text:
\section{Introduction}

The study of dark solitons has attracted considerable theoretical and experimental
attention in various branches of physics. Prominent examples include
nonlinear optics~\cite{Kivshar-LutherDavies} and
atomic Bose-Einstein condensates (BECs)~\cite{djf,SIAMbook},
but also mechanical \cite{mech} and electrical \cite{el} dynamical lattices,
magnetic films \cite{mf}, electromagnetic \cite{gv} and acoustic \cite{acous} metamaterials,
hydrodynamics \cite{ww}, plasmas \cite{plasma}, nematic liquid crystals \cite{nlc},
as well as other nonlocal media \cite{nonloc}, dipolar atomic condensates \cite{chrom},
and exciton-polariton condensates \cite{polar}.

In the context of BECs, a number of experiments have addressed
diverse phenomena including the formation of dark solitons by
laser beams dragged through an elongated BEC~\cite{engels},
their oscillations in the trap~\cite{becker,ourmarkus2}, their
pairwise interactions~\cite{ourmarkus2,ourmarkus3}, as well as their
transverse instability in higher-dimensional settings
and their concomitant decay into vortices and vortex
rings~\cite{watching,jeff,becker2,lamporesi} (see the recent volume~\cite{SIAMbook}
summarizing many of these phenomena). Furthermore,
a sizeable literature has emerged in the topic of multi-component
condensates, where one of the components assumes the form of a dark soliton
(see, e.g., the recent review~\cite{revip} and references therein).
Regarding applications, matter-wave dark solitons have been proposed for use in
atomic matter-wave interferometers~\cite{in1} and as qubits in BECs~\cite{qub}.

Generally, dark solitons are unstable against decay when embedded in a higher dimensional space.
The study of their transverse (or ``snaking'') instability
has been of particular significance since its theoretical inception~\cite{kuzne}
(see also the review~\cite{kidep} and references therein).
However, the instabilities associated with the mutual interactions between multiple dark
solitons in a BEC
have only been partly investigated ---see, e.g., Ref.~\cite{ourmarkus3} for the
quasi-1D setting, as well as the recent work~\cite{mat} for 2D and 3D settings.
Importantly, these works have always considered the role of trap
induced confinement in the corresponding dimensionality of the problem.
In the higher-dimensional cases, examples of stability have been
reported numerically
for suitable parametric regimes suppressing the snaking instability.

In the present work, we analytically and numerically characterize the dynamics of up
to four parallel dark solitons, finding that while the number of unstable eigenmodes
increases as the number of stripes increases, their corresponding growth rates do not
significantly change; nevertheless for large chemical potentials the rates
are found to increase with the stripe number.  Progress on this front is especially relevant in experimental settings that involve solitons produced in the merging or collisions of BECs~\cite{kali}, the interaction of multiple dark solitons~\cite{ourmarkus2,ourmarkus3,jeff,becker2}, or the decay of multiple dark solitons as a generator of vortices~\cite{watching} and two-dimensional (2D) quantum turbulence~\cite{tsubota} in BECs as well as in optics~\cite{tikh}.
The subject of dark soliton decay also continues to attract theoretical attention~\cite{smirnov,hoefer}, including the possibility of ``engineering'' avoidance of this instability~\cite{us}.

In recent work~\cite{aipaper,aipaper2}, we provided a framework
for addressing the transverse instability of a diverse array of structures
including dark soliton stripes, ring dark solitons (extensively studied in
optics~\cite{kivyang,rings,rings1} and BECs~\cite{rings2,rings3,rings4,korneev}),
and spherical shell solitons~\cite{kivyang,carr,wenlong,hau}, as well as
dark-bright solitons in multi-component BECs~\cite{revip}.
Our approach in the present work involves extending this formulation to the case of multi-soliton settings.
We seek to understand how the presence of a secondary
stripe may affect the growth rate of a transverse instability.
To address this problem we combine the adiabatic invariant (AI) of
a single dark soliton stripe~\cite{aipaper2} with the pairwise
interaction between the stripes. This allows us to identify
the equilibrium states of the multiple stripes, and more importantly the
modes of linearization as per the well established
Bogolyubov-de Gennes (BdG) analysis,
around the solitonic multi-stripe solution. Finally, this formulation
enables an exploration of the fully nonlinear stage of the instability
by examining the filament partial differential equation (PDE) for each
of the relevant stripes. While the analytical framework becomes
rather complex as the number of stripes increases, we explore
the relevant instability numerically for larger stripe numbers
(such as 3 and 4).

Our presentation is structured as follows. In Sec.~\ref{theory}
we provide the theoretical analysis of the case of two dark soliton stripes, which we refer to as ``2-stripes.'' In Sec.~\ref{results}, we explore numerically the scenarios of 2-, 3- and 4-stripes
and, where appropriate, compare with the semi-analytical predictions
of the filament theory. Finally, in Sec.~\ref{cc}, we summarize our
findings and present our conclusions, as well as a number of directions for future work.

\section{Theoretical Analysis}
\label{theory}

The model under consideration is the normalized 2D Gross-Pitaevskii
equation (GPE),
describing a condensate confined in a highly oblate trap
along the $z$-axis of frequency $\omega_z$~\cite{SIAMbook}:
  \begin{eqnarray}
    i u_t =-\frac{1}{2} \left(u_{xx}+u_{yy}\right) + |u|^2 u + V(x) u,
    \label{extr}
  \end{eqnarray}
where subscripts denote partial derivatives, and $u(x,y,t)$ denotes the wavefunction.
Here, the density $|u|^2$, length, time, and energy are respectively measured in units of
$2\sqrt{2\pi}a a_z$, $a_z$, $\omega_z^{-1}$, and
$\hbar\omega_z$, where $a$ and $a_z$ are, respectively, the $s$-wave scattering
length and harmonic oscillator
length in $z$-direction. The external potential is given by
\begin{equation}
V(x)=\frac{1}{2} \Omega^2 x^2,
\label{htrap2dd}
\end{equation}
which is independent of the transverse $y$-direction, with $\Omega = \omega_x/\omega_z$
being the trap's aspect ratio.
After this dimension reduction, we carry out a subsequent scaling and consider $\Omega=1$ (see Sec.~\ref{bg} for more details).

The model is supplemented with periodic boundary conditions in the $y$-direction.
Equation~(\ref{extr}), for $V=0$, conserves the Hamiltonian:
\begin{eqnarray}
H=\frac{1}{2}  \iint_{-\infty}^{\infty}
  \left[ |u_x|^2 + |u_y|^2 +
  \left(|u|^2-\mu \right)^2 \right] dx\, dy,
\label{ham}
\end{eqnarray}
where $\mu$ is the chemical potential. In the dimensionless form of the GPE given here,
we consider chemical potentials ranging from the linear limit up to $\mu$=80
in the Thomas-Fermi limit.
This range is sufficient to address the chemical potential and atomic densities in typical experimental BECs; see Ref.~\cite{SIAMbook} for a detailed
discussion on the translation between dimensionless and dimensional
units.

Let us first study the case of two-dark soliton stripes. To describe each stripe,
we consider the following ansatz:
\begin{eqnarray}
u=e^{-i \mu t} \left[
  \sqrt{\mu - v^2} \tanh \left(\sqrt{\mu - v^2} (x-x_0) \right) + i v \right],
\label{dark2a}
\end{eqnarray}
which is the functional form of the quasi-one-dimensional dark soliton solution of Eq.~(\ref{extr}),
for $V=0$, that extends uniformly in the $y$-direction. In the 2D setting under
consideration, Eq.~(\ref{dark2a}) describes a one-dimensional
dark soliton stripe embedded in 2D space,
characterized by its center, $x_0$, and velocity $v={x}_{0t} \equiv dx_0/dt$.
In order to describe the transverse instability-induced undulation of the stripe,
we assume that the center position $x_0$ is not solely a function of $t$, but also
a function of the transverse variable $y$, i.e., $x_0=x_0(y,t)$.
We also wish to consider cases in which the potential $V(x)$ may be non-zero, which involves replacing $\mu$ with $\mu-V(x_0)$ ---representing the effective, or {\em local}, chemical
potential where the dark soliton is sitting--- in Eqs.~(\ref{dark2a}) and (\ref{ham}).
Then, substituting
the ansatz~(\ref{dark2a}) into the Hamiltonian~(\ref{ham}), we obtain the following
``effective energy'' (an adiabatic invariant) of the stripe:
\begin{eqnarray}
  E= \frac{4}{3} \int_{-\infty}^{\infty}
  \left(1 + \frac{1}{2}x_{0y}^2 \right)
  \left(\mu - V(x_0) -x_{0t}^2 \right)^{3/2}  dy.
  \label{dark5}
\end{eqnarray}
Here, the transverse energy contribution (of the $|u_y|^2$ term) has
been accounted for through the term proportional to $x_{0y}^2$.
For convenience, hereafter we use the following compact notation:
$$A=\mu - V(x_0) - x_{0t}^2, \quad B= 1 + \frac{1}{2}x_{0y}^2.$$

Earlier work on the interaction of dark solitons~\cite{akh,kk} in one-dimensional (1D) settings,
including relevant work in the context of quasi-1D atomic BECs~\cite{ourmarkus3,ourmarkus2,coles}, has quantified the interaction
effect between dark solitons. Now, this interaction
becomes a pointwise effect across the stripes, when the interaction
term is integrated along $x$, as per the variational formulation of Ref.~\cite{kk}.
Thus the corresponding energy, incorporating through its last term this interaction
effect, reads:
  \begin{eqnarray}
    E=2 \int_{-\infty}^{\infty}
    \left( \frac{4}{3} A^{3/2} B - 8 A^{3/2} e^{-4 A^{1/2} x_0} \right) dy.
\nonumber
  \end{eqnarray}
Here, we have used the symmetry of the two solitons, which are assumed to
be located at $\pm x_0(y)$. This represents the simplest possible scenario,
where a single dynamical variable, $x_0$ (i.e., the symmetric position of the two solitons),
can adequately describe the dynamics of both. Nevertheless, it should be pointed out that
this scenario is of direct relevance to experiments~\cite{ourmarkus3,ourmarkus2}.
Due to the consideration of two solitons, the energy of each individual
soliton is doubled, hence the factor of $2$ in front of the integral.

We can now find the evolution of the 2-stripe parameter $x_0$ from
the energy conservation, $dE/dt=0$. Indeed, the relevant calculation leads
to the following PDE for $x_0$:
  \begin{eqnarray}
    B \left( {x_0}_{tt} + \frac{V'}{2}\right) + \frac{A}{3} {x_0}_{yy}
    = \frac{V'}{2} {x_0}_y^2 + {x_0}_y {x_0}_t {x_0}_{ty}
\nonumber
\\[1.0ex]
\label{extr2}
     -\left[(V'+ 2 {x_0}_{tt}) (-3 + 4 A^{1/2} x_0) - 8 A^{3/2} \right]
    e^{-4 A^{1/2} x_0},
  \end{eqnarray}
where $V'\equiv \partial V/\partial x_0$. Hereafter, the above equation
will be called the ``adiabatic invariant PDE'' (AI PDE).

