text:
\section{Introduction}
The understanding of neutrino masses and mixing matrix is crucial to
unveil the mystery of lepton flavor structures. The updated SK
analysis of the atmospheric neutrino data gives \cite{Ashie:2005ik}
\begin{equation}
 1.5\cdot 10^{-3}\,\,\, {\rm eV}^{2}< \vert \Delta m_{31}^{2}\vert < 3.4\cdot
 10^{-3}\,\,\, {\rm eV}^{2},  \ \sin^{2}2\theta_{23} >0.92. \label{range23_new}
\end{equation}
This is a  $90\% \, {\rm C.L.}$ range with the best fit values given
by $\sin^{2}2\theta_{23} =1$ and $\Delta m_{31}^{2}=2.1\cdot
10^{-3}\, \, \, {\rm eV}^{2}$ respectively. An earlier result based
upon $L/E$ analysis gives \cite{Ashie:2004mr}
\begin{equation}
 1.9\cdot 10^{-3}\,\,\, {\rm eV}^{2}< \vert \Delta m_{31}^{2}\vert < 3.0\cdot
 10^{-3}\,\,\, {\rm eV}^{2},  \ \sin^{2}2\theta_{23} >0.9. \label{range23}
\end{equation}
at $90\% \, {\rm C.L.}$ where the best fit values are given by
$\sin^{2}2\theta_{23} =1$ and $\Delta m_{31}^{2}=2.4\cdot 10^{-3}\,
\, \, {\rm eV}^{2}$ respectively. The scenario of $\nu_{\mu}\to
\nu_{\tau}$ oscillation for atmospheric neutrinos has been confirmed
by the K2K experiment \cite{Aliu:2004sq,Ahn:2006zz}. Furthermore the
results in the solar neutrino oscillation measurements are also
confirmed by KamLAND reactor measurements
\cite{Eguchi:2002dm,Araki:2004mb}. Combining these measurements, the
LMA solution of the solar neutrino problem is established and the
updated $2\sigma$ parameter ranges are given by \cite{Fogli:2005cq}
\begin{equation}
7.21\cdot 10^{-5}\,\,\, {\rm eV}^{2}< \Delta m_{21}^{2}< 8.63\cdot
10^{-5}\, \, \, {\rm eV}^{2}, \ 0.267< \sin^{2}\theta_{12}< 0.371,
\label{range12}
\end{equation}
with the best fit values $\Delta m_{21}^{2}=7.92\cdot 10^{-5}\, \,
\, {\rm eV}^{2}$ and $\sin^{2}\theta_{12}=0.314$.

Despite the achievements so far in measuring the neutrino mixing
parameters, the sign of $\Delta m_{31}^2$, the mixing angle
$\theta_{13}$ and the CP violating parameter $\delta_{\rm CP}$ in
the mixing matrix remain to be determined. Furthermore, one is keen
to resolve the octant degeneracy of $\theta_{23}$
\cite{Fogli:1996pv}.

The mixing angle $\theta_{13}$ is constrained by the reactor
experiments \cite{Apollonio:1999ae,Boehm:2001ik}. The CHOOZ
experiment \cite{Apollonio:1999ae} gives a more stringent constraint
on $\theta_{13}$ with $\sin^2 2\theta_{13} < 0.1$ for a large
$\Delta m_{31}^2$ (90\% C.L.). A recent global fit based upon
three-flavor neutrino oscillation gives the $2\sigma$ upper bound,
$\sin^2 2\theta_{13}< 0.124$ \cite{Fogli:2005cq}. It is well known
that the mixing angle $\theta_{13}$ can be enhanced by the matter
effect in Earth. The appearance oscillations $\nu_{\mu}\to \nu_e$,
$\nu_e\to \nu_{\mu}$, and the survival mode $\nu_{\mu}\to \nu_{\mu}$
performed in a very-long baseline have been proposed
\cite{Mocioiu:2000st} to probe the angle $\theta_{13}$ and the sign
of $\Delta m_{31}^2$. Furthermore, the aforementioned very long
baseline neutrino experiments as well as future atmospheric neutrino
experiments are proposed to determine the deviation of $\theta_{23}$
to maximality \cite{long_theta23}. In this work, we focus on the
mixing angle $\theta_{23}$. We shall provide a global survey on
ideal neutrino energies in the GeV range and baseline lengths from
$10^3$ km to $10^4$ km for probing the octant of the mixing angle
$\theta_{23}$. The muon neutrino survival probability
$P(\nu_{\mu}\to \nu_{\mu})\equiv P_{\mu\mu}$ and electron neutrino
appearance probability $P(\nu_e\to \nu_{\mu})\equiv P_{e\mu}$ are
both studied for this purpose. We observe that the muon neutrino
survival probability $P_{\mu\mu}$ has complementary dependencies on
mixing angles $\theta_{13}$ and $\theta_{23}$ as the neutrino energy
varies. This property is established by studying the dependencies of
$P_{\mu\mu}$ on $\cos 2\theta_{23}$ and $\sin 2\theta_{13}$ while
keeping other parameters fixed. The choice of the parameter $\cos
2\theta_{23}$ is appropriate as
\begin{equation}
\frac{1}{2}\cos2\theta_{23}=\frac{1}{2}-\sin^2\theta_{23},
\end{equation}
which is a probe to the deviation of $\theta_{23}$ to the best-fit
value $\pi/4$. We find that the dependencies of $P_{\mu\mu}$ on
$\cos 2\theta_{23}$ and $\sin 2\theta_{13}$ at energies near local
maxima of this probability differ drastically from those at energies
near local maxima of the same probability. In the former case, the
probability $P_{\mu\mu}$ is always more sensitive to $\sin
2\theta_{13}$. Furthermore, the $\theta_{23}$ degeneracy is absent
in this case. In the latter case, the probability $P_{\mu\mu}$ is
more sensitive to $\cos 2\theta_{23}$ while the $\theta_{23}$
degeneracy is generally present. Such information is useful for
probing the octant of $\theta_{23}$. We also study sensitivities of
the probability $P_{e\mu}$ to $\cos 2\theta_{23}$ and $\sin
2\theta_{13}$ with other parameters fixed. We only focus on energies
near the local maximum of $P_{e\mu}$ as this probability is not
sensitive to mixing parameters for energies near its local minimum.

This paper is organized as follows. In Section II, we compare results
on the oscillation probability $P_{e\mu}$ obtained by the full
calculation with those obtained by various analytic approximations.
This comparison is essential since analytic approximations will be
employed for discussions in later sessions. To set up the analytic
approximation, we introduce the concept of average density which
varies with the total neutrino path-length inside the Earth.
Applying full calculations and the two-layer analytic approximations
\cite{Freund:1999vc}, we identify the energy values for local maxima
and local minima of neutrino oscillation probabilities $P_{\mu\mu}$
and $P_{e\mu}$ for baseline lengths $1000 \leq L/{\rm km}\leq
12000$. It is found that the two-layer approximation is quite
satisfactory compared to the full calculation for computing these
energy values. In Section III, we first present the dependencies of
$P_{\mu\mu}$ and $P_{e\mu}$ on the CP violation phase $\delta_{\rm
CP}$. It will be shown that, unlike $P_{e\mu}$, $P_{\mu\mu}$ is not
sensitive to the CP violation phase $\delta_{\rm CP}$. We study
numerically the effect of CP violation phase to the appearance
probability $P_{e\mu}$. The result confirms the so-called magic
baseline \cite{Barger:2001yr,Huber:2003ak,Smirnov:2006sm} at
$L\approx 7600$ km where $P_{e\mu}$ is rather insensitive to the CP
violation phase. After discussions on the CP violation phase, we
present the contour graphs of probabilities $P_{\mu\mu}$ and
$P_{e\mu}$ on $\cos 2\theta_{23}-\sin 2\theta_{13}$ plane for
baseline lengths $L=1000, \ 5000, \ 10000$, and $12000$ km. At all
these baseline lengths, we shall see that $P_{\mu\mu}$ is more
sensitive to $\sin 2\theta_{13}$ at energies around its local
maximum while it is more sensitive to $\cos 2\theta_{23}$ at
energies around its local minimum. Such observations are then  justified by
using the two-layer
analytic approximations for neutrino oscillation probabilities. With
this approximation, the baseline lengths and neutrino energies
allowing an unambiguous determination of $\theta_{23}$ through
measuring $P_{\mu\mu}$ are identified.  In Section IV, we discuss the prospects of probing the
$\theta_{23}$ octant via measuring $P_{e\mu}$ and $P_{\mu\mu}$.
We then conclude in the same section.
\section{The comparison of full calculations and analytic approximations }

We begin the discussions with the relation connecting flavor and
mass eigenstates of neutrinos, $\nu_{\alpha}=\sum_i U_{\alpha
i}\nu_{i}$, with $U$ the Maki-Nakagawa-Sakata mixing matrix
\cite{MNS} given by
\begin{equation}
U =\left(\!
\begin{array}{ccc}
c_{12}c_{13} & s_{12}c_{13} & s_{13}e^{-i\delta_{\rm CP}} \\
-s_{12}c_{23}-c_{12}s_{13}s_{23}e^{i\delta_{\rm CP}} &
c_{12}c_{23}-s_{12}s_{13}s_{23}e^{i\delta_{\rm CP}}
& c_{13}s_{23} \\
s_{12}s_{23}-c_{12}s_{13}c_{23}e^{i\delta_{\rm CP}} &
-c_{12}s_{23}-s_{12}s_{13}c_{23}e^{i\delta_{\rm CP}} & c_{13}c_{23}
\end{array}
\!\right)\,,
\end{equation}
where $s_{ij}$ and $c_{ij}$ denote $\sin\theta_{ij}$ and
$\cos\theta_{ij}$, respectively. The value for the Dirac type
CP-phase $\delta_{\rm CP}$ ranges from 0 to 2$\pi$. The evolutions
of neutrino flavor eigenstates are governed by the equation
\begin{eqnarray}
i\frac{d}{dt} |\nu(t)\rangle &=&  \left\{ \frac{1}{2E_\nu}U \left(\!
\begin{array}{ccc}
0 & 0               & 0 \\
0 & \Delta m^2_{21} & 0 \\
0 & 0               & \Delta m^2_{31}
\end{array}
\right)U^\dagger  + \left(\!
\begin{array}{ccc}
V & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{array}
\!\right)\right\} |\nu(t)\rangle \,, \label{evolution}
\end{eqnarray}
where $|\nu(t)\rangle = (\nu_e(t), \nu_\mu(t), \nu_\tau(t))^T$,
$\Delta m^2_{ij} \equiv m^2_{i}-m^2_{j}$ is the mass-squared
difference between the $i$-th and $j$-th mass eigenstates, and
$V\equiv \sqrt{2}G_F N_e$ is the effegtive potential arising from
the charged current interaction between $\nu_e$ and electrons in the
medium with $N_e$ the electron number density. Numerically $V= 7.56
\times 10^{-14}$ $(\rho/[{\rm g/cm^3}])$$Y_e$ [{\rm eV}] with $Y_e$
denoting the number of electrons per nucleon. We take $Y_e\sim 0.5$
in our calculations. One solves Eq.~(\ref{evolution}) by
diagonalizing the Hamiltonian on its right hand side. This amounts
to writing the right hand side of Eq.~(\ref{evolution}) as
$U'H'U^{'\dagger}|\nu(t)\rangle$ with $U'$ the neutrino mixing
matrix in the matter and $H' \equiv {\rm diag}(E_1, E_2, E_3)$ the
Hamiltonian after diagonalization. To obtain various oscillation
probabilities described later, we have used the parametrization in
\cite{profile} for the Earth density profile.

