text:
\section{Introduction}

Quantum mechanics, originally formulated in terms of Hermitian physical observables, has been extended in the past twenty years to include complex operators invariant under parity  and temporal  symmetry transformations. These  $\mathcal{PT}$-symmetric operators \cite{bender,bender01,bender02,bender03,bender04} also have a real spectrum under certain conditions as the $\mathcal{PT}$ symmetry requirement alone does not guarantee the existence of a real spectrum. Actually, the Hamiltonian $H(b)$ contains a free parameter $b$ that may be increased up to a critical value, above which the system undergoes a symmetry breaking phase transition. Below the critical value, all eigenvalues are real and, due to the symmetry $\mathcal{C}$, a properly defined $\mathcal{CPT}$ inner product may be defined to achieve unitary evolution \cite{bender05}. Furthermore, the $\mathcal{PT}$ symmetry is not broken as the eigenvectors of the $\mathcal{PT}$ operator are simultaneous eigenvectors of the Hamiltonian. On the other hand, above the critical value, the phase of the system is said to be spontaneously broken and the Hamiltonian no longer shares a common set of eigenvectors with the $\mathcal{PT}$ operator. Thus, the real eigenvalues give way to complex-conjugated pairs of eigenvalues.

These $\mathcal{PT}$-symmetric Hamiltonians are quite suitable to describe optical structures due to the similarity between the Schr\"odinger equation and the paraxial wave equation. The latter is obtained from Maxwell's relations and describes the propagation of a wave through a medium with balanced gain/loss. Thus, based on the association of the potential function with complex-valued refractive indices, it was shown recently that even non-$\mathcal{PT}$ operators may be used to represent classes of materials with arbitrary gain and loss \cite{yang}. Experimental evidence on systems that simulate $\mathcal{PT}$-symmetric behavior has been carried out in coupled waveguides \cite{makris2008beam,guo2009observation,ruter2010observation}, silicon photonic circuits \cite{feng2011nonreciprocal}, superconducting wires \cite{rubinstein2007bifurcation} and even in classical mechanical systems \cite{bender2013observation}, to cite a few.

The present work is mainly concerned with periodic photonic lattices. In this context, the propagation of wide monochromatic Gaussian beams has been studied in a $\mathcal{PT}$-symmetric periodic structure reporting double refraction and power oscillations which are not present in conservative Hermitian systems \cite{makris}. Also,
it has been demonstrated that the evolution of a paraxial wave under the two-beam approximation
diffracted by a $\mathcal{PT}$-symmetric optical lattice obeys a different sum rule for the intensity of the wave as compared to the Hermitian case \cite{Berry}. Actually, the optical properties of photonic lattices have also been associated with X-rays in crystals, in the sense that these Bragg oscillations have been previously identified with the Pendell\"osung effect in photonic crystals, such as in the 2D case \cite{Mocella}, and in opal 3D photonic crystals \cite{Agio}. Furthermore, experiments on the properties of microwave diffraction in periodic structures have been reported  in 2D artificial dielectric media \cite{Leo}, and in the optical regime in volume holographic gratings \cite{Calvo}. Bragg oscillations have been reported in $\mathcal{PT}$-symmetric photonic lattices \cite{Feynman Jr.17}.

However, the analyses developed in these works rely on the paraxial approximation limiting its applications to the particular case of optical systems for which all spatial scales are much larger than the wavelength of light. In a photonic crystal this condition is not satisfied, as the wavelength is of the order of the periodicity of the structure \cite{Ramakrishna}, and therefore a more accurate nonparaxial approach is highly desirable to unravel the meaning and accuracy of the paraxial Pendell\"osung effect. Recently, a nonparaxial approach to investigate the Pendell\"osung effect in a finite $\mathcal{PT}$-symmetric photonic lattice, via another route, has reported asymmetric changes in the intensity profile of the field as well as transparency changes \cite{bushuev}. It should also be mentioned that the propagation of electromagnetic waves through localized and periodic media under a nonparaxial regime has been recently considered by some authors \cite{malomed,jones}.

In this work, a theoretical analytic investigation on the propagation of a wide beam through a transversal periodic photonic lattice described by a
$\mathcal{PT}$-symmetric
electric permittivity is carried out. Considering
that our study is focused on the Bragg incidence angle, we use a two-waves model to investigate the power
exchange that occurs between a pair of resonant
Bragg modes, within three scenarios: (i) Hermitian Bragg scattering (optical Pendell\"osung effect), (ii) $\mathcal{PT}$-symmetric
Bragg scattering, below and above the symmetry breaking point, and (iii) Bragg scattering at the symmetry
breaking point. To this end, next section is
devoted to a general $n$-waves treatment while
in section III we focus on the simplified two-waves
version. Sections IV, V, and VI deal with the
particular cases described in (i), (ii),
and (iii) respectively.

\section{General theory}

The propagation of monochromatic electromagnetic
fields, $\mathbf{E}(\mathbf{r},t) = \text{Re}
[\mathbf{E}(\mathbf{r})\exp(-i\omega t)]$
and $\mathbf{H}(\mathbf{r},t) = \text{Re}[\mathbf{H}(\mathbf{r})
\exp(-i\omega t)]$,
with angular frequency $\omega$, is governed by Maxwell's
equations (in SI units),
\begin{align}
    \label{pair1}
    \begin{split}
    \nabla\times\mathbf{H}(\mathbf{r}) &= -i\omega\varepsilon_{\text{f}}\varepsilon(\mathbf{r})\mathbf{E}(\mathbf{r}),
    \\
    \nabla\times\mathbf{E}(\mathbf{r}) &= i\omega\mu_{\text{f}}\mathbf{H}(\mathbf{r}),
    \end{split}
\end{align}
where $\varepsilon(\mathbf{r}) = 1 + \chi(\mathbf{r})$ is the space-dependent isotropic electric
permittivity with $\chi$ being the linear electric susceptibility; $\varepsilon_{\text{f}}$ and $\mu_{\text{f}}$ represent the free-space
electric permittivity and magnetic permeability, respectively. Since our objective is to study Bragg resonance induced effects, we assume the dielectric function to be a one-dimensional periodic function of space, $\varepsilon(x+a) = \varepsilon(x)$, with period $a$, which may be written as a Fourier series
\begin{equation}
    \label{eps}
    \varepsilon(x) = \sum_{l \in \mathbb{Z}}\varepsilon_{l}e^{ig_{l}x},
\end{equation}
with $\varepsilon_{l}$ being the Fourier coefficient of the permittivity and $g_{l} = 2\pi l/a$ the one-dimensional reciprocal lattice vector. The first Brillouin zone of the lattice is thus located in the $k$-space domain $-\pi/a \leq k_{x} \leq \pi/a$. After isolating the electric field from the system of equations \eqref{pair1}, we obtain the differential equation satisfied by the electric field alone:
\begin{equation}
    \label{electric}
    \nabla\times\nabla\times\mathbf{E}(\mathbf{r}) = \frac{\omega^{2}}{c^{2}}\varepsilon(x)\mathbf{E}(\mathbf{r}),
\end{equation}
with $c=1/\sqrt{\varepsilon_{\text{f}}\mu_{\text{f}}}$ the vacuum speed of light. Next, we consider the electric field to be polarized in the $y$ direction (TE polarization mode) and propagating in the $(x,z)$ plane in such a way that its wavevector component parallel to the lattice variation is coupled to the edges of the Brillouin zones, i.e., it is Bragg-resonant with the structure
\begin{equation}
    \label{efieldspec}
    \mathbf{E}(x,z) = \hat{y}\sum_{n \in \mathbb{Z}}\psi_{n}(z)e^{ \frac{in\pi x}{a} },
\end{equation}
where $\psi_{n}(z)$ is the spectral amplitude of the electric field at a distance $z$ and $\mathbb{Z}$ is the set of integers. The magnetic field is derived from the electric field and is given by
\begin{equation}
    \mathbf{H}(x,z) = \frac{1}{i\omega\mu_{\text{f}}}\sum_{n\in\mathbb{Z}}\left[ \hat{z}\psi_{n}(z)\frac{i n \pi}{a} - \hat{x}\frac{d\psi_{n}(z)}{dz}\right]e^{ \frac{i n \pi x}{a}},
\end{equation}
where the divergence condition $\nabla\cdot\mathbf{H} = 0$ is satisfied, as can be easily verified. Notice that the choices for the polarization and the direction of the material periodicity are consistent with the constraint $\nabla\cdot\mathbf{D} = 0$ where $\mathbf{D} = \varepsilon_{\text{f}}\varepsilon(x)\mathbf{E}$ is the electric displacement vector. By substituting Equations \eqref{eps} and \eqref{efieldspec} into Equation \eqref{electric} we arrive at the following set of coupled linear second-order ordinary differential equations for the evolution of the spectral amplitudes $\psi_{n}(z)$
\begin{equation}
    \label{evolutionA}
    \frac{d^{2}\psi_{n}}{dz^{2}} =  \frac{\pi^{2}n^{2}}{a^{2}}\psi_{n} - \frac{\omega^{2}}{c^{2}}\sum_{l \in \mathbb{Z}}\varepsilon_{l}\psi_{n-2l}.
\end{equation}
Usually, in a given periodic function $\varepsilon(x)$ its Fourier coefficients $\varepsilon_{l}$ slowly decay as $l$ increases. This happens when the medium properties undergo abrupt changes as occurs
in a stack of two different materials $ABABAB...AB$, for example.
This is because higher frequencies are necessary in the sum \eqref{eps} to take into account the extremely rapid variations of the permittivity. However, in some very tractable cases, only three of these coefficients are nonzero. We will be mainly interested in the following $\mathcal{PT}$-symmetric permittivity
\begin{equation}
    \label{epsilon}
    \varepsilon(x) = \varepsilon_{0} + \varepsilon_{R}\cos\left( \frac{2\pi x}{a} \right) + i\varepsilon_{I}\sin\left( \frac{2\pi x}{a} \right),
\end{equation}
where $\varepsilon_{0}$, $\varepsilon_{R}$ and $\varepsilon_{I}$ are real positive numbers. It is clear from Equation \eqref{epsilon} that the only nonzero Fourier coefficients in the expansion \eqref{eps} are $\varepsilon_{0}$ and $\varepsilon_{\pm1}$ and are given in terms of $\varepsilon_{R}$ and $\varepsilon_{I}$ by $\varepsilon_{\pm1} = (\varepsilon_{R}\pm\varepsilon_{I})/2$. It should be pointed out that, since our interest is to describe the most common optical systems available, we require the real part of the relative permittivity to be greater than 1. For this to be satisfied, one must have $\varepsilon_{0} > 1 + \varepsilon_{R}$. With only three Fourier coefficients for the permittivity function, Equation \eqref{evolutionA} may now be rewritten as
\begin{equation}
    \label{principal}
    \frac{d^{2}\psi_{n}}{dz^{2}} = \alpha_{n}\psi_{n} - \varepsilon_{1}\psi_{n-2} - \varepsilon_{-1}\psi_{n+2},
\end{equation}
where $\alpha_{n} =  \pi^{2}n^{2}/a^{2} - \varepsilon_{0}$ and we have normalized $z\rightarrow \omega z/c$ and $a\rightarrow \omega a/c$. Equation \eqref{principal} is one of the main results of this paper and we now proceed to study its solutions in more detail.

