Measure representation and multifractal analysis of complete genomes

This paper introduces the notion of measure representation of DNA sequences. Spectral analysis and multifractal analysis are then performed on the measure representations of a large number of complete genomes. The main aim of this paper is to discuss the multifractal property of the measure representation and the classification of bacteria. From the measure representations and the values of the $D_{q}$ spectra and related $C_{q}$ curves, it is concluded that these complete genomes are not random sequences. In fact, spectral analyses performed indicate that these measure representations considered as time series, exhibit strong long-range correlation. For substrings with length K=8, the $D_{q}$ spectra of all organisms studied are multifractal-like and sufficiently smooth for the $C_{q}$ curves to be meaningful. The $C_{q}$ curves of all bacteria resemble a classical phase transition at a critical point. But the 'analogous' phase transitions of chromosomes of non-bacteria organisms are different. Apart from Chromosome 1 of {\it C. elegans}, they exhibit the shape of double-peaked specific heat function.Comment: 12 pages with 9 figures and 1 tabl

Stochastic particle packing with specified granulometry and porosity

This work presents a technique for particle size generation and placement in arbitrary closed domains. Its main application is the simulation of granular media described by disks. Particle size generation is based on the statistical analysis of granulometric curves which are used as empirical cumulative distribution functions to sample from mixtures of uniform distributions. The desired porosity is attained by selecting a certain number of particles, and their placement is performed by a stochastic point process. We present an application analyzing different types of sand and clay, where we model the grain size with the gamma, lognormal, Weibull and hyperbolic distributions. The parameters from the resulting best fit are used to generate samples from the theoretical distribution, which are used for filling a finite-size area with non-overlapping disks deployed by a Simple Sequential Inhibition stochastic point process. Such filled areas are relevant as plausible inputs for assessing Discrete Element Method and similar techniques

The Hera

The Hera Au–Pb–Zn–Ag deposit in the southeastern Cobar Basin of central New South Wales preserves calc-silicate veins and remnant sandstone/carbonate-hosted skarn within a reduced anchizonal Siluro-Devonian turbidite sequence. The skarn orebody distribution is controlled by a long-lived, basin margin fault system, that has intersected a sedimentary horizon dominated by siliciclastic turbidite, with lesser gritstone and thick sandstone intervals, and rare carbonate-bearing stratigraphy. Foliation (S1) envelopes the orebody and is crosscut by a series of late-stage east–west and north–south trending faults. Skarn at Hera displays mineralogical zonation along strike, from southern spessartine–grossular–biotite–actinolite-rich associations, to central diopside-rich–zoisite–actinolite/tremolite–grossular-bearing associations, through to the northern most tremolite–anorthite-rich (garnet-absent) association in remnant carbonate-bearing lithologies and sandstone horizons; the northern lodes also display zonation down dip to garnet present associations. High-T, prograde skarn assemblages rich in pyroxene and garnet are pervasively replaced by actinolite/tremolite–biotite-rich retrograde skarn which coincides with the main pulse of sulfide mineralization. The dominant sulfides are high-Fe–Mn sphalerite–galena–non-magnetic high-Fe pyrrhotite–chalcopyrite; pyrite, arsenopyrite; scheelite (low Mo) is locally abundant. The distribution of metals in part mimics the changing gangue mineralogy, with Au concentrated in the southern and lower northern lode systems and broadly inverse concentrations for Ag–Pb–Zn. Stable isotope data (O–H–S) from skarn amphiboles and associated sulfides are consistent with magmatic (or metamorphic) water and sulfur input during the retrograde skarn phase, while hydrosilicates and sulfides from the wall rocks display comparatively elevated δD and mixed δ34S consistent with progressive mixing or dilution of original magmatic (or metamorphic) waters within the Hera deposit by unexchanged waters typical of low latitude (tropical) meteoritic waters. High precision titanite (U–Pb) and biotite (Ar–Ar) geochronology reveals a manifold orebody commencing with high-T skarn and retrograde Pb–Zn-rich skarn formation at ≥403 Ma, Au–low-Fe sphalerite mineralization at 403.4 ± 1.1 Ma, foliation development remobilization or new mineralization at 390 ± 0.2 Ma followed by thrusting, orebody dismemberment at 384.8 ± 1.1 Ma and remobilization or new mineralization at 381.0 ± 2.2 Ma. The polymetallic nature of the Hera orebody is a result of multiple mineralization events during extension and compression and involving both magmatic and likely formational metal sources