text:
\section{Introduction}

Red supergiants (RSGs) represent an important but still poorly characterized
evolutionary phase of massive stars. As He-burning evolved stars, their
surfaces present very cool effective temperatures between 3400 and 4100 K
(spectral type of late-K to M) and average luminosities 20~000 to 300~000
$L_{\odot}$ \citep{Levesque2005, Levesque2006}. RSGs are amongst the largest
stars, with radii up to 1500 $R_\odot$ and masses in the 10-25 $M_{\odot}$
range \citep{Levesque2005, Massey2008, Levesque2010}. The resulting low
gravity has the consequence that material from the outer envelope can easily
escape to the interstellar medium, giving rise to circumstellar envelopes
\citep{Danchi1994} and very significant mass-loss rates ranging between
$10^{-8}$ to $10^{-4} M_{\odot}$ $\text{yr}^{-1}$ \citep{Massey2005,
  Verhoelst2009, Sargent2011}. The actual mechanism of the mass loss is still
unknown but is likely to involve the combined effects of turbulent pressure
from large convection
cells and radiation pressure on molecular lines \citep{Josselin2007}, as well
as
stellar magnetism \citep{Grunhut2010, Auriere2010} and Alfv{\'e}n winds
\citep{Cuntz1997, Airapetian2010}. Through these processes, RSGs are key
agents of nucleosynthesis and chemical enrichment of the Galaxy.

In the last decade, photometric and spectroscopic observations have allowed
several breakthroughs in our understanding of their dynamical convective
patterns. RSGs have long been known for their semi-regular short term optical
variations with periods of the order of hundreds of days \citep{Kiss2006}.
Historically, this
variability was usually attributed to radial pulsation, and while this path is
still being investigated \citep{Yang2012}, the full explanation is now thought
to involve variation of a few large granules on the surface of the RSGs. Such
huge convection cells are suggested by theory and simulations
\citep{Schwarzschild1975, Stothers2010}, and supported by recent spectroscopic
observations that detected large amounts of material moving through the
photosphere of RSGs \citep{Josselin2007, Gray2008, Ohnaka2009, Ohnaka2011,
Ohnaka2013}.

Modeling these convection effects requires a precise determination of the
temperature of the RSGs. The last decade of measurements of effective
temperatures of RSGs seemed to indicate much cooler temperatures than
predicted by stellar evolutionary theory, until \citet{Levesque2005} used
MARCS stellar atmosphere models with state-of-the art (at the time) treatment
of molecular opacities \citep{Gustafsson1975, Plez2003} to fit
moderate-resolution optical spectrophotometry of Galactic RSGs. They derived a
warmer effective temperature scale for RSGs of Galactic metallicity than
previous studies, in rough agreement with the Geneva evolutionary tracks
\citep{Meynet2003, Levesque2006}. Long-baseline interferometry brings unique
insights to the study of RSGs. Because optically resolving RSGs by
interferometry gives direct access to their angular diameters, it is
complementary to spectrophotometry. In a recently published survey of~$74$ RSGs
with the Palomar Testbed Interferometer (PTI), \citet{vanBelle2009}
thus derived a slightly warmer temperature scale than that of
\citet{Levesque2005}.

Convection processes are involved in the creation of hotspots, and determining
how the formation and evolution of hotspots is correlated to the fundamental
stellar parameters is a difficult task. The presence of spots and large
convection cells affects the estimation of these fundamental parameters,
as it leads to short-term photometric variability \citep{Chiavassa2011} in
addition to long-term effects \citep{Kiss2006}, while also producing photocenter shifts
that throw off diameter determination \citep{Chiavassa2009}.

High angular resolutions techniques are becoming essential tools to
understand these hotspots. Using aperture masking at the William Herschel
Telescope, \citet{Buscher1990} and \citet{Tuthill1997} found bright asymmetries at visible
wavelengths on the surface of M-supergiants ($\alpha$ Ori $\alpha$~Sco,
$\alpha$~Her), with timescale variations of order a few months possibly
explained by the presence
of hotspots. Due to its large angular size, $\alpha$ Ori then became the
best-studied individual RSG in terms of multi-wavelength surface
imaging. Using the COAST interferometer, \citet{Young2000} found a strong
variation in the apparent asymmetry as a function of wavelength, with the
detection of hotspots in the visible, but only featureless disk in
J-band. This has led to the suggestion that the bright spots are unobscured
regions of elevated temperature, seen
through a geometrically-extended and line-blanketed atmosphere, in which the
features are seen along lines of sight for which the atmospheric opacity has
been reduced as the result of activity (e.g. convection) at the stellar
surface. In H or J band, the continuum opacity is close to minimum in these
cool atmospheres \citep{Woodruff2009}, one would expect to see the photosphere,
with
negligible or no evidence of hotspots at this band.

However, interferometric observations of AGB stars (somewhat less massive and
less luminous than RSGs) have revealed that a significant fraction of these
present strong closure phase signals \citep{Ragland2006}. These signals may be
explained by unresolved bright spots, though circumstellar emission could not
ruled out. While the envelopes and dust shells of several RSGs have been
successfully imaged and shown to be very often asymmetric \citep{Monnier2004a,
Kervella2011}, resolving actual surface features has proved more difficult. It
is only recently that \citet{Haubois2009} reported the unambiguous detection of
two hotspots on $\alpha$ Ori by the IOTA interferometer in H band, while
\citet{Chiavassa2010a} found a similar number of spots in the same band on
VX~Sgr using with VLTI/AMBER. These spots are thought to be the imprint of
giant convection cells based on 3D stellar convection models
\citep{Freytag2002, Chiavassa2009, Stothers2010, Chiavassa2010b}.

We present in section \ref{sec:obs} of this paper our observations of two RSGs
from the Per OB1 association, T~Per and RS~Per, using the world-leading
resolution of the CHARA Array to resolve their surface in H-band. Then in
Section~\ref{sec:modeling} we attempt to model the stellar surface asymmetries
as spots, and we devise a procedure to determine the probabilities of these
models based on state-of-the-art Bayesian techniques. Using our best estimates
of the stellar diameters, we then derive the linear sizes, bolometric fluxes,
and temperatures of both stars. Finally in
Section~\ref{sec:image_reconstruction} we present model-independent images of
both RSGs obtained with the latest version of the software SQUEEZE and a new
regularizer developed for spotted star reconstruction.

\section{Observations} \label{sec:obs}

\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{tper_uv.eps}%
\includegraphics[width=0.5\linewidth]{rsper_uv.eps}
\caption{Combined ({\it u, v}) coverage of our observations of
T~Per (left) and RS~Per (right). The telescope configuration used
was S2-E2-W1-W2. The radial dispersion is due to the use
of MIRC low spectral mode with 8 channels.}
\end{figure}

\begin{deluxetable}{ccccc}
\centering
\tabletypesize{\scriptsize}
\tablecaption{\label{log} Reduction log for T~Per and RS~Per. $N_{\rm block}$
refers to the number of
data blocks. All calibrated OI-FITS data are available upon request.}
\tablewidth{0pt}
\tablehead{\colhead{Date (UT)} & \colhead{Target} & \colhead{$N_{\rm block}$} &
\colhead{Calibrators} & \colhead{Flux calibration}}
\startdata
2007 Jul 28 & T~Per & 2 & HD~9022 & Chopper \\
2007 Jul 29 & T~Per & 1 & $\upsilon$~And & Fiber \\
2007 Jul 30 & RS~Per & 1 & $\upsilon$~And & Chopper\\
2007 Jul 31 & RS~Per & 1 & 37~And & DAQ \\
2007 Aug 2 & RS~Per & 2 & $\sigma$~Cyg, $\upsilon$~And & DAQ\\
\enddata
\tablecomments{ Calibrator diameters (mas): \\
HD~9022 = $1.05\pm0.02$ \citep{Merand2005}.\\
$\upsilon$~And = $1.097\pm0.009$ \citep{Zhao2011}, UD model. \\
37~And = $0.676\pm0.034$, \citet{Kervella2008}. \\
$\sigma$~Cyg = $0.542\pm0.021$ M\'erand 2008, private comm.}
\label{tab:calibrators}
\end{deluxetable}

\subsection{RS~Per and T~Per}

In the following we will present our observations of two Red Supergiants from
the Per OB1 association, RS~Per (HD
14488) and T~Per (HD 14142). RS~Per is a firmly established member of the
$\chi$~Per/NGC~884 cluster, while T~Per lies about 2 degrees North above the
Double Cluster.
Both are M~supergiants, with RS~Per classed as M4I, and T~Per as M2I.  Based on
previous results \citep{Gonzalez2000, Slesnick2002, Levesque2005}, T~Per has a
temperature typical of most M~supergiants in the Per OB1 association (average
temperature in the litterature $T \simeq 3850$ K), while RS~Per is thought to
be slightly cooler ($T \simeq 3500$~K). It
is  interesting to note that they both display comparable long photometric
periods,
$2500 \pm 460$~days for T~Per, $4200 \pm 1500$ days for RS~Per
\citep{Kiss2006}, thought to be related to a global pulsation mode. RS~Per also
displays a shorter period of
$245$ days.

\subsection{CHARA/MIRC observations}

Our observations were carried out on five nights in July-August 2007 at the
Georgia State University Center for High Angular Resolution Astronomy (CHARA)
interferometer
array using the Michigan Infra-Red Combiner (MIRC). The CHARA array, located on
Mount Wilson, consists of six 1~m telescopes. Thanks to its 15~baselines ranging
from 34 m to 331 m, it achieves the highest angular resolution of optical
interferometers, up to $\sim$0.5 mas in $H$~band \citep{tenBrummelaar2005}.

The Michigan InfraRed Combiner (MIRC) instrument was used to combine the H-band
light
($1.5$-$1.8 \mu$m) of four CHARA telescopes at low spectral resolution
(R=$30$). This
provided six visibilities, four closure phases, and four triple amplitudes
simultaneously in each of the eight 30-nm wide spectral channels
\citep{Monnier2004b, Monnier2006}. Using the same W1-W2-S2-E2 configuration of
CHARA that was used for surface imaging of Altair \citep{Monnier2007}, we
achieved adequate
({\it u,v}) coverage of each target for imaging. The longest baseline in this
configuration is~$251.3$~m, corresponding to a resolution of~$1.3$ mas at~$1.6
\mu$m. We secured 4 data blocks for RS~Per and 3 for T~Per, each data block
corresponding to a continuous observation of a target during about 20~minutes.

The data were reduced by the latest version of the MIRC pipeline written by
John Monnier (as of November 2012) and previously described in
\citet{Monnier2007}. The pipeline computes the squared visibilities using
Fourier Transforms, then averages them. The bispectrum is formed using the
phases and amplitudes of three baselines that form a closed triangle. For each
data block we use the best method available for amplitude calibration: for
T~Per the fluxes were estimated by the chopper method, and for RS~Per both the
chopper and DAQ method \citep{Monnier2008}. Our targets were observed along
reference calibrators to correct for
the usual transfer function variations that occur during the night due to
atmospheric and optical changes
in the beam path \citep{Perrin2003}. Our observations were typical of
July-August weather, with transfer functions remaining very stable (less than
0.2 drop in visibility during the nights).

