text:
Лига на конференциите 2023/24 е 3-ото издание на третия по сила турнир в Европа. Финалът на турнира ще се играе на 29 май 2024 г. Победителят в турнира се класира за груповата фаза на следващото издание на Лига Европа. Представителите на Русия са наказани да не участват в турнира поради руското нападение срещу Украйна.

Квалификационни кръгове

Първи квалификационен кръг
Жребият за предварителния кръг се тегли на 21 юни 2023 г. Първите срещи са на 13 юли 2023 г., а реваншите – на 20 юли 2023 г.

Класирали се отбори

Втори квалификационен кръг
Вторият квалификационен кръг се дели на два потока – шампионски и основен. В шампионския поток се състезават 17 отпаднали шампиона от първия квалификационен кръг и три шампиона, отпаднали от предварителния кръг на Шампионска лига 2023/24. В основния поток се включват 54 отбора, както и 36-те победителя от първия квалификационен кръг.

Жребият за втория квалификационен кръг се тегли на 21 юни 2023 г. Първите срещи са на 27 юли 2023 г., а реваншите – на 3 август 2023 г.

Класирали се отбори
Шампионски поток

Основен поток

Трети квалификационен кръг
В третия квалификационен кръг се включват седем нови отбора в основния поток.

Жребият за третия квалификационен кръг се тегли на 24 юли 2023 г. Първите срещи са на 10 август 2023 г., а реваншите – на 17 август 2023 г.

Класирали се отбори
Шампионски поток
  1 отбор от втория квалификационен кръг (шампионски поток), класирал се без игра
  9 победителя от втория квалификационен кръг (шампионски поток)

Основен поток

Плейоф
Жребият за плейофите се тегли на 7 август 2023 г. Първите мачове са на 24 август 2023 г., а реваншите – на 31 август 2023 г. В този кръг се включват пет нови отбора, както и отпадналите отбори от третия квалификационен кръг на Лига Европа 2023/24.

Класирали се отбори
Шампионски поток

Основен поток

Групова фаза
Жребият се проведе в Нион (Швейцария) на 1 септември 2023 г. 32-та отбора са разделени в 4 урни в зависимост от коефициентите им в ранглистата на УЕФА. Отборите са изтеглени в осем групи по четири отбора, като два отбора от една държава не могат да попаднат в една група.

В групата отборите играят на принципа "всеки срещу всеки" на разменено гостуване. Мачовете се играят на 21 септември, 5 октомври, 26 октомври, 9 ноември, 30 ноември и 14 декември 2023 г. Победителите от всяка група се класират за елиминационната фаза, докато завършилите на второ място ще играят в предварителния елиминационен кръг срещу осемте отбора, завършили на трето място в груповата фаза на Лига Европа 2023/24.

Класирали се отбори
  22 победителя от плейофите
  10 отпаднали от плейофите на Лига Европа 2023/24

Вижте също
 Шампионска лига 2023/24
 Лига Европа 2023/24

Източници

Външни препратки
 Сайт на УЕФА за Лига Европа

Сезон 2023/24 във футбола
Лига на конференциите

redpajama_set_name: RedPajamaWikipedia


For many decades, especially since the Franco-Prussian war of 1870-1871, stereotypes about French decadence had dominated foreign images of France. Decadence and racial degeneration was related to the allegedly political and military weaknesses of France and the growing effeminacy of the French nation visualized by 'irrational' Symbolist art.
This was also the case in the Netherlands. During the war, pro-German intellectuals reinforced this popular imagery about a frivolous France at the same time applauding the military force, the decisiveness, and the manliness of Germany and German culture. In anti-German circles, French military victories were particularly useful in debunking these images and demonstrating a renewed French power. In these radically pro-French and often nationalist Dutch circles, to which the cartoonist Braakensiek belonged, the Battle of the Marne in September 1914 and the Battles of Verdun and the Somme in 1916 were interpreted as powerful proof of a resurrected France. This 'purified' French culture was able to serve as an example again to the Dutch nation. See also 'Latijnsche Lente' [Latin Spring] of Jan Greshoff in 1918.
Johan Braakensiek, 'Wie spreekt er nu nog van het décadente Frankrijk? De strijd om Verdun', De Amsterdammer, 5 March 1916, addendum.
Cartoon 'De strijd om Verdun'," Cultural Exchange in a Time of Global Conflict, accessed April 21, 2019, http://sourcebook.cegcproject.eu/items/show/222.


text:
Safe and resilient forests: Commission works for wildfire prevention in Europe and globally
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European Commission Press release Brussels, 22 Mar 2021 Today, following the International Day of Forests, the Commission has published new guidelines to facilitate a better understanding of land-based wildfire prevention and effective responses.
(άρθρο στα ελληνικά) The ultimate platform to handle extreme weather events
22 Mar Research & Innovation
Article - MEPs want a safer and more sustainable tourism after Covid
19 Mar Covid-19

redpajama_set_name: RedPajamaCommonCrawl


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Amazing quality. Amazing service. And a genuinely nice guy. Look no further for a home inspector.


text:
\section{Introduction}

We have come a long way since Neils Bohr proposed his principle of
complementarity in 1928 \cite{bohr}, but instead of fading away, the topic
has increasingly become more interesting and involved. Wootters and Zurek
were the first ones to quantitatively analyze the phenomenon of complementarity
or wave-particle duality, as it is more commonly called \cite{wootters}.
Greenberger and Yasin analyzed the problem with the assumption that unequal
beams in a two-path interferometer allows for predicting, to a certain
degree, which of the two paths the quanton followed. They established
a duality relation \cite{GY}
\begin{equation}\label{dualitygy}
   {P}^{2} + {V}^{2} \le  1,
\end{equation}
which involved a \emph{path predictability} ${P}$ and an interference
visibility, which is just the fringe contrast
$V=(I_{max}-I_{min})/(I_{max}+I_{min})$, $I_{max},I_{min}$
being the maximum and minimum intensities in a region on the screen. Here, equal beams would imply no path information.
It was further refined by Jaeger, Shimony and Vaidman \cite{jaeger}.
This approach, however, does not take into account the fact that even when the
two beams are equal, one may introduce a probe to find out which of
the two paths the quanton followed. Such a scenario was considered by
Englert \cite{englert}, where he studied a two-path interferometer in the presence of
a path-detector. He arrived at a duality relation
\begin{equation}\label{dualitye}
   {D}^{2} + {V}^{2} \le  1,
\end{equation}
involving a \emph{path distinguishability} ${D}$ and the fringe
contrast ${V}$. After a lull of nearly two decades, the issue
of wave-particle duality saw a resurgence when the concept of
complementarity was quantitatively extended to mulitpath interference
\cite{cd15,nduality,bagan}. The multipath complementarity relations used
a \emph{coherence} introduced in the context of quantum information
theory \cite{plenio}, instead of conventional interference visibility.
This coherence measure has been shown to be a good quantifier of the wave
nature of a quanton \cite{coherence}.
The duality relation, based on path-predictability, was also generalized
to the multipath case using coherence \cite{roy}. However, the two kinds of duality
relations, one based on predictability, and the other on distinguishability,
remained separated.

\begin{figure}
\centerline{\resizebox{8.0cm}{!}{\includegraphics{npath.pdf}}}
\caption{A schematic representation of a multipath interference experiment, with which-way detection.
}
\label{npath}
\end{figure}

Jakob and Bergou \cite{triality1} were the first to point out that, in
two-path interference,
the predictability and distinguishability were connected through
entanglement, and the duality relation (\ref{dualitye}) can be written as
a triality relation between predictability, visibility and concurrence
\cite{concurrence}, which is a measure of entanglement. This was followed
by a similar realization in classical optics \cite{triality2}.
This idea was later investigated in a multipath quantum setting,
and a multipath predictability, coherence \cite{plenio} and entanglement
were shown to follow a triality relation \cite{triality3}. While that
analysis used a robust measure of coherence, the quantifier of
entanglement could not be shown to be a good entanglement measure.
Although the analysis brought out the role of entanglement in multipath
complementarity, it could not be rigorously quantified.

In the following, we investigate the issue of complementarity in multipath
interference and show that a robust entanglement measure, namely
I-concurrence \cite{rungta}, plays an essential role in it.