\section{Two-waves model}

Let us consider that only two spectral modes, $\psi_{-1}(z)$ and $\psi_{1}(z)$, are coupled during propagation. If this is the case, Equation \eqref{principal} gives
\begin{align}
    \label{pair2}
    \begin{split}
    \frac{d^{2}\psi_{1}}{dz^{2}} = \alpha\psi_{1} - \varepsilon_{1}\psi_{-1},
    \\
    \frac{d^{2}\psi_{-1}}{dz^{2}} = \alpha\psi_{-1} - \varepsilon_{-1}\psi_{1},
    \end{split}
\end{align}
where $\alpha = \alpha_{\pm1} = 1 - \varepsilon_{0}$ and we have chosen $a = \pi$ without loss of generality. We solve this system by first writing it in standard form $(d/dz)\mathbf{\Psi} = \mathbf{A}\cdot\mathbf{\Psi}$. Explicitly, the matrices $\mathbf{\Psi}$ and $\mathbf{A}$ are given by
\begin{equation}
\label{system2}
\frac{d}{dz}
    \begin{bmatrix}
    \psi_{-1} \\
    \phi_{-1} \\
    \psi_{1} \\
    \phi_{1}
    \end{bmatrix}
    =
    \begin{bmatrix}
    0 & 1 & 0 & 0\\
    \alpha & 0 & -\varepsilon_{-1} & 0 \\
    0 & 0 & 0 & 1 \\
    -\varepsilon_{1} & 0 & \alpha & 0
    \end{bmatrix}
    \begin{bmatrix}
    \psi_{-1} \\
    \phi_{-1} \\
    \psi_{1} \\
    \phi_{1}
    \end{bmatrix},
\end{equation}
where $\phi_{\pm1} = d\psi_{\pm1}/dz$. We now proceed in the standard way of calculating its eigenvalues $r_{j}$ by using $\text{det}(r\mathbf{I}-\mathbf{A})=0$, which gives the fourth-degree characteristic polynomial $r^{4} - 2\alpha r^{2} + (\alpha^{2} - \varepsilon_{1}\varepsilon_{-1}) = 0$. The four eigenvalues are given by
\begin{align}
    \label{eigen}
    \begin{split}
        r_{1} &= -\sqrt{1-\varepsilon_{0} - \frac{1}{2}\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}},\\
        r_{2} &= +\sqrt{1-\varepsilon_{0} - \frac{1}{2}\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}},\\
        r_{3} &= -\sqrt{1-\varepsilon_{0} + \frac{1}{2}\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}},\\
        r_{4} &= +\sqrt{1-\varepsilon_{0} + \frac{1}{2}\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}.\\
    \end{split}
\end{align}
Figure \ref{complexplane} depicts the dynamics of the eigenvalues \eqref{eigen} as $\varepsilon_{I}$ increases from zero to 1.5 with the values of $\varepsilon_{R} = 1$ and $\varepsilon_{0} = 3$ fixed. If $\varepsilon_{I} = 0$, four distinct pure imaginary
numbers are shown in part (a) of Figure \ref{complexplane} corresponding to $r = \pm\sqrt{-2\pm1/2}$. On the other hand, when the loss present in the complex
permittivity is balanced by the gain, $\varepsilon_{I} = \varepsilon_{R} = 1$, two eigenvalues collide at $r = \pm i\sqrt{2}$ giving rise to a system of two eigenvalues
with multiplicity two. As we will show below, this drastically alters the
dynamics
of the propagating waves. When $\varepsilon_{I} > 1$, the four
eigenvalues become
distinct once more with nonzero real
parts. There are, therefore,
three different behaviors of the field evolution depending
on the value of $\varepsilon_{I}$ and
we will study each case in detail.

\begin{figure}
\includegraphics[width=0.5
\textwidth]{eigen.eps}
\centering
\caption{Real and imaginary parts of the eigenvalues below
(left panel), at (middle panel), and above the critical point. There
are four eigenvalues before they collide at the critical point where they merge
into two eigenvalues, and give way to a complex conjugated pair. In this figure, $\varepsilon_{R} = 1$ and $\varepsilon_{0} = 3$.}
\label{complexplane}
\end{figure}

The eigenvectors corresponding to the eigenvalues \eqref{eigen} are given by
\begin{align}
\label{eigenvec}
\begin{split}
    \mathbf{u}_{1} =
        \begin{bmatrix}
            \frac{-\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}{(\varepsilon_{R}+\varepsilon_{I})\sqrt{1-\varepsilon_{0} - \frac{1}{2}\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}} \\
            \frac{\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}{\varepsilon_{R}+\varepsilon_{I}} \\
            -\frac{1}{\sqrt{1-\varepsilon_{0} - \frac{1}{2}\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}} \\
            1\\
        \end{bmatrix},
\\
    \mathbf{u}_{2} =
        \begin{bmatrix}
            \frac{\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}{(\varepsilon_{R}+\varepsilon_{I})\sqrt{1-\varepsilon_{0} - \frac{1}{2}\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}} \\
            \frac{\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}{\varepsilon_{R}+\varepsilon_{I}} \\
            \frac{1}{\sqrt{1-\varepsilon_{0} - \frac{1}{2}\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}} \\
            1\\
        \end{bmatrix},
\\
    \mathbf{u}_{3} =
        \begin{bmatrix}
            \frac{\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}{(\varepsilon_{R}+\varepsilon_{I})\sqrt{1-\varepsilon_{0} + \frac{1}{2}\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}} \\
            \frac{-\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}{\varepsilon_{R}+\varepsilon_{I}} \\
            -\frac{1}{\sqrt{1-\varepsilon_{0} + \frac{1}{2}\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}} \\
            1\\
        \end{bmatrix},
\\
    \mathbf{u}_{4} =
        \begin{bmatrix}
            \frac{-\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}{(\varepsilon_{R}+\varepsilon_{I})\sqrt{1-\varepsilon_{0} + \frac{1}{2}\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}} \\
            \frac{-\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}{\varepsilon_{R}+\varepsilon_{I}} \\
            \frac{1}{\sqrt{1-\varepsilon_{0} + \frac{1}{2}\sqrt{\varepsilon_{R}^{2}-\varepsilon_{I}^{2}}}} \\
            1\\
        \end{bmatrix},

\end{split}
\end{align}
such that $\mathbf{A}\cdot\mathbf{u}_{j} = r_{j}\mathbf{u}_{j}$ for $j = 1,2,3,4$. To verify that the set of eigenvectors \eqref{eigenvec} is linearly independent we construct the $4\times 4$ matrix $\mathbf{U} = [\mathbf{u}_{1}\hspace{0.1cm}\mathbf{u}_{2}\hspace{0.1cm}\mathbf{u}_{3}\hspace{0.1cm}\mathbf{u}_{4}]$ with the columns formed by the eigenvectors \eqref{eigenvec} and calculate its determinant as a function of $\varepsilon_{I}$ with $\varepsilon_{R} = 1$ and $\varepsilon_{0} = 3$ fixed. Figure \ref{det} shows that for every value of $\varepsilon_{I} \neq 1$ the determinant is nonzero and, therefore, the set \eqref{eigenvec} is linearly independent. The particular case where $\varepsilon_{I} = 1$ will be treated separately later. Note also that this corresponds to the situation in Figure \ref{complexplane} where the eigenvalues collide. The general solution of the system \eqref{system2} is given by \cite{brauer}
\begin{equation}
\label{general}
    \mathbf{\Psi}(z) = c_{1}e^{r_{1}z}\mathbf{u}_{1} + c_{2}e^{r_{2}z}\mathbf{u}_{2} + c_{3}e^{r_{3}z}\mathbf{u}_{3} + c_{4}e^{r_{4}z}\mathbf{u}_{4},
\end{equation}
where $c_{j}$ are arbitrary constants determined by the initial conditions.
In order to write the $c_{j}$'s in terms of $\psi_{j}(0)$ and
$\phi_{j}(0)$ it is necessary to inspect Equation \eqref{general}
at $z = 0$. By using the matrix $\mathbf{U}$ and considering the
column vector $\mathbf{C} = [c_{1}\hspace{0.1cm}c_{2}\hspace{0.1cm}c_{3}\hspace{0.1cm}c_{4}]^{T}$,
where $T$ is the transpose operation, one may write $\mathbf{\Psi}(0) = \mathbf{U}\cdot\mathbf{C}$ and, after calculating the
inverse of $\mathbf{U}$, the constants $c_{j}$'s may be
written as a function of $\mathbf{\Psi}(0)$: $\mathbf{C} = \mathbf{U}^{-1}\cdot\mathbf{\Psi}(0)$. This will give us the
general solution for $\varepsilon_{I} \neq \varepsilon_{R}$
in terms of the initial conditions.

\begin{figure}[ht]
\includegraphics[width=0.25\textwidth]{det.eps}
\centering
\caption{Determinant of the matrix $\mathbf{U}$ as a function of
$\varepsilon_{I}$, with $\varepsilon_{R} = 1$ and $\varepsilon_{0} = 3$ fixed.
Since the determinant is different from zero whenever $\varepsilon_{I} \neq 1$,
the set \eqref{eigenvec} is linearly independent provided we exclude this
particular value of $\varepsilon_{I}$. }
\label{det}
\end{figure}

