text:
Home ANS Reports	Lahore High Court has asked Pakistan's Federal Investigation Agency not to stop two Christians from going abroad
Lahore High Court has asked Pakistan's Federal Investigation Agency not to stop two Christians from going abroad
by Dan Wooding June 19, 2015
written by Dan Wooding June 19, 2015
By Dan Wooding, Founder of ASSIST Ministries and the ASSIST News Service
LAHORE, PAKISTAN (ANS — June 19, 2015) – The Lahore High Court (LHC) in Pakistan, has ordered the country's Federal Investigation Agency (FIA) not to create hindrances for two Christian siblings who wanted to visit Sri Lanka.
Rana Tanveer, writing The Express Tribune, said that FIA submitted a letter before the court saying that according to Sri Lankan Immigration authorities, more than 1,400 Pakistani asylum seekers, mainly Ahmedis, Christians and Shias, have registered with the United Nations High Commission for Refugees (UNHCR) in Sri Lanka.
An FIA deputy director said that on June 24, 2014, Pakistan's high commission in Colombo had written a letter to FIA headquarters stating that the Sri Lankan government had initiated action against Pakistani asylum seekers on June 9, 2014.
The letter said that 143 male asylum seekers had been detained for questioning at Boossa and Mirihana detention facilities in Sri Lanka.
Authorities there said in the letter that they had been acting against the asylum seekers involved in "criminal activities".
The United Nations High Commissioner for Refugees (UNHCR) has warned that any action leading to deportation will be a violation of international humanitarian laws. "The matter is between the UNHCR and the Sri Lankan government… but immigration authorities might consider putting in place some measures to check the movement of asylum seekers to Sri Lanka," the letter said.
In her story, Rana Tanveer went on to say, "The court ordered the FIA to remain within the four corners of law and stop harassing the Christian siblings."
Petitioners Irfan Masih and his sister Maria Batool, residents of Kasur, had accused the FIA of offloading them twice from Sri Lanka-bound flights. They said they had been invited to visit Sri Lanka by a family friend, KA Nalika Damayanthi, a Sri Lankan national."
Their counsel, Advocate Mushtaq Gill, said the petitioners had obtained visas and sponsor letters after due process. He said they had purchased tickets of Mihin Lanka (PVT) Ltd, a Sri Lankan airline, for departure on May 12 from Lahore to Colombo. However, at Allama Iqbal International Airport, FIA officials had stopped them and asked them if they had certain documents on them. He said that they showed them the documents but the officials did not allow them to board the plane.
A few days later, he said, they had bought new tickets and tried to board a flight to Colombo on June 1 from Allama Iqbal International Airport. They received their boarding cards but were once again stopped from boarding the flight.
Advocate Mushtaq Gill had previously said that citizens whose passports mentioned Christian as the religion were often asked to provide assurance that they were not travelling abroad to seek asylum. Gill said when he was travelling to Italy in December 2014, he had been approached by FIA officials at the airport who claimed that he was intending to seek asylum in Italy. "I was finally allowed to travel after I asked some officers to intervene," he said.
Gill added that, as citizens of Pakistan, Christians were entitled to fundamental rights guaranteed by the Constitution. He said his clients' right to freedom of movement had been violated because of their faith. He said his clients had no intention to seek asylum.
"The fact that so many Christians are seeking asylum abroad, speaks volumes of the persecution they face in this country. Christians here face discrimination; mob violence; misuse of blasphemy laws; inequality before law; threats and harassment; and unequal job opportunities."
He said that if that was not the case, then his clients, being equal citizens of Pakistan, had every right to visit any country in the world. He asked the court to direct the Lahore FIA director not to stop them from flying abroad.
Photo captions: 1) Arrivals lounge at Allama Iqbal International Airport, Lahore. 2) Advocate Gill. 3) Dan Wooding doing a TV report.
About the writer: Dan Wooding, 74, is an award-winning journalist who was born in Nigeria of British missionary parents, and is now living in Southern California with his wife Norma, to whom he has been married for nearly 52 years. They have two sons, Andrew and Peter, and six grandchildren who all live in the UK. He is the author of some 45 books, the latest of which is "Mary: My Story from Bethlehem to Calvary," which you can read at: http://marythebook.com/.
Note: If you would like to help support the ASSIST News Service, please go to www.assistnews.net and click on the DONATE button to make you tax-deductible gift (in the US), which will help us continue to bring you these important stories. You can also make out a check to ASSIST and mail it to PO Box 609, Lake Forest, CA 92609, USA.
** You may republish this and any of our ANS stories with attribution to the ASSIST News Service (www.assistnews.net)
Dan Wooding
Dan Wooding, 79, is an award-winning journalist who was born in Nigeria of British missionary parents, Alfred and Anne Wooding from Liverpool, and is now living back in the UK with his wife Norma, to whom he has been married for 57 years. They had lived in the US for 36 years and returned home to be close to their two sons, Andrew and Peter, and six grandchildren. Dan continues to write and conduct radio interviews for ANS. Dan is one of the few Christian journalists to ever be allowed to report from inside of North Korea. His life story has been turned into a screenplay by screenwriter, Claire Hutchinson. For more information contact Dan at danjuma1@aol.com.
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Moviegoers saw a real-life scare with a happy ending this Fourth of July weekend, when the Dix Hills Fire Department Rescue Squad saved a man in cardiac arrest in the theater.
But the end of the night was not the end of the action: the next day, the squad rescued a man who went into cardiac arrest at a residence.
According to Chief Bill Stio, who was present for the movie theater rescue, the department does "maybe four or five" cardiac arrest rescues a year.
Still, Cavalieri, who has been a medic since 1980, said that "nothing" surprises him anymore.
"It's either really slow or really busy," he said.
On Saturday night, Cavalieri was on his way out of the department's headquarters down the road from the Elwood Cinemas on Jericho Turnpike when he got the call about a man in cardiac arrest at the theater. His response time, he estimated, was about one minute. Third Assistant Chief Alan Berkowitz happened to be at a traffic light opposite the theater and reported to the scene, followed by others.
The 67-year-old patient was lying in the aisle of the theater when officials arrived, fire officials said. He lost his pulse and went into cardiac arrest. Berkowitz started performing CPR and hooked the patient up to a defibrillator, and Berkowitz and Cavalieri then continued CPR.
The patient was then taken to Huntington Hospital by the Dix Hills Rescue Squad ambulance, accompanied by the captain of the Dix Hills Rescue Squad, paramedic Scott DiPino.
The next day, on Sunday afternoon around 3:35 p.m., the department got a call about a 92-year-old man choking on food and going into cardiac arrest at a residence. Cavalieri responded again, along with Tony Hunt, Advanced EMT-CC Eytan Pick and Suffolk County police. A Dix Hills Rescue Squad ambulance brought the man to Huntington Hospital.
Dix Hills wasn't the only department making cardiac arrest saves over the weekend. On Saturday night, Suffolk County police officers saved a third individual suffering cardiac arrest in Huntington village.
Around 7:45 p.m., the department got a call about an 80-year-old man choking at Sur Steakhouse on New York Avenue.
The man went into cardiac arrest, police said, as Officer David Weymouth tried to perform the Heimlich maneuver.
The man, whom police did not identify, lost consciousness. Police shocked him with an internal defibrillator and performed chest compressions. The man regained consciousness, police said, and was taken to Huntington Hospital.
Dabes Das, a server at Sur, was in the restaurant at the time of the incident.
The children were taken outside, Das said, and the adult guests also cleared out to make sure that the officers and paramedics had the space to work.


Here are 3 little bears I have made ready to go to Melbourne with me. I fly out Friday for a week of 3x 2 day workshops at Bear Essence. I have been busy making mink kits and a few bears to take along for the ride.


Tropical fishes flashcard for kids. Colorful application to keep your kids engaged, learn to paint fishes and build motor skills. Join the dots in the color of your choice to draw different tropical fishes. This application has collection of pictures with fish outlines to draw and additional illustrations with visualization and puzzles. Draws as you move the finger. Tags: kids, children, finger paint, draw, learn, connect dots, letters, fish, shapes, motor skills, flashcard, puzzle.


text:
\section{introduction}
The epoch of reionization (EoR) is a complex and information-rich stage in the history of our
Universe, during which the first galaxies formed and the intergalactic medium (IGM) transits from neutral to ionized
(e.g. \citealt{2018PhR...780....1D}).
The Lyman-$\alpha$ absorption spectra of high redshift quasars show that reionization is nearly complete
at $z\approx6$ \citep{Fan:2006dp}, while the latest cosmic microwave background (CMB) data from the Planck satellite
sets the average redshift of EoR to be $z_{re}=7.82$ \citep{Akrami:2018vks}.
Recently, the Experiment to Detect the Global Epoch of Reionization Signature (EDGES) claims to
detect a strong global 21cm absorption signal at redshift $z\sim 18$ corresponding to the formation of the first luminous
objects \citep{2018Natur.555...67B}, though the claimed signal is too strong to be consistent with standard cosmological
model, and this result still needs further confirmation from more experiments.
Besides the basic timing of reionization, however, more details
about this process, such as the nature and properties of the ionizing sources and the scale and morphology
of the ionization field are still very uncertain. Using the 21 cm transition of neutral hydrogen as the tracer of
the neutral IGM, various experiments
are built or being designed in order to detect the 21 cm signals from the EoR, including the current GMRT \citep{Paciga:2010yy},
MWA \citep{Tingay:2013ypa}, PAPER \citep{Parsons:2009in}, and LOFAR \citep{vanHaarlem:2013dsa},
and the upcoming HERA \citep{DeBoer:2016tnn} and SKA-low \citep{Maartens:2015mra}.
The 21 cm power spectrum may be the most comprehensively studied statistics, and
it is also probably the first statistical signal to be measured in the near future.
Nevertheless, much more information is expected to be extracted from other 21 cm statistics beyond
the power spectrum, as the reionization process involves various non-linear processes,
and the ionization field is expected to be highly non-Gaussian.
Indeed, evolutionary features in the skewness (e.g. \citealt{Wyithe:2007if}), kurtosis (e.g. \citealt{Kittiwisit:2017jia}), and bispectrum (e.g. \citealt{Shimabukuro:2015iqa}) of the 21 cm brightness fields, among others, have been explored.

According to our current understanding, reionization began with the formation of first stars and galaxies
in high density regions, which photoionized the gas in the surrounding regions and form individual ionized bubbles.
As more and more galaxies form, the bubbles grow in size and number, at some point they
start to connect with each other, going through a percolation process, and eventually the ionized regions overlap with
each other and most of them are connected as a whole. The remaining neutral regions are then one-by-one
cut off from each other and become isolated islands. The reionization process
is completed with the shrinking and disappearing of these islands.