\section{Preliminaries}

\subsection{Visibility measure}

Two decades back it was experimentally demonstrated that in multipath
interference, conventional visibility, defined as fringe contrast, can
\emph{increase} under path-selective decoherence or selective path
information \cite{mei}. Subsequent debate concluded that conventional
visibility does not quantify the wave nature of a quanton in multipath
interference, and cannot be used to analyze the notion of Bohr's complementarity
\cite{luis,bimonte1,prillwitz}. In the experiment of Mei and Weitz \cite{mei},
in a multipath interference, one particular path was given an additional
180$^\circ$ phase flip. A selective decoherence was applied on the particular
path, by scattering photons off the quanton. Counter-intutively, this resulted in an increase in the fringe contrast of the interference pattern.

We use the normalized Hilbert-Schmidt coherence to define a generalized visibility for a quanton passing through a multipath interferometer (see FIG. \ref{npath})
\begin{equation}
\mathcal{V}^{2} \equiv \frac{n}{n-1}\sum_{i\neq j} |\rho_{ij}|^{2} = \mathcal{C}_{HS} ,
\label{VHS}
\end{equation}
where $\mathcal{C}_{HS}$ is the normalised Hilbert-Schmidt coherence. The system is assumed to have a $n$-dimensional Hilbert space, which arises out of the quanton passing through $n$ paths. The states corresponding to the quanton following each path are mutually orthogonal, and can be used to construct a Hilbert space basis. The density matrix element $\rho_{ij}$ is taken between two such states. This visibility
satisfies all the criteria proposed by D{\"u}rr for a valid measure of
interference and wave properties \cite{durr}. We note in passing that, in the
recently proposed resource theory of coherence by Baumgratz et al. \cite{plenio},
Hilbert-Schmidt norm has been shown to not be a robust coherence monotone,
as it may increase under some incoherent operations. Nevertheless, it has been recently highlighted that in addition to having simpler structure, the Hilbert-Schmidt coherence has information theoretic significance, in particular, through its manifestation as quantum uncertainty \cite{Luo}. Furthermore, the shortcoming of monotonicity is absent in the genuine quantum coherence framework \cite{Vicente}. Therefore, Hilbert-Schmidt coherence may
still be good enough to quantify visibility in multipath interference. It is worth noting that, for the two slit interference case, the
generalized visibility reduces to $\mathcal{V} = 2|\rho_{12}|$, which can be easily
shown to be equal to the usual visibility measure ${V} = (I_{max}
- I_{min})/(I_{max} + I_{min})$.

Consider a quanton passing through $n$-path interferometer, which could
have a multi-slit or some kind of beam splitter, as the first element.
The state corresponding to the $i^{th}$ path can be represented by the pure
state $|\psi_i\rangle$. In general the density operator of the quanton
may be mixed, and will have the general form
\begin{equation}
  \rho = \sum_{j=1}^n \sum_{k=1}^n \rho_{jk} |\psi_j\rangle\langle\psi_k|.
\end{equation}
The diagonal elements represent the fractional populations of the various beams.
We allow the possibility that the phase in $i^{th}$ beam may be shifted by
$\theta_i$, in order to analyze the experimental scenario of Mei and Weitz
\cite{mei}.
On coming out, the state of the quanton is
\begin{equation}
  \rho = \sum_{j=1}^n \sum_{k=1}^n \rho_{jk} |\psi_j\rangle\langle\psi_k|
  e^{i(\theta_j-\theta_k)},
\end{equation}
where $\rho_{jk}$ are assumed to be real without loss of generality, as any phases can be absorbed in the exponential factor.
In the multi-slit interference experiment, after coming out, the beams spread
and overlap and are registered at different positions on the screen. In another
kind of multipath interference, the beams may be split and recombined,
as happens in a Mach-Zehnder interferometer. In general, we may assume that
each beam is split into new channels, whose states may be represented
by $|\xi_i\rangle$. The simplest case would be where
all the original beams have equal overlap with a
particular output channel, say $|\xi_i\rangle$. This translates to an
assumption that $\langle\xi_i|\psi_k\rangle = A_i$ is same for all $k$.
The probability $I$ of finding the quanton in the $i^{th}$ output channel
(not the $i^{th}$ path) is then
given by $I = \langle\xi_i|\rho|\xi_i\rangle$. For the present case,
this probability is given by
\begin{eqnarray}
I &=& |A_i|^2 \Big[ \sum_{j=1}^n \rho_{jj} +
\sum_{j \neq k}\rho_{jk} e^{i(\theta_j-\theta_k)} \Big] \nonumber\\
  &=& |A_i|^2 \Big[1 +
\sum_{j \neq k}\rho_{jk} e^{i(\theta_j-\theta_k)} \Big] \nonumber\\
  &=& |A_i|^2 \Big[1 +
\sum_{j \neq k}|\rho_{jk}| \cos(\theta_j-\theta_k) \Big] .
\label{ninterf}
\end{eqnarray}
If one were to simulate Mei and Weitz experiment in this situation,
one would first change the phase of the $\ell$'th path as
$\theta_{\ell} \rightarrow \theta_{\ell}+\pi$. It is to be noted that our visibility $\mathcal{V}$, given by (\ref{VHS}), is unaffected
by this phase change, whereas the fringe contrast does get affected.

If one wants to know which path the quanton followed, one needs to have
the quanton paths entangled with a path-detector.
The combined state of the quanton and the path-detector, after the two
have interacted, will be of the form
\begin{equation}
  \rho' = \sum_{j=1}^n \sum_{k=1}^n \rho_{jk} |\psi_j\rangle\langle\psi_k|
  e^{i(\theta_j-\theta_k)}\otimes |d_j\rangle\langle d_k|,
\end{equation}
where $\{|d_i\rangle\} $ are the states of the path detector, assumed to be
normalized, but not necessarily mutually orthogonal.
The reduced density operator of the quanton is obtained by tracing over the
path-detector states:
\begin{equation}
  \rho_r' = \sum_{j=1}^n \sum_{k=1}^n \rho_{jk} |\psi_j\rangle\langle\psi_k|
  e^{i(\theta_j-\theta_k)} \langle d_k|d_j\rangle .
\end{equation}
In order to reproduce the Mei and Weitz experimental situation, we assume
that the path-detector can only tell if the quanton passed through path
$\ell$ or not, it cannot discriminate between any other paths. This is
achieved by having all the path detector states being identical,
(say) equal to $|d_1\rangle$, and only $|d_{\ell}\rangle$ being different
from $|d_1\rangle$. Now if one were to calculate the visibility, as
defined by (\ref{VHS}), for this state of the quanton, it will turn out
to be
\begin{equation}
\mathcal{V}'^{2} = \frac{n}{n-1}\sum_{i\neq j} |\rho_{ij}|^{2}
|\langle d_k|d_j\rangle|^2 .
\label{VHS'}
\end{equation}
Since $|\langle d_i|d_j\rangle|=1$ for all $i,j$ except those involving $\ell$,
one can easily see that
\begin{equation}
\mathcal{V}'^{2} < \frac{n}{n-1}\sum_{i\neq j} |\rho_{ij}|^{2}
\end{equation}
or
\begin{equation}
\mathcal{V}'^{2} < \mathcal{V}^{2} ,
\end{equation}
which means that the visibility will always decrease if one tries to find out
if the quanton passed through path $\ell$ or not. Thus the new visibility
works satisfactorily even for Mei and Weitz experiment, where conventional
visibility fails.

The next question we address is, how to measure this visibility in an
interference experiment. The probability given by (\ref{ninterf}), can
also be interpreted as the intensity at a position on the screen, or in
an output channel. In general it depends on the phases of the paths.
D\"ur has shown that the second moment of this interference pattern \cite{durr},
\begin{equation}
\langle (\Delta I)^2\rangle_{\theta} = \tfrac{1}{n^2}
\sum_{i\neq j} |\rho_{ij}|^{2} ,
\end{equation}
where $\Delta I = I - \langle I\rangle_{\theta}$, and
$\langle\dots \rangle_{\theta}$ denotes the average over all phases.
Thus the new visibility can be written as
\begin{equation}
\mathcal{V}^{2} = \tfrac{n^3}{n-1} \langle (\Delta I)^2\rangle_{\theta},
\end{equation}
which means, it can be measured if one can design an experimental
arrangement to vary the phases of all paths independently, and do an averaging
over them. This is one method of experimentally obtaining the new visibility.

