Zenab, centre, with the Huntingdon fire crew who helped put out the fire that started under her bed.
A mum has told of the terrifying moment her 18-year-old daughter woke up to find her bed was on fire.
Lisa Attryde and her four teenage children were forced to flee their Hinchingbrooke Park home after being alerted to the blaze in the early hours of Monday (June 1).
"My daughter, Zenab, was screaming because she woke up surrounded by fire," said Lisa. "I threw a bucket of water over it but it didn't do anything. I said 'Everyone out, get down the stairs'. It was horrible, absolutely horrible.
Zenab, who suffered from shock but was otherwise uninjured, her mum, sisters Amina, 19, and Tabs, 15, and brother Mo, 16, all escaped unharmed.
Once outside, Lisa said the family were joined by friends who tried to put out the flames, which were in a front bedroom. A ladder was found and buckets were passed between a human chain.
Two fire engines from the Huntingdon's fire station were sent to the terrace house in The Shrubbery at 3.12am, arriving at 3.21am, with both there in less than 15 minutes.
Firefighters wearing breathing apparatus went inside and found a smouldering mattress, which was pushed out of the window, before they made sure the property was safe. The rest of the room was heavily smoke damaged and many of the clothes belonging to Zenab, who is doing A-levels at Hinchingbrooke School, were ruined.
Lisa, who has lived in the house for nearly two years, said the fire had started underneath the bed but the cause remained a mystery.
Group Commander Chris Parker, who is responsible for community fire safety at Cambridgeshire Fire and Rescue Service, advised people not to put themselves at risk. He said: "When the crews arrived at the scene, some of the residents were attempting to put out the fire, which could have put them at risk of injury.


A jingle of bells announced LaplandUK's entrance into our life.
The Christmas tree was finally bought and decorated, the bath had been run and the children plunged into it (the youngest clinging to the sides of the bath like a squid over a saucepan). As they were decanted into their pjs, we asked them if they had heard a strange tinkling noise from downstairs.
Under the tree lay a beautiful box (freezing cold as it had come from the North Pole) containing two letters from Father Christmas, wax sealed and individually addressed to the girls. Children this year have been so good that he was certain that the elves would need extra hands in the toy factory, would they mind coming to help?
My eldest was so delighted that she went to sleep clutching the box and took it to school with her for the next week. Bedtime behaviour improved immeasurably when I reminded both girls that they'd be meeting Father Christmas in a week's time, which is my kind of seasonal treat.
Finally, Saturday arrived and, en famille, we travelled down to the St Anne's Manor Hilton near Bracknell. This hotel has a special link with LaplandUK and you can get discounts if you book your tickets with them at the same time. A family room there consists of two kingsize beds in one room, a bathroom and a tv – what more could a family need?
Food, as it turned out. The restaurant was quite busy (and expensive) so we took our chances with a pub nearby. I'll not name names but I'll be unlikely to return there. Admittedly it was one of the last Saturdays before Christmas but it was grubby, manic and packed to the brim. We retreated back to the hotel, had a quick drink in the bar and then went back to our rooms.
The kids were enormously excited to be sleeping in the same room together, with the prospect of seeing the big FC the next day. I honestly thought they might never sleep again but by 9 they were drooping and quickly went off, as did we.
At breakfast the next morning, the husband took the kids off whilst I packed our things and checked out of the room. They had a fab time in the swimming pool (and jacuzzi) for an hour or more which shows the benefit of staying at a hotel with these kinds of facilities when you have kids. Even more beneficially, I had a coffee to myself and actually read a bit of a book. Hurrah.
The next bit of the day took something of a nosedive. I'd thought that, as Ascot was nearby, we might stop off and have a wander down the pretty (as I recalled it) high street. Turns out I was thinking of somewhere else entirely. With two fractious kids in the car, revving up to see Santa, we had to make a quick choice as to what to do with our next few hours. Faced with a choice between Windsor and Maidenhead, I chose the latter, thinking we'd not have time to do the castle and, anyway, wasn't Maidenhead down by the river so probably a bit like Richmond or something?
No. No, readers, it was not. It might once have been a pretty market town but had since been rolled in concrete, picking up a few chain shops and large derelict buildings on the way, and tied in a bow of dual carriageway ringroads. I held the kids' hands tight as we walked across a flyover and bundled through a Sainsbury's car park into a bleak town centre only to find that the only place selling food was McDonalds. Apologies, Maidenhead, but Richmond you are not. If anyone would like to suggest places in Maidenhead that we could have gone to, I'll save them up for next time we're down there. Otherwise, I'll suggest that anyone with time to spare in that area might instead head for Windsor, Cookham or even Cliveden.
Finally, FINALLY, it was nearing 2:30pm and just about time to go to LaplandUK for our entry time of 3pm. The car park is in a large coniferous woodland (the Enchanted Forest) with clearly signed areas and direction markers and there were loads of helpful attendants at hand to point out our route. As we came to the entrance, the eldest was excited to see a little elfin house with a note from one of the woodland elves we'd already met on LaplandUK's website. Eeko was out berry picking so we'd have to catch her later.
Upon walking into the arrivals hall, the atmosphere instantly picked up, with places to sit and a little canteen serving warm food and drinks. It was bustling excitedly, with a signing in area where we were quickly checked in. The children were directly handed their LaplandUK passports, an elf newspaper and a pouch of elf jingles I'd previously bought (1 jingle = £1) underscoring that the children were the most important visitors here.
Elves whom we'd seen on the website were wandering around the hall, engaging with children and whipping up the excitement. We were stickered up (Team Reindeer rather than Team Husky for us – A-ruuf!) by the elves then we were invited beyond the wall of suitcases and through a twisting tunnel to a space with a gnarled oak tree growing through the middle.
Sage, a woodland elf, welcomed us and eventually Eeko made her appearance (much to my girls' delight). Together they told the tale of Father and Mother Christmas's journey to the world of the elves in Lapland. At the end of this performance the doors were opened onto a snow-covered wonderland. I was so thrilled that I totally failed to take any photos and the gasps of excitement from the children (and me!) were audible. We were entering a world quantitively different to the one we were leaving behind. That this magical transformation was so seamless is down to the production team and I almost felt a bit tearful at the dedication to their craft. They have created something very special here.
The first snow-covered path lead to a toy factory where Whittle the Toymaster was impatiently awaiting our arrival. Children were ushered through a tiny door that adults couldn't squeeze through and they sat down at work benches to watch what happened next.
We were introduced to Conker (the naughty elf trying to work harder to win his elf cap's jingle bell) and Wish (the elf who collects children's wishes and writes Santa's list). Wish sat next to my eldest who quivered with delight at this special attention.
The children were shown how to make a fluffy stuffed penguin and everyone was given a basket of the necessary bits. The youngest set to with a determined ferocity to get the job done and was delighted to finish it off all by herself. All the baskets were delivered to the Wrapping Room through a hatch and the elves came round to stamp the passports on the Toy Factory page.
We waited until everyone had filed out as someone must have accidentally picked up the eldest's passport, leaving us with only one. Whittle swiftly found her a spare, stamped it and, when he realised she was keen to meet Pixie Mixie next, gave her a little stuffed heart to pass on. She was so pleased to have a special assignment that it entirely took the sting out of losing her original passport. I was mightily impressed at that bit of quick thinking and excellent customer service on Whittle's behalf; top marks that elf.
We travelled to Mother Christmas's kitchen next and the children listened to a story then decorated their own gingerbread men at stations specially lined up for them. Our two were well into the swing of things by then and needed no encouragement to get involved and earn their next passport stamp. We stowed away the gingerbread and the next twisty path lead us to the elf village.
Here there was everything you might need to divert yourself for 1.5hrs or so, until your important appointment with Father Christmas. We headed straight for the ice rink where the eldest floated off under a sea of sparkly lights and the youngest hacked at the ice with a vengeance and a pair of strap-on skates.
Our next visit was to Pixie Mixie's sweetshop where we met the lady herself and handed over the heart. I've no idea if we were the unwitting pawns in a love story there or not but our two were chuffed to have completed their mission and we went inside to fill up on elfin pic'n'mix, paid for with jingles. 4.5 jingles was a fair amount for some sweets but compared to the (admittedly wonderful looking) gingerbread houses at £25+, we found it a bargain!
There were huskies to pet, different elves to meet, food stands to visit, shops to meander around and even a little post office. Here you could send your wish list to Father Christmas or real postcards to friends and family – a lovely touch.
What is clear is that someone has taken the time to stand back and look at all aspects of the experience, especially from child height, and to design it so that the feeling of magic is never suspended. Even the toilets and the ice-skate stand are housed in "reindeer hide" teepees and the necessary electronics are hidden behind props. As a rather picky adult, it's something of a relief to surrender yourself and your grown-up cynicism into excellent and assured hands.
Storm Deidre came back to visit whilst we were in the Elf Emporium and made the last 20 minutes or so fairly soggy but there was plenty of under-cover space to hide out and some brave souls continued to skate on the central ice rink. At the appointed time we met at the mouth of another twisty path to wend our way to Father Christmas's cottage in the woods.
At first we walked past some reindeers and walked into something of a holding pen. You enter personalised details about your children before you arrive and this is the point at which they double check them and iron out any issues to make sure that the last, most important, part of the visit is absolutely perfect. The screens are, as before, hidden inside massive ledgers to add to the effect.
At last! Our names were called and we followed a chatty elf into the forest. It was properly howling down at this point but the anticipation kept us hopping along over the puddles with excitement. There was a short hiatus outside the hut and then the door opened, revealing the most Christmassy Father Christmas I'd ever seen. Even the voice was perfect, as was his outfit.
There was a small banquette to his side, especially for the children and he spoke directly to them using a mix of pre-gleaned information and genial good sense. They were captivated.
Since first hearing about LaplandUK, my eldest had been particularly concerned that Father Christmas might feel left out, giving so many presents and yet not receiving any. It was such a simple thought but it really struck me. She instantly set to work, writing him a Christmas card and finding him a present to take with her. The youngest tested out her brand new writing skills and managed a whole 'Santa' with only a very little help. A visibly moved FC took these little heartfelt gifts with grace and for me, the soul of Christmas was given and received. I wish I could have distilled that moment and stoppered it up for my babies to use whenever they felt affected by life or other people. I will never forget it and I hope I shall always be able to remind them of the kindness of which they are capable.
Thankfully, both children were on the Good List (though it's been touch and go at times this year) so they were given a lovely cuddly husky toy – and a jingle bell for being so helpful. For my two, with their adoration of anything dewy-eyed and cuddly (and noisy), Santa really couldn't have done better.
A few photographs later, one of which you could have printed out complimentarily, and we were on our way back into the forest towards the exit. There was a shop to negotiate first but a few quick strops later and we were out into the car park. At this point it was nearing 7pm and there was school tomorrow with a 2.5hr journey between us and bed. After some heavy-going traffic, both kids fell asleep and we were able to decant them into bed with relative ease.
On reflection some days later, there are a few things that still stand out about the experience.
This is all about the children. The experience is designed from their point of view; they're the first to be spoken to and consulted about their interests and wants. This shouldn't be such a big surprise, especially at this time of year, but it is.
The experience is really well designed. There's barely a break in the magic and it feels like you're in good hands. What you are given is generally really good quality.
No one stepped out of character the whole time we were there. That's some excellent staff training that must have to be refreshed every couple of weeks to keep everyone perky (whilst wearing elf hats).
It is expensive, most certainly, but to me it felt worth it because of the length of visit and the quality of the experience, as well as the pre-visit communication and excellent website.
There is nothing like this for children in our area, which is a shame. Perhaps it is proximity to London and London-level expectations, the price of tickets or the length of time they've been doing it – or all three – but it's a hell of an interactive 4 hours. It left me feeling pathetically grateful that they'd designed something so wonderful for children, let alone adults.
Would we go again? In a word, yes. I'd try a different time of day and organise our time outside LaplandUK better but the experience itself was impressive enough to make a return journey.
Thank you LaplandUK, it's been a blast!
This experience gets the full Plums Up!