The calibrators were modeled as uniform discs as indicated
in Table~\ref{tab:calibrators}. Note that $37$~And has recently been resolved
by MIRC as a binary ; however the flux ratio of the components is greater than
1:100 and thus this does not significantly impact our calibration.

As the brightness distributions of both targets is not expected to vary
significantly during our observing run (see Table~\ref{tab:calibrators} for the
exact observing dates), all nights were combined into a single data
file for each target, resulting in data sets that total 419 power spectra and
264 bispectra for T~Per and 523 power spectra and 326 bispectra for RS~Per.
Systematic errors are taken into account by applying additive and
multiplicative errors on the data. All the following nominal values were
determined based on the expertise of the MIRC group with MIRC 2007 data
(Monnier, private comm.), and based on the in-depth study of $\upsilon$~And
data
acquired during the same nights \citep{Zhao2011}. Additive errors, that correct
for biases at low fringe contrast were set to $2 \times 10^{-4}$ for squared
visibilities and $10^{-5}$ for triple amplitudes. Multiplicative errors, that
correct for the
uncertainties in the transfer function, were $20\%$ on squared visibilities
and $30\%$ on triple amplitudes. Based on the analysis of the closure phase
statistics made by \citet{Zhao2011}, an error floor of $1 \ensuremath{^\circ}$ is chosen on
closure phases. To account for the unreliability of closure estimation at low
flux, each closure error is further increased by $30/S_\text{T3amp}^2$ degrees,
where $S_\text{T3amp}$ is the signal-to-noise of the corresponding triple
amplitude. Finally, to account for the difficulty of estimating rapidly varying
closures, an error equal to 10\% of the closure gradient in the spectral domain
is
further added.

\section{Model-fitting}\label{sec:modeling}

\begin{figure}
\centering
\includegraphics[width=\linewidth]{tper_pow.eps}
\includegraphics[width=\linewidth]{tper_clos.eps}
\caption{Power spectrum and closure phase fits for T~Per. }
\label{fig:fits_tper}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=\linewidth]{rsper_pow.eps}
\includegraphics[width=\linewidth]{rsper_clos.eps}
\caption{Power spectrum and closure phase fits for RS~Per.}
\label{fig:fits_rsper}
\end{figure}

All the available square visibilities and closure phases are plotted on
Fig.~\ref{fig:fits_tper} and Fig.~\ref{fig:fits_rsper} as a function of their
spatial frequency. The power spectrum curves are typical of limb-darkened
stellar discs, while the closure phases clearly depart from zero, indicating
the presence of strong resolved asymmetries on the stellar surfaces. Based on
the previous interferometric results on M~supergiants in the literature, we
expect these to be due to the presence of spots.

\subsection{Spotless models: limb-darkening}\label{sec:ldd}

\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{tper_ldd.eps}%
\includegraphics[width=0.5\linewidth]{rsper_ldd.eps}
\includegraphics[width=\linewidth]{atlas_ldd.eps}%
\caption{Constraints on the limb-darkening. Top panel: $\chi^2$ surface for the
linearly limb-darkened discs of T~Per (left) and RS~Per (right) based on
interferometric data. Bottom panel: SATLAS limb-darkening models
for a range of temperature, gravity, and mass values compatible with previous
observations of RS~Per and T~Per.}
\label{fig:ldd}
\end{figure}

Before attempting a spot search, we first sought to roughly characterize the
size and brightness distribution of the stellar discs. Our model-fitting code
FITNESS was used to fit several limb-darkening models (square root, quadratic,
power law) to the power spectra and triple amplitudes. FITNESS is a
straightforward combination of grid search to identify the
global $\chi^2$ minima and Levenberg-Marquardt to refine the parameters. The
best fits were obtained for the linear law and the Hestroffer power law
\citep{Hestroffer1997}, but they both show the existence of a strong
covariance between the limb-darkened angular diameter and the limb-darkening
coefficient. The issue is illustrated on Figure~\ref{fig:ldd} (top), where the
reduced $\chi^2$ surface is plotted as a function of both parameters. For both
targets, the problem is mainly due to the lack of high signal-to-noise data on
the first visibility lobes. To increase the precision of the fit on the
angular diameter, the limb-darkening coefficients have to be constrained.

\citet{Haubois2009} reported successfully fitting the visibility curve of
$\alpha$~Ori (M2 type, $T_{\text{eff}} \simeq 3600$~K) with a linear
coefficient $\alpha = 0.43 \pm 0.03$ (roughly corresponding to a Hestroffer law
with coefficient~$0.3$--$0.4$). Beyond this empirical result, it seems
non-obvious whether conventional plane-parallel 1D radiative codes such as
ATLAS \citep{Kurucz1992, Castelli2004} or MARCS \citep{Gustafsson1975} may be
reliably predict the intensity profiles of RSGS. RSGs are notoriously
difficult to model: their atmospheres are very extended, which invalidates the
assumption of plane-parallel geometry, and their very cool temperatures
require an advanced treatment of molecular opacities. However more recent
codes that assume spherical geometry such as MARCS-spherical
\citep{Gustafsson2008}, SATLAS \citep{Lester2008} and PHOENIX
\citep{Hauschildt1999} have demonstrated successful results on comparably cool
M~giants or supergiants \citep{Wittkowski2004, Wittkowski2006, Wittkowski2012}.

We used the latest SATLAS code (with improved ODF treatment and fixed H2O
lines) to weakly constrain the limb-darkening in H~band for both RSGs, with
parameters based around the values found in \citet{Gonzalez2000} and
\citet{Slesnick2002}: temperatures ranging from 3100~K to 4000~K (steps of
100K), $\log g = -0.5$ to
$0.5$ and a fixed metallicity $[\text{Fe/Z}]=-0.5$ \citep{Gonzalez2000}.
Figure~\ref{fig:ldd} (bottom) presents the
results of these simulations as a band of possible brightness distributions.
The intensity profiles
are weakly dependent on the temperature and are mostly determined by the mass
and surface gravity. They are characteristics of spherical codes, showing a
sudden drop of intensity at the Rosseland radius, where the Rosseland mean
opacity equals unity and where most photons escape the atmosphere. As shown on
Figure~\ref{fig:ldd}, the brightness distributions can adequately be bounded by
two Hestroffer laws with coefficients~$0.29$ and~$0.36$. Injecting this prior
into the fit, we found the Hestroffer limb-darkening coefficients to be $\alpha
= 0.32 \pm 0.2$ for T~Per and $\alpha = 0.34 \pm 0.2$ for RS~Per. Assuming that
both RSGs have similar masses, as the angular diameter of T~Per is smaller, we
expect a stronger gravity at its surface, which indeed corresponds to a lower
limb-darkening coefficient.

Taking into account all statistical errors due to the
visibility measurements and the calibration via data bootstrapping, we also
obtained the following
limb-darkened diameters: for T~Per: $\theta_{\rm LD} = 2.01\pm 0.03$~mas, with
$\chi^2=1.92$ at the nominal values. For RS~Per, $\theta_{\rm LD} =
3.05\pm 0.05$~mas and with $\chi^2=2.37$.  Because non-zero closure
phases cannot be fitted by a limb-darkening model, the ``full'' $\chi^2$ --
including the closure phase data -- are larger, $\chi^2 = 7.8$ for RS~Per and
$\chi^2 = 9.4$ for T~Per, unambiguously indicating the presence of significant
asymmetries on the stellar surfaces.

\subsection{Models with one or two spots}

\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{tper_chi2one.eps}%
\includegraphics[width=0.5\linewidth]{tper_chi2two.eps}
\includegraphics[width=0.33\linewidth]{tper_onespot.eps}%
\includegraphics[width=0.33\linewidth]{tper_brightspot.eps}%
\includegraphics[width=0.33\linewidth]{tper_twospots.eps}
\caption{Simple modeling of T~Per: likelihood maps for one- and two-spot models
(top); corresponding best fitting images for a dark spot, bright spot and two
spots (bottom).}\label{fig:tper_spots}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{rsper_chi2one.eps}%
\includegraphics[width=0.5\linewidth]{rsper_onespot.eps}
\caption{Simple modeling of RS~Per: likelihood map of the spot location (left)
and best fitting image with a dark spot (right).}\label{fig:rsper_spots}
\end{figure}

\begin{deluxetable}{lcccc}
\centering
\tabletypesize{\scriptsize}
\tablecaption{Model-fitting Results for T~Per (angles given East of North).}
\tablewidth{0pt}
\tablehead{ Fit results & \colhead{No spot} & \colhead{Dark spot} &
\colhead{Bright spot} & \colhead{Two spots} }
\startdata
$\chi^2$ & $9.4$ & 2.24 & 2.64 & 1.95 \\
$\log Z (\pm 0.02)$ & $-0.35$ & $0.87$ & $1.23$ & $0.20$ \\
$\theta_{\star}$ & 2.01 & 2.02 & 2.02 & 2.02 \\
$f_{\text{spot}}$ & $\ldots$ & 4 \% & 5\% & 3\%, 4\% \\
$(r_{\text{spot}}, \theta_{\text{spot}})$ & $\ldots$ & $0.21, -135 \ensuremath{^\circ}$ &
$0.22,
134 \ensuremath{^\circ}$ & $0.22, 134 \ensuremath{^\circ}$ \\
& & & & $0.73, 238 \ensuremath{^\circ}$ \\
\enddata
\label{tab:tper_fits}
\end{deluxetable}

\begin{deluxetable}{lcc}
\centering
\tabletypesize{\scriptsize}
\tablecaption{Model-fitting Results for RS~Per (angles given East of North).}
\tablewidth{0pt}
\tablehead{ Fit results & \colhead{No spot} & \colhead{Single dark spot} }
\startdata
$\chi^2$ & $7.8$ & 1.2 \\
$\log Z (\pm 0.05)$ & $-0.35$ & $0.32$ \\
$\theta_{\star}$(mas) & 3.05 & 3.06 \\
$f_{\text{spot}}$ & $\ldots$ & 4 \% \\
$r_{\text{spot}}$(mas), $\theta_{\text{spot}}$ & $\ldots$ & $1.43, 147 \ensuremath{^\circ}$
\\
\enddata
\label{tab:rsper_fits}
\end{deluxetable}

The most economical assumption to explain the closure phases is the presence
of spots on the stellar surface. The formation of complex granulations is
expected on the surface \citep{Freytag2002, Chiavassa2011}, and at the
resolution and dynamic contrast provided by interferometry, these appear as
compact spots. Here we attempted to search only for the most prominent
features, with the assumption that the stellar surface could be described as a
limb-darkened disc with a limited number of these spots. Previous studies on
$\alpha$~Ori demonstrated that spots may be modeled well by Gaussians or
uniform ellipses \citep{Young2000, Haubois2009}. We also chose
to use ellipses, so that each spot is modeled by six parameters: its
coordinates on the stellar surface, its size, its flux contribution, its
orientation angle and its ellipticity. Our priors on these parameters were
flat. During model-fitting, spots were not constrained to be brighter than the
stellar surface (hot) and thus dark (cold) spots were not ruled out. Spots
lying on the circumference of the stellar disc were also searched for.