\begin{figure}[tb]
\begin{center}
$\begin{array}{c}
\includegraphics[width=9.5cm]{Fdensity.eps}
\end{array}$
\end{center}
\caption{The average Earth density along the path traversed by the
neutrino as a function of the path length $L$.} \label{Fdensity}
\end{figure}
For analytic calculations, we employ the two-layer approximation for
the Earth density profile \cite{Freund:1999vc}. Given a path-length
$L$ for a neutrino traversing the Earth medium, one can divide $L$
into the sum $L=L_1+L_2+\cdots L_n$ with each $L_i$ corresponding to
a region with a specific matter density. The average density for
this path-length is then given by $\rho=(\rho_1L_1+\rho_2L_2+\cdots
\rho_n L_n)/L$. The Earth medium can be categorized as the Earth
mantle and the Earth core. If a neutrino only traverses the Earth
mantle, we shall use the one-density approximation for the analytic
calculation with the density defined by the above prescription.
However, if a neutrino traverses both the Earth mantle and the Earth
core, one should write the total neutrino path-length as
$L=2L_m+L_c$ with
\begin{eqnarray}
L_m&=&R\left(\cos\theta_n-\sqrt{\frac{r_c^2}{R^2}-\sin^2\theta_n}\right),\nonumber
\\
L_c&=&2R\sqrt{\frac{r_c^2}{R^2}-\sin^2\theta_n}, \label{core_mantle}
\end{eqnarray}
where $R=6371$ km and $r_c=3480$ km are the radii of the entire
Earth and the Earth core respectively while $\theta_n$ is the
incident Nadir angle of the neutrino. We note that the critical
Nadir angle for a neutrino to pass the Earth core is $33.17^{\circ}$
corresponding to $L=10674$ km. For $L> 10674$ km, one separately
defines average densities within the path-length $L_m$ and the
path-length $L_c$ respectively. The average densities as functions
of the neutrino path-length is shown in Fig.~\ref{Fdensity}. For
$L\leq 10674$ km, there is only one curve for the average density,
which is represented by the solid line in the figure. Beyond this
distance, one can define the average density in the core and the
average density in the mantle, which are represented by dashed and
dotted lines respectively. Alternatively, one can also define single
average density for $L> 10674$ km by ignoring the distinction
between the mantle and the core. This is seen from the solid line
for $L>10674$ km. However, in our analytic calculations, we shall
adopt the two-density approach for $L>10674$ km.
\begin{figure}[tb]
\begin{center}
$\begin{array}{c}
\includegraphics[width=9.5cm]{FpmmeL11400.eps}
\end{array}$
\end{center}
\caption{A comparison of $P_{e\mu}$ obtained by the full numerical
calculation and various approximations. The thick solid curve
denotes the result by the full numerical calculation. The
dotted-dashed curve denotes the result by setting $\Delta
m_{21}^2=0$ in the full numerical calculation. The dashed curve
represents the result obtained by the two-layer approximation in the
leading order of $\tau\equiv \Delta m_{21}^2/\Delta m_{31}^2$. The
dotted curve denotes the result obtained by one-density
approximation in the leading order of $\tau$ while the thin solid
curve is that obtained by the one-density approximation in the
next-to-leading order of $\tau$. } \label{FpmmeL11400}
\end{figure}

For analytic calculations, we only compute oscillation probabilities
up to the lowest order in $\tau\equiv \Delta m_{21}^2/\Delta
m_{31}^2$. In other words, we set $\Delta m_{21}^2$=0 in analytic
calculations and consequently the mixing angle $\theta_{12}$ and the
CP phase $\delta_{\rm CP}$ drop out from the oscillation
probabilities. The probabilities $P_{\mu\mu}$ and $P_{e\mu}$ in the
two-layer approximations are given
by\cite{Chizhov:1999he,Akhmedov:1998ui,Petcov:1987cd,Bernabeu:2001xn,Hsu_thesis}:
\begin{eqnarray}
P_{\mu\mu}&=&\cos^4 \theta_{23}+\left(u^2+v^2\right)\sin^4
\theta_{23}+2\cos^2\theta_{23}\sin^2\theta_{23}\left(u\cos t+v\sin
t\right),\nonumber \\
P_{e\mu}&=&\sin^2 \theta_{23}\left(1-u^2-v^2\right).\label{analytic}
\end{eqnarray}
The quantities $u$, $v$ and $t$ are defined as
\begin{eqnarray}
u&=&\cos(2\phi^m)\cos(\phi^c)-\cos(2\theta_{13}^c-2\theta_{13}^m)\sin(2\phi^m)\sin(\phi^c),\nonumber
\\
v&=&-\cos(2\theta_{13}^m)\left[\sin(\phi^c)\cos(2\phi^m)\cos(2\theta_{13}^c-2\theta_{13}^m)+\cos(\phi^c)\sin(2\phi^m)
\right]\nonumber \\
&&+\sin(2\theta_{13}^m)\sin(\phi^c)\sin(2\theta_{13}^c-2\theta_{13}^m),\nonumber
\\
 t&=&\frac{(M_{13}^2)^m+(m_{13}^2)^m}{4E}\times
2L^m+\frac{(M_{13}^2)^c+(m_{13}^2)^c}{4E}\times L^c,
\end{eqnarray}
where
\begin{eqnarray}
\phi^{m(c)}&=&\frac{\Delta_{31}^{m(c)}}{4E}L^{m(c)},\nonumber \\
(M_{13}^2)^{m(c)}&=&(\Delta
m_{31}^2+A_e^{m(c)}+\Delta_{31}^{m(c)})/2,\nonumber \\
(m_{13}^2)^{m(c)}&=&(\Delta
m_{31}^2+A_e^{m(c)}-\Delta_{31}^{m(c)})/2,
\end{eqnarray}
with
\begin{equation}
\Delta_{31}^{m(c)}=\sqrt{(\Delta m_{31}^2\sin
2\theta_{13})^2+(A_e^{m(c)}-\Delta m_{31}^2\cos 2\theta_{13})^2}.
\end{equation}
 The superscripts $m$ and $c$ denote quantities defined in the
Earth mantle and the Earth core respectively. For neutrinos
traversing only the Earth mantle, one simply sets $L_c=0, \ 2L_m=L$
in the above equations and recovers well known expressions for
$P_{\mu\mu}$ and $P_{e\mu}$ in the one-density approximation
\cite{Akhmedov:2004ny}.

\begin{figure}[tb]
\begin{center}
$\begin{array}{cc}
\includegraphics*[width=6.2cm]{Fpmme_peak.eps} &
\includegraphics*[width=6.2cm]{Fpmmm_peak.eps}
\end{array}$
\end{center}
\caption{Left panel: the energy at the local maximum of $P_{e\mu}$,
as a function of $L$. Right panel: energies at local maxima and
local minima of $P_{\mu\mu}$, as functions of $L$.  } \label{maxmin}
\end{figure}
The accuracy of two-layer approximation is shown in
Fig.~\ref{FpmmeL11400} with a comparison of this approximation to
the full numerical calculation and other approximations. In the
calculations, we have assumed the normal mass hierarchy and taken
$\sin2\theta_{13}=0.3$, $\cos2\theta_{23}=0$, $\delta_{\rm CP}=0$,
$\Delta m_{31}^2=2.4\times 10^{-3}$ eV$^2$, $\Delta
m_{21}^2=8.2\times 10^{-5}$ eV$^2$, and $\tan^2\theta_{12}=0.39$
\cite{Bahcall:2004ut}. This set of parameters will be adopted for
later calculations unless specific mentioning of other choices. This
set of parameters differ from the most updated best-fit values
quoted right after Eq.~(\ref{range12}). However, both set of
parameters give undistinguishable results on $P_{e\mu}$ and
$P_{\mu\mu}$ in the energy range concerned here. A comparison made
at $L=11400$ km has two purposes. First of all, it is known that the
series expansion in the parameter $\tau$ is valid for $L/E_{\nu}\ll
10^4$ (km/GeV) \cite{Akhmedov:2004ny,Mocioiu:2001jy}. Hence analytic
calculations performed at this baseline length test the marginal
region of the condition $L/E_{\nu}\ll 10^4$ (km/GeV). Secondly this
path-length implies that the neutrino traverses both the Earth
mantle and the Earth core. Therefore it is also a good test to the
two-layer approximation. It is seen that the two-layer
approximation, unlike the one-layer approximation, reproduces well
the peak energies of $P_{e\mu}$, while it gives peak probabilities
deviating from those obtained from the full calculation by
$15\%-20\%$. We also see that the two-layer approximation agrees
well with the full calculation in the limit $\Delta m_{21}^2=0$.

For later analysis, we compute energies at local maxima of
$P_{e\mu}$ and those at local maxima and local minima of
$P_{\mu\mu}$ for the baseline range $1000\leq L/{\rm km}\leq 12000$.
The results are depicted in Fig.~\ref{maxmin}. We do not study local
minima of $P_{e\mu}$ since their values are not sensitive to mixing
angles $\theta_{13}$ and $\theta_{23}$. It is seen that the analytic
approximation is satisfactory for computing energies at local maxima
and local minima of neutrino oscillation probabilities. We point out
that the energy curves in Fig.~\ref{maxmin} are calculated with
$\sin2\theta_{13}=0.3$ and $\cos2\theta_{23}=0$. It is found that
these curves are not sensitive to the values of $\sin2\theta_{13}$
and $\cos2\theta_{23}$.

\section{Conditions for the absence of $\theta_{23}$ degeneracy in $P_{\mu\mu}$ and $P_{e\mu}$ at different energies}

\subsection{The dependencies of $P_{\mu\mu}$ and $P_{e\mu}$ on $\delta_{\rm CP}$}
Before concentrating on $\theta_{13}$ and $\theta_{23}$ dependencies
of neutrino oscillation probabilities, we first study the CP phase
dependencies with the full numerical calculations.
\begin{figure}[tb]
\begin{center}
$\begin{array}{cc}
\includegraphics*[width=6.2cm]{FL1000cp.eps} &
\includegraphics*[width=6.2cm]{FL5000cp.eps}
\\
\includegraphics*[width=6.2cm]{FL10000cp.eps} &
\includegraphics*[width=6.2cm]{FL12000cp.eps}
\end{array}$
\end{center}
\caption{The CP phase dependencies of $P_{\mu\mu}$ and $P_{e\mu}$
for $L=1000$ km, $5000$ km, $10000$ km and $12000$ km respectively.
The probability $P_{\mu\mu}$ is described by the thick curve while
$P_{e\mu}$ is described by the thin curve. }
\label{cp-phase}
\end{figure}
It is easily seen from Fig.~\ref{cp-phase} that $P_{\mu\mu}$ is not
sensitive to the CP phase for all distances displayed. On the other
hand, $P_{e\mu}$ is rather sensitive to the CP phase for $L=1000$ km
and $5000$ km. In order to quantify the CP phase dependence of
$P_{e\mu}$, we study peak values of $P_{e\mu}$, which occur at
energies described by the curve {\bf max1} in Fig.~\ref{maxmin} for
different baseline lengths. This peak value for a specific baseline
length depends on the CP violation phase $\delta_{\rm CP}$ and we
denote the maximum and the minimum of this value as $P_{e\mu}^{\rm
max}$ and $P_{e\mu}^{\rm min}$ respectively. The difference and the
ratio of these two values as functions of the baseline length $L$
are shown in Fig.~\ref{emu-cp}.
\begin{figure}[tb]
\begin{center}
$\begin{array}{cc}
\includegraphics*[width=6.2cm]{FPem_diff.eps} &
\includegraphics*[width=6.2cm]{FPem_rat.eps}
\end{array}$
\end{center}
\caption{The difference and the ratio of $P_{e\mu}^{\rm max}$ and
$P_{e\mu}^{\rm min}$ as functions of the baseline length.}
\label{emu-cp}
\end{figure}
It is interesting to note that the ratio $P_{e\mu}^{\rm
min}/P_{e\mu}^{\rm max}$ increases monotonically with the baseline
length until $L=7600$ km. The ratio begins to decrease for a larger
baseline but remains larger than $90\%$. In fact, one can see that
$P_{e\mu}^{\rm max}$ and $P_{e\mu}^{\rm min}$ differ by less than
$10\%$ for $L\geq 6500$ km. We point out that $1-P_{e\mu}^{\rm
min}/P_{e\mu}^{\rm max}$ reaching to minimum at $L=7600$ km confirms
the so-called magic baseline for the probability $P_{e\mu}$
\cite{Barger:2001yr,Huber:2003ak,Smirnov:2006sm}.