The next step is to examine the stationary states of this PDE and their stability.
As we know, there exists a homogeneous (independent of $y$) solution
corresponding to the two parallel
soliton stripes. Retrieving that, as well as its linearization, yields information
about the existence and stability of the 2-stripe state, and more specifically on how
the presence of a second stripe affects the transverse (in)stability of the first one.

More specifically, we seek a symmetric pair of soliton stripes with $x_0$
independent of $y$ that yields the following algebraic (transcendental)
equation for $x_0$ (see, e.g., Ref.~\cite{ourmarkus3} for a relevant analysis):
  \begin{eqnarray}
    -\frac{V'}{2}=e^{-4 A_0^{1/2} x_0}
    \left[V'(-3 + 4 A_0^{1/2} x_0) - 8 A_0^{3/2} \right],
    \label{extr4}
  \end{eqnarray}
where $A_0=\mu-V(x_0)$.
Notice that results stemming from Eq.~(\ref{extr4}) are expected to be more accurate
in the framework of the so-called ``particle approximation'', whereby individual
solitons feature a particle-like nature; this situation corresponds to the case of
sufficiently large values of the chemical potential $\mu$, the so-called Thomas-Fermi (TF)
large density limit.
Thus, this step leads to the determination of the equilibrium positions $\pm x_0^{(\rm{eq})}$
of the constituent stripe solitons forming the stationary stripe pair. Then,
the stability of $x_0^{(\rm{eq})}$ can be studied by introducing the ansatz
\begin{equation}
x_0=x_0^{(\rm{eq})} + \epsilon X_1(t) \cos(k_n y),
\nonumber
\end{equation}
with $k_n=n\pi/L_y$ denoting the transverse perturbation wavenumbers, and $L_y$ being
the size of the computational domain in the $y$-direction ---see below. Then, we
linearize with respect to the small-amplitude perturbation $X_1(t)$, and
determine whether such a stationary stripe pair is robust under transverse
modulations or not. By doing so, we obtain a rather elaborate expression that
can be summarized as
  \begin{eqnarray}
    R X_{1tt}= - \left[ \frac{1}{2}V''(x_0) - \frac{1}{3}k_n^2 A_0 + S \right] X_1.
\nonumber
    \end{eqnarray}
Here, $A_0=A(t=0)$ and the coefficients $R$ and $S$ are given by:
\begin{eqnarray}
R&=&1 +2 (-3 + 4 A_0^{1/2} x_0) e^{-4 A_0^{1/2} x_0},
\nonumber
\\[2.0ex]
\nonumber
S&=& R \left[-4 S_1 \left( V'(x_0) S_2-8 A_0^{3/2}\right)+ 4V'(x_0) S_1 \right]
\\
\nonumber
      &&+ \left[V''(x_0) S_2
      +12 V'(x_0) A_0^{1/2}\right] R_0,
\end{eqnarray}
where $S_0=e^{-4 A_0^{1/2} x_0}$, $S_1=A_0^{1/2} - V' A_0^{-1/2} x_0/2$, and
$S_2=-3 + 4 A_0^{1/2} x_0$.
Note that here, for simplicity, we have used $x_0$ instead $x_0^{(\rm{eq})}$;
furthermore, both $R$ and $S$ are evaluated at the equilibrium position $x_0=x_0^{(\rm{eq})}$. With
the equation of motion for a generic perturbation $X_1$, we can look for
normal mode frequencies by setting
$$X_1(t) = X_1^{(0)} \exp(\lambda t),$$
where $X_1^{(0)}$ is a constant amplitude,
and $\lambda$ is the eigenvalue of the normal mode $n$.

In the numerical section below, we compare this prediction about multi-stripe
stability with detailed computations of the spectrum at the 2D GPE level. This
is done upon performing the standard Bogoliubov-de Gennes (BdG) analysis (see details, e.g.,
in Ref.~\cite{SIAMbook}). Moreover, given the favorable comparison reflected in our results,
it is relevant to examine the full AI PDE dynamics
of Eq.~(\ref{extr2}) against the corresponding 2D dynamical evolution
of the GPE. This will help us to build a systematic appreciation of
the role of soliton interactions in enhancing or mitigating transverse
instabilities. It will also serve as a stepping stone towards generalizing
this to a larger number of stripes, by means of the (AI PDE) extension of the
significantly simpler, ODE-based, 1D picture of Refs.~\cite{ourmarkus3,coles}.

\section{Numerical results}
\label{results}

\subsection{Preliminaries}
\label{bg}

It is worth noting that the theoretical analysis in the last section applies
to a generic potential $V(x)$ varying slowly on the soliton scale. In
what follows, we focus on the experimentally relevant harmonic trap described by
Eq.~(\ref{htrap2dd}).
For all of the numerical computations we set the trap strength $\Omega=1$.
However, it is important to mention that,
after a scaling transformation, smaller values for $\Omega$ would
correspond to larger values of the chemical potential $\mu$.
Specifically, by defining the rescaled variables
$(\bar{x},\bar{y})=\bar{\Omega}^{-1/2}\,(x,y)$, $\bar{u}=\bar{\Omega}^{1/2}\,\,u$,
and $\bar{\mu}={\bar{\Omega}}\,\mu$,
Eq.~(\ref{extr}) with $\Omega=1$ transforms to the same equation but with
arbitrary $\bar{\Omega}$.

As for our computational domain we use $(x,y)\in[-L_x,L_x]\times[-L_y,L_y]$ with
periodic boundary conditions in $y$.
The values of $L_x$ and $L_y$
will be chosen as $L_x=16$ and $L_y=2$, $L_y=4$, or $L_y=8$. In terms of
physical
parameters, and for $L_y=4$, one may estimate the system parameters corresponding to a $^{87}$Rb
condensate confined in a
parabolic trap with $\omega_z=2\pi\times 100$~Hz. In this case, the number of atoms
(resulting from the normalization of the wavefunction) is given by:
$$N=\frac{4L_y}{3\sqrt{\pi}} \left(\frac{a}{a_z} \right)\mu^{3/2}.$$
For $^{87}$Rb, the $s$-wave scattering length is $a=5.3$~nm. The
trapping frequency $\omega_z$ corresponds to a harmonic oscillator
length $a_z=\sqrt{\hbar/(m\omega_z)}=2.7~\mu{\rm m}$.
With these parameters, typical numbers of atoms, as well
as respective values of the healing length $\xi=\hbar/\sqrt{2m g_{2D} n_{2D}}$
(where $g_{2D}=2\sqrt{2\pi} a a_z\hbar \omega_z$ is the effective 2D interaction
strength and $n_{2D}$ the peak density \cite{SIAMbook}), are as follows:
for a (dimensionless) chemical potential
$\mu=1$, one has $N\sim1400$ atoms and $\xi \sim 1.9~\mu{\rm m}$;
for $\mu=40$ the respective values are $N \sim 3.5 \times 10^5$ atoms and $\xi \sim 0.3~\mu{\rm m}$,
while for $\mu=80$, we have $N \sim 10^6$ atoms and $\xi \sim 0.2~\mu{\rm m}$.
Notice that the above characteristic values of the chemical potential
correspond to various numerical results that will be presented below. Furthermore,
in the simulations depicting stripe dynamics, the time unit $t=1$ corresponds to $\sim 2$~ms.

With respect to our numerical simulations, we
use a computational framework, similar to our earlier
works~\cite{aipaper,aipaper2,wenlong}. This is based
on finite differences to approximate partial derivatives and the
partial wave method to reconstruct the spectrum for the full (2D)
system by computing a handful of 1D ($x$-) spectra.
To fully resolve the 1D spectra we used 64,000 mesh points
over the interval $-16\leq x \leq 16$.

\subsection{Two dark soliton stripes}

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=\columnwidth]{steady_states.eps}
\caption{(Color online)
Cross sections ($y={\rm const.}$) along the $x$-direction of typical wavefunctions
$\Psi$ [which are found from the GPE~(\ref{extr}) using
$u(x,y,t)=\Psi(x) \exp(-i\mu t)$]
corresponding from top to bottom to one, two, three and four dark solitons,
respectively. In all cases $\Omega=1$ and $\mu=5$ (left) and $\mu=40$ (right)
correspond to chemical potential values close to the linear (small density)
and Thomas-Fermi (large density) limits, respectively.
Note that these 2D stationary states are homogeneous in the $y$-direction,
as the potential (\ref{htrap2dd}) is only $x$-dependent.
}
\label{States}
\end{center}
\end{figure}

In the linear, low-density limit of Eq.~(\ref{extr}), each of the dark
soliton multi-stripe states corresponds to an eigenstate of the simple harmonic
oscillator. That is, at chemical potential $\mu=(n+1/2)\Omega$,
the $n$-th harmonic oscillator eigenfunction is a starting point for
the continuation of a nonlinear state with $n$ stripes (see, e.g., Ref.~\cite{alf}). We thus
use parametric continuation towards higher values of the chemical
potential, gradually tending to the large chemical potential limit.
In Fig.~\ref{States} we depict the different steady states with one
to four stripes for the small and large density limits.
It is important to stress that it is in the Thomas-Fermi (large density) limit that
we expect the above developed theory to be valid. This is because, in
that limit, the dark-soliton stripe width $\propto \mu^{-1/2}$
tends to $0$, thus justifying its consideration as a filament (without
internal dynamics).

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=\columnwidth]{plot_x0.eps}
\caption{(Color online)
Top: Equilibrium position $x_0=x_0^{({\rm eq})}$ for the 2-stripe, as
obtained from the GPE~(\ref{extr}) (red line)
and the AI PDE model~(\ref{extr2}) (blue circles).
Bottom: Difference $\Delta x_0$ between the equilibrium position from the
GPE~(\ref{extr}) and the one predicted by AI PDE model~(\ref{extr2}).
Notice the remarkably good agreement even near the linear limit.
}
\label{fig:EquiDS2}
\end{center}
\end{figure}

We start with the equilibrium points of the (homogeneous) stationary
stripes. Here, the comparison of the analytical prediction of Eq.~(\ref{extr4}) with
the full numerical results of the GPE is depicted in Fig.~\ref{fig:EquiDS2}.
A remarkably good agreement is found between the two, for all of the considered values
of the chemical potential, with the result indeed becoming essentially exact
for sufficiently large values of $\mu$ (five digits of precision for $\mu \approx 80$).
In some sense, however, this agreement
should be expected, given the corresponding 1D results of Ref.~\cite{coles},
as well as the effectively quasi-1D nature of the pertinent equilibria.
A far more challenging test of the theory lies in the examination of the
corresponding linearized modes.