Fitting spots is a difficult numerical problem due to the properties of the
$\chi^2$. First, while the bispectrum probability density is generally
approximated by a convex normal distribution \citep{Meimon2005, Thiebaut2008},
this approximation breaks down for small triple amplitudes, e.g. for very
resolved targets such as these RSGs. Therefore we revert to use separate
$\chi^2$~expressions for closures and triple amplitudes. The likelihood
expression for the closure phases may then be chosen based $2\pi$-wrapped
normal distribution \citep{Haniff1991} or the von~Mises distribution, and in
general is non-convex. Moreover, because the phase information is only partially
retrieved from closure phases, the $\chi^2$ is multimodal,
i.e. there exist local minima into which minimizers can easily get trapped
\citep{Meimon2008}. The $\chi^2$-minimization strategy has then to take both
non-convexity and multimodality into account. Due to the relatively large
number of parameters (eight to fourteen: two for the stellar disc description,
plus six per spot), our strategy consisted in a grid search on the positions
of the spots, with a three-step Levenberg-Marquardt minimization at each given
position. During the first step, only the stellar disc parameters (diameter
and Hestroffer coefficient) and the spot flux are allowed to vary. During the
second step, the shape of the spots (size, aspect ratio, orientation) is
optimized, then in the third step consists all the parameters become free to
settle.

Figure~\ref{fig:fits_tper} and Figure~\ref{fig:fits_rsper} show that overall
the fits provided by our models are not very satisfactory on the short
baselines, where our models underestimated the visibilities. This is due to
our naive assumption of a linearly limb-darkened disc model, compared to more
refined models (e.g. SATLAS, Figure~\ref{fig:ldd}), and possibly to the
presence of circumstellar material further obscuring the stellar discs at
their edges. Note that model-independent image reconstruction, carried out in
Section~\ref{sec:image_reconstruction}, also shows evidence for strong
darkening at the periphery. However these considerations do not significantly
affect our spot analysis, relying on medium and long baseline
visibilities. Figure~\ref{fig:tper_spots} and Figure~\ref{fig:rsper_spots}
presents the $\chi^2$ surface as a function of the spot position, as well as
the corresponding best one-spot and two-spot models for T~Per and RS~Per. In
all cases, we found that the total flux contribution of the spots represent
roughly $\sim 4\%$ of the stellar flux. The reduced $\chi^2$ and parameters
for these models are given in Table~\ref{tab:tper_fits} and
\ref{tab:rsper_fits}, with error bars derived using the classic bootstrapping
technique. For T~Per, our results imply the presence of a spot on along the
diagonal NW-SE. Based solely on the $\chi^2$ metrics, a dark spot in the SE
quadrant ($\chi^2 = 2.24$), or a bright spot on the NW quadrant seem equally
probable ($\chi^2 = 2.35$). There is also a slight decrease of $\chi^2$
($\chi^2 = 1.9$) when attempting to fit an additional spot to the dark spot
model. For RS~Per, the results are clearer, with evidence of a single dark
spot in the SW. In particular no solution involving any bright spot could be
found.

\subsection{Bayesian spot model selection}

In general the reduced-$\chi^2$ metric is ill-adapted to truly assess the
relative probabilities of models \citep{Marshall2006}. The $\chi^2$ decrease
that results from the addition of a new set of spot parameters can be due to
modeling a real spot or simply to over-fitting, with emergence of artifacts
due to imperfect ({\it u,v}) coverage. Here we present a general framework to
treat the problem of fitting spots, based on Bayesian model
selection. Model-fitting consists in estimating the most probable model
coefficients $\V{C}=\{ c_1, c_2, \ldots c_n\}$ of a model $\V{M}_i$. To do so
we actually maximize the posterior probability $p(\V{C}|\V{D},\V{M}_i)$:
\begin{equation}
 p(\V{C}| \V{D}, \V{M}_i)= \frac{p(\V{D}|\V{C},\V{M}_i)
p(\V{C}|\V{M}_i)}{p(\V{D}|\V{M_i})} , \label{eq:bayes}
\end{equation}
where $p(\V{D}|\V{C},\V{M}_i)$ is the likelihood of the model coefficients,
$p(\V{C}|\V{M}_i)$ is the prior probability of the coefficients, and
$p(\V{D}|\V{M_i})$ is the marginal likelihood, also often called ``Bayesian
evidence'' in astronomy. The evidence appears in Eq.~\ref{eq:bayes} as the
denominator, its role being to normalize the posterior probability.  For a
given model $\V{M_i}$, the evidence is constant. To determine the $\V{C}$
coefficients it is then sufficient to maximizing the denominator only: i.e the
likelihood (i.e. $\chi^2$) under prior constraints (mostly physical
constraints such as positivity for the stellar diameters, spots within the
stellar discs).  However when comparing two spot models, the ratio of their
evidence is to be considered. The ratio of the probabilities of two models
$\V{M}_1$ and $\V{M}_2$ given the data can be expressed as:
\begin{equation}
\frac{p(\V{M_1}|\V{D})}{p(\V{M}_2|\V{D})}= \frac{p(\V{M}_1)}{p(\V{M}_2)}
\frac{p(\V{D}|\V{M_1})}{p(\V{D}|\V{M_2})} \label{eq:model_selection}
\end{equation}
where $p(\V{M}_i)$ is the {\it a priori} probability of model $\V{M}_i$. As we
have no specific preference for a model in the absence of data,
$p(\V{M}_1)/p(\V{M}_2) = 1$, and therefore the most probable model corresponds
to the model with the largest evidence. For a given data set, the evidence
$Z(\V{M_i}) = p(\V{D}|\V{M_i})$ for model $\V{M_i}$ is defined as the
marginalized likelihood:
\begin{equation}
Z(\V{M_i}) = \int\limits_{C_1}\ldots\int\limits_{C_n} p(\V{D}|\V{C},\V{M})
p(\V{C}|\V{M})
dC_1 \ldots dC_n. \label{eq:evidence_marginalization}
\end{equation}
Computing the evidence and its associated error bar with good precision
requires the exploration and integration of the posterior probability by
specialized Monte-Carlo Markov Chain algorithms. Our model-fitting code
FITNESS uses the MultiNest library \citep{Feroz2008, Feroz2009} to compute the
logarithm of the evidence $\log Z$ with the Nested Sampling algorithm
\citep{Skilling2006}. Because the ratio of evidence intervenes in
Eq.~\ref{eq:model_selection}, differences of $\log Z$ encode the relative
model probabilities and can be interpreted (with caution) using the Jeffrey's
scale \citep{Kass1995}. Contrary to the reduced-$\chi^2$, $\log Z$ does not
directly take into account the raw number of parameters, but it is based on
their actual relevance to the fitting process. A good model has the minimal
number of parameters required to explain the data (Occam's razor), which
corresponds to a high $\log Z$. Bad models may be less predictive, or may be
too generic due to the overabundance of parameters, and the are characterized
by low $\log Z$. We give the $\log Z$ for all our models in
Table~\ref{tab:tper_fits} and Table~\ref{tab:rsper_fits}.  For T~Per, $\log Z$
points overwhelmingly in favor of the single bright spot model. Despite having
better $\chi^2$, the single dark spot and the two-spot models are found to be
much less probable. For RS~Per, a comparison of the $\log Z$ for the spotted
and non-spotted models indicate that the dark spot in the SW is probably real,
though with a low confidence index. Both these results will be confirmed by
image reconstruction in Section~\ref{sec:image_reconstruction}.

\subsection{Effective surface temperatures}\label{sec:temperatures}

The effective temperature of a star $T_{\rm eff}$ and its bolometric flux
$F_{\rm bol}$ follow the Stefan-Boltzmann law, $F_{\rm bol} = \sigma T_{\rm
  eff}^4$. The measured bolometric flux on Earth $f_{\rm bol}$ is weaker by a
factor $\theta^2/4$, where $\theta$ is the angular diameter of the star. The
effective temperature is then given by:
\begin{equation}
T_{\rm eff}= \left(\frac{4 f_{\rm bol}}{\sigma_B
\theta^2}\right)^{\frac{1}{4}},\label{eq:temperature}
\end{equation}
where $\sigma_B$ is the Stefan-Boltzmann constant. As recommended by
\citet{Scholz1987}, $\theta$ is chosen to be the Rosseland angular diameter.
Considering the relatively low signal-to-noise of the data, we assume here the
Rosseland diameter to be equal
to the limb-darkened diameter $\theta_{\text{LD}}$ fitted in~\ref{sec:modeling}.

\begin{figure}
\centering
\includegraphics[width=\linewidth]{tper_sed.eps}\\
\includegraphics[width=\linewidth]{rsper_sed.eps}%
\caption{Spectral energy distributions of T~Per (top) and RS~Per (bottom). The
plain
lines show the dereddened SATLAS fit to the optical and near-IR parts of the
spectra.}\label{fig:seds}
\end{figure}

To compute $f_{\rm bol}$ for our targets, we derived the spectral energy
distributions (SEtDs) from public catalog records. Visible and near-ultraviolet
data were
obtained from Johnson UBVRI measurements \citep{Johnson1966, Mendoza1967,
Morel1978, Ducati2002} and from
\citet{Slesnick2002}. In addition we used observations in the Geneva
\citep{Rufener1999}, Str\"omgren {\it uvby$\beta$} \citep{Marco2001} and
Vilnius UPXYZVS systems \citep{Straizys1995}. The near-infrared
data (JHKs) was obtained from \citet{Morel1978} and \citet{Ducati2002}, as well
as 2MASS \citep{Currie2010,
Skrutskie2006}. Because the 2MASS data is saturated for both stars, the
corresponding JHK fluxes are estimated using the less accurate profile method.
Mid-infrared data was acquired by ISO-SWS \citep{Sloan2003}, AKARI/IRC
\citep{Ishihara2010}, WISE \citep{Wright2010,Cutri2012}, IRAS/LRS
\citep{Neugebauer1984}, and the Midcourse Space Experiment Point Source
Catalog \citep{Egan2003}. Far-infrared data came from IRAS
\citep{Neugebauer1984} and AKARI/FIS \citep{Ishihara2010} observations.

The SEDs were de-reddened by adopting the extinction parameters found for the
Double Cluster in \citet{Slesnick2002}, i.e. a distance modulus of $11.85 \pm
0.05$ and color excesses of $E(B-V) = 0.53 \pm 0.02$ for RS~Per and $E(B-V) =
0.56 \pm 0.02$ for T~Per. Based on the analysis of \citet{McCall2004} and the
recommendations of \citet{Massey2005}, we attempted to de-redden the data
using two different empirical laws for the reddening curves: first using the
reddening curve from \citet{Cardelli1989} updated in the near-uv with
coefficients from \citet{ODonnell1994}, and with a total-to-selective ratio of
absorption $R_V= 4.15$ ; and second using the curve derived by
\citet{Fitzpatrick1999} with $R_V = 3.8$. In both cases we extended the
de-reddening to the longest wavelengths, using equations from
\citet{Chiar2006} for $\lambda > 5\mu$m. Figure~\ref{fig:seds} presents the
final de-reddened SEDs using the Cardelli de-reddenning.

Both SEDs show significant amount of circumstellar emission in the mid-IR and
far-IR, though is this much more pronounced for RS~Per. The infrared excess of
RS~Per around $7.6 \mu$m is attributed to PAH emission \citep{Verhoelst2009},
and a peak at 9.7 $\mu$m indicate strong silicate emission
\citep{Speck2000}. Both constitute evidence of ongoing dust
production. Moreover its far-infrared excess at 60$\mu$m is characteristic of
extended circumstellar emission \citep{Stencel1988, Stencel1989} and indicates
significant mass-loss through a circumstellar outflow whose typical size can
be estimated to about 4 arcminutes \citep{Stencel1989}. In contrast, T~Per
does not appear as active, but still displays broad dust emission between 9-13
$\mu$m range.