\subsection{The dependencies of $P_{\mu\mu}$ and $P_{e\mu}$ on mixing angles $\theta_{13}$ and $\theta_{23}$}
Having studied CP phase dependencies of oscillation probabilities,
we now focus on $\theta_{13}$ and $\theta_{23}$ dependencies. In
this study we set the CP phase $\delta_{\rm CP}$ equal to zero.
\begin{figure}[tb]
\begin{center}
$\begin{array}{cc}
\includegraphics*[width=6.2cm]{FL1000_sc.eps} &
\includegraphics*[width=6.2cm]{FL5000_sc.eps}
\\
\includegraphics*[width=6.2cm]{FL10000_sc.eps} &
\includegraphics*[width=6.2cm]{FL12000_sc.eps}
\end{array}$
\end{center}
\caption{The $\theta_{13}$ and $\theta_{23}$ dependencies of
$P_{\mu\mu}$ and $P_{e\mu}$ for $L=1000$ km, $5000$ km, $10000$ km
and $12000$ km respectively. The probability $P_{\mu\mu}$ is
described by the thick curve while $P_{e\mu}$ is described by the
thin curve. } \label{theta1323}
\end{figure}
The results are presented in Fig.~\ref{theta1323}.  It is easily
seen that the values of $P_{\mu\mu}$ at its local maximum and local
minimum depend on mixing angles $\theta_{13}$ and $\theta_{23}$
while only the local maximum of $P_{e\mu}$ depends on these
parameters. This confirms our earlier comments concerning the left
panel of Fig.~\ref{maxmin}. We point out that the differences
between solid and dotted curves in Fig.~\ref{theta1323} reflect the
effect of $\sin2\theta_{13}$; while the differences between solid
and dashed curves there reflect the effect of $\cos2\theta_{23}$.

\begin{figure}[tb]
\begin{center}
$\begin{array}{cc}
\includegraphics*[width=6.2cm]{Fcontour_pmmm_L1000.eps} &
\includegraphics*[width=6.2cm]{Fcontour_pmmm_L5000.eps}
\\
\includegraphics*[width=6.2cm]{Fcontour_pmmm_L10000.eps} &
\includegraphics*[width=6.2cm]{Fcontour_pmmm_L12000.eps}
\end{array}$
\end{center}
\caption{The contour graphs of the muon neutrino survival
probability $P_{\mu\mu}$ on the  $\cos 2\theta_{23}-\sin
2\theta_{13}$ plane. At $L=1000$ km, the local minimum of
$P_{\mu\mu}$ on the curve {\bf min1} occurs at $E=1.89$ GeV. We plot
the contour graph of $P_{\mu\mu}$ by averaging this probability over
an $1$ GeV energy range centered at the above local minimum. At
$L=5000$ km, the local maximum of $P_{\mu\mu}$ on the curve {\bf
max1} occurs at $E=4.75$ GeV while the local minimum of this
probability on the curve {\bf min1} occurs at $E=9.24$ GeV. We plot
the contour graphs of $P_{\mu\mu}$ in the energy range $4.25\leq
E/{\rm GeV}\leq 5.25$ for the former case and $8.74\leq E/{\rm
GeV}\leq 9.74$. The same type of convention applies to $L=10000$ km
and $12000$ km.} \label{contour-pmm}
\end{figure}
We now present contour graphs of $P_{\mu\mu}$ and $P_{e\mu}$ on the
$\cos 2\theta_{23}-\sin 2\theta_{13}$ plane. The range for
$\cos2\theta_{23}$ is chosen such that $\sin2\theta_{23}>0.9$
\cite{Ashie:2004mr}, i.e., $-0.316<\cos2\theta_{23}<0.316$; while
$\sin^2 2\theta_{13}$ is chosen to be less than $0.1$, i.e.,
$\sin2\theta_{13}<0.316$. The contour graphs of $P_{\mu\mu}$ at
different baseline lengths are presented in Fig.~\ref{contour-pmm}.
Except for $L=1000$ km, we have shown contours of $P_{\mu\mu}$ for
energies in the vicinity of both local maximum and local minimum of
this probability. The contour for the local maximum of $P_{\mu\mu}$
at $L=1000$ km is not shown since $P_{\mu\mu}$ at this energy and
baseline length is not sensitive to mixing angles $\theta_{13}$ and
$\theta_{23}$. For $L=5000$ km, $10000$ km and $12000$ km, it is
seen that the contours at local maxima of $P_{\mu\mu}$ and those at
local minima of $P_{\mu\mu}$ behave rather differently. The former
are in general more parallel to the $\cos2\theta_{23}$-axis while
the latter are generally more parallel to the
$\sin2\theta_{13}$-axis. We note that the local maximum ({\bf max2})
of $P_{\mu\mu}$ at $L=12000$ km can vary from $0.9$ to a much
smaller value, 0.45, which is a result of significant matter
effects. Similarly, due to large matter effects, the local minimum
({\bf min2}) of $P_{\mu\mu}$ at $L=10000$ km can vary from $0$ to a
much larger value, $0.4$. We also notice that, at this baseline
length, the $\theta_{23}$ degeneracy is absent for $P_{\mu\mu}>0.1$.
In general, such a degeneracy is also absent for energies near local
maxima of $P_{\mu\mu}$. However, the probabilities are not sensitive
to $\cos2\theta_{23}$ in those cases. For comparisons, we also
present contour graphs for the appearance probability $P_{e\mu}$ at
different baseline lengths.
\begin{figure}[tb]
\begin{center}
$\begin{array}{cc}
\includegraphics*[width=6.2cm]{Fcontour_pmme_L1000.eps} &
\includegraphics*[width=6.2cm]{Fcontour_pmme_L5000.eps}
\\
\includegraphics*[width=6.2cm]{Fcontour_pmme_L10000.eps} &
\includegraphics*[width=6.2cm]{Fcontour_pmme_L12000.eps}
\end{array}$
\end{center}
\caption{The contour graphs for the oscillation probability
$P_{e\mu}$ on the $\cos 2\theta_{23}-\sin 2\theta_{13}$ plane. We
plot contours of $P_{e\mu}$ at energies near the local maximum ({\bf
max1}) of this probability. } \label{contour-pem}
\end{figure}
It is clearly seen that $P_{e\mu}$ is only sensitive to
$\sin2\theta_{13}$ for most cases. The sensitivity to
$\cos2\theta_{23}$ only occurs at very long baseline lengths and
large values of $\sin2\theta_{13}$. For example, at $L=10000$ km,
$P_{e\mu}$ becomes sensitive to $\cos2\theta_{23}$ as
$\sin2\theta_{13}$ approaches $0.3$. At $L=12000$ km, $P_{e\mu}$
becomes sensitive to $\cos2\theta_{23}$ when $\sin2\theta_{13}$ is
greater than $0.2$.

\subsection{A global look at the absence of $\theta_{23}$ degeneracy}
In this subsection, we focus on $\theta_{23}$ dependencies of
$P_{\mu\mu}$ and $P_{e\mu}$ for general baseline lengths. The
two-layer analytic approximations for $P_{\mu\mu}$ and $P_{e\mu}$
will  be employed for our discussions, and observations in the
previous subsection shall be justified. It is instructive to rewrite
Eq.~(\ref{analytic}) in polynomials of $\cos2\theta_{23}$:
\begin{eqnarray}
f(y,z)&=&-\alpha  y^2+(\alpha+\beta)y+(1-\beta), \nonumber \\
g(y,z)&=&-\gamma (y-1),
 \label{quadratic}
\end{eqnarray}
with $f(y,z)\equiv P_{\mu\mu}$, $g(y,z)\equiv P_{e\mu}$, $y\equiv
\cos 2\theta_{23}$ and $z\equiv \sin 2\theta_{13}$. Furthermore,
\begin{eqnarray}
\alpha&=&-\frac{1}{4}\left[\left(u-\cos t\right)^2+\left(v-\sin
t\right)^2\right],\nonumber \\
\beta&=&\frac{1}{2}\left(1-u^2-v^2\right)+\frac{1}{4}\left[\left(u-\cos
t\right)^2+\left(v-\sin t\right)^2\right],\nonumber \\
\gamma &=&\frac{1}{2}\left(1-u^2-v^2\right).
\end{eqnarray}
We note that the $\sin2\theta_{13}$ dependencies of $P_{\mu\mu}$ and
$P_{e\mu}$ reside in quantities $u$, $v$, $\cos t$ and $\sin t$.
These quantities also depend on the baseline length $L$ and the
neutrino energy $E$. Hence the coefficients $\alpha$, $\beta$ and
$\gamma$ also depend on the baseline length $L$ and the neutrino
energy $E$. It is interesting to note that $\alpha+\beta=\gamma$.
Therefore we have
\begin{equation}
P_{\mu\tau}=\alpha\left(y^2-1\right),
\end{equation}
using $P_{\mu e}+P_{\mu\mu}+P_{\mu\tau}=1$ and $P_{\mu e}=P_{e\mu}$
with our choice of $\delta_{\rm CP}=0$.
\begin{figure}[tb]
\begin{center}
$\begin{array}{c}
\includegraphics[width=9.5cm]{pem.eps}
\end{array}$
\end{center}
\caption{The coefficient $\alpha(z)+\beta(z)$ calculated along the
energy curve {\bf max1} in the left panel of Fig.~\ref{maxmin}. The
values of $\sin2\theta_{13}$ are taken to be $0.1, \ 0.2$ and $0.3$
respectively. } \label{pem}
\end{figure}
The contour structure of $P_{e\mu}$ is straightforward as $g(y,z)$
is only a linear function of $y$. Hence no $\theta_{23}$ degeneracy
presents in the contour graphs depicted in Fig.~\ref{contour-pem}.
Additionally, the sensitivity of $P_{e\mu}$ to $\cos2\theta_{23}$ is
$dg(y,z)/dy=-(\alpha(z)+\beta(z))$. The coefficient $\alpha+\beta$
evaluated along the energy curve {\bf max1} in the left panel of
Fig.~\ref{maxmin} are plotted in Fig.~\ref{pem} for
$\sin2\theta_{13}=0.1, \ 0.2$ and $0.3$. For $\sin2\theta_{13}=0.3$,
$\alpha+\beta$ reaches to the maximal value, 0.5, for $L\simeq
10500$ km. For $\sin2\theta_{13}=0.1$ and $0.2$, $\alpha+\beta$
rises quickly as the baseline length $L$ surpasses $10674$ km. We
note that the value of $P_{e\mu}$ is proportional to $\alpha+\beta$.
Hence $\alpha+\beta$ shown in Fig.~\ref{pem} is its own maximal
value for each baseline length $L$.