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.90\columnwidth]{spectrum_L2.eps}
\\[2.0ex]
\includegraphics[width=0.90\columnwidth]{spectrum_L4.eps}
\caption{(Color online)
Comparison between the two-dark soliton stripes' stability spectra
for the full GPE and the analytical prediction based on the AI PDE.
Depicted are the real ($\lambda_r$; top subpanels) and imaginary
($\lambda_i$; bottom subpanels) parts of the stability eigenvalues,
$\lambda=\lambda_r + i\,\lambda_i$, vs.~the chemical potential $\mu$
(note that $\lambda_r$ is scaled by $\sqrt{\mu}$).
For the numerical domain we use $L_x=16$, as well as $L_y=2$ (top
set of panels) and $L_y=4$ (bottom set of panels).
Red and blue dots correspond to the real and imaginary parts of the spectrum
from the full GPE model, while pink and orange thick curves correspond
to the real and imaginary parts for the effective AI PDE model.
The thick green horizontal line is the single-stripe $n=0$ (stable) in-phase mode
Im$(\lambda)=\Omega/\sqrt{2}$ while the thick violet curves depict the (unstable)
$n\geq1$ in-phase modes; see Eq.~(\ref{eq:IPkn}).
The thick gray horizontal lines correspond to the 1D TF spectrum; see
Eq.~(\ref{eq:TFspectrum}).
}
\label{DS2spectrum}
\end{center}
\end{figure}

Once we have identified the steady states for $N$ dark soliton stripes,
we proceed to compare their respective spectra of the BdG analysis of
the GPE (``BdG/GPE'' hereafter) with the corresponding predictions
of the AI PDE, Eq.~(\ref{extr2}).
At this point, it should be recalled that, for mathematical simplicity,
we have restricted consideration to two dark soliton stripes symmetrically
placed around the center of the trap (in line with, e.g., the experiments
of Refs.~\cite{ourmarkus2,ourmarkus3}). Therefore, the AI theory will
naturally capture only the normal modes corresponding to dark soliton stripes
oscillating {\it out-of-phase} (OOP); for simplicity these modes will
be referred hereafter to as OOP modes.
Figure~\ref{DS2spectrum} depicts the spectra obtained via
BdG/GPE [(red and blue) dots] and AI PDE [thick (pink and orange) curves] for the
2-stripe steady state. It is relevant to mention that
the spectra have a strong dependence on the numerical domain,
namely $(x,y)\in[-L_x,L_x]\times[-L_y,L_y]$, and particularly
on $L_y$.
Specifically, since the snaking instability of dark soliton stripes
is only present for relatively small wavenumbers, reducing the length
of the domain in the $y$-direction results in long wavelengths being
suppressed (i.e., not accessible) on this smaller domain. As a result,
as $L_y$ is reduced, more (long-wave) modes are suppressed and only
shorter wavelength eigenmodes will be unstable (cf.~compare the $L_y=2$
and the $L_y=4$ spectra in Fig.~\ref{DS2spectrum}). In fact, for
small enough $L_y$, no unstable wavelengths will fit in the domain
and the solutions will be effectively stable in a manner akin to the
stabilization of transverse dark solitons in elongated BECs
reported in Ref.~\cite{mat}.
Therefore, we have selected two typical $L_y$ values to compare
the BdG/GPE and AI PDE. The results for $L_y=2$ and $L_y=4$ are shown
in Fig.~\ref{DS2spectrum} (see top and bottom sets of panels, respectively).
As can be seen from the figure, all of the AI PDE modes referring to the soliton stripes
are also present in the original BdG/GPE.

It is crucial to note that the AI PDE
cannot capture modes referring to the background (stripe-less configuration).
These background modes correspond to both longitudinal and transverse
modes. The longitudinal background modes in our system correspond to the collective
oscillations of a 1D trapped BEC, characterized by the imaginary eigenvalues
$\lambda_\ell=i\omega_\ell$, where the corresponding frequencies are given by \cite{menstr}:
\begin{equation}
\label{eq:TFspectrum}
\omega_\ell = \sqrt{\frac{\ell(\ell+1)}{2}}\,\Omega.
\end{equation}
Note that in our notation, instabilities are characterized by a positive real
part of the eigenvalue $\lambda$, which in turn corresponds to an imaginary part
on the corresponding eigenfrequency $\omega$.
The frequencies of the longitudinal background modes are depicted by the thick gray
horizontal lines in Fig.~\ref{DS2spectrum}, which give a good approximation
of the corresponding frequencies of the full BdG/GPE modes
---especially as $\mu$ becomes larger.
Another set of modes that the AI PDE is not able to capture
corresponds to in-phase (IP) oscillating dark soliton stripes
(hereafter, these will be called IP modes). Nevertheless, one can approximate
the relevant oscillation frequency as follows. According to the AI analysis
the oscillatory modes of a {\em single} dark soliton in a 1D trap, are
characterized by the frequencies~\cite{aipaper2} (see also Ref.~\cite{coles}):
\begin{equation}
\label{eq:IPkn}
\lambda_n=i\,\omega_n = \sqrt{\frac{1}{3}\mu k_n^2-\frac{1}{2}\Omega^2},
\end{equation}
where $k_n= n\pi/L_y$. Then, for in-phase oscillating soliton stripes
and large chemical potentials,
one may approximate the oscillation frequency of the relevant IP modes
by Eq.~(\ref{eq:IPkn}).
This is because for such IP modes, the distance between the stripes
remains the same during the evolution and thus the interaction
(depending on their relative distance) effectively does not affect
the motion.
These modes are depicted by the violet curves in Fig.~\ref{DS2spectrum}.
A relevant example concerns the appearance of
the important stable IP mode, namely the $k_n=0$ mode (see thick green line)
in the full BdG/GPE spectrum shown in Fig.~\ref{DS2spectrum}.
The eigenfrequency of this mode corresponds to the oscillation
frequency Im$(\lambda)=\Omega/\sqrt{2}$ of a single- \cite{buschanglin}
or multiple-in-phase \cite{ourmarkus3} solitons.
However, one should not expect that the frequencies of the IP modes in the
full BdG/GPE will be
identical to $\omega_n$ in Eq.~(\ref{eq:IPkn}):
this is due to the fact that,
for the same chemical potential $\mu$, the solitons of
different $n$ are placed at different positions and hence also have different
local chemical potentials. This results in the {\em collective} oscillation
for the multi-soliton stripe state to have a frequency that is slightly larger
than the single-dark soliton prediction~(\ref{eq:IPkn}).
Here it should be pointed out that the convergence of the full BdG/GPE
and the $n=0$ IP modes in the TF limit, as shown in Fig.~\ref{DS2spectrum},
can simply be understood as follows:
as $\mu$ increases, the interactions become increasingly short-ranged and, hence,
the solitons are all pushed towards the center of the trap. Thus, they should all
oscillate with the same IP frequency ($\Omega/\sqrt{2}$) at the bottom of the well.
We shall see this mode again when we generalize to 3- and 4-stripes in the
next subsection.

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=\columnwidth]{GPE_123_DSS_A1e-3.eps}
\caption{(Color online)
Dynamics for in-phase modes corresponding, from top to bottom,
to the 1-, 2-, and 3-stripe states for $\mu=40$.
The colorbars on the right-hand side correspond to the density $|u(x,y,t)|^2$.
The system was initialized at $t=0$ with an $N$-stripe state perturbed
by the mode $A\,\cos(k_n y)$ in the transverse direction
where $k_n=n\pi/L_y$ with $A=10^{-3}$, $n=5$, and $L_y=8$
(only the portion corresponding to $-5\leq y\leq5$ at the
times indicated is shown).
Note that the dynamics, including the growth rate,
seem to be closely analogous in the different cases.
}
\label{fig:123DSS_IP}
\end{center}
\end{figure}

Similar to the results for the $n=0$ IP mode, the $n\geq1$ predictions
of Eq.~(\ref{eq:IPkn}) ---see the thick violet curves in Fig.~\ref{DS2spectrum}---
also fare favorably when compared to the full BdG/GPE spectra.
In this case, the lower the order $n$ of the mode, the better the approximation
in Eq.~(\ref{eq:IPkn}) is, and all results asymptotically match as
$\mu\rightarrow\infty$.
It is evident that the modes of the full BdG/GPE analysis
arise in pairs i.e., IP and OOP for the case of 2 stripes.
Similarly, we will see below that the modes arise in triplets
for 3 stripes, groups of 4 for 4 stripes, etc. Among these,
we have confirmed that the lowest growth rate corresponds
to the IP excitation, while the higher growth rate to the OOP one.

An example of the relevant dynamics of in-phase evolution of
multi-soliton stripes is
depicted in Fig.~\ref{fig:123DSS_IP} for the case of the $n=5$ IP
mode for the 1-, 2-, and 3-stripes and for a
relatively large chemical potential $\mu=40$. As can be seen from the
figure, the instability evolutionary dynamics
(and thus the associated growth rates) seem to be largely independent
of the number of
stripes. Furthermore, the actual destabilization evolution of the stripes
even in the nonlinear regime (but before the stripes break into pairs
of vortices) seems to also be largely independent of the number of stripes.
Hence, the IP mode excitations behave similarly to the case of a single
stripe.

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=\columnwidth]{eigenvecs_NDS2_mu40N.eps}
\caption{(Color online)
Eigenfunctions corresponding to the in-phase (IP; left) and out-of-phase
(OP; right) unstable modes of the stationary 2-stripe state $\Psi(x)$
for $L_y=2$ and $\mu=40$.
Shown are the $k_1$ modes with
transverse dependence given by $\cos(k_n y)$ with $k_n=n\pi/L_y$.
The eigenmodes corresponding to other values of $n$ are very
similar (results not shown here).
The thick solid (blue) and dotted (red) lines correspond, respectively,
to the real and imaginary parts of the eigenfunction $w(x)$.
The corresponding normalized steady state, $\Psi(x)/\sqrt{\mu}$,
is depicted by the thin black line.
Note that the real part of the eigenmodes have localized ``humps'' that,
when out-of-phase, produce in-phase motion of the dark solitons and
vice versa. The reason for this apparent contradiction is that the
dark solitons are themselves of opposite phase: in this figure the
left soliton corresponds to a $-\tanh$ while the right one corresponds
to a $+\tanh$.
}
\label{fig:eigenvecs}
\end{center}
\end{figure}

\begin{figure*}[htb]
\begin{center}
\includegraphics[width=0.90\textwidth]{dyn_2DS_mu40_xc045_Ly2_n1_A1e-2.eps}
\\[2.0ex]
\,
\includegraphics[width=0.905\textwidth]{dyn_2DS_mu40_xc045_Ly8_n5_A1e-2.eps}
\caption{(Color online)
Dynamical destabilization and collision of two dark soliton stripes.
The background colormap corresponds to full GPE numerics while
the green overlaid curves correspond to the AI reduction
The corresponding systems are initialized symmetrically with
the right dark soliton stripe at
$x_0(y) = \xi_0 + \sum_{n=1}^{\nu}\varepsilon_n\,\sin(2\pi ny/L_y+\varphi_n)$
with $\varepsilon_n=0.01$, $\varphi_n=(n-1)L_y\pi/10$,
$\xi_0=0.45$ (i.e., close to the steady state equilibrium
$x_0^{(\rm{eq})}=0.368$), and $\mu=40$.
The top two rows of panels correspond to a single-mode
perturbation ($\nu=1$) with $L_y=2$ while the bottom two rows
of panels correspond to a perturbation containing five modes ($\nu=5$)
and $L_y=8$.
Within each set of panels the top and bottom rows (and their colorbars) correspond
to the density ($|u(x,y,t)|^2$) and phase ($-\pi$ to $\pi$) of the field at the
indicated times.
}
\label{fig:dyn1}
\end{center}
\end{figure*}