\section{Hermitian Bragg oscillations (Optical Pendell\"osung effect)}

For comparison purposes with the paraxial approximation, let us begin considering the simplest case of a medium in the absence of gain or loss, with a real electric permittivity ($\varepsilon_{I} = 0$), so that the lattice is Hermitian. By borrowing a very useful
nomenclature from two-level atomic systems, we define the population inversion function as the difference between the spectral energy content in modes $\psi_{1}$ and $\psi_{-1}$: $W = |\psi_{1}(z)|^{2}-|\psi_{-1}(z)|^{2}$. We define $W_{1}$ to be the population inversion function whose initial spectral energy is fully concentrated within mode $\psi_{1}$, i.e., $\{\psi_{1}(0),\psi_{-1}(0) \} = \{1,0\}$, and $W_{-1}$ to be the population inversion function whose initial spectral energy is fully within mode $\psi_{-1}$, i.e., $\{\psi_{1}(0), \psi_{-1}(0) \} = \{0,1\}$. After a lengthy but straightforward calculation,
it may be shown that under these circumstances, the population inversion functions are given by
\begin{equation}
W_{\pm1} = \pm\cos(\gamma_{-}z)\cos(\gamma_{+}z),
\end{equation}
which are symmetric, as expected, and
\begin{equation}
\gamma_{\pm} = \text{Im}\left(\sqrt{1-\varepsilon_{0} \pm \frac{\varepsilon_{R}}{2}}\right).
\end{equation}

\begin{figure}[h]
\includegraphics[width=0.40\textwidth]
{population_inversion_e_i_0.eps}
\centering
\caption{Evolution of the population inversion functions $W_{1}$ (continuous line) and $W_{-1}$ (dotted line) for (a) $\varepsilon_{0} = 3$, (b) $\varepsilon_{0} = 5$ and (c) $\varepsilon_{0} = 7$ with $\varepsilon_{R}= 1$ and $\varepsilon_{I} = 0$.}
\label{population_inversion_e_i_0_fig}
\end{figure}
Figure \ref{population_inversion_e_i_0_fig} illustrates the population inversion for three values of $\varepsilon_{0}$ with
$\varepsilon_{R}=1$. First thing we note is that it is a conservative process, as the sum of the power contained in the the resonant Bragg modes is always equals to the input power. Compared to the paraxial case \cite{Feynman Jr.17}, the oscillations exhibit a richer structure. It is clear that two superposed oscillations occur: the envelope, with a much longer spatial period, modulating the phase-like oscillation. The resulting motion is quasi-harmonic in the sense that the envelope amplitude and phase are not exactly constant, although their variation is negligible compared to the faster oscillation. As $\varepsilon_{0}$ increases, the period of the phase oscillations decreases while the modulation cycle increases. This beating behavior is better illustrated by finding the spatial periods of these oscillations and they are given, respectively, by
\begin{equation}
    \Lambda_{\text{p,e}} = \frac{2\pi}{\gamma_{-}\pm\gamma_{+}}
\end{equation}
where $\Lambda_{\text{p}}$ ($\Lambda_{\text{e}}$) stands for the shorter (larger) phase- (envelope-)like oscillation periods. The real part of the electric field $\mathbf{E}(x,z)$ is illustrated in Figure \ref{eletric_field_e_i_0_fig} for $\varepsilon_{0}=3$ and $\varepsilon_{R}=1$. Both initial conditions lead to exactly the same interference pattern, meaning that there is no preferential spatial mode for which energy flows, that is, the energy is shared equally by both modes, and the sum of the power within each mode is equals to the input power, as expected for unitary evolution. The interference pattern obtained in either case, exhibit a transversal variation of contrast following the permittivity function. Minimum values of the permittivity
lead to lower contrast so that in these regions the pattern become dim.

\begin{figure}[h]
\includegraphics[width=0.40\textwidth]
{eletric_field_e_i_0.eps}
\caption{Spatial evolution of the
real part of the electric field
in nonparaxial electromagnetic
Hermitian system for (a) $\left\{\psi_{1}(0),\psi_{-1}(0)
\right\}=\left\{1,0\right\}$
and (b) $\left\{\psi_{1}(0),\psi_{-1}(0)\right\}=\left\{0,1\right\}$
with $\varepsilon_{0} = 3$ and $\varepsilon_{R} = 1$. The black lines in both panels represent the Hermitian electric permittivity with the upper axes indicating its values.}
\label{eletric_field_e_i_0_fig}
\end{figure}

\section{$\mathcal{PT}$-Symmetric Bragg oscillations with $\varepsilon_{I}\neq1$}

In the next two sections we consider systems for which the electric permittivity has a non-zero imaginary part. Let us begin with
the system below the symmetry breaking point, i.e., $0\leq\varepsilon_{I}\leq1$. The population inversion functions in this case are given by
\begin{multline}
W_{-1}=\frac{1-\beta^2}{4\beta^2}\cos^2(\gamma'_{-}z)+
\frac{1-\beta^2}{4\beta^2}\cos^2(\gamma'_{+}z)\\
-\frac{1+\beta^2}{2\beta^2}\cos(\gamma'_{-}z)\cos(\gamma'_{+}z)
\end{multline}
and
\begin{multline}
W_{1}=\frac{1-\beta^2}{4}\cos^2(\gamma'_{-}z)+\frac{1-\beta^2}{4}
\cos^2(\gamma'_{+}z)\\
+\frac{1+\beta^2}{2}\cos(\gamma'_{-}z)\cos(\gamma'_{+}z),
\end{multline}
where
\begin{equation}
\beta=\frac{\sqrt{\varepsilon^2_{R}-\varepsilon^2_{I}}}
{\varepsilon_{R}+\varepsilon_{I}}
\end{equation}
and
\begin{equation}
\gamma'_{\pm}=\text{Im}\left(\sqrt{1-\varepsilon_{0}\pm\frac{1}{2}
\sqrt{\varepsilon^2_{R}-\varepsilon^2_{I}}}\right).
\end{equation}
\begin{figure}[h]
\includegraphics[width=0.40\textwidth]
{population_inversion_e_i_less_1.eps}
\centering
\caption{Evolution of the population inversion functions $W_{1}$ (continuous line) and $W_{-1}$ (dotted line) for (a) $\varepsilon_{0} = 3$, (b) $\varepsilon_{0} = 5$ and (c) $\varepsilon_{0} = 7$ with $\varepsilon_{R}= 1$ and $\varepsilon_{I} = 0.5$.}
\label{population_inversion_e_i_less_1_fig}
\end{figure}
Figure \ref{population_inversion_e_i_less_1_fig} illustrates the population inversion functions for three values of $\varepsilon_{0}$ while $\varepsilon_{R}$ is fixed at 1. When $\varepsilon_{I}\neq0$ the symmetric behavior of the population inversion functions exhibited by the Hermitian case no longer exists and this feature is clearly shown in Figure \ref{population_inversion_e_i_less_1_fig}: $W_{-1}$ now oscillates with an amplitude larger than $W_{1}$ during most part of the propagation and, in fact, as $\varepsilon_{0}$ increases it can be seen that the oscillatory behavior of $W_{-1}$ becomes much more evident than that for $W_{1}$, which oscillates with a very small amplitude compared to the amplitude of $W_{-1}$. Phase-like and envelope-like oscillations are still present below the symmetry breaking point, and with the same beating behavior as before, with some differences though. The spatial periods are now given by
\begin{equation}
\Lambda'_{\text{p}}=\frac{2\pi}{2\gamma'_{-}}
\end{equation}
and
\begin{equation}
\Lambda'_{\text{e}}=\frac{2\pi}{\gamma'_{-}-\gamma'_{+}}.
\end{equation}
Comparing to the Hermitian case, the phase-like spatial periods become shorter while the envelope ones become longer. Another feature when the system is below the symmetry breaking point is a non-zero average value for the population inversion functions reflecting the fact that energy is not shared equally by both modes. By noting that the cosine square function and the product of two cosine functions (with different arguments) give average values equal to $1/2$ and zero, respectively, over one complete oscillation, the population inversion averages are given by
\begin{equation}
\langle W_{\pm1} \rangle = \frac{\varepsilon_{I}}
{2(\varepsilon_{R}\pm
\varepsilon_{I})}.
\end{equation}
These averages are illustrated in Figure \ref{average_W_fig} (note a diverging behavior in $W_{-1}$ as $\varepsilon_{I} \rightarrow  1$). Using the same values of $\varepsilon_{R}$ and $\varepsilon_{I}$ as in Figure \ref{population_inversion_e_i_less_1_fig}, one may obtain $\langle W_{1} \rangle \approx 0.16$ and $\langle W_{-1} \rangle \approx 0.5$.
\begin{figure}[h]
\includegraphics[width=0.35\textwidth]
{average_W.eps}
\centering
\caption{Population inversion averages $\langle W_{1} \rangle$ (continuous line) and $\langle W_{-1} \rangle$ (dashed line). Note the Hermitian case ($\varepsilon_{I}=0$) where both averages are zero).}
\label{average_W_fig}
\end{figure}
These values for the population inversion averages reflects the fact that there is a privileged mode in the sense that irrespective of the initial condition the spectral energy seems to flow to a particular mode, $\psi_{1}$. More specifically, choosing the spectral energy input at mode $\psi_{1}$, what happens next is that the energy oscillates to and from $\psi_{-1}$ with a quite small amplitude. Furthermore, considering mode $\psi_{-1}$ as the input, the energy transfer to the privileged $\psi_{1}$ mode is enhanced, in the sense that the overall picture is the same, except that now, the amplitude in mode $\psi_{1}$ is much larger than in mode $\psi_{-1}$. This unbalanced energy distribution is clearly seen to diverge at the symmetry breaking point in Figure \ref{average_W_fig}.

