The Good Dinosaur is a story that takes place if dinosaurs still walked the Earth. It's centered on a young dinosaur, Arlo, who is afraid of everything and can't seem to make his mark in life or with his family. After a series of tragic accidents Arlo ends up lost, miles from his home, and blames a "critter" (a human boy) for all of his misfortune. Somehow, he must find his way back home through the dangerous countryside. He reluctantly starts a friendship with the aforementioned human boy he names "Spot" as they struggle to survive.
The movie gets a lot of humorous mileage out of the dynamic duo of Arlo and Spot. Arlo is the emotional core of the movie. Despite his fearful nature, he's really a brave and lovable goofball with a heart of gold. Spot, meanwhile, is his mirror opposite--wild, unkempt, brave, and extremely loyal. He's a daring rascal who has his own tragic past. Their budding friendship never feels forced. They feed, protect, and learn about the other and get into several crazy mishaps along their journey. Spot becomes the very catalyst for Arlo's transformation from coward to hero. He inspires Arlo to be brave and helps him to grieve. Their relationship grows from one of resentment (on Arlo's part) to one of true friendship.
Although The Good Dinosaur isn't one of Pixar's "great" films, it's still a funny and entertaining movie. It's brilliantly animated and voiced with the professional ease you've come to expect from a Pixar film. The movie plays on western tropes like cattle herding, rustling, and just plain old farming. This may sound a tad uninspired but it's often played for laughs. The antagonists are terrifying in this otherwise sanitized world and have a neat "reverse Jaws" moment near the end of the film, but they aren't very memorable and only appear briefly. The other characters although humorous were never deeply explored, so we only really get to know Arlo and Spot. Unlike Pixar's other films which have more complex themes The Good Dinosaur's are relatively simple: Arlo must learn to overcome his fears and realize that having fear isn't the same thing as not having courage. He also learns the value of family, friendship, and most of all acceptance. Acceptance of fear, pain, and loss.
The Good Dinosaur is fast flowing and easy on the eyes. It's only drawback is that its story is relatively simple, which isn't really a problem, except in regards to Pixar's previous films like Wall-E, UP!, or Toy Story 3 (to name a few). This film takes the well worn coming of age tale and adds a new spin with the "dinofied" American West as its setting. It's just not as original or memorable as their previous classics. In any case, this is a solid addition to the Pixar canon, a touching tale of loss, overcoming one's fears, and the importance of the bonds of friendship and family. Pixar is as reliable as the sun rising in the east, and once again they've made another quality film. So take your kids, or go see it if you like first rate animation; either way, you can't go wrong.


I have owned quite the plethora of electronics in my life. A commonality between most of these devices' screens is frozen or dead pixels. This is probably the most annoying thing about buying new hardware—your LCD, or worse, LED display has one or more pixels that continues to stay lit. Most of the time, this will appear in the form of a brightly colored pixel that never changes, or a pixel that never displays the right color. Once you notice it's there, you just can't stop staring at it. It mocks you when your entire display lights up like a fireworks show while viewing a night sky in Skyrim.
There are loads of methods for fixing stuck pixels, but no one tells you that some pixels can't be fixed, or why. 95% of pixels can be fixed, but there is that other 5% that stops you from enjoying the beauty of your 60 inch LED display. These are mostly caused by broken transistors, which are impossible to fix (unless you think your soldering skills surpass those of a machine that puts the solder runs on PCBs). Today, Null Byte is going to offer both the common and lesser known methods for fixing stuck pixels, while debunking rumors and "guaranteed" fixes.
There are a number of types of dead pixels, as well as ways to fix (or not fix) them. Let's take a look at the possibilities.
Three sub-pixels make up one pixel—one for red, green and blue, respectively.
Dark dots: These are caused by dead transistors. Unfixable.
Portions of pixels are the wrong color or otherwise displayed improperly: A partial sub-pixel defect from the RGB film layer being cut improperly cannot be fixed.
Bright dots: This is caused by a wonky transistor that allows light through all of the sub pixels, or none of them.
Nothing is on the screen: This is caused by the monitor not being plugged in!
Software is the first step to take when you want to fix a stuck pixel, because it is the least likely to dig your screen into a further hole of ugliness (it is still possible to damage it further this way). This method worked for two of my stuck pixels, and I have heard it works about 40% of the time. I would vouch for that, but some companies sell software and claim it fixes 95% of stuck pixels. This is a blatant lie.
Download Stuck Pixel Sweeper. It's a Java program, so it works on all platforms!
I would recommend running the software for 20 minutes, and if the pixel isn't fixed, run it for an hour. If that fails, move on.
The high contrasts of the image might fix the pixel and allow light to pass through properly. This type of contrast method has also been known to slightly enhance image quality, which is trivial. I've seen it work, and I've seen it not work. A better alternative software, if you want to pay for it, is JScreenFix, another Java applet that flashes each pixel individually, 60 times per second.
People will swear on their lives that hardware solutions like PixelTuneUp work. I am actually one of these people, after using one in a computer tech lab on a student's monitor. The results are breathtaking, and some hardware devices are even compatible with HDTVs. PixelTuneUp actually enhances video quality greatly and reduces the likelihood of ghosting or burning. It's easy to use, too.
Plug the device into a VGA or DVI port, and let it run for 20 minutes. If the pixels can be repaired, this will likely fix it.
Image of DVI and VGA from right to left.
This works much like the software method. The hardware sends specific signals and displays high contrast colors on opposing ends of the UV visible spectrum. This can make sub-pixels that are stuck display properly by stressing the pixels with extreme contrasts, and attempt to force the pixel to render them.
I have heard hundreds of times that cloth methods work. They do not. The only circumstance that could possibly allow any of these silly methods to work would be if a transistor was loose and you somehow pressured the transistor so the solder run was complete again. I have also tried it myself, numerous times without prevailing. If you have an experience where this has worked for you, let me know! I'd love to know if it actually works for some people.
The method is simple, however. Just tap the screen, gently, or apply pressure directly to the pixel with a soft cloth and it supposedly becomes "unstuck".
Now, this doesn't mean the pixel doesn't get removed. I actually have seen it remove stuck pixels, but it doesn't fix anything—in fact, it actually breaks it more. You are just forcing liquid crystals outside of their proper place into another, so it will create a blending effect.
Hey there, thanks for sharing this article! I have a cintiq monitor that arrived with an intense dead pixel problem upon arrival. I guess that is what I get for getting it refurbished... I'm going to try this out and hopefully it works. I'll tell you how it goes!
On another note, I actually DID succeed using the poking the dead pixel until it goes away method. I got my Asus monitor with a dead pixel on arrival, brand new. Just one bright green pixel in the top right corner. I poked it a few times, and viola! Miracles of all miracles, it disappeared and hasn't come back since, four years later. The blue and red and green of that grid space were functioning normally again. I consider myself lucky.
I just tried this on my monitor and it fixed within a few taps of my finger. It works!
Cloth trick has worked for me. Had a few stuck pixels at the bottom of the screen after cleaning it, so I wrapped a screwdriver with a microfiber cloth and gave it a good jab. It's been just fine ever since.
I bought a new 42 inch lcd led tv 2 days ago I know this isn't exacally a dead pixel situation.
I believe they call it clouding but during dark scenes and dark space type movies you could see 3 large spots that where much brighter then the rest of the screen and just for the hell of it I decided to wipe the whole screen with the back of my hand and after doing so the bright spots vanished. It was like when you put a screen protector onto your phone and your chasing a bubble out.I had no idea what had happened so after that I did some research and discovered that what I had was called clouding and that rubbing it as I did could work.
There appeared to be two sides, for some it worked for others it didn't work. I guess my point is if you heard that one method has worked for some people, then it could very well work in some cases so I would say before doing the software resolution in this article try massaging the screen 1st and then go from there.


text:
Mira Rajput Reveals What She Felt Like When She Met Shahid For The First Time... At 16!
Srishti Gupta | Feb 6, 2019
Mira Rajput and Shahid Kapoor have been married for over three years now. But, back then, when Shahid announced he's marrying Mira, who is 13 years his junior, a lot of people were surprised. The shock wasn't only due to the age gap but also due to the fact that it was an arranged marriage and they'd only met a handful times before deciding to tie the knot in a private ceremony. However, as time has passed and their family has grown with cute little additions Misha and Zain, they've proved that love cannot be defined by any societal norms.
Recently, Mira held an AMA on her Instagram account and somebody asked her what it was like meeting Shahid for the first time. Her response was quite surprising. She said "Just like meeting anyone for the first time. Interesting. It was actually when I was 16 and we were at a common family friend's house for a concert by a Sufi singer. Both our dads love that kind of music."
Shahid had also, once in an interview, revealed what it was like the first time he met his now wife Mira. "It was a lovely evening and light was falling on her face. She just turned towards me and smiled and said something. I was like she is so young but I like her, I thought if something is wrong with me," he said
Almost there! Don't forget to tune into @colorsinfinitytv, 7:30 PM today to watch @shahidkapoor get candid with @jiteshpillaai on season 2 of #FamouslyFilmfare. @americanexpress @mynykaa
A post shared by Filmfare (@filmfare) on Jan 20, 2019 at 4:19am PST
Another interesting question that a follower asked her was, "What did you REALLY do to lose the pregnancy weight?" She had a pretty positive reply to this too - "I really worked hard and still am. Try and be the best version of yourself and stay happy. Workout, eat healthy and have fun."
POPxo is now available in six languages: English, Hindi, Tamil, Telugu, Marathi and Bangla.
AWESOME NEWS! POPxo SHOP is now Open! Get 25% off on all the super fun mugs, phone covers, cushions, laptop sleeves, and more! Use coupon code POPXOFIRST. Online shopping for women never looked better!
Srishti Gupta
Deputy Features Editor
Home >; Wedding >; Life
Here's Why A Wedding Gift Registry Is A Revolutionary Concept!
Dear Bestie, Can We Too Please Dance On *Lamberghini* At My Sangeet?!

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}
\label{sec:intro}

Weak lensing (WL) is one of the most promising cosmological probes since it directly traces the integrated gravitational potential along the line-of-sight (LoS) without any assumption on the relation between luminous matter and dark matter~\citep[see][for reviews]{Mandelbaum18,Kilbinger15,WMM13,BS01_review}.
It plays an essential role in ongoing surveys such as
the Dark Energy Survey (DES\footnote{\href{https://www.darkenergysurvey.org}
{\nolinkurl{https://www.darkenergysurvey.org}}}),
the Kilo-Degree Survey (KiDS\footnote{\href{http://www.astro-wise.org/projects/KIDS/}
{\nolinkurl{http://www.astro-wise.org/projects/KIDS/}}}), the
Hyper Suprime Cam Subaru Strategic Program (HSC\footnote{\href{http://www.naoj.org/Projects/HSC/HSCProject.html}
{\nolinkurl{http://www.naoj.org/Projects/HSC/HSCProject.html}}}),
and future surveys such as the
Rubin Observatory's Legacy Survey of Space and Time (LSST\footnote{\href{https://www.lsst.org}
{\nolinkurl{https://www.lsst.org}}}), the
\textit{Roman Space Telescope}\footnote{\href{https://roman.gsfc.nasa.gov}
{\nolinkurl{https://roman.gsfc.nasa.gov}}} and
\textit{Euclid}\footnote{\href{https://sci.esa.int/web/euclid}
{\nolinkurl{https://sci.esa.int/web/euclid}}}.
The currently ongoing, so-called Stage-III weak lensing surveys have achieved constraints on $S_8\equiv\sigma_8(\Omega_m/0.3)^{0.5}$ at the 3--5 per cent precision level.
Constraints on $w_0$ range around a $40$ per cent precision level  using cosmic shear only~\citep{DES_Y3_WL2,DES_Y3_WL1,SubaruHSC_shear19,KiDS_shear20,KiDS+VIKING450xDES-Y1_shear}.
This precision has been improved by combining cosmic shear with other probes such as galaxy galaxy lensing, galaxy clustering, CMB lensing, Supernovae, baryon acoustic oscillation (BAO), redshift space distortion (RSD) etc~\citep{DES_Y1_3x2pt,DESY1xPlanckxSPT_6x2pt,KiDS1000_3x2pt}.
The near-future Stage-IV surveys are going to push this frontier to sub per cent level on $S_8$ and per cent level on the equation-of-state (EoS) of dark energy~\citep{WFIRST_AFTA,LSST_SRD18,Euclid_DSR,SKA_RedPaper}.