Notice that (\ref{VHS}) represents a sum over pairs of paths. If one were
to modify the $n$-path interference experiment by blocking all paths except
one pair $i,j$, the \emph{conventional visibility} of the interference of
that pairs of paths will be given by
\begin{equation}
{V}_{ij} = \frac{2|\rho_{ij}|}{\rho_{ii}+\rho_{jj}}.
\end{equation}
Now one can repeat the experiment with another pair of paths, and so on, until
one has gone over all path pairs. If all paths are equally probable,
$\rho_{ii}=\rho_{jj}=\frac{1}{n}$, ${V}_{ij} = n|\rho_{ij}|$.
The \emph{mean square} of the visibilities, of all path pairs, is given by
\begin{equation}
\tfrac{2}{n(n-1)} \sum_{\text{pairs}}{V}_{ij}^2 =
\tfrac{n}{n-1}\sum_{i\neq j}|\rho_{ij}|^2 = \mathcal{V}^2 .
\end{equation}
This is a very interesting result, which shows that the multipath visibility
$\mathcal{V}$ is the \emph{root mean square} of the fringe contrasts of
interference from all path pairs. So, another way $\mathcal{V}$ can
be measured is by opening only a pair of paths at a time, and measuring
conventional visibility, and then taking root mean square over all path
pairs. Such a procedure is very much feasible, and selectively opening
path pairs has already been experimentally demonstrated \cite{padua}.
If the paths are not equally probable, the procedure needs to be slightly modified. It can be shown that
$\tfrac{n}{2(n-1)} \sum_{\text{pairs}}(\rho_{ii}+\rho_{jj})^2{V}_{ij}^2 =
\ \mathcal{V}^2$.

\subsection{Predictability measure}
A generalized predictability can be defined as,
\begin{equation}\label{pred1}
  \mathcal{P}^{2}   = \sum_{i =1}^{n}\rho_{ii}^{2} - \frac{1}{n-1}\sum_{i\neq j}\rho_{ii}\rho_{jj} = 1 - \frac{n}{n-1}\sum_{i\neq j}\rho_{ii}\rho_{jj}
\end{equation}
where $\rho$ is the density matrix of the quanton and $n$ is the
dimension of the density matrix (number of paths). As is evident from
the above expression $\mathcal{P}$ varies from zero to one, therefore
normalized. Although defined in a very different manner, it turns out that
(\ref{pred1}) is identical to the predictability defined by D\"urr \cite{durr}.
To show that (\ref{pred1}) is a good measure of generalized
predictability, we show that it follows all of D{\"u}rr's criteria.\\
(i) $\mathcal{P}$ is a polynomial function of $\rho_{ii}$, therefore
a continuous function involving only the diagonal elements.\\ (ii)
When the quanton's path is known for sure, i.e., $\rho_{ii} = 1$ and
$\rho_{jj} = 0~~ \forall ~~j \neq i$ (only $i^{th}$ slit is open),
predictability  reaches its global maximum i.e., $\mathcal{P} =
1$.\\ (iii) When quanton's probability of going through all paths
are equally likely, i.e., $\rho_{ii} = \frac{1}{n}~~\forall~~i$,
generalized predictability is zero, since $\mathcal{P}^{2} = 1 -
\frac{n}{n-1}\sum_{i\neq j}\frac{1}{n^{2}} = 0$.\\ (iv) A change of
probabilities (diagonal elements $\rho_{ii}$) towards equalization leads
to decrease in the generalized predictability. To show that, consider
$\rho_{11} < \rho_{22}$ and a small parameter $0<\varepsilon < \rho_{22}
- \rho_{11}$. A shift in probabilities, $\Tilde{\rho}_{11} = \rho_{11}
+ \varepsilon$ and $\Tilde{\rho}_{22} = \rho_{22} - \varepsilon$, with
other elements unchanged yields the following,
\begin{equation}
    \mathcal{P}^{2} - \Tilde{\mathcal{P}}^{2} = \frac{2n\varepsilon}{n-1}\left(\rho_{22} - \rho_{11} -\varepsilon\right).
\end{equation}
Since, $\varepsilon>0$ and $\varepsilon < \rho_{22} - \rho_{11}$, one obtains $\mathcal{P} > \Tilde{\mathcal{P}}$, therefore, a decrease in predictability.

Therefore, generalized predictability as defined in (\ref{pred1}) satisfies D{\"u}rr's criteria. Furthermore, for two beam interferometer case ($n=2$), it reduces to,
\begin{equation}
    \mathcal{P} = |\rho_{11} - \rho_{22}|
\end{equation}
which matches with the predictability proposed by Greenberger and Yasin
\cite{GY}.

\subsection{Path distinguishability}
A multipath distinguishability has been proposed earlier as \cite{nduality}
\begin{equation}\label{dis1}
      \mathcal{D}^{2} = 1 - \left(\frac{1}{n-1} \sum_{i\neq j}\sqrt{\rho_{ii}\rho_{jj}}|\langle d_{i}|d_{j}\rangle|\right)^{2},
\end{equation}
which can be related to unambiguous quantum state discrimination.
We define the path-distinguishability $\mathcal{D}$ in a different way:
\begin{equation}\label{dis2}
    \mathcal{D}^{2} = 1 - \frac{n}{n-1} \sum_{i\neq j}\rho_{ii}\rho_{jj}|\langle d_{i}|d_{j}\rangle|^{2}.
\end{equation}
In the spirit of complementarity, our proposed distinguishability
measure satisfies the following basic criteria for being a reliable path
quantifier \cite{durr}:  \\(i) When the detector states $\{{|d_{i}\rangle}\}$ form
an orthonormal basis, i.e., $\langle d_{i}|d_{j}\rangle = \delta_{ij}$,
the path distinguishability $\mathcal{D}$ is maximum ($\mathcal{D} = 1$),
since in this case all the paths can be unambiguously discriminated.
\\  (ii) When all the detector states are parallel, i.e., state of
quanton and the detector is separable, and probability through all
the slits are equal, i.e., $\rho_{ii} = 1/n~\forall i$, then the path
distinguishability $\mathcal{D}$ is minimum ($\mathcal{D} = 0$). \\(iii)
Whenever the detector states $|d_{i}\rangle$ and $|d_{j}\rangle$ are made
more orthogonal i.e., with an increment in $|\langle d_{i}|d_{j}\rangle|$,
the distinguishability increases. \\(iv) Distinguishability and visibility
both can not increase simultaneously under any operation, which is evident
through the fact $\mathcal{D}^{2} + \mathcal{V}^{2} = 1$.

For the case of two paths, (\ref{dis2}) reduces to the distinguishability
defined by Englert \cite{englert}. Next we address the issue of measuring
this distinguishability. Taking cue from the visibility, we note that if
one were to close all paths, except paths $i,j$, the path distinguishability,
based on minimum error state discrimination, is given by
\begin{equation}
{D}_{ij} = \sqrt{1 - \frac{4\rho_{ii}\rho_{jj}}{(\rho_{ii}+\rho_{jj})^2}
|\langle d_{i}|d_{j}\rangle|^{2}},
\end{equation}
which is essentially Englert's distinguishability, generalized for unequal path probabilities by using the Helstrom bound \cite{helstrom}.
As done in the case of visibility, one can repeat the interference experiment by selectively
opening different pairs of slits, while measuring the distinguishability. When all the path are equally probable, the
\emph{mean square} of the distinguishabilities, from all pairs of paths,
is given by
\begin{equation}
\tfrac{2}{n(n-1)} \sum_{\text{pairs}}{D}_{ij}^2 =
1 - \frac{n}{n-1} \sum_{i\neq j}\rho_{ii}\rho_{jj}|\langle d_{i}|d_{j}\rangle|^{2}
 = \mathcal{D}^2,
\end{equation}
which is the same as (\ref{dis2}). Thus the distinguishability too can be
measured experimentally, as the \emph{root mean square} of
conventional distinguishabilities, from all path pairs. When the paths are not equally probable, the distinguishability can be measured through the conventional two-slit distinguishability from path pairs $D_{ij}$ and the path probabilities $\rho_{ii}$ as following,
\begin{equation}\label{disuneq}
    \mathcal{D}^{2} = 1 - \frac{n}{2(n-1)}\sum_{pairs}(\rho_{ii} + \rho_{jj})^{2}(1-D_{ij}^{2}).
\end{equation}

It is not difficult to see that our $n$-path predictability may also be expressed in terms of the conventional two-slit predictability for path pairs and their intensities, in a manner similar to that of distinguishability in  (\ref{disuneq}).
This has not been recognized earlier, although the predictabilities proposed by Greenberger
and Yasin \cite{GY} and D\"urr \cite{durr} have been around for a long time.

