The Fa,b,c conjecture, I

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and one part of the conjecture was proved. The conjecture completely determines all finite members of the family. Here we prove another part of the conjecture and foreshadow a paper which completes the proof of the other three parts.

The Fa,b,c conjecture is true, II

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and subsequently two parts of the conjecture were proved. The conjecture completely determines all finite members of the family. Here we complete the proof of the conjecture by giving proofs for the remaining three parts. (c) 2006 Elsevier Inc. All rights reserved.

CemaT1 is an active transposon within the Caenorhabditis elegans genome

The maT clade of transposons is a group of transposable elements intermediate in sequence and predicted protein structure to mariner and T-C transposons, with a distribution thus far limited to a few invertebrate species. In the nematode Caenorhabditis elegans, there are eight copies of CemaT1 that are predicted to encode a functional transposase, with five copies being >99% identical. We present evidence, based on searches of publicly available databases and on PCR-based mobility assays, that the CemaT1 transposase is expressed in C. elegans and that the CemaT transposons are capable of excising in both somatic and germline tissues. We also show that the frequency of CemaT1 excisions within the genome of the N2 strain of C. elegans is comparable to that of the Tc1 transposon. However, unlike T-C transposons in mutator strains of C elegans, maT transposons do not exhibit increased frequencies of mobility, suggesting that maT is not regulated by the same factors that control T-C activity in these strains. Finally, we show that CemaT1 transposons are capable of precise transpositions as well as orientation inversions at some loci, and thereby become members of an increasing number of identified active transposons within the C. elegans genome. (C) 2004 Elsevier B.V. All rights reserved.

Improved slope adjustment functions for soil erosion prediction

Numerous studies in the last 60 years have investigated the relationship between land slope and soil erosion rates. However, relatively few of these have investigated slope gradient responses: ( a) for steep slopes, (b) for specific erosion processes, and ( c) as a function of soil properties. Simulated rainfall was applied in the laboratory on 16 soils and 16 overburdens at 100 mm/h to 3 replicates of unconsolidated flume plots 3 m long by 0.8 m wide and 0.15 m deep at slopes of 20, 5, 10, 15, and 30% slope in that order. Sediment delivery at each slope was measured to determine the relationship between slope steepness and erosion rate. Data from this study were evaluated alongside data and existing slope adjustment functions from more than 55 other studies from the literature. Data and the literature strongly support a logistic slope adjustment function of the form S = A + B/[1 + exp (C - D sin theta)] where S is the slope adjustment factor and A, B, C, and D are coefficients that depend on the dominant detachment and transport processes. Average coefficient values when interill-only processes are active are A - 1.50, B 6.51, C 0.94, and D 5.30 (r(2) = 0.99). When rill erosion is also potentially active, the average slope response is greater and coefficient values are A - 1.12, B 16.05, C 2.61, and D 8.32 (r(2) = 0.93). The interill-only function predicts increases in sediment delivery rates from 5 to 30% slope that are approximately double the predictions based on existing published interill functions. The rill + interill function is similar to a previously reported value. The above relationships represent a mean slope response for all soils, yet the response of individual soils varied substantially from a 2.5-fold to a 50-fold increase over the range of slopes studied. The magnitude of the slope response was found to be inversely related ( log - log linear) to the dispersed silt and clay content of the soil, and 3 slope adjustment equations are proposed that provide a better estimate of slope response when this soil property is known. Evaluation of the slope adjustment equations proposed in this paper using independent datasets showed that the new equations can improve soil erosion predictions.