# The Loneliest Galaxies in the Universe: A GAMA and GalaxyZoo Study on Void
Galaxy Morphology

Lori E. Porter,1 Benne W. Holwerda,1 Sandor Kruk,2,3 Maritza Lara-López,4
Kevin Pimbblet,5 E-mail<EMAIL_ADDRESS>Christopher Henry,1 Sarah
Casura,6 and Lee Kelvin7
1Department of Physics and Astronomy, University of Louisville, 102 Natural
Sciences Building, Louisville, KY 40292, USA
2Max-Planck-Institut für extraterrestrische Physik (MPE), Giessenbachstrasse
1, 85748 Garching bei München, Germany
3European Space Agency, ESTEC, Keplerlaan 1, NL-2201 AZ, Noordwijk, the
Netherlands
4Departamento de Física de la Tierra y Astrofísica, Instituto de Física de
Partículas y del Cosmos, IPARCOS, Universidad Complutense de Madrid (UCM),
28040 Madrid, Spain
5 E.A. Milne Centre for Astrophysics, University of Hull, Cottingham Road,
Kingston-upon-Hull, Hull HU6 7RX, UK
6 Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg,
Germany
7Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane,
Princeton, NJ 08544, USA

(Accepted 2023 April 10. Received 2023 April 10; in original form 2023
February 24)

###### Abstract

The large-scale structure (LSS) of the Universe is comprised of galaxy
filaments, tendrils, and voids. The majority of the Universe’s volume is taken
up by these voids, which exist as underdense, but not empty, regions. The
galaxies found inside blackthese voids are expected to be some of the most
isolated objects in the Universe. This study, using the Galaxy and Mass
Assembly (GAMA) and Galaxy Zoo blacksurveys, aims to investigate basic
physical properties and morphology of void galaxies versus field (filament and
tendril) galaxies. We use void galaxies with stellar masses black($\rm M_{*}$)
of $10^{9.35}M_{\odot}<M_{*}<10^{11.25}M_{\odot}$, and this sample is split by
identifying blacktwo redshift-limited regions, 0 < z < 0.075, and, 0.075 < z <
0.15. To find comparable blackobjects in the sample of field galaxies from
GAMA and Galaxy Zoo, we identify black‘twins’ of void galaxies as field
galaxies within $\pm$0.05 dex and $\pm$0.15 dex blackof $\rm M_{*}$ and
blackspecific star formation rate. blackWe determine the statistical
significance of our results using the Kolmogorov-Smirnov (KS) test. We see
that void galaxies, in contrast with field galaxies, seem to be disk-dominated
and have predominantly round bulges black(with > 50% of the Galaxy Zoo
blackcitizen scientists agreeing that bulges are present).

###### keywords:

galaxies: evolution – galaxies: spiral – galaxies: structure – galaxies:
formation

††pubyear: 2023††pagerange: The Loneliest Galaxies in the Universe: A GAMA and
GalaxyZoo Study on Void Galaxy Morphology–The Loneliest Galaxies in the
Universe: A GAMA and GalaxyZoo Study on Void Galaxy Morphology

##  1 Introduction

Void galaxies are expected to be some of the most isolated objects in the
Universe. However, their standard morphology, and how it compares to galaxies
in denser regions of the Universe, remains a topic of debate. Studying
galactic morphology, how galaxies are classified, and possible links between
physical properties and morphological type is essential to further developing
our understanding of galaxy formation and evolution.

Galaxy environment is arguably one of the most important factors in
determining what shape a galaxy takes (Dressler, 1984; Postman et al., 2005;
Hambleton et al., 2011; Buta et al., 2015). With this dependence on
environment, it is not unreasonable to believe that the secluded nature of
void galaxies could have a substantial effect on their morphology. With fewer
merging galaxies in these underdense regions, a lack of clusters, and less
material for accretion, the evolution of these galaxies is highly likely to be
driven by internal processes. As a result, void galaxies are optimal natural
laboratories for studying how galaxies evolve in isolated environments, which
can possibly explain how important morphological features form (Kormendy,
1979; Combes & Sanders, 1981). While Hambleton et al. (2011) points out
weaknesses in relying on broad morphological classifications, it is first
important for us to understand these broad categorical distinctions in void
galaxy morphology before we can study the finer details.

Understanding the basic morphology of void galaxies (if one exists) provides a
gateway to possibly linking other physical properties of void galaxies with
environment. There also blackexist well-known relations involving morphology,
environment, and other galaxy properties, such as the blackstar formation rate
(SFR)-$\rm M_{*}$-morphology relation (Blanton et al., 2003; Kauffmann et al.,
2003; Wuyts et al., 2011; Kelvin et al., 2014), environment and mass-quenching
(Peng et al., 2010), and star formation-morphology (Kennicutt, 1998; Williams
et al., 2009; Barro et al., 2013; Kelvin et al., 2018). For example, galaxies
in denser environments have been found to be redder in color, have lower star
formation rates, and be more elliptical, typically caused by the neighboring
galaxies and higher incidents of mergers (Dressler, 1984; Kauffmann et al.,
2003; Lotz et al., 2008, 2011; Peng et al., 2010; Bell et al., 2012; Alpaslan
et al., 2015; Woo et al., 2015). On the other hand, galaxies in the lower-
density areas are usually largely dominated by spiral galaxies (Dressler,
1984).

Rojas et al. (2004) blackidentify nearly a thousand void galaxies blackin the
Sloan Digital Sky Survey (SDSS) using a nearest neighbor analysis. blackThey
investigate the blackSérsic index in two populations, wall galaxies (non-void
galaxies, also known as tendril and filament galaxies) and void galaxies in
two distance groups: near and distant. blackThis results in a total of two
statistical tests being conducted: a comparison of the blackSérsic index in
the nearby void galaxies versus nearby wall galaxies, and distant void
galaxies versus distant wall galaxies. blackThey find no significance in the
Kolmogorov-Smirnov statistics between the nearby groups, but statistical
significance in the distant sample.

These are conflicting results, and result in an inconclusive study in terms of
galaxy morphology. However, Rojas et al. (2004) blackdo determine that void
galaxies appear to be bluer in color and fainter than wall galaxies in both
the nearby and distant samples.

In addition, other studies agree with the conclusion that void galaxies are
expected to have higher specific star formation rates (sSFR) and retain more
of a blue color as compared to similar galaxies in more dense environments
(Rojas et al., 2004, 2005; Hoyle et al., 2012; Moorman et al., 2015; Penny et
al., 2015; Moorman et al., 2016; Beygu et al., 2016, 2017; Florez et al.,
2021). However, Kreckel et al. (2014) blackdisagree, stating that in their
sample of 61 void galaxies in the Void Galaxy Survey (VGS), there appeared to
be no evidence for bluer colors at a fixed luminosity (although the authors
note their small sample size and the need for control of all variables), and
that void galaxies have similar gas disks to galaxies in denser environments.
The analysis of nine void galaxies from SDSS Data Release 7 (DR7) by Fraser-
McKelvie et al. (2016) black and Ricciardelli et al. (2014) also suggest that
the isolation of void galaxies has no effect on the SFR. black Rosas-Guevara
et al. (2022), on the other hand, blacknote that similarities in SFR seem to
vary depending on stellar mass ($M_{*}$).

Rojas et al. (2005) blacksuggest that void galaxies have more spirals than
their counterparts in denser environments, with Van de Weygaert et al. (2011)
suggesting that they maintain a late-type morphology. In addition, Beygu et
al. (2016) blackfind that void galaxies from the Void Galaxy Survey typically
have a lower blackSérsic index (n $<$ 2), typically blackindicative of more
disky galaxies, but concludes that void galaxies do not seem to have a
specific type. blackblackConversely, Penny et al. (2015) blackfind that void
galaxies do not exhibit a different morphology than those in denser
environments, in addition to other properties mentioned above.

Pustilnik et al. (2019)’s analysis of dwarf galaxies in voids blackshows that
these galaxies typically have morphologies consistent with irregular
(morphologies that are neither elliptical nor spiral) and late-type spiral
galaxies, blackquantitatively suggesting that 7% of local void galaxies are
early-types, 41.6% are some type of spirals, and 43.2% are irregular. The
remaining galaxies are either blue compact objects or lenticulars.

black Florez et al. (2021) blacksuggest that void galaxies altogether follow a
specific evolutionary path, dependent on the dark matter halo. When
investigated at a fixed mass, void galaxies here agree with previous results
in that they are bluer, star-forming, and gas-rich, and that these trends
persist with morphology as well. The authors note that this is likely due to a
galaxy assembly bias, and indeed find that the trends are replicated when
galaxy properties are matched to halo properties.

blackIndeed, simulations and theory further bolster the need to investigate
correlations between galaxy environment and morphology. Croton & Farrar (2008)
blackinvestigate a population of quenched late-type void galaxies, comparing
their luminosity functions to galaxy formation models built from Millenium
simulations. blackTheir results suggest that despite their large-scale
environmental differences, galaxies residing in similar dark matter halo
masses will retain similar properties.

black Rosas-Guevara et al. (2022) blackprovide a new perspective by using the
EAGLE hydrodynamical cosmological simulations to investigate void galaxy
properties and their assembly histories. After controlling for the effect of
stellar halo mass, Rosas-Guevara et al. (2022) finds that their sample of most
isolated void galaxies have the fewest positive gas-phase metallicity
gradients present. This finding alludes to the possible association between
external processes and feedback events in isolated environments, which implies
that these most-isolated galaxies have fewer instances of mergers than their
analogues in denser environments.

