It is known that if the Gaussian curvature function along each meridian on a surface of revolution (R2, dr2 + m(r) 2 do2 ) is decreasing, then the cut locus of each point of 0-1(0) is empty or a subarc of the opposite meridian 0-1(4 Such a surface is called a von Mangoldt's surface of revolution. A surface of revolution (]I �2, dr2 + m(r)2 is called a generalized von Mangoldt surface of revolution if the cut locus of each point of 0-1(0) is empty or a subarc of the opposite meridian 0-1(7r).For example, the surface of revolution (R2, dr2 + mo(r)2d & theta;2), where mo(x) = x/(1 + x2), has the same cut locus structure as above and the cut locus of each point in r-1((0, oo)) is nonempty. Note that the Gaussian curvature function is not decreasing along a meridian for this surface. In this article, we give sufficient conditions for a surface of revolution (R2, dr2 + m(7.)202) to be a generalized von Mangoldt surface of revolution. Moreover, we prove that for any surface of revolution with finite total curvature c, there exists a generalized von Mangoldt surface of revolution with the same total curvature c such that the Gaussian curvature function along a meridian is not monotone on [a, oo) for any a > 0.

Exact expressions for the relationship between angles of incidence and reflection from a boundary wall in nonlinear dissipative particle models are extremely rare. Here, we study a particle model of a camphor disk floating on water in a low speed limit, for which the model was derived. We begin with a very rough and inaccurate approximation, based in part on a Hamiltonian limit of the model, and then, using symmetry arguments supported by a series of experiments, show that this rough approximation can likely be repaired by introducing a factor dependent upon model parameters, then extract the full parameter dependence of this factor, and finally conjecture a simple and exact asymptotic relationship between the angles of incidence and reflection. There are reasons to believe that this asymptotic relationship may be universal for such models in their corresponding limits.

There are not so many kinds of surface of revolution whose cut locus structure have been determined, although the cut locus structures of very familiar surfaces of revolution (in Euclidean space) such as ellipsoids, 2-sheeted hyperboloids, paraboloids and tori are now known. Except for tori, the known cut locus structures are very simple, i.e., a single point or an arc. In this article, a new family {Mn}n of 2-spheres of revolution with simple cut locus structure is introduced. This family is also new in the sense that the number of points on each meridian which assume a local minimum or maximum of the Gaussian curvature function on the meridian goes to infinity as n tends to infinity. Thus, our family includes surfaces which have arbitrarily many bands of alternately increasing or decreasing Gaussian curvature, although each member of this family has a simple cut locus structure.

In this empirical study, we show that the shape of the distribution of relative prices of basic food and drink items has been extraordinarily robust, from ancient Egypt to modern Chile, whether there be peace and economic stability, war, revolution, depression or hyperinflation. The width of the distribution of log prices does not deviate significantly from a specific value, which would appear to be universal. This property of relative prices has not changed over the past three thousand years, wherever there have been food markets, despite great differences in culture, institutions, and the particular food and drink items consumed.

Multilayers of Gd/Co produced by sputter deposition are observed to be amorphous for a wide range of bilayer periods. This structure is largely the result of an amorphization reaction during the deposition between crystalline Gd and newly arriving Co atoms. We explore this reaction by producing multilayers of Gd/Co/Cr, and examining the resulting microstructure. We observe both interfacial disordering due to a layer thickening mechanism and evidence for growth of the amorphous phase from Gd grain boundaries. The reaction is enhanced by the presence of a large number of crystalline defects in the Gd layers.

Viral capsids ensure viral genome integrity by protecting the enclosed nucleic acids. Interactions between the genome and capsid and between individual capsid proteins (i.e., capsid architecture) are intimate and are expected to be characterized by strong evolutionary conservation. For this reason, a capsid structure-based viral classification has been proposed as a way to bring order to the viral universe. The seeming lack of sufficient sequence similarity to reproduce this classification has made it difficult to reject structural convergence as the basis for the classification. We reinvestigate whether the structure-based classification for viral coat proteins making icosahedral virus capsids is in fact supported by previously undetected sequence similarity. Since codon choices can influence nascent protein folding cotranslationally, we searched for both amino acid and nucleotide sequence similarity. To demonstrate the sensitivity of the approach, we identify a candidate gene for the pandoravirus capsid protein. We show that the structure-based classification is strongly supported by amino acid and also nucleotide sequence similarities, suggesting that the similarities are due to common descent. The correspondence between structure-based and sequence-based analyses of the same proteins shown here allow them to be used in future analyses of the relationship between linear sequence information and macromolecular function, as well as between linear sequence and protein folds.IMPORTANCE Viral capsids protect nucleic acid genomes, which in turn encode capsid proteins. This tight coupling of protein shell and nucleic acids, together with strong functional constraints on capsid protein folding and architecture, leads to the hypothesis that capsid protein-coding nucleotide sequences may retain signatures of ancient viral evolution. We have been able to show that this is indeed the case, using the major capsid proteins of viruses forming icosahedral capsids. Importantly, we detected similarity at the nucleotide level between capsid protein-coding regions from viruses infecting cells belonging to all three domains of life, reproducing a previously established structure-based classification of icosahedral viral capsids.

