Erosion versus construction: The origin of Venusian channels

Lava channels are a common feature in the volcanic regions of the Moon, and have now been observed on Venus. There has been much debate about the origin of lunar channels as to whether they are the result of erosional (either thermal or mechanical) or constructional processes. It is necessary to determine the criteria to distinguish between the different types of channels. The clearest evidence is that the presence of levees indicates that the channel experienced a constructional phase for a period. One example of a channel of this type in the southeast region of Aphrodite Terra appears to show both erosional and constructional characteristics. It is approximately 700 km long with an average width of about 1 km. It drops a distance of 700 m from beginning to end, which means that the average slope is 0.06 degrees. Its source may have been a graben situated at the northwest end of the channel. It appears to have different origins along its length. The lack of levees near the source suggests that the channel is erosional in this region. The presence of levees indicates that a constructional phase has occurred. These are formed by lava repeatedly splashing over the channel sides and solidifying. Evidence of levees is seen further away from the source. However, the presence of levees does not mean that the lava was not also eroding and deepening the channel. Thus, in conclusion, our example channel is very sinuous and there is evidence of erosion. There may also have been overflow here. In its middle reaches it roofs over and has the characteristics of a lava tube. In the lower reaches there is strong evidence for the presence of levees indicating construction. On Earth, limited amounts of erosion may occur in basaltic lava channels, although not nearly on the same scale as on the planets just mentioned. For lava erosion on Earth to occur to a comparable extent, excessive eruption times are required. However, low-viscosity komatiite lava may erode to a larger extent and there is direct evidence that carbonatite lava erodes when the underlying strata is also carbonatite. Previously, it has always been assumed that for thermal erosion to occur the flow must be turbulent. Recent findings indicate that this may be a false assumption and that laminar flow may be effective in eroding the substrate

What the success of brain imaging implies about the neural code

The success of fMRI places constraints on the nature of the neural code. The fact that researchers can infer similarities between neural representations, despite fMRI’s limitations, implies that certain neural coding schemes are more likely than others. For fMRI to succeed given its low temporal and spatial resolution, the neural code must be smooth at the voxel and functional level such that similar stimuli engender similar internal representations. Through proof and simulation, we determine which coding schemes are plausible given both fMRI’s successes and its limitations in measuring neural activity. Deep neural network approaches, which have been forwarded as computational accounts of the ventral stream, are consistent with the success of fMRI, though functional smoothness breaks down in the later network layers. These results have implications for the nature of the neural code and ventral stream, as well as what can be successfully investigated with fMRI

Geodesic Flow on the Normal Congruence of a Minimal Surface

We study the geodesic flow on the normal line congruence of a minimal surface in ${\Bbb{R}}^3$ induced by the neutral K\"ahler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description of minimal surfaces in ${\Bbb{R}}^3$ and relate it to the classical Weierstrass representation.Comment: AMS-LATEX 8 pages 2, figure

Mobility of a class of perforated polyhedra

A class of over-braced but typically flexible body-hinge frameworks is described. They are based on polyhedra with rigid faces where an independent subset of faces has been replaced by a set of holes. The contact polyhedron C describing the bodies (vertices of C) and their connecting joints (edges of C) is derived by subdivision of the edges of an underlying cubic polyhedron. Symmetry calculations detect flexibility not revealed by counting alone. A generic symmetry-extended version of the Grübler-Kutzbach mobility counting rule accounts for the net mobilities of infinite families of this type (based on subdivisions of prisms, wedges, barrels, and some general inflations of a parent polyhedron). The prisms with all faces even and all barrels are found to generate flexible perforated polyhedra under the subdivision construction. The investigation was inspired by a question raised by Walter Whiteley about a perforated polyhedron with a unique mechanism reducing octahedral to tetrahedral symmetry. It turns out that the perforated polyhedron with highest (OhOh) point-group symmetry based on subdivision of the cube is mechanically equivalent to the Hoberman Switch-Pitch toy. Both objects exhibit an exactly similar mechanism that preserves TdTd subgroup symmetry over a finite range; this mechanism survives in two variants suggested by Bob Connelly and Barbara Heys that have the same contact graph, but lower initial maximum symmetry.Supported by EPSRC First Grant EP/M013642/1.This is the final version of the article. It first appeared from Elsevier via https://doi.org/10.1016/j.ijsolstr.2016.02.00