Clearly, results and sampling of void galaxies remain diverse across studies
and often lead to conflicting results. Therefore, this study aims to remedy
this problem by using new data and a variety of perspectives.

Alpaslan et al. (2014) introduces a new spectroscopically complete catalogue
of the large-scale structure (LSS) of the Universe called the Galaxy and Mass
Assembly (GAMA) Large Scale Structure Catalogue (GLSSC), comprising over forty
thousand galaxies. blackThey identify blackeach galaxy as belonging to either
filaments (the largest structure), tendrils (the second-largest structure, and
substructure of filaments), or voids. Because of the introduction of tendrils,
in addition to filaments, galaxies can be more accurately grouped according to
their environment.

This study introduces the idea of combining the powerful sample created by
Alpaslan et al. (2014) with the resources in Galaxy Zoo, to complete an
observational analysis on void galaxy morphology. This paper is organized as
follows: we begin by reviewing the surveys from which our sample is selected
in Section 2, specifically elaborating on how void galaxies are identified in
Section 2.1.2, and how we selected our analysis sample in Section 2.3. We go
over our results from both GAMA and Galaxy Zoo in Section 3, discuss
interpretations in a physical sense and compare with previous literature in
Section 4, and finally briefly summarize this study in Section 5.

##  2 Data

All galaxies are identified from the Galaxy And Mass Assembly (GAMA) survey
(Driver et al., 2009; Liske et al., 2015). We combine the GAMA Data Release 3
(Baldry et al., 2018) and the KiDS (de Jong et al., 2013; De Jong et al.,
2015, 2017; Kuijken et al., 2019) imaging, with MAGPHYS computing the stellar
mass and specific star formation rate (sSFR) blackutilized in this study (Da
Cunha et al., 2008). In addition, we use the GLSSC from Alpaslan et al. (2014)
to identify void galaxies, and morphology voting is from the Galaxy Zoo GAMA-
KiDS project.

###  2.1 GAMA

GAMA is a highly complete (>98% to r < 19.8 mag) spectroscopic and
multiwavelength imaging survey conducted with the intent to investigate large-
scale structure (LSS) in the local Universe black(z < 0.6) on kpc to Mpc
scales (Driver et al., 2009, 2011, 2022; Baldry et al., 2018). The survey now
consists of blackfive regions, three of which are equatorial regions of 5
degrees in declination and 12 degrees in right ascension, blackcovering a
total of nearly black250,000 galaxies. Additional photometric data was
collected on each galaxy in 20+ bands at multiple wavelengths (Liske et al.,
2015; Driver et al., 2016; Baldry et al., 2018; Driver et al., 2022). This
specific study uses GAMA Data Release black4, detailed in Driver et al.
(2022), where the galaxies’ Sérsic indices and effecive radii are computed by
Kelvin et al. (2012) blackin SersicPhotometryv09. With such a large and
complete sample of high resolution data, we are well-equipped to study the
selected population of galaxies.

####  2.1.1 MAGPHYS

blackAs part of GAMA, the MAGPHYS v06 spectral energy distribution (SED) fit
data products (Da Cunha et al., 2008; Driver et al., 2009, 2011; Da Cunha et
al., 2015) to calculate physical properties such as specific star formation
rate (sSFR), redshift, and stellar mass, accounting for the emission from
stellar populations, and both dust attenuation and emission. For further
details on MAGPHYS, we direct the reader to Da Cunha et al. (2008) and Da
Cunha et al. (2015). blackThis allows us to further select field galaxies for
comparison that are effectively identical to void galaxies in terms of star
formation, as described in Section 2.3.

####  2.1.2 Void Galaxies

Void galaxies are defined by Alpaslan et al. (2014) as a galaxy that is at a
minimum 4.56h-1 Mpc from the nearest tendril galaxy, which are a minimum of
4.12h-1 Mpc from filaments. This survey samples galaxies from various stellar
mass groups, which allows for trends caused by environment to be more
prevalent than trends in galaxies caused by mass. Alpaslan et al. (2014) and
Alpaslan et al. (2015) then use data from Pan et al. (2012), to identify a new
sample of void galaxies that are truly isolated, and prove that many galaxies
previously identified as voids may actually be tendril galaxies. As a result,
the galaxies identified blackby FilamentFindingv02 in Alpaslan et al. (2014)
are expected to truly be some of the most isolated objects in the Universe.
These parameters and the high resolution of GAMA allow us to be blackmore
confident that these void galaxies are truly isolated. For ease, we will now
refer to any galaxy that is not a void galaxy (i.e, a tendril or filament
galaxy) as a field galaxy.

Figure 1:  The Galaxy Zoo decision tree for the GAMA-KiDS GZ survey.
Participants begin at the top of the tree with the first question, color-coded
by the key visible in the bottom-left, and move their way throughout the tree
based on their answers to each question. This study focuses on questions T00,
T02, T03, T04, T07, and T09. blackNote that later in this study for question
T09, to avoid redundancy, we simply combine the answers for "merging", "tidal
debris", and "both", effectively limiting the possible answers to T09 to "Yes"
or "No."

###  2.2 GAMA-KiDS Galaxy Zoo

Our analysis on void galaxy morphology is largely based on the GAMA-KiDS
Galaxy Zoo survey (Kelvin et al. in prep.). 49,851 galaxies are selected from
GAMA equatorial fields with a maximum redshift of z=0.15 for use in
morphological classification, with questions in the survey following the
structure shown in Figure 1. Comprehensive voting fractions are then
evaluated, with each voting fraction representing the portion of the
population that vote for a specific component’s presence (or lack thereof)
blackaccording to the question. For example, in question T01, "Could this be a
disk viewed edge-on?", we see there are two possible answers for individuals
to choose from: yes and no. Therefore the votes are stored in two categories,
those of "yes" and those of "no". If 25% of the population votes that a
specific galaxy could be viewed edge-on, blackan answer of "yes" according to
the question, then the voting fraction of "edge-on" would be 0.25, and the
voting fraction of "not edge-on" is 0.75. All answers to a specific question,
when added together, must have a voting fraction of 1, which represents 100%
of the population that answered the question.

As a result of the decision tree and tiered questions, not all participants
will answer each question; higher tiers, denoted by color on Figure 1, may
have fewer votes than the grey tiers that each participant answers. For
example, the 4th tier questions will only be answered by participants that
vote in favor of a galaxy having features, being face-on, and appearing to
have a spiral pattern. This means that if we start with a small sample size,
higher-tier questions run into the realm of small-number statistics.

As a citizen science project, blackit is important to note that Galaxy Zoo can
be susceptible to human bias. However, with extensive available data, Galaxy
Zoo has been used in conjunction with GAMA blackto minimize this bias and take
full advantage of the data. blackSuch studies include identifying dust lanes
in edge-on galaxies (Holwerda et al., 2019), strong gravitational lensing
(Knabel et al., 2020), green valley galaxy morphology (Smith et al., 2022),
and blackinvestigating a possible correlation between the number of spiral
arms in spiral galaxies and star formation (Porter-Temple et al., 2022).

###  2.3 Sample Selection

Figure 2: The complete samples of data from GAMA and GalaxyZoo. Void galaxies are denoted as black stars, whereas other galaxies in GAMA and GalaxyZoo are cyan circles. The yellow highlighted region represents the redshift-limited portion of this study, where left and right panels show the difference in the population of comparable field galaxies to void galaxies.  Table 1: blackSummary of the number of galaxies present for each sample, before conducting analysis. This table does not define the number of galaxies that exist in a certain morphology, for example, but instead the number of galaxies present in the cumulative population histograms beginning with Figure 6. Note that later in this study for question T09, to avoid redundancy, we simply combine the answers for "merging", "tidal debris", and "both." |  black0 < z < 0.075 |  black0.075 < z < 0.15
---|---|---
| Void Galaxies | Twins ($\pm 0.05$ dex) | Twins ($\pm 0.15$ dex) | Void Galaxies | Twins ($\pm 0.05$ dex) | Twins ($\pm 0.15$ dex)
blackSérsic Index, Effective Radius | 58 | 350 | 1334 | 444 | 4831 | 15710
T00: Features | 57 | 349 | 1325 | 436 | 4614 | 14843
T02: Bar | 43 | 240 | 860 | 227 | 1986 | 6116
T03: Spiral | 36 | 199 | 758 | 242 | 2230 | 6618
T04: No Central Bulge | 26 | 179 | 652 | 178 | 2721 | 8772
T04: Obvious Central Bulge | 50 | 320 | 1224 | 308 | 3896 | 12486
T04: Dominant Central Bulge | 50 | 288 | 1133 | 289 | 3518 | 11444
T07: Edge-on: Rounded Bulge | 29 | 338 | 1252 | 159 | 4293 | 13918
T07: Edge-on: Boxy Bulge | 15 | 147 | 603 | 110 | 2728 | 9077
T07: Edge-on: No Bulge | 19 | 209 | 826 | 112 | 3096 | 10128
T09: Evidence of Mergers | 55 | 350 | 1334 | 425 | 4828 | 15702

To conduct our analysis, it is first important to ensure that we are only
investigating a range of galaxies in which we are sure that our samples of
both field and void galaxies are complete. Because Galaxy Zoo has a maximum
redshift of $\rm z_{max}$ = 0.15, our blackmaximum redshift of this sample is
blackalso limited to $\rm z_{max}=0.15$. Furthermore, we limit our total
stellar mass range to that of $\rm
10^{9.25}M_{\odot}<M_{*}<10^{11.25}M_{\odot}$ black, as this mass range is
home to our identified void galaxies, and is most easily compared to previous
literature on void galaxies.

blackThis study’s primary focus is to determine whether void galaxies and
similar field galaxies have a differing average morphology. This means that we
are attempting to test for significance in the two samples where the primary
difference is the environment (void vs field).

blackIt is known that morphological features in galaxies can be redshift-
dependent; galaxies residing around z=0 are a different population than those
at z=0.1. To ensure we are taking blackredshift into consideration while
maintaining an appropriate sample size to allow for reasonable statistics, we
divide our sample into two: one consisting of black 0 < z < 0.075 (yellow
shaded region of Figure 2) and another blackof 0.075 < z < 0.15 (unshaded
portion of Figure 2). We can now effectively refer to these samples as our
"local" galaxies (0 < z < 0.075) and "distant" galaxies (0.075 < z < 0.15),
similar to Rojas et al. (2004).