However, weak lensing analyses from next generation galaxy surveys face several challenges. Firstly, standard weak lensing measurements require a large galaxy sample that includes predominantly faint galaxies in order to overcome limitations from intrinsic ellipticity noise.
Secondly, photometric redshift (photo-$z$) estimation and shear calibration are inherently hard for faint galaxies and pose severe systematic uncertainties~\citep[e.g.,][]{Mandelbaum18} that must be modelled and controlled in future surveys.
In order to overcome the first limitation the following novel methods have been proposed to directly infer the intrinsic galaxy shape:

    i) \textit{Radio polarization}: Observations have revealed azimuthal magnetic fields across the disc in the Milky Way and nearby spiral galaxies~\citep[e.g.~][]{HMQ_99,Beck07}.
    When the galaxy is not perfectly aligned face-on towards the observer, Faraday rotation caused by the LoS component of the galactic magnetic field and free electrons will change the position angle (PA) of polarized synchrotron radiation.
    This results in inclination-dependent integrated polarization when the galaxy is not spatially resolved~\citep[][]{SKBT_09,SR12}.
    Since gravitational lensing preserves the position angle, \cite{BB_11a} proposed to utilize polarization information to calibrate the intrinsic inclination of spiral galaxies.
    However, typically only few per cent of the radiation is polarized, thus $\mu$Jy sensitivity is required to ensure a large enough sample with meaningful SNR.
    The relation between inclination and polarization as a function of environments and redshifts are further uncertainties in this method. Potentially, SKA will enable these type of measurements ~\citep{BB_11b,WBB_15,SKA_WL_3}.

    ii) \textit{Galaxy rotation velocity field}: This method was first proposed by~\cite{Blain02} and~\cite{Morales06}.
    The idea is described as follows: weak lensing only linearly distorts the 2D position of photons, but keeps the frequency unchanged.
    By measuring the projected 2D rotation velocity field of late-type galaxies, we can partially constrain the shapes before lensing assuming a disc kinematics model (see Sect.~\ref{sec:KL} for detailed description).
    The rotation velocity could be measured both in optical/NIR bands traced by nebular emission lines, and in radio/submm wavelength traced by the CO rotational ladder or H\,\textsc{i} 21 cm emission. To fully break the degeneracy, one still needs information on either the direction of the shear field or the circular velocity of the disc.
    \cite{DSM_15b,DSM_15a} proposed to estimate the direction of the shear field from the orientation of lens galaxies or clusters, and \cite{GTF20} obtained the first measurement from low redshift galaxy-galaxy lensing systems, with an averaged measurement of tangential shear $\langle \gamma_\mathrm{t} \rangle=0.020\pm0.008$ over 18 low-$z$ galaxies. While \cite{GTF20} primarily used the velocity map for their measurements, \cite{DiGiorgio21} further improved this approach by modelling the major and minor axes in photometry images of source galaxies.
    \cite{Eric13,SKH+22} developed kinematic lensing in the context of cosmic shear rather than galaxy-galaxy lensing. Specifically, they built estimators for both shear components taking advantage of scaling relation of galaxies, e.g. the Tully-Fisher relation\citep[TFR,][]{TF1997}, to infer the circular rotation velocity of spiral galaxies. This will not only suppress the shape noise, but also decrease other systematic uncertainties like redshift error, shear calibration bias, and intrinsic alignment (see Sect.~\ref{sec:sys}). These improvements not only increase the cosmological constraining power of a tomographic WL survey, but also enable meaningful BAO detection from 2D tomography shear power spectra~\citep{DSH+19}. We note that synthesising methods of radio/optical/NIR rotation curves and radio polarization can produce more robust and precise measurements ~\citep{SKA_WL_3,BHH_18}.

Among the next generation telescopes the \textit{Roman Space Telescope}~\citep{WFIRST_AFTA,Roman_general} has the most promising instrument capabilities, specifically high resolution grism and wide-field imaging, to conduct a self-contained KL survey.
The ESA/NASA \textit{Euclid} mission could in principle also perform a KL measurement, the only concern is the slightly lower grism resolution and related uncertainty in measuring kinematics.

The \textit{Roman Space Telescope}\ has several primary science goals ranging from the search of habitable exoplanets to the origin and evolution of our universe.
It will perform multiple surveys including a microlensing survey, exoplanets direct imaging, a type-Ia supernovae (SNIa) survey and, the main focus of this paper, a wide-field imaging and spectroscopic survey, the so-called High Latitude Survey (HLS).
The HLS is designed to combine multiple cosmic probes, e.g. weak lensing, photometric galaxy clustering, galaxy clusters, BAO and RSD to optimize systematics control \citep[c.f.][]{WFIRST_MultiProbe}.

In the current 1.6 year \textit{HLS reference survey design} the HLS is composed of the High Latitude Imaging Survey (HLIS) and High Latitude Spectroscopy Survey (HLSS).
The HLIS will map 2,000 deg$^2$ of the sky in \textit{Y}, \textit{J}, \textit{H} and \textit{F184} bands with a $5\sigma$ point-source depth of M$_{\mrm{AB},\mathit{J}}$=26.70.
HLSS will measure slitless galaxy spectra in the same footprint with $7\sigma$ flux sensitivity down to $1.0\,(1.8)\times10^{-16}\rm{erg\,cm^{-2}\,s^{-1}}$ for a point source (extended source, respectively).
This reference design will be updated and improved with input from the community in order to maximize the scientific return ~\citep[e.g., see ][for a wide survey design that overlaps with the LSST footprint]{WFIRST-LSST}.

This work builds on the kinematic lensing idea as developed in ~\cite{Eric13}. We explore how well the combination of shape measurements from the HLIS and rotation curves extracted from the HLSS data allow for a KL analysis that self-calibrates the intrinsic galaxy shape, thereby significantly reducing the impact of shape noise. We further examine the improved constraining power of the KL measurement with respect to systematic uncertainties and compare our forecasts to the standard \textit{Roman} WL reference survey. As a first step, this work predicts the constraining power on $S_8$-$\Omega_\mrm{m}$ and $w_0$-$w_p$ with shear-shear angular power spectra as the only observable, however we note that an extension to a multi-probe analysis is straightforward and a topic of future work.

The paper is structured as follows: In Sect.~\ref{sec:KL} we briefly review the KL theory. We then specify our scenario definitions and parameter settings in Sect.~\ref{sec:simulation_settings}. Likelihood modelling, including data vector, covariance matrix and systematics, are described in Sect.~\ref{sec:CosmoLike}. We present our results in Sect.~\ref{sec:results}, and conclude in Sect.~\ref{sec:conclusions}. More details on cosmic shear estimation via KL and effective shape noise evaluation are derived in Appendices~\ref{sec:appd_a} and~\ref{sec:shape_noise_estimation_details}.

\begin{figure*}
    \centering
    \includegraphics[width=\linewidth]{figures/v3_figs/illustration_obsdata_v3_show_diff.png}
    \caption{An illustration of the shear effects on photometry image, kinematic map and grism image.
    \textbf{Panel a:} The projected photometric isophotes (black dashed contour) and LoS velocity map (blue-red dashed contour) as observed in the source plane $X_\mrm{S}$-$Y_\mrm{S}$.
    \textbf{Panel b:} The projected photometry isophotes observed in the image plane $X_\mrm{O}$-$Y_\mrm{O}$ (grey-black filled contour). As a reference, we also plot the original isophotes before lensing as grey dashed contours. To illustrate the shear distortion better, we take 4 example points on the major and minor axes of the source plane galaxy (the open circles), and show their positions on image plane as filled circles. The displacements are shown in black solid line segments.
    \textbf{Panel c:} The projected disc velocity map observed in the image plane (blue-red filled contour). We indicate redshift as red and blueshift as blue, relative to the systemic redshift. As a reference, we also plot the original LoS velocity distribution in dashed contour, as in panel a.
    \textbf{Panel d:} A \textit{Roman} Wide-Field Instrument (WFI)/$H$-band image. From left to right, we show the noise-free simulated data in the image plane (shear-on), the source plane (shear-off), and a 10-times-enhanced difference between the image and source plane.
    \textbf{Panel e:} A \textit{Roman} WFI/Grism image, with dispersion along $Y_\mathrm{O}$ direction. From left to right we show shear-on, shear-off and the 10-times-enhanced difference, similar to panel d.
    All these panels assume $(\kappa,\gamma)=(0.0, 0.1)$.}
    \label{fig:illustration_src2obs}
\end{figure*}

\section{Kinematic lensing}
\label{sec:KL}
In short, KL is based on the fact that gravitational lensing induced by the large scale structure of the Universe changes the trajectories of photons travelling through space, however their frequencies remain unchanged. The former implies that the shape of a galaxy, aka the photometric image, is distorted when it reaches the observer. The latter implies that the original position of photons can be tightly constrained by the velocity field of a disc galaxy, aka the spectroscopically measured frequency map.

To quantitatively study the distortion patterns of photometric and kinematic maps under cosmic shear, we firstly define the source plane $X_\mrm{S}$-$Y_\mrm{S}$ as the 2D comoving frame at the position of source galaxy, and the image or observed plane $X_\mrm{O}$-$Y_\mrm{O}$ as the 2D plane at the observer.
We assume throughout the main sections in this paper that $X_\mrm{O}$-$Y_\mrm{O}$ are aligned with the major-minor axes of the observed galaxy image.
The remapping of the 2D position of photons $\bm \theta$ due to cosmic shear from the source plane to the image plane can be described as $\bm{\theta}_{\mrm{S}}=\mat{A}\bm{\cdot}\bm{\theta}_\mrm{O}$, where the shear transformation matrix is defined as
\begin{equation}
\label{eqn:shear_mat_def_sect2}
    \mat{A} \equiv \frac{\partial\bm{\theta}_\mrm{S}}{\partial\bm{\theta}_\mrm{O}}= (1-\kappa)
    \begin{pmatrix}
    1-g_+ & - g_\times \\
    -g_\times & 1+g_+
    \end{pmatrix}
\end{equation}
and $g= \gamma / (1- \kappa)$ is the reduced shear that can be expressed as a complex number $\bm{g}=g_++ig_\times$ (please see Appendix \ref{sec:appd_a} for a derivation in general coordinates).

We further illustrate the KL concept in Fig.~\ref{fig:illustration_src2obs}:
\begin{itemize}
    \item Panel a: We show the shape and velocity distribution of the source galaxy without shear distortion.
    \item Panel b: When shear is applied, the distortion pattern on the photometry shape is manifested as a rotation of the image and a change of ellipticity.
    \item Panel c: The distortion pattern of the velocity field is described by a non-axisymmetric transformation.
    \item Panel d: We generate a simulated \textit{Roman} WFI/$H$-band image, with and without shear. The quadrupole structure in the difference map shows how photometry image responds to shear.
    \item Panel e: We generate a simulated \textit{Roman} WFI/Grism image with and without shear. The two distinct patterns in shape (panel b) and velocity distortions (panel c) are combined in the grism image, resulting in the S-shape difference map. The different shear responses in panel d and e give us information on the galaxy intrinsic orientation. This additional information compared to traditional WL, where the intrinsic orientation is treated as an unconstrained noise source, leads to the significant signal-to-noise increase of KL over WL.
\end{itemize}

In the following we detail the methodology of KL shear inference structured into 3 parts: the photometric measurement of the galaxy shapes (Sect.~\ref{sec:KL_morph}), the spectroscopic measurement of the galaxy kinematics (Sect.~\ref{sec:KL_kine}), and the integrated modelling of shapes and kinematics (Sect.~\ref{sec:KL_intg}).

\subsection{Photometric data - galaxy shape}
\label{sec:KL_morph}
To measure galaxy shapes, we use the conventional complex quadratic estimators
\footnote{We are choosing different ellipticity definition than \cite{Eric13} because equation~(\ref{eqn:quadratic_estimators_def}) has simpler transformation rule under shear and is an unbiased estimator of shape~\citep{SS97}}
\begin{equation}
\label{eqn:quadratic_estimators_def}
    \hat{\bm{\epsilon}} = \hat{\epsilon}_1 + i\hat{\epsilon}_2= \frac{I_{11}-I_{22}+2iI_{12}}{I_{11}+I_{22}+2\sqrt{I_{11}I_{22}-I_{12}^2}},
\end{equation}
where
\begin{equation}
\label{eqn:Iij_def}
    I_{ij}=\frac{\int I(\bm{\theta})\theta_i\theta_j\mathrm{d}^2\bm{\theta}}{\int I(\bm{\theta})\mathrm{d}^2\bm{\theta}} \,(i,j=1\,\mrm{or}\,2)
\end{equation}
is the 2nd moment of the photometric flux in the galaxy image, with 1 and 2 indicating $X$ and $Y$ components. The original shape before lensing, the so-called intrinsic ellipticity, is denoted as $\hat{\bm{\epsilon}}^\mrm{int}$ and can be expressed through equation~(\ref{eqn:quadratic_estimators_def}) using the intrinsic flux moments of the galaxy.
We can relate the observed ellipticity $e_\mrm{obs}\equiv|\hat{\bm{\epsilon}}|$ to the intrinsic ellipticity $e_\mrm{int}\equiv|\hat{\bm{\epsilon}}^\mrm{int}|$ as (see Appendix~\ref{sec:appd_a})

\begin{equation}
\label{eqn:eobs-eint}
\begin{aligned}
    e_\mrm{int}^2-e_\mrm{obs}^2+2(1-e_\mrm{int}^2)g_+e_\mrm{obs}+(e_\mrm{int}^2e_\mrm{obs}^2-1)g^2=0.
\end{aligned}
\end{equation}
Neglecting terms $\bigo{g^2}$, we derive
\begin{equation}
\label{eqn:shape_result}
    g_+=\frac{e_\mrm{obs}^2-e_\mrm{int}^2}{2e_\mrm{obs}(1-e_\mrm{int}^2)},
\end{equation}
which gives the $g_+$ component of the shear, if both $e_\mrm{int}$ and $e_\mrm{obs}$ are measured.

\begin{figure}
	\includegraphics[width=\linewidth]{figures/v3_figs/illustration_g+gx.png}
    \caption{An illustration of the shape and LoS velocity transformation patterns for the different cosmic shear components. We show the impact of $g_+$ on the left and the impact of $g_\times$ on the right. In both the left and the right panels, the observed sheared galaxy shapes are indicated as filled elliptical contours and the original shapes are indicated as unfilled dashed elliptical contours. The observed LoS velocity distributions are shown in solid blue-red contours while the original LoS velocity distributions are plotted as the dashed blue-red contours.
    }
    \label{fig:shear_illus_2}
\end{figure}

We further illustrate the transformation of the photometric components under shear in Fig.~\ref{fig:shear_illus_2}, where the unfilled black dashed contours correspond to the source plane and the black filled contours correspond to the image plane. As shown, $g_+$ changes the ellipticity, while $g_\times$ also rotates the PA. We will further explain in Sect.~\ref{sec:KL_intg}, how $e_\mrm{int}$ can be inferred from  kinematics measurements in combination with the TFR.