To determine the effective surface temperature, integration of the
spectrophotometric data has to be restricted to photospheric emission. To this
purpose we fitted SATLAS models only to the ultraviolet, visible and
near-infrared wavelengths where the stellar photosphere clearly dominates the
emission (i.e. $< 3 \mu$m). The SATLAS models were using ODF sampling with
improved H2O lines and the following parameters: sub-solar metallicity ${[\rm
    Fe/Z]} = -0.5$, based on the assumed typical metallicity of the double
cluster ${[\rm Fe/Z]} = -0.35$ from \citet{Gonzalez2000}; a medium
micro-turbulence level $\chi_t = 5$~km/s ; surface gravities $\log g = -0.5$
to $0.5$, and total mass $7-25 M_{\odot}$, typical of M~supergiants; effective
temperatures range $T = 3300-4000$~K, based on previous estimates
\citep{Gonzalez2000, Levesque2005, Verhoelst2009}. In order to check the
independence of our results from the specificities of SATLAS, we also fitted
spherical MARCS models using the same parameters, and we obtained identical fit
results. We
found that the SED of T~Per was fitted well by models with temperatures in the
3700K--3800K range and $\log g\simeq 0$; and for RS~Per, temperature of
3500K--3600K and $\log g \simeq -0.5$.

To derive the bolometric fluxes, the photosphere SEDs was integrated with a
Gaussian quadrature algorithm (in logarithm space). The SATLAS model was used
instead of the actual SED only for wavelengths affected by circumstellar
emission (i.e. $> 3 \mu$m). Our estimates of bolometric fluxes and the derived
absolute bolometric magnitude) are presented in Table~\ref{tab:sed_fits}. The
1-$\sigma$ errors are mostly dominated by the uncertainties arising from the
de-reddening parameters, and from the probable inclusion of circumstellar
emission. We note that our estimate of RS~Per's absolute bolometric magnitude,
$\text{Mbol}=-7.47 \pm 0.12$, falls in the middle range of literature values:
$-7.21$ in \citet{Slesnick2002}, $-7.48$ in \citet{Gonzalez2000}, $-7.74$ in
\citet{Verhoelst2009}, and $-8.15$ in \citet{Levesque2005}.

Using Equation~\ref{eq:temperature}, we derive the effective temperatures $T =
3685 \pm 30~K$ for T~Per and $T= 3470 \pm 90~K$ for RS~Per. Our error bars
take into account both the spectrophotometric and interferometric errors. The
dominant uncertainties lie in interstellar reddening: though relatively
well-characterized, the extinction to the Double Cluster is considerable due
to its distance, and the choice of de-reddening law significantly affect the
bolometric magnitude. These temperatures are consistent with previous
literature estimates \citep{Gonzalez2000, Slesnick2002,
  Verhoelst2009}. Figure~\ref{fig:tempscales} presents our results in relation
with four RSG temperature scales from the literature. Both scales from
\citet{Humphreys1984} and \citet{Massey2003} were derived by averaging
previous observations from public catalogs, but they most likely suffered from
de-reddening issues, underestimating the RSG
temperatures. \citet{Levesque2005} used spherical-geometry MARCS models (with
the
then-new opacity sampling method, later published in \citet{Gustafsson2008})
and improved de-reddening of the sources, reconciling the observations with
both predicted temperatures and evolutionary tracks. Finally,
\citet{vanBelle2009} estimated the temperature by fitting the SED with stellar
templates derived from \citet{Pickles1998} in place of synthetic models, and
independently estimated stellar diameters using the interferometer PTI
(Palomar Tested Interferometer). Note that the spatial resolution of our CHARA
observations is at least twice that of PTI, therefore it should provide more
reliable diameter estimates.

Our results confirm the hotter temperature scales of RSGs, falling in-between
the results of \citet{Levesque2005} and \citet{vanBelle2009} for T~Per, and
slightly under the Levesque's curve for RS~Per. Hence, and taking into account
the limits of our analysis (noisy 2007 data compared to current CHARA/MIRC
data), we are reasonably confident in the quality of our temperature estimates.

\begin{deluxetable}{ccc}
\centering
\tabletypesize{\scriptsize}
\tablecaption{Estimated physical parameters of T~Per and RS~Per.}
\tablewidth{0pt}
\tablehead{ & \colhead{T~Per} & \colhead{RS~Per} }
\startdata
$R_{\text{ross}}$ ($R_{\odot}$) & $ 510 \pm 20$ & $ 770 \pm 30 $ \\
$M_{\rm bol}$ & $-6.90 \pm 0.07$ & $-7.47\pm 0.12$ \\
$T_{\rm eff} (K)$ & $3750 \pm 60$ & $3470 \pm 90$ \\
$M_{\star} (M_{\odot})$ & 9-12 & 12-15 \\
$\log L/L_{\odot}$ & $4.66 \pm 0.04$ & $4.89 \pm 0.05$ \\
$\log g$ (cgs) & $0.06 \pm 0.05$ & $-0.2 \pm 0.05$ \\
\enddata
\label{tab:sed_fits}
\end{deluxetable}

\begin{figure}
\centering
\includegraphics[width=\linewidth]{temperature_scales.eps}
\caption{Effective temperatures for T~Per and RS~Per, compared to four
temperatures scales from the literature. Our results confirm the hotter scale
of \citet{Levesque2005} and \citet{vanBelle2009}.}\label{fig:tempscales}
\end{figure}

\subsection{Linear radii, luminosity, mass, and surface gravity}

Assuming a distance of $d = 2345 \pm 55$ pc \citep{Slesnick2002}, our
estimates of the linear radii are $R_{\text{ross}}=510 \pm 20 R_{\odot}$ for
T~Per and $R_{\text{ross}}=770 \pm 30~R_{\odot}$ for RS~Per. This corresponds
to luminosities $\log L/L_{\odot} = 4.66 \pm 0.04$ for T~Per and $\log
L/L_{\odot} = 4.90 \pm 0.05$ for RS~Per, comparable to that of $\alpha$~Ori.
To get estimates of the stellar masses, we used the most recent evolutionary
tracks from \citet{Ekstrom2012} and the new Geneva tracks from
\citet{Neugent2012}, that both demonstrated their (relative) reliability on
RSGs. The range of possible masses appears to be $M= 9-12 M_{\odot}$ for
T~Per, and $M= 12-15 M_{\odot}$ for RS~Per, which translates into $\log g =
0.06 \pm 0.05$ for T~Per and $\log g = - 0.2 \pm 0.05$ for RS~Per. These
results support the assumptions made during our selection of SATLAS models in
sections~\ref{sec:ldd} and~\ref{sec:temperatures}.

\section{Image reconstruction} \label{sec:image_reconstruction}

\subsection{Regularized maximum likelihood}

As four telescope data is secured on both objects, there exists enough phase
information in our data sets to attempt ``model-independent
image reconstruction''. Here the prefix ``model-independent'' signifies that
the image reconstruction process will not rely on a specific astrophysical
model. The target image $\V{i}$ is modeled as an array of pixel
fluxes~$\widehat{\V{i}}=\{i_0, \ldots i_{n-1}\}$.

As the data is assumed to be normally distributed, to each image we can
associate a $\chi^2(\V{i})$ metric that measure the distance between the
observed data (power spectra and bispectra) and the same quantities derived
from the current image. Maximizing the likelihood of the image by minimizing
its $\chi^2$ unfortunately does not lead to reasonable images. The reason is
that image reconstruction belongs to the class of ``ill-posed'' inverse
problems: the number of pixels to reconstruct is typically a few thousand,
while we only have a few hundreds interferometric data points. Under these
conditions, maximum likelihood leads to an overfitting the data. It is thus
essential to ``regularize'' the solution by introducing reasonable but
noncommittal prior expectations about the image. This is usually done through
regularization functions that control the flux distribution within the image.
In addition to preventing over-fitting, good regularizers fulfill other
roles. As underlined during model-fitting, the $\chi^2$ is heavily
multimodal. Most classic regularization function $R(\V{i})$ effectively allow
to discriminate between these local minima and thus ease minimization of
Eq.~\ref{eq:reconst}. In effect, regularizers help extrapolate the missing
information from the phase lost to the atmosphere and the gaps in the data
coverage of the ({\it u,v}) plane. A competent choice of regularizers ensures
that high frequencies are extrapolated well, and image reconstruction has
demonstrated it achieves super-resolution \citep{Renard2011}, i.e. that the
effective resolution of the reconstructed images is typically about three to
four times greater than the interferometer resolution.

This regularized maximum likelihood approach constitutes the current framework
for image reconstruction in optical interferometry \citep{Baron2010,
  Thiebaut2010}. Formally, the target image minimizes the sum of the
$\chi^2(\V{i})$ metric and of $K$~regularizers $R_k(\V{i})$:
\begin{equation}
\widehat{\V{i}} = \underset{i \in \mathbb{R}^n}{\operatorname{argmin}} \left \{
\chi^2 (\V{i}) + \sum_{k=1}^{K} \mu_k R_k(\V{i}) \right \}\label{eq:reconst} ,
\end{equation}
under the constraints of image positivity ($\forall n, i_n \ge 0$) and of
normalization of the image to unity ($\sum_n i_n = 1$). The
factors~$\mu_k$ in Eq.~\ref{eq:reconst} control the relative weight of the
$\chi^2$ and regularization terms.

\subsection{Reconstructing spotted stars with current
software}\label{sec:oldreg}

Reconstructing spotted stars is currently difficult with available
software. To date, the only published model-independent interferometric
reconstructions of stellar spots are that of the large convection cells of
$\alpha$~Ori \citep{Young2000, Haubois2009, Chiavassa2010a} and of VX Sgr
\citep{Chiavassa2010b}. Resolving spots entails that the stellar disc is
proportionally much larger, which implies very low visibility amplitudes, and
consequently bad signal-to-noise. Moreover, the conventional convex
approximations of the $\chi^2$ expression should then be ruled out. And as
exemplified by the difficult reconstruction of VX Sgr, the minimization of the
non-convex $\chi^2$ is very prone to appearance of artifacts when using
conventional tools such as BSMEM~\citep{Baron2010} or
MIRA~\citep{Thiebaut2010}.

To solve this issue we suggest the use of non-convex reconstruction codes,
such as those based on Markov Chain Monte Carlo (MCMC) approach. In this
paper, the software SQUEEZE \citep{Baron2010} was used to obtain the
reconstructions presented in this paper. SQUEEZE uses parallel tempering to
tentatively find the global minimum of the criterion in Eq.~\ref{eq:reconst},
and therefore is well-adapted to non-convex problems. SQUEEZE is
multi-threaded, with each thread conducting minimization by simulated
annealing at a different temperature and starting with a different random
seed. Compared to its predecessor MACIM \citep{Ireland2006}, it is less
sensitive to the initial condition of the Markov Chains (i.e. the starting
image). Thus, the quality of its reconstructions mostly depends on the choice
of regularization.