The black0 < z < 0.075 sample will be important when analyzing voting
fractions of morphologies such as the presence of a bar (questions T02 and
T07) or tidal debris (question T09), as Kruk et al. (2018) blackfind that few
bars are accurately resolved above a redshift of z = 0.1, and therefore limit
their sample for bars to z = 0.06. Similarly, Porter-Temple et al. (2022),
which utilizes the same GAMA and Galaxy Zoo data to investigate the number of
spiral arms (another morphological feature), blacklimit their sample to $\rm
z_{max}$ = 0.08. These redshift cuts ensure that the data gathered by Galaxy
Zoo is from sufficiently resolved galaxy images. Our study is slightly more
complicated in the fact that we investigate a wide range of morphological
components, some of which do not require such precise resolution, such as
features (question T00), spiral arm patterns (question T03), and discerning
between the presence of a bulge or not (questions T04 and T07).

blackHowever, because we are interested in ensuring that the primary
difference between our void and field galaxies is their environment, we
further limit the sample of field galaxies by identifying directly comparable
galaxies, which we refer to as black‘twins’ of the void galaxies. In terms of
redshift, we acknowledge that the black‘distant’ 0.075 < z < 0.15 is still a
large redshift range, and therefore require that, in order for a field galaxy
to be identified as a twin to a void galaxy, it must have a redshift within
$\pm 0.025$ of an identified void galaxy.

blackWe define star formation rates and stellar mass to be equally important
in identifying void galaxy analogues. Therefore, black‘twins’ are also
required to be any field galaxy that is within $\pm 0.05$ dex or $\pm 0.15$
dex of a void galaxy in terms of sSFR and $\rm M_{*}$. The intention behind
this is to identify a small subset of galaxies that are almost exactly
identical to the void galaxies ($\pm 0.05$ dex) in terms of properties, but
due to observational uncertainties in terms of properties such as sSFR, we
allow for the second, larger sample of comparable field galaxies ($\pm 0.15$
dex). Keeping both definitions of ’twins’ is important to ensure we are
maintaining similar samples, all while providing an appropriate number of
field galaxies to compare with the void galaxies (see Table 1).

blackIn summary, we have two samples of void galaxies and their field galaxy
black‘twins’: 0 < z < 0.075, and 0.075 < z < 0.15. The former redshift range
requires that, to be a black‘twin’, a field galaxy must have a sSFR and $\rm
M_{*}$ within $\pm 0.05$ or $\pm 0.15$ dex of a void galaxy. The latter
redshift sample implements the same sSFR and $\rm M_{*}$ requirement, but
imposes the additional restraint that the field galaxy is also within $\pm
0.025$ in redshift of the same galaxy. If a field galaxy does not meet all
requirements for a specific void galaxy, it will not be identified as a
black‘twin’. blackTo remain complete, we later conduct an analysis and
statistical significance testing on all subgroups.

blackThe overall numbers of the galaxies within our analysis (void galaxies,
field galaxies within $\pm 0.05$ dex, and field galaxies within $\pm 0.15$
dex) are documented in Table 1. Note that in the Galaxy Zoo questions, this
table does not provide the number of galaxies with that specific morphological
feature (e.g., the bar voting fraction row does not say how many galaxies have
bars), but rather the total number of galaxies for which we have voting
results.

##  3 Results

After constraining our sample, we analyze and compare the physical properties
of the void galaxiesblack, and compare them to the field galaxy analogues. The
properties included here will be directly relevant to morphology: blackSérsic
index, specific star formation rate (sSFR), and effective radius. Once we
understand the distribution of these components, we can look at specific
morphological voting in Galaxy Zoo.

###  3.1 Physical Properties

Figure 3: Physical properties of galaxies in both samples with redshift black0
< z < 0.075, GAMA black‘twins’ within $\pm 0.05$ dex (left panels) and $\pm
0.15$ dex (right panels). The top panels show specific star formation rate
(sSFR) as a function of stellar mass ($\rm M_{*}$), and the bottom panels show
effective radius ($\rm R_{eff}$; kpc) as a function of $M_{*}$. Points are
colored by their blackSérsic index. blackThe solid black line in the bottom
panels represents the least squares regression line from jacknife resampling,
the equation and error for which can be found in Table 2. Dashed black lines
represent the $\pm 1\sigma$ error.

The physical properties of the galaxy, including the rate at which they are
actively producing stars and their effective radius, provide useful
information about their history and distribution in the Universe. The
following Figures, beginning with Figure 3, allow us to investigate these in
our sample.

black Figure 3 displays the local sample (0 < z < 0.075). In the top panels,
it is clear that the diskier (n < 2; blackshades of blue in Figure 3) galaxies
have blackspecific star formation rates that are nearly two orders of
magnitude larger than the elliptical galaxies (n $\sim$ 4; blackyellow/green
in Figure 3) . In the bottom panels, we see that these ellipticals have
blacksimilar effective radii to the disks, but maintain a similar or slightly
higher (up to an order of magnitude) stellar mass. blackThroughout all of
Figure 3, but most evident in the top panels with sSFR, each
blackmorphological group appears to cluster together. While there is some
slight variation, disk and elliptical galaxies are clearly separated in the 0
< z < 0.075 sample.

If we consider the sample of galaxies blackin the redshift range of
black(0.075 < z < 0.15; Figure 4), we still see this result. While there is a
significantly bigger population of galaxies due to the extended sample size,
we can still clearly discern that in terms of sSFR (top panels), disk and
elliptical galaxies reside in their own regimes.

We note here that we include no analysis on the difference in sSFR between
void and field galaxies, as we use this property to constrain our sample of
field galaxies to those that are intrinsically similar to the sample of void
galaxies.

Figure 4: Physical properties of galaxies in both samples with redshift
black0.075 < z < 0.15, GAMA black‘twins’ within $\pm 0.05$ dex (left panels)
and $\pm 0.15$ dex (right panels). The top panels show specific star formation
rate (sSFR) as a function of stellar mass ($\rm M_{*}$), and the bottom panels
show effective radius ($\rm R_{eff}$; kpc) as a function of $M_{*}$. Points
are colored by their blackSérsic index. blackThe solid black line in the
bottom panels represents the least squares regression line from jacknife
resampling, the equation and error for which can be found in Table 2. Dashed
black lines represent the $\pm 1\sigma$ error.

####  3.1.1 Size-Mass Relation and Effective Radius

Table 2: blackSlope, error, y-intercept, and p-value for the least squares regression lines in the bottom panels of Figures 3 and 4, obtained via jacknife resampling. Error is 1$\sigma$ in regards to the slope. Bold p-values represent significance for a relationship between stellar mass ($\rm M_{*}$) and effective radius ($\rm R_{eff}$).  |  black0 < z < 0.075 |  black0.075 < z < 0.15
---|---|---
| Void Galaxies | ‘Twins’ $\pm$0.05 dex | ‘Twins’ $\pm$0.15 dex | Void Galaxies | ‘Twins’ $\pm$0.05 dex | ‘Twins’ $\pm$0.15 dex
blackSlope | 0.12 | -0.01 | 0.13 | 0.12 | 0.12 | 0.12
blackError |  $\pm$0.05 |  $\pm$0.11 |  $\pm$0.02 |  $\pm$0.03 |  $\pm$0.01 | 0.004
blackY-intercept | -0.66 | 0.72 | -0.77 | -0.61 | -0.63 | -0.67
blackP-value | 0.01 | 0.88 | <0.01 | <0.01 | <0.01 | <0.01

The size of the galaxies in question is a basic morphological property that
can be telling about the galaxy’s history. As a result, the relationship
between effective radius and stellar mass, often known as the galaxy size-mass
relation, is thought to be another indicator of evolution in a galaxy (Van der
Wel et al., 2014; Genel et al., 2018; Mowla et al., 2019; Kawinwanichakij et
al., 2021; Suess et al., 2021; Yang et al., 2021; Nedkova et al., 2022).
Typically, this relation can be understood as larger galaxies tend to also be
more massive, which is commonly thought to be a result of mergers (Hernquist,
1989; Robertson et al., 2006; Naab et al., 2010). In the bottom panels of
Figures 3 and 4, we use jacknife sampling to accurately fit the size-mass
relation, represented by the solid black line.

Focusing specifically on the size of these galaxies, Figure 5 blackrepresents
a similar cumulative histogram of the effective radii to see whether there is
a difference in size between void galaxies and their field counterparts.
blackHere, we see that most galaxies in both samples reside within 1-10 kpc,
as expected. blackIt is interesting to note that, in Figure 4, the line of
best fit is nearly identical across the void galaxies and all samples of field
galaxies, unlike Figure 3, though we note the importance of sample size. When
conducting Kolmogorov-Smirnov (K-S) testing, we blackonly find significance in
the $\pm 0.05$ dex, 0.075 < z < 0.15, sample (see Table 3, Figure 5).