Finally, as concerns the spectra, it is worth mentioning that
there exist other eigenmodes corresponding to the background
(rather than the dark soliton stripes).
For instance, there exist imaginary eigenvalues that appear in pairs
(starting at the linear limit) and that monotonically increase as a
function of $\mu$. These eigenvalue pairs seem to quickly approach
(asymptotically) each other as $\mu$ is increased (for the $L_y=4$
case they visually coalesce around $\mu\approx 20$; see
the relevant monotonically increasing blue curves in the bottom
panel of Fig.~\ref{DS2spectrum}).
Each of these eigenmode pairs corresponds to undulations of the background's
edges where the left and right ends oscillate with progressively
higher wavenumbers, the higher the mode frequency.
These oscillations are in- or out-of-phase between the two edges
(at opposite $x$'s), yet as
the chemical potential increases, and so does the separation between
the edges, the former and latter tend to oscillate with the same frequency.
We do not describe further these modes as they only pertain to benign
(i.e., purely oscillatory) perturbations
away from the dark soliton stripes.

With the above observations in mind, let us now summarize a
number of key features of the multi-stripe spectra:
\begin{itemize}
\item[(1)] Our theory correctly captures with good accuracy the {\it stable} $n=0$
out-of-phase (OOP) oscillation mode (see analysis in the end of Sec.~\ref{theory}) of the two stripes,
in line with the pertinent 1D theory~\cite{coles}.

\item[(2)] The oscillation frequency of the stable $n=0$ in-phase (IP) mode for the 2-stripe state
can be well approximated by the frequency for the 1-stripe state in the trap;
this is confirmed in the full BdG/GPE spectrum.
\item[(3)] Our theory detailed above in Sec.~\ref{theory}
only captures the OOP modes. The IP modes appear to be
independent of the interaction, and hence essentially
equivalent to the single-stripe results of
Ref.~\cite{aipaper2} in the TF limit. This also refers to the 3- and 4-stripe case
(see below).

\item[(4)] Each of the finite $k_n$ transverse wavenumber modes,
compared with the single-stripe case, splits into two. This has a
natural explanation as the number of stripe degrees of freedom has been
doubled. In a similar vein, there are three sets of branches for the 3-stripe case,
and four branches for the 4-stripe case (see below).
In Fig.~\ref{fig:eigenvecs} we depict the longitudinal dependence
of the IP and OOP modes extracted from the full BdG/GPE.
As expected, for two stripes there are two ``normal'' modes for each
$k_n$ corresponding to the IP and OOP ones.
\item[(5)] Despite the increase in the multiplicity of the normal modes,
different normal modes of the same $k_n$ mode have similar growth rates,
also similar to those of a single dark soliton stripe. Therefore, the
increase of the number of solitons creates more instabilities, but does
not substantially increase the instability growth rate.
Nevertheless, as we will show below, for large $\mu$ there is a monotonic
(albeit weak) increase of the growth rate of the instabilities with
the stripe number.
It also appears
that the branches of the same unstable $k_n$ mode for the two stripes
converge together in the TF limit.
\item[(6)] There is also one interesting difference near the linear limit.
In contrast to the single stripe, which has a narrow fully stable regime
near the linear limit, many stripes (including the following
cases of 3- and 4-stripes)
studied here all become unstable right from the linear limit.
Note the small ``bumps'' in $\lambda_r$ near the linear limits
(cf.~inset in the top panel in Fig.~\ref{DS2spectrum}).
This instability is analogous to the one observed in the corresponding
quasi-1D~\cite{ourmarkus3} and 1D~\cite{coles} cases, arising from
opposite energy mode collision and
being associated with complex eigenvalues.
However, before the latter is stabilized
(as in 1D), transverse modes start yielding unstable growth
(via real eigenvalues). This causes
the multi-stripe configurations to be susceptible to instability for
{\it all} the values of chemical potentials considered herein.
\end{itemize}

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.90\columnwidth]{spectrum_L2_3DS.eps}
\includegraphics[width=0.90\columnwidth]{spectrum_L2_4DS.eps}
\caption{(Color online)
Similar to Fig.~\ref{DS2spectrum} (for 2-stripes), but now for
the 3- and 4-stripe cases, for $L_x=16$ and $L_y=2$.
}
\label{DS34spectrum}
\end{center}
\end{figure}

The results presented above indicate that the AI PDE is able to approximate
very well the (linear OOP) modes that it is designed to capture. However, our
ultimate goal with the AI method is not only to obtain the BdG modes,
but more importantly to obtain a reduced AI PDE that is also able to capture
the (linear and) nonlinear dynamics of the stripe dynamics.
We therefore now compare the dynamics of the full GPE and of the AI PDE.
We initialize typical symmetric stripes of the following form
\begin{equation}
x_0(y,t=0) = \pm( \xi_0 + p(y)),
\end{equation}
where $\xi_0$ is the initial location of the stripes and $p(y)$
is a perturbation to accelerate the destabilization dynamics.
We depict in Fig.~\ref{fig:dyn1} two typical cases that compare
the full GPE dynamics (see background colormap) and the AI PDE dynamics
(see overlaid green curves).
The first case (see top set of panels) corresponds to an initial position
close to stationary equilibrium $x_0^{(\rm{eq})}$ perturbed by a single
mode ($n=1$ for $L_y=2$) with amplitude 0.01.
The second case (see bottom set of panels) corresponds to the same initial
position of the stripe but now perturbed by five different modes (see caption
for more details); see figure caption for details on the perturbation
$p(y)$ used in these two cases.
As can be noticed from the figure, for both cases, the AI PDE is able
to capture (a) the initial growth of the perturbation (in accordance with
our previous results on the BdG spectra), (b) the strong interactions between
the stripes that include collision and bounce-back, and importantly
(c) even some of the
nonlinear stripe dynamics before the stripes finally break into vortices.
It is remarkable that indeed the AI PDE is able to capture the full GPE
dynamics even when the stripes are interacting quite strongly.

\subsection{3- and 4-stripe states}

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=\columnwidth]{eigenvecs_NDS3_mu40.eps}
\\[2.0ex]
\includegraphics[width=\columnwidth]{eigenvecs_NDS4_mu40.eps}
\caption{(Color online)
Same as Fig.~\ref{fig:eigenvecs} but for the 3-stripe (top)
and 4-stripe (bottom) states.
Parameters correspond to $L_y=2$ and $\mu=40$ for the
transverse modes involving the motion of the dark soliton stripes.
The notation $\pm1:\pm1:\pm1$ is used to denote a normal mode
that has a displacement from the steady state of the first,
second, and third dark soliton in the positive (+) or negative
($-$) direction. The same notation is used for the 4-stripe case.
}
\label{fig:eigenvecs34}
\end{center}
\end{figure}

\begin{figure}[tbp]
\begin{center}
\includegraphics[width=0.75\columnwidth]{Statistics_trim.eps}
\caption{(Color online)
Top panel: Comparison of the fully in-phase oscillation mode $(n=0)$ frequency
for different numbers of dark soliton stripes using the same $L_y=2$.
DS$N$ denotes the $N$-stripe state.
Note that they all converge to the 1D single dark soliton results
$\Omega/\sqrt{2}$ corresponding to the IP oscillation of the $N$-stripes.
Bottom panel: The most unstable mode growth rate for different numbers of dark soliton
stripes. Note there is an interesting crossover behavior. The growth rate
is larger for the 1-stripe state near the linear limit but in the TF limit,
more dark solitons are more unstable. Moreover, in the latter limit
there is a (weak, yet) monotonic increase of the growth rate with $N$.
}
\label{Statistics}
\end{center}
\end{figure}

In this section, we consider the cases of 3- and 4-stripe states,
and study their spectra and dynamics. The dependence of the real and imaginary parts
of the eigenvalues on the chemical potential is shown in Fig.~\ref{DS34spectrum}
for both cases.
Besides the presence of the same background modes as the ones describe
above for the 2-stripe case, we can clearly see the multiplicity of
the inter-stripe vibrational
modes.  The 3-stripe case has three modes while the
4-stripe case has four.
As explained above, this multiplicity stems from the different normal
modes of vibration of the $N$-stripe solution. Indeed, we have
extracted the longitudinal dependence of the normal modes for $n=2$
as depicted in Fig.~\ref{fig:eigenvecs34}. As can be observed from the
figure, the 3- and 4-stripe cases have, respectively,
three and four normal modes.

It is also evident, more so in the 3- and 4-stripe case
when compared to the 2-stripe case, that in comparison, e.g.,
with Fig.~2 of Ref.~\cite{aipaper2},
the higher $N$ is, the more unstable the
corresponding state becomes in the TF limit.
This makes intuitive
sense, as the differential repulsion of the stripes at different
locations (in the presence of perturbations) can be expected to lead to
enhancement of the undulations and ultimately of the instability
growth rate.
This is more concretely quantified in Fig.~\ref{Statistics}. The top panel
clearly shows
that the IP modes converge, in the TF limit,
to the same frequency of IP oscillations for the different stripes.
On the other hand, the bottom panel shows, interestingly, that
the single-stripe state is the one that bifurcates into instability
the earliest.
Nevertheless, and going towards the analytically tractable
limit of large $\mu$, we observe that there exists
a crossover. As a result, more
soliton stripes lead to higher ---but only slightly higher---
growth rates. Nevertheless, the scales of the growth rates of
different numbers of stripes remain
quite proximal.

