text:
\section{Introduction}
The 2020 Astronomy and Astrophysics (Astro2020) Decadal Survey report\cite{Astro2020} recommended a large infrared / optical / ultraviolet (IR/O/UV) telescope aiming to obtain spectra of a robust sample of $\sim$25 potentially habitable exoplanets. While the telescope design has yet to be defined for this mission, preliminary modeling has shown that the minimum aperture size to achieve this scientific goal is likely $\sim$6 meters (inscribed) assuming an off-axis, unobscured telescope equipped with a coronagraph instrument\cite{Stark2019}\,. The Large UV/Optical/IR Surveyor (LUVOIR) report\cite{LUVOIR_finalReport} discussed two segmented telescope concepts with coronagraph instruments capable of exceeding these scientific goals: LUVOIR-A and LUVOIR-B, with respective diameters of 15~m (13.5~m, inscribed) and 8~m (6.7~m, inscribed).

To directly image Earth-sized exoplanets (``exoEarths'') with any telescope design, a coronagraph instrument must provide a stable raw contrast of $\sim$10$^{-10}$, which requires an extremely stable wavefront. Segmented telescopes present unique challenges for high-contrast imaging, such as segment gap obscurations and potentially more dynamic wavefront errors at the most critical mid spatial frequencies. To understand the implications of these issues, NASA's Exoplanet Exploration Program initiated the Segmented Coronagraph Design and Analysis (SCDA) study to assess the viability of imaging exoEarths with segmented space telescopes. To this end, the SCDA modeling team has optimized coronagraph mask designs for segmented telescopes, demonstrated their abilities to reach contrast levels below $10^{-10}$ in simulation\cite{Ruane2017_SPIE,Sirbu2020,Juanola2022}\,, and predicted their scientific yields in an idealized, unaberrated, and stable regime\cite{Stark2019}\,. SCDA also studied the sensitivity of these coronagraphs to optical aberrations and found that a raw contrast level of $\sim$10$^{-10}$ is maintained in the image if the optical path differences caused by segment phasing errors does not exceed $\sim$10~pm~RMS\cite{Pueyo2019,Juanola2022}\,, which is three to four orders of magnitude more stable than the James Webb Space Telescope (JWST)\cite{Lightsey2004,Lightsey2018}\,.

A future segmented flagship mission will have the advantage of JWST heritage to reduce risk and cost of a segmented architecture\cite{Feinberg2016} as well as more recent advances in telescope metrology strategies to reduce motions at the primary mirror level\cite{Bolcar2016, Feinberg2017, Saif2017, Lou2018}\,. In addition, the coronagraph instrument may use a closed-loop wavefront sensing and control (WS\&C) architecture, similar to an adaptive optics (AO) system on a ground-based telescope, to correct dynamic aberrations using the combination of one or more deformable mirrors (DMs) and a wavefront sensor (WFS)\cite{Pueyo2019WP}\,. In this paper, we assess the capability of such a AO system to minimize dynamic aberrations in the coronagraph instrument, stabilize the high-contrast performance in the long-exposure science images, and relax the demanding constraints on the mechanical stability of the telescope. Throughout this paper, we make use of a telescope  finite element model based on the LUVOIR-A design as an informative example, which is the most advanced of its kind prior to the release of the Astro2020 decadal survey report. In future work, these simulations will be adapted to a smaller diameter telescope architecture that is more representative of the flagship mission recommended by the decadal survey. However, the AO performance predictions presented herein highlight the benefits and limitations of a coronagraph instrument with a high-order AO capability on a future space telescope and the developed methods are essential for deriving accurate telescope stability requirements.

In Section~\ref{sec:Statistics_Wavefront}, we introduce the dynamical aberrations assumed for this study whose spatio-temporal properties are based on a finite element model of a large segmented telescope similar to the LUVOIR-A architecture. The resulting wavefront time series is projected into a modal basis for the purpose of AO correction. In Section~\ref{sec:AOsystem}, we develop an analytical model of an AO system and derive its temporal response. In Section~\ref{sec:OptimizationAndResults}, we optimize the response of the AO system to minimize the wavefront residuals under specific observing circumstances. Then, using an end-to-end forward model of the coronagraph instrument, we predict the closed-loop contrast performance and the exoEarth candidate yield gain provided by the optimized AO system.

\section{Spatio-temporal characteristics of the dynamical wavefront}
\label{sec:Statistics_Wavefront}
\subsection{Structural dynamics of a large segmented telescope}

The remaining wavefront error residuals after a closed-loop adaptive optics system depends on the spatio-temporal properties of the input (or "open-loop") wavefront aberrations. Lockheed Martin (LM) developed a model of the LUVOIR-A observatory, that integrates the flexible-body dynamics of both the spacecraft bus and the optical payload, a linear optical model of the Optical Telescope Assembly (OTA), control systems for maintenance of payload LOS on the target star, and observatory disturbances that contribute to time-domain variation in the wavefront\cite{Dewell2019}\,. The principal components of this integrated model are described in the following paragraphs. These perturbations are driven by the dynamic interaction of flexible structures with the noise and disturbances of the multi-stage pointing control system.

\paragraph{Spacecraft and payload structural dynamics} The flexible-body dynamics are modeled by a set of linear ordinary differential equations, based on the normal vibration modes computed from a Finite Element Model (FEM) of the respective structures. The second-order vibratory dynamics are diagonalized by the mode shapes, using a set of generalized modal coordinates, and a mode shape matrix converts input physical disturbances (typically forces and torques disturbing the structure) into the modal degrees of freedom, and also converts the generalized coordinates to physical displacement and rotation of important physical location on the structure, such as primary mirror segments. For the modeled LUVOIR-A architecture, the spacecraft mass was 11,490~kg, the payload mass was 23,128~kg; significant structural modes below 250~Hz were extracted from the FEM to capture the dominant structural dynamics.

\paragraph{Vibration isolation and pointing models} To reduce dynamic wavefront errors well below 1 nm RMS and achieve low residual line of sight (LoS) error, the model architecture includes passive isolation between the spacecraft Control Moment Gyroscope (CMG) actuators and surrounding structure, as well as a non-contact pointing stage between the spacecraft and the sensitive science payload. Pointing errors are sensed by the fine guidance mode of LUVOIR's High Definition Imager and controlled in two stages, by a fast steering mirror feeding back to the Fine Guidance Sensor (FGS) with a 5~Hz closed-loop bandwidth, and the Vibration Isolation and Precision Pointing System (VIPPS) controlling the overall payload rigid-body angular degrees of freedom over a 0.05~Hz bandwidth. VIPPS is a non-contact spacecraft-to-payload architecture whereby payload inertial rigid-body attitude is controlled by voice-coil actuators while payload-spacecraft relative alignment is sensed by non-contact sensors. This sensed interface alignment error is used to compute the spacecraft CMG torque in real-time to maintain positive stroke and gap at the non-contact interface during payload imaging\cite{Pedreiro2003}\,. While no structural contact exists as a load path, residual coupling from spacecraft/payload power and data cables were modeled. The cable stiffness was computed from payload and spacecraft mass properties, such that the translational cable suspension modes were equal to 3~mHz, and the rotational modes were 0.5~mHz.

\paragraph{Linear optical line-of-sight and wavefront error model} Variations in LoS and telescope exit pupil Optical Path Difference (OPD) due to structural dynamic response was modeled as a linear matrix multiplier on the 6-DOF translation and rotation of the 120 hexagonal primary mirror segments, secondary and tertiary mirror, fast steering mirror, and coronagraph instrument. The first-order LoS sensitivity was thus a 2$\times$744 matrix, transforming the 744 displacement degrees of freedom (124$\times$6) into two LoS perturbations. For OPD, the exit pupil was sampled over a 128$\times$128 grid. Thus, the OPD sensitivity was modeled as a 16,384$\times$744 matrix sensitivity, transforming the 744 displacement degrees of freedom into an OPD vector, where each element represents the scalar OPD at a given location in the 128$\times$128 grid.

\paragraph{Modeled disturbances and error sources} The integrated model incorporated disturbances arising from the CMG exported force and torque, VIPPS interface voice coil actuator current drive noise, FGS noise, steering mirror exported loads and servo control error, and VIPPS non-contact sensor noise. Exported loads from CMGs were based on measured harmonic data, with an additive frequency-dependent Model Uncertainty Factor (MUF). Voice coil current drive noise was modeled as additive force noise with specified RMS force, and shaped by a low-pass filter.

\paragraph{}With these physical and parametric disturbance models, three different time series were generated with RMS OPD error of 3.2~pm, 9.9~pm and 114~pm, which we refer to as sample A, B and C, respectively. The three disturbance cases were realized by scaling both the CMG exported loads and the VIPPS voice coil current noise, which were determined to have the highest sensitivity to overall RMS wavefront error. Sample A represents a stable and optimistic scenario, sample B has roughly the level of error specified in the LUVOIR report\cite{LUVOIR_finalReport}\,, while sample C represents a more pessimistic case with $\sim$10$\times$ larger wavefront errors than B. The derived LoS error for all sample B was $<$0.1 milli-arcseconds, which is three times lower than the requirement specified in the LM SLSTD Phase 1 Final Report\cite{LMC2019}\,. While the LoS error is usually dominant in the overall error budget if uncontrolled, we assume that it is negligible because of its relatively small impact on the image contrast. Each data set has a duration of T = 20s, representing the telescope wavefront errors in steady state with residual vibrations. They are sampled with 8000 OPD maps resulting in an effective sample rate of 400 Hz. The feasibility of these levels of stabilization with a 15-m segmented space telescope is beyond the scope of this paper. The telescope structure assumed in our model has not been anchored to test data or optimized for stability. In addition, metrology-based segment position sensing and control models have yet to be incorporated into the integrated model. Therefore, some wavefront patterns contained in the data sets and later presented in this publication may be mitigated through a future modification of the mechanical design or via telescope metrology\cite{Lou2018}\,. For the purposes of this study, we ignore dynamic aberrations at temporal frequencies $\lesssim$1~Hz because we expect those to be mitigated with the aforementioned telescope model improvements and negligible with respect to the high temporal frequency residuals.