The  widely adopted ``bubble model'' assumed isolated-bubbles topology for the early stage of
reionization \citep{Furlanetto:2004nh}, and several semi-numerical simulation programs have been
developed based on this idea \citep{Zahn:2006sg,Mesinger:2010ne}).
It is important to know the realm in which the isolated-bubbles topology applies, before such simulations
are used for interpreting the upcoming observational data.
Recently, it has been recognized that the bubble overlap happens at fairly high neutral
fractions \citep{Xu:2013npa,Furlanetto:2015hqp}, casting doubts on the applicable range of the models based on the
idea of isolated bubbles, as its basic premise is invalid except for a very brief periods.
At a later stage, when most of the space have been reionized, the neutral regions become isolated,
and one could then treat them as neutral islands \citep{Xu:2013npa}, but
again we need to know the point at which the topological phase transition happened and the
model based on the island picture can apply.

The two-dimensional and three-dimensional topology of the ionized regions during the EoR have been
investigated in a number of
researches \citep{Gleser:2006su,2008ApJ...675....8L,2014JKAS...47...49H,Wang:2015dna}
\citep{2018JCAP...10..011K,Bag:2018zon,Bag2019MNRAS}.
While the neutral fraction, matter density and spin temperature of the hydrogen atoms may all affect
the 21cm signal,  \citet{Yoshiura:2016nux} demonstrated that the MFs of the
21cm field is determined primarily by the neutral fraction, so that it provides a very powerful tool to
study the topological evolution process during reionization.

Here we aim to quantify the topological structure  of the 21 cm brightness field in terms of the MFs,
and provide a full description of the evolutionary features of the 21 cm signal through the reionization process.
Using the Minkowski functionals and the statistics of ionized and neutral regions, we try to gain an understanding of
how the topology of the neutral and ionized regions evolve.

In Section 2,  we briefly introduce the excursion set theory of reionization, and
the semi-numerical simulations, on which our topological analysis is based. The computation of MFs
is given in Section 3.  The evolutionary features in the topology
of the 21 cm brightness field are presented in Section 4, with each subsection dedicated to a stage of EoR.
Section 5 compares the topology evolution in the 21cmFAST and the IslandFAST.
We then discuss the feasibility to measure the MFs with SKA in Section 6,
before summarizing the main results in Section 7.

\section{Semi-numerical simulations}
In order to generate the ionization field and the corresponding 21 cm brightness temperature map during reionization,
we use the semi-numerical simulations of the 21cmFAST \citep{Mesinger:2010ne} program as well as
the IslandFAST\citep{Xu:2016nmi}, which is designed to have a more accurate description at the late stage of the reionization.
The semi-numerical simulations are based on the excursion set theory of structure
formation (\citealt{Bond:1990iw}, \citealt{Lacey:1993iv}, \citealt{Zentner:2006vw}), in which the formation of
luminous objects are determined by the over-density on the corresponding mass scales, and the ionization of the region
is determined by the balance of ionizing photon supply and the number of baryons to be ionized--in the presence of recombination,
each baryon may also require multiple photons to keep it ionized during the time being considered.
The 21cmFAST program was developed based on the ``bubble model'' of reionization \citep{Furlanetto:2004nh}
which assumes an isolated-bubble topology of the ionization regions.
To obtain a more accurate description of the reionization process after percolation of the ionized regions, the ``island model''
\citep{Xu:2013npa} and the corresponding semi-numerical code IslandFAST \citep{Xu:2016nmi} were developed,
assuming a topology of isolated neutral islands in the ionization field.
Strictly speaking, the ``bubble model'' should be applied only before the connection of individual bubbles,
while the ``island model'' should be used only after the isolation of the neutral patches, and during the mid-stage
of reionization when the percolation occurs, neither of these model is completely accurate.
Within the framework of the excursion set theory, the watershed happens when the density barrier
crosses the coordinate origin on the $\delta-S$ plane.

Although the ionized bubbles are isolated only at the early stage of reionization, it was found that the statistical predictions from
the 21cmFAST still have a reasonable agreement with full radiative transfer hydrodynamical simulations
for most epochs during reionization \citep{Zahn:2006sg}. In this paper
we will use the 21cmFAST to simulate the whole process of reionization, and analyze
the topology of reionization. Using the MFs, we will identify the point
at which neutral regions are divided into discrete pieces, after that the neutral island gives a better
description of the hydrogen distribution. For the late stage, we also perform the IslandFAST simulation, which
begin with an initial state generated with 21cmFAST, but then evolve the reionization sequence using the
IslandFAST rules.

We assume an ionizing efficiency parameter of $\zeta = 20$, and a minimum virial temperature of
$10^4$ K for halos hosting ionizing sources as our fiducial model.
For the IslandFAST, an empirical model for the ionizing background is adopted, based on the
observed number density of Lyman limit systems near redshift 6 \citep{2010ApJ...721.1448S}.
The simulation box has comoving length of 1 Gpc on a side and $500^3$ cubic cells.

The EoR experiments measure the 21 cm brightness temperature,
given by (e.g. \citealt{Furlanetto:2006jb}):
\begin{eqnarray}
T_b (z)&\approx& 27x_{\rm HI}(1+\delta_{m})\left(\frac{H}{{\rm d}v_{r}/{\rm d}r+H}\right)
\left(1-\frac{T_{\gamma}}{T_{\rm S}}\right) \nonumber \\
 &&\left(\frac{1+z}{10}\frac{0.15}{\Omega_{m}h^2}\right)^{1/2}\left(\frac{\Omega_{b}h^2}{0.023}\right)[{\rm mK}],
\end{eqnarray}
where $H$ is the Hubble parameter, $\Omega_{m}$ and $\Omega_{b}$ are the matter and
baryon density parameters respectively, $T_{\gamma}$ is the CMB temperature and
${\rm d}v_{r}/{\rm d}r$ is the radial gradient of the peculiar velocity.
The topology of $T_b$ contains the three-dimensional information about the neutral fraction $x_{\rm HI}$,
matter overdensity $\delta_{m}$, spin temperature $T_{\rm S}$, as well as the radio velocity gradient.
The spin temperature is an weighted average of the gas kinetic temperature and the CMB temperature.
At the cosmic dawn, when the first stars and galaxies formed, the spin temperature might be driven below the CMB temperature
by the Wouthuysen-Field mechanism of the Lyman-$\alpha$ photons, producing an absorption
trough \citep{Chen:2003gc}. However, for the major part of the epoch of reionization, especially when the ionization
fraction became significant, the gas would have already been heated well above the CMB temperature, thus the tomographic
signal would be found 21cm emission. Below for simplicity  we assume
$T_{\rm S} \gg T_{\gamma}$ in the analysis.
While the density fluctuations also contribute to $T_b$ fluctuations, the ionization can set
the brightness directly to 0. Therefore, the features in the MFs of $T_b$
during reionization are dominated by the $x_{\rm HI}$ distribution \citep{Yoshiura:2016nux}.
We will focus on the topology of $T_b=0$ contours.

\section{Minkowski Functionals}

To quantify the morphological structure of the reionization, we calculate the
MFs \citep{Minkowski1903} of the $T_b$ field, for which there are only four independent ones in three
dimensional space \citep{1997ApJ...482L...1S}.  A typical set of MFs in the three dimensional space is:
\begin{equation}
V_0(\nu)=\frac{1}{V}\int_{V}{\rm d}^{3}x~ \Theta[u(\mathbf{x})-\nu\sigma]
\end{equation}
\begin{equation}
V_{1}(\nu)=\frac{1}{6V}\int_{\partial F_{\nu}}ds
\end{equation}
\begin{equation}
V_{2}(\nu)=\frac{1}{6\pi V}\int_{\partial F_{\nu}} {\rm d}s~ [\kappa_{1}(\mathbf{x})+\kappa_{2}(\mathbf{x})]
\end{equation}
\begin{equation}
V_{3}(\nu)=\frac{1}{4\pi V}\int_{\partial F_{\nu}} {\rm d}s ~\kappa_{1}(\mathbf{x})\kappa_{2}(\mathbf{x})
\end{equation}
where $\Theta$ denotes the Heaviside step function, $u(\mathbf{x})$ is the random field being studied, $\sigma$ is the
root mean square (rms) of the field, and $\nu=u_{\rm thr}/\sigma$ is the relative threshold. $V$ denotes the three dimensional
space being studied, $x$ denotes the comoving coordinates, $\partial F_\nu$ denotes the contour surface formed by
 $u(\vec{x})=\bar{u}+\nu\sigma$,  $\kappa_{1,2}$ are the principle curvatures of $\partial F_\nu$.
 These MFs, in order, describes the volume, surface area, mean curvature and the Gaussian curvature of the excursion sets,
   i.e. regions in which the field $u$ exceeds certain threshold. By the Gaussian integration theorem, $V_3$ is also
the Euler characteristic, which is related to the genus by $g=1-\chi/2$, which describes the topology of the excursion set, with
 $g V$ = (number of tunnels) - (number of isolated surfaces)+1.

We smooth the $T_b$ field with the simple average and a smoothing scale of $4^3$ cells (8 Mpc a side).
The 21cm fluctuation $T_b/\sigma_{T_b}$ is used as the probe field,  and as we discussed above,
 the $T_b=0$ contours  trace the ionization fronts.
 During the reionization, at least in popular reionization models with soft ionizing photon sources, the
 boundary between the ionized regions and neutral regions are sharply defined. At such boundary $T_b=0$,
 thus we may watch for the $T_b=0$ point in the MF for the
evolution of ionized regions. Other points in the MFs reflect also the change in the density of the neutral hydrogen field, though
being affected by many factors it is more difficult to interpret.

 We use the Koenderink method \citep{Koenderink1984} to
 calculate the MFs. This method obtain the principal curvature by calculating
 the first and second order partial derivatives of the field, and transforms the surface integrals to volume integrals for
 computation using the Gaussian theorem.