Figure 5: Cumulative histogram of effective radius values. Void galaxies are
denoted in black, whereas twins of the void galaxies in GAMA are in cyan. Left
panels represent twins chosen within $\pm 0.05$ dex of void galaxies, whereas
right panels represent twins chosen within $\pm 0.15$ dex. blackMost panels
show that roughly half of their populations lie within $\rm R_{eff}$ of
$10^{0.5}$ (3.16) kpc.

####  3.1.2 blackSérsic Index

The blackSérsic index is one of the simplest ways to gain insight into the
morphological distribution of galaxies. Plotting histograms of these values,
blackcalculated by Kelvin et al. (2012), allows us to immediately see what the
general distribution of galaxy morphology based on the light profile appears
to be, with disky galaxies residing around n < 2, and ellipticals around n
$\sim$ 4\. In addition, this allows for a direct and normalized analysis
between the samples of void and field galaxies.

For each population of galaxies in Figure 6, we see a clearly defined peak in
the distributions of blackSérsic index at n < 2, with all subsamples having
roughly blackhalf of their galaxies with a blackSérsic index of n < 2black,
and 75% with n < 3, showing that most galaxies in each distribution appear to
be late-type, or disky. Therefore, we immediately see that both void galaxies
and their black‘twins’ in redshift, stellar mass, and sSFR are disk-dominated.
This fact is not changed whether we look at the $\pm$0.05 dex (left panels of
Figure 6) or $\pm$0.15 dex samples of twins (right panels). blackWhile for the
black‘local’ sample we need to be careful in over-interpreting results due to
the smaller sample size of void galaxies, we do find the differences to be
statistically significant for both subsamples of field galaxies within 0.075 <
z < 0.15 (upper panels of Figure 6; see also Table 3).

Figure 6: Histogram of blackSérsic index (n) values. Void galaxies are denoted
in black, whereas twins of the void galaxies in GAMA are in cyan. Left panels
represent twins chosen within $\pm 0.05$ dex of void galaxies, whereas right
panels represent twins chosen within $\pm 0.15$ dex. blackAll panels show that
about 50% of the their populations have a Sérsic index of n < 2, and 75% with
n < 3, showing disk-dominated samples, as ellipticals are n $\approx$ 4\.

###  3.2 GalaxyZoo

Table 3: Significance testing results blackusing the two-sample Kolmogorov-Smirnov test for morphological features between void galaxies and their twins, under the null hypothesis that both samples come from the same distribution. Bold p-values denote significant results black(p-value < 0.05).  |  black0 < z < 0.075 |  black0.075 < z < 0.15
---|---|---
|  $\pm$0.05 dex |  $\pm$0.15 dex |  $\pm$0.05 dex |  $\pm$0.15 dex
| Test Statistic | P-value | Test Statistic | P-value | Test Statistic | P-value | Test Statistic | P-value
blackSérsic Index | 0.10 | 0.66 | 0.07 | 0.94 | 0.09 | <0.01 | 0.13 | <0.01
Effective Radius | 0.14 | 0.24 | 0.09 | 0.72 | 0.09 | <0.01 | 0.03 | 0.88
T00: Features | 0.06 | 0.99 | 0.11 | 0.45 | 0.10 | <0.01 | 0.13 | <0.01
T02: Bar | 0.09 | 0.93 | 0.08 | 0.92 | 0.08 | 0.14 | 0.10 | 0.02
T03: Spiral | 0.25 | 0.04 | 0.27 | 0.01 | 0.08 | 0.09 | 0.10 | 0.01
T04: No Central Bulge | 0.27 | 0.05 | 0.33 | <0.01 | 0.39 | <0.01 | 0.42 | <0.01
T04: Obvious Central Bulge | 0.25 | 0.01 | 0.18 | 0.08 | 0.28 | <0.01 | 0.30 | <0.01
T04: Dominant Central Bulge | 0.11 | 0.60 | 0.13 | 0.33 | 0.29 | <0.01 | 0.32 | <0.01
T07: Edge-on: Rounded Bulge | 0.43 | <0.01 | 0.46 | <0.01 | 0.60 | <0.01 | 0.62 | <0.01
T07: Edge-on: Boxy Bulge | 0.37 | 0.03 | 0.42 | 0.01 | 0.57 | <0.01 | 0.60 | <0.01
T07: Edge-on: No Bulge | 0.37 | 0.01 | 0.40 | <0.01 | 0.56 | <0.01 | 0.59 | <0.01
T09: Evidence of Mergers | 0.13 | 0.37 | 0.13 | 0.27 | 0.09 | <0.01 | 0.11 | <0.01
Figure 7: Histogram comparing the voting fraction for question T00 (presence
of features) in both samples, with a normalized frequency. GAMA black‘twins’
are denoted in cyan, and void galaxies are denoted in black. Left panels
represent twins chosen within $\pm 0.05$ dex of void galaxies, whereas right
panels represent twins chosen within $\pm 0.15$ dex. blackNote that values of
black‘0’ mean that no blackcitizen scientists answered the question with
black‘yes’, while black‘1’ means all answered black‘yes’, or in favor of the
specific morphological component (i.e., features). blackIn the local sample
(top panels), 75% of the population has voting fractions greater than 0.5,
indicating that a majority of the galaxies have features present, while the
further sample (bottom panels) only have 25-50% of their population in the
same range, meaning that features are much less common in this further
redshift range.

Similar to the blackSérsic index and effective radius, we now investigate the
voting fractions from the selected Galaxy Zoo questions. Here, we focus our
attention on the following questions from Figure 1:

  * •

T00 - Is the galaxy in the centre of the image simply smooth and rounded, or
does it have features?

  * •

T02: Is there any sign of a bar feature through the centre of the galaxy?

  * •

T03: Is there any sign of a spiral arm pattern?

  * •

T04: How prominent is the central bulge, compared with the rest of the galaxy?

  * •

T07: Does the galaxy have a bulge at its centre?

  * •

T09: Is the galaxy currently merging or is there any sign of tidal debris?

We choose to skip question T01 (black"Could this be a disk viewed edge-
on?black") because edge-on galaxies are not a type of morphology that can be
caused by environment; edge-on galaxies are merely a result of the viewing
angle, so this specific question is not relevant to this study. Therefore, we
skip to question T07 which contains the morphological information for galaxies
viewed at such an angle.

We also choose to skip questions T05 (black"How tightly wound do the spiral
arms appear?black") and T06 (black"How many spiral arms are there?black")
because we are simply interested in whether the spiral morphology itself is
present as opposed to the intricacies involved.

Figure 8: Histogram comparing the voting fraction for question T02 (black"Is a
bar present?black") in both samples, with a normalized frequency. GAMA
black‘twins’ are denoted in cyan, and void galaxies are denoted in black. Left
panels represent twins chosen within $\pm 0.05$ dex of void galaxies, whereas
right panels represent twins chosen within $\pm 0.15$ dex. blackIn all
samples, 75% of the population has voting fractions less than 0.5, so most
galaxies here do not have a visible bar.

Figure 7 is the beginning of our comparisons in Galaxy Zoo with question T00
(black"Is the galaxy in the centre of the image simply smooth and rounded, or
does it have features?black"). Immediately, we can see that the samples are
blackrelatively similar. blackIn the near sample, we can clearly tell that
both the field and void galaxies within our physical parameters are dominated
by the presence of features, especially compared to the galaxies at higher
redshifts (0.075 < z < 0.15). When we conduct the two-sample Kolmogorov-
Smirnov (K-S) test between the void and field galaxies (see Table 3), we see
significant results in this further redshift range, but low test statistics,
indicating that we can be confident in the samples’ similarity.

Figures 8 and 9 address questions T02 and T03, which ask about the presence of
a bar or spiral, respectively. Here we again note the importance of consulting
the local region (0 < z < 0.075; top panels of Figure 8) for the presence of
bars, as bars are not well resolved at higher redshifts, and Kruk et al.
(2018) similarly limited their sample to z=0.06. blackIn the case of bars, we
see low test statistics across all subsamples, and find significance in the
$\pm 0.15$ dex, 0.075 < z < 0.15 subsample. This indicates almost no
difference in the presence of bars in void galaxies and field galaxies. This
is an interesting result in itself, as bars may be formed by secular
processes, yet we find no difference between the two galaxy populations. In
Figure 9, we see that spirals dominate both the void and field galaxie.
However, at redshifts of 0 < z < 0.075 (upper panels), void galaxies seem to
have a higher fraction of spirals. This is supported by the K-S test, which
reveals moderate test statistics ($\sim$0.25) for the local group, and low
test statistics for the further group ($\sim$0.09), including significance for
three of the four subsamples.

Figure 9: Histogram comparing the voting fraction for question T03 (presence
of spiral blackarm pattern) in both samples, with a normalized frequency. GAMA
black‘twins’ are denoted in cyan, and void galaxies are denoted in black. Left
panels represent twins chosen within $\pm 0.05$ dex of void galaxies, whereas
right panels represent twins chosen within $\pm 0.15$ dex. blackIn the top
panels, about 75% of each population has voting fractions above 0.5, showing
majority spirals. The bottom panels are more evenly distributed, with roughly
half of the populations at a voting fraction above 0.5.