\subsection{Modal decomposition of the dynamic errors}
To model the AO performance, we decompose the OPD maps into modes. The full AO system will effectively have independent control loops for each mode running in parallel to maximize efficiency. We use principal component analysis (PCA) to create an orthonormal basis unique to each time series, which maximizes the variance of the phase projected on the first modes\cite{Roddier1999}\,. In this respect, PCA minimizes the mean square error that would result from a modal truncation. Numerically, the PCA is calculated using singular value decomposition (SVD) of the discrete OPD data set. If $X$ stands for the matrix representing the OPD data set, the SVD of $X$ can be written as $X=U\Sigma V^T$, where $\Sigma$ is a rectangular diagonal matrix with the singular values of $X$ sorted in ascending order. $U$ and $V$ are two square matrices whose vectors are orthogonal and called respectively left and right singular vectors. Under this formalism, the principal components are $P=V^T$. Appendix \ref{sec:orthonormal_basis} derives statistical properties of the orthonormal basis relevant to the analysis below.

\begin{figure}[t]
    \centering
	\includegraphics[width=\linewidth]{PCA_modes.pdf}
	\caption{The first ten principal components of the ``sample B" OPD time series ($\sim$10~pm~RMS). The number in the upper left of each panel is the percentage of the total variance represented by each mode.}
	\label{fig:PCA_modes}
\end{figure}

Figure~\ref{fig:PCA_modes} shows the first ten principal components of the decomposition of time series B. Here, the first three modes account for 76\% of the total variance and are characterized by a strong vertical shape; thus, the wavefront error is dominated by a small number of structural modes. These effects may be mitigated with a future mechanical optimization of segmented telescope architectures or by advanced telescope metrology. For instance, in our model, a 10x increase in damping of only 5 modes on the payload structure reduces the sample B wavefront error to 2.5~pm RMS. Since the eight first modes represent 96\% of the total variance, we only control these eight modes in our AO performance analysis for sample B, which allows us to simplify subsequent numerical calculations with a minor loss of precision. Except for the second principal component, we note that each mode is dominated by mid-spatial frequencies induced by segment phasing errors.

\begin{figure}[t]
    \centering
	\includegraphics[width=\linewidth]{PSD_Example_10pm.pdf}
	\caption{Power spectral densities of the first ten principal components for the ``sample B" OPD time series (i.e. for the spatial modes shown in Fig.~\ref{fig:PCA_modes}).}
	\label{fig:PCA_PSD}
\end{figure}

We calculate the temporal power spectral densities (PSDs) for each of the modes in the PCA basis. Figure~\ref{fig:PCA_PSD} shows the result for time series B. The PSDs obey power laws with exponents between -1.5 and -2 for the first ten principal components. Moreover, the variances are dominated by a few localized vibrations at 16.5~Hz in the first and third modes and 0.9~Hz in the second. In fact, the 16.5~Hz vibration accounts for 20\% of the total variance. With this information in mind, there may be considerable room for optimization of the telescope mechanical architecture to improve its dynamic stability by damping this, and other, specific vibration modes. Otherwise, the correction of these vibrations requires an AO control loop bandwidth significantly greater than the vibration frequency.

There are some drawbacks to the basis we have selected. First, the AO system architecture is not taken into account; a better option may be to adapt the basis such that the AO hardware optimally senses and corrects the first modes. For example, the DM may not be able to accurately correct the derived modes because of its finite number of actuators and resulting fitting errors. Additionally, the WFS may not have the resolution to differentiate between the modes accurately. In this paper, we optimize the number of pixels in the WFS to provide the best correction for the derived PCA modes. Secondly, correcting the first PCA modes in order of their OPD variance minimizes the resulting OPD error, but does not necessarily provide the best coronagraph contrast performance. Optimized coronagraphs for LUVOIR are, for instance, more sensitive to mid-spatial aberrations than to low-order aberrations with equal variance. The PCA decomposition might not capture modes with low--but not negligible--variance that have a high impact on the contrast performance of the instrument. In the following sub-section, we carry out contrast calculations using the PCA decomposition and confirm that the modes are mostly ordered by their impact of contrast despite these potential pitfalls.

\subsection{Contrast calculation}
\label{subsec:Modal_Contrast}
We use a ``compact" end-to-end model of the coronagraph instrument i.e. all the aberrations are collapsed down into the input pupil plane and only Fourier propagation is employed in between optical planes, assuming no particular testbed design nor coronagraph internal aberrations from spectral or polarization errors) to estimate the contrast change due to each OPD error map. The numerical simulation uses the PROPER\cite{Krist2007} and FALCO\cite{Riggs2018} software packages to generate images for each of the 8000 OPD time steps in a 20\% spectral bandwidth centered at 550nm using LUVOIR's narrow field-of-view binary Apodized Pupil Lyot Coronagraph (APLC)\cite{Pueyo2019, Juanola2022}\,. The APLC attenuates the starlight with a binary apodizer optimized with respect to the telescope architecture, inner working angle and spectral bandwidth that is introduced at a relayed telescope pupil, a focal plane mask (here of radius 26.5~mas) to occult the core of the stellar Point Spread Function (PSF) associated with a Lyot stop  in the following pupil plane whose inner and outer diameters are 12\% and 98.2\%, respectively, of the pupil diameter. The resulting region where the starlight is attenuated, or ``dark hole" (DH) is an annulus between 3.5 and 12.0~$\lambda/D$ from the star. For time series B, we find that the mean intensity, normalized by the maximum of the unocculted PSF, is equal to $9.5\times10^{-11}$ in the DH. Comparing this result with the normalized intensity induced by sample B that is reduced to its first 10 principal components, the mean difference between the normalized intensity at each time steps is $4.2\times10^{-13}$ while the standard deviation of the differences is $8.8\times10^{-13}$. Considering only the first 10 principal components therefore induces $<$1\% error in the contrast calculation.

\begin{figure}[t]
    \centering
	\includegraphics[width=\linewidth]{Contrast_per_mode.pdf}
	\caption{Contrast change in the image plane due to 10~pm RMS of each principal component (ordered one to ten from left to right). The RMS normalized intensity calculated in the dark hole is also displayed in the upper left of each panel ($\times 10^{-10}$).}
	\label{fig:PCA_intensity}
\end{figure}
In Fig.~\ref{fig:PCA_intensity}, we show the change in contrast induced by the first individual PCA modes when the spatial variance at coronagraph entrance pupil is equal to 10~pm RMS. Figure~\ref{fig:DeltaE_vs_OPD} shows the mean normalized intensity $|\Delta E_i|^2$ induced by each individual mode $i$ at the science detector versus the level of OPD error for the first 10 modes. The simple quadratic relationship allows us to easily estimate the contrast impact of the OPD data sets by scaling to any amount of OPD error. In both Figs.~\ref{fig:PCA_intensity} and \ref{fig:DeltaE_vs_OPD}, it is evident that the contrast is most sensitive to the first and third principal components. Indeed, 10~pm RMS of these modes individually bring the mean contrast in the DH above $10^{-10}$. Conversely, the second principal component has a relatively small effect on the contrast. In time series B, the order of magnitude of the contrast induced by the second component ($2.3\times10^{-12}$) is similar to the contrast induced by the fourth ($1.6\times10^{-12}$) despite the $>$3$\times$ larger OPD variance in the second mode. For the other components, the mean contrast values are roughly the same for a constant OPD variance. This justifies using the PCA decomposition because the contrast impact of each mode in the time series (for the most part) decreases with the mode number and the contrast error due to truncation is negligible. In the remainder of this publication, the long-exposure post-AO contrast performance is calculated using Eq.~\ref{eq:MeanContrast_calculation} in appendix~\ref{sec:long_exp_contrast}.

Table~\ref{table:modeParams} summarizes the OPD error by mode for each time series and the relative impact of each mode on the contrast. The impact of each mode on contrast is roughly proportional to the product of the last two columns. See Appendix \ref{sec:timeseries_properties} for more detail on the properties of time series A and C.

\begin{figure}[t]
    \centering
	\includegraphics[width=8cm]{DeltaE_vs_OPD.png}
	\caption{Normalized intensity induced by each of the first ten PCA modes with respect to the level of aberration at the central wavelength.}
	\label{fig:DeltaE_vs_OPD}
\end{figure}

\begin{table}[htp]
	\caption{Modal decomposition properties of each time series. The first column is the mode number. For each time series, the three columns are (1)~the RMS OPD error in units of pm, (2)~the percentage of the OPD variance explained by each mode, and (3)~the RMS $|\Delta E|^2$ at the central wavelength for a 10~pm~RMS wavefront error scaled by $10^{10}$.}
	\centering
	\begin{tabular}{|c|*{3}{C{1cm}}|*{3}{C{1cm}}|*{3}{C{1cm}}|}
        \toprule
       PCA Mode & \multicolumn{3}{c|}{Time series A} & \multicolumn{3}{c|}{Time series B} & \multicolumn{3}{c|}{Time series C}\\
		\midrule
         & OPD & \%Var & $|\Delta E|^2$ & OPD & \%Var & $|\Delta E|^2$ & OPD & \%Var & $|\Delta E|^2$ \\
		\midrule
		1 & 2.0 & 39.8 & 0.1 & 6.3 & 41.0 & 1.0 & 73.7 & 41.9 & 0.2\\
        \midrule
        2 & 1.4 & 18.9 & 0.2 & 5.1 & 26.1 & 0.0 & 59.2 & 27.0 & 0.9\\
        \midrule
        3 & 0.9 & 7.9 & 0.1 & 2.9 & 8.9 & 0.9 & 29.4 & 6.7 & 0.7\\
        \midrule
        4 & 0.9 & 7.1 & 0.2 & 2.7 & 7.6 & 0.1 & 28.9 & 6.4 & 0.4\\
        \midrule
        5 & 0.8 & 6.7 & 0.3 & 2.2 & 4.8 & 0.1 & 25.2 & 4.9 & 0.1\\
        \midrule
        6 & 0.6 & 3.0 & 0.2 & 1.9 & 3.5 & 0.1 & 21.2 & 3.5 & 0.1\\
        \midrule
        7 & 0.5 & 2.8 & 0.9 & 1.5 & 2.4 & 0.2 & 18.7 & 2.7 & 0.2\\
        \midrule
        8 & 0.4 & 1.9 & 0.3 & 1.3 & 1.8 & 0.3 & 16.7 & 2.1 & 0.2\\
        \midrule
        9 & 0.4 & 1.7 & 0.4 & 0.9 & 0.9 & 0.2 & 12.4 & 1.2 & 0.2\\
        \midrule
        10 & 0.4 & 1.4 & 0.2 & 0.7 & 0.5 & 0.2 & 10.3 & 0.8 & 0.2\\
        \midrule
		\bottomrule
	\end{tabular}
	\label{table:modeParams}
\end{table}