Before moving on to measuring the simulation results, we first consider the case of random Gaussian field,
which gives a good description of primordial density field of the large scale structure in the standard cosmology model.
The analytical form of the MFs are known in this case:
 \begin{eqnarray}
 V_0&=&\frac{1}{2}-\frac{1}{2} \Phi(\frac{\nu}{\sqrt{2}})\\
 V_1&=&\frac{2}{3}\frac{\lambda}{\sqrt{2\pi}}e^{-\nu^2/2}\\
 V_2&=&\frac{2}{3}\frac{\lambda^2}{\sqrt{2\pi}} \nu e^{-\nu^2/2}\\
 V_3&=&\frac{\lambda^3}{\sqrt{2\pi}}(\nu^2-1) e^{-\nu^2/2}
 \end{eqnarray}
 where $\nu=\delta/\sigma$, $\lambda=\sqrt{|\xi^{''}(0)|/(2\pi\xi(0))}$ where $\xi(r)$ denotes the  correlation function at zero,
 and $\Phi(x)=\frac{2}{\sqrt{\pi}} \int_0^x dt ~e^{-t^2}$ is the Gaussian error integral. We plot the MFs of a Gaussian
random field in Fig.~\ref{figGauss} for reference, and use them to check our code for numerically measuring the MFs.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.23\textwidth]{Gaussian0.pdf}
\includegraphics[width=0.23\textwidth]{Gaussian1.pdf}\\
\includegraphics[width=0.23\textwidth]{Gaussian2.pdf}
\includegraphics[width=0.23\textwidth]{Gaussian3.pdf}\\
\caption{MFs for a Gaussian random field with $\bar{u}=0$ and $\sigma=0.5$. Red solid line denotes analytical solution and blue solid line denotes the result of numerical algorithm, which are almost identical. The resolution in this case is $128^3$.}
\label{figGauss}
\end{figure}

We can also gain some insights on the interpretation of the MFs from this plot.  The left end of the plot corresponds to
extreme under-density,  so the contours  there would have very small total surface area ($V_1 \sim 0$), and as the surface
is oriented from high density to low density, it enclosed most of the volume ($V_0 \sim 1$).
As the density increases, the enclosed volume fraction $V_0$ decreases, which drops to zero at the right end
for the  extremely large over-density fluctuations. During the same process, the area of the contour surface $V_1$ initially
increases as we move to more probable field values, reaching a maximum at the mean value of $\nu=0$, then starts
decreasing again to smaller values at large over-densities.  The mean curvature $V_2$ at $\nu<0$ is negative due to the
orientation of the contour surface and positive at $\nu>0$, crossing zero at the mean field value of $\nu=0$.
It approaches zero at large $|\nu|$, as the number and contour surface of such extreme points rapidly decrease, though the
curvature itself is large. The maximum and minimum of $V_2$ is reached near $\nu=1$ and $-1$ respectively.
 However, $V_2$ is not frequently used in cosmological applications.
The $V_3>0$ peaks at a moderately large $|\nu|$ indicated that $g<0$, i.e. the number of tunnels smaller than the
number of isolated surfaces, while the  case $V_3<0$ near $\nu=0$ is just the opposite, where we would have a ``sponge"
topology with complex multi-connected iso-density surfaces.

\begin{figure*}[tbp!]
\centering
\includegraphics[width=\textwidth]{MF.png}
\caption{The Minkowski functionals at different redshifts. From top to bottom are $V_0, V_1, V_2, V_3$ respectively,
and from left to right, for each panel the MF at three redshifts (marked on the plot) are shown.}
\label{figMF}
\end{figure*}

\section{Stages of Reionization}

In the bubble model, it is noted that the ionized bubbles first formed in high
density peaks where the star formation rate is high, and as redshift decreases,
more bubbles appear and existing bubbles grow in size, eventually  they would overlap with each other
\citep{Furlanetto:2004nh}, then most of the space is reionized, with only a small fraction of low density regions
remain as neutral islands, and afterwards they also disappeared quickly.
After that, the hydrogen reionization is complete and the neutral hydrogen is only found within the high
density clumps of galaxies or minihalos.
However, it has been recognized recently that the percolation of the ionized bubbles could occur
when the average ionized fraction is still very low \citep{Xu:2013npa,Furlanetto:2015hqp}, so strictly speaking,
the {\it bona fide} isolated bubble picture is only valid for a very brief period.

Armed with the  MFs, we can now study the history of reionization quantitatively. However, we shall use a modified form.
We shall plot the $V_i$ not as a function of the temperature fluctuation normalized with the variance,
$\delta_T = (T_b-\bar{T_b})/\sigma_{T_b}$, but simply as a dimensionless brightness temperature
$T_b/\sigma_{T_b}$.
The advantage of using this is that the boundary between neutral and ionized regions have $T_b=0$, which we can easily
mark, while in the conventional definition this point changes with $\bar{T_b}$.

The redshift evolution of the MFs are plotted in Fig.~\ref{figMF}, where the MFs $V_0,V_1,V_2,V_3$ are shown from top
to bottom, the results at different redshifts are plotted on the four columns from left to right in descending order, and within
each panel results for three redshifts are plotted.

Using the MFs as a classification tool, we find that the reionization history
can be divided into the following five stages according to morphology:
\begin{itemize}
\item {\bf The Ionized Bubbles stage}.
Initially the MFs of the 21cm brightness temperature field are almost identical with the case of a
Gaussian random field. A  small number of isolated ionized bubbles begin to appear in the volume at high peaks of the
density field.
\item {\bf The Ionized Fibers stage}. From $x_{\rm HI}\sim0.9$ to $x_{\rm HI}\sim0.7$,  more and more
bubbles get connected to form a large fiber-like structure extending the whole simulation box.
While such ionized structures do not look exactly as the originally envisioned bubbles, they can still be regarded as
connected bubbles embedded in the neutral box.
\item {\bf The Sponge stage}.
When $x_{\rm HI}$ drops below 0.7, we begin to see that most of the ionized regions get connected,
with the neutral and ionized regions intertwined with each to form a sponge-like complex structure.
\item{\bf The Neutral Fibers stage}.
When the neutral fraction drops below 0.3, the neutral regions begin to look like a large fiber embedded in the
ionized regions. This stage mirrors the ionized fiber stage before the sponge stage.
\item {\bf The Neutral Islands stage}.
As reionization progresses further, the connections between the neutral regions get cut off. When $x_{\rm HI} < 0.16$,
the remaining large neutral regions become islands, and continue to shrink and disappear in the end.
\end{itemize}

Below, we study the evolving MFs and the stages of reionization in detail.
The transition neutral fraction between each stage and the corresponding features in MFs are summarized
in Table~\ref{table:1}.

\subsection{The Ionized Bubbles stage}
In Fig.~\ref{figMF}, the first column from left shows the earliest stage of the reionization process. The three curves
in the figure are for redshift $z=13$ (red solid line), $z= 10.75$ (blue dashed line), and $z=9.75$ (brown dash-dotted line),
and the corresponding neutral fractions are $x_{\rm HI}= 0.9975, 0.9573, 0.9025$ respectively (At the mass
resolution considered here, the difference between the volume and mass-weighted neutral fractions are not large, we
shall use the volume neutral fraction in all discussions in this paper.)
The general impression on the MFs of this stage is that they are very close to the Gaussian case, with only minor deviations.

At the beginning of reionization ($z=13$), almost all of the gas are neutral, and the 21 cm brightness field are
dominated by the density fluctuations. The MFs of the $T_b$ field follow those of a Gaussian field.

As the ionized bubbles formed,  the neutral hydrogen field deviates from the Gaussian case. Inside the ionized regions
 $T_b=0$, and the boundary between the ionized region and neutral regions are sharp, at least for the soft
 ionizing sources such as stars, so we  expect that the volume $V_0(T_b)$ should drop steeply
 just above the point $T_b=0$, as a fraction of the volume
 $x_i=1-x_{\rm HI}$ is now ionized and has $T_b=0$. It should rejoin the original Gaussian curve at a height of
 $V_0=x_{\rm HI}$, if the brightness temperature field remain unchanged outside ionized region. Due to the effect of
 smoothing, the actual drop of $V_0$ is not  so steep. In fact for $x_{\rm HI} \approx 0.96 $ case, the  difference from
 the Gaussian curve is very small, perhaps because the bubbles are still smaller than the smoothing scale.
  But we do see that for the $x_{\rm HI} \approx 0.90$ case, the $V_0$ decreases at $T_b>0$ and
  approaches the Gaussian curve at a value close to $x_{\rm HI}$. The same is true for
  the surface area $V_1$, which for $x_{\rm HI}\approx 0.96$
  the change is unnoticeable, but for $x_{\rm HI} \approx 0.90$  the increase in $V_1$ is quite obvious.

The nature of the ionized region can be revealed by $V_3$ which is related to the topology of the field.
It has an increase at $T_b>0$, showing an excess of contour surfaces, corresponding to the
formation of bubbles. The trough of $V_3$
at the mean brightness temperature also deepens, perhaps due to structure growth, but this is more complicated and
not relevant to the main purpose of our study, so we will not discuss it further.

\begin{figure} [htbp]
\centering
\includegraphics[width=0.28\textwidth]{3DBox1.pdf}\\
\includegraphics[width=0.28\textwidth]{3DBox2.pdf}\\
\includegraphics[width=0.28\textwidth]{3DBox3.pdf}
\caption{The largest ionized region(blue) and other ionized regions(red) at $z=13.0, x_{\rm HI}=0.9925$ (top),
$z=10.75, x_{\rm HI}=0.9573$(middle), and $z=9.75, x_{\rm HI}=0.9027$ (bottom).
The neutral regions are left transparent. }
\label{fig3DBoxA}
\end{figure}

The simulation box at the three redshifts is shown in Fig.~\ref{fig3DBoxA}, where the ionized regions are shown in red,
except the largest ionized region which is colored blue, while the neutral region are left transparent. We plot the simulation
box in this way to highlight the nature of the largest ionized region. We see that at $z=13$, there are already numerous
ionized bubbles, but they are all very small, so that after smoothing
with a relatively large scale (8 Mpc), one would recover almost the exact Gaussian field.
At $z=10.75$, the density of the ionized regions increased, and some of them merge to form large ionized regions, but
even the largest ionized region is still very small. At $z=9.750$, however, even more ionized regions appear, and
begin to get connected with each other to form a large ionized region.
This result is consistent with the findings of \cite{Furlanetto:2015hqp} that one large ionized bubble formed at around
$\bar{x}_{\rm HI}\approx 0.9$.

