis community that is one of the most active in the Denver area. We offer a full summer schedule of tennis, lessons, clinics and activities. Facility highlights include 6 lighted outdoor tennis courts, four lane 27-meter swimming pool with diving area, children's' wading pool, sand volleyball and basketball courts, snack shop, and large gazebo with picnic areas and grills.
Ideal Candidate is a self starter and team player. Someone who can sell themselves and the tennis professionals they work side by side with.
Qualified candidate must be trained, certified, qualified and accredited for assigned services activities as required by federal, state or local codes and regulations. Proven capability and experience as a tennis professional.
Please send resume to Noah.BSTC@gmail.com.
Crestmoor Community Association in Denver, CO is seeking an assistant tennis professional. The position is full time from June-August. Position requires part time hours in April, May, September and October. The tennis professional is responsible for assisting the Director of Tennis in the administration and implementation of the tennis program. Candidates should have previous teaching and playing experience.
Position is available for start in April of 2019.


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redpajama_set_name: RedPajamaGithub


Start an East Stroudsburg Borough real estate search to find a tight knit community with lots of great amenities. This is a great place to move, whether you're raising a family or are happily child-free. The schools in the area all give a solid performance on state standardized testing, rating higher than average in several areas. There are six elementary schools, two middle schools, and two high schools. Parents who are interested in parochial education should check out Notre Dame Elementary and Junior and Senior High School, in the Catholic diocese of Scranton. St. Paul's Lutheran School is another highly rated option. East Stroudsburg University is an excellent option for higher education close to home.
In addition to good schools, which means that East Stroudsburg Borough homes tend to maintain their value, the city maintains many great services for residents. There are great parks, with a summer recreation program at Dansbury Park and public pool. The city also owns Terra Greens Golf Course.
The Shawnee Mountain Ski Area provides great skiing and is very beginner friendly. Season passes are available, as are lessons in skiing and snowboarding for all levels of experience.
There are plenty of everyday amenities, too. The downtown area is being revitalized by the Eastburg Community Alliance (or ECA). The ECA promotes downtown businesses and helps to raise money to improve the infrastructure of downtown buildings. There is a great calendar of events, celebrating local artists, business, and bringing the community together for holidays. Search East Stroudsburg Borough homes and find your place in this fun community.


text:
Sciences et techniques
 En astronomie, le Grand Rift est une nébuleuse obscure voilant une partie de la Voie lactée.

Toponyme
 La vallée du Grand Rift est un ensemble géographique et une formation géologique en Afrique.

redpajama_set_name: RedPajamaWikipedia


Meet Mary Jane Anderson, because of her ROP class she was selected to be part of an Intern Program.
ROP Metal Fabrication instructor shares how ROP courses benefit the students who take them.
The opportunity that the ROP program provides our students is unmatched, and something that cannot be duplicated or replicated by any school district.
ROP is a critical partner to our district because they provide students with the opportunity to explore and experience career technical education courses.
Hart High School ROP Specialist shares the pride in her program.
This event showcases what career possibilities await kinder students in their future through engaging activities and positive relationships with peers, mentors, and adults.
Preparing students for our 21st-century economy.
Superintendent of TUSD says ROP courses have tremendous value to students and are provided by ROP at a cost that districts cannot match. ROP is efficient.
Coastline ROP plays a key role in student engagement and successful educational environment.


I mostly blog about mental health and illness, as a result many of my followers and readers are people who may be experiencing their own difficulties.
I am always a friendly ear to listen should it be needed. I'll happily discuss mental health/wellness/illness with anyone – after all, that is one of the aims of this blog – to normalise discussion around mental health & illness.
However, I am NOT a doctor, psychiatrist, counsellor, psychologist, etc. I can tell you what works for me, how I dealt with particular situations and I can share my experiences but I can't tell you what to do apart from recommending that you share your situation with someone you trust if you haven't done so already & seeking professional help if you think that is right for you.
It would be a disservice to you if I told you to do something because 'It works!' or 'It will make you better!', that may be the case for me but not for you and telling you those things could be damaging and dangerous.
Whenever I post something relating to mental health or wellness I will include a link at the bottom of the post – this link will bring you to a page with a list of charities & support services should you need help, advice or information. Do not be afraid to seek it out, it's what those organisations are there for. If you are reading from a country other than Ireland a quick Google search will help you find similar support services near you. Alternatively, you can contact one from the list below and ask them if they could point you in the right direction.
Reading about someone else's experiences with mental ill health can be comforting but it can also be triggering so please look after yourself.


COMMUNIQUE #2 The Kallikak Memorial Bolo & Chaos Ashram: A Proposal. NURSING AN OBSESSION FOR Airstream trailers–those classic miniature dirigibles on wheels–& also the New Jersey Pine Barrens, huge lost backlands of sandy creeks & tar pines, cranberry bogs & ghost towns, population around 14 per sq. mile, dirt roads overgrown.
Adrian Flux can find affordable and comprehensive car insurance for dancers, musicians and broadcasters – protecting your pride and joy for a reasonable price.
A Coventry man who led police on a 130mph chase in a stolen car with fake plates – with his two brothers in the vehicle – was jailed for 15 months. The chase along.
1.5 What's temporary storage? Definition of a temporary storage. Temporary storage means the situation of Non-Union goods temporarily stored under customs supervision in the period between their presentation to customs and their placing under a customs procedure or re-exported.
Bulgaria's head of insurance supervision resigned on Tuesday, bowing to pressure.
Compared with other financial instruments such as mutual funds or even a bank.
Jan 5, 2013. How younger drivers can beat the car insurance trap – and even drive a. huge headaches if a claim is made – with some firms refusing to pay out. to cut costs is to add under 25s to insurance policies on a temporary basis.
Mar 15, 2018. Proving you have car insurance cover in your home country (is your. Several French insurers refused to consider Rosa's driving record in Italy.
However, we will refund your excess if your vehicle is. Thank you for choosing to insure your vehicle. Temporary cover when you change your vehicle. iv fails or refuses to stop, or remain at the scene, following an accident (as required.
PLANS to build a 200-space public car park in Kenavon Drive have been refused amid fears of an increase in traffic. car parking is long-stay but will reduce to 35 per cent when the temporary cart p.
Frequently Asked Questions about short term insurance. in their own car! Are you looking for Learner Driver Car Insurance? Check out our Learner FAQs here.
Travelers insurance is one of those things that people either refuse to leave home without or decide to just. They range from basic coverage for car rentals and.
The court heard that Bagley 'must have seen the police car on the motorway.
Jun 19, 2013. Your car insurance policy is a legal agreement between you and the. where your policy is cancelled and the claim is denied, you'll be left.