Figures 10, 11, and 12 represent the answers for question T04, which asks
about the prominence of the central galaxy bulge compared to the rest of the
galaxy (for those not identified as edge-on). blackTest statistics for this
question are higher, suggesting the first difference in void and field
galaxies is the prominence of the bulge. blackIn particular, we can note that
the consensus of Figure 12 is that void galaxies in all samples have a bulge
present. All three of these questions appear to be highly significant at 0.075
< z < 0.15, but lose some of their significance in the local sample. This
could be due to a variety of factors, including the limited sample size for
lower redshifts. Question T04 likely needs higher-resolution images to
determine an accurate answer. A larger sample size and highly-resolved images
would be best to follow-up on the dominance of central bulges in field and
void galaxies, particularly to determine whether this is, in fact, a
resolution issue, or whether this is a fundamental morphological difference
between void and field galaxies at higher redshifts.

Figure 10: Histogram comparing the voting fraction for question T04 (black"How
prominent is the central bulge, compared with the rest of the galaxy?black")
with answers for black‘obvious bulge’ in both samples, with a normalized
frequency. GAMA black‘twins’ are denoted in cyan, and void galaxies are
denoted in black. Left panels represent twins chosen within $\pm 0.05$ dex of
void galaxies, whereas right panels represent twins chosen within $\pm 0.15$
dex. blackEach sample has 75+% of their voting fractions above 0.5, so most
bulges can be classified as obvious.  Figure 11: Histogram comparing the
voting fraction for question T04 (black"How prominent is the central bulge,
compared with the rest of the galaxy?black") with answers for black‘dominant
bulge’ in both samples, with a normalized frequency. GAMA black‘twins’ are
denoted in cyan, and void galaxies are denoted in black. Left panels represent
twins chosen within $\pm 0.05$ dex of void galaxies, whereas right panels
represent twins chosen within $\pm 0.15$ dex. blackGalaxies in the local
regime (top panels) do not appear to have dominant bulges, nor do field
galaxies in the further redshift range (bottom panels). Field galaxies in the
latter regime appear to be evenly split.  Figure 12: Histogram comparing the
voting fraction for question T04 (black"How prominent is the central bulge,
compared with the rest of the galaxy?black") with answers for black‘no bulge’
in both samples, with a normalized frequency. GAMA black‘twins’ are denoted in
cyan, and void galaxies are denoted in black. Left panels represent twins
chosen within $\pm 0.05$ dex of void galaxies, whereas right panels represent
twins chosen within $\pm 0.15$ dex. blackAll samples in the top panels have
75% of their population within a voting fraction of 0.25, meaning participants
strongly disagree with there being no bulge. In the bottom panels, this
remains true for void galaxies, but field galaxies appear to be evenly split.
Figure 13: Histogram comparing the voting fraction for question T07 about
edge-on galaxies (black"Does the galaxy have a bulge at its center?black")
with answers for black‘rounded bulge’ in both samples, with a normalized
frequency. GAMA black‘twins’ are denoted in cyan, and void galaxies are
denoted in black. Left panels represent twins chosen within $\pm 0.05$ dex of
void galaxies, whereas right panels represent twins chosen within $\pm 0.15$
dex. black75+% of all samples have a voting fraction greater than 0.5,
indicating participants largely agree with the edge-on bulge being rounded.
Figure 14:  Histogram comparing the voting fraction for question T07 about
edge-on galaxies (black"Does the galaxy have a bulge at its center?black")
with answers for black‘boxy bulge’ in both samples, with a normalized
frequency. GAMA black‘twins’ are denoted in cyan, and void galaxies are
denoted in black. Left panels represent twins chosen within $\pm 0.05$ dex of
void galaxies, whereas right panels represent twins chosen within $\pm 0.15$
dex. blackIn all panels, most void galaxies (75-90%) do not have voting
fractions that represent the presence of a boxy bulge. More than 25% of field
galaxies in the top panels appear to have a boxy bulge, while in the bottom
panels this number raises to more than 50%.  Figure 15: Histogram comparing
the voting fraction for question T07 about edge-on galaxies (black"Does the
galaxy have a bulge at its center?black") with answers for black‘no bulge’ in
both samples, with a normalized frequency. GAMA black‘twins’ are denoted in
cyan, and void galaxies are denoted in black. Left panels represent twins
chosen within $\pm 0.05$ dex of void galaxies, whereas right panels represent
twins chosen within $\pm 0.15$ dex. blackSimilar to Figure 12, void galaxies
in all panels and field galaxies in the upper panels all appear to have a
bulge, while most field galaxies in the lower panels do not.  Figure 16:
Histogram comparing the voting fraction for question T09 (black"Is the galaxy
currently merging or is there any tidal debris?black") with answers for
black‘merging’, black‘tidal debris’, or black‘both’ in void and field
galaxies, with a normalized frequency. GAMA black‘twins’ are denoted in cyan,
and void galaxies are denoted in black. Left panels represent twins chosen
within $\pm 0.05$ dex of void galaxies, whereas right panels represent twins
chosen within $\pm 0.15$ dex. blackMergers do not appear to be occurring in
most of the galaxies included in this study.

Next, Figures 13, 14, and 15 represent the answers for question T07, which
asks about the shape of central galaxy bulge (if one exists) for galaxies
identified as being viewed edge-on. Test statistics for this question are
higher than the face-on group (question T04), suggesting an even higher
contrast between the two types of galaxies blackat this viewing angle. All
three of these questions appear to be highly significant for all subsamples.
Investigating these histograms tells us that people remain in general
agreement with edge-on bulges being rounded in all samples (Figure 13), where
Figure 14 shows a strong disagreement with the presence of boxy bulges in void
galaxies. Similarly, a majority of votes in Figure 15 shows that people
strongly disagree that void galaxies have no bulge. Therefore, we can conclude
that void galaxies are extremely likely to always have a bulge present when
viewed edge-on.

blackWe blackagain note the importance of redshift when it comes to discerning
between round and boxy bulges in edge-on galaxies. When viewing a galaxy edge-
on, it can be much easier to see that a bulge is present than it is to see the
exact shape of said bulge. Especially in less-resolved images, bulges that are
actually boxy may appear to be rounded, and we caution against this bias when
seeing this result, blackand therefore recommend using only the 0 < z < 0.075
sample for forming a conclusion about the shape of an edge-on bulge in
question T07.

Finally, question T09 ("Is the galaxy currently merging or is there any sign
of tidal debris?") can be investigated by referencing Figure 16. For
simplicity, we are more concerned with identifying the general presence of
mergers as opposed to the identification method (tidal debris, visible
mergers, or both). Because question T09 has four possible choices, if we then
group the three positive identifications of mergers together into simply,
"Evidence of Mergers", it then becomes redundant to include "Neither", as the
sum of all four must equal one, and they will then have the same statistics.
From this point on, we will only refer to question T09 as, black"Evidence of
mergers?" with the general answers being "Yes (presence of tidal debris,
visible mergers, and/or both)", or "No".

This question and all four possible answers are extremely relevant to this
study, as the presence of merging galaxies and tidal debris are direct
consequences of denser environments. It is with simple logic that we would
hypothesize void galaxies have a much lower possibility of either of these
occurring due to their isolated nature, but our results contradict this
assumption.

blackFrom Figure 16, there is a strong general disagreement for the presence
of mergers in void and comparable field galaxies. We can effectively conclude
that there does not appear to be signs of active merging in our sample
black,especially because we do not find any form of statistical significance.
However, this Galaxy Zoo question only accounts for mergers in-progress
(presence of a merging satellite) or relatively recently (tidal debris). This
does not account for past mergers that may be revealed through an analysis of
star formation histories. blackIn addition, because we limit our definition of
void galaxy black‘twins’ to be within either $\pm 0.05$ or $\pm 0.15$ dex in
terms of stellar mass and sSFR, this could likely account for the lack of
mergers. Merging galaxies are known to cause a significant increase in both
star formation rates and stellar mass. Therefore, not allowing for field
galaxies to have a significantly higher $\rm M_{*}$ or sSFR could be why we do
not see strong signs of mergers.

##  4 Discussion

Through investigating true void galaxies identified by Alpaslan et al. (2014),
we are able to uncover what (if any) blackeffect the environment has on local
galaxy evolution. For the most part, we find that our results align with
previous literature, and any deviations can be logically explained.

Rojas et al. (2004) uses nearest-neighbor statistics in SDSS to investigate
the blackSérsic index of void galaxies and black‘wall’ galaxies. Similar to
the work done here, blackthey blackemployed the Kolmogorov-Smirnov test to
test for blacksignificance in the difference between Sérsic index
distributions of their subsamples (void and wall galaxies, near and far), and
found significance in the far sample. blackHere, we also find no K-S
significance in our local galaxies, with it only being evident for our far
sample, but with low test statistics. From Galaxy Zoo, the 0.075 < z < 0.15
sample stands out for a few questions: in many cases, we see extremely high
significance that is not replicated in the near sample, 0 < z < 0.075. blackIt
is possible that these results are due to the low sample size of our "local"
region, as the statistical significance tests (i.e., the Kolmogorov-Smirnov
test) are normalized by the sample size, and therefore small sample sizes are
less optimal for performing such tests. blackIt is also worth notice that the
"near" sample from Rojas et al. (2004) uses a maximum redshift ($\rm z_{max}$)
of 0.025, where ours is 0.075, and for their far sample, $\rm z_{max}$ =
0.089, while ours is z = 0.15. blackClearly, how redshift is analyzed has a
clear significance to results.