Let us now turn to the spatial evolution
of the real part of the electric field $\mathbf{E}(x,z)$, which is illustrated
in Figure \ref{eletric_field_e_i_less_1_fig}
for $\varepsilon_{0} = 3, \varepsilon_{R} = 1$, and $\varepsilon_{I} = 0.5$. This spatial
pattern reflects the dynamics demonstrated
by the population inversion functions
in Figure
\ref{population_inversion_e_i_less_1_fig}. Like the Hermitian case, the transverse
interference pattern is composed by cycles of bright and dark fringes of interference separated by smaller cycles of low contrast fringes. But now, as the maximum value attained by the envelope amplitude of the population inversion function also varies, low contrast regions appears periodically in the propagation direction. These regions correspond to locations where the energy content is minimum and thus the periodical pattern is almost gone, and one may see them in Figure \ref{eletric_field_e_i_less_1_fig} as blurred sections along both the propagation and transverse direction.
\begin{figure}[h]
\includegraphics[width=0.40\textwidth]{eletric_field_e_i_less_1.eps}
\caption{Spatial evolution of the real part of the electric field below the symmetry breaking point for (a) $\left\{\psi_{1}(0),\psi_{-1}(0)\right\}= \left\{1,0\right\}$ and (b) $\left\{\psi_{1}(0),\psi_{-1}(0)\right\}= \left\{0,1\right\}$ with $\varepsilon_{0} = 3$, $\varepsilon_{R} = 1$ and $\varepsilon_{I} = 0.5$. The black lines in both panels represent the real (continuous line) and imaginary (dashed line) parts of the electric permittivity and the dotted line separates the regions of gain and loss. The upper axes indicate few values of the permittivity.}
\label{eletric_field_e_i_less_1_fig}
\end{figure}
Let us now investigate the system behavior above the symmetry breaking point, that is, for $\varepsilon_{I}>1$. In this case, the eigenvalues of the matrix $\textbf{A}$ have both real and imaginary parts (Figure \ref{complexplane}) revealing an entirely different evolution from the previous ones, found in the last section. The population inversion functions are now given by the expressions
\begin{widetext}
\begin{multline} \label{eq26}
        W_{-1}  = \frac{1-\tilde{\beta}^2}{4\tilde{\beta}^2}[\sinh^{2}(\tilde{\gamma}_{-}z) + \cos^{2}(\tilde{\gamma}_{-}'z)] + \frac{1-\tilde{\beta}^2}{4\tilde{\beta}^2}[\sinh^{2}(\tilde{\gamma}_{+}z) + \cos^{2}(\tilde{\gamma}_{+}'z)] \\
         - \frac{1+\tilde{\beta}^2}{2\tilde{\beta}^2}\left[  \cosh(\tilde{\gamma}_{-}z)\cosh(\tilde{\gamma}_{+}z)\cos(\tilde{\gamma}_{-}'z)\cos(\tilde{\gamma}_{+}'z) + \sinh(\tilde{\gamma}_{-}z)\sinh(\tilde{\gamma}_{+}z)\sin(\tilde{\gamma}_{-}'z)\sin(\tilde{\gamma}_{+}'z) \right]
\end{multline}
and
\begin{multline} \label{eq27}
        W_{1}  = \frac{1-\tilde{\beta}^2}{4}[\sinh^{2}(\tilde{\gamma}_{-}z) + \cos^{2}(\tilde{\gamma}_{-}'z)] + \frac{1-\tilde{\beta}^2}{4}[\sinh^{2}(\tilde{\gamma}_{+}z) + \cos^{2}(\tilde{\gamma}_{+}'z)] \\
         + \frac{1+\tilde{\beta}^2}{2}\left[  \cosh(\tilde{\gamma}_{-}z)\cosh(\tilde{\gamma}_{+}z)\cos(\tilde{\gamma}_{-}'z)\cos(\tilde{\gamma}_{+}'z)  + \sinh(\tilde{\gamma}_{-}z)\sinh(\tilde{\gamma}_{+}z)\sin(\tilde{\gamma}_{-}'z)\sin(\tilde{\gamma}_{+}'z) \right],
\end{multline}
\end{widetext}
where
\begin{equation}
    \tilde{\beta} = \frac{\sqrt{\varepsilon_{I}^2-\varepsilon_{R}^2}}{\varepsilon_{R}+\varepsilon_{I}},
\end{equation}
\begin{equation}
    \tilde{\gamma}_{\pm} = \text{Re}\left( \sqrt{1-\varepsilon_{0} \pm\frac{i}{2}\sqrt{\varepsilon_{I}^2-\varepsilon_{R}^2}} \right)
\end{equation}
and
\begin{equation}
    \tilde{\gamma}_{\pm}' = \text{Im}\left( \sqrt{1-\varepsilon_{0} \pm\frac{i}{2}\sqrt{\varepsilon_{I}^2-\varepsilon_{R}^2}} \right).
\end{equation}
Equations \eqref{eq26} and \eqref{eq27} clearly show an unbounded behavior due to the hyperbolic functions. Figure \ref{population_inversion_e_i_greater_1_fig} illustrates the population inversion functions on propagation, for three different values of $\varepsilon_{0}$ with $\varepsilon_{R}=1$ and $\varepsilon_{I}=1.5$.
\begin{figure}[h]
\includegraphics[width=0.40\textwidth]
{population_inversion_e_i_greater_1.eps}
\centering
\caption{Evolution of the population inversion functions $W_{1}$ (continuous line) and $W_{-1}$ (dotted line) for (a) $\varepsilon_{0} = 3$, (b) $\varepsilon_{0} = 5$ and (c) $\varepsilon_{0} = 7$ with $\varepsilon_{R}= 1$ and $\varepsilon_{I} = 1.5$.}
\label{population_inversion_e_i_greater_1_fig}
\end{figure}
Besides the asymmetry between $W_{1}$ and $W_{-1}$, in this case the oscillations persist, however now they exhibit an unbounded oscillatory behavior. At the very beginning of the propagation the amplitude oscillations are quite small but they increase quickly and grow indefinitely. As before, the oscillation amplitude grows faster by choosing the initial condition $\left\{\psi_{1}(0),\psi_{-1}(0)\right\}=\left\{0,1\right\}$, and also all the energy is quickly transferred to mode $\psi_{1}$, whatever initial condition one considers.

\begin{figure}[h]
\includegraphics[width=0.40\textwidth]
{eletric_field_e_i_greater_1.eps}
\caption{Spatial evolution of the real part of the electric field above the symmetry breaking point for (a) $\left\{\psi_{1}(0),\psi_{-1}(0)\right\}=\left\{1,0\right\}$ and (b) $\left\{\psi_{1}(0),\psi_{-1}(0)\right\}=\left\{0,1\right\}$
with $\varepsilon_{0} = 3$, $\varepsilon_{R} = 1$ and $\varepsilon_{I} = 1.5$. The black lines in both panels represent the real (continuous line) and imaginary (dashed line) parts of the electric permittivity and the dotted line separates the regions of gain and loss. The upper axes indicate few values of the permittivity.}
\label{eletric_field_e_i_greater_1_fig}
\end{figure}

Let us now turn to Figure \ref{eletric_field_e_i_greater_1_fig} where  the real part of the electric field $\mathbf{E}(x,z)$ is depicted for $\varepsilon_{0} = 3$, $\varepsilon_{R}=1$ and $\varepsilon_{I}=1.5$. As before, this pattern reflects the population inversion dynamics (Figure \ref{population_inversion_e_i_greater_1_fig}), where at the beginning of propagation, both initial conditions lead to a tiny electric field which grows considerably as propagation continues. The interference fringes begin to appear quite faintly but then, the fringe contrast increases intensely quite rapidly.

\section{$\mathcal{PT}$-SYMMETRIC BRAGG OSCILLATIONS AT THE
SYMMETRY BREAKING POINT ($\varepsilon_{I} = 1$)}

As we have seen above, in this case the eigenvectors  become degenerate with  double multiplicity so that the general solution is given by \cite{brauer}

\begin{equation}
\mathbf{\Psi}(z) = \sum_{j=1}^{k}e^{r_{j}z}\left[\sum_{p=0}^{n_{j}-1}
\frac{z^{p}}{p!}\left(\mathbf{A}-r_{j}\mathbf{I}
\right)^{p}\right]\cdot \mathbf{u}_{j},
\end{equation}
where $k$ is the number of eigenvectors $\mathbf{u}_j$, $n_j$ is the multiplicity of the respective eigenvalues and $\mathbf{I}$ is the $4\times4$ identity matrix. It can be shown that
\begin{equation}
\mathbf{\Psi}(z) = \begin{bmatrix}
\psi_{-1}(0)\cos\left(\tilde{\alpha}^{1/2}z\right) \\
-\tilde{\alpha}^{1/2}\psi_{-1}(0)\sin\left(\tilde{\alpha}^{1/2}z\right) \\
\psi_{1}(0)\cos\left(\tilde{\alpha}^{1/2}z\right)-\frac{\psi_{-1}(0)}{2\tilde{\alpha}^{1/2}}z\sin\left(\tilde{\alpha}^{1/2}z\right) \\
-\frac{\psi_{-1}(0)}{2}z\cos\left(\tilde{\alpha}^{1/2}z\right)-\frac{\psi_{-1}(0)+\tilde{\alpha}\psi_{1}(0)}{\tilde{\alpha}^{1/2}}\sin\left(\tilde{\alpha}^{1/2}z\right)\\
\end{bmatrix},
\end{equation}
where $\tilde{\alpha}=\varepsilon_{0}-1$. The population inversion functions for this case are given by
\begin{equation}
W_{-1}=\frac{1}{4\tilde{\alpha}}z^{2}\sin^{2}(\tilde{\alpha}^{1/2}z)-\cos^{2}(\tilde{\alpha}^{1/2}z)
\end{equation}
and
\begin{equation}
W_{1}=\cos^{2}(\tilde{\alpha}^{1/2}z).
\end{equation}
\begin{figure}[h]
\includegraphics[width=0.40\textwidth]
{population_inversion_e_i_equals_1.eps}
\centering
\caption{Evolution of the population inversion functions $W_{1}$ (insets) and $W_{-1}$ (dotted line) for (a) $\varepsilon_{0} = 3$, (b) $\varepsilon_{0} = 5$ and (c) $\varepsilon_{0} = 7$ with $\varepsilon_{R}= 1$ and $\varepsilon_{I} = 1$. The continuous line is the parabola $[4 (\varepsilon_0 -1)]^{-1} z^2.$}
\label{population_inversion_e_i_equals_1_fig}
\end{figure}
Figure \ref{population_inversion_e_i_equals_1_fig} illustrates the population inversion functions for three values of $\varepsilon_{0}$ while $\varepsilon_{R}$ is fixed at 1 . In contrast with the paraxial result for which $W_{1}=1$ constant \cite{Feynman Jr.17}, here at the symmetry breaking point we find no occurrence of mode trapping. Actually here, we find that $W_{1}$ oscillates harmonically transferring power to and from efficiently, while the amplitude of the $W_{-1}$ oscillation increases with $z^{2}$. Furthermore, as $\varepsilon_0$ increases, the growth of the amplitude of the oscillations becomes slower. Thus, at the symmetry breaking point, we find a quite asymmetric dynamics comparing $W_{-1}$ and $W_{1}$ and both dynamics are strikingly contrasting with the paraxial Bragg oscillations reported in \cite{Feynman Jr.17}.

\begin{figure}[h]
\includegraphics[width=0.40\textwidth]{eletric_field_e_i_equals_1.eps}
\caption{Spatial evolution of the real part of the electric field
at the symmetry breaking
point for (a) $\left\{\psi_{1}(0),\psi_{-1}(0)\right\}=\left\{1,0\right\}$
and (b) $\left\{\psi_{1}(0),\psi_{-1}(0)\right\}=\left\{0,1\right\}$
with $\varepsilon_{0} = 3$, $\varepsilon_{R} = 1$ and $\varepsilon_{I} = 1.0$.
The black lines in both panels represent the real (continuous line)
and imaginary (dashed line) parts of the electric permittivity and the dotted line separates
the regions of gain and loss. The upper axes indicate
few values of the permittivity.}
\label{eletric_field_e_i_equals_1_fig}
\end{figure}

Finally, let us turn to Figure \ref{eletric_field_e_i_equals_1_fig} where we present the
spatial distribution of the electric field at the symmetry breaking point, with parameters
$\varepsilon_{0} = 3$, $\varepsilon_{R} = 1$ and $\varepsilon_{I} = 1$. The asymmetric behavior
of the modes is clear. By choosing mode $\psi_{1}$ as the input, one obtains interference
fringes of constant contrast. On the other hand choosing mode $\psi_{-1}$ as the input,
the fringes appear with a linear increasing contrast along the
propagation direction.