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You are here: Home / Sports / NBA / Are The Mavericks Proving They're More Than A One-Man Team?
Are The Mavericks Proving They're More Than A One-Man Team?
(Photo by Ron Jenkins/Getty Images)
When the Dallas Mavericks began their best-of-seven Western Conference semifinal series against the Phoenix Suns, most assumed they would be sent to summer vacation pretty quickly.
The Suns, people reasoned, were a well-balanced team that is greater than the sum of its parts, while the Mavericks were just a one-man team.
Phoenix won the first two games, despite two otherworldly performances from Luka Doncic, and it looked like a sweep was a real possibility.
Dallas then took Game 3, 103-94, and many dismissed it as an aberration and felt that the Suns would reassert themselves in Game 4.
Instead, the Mavs not only took Game 4, 111-101, but they found some things that worked well for them.
Luka Doncic stuns the defense with the up & under and showing us all off with his elite footwork! 👀🔥 pic.twitter.com/x4Ld8XYuN1
— ClutchPoints (@ClutchPointsApp) May 7, 2022
Most importantly, they have gotten Doncic some much-needed help.
Doncic Hasn't Been A Solo Act In Dallas' Two Wins
The Slovenian native has been sensational in this series.
He put up 45 points, 12 rebounds, and eight assists in Game 1, then followed that up with 35 points and seven assists in Game 2.
However, he didn't get enough assistance on either end of the floor, and Phoenix cruised to victory in both contests.
But the tide started to turn in Game 3.
Doncic had 26 points, 13 rebounds, and nine assists, but guard Jalen Brunson exploded for 28 points and five assists to help the Mavs' cause.
Then on Sunday, Brunson scored 18 points, while Dorian Finney-Smith contributed 24 points and went 8-of-12 from 3-point range.
What made that victory all the more impressive was that Doncic had a bad shooting game, making just 9-of-25 shots from the field and 1-of-10 from 3-point land.
Dallas Has Also Been Winning With D
In the regular season, the Suns were a well-oiled machine, ranking fourth in offensive rating while scoring 114.8 points per game, which was fifth in the NBA.
They were true to form in the first two games of this series, scoring 121 and 129 points, respectively, while shooting over 50 percent from the field in both contests, including a nova-like 64.5 percent in Game 2.
But afterward, Dallas started clamping down on the squad that won more regular season games than any other this year.
Phoenix shot under 50 percent in Game 3 and Game 4, and the Mavericks did not allow a single Suns player to reach 20 points in Game 3.
On Sunday, Devin Booker went for 35 points, but no one else had more than 15 points.
In particular, Chris Paul, whom everyone expects to play big in such games, only took four shots all day, making two of them and scoring just five points in 23 minutes before fouling out.
Chris Paul has fouled out of Game 4 after this play on Jalen Brunson. pic.twitter.com/r5ooajNzCw
— ESPN (@espn) May 8, 2022
Brunson Might Be The Key Moving Forward
In the first round of the playoffs versus the Utah Jazz, Brunson looked like a budding star, averaging 27.8 points a game while shooting 48.4 percent from the floor and 36.4 percent from downtown.
Other than Doncic, he is the only other player the Mavs have who can get his own shot against a set halfcourt defense.
Doncic can, and likely will, have at least one more superhuman game in this series, but it won't matter if he doesn't get enough help, especially on the offensive end.
Filed Under: Dallas Mavericks Rumors And News (Updated Daily), NBA Tagged With: Dallas Mavericks
More Dallas Mavericks News
The Mavericks Have Suddenly Fallen Far
Luka Doncic Wasn't Happy At The End Of Latest Loss
2 Things Luka Doncic Still Needs To Improve This Season
Detailing The Insane Tear Luka Doncic Has Been On Lately
NBA Analyst Knows How To Help The Mavericks
Luka Doncic Makes Big Demand For The Mavericks
Luka Doncic Asks For Help In Fan-Made Art
Newest Mavericks Star Talks His Relationship With Coach
Mavericks Owner Chimes In To Complain About The Refs
Luka Doncic Joins Michael Jordan In NBA History
Luka Doncic Talks About His Future In The NBA
Luka Doncic Showed Off His Magic Thursday Night
Luka Doncic Consistently Plays Hard Against A Rival Team
Mavericks Owner Did Not Look Happy After Tuesday's Loss
The Mavericks Are Talking About Possible Trades
Luka Doncic Took A Tumble On Tuesday Night
The Mavericks Are Waiting On News About Their Biggest Star
The Mavericks Struggle Without Their Superstar
How Good Are The Mavericks Without Luka Doncic?
NBA Analyst Says There Is No Doubt About 2 Best Players In The NBA
The Mavericks Make A Surprising Roster Move
Luka Doncic Explains His Scoring Mentality In Each Game
Charles Barkley Gives His True Opinion Of Dallas Mavericks
Luka Doncic Leads The League With His Special Shot
Are The Mavericks Proving They're More Than A One-Man Team?