\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.90\columnwidth]{GPE_2DSS_rand1e-1.eps}
\\[0.5ex]
\includegraphics[width=0.90\columnwidth]{GPE_2DSS_rand1e-2.eps}
\\[0.5ex]
\includegraphics[width=0.90\columnwidth]{GPE_2DSS_rand1e-4.eps}
\\[0.5ex]
\includegraphics[width=0.90\columnwidth]{GPE_2DSS_rand1e-12.eps}
\caption{(Color online)
Dynamical destabilization of 2-stripe states
using different small random perturbations.
Each set of two rows of panels corresponds, from top to bottom, to
two different realizations for a random perturbation of amplitude
$10^{-1}$,
$10^{-2}$,
$10^{-4}$,
and
$10^{-12}$,
respectively.
}
\label{fig:D2rand}
\end{center}
\end{figure}

\begin{figure*}[htb]
\begin{center}
\includegraphics[width=0.9\textwidth]{dyn_3DS_mu40_rand1e-4_Ly8.eps}
\includegraphics[width=0.9\textwidth]{dyn_4DS_mu40_rand1e-4_Ly8.eps}
\caption{(Color online)
Dynamical destabilization of the 3- and 4-stripe states
as obtained from the full GPE. In these cases, we have added a small
($10^{-4}$ amplitude) random noise.
Both states, following the spectral picture, break with the most unstable
mode, and  give rise to numerous vortex pairs.
Note that despite the existence
of more unstable modes, the maximum decay rates are about the same
for different number of stripes.
}
\label{D3}
\end{center}
\end{figure*}

Finally, we have performed simulations to study the dynamics
when random noise is added to the stationary state.
In this case we do not compare with the AI PDE dynamics as
our analytical characterization captures the OOP modes (in terms
of their nonlinear dynamics) but not the IP ones. Given that
random perturbations excite both, a more elaborate and less straightforwardly
tractable AI approach without the assumption of symmetric center positions
would be needed for comparison here.
In Fig.~\ref{fig:D2rand} we depict the dynamics ensuing from the
2-stripe state perturbed by a small, uniformly distributed random perturbation.
For each perturbation size we show two typical runs and, from top to
bottom, we depict the cases for random perturbations of
diminishing amplitude. Surprisingly, as the perturbation is set to
smaller values, the full GPE dynamics tends to a {\em symmetric OOP}
configuration for the two stripes.

In Fig.~\ref{D3} we depict the dynamical destabilization for the
3- and 4-stripe cases.
The BdG spectra depicted in Fig.~\ref{DS34spectrum}, computed for
$L_y=2$ suggest that the dominant unstable mode for $\mu=40$
should be the $n=3$ one which corresponds to the $n=6$ mode
in Fig.~\ref{D3} as in this latter case we used $L_y=4$.
The dynamics indeed follows this prediction until
each stripe breaks into vortex pairs.
It is, arguably, not entirely straightforward to define a precise breaking
time, as this is a continuous process, but both states start to bend
around $t=1$ and therefore the two states break at about
the same time scale, as expected from the spectra.
It should be noted that for the 3-stripe case, the AI approach is
conceptually straightforward to construct, generalizing the
energy functional of Eq.~(\ref{dark5}), as for OOP configurations
the dark soliton in the middle is centered at $x=0$ and the
relevant center positions are $-x_0$, $0$ and $x_0$.
However, the resulting expressions are particularly tedious and
hence we do not attempt to give them here.

We now comment on the possibility
of generating quantum turbulence from the transverse-instability-induced
dynamics of multiple dark soliton stripe states. This scenario was considered
and investigated in Ref.~\cite{tsubota} for an initial configuration different from
that used in this work, namely for a square grid of many dark soliton stripes in a
spatially uniform condensate. In our case, Fig.~\ref{D3} (see panels corresponding
to $t=1.6$) suggests that the instability-induced generation of vorticity could also
lead to quantum turbulence. Nevertheless, the state of quantum turbulence that
is induced by the decay of a series of dark soliton stripes is likely to lack the
vortex clustering, as well as the
statistical signatures of classical and quantum two-dimensional
turbulence~\cite{Bra2012.PRX2.041001,Ree2014.PRA89.053631,Bil2014.PRL112.145301}.
Nonetheless, weak correlations and small clusters can build after some
vortex-antivortex annihilation~\cite{Sim2014.PRL113.165302}, which we surmise is one of
the more interesting effects that could be observed for this type of turbulent
state. In any case, a pertinent systematic study of such effects is beyond the
scope of this work.

\section{Conclusions \& Future Work}
\label{cc}

In the present work, we have extended considerations of the solitonic
stripes as filaments to the realm of multi-stripes, taking into
consideration their pairwise interactions. We have seen how this
allows one to evaluate the equilibrium position of multi-stripe
states. Perhaps more importantly, this also enables the consideration
of the linearized eigenmodes around such an equilibrium. These
modes can be partitioned into in-phase and out-of-phase ones. The in-phase
ones are similar to
the single-stripe modes. On the other hand,
the out-of-phase ones introduce additional growth modes of the transverse
instability. Despite the larger number of instabilities, the maximum growth
rates remain comparable to that of a single stripe, although we have found a
weak monotonic dependence thereof on the the number of stripes $N$
in the large chemical potential limit.
In addition to this linearization picture, we have explored the full
dynamics of the two stripes, always in good agreement with the
filament (AI PDE)
method results which consider each of the stripes as a reduced PDE
for the stripe center $x_0(y,t)$. We have extended the numerical
consideration of such stripe interaction scenarios to the case
of 3- and  4-stripe settings, obtaining a natural generalization
of the two-stripe results.

This effort paves the way for a number of future possibilities.
One of the most intriguing ones, in line with the experimental
thesis results of Ref.~\cite{kali}, is to examine the interaction of
a quasi-1D pattern (like the stripe) and a genuinely 2D pattern,
like the vortex. This has been associated with a nonlinear variant
of the famous Aharonov-Bohm effect in Refs.~\cite{neshev1,neshev2}.
Yet, it has not been systematically explored at the level of a
filament theory as the one presented herein, which could shed
quantitative light in the relevant dynamics. Moreover, this
is an especially appealing problem at the interface of dimensionalities
and at the interface between differential and integral equations
(preliminary calculations suggest that the vortex has a distributed
effect on the stripe, while the stripe has an integrated effect
on the motion of the vortex).  A version of this problem that
could be radially symmetric and hence simpler to tackle could
be that of a ring dark soliton with a vortex sitting in its center.
One can also go beyond 2D settings and consider effective
PDEs for 1D filaments such as vortex rings embedded in 3D
space as in the recent works of Refs.~\cite{ruban2,ticknew} and then
attempt to generalize these incorporating ring-ring interaction
to account for multi-vortex-ring settings~\cite{leapfrog2,leapfrog3,ourrecent}.
These directions will be considered
in future studies.

\acknowledgments

W.W.~acknowledges support from the Swedish Research Council Grant
No.~642-2013-7837 and Goran Gustafsson Foundation for Research in
Natural Sciences and Medicine.
P.G.K.~gratefully acknowledges the support of
NSF-PHY-1602994, as well as from  the Greek Diaspora
Fellowship Program.
R.C.G.~gratefully acknowledges the support of NSF-PHY-1603058.
B.P.A.~gratefully acknowledges the support of NSF-PHY-1607243.