text:
Q: Dealing with large slowdown when moving PyTorch code to GPU I have a Graph Neural Network model I have written using Pytorch. On my CPU I am not getting fantastic performance, so I tried to port it over to a V100 GPU I have access to. In this process, I have received a huge performance decrease (around 10times slower).
I have two ideas of where might be the issue, but I would like some input to try get the optimum performance from my model. The first problem might be coming from my custom graph convolutional layer:
class GraphConvLayer(torch.nn.Module):
    """
    Based, basically, on https://arxiv.org/abs/1609.02907
    Have some modifications:
    https://towardsdatascience.com/how-to-do-deep-learning-on-graphs-with-graph-convolutional-networks-7d2250723780
    This helped:
    https://pytorch.org/docs/master/notes/extending.html

    """
    def __init__(self, input_features, output_features, device, bias=True):
        super(GraphConvLayer, self).__init__()

        self.input_features = input_features
        self.output_features = output_features
        self.device = device

        self.weight = nn.Parameter(torch.FloatTensor(self.input_features, self.output_features))

        if bias:
            self.bias = nn.Parameter(torch.FloatTensor(self.output_features))
        else:
            self.register_parameter('bias', None)

        # Not a very smart way to initialize weights
        self.weight.data.uniform_(-0.1, 0.1)
        if bias is not None:
            self.bias.data.uniform_(-0.1, 0.1)

    def forward(self,input, adj):
        # Here, we put in the forward pass:
        # Our forward pass needs to be:
        # D^-1 * (A + 1) * X * weights
        input, adj = input.float(), adj.float()

        Identity = torch.eye( len(adj[0]), device = self.device)
        A_hat = adj + Identity

        D = torch.sum(A_hat, dim=0)
        len_D = len(D)
        zero = torch.zeros(len_D,len_D, device = self.device)
        mask = torch.diag(torch.ones_like(D, device = self.device))
        D = mask*torch.diag(D) + (1. - mask)*zero

        D_inv = torch.inverse(D)
        out = torch.mm(input, self.weight)
        out = torch.spmm(A_hat,out)
        out = torch.spmm(D_inv, out)

        if self.bias is not None:
            return out + self.bias
        else:
            return out

        return out

    def extra_repr(self):
        # (Optional)Set the extra information about this module. You can test
        # it by printing an object of this class.
        return 'node_features={}, length of weights={}, bias={}'.format(
            self.node_features, self.input_features, self.bias is not None
        )

Specifically, in the forward pass I am doing a selection of transformations that are described in the towardsdatascience link in the class. Is there something here that is causing this large slow-down? It seems to me that the tensors are all being initialised on the GPU.
Secondly, as all my graphs are different sizes I am being forced into using a batch size of 1. In my training loop I have this:
        for batch in tqdm(train_loader):
            opt.zero_grad()
            adjacency, features, _, nodes = batch
            adjacency = adjacency.to(device)
            features = features.to(device)
            nodes = nodes.to(device)

            output = model(features[0], adjacency[0])

            loss = F.nll_loss(output, nodes[0])
            loss.backward()
            opt.step()

This means (as I interpret it) that every single piece of data is being moved to the GPU individually, every loop. This seems like an obvious cause of inefficiency. Is there a way to move all the data into GPU memory at once, outside the training loop, allowing me to remove the adjacency = adjacency.to(device) lines?
Any help would be really appreciated.

A: Your problem is almost guaranteed to be bound by the memory movement to the GPU, especially since you mention your singular batches.
The only ways that may help you speed up the current implementation might be to look into memory maps, which we are not able to see whether or not you are already using them based on the provided code.
Other than that, even with differently sized adjacency matrix, padding might be a valid strategy, if you manage to sort your batches by somewhat equal sizes.
Your forward() function is also clearly not optimized and might be able to deliver some sort of speedup, but I would expect optimization towards better batching to be of much greater improvement.

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction}
\label{sec1}
Early-type galaxies show a large variety in spatial and kinematic
structure \citep[e.g.,][and references
therein]{1996ApJ...464L.119K,2011MNRAS.414..888E}.  Among early types
with typical luminosities ($L^*$) or stellar masses, most have
disk-like properties in that they are axisymmetric, rotating and
intrinsically flat, even though their light profiles are significantly
more concentrated than those of late-type, star-forming $L_*$
galaxies.  More massive early-type galaxies are rounder, triaxial, and
slowly rotating.  Given these fundamental differences, one may surmise
that disk-like and spheroid-dominated galaxies have different
evolutionary paths and formation mechanisms.  Here we empirically
address this issue by analyzing the shape distribution of early-type
galaxies as a function of redshift.  Our reconstruction of the
internal structure of early-type galaxies at different cosmic epochs
will provide insight into the assembly history of massive, triaxial
galaxies as well as the evolutionary path of less massive, disk-like
early-type galaxies.

The internal structure of galaxies has been studied by means of analyzing projected shape distributions for several decades.  Early on, axisymmetric structure was assumed to describe the three-dimensional light profile of galaxies, that is, the projection of simple oblate and prolate models was used \citep{1926ApJ....64..321H, 1970ApJ...160..831S, 1978MNRAS.183..501B, 1983AJ.....88.1626F}. Then the triaxial model family \citep{1977ApJ...213..368S, 1985MNRAS.212..767B, 1991ApJ...383..112F} was considered to account for observational evidence that local early-type galaxies are not axisymmetric \citep{1992ApJ...396..445R, 1992MNRAS.258..404L, 1995AJ....110.1039T, 2007ApJ...670.1048K, 2008MNRAS.388.1321P, 2010A&A...521A..71M}. \citet{1996AJ....111.2243T} showed that the projected axis ratio distribution of early-type galaxies is accurately described by a model that consists of an oblate and a triaxial set of objects. Brighter galaxies tend to be more triaxial (non-axisymmetric) than fainter galaxies, which are more axisymmetric and intrinsically flatter \citep{2005ApJ...623..137V}.
This two-component model does not provide a mathematically unique
solution, but is physically plausible, in line with the kinematic
distinction of `fast rotators' and `slow rotators' \citep[e.g.,][]{2011MNRAS.414..888E}.

\citet[hereafter vdW09]{2009ApJ...706L.120V} used stellar masses instead of luminosity, and described the projected axis ratio distribution of early-type galaxies. In addition to enabling a more immediate comparison with galaxy formation models, the use of stellar masses instead of luminosities simplifies the interpretation of evolution with redshift \citep[][hereafter H12]{2012ApJ...749...96H} \citep[also see][]{2009ApJ...693..617H} vdW09 and H12 found that at all redshifts $z\lesssim1$ there is a quite sudden transition in the projected axis ratio distribution at a stellar mass of $\sim10^{11}M_\odot$. At lower masses the projected axis ratio distribution is broad, indicative of a large fraction of disk-like early-type galaxies, which have a ceiling mass of $\sim2\times10^{11}M_\odot$, above which essentially all early-type galaxies are intrinsically round. H12 provide a quantitative analysis by describing the projected axis ratio distribution of early-type galaxies, and its evolution with redshift by the aforementioned two-component model. Overall, they found little evolution between $z=0.8$ and the present. \citet{2011ApJ...730...38V} and \citet[hereafter C13]{2013ApJ...762...83C} extended these studies to higher redshift. They found that massive early-type galaxies at $z\gtrsim 1.5$ are flatter than at the present. Their implied disk-like structures show that these galaxies formed while gas had time to settle into disks.

The vdW09, H12, and C13 samples were selected by (a lack of) star formation activity \citep[also see][]{2007ApJ...655...51W,2009ApJ...691.1879W}.  Such a selection can effectively be used as a proxy for a (visual) morphological classification, as a smooth light profile is the main criterion for the visual classification of an early-type galaxy, which usually corresponds to low star-formation activity \citep[also see][]{2012ApJ...748L..27P}.  A practical advantage of a star formation selection is that it allows for the consistent selection of high-redshift samples, for which visual classification is difficult or impossible.  Furthermore, since we are investigating the evolution of structural properties, the use of structural parameters such as concentration or S\'ersic index to select early-type galaxies are prone to introducing biases.

So far, these results have been rather qualitative. In this paper, we provide a more quantitative description of the internal structure of $z=1-2.5$ early-type galaxies down to $M\sim10^{10}$.
The Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey \citep[CANDELS, ][]{2011ApJS..197...35G,2011ApJS..197...36K}, a 902 orbit Hubble Space Telescope (HST) multi-cycle treasury program, provides high-resolution near-infrared imaging aimed at investigating the structural and morphological properties of galaxies to $z\sim3$ in the rest-frame optical. \citet[hereafter vdW12]{2012ApJS..203...24V} used \texttt{GALFIT} \citep{2010AJ....139.2097P} to measure the global structural parameters of $\sim$ 100,000 galaxies in CANDELS. We draw from this work to construct a sample of 569 $z>1$ early-type galaxies with accurately measured axis ratios.

The structure of this paper is as follows. In Section~\ref{sec2} we describe the data and select our sample of early-type galaxies.
In Section~\ref{sec3} we analyze the structural parameters of early-type galaxies and their evolution since $z\sim2.5$ and as a function of stellar mass. In Section~\ref{sec4} we describe our models to reconstruct the intrinsic shape distribution. In Section~\ref{sec5} we investigate the internal structure of early-type galaxies and its evolution. In Section~\ref{sec6} and \ref{sec7} we discuss and summarize our results.

We use AB magnitudes and adopt the cosmological parameters ($\Omega_M$,$\Omega_\Lambda$,$h$)=(0.27,0.73,0.70) in this paper.

\section{Data}
\label{sec2}

\begin{figure}[ht]
\centering
\includegraphics[width=1.0\columnwidth]{ca_fig_m_h}
\caption{CANDELS $H_{F160W}$ magnitude vs. stellar mass at different redshifts. The red crosses represent early-type galaxies, selected as described in Section~\ref{sec2_3} and illustrated in Figure~\ref{ca_fig_uvj}.  The black symbols represent all galaxies. We adopt $H_{F160W}=24.5$ as our magnitude limit: vdW12 showed that size and shape measurements are better than 10\% down to this limit.  This leads us to adopt a stellar mass limit of $\log(M_*/M_{\odot})>10$, ensuring robust structural parameter estimates for all galaxies in our sample up to $z\sim 2.5$.}
\label{ca_fig_m_h}
\end{figure}

\begin{figure}[ht]
\centering
\includegraphics[width=1.0\columnwidth]{ca_fig_uvj}
\caption{Rest-frame $U-V$ vs.~rest-frame $V-J$ colors for galaxies in four redshift bins.  As shown, e.g., by \citet{2009ApJ...691.1879W}, the black polygons effectively separate star-forming and quiescent galaxies, which we use in this paper to select our early-type sample.  The symbols' color coding corresponds to the S\'ersic index $n$, the symbol size (area) with stellar mass surface density ($M_*/2\pi q R_{\rm{eff}}^2$), and symbol shape with observed, projected axis ratio $q$. The color-color selection separation of early- and
late-type galaxies corresponds well with their structural properties
in the sense that early-type galaxies have high S\'ersic indices and
large surface mass densities.}
\label{ca_fig_uvj}
\end{figure}

\subsection{Multi-wavelength Data and SED Fitting}
\label{sec2_1}
In this paper, we use imaging and multi-wavelength catalogs from CANDELS in
the Great Observatories Origins Deep Survey-South field
\citep[GOODS-S, ][`wide' over 4'$\times$10' and `deep' over 7$\times$10']{2004ApJ...600L..93G}
and Ultra Deep Survey field \citep[UDS; ]['wide' over 9'$\times$24']{2007MNRAS.379.1599L}.
The deep near-infrared HST survey allows us to select early-type galaxies up to $z=2.5$.
The details of the multi-wavelength catalogs are described in Guo et al., (2013, GOODS-S), \citet[][UDS]{2013ApJS..206...10G}, and \citet[][IRAC SEDS catalog]{2013ApJ...769...80A}.

The method and algorithms for acquiring photometric redshifts, rest-frame colors and stellar masses
are described by \citet{2011ApJ...742...96W}.
Briefly, photometric redshifts are estimated
by EAzY \citep{2008ApJ...686.1503B} and available
spectroscopic redshifts are included.
The stellar masses, star-formation rates, and rest-frame colors
are estimated by FAST \citep{2009ApJ...700..221K}.
The \citet{2003MNRAS.344.1000B} model,
and a \citet{2003PASP..115..763C} stellar initial mass function is adopted.
A range of ages, star formation histories and extinction
parameters is explored.