The size distribution of the ionized regions at each redshift is
shown in Figure \ref{figSD1} in units of box cells. We have made the plot such that the few
 largest cells appear individually as distinct
spikes at the large size side in the figure.  We can see that a very large ionized region appeared at $z=9.75$ box,
its size exceeds other ionized regions by orders of magnitude.  Such a large ionized region starts to ``suppress''
the growth of more ionized regions, in the sense that the newly formed ionized regions are more likely to encounter
this giant one and become annexed before growing to large scale by itself.
When the Universe is only $5\%$ ionized, there are still numerous ionized regions
with comparable sizes of the order $10^4 ~ V_{\rm cell}$. However, the number of these is reduced when the largest ionized
region formed at $x_{\rm HI}\sim0.9$, and the volume of other ionized regions stay much lower. The value of the
distribution function at small volume is still rather large, the small bubbles are not significantly affected. Recall that due to
the well known biased formation of structures, the larger bubbles are likely formed in large regions with high average
density, while the many smaller bubbles are more likely to form in regions of lower average densities,
so the isolated bubble assumption could still be applied to these after this stage.

\begin{figure} [!htbp]
\centering
\includegraphics[width=0.4\textwidth]{combinedSD1.pdf}
\caption{The size distribution of ionized regions at $z=13.000$, $\bar{x}_{\rm HI}=0.9925$ (top panel),
 $z=10.750$, $\bar{x}_{\rm HI}=0.9573$ (center panel) and $z=9.750$, $\bar{x}_{\rm HI}=0.9027$ (bottom panel).
 }
\label{figSD1}
\end{figure}

\subsection{The Ionized Fibers stage}

The second column of Fig.~\ref{figMF} from left shows the MFs of the second stage of the reionization process.
The three curves are for $z=8.875, x_{\rm HI}=0.792$ (red solid line),  $z=8.5, x_{\rm HI} =0.7230$(blue dashed line) and
$z=8.25, x_{\rm HI}=0.6569$ (brown dash-dotted line). The MFs around the ionization boundary $T_b=0$ are clearly different
from the Gaussian field in this stage.

As noted above, at $x_{\rm HI}\sim 0.9$ a large ionized region formed, which goes through the
whole simulation box. The formation of a connected ionized region which is infinitely large, or going through the
whole box volume in a simulation, marks the point of percolation of ionized regions \footnote{Note that here
we distinguish percolation of ionized regions and the overlap of such regions. The former
refers to the point of forming an infinitely large ionized region (in a simulation, one which goes through the whole simulation
box), while the latter refers that most of the ionized regions get connected with each other.  We did not distinguish
these two but lumped them together as a single stage in \citet{Xu:2013npa}.
As there are substantial difference in the  neutral fractions and
redshifts of these two events, we now distinguish them. In \citet{Furlanetto:2015hqp},  ``percolation"
refers to what we called bubble overlap here. However, the present usage is more in line with the usual
definition of percolation theory \citep{2015PhR...578....1S}.
So the percolation threshold is $p_c \approx 0.9$ for our simulation}.
Not all of the ionized regions are connected at this point, however, as is clearly shown in Fig.~\ref{fig3DBoxA}.
But as a matter of fact, even to the very late stage of reionization, there may still be
some isolated ionized regions referred to as ``bubbles-in-island" in \citet{Xu:2013npa}
which are not connected. At best, one can say that most of the ionized regions get connected in this era.

After the formation of this large ionized region, as redshift decreases, more and more ionized regions get connected.
The MFs near $T_{\rm b}=0$ changed appreciably. Now for $V_0$ the drop above $T_b=0$ is more
apparent, and it rejoins the near-Gaussian case at $V_0 \sim x_{\rm HI}$ as we discussed earlier.
The surface area $V_1$ at $T_{\rm b}=0$ contours increase continuously, as ionized regions of
large size formed.  An additional local peak near $T_b \sim 0$ appeared
when the global neutral fraction reaches $x_{\rm HI}\sim0.70$. Meanwhile, the trough in the mean curvature $V_2$
and the peak in the Euler characteristic $V_3$ shifts toward left, also reaching $T_b \sim 0$ at $x_{\rm HI}\sim0.70$.
The position of these peaks and trough are slightly above $T_b = 0$ thanks to the smoothing effect.
These features in $V_1, V_2$ and $V_3$  near $T_b = 0$ indicates that there is a very large area and complicated
topology and morphology for the ionized region, which is an nature outcome of the connection of the ionized regions.
We shall refer to this point as the overlap of ionized regions.

As discussed in last subsection, the largest region which now permeates much of the volume has the
effect of annexing the other large ionized regions. The  size distribution of ionized regions is shown in Fig.\ref{figSD2}.
The few largest ionized regions of $\sim 10^4 ~V_{\rm cell}$ in Fig.~\ref{figSD1} now disappears,
as most of the ionized regions get connected with each other. However, the number of small bubbles remain numerous,
showing that not all ionized regions are connected.

\begin{figure} [!htbp]
\centering
\includegraphics[width=0.4\textwidth]{combinedSD2.pdf}
\caption{The size distribution of the ionized regions at $z=9.75, x_{\rm HI}=0.90275$ (top),
$z=8.5, x_{\rm HI}=0.723$ (middle) and $z=8.25, x_{\rm HI}=0.6569$ (bottom).
}
\label{figSD2}
\end{figure}

\begin{figure} [!htbp]
\centering
\includegraphics[width=0.28\textwidth]{3DBox4.pdf}
\caption{The largest connected ionized region at $z=8.25$.}
\label{fig3DBoxB}
\end{figure}

We show the largest ionized region after the overlap of ionized regions
in Figure \ref{fig3DBoxB}. It is difficult to identify the beginning of overlap visually, but the
additional peak in the Minkowski Functional $V_1$ curve at around $T_b = 0$ give a cue for
its occurrence. The typical global neutral fraction at which overlap happens is found to be $\bar{x}_{\rm HI}\sim0.70$, which is
consistent with the findings of \citet{Furlanetto:2015hqp} and \citet{Bag:2018zon}.

\subsection{The Sponge Stage}
The MFs during next stage of reionization is shown in the third column from left in Fig.~\ref{figMF}. Here all three
curves are from an epoch after the overlap,  for $z= 7.875, x_{\rm HI}=0.525$ (red solid line),
$z= 7.5, x_{\rm HI}=0.3352$ (blue dashed line), and $z=7.375, x_{\rm HI}=0.2548$.

After the point of overlap, the whole box consists one large ionized region with small neutral
regions inside, and one large neutral region, with small ionized regions inside.
The two  are intertwining with each other in a sponge-like morphology, as shown in Figure \ref{figHBoxA}.

\begin{figure}[!htbp]
\centering
\includegraphics[width=0.28\textwidth]{sponge.pdf}
\caption{The largest ionized region(red) and the largest neutral region(blue) at $z=7.875$. }
\label{figHBoxA}
\end{figure}

The evolution of the topological structure is best shown with the
 Euler characteristics $V_{3}$. The Euler characteristics can tell the difference between
 a solid sphere in an empty space, which has a positive $\chi$, and holes inside a solid object,
which has a negative $\chi$. The Euler characteristics is additive, so whether the $V_{3}$ value is positive or negative
can be used to determine whether the neutral region or ionized region is the dominating one.

\begin{figure} [!htbp]
\centering
\includegraphics[width=0.4\textwidth]{combinedSD3.pdf}
\caption{The size distribution of ionized regions and neutral regions at $\bar{x}_{\rm HI}=0.5250$.
}
\label{figSD3}
\end{figure}

Initially, $V_{3}$ has a positive peak around $T_b = 0$, reflecting the fact that even down
to $x_{\rm HI} \sim 0.5$, the ionized regions are still in some sense surrounded by neutral regions.
When the neutral fraction drops to around 0.3, however, the $V_{3}$ at $T_b = 0$ become negative.
This is the sign that there are similar number of ``holes" (neutral regions inside ionized region) to
that of ``balls" (ionized regions inside neutral region).
We note that there is an asymmetry in the evolution of topology as a function of the global neutral fraction, which may
help to explain why the analytical ``bubble model'' and semi-numerical models based on the same idea works fairly well statistically
throughout most of the epoch of reionization.

The other MFs also show interesting evolution during this stage. The volume fraction $V_0$ now exhibits a cliff-like initial drop at
$T_b \sim 0$, then it changes to a shallower decrease. This very steep initial drop does not reach $x_{\rm HI}$ however,
but only down some point higher than it. In earlier discussions we noted that the smoothing  effect make the drop of $V_0$
less steep. The appearance of the very steep initial drop shows that at this stage of reionization, some very large ionized regions
are present, so that they are not affected by the smoothing. However, some of the ionized regions are still small which
are subject to the smoothing effect, so the $V_0$ changes to a more gentle decline before reaching $x_{\rm HI}$.
Looking more carefully, there is a small bounce at the bottom of its initial drop. As $V_0(x) $ is the fraction of volume
with $T_b>x$, it should be monotonically decrease.
The peak in the surface area $V_1$ and the trough in the mean curvature $V_2$ at $T_b\sim 0$ becomes more prominent,
consistent with the impression that the interface between the neutral and ionized regions are highly complicated for the
sponge-like topology in this stage.

The fact that the neutral region still surrounds the ionized regions after the Universe is $50\%$ ionized can also be seen
using the size distribution of ionized region as shown in Figure \ref{figSD3}. Both the largest neutral region and the largest
ionized region appear as a dominant cell cluster in this figure, and they have comparable volumes.
However, the number of small ionized regions and neutral regions have a significant difference, with many more (two orders of
magnitude higher) ionized regions than its neutral counterparts. The bubbles are much more numerous than the
islands, hence the positive Euler characteristics.

\subsection{The Neutral Fibers Stage}

As the redshift decreases further, most of the cosmic volume become occupied by the ionized regions,
and we expect to enter a neutral fibers stage,  which in some sense can be regarded as
the mirror of the ionized fiber state: the neutral regions
are now embedded within the ionized regions, but most of the neutral regions are connected.

\begin{figure} [!htbp]
\centering
\includegraphics[width=0.28\textwidth]{3DBox5.pdf}
\includegraphics[width=0.28\textwidth]{3DBox6.pdf}
\caption{The largest neutral region(blue) and other neutral regions(red) at $z=7.35, x_{\rm HI}=0.2548$ (top)
and $z=7.25, x_{\rm HI}=0.1601$. The ionized regions are left transparent.}
\label{figNuFibersBox}
\end{figure}

Two curves in the last column of Fig.~\ref{figMF} are the MF during this stage. The first curve, which is the same as the
last curve of the last stage, with $z=7.375, x_{\rm HI}=0.2548$ (red solid line), and the second has
$z=7.25, x_{\rm HI}=0.1601$ (blue dash line).

Now the $V_0$ has an even larger steep initial drop at $T_b=0$,
though still not down to $x_{\rm HI}$ during this steep drop due to the smoothing effect.
The surface area $V_1$ at $T_b=0$ decreases a bit as the neutral region begin to shrink.  The negative trough
of $V_2$ also become less deep. The trough of $V_3$ deepens however, showing that there are more ``tunnels"
than the "holes", and the neutral region remain to have a highly complicated topology.
However, at $x_{\rm HI}=0.16$ the $V_{3}$ drops to a minimum, approaching the percolation threshold.

