The cratering record in the inner solar system: Implications for earth

Internal and external processes have reworked the Earth's surface throughout its history. In particular, the effect of meteorite impacts on the early history of the earth is lost due to fluvial, aeolian, volcanic and plate tectonic action. The cratering record on other inner solar system bodies often provides the only clue to the relative cratering rates and intensities that the earth has experienced throughout its history. Of the five major bodies within the inner solar system, Mercury, Mars, and the Moon retain scars of an early episode of high impact rates. The heavily cratered regions on Mercury, Mars, and the Moon show crater size-frequency distribution curves similar in shape and crater density, whereas the lightly cratered plains on the Moon and Mars show distribution curves which, although similar to each other, are statistically different in shape and density from the more heavily cratered units. The similarities among crater size-frequency distribution curves for the Moon, Mercury, and Mars suggest that the entire inner solar system was subjected to the two populations of impacting objects but Earth and Venus have lost their record of heavy bombardment impactors. Thus, based on the cratering record on the Moon, Mercury, and Mars, it can be inferred that the Earth experienced a period of high crater rates and basin formation prior to about 3.8 BY ago. Recent studies have linked mass extinctions to large terrestrial impacts, so life forms were unable to establish themselves until impact rates decreased substantially and terrestrial conditions became more benign. The possible periodicity of mass extinctions has led to the theory of fluctuating impact rates due to comet showers in the post heavy bombardment period. The active erosional environment on the Earth complicates attempts to verify these showers by erasing geological evidence of older impact craters. The estimated size of the impactor purportedly responsible for the Cretaceous-Tertiary mass extinctions is 10 km in diameter. Thus impactors greater than or equal to the size postulated for K-T impactor are rare within the inner solar system since the end of heavy bombardment

Relative chronology of Martian volcanoes

Impact cratering is one of the major geological processes that has affected the Martian surface throughout the planet's history. The frequency of craters within particular size ranges provides information about the formation ages and obliterative episodes of Martian geologic units. The Barlow chronology was extended by measuring small craters on the volcanoes and a number of standard terrain units. Inclusions of smaller craters in units previously analyzed by Barlow allowed for a more direct comparison between the size-frequency distribution data for volcanoes and established chronology. During this study, 11,486 craters were mapped and identified in the 1.5 to 8 km diameter range in selected regions of Mars. The results are summarized in this three page report and give a more precise estimate of the relative chronology of the Martian volcanoes. Also, the results of this study lend further support to the increasing evidence that volcanism has been a dominant geologic force throughout Martian history

TIDY, a complete code for renumbering and editing FORTRAN source programs. User's manual for IBM 360/67

TIDY, a computer code which edits and renumerates FORTRAN decks which have become difficult to read because of many patches and revisions, is described. The old program is reorganized so that statement numbers are added sequentially, and extraneous FORTRAN statements are deleted. General instructions for using TIDY on the IBM 360/67 Tymeshare System, and specific instructions for use on the NASA/AMES IBM 360/67 TSS system are included as well as specific instructions on how to run TIDY in conversational and in batch modes. TIDY may be adopted for use on other computers

Depth-diameter ratios for Martian impact craters: Implications for target properties and episodes of degradation

This study determines crater depth through use of photoclinometric profiles. Random checks of the photoclinometric results are performed using shadow estimation techniques. The images are Viking Orbiter digital format frames; in cases where the digital image is unusable for photoclinometric analysis, shadow estimation is used to determine crater depths. The two techniques provide depth results within 2 percent of each other. Crater diameters are obtained from the photoclinometric profiles and checked against the diameters measured from the hard-copy images using a digitizer. All images used in this analysis are of approximately 40 m/pixel resolution. The sites that have been analyzed to date include areas within Arabia, Maja Valles, Memnonia, Acidalia, and Elysium. Only results for simple craters (craters less than 5 km in diameter) are discussed here because of the low numbers of complex craters presently measured in the analysis. General results indicate that impact craters are deeper than average. A single d/D relationship for fresh impact craters on Mars does not exist due to changes in target properties across the planet's surface. Within regions where target properties are approximately constant, however, d/D ratios for fresh craters can be determined. In these regions, the d/D ratios of nonpristine craters can be compared with the fresh crater d/D relationship to obtain information on relative degrees of crater degradation. This technique reveals that regional episodes of enhanced degradation have occurred. However, the lack of statistically reliable size-frequency distribution data prevents comparison of the relative ages of these events between different regions, and thus determination of a large-scale episode (or perhaps several episodes) cannot be made at this time

Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and Kajino based on the heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true in the examples that have been analyzed in the existing literature

