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buy artwork The Universe - Superclusters and Voids by Martin Krzywinski
THE ENTIRE UNIVERSE | Put it on your wall. (buy artwork / see all my art)
If you like space, you will love this. The 2017 π Day art imagines the digits of π as a star catalogue with constellations of extinct animals and plants. The work is featured in the article Pi in the Sky at the Scientific American SA Visual blog.
If you like space, you'll love my the 12,000 billion light-year map of clusters, superclusters and voids. Find the biggest nothings in Boötes and Eridanus.The largest map there is shows the location of voids and galaxy superclusters in our visible universe.

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from an undefined
place,
undefined
create (a place)
an account
of us
— Viorica Hrincu

Sometimes when you stare at the void, the void sends you a poem.

Universe—Superclusters and Voids

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The Universe — Superclustesr and Voids. The two supergalactic hemispheres showing Abell clusters (blue), superclusters (magenta) and voids (black) within a distance of 6,000 million light-years from the Milky Way.

The average density of the universe is about `10 \times 10^{-30} \text{ g/cm}^3` or about 6 protons per cubic meter. This should put some perspective in what we mean when we speak about voids as "underdense regions".

expressing distances in the universe

1 · Light-travel and comoving distance

Distances in the universe can be expressed as either the light-travel distance or the comoving distance to the object. The first tells us how long light took to travel from the object to us.

For example, the furthest object observed is the galaxy GN-Z11 and its light-travel distance is 13 billion light-years (Gly).

But because space has expanded during the time the light from GN-Z11 has been travelling to us, the galaxy is now actually much further away. This is measured by its comoving distance which accounts for space expansion, which is 29.3 Gly for GN-Z11.

The redshift, `z`, is commonly used to specify distance, since it's a quantity that can be observed. For GN-Z11, `z = 11.09`.

All distances on the poster are expressed in terms of the light-travel distance.

2 · Calculating distances

To calculate these distances, the redshift `z` is used along with a few cosmological parameters.

The Hubble parameter, `H(z)`, is the function used for these calculations. It can be derived from the Friedmann equation. $$ H(z) = H_0 \sqrt { \Omega_r({1+z})^4 + \Omega_m({1+z})^3 + \Omega_k({1+z})^2 + \Omega_\Lambda } $$

The values of the parameters in `H(z)` are being continually refined and the values of some depend on various assumptions. I use the Hubble constant `H_0 = 69.6 \text{ km/s/Mpc}`, mass density of relativistic particles `\Omega_r = 8.6 \times 10^{-5}`, mass density `\Omega_m = 0.286`, curvature `\Omega_k = 0` and dark energy fraction `\Omega_\Lambda = 1 - \Omega_r - \Omega_m - \Omega_k = 0.713914`.

Bennett, C.L. et al The 1% Concordance Hubble Constant Astrophysical Journal 794 (2014)

Now given a redshift, `z` the light-travel distance is $$ d_T(z) = c \int_0^z \frac{dx}{({1+x})E(x)} $$

The age of the universe can be computed from this expression. The edge of the universe has an infinite redshift so w can calculate it using `\lim_{z \rightarrow \infty} d_T(z)`.

The comoving distance to the object with redshift `z` is $$ d_C(z) = c \int_0^z \frac{dx}{E(x)} $$

It's convenient to express the above integrals by making a variable substitution. Using the scale factor `a = 1/(1+z)`, $$E(a) = H_0 \sqrt { \frac{\Omega_r}{a^2} + \frac{\Omega_m}{a} + \Omega_k + a^4\Omega_\Lambda } $$

The light-travel distance is $$D_T(z) = c \int_a^1 \frac{dx}{E(x)}$$

The comoving distance is $$D_C(z) = c \int_a^1 \frac{dx}{xE(x)}$$

The light-travel distance to the edge of the universe is $$D_{T_U}(z) = c \int_0^1 \frac{dx}{E(x)}$$

and the light-travel distance from the edge of the universe to the object as we're observing it now is $$D_{T_0}(z) = c \int_0^a \frac{dx}{E(x)}$$

which can be interpreted as the age of the object when it emitted the light that we're seeing now.

The proper size of the universe is the comoving distance to its edge, $$D_{C_U}(z) = c \int_0^1 \frac{dx}{xE(x)}$$

3 · Distance calculator

Below you can You can download the full script.

### Cosmological distance calculator
### Martin Krzywinski, 2018
#
# The full script supports command-line parameters
# http://mkweb.bcgsc.ca/universe-voids-and-superclusters/cosmology_distance.py

z  = 1                     # redshift 
a  = 1/(1+z)               # scale factor
Wm = 0.286                 # mass density
Wr = 8.59798189985467e-05  # relativistic mass
Wk = 0                     # curvature
WV = 1 - Wm - Wr - Wk      # dark matter fraction
n  = 10000                 # integration steps

# Hubble parameter, as function of a = 1/(1+z)
def Ea(a,Wr,Wm,Wk,WV):
    return(math.sqrt(Wr/a**2 + Wm/a + Wk + WV*a**2))