IF YOU ARE GETTING MARRIED!
Don't forget that it is your responsibility to get the marriage license!
Remember to bring the license to the wedding so it can be signed and filed.
I do the legal filing after the wedding.
BASIC CIVIL CEREMONIES are available for those who want a traditional service. Don't settle for a Justice of the Peace when there are many other options to make your ceremony uniquely yours.
It doesn't have to be complicated to be special.
I can help. I will provide you with a wide variety of options for locations, vows and other ceremony elements which you can choose to express your heart.
I can also provide a Discussion List for Couples to help you address a lot of partnership situations before they become a dispute.
Communication and Trust are the keys to a lasting, happy relationship. And these two things go hand in hand!
Special jewelry from family members or in memory of them make the day very special.
For many, the celebration of an important life event is a bit sorrowful because someone special is not there to share in the event.
If the person is separated because of distance or health, Skype or Facetime is a wonderful option to allow them to witness or even participate in the ceremony via tech.
Carrying a memento of the loved one with you or at a special location for your guests can see is a loving way to include those that are missing.
Having a special letter from them included in your ceremony or reception is also a good option.
If there are deceased individuals that you want to honor, leaving special chairs for them is a visual way to welcome their connection. A picture of the missing individual, helps other guests to understand the absence.
Your ceremony can also include candles lighted for these individuals or a personal item included in your flowers or other items carried during the ceremony.
I LOVE Pinterest! There are so many ideas there for your planning, photography, ceremony.
Rites of Celebration has a page -- check out what I have already found.
Let's Ride pedicab service can be a solution to your parking concerns.
Phoenix Wedding Limos for transportation on your special day.


text:
Q: Prevent duplicates in a SP list. I am using Javascript I am trying to prevent duplicates in a SP list but my code does not work.
e.g if an item "James" exists in my list it should not be possible to add same item instead an alert message should show up "Item already exists". but if item "James" does not exist than it should be added.
 var clientContext = new SP.ClientContext.get_current();
    var hostWebUrl = decodeURIComponent(getQueryStringParameter("SPHostUrl"));
    var parrentConetxt = new SP.AppContextSite(clientContext, hostWebUrl);
    var parrentWeb = parrentConetxt.get_web();
    var list = parrentWeb.get_lists().getByTitle("testList");
    var items = list.getItems("");
    var createItem = new SP.ListItemCreationInformation();
    var newItem = list.addItem(createItem);

    function add() {
    clientContext.load(items);
    clientContext.executeQueryAsync(onS);

}

    function onS() {
    var Enumerator = items.getEnumerator();

    while (Enumerator.moveNext()) {
        var currentItem = Enumerator.get_current();
        if (currentItem.get_item("Title") = $("#txtTitle").val())
        {
            alert("Item alredy exists");
        }
        else {
            newItem.set_item("Title", $("#txtTitle").val());
            newItem.update();
        }
        clientContext.load(list);
        clientContext.executeQueryAsync(onF);
    }
}

    function onF() {
    alert("Error");
}

A: Lists columns have this functionality built in. Simply enable the enforce unique values option on your desired column.
Then you try to add your item like normal in your JavaScript code. Any error you will receive in the callback and you can handle however you'd like at that point.
Let the built in SharePoint functionality work for you.

redpajama_set_name: RedPajamaStackExchange


Marcus Ulpius Traianus Maior (c. 29 AD – before 98 AD; Latin: Maior, "the elder") was a Roman senator who lived in the 1st century. He was father to the Roman Emperor Trajan.
Reverse of Roman aureus struck under Trajan, c. 115 AD, commemorating Marcus Ulpius Traianus after his deification.
Traianus belonged to the gens Ulpia, originating from the Umbrian City of Tuder, and was born and raised in the city of Italica (modern Santiponce, near Seville, Spain) in the Roman Province of Hispania Baetica. The Ulpii lived there from 206 BC, when the town was founded by Publius Cornelius Scipio, resettling wounded and invalid veterans of the wars against Carthage. The Ulpii, like the Aelii and the Traii belonged to the leading Hispano-Roman families of the city. From the latter family came a branch of the ancestors of Traianus, which intermarried with the Ulpii, originating the cognomen Traianus. Since the father of Traianus joined the ranks of the Patricians in Rome, it is very likely that his grandfather had already belonged to the Roman Senate. His mother's origin is unknown. His sister Ulpia would be the mother of praetor Publius Aelius Hadrianus Afer (father of the Emperor Hadrian). Traianus married a Roman noblewoman called Marcia. She was the elder sister of Marcia Furnilla, the second wife of future Emperor Titus, and consequently was in a position to help the career of her husband. They had two children, a daughter called Ulpia Marciana and a son, the future Roman Emperor Trajan. He was the maternal grandfather to Salonina Matidia; a maternal uncle to praetor Publius Aelius Hadrianus Afer and a paternal great-uncle to Hadrian.
Traianus was possibly a senator by the reign of Claudius. Before 67 AD, Traianus might have commanded a legion under the Roman General Gnaeus Domitius Corbulo. Under Vespasian (who was the Roman Governor of Judea), Traianus commanded the Legio X Fretensis during the First Jewish–Roman War between 67-68 AD. During this time he came into favour with the future emperor.
As a result of his military successes, Vespasian awarded Traianus the governorship of an unknown Roman province and a suffect consulship. Paul Gallivan dated M. Ulpius Traianus the Elder to 70 based on his arrangement of the fragments of tablet E of the Fasti Ostienses; however, subsequent recovery of fragments allowed Ladislav Vidman to date Ulpius Traianus' tenure to September–October 72. He was appointed governor of Cappadocia-Galatia (70/71 AD). He then served as governor of Syria in 73/74 AD, followed by a term as proconsul of Roman Asia in 79/80 AD. At an unspecified time he served as Governor of Hispania Baetica. During his time in Syria, Traianus prevented a Parthian invasion.
Traianus lived out his final years in honor and distinction. Indirect evidence suggests that he may have died before his son became emperor in 98 AD. Around 100 AD his son Trajan founded a colony in North Africa. This colony became a town and was called Colonia Marciana Ulpia Traiana Thamugadi (modern Timgad, Algeria). His son named this town in honour of him, his late wife and his daughter. The colony's name is also a tribute to his sister and his paternal ancestors. In 113 AD, Traianus was deified by his son, and his titulature reads divus Traianus pater.
^ a b c d e Strobel, Karl (2010). Kaiser Traian (in German). Regensburg: Friedrich Pustet. p. 40. ISBN 9783791721729.
^ a b c d Strobel, Karl (2010). Kaiser Traian (in German). Regensburg: Friedrich Pustet. p. 41. ISBN 9783791721729.