The contour structure of $P_{\mu\mu}$ can be analyzed through the
quadratic polynomial $f(y,z)$ in $y$. If $-\alpha\gg \alpha+\beta$,
generally there are two solution curves for $f(y,z)=p$ compatible
with the ranges of $y$ and $z$ where $p$ is a given value for
$P_{\mu\mu}$. Let us suppose that $z\equiv \sin2\theta_{13}$ is
measured in the future \cite{Ardellier:2006mn,Wang:2006ca} with a
central value $z_0$. The two solution curves for the equation
$f(y,z)=p$ then intersect with the straight line $z\equiv
\sin2\theta_{13}=z_0$ at two points $(y_1,z_0)$ and $(y_2,z_0)$.
This is actually what we have seen in Fig.~\ref{contour-pmm} for
local minima of $P_{\mu\mu}$. If, on the other hand, $-\alpha\simeq
\alpha+\beta$ or even $-\alpha\ll \alpha+\beta$, there exists only
one solution curve for the equation $f(y,z)=p$. This is because that
the two points $(y_1,z_0)$ and $(y_2,z_0)$ can not simultaneously
satisfy the constraint $-0.316<y<0.316$ since $\vert
y_1+y_2\vert=-(\alpha+\beta)/\alpha\geq 1$. This is actually what we
have seen in Fig.~\ref{contour-pmm} for local maxima of
$P_{\mu\mu}$. To justify this observation, it remains to show that
the coefficient $-\alpha$ dominates over $\alpha+\beta$ at energies
corresponding to local minima of $P_{\mu\mu}$ while the latter
dominates over the former at energies corresponding to local maxima
of $P_{\mu\mu}$.
\begin{figure}[tb]
\begin{center}
$\begin{array}{cc}
\includegraphics[width=6.2cm]{Falbe_s02.eps} &
\hspace{1cm}
\includegraphics[width=6.2cm]{Falbe_s03.eps}
\end{array}$
\end{center}
\caption{The coefficients $-\alpha$ and $\alpha+\beta$ evaluated
along energy curves in the right panel of Fig.~\ref{maxmin}. The
coefficients are calculated with $\sin2\theta_{13}=0.2$ and $0.3$ on
the left and right panels respectively. The thick curves denote
values of $-\alpha$ while thin curves denote those of
$\alpha+\beta$. For solid and dotted curves, the thick curves
generally dominate over the corresponding thin ones. For dashed and
dotted-dashed curves, the thin curves generally dominate over the
thick ones.} \label{coefficient}
\end{figure}
This is clearly demonstrated in Fig.~\ref{coefficient} where the
coefficients $-\alpha$ and $\alpha+\beta$ are evaluated along energy
curves in the right panel of Fig.~\ref{maxmin}. We have calculated
the coefficients with $\cos2\theta_{23}=0$ and
$\sin2\theta_{13}=0.2, \ 0.3$ respectively. We remark that other
choices for $\cos2\theta_{23}$ do not produce noticeable changes on
the energy curves where $-\alpha$ and $\alpha+\beta$ are evaluated.

It is easily seen that $\alpha+\beta$ always dominates over
$-\alpha$ when these coefficients are evaluated at energies along
{\bf max1} or {\bf max2} in the right panel of Fig.~\ref{maxmin}. In
such cases, the $\theta_{23}$ degeneracy is absent in the solutions
of $f(y,z)=p$. Namely there exists only one solution curve for the
above equation. Reversely, $-\alpha$ always dominates over
$\alpha+\beta$ when these coefficients are evaluated at energies
along {\bf min1}. The situation is slightly more complicated when
these coefficients are evaluated at energies along {\bf min2}. In
this case $-\alpha$ no longer dominates over $\alpha+\beta$ for
baseline lengths around $10^4$ km. In fact, with
$\sin2\theta_{13}=0.3$, $\alpha+\beta$ is even larger than $-\alpha$
for $9000\leq L/{\rm km}\leq 10500$. This explains the contour
structure of $P_{\mu\mu}$ at $L=10000$ km (see
Fig.~\ref{contour-pmm}) where the straight line $z=0.3$ only
intersects one equal probability curve $f(y,z=0.3)=p$. The straight
line $z=0.2$ also behaves the same except for a very small $p$. We
reiterate that the range for $y\equiv \cos2\theta_{23}$ is $-0.316<
y< 0.316$ due to the constraint $\sin^2 2\theta_{23}>0.9$
\cite{Ashie:2004mr}. Therefore, given $z=z_0$, the equation
$f(y,z_0)=p$ could have only one solution for $y$ if
$-(\alpha(z_0)+\beta(z_0))/\alpha(z_0) > 0.632$. In other words,
such values of $-(\alpha(z_0)+\beta(z_0))/\alpha(z_0)$ lead to the
absence of $\theta_{23}$ degeneracy. In fact, the condition for the
absence of $\theta_{23}$ degeneracy is even more relaxed. To see
this, let us divide our discussions according to the true octant of
$\theta_{23}$.
\subsubsection{ {\bf min2}, $\theta_{23}<\pi/4$}
Since $\alpha<0$ and $\alpha+\beta>0$, the two solutions for $y$ in
$f(y,z_0)=p$ are both negative for $1-\beta(z_0)-p>0$ while they
have opposite signs for $1-\beta(z_0)-p<0$. If the true value of
$\theta_{23}$ is less than $\pi/4$, i.e., the true value of $y$ is
positive, then the experimental measurement should give
$1-\beta(z_0)-p<0$ so that a positive solution for $y$ exists. With
$1-\beta(z_0)-p<0$, the two solutions for $f(y,z_0)=p$ have opposite
signs and the negative solution has a larger absolute value. The
negative solution will violate the constraint $-0.316<y$ if
$-(\alpha(z_0)+\beta(z_0))/\alpha(z_0)
> 0.316$.  For $z_0=0.2$,
$-(\alpha(z_0)+\beta(z_0))/\alpha(z_0)
> 0.316$ is valid for $8300\leq L/{\rm km}\leq 10770$. For $z=0.3$, the
above baseline range is extended to $7410\leq L/{\rm km}\leq 10790$.
\subsubsection{ {\bf min2}, $\theta_{23}>\pi/4$}
With a true value of $\theta_{23}$ greater than $\pi/4$, i.e., the
true value of $y$ less than zero, the value of $1-\beta(z_0)-p$ can
either be positive or negative. The condition
$1-\beta(z_0)-p>(<)\,0$ is equivalent to the condition
$\left|y\right|<(>)\left(\alpha(z_0)+\beta(z_0)\right)/\left(-\alpha(z_0)\right)$.
For $-(\alpha(z_0)+\beta(z_0))/\alpha(z_0)
> 0.316$, one must have $1-\beta(z_0)-p>0$. Hence there exist two
negative solutions for $y$. In this case, the corresponding
solutions for $\theta_{23}$ are both located in the same octant. For
$0.316< -(\alpha(z_0)+\beta(z_0))/\alpha(z_0)<0.632$, the spurious
solution for $y$ may or may not violate the constraint $y>-0.316$.
For $-(\alpha(z_0)+\beta(z_0))/\alpha(z_0)
> 0.632$, the spurious solution for $y$ must violate the constraint
$y>-0.316$, hence the $\theta_{23}$ degeneracy is surely absent. For
$\sin2\theta_{13}=0.2$, the condition
$-(\alpha(z_0)+\beta(z_0))/\alpha(z_0) > 0.632$ can not be achieved
along {\bf min2}. For $\sin2\theta_{13}=0.3$, the above condition is
satisfied for $8270\leq L/{\rm km}\leq 10720$. For
$-(\alpha(z_0)+\beta(z_0))/\alpha(z_0< 0.316$, $1-\beta(z_0)-p$ can
either be positive or negative. For $1-\beta(z_0)-p>0$, both
solutions for $y$ are negative and satisfying the constraint $y
> -0.316$. For $1-\beta(z_0)-p<0$, both solutions for $y$ satisfy the
constraint $-0.316<y<0.316$. However their corresponding
$\theta_{23}$ angles are situated in different octants.

Let us summarize the results obtained in this subsection. The
coefficient $\alpha+\beta$ dominates over $-\alpha$ for energy
values along curves {\bf max1} and {\bf max2} for all baseline
lengths. Hence the $\theta_{23}$ degeneracy is absent along these
energy curves for all baseline lengths. The situation along the
curve {\bf min1} is just the opposite, the coefficient $-\alpha$
dominates over $\alpha+\beta$ for all baseline lengths. Hence the
$\theta_{23}$ degeneracy is present for all baseline lengths in this
case. The issue of $\theta_{23}$ degeneracy becomes more complicated
along {\bf min2}, which we have discussed according to the true
octant of $\theta_{23}$. Along the energy curve {\bf min2}, the
non-degeneracy baseline range is larger for the $\theta_{23}<\pi/4$
case.

\section{Discussions and Conclusions}
We have presented the baselines and energies ideal for probing the
octant of $\theta_{23}$ through neutrino oscillations. The
appearance mode $\nu_e\to \nu_{\mu}$ can be studied in a very long
baseline with the facility of neutrino factory \cite{nu_factory} or
the more recent proposed $\beta$ beam \cite{Zucchelli:2002sa}.  As
said, the sensitivity of $P_{e\mu}$ to $\theta_{23}$ is
$dg(y,z)/dy=-(\alpha(z)+\beta(z))$ where $g(y,z)$ represents
$P_{e\mu}$ in the analytic approximation given by
Eq.~(\ref{quadratic}). The maximal value of $\alpha+\beta$ for each
baseline length is shown in Fig.~\ref{pem}. At the magic baseline,
$L=7600$ km, $\alpha+\beta=0.06, \ 0.21$ and $0.38$ for
$\sin2\theta_{13}=0.1, \ 0.2$ and $0.3$ respectively. For a
sufficiently large $\sin2\theta_{13}$ and a baseline length close to
the magic value \cite{Barger:2001yr,Huber:2003ak,Smirnov:2006sm},
$P_{e\mu}$ is ideal for probing the octant of $\theta_{23}$.

The probability $P_{\mu\mu}$ is also relevant in neutrino
oscillation experiments with neutrino factories. The sensitivity of
this probability to $\theta_{23}$ is determined by the derivative
\begin{equation}
r\equiv \frac{dP_{\mu\mu}}{d\cos2\theta_{23}}=-2\alpha
\cos2\theta_{23}+\left(\alpha+\beta\right).
\label{sensitivity}
\end{equation}
Since $\alpha$ is negative, the sensitivity $r$ is larger for $\cos
2\theta_{23}>0$, i.e., $\theta_{23}<\pi/4$. For a measurement
performed around a local maximum of $P_{\mu\mu}$, the sensitivity to
$\theta_{23}$ is completely determined by the coefficient
$\alpha+\beta$, since the coefficient $\alpha$ is generally rather
suppressed in this case. Along the energy curve denoted by {\bf
max1}, $\alpha+\beta$ peaks at $7480$ km for $\sin2\theta_{13}=0.2$
and it peaks at $L=7350$ km for $\sin2\theta_{13}=0.3$. The values
of $\alpha+\beta$ at those peaks are $0.17$ and $0.32$ respectively.
Along the curve {\bf max2}, $\alpha+\beta$ peaks around $L=10750$ km
for both $\sin 2\theta_{13}=0.2$ and $0.3$ with values  $0.43$ and
$0.48$ respectively.