To select the best regularizer, we generated a synthetic test dataset
simulating the observation of a spotted star using the OIFITS-SIM tools
\citep{oifitssim}. The original image used to create the data was chosen as
the T~Per "bright spot" model from Figure~\ref{fig:tper_spots}, and we use the
same ({\it u,v}) coverage and signal-to-noise as the actual T~Per data.  We
then reconstructed the stellar surface using the two most successful
regularizers as benchmarked by \citet{Renard2011}: maximum entropy and total
variation~\citep{Rudin1992}. Maximum entropy was implemented using the
multiplicity expression from \citet{Sutton2006}, which is well adapted to our
MCMC implementation:
\begin{equation}
R_{\Gamma}(\V{i}) = \sum_{n} \log \Gamma(i_n +1).
\end{equation}
where $i_n$ is the flux in pixel $n$. Total variation (hereafter, TV) is
defined as the $\ell_1$ norm of the spatial gradient $\V{g}$:
\begin{equation}
R_{\text{TV}}(\V{i}) = \ell_1(\V{g}) = \sum_{n} |g_{n}| .
\end{equation}
Several practical expressions are available to discretize $\V{g}$ on the image
grid. In the context of this paper, we implemented the classic isotropic
formulation of $\V{g}$, i.e. for each pixel coordinate $(n, m)$ in the
two-dimensional image~$\V{i}$, the local gradient was given by:
\begin{equation}
g_{n,m}(\V{i}) = \sqrt{|i_{n+1, m}-i_{n,m}|^2 + |i_{n, m+1}-i_{n,m}|^2}.
\end{equation}
Figure~\ref{fig:reconst_compare} compares regularization obtained with both
these regularizers on our synthetic dataset (the full reconstruction procedure
is detailed in Section~\ref{sec:reconst_proc}). Our results demonstrate that
the maximum entropy image suffers from several flaws: the stellar background
is excessively non-uniform, and the precise location of spot is lost. The
total variation reconstruction is definitively superior on both
aspects. Moreover, and unlike maximum entropy, total variation does not
require an additional prior to constrain the flux to stay within a given
diameter. The good performance of total variation are in line with the
empirical results of \citet{Renard2011} but also theoretical
predictions. Total variation is indeed a direct application of the Compressed
Sensing theory, a recent mathematical framework that supersedes the
conventional Shannon sampling theorem when applied to sparse images, i.e.,
images that may be described with small number of non-zero coefficients in
some give basis. Here, on first order, our model spotted star consist of a
(mostly) uniform disc with compact spots or cells. The spatial gradient of the
image is sparse, with only the perimeters of the stellar disc and the spots as
non-zero components. Total variation enforces the sparsity of the spatial
gradient so that the reconstruction is piecewise constant with sharp
transitions, though this is not apparent on Figure~\ref{fig:reconst_compare}
as these images are actually Markov Chain averages as explained further in
Section~\ref{sec:reconst_proc}.

\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{reconst_original.eps}%
\includegraphics[width=0.5\linewidth]{reconst_maxent.eps}
\includegraphics[width=0.5\linewidth]{reconst_tv.eps}%
\includegraphics[width=0.5\linewidth]{reconst_bm.eps}%
\caption{Reconstructions of a synthetic spotted star with the same same {uv}
coverage and signal-to-noise as the T~Per data. Top left: the original image
convolved to the expected
  effective resolution (using a super-resolution factor of~3); Top right:
  reconstruction regularized by maximum entropy and a prior constraining the
  flux to stay within the stellar diameter; Bottom left: reconstruction
  regularized by total variation ; Bottom right: reconstruction regularized by
  the spot regularizer presented in
  Section~\ref{sec:newreg}. }\label{fig:reconst_compare}
\end{figure}

\subsection{A novel regularizer for spotted stars}\label{sec:newreg}

To derive a novel regularizer for use on spotted stars, we built upon the idea
of spatial gradient sparsity, adding two noncommittal requirements. The first
requirement is that for a given flux to distribute into possible spots, the
regularizer should prefer a single spot to two spots, as per Occam's razor
prescription. The second requirement is that for a given flux to attribute to
a spot, the size of the spot should be determined solely by the data. This
implies that the regularizer value should be independent of the spot size.

It is straightforward to demonstrate that TV violates this second
requirement. Let us consider an idealized stellar disc, and two cases: either
two small spots of diameter $D$, or a single large spot of diameter $2D$. Let
us assume the brightness distribution of the disc and the spots as uniform, so
that the spatial gradient is null everywhere except on the perimeters of these
components. The actual contribution of the spots to the spatial gradient is
then proportional to the spot perimeters -- equal to $2 \pi D$ in both cases
-- multiplied by the flux density for each case. Assuming that a combined flux
$F$ is emitted by the spots, the spot flux density is then $F / ( \pi D^2)$
for the single spot case, and $2 F / ( \pi D^2)$ for the two spot
case. Consequently the total variation is $\operatorname{TV}(\text{one spot})
= F/D$ for a single spot and $\operatorname{TV}(\text{2 spots}) = 2F/D$ for
two spots. While this implies that TV does favor a single spot, this also
demonstrates that the regularization depends on the size of the spot, and
therefore it may bias a reconstruction toward larger spots.

In contrast the regularizer $R_{\text{spot}}$ defined by:
\begin{equation}
R_{\text{spot}}(\V{i}) = \ell_{\frac{1}{2}}(\V{g}) = \left(\sum_{n}
\sqrt{|g_{n}|} \right)^2 .
\end{equation}
meets both our requirements for an ideal regularizer, with
$R_{\text{spot}}(\text{one spot}) = 4 \pi F$ and $R_{\text{spot}}(\text{two
spots}) = 8 \pi F$.
Figure~\ref{fig:reconst_compare} confirms our analysis, and our spot
regularizer demonstrates a significant improvement over total variation.

\subsection{Reconstruction procedure and results}\label{sec:reconst_proc}

The instrumental resolution is given by the largest CHARA baseline in our data
sets (S2-W1 or E2-W1, $\simeq 250$ meters), corresponding to~$1.3$ mas in H
band. Taking into account a super-resolution factor of four, the effective
resolution of the reconstructed images should be about $0.3$~mas. In order to
avoid excessive pixellation of the images, the actual resolution of the
reconstruction was set to $0.1$~mas. We ran five batches of multi-threaded
SQUEEZE with $16$~threads each, corresponding to a total of $80$~independent
Markov chains that were averaged to reconstruct the final images. The number
of pixel elements in each chain was set to~$5000$, with a length of~$500$
iterations. In addition to the spot regularizer derived in the previous
section, we made use of the fitting results from section~\ref{sec:ldd} to
constrain the reconstruction. The fitted limb-darkening discs were used to
initialize the chains to sensible starting points.The factors~$\mu_k$ were
chosen so that the actual reduced $\chi^2$ is roughly unity for the
reconstructed image.  The final reconstructions are presented on
Figure~\ref{fig:images}. For T~Per, the spot location in North West quadrant
agrees with the conclusions of Bayesian model selection. For RS~Per, there is
indeed a darker area in the South West. However the correct interpretation is
unclear: this may be a dark spot, or most of the surface could be understood
as a temporary hot convection cell. Without data outside the 2007 July/August
period, we cannot conclude from this single RS~Per image. To exclude the
possibility that the surface
features on Figure~\ref{fig:images} are due to ({\it u,v}) coverage or to
noisy data, we ran an ''artifact test" on both targets. We generated synthetic
observations of the limb-darkening discs derived from model fitting, with
exactly the same ({\it u, v}) coverage and signal-to-noise as the real data
sets. We then reconstructed the images using the same procedure outlined
above, and we found that the reconstructions did not display any significant
surface features.
\begin{figure}
\centering
\includegraphics[width=0.5\linewidth]{tper_image.eps}%
\includegraphics[width=0.5\linewidth]{rsper_image.eps}%
\caption{Reconstructed images of T~Per (left) and RS~Per (right) with the
  SQUEEZE-MCMC engine and the ''spot regularizer'' presented in
  section~\ref{sec:newreg}. The angular diameters estimated by model-fitting
  are indicated by white circles.}\label{fig:images}
\end{figure}

\section{Discussion and Conclusion}

We have analyzed the CHARA/MIRC data taken in H~band on two red supergiants
T~Per and RS~Per and presented evidence for the existence of spots on their
surfaces. For this we developed a set of tools dedicated to the analysis of
spotted stars. As the utility of simple model-fitting procedures is limited
for spotted stars, we demonstrated that Bayesian model selection is capable of
assessing the relative probabilities of various models, the Bayesian evidence
constituting a more reliable metric than the reduced $\chi^2$. Our results on
T~Per confirm that hot spots can indeed be observed in $H$-band. If considered
together with similar results on $\alpha$~Ori by \citep{Haubois2009} and on
VX~Sgr by \citep{Chiavassa2010a}, it seems we should expect a significant
proportion of RSGs to have bright spots, as is thought to be the case for AGB
stars \citep{Ragland2006}. Considering the typical continuum opacity curves in
such cool atmospheres \citep{Woodruff2009}, the continuum opacity should be
close to
minimum in H~band, where our MIRC observations took place. These spots must be
generated very
close to the photosphere, and therefore it seems currently doubtful that their
enhanced contrast may be explained by opacity effects.
As the correct approach to model these objects is not really to model
spots, but to interpret the surface in terms of convective cells using 3D
models \citep{Chiavassa2010b}, inhomogeneous granulation temperatures may
explain the
spots. Our detection of a ''dark spot`` on RS~Per probably corresponds to a
cooler
granulation, imaged with the reduced dynamic contrast typical of current
interferometry.

We also found that classic regularizers are hardly adequate to reconstruct
model-independent images of spotted surfaces. Hence we derived a novel
regularizer tailored for this task, based on simple Compressed Sensing and
Occam's razor principles. Our reconstructions of T~Per and RS~Per were found
to essentially agree with the Bayesian spot selection.

It should be underlined that the data quality from MIRC circa 2007 was a major
limiting factor in the present analysis. Fortunately since 2007, the MIRC
combiner underwent a series of hardware upgrades which drastically improved
its performance. MIRC-6T can now simultaneously combine all six CHARA
telescopes with thrice higher signal-to-noise and much lower systematic
errors. A survey of several RSGs over longer periods of time with MIRC-6T
would allow to conclude to whether spots on M~supergiants are ubiquitous, and
in particular if a relationship can be found between circumstellar
activity/infrared excess and the complexity of observed surface features. Our
future work will thus focus on the analysis of new RSG data collected with
MIRC-6T, with a systematic application of Bayesian model selection to
3D~hydrodynamical models, and the development of better reconstruction
algorithms for RSGs.

\acknowledgments

The authors would like to acknowledge funding from the NSF through award
AST-0807577 to the University of Michigan, as well as funding by the
Australian Research Council and the ``Lend\"ulet Fiatal Kutat\'oi Program'' of
the Hungarian Academy of Sciences for the initial work on these objects.