\subsection{Galaxy Structural Parameters}
\label{sec2_2}
The structural parameters (radii, S\'ersic indices and projected axis ratios) are taken from vdW12 who fit single S\'ersic profiles to individual galaxies with \texttt{GALFIT}.
Many of the galaxies in our sample are very small ($\sim$ 1kpc), close to the resolution limit. If the point spread function (PSF) is precisely known, this is not a problem as shown by vdW12, at least under the assumption that the characterization of the light profile by a single S\'ersic component is reasonable. In order to test the sensitivity of our results to errors in the PSF model, we refit our sample with the `wrong' PSF: if we convolve the S\'ersic profile with the F125W PSF model in order to fit the F160W images, the resulting axis ratios are larger, but not to the extent that our results are affected. Since we know the F160W PSF with much better accuracy than the $\sim 15\%$ difference between the F125W and F160W PSFs (FWHM$_{F125W}\sim0''.20$; FWHM$_{F160W}\sim0''.17$), we conclude that errors in our PSF model do not affect our results.

\subsection{Sample Selection}
 \label{sec2_3}
Combining the multi-wavelength and structure parameter catalogs, we have an initial sample of 56,010 objects (21,889 in GOODS-S and 34,121 in UDS).
Size and shape measurements are accurate and precise to 10\% for galaxies with $H_{F160W}\sim24.5$ (see vdW12).
We adopt a stellar mass limit of $M=10^{10}M_\odot$, which allows us to consistently compare galaxies at all redshift $z<2.5$ (see  Figure~\ref{ca_fig_m_h}). We reject stars by including only objects with $J-H>0.15$.  We only include galaxies with good {\texttt GALFIT} fits (flag=0; 87\% of the remaining sample) from the vdW12 catalog and ignore 13\% with suspect fits (flag=1) or bad fits (flag=2).  This mass-selected sample with reliable structure measurements consists of 2,827 objects.

\setcounter{footnote}{0}

To separate quiescent galaxies from star-forming galaxies, we use color-color selection criteria as shown in Figure~\ref{ca_fig_uvj},
following: $(U-V)>0.88\times(V-J)+0.49$, $(U-V)>1.3$ and $(V-J)<1.6$.
\footnote{To compute the rest-frame $U$, $V$, and $J$ band fluxes, we use the $UX$ and $V$ Bessell filters and the Palomar $J$ filter.}
We define these as early-type galaxies and the remainder as late-types.
This approach follows the technique outlined by, \citet[e.g.,][]{2009ApJ...691.1879W},
but the color selection criteria are slightly different to account for differences
in filter transmission curves and small offsets in the flux measurements.
In Figure~\ref{ca_fig_uvj} it can be seen that this star-formation activity- based selection corresponds well with the S\'ersic index, indicating that our selection by star formation activity is effectively equivalent to a concentration-based definition of early type \citep[also see][]{2008ApJ...682..355B,2011ApJ...742...96W,2012ApJ...753..167B,2012ApJ...753..114W} over the full redshift range probed here. As noted before, star-formation activity is strongly anti-correlated with S\'ersic index and surface mass density, up to at least $z=2.5$.
Even though in this paper we emphasize the diskiness
of early-type galaxies,  it is also apparent in Figure~\ref{ca_fig_uvj} that
late-type galaxies are still flatter, that is, more disk-like, than early-type galaxies at all redshifts.

The final sample of mass-selected early-type galaxies with reliable (flag=0) structure measurements consists of 880 galaxies in the redshift range $0.6<z<2.5$.
The numbers of galaxies in different redshift bins are shown in Table~\ref{number}.
We create three stellar mass bins for CANDELS with a roughly equal number of galaxies.

\begin{table}[ht]
\caption{Sample Sizes}
\label{number}
\centering
\begin{tabular}{|c|c|ccc|}
\hline
$\log(M_*/M_\odot)$  & $10.1-11.5$ & $10.8-11.5$& $10.5-10.8$ & $10.1-10.5$ \\
\hline
Redshift  &  \multicolumn{4}{c|}{Numbers} \\
\hline
SDSS & 32842 & 13640 & 13991 & 5211 \\
H12 & 1321 & 384 & 475 & 462\\
$1<z<2.5$ & 569 & 197 & 168 & 204 \\
$0.6<z<0.8$ & 220 & 47 & 67 & 106 \\
$0.8<z<1.3$ & 256 & 78 & 66 & 112 \\
$1.3<z<1.8$ & 244 & 88 & 71 & 85 \\
$1.8<z<2.5$ & 147 & 55 & 47 & 45 \\
\hline
\end{tabular}
\end{table}

The SDSS sample from H12 is used as a low-redshift benchmark. Here, the early-type galaxies are selected by an equivalent color-color criterion.
We verified that rejecting all SDSS color-color selected early-type
galaxies with detected $H\alpha$ emission ($\sim 18\%$ of the sample)
does not change our results. Even though the galaxies with detected
emission lines are on average somewhat flatter than their counterparts
without emission lines, the axis ratio distribution analyzed in the
subsequent sections is not significantly altered.

Sufficiently deep emission-line data are not available for the
galaxies in CANDELS. Instead, we search for detections in public MIPS
24$\mu$m imaging in the
UDS\footnote{http://irsa.ipac.caltech.edu/data/SPITZER/SpUDS} and
cataloged MIPS 24$\mu$m flux measurements from \citet{2008ApJ...682..985W} in
GOODS-S.  Removing the $3\sigma$ detected objects ($\sim 16\%$) does
not change the projected axis ratio distributions significantly.  We
conclude that the evolutionary trends with redshift are not sensitive
to the inclusion of contaminating populations of star-forming galaxies
and/or active galactic nuclei.

\begin{figure}[ht]
\centering
\includegraphics[width=1.0\columnwidth]{ca_fig_m_q}
\caption{Projected axis ratio vs. stellar mass for early-type galaxies in CANDELS in four redshifts bins. The symbols' color coding corresponds to the S\'ersic index $n$, the symbol size represents the radius in kiloparsecs. High-mass early-type galaxies are rounder and have higher S\'ersic indices than low-mass early-type galaxies, but these trends apparently weaken at $z\sim 2$.  At all redshifts, flatter galaxies have lower S\'ersic indices, indicating that the population exists of a mix of different types of galaxies, and that variation in projected shape is not only the result of different viewing angles.  The thin vertical lines indicate the mass bins that we use in this paper,} and are chosen to contain similar numbers of galaxies.
\label{ca_fig_m_q}
\end{figure}
\begin{figure}[ht]
\centering
\includegraphics[width=1.0\columnwidth]{ca_fig_z_evolution}
\caption{Evolution of the projected axis ratios for galaxies in three mass bins (color coding). The filled symbols are median values of previously published results.  The dashed lines represent fits to the redshift-axis ratio distribution of the individual objects in the CANDELS sample, anchoring to the median axis ratio of present-day galaxies.  The shaded area indicates the $1-\sigma$ uncertainty. See the text for details on the fitting method.  The most significant evidence for evolution is seen for the massive galaxies: these are progressively flatter at higher redshift.}
\label{ca_fig_z_evolution}
\end{figure}
\begin{figure*}[ht]
\centering
\includegraphics[width=0.9\textwidth]{ca_fig_q_hist}
\caption{Redshift evolution of the projected axis ratio distributions in different mass bins.  The top row of panels shows cumulative distributions; the bottom row shows binned histograms.  The colored lines and histograms represent the $1<z<2.5$ CANDELS early-type galaxy sample; the gray/black lines represent the present-day early-type galaxy sample from SDSS.  The right most panels combine the cumulative histograms for the present-day sample (top) and high-redshift sample (bottom), separated according to the mass bins. Probabilities that the distributions are consistent with each other from two statistical tests (Kolmogorov-Smirnov and Mann-Whithney) are given in the bottom panels.  The samples high- and low-mass bins show evidence for evolution in opposite directions: whereas high-mass galaxies are flatter at high redshifts, low-mass galaxies are rounder.}
\label{ca_fig_q_hist}
\end{figure*}
\section{Evolution of the projected axis ratio distribution}
\label{sec3}
In Figure~\ref{ca_fig_m_q} we show the axis-ratio distributions of early-type galaxies as a function of stellar mass for a number of redshift bins from $z=0.6$ to $z=2.5$. Half-light radii ($R_{eff}$) and S\'ersic indices ($n$) are represented by varying the symbol size and color coding, respectively.  Over the whole stellar mass range probed here the typical $R_{eff}$ and $n$ increase from $z\sim2.5$ to later times, while non-starforming galaxies with exponential light profiles are rare at all redshifts.  As previously reported by vdW09, H12, and C13, the most massive galaxies are the roundest, which can be seen here in particular at $z\sim 1$; at higher redshifts the probed volume is too small to include a sufficiently large number of very massive galaxies.

The main results presented in this paper can all be qualitatively seen in Figure~\ref{ca_fig_m_q}.  First, as was also shown by C13, there are many flat early-type galaxies with mass $\sim 10^{11} M_{\odot}$ at $z>1$. Second, and contrarily, there are not many flat early-type galaxies with mass $\sim 10^{10} M_{\odot}$ at $z>1$.  The overall tendency is that the dependence of shape on galaxy mass is weak at $z>1$ and strong at $z<1$. To investigate these indications of structural evolution in a quantitative way, we will model the projected axis ratio distributions to infer the intrinsic shape distribution in Section~\ref{sec5}.

But first, we will establish the significance of these trends in a model-independent manner. In Figure~\ref{ca_fig_z_evolution}, we perform least-squares fits to the axis ratios of the full $0.6<z<2.5$ sample separated into three mass bins, anchored by the low-redshift median values from the SDSS sample to which we assign a 0.01 systematic uncertainty (see H12).  The uncertainties on the least-square fits are obtained by bootstrapping the sample and perturbing the photometric redshift ($z_{phot}$) and the projected axis ratio by their measurement uncertainties. Moreover, uncertainties in stellar masses ($M_*$) are included in two steps: first, the perturbation in photometric redshift is propagated ($M_* \propto  (1+z)^4$) and, second, a random mass uncertainty of 0.2 dex \cite[see, e.g., ][]{2006ApJ...652...97V} is included. Figure~\ref{ca_fig_z_evolution} shows that there is significant evolution in the projected axis ratios for massive galaxies, with the projected axis ratios decreasing toward high redshift, and we find marginal evidence for increasing projected axis ratios with redshift for the lowest-mass sample.

We now turn to the full distribution of axis ratios, which, compared to evolution in the average or median, enables more sensitive tests for structural evolution. In Figure~\ref{ca_fig_q_hist}, we compare the axis ratio distributions
of our $1<z<2.5$ early-type galaxies with local early-type galaxies
(see vdW09 and H12) by means of cumulative distributions and of histograms. Figure~\ref{ca_fig_q_hist} shows that for $\log(M_*/M_{\odot})>10.8$, high-redshift
galaxies are flatter (have smaller projected axis ratios) than local
galaxies, while for $\log(M_*/M_{\odot})<10.5$, high-redshift galaxies
are rounder. We use Kolmogorov-Smirnov (K-S) and Mann-Whitney U (M-W)
tests to show that these trends are significant at the $5\sigma$ and
$3\sigma$ level, respectively.  These quantitative comparisons confirm
the hints seen in Figure~\ref{ca_fig_m_q}.

While the flattening of high-mass galaxies is consistent with previous
results \citep[][, and C13]{2011ApJ...730...38V,2012MNRAS.427.1666B,2012ApJ...745..179W,2013MNRAS.428.1460B},
the 3$\sigma$-level evidence that low-mass early types were rounder at earlier epochs is surprising. One could
suspect that systematic shape measurement errors may prevent us
from recovering the actual flatness of the small, faint galaxies in
this sub-sample.  However, the simulations performed by vdW12 indicate
that shapes and sizes can be recovered with high accuracy down to the
regime probed here.  Note, however, that those
simulations were performed with ideal S\'ersic profiles, not with real
galaxy light profiles.  In addition, we can ask whether
mismatches in the PSF model matter.  In
order to test this we rerun the profile fits on the F125W images of
this sub-sample of low-mass early-type galaxies. For this test
we replace the F125W PSF model, which we assume to be accurate,
with the F160W PSF model.  We know that the F160W PSF model is too
broad to describe the light profiles of point sources in the F125W
imaging (by $\sim 15\%$).  Therefore, the projected axis ratio will
now be underestimated (objects will appear flatter than they are).
Even with this crudely wrong PSF model we find that the axis ratios of
the low-mass $z>1$ early types are not flatter than the axis
ratios of their present-day counterparts.  Given that the uncertainty
in our PSF models is much smaller than the difference between the
F125W and F160W PSF models, we can safely conclude that the observed
evolution in the axis ratio distribution for low-mass early-type
galaxies is not due to uncertainties in our PSF models.

