You will be presented with the full text of a science research paper. Please write an abstract for this paper. Your response should include the abstract and no additional text.

Paper text:
neyman and scott ( 1952 , 1953b ) , using statistical techniques based on counts - in - cells , showed that the galaxy distribution is statistically clustered rather than statistically uniform , and on the other , abell actually identified from palomar sky survey plates , 2712 operationally well - defined rich clusters of galaxies ( abell 1958 ) . to better describe the clustering property , the two - point correlation function ( peebles 1973 ) and continual high order correlation functions ( croton et al 2004 ) are widely used .
high density regions , such as filaments ( wu et al . 2012 ) , superclusters ( connolly et al . 1996 ) and low density regions , such as voids ( danny et al . 2012 ) , are discovered and well discussed . at the same time , people begin to have interest for the comparison of high density and low density region .
if the early universe is grown from quantum fluctuations , then positive and negative fluctuations will have the same probability and a sponge - like structure ( high density regions have the same topology with low density regions ) is doomed ( gott 1986 ) . with the evolution dominated by gravitational instability ,
the sponge - like structure is most likely remained whatever the growth stays in the linear regime or is damped ( bond & szalay 1983 ) .
gott ( 1986 ) found that both two regions have similar properties from the measured density contours , such as sponge - like shape , connectedness .
however , gott ( 1986 ) mentioned a direct test more than measuring density contours is needed .
here we use the hexagon cell method to investigate the equivalent of high density and low density regions .
our hexagon cell method is inherited from the dodecahedron cells ( kiang 2003 , kiang et al 2004 ) ; it is actually a 2-d application of dodecahedron cells method .
different cells have been applied to analyze the topology of galaxy distribution , such as truncated octahedrons ( coxeter 1937 ; gott 1967 ; gott 1986 ) , voronoi foams ( icke and weygaert 1987 ) , dodecahedron cells ( kiang 2004 ) ; 2d topological structure of the observed universe has been investigated by variety of methods , such as genus method ( davies & coles 1993 , colley 1997 , hoyle & vogeley 2001 , hoyle et al 2002 ) , percolation and ?
lamentarity ( pandey & bharadwaj 2008 ) .
colley ( 1997 ) found that the 2d genus of the las campanas redshift survey is very close to a gaussian random field , hoyle claimed the genus of 2 degree field galaxy redshift survey team ( 2dfgrs ) and sloan digital sky survey ( sdss ) reveals a smaller number of isolated voids than clusters ( hoyle & vogeley 2001 , hoyle et al 2002 ) .    the motivation of this paper is to investigate the topological relation between low density regions ( such as voids ) and high density regions ( such as clusters ) to get more understanding of the early universe .
our article is organized as follows . in section 2
we present the hexagon cells method . in section 3
we study the data from the 2mass .
we summarize the results in section 4 and have conclusions in section 5 .
if we partition the 2-d space into cells with the shape of hexagon , we can get hexagonal lattice .
hexagonal lattice is one of the five 2d lattice types and is the only lattice which can fill the 2d space inseparably with more edges than square . in the natural world
, honeycomb is an interesting example of hexagonal lattice . for bees , hexagon is the most efficient shape for the bees living and storing of food . in the reality ,
the hexagon structure provides the maximum strength and that it is used in designing airplane wings and satellites walls .
the reason of using hexagon cells in this paper is that we want to have the direction detection as many as possible for our unit cells .
hexagon cells could detect the neighbors in six directions and provide us the rich topology information , and at the same time fill in the space without overlap or missing region .
for an application of hexagon method on galaxy distribution , similar with the definition of rhombic cell in kiang ( 2003 ) , if a hexagon cell contains no galaxies , then we call it an empty cell ; otherwise , it is a filled cell . automatically empty cells represent the low density region and filled cells represent the high density region . by this definition
, we could discover if the filled and empty regions have the same morphology and give us a quantitative description of the topology .
we know the hexagons have 6 neighbors and 6 edges shared with neighbors .
if two neighbor cells are both filled or both empty , then we define their common edges as inner edge ; otherwise we call it as outer edge .