\subsection{Spectroscopic data - galaxy kinematics}
\label{sec:KL_kine}

We define the shear transformation of the LoS velocity distribution from source to image plane $v_\mrm{LoS}^\prime$ as
\begin{equation}
\label{eqn:formal_velocity}
    v_\mrm{LoS}^\prime(\bm{\theta}_\mrm{O})=v_\mrm{LoS}(\bm{\theta}_\mrm{S})=v_\mrm{LoS}(\mat{A}\bm{\cdot}\bm{\theta}_\mrm{O}),
\end{equation}
where $v_\mrm{LoS}(\bm{\theta}_\mrm{S})$ is the LoS velocity distribution in the source plane.

The expression for $v_\mrm{LoS}(\bm{\theta}_\mrm{S})$ in general coordinates is discussed in Appendix~\ref{sec:appd_a}. However, we can gain useful insight by considering the limiting case, where the intrinsic inclination angle $i$ is reasonably large such that the change in PA induced by cosmic shear is much smaller than
\footnote{For nearly face-on source galaxies, a weak shear distortion can change the PA of the photometric major axis significantly, and the expansion of the LoS velocity distribution in the image plane as a Taylor series in $g_{+/\times}$ breaks down.}.
The maximum $v_\mrm{LoS}^\prime$ along the $X_\mrm{O}$-$Y_\mrm{O}$ axis $v_\mrm{major/minor}^\prime$ in the image plane are given by (neglecting terms higher than or equal to $\bigo{g^2}$)
\begin{equation}
\label{eqn:vminor}
    \begin{aligned}
    v^\prime_\mrm{major}&=-v_\mrm{TF}\,\sin{i},\\
    v^\prime_\mrm{minor}&=
    v_\mrm{TF}\,\sin{i}\,\cos{i}\,(1+\frac{1+e_\mrm{obs}^2}{2e_{\mrm{int}}})g_\times\,,
    \end{aligned}
\end{equation}
where $v_\mrm{TF}$ is the asymptotic circular rotation velocity inferred from the TFR (see Sect.~\ref{sec:KL_intg}).
Thus $v_\mrm{major}^\prime$ is a good proxy of $\sin{i}$, and $v_\mrm{minor}^\prime$ is directly probing $g_{\times}$, which are also consistent with Fig.~\ref{fig:shear_illus_2} (the solid and dashed blue-red contours): The LoS velocity along $X_\mrm{O}$ axis is agnostic against $g_+$ and $g_\times$, but the velocity along $Y_\mrm{O}$ is sensitive to $g_\times$ due to its non-axisymmetric impact.

We note that \cite{Miller13} suggest that for typical disc galaxies, the rotational velocity converges to the asymptotic rotational velocity at 2.2 times the galaxy scale radius ($r_{2.2}$). Our method requires that we selected galaxies where velocity measurements beyond $r_{2.2}$ can be made with sufficient SNR.

Kinematic measurements based on slitless spectroscopy, such as the \textit{Roman Space Telescope}\ grism, are challenging. The Doppler shift information is entangled with the galaxy spectrum and the photometric profile as shown in panel e in Fig.~\ref{fig:illustration_src2obs}.
Encouragingly, ~\cite{OC20} have successfully measured galaxy kinematics at a precision of $\pm$40 km$\,$s$^{-1}$ using the \textit{HST} grism (the \textit{Roman Space Telescope}\ grism will have a factor of 3--4 higher resolution).

\subsection{Integrated Modelling}
\label{sec:KL_intg}

In order to break the degeneracy between intrinsic shape and cosmic shear, we first isolate $v_\mrm{TF}$ from $v_\mrm{major}^\prime$.
The TFR allows us to express ~\citep{R11}
\begin{equation}
\label{eqn:TFR}
    \mrm{log}_\mathrm{10}(v_{\mrm{TF}})=a + b\, (M_\mrm{B}-M_\mrm{p})\,,
\end{equation}
where $M_\mrm{B}$ is the absolute magnitude and $M_\mrm{p}$ is the pivot value, which is the weighted sample mean of $M_\mrm{B}$. $a$ and $b$ are the zero-point and the slope of the scaling relation.
The intrinsic scatter of the TFR calibrated in $i$-band is 0.049 dex and even smaller scatter can be achieved with more colour information~\citep{R11}.

Once $i$ is inferred per galaxy from the TFR and velocity measurement $v_\mrm{major}^\prime$, the intrinsic ellipticity $e_\mrm{int}$ is derived from a simple geometric relation
\begin{equation}
\label{eqn:eint_geo}
    e_{\mrm{int}}=\frac{1-\sqrt{1-(1-q_z^2)\sin{^2i}}}{1+\sqrt{1-(1-q_z^2)\sin{^2i}}}\,,
\end{equation}
where $q_z$ is the ratio of scale height to scale radius of the disc galaxy.
Typical $q_z$ is around 0.25, and is larger for galaxies at higher redshift, since disc galaxies are more turbulent at earlier time~\citep{Ubler:2017pik}.
When estimating shear for individual galaxies, $q_z$ is not known perfectly and should be treated as a nuisance parameter in the KL shear inference pipeline.

Combining equation~(\ref{eqn:shape_result}), (\ref{eqn:vminor}), (\ref{eqn:TFR}) and (\ref{eqn:eint_geo}), we derive
\begin{equation}
\label{eqn:reduced_shears}
    \begin{aligned}
    \hat{g}_+ &= \frac{e_\mrm{obs}^2-e_\mrm{int}^2}{2e_\mrm{obs}^2(1-e_\mrm{int}^2)},\\
    \hat{g}_\times&=|\frac{v_\mrm{minor}^\prime}{v_\mrm{major}^\prime}|\frac{2e_\mrm{int}}{\cos{i}\,(2e_\mrm{int}+1+e_\mrm{obs}^2)}\,,
    \end{aligned}
\end{equation}
which allows us to estimate both shear components given the measured ellipticity $e_\mrm{obs}$, the measured velocities $v_\mrm{minor}^\prime$ and $v_\mrm{major}^\prime$, the inclination angle $i$ as computed in equation~(\ref{eqn:vminor}) and (\ref{eqn:TFR}), and the inferred intrinsic ellipticity $e_\mrm{int}$ as computed in equation~(\ref{eqn:eint_geo}).

In practice, instead of directly using the estimators described in equation~(\ref{eqn:reduced_shears}), we recommend building a generative full-forward model to predict the sheared galaxy photometry and grism images at pixel level. Such a generative model has to account for realistic systematics, e.g. point-spread function (PSF), galaxy morphology and aspect ratio $q_z$, and uncertainties in the TFR.

\section{Galaxy sample characteristics}
\label{sec:simulation_settings}

Based on the reference survey design further described in \cite{WFIRST_MultiProbe} we compare two science cases:
\begin{itemize}
    \item \textbf{Traditional Weak Lensing (WL)}: cosmological information from shear-shear two-point statistics using the reference survey HLIS imaging dataset only.
    \item \textbf{Kinematic Lensing (KL)}: cosmological information from shear-shear two-point statistics using both photometric and spectroscopic data. This effectively limits our galaxy sample to that of the HLSS dataset and even adds some additional constraints.
\end{itemize}

\subsection{The WL galaxy sample}
\label{sec:sampleselection_WL}

The WL sample assumed here is the same as for the reference \textit{Roman Space Telescope}\ HLIS ~\citep{WFIRST_MultiProbe}. Based on the CANDELS~\citep{CANDELS} catalogue, realistic sources are selected following \cite{hemmati2019}. The reference HLIS is expected to have a $5\sigma$ depth of 26.54 in \textit{H}-band; given that the depth of the CANDELS (the GOODS-South Field, which is one of the two CANDELS Deep Program fields) reaches a $5\sigma$ point source limit of 27.6 mag in \textit{F160W}, we can assume that the catalogue is complete.
The specific selection criteria for our WL sample are
\begin{itemize}
    \item \textit{J}+\textit{H} band combined SNR $>18$
    \item ellipticity measurement error $\sigma(\bm{\epsilon})<0.2$\footnote{In this and only in this criterion, we take $\bm{\epsilon}=(I_{11}-I_{22}+2iI_{12})/(I_{11}+I_{22})$, as in~\cite{BJ02}. $\sigma(\bm{\epsilon})$ is defined as rms per $\bm{\epsilon}$ component, i.e. the observed shape uncertainty due to image noise, PSF and pixelization. Note that this is different from shape noise, which captures the uncertainty from random intrinsic inclination angle.}
    \item spatial resolution factor $R>0.4$\footnote{$R\equiv(1+\mrm{EE50}_\mrm{PSF}^2/r_\mrm{eff,gal}^2)^{-1}$, where $\mrm{EE50}$ is the 50 per cent encircled energy radius and $r_\mrm{eff,gal}$ the galaxy effective radius~\citep{ETC}.}
\end{itemize}
The resulting average number density is 51 arcmin$^{-2}$, and the redshift distributions including the split into 10 tomographic bins of equal number of galaxies are shown in Fig.~\ref{fig:zdist} (green lines).

\subsection{The KL galaxy sample}
\label{sec:sampleselection_KL}
We use the COSMOS Mock Catalogue~\citep[CMC, ][]{CMC} to infer the number density and redshift distribution of source galaxies that qualify for a KL measurement with the \textit{Roman Space Telescope}. Based on the observed COSMOS catalogue, the CMC fits a template for each galaxy using the observed spectral energy distribution and predicts its photometry and emission line strength ($\mrm{H}\,\alpha$, [O\,\textsc{iii}], etc.). The emission line fluxes are calculated from empirical relations between emission line fluxes and dust-corrected UV star formation rates and are further calibrated with a spectroscopy sample~\citep[see Sect.~2.2.3 in ][and reference therein for more details.]{CMC}\par

We select galaxies with high SNR to ensure robust rotation velocity measurements, and also require that our galaxies have sufficient angular size such that the rotation velocity converges to $v_{\rm{TF}}$ at 2.2 times the scale radii.
We impose the following criteria
\begin{itemize}
    \item At least one of the emission lines ($\rm{H}\,\mrm{\alpha}, \rm{H}\,\mrm{\beta}$, [O\,\textsc{iii}]) tracing the disc kinematic of galaxy is resolved within the grism's spectral range.
    \item Emission line flux reach $7\sigma$ point-source detection limit, which is $10^{-16}\ \rm{erg\,s^{-1}\,cm^{-2}}$
    \item Half-light radius $\geq$ $0.1\arcsec$. As a comparison, the \textit{Roman Space Telescope} PSF is around $0.1\arcsec$
    \item \textit{z}-band magnitude $\leq$24.5
\end{itemize}

The resulting source galaxy density is 8.13 arcmin$^{-2}$. We further require that the galaxy sample also satisfies the criteria in Sect.~\ref{sec:sampleselection_WL}, however the HLIS selection criteria don't lead to a further reduction of the KL sample.
We further multiply this number by a factor of 0.5, in order to account for observational inefficiencies, arriving at 4 arcmin$^{-2}$ as the number entering our likelihood analysis. The redshift distributions are depicted in Fig.~\ref{fig:zdist} (the red/blue lines for $N_{\mrm{tomo}}=10/30$ scenario).

We also compare this galaxy number density with other estimations in the literature.
The EL-COSMOS catalogue~\citep{sti20} is based on the updated COSMOS2015 catalogue~\citep{COSMOS2015} and more physically motivated emission line modelling.
Applying the same cuts on the emission line SNR\footnote{The EL-COSMOS catalogue does not have half-light radius attribute, so we neglect the criterion of hlr $\geq 0.1\arcsec$. However the resulting bias is negligible since almost all the galaxies satisfy this criterion.}, we obtain $n_{\mathrm{gal}}\approx 12\,\mathrm{arcmin}^{-2}$, before accounting any observational inefficiency.
\cite{zbw19}, on the other hand, uses semi-analytic modelling to predict the H$\,\alpha$ emitter density for $Euclid$ and $Roman$.
For a combined $z$=0.5--3.0 [O\,\textsc{III}] and H$\,\mathrm{\alpha}$ sample with high-redshift dust extinction model, the galaxy surface number density is around 4.14 arcmin$^{-2}$ without any observational inefficiency considered.