\section{Analytical modeling of an adaptive optics system}
\label{sec:AOsystem}
\subsection{Wavefront Sensing and Control architecture}
In this study, we first assume that static aberrations are compensated before the science operations using conventional focal plane wavefront sensing and control techniques\cite{GiveOn2007SPIE,GiveOn2011}\,. The intensity in the DH is therefore at its minimum and the raw contrast is only limited by the coronagraph's diffraction pattern. We then introduce dynamical telescope aberrations that occur during the science operations and cause stellar leakage in the DH. To correct these aberrations, we need to use a wavefront sensor that (1)~operates simultaneously with science observations, (2)~has a sufficient spatial resolution to sense for segment phasing errors, (3)~is sensitive to picometer level phase aberrations, and (4)~is in a common beam path with the coronagraph. We therefore consider the example of a Zernike Wavefront Sensor (ZWFS) built in to the coronagraph's focal plane mask (FPM), which reflects out-of-band light using a dichroic on the FPM substrate (while part of the in-band light can also be reflected by an occulting spot on the FPM). This type of in-situ ZWFS design has been shown to be sensitive to picometer-level wavefront variations in the laboratory\cite{Ruane2020}\,. For the sake of simplicity, our simulation effectively assumes an ideal in-band ZWFS that collects all of the light passing through the 20\% bandwidth visible filter. In reality, the ZWFS may operate in a different band than science observation's filter, but this distinction is not important to our analysis. In accordance with the small level of aberrations expected, we consider the relationship between measured intensity in the ZWFS and the phase to be linear during operations. The sensitivity of a ZWFS is often parameterized by $\beta$, which relates the phase error to the photon noise\cite{Guyon2005}\,. Here, we round $\beta = 1$ at each wavelength and spatial frequency in a Fourier basis, while $\beta$ has recently been derived more precisely considering the realistic diffraction from the focal plane mask\cite{Ruane2020}\,. We ignore any artifact or bias originating from the WFS detector.
Our assumed telescope and WFS parameters are summarized in Table~\ref{table:TelescopeParameters}. For the correction, we ignore fitting errors due to the finite number of DM actuators and confirmed that the residuals are negligible for a 64$\times$64 actuator DM and the OPD modes derived above. The DM that is conjugated to the telescope pupil is used to correct for both static aberrations and the dynamical aberrations sensed with the ZWFS.

\begin{table}[htp]
	\caption{Telescope Specifications used to analyze the AO system performance. The throughput is the optical transmission from the telescope primary mirror to the wavefront sensor (quantum efficiency included). The detector read out noise (RON) is assumed to be 1 electron per pixel which is conservative with respect to state-of-the-art detectors in AO ($\sim0.3e^-$ for the EMCCD) and the arisen of more advanced detectors like MKIDs\cite{Mazin2012}\,. This value multiplies by 10 the RON/photon noise ratio in Eq.~\ref{eq:SNR-1} with respect to the 0.3$e^-$ value adopted in Douglas et al.}
	\centering
	\begin{tabular}{lcc}
		\toprule
		Inscribed diameter & $D$ & 14~m \\
		\midrule
		 Throughput & $\mathcal{T}$  & 0.3 \\
		 \midrule
		 Central wavelength & $\lambda$  & 545~nm \\
		 \midrule
		 Spectral bandwidth & $\Delta\lambda/\lambda$ & 20\% \\
		 \midrule
		 WFS detector RON & $\sigma_{RON}$ & 1$e^-$ \\
		 \midrule
		 Vega photon flux & $\Phi_{Vega,ph}$ & 10$^8$ m$^{-2}$s$^{-1}$nm$^{-1}$\\
		\bottomrule
	\end{tabular}
	\label{table:TelescopeParameters}
\end{table}

\subsection{System frequency response}
To stabilize the wavefront variation, a conventional linear AO system acts like a temporal filter on the modal coefficients at a given time $a_i(t)$. The corrected coefficients, $a^\prime_i(t)$, are given by the convolution between the impulse response and the input modal coefficient in the time domain:
\begin{equation}
\label{eq:input_output}
a^\prime_i(t)=h_i(t)\ast a_i(t) \quad ,
\end{equation}
where $h_i(t)$ is the AO impulse response function.
According to the convolution theorem, the Fourier transform of a convolution of two signals is the product of their Fourier transforms. Then, the square of the Fourier transform of Eq.~\ref{eq:input_output} gives the PSD:
\begin{equation}
\label{eq:TFdefinition}
PSD^\prime_i(f)=|H_i(f)|^2\cdot PSD_i(f) \quad ,
\end{equation}
where $H_i(f)$ is the AO transfer function of the $i^{th}$ mode and $f$ is the temporal frequency. However, the AO system also introduces noise during the correction process. The resulting PSD of each mode is a function of the input wavefront error and noise:
\begin{equation}
\label{eq:PSDcorrection}
PSD^\prime_i(f)=|H_i(f)|^2\cdot PSD_i(f)+|H_{N,i}|^2\cdot N_i(f) \quad ,
\end{equation}
where $H_{N,i}(f)$ and $N_i$ stands respectively for noise transfer function and the squared Fourier transform of the noise distribution introduced when sensing the $i^{th}$ mode.

\begin{figure}[t]
    \centering
	\includegraphics[width=0.8\linewidth]{AOloop.pdf}
	\caption{Block diagram of an AO control loop for a single mode in the case of a simple integrator.}
	\label{fig:AOloop}
\end{figure}

The block diagram in Fig.~\ref{fig:AOloop} represents the AO temporal model assumed for this study. The total temporal response of the system includes contributions from the wavefront sensor, the controller, the servo-lag error, and the digital-to-analog converter (DAC) which applies the signal to the DM. The transfer function of each individual subsystem is derived in appendix~\ref{sec:AO_loop_TF}. The DM transfer function is not taken into account here but could be readily included in future studies. According to this scheme, the wavefront residuals are given by
\begin{equation}
R_i=W_i-H_{WFS} H_{con,i} H_\tau H_{DAC} R_i\quad ,
\end{equation}
where $R_i$ and $W_i$ are the Fourier transforms of the corrected (residual) and input wavefronts, respectively. We can therefore derive the rejection transfer function as:
\begin{equation}
\label{eq:correction_TF}
H_i=\frac{1}{1+H_{WFS} H_{con,i} H_\tau H_{DAC}}\quad .
\end{equation}

We also derive an analytic expression for the noise transfer function only considering wavefront sensor noise (i.e. electronic read out noise) and photon noise injected before the controller as shown in Fig.~\ref{fig:AOloop}. The noise transfer function relates the residual signal introduced by the system in the presence of only noise. In that case,
\begin{equation}
R_i= - H_{con,i} H_\tau H_{DAC} ( N_i + H_{WFS} R_i ) \quad .
\end{equation}
and noise transfer function is
\begin{equation}
\label{eq:noise_TF}
H_{N,i}= - \frac{H_{con,i} H_\tau H_{DAC}}{1+H_{WFS} H_{con,i} H_\tau H_{DAC}} \quad .
\end{equation}

\subsection{Optimization of the temporal response}
\subsubsection{Optimized integrator}
Figure~\ref{fig:TransferFunction} shows the squared modulus of the rejection and noise transfer functions with respect to the gain $g_i$ in the case of a simple integrator (see Eq.~\ref{eq:TF_integrator} in appendix~\ref{sec:AO_loop_TF}) assuming a pure delay of 1 frame. On one hand, the rejection transfer function shows that the telescope stability requirements can be relaxed for frequencies $\lesssim1/10$ of the WFS sampling frequency. For example, assuming a 100~Hz control loop and zero noise, an original telescope stability requirement of 10~pm RMS for a 1~Hz disturbance would be relaxed to 30~pm RMS using an integrator gain of 0.2 and to 100~pm~RMS for a gain of 0.6. The AO cutoff bandwidth (i.e., the maximum frequency where $|H_i|^2 < 1$) also increases with the gain. On the other hand, the signal is amplified for temporal frequencies higher than the AO bandwidth and the amplification increases with the gain. Moreover, the integral of the noise transfer function also increases with the gain. Therefore, the gain needs to be optimized to balance the correction of the incoming wavefront and the propagation of noise in the system as well as avoiding any substantial amplification of wavefront variations that are too fast for the AO system to correct. The gain should be optimized separately for each mode, depending on both the modal PSD and the noise amplitude, in order to get the minimal residual:
\begin{equation}
\label{eq:optimize_SI}
g_i=\text{argmin}\,\sigma_{T,i}^2(g_i,SNR) \quad .
\end{equation}

\begin{figure}[t]
    \centering
	\includegraphics[width=0.8\linewidth]{Transfer_Function4.pdf}
	\caption{Squared modulus of the rejection transfer function (left panel) and noise transfer function (right panel) with varying AO gain. The sampling frequency is 100~Hz and the pure delay is equal to 1 frame.}
	\label{fig:TransferFunction}
\end{figure}

\subsubsection{Predictive controller}
The correction provided by an integrator is limited by the AO bandwidth and, as a result, faster vibrations will not be corrected by AO system. A potential solution is to replace the integrator with a predictive control algorithm. Indeed, such methods are able to partially mitigate some localized vibrations in the perturbation's PSD that are faster than the integrator AO bandwidth. However Bode's theorem imposes restrictions on the shape of the rejection transfer function \cite{Guesalaga2012}\,. Indeed, the overall integral of the rejection transfer function is fixed by the sampling frequencies and hardware delays. It follows that the perturbation rejection tends to be worse in the vicinity of the targeted vibration frequency with respect to the simple integrator case. The predictive controller also has to be shaped according to the open-loop PSD. Prior knowledge of the perturbation is therefore required to optimize the controller coefficients (see Eq.~\ref{eq:Predictive_controller} in appendix~\ref{sec:AO_loop_TF}) and minimize the residuals:
\begin{equation}
\label{eq:optimize_PC}
(a_0,...,a_p,b_1,...,b_q)_i=\text{argmin}\,\sigma_{T,i}^2(a_0,...,a_p,b_1,...,b_q)_i \quad.
\end{equation}
This PSD knowledge requirement limits the performance of predictive control on ground-based facilities\cite{vanKooten2019}\,. For example, observing conditions can quickly change subject to properties of the air turbulence in the atmosphere and telescope dome. As a result, predictive control may require a reevaluation of the perturbation's PSD that is too frequent to be conveniently applied. On the other hand, space-based telescope might offer a steady state where the coefficients may not require regular re-optimization. The wavefront errors would therefore be described by consistent and potentially well-characterized spatial modes and temporal PSDs.

Both predictive control and a simple integrator require some knowledge of the perturbations to minimize the residuals.
In practice, minimizing the integral in Eq.~\ref{eq:PSDcorrection} is equivalent to minimizing:
\begin{equation}
\int |H_i(f)|^2\cdot PSD_{meas,i}(f) \, df \quad ,
\end{equation}
where $PSD_{meas,i}$ is the PSD measured by the AO wavefront sensor in open loop\cite{Dessenne1998}\,. The corresponding time series can therefore be measured directly and the parameters of the controller can be optimized based on those measurements. However, we use the full Eq.~\ref{eq:PSDcorrection} in this report since we already have prior knowledge of the OPD time series of aberrations.