This work is based on observations collected at the Center for High Angular
Resolution Astronomy (CHARA) operated by the Georgia State University at
Mt. Wilson, California. This research also relied on observations with AKARI,
a JAXA project with the participation of ESA, and made use of data products
from the Wide-field Infrared Survey Explorer (a joint project of the
University of California, Los Angeles, and the Jet Propulsion
Laboratory/California Institute of Technology, funded by the National
Aeronautics and Space Administration), and from the Two Micron All Sky Survey
(a joint project of the University of Massachusetts and the Infrared
Processing and Analysis Center/California Institute of Technology, funded by
the National Aeronautics and Space Administration and the National Science
Foundation).

redpajama_set_name: RedPajamaArXiv


text:
Centrohelidní slunivky (Centroplasthelida, s mladšími synonymy Centrohelea či Centroheliozoa) je velká skupina jednobuněčných eukaryot dříve řazená do nepřirozené skupiny slunivek (Heliozoa). Taxon s původním mezinárodním jménem Centrohelida ve svém vymezení obsahoval i řád Gymnosphaerida, dnes řazený mezi Cercozoa, a proto je z dnešního pohledu polyfyletický a jako nepřirozený by se neměl používat.

Centroplasthelida zahrnují pohyblivé i nepohyblivé zástupce, žijící v sladkovodních i mořských vodách, zejména v určité hloubce.

Popis
Jedinci jsou jednobuněční a kulovitého tvaru, obvykle asi 30-80 μm v průměru. Z jejich těla vychází bezpočet dlouhých panožek, axopodií, které jsou upevněné na mikrotubulární vlákna. Tyto panožky jim umožňují pohyb a aktivní získávání potravy.

Některé druhy nemají kolem buňky žádný plášť, většina však je obklopena želatinózním obalem s množstvím šupinek a ostnů, které vznikají v speciálních váčcích a chemicky se mohou zakládat na organických látkách, nebo na křemíku. Na rozdíl od ostatních slunivek, které mají mitochondrie s trubičkovitými (tubulárními) kristami, mají mitochondrie centrohelidních slunivek kristy ploché.

Systematika
Evoluční pozice centrohelidních slunivek byla dlouho nejasná. V současnosti (rok 2022) je tato skupina řazena na základě molekulárně biologických analýz do kmene Haptista jalo sesterskou skupinu haptofyt, i když některé nedávné analýzy naznačují i jiná možná umístění. V systému Cavaliera-Smithe tvoří třídu monotypicého podkmene Heliozoa. Již fylogenetická analýza z r. 2011 potvrdila s vysokou spolehlivostí přirozenost této třídy, která je potvrzována i v následných analýzách.

Aktuální (rok 2022) klasifikace do úrovně čeledí (rody jen výčtem v závorce):

 Kmen: Haptista
 Třída: Centroplasthelida  [Centrohelea ; Centroheliozoa ; ne však Centrohelida ] – centrohelidní slunivky
 Incertae sedis Centroplasthelida:
 Rody: Parasphaerastrum, Meringosphaera
 Čeleď: Spiculophryidae  (Spiculophrys, Heteroraphidiophrys)
 Řád: Panacanthocystida
 Podřád: Chalarothoracina
 Infrařád: Acanthocystida
 Čeleď: Acanthocystidae  (Acanthocystis)
 Čeleď: Raphidocystidae  (Raphidiocystis)
 Infrařád: Chthonida
 Čeleď: Yogsothothidae  (Yogsothoth, Pinjata)
 Podřád: Marophryina
 Čeleď: Marophryidae  (Marophrys)
 Řád: Pterocystida – pravděpodobně parafyletický
 Podřád: Raphidista
 Čeleď: Choanocystidae  (Choanocystis)
 Čeleď: Raphidiophryidae  (Raphidiophrys, ?Polyplacocystis)
 Podřád: Pterista
 Čeleď: Clypiferidae  (Clypifer)
 Čeleď: Oxnerellidae  (Oxnerella)
 Čeleď: Pterocystidae  – parafyletická (Pterocystis, Chlamydaster, Khitsovia, Pseudoraphidiocystis, Pseudoraphidiophrys, Raineriophrys syn. Raineria syn. Echinocystis, Triangulopteris)
 Čeleď: Heterophryidae  (Heterophrys, Sphaerastrum)

Vzhledem k tomu, že analýzy environmentálních vzorků identifikovaly mnoho dosud nepopsaných linií na úrovni rodů i čeledí, a protože pravděpodobně dojde k rozdělení taxonů, které byly identifikovány jako nepřirozené, lze očekávat, že výše uvedený systém dozná podstatnějších změn.

Vzájemnou příbuznost vyšších taxonů podle současných (rok 2022) představ ukazuje následující fylogenetický strom:

Poznámky

Reference

Externí odkazy

Chromalveolata

redpajama_set_name: RedPajamaWikipedia


Problem Description: I placed the order thru your online store for CoPilot Live Premium Android, using a Dell Windows XP PC to place the order. I received this download link via email http://www.copilotlive.com/store/download.asp, but after I enter the pertinent info, when I click on the "download" button, it just causes another window to pop up with another download button. Clicking the download button does not cause a download to start. Please let me know what I need to do to make this work.
Some of our customers have experienced difficulties downloading CoPilot via Internet Explorer. If you are using Internet Explorer, I would suggest you try downloading CoPilot via Mozilla Firefox or Google Chrome.Please be aware that the web browser you are using and/or your browser settings can affect the downloading of an application.
I don't use Internet Explorer. I was using Firefox 13.0.1 when it would not let me download the CoPilot for Android that I purchased. I would like to get the product I bought. Surely you must have a way for me to download it.
Please try using a different web browser than the one you are currently using.
When I click on the "download" button, it simply brings up another page with another download button, and when I click on this button, nothing happens.
Please note that I have "simple" home internet access - these computers are not protected by any kind of firewall or protective software that might interfere with a download. I download things all the time from many other sites without any problems like I'm having downloading from your site.
Please advise what WILL work, rather than just "try something else"
I realize I am trying to use a Windows PC to download an Android version of CoPilot (and I have a good reason), but ALK sure hasn't even hinted that's the problem. Surely the file download functionality of ALK's website cannot be platform-specific.
Update: I had a friend try to download CoPilot using the link I was given. They were using a Mac at a different location than my computers. And they had the same result - clicking on the download button just brings up another window with another download button (that does nothing when clicked).
Guess you'll have to do it on an Android. You've tried everything else!
Does anyone already have this file?
If you download it with your Android device, the file will be on the phone. You just need a file browser to hunt it down, but it will be there.
I just tested the site, and downloaded the APK file without any issues from the link you were sent. Have you tried downloading the APK file directly to your mobile device? This is recommended.
My reply: Specifically which url did you download it from? And specifically what did you use to download it?
I downloaded the APK from http://www.copilotlive.com/store/quickstart.asp. I was able to do so using Google Chrome on a Windows 7 PC. I've also been able to use this URL to download the APK straight to my mobile phone in the past.
Jason - I went back to http://www.copilotlive.com/store/quickstart.asp again, and just happened to click on the "QR code" that is located under the line "Step 1: Download CoPilot Live APK Download the 'com.alk.copilot.alkdirect.apk' file directly to your Android smartphone/tablet" and it opened up a normal download window (with a save as).
I had no idea this QR code was a link. It does not look like any clickable download link on any other website, and there is NO text anywhere saying to click on the QR code. I'm sure I'm not the only one who would not recognize that QR code as a clickable link. But now, after who knows how many messages back-and-forth to Sebastien and yourself, I finally stumbled on to it. There is no reason it should be this difficult to download your software.
Which brings me to my next problem, since I plan to get the laptop version as well. Under the "CoPilot Live v8 Laptop" it says: "Step 1 - Download CoPilot Live v8 laptop software and maps to your laptop - Click on the download link above and save the .EXE file to a location on your laptop."
But I do not see that "download link" anywhere on that page. Please let me know WHERE that link is.
In addition to downloading the app, you will also need an Internet connection on your device to activate CoPilot and download the maps. You are welcome to use an Internet mobile connection but please be aware that we strongly recommend a WiFi connection as it is more stable and will take less time to download.
The link you gave below: http://www.copilotlive.com/store/com.alk.copilot.alkdirect.apk works without any problem on my WinXP pc. It was never an issue of which OS/browser to use.
Since your previous message, I had finally realized that the QR code at http://www.copilotlive.com/store/quickstart.asp is a clickable link (the same link you gave in your latest email). I had no idea this QR code was a clickable link, since it does not look like a normal clickable download link on other websites, and there is no text anywhere saying to "click on the QR code." I'm sure I'm not the only one who would not recognize that QR code as a clickable link. In the meantime I was able to get my Toshiba Thrive tablet connected to the internet via a wired USB-Ethernet connection, so that should provide the most stable download of all.
I now have my Toshiba Thrive tablet (freshly updated to Android 4) connected to the internet (wired LAN connection via a Linksys USB300M USB ethernet adapter). Using the Thrive, when I go to the link ALK originally provided, I STILL get the same result after entering the requested information and pressing the download link button merely brings up another window with another download link that does not work!
I guess I'm glad I already have it on my PC. I can't honestly remember the download but think they provided a couple of links. It certainly wasn't that difficult fortunately.
which are referred to on the "Quickstart Setup" page: "Click on the download link above" - but isn't actually anywhere on that page.
I didn't want to post the links in an open forum, but if anyone needs these links, let me know.
We need to download a few files to get you started with OnDemand Maps. This should only take a few minutes.
My only option on this page is the red bar at the bottom labled "Quit CoPilot"
How long should I wait? It seems like it has been far too long already.
FWIW, the Thrive tablet has a fully functional internet connection, which is working fine. I just checked it by pulling up the latest google news page and local weather, so I know the problem is not a lack of a good internet connection.
"You will need to finish downloading your first map to start using CoPilot Live. If you quit, your download will automatically resume when CoPilot is restarted or you may download your map with CoPilot desktop management software. Access CoPilot Central at www.copilotlive.com/central"
Oh goody. ALK is sending me on yet another wild goose chase. Naturally I tried that url. And guess what? It doesn't work either. It automatically redirects to a different URL on the UK version of their website.
This is beyond ridiculous. The rudimentary navigation functions in S&T are looking better all the time. Maybe someday ALK will get their act together. More likely Google will make a standalone nav program for Android that will be better, and certainly will be a lot easier to install.
How do I download maps to my Android phone/Tablet?
Installing CoPilot Live on an Android phone is a two stage process. You first need to install the application on your mobile device, then download your required map region to your device's memory card.
1) Install the application on your mobile device. If you have purchased CoPilot Live from Google Play (Android Market), the application should download and install automatically. If you purchased CoPilot Live from the CoPilot Live online store or from a reseller you will need to download and install the application by going to to the links provided in your receipt/order confirmation email.
So what ALK is saying now is that the maps can ONLY be installed over a Wi-Fi network connection. Even though ALK tech Sebastien previously told me that a Wi-Fi connection is the "preferred" connection (compared to a cellular network, for obvious reasons). After many emails, in all of which I told them I was connecting via a wired USB ethernet adapter, and after successfully downloading and installing the CoPilot app itself via my USB-Ethernet adapter, this was the very first indication of any requirement to download anything via Wi-Fi.
So I went and got a Wi-Fi router, hooked it up, and what do you know? Where it had stalled out at the "OnDemand Maps" step before, when connected via Wi-Fi instead of via wired ethernet, it proceeded without further delay, and downloaded the full 1.3GB North American map without any further problems.
I proceeded to take the Thrive tablet outside to see how quickly it locked on to the GPS satellites, and although the GPS lock was established fairly quickly, when I launched CoPilot, it still took nearly two minutes to acquire the location, even though it showed seven GPS satellites with fairly strong signal bars.
My subsequent experience (which is limited to about 15 minutes walking up & down the street) is not too positive. CoPilot locked up (I think) twice during this time. I could get back to the home screen, where eveything else worked, but all that was where CoPilot was supposed to be was a blank black screen. I had to reboot the Thrive to clear this problem. Maybe I should have tried CoPilot before I updated the Thrive to Android 4.0.4, but I wanted to do that first, before any applications were installed. And I had no problem installing the two OS updates via my USB-ethernet adapter (or doing anything else via this internet connection, except installing CoPilot's map data).
UPDATE: I was just able to duplicate one of the circumstances that locks up CoPilot: clicking on "Route Demo" freezes the screen in CoPilot. I can go back to the home page, where everything seems to work normally, but if I then try to go back to CoPilot, the screen is completely black except for the task bar at the bottom, and the only way to clear this is to reboot the Thrive tablet.
• Where can I download ALK CoPilot?