Now we proceed in the next two sections to reconstruct the intrinsic structural properties of early-type galaxies as a function of stellar mass and redshift. We explore a variety of approaches that employ different model families and search for solutions by assuming random viewing angle distributions for our samples. In Section~\ref{sec4} we apply an analytical approximation to reconstruct the intrinsic axis ratio distribution of axisymmetric model families. In Section~\ref{sec5} we project model distributions that represent a combination of axisymmetric and triaxial families in order to reproduce the observed distributions of projected axis ratios and to find best-fitting solutions.
\begin{figure*}[ht]
\centering
\includegraphics[width=1.0\textwidth]{ca_fig_deprojections}
\caption{Projected axis ratio ($q$) distributions in gray/black and
deprojected, intrinsic axis ratio ($\gamma$) distributions in
blue/orange, inferred as described in Section~\ref{sec4}. Observed, projected axis ratio distributions (black histograms) are represented by eighth-order polynomials (black lines) and then analytically deprojected according to Equation~(\ref{deproj_1}) to infer the intrinsic shape distribution of axisymmetric model populations (oblate in blue; prolate in orange). The dashed lines below and above the solid lines represent the 16 and 84 percentile confidence intervals obtained from bootstrapping
($n=10,000$).  The vertical lines show the 16, 50, and 84 percentiles
of the deprojected intrinsic axis ratios.  The top row of panels shows present-day early-type galaxies from SDSS; the bottom row shows $1<z<2.5$ early-type galaxies from CANDELS.}
\label{ca_fig_deprojections}
\end{figure*}
\section{Analytical Reconstruction of the Intrinsic Shape Distribution}
\label{sec4}
For an oblate ellipsoid at the origin of a Cartesian coordinate system, the intrinsic shape can be written as $x^2+y^2+z^2/\gamma^2=1$,
where $\gamma$ ($0<\gamma\leq 1$) is the intrinsic axis ratio between the (one) short axis and the (two) long axes. For a prolate ellipsoid, the intrinsic shape can be written as
$x^2/\gamma^2+y^2/\gamma^2+z^2=1$, where $\gamma$ ($0<\gamma\leq 1$) is the intrinsic axis ratio between the (two) short axes and the (one) long axis.
The intrinsic axis-ratio distribution, $\psi(\gamma)$, can be inferred as prescribed by \citet{1983AJ.....88.1626F}:
\begin{subequations}
\begin{align}
& \psi_O(\gamma)=\frac{2}{\pi}\sqrt{1-\gamma^2}\frac{d}{d\gamma}\int^q_0
\frac{\phi_O(q)dq}{\sqrt{\gamma^2-q^2}} \\
& \psi_P(\gamma)=\frac{2}{\pi}\frac{\sqrt{1-\gamma^2}}{\gamma^2}\frac{d}{d\gamma}\int^q_0
\frac{\phi_P(q)q^3 d q}{\sqrt{\gamma^2-q^2}},
\end{align}
\label{deproj_1}
\end{subequations}
where $\phi$ is the projected axis-ratio distribution, and
the subscripts $O$ and $P$ refer to the oblate and prolate case, respectively.
If we describe the projected axis-ratio distribution by a power law ($\phi(q)=(m+1)q^m$ with $m>-1$), we can rewrite
Equation~(\ref{deproj_1}) analytically:
\begin{subequations}
\begin{align}
& \psi_O(\gamma)=\frac{2\gamma^{m-1}\sqrt{1-\gamma^2}}{B(0.5m,1.5)} \\
& \psi_P(\gamma)=\frac{2\gamma^{m}\sqrt{1-\gamma^2}}{B(0.5m+0.5,1.5)},
\end{align}
where $B(x,y)$ is the beta function.
\label{deproj_2}
\end{subequations}
The reconstructed intrinsic axis ratio distribution should be non-negative if an oblate or prolate model is a good description of the data.
\subsection{Application}
\label{sec4_1}
Figure~\ref{ca_fig_deprojections} shows the results of the deprojection outlined above.  We use an eighth-order power law, $\phi(q)=\Sigma^{8}_{m=0} C_m (m+1)q^m$, to describe the observed projected axis ratio distributions (black lines in Figure~\ref{ca_fig_deprojections}).
The dashed lines show the 16 and 84 percentile confidence intervals
obtained from bootstrapping \citep[e.g.,][]{1995AJ....110.1039T,1996AJ....111.2243T,1996ApJ...461..146R,1996ApJ...471..822R}.
The reconstructed intrinsic shape distributions for
the oblate and prolate models (shown in thick blue and orange lines,
respectively) are sometimes slightly negative, but the uncertainties
are such that this can be attributed to the limited sample size.
The distributions are very broad; that is, in narrow ranges of mass, galaxies display a large variety in intrinsic shape, and the population cannot consist of objects that are all similar in intrinsic thickness.  This is true both for present-day galaxies and for $z>1$ galaxies. Changes in the intrinsic shape distribution with redshift mirror changes in the projected shape distribution: high-mass galaxies were on average flatter at $z>1$, and low-mass galaxies were rounder.  Especially for the large, present-day samples, there is a clear hint that multiple components (galaxy populations) are needed to describe the intrinsic shape distribution, which we will explore below.
\section{Projection of Axisymmetric and Triaxial Models}
\label{sec5}
Following \citet{1985MNRAS.212..767B} Equation (11) and (12), we project a triaxial ellipsoid (written as $m^2=x^2/a^2+y^2/b^2+z^2/c^2$, at the origin of Cartesian coordinate system) and compute the projected axis ratio $q$ as follows:
\begin{subequations}
\begin{align}
& A=\frac{\cos^2\theta}{\gamma^2}\Biggl(\sin^2\phi+\frac{\cos^2\phi}{\beta^2}\Biggl)+\frac{\sin^2\theta}{\beta^2} \\
& B=\cos\theta\sin2\phi\Biggl(1-\frac{1}{\beta^2}\Biggl)\frac{1}{\gamma^2} \\
& C=\Biggl(\frac{\sin^2\phi}{\beta^2}+\cos^2\phi\Biggl)\frac{1}{\gamma^2} \\
& q(\theta,\phi;\beta,\gamma)=\sqrt{\frac{A+C-\sqrt{(A-C)^2+B^2}}{A+C+\sqrt{(A-C)^2+B^2}}},
\end{align}
\label{proj_1}
where ($\theta$,$\phi)$ are the polar and azimuthal viewing angles in
a spherical coordinate system, and $\beta=b/a$ and $\gamma=c/a$.  Note
that $\beta=1$ and $\beta=\gamma$ correspond to the special,
axisymmetric cases (oblate and prolate, respectively).
\end{subequations}
In order to account for variations in intrinsic shape, we assume a Gaussian
distribution for the triaxiallity $T$($=[1-\beta^2]/[1-\gamma^2]$) and
ellipticity $E$($=1-\gamma$) with dispersion $\sigma_T$ and
$\sigma_E$.

For a given set of parameters ($T$,$E$,$\sigma_T$,$\sigma_E$), we
numerically generate distributions for $\beta$ and $\gamma$.  Then, a
random viewing angle ($\theta$,$\phi$) is assigned to each of the
elements of the distribution (100,000 in our case) such that with
Equation~(\ref{proj_1}) the projected axis ratio distribution can be
generated.  This distribution corresponds to the probability
distribution $p(q_{model})$.

For nearly round ($q\sim1$) galaxies, random noise will always
cause the measured $q$ to be an underestimate as the position
angle of the long axis becomes ill-determined. This affects the
projected axis-ratio distribution as described by
\citet{1995ApJ...447...82R} (Equation (C5)):
 \begin{equation}
P_e(\epsilon,\epsilon_e,\Delta\epsilon)=\frac{\epsilon}{\Delta\epsilon^2}
I_o\biggl(\frac{\epsilon\epsilon_e}{\Delta\epsilon^2}\biggl)
\exp\biggl(-\frac{\epsilon^2+\epsilon_e^2}{2\Delta\epsilon^2}\biggl),
\label{proj_2}
\end{equation}
where $\epsilon$($=1-q$) is the measured ellipticity,
$\epsilon_e$ is the expected ellipticity, $\Delta\epsilon$ is the
measured error, and $P_e$ is the expected ellipticity distribution.
We numerically implement the difference between $\epsilon$ and
$\epsilon_e$ to correct the generated probability distribution
$p(q_{model})$.  We adopt fixed values $\Delta\epsilon=\Delta
q$ for each of the data sets used here: 0.03 and 0.05 for the
low- and high-$z$ data sets from H12, and 0.04 for the CANDELS data set.

The total likelihood $L$ for a measured set projected axis ratios
$q_{data}$ and a given set of model parameters $T$, $E$, $\sigma_T$,
and $\sigma_E$ is given by $L=\Sigma_{q_{data}} \log
p(q_{data}|q_{model}) $, where $p$ has a minimum value of 0.01.

$L$ is computed for a grid of model parameters, chosen in various ways
for the different approaches explored below, such that the maximum
likelihood model can be located in the grid and the best-fitting model
is identified.

In order to obtain uncertainty estimates on the best-fitting model
parameters, we bootstrap the observed data ($q_{data}$), also
perturbing $q_{data}$ by the measurement uncertainty and perturbing
the redshift and stellar mass estimates as described in Section~\ref{sec3}.
\begin{figure}[ht]
\centering
\includegraphics[width=1.0\columnwidth]{ca_fig_triaxial}
\caption{Histograms show observed distributions of projected axis ratios for present-day early-type galaxies from SDSS (upper row) and at $1<z<2.5$ from CANDELS (bottom row), each in three mass bins.  The colored lines represent the best-fitting, single-component models with Gaussian distributions for intrinsic axis ratios, with the oblate model in blue, the prolate model in orange, and the triaxial model in red. See Section~\ref{sec5_1_1} for details.  The mean and dispersion of the best-fitting Gaussians are listed in Table \ref{model_single}.}
\label{ca_fig_triaxial}
\end{figure}

\subsection{Application}
\label{sec5_1}
\subsubsection{Single-component Model for the Intrinsic Shape}
\label{sec5_1_1}