\section{Conclusions}

Within the frame of Maxwell's equations, we have analyzed the process of energy transfer between a pair of resonant Bragg non-paraxial modes in $\mathcal{PT}$-symmetric photonic lattices. To this end we have used a simple two-waves analytic model to solve the wave equation, and so obtain the mode dynamics for the Hermitian lattice ($\varepsilon_I=0$) as well as for the complex one ($\varepsilon_I\neq 0$). In the Hermitian lattice, the population inversion functions exhibit a beat-like evolution profile, which is reflected in the diffraction pattern of the electric field, and the sum of the energy contained in each mode is always equals to the incident power. Furthermore, there is no asymmetry in the mode dynamics: one may choose mode $\psi_{1}$ or $\psi_{-1}$ as the input, to observe the same dynamics. This is a contrasting feature with the complex lattices which exhibit severe nonreciprocal unidirectional propagation. Furthermore, the sum of the mode energies is not equal to the input energy. Also, in this case a symmetry breaking phase transition occurs for a critical value of the imaginary part of the electric permittivity, at which four real eigenvalues collide and merge into a pair. Above the critical value each member of the pair gives way to a pair of complex values. Therefore, one finds dramatically different dynamics in each case. When the $\mathcal{PT}$ symmetry is not broken, one obtains population inversion oscillations with variable amplitude. At the critical point where the eigenvalues are degenerated, the beat-like pattern of the population inversion disappears and depending on which mode one chooses for the input, one may find harmonic oscillations ($\psi_{1}$) or oscillations whose envelope may grow indefinitely ($\psi_{-1}$).

Therefore, our results have shown that within the framework of non-Hermitian photonic lattices, which are well suited to describe periodic optical systems with balanced gain/loss profile, a variety of different beam dynamics is unveiled. Apart from their fundamental interest, our results suggest new routes for modal tailoring and control based on $\mathcal{PT}$-symmetric photonic lattices.

\section*{Acknowledgements}

The authors would like to acknowledge the Brazilian Agencies CNPq,
CAPES and FAPEAL for financial support.

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Reform and Modernity in Islam: The Philosophical, cultural and political discourses among Muslim reformers, IB Tauris, London, 2013.
2018, "Secular time and the poetics of re-enchantment", exhibition catalogue essay in eleven – Waqt al-Tagheer: Time of change, Ace Open gallery, 80-83.
2016, "Refugee Art Project – Borderless voices: Art from the Villawood detention centre', exhibition catalogue essay in Telling Tales: Excursions in Narrative Form, MCA Australia, 70-79.
2013, Eulogy for Ahmad Ali Jafari, Overland.
2013, "Progressive Islam and Quranic Hermeneutics: The Reification of religion and theories of religious experience", book chapter in Muslim Secular Democracy: Voices From Within (eds Lily Zubaidah Rahim & Naser Ghobadzadeh), Palgrave Macmillan.
2012, "Literary Romanticism and Islamic Modernity: The Case of Urdu Poetry", South Asia: Journal of South Asian Studies, January 2012, 1-22.
2011, "The Art of Exile", Literature and Aesthetics, Vol. 21, June 2011, 10-18.
2011, "Abu Ghraib in the Art of Ayad Alkadhi", Third Text: Critical Perspectives on Contemporary Art and Culture, Vol. 25, Issue 3, May 2011, 1-10.
2009, '"We are integrating you": Western Muslims and the Danish Cartoon Controversy', Art(e)fact Magazine 1, 23.
Here is a story on Radio National's Encounter program in which I participated. It explores themes from the 'Competing Visions in the Muslim world' symposium at the University of Sydney in 2013.
Here is my talk, titled 'Progressive Islam and Quranic Hermeneutics', which was delivered at the Spirited Voices from the Muslim World conference in the University of Sydney in 2011.
2017, Unstitching Fortress Europe (book review of Kate Evan's Threads from the refugee crisis), Overland.
2006, Review of 'Subaltern Studies XI: Community, Gender and Violence', P Chatterjee and P Jeganathan (eds), Asian Studies Review 30 (2), 204-206.
2005, Review of 'The 'Ulama of Farangi Mahal and Islamic Culture in South Asia', by Francis Robinson, Asian Studies Review 29 (3), 318-319.
August 2013, 'Towards a theory of Islamic Secularism', Competing Visions in the Muslim World: Rebuilding States and Reinvigorating Civil Society, University of Sydney.
December 2011, 'The Multiple Interpretations of Jihad', Imams, Academics and Muslim Youths Workshop, University of Western Sydney.
December 2011, 'The Art of Exile', Fear+Hope: Asylum Seekers in Australia, University of Sydney.
October 2011, 'The Art of Hazara Asylum Seekers in Australian Detention Centres', Freedom From Persecution? The Question of Afghanistan, University of Technology, Sydney.
September 2011, 'Philosophical Sufism, Muslim Reform and the Reification of Islam', Sufism for a New Age: Twenty-first Century Neo-Sufism, Cosmopolitan Piety and Traditionalist Responses, University of Western Sydney.
April 2011, 'Progressive Islam and Quranic Hermeneutics', Spirited Voices from the Muslim World, University of Sydney.
November 2010, ''We are not of the East or the West': Ameen Rihani and Muhammad Iqbal', Ameen Rihani International Conference: A Century of Engaging Humanism, University of Sydney.
July 2009, 'The Islamic Fundamentalist view of Women', paper presented at School of Languages and Cultures Research Day, University of Sydney.
September 2008, 'Islamic Reform and the Discourses of Modernity', History, Modernity and the Muslim world: Between Europe and Asia Conference, University of Sydney.
June 2006, 'Islamic modernism and the birth of the Salafiyya' paper presented at School of Languages and Cultures Research Day, University of Sydney.
September 2005, 'Islamic fundamentalism and the theory of Divine Sovereignty', paper presented at the School of Languages and Cultures Research Day, University of Sydney.


text:
Q: How should I handle undefined references with XML::Simple? I'm parsing a XML file with XML::Simple using these options
my $xml = XML::Simple->new(ForceArray => 1, KeyAttr => 1, KeepRoot => 1);

This is a sample xml document
<ip>
    <hostname>foo</hostname>
    <info>server</info>
    <soluton>N/A</solution>
    <cats>
        <cat>
            <title>Baz</title>
            <flags>0</flags>
        </cat>
        <cat><title>FooBar</title></cat>
    </cats>
</ip>
<ip>
    <info>client</info>
    <diagnosis>N/A</diagnosis>
    <cats>
        <cat><title>Foo</title></cat>
        <cat>
            <title>Bar</title>
            <update>Date</update>
        </cat>
    </cats>
</ip>

As you can see, not every node has the hostname attribute, which causes my script to die with an "Can't use an undefined value as an ARRAY reference" error when I try to get the hostname
   $nb = "@{ $_->{hostname} }";

There are several optional elements in the xml (more than a dozen). How should I handle that?
Should I check the existence of the element prior to the assignment?
if ( @{ $_->{hostname} ) { $nb = "@{ $_->{hostname} }" }
if ( @{ $_->{solution} ) { $s  = "@{ $_->{solution} }" }
if ( @{ $_->{diagnosis} ) {...}

Should I use an eval block?
eval { $nb = "@{ $_->{hostname} }" };

Maybe
eval {
    $nb = "@{ $_->{hostname} }";
    $s  = "@{ $_->{solution} }";
    $d  = "@{ $_->{diagnosis} }";
};

Is there a better way?

A: First at all, do you really need 'ForceArray' option enabled? Maybe it's better to use scalar values and check for arrays where they (possible) are?
Solutions for references to array that-may-be-undefined I use is:
my $string = join '', @{ $var || [] };

Which means "dereference variable or empty anonymous arrayref".
In your case it will be
$nb = join '', @{ $_->{hostname} || [] };

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WALCOM 2021 — 15th International Conference and Workshops on Algorithms and Computation
28 Feb 2021 - 02 Mar 2021 • Yangon, Myanmar
Organized in cooperation between University of Information Technology and Japan Advanced Institute of Science and Technology
The 15th International Conference and Workshop on Algorithms and Computation (WALCOM) is intended to provide an international forum for researchers working in the areas of algorithms and computation. WALCOM 2021 will be held during February 28 – March 2, 2021 at University of Information Technology, Yangon, Myanmar.
Approximation Algorithms, Algorithmic Graph Theory and Combinatorics, Combinatorial Algorithms, Combinatorial Optimization, Computational Biology, Computational Complexity, Computational Geometry, Discrete Geometry, Data Structures, Experimental Algorithm Methodologies, Graph Algorithms, Graph Drawing, Parallel and Distributed Algorithms, Parameterized Algorithms, Parameterized Complexity, Network Optimization, Online Algorithms, Randomized Algorithms, String Algorithms
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https://www.uit.edu.mm/walcom-2021/
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Plan a trip to the beach on a sunny day to walk on the sand, collect seashells and swim in the ocean. Make sure to pack the essentials for the day, including sunscreen lotion, nonperishable food and cold beverages. Make the beach a learning experience by bringing along books to look for certain types of sea animals or finding particular types of boats.
Summer is the perfect time for a camping trip, and you can use a camper or a tent for your overnight stays. There are parks that permit camping, but make sure to understand the rules that might include bringing in your own fuel for campfires. Planning a camping trip takes some time, but it can help your children to learn more about nature.
On an extremely hot day, you can still have fun by visiting a museum for the day. There are different types of museums, including museums that have paintings or museums that display science exhibits. You can also find aviation museums, historical museums and military museums.
A cool summer night is the best time to use a telescope in your backyard to look at the stars and the planets. If your home is near to numerous streetlights, then find a field away from the city where you can look at the nighttime sky. Have a book from the public library to help you find the constellations.
Children and adults love swimming in a relaxing pool at home, and the custom pools Ft. Worth, Texas families want are available from professional designers. Rather than using a community swimming pool, you can have one of these items customized to fit in your own backyard.
Don't plan all of your summer activities during one week because you and your children will also need some downtime for relaxing after a busy day.