For a measurement performed around a local minimum of $P_{\mu\mu}$,
the sensitivity to $\theta_{23}$ is determined by both coefficients
$-\alpha$ and $\alpha+\beta$. Along the energy curve denoted by {\bf
min1}, the coefficient $-\alpha$ is always close to unity while the
coefficient $\alpha+\beta$ is always suppressed for all baseline
lengths. It is understood that the magnitude of $\alpha+\beta$
determines the size of matter effects. Hence the matter effect is
small at energies along the curve {\bf min1}. The suppression of
$\alpha+\beta$ compared to $-\alpha$ leads to the $\theta_{23}$
degeneracy as discussed before. The behavior of $P_{\mu\mu}$ along
the energy curve {\bf min2} is more interesting. If the true value
of $\theta_{23}$ is less than $\pi/4$, the $\theta_{23}$ degeneracy
from the measurement of $P_{\mu\mu}$ is absent in the baseline range
$8300\leq L/{\rm km}\leq 10770$ for $\sin 2\theta_{13}=0.2$. The
above non-degeneracy baseline range extends to $7410\leq L/{\rm
km}\leq 10790$ for $\sin 2\theta_{13}=0.3$. On the other hand, if
the true $\theta_{23}$ is greater than $\pi/4$, the non-degeneracy
baseline range does not exist along the energy curve {\bf min2} for
$\sin 2\theta_{13}=0.2$. For $\sin 2\theta_{13}=0.3$, the
non-degeneracy baseline range is $8270\leq L/{\rm km}\leq 10720$.

The existence of non-degeneracy baseline range along the energy
curve {\bf min2} has important implications. It can be seen from
Fig.~\ref{maxmin} that the curve {\bf min2} lies in between curves
{\bf max1} and {\bf max2}. Since the degeneracy of $\theta_{23}$ is
absent on both {\bf max1} and {\bf max2} for all baselines, it is
possible that there exists a non-degeneracy region spanned by ranges
of the baseline length and the neutrino energy. For example, with
$\sin2\theta_{13}=0.2$ and a true value of $\theta_{23}$ less than
$\pi/4$, the $\theta_{23}$ degeneracy is absent for $8300\leq L/{\rm
km}\leq 10770$ for energies along curves {\bf max2}, {\bf min2} and
{\bf max1}. It is of great interest to investigate if the
$\theta_{23}$ degeneracy is also absent for any neutrino energy
larger than the value on {\bf max2} and smaller than that on {\bf
max1}. By taking all these energies into account, we find that the
$\theta_{23}$ degeneracy is absent for $8550\leq L/{\rm km}\leq
10680$. For a true value of $\theta_{23}$ greater than $\pi/4$ and
$\sin2\theta_{13}=0.3$, the $\theta_{23}$ degeneracy is absent for
$8270\leq L/{\rm km}\leq 10720$ for energies along curves {\bf
max2}, {\bf min2} and {\bf max1}. However, with all energies between
curves {\bf max2} and {\bf max1} considered, we find that the
$\theta_{23}$ degeneracy is absent for $8450\leq L/{\rm km}\leq
10680$. The non-degeneracy baseline range corresponding to different
combinations of $\theta_{23}$ and $\theta_{13}$ values are
summarized in Table~I.
\begin{table}[bt]
\begin{center}
\caption{The baseline range in which the $\theta_{23}$ degeneracy is
absent in the probability $P_{\mu\mu}$ for all energy values between
the curves {\bf max2} and {\bf max1}. The entry corresponding to
$\theta_{23}>\pi/4$ and $\sin2\theta_{13}=0.2$ is left blank since,
with such set of parameters, there exists no baseline length where
the condition for the absence of $\theta_{23}$ degeneracy can be
satisfied. }
\begin{tabular}{|c|c|c|}\hline
$\theta_{23}$ octant & $\sin2\theta_{13}=0.2$ &
$\sin2\theta_{13}=0.3$ \\ \hline $\theta_{23}<\pi/4$ & $8550\leq
L/{\rm km}\leq 10680$ & $7950\leq L/{\rm km}\leq 10700$ \\
\cline{2-3} $\theta_{23}>\pi/4$ &  &$8450\leq L/{\rm km}\leq
10680$\\ \hline
\end{tabular}
\end{center}
\label{table}
\end{table}

It is interesting to compare measurements on $P_{e\mu}$ and
$P_{\mu\mu}$ since both oscillations appear in experiments with
neutrino factories \cite{nu_factory}. The main issue for comparison
is on the determination of the true $\theta_{23}$ value under the
assumption that both the sign of $\Delta m_{31}^2$ and the value of
$\sin2\theta_{13}$ are known. Let us begin the discussion with a
true value of $\theta_{23}$ less than $\pi/4$ and
$\sin2\theta_{13}=0.2$. For $L< 8550$ km, the appearance mode
$\nu_{e}\to \nu_{\mu}$ is useful for probing the octant of
$\theta_{23}$, in particular for $L$ close to the magic value,
$7600$ km. However, the survival mode $\nu_{\mu}\to \nu_{\mu}$ is
not as useful since the $\theta_{23}$ degeneracy is absent only at
energies near {\bf max1} and {\bf max2}. Concerning the sensitivity
to $\theta_{23}$, we note that the differentiation of $P_{e\mu}$
with respect to $\cos2\theta_{23}$ is $-(\alpha+\beta)$. The value
of $\alpha+\beta$ increases with $L$ as shown in Fig.~\ref{pem}. It
is $0.21$ at $L=7600$ km, and $0.26$ at $L=8550$ km. For $8550\leq
L/{\rm km}\leq 10680$, both $\nu_e\to \nu_{\mu}$ and $\nu_{\mu}\to
\nu_{\mu}$ are useful for probing the octant of $\theta_{23}$. We
note that peak positions of $P_{e\mu}$ are mostly around $6$ GeV.
Hence they overlap with the non-degeneracy energy range of
$P_{\mu\mu}$. From Eq.~(\ref{sensitivity}) and our assumption of
$\theta_{23}<\pi/4$, we find that $P_{\mu\mu}$ is more sensitive to
$\theta_{23}$ as compared to $P_{e\mu}$ for the same neutrino
energy. For $L>10680$ km, $\nu_e\to \nu_{\mu}$, is again the only
useful mode for probing the octant of $\theta_{23}$.

Let us turn to the case where the true value of $\theta_{23}$ is
greater than $\pi/4$ and $\sin2\theta_{13}=0.2$. In such a case, the
value for $P_{e\mu}$ is enhanced compared to that with $y>0$.
Furthermore $P_{e\mu}$ is always more sensitive to
$\cos2\theta_{23}$ as compared to $P_{\mu\mu}$ for the same neutrino
energy. It is clear that the $\nu_e\to \nu_{\mu}$ appearance mode is
more useful for probing $\theta_{23}$ regardless the baseline
length. Although there exists a baseline range where the
$\theta_{23}$ degeneracy is absent in $P_{\mu\mu}$ for neutrino
energies between curves {\bf max2} and {\bf max1}. However this
requires a large value of $\sin2\theta_{13}$, such as
$\sin2\theta_{13}=0.3$.

It is essential to remark that the above non-degeneracy baseline
range is not sensitive to the value of $\Delta m_{31}^2$, which we
have so far taken to be $2.4\cdot 10^{-3}$ eV$^2$. Changing the
value of $\Delta m_{31}^2$ only shifts the probability curves in
Fig.~\ref{cp-phase} and Fig.~\ref{theta1323} so that positions for
local maxima and local minima of these probabilities shift
accordingly. However, the maximal or minimal values of these
probabilities remain unchanged. In other words, although the energy
curves in Fig.~\ref{maxmin} are shifted, the coefficients $-\alpha$
and $\alpha+\beta$ plotted in Fig.~\ref{coefficient}, which combine
to form $P_{e\mu}$ and $P_{\mu\mu}$ (see Eq.~(\ref{quadratic})),
remain the same. The values of these coefficients as functions of
the baseline length $L$ then determine the non-degeneracy baseline
range.

In conclusion, we have studied the probabilities $P_{e\mu}$ and
$P_{\mu\mu}$ for very long baseline neutrino oscillations. We focus
on sensitivities of these probabilities to mixing angles
$\theta_{13}$, $\theta_{23}$ and the CP violation phase $\delta_{\rm
CP}$. Taking $\delta_{\rm CP}=0$ as an example, we presented contour
graphs of $P_{e\mu}$ and $P_{\mu\mu}$ in the
$\sin2\theta_{13}-\cos2\theta_{23}$ plane for baseline lengths
$L=1000$ km, $5000$ km, $10000$ km and $12000$ km. The energy values
chosen for such studies are in the vicinities of either local minima
or local maxima of neutrino oscillation probabilities. For each
baseline length, we have found that $P_{\mu\mu}$ is more sensitive
to $\sin 2\theta_{13}$ at energies around its local maxima while it
is more sensitive to $\cos 2\theta_{23}$ at energies around its
local minima. On the other hand, the appearance probability
$P_{e\mu}$ is sensitive to $\sin2\theta_{13}$ and $\cos2\theta_{23}$
only near its local maximum. Such findings have been applied to
probe the octant of mixing angle $\theta_{23}$ assuming that the
angle $\theta_{13}$ and the sign of $\Delta m_{31}^2$ are known. The
appearance probability $P_{e\mu}$ is non-degenerate in
$\theta_{23}$. The sensitivity of $P_{e\mu}$ to $\cos2\theta_{23}$
is studied for baseline lengths from $1000$ km to $12000$ km. We
also studied the sensitivity of $P_{\mu\mu}$ to $\cos2\theta_{23}$
for the same range of baseline length. We have identified the ranges
of neutrino energy and baseline lengths where the $\theta_{23}$
degeneracy is absent. We have pointed out that, for a true value of
$\theta_{23}$ less than $\pi/4$ and a baseline length between $8000$
and $10000$ km, the survival mode $\nu_{\mu}\to \nu_{\mu}$ is
equally good as the appearance mode $\nu_{e}\to \nu_{\mu}$ for
probing the octant of $\theta_{23}$.

\section*{Acknowledgements}
G.L.L likes to thank D. Indumathi for informative discussions. This
work is supported by National Science Council of Taiwan under the
grant number NSC 94-2112-M-009-026.

redpajama_set_name: RedPajamaArXiv


In the wake of last season's glorious "The Norman Conquests," it's especially gratifying to be presented with a brand new play by its peerless author, Alan Ayckbourn, and to find that 26 years after writing that masterful trilogy, he's still in fine fettle.
The play – his 73rd -- is hot off the press as it were, having been directly imported to New York from Ayckbourn's Stephen Joseph Theatre Company in Scarborough, England where it premiered only last month. And it's his third play to be presented as part of the annual Brits Off Broadway festival.
"My Wonderful Day," though not a trilogy or a two-parter like some of Ayckbourn's other works, proves every bit as ingenious, exploring, as it does, the world of adults from the unique perspective of a child.
The child in question is Winnie, the eight-going-on-nine year old daughter of Laverne (Petra Letang), housecleaner to smarmy, self-centered TV host Kevin (Terence Booth). She's played by the extraordinary Ayesha Antoine, who is, in fact, 28 years old. Her impersonation is so authentic that if you didn't check your program, and see her hefty list of credits, you'd assume she was at most, 12 or 13.
Single mother Laverne brings Winnie to work as the girl professes to not feeling well. Laverne is large with child, whom she has already named Jericho Alexander Samson ("That should keep him out of trouble, shouldn't it?" a character later wryly observes). After the birth, Laverne fantasizes about moving her family to Martinique.
In preparation, Laverne insists that she and Winnie speak nothing but French one day each week. "Oui, mamam," dutifully answers little Winnie repeatedly.
Laverne parks Winnie on the sofa to do her homework: an essay on her "most wonderful day." With that setup, you just know the girl will get plenty of fodder before the play is done.
When Laverne's water breaks, Winnie is left in the care of Kevin, his kind-hearted secretary and (we learn) mistress Tiffany (Ruth Gibson), and hung-over best friend and business partner Josh (Paul Kemp).
Both Kevin and Josh assume the girl speaks no English, leading to all kinds of candid revelations in front of Winnie who takes it all in as she writes in her notebook. Eventually, Kevin's fearsome wife Paula (Alexandra Mathie) returns home just as, wouldn't you know, Kevin and Tiffany have retired to the bedroom upstairs.
Ayckbourn already establishes the girl as a smart, sensitive child so we understand she is far from oblivious to the extraordinary happenings around her, and thanks to Antoine's performance – wide-eyed, slack-jawed languor – we seem to know precisely what she's thinking, silent and uncommunicative though she is.
Much as Strindberg broke ground with long stretches of naturalistic silence, Ayckbourn pushes the envelope with a lengthy kitchen scene that has Winnie laboriously reading "The Secret Garden" to Josh who soon succumbs to snoring sleep.
"You have seen the last of my childish, thoughtless tantrums," she assures Winnie. With her husband upstairs with Tiffany, Ayckbourn makes sure we know that is a promise soon to be broken.
Roger Glossop's set is a model of clever economy. With three playing areas -- left to right, a kitchen, living room, and office -- one gets the scope of the whole of Kevin's house thanks to Mick Hughes' clever lighting scheme.
As you'd expect, Ayckbourn has directed his play (performed without an interval) masterfully.