In Fig.~\ref{figNuFibersBox} we show the largest neutral region in blue and all other neutral regions in red, while ionized
regions are transparent. We can see the largest neutral region has a fiber-like morphology, similar to the
ionized regions during the ionized fiber stage. At the lower redshift with $x_{\rm HI}=0.16$,
the size of the largest fiber decrease, and some of its  branches are cut off by ionization and become small,
independent neutral regions.

\subsection{The Neutral Islands Stage}

As the reionization progress further, the connected network of neutral regions gradually break into pieces and become
isolated neutral islands. The last curve in the last column of Fig.~\ref{figMF}, $z=7.1, x_{\rm HI}=0.023$  shows this final stage
of reionization.

\begin{figure}[!hbt]
\centering
\includegraphics[width=0.28\textwidth]{3DBox7.pdf}
\caption{The largest neutral region(blue) with other neutral regions(red) as simulated with 21cmFAST
at $z=7.1, x_{\rm HI}=0.023$, ionized cells are
left transparent.}
\label{figIslandBox}
\end{figure}

 The volume fraction $V_0$ now drops as a cliff at $T_b>0$, to almost zero, then bounces back to a value
 slightly larger than $x_{\rm HI}$,  due to smoothing.  For the surface area $V_1$, the peak at $T_b=0$ lowers as the
 number and area of the neutral region is decreasing, and at higher $T_b$ it almost vanished. The trough at
 $T_b=0$ for the mean curvature $V_2$ and the Euler characteristic $V_3$ also has the same vanishing trend. Furthermore,
 during the Neutral Fibers stage there is still some peaks in $T_b \gg 0$, indicating the presence of some dense clumps
 inside the large neutral region, these now also disappeared. At this point, most neutral regions are
isolated, contributing the number of ``holes'', and the island model description becomes applicable.

After the neutral islands become isolated, they continue to shrink and disappear, resulting the decreasing
value of $V_3$ around $T_b \sim 0$. Eventually, all the islands are ionized and $V_3$
returns to 0 as the reionization is completed. In Fig.\ref{figIslandBox} we show the largest neutral region
in blue, and other neutral regions in red. Here we see even the largest neutral region is now relatively small, but there
are still numerous small islands. However, all of these neutral will be reionized eventually.

\begin{figure} [!htbp]
\centering
\includegraphics[width=0.35\textwidth]{21cmFAST.png} \\
\includegraphics[width=0.35\textwidth]{IslandFAST.png}
\caption{The evolution of $V_{3}$ simulated with 21cmFAST ({\it top panel}) and IslandFAST ({\it bottom panel}).
}
\label{figDiff}
\end{figure}

\section{IslandFAST vs. 21cmFAST}

\begin{figure*} [!ht]
\centering
\subfigure[$\bar{x}_{\rm HI}=0.1601$, 21cmFAST] { \label{fig:a}
\includegraphics[width=0.28\textwidth]{21SD1.pdf}
}
\subfigure[$\bar{x}_{\rm HI}=0.0988$, 21cmFAST] { \label{fig:b}
\includegraphics[width=0.28\textwidth]{21SD2.pdf}
}
\subfigure[$\bar{x}_{\rm HI}=0.0687$, 21cmFAST] { \label{fig:c}
\includegraphics[width=0.28\textwidth]{21SD3.pdf}
}   \\
\subfigure[$\bar{x}_{\rm HI}=0.1664$, IslandFAST] { \label{fig:d}
\includegraphics[width=0.28\textwidth]{islandSD1.pdf}
}
\subfigure[$\bar{x}_{\rm HI}=0.1082$, IslandFAST] { \label{fig:e}
\includegraphics[width=0.28\textwidth]{islandSD2.pdf}
}
\subfigure[$\bar{x}_{\rm HI}=0.0769$, IslandFAST] { \label{fig:f}
\includegraphics[width=0.28\textwidth]{islandSD3.pdf}
}
\caption{Size distribution of neutral regions in each neutral fraction from $x_{\rm HI}\sim0.17$ to
$\bar{x}_{\rm HI}\sim0.07$. The top panel are results of 21cmFAST, and the bottom panel are results for islandFAST.\\}
\label{figSD4}
\end{figure*}

In the above, the evolution of the ionization field were obtained by using the 21cmFAST  semi-numerical simulation.
However, the external photons from the ionizing background may play an important role in the later stages of reionization.
This is taken into account by the IslandFAST model. Here we make a re-analysis of the later stages by comparing the
results of the 21cmFAST and IslandFAST simulations. The IslandFAST requires an input on the external ionizing
background at the start, though afterwards the ionizing background at each later redshift is derived self-consistently.
Here we started the IslandFAST simulation at $x_{\rm HI}=0.17$, using the
output of the 21cmFAST at that redshift as initial condition. We then compare the subsequent topological
evolution for the two models.

The evolution of $V_{3}$ as simulated with IslandFAST and 21cmFAST are shown in Figure \ref{figDiff}. As the
evolution in the two models are different, we take the results at approximately equal neutral fractions.

For the 21 cm field simulated with 21cmFAST, the $V_{3}$ at $T_b=0$ simply increases monotonically during this era,
indicating a continuous decrease in the number of individual islands. For the IslandFAST, however,
$V_{3}$ at $T_b = 0$ first decrease to a lower minimum, then begin to increase.
The further decrease in $V_{3}$ for the IslandFAST simulation reflects the process that the relatively large
neutral regions are being divided into smaller ones because of the bubbles-in-island effect, as well as the
increasing ionizing background. This process creates more ``holes", resulting in a more negative
$V_{3}$ around $T_b = 0$. Eventually, the isolated neutral islands are consumed by the ionizing background,
and similar to the case with 21cmFAST, the $V_3$ at $T_b=0$ eventually vanishes.

In Fig.~\ref{figSD4} we plot  the size distribution function of the two simulations at three comparable
neutral fractions (the neutral fractions are derived from the simulation snapshots, so they can not be made exactly equal).
The top panels (a,b,c) show the 21cmFAST results, while the bottom panels (d,e,f) show the IslandFAST result.
For 21cmFAST, the neutral region simply shrinks as the neutral fraction decreases, so that the whole neutral region size distribution simply shifts toward smaller ones, but a very large neutral cluster is always present. For IslandFAST,
however, at certain point the largest neutral region breaks into disconnected pieces around $x_{\rm HI}\sim0.1$, so the
largest island disappears, while the number of smaller ones is nearly constant or even get an increase during this
process.  This evolution in the  number of neutral islands  as a function of average
neutral fraction is also plotted in Fig.~\ref{figIslandnumber}.  At the starting point
$x_{\rm HI}=0.17$, the number of islands in the 21cmFAST simulation and the IslandFAST simulation are the same.
As  $x_{\rm HI}$ decreases, however, the two models diverge. For 21cmFAST, the  number of neutral regions as well
as the volume of the largest neutral region decreases monotonically. For IslandFAST, as $x_{\rm HI}$ drops
to $\approx 0.1$, the large neutral region breaks into a number of smaller islands, with a
sudden increase of the number of neutral regions. Of course, for either code, the number of islands approaches zero
with $x_{\rm HI} \to 0$.

\begin{figure}[!htbp]
\centering
\includegraphics[width=0.4\textwidth]{islandnumber.pdf}
\caption{The number of islands as a function of average neutral fraction as simulated with 21cmFAST and IslandFAST.}
\label{figIslandnumber}
\end{figure}

From these results, we observe that during the late stage of the reionization, the IslandFAST simulation predicts that
the largest neutral region gets cut off into multiple pieces, while in the 21cmFAST it shrinks, though at some point
it must also be broken off into two or a few pieces, as it no longer percolate through the whole box.
This is not surprising, the IslandFAST takes the ionization caused by external photons into account explicitly,
such photons are more uniformly distributed, and would more likely to cut through the links between the neutral regions
at the same time, and this perhaps provides a better description of the topological evolution during the late stage of EoR.

\section{Observablity}

We now study the feasibility of using the MFs to distinguish the
various stages. The reionization process are very complicated and there are a very wide range of possibilities, it is not possible
to cover or even explore all these possibilities here. For example, For example, if the ionizing photon spectrum are
produced by quasars or decaying particles and very hard, many regions will be partially ionized and the scenarios
would be entirely different. Instead, we  will use our fiducial model to illustrate how the MFs
can be used as a quantitative tool to distinguish these stages, and similar analysis with the MFs can be performed on models
not too different. For simplicity, we select one feature for each stage transition and list them in Table \ref{table:1}, but
we do NOT claim that these are universal criteria applicable to all models.

\begin{table} [htbp]
\begin{center}
\caption{A summary of the MF features at transition points}
\begin{tabular}{lll}
\hline  \hline
Stage$^\star$  & $\bar{x}^c_{\rm HI} $ & Feature\\
\hline
1 $\to$ 2 & 0.9 & The fractional difference of the \\
&& two peaks of $V_3 > 0.1$   \\
\hline
2 $\to$ 3 & 0.7 & The trough in $V_2$ shifts leftwards \\
 && to $T_b \approx 0$ \\
\hline
3 $\to$ 4 & 0.3 & $V_3$ around $T_b\sim0$ becomes negative \\
\hline
4 $\to$ 5 & 0.1 or 0.16$^\dagger$ & The trough in $V_3$ reaches its minimum \\
\hline
\hline
\end{tabular}
\end{center}
\footnotesize $^\star$ The numbered stages are 1.the Ionized Bubbles stage, 2. the Ionized Fibers stage,
3. the Sponge stage, 4. the Neutral Fibers stage and 5. Neutral Islands stage.\\
\footnotesize $^\dagger$ The mean neutral fraction at the last transition is about 0.16 in 21cmFAST and about 0.10 in islandFAST.
\label{table:1}
\end{table}

For the Square Kilometer Array phase one low frequency experiment (SKA1-low), the
angular and frequency resolutions are much finer than the comoving smoothing scale (16 Mpc) used for our MF measurement,
so instrumental smearing is negligible. We assume the per pixel noise is Gaussian and given by (e.g. \citealt{Watkinson:2013fea}):
\begin{eqnarray}
\sigma_{\rm{noise}}&=&2.9 \left(\frac{10^5\rm{m^2}}{A_{\rm{eff}}}\right)\left(\frac{10'}{\Delta\theta}\right)^2
\left(\frac{1+z}{10.0}\right)^{4.6}\nonumber \\
&&\times \sqrt{\frac{1\,\rm{MHz}}{\Delta\nu}\frac{100\, \rm{hours}}{t_{\rm{int}}}} \rm{mK},
\end{eqnarray}
with the system temperature $T_{\rm sys}\approx T_{\rm sky}$ with \citep{10.1093/mnras/stv2601}
\begin{equation}
 T_{\rm sky} = 180 \left(\frac{\nu}{180 \ensuremath{\, {\rm MHz}}}\right)^{-2.6} \rm{K}.
\end{equation}
The array sensitivity $A_{\rm{eff}}/T_{\rm{sys}}$ is modeled according to the SKA performance document\footnote{\url{https://astronomers.skatelescope.org/wp-content/uploads/2017/10/SKA-TEL-SKO-0000818-01_SKA1_Science_Perform.pdf}},
and we assume an integration time of 1000 hours. For $z=8.5$ and $\bar{x}_{\rm HI}=0.72$ in
our fiducial model, the
signal to noise ratio  $\approx$10 per smoothing pixel ($(16 \ensuremath{\,{\rm Mpc}})^3$).