When it comes to the physical properties, we note that while most previous
literature conducts analysis on the star formation rates of void galaxies
compared to those in denser environments, we refrain from doing so because we
have specifically selected field galaxies to be similar in blackspecific star
formation (within $\pm 0.05$ and $\pm 0.15$ dex).

We remain in general agreement when it comes to previous findings on void
galaxy morphology as a whole. We find that void galaxies are dominated by
late-type, or disky, galaxies (Van de Weygaert et al., 2011; Beygu et al.,
2016; Pustilnik et al., 2019). blackWe note that we have inconclusive results
with regard to findings from Rojas et al. (2005) stating that void galaxies
have more spiral galaxies. We find that both field and void galaxies are both
dominated by spirals, and Figure 9 appears to show that there are more spirals
in void galaxies in the local regime. This is supported by higher test
statistics in this redshift range from Table 3. However, the higher redshift
field and void galaxies appear to have little difference in the voting
fraction of spirals, and show lower test statistics. Nearly all of these test
statistics have high significance.

blackFor question T07 ("Does the galaxy have a bulge at its center?"), we note
the difference in samples (and high K-S test statistics), displayed
graphically in Figure 15. A large majority of the Galaxy Zoo blackcitizen
scientists disagree with the fact that void galaxies have no bulge, indicating
that they nearly always have a bulge present, and that this bulge is
blackusually rounded.

From an inside-out galaxy formation perspective, the definite presence of
bulges, blackparticularly those that are obvious/dominant round ones, makes
sense. In such a galaxy formation model, the inner bulge is the oldest part of
the galaxy, and blackslowly accretes surrounding material to form the disk
(Kepner, 1999; Robertson et al., 2004; Van Dokkum et al., 2010; Nelson et al.,
2012, 2016). In the case of our void galaxies, as a result of their isolation,
the lack of material to accrete would result in the bulge being far more
dominant than the disk. This follows the results that we see in the Galaxy Zoo
voting fractions for obvious and dominant bulges, blackthe bulge shapes, and
the dominance of disk galaxies (which is also supported by the GAMA Sérsic
index).

blackOn the topic of bulges, we found earlier that there is a strong
disagreement for the presence of bars and boxy bulges in the samples,
especially for the void galaxies (see Figures 8 and 14). There currently exist
several arguments in literature, such as those by Kruk et al. (2019) and
Peschken & Łokas (2019), that bars can be tidally induced. blackThrough
logical reasoning, one could assume that these tidally-induced bars would
therefore happen at higher rates in denser environments, which has the
potential to explain Figure 14. Question T09 in Figure 16 shows little
evidence of mergers, one sign of which includes tidal debris, and therefore
these two questions may be linked. We previously explained that reducing the
accepted stellar mass and specific star formation rates for analogue void
galaxies has likely affected our results on mergers. Therefore, if these tidal
interactions from nearby galaxies can cause bars to form in galaxies, our
reduction in stellar mass and star formation may also be affecting the results
for barred (or boxy edge-on) galaxies.

##  5 Conclusions

In this paper we presented an overview of void galaxies identified by Alpaslan
et al. (2014), focusing on the properties of blackSérsic index, stellar mass,
specific star formation rate, and effective radius. In addition, we used the
Galaxy Zoo Survey to investigate the morphological voting fractions, with the
goal of determining blackthe typical void galaxy morphology, and whether void
galaxies are morphologically different from their field galaxy counterparts.
We can summarize our findings through the following points:

  1. 1.

blackBoth void and field galaxies, as seen in the Sérsic indices (Figure 6)
and presence of features in Galaxy Zoo (Figure 7), are dominated by disk
galaxies. However, we do not find evidence that void galaxies exhibit a higher
fraction of disks.

  2. 2.

In all subsamples of blackfar edge-on galaxies, we see strong indicators that
the bulges of void galaxies are round as opposed to boxy, blackand results are
highly suggestive that void galaxies almost always have a bulge (Figure 15,
Table 3). blackThe significant differences in rounded edge-on bulges are also
found in our local sample.

  3. 3.

Neither field nor void galaxies appear to show strong evidence of mergers
occurring, despite their difference in environment density. blackHowever, this
is likely due to our imposed restraint on stellar mass and star formation
rates, as mergers are known to cause a strong increase in both quantities.

  4. 4.

We see little difference in the results for how we define the void galaxy
counterparts in GAMA (black‘twins’), blackwhether we select stellar mass and
specific star formation rates within $\pm 0.05$ dex or $\pm 0.15$ dex, but
redshift appears to have an affect.

Overall, we see that void galaxies are rather similar to field galaxies,
especially in a limited redshift range for the local Universe. However, we do
see evidence from our conclusions that point to how isolated galaxies may
evolve differently from their counterparts in filaments and tendrils.

While our results primarily match previous literature, this study still
consists of few void galaxies and analogues, therefore relying on a smaller
sample size to conduct analyses compared to the wealth of field galaxies
available with GAMA. Investigating the star-formation histories of these
galaxies, blacksuch as using data from studies such as Bellstedt et al.
(2020), would be ideal to determine how these galaxies are fueled, and whether
these assembly histories differ for void galaxies. blackSimilarly, studying
the B/D ratios (e.g., Casura et al. (2022)) of these samples could also
provide morphological information beyond the scope of this paper. In addition,
employing techniques to identify a larger catalog of void galaxies would be
ideal in order to perform further analysis. Future study into the history and
morphology of void galaxies would provide a more quantitative understanding of
whether they are truly different from those in denser parts of the Universe,
and whether their isolation is the specific cause.

## Acknowledgements

The material is based upon work supported by National Aeronautics and Space
Administration (NASA) Kentucky award no. 80NSSC20M0047 blackOGMB 220984 (NASA-
REU to B.W. Holwerda and L.E. Porter).

This research made use of ASTROPY, a community-developed core PYTHON package
for astronomy (AstropyCollaboration et al., 2013, 2018), blackDR4 of the
Galaxy and Mass Assembly Survey (Driver et al., 2022), and Galaxy Zoo (Kelvin
et al. in prep). We are grateful to members of GAMA and Galaxy Zoo for
contributing to this paper.

## Data Availability

blackThe data for this project are available from the GAMA DR4 website
(http://www.gama-survey.org/dr4/).

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# Imitation-Based Active Camera Control with Deep Convolutional Neural Network

Christos Kyrkou,
KIOS Research and Innovation Center of Excellence
University of Cyprus
1 Panepistimiou Avenue, Nicosia Cyprus
<EMAIL_ADDRESS>
ckyrkou@gmail.com,www.christoskyrkou.com

###### Abstract

The increasing need for automated visual monitoring and control for
applications such as smart camera surveillance, traffic monitoring, and
intelligent environments, necessitates the improvement of methods for visual
active monitoring. Traditionally, the active monitoring task has been handled
through a pipeline of modules such as detection, filtering, and control. In
this paper we frame active visual monitoring as an imitation learning problem
to be solved in a supervised manner using deep learning, to go directly from
visual information to camera movement in order to provide a satisfactory
solution by combining computer vision and control. A deep convolutional neural
network is trained end-to-end as the camera controller that learns the entire
processing pipeline needed to control a camera to follow multiple targets and
also estimate their density from a single image. Experimental results indicate
that the proposed solution is robust to varying conditions and is able to
achieve better monitoring performance both in terms of number of targets
monitored as well as in monitoring time than traditional approaches, while
reaching up to 25 FPS. Thus making it a practical and affordable solution for
multi-target active monitoring in surveillance and smart-environment
applications.

_K_ eywords Real-Time Active Vision, Smart Camera, Deep Learning, End-to-End

##  1 Introduction

Active vision systems (i.e., movable cameras with controllable parameters such
as pan and tilt) have received much attention in recent years due to their
extended coverage, flexibility, cost-efficiency compared to static vision
systems [1]. Active cameras can be used to track targets (i.e. follow them)
and can provide continuous monitoring of an area reliably and robustly and are
increasingly being used for various applications ranging from surveillance[2]
to intelligent interactive environments[3]. However, there is a limited number
of cameras that human operator can monitor and control hence, there is a need
for for automated, robust, and reliable systems for active vision. In
addition, there are additional challenges for systems operating with battery
limitations or in remote locations and with requirements for rapid deployment
in temporary installations necessitating reduced computational cost and
simpler active vision systems.

Existing approaches for automated active vision decompose the active control
problem into separate modules, such as detection, tracking, and control [4],
and employ different algorithms at each step. Such examples include motion
detection, background modelling/subtraction, and lastly tracking by detection.
The former two are widely used in static camera scenarios [5] due to their
relative computational efficiency however, for active cameras that move and
exhibit constant background change the latter methods are preferred since they
are more widely applicable. Such techniques are often augmented with post-
processing filters that increase the computational complexity and may also
susceptible to false alarms and outliers. Hence, existing methods that rely on
hand-crafted features, motion models, and modeling of the camera views are not
optimized for active vision scenarios.

Figure 1: (top) Traditional multi-stage active monitoring vs. (bottom) End-to-
end control with deep neural network (DNN). The DNN learns though examples how
to control the camera to simultaneously recognize targets and keep them in its
Field-of-View (FoV).