For the first time ever on a headlining tour, Adam McIlwee, the Pennsylvania electronic angst auteur who records as Wicca Phase Springs Eternal, has gone out with a stage backdrop, and it's impressive. But last week in Brooklyn, he didn't use it. No need, really, as the artist was performing in front of one of the most dramatic views a New York venue has to offer: the elevated tracks of the J, M and Z trains, which rumble by periodically mid-set, just outside the beloved indie venue Market Hotel.
It feels like a moment for Wicca Phase. Maybe not a splashy, look-at-me moment, but then, flexing is not really for McIlwee, who at 29 has already logged several notable chapters in an unlikely musical path, one that's bridged punk, hip-hop, emo, and most recently evolved into singer-songwriter acoustics. He's still based in his native Scranton, PA, where in the late 2000's he fronted the indie outfit Tiger's Jaw, until more electronic and experimental tendencies led him to split from the band in 2013, to devote himself fully to Wicca Phase Springs Eternal. It was a solo project with a work-in-progress identity, but one with beats, synths and general gloom at its core. McIlwee has played with sounds and themes over numerous EP's and singles: outsider visual art, comics, the occult and conspiracy theories have at times inflected his songs, as have fraught relationships. But he's never confronted domestic drama quite as head-on as he does on Suffer On, his second full-length, released last month and a record that marks something of a reset in the way McIlwee approaches creating music.
Signature Wicca Phase issues of connection and anxiety once again pepper Suffer On, but their musical backdrop has been tweaked. His familiar trap rhythms are still prominent—McIlwee worked again with frequent beatmaking collaborator DØVES—and a handful of tracks are fully synth-based, including the record's infectious breakout single "Just One Thing". But a remarkable amount of Suffer On puts acoustic guitar front and center. Previous Wicca Phase releases have dabbled in it, but never to this extent—one song, "Crushed", is little more than guitar and McIlwee's increasingly confident voice. It's a refreshing new look for McIlwee, casting him for the first time as a millennial iteration of the sort of singer-songwriters he's long admired—Leonard Cohen, Nick Cave and Phil Elverum—and moving him further away from "emo rap" – a tag he's been eager to shake, and one that which comes in large part from his best-known affiliation.
Wicca Phase, along with the like-minded outsider musician Cold Hart, co-founded GothBoiClique, the celebrated collective made up of nine genre-bending boys, punk-bred magpies in various musical styles but who more than anything became synonymous with the melding of revivalist emo and trap – a formula that has in recent years transcended the underground to become a signature sound of late 2010's hip-hop. The LA-based GBC existed for several years in a very passionate corner of the musical fringe, until being thrust into much greater notoriety in 2016 with the inclusion of a charismatic newcomer who went by the name Lil Peep. Gus Åhr's time with GBC was short—a little more than a year after joining the group, the "Crybaby" supernova was gone, far too soon. With Peep's November 2017 passing, the C-suite label honchos came calling, eager to catch whatever residual clout they could by signing GBC's various members. None of them received more suit-wooing than Wicca Phase, but in the end, McIlwee went with Run For Cover, the indie stalwarts with whom he'd had a long relationship.
McIlwee himself calls Suffer On a "depressing" album, and while it's no emotional walk in the park, depression is relative, and it's nowhere near the level of druggy misery of, say, part two of his late friend Peep's Come Over When You're Sober. Those guitars point to a new, uncharted, and hopefully prosperous future for Wicca Phase Springs Eternal, and his Market Hotel show was anything but a downer. A few hours before he took the stage, I sat down with a good-spirited McIlwee at a nearby Bushwick bar.
So, Adam! The tour began last night in Philly. How was that? I know you had tweeted about having a ton of anxiety before it.
Adam McIlwee: [laughs] Yeah! I get anxious normally, especially before tours. I mean I am a naturally anxious person, but Philly is kind of like a hometown show, and the guest list was, we had like 80 people on the guest list. Capacity was like over 100 per cent. So it was a little crazy, but it ended up being good. It was a cool show.
Is most of the new album Suffer On in the set at the moment?
McIlwee: Yeah, we're doing seven. Seven out of ten?
You play a lot of acoustic guitar on the record. Are you doing it in the show as well?
McIlwee: No I don't play any guitar in the show. I did play all of the guitar on the record, but with this being my first longer headlining tour I was already nervous enough, and I didn't want to throw in the added element of live guitar, yet. I figured I would just play the regular tracks. I mean I have live mixes of them, so if there's harmonies or something, they're still in there, but the vocals are taken out. I was just a little bit too nervous to start with the guitar, on this tour. I have some stuff in the summer, like one-off shows where I might try it.
You've had guitar here and there on past Wicca Phase releases, but never like this. How did that come about?
McIlwee: With this album coming out on a proper label, I knew that I would want to handle most of the production myself. The way my other stuff worked was I would just get beats from people, be it one producer sending me a bunch of beats and I would just use all of those for a project, or multiple producers sending me beats, and I would record over 20 songs or something and try and pick the ones that fit most cohesively. When you do that, it's the producer dictating where the song goes. I think that there's some sort of internal thing that happens when you hear a beat for the first time, where you think, "this song is already half way there." It's already half way to completion, right? And I have to work my part over it. So I knew doing this album that I would want to write it from scratch. I would want it to be all me, in the sense that I would pick the kinds of songs that were on the record. So when I started writing it, I was doing it on guitar just for rough ideas, and the more I was writing, the more I realized that the guitar parts were becoming integral to the song, and the way I was writing vocals around certain guitar parts. And so I realized, I have to put this guitar part on there. I can't substitute it with synthesizers or something. Now, there are some songs that are just keyboard, pads, 808 bass and drum patterns….
"Just One Thing", for instance, doesn't have guitar.
McIlwee: Exactly. And that's pretty much just a bass synth, a very aggressive drum beat and a little bit of pad just to give it some space-iness. But yeah it just seemed like guitar was integral. It's what I play the most, and so it ended up being where like eight of the songs have heavy guitar on them.
Songs like "Crush" and "Contact" really cast you in an acoustic singer-songwriter light that's pretty new, considering most people think "emo trap" or something when then think of Wicca Phase. Do you think that this record kind of evolves the perception of who you are and what you do?
McIlwee: I hope so. That was the intent, too. Because some of my favorite types of artists are singer-songwriter types. When I was in middle school, like 12 years old, Bright Eyes was like it for me. Pretty much everyone on Saddle Creek Records. I was never into like emo, in the traditional sense. I was into more the indie side of just, depressing songwriters. And from there, my favorite artists have always been singer-songwriters. And that's a lot to do with my family, my uncles are really into Leonard Cohen, and so growing up I was listening to that a lot. Bob Dylan was always a major influence for me, Nick Cave, of course. He's probably number one for me. But even newer, like Bonnie "Prince" Billy, Phil Elverum [Mount Eerie], they're my favorites. And I understand that what I'm doing isn't exactly in their vein, but I thought that if I want to re-direct, because—I know this "emo rap" craze isn't gonna last forever, right? And it's not like I ever intended to make that kind of music, it's kind of just what happened naturally. But I thought, this is kind of my chance to show people what I really have for the first time. Because this is the first time I'm getting a major PR push, a label backing me and supporting me—I can pivot a little bit, and take things in the direction that I want to go in the future, over the next five to ten years. And I thought having songs with guitar would help me do that.
You ended up releasing this on Run For Cover, who you have a long relationship with, but you had some big labels sniffing around?
McIlwee: Yeah well, when I first started Wicca Phase and I was in Tiger's Jaw, I was doing blogging on Run For Cover's website, as Wicca Phase, and they've always been really supportive. And around 2017 we started talking about what me being on Run For Cover would look like, and I was weighing it. But after Peep died—very shortly after Peep died, I started getting offers, major label offers. Very quick. And sometimes it wasn't even from labels themselves, but just like industry executives, who took note of Peep, who maybe weren't fully aware of Peep was before he passed, but then the public response to his passing was so overwhelming—it kind of forced people to notice. And I think that's pretty typical. When someone dies and you might not know who they are but everyone else is talking about them, and your ears kind of perk up and wonder, "Well, how did I miss this?" And I think that's what a lot of people were doing. So, naturally, they came to me and to others in GothBoiClique. There were offers being floated my way, but I just felt uncomfortable with the idea that someone would be so quick to give me so much money when a few months before they might not have known who I was. And it's a largely untested genre—or at least it was at that point. This was before Juice WRLD, just as Post Malone was beginning to—right when "rockstar" was first hitting—so kind of untested. And to be honest, I understand that advances from a record label are essentially a loan, and that money has to be made back. And in many cases the money that you're given is all the money that you're gonna see unless you're confident that you can make that money back. I am not confident that I can make a major label a million dollars back. I'm not! But I know that I can make an independent record label a few dozen thousand dollars back. I can do that, and once that money is paid back, then I start getting my own checks—I know I can do that.