redpajama_set_name: RedPajamaArXiv


text:
Finally the time has come for the return of Seton Hall University basketball. Tonight the Pirates open up the 2017-18 season by taking on the Knights of Farleigh Dickinson. Seton Hall opens the year ranked #23 in the country.
Khadeen Carrington, Desi Rodriguez, and Angel Delgado form a trio of seniors that the Hall hopes to ride deep into March this year. Expectations are sky high for the Pirates for the first time in over a decade.
Tonight expect to see the Hall roll with a deep lineup featuring newcomers Myles Cale, Jordan Walker and Sandro Mamukelashvili. The Pirates will look to kick off non-conference play on a good note against a team they have had a fair amount of success against in the past.
You can catch the game tonight on FS2 at 6:30. As always, Hazard Zet Forward.
Inside The Enemy Ship: Providence Friars – Home Edition
Welcome to the latest edition of Inside The Enemy Ship, featuring recurring guest on the site, Kevin McNamara from The Providence Journal! He was kind enough to answer some questions about the upcoming game!
BBA: What do you think of the team's 14-10? Does it accurately reflect the team?
McNamara: They let two games slip away – DePaul, St. John's – and being 16-8 would be a major difference right now.
BBA: Who do you consider Providence's biggest Big East rival?
McNamara:
BBA: What do you think of the Secondary Mascot concept that Providence is trying?
McNamara: I've given it 1.5 seconds of thought.
BBA: After their exit against Villanova in the semi-finals of the Big East Tournament last year, what do you see them doing this BET?
McNamara: If they can reach the semis for the 4th year in a row, they should hold a parade in Downtown Providence.
BBA: Record aside, who do you think is the worst team in the Big East?
McNamara: DePaul, but they're getting better.
BBA: Who do you consider the biggest challenge to Nova in the Big East this season? What rank do you see them ending up nationally by season's end?
McNamara: Butler is the 2nd best team. Nova will remain top 5, really benefit by injuries to Edmund Sumner (X) and Maurice Watson (Creighton).
BBA: Earlier this season, Cartwright and Bullock were both major reasons Seton Hall lost the first match up between these two teams earlier this year. Are they the two players Seton Hall should be most worried about again?
McNamara: For sure. Both must play well for Providence to go for the sweep.
BBA: What Pirates do you think the Friars should be most worried about?
McNamara: The Big Three: Delgado-Carrington-Rodriguez.
BBA: Which teams from the Big East will ultimately end up making the NCAA tournament?
McNamara: Villanova, Butler, Creighton, Xavier for sure. I can see 2 more with Marquette, PC and Seton Hall still holding chances
BBA: Final Score Prediction for the upcoming game?
McNamara: Seton Hall 72 Providence 67
Thanks again to Mr. McNamara for taking the time to talk with us! Check him out on twitter @KevinMcNamara33 and online here. These two teams tip off tonight at 8:30 from the Rock, and for those who can't be there, you can catch it on FS1. Seton Hall hopes to remain in and around the NCAA bubble with a win, as Angel Delgado looks to solidify the title of the nation's top rebounder! As always, Hazard Zet Forward
Vincent M. Santore
Inside The Enemy Ship, Seton Hall MBB
Pirate Talk with Bill Olshefski
A few weeks ago, I had the pleasure of interviewing Bill Olshefski, a basketball super fan, who has worked in my mother's office for as long as she has been there. Once he learned that her son (me), went to Seton Hall, for years he would always talk to her about the games, watching as many as he could, and telling her what the team did well and what they could have done better. Since he is retiring very shortly, I realized after all these years, I needed to meet this man who I have heard so many good things about. The day after a rough loss to Creighton, I was really interested in what he had to say about the game.
When I walked into the school administration building where my mother works, she said I'll be able to find Bill by listening for him singing or whistling, and she was absolutely right. From the moment I stepped in the building, even over the sounds of the industrial vacuum cleaner, I hear Bill singing.
After I introduced myself and we sat down for this interview in one of the break rooms, before I started asking questions, in a surprise change of events, he actually had questions for me, quizzing me on the ins and outs of not just Seton Hall basketball, but the school as a whole, and while I did pretty well, he did stump me on how many acres Seton Hall's campus is (for the record, it's 58). Then, he had a more interesting question: "Who the heck is Madison Jones?". When I told him he was a transfer from Wake Forest he said, very bluntly and with a laugh "well, he should have stayed there." Immediately after talking to him, you can tell how much he loves this game.
What consistently amazed me in talking to Bill was all the amazing stories throughout different eras of basketball that he has from simply being in the right place at the right time. An avid basketball player through his Junior year at King's College, he walked on the team knowing he wasn't going to get much playing time but did simply to prove to everyone that he really wanted to make the team, which he did. "I think I got in about maybe four games, but I had a lot of fun let me tell ya. We had a great team that year, we were 26 and 4 and won the league that year. One guy averaged more than 30 points a game!" It became apparent that when it came to basketball, there was little that Bill didn't remember. Effortlessly bringing up Angel Delgado's stat line from his dominant game against Rutgers (19 points, 16 rebounds) and Carrington's Garden State Hardwood Classic MVP trophy, to accurately predicting that Delgado will lead the nation in rebounds per game (which he does after last night's 20 rebound effort last night against #11 Butler, averaging 12.9), I was consistently amazed by the sheer amount of knowledge that he had and wanted to share. I was more than happy to listen. Back when the Eastern Basketball League was still around, he would routinely go to Wilkes-Barre Baron games to see famous Kentucky center Bill Spivey, who despite his amazing talent, never made it into the NBA because of an alleged point-shaving scandal, but according to Bill "that boy could play. I used to love watching him and Richie Gaines (a Seton Hall alum, as I later found out). You couldn't do anything against him beneath the board, he was so big he'd just push you out of the way." This to me highlights his basketball fandom. It didn't matter what level, or who was playing, he would take any chance he could to see the sport that he loved.
Much like many of the Seton Hall fans, he has been fed up with the officiating this year. "These guys are hired to tell the truth," Bill said taking a more serious tone than almost any other part of the interview. "The issue is that it is becoming rarer that they actually are. Villanova gets every call available, but they should never change the rules just because the team is someone."
Of all of Bill's stories, the most interesting story (in my opinion) about his time with Hall of Famer (and Villanova legend), George Raveling. When Bill was in high school, they were both regularly selected to their division's "all-star" games. "I would tell him 'George, I'm getting tired of seeing you! Every game I play, you're there!' I played four years against him, and God was he good. You could never, ever beat him. One time he told me when we were playing on the same team 'look Bill, when we get out there, give me the ball and we'll win this game.' I looked at him like he was crazy since we we're down 15 at the half and the other side was really good too. But I gave him the ball anyway, and wow, every shot fell into the net. I never doubted him after that."
In what was an amazing stroke of fortune a week or so after I talked to Bill, Raveling was actually interviewed during the Seton Hall – Villanova game on MLK day. For those who are unaware, this is exceptionally special since Raveling was on the stage with Martin Luther King Jr. as he delivered his famous "I Have a Dream" speech, and to this day still has the typewritten original copy. Not only was the man a basketball legend but was there for such an important piece of civil rights history, and the fact that Bill had a personal relationship with him for so many years, speaking about him with the way someone talks about an old friend is something I won't soon forget. "I should reach out to him," Bill said. "I'd bet he'd remember me."
His love for basketball extends well beyond just college basketball, and we spent a good portion of the 90 plus minutes we spent talking about the enjoyment he got from watching the Golden State Warriors. "Wow what a well-oiled machine that team is. Steve Kerr doesn't even have to coach, that team can handle everything themselves from the court. They are unbelievable, it's crazy. By the time I had finished brushing my teeth, they were up by 20 points on Toronto. Every time I turn on the TV they are up 30 or 40 points. Durant went there because he wants to win. Who could blame him. Watching them play is like watching a movie. The way they pass is like nothing I've ever seen." Coming from Bill, someone who has seen so much basketball in his life, that really means something. "I love the Golden State Warriors. I love them. They don't even need a coach. No matter what time of the day the game is on, I'm watching it."
Beyond basketball, Bill shared so much from is 70 plus years of life experiences, giving advice from everything from tips on going on job interviews, to how to properly save for retirement, which included started putting $100 from each of your paychecks into a savings account. We talked about Carli Lloyd and her new book, our mutual love for Jason Kidd, what we thought about Jeremy Lin and "Linsanity", and how his son-in-law and I both work for Lockheed Martin. He has the kind personality of someone who you can talk to about literally anything.
At the end of the interview, one of my final questions "was what is your favorite Seton Hall memory?" and without hesitation he said, grinning ear to ear, "beating Villanova. It was huge. It was huge, and people didn't realize just how huge it was at the time. Not only for the conference but as far as enrollment and recruiting are concerned, it was huge. I couldn't believe it was happening, and then suddenly, boom! The Big East is a tough conference, but this proved that so many of those teams have the ability to beat anyone in the country." With four, soon to be five nationally ranked teams, it looks like he was dead on, again.
We could have kept talking for hours on end, but he had so generously given me about 90 minutes of his time, so after a tremendous interview, I thanked him for his time and headed to leave. "One more thing," he said with a smile on his face as I was headed to the door; he lifts his hoodie up to reveal a Seton Hall basketball t-shirt. There is no doubt that this guy loved the game, and it was my genuine pleasure taking the time and listening to everything he had to say. A big thank you to Bill, and best of luck in your retirement. I hope you find many more stories to share.
Inside The Enemy Ship: Butler Bulldogs – Home Edition
Welcome to the the latest edition of Inside the Enemy Ship, your exclusive look into the upcoming Seton Hall game through the lenses on the opponnet! This time, we have had the pleasure of talking to Grant Anschuetz! Check below for what he thinks about the upcoming game! [EDITOR'S NOTE: The following interview took place before #1 Villanova was upset by Marquette late last night, hence why they are referred to as undefeated in the interview]
BBA: What do you think of the team's 17-3 record and #11 national ranking? Does it accurately reflect the team?
Anschuetz: Overall, I would say it does accurately reflect this team. Butler has proven time and time again this year they can win against solid opponents. They are 5-1 against ranked teams this year, including wins over Arizona and Villanova.
BBA: How did it feel going into overtime against DePaul after two straight wins?
Anschuetz: That game was the epitome of the saying that there are no off games in a conference like the Big East. The Bulldogs got off to such a poor start in the first half that I think there was a feeling of relief to make it to overtime and have a fresh five minutes after trailing for the majority of the game.
BBA: Who do you consider Butler's biggest Big East rival?
Anschuetz: To me, Butler's biggest Big East rival is Xavier. That answer is solely based off of how hostile the arena becomes whenever those two teams hit the floor, especially between fans.
BBA: Do you think the Big East has been a good home for Butler compared to the Horizon League?
Anschuetz: Yes. Although the change has led to tougher competition, the national exposure and ability to attract higher ranked recruits is a positive thing for the program.
BBA: How far do you now expect Butler to go into the NCAA Tournament?
Anschuetz: In this year's NCAA Tournament, I believe Butler can realistically make it to the Elite Eight. With that being said, based on 2010-2011, a trip to the National Championship is not out of the question.
BBA: After last season's early exit during the Big East tournament, what do you see the Bulldogs doing this year?
Anschuetz: I could see Butler making it at least one more round deeper into the Big East tournament. It is always hard to predict how hot a team is going to be down the stretch, but they should make it farther than last year.
BBA: Roosevelt Jones and Kellen Dunham played huge roles in making sure that Butler was the only Big East team that Seton Hall didn't beat last season. Who is going to fill their roles?
Anschuetz: Kelan Martin, Kamar Baldwin and Kethan Savage have all performed well for the Bulldogs as of late. Senior Andrew Chrabascz is a crafty player down low and is also a great facilitator.
BBA: Which player should the Seton Hall Pirates be the most worried about meeting on the court? Why?
Anschuetz: The Pirates should be most worried about Kamar Baldwin. Specifically, the guards for Seton Hall because Baldwin is known for making big steals in big moments. His defensive presence is just as strong as his offensive presence.
BBA: Who do you consider the biggest challenge to Nova in the Big East this season? How about nationally? Butler is still the only team to beat them so far!*
Anschuetz:The biggest challenge to Villanova before the injury to Maurice Watson was Creighton. Now, I have to go with Butler since they are the highest ranked Big East team who has beaten them.
Anschuetz: From the Big East, I believe Villanova, Butler, Creighton are basically locks at this point. Marquette, Xavier and Seton Hall all have a realistic chance to make it.
Anschuetz: Final Score Prediction = Butler 72 Seton Hall 65
Once again, thanks to our new friend Grant Anschuetz for taking the time to talk to us! He can be found on twitter @Granschuetz and on Slump Sports!
Tip-off is tonight at The Rock at 8:30 PM! If you can't make it there in person, it will be broadcast nationally on FS1. Be sure to check by later for the game recap, and as always Go Pirates and Hazard Zet Forward!
Angel Delgado, Desi Rodriguez, Grant Anschuetz, Indiana, Kamar Baldwin, Kellen Dunham, Roosevelt Jones, Seton Hall, Xavier

redpajama_set_name: RedPajamaCommonCrawl


On Friday 11th November, year 6 travelled into London and all the way to Waterloo station to visit the British Film Institute's Imax theatre. The children watched a 3D film, called Fly me to the Moon, on one of the biggest 3D screens in Europe. The children were quite literally blown away by the experience.


A perfect 10 in a great location. Nothing to do here but move in. Three bedrooms & three baths. Numerous extra features including hardwood floors, gas fireplace, custom blinds, granite counters throughout, gas stove, BI microwave, ensui te with separate shower & tub, large private south facing deck with hot tub, double garage with room for extra storage. This is better than new, no HST and landscaping is complete. Call now to view, you will not be disappointed.