I so love this editorial because it is so me (and I know, you too!). I have been blogging full-time for quite a long time now and this have been how my daily routine already looks like. Checking instagram while having coffee, answering emails in bed, browsing the web to find post inspirations, taking selfies and the list goes on. . .


Lyme disease, or 'Borreliosis', is a bacterial infection passed to humans through a tick bite. It is currently the fastest growing vector-borne disease. The bacteria is shaped like a corkscrew (called a spirochete) which enables it to burrow through body tissue which most other bacteria wouldn't be able to penetrate.
Infection starts with a tick bite and symptoms usually follow a few days or weeks after a bite. The first signs are an erythema migrans (EM), or "bulls eye" rash that generally radiates outwards from the source of the bite. Presence of a rash is a strong indicator of infection with Lyme disease although it might not be present in up to 50% of patients. Chronic flu like symptoms and fatigue are usually experienced soon after an infection.
Occasionally, the patient may carry Lyme disease but have no outwardly obvious symptoms. Ill health may crop up years later following an illness or period of stress. This leads to disseminated (or late) Lyme disease, where symptoms are similar to Multiple Sclerosis, Chronic Fatigue Syndrome or Parkinson's disease. Lyme disease can lead to joint pain, weakness, muscle aches, pelvic pain, visual problems, tremors, headaches and heart problems, and can even result in paralysis and loss of sight. For a full list of symptoms click here.
Treatment is by a course of antibiotics and if caught and treated within a few weeks it is normally successful. However infections lasting more than a few weeks become increasingly difficult to treat needing long courses of antibiotics and in some cases intravenous antibiotics may have to be used. Symptoms become more varied and debilitating the longer an infection is left untreated. Chronic Lyme disease occurs in patients who remain untreated for a long time.
Testing techniques for Lyme disease have limitations and can prove to be falsely positive or negative. Therefore it is important to take into account the clinical history of a tick bite or exposure to ticks.


text:
A Superworld – Power Girl: Gods and Mortals, Part 3
Written by erikphandel :: [Wednesday, 26 August 2015 17:50] Last updated by :: [Wednesday, 08 June 2016 10:27]
1276 A Superworld – Power Girl: Gods and Mortals, Part 3 /index.php/library/sort-by/title/item/1276-a-superworld-power-girl-gods-and-mortals-part-3
It was a cold night in the middle of the Texan desert. So-Hyun did not mind, despite being dressed less than appropriately for almost sub-zero temperatures. Claire was shivering and holding to her friend strongly.
"Look, we can still give up and go back home. I don't know how you convinced to go this far." So-Hyun said, her face frowned and worried.
"You came here because you're even madder at Luthor than I am! C'mon, let's get that bitch something to cry about." Ignoring the cold, she released So-Hyun and ran towards the super-secret lab that was home to Lex Luthor's metahuman researches. The building was protected with a tall wire fence, electrified and filled with cameras.
"Power Girl, a little help here?"
So-Hyun sighed, but knew there was no stopping Claire now. She was stubborn, to say the least. She grabbed her and floated upwards, going across the fence easily. Only a huge metal door separated them from the lab.
So-Hyun tried to spy inside with her x-ray vision, but for some reason she could not see anything from the lab.
"Luthor must have added a lead layer to the lab's walls. She's good. But she can't do nothing to stop you, girl."
So-Hyun rested her hands on the metal door, and breathed slowly. She pressed her fingers against it, to grab a hold on it. Her finger dug into the dense, thick metal like it was made of butter. Putting more strength in her arms, she opened them slowly, and could clearly hear the creak of the metal trying to maintain its structure, and failing. With little effort, she managed to open a gap on the door so big that them both could easily enter the laboratory.
"Wow…" Claire was always amazed by the super-strength feats of her friend. She entered, sliding her fingers through almost a meter of thick steel that was the door her friend so easily opened.
The place was dark and cold. Machines that could never be turned off hummed at the background, and several LED lights blinked randomly all across the room. So-Hyun walked towards the enormous particle accelerator, and turned some buttons and switches on. The equipment quickly came to life, and then coughed and buzzed for several seconds before shutting down again.
"Looks like we have a lot of work to do."
"Don't worry, I can handle that." So-Hyun vanished in a white and red blur, and all the dirty and exploded parts of the accelerator began to rearrange themselves. She connected loose cables and substituted fried parts faster than Claire's eyes could follow. At one point, she had to lift an entire section of the accelerator to fix the lower circuitry, and did in half a minute an operation that would take a whole week without superhuman help. In just a few moments, the accelerator was as good as new.
"Well, now you made me jealous." Said Claire, completely amazed.
"You don't have to be. Soon, you'll be as awesome as I am."
"You really think so?"
"Of course I do! Why would the result be different anyways? This is a scientific experiment. We just have to do everything right."
She turned on the accelerator, which this time emitted noises far more healthy and pleasurable to the two of them. The whole room began to shake under the power of the machine. Soon, their eyes were filled with a bizarre light. It happened again. Inside the accelerator laid a connection with the very source of the universe. And yet…
"Wait a minute, Claire. Something is wrong."
"Wrong? What do you mean?" Clair was mesmerized by what was happening, and could not take her eyes off the strange structure of light and darkness inside the machine.
"There's something … Different this time. This … Thing, it was not as bright when I did it. And it was not green."
Claire was not even listening at this point. She just pressed the button to open the observation panel, and strode slowly inside the machine. "But it's so … beautiful …"
"Claire, NO!"
It was too late. Claire touched the source with her hand. Instead of the usual orgasmic pleasure that everyone that connected to the source felt, Claire felt a sting in her fingers. Slowly, an unbearable pain took over her hands, and then her arms, and made her cry and scream in agony. So-Hyun tried to separate her friend from the source, but even her superhuman strength could not perform that task.
"Foolish humans!" an otherworldly voice echoed through the room. "You toy with powers beyond your comprehension! You think this is science? You think you can just sap from my source of power as you see fit? I shall punish your arrogance!"
Claire's body twisted in such pain no one has ever felt before in human history. Her mind went numb and her thoughts went silent, and she wished she was dead so this pain could be over. Her body began changing.
"I will mark you as an example! Everyone in this planet that sees you, and what you did to yourself, shall know the forces of the universe are not to be trifled with."
Claire's muscles began to grow. First her arms and legs, her biceps ripping through her shirt. She grew in height and size, and her blue eyes turned bright green. Her tight jeans and t-shirt were in shreds as her massive muscles now demanded to be free. Her breasts grew proportionally, popping her bra open in instants. With a last deafening scream of pain, her pale skin turned bright green. The source vanished, stopping the pain and making Claire fall to her knees. She breathed heavily and cried silently.
"Kimmie …" she managed to say after a long silence. "What happened to me?"
"I … Claire … Oh man …"
She raised her hands and looked at them. "I just wanted to beautiful and powerful like you … Kimmie."
"Claire, please, calm down."
"WHAT HAPPENED TO ME?" she yelled, and in an uncharacteristic spasm of rage, swung her huge arm in So-Hyun's direction. Half of the observation panel flew across the room when her hand hit it.
"Wow. Claire, you have to calm down. We can fix this. Just-"
Claire was not listening anymore. In pure rage, she lunged at So-Hyun with unbelievable strength.
Alexis Luthor woke up to the sound of the alarm in her lab. With a perverse smile on her face, she put on her power suit, and woke up her little experiment.
Claire landed another violent punch on So-Hyun's belly. Despite her superhuman durability and resistance, Claire's punch hurt So-Hyun unlike anything had ever hurt her in her life, not even Thor's hammer. She flew across the room, making a huge hole in every wall she smashed, until she landed a few miles outside the lab, in the middle of the desert. She tried to recuperate, but Claire was already on her. With her two overgrown hands, she squeezed Power Girl's neck.
"Cl-Claire … Hgnnnnn. Stop … This …"
Claire was not listening. She would have killed So-Hyun, had not a laser bullet hit her in the head. It did not hurt her, but it distracted her. She turned around and forgot about So-Hyun for a moment, loosening her grip.
"You … YOU SUED KIMMIE!" she yelled.
"Wait, what? You were just trying to ki-"her surprise was interrupted when Claire hurled an enormous chunk of earth in her direction. Her reflexes activated the hydraulic muscles from her power armor, putting her away from danger just in time with a side roll.
"Call in the Rogue. NOW!" said Luthor putting her fingers on her ear.
An helicopter approached, but Claire didn't care. She jumped at Luthor almost in a flash of speed. Luthor tried to counter her strength, foolishly trusting too much on her power armor. She held both of Claire's hands with hers, and tried to push her away. However, she soon began to hear the creaks and snaps of the inner mechanics of her armor giving up on Claire's superhuman strength. One person jumped out of the helicopter, and it began to shoot Claire with a built-in machine gun. As soon as the bullets entered Claire skin, it began to heal almost immediately. When the bullets finished penetrating her skin, the wound they had just made was already healed, and the pure force of her healing muscles reduced the bullets to dust. It nevertheless managed to divert Claire's attention again.
"I tire of your little toys …" she whispered, and jumped towards the flying helicopter. Easily reaching it, she grabbed the machine's tail and, with a mid-air spin, flung it towards Luthor. So-Hyun knew not even her armor could withstand an explosion like that, so she used her super-speed to rush in front of her and grabbed the helicopter before it hit the ground.
"Are you all right?" asked So-Hyun to the helicopter's pilot. The poor man was wide eyed with a mix of pure terror of the green behemoth that was flinging helicopters like they were baseballs and marvel for having just been saved by the most beautiful Asian woman he had ever seen in his life. He passed out in emotion.
"I hope you are" she sighed, putting the chopper down gently. She flew towards Claire, who was standing several meters from her, spewing rage and spit from her mouth. Before Claire could have any reaction, So-Hyun slapped her right cheek with all the strength she had, knocking one of Claire's teeth out of her mouth.
"AND YOU STOP THIS CHILDISH TANTRUM THIS INSTANT, CLAIRE!" she shouted at a completely astonished Claire. "EITHER YOU CALM DOWN RIGHT NOW, OR I WILL NEVER EVER TALK TO YOU AGAIN, DO YOU UNDERSTAND?"
"Kimmie …" she began to cry. So-Hyun hugged her, and Claire finally calmed down. Just as things began to get better for them, they felt a cold touch on their shoulders, and both of them passed out, dropping to the ground.
Luthor disposed of her broken suit, and walked slowly towards the two knocked out metahumans, rubbing her hands in pleasure.
"Good job, Rogue." She said to the pale, skinny girl standing behind the two. "Now, what shall I do with those two …"
Categories SWM Library | A Superworld

redpajama_set_name: RedPajamaCommonCrawl


text: Q: Select Mapped Devices with FolderBrowserDialog using Mono Is there any way to allow FolderBrowserDialog to show up other devices or mapped drives in OSX? I Have a network mapped directory and it doesn't appear in the list.