This number is somewhat different compared to the estimation from the EL-COSMOS catalogue, especially given both of them are calibrated with the $\mathrm{H}\,\alpha$\ luminosity functions from HiZELS~\citep{Sobral13}.
However, we note that the $\mathrm{H}\,\alpha$\ luminosity functions predictions in \cite{sti20} and \cite{zbw19} do not agree perfectly with each other, and $\mathrm{H}\,\alpha$\ emitters at $z\approx 1$, where our $\mathrm{d} N/\mathrm{d} \Omega\mathrm{d} z$ peaks, are not included in the HiZELS luminosity functions.
Thus we think the difference in galaxy number density is a reasonable manifestation of the significant differences in these two methods.
Our number (8 arcmin$^{-2}$ without accounting for observational inefficiencies) falls somewhere between these two results.
We note that the same trend is also found in \cite{FC20}, where the authors show that the number density of both the $\mathrm{H}\,\alpha$\ and the [O\,\textsc{III}]\ samples in \cite{zbw19} are somewhat lower than the predictions from HiZELS~\citep{ksm15}.

Another estimate is obtained from table~2-2 in \cite{WFIRST_AFTA}, which predicts a sample of 17.8 million emission line galaxies ($\mathrm{H}\,\alpha$\ and [O\,\textsc{III}]) in a 2,200 deg$^2$ survey, or 2.25 arcmin$^{-2}$. This number however includes observational inefficiencies, and is based on the old HLSS design, where only emission line galaxies within $1.06\leq z\leq 2.77$ are observable.
Since in our reference HLSS sample, $\mathrm{H}\,\alpha$+[O\,\textsc{III}]\ emitters within $1.06\leq z\leq 2.77$ take up 61.91 per cent of the total sample, an approximate scaling of the prediction in ~\cite{WFIRST_AFTA} gives 3.63 arcmin$^{-2}$, which is very similar to the number assumed in this paper.

We conclude that our assumed number density of galaxies is in line with other estimates in the literature even though these are based on different techniques such as semi-analytic modelling and analytic models based on an assumed luminosity function.
We also consider the reduction of the number density estimate by a factor of 2 to account for observational inefficiencies as conservative.

\begin{figure}
	\includegraphics[width=\columnwidth]{figures/v3_figs/zdistribution_tomo_new_ngal.pdf}
    \caption{The redshift distribution of source galaxies per tomographic bin in traditional weak lensing method (the green solid lines, according to the baseline \textit{Roman Space Telescope} HLIS), kinematic lensing method with 10 tomography bins (the red solid lines, according to baseline \textit{Roman Space Telescope} HLSS), and kinematic lensing method with 30 tomography bins (the blue solid lines, offset by 10 arcmin$^{-2}$ for better visualisation).}
    \label{fig:zdist}
\end{figure}

\subsection{Shape Noise}
\label{sec:shape_noise}

For our WL sample we assume a shape noise level of 0.26 per component and $\sigma_{\bm{\epsilon}}^\mrm{WL}=0.37$ in quadrature, which is standard across the community~\citep[see e.g.,][]{Chang13}.
The shape noise of our KL sample is $\sigma_{\bm{\epsilon}}^\mrm{KL}=0.035$ in quadrature, which we explain further below.

From the source selection criteria in Sect.~\ref{sec:sampleselection_KL} we know that the faintest sources in the KL sample have $r$-band magnitudes around 26, and 95.7 per cent of the sample has $M_r<25$.
The LSST Year 10 $5\sigma$ $r$-band limit is 27.5, which means most of our KL sample have $r$-band SNR higher than 50.
Also, according to the CMC catalogue, 97.1 (69.3) per cent of the sample have hlr larger than 1 (2) times the typical PSF hlr of \textit{Roman Space Telescope}, and 39.3 per cent of the sources have hlr larger than the LSST $r$-band PSF.

Given the high S/N we expect the dominant contribution to KL shape noise to come from velocity measurement error and the intrinsic scatter of TFR. To estimate this effective shape noise per galaxy, we build an error model for the KL observables and numerically calculate the maximum likelihood estimate (MLE).

The exact details of the procedure can be found in Appendix.~\ref{sec:shape_noise_estimation_details}. In short, we create random samples of KL model parameters $\bm{X}_\mathrm{model}$=($e_\mrm{int}$, $\phi$, $\bm{g}$, $v_\mrm{TF}$) where $\phi$ is the intrinsic PA of the galaxy image in source plane. For each realization, we calculate the data vector of observables $\bm{Y}$=($\hat{\bm{\epsilon}}$, $v_\mrm{major}^\prime$, $v_\mrm{minor}^\prime$, $M_\mrm{B}$) according to equation~(\ref{eqn:estimators_image_to_source}), (\ref{eqn:galaxy_frame_source_plane_velocity}) and (\ref{eqn:TFR}).
Realistic measurement errors are then added to those observables. These errors determine the covariance matrix for the multivariate Gaussian log-likelihood function $\mrm{ln}(p(\bm{Y}|\bm{X}_\mathrm{model}))$.
We then call optimization routines to get MLE solution of $\bm{g}_{i}$ for each realization.
The shape noise is finally computed as the $\sigma^{-2}(g_{+/\times})$ weighted standard deviation among the random sample.

\begin{figure}
    \centering
    \includegraphics[width=\linewidth]{figures/v3_figs/shape_noise_velocity_error_v2.png}
    \caption{Here we show the effective shape noise $\sigma_{\bm{\epsilon}}$ as a function of velocity measurement errors $\sigma_v$. Blue for the $g_+$ component and orange for the $g_\times$ component. The shape noise is calculated as weighted standard deviation of the random sample, while the error bars on shape noise are estimated via a bootstrap method.

    The $g_\times$ data points are slightly offset for better visualization. }
    \label{fig:shape_noise_velocity_error}
\end{figure}

We show the shape noise as a function of velocity measurement uncertainty $\sigma_v$ in Fig.~\ref{fig:shape_noise_velocity_error}, with the blue and orange points for $g_+$ and $g_\times$.
As we can see, for $\sigma_v>10$ km$\,$s$^{-1}$, the shape noise is linearly increasing with $\sigma_v$.
For $\sigma_v<10$ km$\,$s$^{-1}$, the shape noise is gradually being saturated by the intrinsic scatter of TFR.

We note that a similar galaxy kinematic measurement on grism data has already been carried out recently by~\cite{OC20}, although without accounting for cosmic shear distortions.
The authors built a forward modelling pipeline and applied it to the \textit{Hubble Space Telescope} based datasets, 3D-HST and GLASS.
\cite{OC20} table~2 shows the kinematic measurements of 4 galaxies.
The rotation velocity uncertainties are 30--40 km$\,$s$^{-1}$ for single roll exposures and $15$ km$\,$s$^{-1}$ if more roll angles are available.
The higher spectral resolution of \textit{Roman Space Telescope}\ grism, its grism observing strategy, and the bright nature of our KL sample, should enable typical KL velocity measurement errors to be 15 km$\,$s$^{-1}$ or better.
Using Fig.~\ref{fig:shape_noise_velocity_error}, this translates to a shape noise of $\sim 0.025$ per component, or 0.035 in quadrature.

Similar kinematic lensing measurements have also been conducted by \cite{GTF20,GTF21,DiGiorgio21}.
Those works are different from ours in both theoretical methodology and the instrument used for observations: they use the lens galaxies position rather than the TFR to provide extra information on $g_+$, and use ground-based integral field units (IFU) rather than space-based grism.
Thus their sample is focused on low-$z$ bright and well-resolved disc galaxies in galaxy-galaxy lensing systems, where the tangential shear contributed by the lens galaxies dominate over the cosmic shear effect.
The resulting sample contains 18 galaxies with an averaged tangential shear of $\langle\gamma_\mrm{t}\rangle=0.020\pm 0.008$.
The effective shape noise per galaxy originated from velocity measurement uncertainty ($\sigma_\gamma$ in their table~3) is 0.013.

Despite the very different nature between their sample and ours, the two samples have comparable photometric SNR and spatial resolution factor ($R\approx 0.8$).
The difference in shape noise could come from velocity resolving power $\mathcal{R}_\mrm{kin}=\frac{c}{(1+z)\mathcal{R}}$, the velocity dispersion per pixel.
For the sample in~\cite{GTF20}, $\mathcal{R}_\mrm{kin}\approx 90$, while for \textit{Roman Space Telescope}\ grism $170<\mathcal{R}_\mrm{kin}<330$.
Assuming that shape noise scales as $\mathcal{R}_\mrm{kin}$, then we expect the shape noise of our KL sample is 2--4 times larger, which is 0.025--0.051 and is consistent with our $\sigma_{\bm{\epsilon}}^\mrm{KL}$.

\cite{DiGiorgio21} also studied shape noise as a function of inclination angle, image PA uncertainty and velocity error.
For $\sigma_v$=10--20 km$\,$s$^{-1}$, $\sigma_\mrm{PA}$=1--6 deg and $i<45$ deg, the shape noise ranges from 0.015 to 0.08, which is of the same order as our result.

A comprehensive kinematic lensing shape noise study, highly relevant to our work, is presented in~\cite{WS19}, which considers TFR as an ingredient to break intrinsic shape-shear degeneracy.
The authors utilized Fisher matrix analysis to map out shape noise as a function of various variables, including inclination angle, TFR scatter, orthogonal-slits measurement v.s. IFU velocity map, velocity measurement uncertainty, etc.
Assuming that the shape noise measured at $i=\pi/4$ is a good representation of the ensemble average, we expect to see a shape noise of 0.036--0.054 for orthogonal-slit measurement with $\sigma_v\approx 20$ km$\,$s$^{-1}$ and a fiducial $g\approx 0.05$.

A detailed study of KL shape noise is presented in \cite{SKH+22}, where the authors build a slit-spectrum-based KL shear inference pipeline and study shape noise as a function of SNR, intrinsic ellipticity, spectral resolution, and TFR uncertainty using Keck/DEIMOS-like simulated data. Keck/DEIMOS has higher spectral resolution but worse PSF control compared to \textit{Roman} grism. \cite{SKH+22} find the average shape noise of a galaxy sample to be $0.02$--$0.06$.

Given the differences between the KL implementation of this paper compared to the aforementioned, which range from instrumentation to sample selection to methodology, we note that these comparisons serve as sanity checks rather than direct comparisons.
A more realistic shape noise calculation requires a more sophisticated pipeline and has to deal with complexities like non-axisymmetric disc structure, magnification-shear degeneration and other systematics, which are beyond the scope of this work.
We conclude that $\sigma_{\bm{\epsilon}}^\mrm{KL}=0.035$ is a good assumption in order to explore the science outcome of a KL survey conducted with \textit{Roman Space Telescope}, and to explore multi-probe and cross-survey synergies using KL.