text:
package com.intellij.refactoring.makeStatic;

import com.intellij.java.refactoring.JavaRefactoringBundle;
import com.intellij.openapi.util.NlsContexts;
import com.intellij.openapi.util.text.StringUtil;
import com.intellij.psi.PsiElement;
import com.intellij.psi.PsiMember;
import com.intellij.refactoring.RefactoringBundle;
import com.intellij.usageView.UsageViewBundle;
import com.intellij.usageView.UsageViewDescriptor;
import com.intellij.usageView.UsageViewUtil;
import org.jetbrains.annotations.NotNull;

public class MakeMethodOrClassStaticViewDescriptor implements UsageViewDescriptor {

  private final PsiMember myMember;
  private final @NlsContexts.ListItem String myProcessedElementsHeader;

  public MakeMethodOrClassStaticViewDescriptor(PsiMember member
  ) {
    myMember = member;
    String who = StringUtil.capitalize(UsageViewUtil.getType(myMember));
    myProcessedElementsHeader = JavaRefactoringBundle.message("make.static.elements.header", who);
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  @NotNull
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  public String getCodeReferencesText(int usagesCount, int filesCount) {
    return RefactoringBundle.message("references.to.be.changed", UsageViewBundle.getReferencesString(usagesCount, filesCount));
  }
}

redpajama_set_name: RedPajamaGithub


text:
A Playful Take on Serious Matters: The Center for Urban Pedagogy
By Rebecka Gordan for [ polis ] blog:
Collecting my thoughts after six months as an architectural reporter in New York City, one of my most memorable encounters was undoubtedly with the Center for Urban Pedagogy (CUP). I wrote three articles on this Brooklyn-based organization, two in print and one online. What makes this non-profit so special is the way it combines art, design and visuals toward its well-targeted goal: to demystify the complex mechanisms of the city. With a strong emphasis on public participation, the relatively small core of staff starts several projects by teaming up with another NGO, specializing in a certain issue in the city. Together they track a critical issue that needs further explanation.
This past summer, 15 Bronx public high-school students came together to break down the Community Benefit Agreements, CBAs, which are unofficial agreements between a real-estate developer and a community. The result: an educational poster.
One outcome of this strategy is the project "Making Policy Public", which includes a series of foldout posters that are published four times a year. Created in close collaboration with policy advocates and design professionals, these posters are giving much-needed answers to vulnerable groups in the city. One issue, for example, calledVendor Power! explains the rights of New York's circa 10 000 street vendors. Another recent triple-launch focus on non-citizens, youth, and formerly incarcerated people–outlining the situations they face on the fringes of the criminal justice system with titles such as I Got Arrested! Now What? and Immigrants Beware!
The foldout poster Vendor Power! was designed by Candy Chang and included in the National Design Triennial: Why Design Now?, on show at the design museum Cooper-Hewitt in New York until the 9th of January 2011.
CUP is also engaging the community through workshops and other teaching tools. On a slushy Friday last February, I participated in one such workshop, in connection with the launch of the Affordable Housing Toolkit, part of CUP's "Envisioning Development Toolkit" series. In an empty corner store on the Lower East Side, CUP staff member John Mangin explored the mechanisms of the city's affordable housing policy together with a group of housing advocates, who aimed to use the kit to educate the tenants they already worked with. Opening the red box we found a colorful felt chart, an informational book, and a post card with the address to an online map. The purpose: to teach participants about income demographics, rent levels and the technical definitions of affordable housing–thereby empowering them to dare to ask the crucial question: "Affordable to whom?"
John Mangin, who has a background in policy and law, said that in the last few years the government has been getting better at recognizing its obligation to educate the public. Nevertheless, many decisions are made without adequate public participation, even if there are channels written in the city and state law for public participation to happen. "Our mission is kind of twofold," he said. "First, we want to help people understand how things work. But secondly, we would like people to want to participate. And that's where the designers and artists come in."
The Affordable Housing Toolkit from 2010 was designed Glen Cummings, MTWTF. CUP staff member John Mangin explains the educational felt chart.
But it is not only graphical experts that make CUP's urban education so engaging. Another branch is the youth education programs, varying in length with a reach of over 500 students each year. Here, the students themselves create the educational artwork, ranging from videos to comic books, models and exhibitions. In the longer "Urban Investigations" the students make site visits and conduct interviews with the help of a teaching artist. The programs are focused on specific questions: Where does our garbage go? Can illegal basement apartments be legalized? Why are there homeless people when some buildings stand empty?
In the spring of 2008, students from New Settlement's Bronx Helpers interviewed officials and researchers on the food that is sold in the bodegas of Bronx. The project resulted in the film Bodega Down Bronx.
In the project "Re-inventing Grand Army Plaza" from 2008, students from College Now investigated what it would take to be allowed to build on the old square in front of Prospect Park, Brooklyn.
Three weeks after the toolkit workshop, I rode my bike to an old cannery in Brooklyn to meet with Christine Gaspar, CUP's Executive Director. Surrounded by semi-finished sewage models, piles of Lego, golden paint bottles and rulers, she explained why she decided to join CUP in 2009, after providing architectural and planning services to low-income communities recovering from Hurricane Katrina: "The more people that actually understand how the city works, the more people can be represented in shaping it–whether it is through their vote or holding the developers or elected officials accountable for their actions," she said. CUP's persistent work–creating playful products on serious matters in collaboration with those that want and need to know–makes an important contribution to the democratization of the city. As Christine Gaspar put it: "We cannot put money in people's hands–but we can give them power through knowledge". And while the CUP staff are continuing their work in their little office in the Gowanus plant, hopefully similar strategies will follow in other cities.
Credits: CBA poster developed together with CUP Teaching Artist Hatuey Ramos-Fermin, and Teaching Assistant Prudence Katzewas. Image on street vendor from CUP. Image on toolkit from CUP.Image on John Mangin by felt chart from CUP. Image on students conducting interview from CUP.Image on students at table from CUP.
Posted by Rebecka at 3:00 AM
Labels: affordable housing, New York City, participation, public policy, Rebecka Gordan, the Center for Urban Pedagogy, urban development
Categorized as Press
Los taxis de NY que no son amarillos en Diálogo Digital
Dispatching Art In Real Time


A few days ago I got back from a trip to a conference in Tartu, Estonia. The conference was a gathering of mostly European political scientists although there were a few participants from the US, Latin America and Asia as well. The workshop I was directing explore the increasingly prominent role that emerging powers, such as China, India, Brazil and Turkey among others are playing in the processes of post-conflict reconstruction and peacebuilding. We spent a few days exploring the reasons behind the emerging powers growing prominence in international relations, the divergences between them and traditional donors as well as the differences within this heterogeneous group of states.
While the discussions were very interesting, what struck me was what was happening outside of these meetings. I traveled to Tartu through Copenhagen in Denmark and through Riga in Latvia. And the journey and the theme of the workshop made me think about the extent to which globalization processes have fundamentally reshaped the relationships between people and between states and to what extent the organization of political space has in many ways persisted despite the changes. Perhaps within the European Union these tensions between change and continuity can be seen more starkly than elsewhere. Those who are admitted into this political space and those who are not or are admitted grudgingly and with restrictions reinforce hierarchies of global power and political access. On the beautiful, old streets of Riga and the seemingly endless forests and fields between Riga and Tartu, these hierarchies and problems of access could not be seen. There were no horrific images of boats full of migrants capsizing in the Mediterranean, no reports of people being smuggled in cramped trucks or trekking on foot for weeks. Riga, experiencing unusually sunny and warm whether was filled with sauntering tourists gazing at remains of the Hanseatic League era and locals and visitors sitting at the many outdoor cafes sipping beer. In fact, there was little sense of international borders. I entered the Schengen Area arriving from Washington, DC in Copenhagen. Here a bored border guard barely glanced at my American passport and did not bother stamping it. Once in, the only way I new I was entering a different country was the ring of my cell phone to inform me that a different service provider would now be taking care of my mobile needs. I was travelling in what felt like a borderless world, so fully wired that I could find wifi on my phone while strolling down city streets and following the unfolding protests in Istanbul in the bucolic parks of sleepy Tartu.
But others arriving at the workshops told a story of a very different world. The passengers exiting a plane from Istanbul where greeting by border guards who seemed poised for a verbal altercation and who carefully scanned all documents. A workshop participant who lives in London but travels on a Chinese passport waited for weeks for her visa and arrived in Estonia at the last minute and then was forced to stay after the conference ended because of the very complicated visa regulations that dictated her movements within the Schengen Area. Other workshop participants told stories of their failed attempts to invite colleagues from South East Asia to their German university. Not everyone would be granted entry into the borderless world of the Schengen. The world might have become more interconnected but not less segmented.