\section{Complementarity}
Consider a quanton passing through a $n$-path interferometer, such that its quantum state is given by the following pure state,
\begin{equation}\label{pure1}
    |\psi\rangle = \sum_{i=1}^{n}c_{i}|\psi_{i}\rangle,
\end{equation}
where, $c_{i}\in \mathbf{C}$. The density operator for the quanton can be written as $\rho = \sum_{i,j}c_{i}c_{j}^{*}|\psi_{i}\rangle\langle\psi_{j}|$.
Using (\ref{VHS}) and (\ref{pred1}),
one obtains a $n$-path duality relation as follows. The sum of the squares of the predictability and visibility is given by
\begin{eqnarray}\label{duality1}
    \mathcal{P}^{2} + \mathcal{V}^{2} &=& 1 - \frac{n}{n-1}\sum_{i\neq j}\left(\rho_{ii}\rho_{jj}-|\rho_{ij}|^{2}  \right) .
\end{eqnarray}
Since for the pure state given by (\ref{pure1}) $\rho_{ij}
= c_{i}c_{j}^{*}$ resulting in $\rho_{ii}\rho_{jj} =
|\rho_{ij}|^{2}$, the duality relation saturates
for the pure state case. When a quanton is given by an ensemble
$\{(p^{\alpha},~ |\psi^{\alpha}\rangle)\}$, where $p^{\alpha}
\geq 0$ with $\sum p^{\alpha} = 1$, and $|\psi^{\alpha}\rangle =
\sum_{i}c^{\alpha}_{i}|\psi_{i}\rangle$. The resulting density
matrix is mixed with the elements given by $\rho_{ij} =
\sum_{\alpha}p^{\alpha}c_{i}^{\alpha}c_{j}^{\alpha *}$ :
\begin{equation}
    \rho_{ii}\rho_{jj}-|\rho_{ij}|^{2} = \sum_{\alpha}\left\lvert c_{i}^{\alpha}\right\rvert^{2} \sum_{\beta}\lvert c_{j}^{\beta}\rvert^{2} - \abs{\sum_{\alpha}c_{i}^{\alpha}c_{j}^{\beta *}}^{2} \geq 0.
\end{equation}
Here, the last inequality follows from the Cauchy-Schwartz inequality. Therefore, in general we have the following $n$-path duality relation,
\begin{equation}
    \mathcal{P}^{2} + \mathcal{V}^{2} \leq 1,
\end{equation}
which saturates for pure $\rho$. This result was already derived by
D\"urr \cite{durr}, but now sets the stage for investigating the case where
there is a path-detector in place, which can perform a which-path or
which-way detection.

Consider an interferometer with an added path-detecting device, such that the
quanton going through the $n$ paths is described by the state
\begin{equation}
    |\Psi\rangle = \sum_{i=1}^{n}c_{i}|\psi_{i}\rangle|d_{i}\rangle,
\end{equation}
where, $|\psi_{i}\rangle$ is the state of the quanton corresponding to its passing through the $i^{th}$ path, and $|d_{i}\rangle$ is the state of the path-detector, corresponding to that possibility. The states $\{|d_{i}\rangle\}$ are assumed to be normalized, but not necessarily orthogonal.

The reduced density operator of the quanton, after tracing over the path-detector states is,
\begin{equation}\label{reduceddensity1}
    \rho_{r} = \sum_{i,j}c_{i}c_{j}^{*}\langle d_{j}|d_{i}\rangle~|\psi_{i}\rangle\langle \psi_{j}|.
\end{equation}
In terms of the density operator for the quanton in the absence of the path-detector, one can write  (\ref{reduceddensity1}) as,
\begin{equation}
    \rho_{r} = \sum_{i,j}\rho_{ij}\langle d_{j}|d_{i}\rangle~|\psi_{i}\rangle\langle \psi_{j}|
\end{equation}
 For this reduced density operator, one can write (\ref{duality1}) as,
 \begin{equation}\label{duality2}
 \begin{aligned}
     \mathcal{P}^{2} + \mathcal{V}^{2} =& 1 - \frac{n}{n-1}\sum_{i\neq j}\rho_{ii}\rho_{jj}+\frac{n}{n-1}\sum_{i\neq j}|\rho_{ij}|^{2}|\langle d_{j}|d_{i}\rangle|^{2}\\ =& 1 - \frac{n}{n-1}\sum_{i\neq j}\rho_{r_{ii}}\rho_{r_{jj}}+\frac{n}{n-1}\sum_{i\neq j}|\rho_{r_{ij}}|^{2}
     \end{aligned}
 \end{equation}
One can define a normalized entanglement measure $\mathcal{E}$ such that,
\begin{equation}
    \mathcal{E}^{2} = \frac{n}{n-1}\sum_{i\neq j}\left(\rho_{r_{ii}}\rho_{r_{jj}} - |\rho_{r_{ij}}|^{2} \right) = \frac{n}{2(n-1)}E^{2}
\end{equation}
where $E$ is the generalized concurrence \cite{gconc}, and coincides
with I-concurrence \cite{rungta}, when the bipartite state under consideration is a pure state. Eqn. (\ref{duality2}) can then be written as,
\begin{equation}
    \mathcal{P}^{2} + \mathcal{V}^{2} = 1 - \mathcal{E}^{2},
\end{equation}
or as a triality relation,
\begin{equation}\label{triality}
     \mathcal{P}^{2} + \mathcal{V}^{2} + \mathcal{E}^{2}= 1 .
\end{equation}

Therefore, the generalized predictability, Hilbert-Schmidt coherence,
and I-concurrence obey a tight triality relation. It is interesting
to note that the path-distinguishability measure, as defined in the
previous section, is related to the generalized predictability through
I-concurrence as follows,
\begin{equation}\label{DPE1}
   \mathcal{D}^{2} =  \mathcal{P}^{2} + \mathcal{E}^{2} .
\end{equation}
This above relation shows that the two different kinds of path knowledge,
predictability and distinguishability, are quantitatively connected through
a measure of entanglement, the I-concurrence. It very naturally generalizes
Englert's duality relation (\ref{dualitye}) to multipath interference:
\begin{equation}\label{nduality}
   \mathcal{D}^{2} + \mathcal{V}^{2} =  1.
\end{equation}
Needless to say, Englert's duality relation is recovered for $n=2$.
Since the above relation is an equality, it is obvious that this
multipath distinguishability does not suffer from the shortcoming of
D\"urr's multipath distinguishability, pointed out by Bimonte and
Musto \cite{bimonte2}.

A triality connection between predictability, coherence and entanglement
has been shown earlier \cite{triality3}, but that relation does not
involve an entanglement monotone. Here, we have shown that a good
entanglement measure, the I-concurrence, is an integral part of complementarity
in multipath interference. For $n=2$, (\ref{triality}) reduces to
\begin{equation}\label{triality2}
     {P}^{2} + {V}^{2} + \mathcal{E}_2^{2}= 1 ,
\end{equation}
where is ${P}$ is the predictability of Greenberger and Yasin \cite{GY}, ${V}$ is
the fringe contrast, and $\mathcal{E}_2$ is the concurrence \cite{concurrence}.
This two-path result is the same as that derived earlier by Jakob and
Bergou \cite{triality1}, and it is satisfying to see that our general
multipath relation reduces to it in the appropriate limit. In addition,
for $n=2$ the relation (\ref{DPE1}) reduces to
\begin{equation}\label{DPE}
   {D}^{2} =  {P}^{2} + \mathcal{E}_2^{2} ,
\end{equation}
where ${D}^{2}$ is Englert's distinguishability \cite{englert},
${P}$ is the predictability \cite{GY}, and $\mathcal{E}_2$ is the
concurrence, a known result due to Jakob and Bergou \cite{triality1}.