\section{Performance improvement provided by AO}
\label{sec:OptimizationAndResults}
\subsection{Residual variance and stellar magnitude}
In this section, we calculate the closed-loop AO residuals assuming the incoming perturbations described in Sec.~\ref{sec:Statistics_Wavefront}. We have shown that the performance depends on the SNR of the WFS measurement and thus on the magnitude of the AO guide star. We therefore optimized the controller gain as a function of the stellar magnitude between -4 and 11 to cover the broad stellar sample targeted by LUVOIR-A\cite{LUVOIR_finalReport}\,. The resulting gains are used to minimize the residual PSD of each independent mode derived in Sec.~\ref{sec:Statistics_Wavefront}. The noise PSDs of such modes are modeled using the method described in appendix \ref{sec:WFSphotonnoise}. The AO rejection and noise transfer functions are calculated through Eq.~\ref{eq:correction_TF} and Eq.~\ref{eq:noise_TF} respectively.

\subsubsection{Optimized integrator}
\begin{figure}[t]
    \centering
	\includegraphics[width=\linewidth]{VariancevsMagnitudeComparison.pdf}
	\caption{Left: Standard deviation of the residual wavefront after a conventional AO correction (optimized integrator) running at 1~kHz. Right: Same plot using predictive control at 100~Hz. The input dynamical aberrations is time series B (total open-loop RMS OPD error of 9.9~pm~RMS). The residual of the eight first principal components is also shown. These plots demonstrate the optimized integrator can be used to minimize the total wavefront errors if $M_V<2$ while predictive control can work on stars as faint as $M_V<8$. }
	\label{fig:Variance_Magnitude}
\end{figure}
We first assume the controller is a simple integrator, the servo-loop frequency sampling is 1~kHz, and the WFS is sampled with 64 pixels across the beam. We also assume 1 frame of pure delay. The other relevant parameters are given in Table~\ref{table:TelescopeParameters}. The gain is optimized for each mode via a Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. For a wavefront error following the statistics of time series B, we plot the residual wavefront standard deviation as well as each mode residual standard deviation with respect to the stellar magnitude in Fig.~\ref{fig:Variance_Magnitude}. For an initial wavefront variation of about 10~pm RMS, the AO system brings an improvement when the visible magnitude of the observed star is $<$1 (i.e. brighter than 1st magnitude). Above this magnitude (i.e. fainter than 1st magnitude), the modal noise $N_i$ is too high for the AO system to correct any modes and all the modal gain are set to 0. Between $M_V=0.2$ and $M_V=1$, only the first principal component is controlled by the AO system. Indeed, the ratio between $PSD_i$ and $N_i$ in Eq.~\ref{eq:PSDcorrection} is the highest for this mode owing to the PCA decomposition. This means that, for the assumed pixel sampling and exposure time, no other mode or decomposition can be corrected for stellar magnitude above 1. A longer exposure time could be used to correct slow varying drifts when observing stars at higher magnitudes. However, most of the OPD variance would remain uncorrected and the AO system would not bring any significant modifications in the OPD statistics. This result implies that a laser guide star (LGS) may be required to stabilize all the mid-order spatial modes under 10~pm RMS if the AO controller is an integrator. Figure~\ref{fig:Variance_Magnitude} also shows that the total standard deviation would be divided by two for $M_V=-2.3$, which is brighter than a typical star in a direct imaging survey.

\subsubsection{Predictive control}
The numerical simulations above assumed an optimized integrator. We expect better performance with predictive control since it should be able to focus on mitigating vibrations (e.g. at 0.9~Hz and 16.5~Hz in time series B). Figure~\ref{fig:PCA_PSD_PC} shows the PSD of the first three modes before and after correction with predictive control for $M_V=3$. The loop is assumed running at 100~Hz in order to increase the signal-to-noise ratio by $\sqrt{10}$ with respect to the simulation in Fig~\ref{fig:Variance_Magnitude}. We choose $p=q=2$ in Eq.~\ref{eq:Predictive_controller} which implies that we optimize five different parameters in Eq.~\ref{eq:optimize_PC}. We use a constrained optimization method to minimize the cost function in the frequency domain and the parameters are all bounded in between -1 and 1, except $a_0$ whose value is between 0 and 1. While these bounds and algorithms have shown reliable results, the use of recursive algorithms applied in the time domain such as Kalman estimators \cite{Leroux2004,Kulcsar2006,Poyneer2010} whose parameters are optimized by solving a Riccati's equation \cite{Guesalaga2012,Males2018b} may be required to ensure the stability and robustness of the correction. Their implementation is beyond the scope of this work.

\begin{figure}[t]
    \centering
	\includegraphics[width=\linewidth]{PSD_Mv3_10pm_PC_bnd1.pdf}
	\caption{PSDs of the first three principal components of time series B before (grey) and after (red) correction with an AO system running at 100~Hz with a predictive controller. The wavefront sensor is sampled at 64~pixels across the beam and the magnitude of the target star is equal to 3 in V-band. As desired, the predictive controller reduces the highest magnitude peaks of the PSD, thereby reducing the dynamical wavefront error substantially.}
	\label{fig:PCA_PSD_PC}
\end{figure}

Predictive control helps correct one specific vibration for each mode in Fig.~\ref{fig:PCA_PSD_PC}. To do so, the signal is also amplified at other frequencies, as expected from Bode's theorem, which limits further mitigation of these modes. However, the variance residuals is minimized overall. The right panel of Fig.~\ref{fig:Variance_Magnitude} shows the standard deviation of the residuals with respect to the observed star magnitude. Predictive control is able to minimize the wavefront variance with stars brighter than $M_V=10$ which constitutes the majority of the natural stars that will be targeted by a future direct imaging mission. This represents an important improvement with respect to the optimized integrator.

\subsection{Contrast predictions}
\label{subsec:Contrast_Performance}
We reproduced an equivalent analysis for time series A and C where we find a similar but not identical PCA decomposition (see Appendix \ref{sec:timeseries_properties} for more detail on the time series statistics). The modes are then corrected independently with optimized AO systems. For the three time series samples, Fig.~\ref{fig:Contrast_vs_magnitude} shows the normalized intensity in the DH annulus of the narrow field-of-view APLC coronagraph, calculated by Eq.~\ref{eq:MeanContrast_calculation}, versus the magnitude of the AO guide star. Here, the residuals for samples A, B and C are all calculated using an optimized integrator running at 1~kHz. We also present the normalized intensity when the time series B and C are corrected with predictive control. The best contrast result between a servo-loop frequency of 100~Hz and 1~kHz is adopted at each magnitude.

\begin{figure}[t]
    \centering
	\includegraphics[width=10cm]{Intensity_Magnitude.pdf}
	\caption{Mean normalized intensity in the dark hole after the wavefront being corrected by an AO system. The AO performance depends on the magnitude of the observed star and on the initial level of turbulence. Purple, pink and orange curves use respectively samples A, B and C as inputs of the simulations. Continuous lines represent results for the optimized integrator while the dashed lines are for predictive control.}
	\label{fig:Contrast_vs_magnitude}
\end{figure}

First, Fig.~\ref{fig:Contrast_vs_magnitude} shows that AO is not required in the best case scenario (time series A). Indeed, the wavefront is already low enough before any correction that the normalized intensity is dominated by the static diffraction pattern of the APLC. Sample B's scenario is quite different. If the overall contrast budget for the telescope is on the order of $10^{-10}$, minimizing dynamical aberrations is required because the normalized intensity due to the dynamics alone is $9.45\times10^{-11}$ for sample B in open loop. However, a simple integrator would require a LGS to achieve a significant correction. A $M_V=-4$ star, for instance, would improve the contrast down to sample~A's contrast performance. The coronagraph performance also benefits from predictive control by mitigating the strong vibrations in the first and third principal components. For $M_V<8$, the variance of these two modes is reduced which decreases the dynamical aberrations significantly. Finally, in the worst case scenario where the wavefront is above 100~pm RMS (sample C), the AO system is able to correct aberrations with natural guide stars for either controller. However, predictive control provides better contrast results. Again, there are two different regimes. For natural guide stars, the AO loop should run at $\sim$100~Hz because higher frequencies would make the WFS photon starved leading to insufficient sensitivity. For brighter stars, or LGS, the correction remains limited at such frequencies since the pm level sensitivity has been already reached while high frequency vibrations remain uncorrected. Decreasing the WFS exposure time to correct for these vibrations when observing brighter stars improves the performance. With such an optimization and the essential contribution of a LGS, it is possible to achieve a normalized intensity of $10^{-10}$ in this 100~pm RMS scenario. For the most cost-effective approach, it may be optimal to avoid launching additional spacecrafts for the LGS and consider strategies that minimize the overall dynamical aberrations levels at the telescope level to a few tens of pm RMS and take advantage of the internal AO system to correct the residual wavefront error within the coronagraph instrument.

\subsection{Yield improvement provided by AO}
\label{subsec:yield_performance}

A useful performance metric for a high-contrast imaging mission is the overall exoplanet yield since it takes into account the properties of the target sample including stellar type and diameter, as well as the instrument properties and a given resource budget (mission time, spacecraft fuel). The yield of potentially Earth-like planets, or exoEarth candidates (EECs), in particular has been used extensively to compare different flagship mission concepts proposed as part of the Astro2020 decadal survey. Here, the yield is defined as the expected number of detected EEC at $SNR>7$ in V-band. We require each system to be observed a minimum of six times for planet detection and orbit determination and budget for spectral characterization observations to search for water vapor at 950~nm on each detected EEC (spectral resolution $R=70, SNR=10$). In this section, we use the Altruistic Yield Optimization\cite{Stark2014} (AYO) to understand the impact of the AO system on the estimated EEC yield of a direct imaging mission that makes use of a large segmented telescope. We make identical assumptions to those listed in previous AYO studies\cite{Stark2019}\,. Briefly, we use the same definition of EECs as the LUVOIR and HabEx Study final reports\cite{LUVOIR_finalReport,HabEx_finalReport}\,, adopt a self-consistent occurrence rate of $\eta_\text{Earth}=0.24$, and assign all EECs an wavelength-independent geometric albedo of 0.2. We model a total of 2 years of science time including overheads while setting the maximum single observation time to two months. AYO then optimizes the target selection, exposure time, and cadence of all observations to maximize the EEC yield given our instrument models.

For simplicity, we assume a single guide star magnitude for the whole mission. This is equivalent to using a laser guide star for all observations. We do not consider any fuel limitations or overheads related to the separated LGS spacecraft. While yield studies have shown these are major limitations for a starshade\cite{HabEx_finalReport,Seager2015}\,, here we expect smaller impacts as the LGS may be significantly closer to the telescope, less massive, and thus requires less fuel and time to re-position itself or more than one LGS spacecraft could be deployed. For each guide star magnitude, the raw contrast maps are provided through the results in Sec.~\ref{subsec:Contrast_Performance}.