\begin{table*}
	\centering
	\begin{tabular}{l|cccc}
	\toprule
	Cosmology Parameters & \multicolumn{2}{c}{Fiducial} & \multicolumn{2}{c}{Prior}\\
	\midrule
	$\Omega_\mrm{m}$&\multicolumn{2}{c}{0.3156}&\multicolumn{2}{c}{flat[0.095, 0.585]}\\
	$\sigma_8$&\multicolumn{2}{c}{0.831}&\multicolumn{2}{c}{flat[0.5, 1.1]}\\
	$n_s$&\multicolumn{2}{c}{0.9645}&\multicolumn{2}{c}{flat[0.84, 1.06]}\\
	$\Omega_\mrm{b}$&\multicolumn{2}{c}{0.0491685}&\multicolumn{2}{c}{flat[0.005, 0.095]}\\
	$h_0$&\multicolumn{2}{c}{0.6727}&\multicolumn{2}{c}{flat[0.4, 0.9]}\\
	$w_0$($\Lambda$CDM)&\multicolumn{2}{c}{-1}&\multicolumn{2}{c}{flat[-2.1, 0]}\\
	$w_a$($\Lambda$CDM)&\multicolumn{2}{c}{0}&\multicolumn{2}{c}{flat[-2.6, 2.6]}\\
	$w_0$($w$CDM 1)&\multicolumn{2}{c}{-0.289}&\multicolumn{2}{c}{flat[-1.389, 0.711]}\\
	$w_a$($w$CDM 1)&\multicolumn{2}{c}{-2.21}&\multicolumn{2}{c}{flat[-4.18, 0.39]}\\
	$w_0$($w$CDM 2)&\multicolumn{2}{c}{-1.249}&\multicolumn{2}{c}{flat[-2.349, -0.249]}\\
	$w_a$($w$CDM 2)&\multicolumn{2}{c}{0.59}&\multicolumn{2}{c}{flat[-2.01, 3.19]}\\
	\toprule
	\thead{Survey\\Parameters}&\multicolumn{2}{c}{WL}&\multicolumn{2}{c}{KL}\\
	\midrule
	$\Omega_{\mrm{s}}$ [deg$^2$]&\multicolumn{2}{c}{2,000}&\multicolumn{2}{c}{2,000}\\
	$n_{\mrm{src}}$ [arcmin$^{-2}$]&\multicolumn{2}{c}{51}&\multicolumn{2}{c}{4}\\
	$\sigma_{\bm{\epsilon}}$&\multicolumn{2}{c}{0.37}&\multicolumn{2}{c}{0.035\,($N_{\mrm{tomo}}=10$)/0.056\,($N_{\mrm{tomo}}=30$)}\\
	\toprule
	\thead{Systematic\\Parameters} & \multicolumn{2}{c}{WL} & \multicolumn{2}{c}{KL}\\
	\hline
	{} & Fiducial & Prior & Fiducial & Prior \\
	\midrule
	$\Delta_{\mrm{z,\,src}}^{i}$&0.0&$\Ndist{0}{2}{-3}$&0.0&$\Ndist{0}{4}{-4}$\\
	$\sigma_{\mrm{z,\,src}}^{i}$&0.01&$\Ndist{0.01}{2}{-3}$&0.002&$\Ndist{0.002}{4}{-4}$\\
	$m^{i}$&0.0&$\Ndist{0}{2}{-3}$&0.0&$\Ndist{0}{4}{-4}$\\
	\hline
	$A_{\mrm{IA}}$&5.92&$\mathcal{N}$(5.92,\,3.0)&-&-\\
	$\beta_{\mrm{IA}}$&1.1&$\mathcal{N}$(1.1,\,1.2)&-&-\\
	$\eta_{\mrm{IA}}$&-0.47&$\mathcal{N}$(-0.47,\,3.8)&-&-\\
	$\eta_{\mrm{IA}}^{\mrm{high}\textit{-}z}$&0.0&$\mathcal{N}$(0.0,\,2.0)&-&-\\
	$Q_1$&0.0&$\mathcal{N}$(0.0,\,16.0)&0.0&$\mathcal{N}$(0.0,\,16.0)\\
	$Q_2$&0.0&$\mathcal{N}$(0.0,\,2.0)&0.0&$\mathcal{N}$(0.0,\,2.0)\\
	$Q_3$&0.0&$\mathcal{N}$(0.0,\,0.8)&0.0&$\mathcal{N}$(0.0,\,0.8)\\
	\bottomrule
	\end{tabular}
	\caption{The parameter settings for different scenarios in \textsc{CosmoLike}\  simulations. We express a flat prior as flat[min,max] where min and max are the boundary of the uniform distribution. We express a Gaussian prior as $\mathcal{N}(\mu,\sigma)$ where $\mathcal{N}$ means normal distribution, $\mu$ is the mean and $\sigma$ is the standard deviation. We fill the IA parameters ($A_{\mrm{IA}}$, $\beta_{\mrm{IA}}$, $\eta_{\mrm{IA}}$, $\eta_{\mrm{IA}}^{\mrm{high}\textit{-}z}$) in KL scenario with `-' to indicate that the IA mitigation method doesn't apply to the KL sample. Note that we had to increase the shape noise for the 30 tomography bins scenario due to numerical stability problems of the covariance matrix.
	We also adopt a conservative redshift uncertainty for the KL sample in this work.
	}
	\label{tab:params_table}
\end{table*}

\section{Simulated Likelihood Analysis}
\label{sec:CosmoLike}

Our KL \textsc{CosmoLike}\ ~\citep{Krause_Tim17} implementation for the simulated analyses follows the widely used Bayesian approach to infer the posterior of cosmological parameters $\bm{p}_{\mrm{co}}$ and nuisance parameters $\bm{p}_{\mrm{nu}}$ from the observables, which are treated as data vector $\bm{D}$, and prior information $p(\bm{p}_{\mrm{co}},\,\bm{p}_{\mrm{nu}}|I)$\footnote{Here we use $I$ to discriminate different external datasets as priors, although we only adopt flat priors on cosmological parameters in this work.}.
We use \textsc{emcee}~\citep{emcee,goodman2010} to sample the posterior
\begin{equation}
\label{eqn:post}
\begin{split}
    p(\bm{p}_{\mrm{co}},\,\bm{p}_{\mrm{nu}}|\bm{D},\,I)&\propto L(\bm{D}|\bm{p}_{\mrm{co}},\,\bm{p}_{\mrm{nu}} ) \times p(\bm{p}_{\mrm{co}},\,\bm{p}_{\mrm{nu}}|I)\\
    &\propto\mrm{exp}\left(-\frac{1}{2} \chi^2 (\bm{p}_\mrm{co},\,\bm{p}_\mrm{nu})\right)\times
    p(\bm{p}_\mrm{co},\,\bm{p}_\mrm{nu}|I).
\end{split}
\end{equation}
We assume that the likelihood $L(\bm{D}|\bm{p}_{\mrm{co}},\,\bm{p}_{\mrm{nu}} )$ in equation~(\ref{eqn:post}) is well-approximated by a multivariate Gaussian \citep{likelihood}.

We define
\begin{equation}
\begin{aligned}
    \chi^2(&\bm{p}_{\mrm{co}},\,\bm{p}_{\mrm{nu}})=\\&(\bm{D}-\bm{M}(\bm{p}_{\mrm{co}},\,\bm{p}_{\mrm{nu}}))^{\rm{T}}\bm{\cdot}\mat{C}^{-1}\bm{\cdot}(\bm{D}-\bm{M}(\bm{p}_{\mrm{co}},\,\bm{p}_{\mrm{nu}})),
\end{aligned}
\end{equation}
where $\bm{M}$ is the model vector evaluated at $(\bm{p}_{\mrm{co}},\,\bm{p}_{\mrm{nu}})$ and $\mat{C}$ the covariance matrix calculated at the fiducial parameter values. We further assume that the covariance matrix $\mat{C}$ of the multivariate Gaussian is constant within the range of parameters considered and do not adopt an iterative inference approach or a full cosmology dependent covariance ~\citep{ESH_09} approach in this work.

\subsection{Data Vector}
We only consider the shear-shear two point statistics as our observable.
In practice, results based on $\bm{\xi}^{ij}_\pm(\theta)$ and $\bm{C}_{\kappa\kappa}^{ij}(\ell)$ do not necessarily agree with each other perfectly~\citep[e.g. see~][]{HSC_Y1_2PCF} due to the weighing of the different scales, however we assume that this difference is negligible for the forecasting purpose of this paper.
Due to the convenience of Fourier space modelling, we choose the angular shear-shear power spectrum as our observable, which in the Limber approximation reads:
\begin{equation}
    \bm{C}_{\kappa\kappa}^{ij}(\ell)=\int \mathrm{d}\chi \frac{q_\kappa^{i}(\chi)q_\kappa^{j}(\chi)}{\chi^2}P_{\delta\delta}(\ell/f_{K}(\chi),\,z(\chi)),
\end{equation}
where
\begin{equation}
    q_\kappa^{i}(\chi)=\frac{3H_0^2\Omega_\mrm{m}}{2c^2}\frac{\chi}{a(\chi)}\int_\chi^{\chi_h}\mathrm{d} \chi'\frac{n_\mrm{src}^{i}(z(\chi'))}{\bar{n}_\mrm{src}^{i}}\frac{\mathrm{d} z}{\mathrm{d} \chi'}\frac{f_K(\chi'-\chi)}{f_K(\chi')}
\end{equation}
is the lens efficiency for the $i$-th bin, and $n_\mrm{src}^{i}(z)$ represents the redshift distribution of source galaxies in the $i$-th bin (c.f. Fig.~\ref{fig:zdist}), with $\bar{n}_\mrm{src}^{i}$ the 2D angular galaxy density within the same redshift bin.
Here, $\chi$ is the comoving distance, $f_K(\chi)$ is the comoving angular diameter distance, $\mathbf{\ell}$ the wave vector and $P_{\delta\delta}(\ell/f_K(\chi),z(\chi))$ is the 3D matter power spectrum.

\subsection{Covariance Matrix}
Consider the covariance matrix between $\bm{C}_{\kappa\kappa}^{ij}(\ell_1)$ and $\bm{C}_{\kappa\kappa}^{kl}(\ell_2)$
\begin{equation}
\begin{aligned}
    \mat{C}&\equiv \langle \Delta \bm{C}_{\kappa\kappa}^{ij}(\ell_1) \Delta \bm{C}_{\kappa\kappa}^{kl}(\ell_2)\rangle\\
    &=\langle (\bm{C}_{\kappa\kappa}^{ij}(\ell) - \langle{\bm{C}}_{\kappa\kappa}^{ij}(\ell)\rangle)(\bm{C}_{\kappa\kappa}^{kl}(\ell_2) - \langle{\bm{C}}_{\kappa\kappa}^{kl}(\ell_2)\rangle)\rangle,
\end{aligned}
\end{equation}
where $\langle{\bm{C}}_{\kappa\kappa}^{ij}(\ell)\rangle$ is the mean angular power spectrum among an ensemble of random realizations.
The covariance matrix \mat{C} is modelled as the sum of a Gaussian part $\mat{C}_{\rm{G}}$ and a Non-Gaussian part $\mat{C}_{\rm{NG}}$. The Gaussian part is~\citep{HB04}
\begin{equation}
\label{eqn:C_G}
\begin{aligned}
    \mat{C}_{\mrm{G}} (\bm{C}_{\kappa\kappa}^{ij}(\ell_1) ,\,\bm{C}_{\kappa\kappa}^{kl}(\ell_2))=&
    \frac{4\pi\delta_{\ell_1\ell_2}}{\Omega_\mathrm{s}(2\ell_1+1)\Delta\ell_1}[\bar{\bm{C}}_{\kappa\kappa}^{ik}(\ell_1) \bar{\bm{C}}_{\kappa\kappa}^{jl}(\ell_1)\\
    &+\bar{\bm{C}}_{\kappa\kappa}^{il}(\ell_1)\bar{\bm{C}}_{\kappa\kappa}^{jk}(\ell_1)],
\end{aligned}
\end{equation}
where
$
    \bar{\bm{C}}_{\kappa\kappa}^{ij}(\ell_1)\equiv
    \bm{C}_{\kappa\kappa}^{ij}(\ell_1)+\delta_{ij}\frac{\sigma^2_{\bm{\epsilon}}}{\bar{n}^{i}_\mrm{src}},
$ $\delta_{ij}$ is the Kronecker delta function, $\sigma_{\bm{\epsilon}}$ is the shape noise of the two shear components, $\bar{n}_{\mathrm{src}}^i$ is the mean source galaxy number density in the tomography bin $i$, $\Delta\ell_1$ is the $\ell_1$ bin width, $\Omega_\mathrm{s}$ is the survey area.
$\mat{C}_{\rm{NG}}$ is further decomposed into $\mat{C}_{\mrm{NG,\,0}}$
\begin{equation}
\label{eqn:C_NG0}
\begin{aligned}
    \mat{C}_{\mrm{NG,\,0}}&(\bm{C}_{\kappa\kappa}^{ij}(\ell_1), \bm{C}_{\kappa\kappa}^{kl}(\ell_2))=\frac{1}{\Omega_s}\int_{|\mathbf{l}|\in\ell_1}\frac{\mathrm{d}^2 \mathbf{l}}{A(\ell_1)}\int_{|\mathbf{l}^\prime|\in\ell_2}\frac{\mathrm{d}^2\mathbf{l}^\prime}{A(\ell_2)}\\
    &\times\int \mathrm{d}\chi\frac{q_\kappa^{i}(\chi)q_\kappa^{j}(\chi)q_\kappa^{k}(\chi)q_\kappa^{l}(\chi)}{\chi^6}\\
    &\times T_\kappa^{ijkl}(\mathbf{l}/\chi,\, -\mathbf{l}/\chi,\, \mathbf{l}^\prime/\chi,\, -\mathbf{l}^\prime/\chi;\,z(\chi)),
\end{aligned}
\end{equation}
where $\int_{|\mathbf{l}|\in\ell_1}$ means the integration range is an annulus in Fourier space of radius $\ell_1$ and width $\Delta\ell_1$, $A(\ell_1)\equiv \int_{|\mathbf{l}|\in\ell_1} \mathrm{d}^2\mathbf{l}$ is the integration area in Fourier space, and $T_\kappa^{ijkl}$ is the trispectrum of cosmic shear~\citep{tj09}. Note that $\mat{C}_\mathrm{G}$ is free from the survey window effects. The super-sample covariance $\mat{C}_{\mrm{SSC}}$~\citep{TH13}
\begin{equation}
\label{eqn:C_SSC}
\begin{aligned}
    \mat{C}_{\mrm{SSC}}&(\bm{C}_{\kappa\kappa}^{ij}(\ell_1), \bm{C}_{\kappa\kappa}^{kl}(\ell_2))=\int \mathrm{d}\chi\frac{q_\kappa^{i}(\chi)q_\kappa^{j}(\chi)q_\kappa^{k}(\chi)q_\kappa^{l}(\chi)}{\chi^4}\\
    &\times \frac{\partial P_{\kappa}(\ell_1/\chi,\,z(\chi))}{\partial \delta_b}\frac{\partial P_{\kappa}(\ell_2/\chi,\,z(\chi))}{\partial \delta_b}\sigma_b(\Omega_\mathrm{s};\,z(\chi)),
\end{aligned}
\end{equation}
which captures the uncertainties originating from the large-scale density modes outside the survey window. Here $\sigma_b(\Omega_\mathrm{s};\,z(\chi))$ is the variance of the background mode over the survey window, and $\frac{\partial P_{\kappa}(\ell_1/\chi,\,z(\chi))}{\partial \delta_b}$ captures the response of the 3D convergence power spectrum to the background density mode $\delta_b$. For more details, see the appendix in~\cite{Krause_Tim17} and reference therein.