Since (\ref{triality}) is an equality for pure quanton path-detector states,
it opens up the possibility of measuring I-concurrence. In an unbalanced
$n$-path interferometer, if the quanton gets entangled with an ancilla system,
its interference visibility will be affected. Since the path predictability
is known from the experimental setting, and can also be measured, and
the interference visibility can be measured, as discussed earlier, one
can actually infer the degree of entanglelment of the quanton with the
ancilla, without probing the ancilla in any way.

\section{conclusion}

In conclusion, we have introduced an interference visibility based on the
Hilbert-Schmidt coherence, and shown that it constitutes a good measure
of wave nature, and does not suffer from the shortcomings of the conventional
fringe contrast, which emerges in certain experiments \cite{mei}. Interestingly,
this visibility can be obtained as a root mean square of the fringe contrasts
from all \emph{pairs of paths}, if the experiment is done by opening only
a pair of paths at a time. Selectively opening pairs of slit in a multi-slit
interference experiment has already been realized \cite{padua}.

A multipath predictability has been introduced, which is a natural
generalization of the two-path predictability of Greenberger and Yasin
\cite{GY}. Interestingly, this multipath predictability
can also be measured using the two-path predictabilities
of pairs of paths. A multipath distinguishability has also been introduced
which, again, can be viewed as root mean square of the two-path
distinguishability (introduced by Englert) of all pairs of paths.
The predictability and visibility introduced here, together with the
I-concurrence (related to entanglement between the quanton and a
path-detector), are shown to follow a tight triality relation. This
brings out the essential role of entanglement in the phenomenon of
complementarity, in the general context of multipath interference.

\begin{acknowledgements}
\end{acknowledgements}
AKR, NKC and PKP gratefully acknowledge the financial support from DST, India through Grant No. DST/ICPS/QuST/Theme1/2019/2020-21/01. NP acknowledges financial support from DST, India through the Inspire Fellowship (registration number IF180414).

redpajama_set_name: RedPajamaArXiv


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Popping or crackling in an outlet. The sudden hush of appliances as a breaker pops. These sounds can indicate a problem with your electrical system, but did you know there are signs to watch out for that are less noisy yet just as serious?
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text:
The Untold Truth Of Pope Francis
Giulio Origlia/Getty Images
By Pauli Poisuo/March 26, 2021 4:09 pm EST
It's not always clear just what exactly a pope does, but many people seem to agree that the incumbent, Pope Francis, looks pretty great doing it. Per Biography, the man born as Jorge Mario Bergoglio has done the majority of his pre-papal life's work in his native Argentina and holds the distinction of being both the first South American pope and the first Jesuit one.
By the time he was elected to take over the Holy See in 2013, he had already developed a solid street cred as a humble, down-to-earth man of the people, and he's very much carried this salt-of-the-earth over to his papacy. If he can get away with it — which he can, what with being the pope and everything — you won't catch him in the opulent regalia he's entitled to (per Garage). Instead, he eschews his predecessors' more expressive wardrobe in favor of more muted fare that Vatican tailors have been known to call "papal athleisure." All in all, he seems like the kind of guy who's doing his level best to match the papal name he chose after the noted charity-focused Italian saint, St. Francis of Assisi (via Encyclopedia Britannica).
Francis' tenure as the pope has been an interesting and eventful one so far, and as you might imagine, the less-known aspects about the pontiff's life are no less fascinating. Today, we'll take a look at the untold truth of Pope Francis.
Pope Francis used to work as a nightclub bouncer
Franco Origlia/Getty Images
Popes tend to be fairly elderly and, as such, aren't exactly known for their physical prowess. However, when you look at Pope Francis outside the papal context, he's a fairly broad-shouldered guy who looks like he might have been pretty strong in his younger days. As Newsweek tells us, this might very much be the case — at least, judging by the fact that when Jorge Mario Bergoglio was a young man, he financed his studies by working as a nightclub bouncer in his home town, the Argentine city of Buenos Aires.
While it's hard to imagine the gentle Francis standing stone-faced at the door, eyeballing the line of party people — let alone hauling drunken revelers toward the exit in a choke hold — this gem of a fact about his early profession leads to the enticing prospect that back in the day, some citizens of Buenos Aires were removed from the premises after having a few too much by none other than the future pope. If nothing else, having a story like that in your back pocket would make you an instant winner at any family gathering.
Pope Francis had part of his lung removed
Being one of the most famous leaders in the entire world and guiding the Catholic Church is no easy feat, and as Time notes, Pope Francis plays the game on extra-difficult mode on account of having only one fully functional lung. A chunk of his right lung was removed when he was young, and when he became the pope in 2013, it was reported that this happened when he was a teenager, presumably due to some infection or another. However, it was noted that the only real adverse effect was that he has less lung capacity than the average person.
In 2020, Francis addressed his lung issue in relation to the COVID-19 pandemic, per CBS. The picture he painted of the health scare of his youth was significantly more grim than one might imagine. He was 21 when he ended up in a ventilator after a misdiagnosis, and his right lung had to be drained of some 34 ounces of fluid before part of it had to be removed altogether. The struggle, he says, nearly killed him. "For months I didn't know who I was, if I would live or die, even the doctors didn't know," Francis described the ordeal. "I remember hugging my mother one day and asking her if I was about to die." He thinks he wouldn't have survived without an experienced nurse, who adjusted his dosage behind the doctor's back.
Pope Francis released a pop rock album
Look, there's really no way to hype up the following information more efficiently than just bluntly stating it — Pope Francis, as Rolling Stone reports, released a pop rock album. That's right up there with that time when Christopher Lee randomly starting a heavy metal career, as unexpected, yet strangely awesome things go.
Of course, Francis didn't give you a bunch of chart-topping, radio-friendly songs about love and loss with his dulcet tones slowly building toward a power chorus. He is still the pope, after all. The 2015 album Wake Up! is a far stranger affair, and as Pitchfork tells us, it actually leans toward progressive rock. The peculiar collection of tunes — that have names like "Wake Up! Go! Go! Forward!" — contains a number of the pope's speeches in various languages, embedded in an assortment of curious musical tracks, many of which come courtesy of Tony Pagliuca of the 1970s prog-rock band Le Orme.
As Pitchfork's reviewer opines, it's all very strange and not always musically impressive. Yet, the very fact that the Vatican set out to release something like this instead of more classic ecclesiastically themed pope record fare speaks volumes of the kind of pope that Francis is.
Pope Francis is a huge fan of tango
Pope Francis might come across as a more laid-back guy than your average pontiff, but you might still have a hard time imagining him tearing up the dance floor. Yet, by his own admission, the pope is a big fan of dancing, and according to the Catholic News Agency, he sees it as a pretty essential extension and expression of a person's happiness. "I liked to be together with other children, playing...dancing our typical dances from Argentina," he has said of his fondness of dancing as a child. "I had a lot of fun."
In his teenage years, the future pope became fond of tango, and according to the BBC, this carried over well into his adult years. "I love it," he enthused about the dance some years before he became the pope. "It's something that comes from deep within me."
The pope's love of the dance has not gone unseen by the people. When Francis turned 78 in 2014, the celebrations involved a huge tango event at St. Peter's Square, where hundreds of dancers turned up.
Pope Francis used to be a chemist
Pope Francis is quite obviously a man of religion – the man of religion, as it happens — but as Forbes notes, he has a surprisingly solid background in science, as well. Back in the day, when he was still young Jorge Mario Bergoglio, he studied in a technical school and received a chemical technician certificate. According to Time, he has also worked as a chemist.
Though the pope eventually entered the ranks of priesthood and doesn't appear to have pursued his early scientific interests further than that, it is pretty cool that the guy in charge of the Catholic Church has a decent understanding of at least one field of science. To be fair, though, National Catholic Reporter notes that the pope's scientific credentials aren't quite as impressive as some people think. Around 2015, media outlets reported that Francis has a master's degree in chemistry, when the diploma he has is actually a título – an Argentine rank that stands somewhere between a high school diploma and a university degree.
Pope Francis loves soccer
Pier Marco Tacca/Getty Images
As Bleacher Report tells us, Pope Francis is very, very fond of association football. Perhaps fittingly to his humble character, the pope's favorite club is the oft-struggling Argentine Premier League-side San Lorenzo, and he's even said to hold a club membership card. "He says he lives in a permanent state of suffering for San Lorenzo," fellow supporter Oscar Lucchini has stated.
On occasion, the pope has found ways to incorporate his favorite sport to his papal duties. As Sports Illustrated tells us, Francis has held many meetings with soccer notables over the years and amassed a bunch of personalized team jerseys in the process. Still, though he's met notables like Lionel Messi and Diego Maradona, his love for San Lorenzo prevails. Per Rome Reports, in 2016 he gave an audience to players from his beloved San Lorenzo and AS Roma, the biggest club in Rome, before the teams met in a charity match — and couldn't resist the opportunity to jokingly dunk on Roma by giving them some San Lorenzo merch.
Interestingly, Francis is far from the first pope to have a warm relationship with soccer. His predecessor, Pope Benedict XVI, was a huge fan of the German club Bayern Munich, and his predecessor John Paul II actually played the game himself as a young man.
The Pope and food
Being one of the most influential people around, you'd expect the pope to be able to eat just about anything he likes. Per NPR, though, Pope Francis is very much not a "caviar and quail's eggs" type of guy. Instead, he has a history of preferring simple fare like salad, chicken, and soup, and though he has been known to partake in the occasional coffee or glass of wine, he generally keeps it pretty simple.
Before he ascended to the papacy, he was also known to cook his meals himself instead of resorting to kitchen staff. Though his current job has him wearing clothes that decidedly aren't chef's whites, his attitude toward food and dining has remained pretty easy-going. As The Washington Post tells us, he has even turned up at the Vatican's employee cafeteria and had lunch at the same table with the workers, making chitchat and even posing for photos.
Though Francis does tend to keep it simple, it doesn't mean that he doesn't like to treat himself every now and then. NBC News reports that he misses being able to pop out for a nice pizza, and according to TMZ, doctors have actually told him to cut back on pasta and other carbs.
Pope Francis doesn't watch TV
According to NBC News, July 15, 1990, was a significant date in the life of Jorge Mario Bergoglio, because this was the last day he watched television. Though the pope presumably has better things to do than keeping up with the latest reality shows in any case, he reportedly went as far as outright promising the Virgin Mary to abstain from that point on and hasn't strayed since. In fact, that's not the only small screen the pope has decided to avoid. Though ABC News reports Francis has called the internet "a gift from God," Cnet.com notes that he doesn't personally use it at all, and that he generally avoids most media — though he does allow himself 10 minutes with the Italian newspaper La Repubblica as part of his morning routine.
While it's unclear precisely what show or life event caused him to swear off the small screen, it quite likely wasn't sports. The decision to avoid TV has brought one significant downside to Francis' life. Since he's located in Vatican and his beloved soccer team, San Lorenzo, is in Argentina, it's hard for him to keep up with their antics without television. However, Francis has reportedly devised a handy workaround to this problem. Apparently, a designated member of the Swiss Guard keeps up with San Lorenzo's games and informs the pope how the team is doing.
Pope Francis lives in a tiny apartment
The Vatican is a pretty impressive place, but that doesn't mean the pope lives in a massive palace. Oh, he has a bunch of pretty awesome dwellings at his disposal, but according to the BBC, Pope Francis made it clear early on that he isn't about to live in the Apostolic Palace, where the luxurious papal apartments make up the top floor. Instead of the glorious dozen-plus rooms with a great view, he was content to move to a comparatively humble two-room apartment in the Domus Santa Marta building near St. Peter's Basilica. This is something of a habit of him, actually. Back when he was the archbishop of Buenos Aires, he also elected to stay out of the local Bishop's Palace in favor of leading a more modest existence.
The apartment arrangements, as America Magazine notes, was only the beginning of Francis' fight against his right to live in excessively palatial places. He was also quick to inform everyone that he wouldn't spend his summers at the pope's lavish summer palace, Castel Gandolfo. When the lack of papal presence caused a slump in the local economy, he reacted by turning the palace into a museum. Still, though the area gets by without regular visits from the pontiff, some of the locals would be cool if the profitable tourism business closed down, if it meant that the papal visits to Castel Gandolfo would resume.
Pope Francis has a complicated relationship with selfies
As The Washington Post notes, Pope Francis has become notable for being the kind of pontiff who doesn't shun from a selfie. From teens to newlyweds and random acquaintances, many people have managed to add a selfie with a smiling Francis to their collection. Still, while the pope may be game to pose and smile, America Magazine tells us that Francis' personal opinion of selfie culture is rather less glowing. In 2018, he discussed an event where he met young people from an international program. "They were all there waiting for me," said Francis. "When I arrived, they made noise, as young people do. I went to greet them and only a few gave their hand. The majority were with their cellphones (saying), 'photo, photo, photo. Selfie!'"
While the pope seems to fully realizes that this is the game, and the many selfies he's smiled for show that he does very much know how to play, it doesn't mean that he particularly likes it. This isn't just an "old man doesn't understand the youth of today" situation, either. Instead, Francis feels that selfies are part of the "virtualized" lifestyle, which can potentially alienate kids from others and cause them to lose touch with the real world. "We must make young people 'grounded' in the real world; to touch reality without destroying the good things the virtual world may have because they are useful," the pope has said. "This is important: reality, concreteness."
Pope Francis is a climate change activist
Bloomberg/Getty Images
As Vatican News and America Magazine report, one of Pope Francis' greatest interests and biggest concerns is the subject of climate change. He communicates with world leaders about the issue and doesn't let anyone forget the fact that the people who the situation hurts the most are the often the ones with the least amount of power to do anything about it. "The effects of the ongoing pandemic and climate change —which are relevant not only for the environment but also for the spheres of ethics, society, economics, and politics — weigh most heavily upon the lives of the poor and vulnerable," he said in a 2020 message to the United Nations.
This isn't just some random hobby the pope picked up during the ongoing COVID-19 pandemic, either. As The Guardian tells us, in 2019 Francis went as far as to declare what he called a "climate emergency," calling action in no uncertain terms. And it goes even further than that. In 2015, The Washington Post reported that the United States presidential candidate Rick Santorum was busy criticizing the pope ... because the pope was busy addressing the climate change issue. All in all, Francis seems to pay a lot of attention to this particular earthly matter.