text:
Objective methods
Subjective measure
Authors: Jérôme Ruel Nuno Trigueiros-Cunha Jean-Luc Puel
Contributors: Sam Irving
Hearing thresholds of an individual may be assessed by both objective and subjective methods. Objective methods are based on recordings of the electrical activity at various stages along the auditory pathway, from the cochlea to the cortex, and do not need the active participation of the individual. On the other hand, subjective methods need the co-operation of the individual being tested, because they rely on the subject's perception of and response to sound.
Auditory potentials reflect the electrical activity of the various neural pathways involved in the coding of sounds. Individual unitary potentials are recorded directly from a single cell or nerve fibre. Compound potentials, recorded at a distance from their origin, reflect the sum of the unit potentials.
The following are three examples of different types of potentials : note the temporal concordance beween the different recordings - at whichever level being measured, the first wave recorded with a latency of 1 ms reflects the auditory nerve action potential. Recording acoustic otoemissions is also an objective method, which specifically allows to check outer hair cells motile properties.
Unit action potentials (experimental technique not used in humans)
A micro-electrode (black arrow) records electrical activity from a single neurone in the auditory nerve. This auditory fibre responds to sound stimulation (red dot) by sending an action potential (AP) towards the brain. The latency between the sound stimulus (red arrow) and the the AP is about 1ms.
Recording of the compound cochlear nerve action potential at the Round Window.
This technique is used in human subjects, and is also known as electrocochleography.
A transtympanic electrode is placed on the promontory, near to the cochlear Round Window, and it records the compound action potential (CAP) of the auditory nerve, which is the synchronous activity of all the individual unit action potentials after sound stimulation (red point).
This potential is more complex than the single unit AP, but the first wave in this potential (N1) corresponds to the single unit AP in the preceding example. The amplitude of the CAP measured between N1-P1 is in the order of several dozen microvolts (µV). Successive responses are added and then averaged to eliminate background electrical noise.
Brainstem Auditory Evoked Potentials (BAEPs)
Surface electrodes placed on the skull allow recording of 5 main waves of electrical activity through the brainstem. Wave I, with a latency of 1 ms, reflects the auditory nerve potential ; waves II to V reflect processing centres in the auditory system.
These potentials are of very weak amplitude (< µV) and therefore averaging of many repeat stimulations (1000 to 2000) is required, in order to be able to differentiate them from background noise. After these early evoked potentials, the same skull electrodes can record later potentials from activity in the thalamocortex (middle latency and cortical auditory evoked responses).
Oto-acoustic emissions (OAEs)
They reflect the activity of outer hair cells, which are the most sensitive cells of the organ of Corti.
OAEs are very useful for screening newborns, but are also widely used as as an objective test in subjects of any age.
Subjective methods (Audiograms)
Tonal audiogram
Pure tone audiograms recorded in a normally-hearing subject over the course of their life. Each curve represents the average hearing loss as a function of age.
(see pathology / presbycusis)
Note: each one of these methods is further developed in specific pages
Last update: 27/12/2016 9:26 am


This morning was calm and quiet. My neighbors are either on vacation or are staying indoors because even though its only 9 o'clock in the morning its already 95 degrees outside. The pavement is literally hot enough to cook an egg and it's not even July. Welcome to the desert.
I eat a variety of things for breakfast depending on my mood. I am not one of those people who can eat the same thing every day. I need to keep it interesting and honestly, I think a varied diet is more healthy.
This morning I had avocado toast with an egg on top. I absolutely love this breakfast. It's so easy, healthy and satisfying. It really starts the day off right. I took the last two slices of gluten free bread out of the bag and popped them in the toaster oven.
Then, I took the end pieces, you know the ones no one ever wants to eat, and I stuck them in a bag in the freezer with several other end pieces and broken slices of gluten-free bread, bagels, and buns. Instead of throwing these unwanted pieces of bread away I save them for breadcrumbs!
I have only found Gluten Free breadcrumbs in a store once (WinCo Foods) and a bought them immediately. They are panko style and work great for anything that needs that crunchy coating, but they are so hard to find! I need a backup.
To make breadcrumbs with your saved bread break the frozen bread up into small pieces and place on a baking tray.
Toast in a toaster oven until the bread is crispy and dry. You will want to stir them about halfway through the cooking time. Cooking time can vary but it shouldn't take more than 10 minutes.
Put bread pieces into a food processor or blender. I use my magic bullet for this. Blend until you have coarse breadcrumbs.
If the breadcrumbs still feel moist you can toast them a bit more before using. Store in the freezer for later use.


text:
Secret Slasha – The Buffy the Vampire Slayer & Angel Slash Fanfiction Secret Santa Project
By Serena Kitt
For A Secret Slasha Dropout
"Of all the caves," Xander said, rubbing the sore spot on the back of his head. It figured, after years of training, years of saving the world (he'd lost count), and now, months of... okay, consoling himself over his ex-ex-fiancee by looking out for newly-minted Slayers, he'd get back into his original line of work. Demon magnet.
"Outside all the villages, in all the countries whose names I can almost pronounce without offending anyone," he continued, "had to be this one. Okay, bring it on. What do you got?" He threw down his stake, convinced the very tall menacing thing was much bigger, and therefore much less worried about death-by-stake-age, than a vampire. Everything has eyes, he joked to himself. This one, they even glow. He thought he should mention it.
"Why do you seek me, mortal?" said the more-menacing-than-a-vampire man (?) on the other end of the cave.
"I don't so much seek you," Xander started, "as I get chained by my ankle to this... stalagmite and drawn into a challenge. That's your first problem." Stalagmite, he was sure.
"Lies. You seek what only I can grant. Like the vampire."
"Mostly, I seek the way out of here," he said.
"What are you willing to give in return?" The fiend might have been raising an eyebrow, if he had them. Xander couldn't tell. He wasn't sure about this whole 'give in return' business, either. He had one less eye to offer than most people who stumbled into this place, maybe he could convince the demon to just throw him back.
"I do a mean Snoopy Dance," Xander offered. "And also, I have a proven track record on saving the girl-- uh, world-- and I'm fond of killing demons though I'm guessing that's not your thing... and here's the part where you tell me there's going to be some kind of test."
"A test? Granted. You have disturbed me, but you may choose what obstacle you face, to leave," he said, and gestured with... were those wings? This guy got scarier by the minute. See? This is why guys don't stop to ask for directions, Xander thought to himself. You go off the trail, stop in one village, guy follows you all the way to a cave, and you end up choosing which friend of the winged devil is going to send you wherever Sunnydale went.
A plume of smoke fanned out from behind the demon. It left Xander coughing and looking ridiculous for a few minutes. When he could see again, two things became apparent. One,
"Hey! I'm naked! No stake and I'm naked? And... still chained to the rock. Great, this is just a dream and I can go now. Anytime..." he almost believed it for a moment, then saw the light in front of him and felt the heat to go with it.
"Choose."
There was a man whose fists were on fire on the left... also naked, and come to think of it, not so bad other than the hands-on-fire part. It's got to be a long time before demons with hands-on-fire start looking good, Xander noticed. And to the right was--
"Spike?! You've got this all wrong, he's a--"
"Oh bollocks this is, you're the one's got it all wrong--" Spike started, then looked down to note that he too was naked. If this was part of the dream, it was definitely not going the way Xander planned. There was no naked Spike in his dreams. Except that one time. Okay, and that other time.
"I hate this dream," Xander said out loud. Spike looked at him a little harder on that one, then realized something.
"What-- say, are you naked? Oh this is definitely not part of the plan," Spike said. Appealing to the demon who smoked you all the way from wherever to get chosen, or not chosen, to let Xander out of the cave, was the brightest idea naked Spike ever had in any of Xander's dreams. "First that soul business, then the pirate captain over there, I know I didn't make any kind of devil's bargain for this," he went on.
"Choose," the demon said again, his voice reverberating through the cave and shaking some dust loose this time. The hands-on-fire guy still looked pretty much ready to go, especially considering the whole not-Spike factor, but then again fighting a bona fide demon guy, while naked, wasn't at all looking good to Xander.
"Have to say I pick Spike. Best out of three?" Xander joked. He was relieved. He'd either kill Spike-- finally, he'd never see that coming-- or he'd let him win, or they'd use the advantage of the vampires with souls' tendency to beat the big bad to get out of there together. At which point then Xander could kill Spike. Or at least run back to his Jeep and leave him by the side of the road.
"Not so fast, choose what? If you're here to find a way to kill Buffy, I got news for you, boy, this one's not an honest salesman," Spike said. He shook his head. "Right, then, what's the deal? Gotta get a renewal on the old soul, then? Knock off some poor unfortunate stumbles into this cave once a year? Easy enough, could at least unchain him and make it fun."
"Spike, we're going to fight," Xander whispered.
"Yeah, and I'm going to kill you and get on about my business. Lot of evil still in LA."
"The choice is made," the demon said, and the hands-on-fire guy looked a little disappointed. He winked-- he actually winked, what demon with hands-on-fire finds it necessary to be subtle-- at Xander and kind of sulked off. Then it was just Xander and Spike. Spike and Xander. By no means sitting in a tree, Xander reminded himself. Have to make that clear when he tells Willow about this. Something interrupted his revelrie, though, something else he hadn't expected.
"Looks like you're not sad to see him go," Spike smirked. He dropped his gaze down to Xander's crotch where, in another development that made this unlike other caves, he was getting an erection.
"Uh... this is magic! Evil, cock-raising magic," Xander shouted. "Everyone gets a little-- excited in the heat of battle. It's a living thing, you wouldn't understand," he said to Spike.
"Give me a chance," Spike said. "Nothing to be ashamed of, brought my own to the party." His hand fell to grasp his own, surprise--vampires have them-- growing cock and walked the few steps toward Xander.
"What's going on here? I trespass on the domain of unholy evil and you-- embarass me to death?"
"Don't think he wants us to fight, love," Spike said. "Just be happy you made the right choice."
A cartoon balloon that said, "Help." would have been appropriate for the face Xander made, and he was sure if he had two eyes, they'd be wider than they'd ever been. Spike put his free hand around the back of Xander's neck and kissed him, hard.
Vampire teeth. Moving down his neck. Much gentler than he expected. Was Spike going to bite him? Xander wasn't so sure now, whether it was magic or not. He was enjoying this too much. Maybe that was part of the magic?
"You know," he said against a gasp as Spike's hand and teeth moved across his shoulder, "I'm only enjoying this because there's magic involved."
"Mm hmm," Spike said, muffled against Xander's awkwardly crossed arms. "Then why," he said, crouching now in front of Xander, "am I having a right good time of it?"
Xander decided not to think on that one. And... that was Spike's mouth on his cock. Vampire teeth. Dangerously close to not being the best thing he'd ever felt. "Ah-- I'm... only enjoying this because you're a demon. It's this thing I have, for demons. Huh?"
Spike's tongue was busy doing things to Xander he didn't think vampires did. Not for Xander, anyway.
"You-- you better be right-- oh-- about getting me off, I mean, out of here," Xander said, shutting his eye and gripping the back of Spike's neck. That seemed to get him more interested, so he started running his fingers through Spike's hair. Because it was Spike. Sucking his cock. In a cave. In Cote d'Ivoire. To fulfill a pact with a demon...
"Sounds like you don't want to leave," Spike said between hasty breaths.
"Who said you could stop?" Xander's eye snapped open to look down at his new favorite champion. Spike went back to it. More enthusiastically this time. Either he'd done it before in his two-hundred odd years, or this wasn't as difficult as Xander thought it would be. Damn, he could have patched things up with Oz way quicker if he'd known that.
"Ow!" Spike said at the sharp pain of Xander squeezing his shoulder.
"No, no, I meant that was good," Xander clarified. Always give compliments. He made a mental note.
There were no more outcries from Spike, only a little more dust cracked loose when Xander shouted, shook the cave, with a shout as he came. He collapsed into Spike's arms-- into Spike's arms? and let himself stay there for a minute as he was sure Spike was laughing with him, not at him. Or laughing at something else entirely Spike-based.
"Chain's gone," Spike said. Xander glanced up at him. He hadn't seen Spike smile exactly like that before, probably because Spike had never smiled at him.
"This... come with the soul?" Xander asked. It wasn't the first thing he wanted to know. He was still interested in leaving the cave, leaving the village, possibly going back to the states where at least the demons could send in the mystery guests locally. But for the moment, he was looking forward to telling the hilarious story of how he got there to the one who had the courtesy to get him out.
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Secret Slasha 2001 | Secret Slasha 2002 | Secret Slasha 2003 | Secret Slasha 2004
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We are committed to providing personal, comprehensive and efficient service to your settlement administration process.
We are Arden Claims Service. An executive team with years of professional experience as arbitrators, judges, mediators, attorneys and accountants. We are committed to providing personal, comprehensive and efficient service to your settlement administration process.
The ACS team has come together to provide you with stellar service in claims administration. We bring a neutral perspective coupled with accounting and legal expertise to ensure every case is individually administered to the highest professional standard.
Martin F. Scheinman, Esq., is the Founder and Chairman of ACS. Marty created ACS to fill the obvious gap in claims administration services — a provider both plaintiff and defense counsel can agree upon. Marty has served as a full-time Arbitrator and Mediator since 1979. During his career, Marty has decided or helped resolve over 20,000 disputes. Marty is widely viewed as one of the busiest and most acceptable neutrals in the United States. His experience includes serving as an industry impartial chairman for several union and management associations covering over 50,000 employees, and as the permanent arbitrator in over 400 contracts in the private and public sector involving thousands of employees. Marty has mediated commercial and employment disputes involving cumulatively over $5 billion dollars.
Scheinman Arbitration and Mediation Services specializes in resolving labor/management disputes as well as commercial, consumer, ad employment matters.
Barry J. Peek, Esq., is the Chief Executive Officer of ACS. Barry's vision for ACS is to continue to offer the uniquely personalized service only a boutique claims administration provider can provide while continuing to enhance the company's product offerings. Barry came to ACS after serving as Co-Chair of the Labor Group of Meyer, Suozzi, English & Klein, P.C.
Angela Ferrante, Esq., is the Chief Operating Officer of ACS. Angela comes to ACS after serving as the Senior Vice President of New York Operations of a nationally recognized claims administration services company. In her past role, Angela was directly responsible for oversight and management of over 100 people.
Laurie Scheinman is the Chief Marketing Officer of ACS. Laurie has spent the past twenty years developing and marketing innovative businesses, including F.A.C.E. I.T Inc., a national psychological wellness program, along with the award-winning philanthropic lifestyle boutique, wit & whim. Laurie holds Masters Degrees in Psychology and Social Work from Columbia University.
William Varon is responsible for overseeing the day to day management of all of ACS's active matters. William is an accountant with a background in business operations including an emphasis on the utilization of technology to meet the fast-paced needs of clients and vendors.
Steve Ostrer is a Certified Public Accountant holding a Juris Doctor from Fordham University School of Law and an MBA from Cornell University Graduate School of Business and Public Administration.
Kate Tierney has managed office operations for the Scheinman companies for more than twelve years. She has coordinated the arbitration and mediation efforts of neutrals Scheinman and Peek and supervised staff activities relating to case administration.