\begin{figure*}
	\includegraphics[width=\columnwidth]{figures/v3_figs/paper_figure_5a_v2.png}
	\includegraphics[width=\columnwidth]{figures/v3_figs/paper_figure_5b_v2.png}
    \caption{Posterior probability distribution of $w_p$-$w_a$(left) and $\Omega_\mrm{m}$-$S_8$(right). The black dashed lines are inferred from traditional weak lensing method. They are marginalized over PZ, M, IA and BA (see Sect. ~\ref{sec:sys} for the definitions of the abbreviations). The blue solid lines are kinematic lensing result marginalized over PZ, M, BA, but not IA. The orange dotted lines are inferred from kinematic lensing method, and assume fiducial nuisance parameters $\bm{p}_\mrm{nu}$, i.e. only sampling $\bm{p}_\mrm{co}$ without systematics modelling. The inner and outer contours show the $68$ per cent and $95$ per cent confidence level. Fiducial cosmological parameters are denoted as horizontal and vertical black dashed lines. In the 1D marginal probability distribution panels, the shaded area indicates the $68$ per cent confidence interval, with the 1$\sigma$ error bar annotated as figure legend, in the same colour scheme.}
    \label{fig:LCDM-WL-KL}
\end{figure*}

\subsection{Systematics Modelling}
\label{sec:sys}
We consider four types of systematic uncertainties in our modelling: redshift uncertainty, multiplicative shear calibration bias, intrinsic alignment and baryonic feedback. The related parameter settings are summarized in Table~\ref{tab:params_table}.
\begin{itemize}
    \item \textbf{Redshift Uncertainty (PZ)}: We assume that redshift errors follow Gaussian distributions for both the WL and the KL scenarios. A galaxy in sample $x$ and in the $i$-th redshift bin with redshift $z_{\mrm{true}}$ has a probability of $p^{i}(z_{\mrm{obs}}|\,z_{\mrm{true}},\,x)$ to be mis-identified to $z_{\mrm{obs}}$:
    \begin{equation}
    \begin{aligned}
        p^{i}(z_{\mrm{obs}}|\,z_{\mrm{true}},\,x)=&\frac{1}{\sqrt{2\pi}\sigma_{z,\,x}^{i}(1+z)}\times\\
        &\mrm{exp}\left[-\frac{(z_{\mrm{true}}-z_{\mrm{obs}}-\Delta_{z,\,x}^{i})^2}{2(\sigma_{z,\,x}^{i}(1+z))^2}\right],
    \end{aligned}
    \end{equation}
    $\Delta_{z,\,x}^{i}$ and $\sigma_{z,\,x}^{i}$ are the bias and the standard deviation of the observed redshift of galaxy sample $x$ in the $i$-th tomographic bin. Thus the photo-$z$ (or spec-$z$ for the KL sample) distribution for the $i$-th tomography bin is
    \begin{equation}
        n_x^{i}(z_\mrm{ph})=\int_{z_{\mrm{min},\,x}^{i}}^{z_{\mrm{max},\,x}^{i}} n_x(z)p^{i}(z_{\mrm{ph}}|\,z,\,x) \mathrm{d} z.
    \end{equation}

    For the WL scenario, we assume the optimistic dataset from LSST Y10 result and \textit{Roman Space Telescope} HLIS full reference survey result, resulting to $\Delta_{z,\,\mrm{WL}}^{i}=0$ and $\sigma_{z,\,\mrm{WL}}^{i}=0.01$~\citep{WFIRST-LSST}. We also add our knowledge of photo-$z$ uncertainty in the likelihood simulation as a Gaussian prior,
    \begin{equation}
        \mrm{ln}(L_{\mrm{prior}}^{\mrm{photo}\textit{-}z})=-\frac{1}{2}\left[(\frac{\Delta_{z,\,x}^{i}-\bar{\Delta}_{z,\,x}^{i}}{\sigma(\Delta_{z,\,x}^{i})})^2+(\frac{\sigma_{z,\,x}^{i}-\bar{\sigma}_{z,\,x}^{i}}{\sigma(\sigma_{z,\,x}^{i})})^2\right],
    \end{equation}
    with $\Delta_{z,\,\mrm{WL}}^{i}\sim \mathcal{N}(0,\,0.001)$ and $\sigma_{z,\,\mrm{WL}}^{i}\sim\mathcal{N}(0.01,\,0.002)$.

    We motivate the redshift error of KL sample by the grism resolution

    $\mathcal{R}^{-1}\approx0.002$.
    We set $(\Delta_{z,\,\mrm{KL}}^{i},\,\sigma_{z,\,\mrm{KL}}^{i})=(0,\,0.002)$ and Gaussian priors $(\mathcal{N}(0,\,4\mrm{e}{-4}),\,\mathcal{N}(0.002,\,4\mrm{e}{-4}))$ for them correspondingly.

    We note that while our WL redshift uncertainty is rather optimistic, our KL choice is very conservative, since with high SNR detection, the grism redshift uncertainty can be orders of magnitude smaller.

    \item \textbf{Multiplicative Shear Calibration Bias (M)}: Uncertainties in galaxy shape measurement come from a variety of sources: image noise, non-perfect galaxy flux profile model, non-linear effects in detector, atmospheric PSF, galaxy blending, etc. Those errors are summarized by the shear calibration bias parameters. We model the multiplicative shear calibration bias with $m^{i}$ (for the $i$-th redshift bin), which modifies the shear-shear angular power spectrum as
    \begin{equation}
        \bm{C}_{\kappa\kappa}^{ij}(\ell) \longrightarrow (1+m^{i})(1+m^{j})\bm{C}_{\kappa\kappa}^{ij}(\ell).
    \end{equation}

    We take the fiducial value $m^{i}=0$ and a Gaussian prior of $\mathcal{N}(0,\,0.002)$ for the WL sample, which is the same as \cite{WFIRST_MultiProbe,WFIRST-LSST}. Since the KL sample is much more brighter and has higher SNR than the WL sample, we set $m^{i}=0$ in the data vector and the prior of $m^{i}$ to be $\mathcal{N}(0,\,4\mathrm{e}{-4})$ for the KL sample.
    We note that existing work on multiplicative shear calibration bias found that $m$ is a function of SNR and galaxy size, and galaxies of $\mathrm{SNR}\,\approx100$ have about 2 times smaller $m$ uncertainty than those of $\mathrm{SNR}\,\approx 10$~\citep{FHH+17,ZSS+18,MLL+18}. Our KL sample approximately follows a log-normal distribution in $r$-band SNR $\mathrm{log}_{10}(\mathrm{SNR})\approx\mathcal{N}(2.62, 0.29)$, while the above papers are focused on galaxies with $\mathrm{SNR}\,\in [10,200]$. This is significantly fainter than most objects in our galaxy sample, which motivates our choice of the KL sample to have 5 times lower $m$ uncertainty in this pilot forecast.

    \item \textbf{Intrinsic Alignment (IA)}:

    The strength of intrinsic alignment of galaxies depends on the type of galaxy considered. A simple theoretical description is that elliptical galaxies are aligned by the tidal field caused by the host dark matter halo profile, while spiral galaxies are aligned by the tidal torquing generated by the host halo angular momentum, which is much weaker than the tidal alignment~\citep{Catelan01}.

    We model intrinsic alignment by including two extra shape correlation terms: The first term affects source galaxies at the same redshift bin $\bm{C}_{\mrm{II}}^{ii}(\ell)$, which models the shape correlation of background galaxies caused by their local tidal field, and the second affects galaxies in different redshift bins $\bm{C}_{\mrm{GI}}^{ij}(\ell)$, where the foreground large-scale structure correlates the orientation a foreground galaxy though tidal alignment or tidal torquing with a background galaxy's shear distortion.
    \begin{equation}
        \bm{C}_{\kappa\kappa}^{ij}(\ell)\longrightarrow \bm{C}_{\kappa\kappa}^{ij}(\ell)+\bm{C}_{\mrm{II}}^{ij}(\ell)+\bm{C}_{\mrm{GI}}^{ij}(\ell).
    \end{equation}

    We adopt the Non-Linear Alignment description of IA ~\citep[NLA, see][]{his04,brk07,Krause16_IA} for red elliptical galaxies, and ignore the contribution from spiral galaxies~\citep[see][and reference therein for more details]{WFIRST-LSST}. We model uncertainties in the NLA model through four different parameters, which are $A_{\mrm{IA}}$ describing the amplitude of IA, $\beta_{\mrm{IA}}$ constraining the luminosity dependence, and $\eta_{\mrm{IA}},\,\eta_{\mrm{IA}}^{\mrm{high}\textit{-}z}$ depicting redshift dependence. The fiducial values and priors are shown in Table~\ref{tab:params_table}.

    However, as we have seen in equation~(\ref{eqn:reduced_shears}), the KL method is unaffected (to leading order) by the traditional IA contamination that plagues WL, since we can in principle isolate the intrinsic shape from the measured shape. Also, the KL sample is dominated by emission line galaxies which mostly have spiral morphology, thus the IA amplitude is expected to be order-of-magnitude smaller than that for the WL sample, which contains lots of elliptical galaxies. As a result, IA uncertainties are negligible for KL and we do not include IA in the KL scenarios.

    \item \textbf{Baryonic Feedback (BA)}: As we approach small scales in cosmic shear, baryonic feedback effects during the formation and evolution of galaxies start to impact our observable through the reduced clustering of matter.
    The resulting modification in the matter power spectrum is a mixture of two leading effects: the feedback distributes baryons to the outskirt of the halo thus suppresses the formation of structure, and the cooling of baryons causes more gravitational collapse towards the halo centre.
    We adopt the principal component analysis technique~\citep[PCA,][]{hem19,ekd15} to mitigate the baryon feedback. The basic idea is to project the impact of baryon feedback on the matter power spectrum on to several principal components (PCs), utilizing a range of simulations that span a variety of baryon physics recipes.
    We assume the real baryon feedback in the universe could be approximated by a linear combination of those PCs, and fit the amplitude $Q_{i}$ of $\mrm{PC}_{i}$. For a more detailed modelling description, see~\cite{WFIRST-LSST}.

    The simulations we select for the principal component space are Horizon-AGN~\citep{dpp16}, Illustris/IllustrisTNG~\citep{wsp18,psn18}, Eagle simulation~\citep{scb15}, Massiveblack-II~\citep{kdc15} and the OWLS AGN simulation~\citep{sdb10,dsb11}.
    We include the first three PCs in the modelling and set the fiducial value of $Q_{i}$ to 0, given that we use a dark-matter-only $\bm{C}_{\kappa\kappa}^{ij}(\ell)$ as our fiducial input data vector. The priors for our baryon mitigation scheme are listed in Table~\ref{tab:params_table}.
\end{itemize}

\section{Simulated kinematic lensing analyses}
\label{sec:results}

In this section, we compare the constraining power of a variety of lensing scenarios, under different cosmology models.
Our metrics of comparison are 2D posterior contours and the standard Figure-of-Merit (FoM, $\sqrt{\mrm{det}[\mat{C}_{p_1 p_2}^{-1}]}$ where $\mat{C}_{p_1 p_2}$ is the covariance matrix between parameter $p_1$ and $p_2$) of $\Omega_\mrm{m}$-$\sigma_8$ and/or $w_0$-$w_a$.
To decorrelate parameters, we replace $\sigma_8$ with $S_8\equiv\sigma_8(\Omega_\mrm{m}/0.315)^{0.35}$ and $w_0$ with $w_p\equiv w_0+(1-1/(1+z_\mrm{p}))w_a$, where the pivot redshift $z_\mathrm{p}=0.4$ is chosen such that the uncertainty on $w(z_\mathrm{p})$ is minimal.