The noise floor that defines the minimally detectable planet-to-star flux ratio is not well known. Its value depends on the signal-to-noise of the observation as well as the differential aberrations between the images used for post-processing. In this study we update the calculation of the noise floor in the AYO code. While previous studies adopted a uniform noise floor independent of stellar magnitude, here we adopt a noise floor proportional to the raw contrast. We therefore consider two cases where the 5$\sigma$ noise floor to be equal to a half and a tenth of the raw contrast at each magnitude. These factors correspond to the expected performance of the Roman Space Telescope Coronagraph Instrument with and without noise, respectively, and without a model uncertainty factor in the initial correction of static aberrations\cite{Ygouf2021} (as also assumed in this study). The noise floor is degraded quasi uniformly in the DH due to the initial aberrations and slowly restored depending on the stellar magnitude thanks to the internal AO system. Since EEC around early type stars have the largest flux ratio with respect to their host stars, it means the earliest type stars are removed from the target list without AO and are then recovered gradually with a decreasing magnitude using AO.

\begin{figure}[t]
    \centering
	\includegraphics[width=10cm]{LGS_AYO_Results4.pdf}
	\caption{EEC yield calculated with AYO assuming a constant guide star magnitude for all observations. The vertical axis is the relative number of EECs with respect to the case of a perfectly stable telescope. We assume the telescope instabilities follow time series C. In closed-loop, predictive control is performed to correct for the aberrations. Dashed lines represent the performance without the use of AO system. The 5$\sigma$ noise floor is either a tenth (orange, circles) or a half (red, squares) of the raw contrast as calculated in Sec.~\ref{subsec:Contrast_Performance}.}
	\label{fig:LGS_yield}
\end{figure}

The AYO results are presented in Fig.\ \ref{fig:LGS_yield}. Without aberrations, 34.1 EECs are detected for the best post-processing scenario and 30.1 in the worst case. We note that these values are considerably lower than the LUVOIR-A yield\cite{LUVOIR_finalReport} because we only model the narrow field-of-view coronagraph designed for LUVOIR-A, while the LUVOIR study used a total of three APLC masks of varying angular scales, and also because of the more pessimistic post-processing noise floor. For the purposes of this work, we therefore emphasize the \textit{relative} yield to estimate the potential gains provided by the AO system. The large difference between the two noise-floor scenarios implies that the yield is mainly limited by the attainable noise floor rather than by the raw contrast. In the case of time series C, 75.1\% and 94.7\% loss in yield is expected without AO for the two post-processing scenarios, respectively. On the other hand, AO associated with a LGS (magnitude $<$ 0) recovers at least 47.2\% of the EECs predicted when the telescope is not affected by dynamic instabilities. A stellar magnitude of -4 allows to recover even more than 92.4\% of EECs. A previous study proposed a 5~Watt LGS spacecraft emitting in visible or near infrared and located at least 40,000~km away from the telescope to simulate starlight with magnitude $<$-4\cite{Douglas2019}\,.

A thorough treatment of the NGS case requires implementing a contrast map for each star in the AYO sample that depends on its magnitude, before overall yield calculation. This modification of the AYO code is currently beyond the scope of this paper and will be presented in future work. In lieu of this, we posit that the LGS scenario at high magnitudes ($3\leq M_V\leq 11$) can inform the NGS scenario. Figure~\ref{fig:LGS_yield} shows that the EEC yield is limited at its best to 18\% and 58\% of the number obtained in the no aberration case when the LGS intensity is limited to NGS-like magnitudes. In the simulation of the LUVOIR-A mission, only ten 3rd magnitude stars are surveyed while the stellar sample includes magnitudes up to 11\cite{LUVOIR_finalReport}\,. To provide an estimated yield with NGS, we therefore weigh each LGS yield by the number of observed stars of same magnitude in the AYO sample. We find the relative yield to be 11.7\% if the 5-$\sigma$ noise floor is the half of the raw contrast. It increases to 42.2\% with the most optimistic noise floor prediction. The mission yield would therefore be multiplied by a factor of 1.7 to 2.2 if the instrument is equipped with an AO system that uses NGS. This result is roughly what is expected for 5th-magnitude stars that dominate the surveyed sample (90 observed stars).

\subsection{Discussion}

\subsubsection{Optimization of the wavefront sensor spatial and temporal sampling}

In Appendix~\ref{sec:WFSphotonnoise}, we discuss how the estimation of modes with significant mid-spatial frequency content could be affected by the spatial sampling of the WFS camera.
Figure~\ref{fig:Performance_vs_Npix} shows the performance of the AO system with respect to the number of pixels across the beam in the WFS plane. We assume five scenarios where $N_{pix}$~=~8, 16, 32, 64 or 128 pixels across the beam.
The figure shows that for any observing scenario, the contrast improves with increasing number of pixels used on the WFS camera.
Indeed, on one hand, the sensitivity of the WFS decreases drastically since it estimates a given mid-spatial frequency aberration with fewer pixels; as a result, $(G^TG)^{-1}$ increases in Eq.~\ref{eq:Mode_PSD_noise} and so does the modal noise.
On the other hand, the relationship between the modal noise and the WFS sampling depends on the noise regime. In the photon-noise limited regime, the total noise of the modal reconstruction is independent of the number of pixels across the beam. In the read-out noise limited regime, the more pixels, the higher is the noise. However, the read-out noise with newer detector technologies is low enough ($RON<1$ electron) that it is negligible with respect to the photon noise, even for stellar magnitude up to 11 where $\sigma_{RON}^2/F_\gamma T=0.06$ for 128 pixels and an exposure time of 10~ms. The WFS is read-out noise limited for stellar magnitudes above 14 with a $RON=1$ electron.

\begin{figure}[t]
    \centering
	\includegraphics[width=10cm]{Contrast_Diagram5.pdf}
	\caption{Normalized intensity versus stellar magnitude as a function of the adaptive optics system characteristics. We assume predictive control under the stability conditions of time series C. Red and blue lines represent the best contrast at each stellar magnitude for an AO system running at 100Hz and 1kHz respectively.}
	\label{fig:Performance_vs_Npix}
\end{figure}

Figure~\ref{fig:Performance_vs_Npix} also shows that a WFS temporal sampling also needs to be optimized.  For natural guide stars with magnitude $M_V\geq3$, the best contrast performance is obtained while running at 100~Hz. For instance, we reach a normalized intensity of $1\times10^{-9}$ with sample C initial perturbation, a stellar magnitude $M_V=5$ and 128 pixels across the beam. For natural guide star where $0<M_V\leq3$, better performance is achieved by increasing the WFS temporal frequency but the resulting contrast remains limited to $>10^{-10}$.
In an LGS scenario ($M_V<0$), an exposure time of $10^{-3}$s is also optimal to reach contrasts down to $10^{-10}$. For such bright stellar magnitude, we did not consider increasing the servo-loop frequency nor the WFS spatial sampling to enhance the contrast performance. Indeed, the performance of the future space-based real time controllers will be limited by the flight-ready computer technology, especially the power consumption, heat dissipation, the size and efficiency of the processors, and the required RAM to make the calculations\cite{Pogorelyuk2021}\,. Future research will determine the highest practical loop frequencies

\subsubsection{Random segment phasing error}

The efficiency of the AO algorithm described above depends strongly on the structural modes in the assumed OPD time series. For the examples above, most of the variance is contained in just a few modes, which assists the WFS measurement thanks to a higher signal-to-noise ratio for these few modes. We can however imagine a worse case where each segment is displaced randomly with respect to its neighbors. For the sake of illustration, we create a new time series where each of the 120 segments has a random piston motion. The total standard deviation is 110~pm RMS (close to sample C for comparison) and each segment carries 1/120th of the total variance. There is no particular vibrations in the segment basis and the temporal PSD is proportional to $f^{-1}$. Following the recipe above to correct for this time series, we first apply PCA, but since each segment movement is random, the variance is distributed among many more modes. The 10 first modes represent only 31.5\% of the total variance. In order to correct for a larger part of the signal in this simulation, we need to consider the 40 first modes that represent 70\% of the total variance. The 80 other modes left over carry individually less than 1\% of the total variance. In this particular time series, the WFS signal per mode is lower than the previous case while the photon noise remains constant and there is no noticeable structure in the principle components. Thus, it is harder for the WFS to distinguish between two separate modes. This induces stronger cross correlations between the modes and higher diagonal terms in the WFS covariance matrix. This can be mitigated with a higher spatial resolution, but at the cost of increasing the computational resources. Figure~\ref{fig:VariancevsMagnitude_RS} shows the standard deviation of the residuals, after the use of a predictive control algorithm running at 1000~Hz, versus the stellar magnitude for such a time series. It shows a dramatic result where the wavefront is not sufficiently corrected, even with the use of a bright LGS, because of the loss of modal signal. This result implies the structures that may be damped by optimizing the design of the telescope are also the easiest modes to correct with the on-board AO system. Therefore, the structures seen in the time series above should be minimized on the sole condition that it does not introduce new modes spread randomly on more segments, even with if the level of optical aberration is globally decreased.

\begin{figure}[t]
    \centering
	\includegraphics[width=10cm]{VariancevsMagnitude_RandomSegments1000Hz.pdf}
	\caption{Correction of a random segment phasing error of 110~pm RMS over the pupil. The standard deviation of the residual aberrations is plotted with respect to the stellar magnitude. We assume a predictive control algorithm running at 1000~Hz and a WFS sampling of 64 pixels across the beam.}
	\label{fig:VariancevsMagnitude_RS}
\end{figure}

\section{Conclusion}
The success of a future segmented space telescopes designed for the direct imaging of exoplanets with a coronagraph instrument strongly depends on the wavefront stability. However, the mechanical structure and payload of segmented telescopes may introduce quickly varying wavefront aberrations at the coronagraph instrument. We showed that wavefront errors induced by the spacecraft instabilities whose level is $\sim$100~pm~RMS would cause a loss of at least 75\% of the Earth-like exoplanet yield if left uncorrected. We therefore considered a range of possibilities to minimize the aberrations upstream of the coronagraph. First, the telescope dynamic aberrations may be optimized by damping some structural modes, or with the use of primary mirror and telescope control mechanisms, to reach an aberration level of about 10~pm RMS (e.g. sample B). This level should be sufficient to recover more than $\sim$90\% of the yield obtained without dynamical optical aberrations.
If the telescope stability is relaxed such that the dynamic wavefront error entering the coronagraph is $>$10~pm~RMS, the internal coronagraph could be equipped with a high-order AO system to partially correct these errors and stabilize the wavefront. Using NGS, we demonstrated the mission yield would be multiplied by a factor of $\sim2$ with a telescope whose initial stability is 100~pm~RMS (sample C). But the performance is limited by the large exposure time needed for a WFS to achieve picometer-level sensitivity with NGS. A separate out-of-band LGS located in the line of sight may be required to recover 100\% of the yield in a similar configuration. Since such a system might limit the mission yield because of limited fuel and large position displacement overheads, internal laser metrology methods should also be considered. Regardless the initial wavefront error, we find that for the steady conditions potentially offered by the space environment, predictive control algorithms are a valuable tool for correcting OPD errors caused by vibrations.

redpajama_set_name: RedPajamaArXiv


Here's today's list of a few hand-picked short-term technical patterns that we are currently eyeing for potential swing opportunities over the coming sessions. These selections are designed to assist the active trader and teach the developing novice in identifying low risk/high probability setups. They are meant to be trade walk-throughs where we show each element of the setup, highlighting the specific techniques we are employing in each case.
To receive alerts when this column is published, use the ticker "BETAX". Please feel free to send any questions/comments/suggestions to Jon Henninger at tapagesetups@briefing.com.
If the highlighted setups happen to not trigger the noted entry point during today's session, I recommend placing a price alert just below/above the mentioned level (below for longs and above for shorts), so that when the opportunity does present itself you will be fully aware of it and ready to execute.