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Dubois, Idaho
Location of Dubois in Clark County, Idaho.
Coordinates: 44°10′26″N 112°13′54″W / 44.17389°N 112.23167°W / 44.17389; -112.23167Coordinates: 44°10′26″N 112°13′54″W / 44.17389°N 112.23167°W / 44.17389; -112.23167
5,148 ft (1,569 m)
217.38/sq mi (83.94/km2)
UTC-7 (Mountain (MST))
UTC-6 (MDT)
www.duboisidaho.com
Dubois (/duːˌbɔɪs/, du-BOISS) is a city in Clark County, Idaho, United States. The population was 677 at the 2010 census. The city is the county seat of Clark County.[4]
The city was named in 1892 for Fred Dubois (1851−1930), the state's prominent politician in its early years.[5] He came to Idaho in 1880 and was the state's first U.S. Senator and served for two non-consecutive terms (1891−97, 1901−07).
Six miles (10 km) north of town is the U.S. Sheep Experiment Station, the county's second largest employer.[6] The station studies sheep breeds to support U.S. sheep farmers. Dubois is near the Caribou-Targhee National Forest, which calls one of its administrative units the Dubois ranger district.[citation needed]
Dubois is located at 44°10′26″N 112°13′54″W / 44.17389°N 112.23167°W / 44.17389; -112.23167 (44.174018, -112.231717),[7] at an elevation of 5,148 feet (1,569 m) above sea level.
According to the United States Census Bureau, the city has a total area of 2.50 square miles (6.47 km2), all of it land.[8]
Est. 2018 588 [9] −13.1%
As of the census[2] of 2010, there were 677 people, 229 households, and 167 families residing in the city. The population density was 270.8 inhabitants per square mile (104.6/km2). There were 265 housing units at an average density of 106.0 per square mile (40.9/km2). The racial makeup of the city was 67.1% White, 0.9% African American, 0.7% Native American, 0.3% Asian, 30.4% from other races, and 0.6% from two or more races. Hispanic or Latino of any race were 49.6% of the population.
There were 229 households of which 41.9% had children under the age of 18 living with them, 58.1% were married couples living together, 9.2% had a female householder with no husband present, 5.7% had a male householder with no wife present, and 27.1% were non-families. 21.4% of all households were made up of individuals and 10.5% had someone living alone who was 65 years of age or older. The average household size was 2.96 and the average family size was 3.46.
The median age in the city was 32.3 years. 32.6% of residents were under the age of 18; 8.4% were between the ages of 18 and 24; 24.6% were from 25 to 44; 22.5% were from 45 to 64; and 11.8% were 65 years of age or older. The gender makeup of the city was 51.6% male and 48.4% female.
As of the census[11] of 2000, there were 647 people, 214 households, and 164 families residing in the city. The population density was 290.1 people per square mile (112.0/km²). There were 245 housing units at an average density of 109.8 per square mile (42.4/km²). The racial makeup of the city was 70.02% White, 1.08% Native American, 0.15% Asian, 0.15% Pacific Islander, 27.51% from other races, and 1.08% from two or more races. Hispanic or Latino of any race were 39.57% of the population.
In the city, the population was spread out with 36.0% under the age of 18, 8.0% from 18 to 24, 27.2% from 25 to 44, 18.4% from 45 to 64, and 10.4% who were 65 years of age or older. The median age was 30 years. For every 100 females, there were 107.4 males. For every 100 females age 18 and over, there were 98.1 males.
Dubois experiences a humid continental climate (Köppen Dfb) with long, cold winters and hot, wetter summers.
Climate data for Dubois, Idaho (1971–2000)
Record high °F (°C)
Average high °F (°C)
(−2.3) 33.0
(0.6) 41.9
Average low °F (°C)
(−12.2) 14.1
Record low °F (°C)
(−33) −26
(−24) 15
(−9) 22
(−1) 2
(−17) 2
(−35)
Average precipitation inches (mm)
(20) 0.71
(23) 13.07
Average snowfall inches (cm)
(6.9) 1.0
Average precipitation days (≥ 0.01 inch)
8.6 6.9 7.1 7.3 9.9 8.5 6.2 5.7 4.5 5.4 7.3 8.3 85.7
Average snowy days (≥ 0.1 inch)
Source: NOAA (normals, 1971–2000) [12]
List of cities in Idaho
^ "2016 U.S. Gazetteer Files". United States Census Bureau. Retrieved Jul 26, 2017.
^ "Population and Housing Unit Estimates". Retrieved June 9, 2017.
^ "Find a County". National Association of Counties. Archived from the original on 2012-07-12. Retrieved 2011-06-07.
^ Pettite, William Stibal (April 26, 1962). "Tiny Clark County long on history". Lewiston Morning Tribune. p. 2.
^ Lee, Sandra L. (February 25, 1990). "Harsh land is home to a hardy breed". Lewiston Morning Tribune. p. 1-centennial.
^ "US Gazetteer files: 2010, 2000, and 1990". United States Census Bureau. 2011-02-12. Retrieved 2011-04-23.
^ "Population and Housing Unit Estimates". Retrieved Jan 5, 2020.
^ "Census of Population and Housing". Census.gov. Archived from the original on April 26, 2015. Retrieved June 4, 2015.
^ "American FactFinder". United States Census Bureau. Archived from the original on 2013-09-11. Retrieved 2008-01-31.
^ "Climatography of the United States NO.81" (PDF). National Oceanic and Atmospheric Administration. Retrieved January 13, 2011.
Wikimedia Commons has media related to Dubois, Idaho.
Clark County School District #161
U.S. Sheep Experiment Station
Clark County official site