we use n to define the number of inner edges .
the physical meaning of n is to find the same kind of neighbors for each hexagon and investigate the aggregation pattern for filled and empty cells . in this way
n is the approximation of the two point correlation function in a specific small scale .
if filled cells are not distributed in space randomly , we can expect the distribution of n will be depart from the well - known binomial form , same thing for empty cells .
this in turn will tell us the morphology similarity and difference of high density and low density regions .
based on the definition of @xmath0 , we could divide the six edges into inner edges and outer edges two groups and consider the connectedness of inner edges or outer edges .
we use @xmath2 to represent the number of connected inner edges group and use @xmath3 to represent the number of connected outer edges group , that is @xmath1 ( see fig .
1 ) . so @xmath4 means a single cell surrounded by 6 unlike neighbors ( same with @xmath5 ) and @xmath6 means a single cell surrounded by 6 like neighbors ( same with @xmath7 ) .
@xmath8 means likely that the cell is on the boundary of the clusters or voids , so its two kind of neighbors are connected separately .
@xmath9 represents a string - like structure and the string penetrates the cell and results in two groups for each of kind neighbors .
@xmath10 is complicated and its special shape possibly implies a mesh structure .
to better understand the @xmath0 and @xmath1 distribution difference between observed and random sample , similar with the method mentioned by kiang ( 2003 ) , we define statistic @xmath12 as a measure of the degree to which the observed frequency of cells exceeds its random expectation for each different structure defined by @xmath0 and @xmath1 .
@xmath13 is for observed sample , @xmath14 is for random sample .      to investigate the uncertainties of the results , we use same method which kiang ( 2004 ) used in rhombic cell analysis .
obviously the present application of hexagon cell analysis revealed that @xmath0 and @xmath1 results are highly sensitive to the exact placing of the grid of hexagon cells . because when the galaxies are fixed , if the cells are moved it will get same galaxies to lie in different cells , we call it as the zero offset .
we start our calculations by placing the centre of our zeroth cell ( 0 , 0 , 0 ) at galactic coordinates ( 0,0,0 ) .
what we found was that if we displace our entire grid of cells by an amount up to and including one unit of a0 , in any combination of the three directions , then the resulting @xmath0 and @xmath15 will generally be different , but slightly .
if we define the length of cell is 1 , we simply consider 4 shifts which are ( 0 , 0.5 ) , ( -0.5,0 ) , ( 0.5,0 ) , ( 0.5,0.5 ) .
the four shifts will be combined with the origin gridding to get average @xmath0 and @xmath15 value with stand deviation .
generally the shift will result in the unequal number of filled and empty cells , but it is very tiny ( around 1/1,000 ) , moreover , it makes more sense for us to keep the length of the cell rather than adjusting it to get equal number of filled and empty cells , so we fix the length of cells when we shift .
the 2mass ( xsc , jarrett et al . 2000 ) data we use is provided by cao et al ( 2006 ) , detailed information can be found in their paper . simply speaking , they select galaxies inside an elliptical isophote with surface brightness of 20 mag @xmath16 in ks band . to have 2-d plane data , they subject the 2mass data to an equal - area projection by the lambert azimuthal algorithm :    @xmath17    where @xmath14 is a relative scale factor , @xmath18 is the galactic latitude and @xmath19 is the galactic longitude .
this hemisphere scheme projects the whole sky into two circular planes , a northern and southern sky .
we select a square with @xmath20 in the central part of each circular plane .
we have two fields of @xmath20 in the northern and southern skies .
the northern square has 323,000 galaxies and the southern includes 342,000 galaxies .
before we analyze the data , we could get the binomial distribution for reference .
the binomial distribution gives the discrete probability distribution @xmath21 of obtaining exactly @xmath22 successes out of @xmath23 bernoulli trials ( where the result of each bernoulli trial is true with probability @xmath24 and false with probability @xmath25 , as given by eq.4 below : ) .