H0   = 69.6            # Hubble constant
c    = 299792.458      # speed of light, km/s
pc   = 3.26156         # parsec to light-year conversion
mult = (c/H0)*pc/1e3   # integrals are in units of c/H0, converts to Gy or Gly
sum_comoving = 0
sum_light    = 0
sum_univage  = 0
sum_univsize = 0

for i in range(n):
    f   = (i+0.5)/n
    x   = a + (1-a) * f # a .. 1
    xx  = f             # 0 .. 1
    ex  = Ea(x,args.Wr,args.Wm,args.Wk,args.WV)
    exx = Ea(xx,args.Wr,args.Wm,args.Wk,args.WV)
    sum_comoving += (1-a)/(x*ex)
    sum_light    += (1-a)/(  ex)
    sum_univsize += 1/(xx*exx)
    sum_univage  += 1/(   exx)

results = [mult*i for i in [sum_univage,sum_univsize,sum_univage-sum_light, \
                            sum_light,sum_comoving]]
print("z {:.2f} U {:f} Gy {:f} Gly T0 {:f} Gy T {:f} Gly C {:f} Gly". \
      format(args.z,*results))

Use the script to generate distances for a given redshift, `z`. For example,

# For galaxy GN-Z11, furtest object ever observed
./cosmology_distance.py -z 11.09
z 11.09 U 13.720 Gy 46.441 Gly T0 0.414 Gy T 13.306 Gly C 32.216 Gly

The galaxy GN-Z11 has a light-travel distance of 13.3 Gly and a comoving distance of 32.2 Gly. We're seeing it now as it was only 0.4 Gy after the beginning of the universe, which is 13.7 Gy old and the distance to its edge is 46.4 Gly.

# For quasar J1342+0928, furthest quasar ever observed
./cosmology_distance.py -z 7.54
z 7.54 U 13.720 Gy 46.441 Gly T0 0.699 Gy T 13.021 Gly C 29.355 Gly

The values for U (age and size of universe), will always be the same for a given set of cosmological parameters for any value of `z`. I include them in the output of the script for convenience.

These values match those generated by Ned's online cosmological calculator for a flat universe.

news + thoughts

Annals of Oncology cover

Wed 14-09-2022

My cover design on the 1 September 2022 Annals of Oncology issue shows 570 individual cases of difficult-to-treat cancers. Each case shows the number and type of actionable genomic alterations that were detected and the length of therapies that resulted from the analysis.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
An organic arrangement of 570 individual cases of difficult-to-treat cancers showing genomic changes and therapies. Apperas on Annals of Oncology cover (volume 33, issue 9, 1 September 2022).

Pleasance E et al. Whole-genome and transcriptome analysis enhances precision cancer treatment options (2022) Annals of Oncology 33:939–949.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
My Annals of Oncology 570 cancer cohort cover (volume 33, issue 9, 1 September 2022). (more)

Browse my gallery of cover designs.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A catalogue of my journal and magazine cover designs. (more)

Survival analysis—time-to-event data and censoring

Fri 05-08-2022

Love's the only engine of survival. —L. Cohen

We begin a series on survival analysis in the context of its two key complications: skew (which calls for the use of probability distributions, such as the Weibull, that can accomodate skew) and censoring (required because we almost always fail to observe the event in question for all subjects).

We discuss right, left and interval censoring and how mishandling censoring can lead to bias and loss of sensitivity in tests that probe for differences in survival times.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Survival analysis—time-to-event data and censoring. (read)

Dey, T., Lipsitz, S.R., Cooper, Z., Trinh, Q., Krzywinski, M & Altman, N. (2022) Points of significance: Survival analysis—time-to-event data and censoring. Nature Methods 19:906–908.

3,117,275,501 Bases, 0 Gaps

Sun 21-08-2022

See How Scientists Put Together the Complete Human Genome.

My graphic in Scientific American's Graphic Science section in the August 2022 issue shows the full history of the human genome assembly — from its humble shotgun beginnings to the gapless telomere-to-telomere assembly.

Read about the process and methods behind the creation of the graphic.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
3,117,275,501 Bases, 0 Gaps. Text by Clara Moskowitz (Senior Editor), art direction by Jen Christiansen (Senior Graphics Editor), source: UCSC Genome Browser.

See all my Scientific American Graphic Science visualizations.

Anatomy of SARS-Cov-2

Tue 31-05-2022

My poster showing the genome structure and position of mutations on all SARS-CoV-2 variants appears in the March/April 2022 issue of American Scientist.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Deadly Genomes: Genome Structure and Size of Harmful Bacteria and Viruses (zoom)

An accompanying piece breaks down the anatomy of each genome — by gene and ORF, oriented to emphasize relative differences that are caused by mutations.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Deadly Genomes: Genome Structure and Size of Harmful Bacteria and Viruses (zoom)

Cancer Cell cover

Sat 23-04-2022

My cover design on the 11 April 2022 Cancer Cell issue depicts depicts cellular heterogeneity as a kaleidoscope generated from immunofluorescence staining of the glial and neuronal markers MBP and NeuN (respectively) in a GBM patient-derived explant.

LeBlanc VG et al. Single-cell landscapes of primary glioblastomas and matched explants and cell lines show variable retention of inter- and intratumor heterogeneity (2022) Cancer Cell 40:379–392.E9.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
My Cancer Cell kaleidoscope cover (volume 40, issue 4, 11 April 2022). (more)

Browse my gallery of cover designs.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A catalogue of my journal and magazine cover designs. (more)

Nature Biotechnology cover

Sat 23-04-2022

My cover design on the 4 April 2022 Nature Biotechnology issue is an impression of a phylogenetic tree of over 200 million sequences.

Konno N et al. Deep distributed computing to reconstruct extremely large lineage trees (2022) Nature Biotechnology 40:566–575.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
My Nature Biotechnology phylogenetic tree cover (volume 40, issue 4, 4 April 2022). (more)

Browse my gallery of cover designs.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A catalogue of my journal and magazine cover designs. (more)

© 1999–2022 Martin Krzywinski | contact | Canada's Michael Smith Genome Sciences CentreBC Cancer Research CenterBC CancerPHSA