Fairy circles are enigmatic features of the Namib desert landscape. They are large, almost perfectly circular patches of barren soil in sparse grassland. Although a matter of continuing debate, we make no attempt to explain their origin. The focus of our approach is a statistical analysis of the spatial patterns. These are easily accessible via aerial and satellite imagery. Observations over extended periods of time have revealed that they have a life-cycle of birth, growth and death. It has also been known for some time that the fairy circles are not randomly distributed. Our novel finding is that the connectivity patterns of fairy circles and metazoan epithelial cells are statistically indistinguishable, while remaining clearly distinct from other commonly observed polygonal patternings. This result identifies an analogy between the microscopic world of epithelial cells and the macroscopic realm of the Namib, suggesting that approaches developed specifically for the analysis of microscopic structures may extend into ecologically relevant, macroscopic dimensions. (C) 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Whole-genome duplication (WGD) is believed to be a significant source of major evolutionary innovation. Redundant genes resulting from WGD are thought to be lost or acquire new functions. However, the rates of gene loss and thus temporal process of genome reshaping after WGD remain unclear. The WGD shared by all teleost fish, one-half of all jawed vertebrates, was more recent than the two ancient WGDs that occurred before the origin of jawed vertebrates, and thus lends itself to analysis of gene loss and genome reshaping. Using a newly developed orthology identification pipeline, we inferred the post-teleost-specific WGD evolutionary histories of 6,892 protein-coding genes from nine phylogenetically representative teleost genomes on a time-calibrated tree. We found that rapid gene loss did occur in the first 60 My, with a loss of more than 70-80% of duplicated genes, and produced similar genomic gene arrangements within teleosts in that relatively short time. Mathematical modeling suggests that rapid gene loss occurred mainly by events involving simultaneous loss of multiple genes. We found that the subsequent 250 My were characterized by slow and steady loss of individual genes. Our pipeline also identified about 1,100 shared single-copy genes that are inferred to have become singletons before the divergence of clupeocephalan teleosts. Therefore, our comparative genome analysis suggests that rapid gene loss just after the WGD reshaped teleost genomes before the major divergence, and provides a useful set of marker genes for future phylogenetic analysis.

Genome composition analysis of di-, tri- and tetra-nucleotide frequencies is known to be evolutionarily informative, and useful in metagenomic studies, where binning of raw sequence data is often an important first step. Patterns appearing in genome composition analysis may be due to evolutionary processes or purely mathematical relations. For example, the total number of dinucleotides in a sequence is equal to the sum of the individual totals of the sixteen types of dinucleotide, and this is entirely independent of any assumptions made regarding mutation or selection, or indeed any physical or chemical process. Before any statistical analysis can be attempted, a knowledge of all necessary mathematical relations is required. I show that 25% of di-, tri- and tetra-nucleotide frequencies can be written as simple sums and differences of the remainder. The vast majority of organisms have circular genomes, for which these relations are exact and necessary. In the case of linear molecules, the absolute error is very nearly zero, and does not grow with contiguous sequence length. As a result of the new, necessary relations presented here, the foundations of the statistical analysis of di-, tri- and tetra-nucleotide frequencies, and k-mer analysis in general, need to be revisited.

When a given tissue must, to be able to perform its various functions, consist of different cell types, each fairly evenly distributed and with specific probabilities, then there are at least two quite different developmental mechanisms which might achieve the desired result. Let us begin with the case of two cell types, and first imagine that the proportion of numbers of cells of these types should be 1:3. Clearly, a regular structure composed of repeating units of four cells, three of which are of the dominant type, will easily satisfy the requirements, and a deterministic mechanism may lend itself to the task. What if, however, the proportion should be 10:33? The same simple, deterministic approach would now require a structure of repeating units of 43 cells, and this certainly seems to require a far more complex and potentially prohibitive deterministic developmental program. Stochastic development, replacing regular units with random distributions of given densities, might not be evolutionarily competitive in comparison with the deterministic program when the proportions should be 1:3, but it has the property that, whatever developmental mechanism underlies it, its complexity does not need to depend very much upon target cell densities at all. We are immediately led to speculate that proportions which correspond to fractions with large denominators (such as the 33 of 10/33) may be more easily achieved by stochastic developmental programs than by deterministic ones, and this is the core of our thesis: that stochastic development may tend to occur more often in cases involving rational numbers with large denominators. To be imprecise: That simple rationality and determinism belong together, as do irrationality and randomness.