As a reaction to the reducing governance standards in listed companies and the heated board room battles, SEBI had formed a committee to re-look into the corporate governance norms in India under the Chairmanship of Mr. Uday Kotak. The Kotak Committee had submitted its report on October 5, 2017. SEBI has now accepted some of the proposals of the Kotak Committee.
· Separation of position of 'non-executive chairperson' from MD/CEO for the largest companies.
· Reasons of resignation of auditors.
· Risk Management Committee to look into the cyber security issues of the company.
· Related party transactions to be disclosed on a half-yearly basis, instead of yearly.
Although implementation of some of these recommendations may increase the level of transparency and reduce the possible sources of conflicts, it will also increase the time spent and cost incurred on compliance by the companies. We are of the view that prescribing principles and giving flexibility in their implementation to the company is better than stipulating a rule-based approach, which encourages a tick box approach to compliance. Many of the provisions will also increase false comfort and moral hazard, as investors will assume that their interests are being taken care of by an independent non-executive chairman, even though that person's appointment, pay and exit are in fact determined by the controlling shareholder.
In 2012, the practice of retaining 1% of the redemption value by the Asset Management Companies (AMCs) out of the exit load charged from investors in mutual fund schemes was discontinued and the AMCs were directed to credit the entire exit load to the scheme. In lieu of the lost revenue, SEBI allowed AMCs to charge an additional expense of up to 20 basis points. In light of exit load in fact being much less, the Mutual Fund Advisory Committee (MFAC) of SEBI placed a proposal to reduce the permitted additional expense from 20 basis points to 5 basis points, which is now accepted by SEBI.
Disclosure: Mr. Sandeep Parekh of Finsec is a member of the MFAC.
Based on the recommendations received from a working group comprised of angel networks, consultants and start-ups, SEBI Board has simplified certain provisions of the SEBI (Alternative Investment Funds) Regulations, 2012 with respect to 'Angel Funds' to facilitate the growth of start-ups and bolster innovation.
The maximum investment amount in any venture capital undertaking by an angel fund has been increased from five to ten crore rupees, and the minimum corpus required of an angel fund has been reduced from ten to five crore rupees. The maximum period of accepting funds by the angel fund from angel investors has been increased to five years from the existing three years period. To simplify the procedure of launching schemes by the angel fund, the requirement of filing the scheme memorandum ten days prior to the launch of a scheme has been replaced with the requirement to file a term sheet containing material information within ten days of launching the scheme. Further, it has been clarified that the provisions of the Companies Act, 2013 shall apply to an angel fund formed as a company.
The relaxation in the regulations may accelerate the growth of angel funds and provide better accessibility of funds to start-ups. The increase in the maximum period will benefit the funds by providing a larger time-frame for them to realize the returns on their investments.
SEBI has decided to revise the enforcement framework for improving the compliance of the SEBI (Listing Obligations and Disclosure Requirements) Regulations, 2015 (Listing Regulations) by listed entities. One of the key highlights of the revised framework is to empower stock exchanges to block the shareholding of promoter and promoter groups (P&PGs) in non-compliant entities as well as their shareholding in other securities. This decision seems to be in line with the existing enforcement framework, wherein the stock exchanges are empowered to act against the P&PGs of non-compliant entities to ensure effective compliance with the requirements of the Listing Regulations.
However, this criterion should not be applied in all cases. Every member of the P&PG should not be penalized and exemptions should be provided to those who have lost effective control over the affairs of non-compliant entities. In circumstances where insolvency professionals and official liquidators are appointed to manage the affairs of non-compliant entities, the P&PGs may lose control over the operation and management of such entities. They are not in a position to direct/compel the management to comply with the requirements of the Listing Regulations. In such situations, it is infructuous to penalize the members of the P&PG as they cannot ensure that non-compliant entities will comply with the requirements of the Listing Regulations. In addition, the obligation on promoters blurs the obligation of the board of directors who are in fact the legally responsible group for any defaults. This distinction will cause some discomfort where the promoter shareholding is limited, say only 15% and thus their obligation vis-à-vis the board ought to be more limited.
Sharing of co-location services: SEBI has now mandated stock exchanges to permit stock brokers to share the co-location services provided by the exchanges. Currently, stock brokers are required to license one exclusive rack for accessing co-location services, even if they have to carry out small trades. In terms of the new mandate, the brokers can now share these racks with other brokers resulting in lesser costs, which would encourage small brokers to do algorithmic trading.
Tick-by-Tick (TBT) Data for free: SEBI has mandated exchanges to provide their TBT data feed for free to the brokers. Currently, exchanges charge a nominal fee for this data and making this zero would reduce entry barriers for small brokers who intend to do algorithmic trading.
Tightening of Order to Trade Ratio: If an algo-trader carries out trades largely at a price beyond ±1% of last traded price of the security, such orders are penalized by the exchanges. The current limit would now reduce to 0.75%. This is a welcome measure, as it would ensure that algo-trades are carried out at a price close to the last traded price to ensure market stability and accurate price discovery.
Unique identifier for each algorithm: SEBI has proposed that each of the trades carried out by way of algo-trading should be tagged with the algorithm generating the trade. This would provide a trail of each trade and act as an efficient risk mechanism tool.
Latency disclosures: SEBI has increased standards of disclosure in terms of the latency, both within the exchange trading infrastructure and also between a reference rack in the co-located facility and the core router of the exchange.
Mock trading: SEBI has recommended better infrastructure such as simulated marker environment for mock testing of algorithmic software.
To further strengthen the equity derivatives market, SEBI has resolved to introduce physical settlement of all stock derivatives, in a phased manner. Stock derivatives which were hitherto settled in cash i.e. by squaring off the exposure on the expiry of the contract, will gradually be available for physical settlement by delivery. Further, changes have been made to the existing entry criteria for introduction of stocks into the derivative segment in line with increasing market capitalizations. Towards this, SEBI has modified the market-wide position limit from three hundred to five hundred crore rupees and the median quarter-sigma order size from ten to twenty-five lakh rupees. Additionally, a minimum deliverable value of ten crore rupees in the cash market of a particular stock has also been introduced. These changes are designed to remove unnecessary, and at times manipulative speculation in the derivatives segment for illiquid or low volume stocks.
The intention is to make all equity derivatives compliant with the new framework within a period of one year. Stocks which fail to meet the enhanced criteria will be sequentially moved from cash to physical settlement and upon continuing failure to meet the enhanced criteria, will be entirely removed from the derivatives segment, based on prescribed timelines. SEBI has also tried to limit the exposure of small investors towards the derivatives segment by prescribing exposure limits based on disclosed income and by requiring rigorous due diligence in cases where such investors wish to invest beyond the exposure limits. The changes are a step in the right direction towards curbing speculation in the derivatives segment, as many instances of mis-selling derivatives products to smaller investors have been uncovered.
In addition to the registrar and share transfer agents (RTA), the companies will also be allowed to obtain assistance from the registered depositories for distribution of returns on investment, such as, dividend. Since the depositories are in direct contact with the investors through various means of communication, their direct involvement will make the process faster and more accessible for the investors. This action by SEBI is probably motivated by the unearthing of a massive fraud at an RTA entity a few years back.
To promote transparency and reduce fraudulent transfer of securities, SEBI has now decided to discontinue with transfers in physical form by amending Regulation 40 of Listing Regulations.
SEBI has initiated a public consultation by issuing a discussion paper on applicability of various securities laws on companies which are undergoing corporate bankruptcy and insolvency process, to address the practical issues which are being faced by such companies.
SEBI has issued a discussion paper for amending the archaic SEBI (Buy-back of securities) Regulations, 1998. It has also proposed changes in the SEBI (Substantial Acquisition of Shares and Takeovers) Regulations, 2011, to make it consistent with the new Companies Act, 2013 and various new securities laws and regulations.


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Home Magazine History Joseon legation in Washington to reopen with national flag for first time...
Joseon legation in Washington to reopen with national flag for first time in 113 years
KOCIS
The building that used to be the Korean legation in the U.S. during Joseon times is of significant value as a cultural property. It's the only Korean legation that retains its original looks, among the diplomatic buildings used by both Joseon and the Korean Empire. Pictured is the building in 1893 (left) and a current picture of the building.
By Kang Gahui and Sohn JiAe
Photos = Cultural Heritage Administration
The building that housed the Joseon legation in Washington, D.C., will now be transformed into a history museum, and a Taegeukgi national flag will be hoisted above the museum for the first time in 113 years.
The Cultural Heritage Administration (CHA) announced on May 15 that restoration work on the legation building, which it bought in 2012, has been complete and that it will open on May 22.
The Joseon government bought the building, just 1.5 km from the White House, in 1889, eight years after it established diplomatic relations with the U.S. in 1882. It cost almost half of the Joseon royal budget that year, which amounted to some USD 25,000. Joseon officials, such as the first minister plenipotentiary Park Jeong-yang, used this building for their diplomatic activities across the U.S. However, the 1905 Protectorate Treaty between Korea and Japan, known as the Eulsa Treaty, deprived Joseon of its diplomatic sovereignty, which stopped all legation activities.
In 1910 when Japan formally annexed Korea, the colonial power purchased the building against the Joseon government's will for just USD 5 and sold it to a U.S. entity for only USD 10. The building then re-entered the full public spotlight in 2003, as that year marked the 100th anniversary of Koreans emigrating to the U.S., and the Korean-American community tried to get back the building, to no avail.
In response, the CHA invested USD 3.5 million in 2012, equivalent to about KRW 39.5 billion, from the National Trust for Cultural Heritage to purchase the building.
Pictured left is the first floor of the Joseon legation in Washington, D.C., in 1893. Pictured right is the room today, as the former legation has been turned into a museum that will open on May 22.
The CHA said that the building is of significant value as a cultural asset, as it is the only remaining building from either Joseon or the Korean Empire that retains its original appearance. It's also the only one that has kept both its interior and exterior intact, among the other 19th-century diplomatic facilities that exist in Washington, D.C. This makes the building even more valuable, both historically and diplomatically, the CHA said.
The first and second floors of the former legation were restored based on written and visual records. The third floor will be used as a hall aimed to promote the historic relationship between Seoul and Washington, D.C., over the past many years. The outside area has been turned into a garden.
The museum will be open free to the public from 10 a.m. to 5 p.m., and it's closed on Mondays.
kgh89@korea.kr
Unsung Hero of Korea's Independence – George Lewis Shaw
Memorabilia of freedom fighters from 1919 on display at former prison
Korean relics displayed at Saudi Arabia's National Museum of Riyadh
Seoul exhibition honors 1,100 years of Goryeo Dynasty artworks
Former Japanese prime minister kneels in front of survivors of atomic bombing


In June, I saw The Internship, and though it was torched by critics and viewers alike, the movie showed me I wasn't taking enough professional risks or going after what I really wanted.
"These are some deep thoughts about a Vince Vaughn movie," joked fellow giggler Anna Swenson, but even the most light-hearted of productions can put you on the right track if you need some guidance. The Internship is about two grown men who lose their jobs and move out West to pursue internships at Google, where they may or may not end up working full-time. Not to spoil the flick for you, but as you can imagine, things pan out for our friends Owen Wilson and Vince Vaughn, and the feel-good story about interning in sunny, inspiring California proves it's fine to intern later in life if that's necessary to build a new career.
I've had more than one internship, some paid, some unpaid, and while I understand the pervasive negative response to unpaid work, I also wish there wasn't such an emphasis on whether or not the position is compensated. What about the internship itself and what it can do for an ambitious individual?
I'm starting an exciting internship next year, and when I told people about it, almost all of them asked right off the bat, "Is it paid? Or just a networking opportunity?" Why has that become the default first question? Yes, it's important to address, especially since unpaid internships can potentially push away talented folks who can't work for free, but why not also inquire about what the internship entails? When you're green, the most valuable thing is the experience itself, not if it comes with a paycheck or stipend.
I understand the concern that unpaid internships keep less-than-privileged people out of certain fields, but that's another discussion entirely, and many unpaid programs offer school credit or flexible scheduling so interns can have part-time jobs on the side. I don't like to say this, but that's just the way it is, and sometimes you have to bite the bullet and be willing to start fresh when embarking on a new adventure. Life is unfair sometimes, but you could be rewarded in the long run. After graduating college in 2010, I held an unpaid internship for two months before it turned into a full-time position, which opened many doors for me in the online media world. I had to begin from the ground up, and doing that a second time is both terrifying and exciting.
Not everyone walks out of internships gainfully employed and insured, and I consider myself lucky to be able to do this, but when asked about my plans for the new year, I don't just want to hear questions about how much money I'll be putting away, because that's my business.
As for internships that are paid, there's always a possibility that the earnings won't be significant. It's just a tough time to be young and unemployed or underemployed, and those with unpaid internships aren't the only ones making sacrifices. Just assume your friends with unpaid internships have a plan to stay afloat, whether by working elsewhere during their off-time or taking odd jobs whenever possible.
Also, it's rude to talk about money. You know better than to ask people how high or low their salary is, so don't put interns in the same awkward, unpleasant boat. We're people too.
What are your thoughts on internships? Is it rude to ask whether the gig is paid? Tell me in the comments.


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News tagged with: statue
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The Story of Kossuth County in USA
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Bud Spencer, Hungarians Favorite Spaghetti Western Star Would be 90 Today
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Completely Reconstructed Vörösmarty Square Opens
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Hungarian Press Roundup: The 30th Anniversary of Martyred 1956 PM Imre Nagy's Reburial
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Plan for New Trianon Memorial Revealed – with Pictures!
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Hungarian Sculptor's Giant Falcon Statue Welcomed Super Bowl Spectators in Atlanta
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The Relocation of Imre Nagy's Statue Draws Controversy
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Statue of Hungarian Primadonna Sári Fedák Unveiled in Beregszász
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Best of Budapest: 6 Statues Commemorating the 1956 Revolution
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Statue of 1st Post-Communist President Unveiled in Budapest
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Statue of Tom Lantos, Hungarian-born former US Congressman, Unveiled in Budapest
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Statue of Actor Bud Spencer Unveiled in Budapest
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← Bud Break and Rain!
Well, I finished weeding and removing the suckers on the upper vineyard last week, and just finished removing the suckers on the first 15 rows on the lower vineyard.
I swear the canes grow as I walk up and down the rows! I've been training the canes in the wires as I work my way up each row, and by the time I walk back down the next row, there are more canes that have reached the wires on the row I just finished.
The berry clusters are forming and it looks like it is going to be a big crop. I just picked up my very own raccoon trap, so we can relocate the little fellows before they eat our grapes.