\subsection{The measurement error of MFs}
Both the 21cm temperature and the thermal noise on each pixel are random. To estimate the error on MFs,
we generate different realizations of the 21cm field as well as the noise, and compute the sample variance.

First we consider the effect of cosmic variance of the 21cm field. We re-simulate the reionization process with 8
independent realizations using the same parameters. The results are shown as
the blue shadows (below the y-axis) in Fig.~\ref{MFs with noise}. As expected, the MFs in the different realizations
are similar and the deviations are small, showing that the MFs are indeed good statistical observables.  This is achieved with
the 1 Gpc box, which at $z\sim 7$ corresponds to an $6.5^\circ \times 6.5^\circ$ area.  For comparison, a fiducial value of the SKA
deep field is about  $20 \deg^2$ \citep{Greig:2019tcg}. Note that the error of the MFs approximately scales as $V^{-1/2}$, as
we verified using the simulation.

\begin{figure} [!htbp]
\centering
\includegraphics[width=0.4\textwidth]{sampling}
\caption{A typical set of MFs with cosmic variance denoted as $\Delta V_{i}$ at $\bar{x}_{HI}\sim0.72$.
The orange shadow (above the y-axis) represents the sampling error from 30 different realizations of thermal noise.
The blue shadow (below the y-axis) represents the sampling error derived from the 8 different realizations of simulation.}
\label{MFs with noise}
\end{figure}

Second, we generate 30 different realizations of thermal noise, and plot the sample variance
with the orange shadow (upper half of the y-axis) in Fig.~\ref{MFs with noise}. The variance between them are also quite small.
However, the thermal noise has a Gaussian distribution, as a result its impacts on the Minkowski functionals are biased.
The observed 21cm field, which is a superposition of the 21cm field and the thermal noise has a more Gaussian distribution than
the 21cm field alone.  The features in the MFs come mainly from the topology of the $T_{\rm b}=0$ contours which
correspond to the boundaries between neutral and ionized regions, i.e. ionizing fronts, such a contour
is sensitive to the addition of the  thermal noise, as already pointed out in previous works on the bubble and island statistics
\citep{Giri:2019pxr, Giri:2017nty}. In  Fig.~\ref{MFs noise}, we show the MFs for the no noise case, the small noise case
which corresponding to the one simulated above, and the large noise case which is obtained by  magnifying the thermal
noise by a factor of 3 so that the signal to noise ratio is $\sim$ 3, the results are shown in  Fig.~\ref{MFs noise}.
The MFs of the small noise case are almost identical to those of the no noise case. However, in the large noise case,
 the shape of MFs becomes very similar to the MFs of Gaussian random field as illustrated in Fig.~\ref{figGauss}, effectively
 wiping out the features of the percolation cluster. The MFs are only effective reionization topology indicators when
 large signal to noise ratio observation data is available.

\begin{figure} [!htbp]
\centering
\includegraphics[width=0.4\textwidth]{noise}
\caption{MFs at $\bar{x}_{\rm HI}\sim0.72$ with no noise, small noise ($\rm SNR \sim 10$) and large noise
($\rm SNR \sim 3$). The $V_2$ and $V_3$ with noise are multiplied by 10 for better view.}
\label{MFs noise}
\end{figure}

\begin{figure*} [!htbp]
\centering
\includegraphics[width=0.9\textwidth]{transition2}
\caption{The simulated observation of MFs and errors taken into account of the light cone effect
at a few redshifts during EoR.  In each column we show the results of two mean neutral fractions
which are before (blue) and after (orange) a transition discussed in this paper. For each the lighter shadow shows the
error taken with a measurement of $(1\ensuremath{\,{\rm Gpc}})^2 \times 48 \ensuremath{\,{\rm Mpc}}$, while
the darker shadow shows the error with a measurement of $(5\ensuremath{\,{\rm Gpc}})^2 \times 48 \ensuremath{\,{\rm Mpc}}$. }
\label{MFs light cone effect}
\end{figure*}

\subsection{The light cone effects}
In the above we have simulated the measurement of MFs at a given time or redshift in a comoving three dimensional box.
However, in real observations one can only make the measurement along the light cone, the near and far sides
of the survey volume correspond to different redshifts. The size of the volume in which the measurement is made must then be
limited, such that the evolution is not too much during the light travel time across the box.
For reionization, this poses a serious problem, because the ionization fraction are changing rapidly.
If one take a redshift interval of $\delta z\sim0.2$ at $z=8.5$, for example, it corresponds to only
about $\delta L\sim 50 \,\rm{Mpc}$ along the line of sight.
As our smoothing length is $R_{\rm{pix}}=16 \,\rm{Mpc}$, a ``realistic'' observation can cover only about
three slices. If such small volume is used, the uncertainties would be significant.  This light cone effect has
been well known in the power spectrum measurement (e.g. \citealt{Datta:2011hv, Datta:2014fna}).

Taking boxes of a thickness of $\delta L=48\ensuremath{\,{\rm Mpc}}$,  we calculate the MFs and the expected errors, the
results are shown in Fig.~\ref{MFs light cone effect}. Here on each column
we plot the results just before(in blue color) or after (in orange color) one of the transition of stages discussed above.
The large lighter shadow depicts the expected error for a survey volume of $(1\ensuremath{\,{\rm Gpc}})^2 \times 48 \ensuremath{\,{\rm Mpc}}$.
Due to the light cone effect, the error is much larger than the
previously discussed sampling errors. Nevertheless, in few cases the differences are still large enough to be
distinguished easily, but in other cases the differences are just comparable to the measurement errors. However,
the measurement error can be reduced by observing a larger sky area. As noted earlier,
the error of MFs roughly scales as $V^{-1/2}$. For a fixed redshift interval limited by the light cone effect, the
error can be reduced to acceptable level by having a larger sky area. We also show in the darker shadow area in
Fig.~\ref{MFs light cone effect} the result with a survey of $(5\ensuremath{\,{\rm Gpc}})^2 \times 48 \ensuremath{\,{\rm Mpc}}$, with the same integration time per
pixel. This would require a quite large amount of observing time, but may still be achieved over several years, and
the process can be speed up if the SKA-low is equipped with multi-beam forming capability.

\section{Discussions}

We have analyzed the evolution of the topological structure of the 21 cm brightness temperature field during EoR
using a set of semi-numerical simulations. The ionized regions have a brightness temperature of $T_b=0$, while the
neutral regions have $T_b>0$. By tracking the  changes of MFs, especially by looking at the
MFs at just above $T_b=0$, one can gain insights on the topology of the ionization-neutral region interface during the
reionization process.

Based on the analysis of the MFs and other statistics, e.g. the size distribution of the neutral and ionized regions,
we find that the topological evolution of the reionization process can be divided into five different stages.
In the first stage where the neutral fraction $x_{\rm HI} \gtrsim 0.9$, there are numerous isolated ionized regions (``bubbles").
As more numerous and larger bubbles formed, the ionized regions begin to connect with each other.
Next, the ionized regions formed cluster structures (``ionized fibers"), with the largest one percolating
through the whole simulation box.  At $x_{\rm HI} \approx 0.7$, most of the ionized regions overlap
with each other, forming a connected structure intertwined with a similar structure of neutral regions, the whole
space of ionized and neutral regions takes the appearance of a ``sponge". As the reionization progress further, the
neutral regions begin to shrink and being surrounded by the ionized regions, at $x_{\rm HI} \lesssim 0.3$, a ``neutral fiber"
stage set in. Finally, the neutral fiber also shrinks and at some point around $x_{\rm HI} \sim 0.16$ it no longer
percolate through the whole simulation box, and we enter the stage of isolated ``neutral islands".

From the results summarized above, we see that strictly speaking, the original assumptions of the bubble model and
island model, namely that  the ionized regions or the neutral regions are isolated, are only valid during the
first or the last stage of the reionization process. During the intermediate stages, the topology of the
region could be fairly complicated, and as a result the numerical model may not be quantitatively accurate, as have been
noted in previous works \citep{Xu:2013npa,Furlanetto:2006jb}.
Nevertheless, it is interesting to note that the semi-numerical simulations which are based on spherical averages
do produce very complex and irregular shaped regions. The bubble model and island model are based on the
balance between the number of photons needed for ionization and the number of photons produced locally (bubble model) and
also the number of photons from the external background (for the island model).
The fiber-like shape in such models originates from the shape of the iso-density contours of the density
fluctuations. Very recently, \citet{Bag:2018zon} used the MFs and cluster statistics to characterize the
topology of the ionized regions, they  also found the fiber-like shapes
of the ionized regions, and using the shapefinder statistics derived from the MFs,
they found that the cross-section of the fibers are nearly constant. The numerical algorithm we adopted is not
suitable for accurate computing of the shapefinder statistics, but this result is consistent with the general picture
of reionization process we delineated above.

Compared with the original assumption, the most important difference for the fiber shaped ionized region
is that they will get some additional ionizing photons from the
connected neighboring cells, i.e. some ionizing photons can propagate along the fibers, so that the ionization may be even
faster. However, if the ionized regions are indeed shaped as fibers, the cross section for the background photon is fairly
limited, and the zigzag path also limit the distance the photons could travel due to finite propagation time and the absorption by
the residue neutral gas in the ionized regions. Thus, even though the original assumption of isolated bubbles is no longer
true during the ionized fiber stage,  we speculate that the model may still give reasonably good predictions.
For the neutral fibers, the inaccuracy of the 21cmFAST model may be larger, as a substantial amount of the photons could
come from the surrounding ionizing background. However, the IslandFAST program may take into account of the surface area
of the actual neutral region, the main difference in topology is that the neutral fibers are more prone to break-up into smaller
islands.