Sir George Scharf (1820-1895), Artist and art historian; first Director of the National Portrait Gallery. Artist associated with 585 portraits, Sitter in 79 portraits.
The (Secret) Ballot Act is passed. By ending open voting in local and general elections, the act reduced the scope for intimidation at hustings, an important step towards democracy. Previously, voters had to mount a platform and announce their choice of candidate to a recording officer, so although most working men had already been enfranchised, employers were able to punish workers who did not vote for their preferred candidate.
George Eliot's novel Middlemarch is published. Exploring the impact of the 1832 Reform Act on provincial England, and charting the changes in class, politics, art and science in the nineteenth-century, Eliot's novel is widely perceived to be one of the best examples of the English realist novel.
The Metaphysical Club is formed in Cambridge, Massachusetts, by William James (brother of author Henry James), Oliver Wendel Holmes Jr, and Charles Sanders Peirce. The group begins to develop the American philosophy of pragmatism, which held that ideas were simply mental constructs that people formed to help them cope with the world, but which did not exist in an ideal realm.


If you came here looking for ways to break into someone's WordPress site, you choose the wrong definition of the word hack. No, this article is all about ways to make WordPress work better for you and your visitors by getting your hands dirty with WordPress' actual code, you know the functions.php files, .htaccess and all that good stuff.
Plugins can contain vulnerabilities that malicious hackers can exploit to gain access to your site and do just about whatever they please.
Plugins can severely slow down your site, thus having a negative effect on your SEO efforts.
Plugins can cause your site to break making it look ugly.
People who develop plugins sometimes forget about them so they stopping working properly when WordPress is updated.
Now, I am not saying don't use any plugins. But if you can do the same thing without one, you will be better off in the long run. So, if you are ready to start making some changes, let's jump right in.
Now you can use custom fields when you write your posts by selecting the key expiration. Set the expiration date in the following format: mm/dd/yyyy 00:00:00.
Yes, it was just that easy.
As it is written, you will display the five most recent sticky posts. Change the number accordingly if you want more or less.
Getting more subscribers could be as easy as reminding your readers. Place this snippet of code right above the Loop and anyone who clicks your previous entries link will see a message making it easy for them to subscribe.
If your blog has a lot of comments, that can be a good thing. What can be even better is if you were to set the author's comments and responses apart from the rest with a different background color.
You will need to change imagefile.extension to the image you wish to use and NAME OF YOUR GRAVATAR to whatever it is you wish to call it.
The posts with the most comments are generally your more popular content. If you want to really captivate your readers, make it easy for them to see which post is really driving the conversation with this hack. All you need to do is place the following code wherever you want your list of posts to be displayed (footer, sidebar, etc.).
The URL to your thumbnail should be changed to the one you uploaded to your site.
I hope you find these hacks useful. Please feel free to share any others that you may know of with the rest of our readers.
Very handy little quick tips. I'll be sure to implement some of these or a quick variation on my next site update.


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Coyotes – "Barking Dogs" 2 Sep 2009
Photo by Paul H. Risk
A lone coyote who thinks he owns our yard strolls leisurely along looking for a peach snack. He thinks they're his, too.
Our home at the north edge of Nacogdoches seems to be in the middle of coyote territory. Related to wolves and domestic dogs, their scientific name, Canis latrans, means barking dog. Often seen trotting through both our back and front yards, they serenade us in the evening with a yipping, howling, wailing, yodeling choir performance. A few can sound like dozens as they vary their voices almost like a ventriloquist. A passing train's whistle or emergency vehicle siren can really set them off. This chorus doesn't thrill our dog though. She prefers to cower in her doghouse when they're around. That's probably a good idea since coyotes like doggy snacks.
Coyotes have been common from ancient times and abound in Native American tales where "Coyote" is cast as a philosopher, a mischievous clown, or an evil trickster whose adventures include stealing food from honest folks. The Aztecs called them coyotl, meaning "holes" (where they spend the first part of their lives), and whether you call them KI-oats (KAH-oats in East Texan) or ki-OH-tees (my preferred pronunciation), we certainly have plenty of them here in Deep East Texas, where population estimates run as high as 15,000!
Why do coyotes make so much noise? They do it to keep in contact with their group, tell other roving bands where they are, help them estimate the abundance of kin, near and distant, and decide whether the neighborhood is just "gittin' too crowded." In spite of the way coyotes sound, a pack usually consists of less than a dozen.
Some people say coyotes are varmints that should be wiped out, swearing that they seriously threaten deer herds and cattle. That's just not true and anyway, exterminating them isn't easy, since the number of pups in a litter increases as coyote population densities decrease. Instead of only five or six to a litter, Mom may produce and be able to care for as many as twelve. The surviving animals also get smarter. It has been said by one detractor that coyotes are "like roaches – you ain't never gonna git 'em all."
A coyote's diet consists mainly of small animals like mice, rats, rabbits, fish, frogs, and snakes. They also consume berries, corn and fruit from farm fields and orchards. Deer and cattle are usually only eaten after they have died from other causes, although newborn calves or those weakened by disease are sometimes killed and eaten by coyotes.
Photo by Debbie DiCarlo / Rex Features
Coyote pups learn early on to howl right along with their elders.
Found in virtually every state, even in towns and cities, adult coyotes average around twenty-five to thirty-five pounds, with a black-tipped tail carried low instead of straight or raised as most domestic dogs and wolves do. Coyotes breed during January and February, giving birth about nine weeks later to between two and twelve pups which stay with the mother at least until fall, but some remain as long as two years before relocating five to ten miles away. A few weeks ago, three coyote pups came into our backyard for a game of tag and a wrestling match.
Coyotes sometimes mate with domestic dogs, becoming coydogs. Be aware that coyotes also purposely lure dogs into the woods where Fido becomes dinner, as the lone decoy coyote is suddenly joined by six or more of his pack mates. Outdoor domestic cats are particularly at risk. Cats are coyote candy!
There is no record of coyote attacks on humans in East Texas. However, in Southern California, where I've seen coyotes sit on a city street and howl at a streetlight, and where some misguided people feed them, there have been attacks on joggers and small children. Like many wild animals when they become too familiar with humans, coyotes lose their natural fear, and a running person, particularly a small one, may be viewed as food.
In any case, Old Man Coyote's call of the wild is definitely a part of nature's symphony in the fields and forests of East Texas and frankly, I kind of enjoy their performances.
Dr. Risk is a professor emeritus in the College of Forestry and Agriculture at Stephen F. Austin State University in Nacogdoches, Texas. Content © Paul H. Risk, Ph.D. All rights reserved, except where otherwise noted. Click paulrisk2@gmail.com to send questions, comments, or request permission for use.
Website by Bradley P. Risk.
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redpajama_set_name: RedPajamaCommonCrawl


text:
Rumored price increase would spell doom for DAZN
Baker Geist Updated January 16, 2020
fight-season_key_visual_used_for_social_headers
160 views January 16, 2020 - 01:01
It's Fight Season On DAZN
One can't fault streaming service DAZN for wanting to make more money. No different from any other service, it wants to maximize revenue and gain a bigger market share, in this case, in the sport of boxing.
A rumored monthly price increase — from $19.99 to $50 — isn't the way to do it. If it does indeed happen, it will alienate boxing fans which will be bad for the sport overall.
As I've said since its debut, DAZN is an innovative product allowing fans the opportunity to see fights overseas that could only be followed by reading publications like Boxing Monthly or searching for less than reliable YouTube streams. I've been treated to the terrific — and underrated — World Boxing Super Series where I was introduced to fighters like Maris Briedis, Yunier Dorticos, Aleksandr Usyk and many more. I've watched heavyweight Dillian Whyte climb the ranks and have been able to watch some entertaining Canelo Alvarez and Gernady Golovkin fights at a value.
That will no longer be the case if the price hike does happen.
While I can't speak to what others' budgets allow, I just don't have an extra $600 dollars a year lying around when presumably I'll receive the same value. Not when I have to budget for standalone pay per view fights as well.
I'm a boxing writer and I'm saying "no". I can't think DAZN's 800,000 U.S. subscribers will react differently.
DAZN is intriguing because of its value and ability to bring fans a wide variety of fights, but a price increase should bring with it more in demand fights on a more consistent basis. Yes, 2019 ended strongly with the rematch of Anthony Joshua and Andy Ruiz and an entertaining, albeit short fight, between Danny Jacobs and Julio Cesar Chavez Jr.
But for more money, December's "fight season" should be the norm rather than the exception.
DAZN Facts and Figures
Employees: 2,600
Launched: 10 August 2016
Chairman: John Skipper (DAZN Group)
Owner: DAZN Group
CEO: Simon Denyer (DAZN Group)
Headquarters: London, England, United Kingdom
Parent: Access Industries
We should get to see fast-rising and current WBO middleweight champion Demetrius Andrade against fellow champion Canelo Alvarez sooner rather than later or a third fight between Alvarez and Gennady Golovkin. We should see DAZN, and Matchroom Boxing promoter Eddie Hearn, work harder to strike deals with other promotional companies so that fans get to see intriguing fights among all of boxing's best.
Some may call such demands unreasonable but they are no more unreasonable than rashly justifying a price hike on a network that lauded itself as the place to watch high quality boxing without the "pain of pay per view."
Perhaps business demands a price increase. My skepticism peaked when Alvarez sign an 11-fight deal worth $365 million in October of 2018 only to be followed by Golovkin's six-fight deal with the network a short time later.
"That's stretching $9.99 pretty far," I thought. "But oh well, they know what they're doing."
If ambition got the best of the brass at DAZN and the price hike is needed for the network to survive, quite frankly it won't. Diehard fans will exit in droves, opting for cheaper options or maybe other forms of entertainment all together.
Not because we don't enjoy boxing or DAZN. But because we've got to, ya know, eat, pay bills, and have money for other things that sometimes interfere with our passion.


text:
The 2008 Nationwide Tour season ran from January 24 to November 9. The season consisted of 30 official money golf tournaments, five of which were played outside the United States. The top 25 players on the year-end money list earned their PGA Tour card for 2009.

Schedule
The following table lists official events during the 2008 season.

Money leaders
For full rankings, see 2008 Nationwide Tour graduates.