\begin{table*}[ht]
\caption{Single-component Fitting Results}
\label{model_single}
\centering
\begin{tabular}{|ccc|cccc|cc|}
\hline
Model &  Mass($\log(M_*/M_\odot)$) & Redshift(z) & $T$ \footnote{$T$ is the mean triaxiality parameter, with standard deviation $\sigma_{\rm{T}}$; these are set to 0 or 1 for the oblate and prolate models.} & $\sigma_T$ & $E$ \footnote{$E$ and $\sigma_{E}$ are the ellipticity (1 minus the intrinsic short-long axis ratio) and its standard deviation.} & $\sigma_E$ & $P_{KS}$ \footnote{The final two columns list the K-S and M-W probabilities that the observed and best-fitting model projected axis ratio distributions are indistinguishable, for a randomly drawn realization of the model distribution with the same number of objects as the observed samples.  These serve as a crude goodness-of-fit test.} & $P_{MW}$ \\
\hline
\multicolumn{9}{|c|}{Single oblate model} \\
\hline
Oblate & 10.8-11.5 & 0.04-0.08 (SDSS) & 0 & 0 & $0.48\pm0.01$ \footnote{Uncertainties are obtained from bootstrapping.} & $0.18\pm0.01$ & *0.00* \footnote{The asterisks (*) represent the significant probability is smaller than 5\%. It implies that the distributions are distinguishable.}& *0.01*\\
Oblate & 10.5-10.8 & 0.04-0.08 (SDSS) & 0 & 0 &  $0.61\pm0.00$ & $0.18\pm0.00$ & *0.00* & *0.01*\\
Oblate & 10.1-10.5 &  0.04-0.06 (SDSS) & 0 & 0 & $0.66\pm0.01$ & $0.13\pm0.01$ & *0.00* & 0.16\\
\hline
Oblate & 10.8-11.5 & 0.6-0.8 (H12) & 0 & 0 & $0.46\pm0.03$ & $0.17\pm0.03$  & 0.21 & 0.20\\
Oblate & 10.5-10.8 & 0.6-0.8 (H12) & 0 & 0 & $0.58\pm0.04$ & $0.17\pm0.04$ & 0.24 & 0.46\\
Oblate & 10.1-10.5 & 0.6-0.8 (H12) & 0 & 0 & $0.58\pm0.03$ & $0.14\pm0.03$  & 0.12 & 0.13\\
\hline
Oblate & 10.8-11.5 & 1-2.5 & 0 & 0 & $0.61\pm0.03$ & $0.18\pm0.03$ & 0.99 & 0.45\\
Oblate & 10.5-10.8 & 1-2.5 & 0 & 0 & $0.59\pm0.04$ & $0.14\pm0.03$  & 0.69 & 0.26\\
Oblate & 10.1-10.5 &  1-2.5 &  0 & 0 & $0.56\pm0.03$ & $0.15\pm0.03$ &  0.41 & 0.34\\
\hline
\multicolumn{9}{|c|}{Single prolate model} \\
\hline
Prolate & 10.8-11.5 & 0.04-0.08 (SDSS) & 1 & 0 & $0.37\pm0.00$ & $0.18\pm0.00$ & *0.00* & 0.34\\
Prolate & 10.5-10.8 & 0.04-0.08 (SDSS) & 1 & 0 & $0.45\pm0.00$ & $0.20\pm0.01$ & *0.00* & 0.07\\
Prolate & 10.1-10.5 &  0.04-0.06 (SDSS) & 1 & 0 & $0.47\pm0.00$ & $0.20\pm0.00$ & *0.00* & 0.35\\
\hline
Prolate & 10.8-11.5 & 0.6-0.8 (H12) & 1 & 0 & $0.36\pm0.02$ & $0.17\pm0.02$& 0.70 & 0.26\\
Prolate & 10.5-10.8 & 0.6-0.8 (H12) & 1 & 0 & $0.42\pm0.03$ & $0.20\pm0.02$ & 0.29 & 0.35\\
Prolate & 10.1-10.5 & 0.6-0.8 (H12) & 1 & 0 & $0.45\pm0.02$ & $0.17\pm0.02$ & 0.24 & 0.41\\
\hline
Prolate & 10.8-11.5 & 1-2.5 & 1 & 0 & $0.44\pm0.03$ & $0.21\pm0.02$ &  0.90 & 0.48\\
Prolate & 10.5-10.8 & 1-2.5 & 1 & 0 & $0.45\pm0.02$ & $0.17\pm0.02$ & 0.55 & 0.37\\
Prolate & 10.1-10.5 &  1-2.5 &  1 & 0 & $0.43\pm0.02$ & $0.17\pm0.02$ & 0.61 & 0.47\\
\hline
\multicolumn{9}{|c|}{Single triaxial model} \\
\hline
Triaxial & 10.8-11.5 &  0.04-0.08 (SDSS) & $0.60^{+0.00}_{-0.08}$ & $0.16^{+0.00}_{-0.12}$ & $0.45^{+0.02}_{-0.00}$ & $0.23^{+0.00}_{-0.01}$ & *0.03* & 0.15\\
Triaxial & 10.5-10.8 & 0.04-0.08 (SDSS) &  $0.92^{+0.00}_{-0.92}$ & $0.00^{+0.66}_{-0.00}$ & $0.47^{+0.16}_{-0.00}$ & $0.24^{+0.00}_{-0.06}$ & *0.00* & 0.12\\
Triaxial & 10.1-10.5 & 0.04-0.06 (SDSS) &  $0.92^{+0.02}_{-0.92}$ & $0.00^{+0.24}_{-0.00}$ & $0.50^{+0.17}_{-0.00}$ & $0.26^{+0.00}_{-0.11}$ & *0.03* & 0.13\\
\hline
Triaxial & 10.8-11.5 & 0.6-0.8 (H12) & $0.76^{+0.00}_{-0.62}$ & $0.92^{+0.00}_{-0.92}$ & $0.44^{+0.06}_{-0.05}$ & $0.20^{+0.05}_{-0.04}$ & 0.82 & 0.34\\
Triaxial & 10.5-10.8 & 0.6-0.8 (H12) & $0.92^{+0.00}_{-0.72}$ & $0.00^{+0.06}_{-0.00}$ & $0.43^{+0.20}_{-0.00}$ & $0.25^{+0.09}_{-0.06}$ & 0.39 & 0.18\\
Triaxial & 10.1-10.5 & 0.6-0.8 (H12)  & $0.92^{+0.04}_{-0.88}$ & $0.00^{+0.28}_{-0.00}$ & $0.47^{+0.18}_{-0.00}$ & $0.21^{+0.04}_{-0.09}$ &  0.40 & 0.26\\
\hline
Triaxial & 10.5-10.8 & 1-2.5 & $0.00^{+0.72}_{-0.00}$ & $0.20^{+0.08}_{-0.20}$ & $0.61^{+0.05}_{-0.10}$ & $0.13^{+0.06}_{-0.05}$ & 0.53 & 0.38\\
Triaxial & 10.8-11.5 &  1-2.5 &  $0.92^{+0.04}_{-0.82}$ & $0.00^{+0.04}_{-0.00}$ & $0.47^{+0.17}_{-0.03}$ & $0.26^{+0.02}_{-0.11}$ & 0.75 & 0.33\\
Triaxial & 10.1-10.5 & 1-2.5 & $0.00^{+0.80}_{-0.00}$ & $0.52^{+0.00}_{-0.52}$ & $0.56^{+0.05}_{-0.07}$ & $0.17^{+0.07}_{-0.03}$ & 0.70 & 0.47\\
\hline
\end{tabular}
\end{table*}

For each of the SDSS (vdW09), COSMOS/GEMS (H12), and CANDELS data sets we search for
the best-fitting triaxial model as described above on a grid spaced as
($\Delta T$, $\Delta \sigma_T$, $\Delta E$, $\Delta \sigma_E$)=(0.04,
0.04, 0.01, 0.01). We separately consider the two special cases:
oblate, with $T=0$ and $\sigma_T=0$; and prolate, with $T=1$ and
$\sigma_T=0$.  As before, the samples are analyzed in bins of stellar
mass and redshift.  The results are given in Table~\ref{model_single}
and a subset are shown in Figure~\ref{ca_fig_triaxial}.  For each best-fitting model we
estimate the goodness-of-fit by computing the K-S and M-W probabilities that the observed $q_{data}$
represent a population of galaxies with a projected axis ratio
distribution $q_{model}$.
Note that our fitting method does not aim to maximize the
probabilities given by these goodness-of-fit indicators.

As noted by H12, the axis ratio distribution of
present-day early-type galaxies cannot generally be accurately
described by a single-component model with Gaussian distributions for
the intrinsic parameters.  The one exception is that massive
early-type galaxies ($\log(M_*/M_{\odot})>10.8$) quite closely resemble a
single, highly triaxial population ($T=0.6$).
At all redshifts up to $z=2.5$
no prolate model fits the data, while an oblate model cannot be ruled
out.  The oblate model fitting results reflect the previously
mentioned evolution in the median axis ratio: the intrinsic
ellipticity for the most massive galaxies increases from $E=0.48$ at
$z<0.1$ to $E= 0.61$ at $z>1$, while it decreases from $E=0.66$ to
$E=0.56$ for galaxies in the mass range
$10.1<\log(M_*/M_{\odot})<10.5$.

\subsubsection{Two-component Model for the Intrinsic Shapes}
\label{sec5_1_2}
\begin{figure*}[ht]
\centering
\includegraphics[width=1.0\textwidth]{ca_fig_par3_pie}
\caption{Histograms show observed distributions of projected axis ratios for present-day early-type galaxies from SDSS (upper row) and at $1<z<2.5$ from CANDELS (bottom row), each in three mass bins.  The green lines represent the best-fitting, two-component models with Gaussian distributions for intrinsic axis ratios as described in Section~\ref{sec5_1_2}. The dashed pink lines respresent the triaxial component; the dotted blue lines represent the oblate component.  The parameters characterizing the Gaussians are given in Tables~\ref{model_sdss} and \ref{model_two}.  The small pie charts represent $f_{ob}$, the oblate fraction, and its uncertainty.  For the CANDELS sample, the triaxial components are assumed to be identical to the best-fitting triaxial components found for the SDSS sample in the same mass bin.  The strong dependence of the oblate fraction on galaxy mass is much weakened at $z>1$.  The most striking feature is the large fraction of oblate, that is, disk-like galaxies in the high-mass bin.}
\label{ca_fig_par3_pie}
\end{figure*}

Because the single-component models with Gaussian distributions for
the intrinsic shape parameters cannot reproduce the shape distribution
of the low-redshift sample, we now explore a different approach.
As shown most recently by H12, a two-component model can accurately
describe the axis-ratio distribution of present-day early-type
galaxies over a large range in mass.  One of these components is
triaxial, precisely of the form used above; the other component is
oblate, with a normally distributed intrinsic axis ratio, with mean
$b$ and standard deviation $\sigma_b$.  Thus, we now have six parameters
that describe the intrinsic shape distribution; the seventh free parameter
is the fraction assigned to the oblate component ($f_{ob}$).  The
spacing of the grid we now use to search for the best-fitting model is
($\Delta f_{ob}$, $\Delta T$, $\Delta \sigma_T$, $\Delta E$, $\Delta
\sigma_E$, $\Delta b$, $\Delta \sigma_b$)=(0.04, 0.04, 0.02, 0.01,
0.01, 0.01, 0.01, 0.01).

\begin{table*}[ht]
\caption{Double-component Fitting Results for $z=0$}
\label{model_sdss}
\centering
\begin{tabular}{|cc||ccccccc|cc|}
\hline
Mass & redshift(z) &  $f_{ob}$ \footnote{$f_{\rm{ob}}$ is the fraction of the oblate component.} & $b$ \footnote{$b$ the intrinsic axis ratio of the oblate component and $\sigma_b$ its standard deviation.} & $\sigma_b$ & $T$ \footnote{$T$ is the mean triaxiality parameter, with standard deviation $\sigma_{\rm{T}}$; these are set to 0 or 1 for the oblate and prolate models.}& $\sigma_T$ & $E$ \footnote{$E$ and $\sigma_{E}$ are the ellipticity (1 minus the intrinsic short-long axis ratio) and its standard deviation.}  & $\sigma_E$  & $P_{KS}$ \footnote{The final two columns list the K-S and M-W probabilities that the observed and best-fitting model projected axis ratio distributions are indistinguishable, for a randomly drawn realization of the model distribution with the same number of objects as the observed samples.  These serve as a crude goodness-of-fit test.} & $P_{MW}$ \\
\hline
10.8-11.5 & 0.04-0.08 (SDSS) & $0.20\pm0.02$ \footnote{Uncertainties are obtained from bootstrapping.} & $0.29\pm0.02$ & $0.07\pm0.01$ & $0.64\pm0.06$ & $0.08\pm0.05$ & $0.41\pm0.02$ & $0.19\pm0.02$& 0.26 & 0.46\\
10.5-10.8 & 0.04-0.08 (SDSS) & $0.56\pm0.06$ & $0.28\pm0.01$ & $0.08\pm0.01$ & $0.68\pm0.12$ & $0.08\pm0.06$ & $0.45\pm0.02$ & $0.16\pm0.03$ & 0.29 & 0.19\\
10.1-10.5 & 0.04-0.06 (SDSS) & $0.72\pm0.06$ & $0.28\pm0.01$ & $0.09\pm0.01$ & $0.48\pm0.08$ & $0.08\pm0.06$ & $0.49\pm0.02$ & $0.12\pm0.02$  & 0.84 & 0.28 \\
\hline
\end{tabular}
\end{table*}

The two-component approach results in a very good description of the
observed axis ratio distributions of present-day galaxies (see Table~\ref{model_sdss}
and Figure~\ref{ca_fig_par3_pie}).  The goodness-of-fit indications from the K-S and M-W
statistical tests suggest that the best-fitting models provide a
realistic view of the intrinsic shape distribution.  Over the entire
galaxy mass range, a highly triaxial ($T\sim 0.6$), yet flattened
($E\sim 0.45$), component combined with an even flatter ($b\sim 0.3$)
oblate component provides a good description of the data, with little
variation in these shape parameters with galaxy mass.  The parameter
that captures the strong mass-dependence in galaxy structure is
$f_{ob}$, the fraction assigned to the second, oblate component: it
rises from $f_{ob} = 0.20\pm 0.02$ at high mass to $f_{ob} = 0.72\pm
0.06$ at low mass.