Were the Suffer On songs all written fairly recently, or are some of them things you'd had around for a while?
McIlwee: Not that long. I started writing it at the end of 2017. I wrote three songs. I wrote "Rest", "Contact" and one other one, I forget which one it was. And then I sat on those three for a few months. I would say it was about six months, where I recorded those three, played a bunch of shows, and then set studio time, like I had studio time booked for June to properly record everything. So I had until June to finish writing the songs, and I would say I wrote the other seven or eight songs within like a two-month period.
And you and DØVES worked on the tracks together?
McIlwee: It was me recording the guitar parts to a click track, and sending like a very rough of a beat, to give him like the tempo and stuff like that—or, just sending the guitars and you know, set to a click track, and a vocal.
Track by track? Would you do as much as you could on one track and then send it to him?
Vocals were pretty much done, demoed at least. Send then to him—most of the time there was no beat behind the song, just guitar and a click track. He would make the beat, and then go to the studio. But me and DØVES had everything finalized before I went to Studio 4.
I know you've drawn on relationships before, but Suffer On seems really relationship-specific.
McIlwee: Yeah definitely. [2018 EP] Corinthiax kind of was a concept record, in the sense that I wanted to write songs about the occult, demons, stuff like that. And that would be the over-arching, I guess "theme" of it, along with relationship stuff woven in. And this is vice versa, I think. I think here you have the relationship at the forefront, and a few occult-y, witch-y aspects, just as metaphors throughout the album—one line here or there. And that's probably because I knew that I had to put all that I had into this album. I didn't want it to seem disingenuous or anything like that, and it was for whatever reason an emotionally heavy time for me. And I think that is a result of the writing process. I was writing these songs pretty much at my grandmother's house. I normally write and record at home, but they were doing work on my house. So I was going up the street to my grandmother's house, and I was just in her basement working. It's just like a work space, there's no internet and there's no phone service. And I think what happened was, I was in my head largely, right? And the more depressing aspects of my life and my relationships—once I wrote the first song, I think they just started compounding, and I think that what was going on was—I couldn't pull from anything else because I didn't have the internet to distract myself. So I was just in that head space, and it just kept going, and the more I thought about it, the more depressing the lyrics got.
To be fair, musically it's not that depressing, including "Just One Thing" which has this great chorus and may be one of the most immediate songs you've ever put out.
Did you kind of know it would be special for you when you created it?
McIlwee: Yeah, when I was writing it, I was thinking that this is the exact type of song that I want to write, in the sense that it's musically fast, and I come from a punk background, that was always my thing. Locally there was a strong punk scene, my local heroes were all punk kids who were like a year older than me, and that's where my love of fast music comes from, and that's why I love a lot of trap music, because it's fast and a lot of progressions are just two chords, right? They're punk songs, in a sense. So musically, it's exactly what I want. It's the type of music that I like and I wish more people would make. So it has that going for it. It's one of the first songs I wrote that has a very obvious chorus to it. And when I wrote the first version of "Just One Thing", the hook wasn't as catchy, and it kind of rambled a little bit. It was kind of convoluted. But when I was recording it with Will Yip at Studio 4, Will suggested that I cut that rambling part, and just keep the immediate, catchy part, and just repeat it. And it worked! Once I heard it recorded I understood that if one of my songs was to resonate with people who don't like my music, this would be the one. If one of my songs had to be on the radio, for whatever reason, that would be the one.
The other one that stood out for me as different is "Put Me In Graves", which is so upbeat.
McIlwee: Yeah well that's a punk song. It's a punk song with 808's. I had never heard a song like that, so I wanted to try it. Other people in GothBoiClique were doing more punk and post-punk type stuff—Yawns especially. I don't know how familiar you are with him, but he really stepped up his production game. When he first joined GothBoiClique, he was doing some production on his own, but mostly he was doing graphic design and stuff. Then he moved to New York and just went for it in terms of production, buying studio time and recording actual drum tracks, taking them back to his apartment and making songs and stuff. And I started to hear the stuff that he was doing, and I was like, "Okay this is what GothBoiClique could be. It doesn't have to be this emo-rap thing, which all of us are bored of anyway, because everyone is doing it. Now any kid can go on YouTube and type in "Lil Peep type beat" and get a beat that sounds like one of ours, right? And sometimes it might be better than ours, because there's been time for people to perfect that type of stuff. They can buy a microphone for 50 dollars, record the song and upload it to Soundcloud all in the same day. Right? It's easy to make this kind of music, and we all want to do something different, we all want to take the next step. Yawns and Fish Narc both started doing that—they just understood that there needed to be an evolution.
I don't know if there's ever been an artist—from Jimmy Eat World to Conor Oberst to Gerard Way—that's loved being called "emo", though I think eventually most of them got to be kind of "whatever" about it. But you really are not a fan of it, are you?
You mean, is Leonard Cohen emo?
McIlwee: You know what I'm saying?
A few months ago, I talked to Dylan, Smokeasac [Peep's producer] about the intensity of a lot of the fans in your corner of the music world, and how so many of them connect with lyrics about anxiety and depression. And he's super willing to try and help people dealing with that to the extent that he can. Do you get that a lot? I think I would be intimidated about being put in the position of like, a counselor to fans.
McIlwee: Yeah [laughs] yeah, I do. I mean if you go to my Instagram messages, they're crazy. In the sense that, people think that because I'm singing about things like different instabilities or insecurities, that I'm an expert in them or that I've found some sort of solution for them. They think, "Oh, this guy is an artist. Of course he's figured this out by now. I'll ask him!" and it's like, "No! I wouldn't still be singing about this stuff if I had any sort of answer." I was interviewed recently, where someone asked me about the title Suffer On, and what I'm trying to say with that. And I basically told them that I have no answers for any of the issues that I'm talking about, or any of the depression that's in my music. I don't have anything! It's still going on, it's here for you to examine and listen to and take it, but you're not gonna find any answers in that record.
So both Dylan and Makonnen, who I spoke with only a couple of weeks ago, have spoken about the beefing and in-fighting that existed around Gus [Peep], both before and after his death. And I know some of those hard feelings involved members of GothBoiClique.
McIlwee: It was during the second tour, the tour he passed on, that things got dicey, where Peep and Tracy were totally not talking. Or if they were, it was confrontational. More so probably Tracy tweeting stuff or whatever, mad about kind of being the Robin to Peep's Batman, which is stuff that we could have worked out, but it's fine. There was never any issues with Smokeasac, there was never any issues with Makonnen, we knew Peep was working with Makonnen in London and stuff. Because prior to that tour, Peep was living in London for a few months. But you hated to see it between Tracy and, and I know how terrible Tracy feels about that now, because who knew how that would have ended? I mean, they were close and they had a falling out, but I don't think either of them ever intended that to be a permanent falling out. Because Gus wasn't really about any sort of public fighting, or anything like that. He just wanted to live his life. He couldn't really be bothered with that. It was the people around him that liked to pick fights, and sometimes that was people that were in GothBoiClique, sometimes it was people who weren't in GothBoiClique. Insecurities can be crazy, especially when you're in such close proximity to someone whose stock is rising so quickly.
There's a GothBoiClique tour on the way, and possibly a second group album?
McIlwee: We have a bunch of songs. We finally managed to get organized, in the sense that we're touring this summer, doing a Europe tour, for about two weeks or something, end of May, cause we're playing Primavera.
McIlwee: Probably six or seven of us. And we're gonna release this album, but we have to finish it. Right now we have four recorded, they're all collabs. I think that on two of those it's me, Tracy, Macned, Cold Hart, Horse Head. So, five people on those songs. On another one, it's me, Horse Head and DØVES, and there's one that's me, Cold Hart and DØVES. So like the first album was Yeah It's True, this one will be Yeah It's True 2—I think!