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Grant Making
Access Online Application
About Theodore Presser
About The Presser Foundation
Advancement of Music
Assistance To Music Teachers
Capital Support
Graduate Music Award
News Release: The Presser Foundation Announces Over $1 Million in Advancement of Music Grants
Posted on Feb 28th, 2020
The Presser Foundation Announces Over $1 Million in Advancement of Music Grants
The Presser Foundation is pleased to announce the selection of seventy-three new multi- and single-year grantees for Advancement of Music. These grants, totaling $823,500 are in addition to $205,000 in existing multi-year grants to seven outstanding music organizations. Advancement of Music provides general operating support to music presenting, music performing and music education organizations in the Greater Philadelphia Area.
William B. McLaughlin, III, Chair of the Advancement of Music Committee, commented, "For the first time in an over one hundred-year history, The Presser Foundation has crossed the threshold of one million dollars in general operating support this fiscal year. It is an honor to provide the largest round of critical funding totaling $1,028,500 to so many musical organizations in and around Philadelphia. As our recently adopted operating values articulate – Music is our purpose. We are committed to supporting the future of music and its excellence."
2019-20 Advancement of Music Grantees (in alphabetical order)
Academy of Vocal Arts
Allentown Symphony Association
Anna Crusis Women's Choir
Annenberg Center for the Performing Arts
Ars Nova Workshop
Artistas y Musicos Latino Americanos (AMLA)
Astral Artists, Inc.
ArtistYear
Bay Atlantic Symphony, Inc.
Berks Youth Chorus
Bowerbird
Bucks County Choral Society
Capital Philharmonic of New Jersey
Chamber Music Society of Bethlehem
Chamber Orchestra of Philadelphia
Chester Children's Chorus
Choir School of Delaware
Choral Arts Philadelphia
CityFest, Inc./Wilmington Children's Chorus
Commonwealth Youthchoirs
Community Conservatory
Community Music School Lehigh Valley
Community Music School of Collegeville
Community Youth Orchestra of Bucks County
Darlington Arts Center
Delaware County Youth Orchestra
Delaware Symphony Orchestra
Dolce Suono Ensemble
Friends of the Wanamaker Organ
Garden State Philharmonic Orchestra
Harrisburg Symphony Association
Kimmel Center, Inc.
Lancaster Symphony Orchestra
LiveConnections
Lyra Society
Lyric Fest
Market Square Concerts
Mendelssohn Club of Philadelphia
Moravian College
Music at Gretna, Inc.
Music for Everyone
Musicopia
Network for New Music
Opera Philadelphia
OperaDelaware
Orchestra 2001
Philadelphia Boys Choir & Chorale
Philadelphia Chamber Music Society
Philadelphia Clef Club of Jazz & Performing Arts
Philadelphia Gay Men's Chorus
Philadelphia Sinfonia Association
Philadelphia Youth Orchestra
Piffaro, The Renaissance Band
Play On, Philly! (POP)
PRISM Quartet, Inc.
Reading Symphony Orchestra
Riverside Symphonia
Settlement Music School
Singing City
State Theatre Regional Arts Center At New Brunswick Inc
Susquehanna Chorale
Symphony in C
Tempesta di Mare, Inc.
Temple University Music Preparatory Division
The Allentown Band
The Bach Choir of Bethlehem
The Friends of Chamber Music of Reading, Inc.
The Georgia E. Gregory Interdenominational School of Music
The Mann Center for the Performing Arts
The Music School of Delaware
The Princeton Festival
Trenton Children's Chorus, Inc.
Trenton Music Makers
Tri-County Concerts Association, Inc.
WRTI90.1FM
The Presser Foundation was established in 1939 under the Deeds of Trust and Will of the late Theodore Presser. It is one of the few private foundations in the United States dedicated solely to music education and music philanthropy. The Presser Foundation supports a broad range of classical symphonic, chamber, choral and vocal music performance and education through general operating and program grants to music organizations; capital grants for music building projects; undergraduate and graduate student awards; and assistance to retired music teachers. Much of the grant making focus of the Foundation is on organizations and institutions in the 75-mile radius surrounding Center City Philadelphia. More information on the Foundation's grant making activity can be found on its website www.presserfoundation.org.
Theodore Presser (1848 – 1925) rose from humble beginnings to become a respected music teacher and publisher. Familiar with the many challenges facing musicians, he established The Presser Foundation which supports music performance and education through undergraduate and graduate scholar awards, operating and program support for music organizations, capital grants for music building projects, and assistance to retired music teachers.
THE PRESSER FOUNDATION
The Presser Foundation was established in 1939 under the Deeds of Trust and Will of the late Theodore Presser. It is one of the few private foundations in the United States dedicated solely to music education and music philanthropy. It is our hope that every institution, organization and individual funded by The Presser Foundation will read about the rich history of The Foundation and the inspiring biography of Theodore Presser.
1501 Cherry Street
(T) 267.519.5350
The Presser Foundation was established in 1939. It is one of the few private foundations in the United States dedicated solely to music education and music philanthropy.
Honoring Thomas M. Hyndman, Jr. December 15, 2020
News Release: The Presser Foundation Announces Nearly $1.6 Million in Special Project Grants to Music Organizations and Undergraduate & Graduate Awards October 27, 2020
Honoring Edith A. Reinhardt September 28, 2020


His research group investigates simulation-based and data-driven computational synthesis of for mechanical, industrial and biomedical systems. The target systems are modeled by utilizing tools and algorithms in computational mechanics, geometric reasoning, image recognition, statistical data processing, and optimized by numerical optimization algorithms. Recent application domains includes lightweight automotive structures, intelligent transportation systems, water desalination systems, energy-efficient production systems, biomedical deformable image registration, and statistical protein energy potentials.
Solar-powered desalination systems for resource-restricted environment. Numerical simulation, optimization, and data mining techniques are utilized to synthesize decision trees among feasible technology alternatives for water desalination systems in rural communities with limited infrastructure access.