To deal with the aforementioned challenges in this paper we propose leveraging
Convolutional Neural Networks (CNN) and end-to-end imitation-learning to
develop an active vision system for monitoring people in surveillance
applications. To the best of our knowledge there has not yet been any attempt
to deal with active tracking of multiple targets in an end-to-end way. In this
work, we investigate it and present its appealing potential. In particular an
Active Camera Deep Controller Network, referred to as ACDCNet, is trained in
an end-to-end manner through imitation learning to associate single image
features with control actions. End-to-end learning approaches allow
encapsulating all the intelligence into the machine learning algorithm thus
can optimizing all processing steps simultaneously and learning the features
to associate with camera control for visual active tracking. In addition, it
can result into smaller less complex smart camera systems.

The proposed approach has been verified by extensive experiments using
simulation to replicate the motion of the camera and targets. Results indicate
that the proposed deep active monitoring approach outperforms some
representative methods, composed of several submodules including object
detection and tracking, for following multiple targets.

##  2 Background and Related Work

The aim of static object tracking is to localize an object in successive video
frames given an annotation the initial frame. It has gained more attention due
to its relatively simpler problem setting [6]. However, the video frames are
considered still and hence the approach is not applicable to active cameras
where in addition to the challenges associated with moving objects and
changing scene perspectives, there is also the issue of controlling the camera
and optimize its position for the given vision task. Since the camera itself
is constantly changing its orientation, object initialization and continuous
tracking pose great challenges. Standard techniques such as foreground
segmentation, motion detection or optical flow may face difficulties as the
background is constantly changing.

The goal of active monitoring in contrast to a static monitoring setting is to
change the camera control parameters in order to maximize a visual-task-
related performance objective such as following one or more targets that are
located within the field-of-view (FoV), in order to improve the overall
surveillance and monitoring capabilities [7]. Active cameras have gained
considerable interest in recent years[8], however, there still does not exist
a generic solution. Conventional solutions for active visual monitoring tackle
the problem by decomposing it into two or more sub-tasks [9]., i.e., object
detection typically using a machine-learning-based classifier/detector, a
tracking algorithms such as Kalman filter, and a control output for the camera
movement. In such case, each task is optimized individually resulting in
highly complex systems with many tuning parameters. Furthermore, this leads to
difficulty in obtaining real-time performance on resource-constraint embedded
camera systems. Different works have investigated the use of active cameras
with one or more degrees of freedom to address the problem of monitoring an
area and are summarized next.

Initial approaches such as [10], followed a master-slave approach used to
track targets at a high resolution. One camera, the master, has a wide FoV and
performs blob detection and uses a Kalman filter to track a target in an area
and by projecting from image plane to world coordinates it controls (pan,
tilt, and zoom) the other active camera, the slave, to follow a target. In
contrast our goal in this work is to improve the tracking performance of a
single camera agent so that it can autonomously follow the majority of targets
in its FoV.

In [11] an Extended Kalman filter is used to jointly track the object position
in the real world as well as estimating the intrinsic camera parameters. The
filter outputs are used as inputs to two PID controllers (one for pan and one
for tilt motion axis) which continuously track a moving target at a certain
resolution. The focus of this work is on tracking only a single target
however, and the objects are assumed to have a predetermined size.

The active camera system proposed in [3] is composed of multiple components in
order to track a subject. The face of the target is identified through a face
detection system and then a tracker is employed to estimate the targets motion
across frames based on previous observations. An online learning approach is
also used to learn the appearance model over time and reduce false detections.
In addition, Gaussian Mixture Models are used to model the body movement in
case the face detection fails. The final part is the controller of the pan-
tilt camera which makes its decision of how to move based on where in the
image the target is positioned and using a set of rules. Such multi-component
system can be difficult to tune and transfer to more resource-constraint
systems that monitor multiple targets.

Finally, in [12] an end-to-end active tracker is proposed for following a
character in the VizDoom video game environment. It uses reinforcement
learning to train an CNN with LSTM to output movement actions for following a
single target. Even though they are somewhat realistic, these scenarios do not
correspond to real-world use cases. Furthermore, the step-based output is not
suitable for the dynamic range needed to control a pan-tilt camera.

In summary, it is evident from the literature that related works make
excessive use of multiple modules composed of hand-crafted models and rules
that must be tuned separately and in most cases track only a single target.
While there has been considerable progression in utilizing deep learning for
static camera tracking there has been relatively few works dealing with deep
learning for active smart camera systems. Hence, in this work we attempt to
bridge the gap between the use of active cameras with deep learning algorithms
by proposing an end-to-end learning approach to simultaneously build a
detector and controller for cameras with pan and tilt motion capabilities.

##  3 Active Camera Control with Deep Learning

###  3.1 Imitation Learning Approach

To solve the problem of active visual control for target following we frame
the problem in an imitation learning setting to be solved in a supervised way.
Under this setting the agent (learner) needs to come up with a policy whose
resulting state-action behaviour matches the expert behaviour. 111Such expert
behaviour can be gathered by appropriate datasets with bounding box
annotations for targets from which the camera movement can be extracted.. For
this specific problem the behaviour is how to control the camera given an
input frame to keep most of the targets in the field-of-view (FoV). It is
assumed that expert state-action pairs are available,
($s_{1},a_{1}$),($s_{2},a_{2}$),…,($s_{N},a_{N}$) where $s_{i}$ are the image
frames and $a_{i}$ are the associated camera actions, such that can form a
training set. The expert behaviors are assumed to be i.i.d and then train a
regressor network end-to-end in a supervised manner, to learn a control
function $f$ that maps observations to actions such that $a_{i}\simeq
f(s_{i})$. In doing so, the desired actions are directly regressed during
inference, without having to explicitly train the network to first detect the
targets (Fig. 1).

A pinhole model [8] is assumed for the camera, and the desired actions are to
control its servo motors along its pan and tilt axes (denoted by $a^{P}$ and
$a^{T}$). Each image $s_{i}$ has resolution $I_{x}\times I_{y}$. Under these
circumstances the pixel distances between the image center to the center of
mass of the targets is analogous to the angle that the servo motors have to
move in order to position the target(s) at the center of FoV (as shown in Fig.
1) [4, 2]. In addition, the motion of the camera when tracking targets in its
FoV is bounded by the half of its horizontal and vertical angles of view
(denoted as $\theta_{x},\theta_{y}$). Accordingly, the motion of the camera in
the pan and tilt axes can be calculated with respect to the viewing angles.
This can be done by first calculating the distance of the camera center from
the target(s) center of mass for the horizontal and vertical direction
($d_{x},d_{y}$), and then use Eq. 1 and 2 to associate the pixel distance to
the camera angles as also illustrated in (Fig. 1). Hence, during the learning
process the objective is to map the input image to normalized pixel
displacement values ($d_{x}/I_{x},d_{y}/I_{y}$), which will then be used to
calculate the corresponding servo motor angle displacements in the pan and
tilt axis. Predicting offsets instead of angles simplifies the problem and
makes it easier for the network to learn. Furthermore, it decouples the
learning process from camera specific parameters.

$\displaystyle
a^{P}\rightarrow\dfrac{d_{x}}{I_{x}}\times\dfrac{\theta_{x}}{2}$ (1)

$\displaystyle
a^{T}\rightarrow\dfrac{d_{y}}{I_{y}}\times\dfrac{\theta_{y}}{2}$ (2)

Figure 2: Example of augmented images from the dataset.

###  3.2 Data Collection and Training

Proper training and testing data are necessary to train a deep CNN regressor
for the visual active monitoring task. To the best of the author’s knowledge
there is no publicly available dataset for active vision surveillance
applications with ground truth camera controls. For this reason existing wide
surveillance image databases, such as the PETS2009[13], used for static
tracking, are re-purposed to develop a simulation framework that allows for
acquiring state-action pairs corresponding to an image frame with the action
in image space needed to position the camera to the center-of-mass of the
targets in the frame. These ground truth information that can be used for both
training and evaluation. In addition, it allows for simulating active cameras
and evaluating performance with real-world images, and capturing and storing
multiple frame sequences with expert ground truth data for bounding box,
density, and camera control. The simulation framework also simulates the
movement of a virtual active camera with pan-tilt control with a fixed FoV
that is able to move within a larger image frame.

Figure 3: Distribution of the pan and tilt values from the images in the
dataset. Figure 4: ACDCNet Architecture: Conceptually comprised of a feature
extractor and a controller that condenses the high level semantic information
to infer an action. Then it regresses the motion for the camera head along the
pan and tilt axes as well as the number of targets in the frame.

An initial dataset of over $3100$ images was generated using the simulation
software and sequence from the PETS2009[13] database in order to train
ACDCNet. Starting at various positions in random frames in the sequence we
calculate the changes in displacement of pan and tilt axes according to Eq. 1
and 2 so that the targets will be positioned at the camera image center in the
next frame. Hence, the training set effectively contains single images sampled
from the sequence, paired with the corresponding pan and tilt displacement
that must be applied. The pan and tilt displacement values are normalized
between $-1$ and $1$ with regards to the maximum motion of the camera in both
axes. As such, it is also possible to apply any mapping function to scale the
output depending on the required configuration. It is also possible to extract
different resolution images with varying number of targets in each one, For
this work images of $320\times 240$ are targeted. It is worth noting that any
input image size can be processed after being re-sized appropriately and from
cameras with different angles of view. Examples of some of the images in the
dataset are shown in Fig. 2

An important part of data preparation is balancing the data. During the data
collection process depending on the motion of successive frames, the target
displacement values may not change significantly in both axes. Also successive
frames may have high correlation and hence little to no motion in both axes.
As a result, as shown in Fig. 3 the distribution of camera motion values might
be imbalanced. To ensure that the learning algorithm does not overfit to the
majority of values around zero, the data in each batch is sampled to contain
high as well as low values so that the network better learns when and how to
move.