text:
Q: JavaFX labels won't show up I am trying to practice with BorderPanes, which so far has been a nightmare. I have tried to get my label to just show up in the window with no avail. Any ideas?
Label arrayLabel = new Label("NUMBERS");
BorderPane.setAlignment(arrayLabel, Pos.TOP_CENTER);

TextField search = new TextField();
Button btn = new Button("search");
HBox searchbox = new HBox(2);
searchbox.getChildren().addAll(search, btn);
searchbox.setAlignment(Pos.CENTER);

BorderPane root = new BorderPane(arrayLabel);
root.setPrefSize(600, 600);
root.setCenter(searchbox);

A: A BorderPane can only have one node in any region. (That node, of course, could be a parent containing arbitrary numbers of other nodes.) The constructor taking a single parameter treats that parameter as the node to be displayed in the center.
So
BorderPane root = new BorderPane(arrayLabel);

is equivalent to
BorderPane root = new BorderPane();
root.setCenter(arrayLabel);

When you subsequently (immediately) then call
root.setCenter(searchbox);

the center node is replaced by searchbox, so arraylabel is no longer part of the BorderPane.
It's not really clear what you intend here: you are essentially trying to put two different UI components (arrayLabel and searchbox) into the same region of the same BorderPane. There's no information (provided either to us, or to the poor BorderPane who is trying to position these nodes) as to how you want these two components positioned relative to each other. What are you actually trying to achieve, in terms of how you want these laid out?


text:
Kate Bush Encyclopedia
Kate Bush Encyclopedia is free to use, but not to operate. Please consider making a small donation to help keep this website online.
Orgonon
Orgonon was the 175-acre (71 ha) home, laboratory and research center of the Austrian-born psychiatrist Wilhelm Reich (1897–1957). Located west of the town center of Rangeley, Maine, and north of Rangeley Lake, the property includes two major buildings and two cabins. Its main building, designed by James B. Bell and built for Reich in 1948, is listed on the National Register of Historic Places (as the Orgone Research Laboratory), and is a significant example of International Style architecture in the state. The name is a play on orgone energy, Reich's principal area of study in his later years.
The main building is the Orgone Energy Observatory, and is where Reich did his research and had his office and library. It is a fieldstone structure, two stories high, with a flat roof. The roughly-centered entry leads into a hallway, with Reich's laboratory on the right and a suite of rooms on the left that included a kitchen, bathrooms, and playroom for Reich's son. The upper level, accessed by stairs at the back of the hall, included a bathroom, office, and living quarters. The walls are finished in knotty pine throughout, with plywood ceilings and vinyl flooring.
The property includes two cabins, which are seasonally available for rental. "Bunchberry", the smaller of the two, has two bedrooms, while "Tamarack" has three. Both have kitchens, and are in secluded settings somewhat apart from the main buildings. Tamarack was used by the Reichs as a residence, and the doctor stipulated that it should be made available to needy children. The trust managing the property donates use of this cabin for four weeks every summer to needy families.
Orgonon is Reich's burial place, and is now open to the public as the Wilhelm Reich Museum. It is referred to in Kate's song Cloudbusting, usually misspelled as Organon.
Orgonon. Wikipedia, retrieved 31 August 2017.
Also in the Kate Bush Encyclopedia:
Garfath, David


The "rosetta" application has been updated to 4.04 for Windows platforms to address the Windows BOINC client 7.8.2 issues. This is a relatively recent version of the Rosetta software source and will eventually replace the "minirosetta" application. Please report issues/bugs in this thread.
Message 87558 - Posted: 24 Oct 2017, 5:45:29 UTC - in response to Message 87457.
This is a relatively recent version of the Rosetta software source and will eventually replace the "minirosetta" application.
There is a roadmap for this "eventually" replacement of app? When you'll abandon the 3.x code?
Message 87680 - Posted: 13 Nov 2017, 6:40:21 UTC - in response to Message 87558.
Message 87720 - Posted: 21 Nov 2017, 19:57:06 UTC - in response to Message 87680.
There's no specific road map. The 3.x versions are still producing "forward folding" results for validating designs successfully.