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For fun, I like to make huge dragons out of snow. I spent an entire day one winter to build the one pictured here (I named him Gary). He was about seven feet high from the ground to the tip of his nose and about twenty feet long from his nose to the tip of his tail. I inserted broken twigs into his mouth to simulate razor-sharp teeth. I had to steal snow from my neighbor's yard because I used all of the snow in my own yard. This is Gary before I made wings for him.


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Fragrance was 2021's big winner, according to The NPD Group, outperforming all other beauty categories with a 49 percent jump in sales versus 2020. For the year, sales of hair products grew 47 percent, makeup grew 23 percent, and skin care sales increased 18 percent.
BY janderson | PUBLISHED January 24, 2022
Fragrance was 2021's big winner, according to The NPD Group, outperforming all other beauty categories during the 12 months with a 49 percent jump in sales versus 2020. The fragrance category registered double-digit growth against both 2020 and 2019, as consumers looked to treat themselves. Sales of perfumes, colognes, and other fragrance juices increased by 61 percent, year over year, as sales of candles, reed diffusers, and other home scents grew by more than 20 percent. The fourth quarter accounted for 45 percent of fragrance category sales revenue in 2021, growing by 35 percent during the critical holiday selling season.
For the year, sales of hair products grew 47 percent, makeup grew 23 percent, and skin care sales increased 18 percent. Sales of fragrance, hair care and skin care in 2021 surpassed 2019 levels. The U.S. prestige beauty industry generated $22 billion in 2021, a 30 percent increase in dollar sales versus 2020.
In 2021, the beauty industry saw continued growth from items that have emerged as big sellers during the pandemic, including perfumes, scented candles, facial exfoliators, nail care, and hair care products. At the same time, makeup foundation, hair styling products, and other segments of the market started to recover as consumers began returning to workplaces, events, and other social activities.
"The beauty industry is unique in its ability to instill self-confidence and change the way people feel," said Larissa Jensen, Beauty Industry Advisor at NPD. "These timeless abilities keep our industry relevant and important in the minds of our consumers — regardless of circumstances or lifestyle changes. As was the case across the retail world, the beauty market faced hurdles in 2020 but proved its resiliency in 2021."
In the spirit of consumers putting their best face forward to re-enter society, face makeup product sales, including foundation, primer, and tinted moisturizer, grew double digits, as did makeup-setting sprays and removers.
The makeup category benefited from a return to consumer interest in makeup artistry, with additional growth observed for cream and stick blushes and other products prevalently used in YouTube videos and other social media. To top that off, brands born from makeup artists and social influencers had the highest revenue gains among all makeup brand types.
Within the hair category, hairsprays, gels, mousses, and other styling products returned to growth in 2021, with hair-styling product sales up 45 percent, versus 2020. The hair styling segment is expected to rise another 15 percent in 2022. Growth will continue through 2024, as people continue to return to more social activities in the months and years ahead, according to new findings from the Future of Hair Report from NPD.
Core skin care product sales, including facial cleansers, creams, and serums, grew between 15 percent and 24 percent, versus 2020. Sales of targeted products, such as eye and lip treatments, also increased. Clinical skin care brands contributed the highest revenue gains to the category. In 2021, clinical surpassed natural as the largest brand type in skincare, based on revenue.
"As we move through 2022, the beauty companies that will thrive are those that harness the industry's unique ability to spread joy, while also recognizing the opportunities of a changed consumer and retail environment," added Larissa. "We can expect more change to unfold in 2022, but, along with these changes, new opportunities for the beauty industry will present themselves."
CEW will be presenting its annual State of the Beauty Industry Report 2022 event February 9 (virtual) bringing together NPD, Mintel, Nielsen, Sparks and Honey, Spate and Google to present key learnings from 2021 and a 2022 forecast on how to best navigate the year. To learn more and register, please click here.
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Nicolette Bosco talks about which beauty products are keeping the beauty counters at ...
CEW Exclusive: Olaplex Launches Dry Shampoo That Treats Scalp Health and Bonds Damaged Hair, Too
The brand's No. 4D formula goes beyond typical oil-absorption to soothe scalp itch ...


Go on an adventure and learn the letters of the alphabet and how to write them with Mr. Pencil. Close the backpack for learning and playtime on the go!"Go-with-Me ABC Backpack™ gives young learners a fun way to explore letters with seven different activity modes. Letter games introduce the alphabet while the music game helps develop hearing and listening skills. With every press of the letter buttons, this toy reinforces the relationship between letter names, sounds and words—setting an important foundation for learning to read.


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With the invention of YouTube and Google, sharing music is a breeze. Today you can also easily find a few lines from a poem, copy and paste the text, and dedicate it to your loved one. One of the hardest parts of sending a postcard to someone fighting in the war during the 20th century was finding a way to fit everything you wanted to say on a small piece of paper. Luckily there was a way around this conundrum which was solved with the creation of the "song postcard". Song postcards featured popular songs, poems, hymns and much more. In Great Britain, the Bamforth Company would produce series of postcards, where if you collected the entire set you would have the chorus to a song. They also had many different themes such as romance and heartbreak and would use live models to convey these emotions. Sometimes they would use women dreaming of their lost beau or thought bubbles filled with a soldier to show that she was thinking of him. These postcards were more than just a piece of paper with some writing on it but were what kept loved ones connected. Song postcards captured the sentiment that people wanted to convey to another but could not express. These cards were also like a time capsule because we can get a sense of what sort of music, themes, and fashion were popular in the day.


If the daily work routine is making your life monotonous then a holiday to some of the hottest tourist destination will be helpful in offering you some relaxation. Therefore, if you are planning to go for a holiday, then going to US will be a wise option. There are many wonderful states and cities in US and Grand Rapids is among one of them that offers some uniqueness to its visitors. Grand Rapids is a city located in the US state of Michigan. Grand Rapids offers some exciting places and a lot of entertainment for its visitors.
If a visitor wants to visit some museums and memorials in Grand Rapids he or she can make a visit to Presidential Museum to see President Ford's tomb or to the Gerald R. Ford Museum which is located on west bank of Grand River. It is the final resting place of 38th president of the US. Grand Rapids offers some amazing and stunning place like the John Ball Park, the Heritage Hill neighborhood and the Wealthy Street.
A visitor can also visit some of the significant building in Grand Rapids such as the DeVos Place Convention Center, the Amway Grand Plaza Hotel, Van Andel Arena and the JW Marriott Hotel. Grand Rapids offers The Urban Institute for Contemporary Arts, houses art exhibits, and the urban clay studio for visitors having a taste for contemporary arts.
Grand Rapids is also home to a numbers of theatres and stages that includes the Meijer Majestic, the DeVos hall, and the Van Andel Arena.
A visitor can also visit the Studio 28 in Grand Rapids which is the first megaplex in the United States. Studio 28 was reopened in 1988 and it has a seating capacity of 6,000.
In Grand Rapids Township, there is the Frederik Meijer Gardens and the Sculpture Park that has 125 acre of a world class botanical gardens and interesting artworks from some of famous sculptors like Mark di Suver, Edgar Degas and Alexander Calder.
The East towns of Grand Rapids and the Heartside District are also a must visit place if a visitor loves to see the counter culture and the music scene of Grand Rapids. A visitor can also have a glance at some of the professional sports events in Grand Rapids like the Baseball and the American football. Numbers of tourist are also flocking into Grand Rapids to enjoy the startling night life in the city.