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

Knowledge-based vision and simple visual machines

The vast majority of work in machine vision emphasizes the representation of perceived objects and events: it is these internal representations that incorporate the 'knowledge' in knowledge-based vision or form the 'models' in model-based vision. In this paper, we discuss simple machine vision systems developed by artificial evolution rather than traditional engineering design techniques, and note that the task of identifying internal representations within such systems is made difficult by the lack of an operational definition of representation at the causal mechanistic level. Consequently, we question the nature and indeed the existence of representations posited to be used within natural vision systems (i.e. animals). We conclude that representations argued for on a priori grounds by external observers of a particular vision system may well be illusory, and are at best place-holders for yet-to-be-identified causal mechanistic interactions. That is, applying the knowledge-based vision approach in the understanding of evolved systems (machines or animals) may well lead to theories and models that are internally consistent, computationally plausible, and entirely wrong

Impact Delivery of Reduced Greenhouse Gases on Early Mars

Reducing greenhouse gases are once again the latest trend in finding solutions to the early Mars climate dilemma. In its current form - as proposed by Ramirez et al. [1], later refined by Wordsworth et al. [2], and confirmed by Ramirez [3] - collision induced absorptions between CO2-H2 or CO2-CH4 provide enough extra greenhouse power 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. To raise surface temperatures significantly by this mechanism, surface pressures must be at least 500 mb and H2 and/or CH4 concentrations must be at or above the several percent level. Both Wordsworth et al. [2] and Ramirez [3] show that the melting point can be reached in atmospheres with 1-2 bars of CO2 and 2-10% H2; smaller concentrations of H2 will suffice if CH4 is also present. If thick weakly reducing atmospheres are the solution to the faint young Sun paradox, 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

Upper estimate of martingale dimension for self-similar fractals

We study upper estimates of the martingale dimension $d_m$ of diffusion processes associated with strong local Dirichlet forms. By applying a general strategy to self-similar Dirichlet forms on self-similar fractals, we prove that $d_m=1$ for natural diffusions on post-critically finite self-similar sets and that $d_m$ is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets.Comment: 49 pages, 7 figures; minor revision with adding a referenc

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

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