Home Opinions Performance vs hollow rhetoric. What will the voters choose?
The year 2014 was a watershed moment in Indian politics. After a long time, the nation had elected a government with a full majority. And Indians felt they had a leader after almost a decade. As I had narrated in my very first article on this website, social media and internet drastically changed the views of public (especially the youth) about politics and Narendra Modi. His stature in the eyes of the public is growing day by day. And it is likely to peak when he steps out to campaign for his re-election.
The urgency and desperation of the Congress ecosystem to oust Modi are visible. Logically speaking, election conversations should start three or four months before the end of Modi's term. But journalists have set a new norm where the possibility of re-election of Modi is discussed during every assembly election (or even a bypoll). Every action of the opposition and every regional/by-election outcome is discussed in the context of 2019 elections by media. This irrational and illogical obsession of the media with this subject is hard to miss. Is the Congress ecosystem afraid of Modi's re-election? Is there a strong desire to ingrain anti-Modi sentiments in the viewers by this ecosystem?
How has the Modi Sarkar fared in the past four years?
The performance of the government on various areas like national security, infrastructure, economy, foreign policy, farm policies and welfare schemes can be debated using statistics and comparing it with the record of past governments. Key achievements of Modi Sarkar in the past four years can be listed as below.
The red corridor is reducing in the area. Maoist affected areas fell from 75 districts in 2015 to 58 districts in 2017.
Demonetisation- lead to massive formalisation in the economy and increase in tax collections.
Electrification of 18,000 villages which were in darkness even after 70 years of independence.
10 crore soil health cards issued. The scheme will enable farmers to choose appropriate fertiliser inputs thereby reducing input costs.
E-NAM (electronic – National Agriculture Market) scheme for better market access to farmers.
Effective implementation of Pradhan Mantri Fasal Bima Yojana to provide insurance cover to farmers.
No charges of corruption against any minister in the centre.
Passed strong legislation against holders of Benami property.
Passed strong ordinance against Fugitive Economic offenders.
Eliminated loopholes in double taxation treaties with countries that help black money holders (Cyprus, Singapore and Mauritius).
Direct benefit transfer of subsidies through Aadhar have contained pilferage to a large extent. 57,000 crore which was earlier pocket by middlemen saved (as of 2017) through this strategy as per the IT minister Ravi Shankar Prasad.
Cancelled registration of 2.24 lakh shell companies.
For the purpose of propaganda, Modi's opponents know that they will fail if they attack statistics of Modi Sarkar. They will strive hard to exploit caste, religion and regional differences to manufacture an atmosphere of anti-incumbency. The details of this conundrum were covered in an earlier article titled 'Data versus Mahaul. Can Modi win the perception battle?' In addition to the natural opposition to Modi, there seems to be a group with the right wing which is impatient and unsatisfied with his actions on Hindutva issues. The size of this group may not be huge, but their concerns seem to be genuine. Apart from these two aspects, it would be hard to identify a visible cause for concern about a strong anti-Modi force in India.
Can 'educated' Hindus overlook the bigotry of sections of the 'minorities'?
Pro-Modi voters know why they must bring him back. Anti-Modi forces are clear as to why they have to vote him out. The swing voters are the ones who are confused. They are concerned about 'Idea of India' and 'secularism' because of the persistent media propaganda.
Educated 'liberal' Hindus speak about the performance of governments on real issues rather than 'divisive agenda'. They not only fail to recognise the achievements of Modi but also fail to recognise the bankruptcy of opposition parties. They are silent on the fact that religious leaders of minorities are actively campaigning against Modi government on the basis of religion alone. The recent comments by an Archbishop and a Maulana against Modi government cannot be ignored.
Talks of united opposition after the failure of BJP to secure a majority in Karnataka have gained momentum, despite BJP emerging as the single largest party with 104 seats. The reason for opposition unity is to save 'democracy' and 'secularism' in India. Apart from vague slogans, the opposition has no clear vision or program to take India forward. Will the public prefer a ragtag opposition whose sole agenda is to remove Modi from Prime Minister's Office? Or will they stand with a politician with impeccable credentials and burning desire to make India a prosperous nation? The answer to this question seems to be obvious.
Personal biases will take precedence over objectivity and facts in some sections of the society during general elections of 2019. They simply do not care about the report card of Modi government. This should worry fence sitters and 'secular' Hindus who constantly evaluate Modi government on 'performance' issues alone. Many educated Hindus claim that BJP is not 'secular' enough. But the blatant anti-Modi rhetoric based on religion does not alarm secularists in India. This is ironical and tragic. The future of the country lies in the hand of those sane voters who can think objectively and vote based on the performance of Modi Sarkar rather than vague slogans of the 'united' opposition.