The whole data is split into $75\%$ for training the CNN regression model, and
$25\%$ of the data was used for testing the final accuracy of the model as
well as to compare with other methods. Furthermore augmentations are
probabilistically applied to the images during training, to increase the
variability and combat over-fitting. The augmentation strategy included some
transformations on the image pixels such as blurring and sharpening, color-
shifting, illumination changes as well as changes in the image orientation
such as translations and horizontal flip with appropriate adjustment of the
target pan and tilt values if a geometric augmentation is applied. The
combinations of all these augmentations resulted in a variety of novel images
that were used for training.

###  3.3 Active Camera Deep Controller Network (ACDCNet)

ACDCNet is trained to perform the regression tasks of estimating the camera
motion displacement and the number of targets in the frame. Figure 4 shows the
network architecture which is conceptually comprised of two main parts, a
feature extractor made up of convolutional layers and a motion controller that
summarizes the feature maps in order to produce the final output values.
Although it is difficult to distinguish the parts of the network that function
primarily as feature extractor and which serve as controller since the system
is trained end-to-end. The input to the CNN is a $320\times 240$ RGB image
which is normalized by dividing the pixels by $255$.

Convolutional Feature Extractor: The layers were designed to perform feature
extraction and were chosen empirically through a series of experiments that
varied layer configurations. There are $7$ major blocks each comprised of a
convolutional layer with leaky relu activation with $\alpha=0.3$ and batch-
normalization layer. Furthermore, dropout is applied at the middle of the sub-
network to combat overfitting with a rate of $0.2$. Overall, the feature
extractor is designed to be inherently computationally efficient to support
use in embedded smart cameras for local control and decision making. For this
reason the first $3$ layers downsample the image to reduce the computational
cost and have a small number of filters, and overall the filters do not exceed
$128$. After the first $3$ layers the resolution is not reduced further to
improve accuracy. The primary goal is to build a small neural network for on-
board processing but alternatively transfer learning techniques using other
backbone networks can also be applied.

Controller Subnetwork: The controller subnetwork is comprised of both
convolutional as well as fully-connected layers. The idea behind this is that
the convolutional layers will condense the information from the feature
extractor; then the final convolution will convert the feature map into a
vector. It is then followed by $2$ fully connected layers with $100$ and $50$
neurons respectively to map the vector to the motion controls. There is a
dropout in between the dense layers and all layers have an elu activation
function for faster convergence. The output of the controller subnetwork is
further processed through a clipped linear activation that bounds the output
between $[-1,\dots,1]$ to estimate the motion in the horizontal and vertical
direction more effectively. The third output neuron that regresses the number
of targets uses a ReLU function to discard negative numbers. Overall, ACDCNet
has a total of $\sim 386,000$ parameters. This results in a small network
which requires $\sim 4$MB, resulting in a lightweight network that can run
even on low-end CPUs.

###  3.4 Network Training

The objective of the learning process is to regress two motion values in the
pan and tilt axes, and the number of targets. Accordingly, the loss function
in Eq. 3 is employed for learning the camera controls and target count. The
Keras deep learning framework [14] with Tensorflow [15] running as the backend
is used for the training of the CNN regressor. The network was trained using a
GeForce Titan Xp, on a PC with an Intel $i7-7700K$ processor, and $32$GB of
RAM. The Adam optimization method was used for training with a learning rate
step-decay approach starting from an initial learning rate of $0.001$, and
decreasing it by a factor of $0.95$ every $5$ epochs. The CNN regressor is
trained for $500$ epochs with a batch size of $32$ resulting in $3100$
generated training images per epoch.

$\displaystyle
L=\dfrac{1}{N_{B}}\sum^{N_{B}}_{j=1}\bigg{[}(y^{true}_{c}(j)-y^{pred}_{c}(j))^{2}+$
$\displaystyle|y^{true}_{d_{x}}(j)-y^{pred}_{d_{x}}(j)|+$
$\displaystyle|y^{true}_{d_{y}}(j)-y^{pred}_{d_{y}}(j)|\bigg{]},$ (3)

##  4 Evaluation and Experimental Results

To compare the proposed method a traditional active tracking pipeline is
implemented following other relevant approaches for active camera control [9].
In this paradigm an object detector is used to localize the targets and a
tracker is applied to filter the detections over time. Finally based on the
filter target positions the camera is moved to position the targets as close
to the center as possible. The control is performed using the simulation
framework as discussed in Section 3.2 and is the same for all methods.

We use the YOLO [16] framework to comparison with single-shot detectors which
are considered more suitable for real-time applications and can be leveraged
for real-time embedded systems. We show herein comparisons with the orignal
smaller YOLO variant referred to as tinyYOLO. Comparisons are also made
against the widely used SVM-HOG pedestrian detection algorithm [17]
implemented in OpenCV [18] and still favored for embedded applications and
especially suitable for low-power systems [2]. On top of the detectors we
apply tracking with Kalman filter (denoted with _T in the Figures) which is a
common approach used in active tracking [8, 11]. The incorporated filtering
handles bounding box associations, maintains trajectories, and handles the
creation and termination of tracks.

The proposed model is evaluated experimentally in a number of ways to
determine its overall performance. For the first experiment we use a test set
of $500$ images not used in the training process, with ground truth camera
motion information in order to calculate how accurate is each method in
estimating the camera motion controls for positioning targets at the center of
its FoV as well as regressing the number of targets. As shown in Fig. 5 the
proposed CNN achieves the lowest error across the different methods. In
practice this means that it will follow the targets better since it has not
have to deal with bounding box localization errors that can steer off the
camera control. In particular, for the case of estimating the number of
targets the other methods can be as off as 1-2 targets. Furthermore, the lower
errors also mean that in cases where there is no target in its FoV the network
has recognized that it should not move, and in case of many targets it
attempts to follow their center of mass thus keeping the majority of them in
view.

The next experiment involved evaluating all the aforementioned methods in the
simulation environment and measure important metrics such as the average
number of targets followed. This provides an indication of how well each
approach manages to keep up with the target motion as well as how many targets
it can keep in its field of view. To conduct these sequences where generated
from the PETS2009[13] dataset for which the ground truth bounding box
annotations is available but have not been used in the training and validation
phases. These sequences provide an additional challenge as they feature
different visual conditions with high density crowd densities and motion
patterns. The images in the sequences are of $768\times 576$ resolution and
the virtual camera FoV is set to $320\times 240$ for all methods so that there
is margin for the camera to move and follow the targets.

The developed simulation framework outlined in section 3.2 models the camera
motion based on the visual input and evaluates its performance. The output of
each vision pipeline is a motion vector that will be passed to the simulator
to perform the action. The camera FoV for all methods is set at the same
initial position. In all cases the objective of the camera is to move in such
a way as to keep the most number of targets in its FoV. We also report the
ground truth motion which represents the motion of the camera when the target
positions are perfectly known.

Figure 5: Errors for the different regressed quantities for each approach.
Figure 6: Average number of targets monitored over time for each approach.
Figure 7: Frames-per-Second (FPS) achieved by each approach. Figure 8: Example
of detection/predictions and estimation for number of targets. A common
mistake by HoG-SVM and YOLO involves missing targets. In addition, other
source of mistake relate to wrong localization with the bounding box. In both
cases leads the camera to move in the wrong direction. Finally ACDCNet is able
to correctly regress the number of targets and chooses to not move the camera
in these frames as the targets are mostly in its FoV. (Best viewed in color)
Figure 9: Example of applying the approach to real-world images. The motion
vector shows the predicted motion that the camera will make to keep the
targets in its field of view. (Best viewed in color)

The results are presented in Fig. 6 and Fig. 7. The proposed system manages to
surpass the other approaches and be close to the optimum based on the number
of targets tracked over the length of the sequences. The proposed approach
also manages to have a performance of $\sim$ 25 frames per second on a CPU.
Since this is a simulation the effect of processing time was not evaluated
directly. However, since the inference time of the other methods is higher it
is expected that in real conditions slower methods will miss even more
targets. Hence, the proposed approach provides a much more efficient way of
building reactive active vision systems that can also be more responsive to
the target motion. Overall the performance gains between the proposed and
other methods can be attributed end-to-end nature of our approach that
associates lower-level-features with control actions and does rely on bounding
boxes. As a result ACDCNet manages to handle more dense targets better. Fig. 8
demonstrates some cases that cause errors in the traditional detection
approaches; while Fig. 9 also demonstrates the fact that the approach can
generalize in out of domain images gathered from real-world settings.

##  5 Conclusion

This work addresses the problem of controlling a smart camera for active
vision applications (surveillance, drones, vehicles, smart environments). One
of the major contributions is that the problem is tackled via end-to-end
learning using deep convolutional neural networks. A CNN architecture referred
to as ACDCNet is proposed that maps input images to pan and tilt motion
command with the goal of keeping targets in its field-of-view. Even with
single frame information the proposed network outperforms other multi-stage
approaches in terms of monitoring efficiency and provides higher frame-rates
while being lightweight. The results are promising and as future work we will
further explore what the network actually learns through its internal
representations, and deploy it in a real experimental setup for further
evaluation.

## Acknowledgment

This work was supported by the European Union’s Horizon 2020 research and
innovation programme under grant agreement No 739551 (KIOS CoE) and from the
Government of the Republic of Cyprus through the Directorate General for
European Programmes, Coordination and Development.

The author would like to acknowledge the support of NVIDIA Corporation with
the donation of the Titan Xp GPU used for this research.

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