Look, first things first, you will not and I repeat, not……see everything on your first visit. Get that idea right out of your head. Say it with me "I will not see everything at Walt Disney World on my trip." This phrase will come in very handy the day you sleep in, or when Dumbo breaks down. Learn it, love it, Live it. We all know a Becky. Becky went for her first visit with her family and they did EVERYTHING. I'm really happy for Becky, but I can tell you they missed out on more than a few things to do. And that's ok!
The first step is to figure out how long you're going to want to go. There are many, many options awaiting you on a visit to Walt Disney World. Not only do you have 4 full Parks to enjoy, but you also have 2 Water Parks, the shops at Downtown Disney, and a slew of Resorts to meander through. Not to mention the other, non-Disney attractions that surround you. SeaWorld, Universal Orlando, Busch Gardens, Gatorland, the brand-spanking-new Legoland, Outlet Shopping, and dare I even mention it, The Holy Land Experience. WHEW!! Again, never going to see EVERYTHING in one visit.
I really recommend that if you going to do Disney, then keep it strictly Disney. Forget trying to pack it all together in 1 day of Parks and then perhaps renting a car to drive to the beach, you need to focus. I suggest that you take at LEAST 7 days. Sounds OUTRAGEOUS but if you're gonna do it, do it right. You have 4 Parks, they are not all the same in size and there will be lots, and I mean lots of walking involved. The Water Parks are so much fun as well, not to mention the 2 mini golf locations on property and Downtown Disney with shops and restaurants and Cirque Du Soleil- La Nouba. You see now what I am talking about. Plan to do 1 Park per day. Yes, it's great to park hop (the art of visiting more than 1 park in a day), but you may spend more time travelling than you do in the parks. I would perhaps throw in a Water Park or Downtown Disney in-between park days so that you're not overwhelmed with children (it will happen!) and people and characters and, well……Disney.
Have your parks, and sleep too!
Whichever Park you decide to start with, you have so much to do and only a finite amount of time to do it. You will want to ensure you get the most bang for your buck. If you plan on sleeping in on this vacation, don't worry, most of the Parks are at least open until 9 or 10 pm. There are also the wonderful days when Disney Resorts offer Extra Magic Hours (or tragic hours for those that work there!). These special hours offer you either an early entry into the Parks prior to the general public, or later hours that extend your fun well into the wee hours. You can grab a guide at your resort when you check-in that details what they are for the week. The best part of Extra Magic Hours is the incredible opportunity to go at your own pace and stretch your time in the parks.
You want a hint, start at the back of the Parks. I know there are those of you that disagree with this comment but if hundreds of guests are crowding the Park at the very same time you decided to go, where is everyone going to start? People with strollers can only move so quickly! So, make yourself look like a seasoned expert and grab a Park map when you get inside the gates and head to the back.
Please do yourself and the Disney Paramedics a favour: Keep drinking water to stay hydrated. Florida is generally a hot and humid place. Your going to be moving and sweating, using up your fluids. It's very easy to get dehydrated when it's 35 degrees Celsius (that's 95 for the Americans). Take a water bottle and skip the $3.00 Dasani. There are fountains at every bathroom, and there are tons of bathrooms.
Take these tips and set the right expectations for your vacation before you set off to the airport. You will be skipping your way through each day of your vacation.
Now, if you will excuse me, I have tickets for La Nouba at Downtown Disney and I hear it is REALLY GOOD!!
Back when I was a Cast Member at Walt Disney World, I had the amazing opportunity to take a backstage tour of The Haunted Mansion. Now this was no ordinary tour, as we got to walk the entire ride and even enter the famous ballroom. This tour is only allowed for Disney Cast Members due to the intimate nature as well as the insurance issues involved. We literally walked within inches of the ballroom dancer animatronics as they twirled around and around. The best part of this tour was learning about the hidden Jack Skellingtons throughout the ride.
During this Cast Member only version of The Haunted Mansion tour, we got the insiders details on the story behind the hidden Jacks. It seems that WDW wanted to get their own version of Haunted Mansion Holiday like the one at Disneyland, but after surveying guests and doing some research they discovered that while Disneyland's guests are mainly locals who can always pop back once the rider is open again, while Walt Disney World caters to a more worldwide guest mix who at best visit every couple of years, or at worst only once in a lifetime. As it requires a month or so to change out the sets for this holiday version of the ride, these once in a lifetime guests can't ride this famous attraction (and don't have the option to come back.) When Disney Imagineering needed to shut down the ride for some well needed maintenance and new effects installed, international guests were very angry when the ride went down for just a few weeks. Shutting down the ride for this long is not usual, but you must remember the ride is generally running nonstop for over 12 hours a day, 365 days a year! Disney realized they didn't want to disappoint guests or make them angry like that every, single year. They simply could not close a signature ride for a few weeks every year.
As a compromise to the disappointed attractions hosts, when The Haunted Mansion went down for refurbishment, Imagineering placed some hidden Jack Skellingtons within the ride. Now to be clear, these are in plain view of the guests on the ride, but almost impossible to spot if you have never seen them or don't have the luxury to walk the ride after hours. They are visible in photos, but as a courtesy to other guests you wouldn't want to impede on their experience by using the flash on your camera. There is really no way for a regular guest to see them. We weren't allowed to take any photos of the tour other than from the perspective of a guest, meaning in a Doom Buggy with the lights off. The next time you ride the Haunted Mansion you can play spot the Hidden Jacks!
1. Jack is on the book in the library flat on the floor to the right side of the Doom Buggy, in front of the table and to the left of the chair.
2. Located to the far right as you enter the attic scene. You almost need to turn backwards to five-o-clock to see a stuffed figure of Jack on a shelf.
3. To the left side of the Doom Buggy in the middle of the floor as you round the corner in the attic, it is the easiest to spot as it's illuminated from above. Jack is clearly visible on the book cover.
4. The fourth is really two that are to the hardest to see. Look right, about 3-o-clock and back pretty far as just as you are leaving the attic. It's a Jack Skellington snow-globe and Sally stuffed toy.
Another cool fact is that the floating Madame Leota in the séance room uses top-secret proprietary technology for the realistic facial projection (not kidding). So valuable to Disney that if the pressure sensitive mats along the ride path are triggered, it gets pulled to the ceiling using a wire it's attached to. This way no one can hop over the railing, steal it and sell it on eBay. Pretty cool!


text:
Q: How to inspect what data react table sends to filter function as argument? I was looking at filtering example from react table filter table records. I wanted to see the data structure received in the following filter function. But my console.log(.. not coming to browser console. How to check that? As per documentation, it should call the text function, but it is likely not calling.
function Table({ columns, data }) {
  const filterTypes = React.useMemo(
    () => ({
      // Add a new fuzzyTextFilterFn filter type.
      fuzzyText: fuzzyTextFilterFn,
      // Or, override the default text filter to use
      // "startWith"
      text: (rows, id, filterValue) => {
        console.log(rows);
        return rows.filter((row) => {
          const rowValue = row.values[id];
          return rowValue !== undefined
            ? String(rowValue)
                .toLowerCase()
                .startsWith(String(filterValue).toLowerCase())
            : true;
        });
      }
    }),
    []
  );

//.....

Example sandbox.

A: React's useMemo hook returns a memoized version of your callback function's return object. It doesn't do anything else. text function won't get executed so you won't see the console.log. Another point is you're giving useMemo a empty dependency list. This means your memoized object never gets updated and it'll be out-of-sync probably.


L-异亮氨酸 产品编号:JS002产品参数-----L-异亮氨酸 中文名称: L-异亮氨酸英文名称: L-Isoleucine分子式: C6H13NO2分子量: 131.
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24 livestreamed virtual hours in the (boring) life of an avatar.
The MOOC that launched our 3 websites: .Re/act, .Re/search, and .Re/cipes plus our Slack chat space, Practice Based Research in the Arts, from Leslie Hill & Helen Paris at Stanford / NovoEd, ran from 9 Oct – 11 Dec 2013. At it's end the Blueberry group decided to continue with once-a-month Google Hangouts. A few of us drifted off, others joined in, and Ciara rechristened our group Mixed Berry Shake.
I think that continuing the monthly meetups is a good idea, even though the attendence is sporatic, and people understandably come and go.
In time, I hope that more on-going collaboratibve teams are formed from within the group, and that a number of single project collaborations are tried as well.
It's been a great learning experience for me to meet you all, and the few things that we've done together, like ONE Night and the LACMA proposal have shown me the way to even better such collaborations in the future.
But I also understand how precious time is fro everyone, and that some may not see the same benefits I've seen. So perhaps a number of options, allowing to some to keep meeting regulatly, others to come and go as thier time and interests dictate and others to simply float away is a way to go.
For 2015, my New Year's resolution will be to go back and writing regular short essays for PBR and to look to find more ways for us to collaboarte from our differnt regions. I think there is something important going on here, even if it is still after one years, in its infancy. I hope that together we can find a way to make it grow.
And I do think another LACMA proposal is a good idea.
I know artists who believe that teaching is an unwise distraction from their work. That artists should focus on production, make, show, and sell work, and earn enough to support yourself.
I know artists who believe that sales are corrupting and that your career is better served by having an income from an activity like teaching, and they your art work isn't beholden to some revenue stream.
For sure both choices have legitimacy. Personally, I favor Choice #2.
I wonder if seeking funding for our work might not be the Magic Dust, the Glue, the Catalyst, we need. Christa has written about the power of deadlines, and getting someone somewhere to believe in your creativity enough to fund it can also be challenging and valuable.
In a busy world we're all challenged with focus and priorities. Collaborating on funded projects might give both internal and external legitimacy to our work. It might give us a chance to bring more of our PB-RITA classmates in on projects.
Michael has the LACMA Art+Technology grant proposal, and Christa's threatening to look some up in the next week. What if we tried to identify a slate of 6 grants to apply for in 2015? And let that work, applying and hopefully executing these projects, be the focus of our Hangouts?
Michael's multi-city interaction projects seem idea in some ways. And Rebecca's City project seems like it or aspects of it could fit with some of Michael's ideas.
Funding might be the cohesive core around which our hangouts could develop more focus around specific projects. Michael and Andrea have talked about the bias of Art History. Getting institutional validation would help to move our ideas and work a little closer to official narratives.
Do you know about any funding opportunities we might apply for?
I agree that meeting monthly and continuing to pursue ways to collaborate is a valuable practice in and of itself. I was thinking that perhaps a group of us could commit to individually writing something for a future issue of MOOC magazine, and we could give ourselves a specific deadline (I love deadlines, as you all know) to make this happen.
Van do you have any content on your mind that you'd like written for a current or future issue? If not, then perhaps we could brainstorm for a theme that we could all write toward.
I also want to continue to add content to our websites and keep in touch and share resources through slack chat. Furthermore, in addition to LACMA, we might be able to search for some other RFPs and work with deadlines to try and come together around an idea for (potentially) funded projects.
Over thanksgiving break, I'll do a bit of research for some other RFPs so that I have something to share at our holiday party on the 8th.
Thanks a million to Vanessa for keeping us going and organized and motivated. I suspect she's got lots of other projects that are driving her harder than this one, and I really do appreciate the energy she continues to share with us. Furthermore, I really want to hear more about her Avatar Field Guide — what IS the difference between the avatar classifications — af̱toportréta and fo̱tográfos móda and fo̱tográfos koultoúra? I looked at a couple of the different examples, and I am too uneducated to discern the differences at this point. I want to learn more. Is the performance in Virtual London related to this project? How can we attend?
BTW Michael, this broadcast formula I finally came up with using XSplit Gamecaster to feed 1080p HD video to the Twitch.tv streaming service looks pretty good. If we ever did something like ONE Night again, it might be a nice way for you to project HD video without having to have a "cameraperson" (logged in, in-world user) on site.
I'm torn — I definitely would like to keep our chats and our contact going. It often seems that the chats are a little too short, so longer hangouts less often might be nice… on the other hand, I know that the fact that they're monthly has made it easier for me to join when I can.
Perhaps it would help to keep the one-hour every-month schedule, but to hold ourselves to a schedule within the hour. For example, we could spend 10 minutes per topic, or give each participant the floor for a set time to let us know what they're up to, and for others to ask questions. One of those timeslots could be free-form conversation; and those who are available can always stay past the hour mark to chat further. It might sound very formal, but a time pressure also might help us each think of what we most want to impart to the group, and ask questions of each other.
http://www.citycreature.wordpress.com. And I'm looking at word-cloud software to help display/interpret the answers to my questionnaire. Let me know if you have suggestions! Fun times.
I've really enjoyed the dialogue and interactions .re/act has supported over the past year and, while the Hangouts do present a challenge in terms of scheduling, I believe they also add value to our exchanges. I quite like Rebecca's suggestion that we occupy 10 minute slots during a hangout and think that structuring the format in this way is worth experimenting with in 2015.
Vanessa, thank you for all the work you've put into creating this space and for your generosity toward the group. I mentioned to Michael that I affectionately refer to the Berries as my "semi-imaginary" friends:-) – thank you all for keeping the energy flowing this year – being involved has meant a lot to me. I also think that Michael and Kate have been instrumental in bringing others to the conversation and in orchestrating (directly and indirectly) meetings in Real Life. For this I am hugely grateful.
I'm looking forward to the December 8th party!! Have been practising my disco moves;-) Or maybe it'll be more Mardi Gras…where's that feather boa I started off with????
Did you get hair extensions??