We found that although the value of MFs are affected by thermal noise, which is more Gaussian than the signal and thus
making the MFs more bland, there remains features which can be  used to distinguish the different stages,
at least with high signal-to-noise measurements (${\rm SNR} \sim 10)$).
However, due to the rapid evolution of the ionization fraction during EoR, the light cone effect put a limit on the usable
redshift bin size ($\Delta z \lesssim 0.2$). For a typical SKA EoR survey with an area of $\sim 40 \deg^2$ and 1000 hour integration
time per pixel, in some cases the MFs can still be distinguished though for many cases the difference
would be comparable to the measurement errors.  To achieve a  good measurement, a larger sky area is needed.
Thus, the evolution of topology is within the reach through 21 cm brightness temperature measurements using SKA-low,
though it may require a survey of many years to complete. The survey time could be shortened if the SKA-low
is equipped with multi-beam forming capability.

The present study is still limited in several ways. Our study is based on semi-numerical models,
which is only an approximation and can not replace a full radiative transfer simulation.
The study of the topology of reionization using the semi-numerical models
may be considered as a self-consistent check on the basic assumptions of the method.
We have limited our presentation to the results obtained for a fiducial model. The
different cosmological and reionization parameters may affect the results. However, from a few exploratory tests,
it seems that as long as the ionizing sources are soft ones which produce clear boundary between the neutral and ionized
regions, and the cosmological parameters and reionization parameters are not too extreme,
the general picture of the evolution presented above should be robust.

\acknowledgements
This work is supported by the Chinese Academy of Sciences (CAS) Frontier Science Key Project
QYZDJ-SSW-SLH017, the National Natural Science Foundation of China (NSFC) key
project grant 11633004, the NSFC-ISF joint research program No. 11761141012, the CAS
Strategic Priority Research Program XDA15020200, the National Key R\&D Program
2017YFA0402603,
the NSFC grant 11773034,
and the MoST grant 2016YFE0100300.
ZTC thanks Jiabei Zhu, Xianyun Jiang for valuable discussions.

redpajama_set_name: RedPajamaArXiv


This web page will show how, and where, NASA faked the lunar approach, lunar orbit, lunar landing, and lunar take off, for all the Apollo Moon landing videos. Contrary to what many believe, the sequences were not shot in a desert, Hollywood studio, or Area 51. There may have been the odd picture taken at Area 51, and a few Apollo pictures that were taken in some remote desert, but the majority of stills and video were performed at Langley Research Center, Hampton, Virginia.
Scientists at NASA knew in the early 60s that a manned mission to the Moon was impossible within 8 years, and a plan to fake the Moon landings was put into operation. NASA's fake Moon pictures were taken at various locations such as KSC, JSC, LRC, and of course the odd one or two desert locations. I would also like to point out to that the art of faking both still photographs, and movie film is as old as photography and film itself.
The 1930's film "King Kong" showed a huge gorilla scaling up the Empire State building. If it's on film are we led to believe it's real? No of course not, but that is exactly what PAN's, (Pro Apollo Nutters) are claiming. Their ridiculous debunking claim is that digital manipulation of photographs and film was not available back in the 1960's, but they did not have digital artifacts back in 1930 when the film "King Kong" was made.
are stored there and not due for declassification until 2026. Other artifacts including the burnt out Apollo 1 capsule which killed Grissom, Chaffe and White. They have the facilities to perform anything, fake backgrounds, simulated orbiters etc. First piece of evidence is the large 250 foot traverse crane shown below. Notice fake Moon crater surface created beneath the crane.
This crane was purposely built in 63/64 to perfect the lunar landing as close as possible to the real thing, and used to suspend both the LM and astronauts. It enabled the mock LM to move in all directions, ie, up down, left right, forward and reverse. Trial runs were so good NASA, opted to use the setup for faking the film of lunar landing, and take off, whereby the flag is blown over.
way as a conventional crane.
The film shown to public of the LM supposedly blasting off from the Moon's surface was also created beneath this crane at LRC. The mock LM was simply attached to the crane, and hoisted very rapidly at the same time a pathetic looking blast off sparks was enacted beneath it. The film was then speeded up for showing to the public, and it is interesting to note that the camera filming this sequence cut short once the LM had reached the crane maximum height. In other words why didn't the camera continue to film the LM until it was out of view? Because it was not possible under the circumstances in which the "lift off" was faked.
The far right picture above is a time lapse sequence taken at night. Notice spotlights on crane gantry, and how it illuminates the ground surface. The mock LM was traversed full length of crane, and simultaneously lowered at the same time in order to create an authentic looking lunar landing, when viewed from within the mock LM itself. Power supply to the mock LM was by cable from crane tower.This enabled a large fan, (fitted beneath the mock LM), to create the dust scatter effect of a rocket engine as it descended to the fake Moon surface.
is how it was done, even if Pro Apollo Nutters say no way. Picture on left, taken at night, looks like a realistic Moon setting.
I am in no doubt that some out there would actually say this photo was taken on the Moon. I have heard so many ridiculous comments from the Pro Apollo Nutters that nothing would surprise me.
the Moon, and likewise Apollo 12 had done the same.
6 months before this picture was taken.
Pictures below show how astronauts were suspended from the crane in order to simulate low gravity. They eventually settled for an upright position with the astronaut suspended by strong elastic/bungee cord, so that his feet were only just touching the ground, the same way as a baby bouncer. You can try it yourself by placing a given weight at the end of an elastic band. As the astronauts walked in a given direction, the overhead crane moved in the same direction. This enabled the astronauts to literally float along in a crude "Moon walk" fashion.
it traversed across the fake lunar surface. The video also shows footage from the camera mounted trolley scanning the Moon surface placards.
a manouvre in space is absolutely ridiculous, and this one video proves beyond any doubt that the film was shot at Langley. This is further detailed later on in the web page. This one film encapsulates all the sequences at the Langley fake Moon studio, and also the exterior crane.
Conclusive proof video footage is fake, but those comedians at NASA claim it as genuine film footage taken from Apollo 8 Command Module as it orbited the Moon.
The video on right shows NASA attempting to simulate one sixth gravity by suspending astronauts in a horizontal position.
Looking down from the top of the gantry on to the simulated Lunar Surface. James Hansen writes: "To make the simulated landings more authentic, [Donald] Hewes and his men filled the base of the huge eight-legged, red-and-white structure with dirt and modeled it to resemble the moons surface. They erected floodlights at the proper angles to simulate lunar light and installed a black screen at the far end of the gantry to mimic the airless lunar "sky." Hewes personally climbed into the fake craters with cans of everyday black enamel to spray them so that the astronauts could experience the shadows that they would see during the actual moon landing." (p. 375) From A.W. Vigil, "Piloted Space-Flight Simulation at Langley Research Center," Paper presented at the American Society of Mechanical Engineers, 1966 Winter Meeting, New York, NY, November 27 - December 1, 1966. "Ground-based simulators are not very satisfactory for studying the problems associated with the final phases of landing. This is due primarily to the fact that the visual scene cannot be simulated with sufficient realism. For this reason it is preferable to go to some sort of flight-test simulator which can provide real-life visual cues. One research facility designed to study the final phases of lunar landing is in operation at Langley. ... The facility is an overhead crane structure about 250 feet tall and 400 feet long. The crane system supports five-sixths of the vehicles weight through servo-driven vertical cables. The remaining one-sixth of the vehicle weight pulls the vehicle downward simulating the lunar gravitational force. During actual flights the overhead crane system is slaved to keep the cable near vertical at all times. A gimbal system on the vehicle permits angular freedom for pitch, roll, and yaw. The facility is capable of testing vehicles up to 20,000 pounds. A research vehicle, weighing 10,500 pounds fully loaded, is being used and is shown [in this picture]. This vehicle is provided with a large degree of flexibility in cockpit positions, instrumentation, and control parameters. It has main engines of 6,000 pounds thrust, throttle able down to 600 pounds, and attitude jets. This facility is studying the problems of the final 200 feet of lunar landing and the problems of maneuvering about in close proximity to the lunar surface." Published in James R. Hansen, Spaceflight Revolution: NASA Langley Research Center From Sputnik to Apollo, (Washington: NASA, 1995), pp. 373-378.
Size does matter believe me, especially when NASA want to create a fake lunar surface as shown in the above picture on left. It literally dwarfs the two men stood in front of it. It's unbelievable the time, trouble and expense that NASA incurred purely to fake the lunar missions. It was of course done purely to convince the world they were the leaders in space. This very large picture, and others were used in conjunction with a rail mounted camera, which also focused on a large rotating PLASTER PARIS model of the Moon, (shown on the right). NASA knew, after Kennedy's speech in 61, that a lunar landing before 1970 was impossible. Realizing this they had no option but to fake the missions. This was Project Apollo, whereby a program was launched at LRC to design props/backgrounds etc, to convince the media they had achieved the goal set by Kennedy.
The high resolution picture above left shows a 20' diameter sphere which can be rotated from below. In the left of that picture can be seen a huge blank placard. This is the scene before LRC staff began work on converting the sphere to an authentic looking Moon complete with craters, ( for lunar approach), and the placards were to be lunar orbit. Notice also the rail track around placards.
These placards formed a gigantic semi circle, which took up the length and breadth within the building. Note moving trolley on the track. This trolley, which had a movie camera mounted on it, was able to scan across the placards, so as to simulate a lunar orbit. When the camera reached the end of the placards it was able to swing through 180 degrees, move up, or down, and continue scanning the placards in reverse at a differing level. (See Youtube video above). Theoretically the camera on trolley, in addition to moving forwards and back, was able to zoom in and out, rotate through a full 360 degrees, and increase or decrease the height level. It first began to film the rotating sphere, (lunar approach), it then swung around and began scanning the fake lunar surface on placards, (lunar orbit).
The picture above right shows a section of the placards after modeling work. Pretty impressive eh? Notice how background is in complete dartkness. Remove bloke from picture and you could easily pass this photo as being taken by Apollo crew orbiting the Moon.
Picture above left is a view taken from cab of the crane, looking down onto fake lunar surface below. Picture above right shows Donald Hewes beneath the Langley crane. Hewes created the fake lunar surface, and was heavily involved in the fake lunar landing and lift off videos.
The pictures above show how LRC made "plaster paris" copies of the Moon craters on the placards. The guy on the left with dividers, is checking that craters are to scale, whilst the guy on the right is spraying the surface to create shadows and dark areas of the Moon, this info being obtained from high resolution images of the Moon, taken with high magnification telescopes.
Notice the sphere in left hand picture after modeling work. This sphere had a light inside, which shone through the translusent surface on the outside, and it enabled the model to have a bright appearance like the Moon itself. The large placards with Moon craters were also backlit with fluorescent tube lights.
Turn off all your lighting, and you end up with the picture shown below left. This is how the Moon would look in the void of space if you could get close enough to it, however no one, not even Armstrong could get anywhere near to the real thing.
The man stood on movie rail track with dividers, is Apollo Program Manager John W Paup. Paup's personality antagonized NASA staff to the point where they ordered Apollo Project Manager, Harrison Storms, to replace him. This he did in 1964, and Paup left NASA at the same time. Paup died at the tender age of 45, and six months before the launch of Apollo 8. It could be that as NASA were using the plaster paris models for showing to the public as being the 'real thing', Paup would immediately recognize the fakery, and as he had a grievance with NASA, he may well spill the beans on them. PAN's claim that if the missions were faked, then someone would have spoken out. Well if dead and gone before the very first fake Moon mission, they can't very well speak out can they?
NASA claim that picture above right is far side of Moon, taken by Apollo 8. Compare this sphere with one shown above it in the left hand picture. It speaks for itself does it not? In all of these pictures notice the black background. This of course made it easier for touching up photos to ensure that background space was indeed black.
The two pictures above prove that you do not need pressurized suits to create an authentic Moon approach or orbit. Take a film whilst approaching the plaster paris model, and it would be enough to convince a gullible audience that film was taken whilst approaching the Moon.
There was no need for NASA to land a man on the Moon before 1970, as the photograph above left shows. Project Apollo staff at Langley had a firm grip on it as early as 1964. Move out the way fellers, this is to be a picture taken by astronauts approaching the Moon.
Picture on right shows Charlie Duke (pointing), and John Young, at the simulator controls for lunar approach/orbit. The picture on TV screen is reminiscent of the pictures we saw on our TV screens. We were told it was the Moon, but the picture showing on TV screen in photograph is not the Moon. It is a camera filming the plaster paris model of Moon. Both John Young and Charlie Duke were heavily involved in faking of the Apollo Moon missions.
So there you have it. I have shown how NASA faked close lunar approach/orbit, and lunar landing and take off, so next time you see a film on TV of any Apollo craft supposedly approaching, orbiting, landing on, or taking off from the Moon, you will know exactly how it was done. However there is more NASA fakery involved in filming the Moon from a much greater distance. You've probably seen the "Incriminating Footage" albeit (Pretty boring eh) video on YT which was supposed to be the Apollo crew filming the Moon from a distance. This video claims to show Earth's shadow moving across the Moons surface, so as to prove it was genuine. Unfortunately, just like other NASA Moon videos, the film is fake, and the pictures below show how it was achieved.
(Top left) Preparing the projection of the Earths shadow (when the lab was still illuminated). Notice camera shrouded in a black cloak, with the lens pointing at a picture of the Moon. The lab lighting was turned off to achieve the objective required.
(Top right) Micro metric system (with vernier) to move Earths shadow across picture of the Moon.
(Bottom right) This picture shows the final set up. The camera is filming the sequence just before the simulated moon eclipse created by the Micro metric system shown above.
How space radiation makes Moon trip impossible.
Clear cut evidence of fakery in the Apollo Moon videos.
Fake Moon Landing,Clavius Moon Base,Clavius.org,moonmovie.com,moonfaker.com,aulis.com.
Here is another method NASA used to give the impression astronauts were in reduced gravity.
A large helium filled balloon was used to take weight off the astronaut actor, so his feet were hardly touching the ground. This would give the impression that astronaut was in reduced gravity, (on the Moon), when in reality they were acting it out at Langley.
Notice floodlight to create a fake Sun, fake Lunar Module, fake lunar soil, and boom camera so as to film the whole sequence, then dish it out to the media as genuine film footage taken on the Moon.
We now go inside the Langley Research Center complex itself to see how they faked the lunar approach, and close orbit of the Moon's surface. We've all seen film supposedly taken from LM as it approached the Moon, and then begin to orbit. The speed at which it changes from lunar approach to orbit is utterly ridiculous, as any craft traveling at that speed would crash straight into the Moon. No one could control a craft in such a way as shown in the film, and in reality no one did. These pictures show exactly how it was done.