These results are very similar to those presented by H12 -- small
differences occur due the choice of different stellar mass bins as
well as a different implementation of the intrinsic variation in the
shape parameters -- the $\sigma$ parameters -- in generating the
probability distributions $p(q_{model})$.

\begin{table*}[ht]
\caption{Double-component Fitting Results for $z=0.6-2.5$}
\label{model_two}
\centering
\begin{tabular}{|cc||ccc|cc||c|cc|}
\hline
\multirow{2}{*}{Mass}  & \multirow{2}{*}{Redshift(z)}
& \multicolumn{5}{c||}{Oblate Parameters Free \footnote{Fix triaxial component in the same stellar mass bins as local galaxies.} } &
\multicolumn{3}{c|}{Oblate Fraction Free \footnote{Fix other parameters in the same stellar mass bins as local galaxies.} }
 \\
 \cline{3-10}
 & &  $f_{ob}$ \footnote{$f_{\rm{ob}}$ is the fraction of the oblate component.} & $b$ \footnote{$b$ the intrinsic axis ratio of the oblate component and $\sigma_b$ its standard deviation.} & $\sigma_b$  & $P_{KS}$ \footnote{The final two columns list the K-S and M-W probabilities that the observed and best-fitting model projected axis ratio distributions are indistinguishable, for a randomly drawn realization of the model distribution with the same number of objects as the observed samples.  These serve as a crude goodness-of-fit test.} & $P_{MW}$  &  $f_{ob}$  & $P_{KS}$ & $P_{MW}$ \\
\hline
10.8-11.5 & 0.6-0.8 (H12) & $0.16\pm0.18$  \footnote{Uncertainties are obtained from bootstrapping.} & $0.33\pm0.10$ & $0.05\pm0.08$  & 0.70 & 0.36 & $0.12\pm0.06$& 0.43 & 0.26 \\
10.5-10.8 & 0.6-0.8 (H12) & $0.48\pm0.23$ & $0.28\pm0.07$ & $0.05\pm0.06$ &  0.21 & 0.24&  $0.49\pm0.08$& 0.22 & 0.24\\
10.1-10.5 & 0.6-0.8 (H12) & $0.56\pm0.12$ &  $0.32\pm0.03$ & $0.06\pm0.04$ & 0.87 & 0.36 &  $0.51\pm0.08$& 0.67 & 0.38\\
\hline
10.8-11.5 & 1-2.5 & $0.60\pm0.24$ & $0.27\pm0.07$ & $0.06\pm0.05$  & 0.71 & 0.49 & $0.59\pm0.10$& 0.54 & 0.40\\
10.5-10.8 & 1-2.5 & $0.60\pm0.25$ & $0.31\pm0.07$ & $0.07\pm0.03$ & 0.87 & 0.37 & $0.53\pm0.14$& 0.61 & 0.33\\
10.1-10.5 & 1-2.5 & $0.52\pm0.24$ & $0.34\pm0.10$ & $0.12\pm0.06$  & 0.69 & 0.46 & $0.38\pm0.11$& 0.12 & 0.16\\
\hline
\multicolumn{10}{|c|}{Redshift Bins of CANDELS} \\
\hline
10.8-11.5 & 0.6-0.8 & $1.00\pm0.31$ & $0.52\pm0.13$ & $0.25\pm0.10$  & 0.96 & 0.44 & $0.35\pm0.20$ & 0.25 & 0.29\\
10.8-11.5 & 0.8-1.3 & $0.84\pm0.21$ & $0.29\pm0.05$ & $0.06\pm0.05$  & 0.99 & 0.50 & $0.81\pm0.20$ & 0.97 & 0.44\\
10.8-11.5 & 1.3-1.8 & $0.48\pm0.28$ & $0.22\pm0.08$ & $0.05\pm0.07$  & 0.89 & 0.46 & $0.59\pm0.16$ & 0.73 & 0.48\\
10.8-11.5 & 1.8-2.5 & $1.00\pm0.27$ & $0.41\pm0.09$ & $0.20\pm0.07$  & 0.97 & 0.44 & $0.51\pm0.21$ & 0.94 & 0.45\\
\hline
10.5-10.8 & 0.6-0.8 & $0.36\pm0.31$ & $0.27\pm0.10$ & $0.05\pm0.09$ & 0.92& 0.46 & $0.42\pm0.24$ & 0.89 & 0.49\\
10.5-10.8 & 0.8-1.3 & $1.00\pm0.28$ & $0.40\pm0.07$ & $0.16\pm0.07$ & 0.99 & 0.49 & $0.53\pm0.27$ & 0.87 & 0.48\\
10.5-10.8 & 1.3-1.8 & $0.64\pm0.31$ & $0.30\pm0.10$ & $0.05\pm0.08$ & 0.67 & 0.30 & $0.63\pm0.24$ & 0.66 & 0.31\\
10.5-10.8 & 1.8-2.5 & $0.56\pm0.32$ & $0.29\pm0.09$ & $0.05\pm0.03$ & 0.93 & 0.39 & $0.55\pm0.28$ & 0.92 & 0.38\\
\hline
10.1-10.5 & 0.6-0.8 & $0.56\pm0.28$ & $0.26\pm0.09$ & $0.05\pm0.08$ & 0.63 & 0.32 & $0.57\pm0.19$ & 0.68 & 0.37\\
10.1-10.5 & 0.8-1.3 & $0.84\pm0.26$ & $0.46\pm0.08$ & $0.17\pm0.10$ & 0.97 & 0.45 & $0.31\pm0.18$ & 0.41 & 0.28\\
10.1-10.5 & 1.3-1.8 & $0.44\pm0.36$ & $0.23\pm0.12$ & $0.19\pm0.10$  & 0.37 & 0.19 & $0.47\pm0.20$ & 0.94 & 0.42\\
10.1-10.5 & 1.8-2.5 & $0.80\pm0.28$ & $0.31\pm0.10$ & $0.05\pm0.06$  & 0.47 & 0.28 & $0.71\pm0.35$ & 0.82 & 0.46\\
\hline
\end{tabular}
\end{table*}

The high-redshift samples are too small to be treated with seven
independent free parameters. However, given the success of the
two-component model in describing the shape distribution of
present-day early-type galaxies, we can use our superior knowledge of
the low-redshift population to inform the model for the high-redshift
population. Because each of the two components are very similar across
the mass range explored here for the low-redshift sample, we assume
that the same components can be used as an appropriate model to
describe the higher-redshift observations.  First, we use the
best-fitting triaxial component for each of the three mass bins, with
fixed intrinsic shape distributions, but let the oblate component vary
arbitrarily.  That is, the parameters $b$, $\sigma_b$, and $f_{ob}$ are
allowed to vary, while the others are kept fixed.  The results are
shown in Table~\ref{model_two} and Figure~\ref{ca_fig_par3_pie}.

For the COSMOS+GEMS and combined ($1<z<2.5$) CANDELS samples we find
that all evolution with redshift can be accounted for by evolution in
$f_{ob}$; no significant changes in $b$ (or $\sigma_b$) are seen.  For
the highest-mass galaxies ($10.8<\log(M_*/M_{\odot})<11.5$) $f_{ob}$ is seen to rise at $z>1$, from
$f_{ob}\sim 0.2$ at $z<1$ to $f_{ob}=0.60\pm 0.24$.  The large
uncertainty is due to the degeneracy between $b$ and $f_{ob}$:
evolution in the average shape can either be accommodated by a change
in the average shape of the galaxies represented by the oblate
component, or by a change in the fraction of oblate galaxies.  The
unsubstantial changes in $b$ ($\sigma_b$) with mass and redshift
motivate us to implement a second restriction to our model: we now
keep all intrinsic shape parameters at the values found for the
low-$z$ SDSS sample, and only allow $f_{ob}$ to vary.

\begin{figure}[ht]
\centering
\includegraphics[width=1.0\columnwidth]{ca_fig_pie}
\caption{The evolution of the oblate fraction of early-type galaxies in different mass bins.  Compared to the results shown in Figure~\ref{ca_fig_par3_pie}, the redshift bins at $z>1$ are now narrower, as indicated, and the intrinsic shape distributions of both the oblate and the triaxial component are kept fixed at the values found for the present-day SDSS sample.  The values of $f_{ob}$ and their uncertainties are given in Table~\ref{model_two}.}
\label{ca_fig_pie}
\end{figure}

This restriction seems justified by the results from the
goodness-of-fit tests: the predicted distribution from the
best-fitting models, even with only a single free parameter
($f_{ob}$), do not significantly differ from the observed
distributions according the the the K-S and M-W tests.
The results are also shown in Table~\ref{model_two} and Figure~\ref{ca_fig_pie}.
We now find that the oblate fraction for the massive galaxies increases from $0.20\pm0.02$
at $z<0.1$ to $0.59\pm0.10$ at $z>1$, a highly significant (4$\sigma$)
change. For galaxies in our middle mass bin ($10.5<\log(M_*/M_{\odot})<11.8$), $f_{ob}$ does not
change with redshift and stays at $\sim 0.5-0.6$, whereas, remarkably,
$f_{ob}$ significantly declines from $0.72\pm0.06$ to $0.38\pm0.11$
for low-mass galaxies ($10.1<\log(M_*/M_{\odot})<10.5$).  The latter was already reflected by the
increased median axis ratio with redshift (see Section~\ref{sec3}).

\section{Discussion}
\label{sec6}
$L^*$ early-type galaxies ($M_*\sim 10^{11}M_\odot$) in the
present-day universe possess a wide range of intrinsic
  shapes: there is no single oblate, prolate, or
triaxial shape that, viewed from any number of random viewing
angles, can account for their projected axis ratio distribution
\citep[e.g., ][]{1992MNRAS.258..404L, 1996AJ....111.2243T}.  We
implemented two methods to describe and model this distribution.
First, we showed that a single family of oblate or prolate structures
with broadly distributed intrinsic axis ratios accurately captures the
observed projected distribution (Section~\ref{sec4} and
Figure~\ref{ca_fig_deprojections}).  Second, we showed that a
combination of triaxial and oblate structures, with normally
distributed intrinsic shapes, works equally well.
This second approach is attractive as the distinction of two components corresponds to the kinematical distinction between `fast rotators' and `slow rotators' \citep[e.g.,][]{2011MNRAS.414..888E}.
Figure~\ref{ca_fig_par3_pie} shows that a triaxial component combined
with a thinner, oblate component provides a good description over a
large range of galaxy masses.  The strong dependence of galaxy
structure on stellar mass is driven by the variation in the relative
abundances of triaxial and oblate objects.  We now discuss the
evolution of the intrinsic shape distribution of early-type galaxies,
based on our analysis presented in Section~\ref{sec3}, \ref{sec4}, and \ref{sec5}.

\subsection{Increased Incidence of Disk-Like, Massive Early-type Galaxies at $z>1$}
\label{sec6_1}

\begin{figure}[ht]
\centering
\includegraphics[width=1.0\columnwidth]{ca_fig_dust}
\caption{The projected axis ratio vs. rest-frame $V-J$ color, mass surface density, and surface brightness for the early-type galaxies selected from CANDELS at redshifts $1<z<2.5$ and more massive than $\log(M_*/M_\odot)>10.8$. The gray lines with error bars from bootstrapping represent running medians.  The lack of a trend in the top panel suggests that these galaxies contain little or no dust; otherwise, galaxies with small axis ratios, that is, those viewed edge-on, would be expected to have redder colors.  The increased surface mass density and surface brightness of the small-axis ratio galaxies (bottom two panels) suggest that these galaxies are oblate rather than prolate; the dashed black lines are the expected projected surface brightness and density for an oblate model, with intrinsic axis ratio $E=0.61$, which is the best-fitting value from the single-component model for this sample (Table~\ref{model_single}).}
\label{ca_fig_dust}
\end{figure}

The cumulative distributions of projected axis ratios of $L^*$
early-type galaxies at $z>1$ and at the present-day show that these
were on average flatter in the past (Section~\ref{sec3}; Figure~\ref{ca_fig_q_hist}).  Our
parameterized modeling approach presented Section~\ref{sec5_1_2}
interprets this as a change in the fraction of the oblate component,
from $0.20\pm0.02$ at $z<0.1$ to $0.59\pm0.10$ at $z>1$.