The money list was based on prize money won during the season, calculated in U.S. dollars. The top 25 players on the tour earned status to play on the 2009 PGA Tour.

Awards

See also
2008 Nationwide Tour graduates

Notes

References

Korn Ferry Tour seasons
Nationwide Tour

redpajama_set_name: RedPajamaWikipedia


The 150211th positive integer is an odd prime number that follows the number 150210 and comes before 150212. One hundred fifty thousand two hundred eleven is 6 digits long.
Q: Is 150211 a prime number?
Q: What is the negative number for 150211?
Q: What is half of 150211?
Q: What is a third of 150211?
Q: What is a quarter of 150211?
Q: What is the square root of 150211?
Q: What is 150211 times Pi?
Q: What is 150211 divided by Pi?
Q: What is the scientific notation for 150211?
Q: What are the divisors for 150211?
Q: What is the factorization of 150211?
Q: What is the sum of divisors of 150211, including itself?
Q: What is the sum of divisors of 150211, excluding itself?
The spelling of 150211 in different languages.
Q: What is the roman numeral for 150211?
Q: What is the digital capacity for 150211?
The number 150211 represented in different base number systems.
List the frequency of characters that make up the number 150211.
List of hash code values for 150211.


Budget cuts brought about by sequestration could force the closure of more than 100 air traffic control facilities — including control towers at smaller airports across the US.
Kissimmee Gateway Airport, which is just outside of Orlando, is on the list of towers which could be shut down April 7th. City leaders say that would put the brakes on one of the main economic drivers in the area.
"It's an economic engine, not only necessarily because of what happens on the field, but also what happens adjacent to it," says Mayor Jim Swan. He says the economic impact of the airport is estimated around $100 million a year. Swan says losing the tower will make it tough to market a $3.2 million dollar business airpark which is being built with state and local funds.
A large part of the airport's traffic includes business jets bringing people to functions at nearby Disney World and conventions on Orlando's International Drive.
Last year the airport saw 129,000 departures and landings from a mix of business jets, and propeller planes. Aviation director Terry Lloyd says losing the control tower- which is operated under a contract with the Federal Aviation Administration- could decrease flights to under 100,000 a year.
"I think it's something that we have a lot of dread [about], and there are a lot of unknowns," he says.
He says having a tower to help manage traffic makes Kissimmee a more attractive destination for business jets.
Aircraft operators also have fuel agreements at airports – like Kissimmee- that guarantee the price of aviation fuel if they land there. Lloyd says those agreements could also be jeopardized by the loss of the tower.
Other airport users say they're concerned about safety. John Calla, vice president of operations for Italico Aviation– a company that plans to import and assemble light sport aircraft at Kissimmee — says he's worried about the mix of traffic if there's no tower. "You see the jets that take off here and the speed they operate," says Calla. "You get a smaller aircraft that's used to flying about 60 miles per hour, integrating with something of that size, and you could get some conflicts.
Florida Congressman Alan Grayson has written to Transportation Secretary Ray LaHood and the FAA urging them to consider the impact of closing the tower.


Working greener practices into your routine not only helps the environment, but it also helps your health and sometimes your wallet too. The term "going green" can consist of simple individual acts like switching to recycled products or to start recycling trash, but can also be done on a much larger scale. In fact, many major corporations are adopting more environmentally friendly practices in their services and day-to-day operations. For example, Google created a "green team" dedicated to finding ways to keep its operations more sustainable, and they found a way to run their data centers using 50% less energy.
Now, I know what you may be thinking, going green sounds great in theory, but what are the costs of going green and are those costs outweighed by the benefits? This article will explore the costs and benefits for small businesses to go green on a small, medium, and large scale.
To begin, take care of the basics.
Replace all incandescent light bulbs with LED light bulbs. This technology might cost a little more than regular light bulbs, but they much longer and use up to 90% less energy.
If you provide bottled water for employees, switch to a water cooler or water filter to purify tap water.
Purchase reusable water bottles. The plastic water bottles are made mostly from polyethylene terephthalate (PET), an oil derived plastic. Each year they generate about two million tons of trash that adds to our landfills here in the U.S.
Implement a recycling program for your business to help in reducing waste. According to the City of Houston's website, commercial waste makes up approximately 40% of total municipal solid waste. Aside from being more environmentally friendly, the more you recycle means the less waste you throw away, which can lower your overall disposal cost. For more information contact your waste disposal company.
An easy alternative is to switch to green energy generated from renewable sources. Most energy is generated by fossil fuels like coal and nuclear power plants. Green energy is an eco-friendly alternative generated from wind, solar, hydro, and biomass sources. Green energy plans, tend to be slightly more expensive, but the impact of switching to green energy leaves much less of a carbon footprint.
If you've implemented the initiatives above and want to make a bigger impact, try these ideas!
Install low-flow toilets. An average low-flow toilet can cost a little over $100, but with all the water you'll save, you can recoup your costs rather quickly, usually within a year and a half.
Install motion sensor lights in rooms that aren't occupied all the time. By installing a motion sensor light switch, you automatically start to save money since the lights only stay on as long as you need them - and no more forgetting to turn them off.
Reduce the use of paper. Not only is it good for the environment, but it also saves you money. Encouraging employees to read all emails and information on their computer first before they decide whether it's necessary to print. Also, promote double-sided printing to lower paper and printing costs.
Ready to make green changes on a much larger scale? Whether you want to redesign the space or start from scratch, it's time to talk about LEED Certification.
To provide some background information, the U.S. Green Building Council (USGBC) is a non-profit community of leaders working to make green buildings available to everyone. And to make a building "green," they established the LEED (Leadership in Energy and Environmental Design) green building certification. This certification can be applied to all building types - commercial and residential - with the goal to promote sustainable building and development practices.
The LEED certification was designed for the environment, but it also makes business sense too, benefiting commercial building owners and tenants. The advantages to redesigning or building a green building not only helps the bottom line, but according to the USGBC, green buildings have proven to make happier and healthier employees and occupants. Green buildings are designed to have a healthier and cleaner indoor environmental quality, which affects employees in a positive way. It leads to improved employee satisfaction (which means less missed time), improved productivity, improved mental/physical health and better recruitment and retention. Having a green building is now a big selling point in recruiting employees (especially younger) because they want to work for companies that are conscious about their impact on the environment.
In addition to benefiting employees, a LEED certified building costs less to operate and maintain. And since green buildings provide immediate and measurable results, building managers and occupants will be able to see lower operating costs as soon as changes are made. There are also tax benefits and incentives for green buildings, which allow for additional savings. Lastly, green buildings are great for public relations and community awareness too. For example, according to the USGBC, "Adobe Systems, Inc., a major software maker, announced in 2006 that it had received three LEED for Existing Building Platinum awards for its headquarters towers; not only did it reap great publicity, but the firm showed that it had garnered a net present value return of almost 20 to one on its initial investment."
Like most things in life, all these benefits of being LEED certified don't come free. There are costs associated with the design and construction (if necessary) to bring a current building up to code or to build a new building. Although I cannot tell you exactly what those costs amount to, it's important to weigh those against the benefits started above.
Now, if becoming LEED certified is not for you, but you are interested in additional ways to make your business greener, check out the LEED project checklists. These checklists outline the specific tasks involved with becoming LEED certified.