Killing is perhaps the most definite form of communication possible. Microbes such as yeasts and gut bacteria have been shown to exhibit killer phenotypes. The killer strains are able to kill other microbes occupying the same ecological niche, and do so with impunity. It would therefore be expected that, wherever a killer phenotype has arisen, all members of the population would soon be killers or dead. Surprisingly, (1) one can find both killer and sensitive strains in coexistence, both in the wild and in in vitro experiments, and (2) the absolute fitness cost of the killer phenotype often seems to be very small. We present an explicit model of such coexistence in a fragmented or discrete environment. A killer strain may kill all sensitive cells in one patch (one piece of rotting fruit, one cave or one human gut, for example), allowing sensitives to exist only in the absence of killer strains on the same patch. In our model, populations spread easily between patches, but in a stochastic manner: one can imagine spores borne by the wind over a field of untended apple trees, or enteric disease transmission in a region in which travel is effectively unrestricted. What we show is that coexistence is not only possible, but that it is possible even if the absolute fitness advantage of the sensitive strain over the killer strain is arbitrarily small. We do this by performing a specifically targeted mathematical analysis on our model, rather than via simulations. Our model does not assume large population densities, and may thus be useful in the context of understanding the ecology of extreme environments.

Rich, T.H., Kear, B.P., Sinclair, R., Chinnery, B., Carpenter, K., McHugh, M.L. & Vickers-Rich, P., 2014. Serendipaceratops arthurcclarkei Rich & Vickers-Rich, 2003 is an Australian Early Cretaceous ceratopsian. Alcheringa 38, 456-479. ISSN 0311-5518.Serendipaceratops arthurcclarkei is one of Australia's most enigmatic dinosaur taxa. Based on a single ulna recovered from Early Cretaceous high-latitude deposits in southeastern Australia, the fossil was originally classified as a neoceratopsian, but subsequently reassigned to Genasauria indet. because of comparisons with atypical thyreophorans. However, a morphometric and structural re-examination of the holotype indicates that it is proportionally distinguishable among dinosaurians and, indeed, manifests decisive statistical compatibility with ceratopsians. Statistical assessment similarly yields a synapomorphy that places the taxon robustly within Ceratopsia. Most certainly, identification of a unique differential character state combination renders S. arthurcclarkei as valid. Its affinity with ceratopsians concurs with proliferating records of other Laurasian dinosaur lineages from the Southern Hemisphere, and may reflect ancient Pangaean dispersals into or out of Gondwana.

Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indiana, USA, August 4 – August 8, 2013.

Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indiana, USA, August 4 – August 8, 2013.

The complex three-dimensional shapes of tree-like structures in biology are constrained by optimization principles, but the actual costs being minimized can be difficult to discern. We show that despite quite variable morphologies and functions, bifurcations in the scleractinian coral Madracis and in many different mammalian neuron types tend to be planar. We prove that in fact bifurcations embedded in a spatial tree that minimizes wiring cost should lie on planes. This biologically motivated generalization of the classical mathematical theory of Euclidean Steiner trees is compatible with many different assumptions about the type of cost function. Since the geometric proof does not require any correlation between consecutive planes, we predict that, in an environment without directional biases, consecutive planes would be oriented independently of each other. We confirm this is true for many branching corals and neuron types. We conclude that planar bifurcations are characteristic of wiring cost optimization in any type of biological spatial tree structure.

In the main text (Figure 1) cone angles were computed for complete branches, i.e. for each branch from the bifurcation point to the next bifurcation or terminal point, because these points are morphologically well defined. In Figure S2 we show the same analysis but for bifurcations to the closest point available in the reconstruction. These first points were selected by those who performed each neuron reconstruction and the corresponding segment lengths tend to be quite variable. Though the proportion of planar bifurcations are smaller than in Figure 1, the difference with random bifurcations remains highly significant for all (KS-test, p-value = 10-5). Assessing the possible effect of shrinkage artefacts in neuronal reconstruction data The dehydration of slices during the histological preparation can induce a pronounced shrinkage in the z-dimension, while shrinkages in other dimensions (x and y) may be much smaller [1,2]. To address the issue of shrinkage [1,2,3,4,5] as well as the systematic errors introduced by histological processes [6], both of which would influence mainly the z-coordinates, we compared bifurcations having planes with different orientations relative to the Z-plane. The bifurcation planes were categorized into 3 groups with bin centers at 15, 45 and 75°. The cone angle distributions of 2