Coverage statistics for sequence census methods

Background: We study the statistical properties of fragment coverage in genome sequencing experiments. In an extension of the classic Lander-Waterman model, we consider the effect of the length distribution of fragments. We also introduce the notion of the shape of a coverage function, which can be used to detect abberations in coverage. The probability theory underlying these problems is essential for constructing models of current high-throughput sequencing experiments, where both sample preparation protocols and sequencing technology particulars can affect fragment length distributions. Results: We show that regardless of fragment length distribution and under the mild assumption that fragment start sites are Poisson distributed, the fragments produced in a sequencing experiment can be viewed as resulting from a two-dimensional spatial Poisson process. We then study the jump skeleton of the the coverage function, and show that the induced trees are Galton-Watson trees whose parameters can be computed. Conclusions: Our results extend standard analyses of shotgun sequencing that focus on coverage statistics at individual sites, and provide a null model for detecting deviations from random coverage in high-throughput sequence census based experiments. By focusing on fragments, we are also led to a new approach for visualizing sequencing data that should be of independent interest.Comment: 10 pages, 4 figure

From non-Brownian Functionals to a Fractional Schr\"odinger Equation

We derive backward and forward fractional Schr\"odinger type of equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [PRL {\bf 96}, 230601 (2006)] provide the correct fractional framework for the problem at hand. In the limit of normal diffusion we recover the Feynman-Kac treatment of Brownian functionals. For applications, we calculate the distribution of occupation times in half space and show how statistics of anomalous functionals is related to weak ergodicity breaking.Comment: 5 page

Standards applicable to performance measurement of solar heating and cooling systems

The advantage of the utilization of existing standards in the performance monitoring of solar heating and cooling systems is discussed. Existing applicable measurement standards and practices are listed

Direct Relationship Between Electrokinetic Surface-charge Measurement of Effluents and Coagulant Type and Dose

AbstractColloidal stability due to rejection between particles with identical charge is a severe problem in water treatment. Pretreatment of industrial effluents such as olive mill or cowshed dairy wastewater includes the addition of “coagulants” aimed at neutralizing the colloids and reducing their rejection. However, the amount and type of coagulant are usually determined by “trial-and-error” jar tests due to the lack of an efficient method to evaluate the effluents' charge. This study presents a method for direct evaluation of the efficiency of type and dose of coagulants based on particle charge detector (PCD) measurements of the colloidal effluents and the coagulant to be used as the neutralizing compound. This presumably trivial procedure is not common, apparently due to the fact that measuring colloidal charge with a PCD is less widely used than ζ potential measurements. A few examples of the effective use of this procedure are presented

Orbital evolution of a test particle around a black hole: Indirect determination of the self force in the post Newtonian approximation

Comparing the corrections to Kepler's law with orbital evolution under a self force, we extract the finite, already regularized part of the latter in a specific gauge. We apply this method to a quasi-circular orbit around a Schwarzschild black hole of an extreme mass ratio binary, and determine the first- and second-order conservative gravitational self force in a post Newtonian expansion. We use these results in the construction of the gravitational waveform, and revisit the question of the relative contribution of the self force and spin-orbit coupling.Comment: 5 pages, 2 figure

The effect of the fuel-cell unit size on the efficiency of a fuel-cell-topped Rankine cycle

Thermodynamic Considerations The fundamental (thermodynamic) reason for interest in fuel cells is the reduction of combustion irreversibility (Obert and Gaggioli, 1963; In ordinary combustion, a fuel is brought in direct contact with oxygen to react, producing oxidation products. The result is a conversion of chemical energy of the fuel to thermal energy of the products Fuel cells, on the other hand, lower the electrochemical potential value of either the fuel or oxygen by first passing ions through an electrolyte and producing electricity in this Currently

Radiative falloff in the background of rotating black hole

We study numerically the late-time tails of linearized fields with any spin $s$ in the background of a spinning black hole. Our code is based on the ingoing Kerr coordinates, which allow us to penetrate through the event horizon. The late time tails are dominated by the mode with the least multipole moment $\ell$ which is consistent with the equatorial symmetry of the initial data and is equal to or greater than the least radiative mode with $s$ and the azimuthal number $m$.Comment: 5 pages, 4 Encapsulated PostScript figures; Accepted to Phys. Rev. D (Rapid Communication

On the formation of black holes in non-symmetric gravity

It has been recently suggested that the Non-symmetric Gravitational Theory (NGT) is free of black holes. Here, we study the linear version of NGT. We find that even with spherical symmetry the skew part of the metric is generally non-static. In addition, if the skew field is initially regular, it will remain regular everywhere and, in particular, at the horizon. Therefore, in the fully-nonlinear theory, if the initial skew-field is sufficiently small, the formation of a black hole is to be anticipated.Comment: 9 pages, ordinary LaTex