A two-tiered approach to assessing the habitability of exoplanets

In the next few years, the number of catalogued exoplanets will be counted in the thousands. This will vastly expand the number of potentially habitable worlds and lead to a systematic assessment of their astrobiological potential. Here, we suggest a two-tiered classification scheme of exoplanet habitability. The first tier consists of an Earth Similarity Index (ESI), which allows worlds to be screened with regard to their similarity to Earth, the only known inhabited planet at this time. The ESI is based on data available or potentially available for most exoplanets such as mass, radius, and temperature. For the second tier of the classification scheme we propose a Planetary Habitability Index (PHI) based on the presence of a stable substrate, available energy, appropriate chemistry, and the potential for holding a liquid solvent. The PHI has been designed to minimize the biased search for life as we know it and to take into account life that might exist under more exotic conditions. As such, the PHI requires more detailed knowledge than is available for any exoplanet at this time. However, future missions such as the Terrestrial Planet Finder will collect this information and advance the PHI. Both indices are formulated in a way that enables their values to be updated as technology and our knowledge about habitable planets, moons, and life advances. Applying the proposed metrics to bodies within our Solar System for comparison reveals two planets in the Gliese 581 system, GJ 581 c and d, with an ESI comparable to that of Mars and a PHI between that of Europa and Enceladus.     

On the exact solutions of pseudorange equations

Three formulations of exact solution algorithms to the system of determined pseudorange equations are derived. It is demonstrated that pseudorange equations are hyperbolic in nature and may have two solutions, even when the emitter configuration is nonsingular. Conditions for uniqueness and for the existence of multiple solutions are derived in terms of the Lorentz inner product. The bifurcation parameter for systems of pseudorange equations is also expressed in term of the Lorentz functional. The solution is expressed as a product of the geometric dilution of precision (GDOP) matrix, representing the linear part of the solution, and a vector of nonlinear term. Using this formulation stability of solutions is discussed     

Use of reduce gravity conditions for the measurements of forces acting against the displacement of liquids inside containers

A setup called Controlled Rotation of Liquids (CROL) has been developed and used to investigate rotational behavior of liquids interacting with solids under reduced gravity conditions. The CROL setup allows us to evaluate the acceleration needed to overcome the interfacial forces that hinder liquid displacement inside different size containers. The well known Wilhelmy equation is used to explain the experimental results. Comparison between experimental results and theoretical predictions are presented and discussed.     

Existence and uniqueness of GPS solutions

The existence and uniqueness of positions computed from global positioning system (GPS) pseudorange measurements is studied. Contrary to the claims of S. Bancroft (1985) and L.O. Krause (1987), in the case of n=4 satellites a fix may not exist, and, if a fix exists, it is not guaranteed to be unique. In the case of n>or=5 satellites, a unique fix is assured, except in certain degenerate cases such as coplanar satellites. An alternate formulation of the direct n=4 pseudorange to three-space position solutions of Bancroft and Krause is presented, and simple tests for existence and uniqueness are derived.<>     

DNA structures and radiation injury.

In the present paper experimental results from radiobiological investigations of the sedimentation behaviour of damaged and restored DNA-subunits attached to the nuclear membrane have been summarized. The studies were carried out preferably with Chinese Hamster cells V79-4 irradiated with different kinds of radiation (gamma-rays, neutrons and carbon ions) using the nucleoid sedimentation technique. Single-strand breaks relax the supercoiled DNA in the subunits resulting in a decreased sedimentation velocity. Rejoining leads to a correct restoration of the structure as can be studied by means of postincubation irradiation. Double-strand breaks release DNA fragments, again leading to an increased sedimentation velocity. If the average number of the induced double-strand breaks per subunit increases to a number higher than one, the measured results suggest that the structures should not be restored completely. The results are compatible with a new repair model developed in our laboratory on the assumption that, firstly, the single DNA subunits are the sensitive target rather than the whole DNA and, secondly, the repair of DNA damage takes place independently in each subunit.     

A divide and conquer approach to least-squares estimation

The problem of estimating parameters &thetas; which determine the mean μ(&thetas;) of a Gaussian-distributed observation X is considered. It is noted that the maximum-likelihood (ML) estimate, in this case the least-squares estimate, has desirable statistical properties but can be difficult to compute when μ(&thetas;) is a nonlinear function of &thetas;. An estimate formed by combining ML estimates based on subsections of the data vector X is proposed as a computationally inexpensive alternative. The main result is that this alternative estimate, termed here the divide-and-conquer (DAC) estimate, has ML performance in the small-error region when X is appropriately subdivided. As an example application, an inexpensive range-difference-based position estimator is derived and shown by means of Monte-Carlo simulation to have small-error-region mean-square error equal to the Cramer-Rao lower bound