\subsection{Comparing Weak Lensing and Kinematic Lensing}
\label{sec:WL-KL}

We compare the constraining power of weak lensing and kinematic lensing method ($N_{\mrm{tomo}}=10$) using three different likelihood setups:
\begin{itemize}
    \item The WL scenario samples $\bm{p}_{\mrm{co}}$ and $\bm{p}_{\mrm{nu}}$, including PZ, M, IA and BA, sampling 35 parameters in total.
    \item The KL scenario samples $\bm{p}_{\mrm{co}}$ and $\bm{p}_{\mrm{nu}}$ including PZ, M and BA, sampling 31 parameters in total.
    \item The KL scenario samples $\bm{p}_{\mrm{co}}$ only, assuming fiducial $\bm{p}_{\mrm{nu}}$, which means it samples only 7 parameters only. The idea of this chain is to study the impact of nuisance parameters in the KL context.
\end{itemize}

We show the posteriors of $\Omega_\mrm{m}$-$S_8$ and $w_p$-$w_a$ inferred from those chains in Fig.~\ref{fig:LCDM-WL-KL}. Compared with traditional weak lensing (the black dashed contours), the kinematic lensing (the blue solid contours, with systematics mitigation) shows noticeable improvement in constraining power on $\Omega_\mrm{m}$-$S_8$ and significant enhancement on $w_p$-$w_a$.
The improvements quantified by the FoM are shown in Table~\ref{tab:FoM}, and $\mrm{FoM}_{w_p\textit{-}w_a}$ has increased by 2.65 times by adopting KL method.
Despite the decrease of effective galaxy number density, the excellent shape noise control benefits the dark energy science significantly.

Another important conclusion is that the constraining power of KL is not systematics-limited given the current configuration of \textit{Roman Space Telescope}\ HLS. From Table~\ref{tab:FoM}, marginalization over spec-$z$ uncertainty and shear calibration bias degrades the FoM by 19.7 per cent, while adding baryon feedback into marginalization brings another 15.7 per cent degradation (also see Fig.~\ref{fig:KL-sys-degrade}). We do not consider other systematics like galaxy blending in kinematic lensing but given the carefully selected high S/N sample, KL is likely more robust against imperfect systematics modelling compared to WL.

\begin{table}
    \centering
    \begin{tabular}{l|c|ccc}
    \toprule
     FoM & WL & \multicolumn{3}{c}{KL($N_{\mrm{tomo}}=10$)} \\
     \hline
     \makecell{Systematics\\Mitigation}  & \makecell{PZ+M+\\IA+BA} & \makecell{PZ+M+\\BA} & PZ+M & no sys\\
     \midrule
    $\mrm{FoM}_{w_p\textit{-}w_a}$ & 10.55 & 38.51 & 47.85 & 59.58\\
    $\mrm{FoM}_{\Omega_\mrm{m}\textit{-}S_8}$ & 5307 & 9017 & 11533 & 13543\\
    \bottomrule
    \end{tabular}
    \caption{The FoMs of $w_p$-$w_a$ and $\Omega_\mrm{m}$-$S_8$, comparing between the WL method and KL method ($N_{\mrm{tomo}}=10$). We calculate the FoM by picking the top 68 per cent points with the highest likelihood in each of the chains, then estimate the covariance matrix from these sub-samples. The columns from left to right show the FoM of i) WL method marginalized over full systematics, including PZ, M, IA and BA (see Sect.~\ref{sec:sys} for the abbreviations and the modelling details) ii) KL method marginalized over PZ, M and BA iii) KL method marginalized over PZ and M, and iv) KL method sampling $\bm{p}_\mrm{co}$ only (no sys).}
    \label{tab:FoM}
\end{table}

\begin{figure}
	\includegraphics[width=\columnwidth]{figures/v3_figs/paper_figure_6_v2.png}
    \caption{Comparison of the $w_p$-$w_a$ KL constraining power degradation from systematics. The systematics modelling includes: i) PZ, M and BA (the blue solid contour) ii) PZ and M (the yellow solid contour) and iii) no systematic modelling, assuming perfect knowledge of systematics (the orange dotted contour). All of the three chains assume KL with $N_{\mrm{tomo}}=10$ and $\sigma_{\bm{\epsilon}}=0.035$.}
    \label{fig:KL-sys-degrade}
\end{figure}

\begin{figure*}
	\includegraphics[width=\columnwidth]{figures/v3_figs/paper_figure_7a_v2.png}
	\includegraphics[width=\columnwidth]{figures/v3_figs/paper_figure_7b_v2.png}
    \caption{Comparing the constraining power on $w_p$-$w_a$ of kinematic lensing survey with different redshift binning strategies and cosmologies.
    In the left panel we assume the fiducial cosmology to be $\Lambda$CDM, while in the right panel, we study the posterior distribution on differential dark energy EoS $\Delta w_p$-$\Delta w_a$ under two $w$CDM fiducial cosmologies, $w$CDM 1: $(w_p,w_a)=(-0.92,-2.21)$ or $(w_0,w_a)=(-0.289, -2.21)$ (the dotted contours, of which the 68 per cent C.L. are annotated without bracket in the 1D posteriors) and $w$CDM 2: $(w_p,w_a)=(-1.08,0.59)$ or $(w_0,w_a)=(-1.249, 0.59)$ (the dashed contours, of which the 68 per cent C.L. are annotated with brackets in the 1D posteriors).
    The green and violet colours correspond to $N_{\mrm{tomo}}=10$ and $N_{\mrm{tomo}}=30$ scenarios. All the chains sample $\bm{p}_\mrm{co}$ only, and assume $\sigma_{\bm{\epsilon}}=0.056$.}
    \label{fig:KL-10-30}
\end{figure*}

\subsection{Kinematic Lensing 10 Tomography Bins v.s. 30 Tomography Bins}
\label{sec:KL10-30}

\begin{table}
    \centering
    \begin{tabular}{l|cc}
    \toprule
      $N_{\mrm{tomo}}$ & 10 & 30\\

     \midrule
    $\mrm{FoM}_{w_p\textit{-} w_a}$ & 27.65 & 31.14\\% 59.58 & 27.65 & 31.14
    \bottomrule
    \end{tabular}
    \caption{The FoM of $w_p$-$w_a$, comparing between different tomography strategies of KL method. The columns from left to right show the FoM of $N_{\mrm{tomo}}=10$ and $N_{\mrm{tomo}}=30$. Both of them sample cosmological parameters only, and assume $\sigma_{\bm{\epsilon}}=0.056$.}
    \label{tab:FoM_10-30}
\end{table}

We compare the performance of 10 and 30 tomography bins KL methods assuming $\Lambda$CDM as the fiducial cosmology.
We run two chains with one assuming 10 tomography bins and the other one assuming 30.
As we mentioned in Sect.~\ref{sec:shape_noise}, we increase the shape noise of the $N_{\mrm{tomo}}=30$ chain to 0.056 to make the covariance matrix positive-definite. We adopt the same setting for the $N_{\mrm{tomo}}=10$ chain for a fair comparison between the two tomography schemes.
Both chains are sampling $\bm{p}_\mrm{co}$ only. For each chain, 560 walkers are deployed and each walker makes 5,000 steps.
We drop the first 0.5M steps as burn-in for each of those.
The posterior distributions on $w_p$-$w_a$ are shown in the left panel of Fig.~\ref{fig:KL-10-30}, and the FoM of $w_p$-$w_a$ are shown in Table~\ref{tab:FoM_10-30}.

The $N_{\mrm{tomo}}=30$ scenario is marginally better than the $N_{\mrm{tomo}}=10$ one (12.6 per cent increase).
There could be two possible reasons for the in-sensitiveness.
The first one is that the observables $C_{\kappa\kappa}^{ij}(\ell)$ are featureless and smooth functions of redshift and scale, hence 10 tomography bins are sufficient to capture most of the information encoded in shear-shear angular power spectrum.
Another possible reason is that in the fiducial $\Lambda$CDM cosmology, dark energy is constant over all the redshift bins, and there is no room for more flexible tomography evolution given the allowed range of $w_p$-$w_a$. We conclude that 10 tomography bins are sufficient to capture the cosmological information in the case considered, but the same must not be true when stronger dark energy evolution across tomography bins is allowed.

In order to discriminate between the two scenarios we explore fiducial data vectors computed from a cosmology with time-evolving dark energy , i.e. $w_a\neq0$. According to the \textit{Planck} 2018 result~\citep[fig.~30 in ][]{Planck2018}, we choose two sets of fiducial parameters: $(w_0,\,w_a)=(-0.289,\,-2.21)$ ($w$CDM 1) and $(w_0,\,w_a)=(-1.249,\,0.59)$ ($w$CDM 2), which correspond to two opposite corners at the edge of $2\sigma$ contour inferred from TT,TE,EE+lowE+lensing+BAO/RSD+WL.
For each set of parameters, we run two chains as we do in the $\Lambda$CDM cases. We show the results in the right panel in Fig.~\ref{fig:KL-10-30}, with the dotted contours assuming fiducial $(w_0,\,w_a)=(-0.289,\,-2.21)$ and the dashed contours assuming fiducial $(w_0,\,w_a)=(-1.249,\,0.59)$. From the posteriors we only see tiny differences between the 10 bins cases and the 30 bins cases (note that these assume the same shape noise level). Thus for scenarios with evolving dark energy within the 1$\sigma$ region allowed by the \textit{Planck} CMB experiment, we can not gain further constraining power by increasing the number of tomographic bins. The observables $\bm{C}_{\kappa\kappa}^{ij}(\ell)$ are smooth in nature and 10 tomography bins are enough to capture most of the information. We note however that more complex dark energy scenarios might benefit from this narrow tomography idea that is feasible with KL.

\section{Conclusions}
\label{sec:conclusions}

In this work we study the performance of a kinematic lensing survey conducted with the \textit{Roman Space Telescope}.
In its reference design the High Latitude Survey covers 2,000 square degrees in the 5-year prime mission with imaging and spectroscopy.
The HLIS will map objects in $Y$, $J$, $H$ and $F184$ bands to a depth of $\mathrm{M}_{\mrm{AB,}J}=26.7$, and the HLSS is targeting emission line galaxies at redshift 0.524--2.855, with 7$\sigma$ flux limit of $1.0\times 10^{-16}\,(1.8\times 10^{-16})\,\mrm{erg}\,\mrm{cm}^{-2}\,\mrm{s}^{-1}$ for point source (extended source), with grism resolution $\mathcal{R}=461(\frac{\lambda}{1\,\mrm{\mu m}})$.
Based on the CANDELS and CMC catalogue we have defined realistic galaxy samples and we get a source galaxy number density of $51\ \mrm{gal\,arcmin}^{-2}$ for weak lensing and $4\ \mrm{gal\,arcmin}^{-2}$ for kinematic lensing (assuming 50 per cent grism success rate). We note that the KL sample number density estimation is also supported by literature using multiple independent methods, like EL-COSMO mock catalogue, SAM-based mock catalogue and luminosity functions.
To estimate the effective shape noise of the KL sample, we design a toy-model for the KL shear estimation process with the \textit{Roman Space Telescope}\ and solve for the MLE shear estimator drawing from the said model. The resulting shape noise ($\sigma_{\bm{\epsilon}}^\mrm{KL}=0.035$) shows a significant improvement over the one in traditional weak lensing ($\sigma_{\bm{\epsilon}}^\mrm{WL}=0.37$).

We demonstrate KL's constraining power by simulating shear-shear only likelihood analyses and comparing to the traditional WL case. For WL, we model a full suite of systematic uncertainties such as photo-$z$ uncertainty, multiplicative shear calibration bias, intrinsic alignment and baryonic feedback. For KL, IA mitigation is unnecessary since the contamination from IA can be calibrated and removed during the isolation the intrinsic shape information in the KL measurement process.

Other prominent WL systematics also experience substantial improvement in the KL case, e.g. redshift uncertainties are insignificant given that we have spectroscopic information, and multiplicative shear calibration bias uncertainties are greatly diminished given the high S/N imaging sample.

Comparing to the standard WL strategy, we find significant improvement in constraining power on $w_p$-$w_a$ (FoM$_{\mrm{KL}}$=3.65 FoM$_{\mrm{WL}}$) and noticeable enhancement on $\Omega_\mrm{m}$-$S_8$ (FoM$_{\mrm{KL}}$=1.70 FoM$_{\mrm{WL}}$).
We also quantify how the FoM$_{\mrm{KL}}$ degrades with different systematics. Compared with the fiducial KL case where no systematics are included, baryonic feedback causes a 15.68 per cent degradation. Redshift uncertainty and shear calibration bias in total contribute another 19.69 per cent degradation in the $w_p$-$w_a$ FoM. Hence, with the current instrument capability of \textit{Roman Space Telescope}, the shear calibration bias and redshift uncertainty are comparable with the baryon feedback.

We also explore how increasing the number of tomographic redshift bins, which is an interesting concept given the reduced shape noise, affects the constraining power on $w_p$-$w_a$. Specifically, we increase the number of tomographic bins from our default of 10 to 30, which significantly increases the size of the covariance matrix. As fiducial input scenarios we consider three dark energy EoS scenarios ($w_0$,$\,w_a$)=(0.0,$\,$0.0)/(-0.289,$\,$-2.21)/(-1.249,$\,$0.59), that are consistent (but at the limits) of the \textit{Planck} 2018 TT,TE,EE+lowE+lensing+BAO/RSD+WL result. We find that no matter whether $w_{\mrm{DE}}$ is evolving or not, increasing the number of tomographic bins does not bring extra information about the EoS of dark energy.
This can be explained by the smoothness nature of $\bm{C}_{\kappa\kappa}^{ij}(\ell)$ with regard to scale and redshift when assuming the standard $w_p$-$w_a$ dark energy parameterization. We note however that more complex dark energy or modified gravity scenarios will likely benefit from the more fine binning in redshift space enabled by KL.