Everyone who's just curious about science - up to the top expert on nuclear fusion - will find something here! Hundreds of the most interesting science questions are answered and are split into 3 categories: Light, Physics and Sound.
What happens to water if you compress it more and more and more... (It can't just disappear)?
What's the temperature of a candle flame?
Can liquid diamond be made and if so, what temperature would be needed?
What on earth would liquid diamond or gold taste like if it was cool enough to drink?
All of these questions and hundreds more will be answered!
are welcome) then don't hesitate to contact me.
then visit the sites dedicated to Q+A at the end of this page.
Currently the following people have contributed to the answers.
How many light bulbs would you need to have it as bright indoors as outdoors?
Why are there 12 notes to the musical scale?
Is there a limit to how sweet or sour something can taste?
How many unique pictures could you ever see?
Is there any way to scientifically prove that people have a 'soul'?
Can the blind see in dreams?
Blue and Yellow really green??
Where is Magenta in the Colour Spectrum?
Tons of light and no heat?? Tons of heat and no light??
Explore the colorful world built entirely using mathematical atoms and molecules. Pictures and animations demonstrate structures colliding and interacting.
Expanding on the questions presented here, this page offers a unique collection of articles about oddities in the science of colour and light.
The greatest optical illusions in the world, and unique to Skytopia, since we created them! Witness the Eclipse of Mars, and see the colour Green and Cyan as you have never seem them before.
www.newscientist.com/lastword A cool Q+A section - for all those 'small mysteries of everyday life'. The site itself is very comprehensive too, with up to date science news and much more.
www.sciencenet.org.uk Another Q+A site with thousands of questions and a neat search feature. This is also the site responsible for the free telephone service - 'Science Line'.
www.madsci.org/submit.html Yet another brilliant site dedicated to answering all your questions about science. This one contains over 25,000 questions, a comprehensive search feature and a forum-style approach to the answers.
www.newton.dep.anl.gov/archive.htm Thousands more questions answered under various topics and sub-topics & search feature.
www.thenakedscientists.com Excellent site with various science articles, a forum and an online radio archive - featuring movies, pictures and audio for download.
All content on this site is copyright D. White 2002 onwards.
Please ask for permission should you wish to use the text or graphic material on these pages.


The Chinese Academy of Agricultural Sciences launches new talent plans to drive innovation at the country's premier agricultural research institution.
The Chinese Academy of Agricultural Sciences (CAAS) is China's leader in agricultural technology. In the 60 years since CAAS was founded, it has always put its scientists at its core and has thus managed to accumulate a rich pool of talent.
CAAS has built a number of well-resourced research platforms. These feature: the world's largest somatic cell bank for domesticated animals and poultry; the second largest genetic resource repository for crops; and, Asia's largest national agricultural library. With two national key scientific engineering projects, six state key laboratories, 22 national crop and domestic animal breeding centres, multiple key laboratories under the Ministry of Agriculture, a number of field stations for scientific observation and testing and several quality inspection centres, CAAS is an agricultural research institution with the most improved and comprehensive facilities in China.
In response to the challenges of inadequate young academic leaders and inappropriate team structure of young talent, CAAS launched the Elite Youth Programme in 2013 as part of its plan to drive science and technology innovation. The programme has helped attract and cultivate a vibrant team of young and mid-career academic leaders.
To further enhance its young talent teams, in 2017 CAAS initiated a Young Talent Plan (2017–2030). This plan aims to increase the academy's under-45 research cohort to approximately 4,750 by 2030 and it would mean that scientists under the age of 45 would account for two thirds of all staff scientists at CAAS. In order to make young researchers a driving force behind agricultural research, CAAS will also reform its human resource development system and incorporate 30 specific measures that address talent acquisition, cultivation, settlement and service support, as well as incentive mechanisms and researcher evaluations. With more open and fluid human resource mechanisms that select superior young researchers based on fair competition, CAAS will create a supportive environment for talent growth that encourages innovation and entrepreneurship.
For new recruits, supporting policies include: an additional subsidy of RMB 100,000–500,000 per year; research funds of RMB 800,000 to 2 million a year; and, a settlement subsidy of RMB 1 million or subsidized housing. In addition, CAAS provides promotion support and helps with graduate student recruitment, children's education and spousal employment.
Aiming to build first-class disciplines and a world-class institute, CAAS is focussing on agricultural genomics and molecular breeding, agricultural information technology and big data, intelligent equipment, novel vaccines, agricultural nanotechnology and other cutting-edge research. It will also promote the innovation of core technologies for new variety development, intelligent agricultural operation, quality control and hazard identification for agricultural products, biological safety and animal nutrition, design and manufacturing of functional food, green agriculture, efficient resource utilization, and environmental control and remediation. CAAS sincerely welcomes researchers both at home and abroad to join it in its endeavours.
The Chinese Academy of Agricultural Sciences retains sole responsibility for content © 2017 The Chinese Academy of Agricultural Sciences.
The table to the right includes counts of all research outputs for Chinese Academy of Agricultural Sciences (CAAS) published between 1 December 2017 - 30 November 2018 which are tracked by the Nature Index.
Countries that import soybeans, instead of growing them for domestic consumption or export, risk increased pollution if they convert existing soybean farms to grow fertiliser-hungry crops.
It is generally accepted that food exporting countries are burdened with the environmental degradation associated with intensive farming, while importing countries reap all the benefits. A team including researchers from the Chinese Academy of Agricultural Sciences examined global data on nitrogen emissions from farming soybeans, wheat, corn, rice, and vegetables.
They found that soybean farmland absorbs nitrogen, whereas the other crops use fertilizer less efficiently, leading to its overuse and accompanying nitrogen pollution, which can damage river ecosystems and water supplies. In China, the world's largest soybean importer, a shift from growing soybean crops to corn and rice increased nitrogen emissions by nearly 125,000 tons between 2010 and 2014.
This highlights the need to re-evaluate the impacts of international trade on importing countries in order to achieve global goals of sustainably increasing food security, while protecting the environment.


Good morning! It's Thursday and it will be what you make it.
Today for lunch we will be having pizza. Tomorrow we will be serving cheeseburgers and fries All of our lunches have a salad bar to pick and choose from.
Any students interested in Health Sciences and in Engineering we will be putting a field visit at WWCC. Please stop by the office to sign up.
Today for lunch we will be having pizza. Tomorrow we will be serving cheeseburgers and fries. All of our lunches have a salad bar to pick and choose from.
The winter dance is on Saturday, January 12th 8-11 pm in the commons. It's $1 per person and you will pay at the dance.