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Dermatologists know that a child's skin is much different from that of adults, and their lifestyles and habits are very different as well. As a result, the skin conditions commonly seen in pediatric dermatology are different from those commonly seen in adults. Children are especially susceptible to infections. Most infections seen in pediatric dermatology are easily treatable, with proper techniques. A child's delicate skin is also more susceptible to the outside world. Childhood rashes such as "eczema" and diaper rash are largely treatable and even preventable, with the right kind of instruction. If your child has a skin condition, let us show you how our years of training and experience in pediatric dermatology can make the difference.
Children are also in closer contact with our pets, making them more susceptible to bites from fleas and ticks. And their world overlaps much more with plants as well, making them prone to botanical allergies from plants such as poison ivy, chrysanthemums, lavender, and wild parsnips.
A child's skin and lifestyle makes them susceptible to many skin infections, most of which are easily treatable by an experienced pediatric dermatologist.
Effective treatment is available for all of these childhood infections. Pediatric skin infections need not be a source of shame or anxiety for you – many children get them! And treatment need not be painful or traumatic for your child. As skin specialists, over the years we have developed gentle, effective treatment techniques designed particularly for children.
What parent is not distressed by a child's itchy red rash that just won't go away? Many children and their parents are frustrated by what is called "ezcema". Some have been told that there is nothing one can do, and that the child will just have to "grow out of it". Others have been given advice, passed on from generation to generation of non-dermatologists, on products or techniques which are disproven or outdated – the "old chestnuts" in pediatric dermatology.
One of the chief functions of the skin is to keep the outside world out – its "barrier function". This waterproof barrier function is provided by the outer keratin layer of the skin, or "stratum corneum". In children, this layer is thinner than in adults, resulting in a less effective barrier to all the things that our skin comes in contact with in the 21st century.
As always, the right treatment begins with the right diagnosis. "Eczema" is not actually a diagnosis at all, but rather a chapter heading in dermatology. The term "eczema" is greek for "dermatitis" which is latin for "rash". What is usually meant by "eczema" is atopic dermatitis, which is present in childhood and goes away during the teenage years. The cause of atopic dermatitis is unknown, and it is thought to be incurable. This diagnosis offers little hope.
Many parents are told that their child's "eczema" is incurable, and they will just have to "grow out of it". This is a hopeless diagnosis. Actually, many cases of eczema can be treated or even prevented.
We see significant hope for many children with "ezcema". Along with a growing number of pediatric dermatologists, at Rustad Dermatology we believe that many cases of eczema are actually forms of contact dermatitis. Contact dermatitis is caused by exposure to a specific allergen or irritant. Children are more susceptible to contact dermatitis because of their less effective barrier function. As opposed to being of unknown cause and incurable, the cause for contact dermatitis often can be found, which makes it both treatable and preventable. This change in opinion about atopic dermatitis has come about with modern patch testing techniques. We have begun to patch test children for allergies, find specific allergens, and effectively prevent their rashes.
If your child has an infection or rash, let us use our training and experience in pediatric dermatology to help you. Many childhood skin conditions are easily treatable, or even preventable with the right information. To schedule a consultation with our board-certified dermatologist, call us at 402.484.6222.