another investigative report exposes Darrell Issa`s witch hunt.
to him to take on his own attorney general.
Shrum and Jonathan Alter will preview the historic vote.
all about American customs and felt more at home in her adopted country.
Oh, wait a minute, I`m sorry, because I`m not a trained Arizona official.
SCHULTZ: The congressman joins me tonight.
And the fate of the nation`s health care will be decided tomorrow.
But either way, single payer is making a comeback.
Eric Holder during a meeting of the House Rules Committee today.
Department of Justice to be uncooperative at every step of the way.
whatsoever. Issa admitted it today.
about the controversial fast and furious case.
wondering why the House is going to go through with the contempt vote.
rush this to the floor tomorrow, just doesn`t smell right to me.
institution, with this particular kind of undertaking.
trafficking never even happened the way the Republicans claim it did.
The Fast and Furious case was one of a dozen the agency was pursuing.
only 200 miles from Mexico.
States. These loose gun laws are a big reason why.
guns. Many of these sales were clearly suspicious.
suspect with no job paid $10,000 for a sniper rifle. Go figure.
with said firearm in his car."
the National Rifle Association, but it also makes a mockery out the truth.
Oversight and Government Reform Committee.
REP. ELIJAH CUMMINGS (D), MARYLAND: Good to be with you, Ed.
we have seen so far on this?
about this, did not authorize it, did not condone it, this whole situation.
history of the United States of America has ever been voted in contempt.
And so, this is really sad and very unfortunate.
today`s hearing. Here it is.
that goes on in every administration.
SCHULTZ: I want to give you an opportunity to respond to that.
invoked here as if it doesn`t even exist.
people to make the determination.
But let me tell you, I think what they`re doing is very political.
And I think that if you -- they need to take a step back.
cooperating and not been working with us.
He has. And he`s done quite a bit to help us.
highway. And that`s what this boils down to.
president took the oath of office.
Holder found out about it, he immediately stopped it, and ordered an I.G.
there`s a bipartisan picnic going on.
SCHULTZ: I understand that all of the key players are there.
SCHULTZ: What`s that atmosphere like?
Issa, you`ve got Boehner, you`ve got the attorney general, the president.
find ourselves in now and tomorrow.
very embarrassing to the country, would you say?
SCHULTZ: Congressman Elijah Cummings, thanks for your time tonight.
SCHULTZ: A sad day in politics tomorrow in America. That`s for sure.
your thoughts on Twitter @EdShow. We want to know what you think always.
Alter and Bob Shrum will weigh in on that and I`ll have commentary.
should not cave to the pressure for the sake of political careers.
will join us on THE ED SHOW later.
Court`s ruling on health care.
from some House Democrats who are pretty nervous.
organization says it will track how members vote tomorrow.
Furious program was designed to restrict gun laws back in October.
no facts to back it up.
Congressman Darrell Issa followed suit at the NRA convention in April.
term on the Second Amendment, you really haven`t evaluated this president.
SCHULTZ: Just red meat to the head-shaking crowd.
does. They`re going to attack him any way they can.
second commercial that might show up in their backyard.
going to vote for contempt and I`m not going to take away your firearms.
That`s all they have to say. And stick with the truth.
abomination of government in this country.
View" columnist, and Democratic strategist Bob Shrum with us tonight.
many do you think will turn on the attorney general and the president?
five of them. But, you know, they should really be ashamed of themselves.
everybody thinks they know about this case is untrue. And they nail it.
viewers to read this article.
president and to get himself in the headlines. I don`t say that lightly.
You know me well enough to know I`m not a bomb thrower.
in the McCarthy era to say, have you no sense of decency, Mr. Chairman?
in contempt. This is a witch hunt of the first order.
should be ashamed of themselves.
attention to this -- and they`re ready to vote on contempt?
dangerous clown, but he`s a clown.
matter -- Jonathan is absolutely right. If you read that "Fortune"
NRA, there was never any connection with this program with gun control.
programs, and that administration was not exactly for gun control.
party members in the House to get their heads screwed on right about this?
Does he play any role at all?
this. It`s out of bounds. This is an improper investigation.
because an awful lot of guns walk out of those shows.
SCHULTZ: Jonathan, what is the political fallout of this?
Representatives that`s in the grip of extremists.
SCHULTZ: What would you compare it to?
to basically make stuff up, that`s what`s going on here.
ALTER: That`s been going on for a long time.
cut opportunity to tell them to stick it.
marching orders from interest groups?
know. They`re an auxiliary of an extremist Republican Party.
crazy as this House of Representatives is.
to make a point about immigration. The stars are part of a pop quiz.
We`ll put you to the test, next.
covers it all, doesn`t it? We`ll show you out of the world poll numbers.
Here`s his "guess the immigrant" quiz.
perform in Phoenix, remember to bring your papers.
American. So let`s consider their names, Jeremy Lin and Tony Parker.
American. And yet this absurdity is the law of Arizona.
is Justin Bieber the face of the immigration debate right now?
what they are, right, pop culture.
I use them because, you know, as I look -- I looked at Justin Bieber.
or you do it, when anyone does it.
you`re under some reasonable suspicion that you`re not in this country.
It`s wrong and it`s bone headed.
serious as this, you laugh at it and you bring a new context.
SCHULTZ: And you can learn from it.
GUTIERREZ: You can learn from it.
against the Arizona law. The justices -- I was there in the courtroom.
revoke the law on that.
respectful of our Constitution and of our American values.
Gosling, what do you think?
GUTIERREZ: Eva Mendes is the American.
another one. Here`s for sports fans, Alex Rodriguez or Jason Bay?
GUTIERREZ: Thank you so much, Ed.
BARACK OBAMA, PRESIDENT OF THE UNITED STATES: Hello, Miami.
It is great to be back in Cleveland.
It`s good to be back in Philadelphia.
SCHULTZ: It don`t mean a thing if you ain`t got the swing.
OBAMA: Let`s get to work.
tomorrow`s big decision on health care.
SCHULTZ: An actual poll from "National Geographic" has the answer.
SCHULTZ: We`ll bring you the results.
leads Mitt Romney with voters in those states 50 to 42.
Also working in the president`s favor, his position on immigration.
In Pennsylvania, the president tops Mitt Romney as well, 45 to 39.
Medved. Great to have all of you with us tonight.
OK, we`re down to four months to go, July, August, September, October.
SCHULTZ: Joy, what does Romney have to do?
besides his business record to really peg him on.
the economy, he`s left himself really vulnerable.
SCHULTZ: But not in the swing states.
change of direction with the same president.
decision -- and immigration. The guy just is not definite on anything.
be focused on precisely that specific agenda.
SCHULTZ: What about that, Richard?
ticket. And that`s why people like to do it just before the convention.
said, Ed, then the president has to keep pretty much hammering Romney.
Republicans who filibustered the Dream Act.
And Romney was against the Dream Act. He stuck with those positions.
to have you with us tonight. Thanks so much.
with them if they got violent.
life before. During the 2008 campaign, he had this to say.
you want the public to find out?
SCHULTZ: Funny story, but it does drive home a pretty serious point.
President Obama is a much stronger leader than Mitt Romney.
yes; six percent of you said no.
joins me for the discussion next. What`s the plan?
right to do this under the Commerce Clause.
for all and they like it.
who think it`s not a good idea.
struck down by the Supreme Court tomorrow?
American judicial history, clearly defying past legal precedent.
think that this law is going to fall apart.
to single payer or Medicare for all?
SCHULTZ: How do you think the Democrats will react to that?
the wrong way. And we`ll make sure that they have the wind at their back.
the campaign trail to embrace single payer?
Clause to help people. And that would be a great thing.
But if they don`t, we need to stand strongly for Medicare for all.
Pelosi about the Supreme Court`s ruling on the health care law.
MADDOW: Thanks, man. I`ll see you tomorrow.


text:
package com.datawar.argdata_warfare;

import android.app.Activity;
import android.os.Bundle;
import android.widget.ListView;

import java.util.Timer;

/**
 * Created by Kill-o-bite on 11/22/2016.
 */

public class Inventory extends Activity {

    ListView inventor;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_splash_screen);

        inventor = (ListView) findViewById(R.id.inventoryList);

    }

    public void addBank(String s, Timer t){

    }

}

redpajama_set_name: RedPajamaGithub


The Eastern District of Wisconsin Bar Association (EDWBA) provides opportunities for involvement through its committees. Committees typically meet monthly. Below is a list of committees with brief descriptions.
The Bankruptcy Committee represents the needs and concerns of the bankruptcy bar, often working closely with the bankruptcy bench. The committee plans CLE seminars and bench-bar luncheons that address these needs and concerns.
The Civil Committee represents the needs and concerns of the civil bar. The committee plans CLE seminars and bench-bar luncheons that address these needs and concerns.
The Criminal Committee represents the needs and concerns of the criminal bar. The committee plans CLE seminars and bench bar luncheons that address these needs and concerns.
The Membership Committee's main goal is to increase membership in the association by reaching out to those newly admitted to practice in the Eastern District as well as those who could benefit from membership. To accomplish this, the committee works closely with other committees.
The Newsletter Committee has the responsibility of publishing the quarterly electronic newsletter. The committee is responsible for story ideas and identifying the appropriate people to write the stories.
The Pro Bono Committee undertakes new pro bono initiatives with the goals of increasing the number of attorneys willing to accept pro bono appointments from the court, ensuring that attorneys are adequately trained to do pro bono work, and to explore new initiatives to assist pro se litigants.
The Program Committee oversees the association's calendar of CLE seminars and bench-bar luncheons. The committee also takes responsibility for planning the Annual Meeting held in April.


text:
Joss Stone Links
[ RETURN TO FULL LISTING ]
Joss Stone Announces Release of New Album, LP1, on July 26. LP1 To Be Released on Stone's Own Label, Stone'd Records And Surfdog Records
Stone'd Records & Surfdog Records are proud to announce their partnership to release Joss Stone's next album, LP1 on July 26, 2011.
As a world-renowned soul singer who Smokey Robinson calls "Aretha Joplin," Joss has sold over 11 million records globally. Having just turned 24, Joss has already amassed a career's worth of successes. She is a Grammy winner, five-time Grammy nominee, and the recipient of several Brit Awards.
Stone recently established her own label, Stone'd Records, and has partnered with Surfdog to release LP1. This is the first album Joss has recorded with total creative freedom. She co-wrote and co-produced it with super-producer and Eurythmics co-founder, Dave Stewart. Together they immersed themselves into a rock n' soul musical odyssey in Nashville, Tennessee, finishing LP1 in only six days.
"This is the most fun I've ever had making a record with Crazy Dave Stewart at the helm, and yes the players in Nashville are unbelievable!!!" says Stone. "This album captures a specific moment in time that was spontaneous and full of creativity."
"Joss can sing with the ferocity of a lioness and dynamically switch to the most delicate whisper in the same phrase," says Stewart. "She is always honest and full of real emotion. It is an honor to work alongside a true artist who understands so much at such a young age."
www.jossstone.com
www.facebook.com/jossstone
www.surfdog.com
STONE'D RECORDS
CONNECT WITH STONE'D RECORDS
©2010-2015 Stone'd Records


Our first-year engineering course we call Engineering Principles is an innovative projects-based, hands-on experience centered around the essence of engineering. You will develop depth of expertise in valuable skills used by engineers. You then gain practical design experience by applying those skills in completing several significant projects.
Makers Fair: develop and build a microcontroller-based product and pitch your idea to a group of potential buyers.
A solid foundation for the engineering knowledge that you acquire over the next three years … and beyond.
"I thoroughly enjoyed the course. This course gave us a real-life experience. We did not just learn about or watch engineers at work - we were engineers at work!"


The Center for Grieving Children offers free support groups for kids and teens ages 5-18 who have experienced the death of a loved one. Each meeting includes creative outlets (like games, arts and crafts, music, and more). Groups are divided by age, and caregiver groups are held concurrently for adults.


text:
Q: not able to route in angularjs in eclipse I am not able routing to other page what the problem I dont know please solve my problem.
I am using Eclipse Java EE IDE for Web Developers.
Version: Mars.1 Release (4.5.1)
Build id: 20150924-1200
// also include ngRoute for all our routing needs
var myApp = angular.module('myApp', ['ngRoute']);

// configure our routes
myApp.config(function($routeProvider) {

  $routeProvider

  // route for the home page
    .when('#/', {

    templateUrl: 'home.html',
    controller: 'mainController'
  })

  // route for the about page
  .when('#/about', {
    templateUrl: 'about.html',
    controller: 'aboutController'
  })

  // route for the contact page
  .when('#/contact', {
    templateUrl: 'contact.html',
    controller: 'contactController'
  });
});

// create the controller and inject Angular's $scope
myApp.controller('mainController', function($scope) {
  // create a message to display in our view

  $scope.username = 'ranjeet';
  $scope.password = 'singh';

  $scope.message = 'Everyone come and see how good I look!';
});

myApp.controller('aboutController', function($scope) {
  $scope.message = 'Look! I am an about page.';
});

myApp.controller('contactController', function($scope) {
  $scope.message = 'Contact us! JK. This is just a demo.';
});

<!DOCTYPE html>

  <link rel="stylesheet" href="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css">

          Angular Routing Example

home

 About

Contact

file structure of my project :
[1

A: Your url values in $routeProvider.when() should not include # which will be set internally if applicable (as by default html5mode is disabled by angular router, so angular does use hash location strategy).
Try changing:
$routeProvider

  // route for the home page
    .when('#/', {

    templateUrl: 'home.html',
    controller: 'mainController'
  })

To
$routeProvider

  // route for the home page
    .when('/', { //do remove # from all registered routes
       // ^^ no "#"
    templateUrl: 'home.html',
    controller: 'mainController'
  })

redpajama_set_name: RedPajamaStackExchange


On Thursdays, If you buy a 60 Minute Jump we will give you 60 more minutes FREE. If you buy 90 Minutes we will give 90 more minutes FREE. We double your time! The last Double Down Promotion ends at 6:00 PM. No other jump times are available on Thursday. Promotion not valid for any other times. Not combinable with any other coupon/offer.


What is news in the property and real estate sectors?
There are millions of property websites, with more being created every day, many around the subject of property, and it's getting harder to know where to turn to for reliable property news and market updates. Technology is having a large affect on the ability for non property related businesses to tap into the new and story based traffic that is of interest to real estate professionals and advisors.
• The LEADER in International For Sale By Owner, TOP ranked web listings portal for International For Sale By Owner, FSBO!