Prospects for the habitability of OGLE-2006-BLG-109L

The extrasolar system OGLE-2006-BLG-109L is the first multiple-planet system to be discovered by gravitational microlensing (Gaudi et al., 2008); the two large planets that have been detected have mass ratios, semimajor axis ratios, and equilibrium temperatures that are similar to those of Jupiter and Saturn; the mass of the host star is only 0.5 M_sun, and the system is more compact than our own Solar system. We find that in the habitable zone of the host star, the two detected planets resonantly excite large orbital eccentricities on a putative earth-mass planet, driving such a planet out of the habitable zone. We show that an additional inner planet of ~>0.3M_earth at <~0.1 AU would suppress the eccentricity perturbation and greatly improve the prospects for habitability of the system. Thus, the planetary architecture of a potentially habitable OGLE-2006-BLG-109L planetary system -- with two ``terrestrial'' planets and two jovian planets -- could bear very close resemblance to our own Solar system.Comment: 11 pages including 4 figures; accepted for publication in ApJ-Letter

Role of Game Theory in Public Health

Game theory, a branch of applied mathematics has been utilized by researchers in various fields including health to arrive at practical solutions to contemporary challenges. The article aims to introduce the subject to medical fraternity in India and recommends that the theory should be included in the syllabus of post graduate students of community medicine so that future generations of public health experts are aware of the theory and its potential use to find tangible solutions to public health issues

GENE EXPRESSION FOLLOWING TRAUMATIC BRAIN INJURY

The pathology which results from traumatic brain injury (TBI) have long been believed to be immediate and irreversible. However, recently it has been shown that, although the primary effects are virtually unavoidable, the secondary effects manifest themselves through biochemical processes set in motion at the time of the injury. These events are frequently mediated through the process of excitotoxicity, which results from a widespread release of excitatory neurotransmitters. These neurotransmitters go on to activate both ionotropic and metabotropic receptors. The signal transduction initiated through these receptor populations gives rise to changes in gene expression. One result of this release of neurotransmitter is an influx of calcium by means of excitatory receptors on the cell. The neurotransmitters upon which most research is focused are glutamate, aspartate, and acetylcholine. Current research is aimed at investigating antagonists to this process as well as elucidating steps within the process. Antagonists primarily function to reduce the calcium toxicity through modulation of receptor activity. However, the therapeutic window for effective antagonist usage is short. Therefore, although they may represent a viable treatment option, they need to be administered as early as possible following the injury to have the greatest effect. The purpose of this paper is to provide a summary of the available literature on TBI and excitotoxicity with a focus on changes in gene regulation. This paper will summarize information on the steps inVolved in the intracellular signaling cascade following brain injury and provide insight to further sites for regulation and treatment. This will also allow for development hypotheses on the possible roles of some of the genes whose expression is already known to be altered

The Mass Distribution Function of Planets

The distribution of orbital period ratios of adjacent planets in extra-solar planetary systems discovered by the {\it Kepler} space telescope exhibits a peak near $\sim1.5$--$2$, a long tail of larger period ratios, and a steep drop-off in the number of systems with period ratios below $\sim1.5$. We find from this data that the dimensionless orbital separations have an approximately log-normal distribution. Using Hill's criterion for the dynamical stability of two planets, we find an upper bound on planet masses such that the most common planet mass does not exceed $10^{-3.2}m_*$, or about two-thirds Jupiter mass for solar mass stars. Assuming that the mass ratio and the dynamical separation (orbital spacings in units of mutual Hill radius) of adjacent planets are independent random variates, and adopting empirical distributions for these, we use Hill's criterion in a statistical way to estimate the planet mass distribution function from the observed distribution of orbital separations. We find that the planet mass function is peaked in logarithm of mass, with a peak value and standard deviation of $\log m/M_\oplus$ of $\sim(0.6-1.0)$ and $\sim(1.1-1.2)$, respectively.Comment: Updated analysis with debiased period ratio data and updated discussion; accepted to Ap

A dynamical mechanism for establishing apsidal resonance

We show that in a system of two planets initially in nearly circular orbits, an impulse perturbation that imparts a finite eccentricity to one planet's orbit causes the other planet's orbit to become eccentric as well, and also naturally results in a libration of their relative apsidal longitudes for a wide range of initial conditions. We suggest that such a mechanism may explain orbital eccentricities and apsidal resonance in some exo-planetary systems. The eccentricity impulse could be caused by the ejection of a planet from these systems, or by torques from a primordial gas disk. The amplitude of secular variations provides an observational constraint on the dynamical history of such systems.Comment: to appear in ApJ-Letter