text:
Another Opinion with Paul Hosse
One of America's leading Independent political sources for those who think for themselves
Our Brave New World: Life Post-COVID-19
As we slowly start to return to life after being confined to our homes these past many weeks, I've wondered what our world will be like post-virus. What will change and what will remain the same? Many states and cities remain on lockdown while a few others are slowly coming around, much like flora in the spring, but will they ever fully blossom again?
The federal government has largely left governors and mayors to decide how quickly or slowly they can reopen. Some recommendations have been suggested such as maintaining "social distancing" of at least six feet, wearing protective masks, regular hand washing or using hand sanitizers, which all sound sensible, but how will it play out in practical daily application? Before we address this and other questions about our "brave new world" (to borrow from Aldous Huxley), perhaps we should take a look at what changes took place following the 1918 Spanish Influenza pandemic.
As you may know, the 1918 influenza outbreak (better known as the Spanish Flu), a strain of the H1N1 virus, first appeared just as World War One was waning. No one knows for sure where it originated. It acquired its infamous name from a Madrid newspaper article which had reported on some of the first cases, including their king, Alfonso XIII, but stated that the virus had originated in France. Meanwhile, American doctors first noted patients with the all too familiar symptoms months earlier at a Kansas army base (many of the patients had been stationed in Europe as well as in Asia).
Unlike the current viral strain, the Spanish Flu was truly a mass killer. More people died due to the flu than died in the war (about 50 million compared to around 20 million war dead). At present just over 264,000 worldwide have died due to COVID-19 with about 4 million infected. Compare that to the 500 million or one-third of the world's population being infected by the Spanish Flu. At the time there were no vaccines. Doctors were at a complete loss. They lacked the high tech specialized labs that we have today or computers capable of running millions of calculations a second. It was all slow trial and error experimentation and knowledge gleaned from each death.
Without a proven vaccine, the best solution was to ask citizens to cover their nose and mouth with whatever they could (most used handkerchiefs or scarves while others used homemade masks). Like today, schools and businesses were closed as were churches, saloons, theaters, and other places where people tended to congregate. Even libraries were closed while mail delivery and garbage pickup became sporadic. Since it was thought that the virus was spread by human contact, some staggering business hours in order to minimize crowds.
Meanwhile, as hospitals quickly filled up with the sick and dying, officials began to covert empty buildings, homes, and gymnasiums. With a lack of available doctors and nurses, medical students were pressed into service to treat the less severe patients, who, as an aside, were often treated with nothing more than common aspirin, then a relatively new "wonder drug" (the German company Bayer held the patent and Germany was an enemy combatant, making the drug hard to come by). And like today, entire communities were quarantined. Those who violated the quarantine were issued a citation ("disturbing the peace") by the local police. Repeated violators were fined or even arrested!
The death rates were so high that funeral homes were filled beyond capacity. Many used ice houses to store the bodies until they could be buried. In rural parts of the country (which at the time made up 49% of the nation), families had "parlor" funerals in their living rooms while graves were dug by family members or friends with the departed buried on the property (it wasn't unusual in the country to have small family cemeteries). Their names and date of death were reported when they could, which could be weeks or months after their death. Some were never reported.
So how did the Spanish Flu change the America? America in 1918 was still in the midst of "The Great War". Industry had been geared up to support the war effort while young men (and a few women) volunteered to go "over there" as the popular battle cry implied. In some ways that was a good thing. It meant much of America's youth were overseas at the height of outbreak.
It also meant that our resources (especially medicine and medical supplies) had to be balanced to support the war effort and flu outbreak "over there" and increasingly at home. Bear in mind too that many of the country's recently graduated medical doctors and nurses, feeling patriotic, had volunteered for military service. Thus, medical students were co-opted to take care of the sick on the home front.
Like today, the flu took its greatest toll on the old , the sick or those with serious underlying medical conditions like cancer, diabetes, heart or lung disease. Another killer at the time which claimed thousands of lives was tuberculosis. "TB" as it's typically called ran rampant in poorer regions of the country like the deep South or in the slums of large cities like New York and Chicago.
Thanks in part to the devastation of the flu and TB among other diseases of the time like the measles, there was calls to eradicate the slums, access to clean water, improved nutrition, particularly for children, and demands for mandatory vaccinations (again, mainly for the children). Hospitals and universities began dedicating more money to the treatment and prevention of these diseases.
By 1920 overall healthcare had improved dramatically. This was due, in part by the lessons learned by the war in the care and treatment of not just the wounded or treatment of the flu, but also mental illness such as "shell shock" or PTSD as we call it today, and other diseases experienced by those who fought in the filth of the trenches. One major improvements was in sanitation.
After the war much of this changed. There was an emphasis on cleanliness. Even hospital food improved (well, relatively. At least they now got healthier meals). Standardized treatment of individuals now became commonplace with added emphasis in prevention. Because more money was going into research, there was more or improved medicines, treatments and vaccines becoming available.
In society in general, there was a new emphasis in cleanliness, be it in restaurants, saloons, or the neighborhood grocery store, which focused on insuring that its vegetables, fruits, and meats were fresh. It became common to wash your hands before dinner and to take regular baths---with soap! It was far from what we would consider acceptable these days, but it was a huge improvement, and it helped jump start movements to improved the quality of life such as water lines to bring clean water to every home, and stronger health codes for better quality control of meat and food processing.
What will the post-COVID-19 world be like? It's hard to say at this point just as it was all but impossible to predict in the waning months of the Spanish Flu pandemic. At first, I expect there will be a lot of "overkill" of precaution. As in 1918, officials are terrified of being accused of doing too much as they are of not doing enough. We'll see some demand everyone wear masks until the impractically of it finally dawns on them or society refuses to comply. Social distancing will likely remain, at least for awhile, but that will soon fade. Humans are social animals. We tend to congregate. It's our nature.
Whereas in 1918/19 there were no "take out" dinners per se, I think we'll see more people doing just that. The result may be fewer restaurants, especially those whose menus don't easily accommodate to pickups. Businesses which deliver food will likely do well along with those who pick up and deliver office supplies, groceries, and fulfill similar needs. We'll see an increase in online shopping across the board. In fact, anything that can be done electronically will do quite well.
There are some things which has to be done in person such as visiting the doctor. Well, maybe. This pandemic took a relatively new technology, "telemedicine", and brought it into the mainstream of healthcare. It allows the doctor or their staff to connect visually over the internet and conduct a virtual office visit. Of course, there are practical limits, but it does allow the physician to actually see and speak with their patient and ascertain their general health and any issues which may necessitate a office visit or trip to the ER. Now, if we can only figure out how to use this in lieu of dentist visits!
Naturally, the patient can provide their weight, temperature, and blood pressure too if they have the equipment at home. Physicians can already check on a number of medical conditions remotely such as heart monitors and CPACS through the use of the internet or electronic transponders. We may also see the increase in doctor directed robots making the rounds in hospitals or nursing homes.
Speaking of robotics, expect to see an increase in automation not just in manufacturing, but also in warehousing and fast food restaurants. The virus pandemic and reliance on "essential" employees has proven to be too unreliable, operationally costly, and increased the risk of a potential infection which would affect not just staffing but insurance costs.
Banks, which are operating mainly through drive-thru tellers, could potentially eliminate inside banking altogether except for appointments, reducing cost and improving security. They could have a dedicated drive-up window to handle investment services or loan applications. What all this means is less demand for low skill/entry level employees. By the way, there's a growing case being made to all but eliminate cash, which some claim is susceptible of carrying germs and viruses.
The result would be the use of credit and debit cards for the majority of transactions. But why stop there? Why not encode a card to include your credit, work, insurance, criminal, and medical histories plus your driver's license and voter ID ? By the way, expect that your vaccination history to be included, which is more likely going to mandatory and less an option. In short, your entire life on one plastic card! You would have just have one card to worry about, but we can do even better than that!
What if, instead of a plastic card to carry around, they could simply implant a microchip in your hand or arm with all your data on it? Just a wave of your hand (or arm as the case may be), and that's all. No more "dirty" money. No more cards to carry or pin numbers to remember. Less risk of ID theft or stick ups! Maybe it could be encoded to unlock your home or car (or even start it!). Well don't laugh, microchips are already being tried in places like Sweden and the trend is growing. Now it's being promoted as a way to cut back on interpersonal contact and reduce the spread of viruses.
Unlike 1918, we have far greater technology available to us. But scientific achievement doesn't translate to moral wisdom, which sadly often lags decades behind. Sometimes longer. In our rush and fear to avoid the next pandemic, let's pause for a moment and reflect on what it is we really want as a society and what price we are willing to pay for it. Remember, earlier Republics and democracies often failed as a result fearful citizens willingness to trade their freedom for security, and ultimately, obtaining neither.
The Influenza Pandemic of 1918
Diseases In The Trenches
Five Bold Predictions For The Post COVID-19 World
Why You're Probably Getting A Microchip Implant Someday
Posted by Paul Hosse at 5/09/2020 10:52:00 AM
Labels: Coronavirus, COVID-19, H1N1, health, Healthcare, hospitals, infectious diseases, Internet, Pandemic, poverty, PPE, preventive care, sanation, Spanish Flu, TB, telemedicine, tuberculosis, vaccinations, virus, WWI
marlem388 said...
Thank you, Paul, for another terrific article...I'm wondering whether we'll be demanding public oversight and some democratic perspective re our technical crafts. If we don't look with a critical eye at the ease and glibness of how digitization achieves connections and preps activities, we surely will be giving up freedom for false security. And if security is our aim, how much can we depend on the validity of the data feedback, whether routinely or during a crisis, if network functions are determined by huge private entities such as Amazon or Google? If public funds were to defray the expense of running these technologies, maybe public ownership and control would make them more accountable to us. It might benefit us if cyber life were a public utility not run for profit. As you and Ben Franklin imply, trading freedom for security will get neither, but protecting ourselves from privateers who blithely seize our freedom may help us seize it back.
Sunday, May 17, 2020 10:06:00 PM
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I'm Paul Hosse (pronounced PAWL HAH-see). I've been a political activist and community organizer for over 40 years. I've served as a Congressional Aide, managed over a 100 campaigns, trained candidates held office, managed a state union, and served on numerous non-profit boards. My articles and book reviews have appeared all over the world. My goal is provide you--the reader--with political editorials from a non-partisan perspective to help you come to your own conclusions.
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redpajama_set_name: RedPajamaCommonCrawl


