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statistics in space


a sample bacterium (Bacillus subtilis) to simulated hypershocks combining influences including pressures across a 5 to 50 GPa (gigapascal) range, over time periods from milliseconds to several seconds, porosity and density of rock habitat, and so on. Analysing the data in SigmaPlot showed DNA resistance to damage and capacity for repair to be the central issue, with wild samples most hardy and peak temperature a critical factor. Survival of ejection was shown to be perfectly feasible, with better than one organism per 10,000 remaining viable even after a 50 GPa shock. Other work has established the feasibility


of ejected organisms surviving long periods of cold vacuum, and of their adaption to a wide range of environments on reactivation. Recent experiments[10]


have shown, for example, that populations of B.subtilis kept GATHERING THE


INFORMATION TO ANSWER SUCH QUERIES CAN BE A PROTRACTED


TASK, BUT THE ACTUAL ANALYSES BASED UPON THEM COULD BE DONE WITH PENCIL AND PAPER BY A TEN YEAR OLD


at the near-inhibitory lower pressure limit of 5kPa (kilopascals) evolve increasing stepwise tolerance, showing statistically greater fitness at the thousandth generation than comparable populations grown at healthier pressures. It is, therefore, far from impossible that viable DNA originating on Mars in an earlier watery phase might have arrived and thrived on Earth. Asteroids can be crudely classified by


orbital type. Those that carry organisms (and other materials, for that matter, including redistribution of the HSEs mentioned below) off in every direction from one planet to another are one class; they are too dispersed to be of economic interest at our present stage of development. Those that gather around libration points 4 and 5, in front of and behind a planet such as Mars along its own orbit, may well be useful at some point in the future. But the easiest target by far is the asteroid belt: relatively dense, well ordered, it also offers the advantage of always (unlike the planets) being equally accessible from Earth’s own orbit at any time. Some of the statistical analysis involved in


planning for missions to the belt (or through it en route to elsewhere) are remarkably unsophisticated. One of my former students, now working for a space programme, tells


14 SCIENTIFIC COMPUTING WORLD


Cumulative distribution of craters on main belt asteroid (2867) Steins, with Poisson estimated error bars. From Keller et al[12]


Sporulation deficiency (left) of B.subtilis spores exposed to simulated planetary impact ejection at preshock temperatures of 20°C (white) and -78.5°C (grey), and shock pressure survival curves (right) at the same preshock temperatures (open and filled circles, respectively). From Moeller et al[9]


me that the most common requests in this area are for mean and standard deviation likelihood estimates. What is the likelihood of a remotely selected asteroid containing such and such a material in useful quantity? What is the likelihood that any specified bit in an information stream beamed across the plane of the ecliptic will be stopped by an intervening asteroid? What is the average point density, or the average mass density, or the predicted element density, of a specified part of the belt in certain specified circumstances? Gathering the information to answer such queries can be a protracted task, and deciding the parameters on which to base assumptions can be a matter for heated debate, but the actual analyses based upon them could be done with pencil and paper by a 10-year-old. At the opposite end of the analytic


scale come calculations such as those[11] showing an intuitively surprising degree of correspondence between elevated planetary


and lunar levels of highly siderophile elements (HSEs) and stochastic impact accretion models. The apparent discrepancy between HSE levels predicted and observed can be explained by impacts if a very specific set of accretion ratios can be assumed: ratios which stochastic analysis bear out. The task of statistical data collection is


often a statistical one – necessarily so, since, to an even greater extent than in planetary exploration, much must be decided on the basis of extremely limited opportunity for direct sampling. Predicting frequency, type, and effect of impacts, for instance, as is required in many of the likelihood estimations mentioned above, draws heavily on probabilistic extrapolation from localised crater counting exercises such as those carried out[12]


by the European


Space Agency’s Rosetta mission. On its way to a 2014 rendezvous with comet 67P/ Churyumov-Gerasimenko, Rosetta was subtasked with close flyby examination of two asteroids, of which 2867 Šteins was the first. Crater counting by Rosetta’s camera shows a distribution of sizes from one large 2,100-metre hole downwards. Image resolution prevents counting of craters below pixel size, but even above that limit there is under representation of smaller impact sites. Poisson distributed assumptions based on observed data both from Šteins and from other asteroids allow extrapolation to populate extended data spaces beyond those directly sampled. Probabilistic decisions also permit data cleaning, and principal component analyses of multiple images give more information on colour variegation (extremely limited in this case, in contrast to other examples) than could be extracted from the images themselves. When those heavy lifter rockets start


heading for Mars and the asteroid belt, and especially if the Ames/DARPA Mars colonisation plan comes to fruition, a very great deal of financial, human and resource investment will be committed to a relatively tiny base of actual solid knowledge. The gap between those certain facts will be spun from theoretical structures based in data analysis. More will rest on scientifically constructed assumption than at any time since Columbus set out across the Atlantic. In computerised data analytic methods we have, on the other hand, far greater confidence and power in the bases and construction of those assumptions.


References and Sources For a full list of the references and sources cited in this article, please visit www.scientific-computing. com/features/referencesoct11.php


www.scientific-computing.com


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