Because the $z>1$ sample is too small to directly distinguish what
structural family the galaxies belong to, we consider independent
evidence for our interpretation that the $z>1$ population largely
consists of flat, oblate objects.  At the present day, flatness is
associated with rotation \citep[e.g.,
][]{2008MNRAS.387...79V,2011MNRAS.414..888E}, but so far such
kinematic evidence has not been extended beyond $z\sim1$
\citep{2008ApJ...684..260V}.  The best direct evidence for our
interpretation that flat galaxies in our sample are indeed disk-like
in structure is that the stellar surface mass density (middle panel of
Figure~\ref{ca_fig_dust}) and the surface brightness (bottom panel of
Figure~\ref{ca_fig_dust}) are larger for galaxies with small projected
axis ratios. This is expected in case the flat galaxies are edge-on
and oblate, but not if they are edge-on and prolate. In the latter
case, the flattest galaxies should have the smallest surface
brightness.  We note that these considerations are only valid for
transparent, that is, dust-poor, stellar systems. This
assumption is supported by the observation that the rest-frame
$V-J$ color does not significantly change with projected axis ratio,
implying little variation in dust attenuation with inclination and,
thus, a low dust content. The lack of star formation activity in
these objects combined with their low dust content indicate that our
sample consists of galaxies with smooth light profiles, and is
therefore comparable to a morphologically classified sample of
early-type galaxies based on visual inspection of images.

Further direct evidence of prominent disks in high-redshift early-type
galaxies comes from two-dimensional bulge-disk decompositions
\citep{2006ApJ...650..706S,2008ApJ...672..146S,2008ApJ...682..303M,2011ApJ...730...38V,2012MNRAS.427.1666B}

Based on these independent lines of evidence, we conclude that at
$z>1$ a substantially larger fraction of $L^*$ early-type galaxies are
disk-like than at $z<1$.  This evolution in structure coincides with
evolution in size
\citep[e.g.,][]{2007ApJ...656...66Z,2007ApJ...671..285T,2008ApJ...677L...5V,
  2008ApJ...688...48V,2012ApJ...746..162N}.  Van der Wel et
al. (2013a, in preparation) showed that the number density of small
($\lesssim 2$kpc) early-type galaxies dramatically decreases between
$z\sim 2$ and the present day \citep[also see][]{,2011ApJ...743...96C,2013arXiv1303.2689C}.
These early types are, as we have shown here, commonly disk-like, such
that we may conclude that individual galaxies evolve from small and
disk-like at $z\sim 2$ to large and round at $z\sim 0$.  The evolution
of size and internal structure  could be driven by a single process,
and merging is usually considered to be the most plausible process \citep[e.g., ][]{2010ApJ...719..844R,2012ApJ...744...85M,2012ApJ...746..162N}.
Major merging and more smooth growth in mass
through accretion and disruption of satellites can account for the
disappearance of prominent disks in $L^*$ early types at $z\sim 2$,
and the observation that the most massive galaxies in the present-day
universe do not host disks (vdW09).

In addition to the growth of individual galaxies, evolution in the
population is driven by the strong increase in the number density of
early-type galaxies between $z\sim 2$ and the present
\citep[e.g.,][]{2004ApJ...608..752B,2007ApJ...665..265F,2011ApJ...739...24B}.
From $z=2$ to $z=1$ the fraction of triaxial galaxies increases, but
this cannot be the result of the formation of `new' early-type
galaxies in the form of triaxial systems from
already-formed early-type galaxies. The absolute number densities
of oblate and triaxial systems both increase over that time span, and we
suggest that all `new' early types start out as compact and disk-like
and subsequently evolve into larger, more triaxial systems
\citep[e.g., ][]{2009ApJ...699L.178N,2012ApJ...744...63O}.  This
suggestion is motivated by the notion that the immediate progenitors
of `new' early-type galaxies will be gas rich and star-forming,
creating suitable circumstances for the formation of disks (see
below), and by the notion that it is implausible that round, triaxial
systems evolve into disk-like systems in the absence of star
formation.  At $z<1$ a natural balance is established between the
addition of `new', disk-like early types and the gradual formation of
triaxial systems, resulting in an almost unchanging, but strongly
varied mix of intrinsic structures, as discussed by H12.

In the scenario described above, galaxies in which star formation is
truncated retain the disk-like structure of their presumed,
star-forming progenitors.  A full discussion of the transition process
is beyond the scope of this paper, but it is important to point out
that while newly formed early-type galaxies retain disk-like
properties, their light (and stellar mass) distributions are more
centrally concentrated than those of equally massive star-forming
galaxies \citep[e.g.,][]{2009ApJ...705..255T, 2011ApJ...742...96W, 2012ApJ...753..167B}.
This implies that a substantial increase in the central
stellar density occurs before or at the time of transition.  A
centrally concentrated starburst fueled by a gas-rich merger is one
possible mechanism to produce bulge-like bodies \citep[e.g.,][]{2006ApJ...648L..21K}.
More recently, violent disk instabilities in a gas-rich
galaxy have been argued to produce clumps that may migrate to the
center on a short time scale, quickly creating a dense stellar body
\citep{2009ApJ...703..785D,2010MNRAS.404.2151C, 2012ApJ...757..120G}.
Whether the gas content of the resulting, dense, disk-like, but
non-star-forming, galaxy has been heated and removed \citep[e.g.,][]{2008ApJS..175..390H} or merely stabilized \citep[e.g.,][]{2009ApJ...707..250M,2012MNRAS.420.3490C} is still debated.

\subsection{Decreased Incidence of Disk-like, Low-mass Early-type Galaxies at $z>1$}
\label{sec6_2}
Sub-$L^*$ early-type galaxies ($M_*\sim 10^{10}M_\odot$) in the local
universe are most often oblate and disk-like.  The comparison with the
cumulative axis ratio distributions of such objects at $z>1$ tells us
that these were less disk-like (see Figure~\ref{ca_fig_q_hist}).  This
may appear to be at odds with the results discussed above,
that is, that massive early types were more disk-like at $z>1$.

Our interpretation of this 3$\sigma$ effect remains largely speculative.
Low-mass early-type galaxies in the present day can be surmised to be
disk-like for the simple reason that their star-forming progenitors
are also disk-like.  Star formation may stop either due to some
internal process or due to environmental effects such as ram-pressure
stripping.  In the latter case the structure of the stellar disk will
remain intact, leading to a very flat early-type galaxy.  At $z\sim 2$
the fraction of satellite galaxies in this mass range is predicted to
be negligible, whereas among the present-day population satellite
galaxies make up $30\%-40\%$ of the total
\citep[e.g.,][]{2008MNRAS.387...79V}. Indeed, the axis ratio distributions
of present-day centrals and satellites are significantly different
\citep{2010ApJ...714.1779V}, but even the present-day centrals are not as
round as their $z>1$ counterparts \citep[also see][]{2011MNRAS.413..921V},.  We suggest that the low-mass
early-type galaxies at $z>1$ are not very disk-like, simply because
their star-forming progenitors were not disk-like at that epoch:
van der Wel et al. (2013b, in preparation) showed that low-mass ($M_*<M_\odot^{10}$) star-forming galaxies
at $z>1$ had not yet attained stable, rotating structures, like they
have at later epochs.  Whether this is related remains to be seen and
hinges on our general lack of understanding of how star-forming galaxies
are transformed into passive, early-type galaxies.

\section{Summary}
\label{sec7}
Projected axis ratio measurements from HST/WFC3 F160W imaging from CANDELS of 880 early-type galaxies at redshifts $1<z<2.5$, complete down to a stellar mass of $\log(M_*/M_{\odot}) = 10$ over the whole redshift range, are used to reconstruct and model their intrinsic shapes.  The sample is selected by low star-formation activity on the basis of $U-V$ and $V-J$ rest-frame colors (see Figure \ref{ca_fig_uvj}, and we demonstrate that these galaxies are dust-poor and transparent: those with flat projected shapes have the same colors as those with round shapes (see Figure~\ref {ca_fig_dust}, top panel).  In addition, the increased surface mass densities and surface brightness of flat galaxies (Figure~\ref{ca_fig_dust}, bottom two panels) suggest that flattening is associated with a disk-like internal structure; prolate galaxies would have lower surface densities when viewed edge-on. Therefore, we conclude that our sample consists of genuine early types, comparable to samples based on visual morphological classification.  We compare the shape distribution of this sample with the shape distribution of early-type at low redshift ($0.04 < z < 0.08$) selected in a similar manner from the SDSS.

Similar to their present-day counterparts, the $z>1$ early-type galaxies show a large variety in intrinsic shape; even at a fixed mass, the projected axis ratio distributions cannot be explained by random projection of a set of galaxies with very similar intrinsic shapes.  We demonstrated this in two ways by assuming that all galaxies are oblate (or prolate): first, an analytical approximation to deproject the observed axis ratio distributions implies that a very broad range in intrinsic shapes is required (Section~\ref{sec4} and Figure~\ref{ca_fig_deprojections}); second, we show that randomly projecting a set of objects with a Gaussian distribution of intrinsic axis ratios cannot match the observed, projected shape distribution (Section~\ref{sec5_1_1} and Figure~\ref{ca_fig_triaxial}).

As was demonstrated for present-day early-type galaxies and up to $z\sim 1$, a two-population model can accurately describe the projected axis ratio distributions. We now extend this to $z=2.5$.  This model, inferred from fitting the axis ratio distribution of the low-redshift sample (Section\ref{sec5_1_2} and Figure~\ref{ca_fig_par3_pie}), consists of a triaxial, fairly round population combined with a flat ($c/a\sim 0.3$) oblate population.  For present-day early-type galaxies the oblate fraction strongly depends on galaxy mass, but at $z>1$ this trend is not seen over the stellar mass range explored here ($10<\log (M_*/M_{\odot})<11.3$).  This is mostly the result of strong evolution in the oblate fraction among high-mass early-type galaxies: for galaxies with mass $\log(M_*/M_{\odot})>10.8$ the oblate fraction increases from $0.20\pm 0.02$ at the present day to $0.59\pm 0.10$ at $1<z<2.5$.  Conversely, we find that the oblate fraction decreases with redshift for low-mass early-type galaxies ($\log (M_*/M_{\odot})<10.5$), from $0.72\pm 0.06$ to $0.38\pm 0.11$. These results are based on the assumption that the intrinsic shapes of the triaxial and oblate population do not evolve with redshift. We refer to Section~\ref{sec5_1_2} for a justification of this assumption and a demonstration that our results and interpretation do not depend on it.

The decreased prevalence of disk-like systems and larger galaxy sizes at lower redshifts point to a scenario in which classical elliptical galaxies gradually emerge over time through merging and the accretion of satellites, at the expense of the destruction of pre-existing disks.  Definitive evidence for the disk-like structure of massive early-type galaxies at $z\sim 2$ should eventually be provided by kinematic evidence for rotation in the stellar body. We speculate that the decreased incidence of disks at early cosmic times among low-mass early-type galaxies can be attributed to two factors: low-mass, star-forming progenitors at $z>1$ were not settled into stable disks to the same degree as at later cosmic times, and the stripping of gas from satellite galaxies is an increasingly important process at lower redshifts.  We refer to Section~\ref{sec6_2} for a discussion.

A joint analysis of shapes, sizes, and S\'ersic indices for late- and early-type galaxies, will provide further insight into the intrinsic structure of high-redshift galaxies, and allow for more constrained deprojection and model construction approaches.  Further improvements will be provided by the extension of the analysis to the full CANDELS data set, drawing samples from all five  fields instead of the two fields used here; at the moment we are still limited by small number statistics at $z\sim 2$ and above.

\acknowledgments
We thank the anonymous referee for helpful comments,
and Steve Willner and Matthew Ashby for useful suggestions.
This work is based on observations taken by the CANDELS Multi-Cycle Treasury Program with the NASA/ESA HST, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.
Y.-Y. C. was funded by the IMPRS for Astronomy \& Cosmic Physics at the University of Heidelberg and the Marie Curie Initial Training Network ELIXIR of the European Commission under contract PITN-GA-2008-214227.