text:
Prestige VDL
Like his sire, Silvano, this Dutch stallion is a star in the competition arena – and the breeding barn. Anyone who was at the Sydney Olympic Games in 2000 will remember Ellen Bontje and Silvano, starring for the Dutch Team. For those who attended the 2012 CDI will remember the grace and power of Prestige VDL in the Grand Prix… Prestige
1997 KWPN Licensed Prestige VDL was champion of his stallion test in Sweden with scores of 8 for walk, 8 for trot and 10 for canter. From the test riders he was awarded 9 for his gaits and 9 for his dressage potential. He was KWPN licensed in 2003 with high scores for gait and dressage talent. Competing with Edward Gal he scored 70%+ in international competition, now he is successfully competing at Grand Prix in Australia, scoring 66.149% in his first season of competition with Sheridyn Ashwood. Prestige VDL has been an extremely popular stallion in Europe and the United States. He is the sire of the approved stallion, Penthagon and many Premium and First Premium mares. His daughter, Beatrice VDL was selected out of approximately 1000 fillies of 2006 to compete in the KWPN National Foal Championships, finishing in 3rd place. His daughter, Ballerina was the top foal of her inspection, while another daughter, Bling, made the USA top ten foal list. Prestige VDL stamps his progeny strongly, producing foals with a good front, powerful gaits, correct conformation and horses that move uphill with a lot of power from the hind leg with a strong canter. They are known for their willingness to work and unrivalled temperament and character… horses that have the mindset and talent to want to compete at Grand Prix Standard. At last in Australia, you have a world class stallion WITH a live foal guarantee.
Stallion 16.3HH:
Aproved: KWPN,SWANA,HANN:
Dressage Index 142 (Highest in Aust.)
$3,850 inc. GST.
(includes booking fee and LFG).
Sheridyn Ashwood
Website: www.sheridyn-ashwood-dressage.com


text:
Lessons of the Great Depression of the 1930s: Create Jobs by Executive Order
By Jeanne Mirer and Prof. Marjorie Cohn
Global Research, December 11, 2017
Theme: Global Economy, Poverty & Social Inequality
First published by GR on November 10, 2010
On May 6, 1935, with the country in the midst of the Great Depression, and with indirect efforts to create jobs having not moved the needle of unemployment rates, President Franklin D. Roosevelt signed Executive Order 7034 and appropriated $4.8 billion for the Works Progress Administration (WPA). The WPA put millions of Americans to work constructing buildings, painting murals to decorate them, and performing plays for audiences that had never before seen a dramatic production. In the process, many were saved from poverty and starvation and the economy began to revive.
Although Congress, as part of the New Deal, had appropriated money specifically for relief, FDR decided to use the money for a direct jobs program by issuing a Presidential executive order. This Executive Order described the agencies to be involved in the program, its structure and procedure for application and allocation of jobs.
The WPA was quickly implemented. By March 1936, 3.4 million people were employed and an average of 2.3 million people worked monthly until the program ended in June 1943. During its existence the WPA employed more than 8,500,000 different persons on 1,410,000 individual projects, and spent about $11 billion. The average yearly salary was $1,100, a living wage at the time. During its 8-year history, the WPA built 651,087 miles of highways, roads, and streets. It constructed, repaired, or improved 124,031 bridges, 125,110 public buildings, 8,192 parks, and 853 airport landing fields.
Today our infrastructure is crumbling, and loss of revenue is forcing many cities and states to cut basic services. About 15 million people have become unemployed since the crisis hit in late 2008; a million and a half of them are construction workers. The need for a direct jobs program is either as great, or even greater than during the Depression.
But, in light of the election results, is such a program possible? Can the President directly create jobs by executive order? The answer is a resounding yes. Remember when the Emergency Economic Stabilization Act of 2008, which created the $700 billion Troubled Assets Relief Program (TARP) was passed, one of the purposes was to preserve homeownership, and promote jobs and economic growth.
Much of the TARP money has been repaid and the administration refers to the profit on the payments. If one assumes an average cost of one job is $50,000, 6 million jobs could be immediately created for $300 billion. 12 million jobs could be created for $600 billion. Because this is already appropriated money, Congressional Republicans could not block it.
This direct job creation would be bold. It would also be highly stimulative. It would not add to the deficit because it is already appropriated money. Furthermore, one third of it would come back immediately in taxes, and more importantly, the growth in demand from this number of added jobs would expand private sector job growth and grow the overall economy.
This bold program would contrast markedly with prior stimulus bills, which were indirect and whose effects have been too slow to manifest themselves. The posture of the Republicans during the last two years has been to prevent the President and Congress from taking bold steps to intervene in the economy to directly create jobs. Then they used the Administration's failure to take bold steps to create jobs to say the "stimulus did not work." They turned the very TARP bailouts they supported into a rallying cry against government intervention in the economy to help people and they characterized as "socialism" any government initiatives such as health care. They decried deficits and opposed any sane tax policies to get the deficit going in the other direction.
By keeping progress in job creation slow and blaming the administration for lack of jobs, the high expectations for the Obama administration became deflated. The loss of jobs exacerbated the mortgage crisis, and banks have been encouraged to foreclose rather than restructure mortgages despite the opposite being explicitly called for the Emergency Stabilization Act.
The people who voted for Obama in 2008 voted for the promised hope and change. Many developed buyer's remorse when what they got a set of policies which protected Wall Street at the expense of Main Street, big business at the expense of workers, and made unnecessary compromises with the right. The so called "enthusiasm gap" created by Republican obstruction and Administration timidity, produced such a deflation in people's morale that it acted as an effective form of voter suppression. The election results can be explained in this fashion.
Some have said that it makes no sense that the voters would go in a more rightward direction because the Obama administration was not "left" enough. But the fact is the Obama administration failed to deliver change and also failed to make the case for progressive policies. The election of Democratic incumbents meant only more of the same. And only 9 million of the 23 million young people who voted in 2008, came out in 2010. This undervote made the difference.
Abraham Lincoln once said: "You can fool some of the people all of the time, and all of the people some of the time but you cannot fool all of the people all of the time." What happened in this election was the right wing was able to fool enough of the people enough of the time to make independents join with rabid right wingers, while at the same time suppressing the progressive electorate.
This country has a lot to do to get its economic house in order. It is heavily dependent on the financial services industry which only promotes speculation and unregulated bubbles. It is largely controlled by the defense industries which have promoted two and possibly more wars. It is beholden to the extractive energy industries, whose owners are funding the "tea party," thus putting environmental amelioration on indefinite hold. And it is more and more influenced by the prison industrial complex which promotes hostility to immigrants, and takes resources from education and other vital areas. For the last 30 years it has relied on anti-union and anti-worker policies, which has forced the hemorrhaging of high paid manufacturing jobs to low cost countries and driven down wages for U.S. workers which can no longer be papered over with unsustainable debt.
The President cannot solve all these problems overnight, but with a stroke of a pen he can use already appropriated money to create millions of good green jobs, and move down the road to recovery much faster. Any opposition to this from the Republicans will expose their hostility to anyone but the richest members of society, and give the progressive movement ammunition to take the offensive.
Jeanne Mirer, who practices labor and employment law in New York, is president of the International Association of Democratic Lawyers. Marjorie Cohn is a professor at Thomas Jefferson School of Law and past president of the National Lawyers Guild.
Copyright © Jeanne Mirer and Prof. Marjorie Cohn, Global Research, 2017
Articles by: Jeanne Mirer and Prof. Marjorie Cohn


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This has been a great addition to the Cutco line! The rounded, upturned blade of the steak knife makes it just like a steakhouse and allows me to feel proud while serving steak to my guests! Can't wait to start seeing these in commercial steak houses, because until then I will be bringing my own knife with me! Cutco all the way for me!


text:
The Witch: Part I. The Subversion (2018) / Hoon Jung Park
By laagi, August 4, 2018 in Korean Cinema
laagi 785
Venomous Lizard
Korean X-Men? Looks pretty damn good to me...
Edited August 4, 2018 by laagi
whitesnake 2,207
King of the Legfighters
The Witch: Part 1. The Subversion is a 2018 South Korean "action, mystery, fantasy" movie directed and written by Park Hoon-jung (The Tiger: An Old Hunter's Tale). The cast includes Choi Woo-sik (Okja), Jo Min-soo (Venus Talk), Park Hee-soon (The Age of Shadows), and Kim Da-mi (in "a breakout performance")
Two synopses - "A high school student with amnesia tries to uncover what has happened to her. All leading her into deeper troubles ultimately revealing a darkness she could not have imagined." (IMDB) and "A female high school student is trained to become a murder weapon. Medical experiments are used on living bodies in the process. While suffering through an identity crisis, she becomes involved in a crime." (asianwiki.com)
Read a favorable film review at - https://www.hollywoodreporter.com/review/witch-part-1-subversion-manyeo-film-review-1123552 - "An often mesmerizing, occasionally kooky but thoroughly entertaining thriller."
International sales rights have been picked up by South Korean sales house Finecut. The movie's international premiere was at the Fantasia International Film Festival in Montreal. (from https://variety.com/2018/film/asia/warner-korea-witch-finecut-1202860346/)
Here's a poster
Edited August 8, 2018 by whitesnake
@whitesnake Thank you for the additional details. Sorry I'm quite lazy when it comes to posting... Just let the trailer do the talking
The Witch is also playing (private screening on September 13th) at the 2018 Toronto International Film Festival. CJ Entertainment picked up distribution rights in HK and Macao, Singapore, Malaysia and Brunei, Indonesia and Thailand. Other companies picked up distribution rights for Japan, Taiwan, and The Philippines. From - https://variety.com/2018/film/asia/the-witch-cj-culture-entertainment-asia-japan-1202933514/
What about distribution in the English-speaking countries? We'd like to see it too. Not everybody is able to attend film festivals.
Youtube trailer with close-captioned English subtitles -
Edited December 6, 2019 by whitesnake
The movie will also be shown during the Busan International Film Festival http://www.biff.kr/eng/html/program/prog_list.asp?c_idx=317&QueryStep=2
@whitesnake I agree we need more of these movies on the local big screen. It's even worse here in Europe. Outside of festivals you can just forget to catch any of these.
I got through watching this one recently, and gave it the full review treatment. Check it out here -
http://cityonfire.com/the-witch-part-1-the-subversion-2018-review/
The Witch: Subversion will get a North America release on Blu-ray and DVD from Well Go USA on March 10, 2020. Info here - https://www.rightstufanime.com/The-Witch-Subversion-Blu-ray


The effort comes in the 10th year that Dr. George D. Ruggieri has served as director of the aquarium, which stretches along the Coney Island boardwalk at West 8th Street in Brooklyn.
For Dr. Ruggieri, who is both a marine biologist and a Jesuit priest, Discovery Cove is the first of three elements needed to achieve ''a complete aquarium'' over the next decade.
Discovery Cove is scheduled to open in the spring of 1988. Its cost will be shared equally by the city and private philanthropy.
The development represents a new approach to the exhibition of marine life, Dr. Ruggieri said.
The Discovery Cove building on the 14-acre aquarium site will be divided into four principal areas dealing with the properties of sand and water, coastal ecosystems, the adaptations of marine animals and the relationship of people to the sea.
All this will be portrayed through live animals, dioramas, graphic and photographic displays, push-button demonstrations and participatory exhibits intended to engage a visitor in the watery world that is home to the smallest invertebrates and the largest mammals. #600,000 Visitors Dr. Ruggieri presides over more than 22,400 aquatic creatures - 20,000 of them corals and anemones - at the aquarium, a division of the New York Zoological Society. Last year, the aquarium attracted 600,000 visitors; its current operating budget is $4 million.
Twenty years ago, the operating budget was $700,000 and the aquarium housed more than 2,500 sea organisms, about 1,000 of them corals and anemones.
''We have no problem about multiplying fishes,'' Dr. Ruggieri observed during an interview in his office.
Sea Cliffs, an indoor-outdoor sequence of coastal habitats for seals, walruses, penguins and sea otters, will stretch 350 feet along the fence separating the aquarium from the boardwalk. Unlike the present grouping of pools, Sea Cliffs will provide underwater viewing of mammals and birds.
The third development project, a $30 million whale-dolphin habitat, has not yet been designed and is five to eight years away, Dr. Ruggieri said.
Nearing completion is a $2 million, city-financed water pumping, filtration and distribution station that ''will satisfy all the future sea-water needs'' of the aquarium, he said.