@xmath26    since for any neighbors of a cell , the probability of a filled or empty cell is the same ( we have the same number of filled and empty cells ) , so @xmath27 and @xmath28 . for an @xmath0 distribution , @xmath29 ( 6 walls for hexagon ) , and n=(0,1,2,4,5,6 ) . from eq . ( 4 ) the probability function of a binomial distribution is ( 1/64 , 6/64 , 15/64 , 20/64 , 15/64 , 6/64 , 1/64 ) for n= ( 0 , 1 , 2 , 3 , 4 , 5 , 6 ) . for @xmath1 , since this is related to specific arrangements , it is better to list all combinations and calculate the probability than using eq.(4 ) .
since there are 6 walls , each wall could be inner wall or outer wall , so the total combinations give @xmath30 arrangements .
if we use `` 1 '' for inner wall , and `` 0 '' for outer wall , we could write number 0  63 with 6-digits binary format , such as 000000 , 000001 .... then the 64 binaries are exactly all possible arrangements of @xmath1 .
we list the results in table 1 :    . [ cols="^,^,^,^,^,^,^,^",options="header " , ]     @xmath31 from @xmath0=6 ( or @xmath6 ) filled cells have a much stronger ( 21@xmath32 for northern sky and 15@xmath32 for southern sky ) aggregation property than empty cells .
this is consistent with hoyle ( 2002 ) who found that the number of isolated voids is smaller than the number of clusters in the 2df survey .
@xmath31 the most general case is @xmath33 ( 20/64 probability for standard distribution ) ; however , we can see the @xmath0 value at @xmath33 is smaller than standard distribution .
this can be explained as that aggregation makes filled and empty cells have more probability on @xmath34 than standard distribution , hence reduce the probability at @xmath33 .
@xmath31 for @xmath0=1 , filled cells are closer ( 12@xmath32 for northern sky and 6@xmath32 for southern sky ) to standard distribution than empty cells , which implies that empty cells have less or longer fiber structure than filled cells as the end of fiber always has @xmath0=1 .
@xmath0=1 must result in a @xmath8 structure , we do not see much difference between filled and empty cells for @xmath8 in table 1 .
this suggests @xmath0=1 structure is the minority in most @xmath8 structures , in other words , @xmath8 includes much more cells on the boundary of filled and empty cells than of the end .
@xmath31 @xmath9 has also significant difference ( 12@xmath32 for northern sky and 8@xmath32 for southern sky ) between filled and empty cells .
empty cells have much more frequently penetrated by filled cells than filled cells penetrated by empty cells , which implies that empty cells have less fiber structure than filled cells and is consistent with @xmath0=1 results .
with a direct measurement by the hexagon cell method , we found there are significant differences in topology between high density regions and low density regions in 2mass data .
the accuracy is assured by the zeroshift technique .
we found low density regions have less fiber structure and are less clustered than high density regions to high accuracy .
the difference could be caused by the evolution , which suggests that evolution might include more things other than gravitational instability ( bond @xmath35 szalay 1983 ) ; or caused by the original asymmetry of quantum fluctuation in the early universe ( turner 1998 ) . overall speaking ,
low density regions have slightly closer topology to random distribution than high density regions .
we also found the topology of 2mass southern sky map is slightly closer to random distribution tan northern sky .
our work provides a supplement for genus analysis , which shows that high density and low density regions have almost identical properties ( park et al , 2001 ; gott 1986 ) or are slightly different ( hoyle et al 2002 ) .
we introduce the new 2-d hexagon technique to probe the topological structure of the universe . 
 the 2-d matter space has been filled with hexagon unit cells , by detecting whether the cell includes matter or not we define the filled cells and empty cells , corresponding to high density region and low density region respectively . 
 the number of the filled cells and empty cells are kept same by controlling the size of the cells . by analyzing the six neighbors of each hexagon we can get and compare statistical topological properties of the high density region and low density region in the universe , in order to have a more understanding of the evolution of the universe . 
 we apply this hexagon method on 2-mass data and discover the significant topological differences between the high density and low density regions , even both of them have significant topological shift from the binomial distribution , or the random distribution .