\bibliographystyle{apj}

redpajama_set_name: RedPajamaArXiv


text:
JUDIE MANCUSO
Long recognized as a leader in California advocating on behalf of animal welfare issues, with a proven track-record that spans decades, Judie Mancuso is the Founder and President.
A small but powerful organization that is unique in its purpose, Mancuso's SCIL is currently working on facilitating numerous groundbreaking laws in 2017; including one that aims to stop the rampant police shootings of innocent dogs and the cat and dog meat trade for human consumption.
Under Mancuso's guidance, SCIL accomplished getting one of the biggest bills done for animals in the world, AB 485 Pet Rescue & Adoption Act, which mandates only rescue and shelter animals be offered in Pet shops, no more supplying stores from cruel puppy mills.
Also, high on the list of her many accomplishments, Mancuso was instrumental passing the Dining With Dogs law that makes it legal for restaurants in California and New York to offer areas for people to dine with their companion canines. More states are expected have followed suit.
With an eye focused on protecting all animals, Mancuso recently made headlines as the organizing force behind the fight to spare the life of local mountain lion P-45 after the Department of Fish and Wildlife issued of a 10-day permit allowing ranchers in Malibu to shoot and kill him after four alpacas were found dead on a farm. The permit was ultimately revoked and the permit holder instead decided to work with Fish and Wildlife, National Park Service and the Mountain Lion Foundation to better to humanly protect their animals from mountain lions, and to implement them. This marks a significant step in the right direction that animal welfare organizations want to ultimately end with the passing of new legislation making it tougher to obtain kill permits.
Mancuso also fought her own City Council's decision to allow the trapping and killing of coyotes in the city. Mancuso's outcry and grassroots support led to the reversal of the decision.
An appointed member of the California Veterinary Medical Board, Mancuso is also currently serving the second and final four-year term.
info@socialcompassioninlegislation.org
Donations to Social Compassion in Legislation, a 501(c)(4) organization are not tax-deductible.
©2018 Social Compassion In Legislation

redpajama_set_name: RedPajamaCommonCrawl


text:
Attention US Festival Fans!
ICON Television Music, UNUSON (Unite Us In Song) and Plum Moving Media have announced a release date, Sept. 3, 2012, for The US Generation - a documentary of the 1982 US Festival.
According to Carlos Harvey of UNUSON (the company Steve Wozniak formed during the US Festival days), "This film is the only authorized and sanctioned documentary of the 1982 US Festival. It captures the cultural essence of the festival and tells the behind-the-scenes stories the fans will appreciate. I've had thousands of calls & emails from attendees over the years about when we'll release a film about the US Festival. After 30 years it seems like the right time so the fans can relive the experience and we can create new fans too."
The release of The US Generation will coincide with the 30th anniversary of the original US Festival which took place over Labour Day weekend in 1982 in the foothills of San Bernardino, California. It was 110 degrees the first day of the festival when the first band, Gang of Four, took the stage on opening day and the rest is precious history.
The original three-day US Festival (the second was held in May 1983) was funded by $12.5 million of Apple co-founder Steve Wozniak's own dollars who at the time was still vice president of the company. Wozniak declared, "I want to throw the party of the century!"
Wozniak paid for the construction of an outdoor concert pavilion (now The San Manuel Amphitheater) which included a temporary stage built with the largest sound system in the world at the time and five large tents which housed the US Festival Technology Exposition.
Day one of the festival included performances by The Ramones, The English Beat, Oingo Boingo, The B-52's, and The Police. Day two featured The Cars, The Kinks, and Pat Benatar, and the final day (Sunday) included The Grateful Dead, Jackson Browne, and Fleetwood Mac.
Watch Steve Wozniak's animated Apple IIe floppy disk-based invitation to the US Festival.
According to the filmmakers the 90-minute documentary will include never-before-seen and digitally re-mastered concert footage, with an "intermingling of history," and "anecdotal stories as told by and seen through the eyes of the event participants."
Steve Wozniak: "The US Festival was not a charity event. It was a rock concert to bring music, technology and people together. It was an event to unite government, industry, science and education to improve the quality of life for everyone."
Photo: Richard Auger via The US Generation Documentary
Quoted material: The US Generation
LABELS: Steve Wozniak, The US Generation, US Festival


text:
Home Free Dividend Report Stock Splits Calendar ANDAU Historical Stock Prices Preferred Stock Newsletter Top Option Ideas Stock Message Boards
ANDAU Historical Price Range
07/14/2021 $11.54 $11.54 $11.54 $11.54 0
About Andina Acquisition Corp Iii - Unit
Andina Acquisition is a shell company.
Andina Acquisition Corp Iii - Unit (ANDAU) has the following price history information. Looking back at ANDAU historical stock prices for the last five trading days, on July 14, 2021, ANDAU opened at $11.54, traded as high as $11.54 and as low as $11.54, and closed at $11.54. Trading volume was a total of 0 shares. On July 15, 2021, ANDAU opened at $11.53, traded as high as $11.53 and as low as $11.53, and closed at $11.53. Trading volume was a total of 100 shares. On July 16, 2021, ANDAU opened at $11.53, traded as high as $11.53 and as low as $11.53, and closed at $11.53. Trading volume was a total of 0 shares. On July 19, 2021, ANDAU opened at $11.10, traded as high as $12.21 and as low as $11.10, and closed at $11.10. Trading volume was a total of 1.10K shares. On July 20, 2021, ANDAU opened at $11.10, traded as high as $11.10 and as low as $11.10, and closed at $11.10. Trading volume was a total of 0 shares.
ANDAU Historical Stock Prices By Date:
Below, we examine the compound annual growth rate — CAGR for short — of an investment into Andina Acquisition Corp Iii - Unit shares, starting with a $10,000 purchase of ANDAU, and working forward through the historical stock price information to today.
Total return: 10.94%
ANDAU Historical Closing Prices
ANDAU Historical Stock Prices | www.HistoricalStockPrice.com | Copyright © 2013 - 2022, All Rights Reserved


text:
IT Vendors Features
Check Point plans to release document security software
Check Point Software Technologies plans to introduce document security software that encrypts and controls access to files across an organisation's various departments and also meets the growing need for corporate users to access company information on mobile devices, a company executive said.
John Ribeiro July 19, 2012
The product is an offshoot of Check Point's 2010 acquisition of data protection startup Liquid Machines and will be offered both as a cloud service managed by Check Point or for deployment by customers in private clouds, said Amnon Bar-Lev, president of Check Point.
Documents in a variety of formats including those created in Microsoft Excel, Word and Adobe Acrobat can be created with different rights assigned to different users, said Bar-Lev. The default can for example be set to ensure that all the documents can only be read by people in the enterprise.
"If someone were to leak out information, then nobody outside can read it," Bar-Lev said. "Then we can start building groups on top of it, allowing only HR or only finance, or only a specific individual to be able to read or do certain things with certain documents." Documents may also be shared outside the organisation with certain restrictions.
The technology, set to debut by the end of this year, will also enable authorised users to access the documents through clients on their smartphones.
Besides its VPN (virtual private network) client for mobile phones, the company also plans to integrate corporate email and calendar into the client in a totally isolated environment, called a sandbox, on the device.
The large number of high-profile hacks and DDoS (distributed denial of service) attacks have increased people's awareness of the importance of security, but enterprise spending on security has not changed dramatically, and is likely to continue at about 5% of IT spending, Bar-Lev said. Security spending is still largely driven by regulation, as it is not seen as directly producing something for the organisation, he added. Current economic conditions including the European debt crisis are also likely to result in a slowdown in overall IT spending, including security.
The Israeli security company, with US headquarters in Redwood City, California, reported that second quarter revenue was about $329 million, a 9% increase over last year's second quarter. Net profit was $150 million, an increase of 17% from 2011's second quarter.
During the quarter, the company introduced its DDoS Protector Appliance, which is designed to handle a new type of "low and slow" DDoS attacks that attack specific applications rather than try to overwhelm the website with a brute force attack that chokes the pipe, Bar-Lev said. In earlier DDoS attacks, the enterprise would count on the service provider to re-route and filter DDoS traffic when there was an attack, but with the changed nature of the attacks, this is not really the best option, he said.
Check Point also introduced the Anti-Bot software blade that can be activated on every Check Point enterprise gateway, monitoring traffic for bots on the network rather than at the endpoints. It saw a requirement for this product as 80% of spam and most DDoS attacks are now executed through bots, Bar-Lev said. Its ThreatCloud, a collaborative network to fight cybercrime, also allows gateways to automatically inform other participating Check Point gateways about bots and where they are originating from. Bots are applications that run automated and repetitive tasks on the internet, and are often used for malicious purposes.
Appliances that combine hardware and software account for over 85% of Check Point's product business, because they give customers simplicity, Bar-Lev said. The company also gives customers the option to buy the software and run it on other appliances or hardware.
Vendors line up to support NAP McAfee and Check Point turn to sandboxing to fend off APTs


Thread: VX220 Owners on here?
So how many of you guys own a VX on here, and where are you all from??
VX220.org has more meets and has a good Q&A section..... I have used the Q&A section a few times and you get a great response.


text:
Biographical Sketch of Henry Rowley
Henry Rowley, immigrant ancestor, was born in England, and died in Barnstable or Falmouth, Massachusetts, in 1673. He was one of the early planters of Plymouth and was a taxpayer as early as 1630. He was admitted a freeman in 1634, after removing to Scituate, where he and his wife Anne joined the church, January 8, 1634. In 1638 he removed with Rev. John Lothrop to the new settlement at Barnstable on Cape Cod. He was a deputy to the general court at Plymouth. In 1650 he removed to West Barnstable, and later to Falmouth. He married (first) Sarah, daughter of William Palmer. He married (second) October 17, 1633, Anne, daughter of Thomas Blossom, who started for New England in the "Speedwell," in 1620, from Holland, but had to return; came to Plymouth in 1629. Children, Moses, mentioned elsewhere; Joseph, said to have gone to the Barbadoes; Sarah, married, April 11, 1646, Jonathan Hatch, of Barnstable and Falmouth.
Rowley,
Barnstable County MA, Barnstable Massachusetts, England, Falmouth Massachusetts, Ontario County NY, Plymouth County MA, Plymouth Massachusetts, Scituate Massachusetts, West Barnstable Massachusetts,


text:
Сент-Амбруа () — муніципалітет у Франції, у регіоні Центр-Долина Луари, департамент Шер
 Сент-Амбруа () — муніципалітет у Франції, у регіоні Окситанія, департамент Ґар

redpajama_set_name: RedPajamaWikipedia


A fascinating little corner of the internet where I share electronics projects I'm working on, designing or modding them myself, and asking you for feedback to improve them. In return you get nicely-drawn schematics and complete circuit descriptions.
This site features posts from the Corelis Support and Engineering team for the purpose of helping to educate other engineers and students alike about Boundary-Scan technology, testing, and maximizing productivity.


text:
Jason and I watch enough television as is without having premium movie channels so we have never spent the extra money on it, however, after hearing the rave reviews from critics and more importantly, my girlfriends, I added HBO to our channel list solely for Girls.
Being touted as the Sex and the City for a younger generation, Girls is a show about four post-collegiate twenty-something girls living in New York City. I caught up yesterday on all three episodes and can say that I absolutely LOVE it. The writing is hilarious, but the best part is the REALNESS of it. It's more real than reality TV...the four main actresses (and supporting cast) all look like real people (I mean as much as you can for Hollywood)! And they speak about real situations facing young women after college, in a sarcastic hilarious way of course.
Some are saying it's a bleak depiction of what real women face, but I would beg to differ...boyfriends, love, dating, drugs, periods, careers, money, sex, abortion, STD's, friendships, parents, being kicked out of the nest, homosexuality, following your dream vs. paying the bills. Maybe us girls, don't have to face every and all of the situations all at once, but I'm sure every girl or woman can relate to at least three on this list!
Fun tidbits of info: Lena Dunham the main character, writes and directs the show too. Allison Williams, who plays Marnie, is Brian Williams (NBC news anchor) daughter. The show is produced by Judd Apatow, of 40-Year Virgin and Knocked Up.
Brian Williams with daughter, Allison Williams
Busy Week
Three Years Ago Today...
No Heat Required: The Perfect Heatless Curls Hair ...
Mommy!
Summer Playlist
The Shops by Target
Weekend Recap: Birthday Edition!
Ombre Revisited
April Birchbox Review
Happy Birthday Sara!
Concert Review: The Fray
Cheering for a Mosquito
It's Been Too Long