Warming Early Mars by Impact Degassing of Reduced Greenhouse Gases

Reducing greenhouse gases are once again the latest trend in finding solutions to the early Mars climate dilemma. In its current form collision induced absorptions (CIA) involving H2 and/or CH4 provide enough extra greenhouse power in a predominately CO2 atmosphere to raise global mean surface temperatures to the melting point of water provided the atmosphere is thick enough and the reduced gases are abundant enough. Surface pressures must be at least 500 mb and H2 and/or CH4 concentrations must be at or above the several percent level for CIA to be effective. Atmospheres with 1-2 bars of CO2 and 2- 10% H2 can sustain surface environments favorable for liquid water. Smaller concentrations of H2 are sufficient if CH4 is also present. If thick CO2 atmospheres with percent level concentrations of reduced gases are the solution to the faint young Sun paradox for Mars, then plausible mechanisms must be found to generate and sustain the gases. Possible sources of reducing gases include volcanic outgassing, serpentinization, and impact delivery; sinks include photolyis, oxidation, and escape to space. The viability of the reduced greenhouse hypothesis depends, therefore, on the strength of these sources and sinks. In this paper we focus on impact delivered reduced gases

Fertility control as a means of controlling bovine tuberculosis in badger (Meles meles) populations in south-west England: predictions from a spatial stochastic simulation model

A spatial stochastic simulation model was used to assess the potential of fertility control, based on a yet-to-be-developed oral bait-delivered contraceptive directed at females, for the control of bovine tuberculosis in badger populations in south-west England. The contraceptive had a lifelong effect so that females rendered sterile in any particular year remained so for the rest of their lives. The efficacy of fertility control alone repeated annually for varying periods of time was compared with a single culling operation and integrated control involving an initial single cull followed by annually repeated fertility control. With fertility control alone, in no instance was the disease eradicated completely while a viable badger population (mean group size of at least one individual) was still maintained. Near eradication of the disease (less than 1% prevalence) combined with the survival of a minimum viable badger population was only achieved under a very limited set of conditions, either with high efficiency of control (95%) over a short time period (1-3 years) or a low efficiency of control (20%) over an intermediate time period (10-20 years). Under these conditions, it took more than 20 years for the disease to decline to such low levels. A single cull of 80% efficiency succeeded in near eradication of the disease (below 1% prevalence) after a period of 6-8 years, while still maintaining a viable badger population. Integrated strategies reduced disease prevalence more rapidly and to lower levels than culling alone, although the mean badger group size following the onset of control was smaller. Under certain integrated strategies, principally where a high initial cull (80%) was followed by fertility control over a short (1-3 year) time period, the disease could be completely eradicated while a viable badger population was maintained. However, even under the most favourable conditions of integrated control, it took on average more than 12 years following the onset of control for the disease to disappear completely from the badger population. These results show that whilst fertility control would not be a successful strategy for the control of bovine tuberculosis in badgers if used alone, it could be effective if used with culling as part of an integrated strategy. This type of integrated strategy is likely to be more effective in terms of disease eradication than a strategy employing culling alone. However, the high cost of developing a suitable fertility control agent, combined with the welfare and conservation implications, are significant factors which should be taken into account when considering its possible use as a means of controlling bovine tuberculosis in badger populations in the UK

Quenched invariance principle for random walks in balanced random environment

We consider random walks in a balanced random environment in $\mathbb{Z}^d$, $d\geq 2$. We first prove an invariance principle (for $d\ge2$) and the transience of the random walks when $d\ge 3$ (recurrence when $d=2$) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.Comment: Published online in Probab. Theory Relat. Fields, 05 Oct 2010. Typo (in journal version) corrected in (26

Optimizing information flow in small genetic networks. II: Feed forward interactions

Central to the functioning of a living cell is its ability to control the readout or expression of information encoded in the genome. In many cases, a single transcription factor protein activates or represses the expression of many genes. As the concentration of the transcription factor varies, the target genes thus undergo correlated changes, and this redundancy limits the ability of the cell to transmit information about input signals. We explore how interactions among the target genes can reduce this redundancy and optimize information transmission. Our discussion builds on recent work [Tkacik et al, Phys Rev E 80, 031920 (2009)], and there are connections to much earlier work on the role of lateral inhibition in enhancing the efficiency of information transmission in neural circuits; for simplicity we consider here the case where the interactions have a feed forward structure, with no loops. Even with this limitation, the networks that optimize information transmission have a structure reminiscent of the networks found in real biological systems

The Alexander-Orbach conjecture holds in high dimensions

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.Comment: 25 pages, 2 figures. To appear in Inventiones Mathematica