Easy With a little sleight of hand and practice. You could soon be performing this very convincing coin vanish.
A coin is shown to the audience and is clearly placed in the fist of one of the magicians hands. The coin is seen to be thoroughly pushed into the fist and then, Kapowee !! Both hands are shown open to see that the coin has completely vanished ?? This trick can be reinforced by showing both sides of the hands to be empty which leaves your audience, even more confused.
The magic trick video below shows the performance of this cool coin trick and then explains the secret to performing it.


Explore the northwest region of Greenland and Disko Bay on this unique Arctic wilderness expedition, and meet the people that call it home.
Sail in the wake of the Old Norse explorers that inhabited the shores of Iceland and Greenland. Explore the settlement of the viking Erik the Red on the way to Iceland and discover the unique history, culture and fascinating heritage.
Take an extraordinary expedition of the Arctic's three best-known islands: Spitsbergen, Greenland and Iceland.
A land where turquoise glaciers descend majestically into glittering fjords, meadows are bright with wildflowers, and humpback and blue whales are frequent visitors to these Arctic waters.
Greenland is the perfect destination for travellers craving a little adventure and freedom to explore at will, which sets itself apart from the energetic nature of major cities. As the world's largest island with almost 80% self-governed, Greenland offers enormous potential to get back to nature and experience breathtaking scenery while still dotted with picturesque villages, with plenty of accommodation, throughout western Greenland.
The capital of Greenland, Nuuk and the quaint town of Ilulissat are destinations like no other that have to be seen to be believed. Almost impossibly beautiful, these colourful seaside towns are set to a backdrop of enormous proportions – grand glaciers, sweeping mountains and iconic UNESCO World Heritage Listed fjord's.
Greenland possesses a wealth of rare beauty with near 24-hour sunshine during the summer and the spectacular naturally occurring Aurora Borellis or Northern Lights illuminating the dark winter sky. This region of the world is truly magnificent, with a variety of ever-changing scenery throughout the enormous land span appealing to even the most seasoned traveller.
What better way to experience Greenland than dog sledding! Take a two hour ride of a several day expedition.
Whale watching is a must in Greenland. With a total of 15 species to spot in the arctic waters, take a whale watching sailing trip and see them for yourself.
Experience a musk ox safari from Kangerlussuaq.
Take a long hot soak in the hot springs on the island of Uunartoq, just off the coast of Qaaqortoq.


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2013-2014 ITH season preview: Penn State Nittany Lions
Alex Bozich
09/12/2013 10:13 am in
With the start of college basketball season on the horizon, we'll be taking a long look at the conference at large as well as Indiana's roster over the next month. Today, we tip off our look at the Big Ten with the Penn State Nittany Lions.
Penn State may have taken a step back last season from a wins and losses perspective, but the rebuilding effort being led by Pat Chambers continues to move along at a program with little historical success on the hardwood.
If there is such a thing as a competitive two-win Big Ten team, Penn State fit the bill a season ago. The Nittany Lions struggled to find their footing after losing Tim Frazier to a torn Achilles' tendon, but finished the conference slate with a home win over eventual national runner-up Michigan and a win at Northwestern. Penn State also played Wisconsin to a narrow 66-63 loss to close the regular season at the Bryce Jordan Center.
With Frazier back in the rotation to go along with D.J. Newbill, Penn State boasts one of the league's best backcourts. Frazier was a first team All-Big Ten selection back in 2011-2012 and while he's never been particularly efficient, he posted a ridiculous assist rate of 45.2 (second nationally) while also averaging 18.8 points, 4.7 rebounds and 2.7 steals per game in his last full season.
Newbill, a junior, had a breakout season in Frazier's absence as he became the go-to scorer and used 30.9 percent of Penn State's possessions, the highest usage among Big Ten players. He's the team's leading returning scorer at 16.3 points per game and also drew 5.8 fouls per 40 minutes last season.
Penn State's backcourt depth took a hit when Jermaine Marshall opted to leave the program, but transfer Allen Roberts should help soften some of the blow of losing Marshall. Roberts, who averaged 12.3 points last season at Miami (OH) and is eligible immediately, will battle John Johnson, a transfer from Pittsburgh who will be eligible the second semester, and freshmen Graham Woodward and Geno Thorpe for minutes.
While Penn State appears to be set in the backcourt with plenty of depth, the frontcourt situation could prevent the Nittany Lions from making a significant leap in the Big Ten standings. Junior Ross Travis, who is the second leading returning rebounder in the conference, returns, but is undersized at 6-foot-6.
Sophomore Brandon Taylor, who averaged 5.3 points and 3.3 rebounds last season, seems like a solid bet to be a starter and 6-foot-9 sophomore Donovan Jack, who returns from a stress fracture, started alongside Travis and Taylor during a recent three-game tour in Belgium, England and France.
Bottom Line: It may not show up in the standings, but Penn State is slowly building a competitive program and the return of Frazier should make a major difference. In Frazier's absence last season, Newbill took on the bulk of his responsibilities, so it will be interesting to watch how those two play together as both rely on having the ball to be effective. If Chambers can get another reliable frontcourt option to emerge alongside the hard-nosed Travis, Penn State has a chance to win its share of home conference games and become more dangerous as the season moves along.
Quotable: "We made strides over the last two years in how we're playing, never giving up, playing at a high level. We had a lot of injuries last year and played a lot of walk-ons, and those kids went after it. They gave it their all. I think people in the Big 10 realize when they play Penn State, they're going to be in a battle. The vision for the program is to be a consistent NCAA tournament team and to be in the top six of the Big 10 on a yearly basis." – Chambers to the CBS affiliate in Philadelphia.
Filed to: 2013-2014 Big Ten preview, Penn State Nittany Lions
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The heat and humidity of summer can take its toll on your body. Dr Sneh Thadani tells us about skin care to beat the summer.
Summers can be severe. The skin feels the heat too. Proper care needs to be taken for it to radiate even when the temperatures rise. Dr. Thadani guides us by giving us some useful pointers. Read on..
Excess heat increases sweat production and the humidity hinders its ability to evaporate away from the skin. This means more oil is available to clog pores which can exacerbate acne. Also, extreme heat and humidity can facilitate bacterial infections such as impetigo and fungal infections like athlete's footor intertrigo, which are rashes seen in body folds. This is that time of the year when a lot of patients who battle those conditions become very uncomfortable.
Nothing is more important than wearing sunscreen (ideally, spf 30) every day. Many dermatologists even recommend layering sunscreens with a chemical blocker first followed by a physical blocking sunscreen which contains zinc and/or titanium. This way the sun's rays are primarily reflected away, but what does get through is then absorbed by the chemical sun-screen beneath.
• Blot sweat from your skin with a clean towel or cloth. wiping sweat off can irritate your skin, which can lead to a breakout.
• Wash sweaty clothes, headbands, towels, and hats before wearing them again.
• Shower and shampoo immediately after getting out of the pool, using fresh, clean water and a mild cleanser or body wash made for swimmers.
• Apply sunscreen before going outdoors, using one that offers broad-spectrum protection, spf 30+, and water resistance.
• Use a mild cleanser to wash your skin. soaps and body washes labeled "antibacterial" or "deodorant" can dry your skin.
• Take showers and baths in warm rather than hot water.
• Slather on a fragrance-free moisturizer after every shower and bath. moisturizer works by trapping water in your skin, so you'll need to apply it within 5 minutes of taking a shower or bath.
• Carry moisturizer with you, so you can apply it after washing your hands and when your skin feels dry.
• Turn up the thermostat if the air conditioning makes your home too dry.
• Steer clear of thick and heavy foundations.
Blocked sweat glands cause this because the sweat cannot get out, It builds up under your skin, causing a rash and tiny, itchy bumps. When the bumps burst and release sweat, many people feel a prickly sensation on their skin.
• Wear light-weight, loose-fitting clothes made of cotton.
• Exercise outdoors during the coolest parts of the day or move your workout indoors where you can be in air-conditioning.
• Try to keep your skin cool by using fans, cool showers, and air-conditioning when possible.
• Check your medication container to find out if it can cause an allergic reaction when you go out in the sun. Medications that can cause an allergic sun reaction include ketoprofen (found in some pain meds) and these antibiotics — tetracycline, doxycycline, and minocycline. If the medicine can cause a reaction, stay out of the sun.
• Protect your skin from the sun. You can do this by seeking shade, wearing sun-protective clothes, and applying sunscreen that offers broad spectrum protection, water resistance, and an SPF of 30 or more.
Read More Article From Dr Sneh Thadani:- Selfies not cool for skin!


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EconomyFinancialThese are the winners of the Great Desert Race
These are the winners of the Great Desert Race
The Great Desert Race, a sporting and tourist event organized by Grupo Expansión and Sabino's Events division, in conjunction with the Government of Sonora, concluded with Pablo Gil as the first place in the men's category of the 75K distance, followed by José Miguel Romero in second place, and Ernesto Rodríguez in third.
In the women's 75K absolute category, Molly Housman took first place, followed by the model and Brazilian Ultra Marathon runner, Sofía Berwig in second place, who along with Pablo Gil, served as the ambassadors of the Great Desert Race.
On October 22 and 23, the Great Desert Race took place in Puerto Peñasco, Sonora, named a World Heritage Site by UNESCO in 2013, to which hundreds of participants who ran were able to witness unique landscapes, where the beach and the desert meet.
The race had different modalities for the different categories of Trail runners: 10K, 25K, 50K and a 75K Ultra Trail. The event is considered one of the most challenging in America.
"We are going for the necessary editions to accredit this event of international stature as are other marathons of this category in the world", said the governor of the state of Sonora, Alfonso Durazo.
In the Ultra Trail Running experience, which brought together runners of more than 10 nationalities and from the Rarámuri and Tohono O'odham communities in the Trail Run modality and the amateur runner community, they demonstrated their high endurance capacity, both physical, as mental.
The participants crossed different ecosystems, between dunes, marshes and the beach to conclude the Ultra Trail 75K, which consisted of 75 kilometers covered in two days, 50 kilometers the first and 25 kilometers the second, with a night camping on the beach next to the sea. In addition to the Mega Desert Run 50K, Beach and Desert Run 25K and Fun Run 10K.
The event served as a showcase for some of the entity's main destinations, such as the Altar Desert, El Pinacate and the Sea of Cortez, places that were presented in the mini-documentary starring the ambassadors of the Great Desert Race, Pablo Gil and Sofia Bergwig.
The award ceremony for this great challenge was attended by Miguel Torruco Marqués, Secretary of Tourism of Mexico, Alfonso Durazo, Governor of Sonora, Célida López, Secretary of Tourism of Sonora, Jorge Pivac, Mayor of Puerto Peñasco and Oscar Castro, local deputy. .
"We are going to see each other here next year with an event that is going to double what happened today," assured Governor Alfonso Durazo.
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