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Police Target Crypto Wallets Linked to Freedom Convoy
Cracking Down
Yazan: Connor Sephton
2d"
The Royal Canadian Mounted Police has written a letter that warns crypto exchanges that they must disclose any information about transactions that are linked to 34 addresses.
Police in Canada have told crypto exchanges to "cease facilitating any transactions" with dozens of wallet addresses as a clampdown on the Freedom Convoy movement continues.
Hundreds of truckers have been protesting against COVID-19 restrictions, with the government declaring that unvaccinated drivers will be turned away at the country's border with the U.S.
Millions of dollars had been raised in support of the truckers through GoFundMe, but the crowdfunding site pulled the plug on the campaign after violence was reported at the protests.
About $1 million in Bitcoin was subsequently raised through a decentralized alternative called Tallycoin — with donors from around the world contributing 22 BTC to a page set up by HonkHonk Hodl. But now, it appears law enforcement agencies are attempting to stop these funds from being used as well.
Earlier this week, Canadian Prime Minister Justin Trudeau invoked the Emergencies Act for the first time ever — and officials broadened the scope of anti-money laundering and terrorist financing rules so they cover all crowdfunding sites, including those that support cryptocurrencies.
The Royal Canadian Mounted Police has written a letter that warns crypto exchanges that they must disclose any information about transactions that are linked to 34 addresses — which include Bitcoin, Ether, Monero, Litecoin and Cardano wallets.
It's unclear how successful Canada will be in stopping those involved in the Freedom Convoy movement from accessing this crypto — and some critics have described the measures as undemocratic.
On Tuesday, Coinbase CEO Brian Armstrong had shared a video of Canada's Deputy Prime Minister Chrystia Freeland announcing the clampdown on digital assets, adding:
"Concerning to see stuff like this happening in any country, especially such an economically free place like Canada. Self-custodial wallets are important!"
Ottawa's police chief has resigned as the unrest continues for a third week — and protesters blocking the streets in the capital's downtown district have been told they risk arrest unless they leave the area now.
In a strongly worded warning, interim police chief Steve Bell said officers have a "methodical and well-resourced plan" to remove this "unlawful" protest in the coming days, adding:
"Some of the techniques we are lawfully able and prepared to use are not what we are used to seeing in Ottawa. But we are prepared to use them where necessary to bring about the safest outcome and restore order."
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MOUNTAIN VIEW, Calif., Nov. 6, 2014 /PRNewswire/ -- CEVA, Inc. (NASDAQ: CEVA), the leading licensor of DSP-based IP platforms for vision, audio, communications and connectivity, today announced that Novatek Microelectronics Corp., a leading fabless chip design company, has selected the CEVA-MM3101 imaging and vision DSP to power its next-generation System-on-Chips (SoC) targeting the surveillance, action camera and automotive markets. Novatek will integrate the programmable CEVA-MM3101 into their SoC designs to add powerful computer vision capabilities including scene analysis, machine vision, depth mapping and object detection in a flexible and power efficient manner.
"Integrating advanced vision processing capabilities with our imaging SoCs allows our customers to design products offering a new level of interactivity with the real world and show real product differentiation," Tommy Chen, Vice President at Novatek. "The CEVA-MM3101 imaging and vision DSP provides the processing horsepower while extending the device battery life and flexibility to implement innovative, intelligent imaging algorithms for any end application."
The CEVA-MM3101 imaging and vision DSP addresses the extreme processing requirements of the most sophisticated computational photography and computer vision applications such as video analytics, augmented reality and advanced driver assistance systems (ADAS). By offloading these performance-intensive tasks from the CPUs and GPUs, the highly-efficient CEVA-MM3101 dramatically reduces the power consumption of the overall system, while providing complete flexibility. The platform includes a vector DSP developed specifically to deal with the complexities of such applications and an extensive Application Development Kit (ADK) to enable easy development environment. The CEVA ADK includes an Android Multimedia Framework (AMF) that streamlines software development and integration effort, a set of advanced software development tools and a range of software products and libraries optimized for the DSP. For more information, visit http://www.ceva-dsp.com/CEVA-MM3101.
Novatek was established in 1997, specializing in display-centered total solutions ranging from full line of display ICs and SoCs for all display applications. The Company is the world's largest supplier of display driver ICs, and is ranked as the world's 12th largest and Taiwan's 2nd largest fabless company in terms of sales revenue in 2013. For more information, please visit the company's website at www.novatek.com.tw.


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