Generally speaking the decrease in shape noise using the KL method changes the intuition of how to optimize cosmological information as a function of survey and systematics mitigation strategy. As shown, intrinsic alignment, photo-$z$ and shear calibration systematics are less worrisome for KL surveys. In contrast, accessing and modelling small scale information, which are already important for WL, will likely become more impactful in the KL case. Also, compared to WL, increasing the survey area will be more important for KL given that the dominant statistical uncertainty for KL is cosmic variance. In particular for \textit{Roman Space Telescope}, where the current reference survey envisions 2,000 deg$^2$, it will be important to explore a wide area KL survey \citep[similar to][]{WFIRST-LSST}, which would also benefit from overlap with ground-based spectroscopic resources.

In summary, we consider KL with the \textit{Roman Space Telescope}\ to be an extremely promising science avenue. It has different challenges than WL (rotation velocity modelling, Tully Fisher Relation uncertainties), but these are likely outweighed by the increase in statistical power and systematics robustness. In this context it is important to note that KL and WL data vectors can be combined in a likelihood analysis; the question is not to replace one with the other but to optimize the joint analysis. Similarly, the combination of KL with other probes such as galaxy clustering, peculiar velocities, CMB lensing, and SZ measurements are exciting opportunities. Lastly, we would like to point out that exploring KL in the context of galaxy cluster mass measurements is an important concept to explore in general and for \textit{Roman Space Telescope}~in particular.

\section*{Acknowledgements}
This work is supported by NASA ROSES ATP 17-ATP17-0173 and NASA 15-WFIRST15-0008 grants. Simulations in this paper use High Performance Computing (HPC) resources supported by the University of Arizona TRIF, UITS, and RDI and maintained by the UA Research Technologies department.

\section*{Data Availability}
The data underlying this article will be shared on reasonable request to the corresponding author.

\bibliographystyle{mnras}

redpajama_set_name: RedPajamaArXiv


Speedpages are a valuable asset to any site. With faster loading, visitors will stay longer and return to your site more often.
As this dzine has described, speed pages can be acomplished in several relatively easy ways.
Break tables whenever possible. Avoid enclosing your site in a single invisible table.
Always add height and width atributes to images.
Reuse logos and navigation elements.
Keep secondary information at the ends of your pages.
Keep style attributes out of HTML.
CSS shortens your pages since you don't have to specify the entire style each and every time its used.
Save CSS definitions to external files.
HTML code pieces are enclosed in single quotes.
Write each codepiece as a function in the external.js file, then link to external.js in the head of your HTML pages.
Remember to use " \ " before apostrophes.
incredible flexibility to change items that are used throughout the site in one place!
Keep these things in mind when making your site, your visitors and your pocketbook will appreciate it.


Video Watch Isibaya 14 February 2018 Full Episode Video. Mzansi Magic Drama Isibaya 14 Feb 2018 Full Episode in HD. Watch Isibaya 14th February 2018 on DStv. Isibaya 14 February 2018 Full Episode Online.
I am very angry because i cant reach isibaya today on internet.Why?Im out of the country i cant get it on my tv.what am i suppose to watch now?
Don't need to be angry we will update the today's telecast soon when the video release….


text:
Das Wasserschloss Untersiemau steht in einem Park am südlichen Rand der oberfränkischen Gemeinde Untersiemau im Landkreis Coburg. Die ältesten Teile des auch als Unteres Schloss bezeichneten Bauwerks stammen aus dem 13. Jahrhundert. Das Schloss wurde im Laufe der folgenden Jahrhunderte mehrfach aus- und umgebaut.

Geografische Lage
Acht Kilometer südlich von Coburg, unweit oberhalb der Einmündung des Siemauer Mühlbachs in die Itz, liegt zwischen Mühlgasse und Leopoldstraße der vom Mühlbach durchflossene, sechs Hektar große Park des Untersiemauer Schlosses auf etwa 300 Meter Höhe. Östlich schließt sich der Schlossteich und danach der Lichtenfelser Forst an.

Geschichte

Sicher ist, dass Untersiemau auf die karolingische Domäne Suomene zurückgeht, die sich im 12. Jahrhundert (wahrscheinlich schon früher) im Eigenbesitz (Allod) der Ritter von Suemen befand, die auf ihrem alten Sitz im Oberen Schloss wohnten. In einer Urkunde aus dem Jahr 1195 wird als Besitzer der Ritter Thiemo de Suemen genannt.

Anfang des 13. Jahrhunderts begann Thiemo mit dem Bau eines Wasserschlosses etwa 300 Meter südlich unterhalb des Oberen Schlosses. Die nächste urkundliche Erwähnung 1499 ist ein aus Geldnot geschlossener Erbpachtvertrag zwischen den Schenken Valentin und Lorenz zu Siemau und den Grafen von Henneberg. 1635 fiel der letzte Siemauer Ritter Georg Friedrich in der Schlacht von Überlingen, sodass der Lehensverwalter Herzog Ernst I. von Coburg die Besitzungen einziehen konnte. Nur zwei Jahre später erwarb Hans Adam von Könitz (1591–1648) Schloss und Park. Die Familie ließ zunächst die durch den Dreißigjährigen Krieg in Mitleidenschaft gezogenen Anlagen renovieren und erweitern und 150 Jahre später die gesamte Innenausstattung im Stil der Zeit erneuern.

1866 starb mit Friedrich Adolf Hermann von Könitz der letzte Herr auf Untersiemau. Das Schloss verfiel zusehends, bis schließlich der Verleger Hermann Louis von Schroedel-Siemau 1911 das Anwesen erwarb und bis 1920 eine Rekonstruktion von Bodo Ebhardt, dem Restaurator der Veste Coburg, durchführen ließ.
Das Schloss befand sich bis 1997 im Besitz der Familie von Schroedel-Siemau. Die neuen Eigentümer ließen zwischen 1999 und 2003 das Gebäude grundlegend sanieren. Da die Sanierung bisher nicht fertiggestellt wurde, ist das Schloss seit 1997 unbewohnt.

Beschreibung

Das ehemalige Wasserschloss mit seinem nahezu quadratischen Grundriss von etwa 70 auf 60 Metern Seitenlänge ist auf 190 cm starken Außengrund- und Erdgeschossmauern errichtet und besteht aus insgesamt fünf Stockwerken. An den nördlichen Gebäudeecken erheben sich zwei runde Türme, die mit ihren Kegeldächern das Walmdach des Hauptgebäudes leicht überragen und so dem Anwesen einen wehrhaften Charakter verleihen.

In der Mitte der südlichen Längsseite des Schlosses befindet sich der über zwei geschwungene Treppen erreichbare Haupteingang, der durch einen sechseckigen Treppenhausturm in alle Stockwerke führt. Diesen Turm krönt ein ebenfalls sechseckiges Kuppeldach mit einem Aussichtsaufsatz (Glocke). Die Ostfassade mit seinen fünf Fensterachsen ist im Erdgeschoss durch einen dreiachsigen Vorbau erweitert.

Die ursprünglich mittelalterliche Schlossanlage erhielt 1911 durch die Umbauten Bodo Ebhards im Stile des Historismus ein völlig verändertes Erscheinungsbild. So wurde der Eingang verlegt und im Erdgeschoss ein falsches Gewölbe aus Holz eingebaut. Verschiedene Türme, romantische Wehrgänge und neu gebaute Ruinenteile sollten den Eindruck eines sehr alten Märchenschlosses erwecken. Im ersten Obergeschoss entstand 1920 ein ovaler Spiegelsaal mit acht ionischen Säulen und ausgemalter Flachkuppel. Der Saal ist mit dem 1791 für Königin Friederike Luise im Berliner Stadtschloss von Carl Gotthard Langhans erschaffenen Pfeilersaal in seiner Anlage und Ausstattung weitgehend identisch. Ob Langhans tatsächlich den Entwurf für den Untersiemauer Spiegelsaal fertigte, ist nicht nachzuweisen. Der Spiegelsaal blieb bei den von 1999 bis 2003 erfolgten Sanierungen erhalten.

Literatur
 Fritz Mahnke: Schlösser und Burgen im Umkreis der Fränkischen Krone. Band. 1. 3. Auflage. Druck- und Verlagsanstalt Neue Presse GmbH, Coburg 1974.

Weblinks

 Ulrich Göpfert: Schloss Untersiemau
 Sanierungsprojekt Schloss Untersiemau 1999-2003

Einzelnachweise

Untersiemau
Untersiemau Wasserschloss
Baudenkmal in Untersiemau
Bauwerk in Untersiemau
Untersiemau

redpajama_set_name: RedPajamaWikipedia


text:
Current School GoalsCurrently selected
Home > School Profile > Current School Goals
Strong Catholic Identity:
By the end of 2021, we will begin the process to revisit and redevelop the School Vision and Mission Statement to reflect our charism and Catholic Identity.
Learning and Teaching:
By the end of 2022,differentiated teachings and learning through individual student reading goals will be evident.
By the end of 2022, improvement in pedagogical practice in the teaching of Mathematics will be evident.
Our People:
By the end of 2022, student learning will improve through implementing individual teacher performance and development processes.
Organisation Efficiency
By the end of 2022, a plan will evolve for increasing enrolments and community awareness of the benefits of children attending Holy Spirit.
By the end of 2022, the first state of our Reconciliation Action Plan will be developed to promote a commitment to create and maintain a culture that is welcoming and safe for Aboriginal and Torres Strait Islander peoples.


Cyclist, mother of 2, DJ, Bauhaus fan and front-end designer. Acting at the intersection of design and programing to answer design problems with honest solutions. Let's make every day ARAZZLE-DAZZLE MUSICAL.
Hydroponics - How About Starting Your Own Hydroponic Garden?
Let's Begin by answering the question what's hydroponics? Well, hydroponics is a innovative method of nurturing crops with the use of a solution full of nourishment; using this new method of cultivating the use of soil or dirt is excluded.
What's Hydroponic Gardening Different from Regular Gardening?
When Growing hydroponics, you will find a huge variety of growing mediums which might be used. Even air might be applied as a hydroponic growing medium.


text:
using Telerik.UI.Xaml.Controls.Primitives.DragDrop;
using Windows.Foundation;
using Windows.UI.Xaml;
using Windows.UI.Xaml.Input;

namespace Telerik.UI.Xaml.Controls.Input.Calendar
{
    internal class CalendarDragInitializer : DragInitializer
    {
        private const double DefaultCalendarStartTreshold = 30.0;
        private Point lastPressedPoint;
        private InputService owner;

        public CalendarDragInitializer(InputService owner, UIElement element)
            : base(element, DefaultCalendarStartTreshold)
        {
            this.owner = owner;
        }

        protected override void StartDrag(object sender, PointerRoutedEventArgs e)
        {
            this.owner.OnDragStarted(this.lastPressedPoint, e);
        }

        [System.Diagnostics.CodeAnalysis.SuppressMessage("Microsoft.Design", "CA1062:Validate arguments of public methods", MessageId = "0")]
        protected override void OnPressed(PointerRoutedEventArgs e)
        {
            var hitPoint = e.GetCurrentPoint(this.owner.Owner.contentLayer.VisualElement).Position;

            if (hitPoint != null)
            {
                this.lastPressedPoint = hitPoint;
            }
        }
    }
}

redpajama_set_name: RedPajamaGithub


LIVERPOOL boss Jurgen Klopp has finally found a formula to make the Reds defensively sound.
That's according to Arsenal legend Ian Wright who reckons the German has created a new solidity to their backline.
After 18 games last season Liverpool had conceded 25 goals.
Then in January Klopp spent £75m to bring Virgil van Dijk to Anfield from Southampton.
And after 18 games this campaign, the Merseysiders have let in just 10.
"Over the years talk of clean sheets has been something of a dirty word — or two — around Anfield," Wright wrote in The Sun.
"While scoring goals has never been a problem for Liverpool, even before Jurgen Klopp arrived, keeping them out at the other end most certainly has.
"Always likely to put two, three or four past opponents but too often having to because of silly mistakes at the back.
Liverpool face Paris St-Germain tonight in an important Champions League clash and Wright reckons the game is the Reds' defence toughest test of the season so far.
"Never mind talk of an awesome foursome or terrible trio, as the Reds' attacking combinations have been called at various times," he continued.
"This year has been more about the fab five. More to the point, the fab defensive five — and that's not something you have said about Liverpool too often.
"Tonight that backline faces arguably its toughest test. They go to the Parc des Princes to take on Paris Saint-Germain, who know they cannot afford to slip up again or the Champions League dream could be over at the group stage.
"For all Neymar, Kylian Mbappe and Edinson Cavani were disappointing in their defeat on Merseyside in September, they are a different prospect on their own patch.
"But there is a difference to Liverpool this season. There's a solidity to them, a quiet efficiency in how they're getting results, like we saw at Watford on Saturday.
"They have just got that confidence in the players at the back.