redpajama_set_name: RedPajamaStackExchange


Your Dog is boarding in our kennels and you want he/she to have a great time playing during the day with his/her friends. We offer a discount to those who use this service while they are staying in the facility. This price is in addition to the boarding rate. For example: Your dog is boarding Monday through Friday and you want he/she to play each day in daycare. You pay a total of $28 per date for your dog to board and play in daycare each day.
$18 is the boarding rate per date.
$10 is the daycare rate per date.


text:
March 13, 2013, 12:46 p.m.
Starting April 1, Burmese publishers can print daily newspapers
LINK: www.theatlantic.com ➚ | Posted by: Caroline O'Donovan | March 13, 2013
For the first time in five decades of authoritarian rule and ironclad media regulation, Burma's media, previously relegated to weekly publications, will be allowed to print daily newspapers. The Atlantic takes an in-depth look at their high hopes and likely struggles.
Kyaw Min Swe, the chief editor of the news journal The Voice Weekly, is one journalist who professes to have long dreamed of publishing a daily newspaper. But like Ko Ko, Kyaw Min Swe has no illusions about the challenges that must be overcome to launch a daily and admits he knows little of how a daily newspaper operates. The Voice is also publishing a daily newspaper in-house to allow reporters and editors to practice on tighter deadlines. But delivering the newspapers to readers hands will be the primary obstacle, Kyaw Min Swe said.
Internet connections, necessary to send design files to printers, remain slow and inconsistent. Much of the country lacks well-paved roads to bear newspaper-laden trucks. Burma still struggles even to provide consistent electricity. As Kyaw Min Swe discussed the challenges of launching a daily newspaper, the power failed several times in the downtown Rangoon building that houses The Voice. "We are just preparing, preparing," he said. "Hopefully we will publish daily paper, but were not confident yet. Well try to publish as soon as possible."
daily newspapers
O'Donovan, Caroline. "Starting April 1, Burmese publishers can print daily newspapers." Nieman Journalism Lab. Nieman Foundation for Journalism at Harvard, 13 Mar. 2013. Web. 30 Jan. 2023.
O'Donovan, C. (2013, Mar. 13). Starting April 1, Burmese publishers can print daily newspapers. Nieman Journalism Lab. Retrieved January 30, 2023, from https://www.niemanlab.org/2013/03/starting-april-1-burmese-publishers-can-print-daily-newspapers/
O'Donovan, Caroline. "Starting April 1, Burmese publishers can print daily newspapers." Nieman Journalism Lab. Last modified March 13, 2013. Accessed January 30, 2023. https://www.niemanlab.org/2013/03/starting-april-1-burmese-publishers-can-print-daily-newspapers/.
| url = https://www.niemanlab.org/2013/03/starting-april-1-burmese-publishers-can-print-daily-newspapers/
| title = Starting April 1, Burmese publishers can print daily newspapers
| last = O'Donovan
| first = Caroline
| date = 13 March 2013
| ref = {{harvid|O'Donovan|2013}}


text:
<!DOCTYPE html>

  <meta charset="UTF-8">

  <title>CSS Containment Test: 'contain: size' applies to inline-block</title>

  <link rel="author" title="Gérard Talbot" href="http://www.gtalbot.org/BrowserBugsSection/css21testsuite/">
  <link rel="help" href="https://www.w3.org/TR/css-contain-1/#containment-size">
  <link rel="match" href="reference/contain-size-027-ref.html">

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Women Taken on Longer Uber Rides Than Men
A new study finds black people face longer wait times, and some women are taken on longer routes than men.
By Prachi Gupta Published: Oct 31, 2016
Findings from a new study suggest that Uber and Lyft drivers are biased against black people and women. The study, conducted in Seattle and Boston by researchers at Stanford University, MIT, and the University of Washington, found that "Across all trips, the cancellation rate for African American sounding names was more than twice as frequent compared to white sounding names." It also found that some women were taken on longer routes than men.
"Other female riders reported 'chatty' drivers who drove extremely long routes, on some occasions, even driving through the same intersection multiple times," the study noted. "As a result, the additional travel that female riders are exposed to appears to be a combination of profiteering and flirting to a captive audience."
"The patterns of discrimination were quite clear and consistent in both cities — and one can only assume it's happening all across the country in other markets," said study co-author Christopher R. Knittel, a professor at the MIT Sloan School of management. "The study has found major areas of racial discrimination within this new industry. It's quite concerning."
The study was executed by four black and four white research assistants, half of whom were men and half of whom were women, who accepted nearly 1,500 rides. In Seattle, the researchers used their real photos on the apps and found that black riders consistently waited as much as 35 percent longer than white riders. In Boston, riders used racially ambiguous photos and adopted either "African American sounding" or "white sounding" names. According to the study, Uber drivers canceled on riders with African American-sounding names more often than white people.
Bloomberg reports on more of the findings:
Lyft and Uber's issues were slightly different. While researchers found that wait times were noticeably longer for black men on both services in Seattle, Lyft drivers didn't cancel on black riders disproportionately. But the researchers said that because Lyft shows riders' names and faces upfront, its drivers could simply screen out black passengers. Uber doesn't show names until after the driver accepts the fare. "In Lyft, you can discriminate without ever having to accept and hit cancel," Knittel said.
In response to the findings of bias, the researchers recommend that rideshare apps offer up-front fares, provide regular internal reviews of driver conduct regarding bias, implement harsher consequences for drivers who cancel after accepting a rider, and not display the rider's name on the app.
Lyft and Uber have responded to the study with similar statements. "Ridesharing apps are changing a transportation status quo that has been unequal for generations, making it easier and more affordable for people to get around — no matter who they are or where they live," said head of North American operations Rachel Holt in a statement emailed to Cosmopolitan.com. "Discrimination has no place in society, and no place on Uber. We believe Uber is helping reduce transportation inequities across the board, but studies like this one are helpful in thinking about how we can do even more."
"We are extremely proud of the positive impact Lyft has on communities of color. Because of Lyft, people living in underserved areas — which taxis have historically neglected — are now able to access convenient, affordable rides," said Adrian Durbin, director of policy communications. "And we provide this service while maintaining an inclusive and welcoming community, and do not tolerate any form of discrimination."
Follow Prachi on Twitter.
Prachi Gupta
Prachi Gupta is an award-winning journalist based in New York. Her first book, about Rep. Alexandria Ocasio-Cortez, is available via Workman Publishing.
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Home Second Amendment Michigan Man Confronts Gun Toting Right Wing Extremists, "Get Your F*cking Guns...
Michigan Man Confronts Gun Toting Right Wing Extremists, "Get Your F*cking Guns Out Our Town."
Far-right gun-toting "boogaloo" right-wing extremists were publicly carrying their guns when they were confronted by residents telling them to get their guns out of their town.
Video of an Ann Arbor, Michigan resident not being intimidated by domestic terrorists:
"Get your fucking guns out of here, man!" — a angry bystander to Boogaloos carrying long guns in Ann Arbor, Michigan (video via @FordFischer) pic.twitter.com/sAszD1cCDY
The boogaloos are fight right-extremists who have sprouted off from white supremacy,neo-nazis, and, more recently, libertarianism. The militias have a stated goal of starting a second civil war.
The reason why they carry long guns in public is to intimidate people, but the Ann Arbor resident wasn't having it. He told the extremists, "We don't need this. We've been through a pandemic. Get your f*cking guns out of here, man."
He continued, "The law is they (the police) are in charge, not you. Get the f*ck out of our town."
The bystander asked the right-wing militia if they were a part of the Capitol attack, and they answered, "The Trumpers? No. God no."
The American people have had enough. They are no longer going to be intimidated by right-wing extremists carrying guns and trying to play cop or soldier on America's streets. Ann Arbor is one of the most liberal college towns in America.
After years of Trump and right-wing extremism, something has changed, as there is growing evidence that most Americans have had enough and aren't going to be bullied by the extreme right anymore.
For more discussion about this story join our Rachel Maddow and MSNBC group.
Follow and Like PoliticusUSA on Facebook
Mr. Easley is the founder/managing editor, who is White House Press Pool, and a Congressional correspondent for PoliticusUSA. Jason has a Bachelor's Degree in Political Science. His graduate work focused on public policy, with a specialization in social reform movements.
Awards and Professional Memberships
Member of the Society of Professional Journalists and The American Political Science Association
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Valmet to replace its first-ever Damatic Classic automation system delivered at Pankaboard's board mill in Finland
Valmet Oyj's trade press release on February 8, 2018 at 11:00 a.m. EET
Valmet will replace the first-ever Damatic Classic automation system delivered with a Valmet DNA automation system at Pankaboard's board mill in Lieksa, Eastern Finland. The system has been operating since 1979. Additionally, Valmet will also upgrade the mill's existing Valmet Damatic XD automation system to Valmet DNA. The new system will increase process availability and improve its performance.
The order was included in Valmet's fourth quarter 2017 orders received. The project will be executed in several stages and completed by mid-2019.
"At Pankaboard, we regard this project as an all-important business development project, and one that an advanced automation system supports well. The new system will enable us to develop our customer need-based and flexible operating model more cost efficiently," says Lauri Junnila, Managing Director, Pankaboard Oyj.
"New information management tools will provide the mill with a whole new dimension to process operations, giving operators access to the trend and event history straight from the operator interface. Together with functional descriptions linked to the controls, this will enable faster troubleshooting," says Juha Mykkänen, Sales Manager, Automation, Valmet.
Information about Valmet's delivery
The new Valmet DNA automation system will replace the current control systems in the stock preparation, on board machines BM2 and BM3, and in the integrated biofuel plant. Pankaboard currently has three generations of Valmet-supplied automation systems: Damatic Classic, Damatic XD and Valmet DNA.
In addition to the automation replacement, Valmet will upgrade the biofuel plant control room. Startup, commissioning, training and spare parts are included in the delivery scope.
Information about Pankaboard
Pankaboard produces high-quality specialty cartonboards for food, luxury beverage, pharmaceutical, food service, graphics and display, as well as laminate industries. The mill is specialized in high-thickness folding boxboards and uncoated cartonboards produced with two distinctly different board machines, BM2 and BM3. Through its own sales offices and sales agent network, Pankaboard has more than 500 customers in 65 countries. The company employs 160 people.
Juha Mykkänen, Sales Manager, Automation, Valmet, Tel. +358 40 543 4704, juha.mykkanen@valmet.com
Kari Silvennoinen, Product Manager, Automation, Valmet, Tel. +358 50 317 0834, kari.silvennoinen@valmet.com
Valmet's net sales in 2017 were approximately EUR 3.2 billion. Our more than 12,000 professionals around the world work close to our customers and are committed to moving our customers' performance forward - every day. Valmet's head office is in Espoo, Finland and its shares are listed on the Nasdaq Helsinki.