Application of the Titius-Bode Rule to the 55 Cancri System: Tentative Prediction of a Possibly Habitable Planet

Following the notion that the Titius-Bode rule (TBR) may also be applicable to some extra-solar planetary systems, although this number could be relatively small, it is applied to 55 Cancri, which is a G-type main-sequence star currently known to host five planets. Following a concise computational process, we tentatively identify four new hypothetical planetary positions given as 0.081, 0.41, 1.51 and 2.95 AU from the star. The likelihood that these positions are occupied by real existing planets is significantly enhanced for the positions of 1.51 and 2.95 AU in the view of previous simulations on planet formation and planetary orbital stability. For example, Raymond et al. (2008) [ApJ 689, 478] argued that additional planets would be possible between 55 Cnc f and 55 Cnc d, which would include planets situated at 1.51 and 2.95 AU. If two additional planets are assumed to exist between 55 Cnc f and 55 Cnc d, the deduced domains of stability would be given as 1.3-1.6 and 2.2-3.3 AU. The possible planet near 1.5 AU appears to be located at the outskirts of the stellar habitable zone, which is however notably affected by the stellar parameters as well as the adopted model of circumstellar habitability. We also compute the distance of the next possible outer planet in the 55 Cnc system, which if existing is predicted to be located between 10.9 and 12.2 AU, which is consistent with orbital stability constraints. The inherent statistical significance of the TBR is evaluated following the method by Lynch (2003) [MNRAS 341, 1174]. Yet it is up to future planetary search missions to verify or falsify the applicability of the TBR to the 55 Cnc system, and to attain information on additional planets, if existing.Comment: 9 pages, 3 figures, 9 tables; accepted by Publications of the Astronomical Society of Japan; to be published on 2012 August 25; Ref.: PASJ 64 (4

Crowded-Field Astrometry with the Space Interferometry Mission - I. Estimating the Single-Measurement Astrometric Bias Arising from Confusion

The accuracy of position measurements on stellar targets with the future Space Interferometry Mission (SIM) will be limited not only by photon noise and by the properties of the instrument (design, stability, etc.) and the overall measurement program (observing strategy, reduction methods, etc.), but also by the presence of other "confusing" stars in the field of view (FOV). We use a simple "phasor" model as an aid to understanding the main effects of this "confusion bias" in single observations with SIM. This analytic model has been implemented numerically in a computer code and applied to a selection of typical SIM target fields drawn from some of the Key Projects already accepted for the Mission. We expect that less than 1% of all SIM targets will be vulnerable to confusion bias; we show that for the present SIM design, confusion may be a concern if the surface density of field stars exceeds 0.4 star/arcsec^2. We have developed a software tool as an aid to ascertaining the possible presence of confusion bias in single observations of any arbitrary field. Some a priori knowledge of the locations and spectral energy distributions of the few brightest stars in the FOV is helpful in establishing the possible presence of confusion bias, but the information is in general not likely to be available with sufficient accuracy to permit its removal. We discuss several ways of reducing the likelihood of confusion bias in crowded fields. Finally, several limitations of the present semi-analytic approach are reviewed, and their effects on the present results are estimated. The simple model presented here provides a good physical understanding of how confusion arises in a single SIM observation, and has sufficient precision to establish the likelihood of a bias in most cases.Comment: 28 pages, 20 figures, 1 table; to appear in December 2007 issue of PAS

Banking Fragility and Disclosure: International Evidence

Motivated by recent public policy debates on the role of market discipline in banking stability, I examine the impact of greater bank disclosure in mitigating the likelihood of systemic banking crisis. In a cross sectional study of banking systems across 49 countries in the 90s, I find that banking crises are less likely in countries with financial reporting regimes characterized by (i) comprehensive disclosure (ii) informative disclosure, (iii) timely disclosure and (iv) more stringent auditing.http://deepblue.lib.umich.edu/bitstream/2027.42/40134/3/wp748.pd

Banking Fragility & Disclosure: International Evidence

Motivated by recent public policy debates on the role of market discipline in banking stability, the study examines the impact of greater bank disclosure in mitigating the likelihood of systemic banking crisis. In a cross sectional study of banking systems across forty-nine countries in the nineties, it finds evidence that banking crises are less likely in countries with regulatory regimes that require extensive bank disclosure and stringent auditing.http://deepblue.lib.umich.edu/bitstream/2027.42/57254/1/wp874 .pd

Consistency of maximum likelihood estimation for some dynamical systems

We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimation. Finally, we exhibit classical families of dynamical systems for which maximum likelihood estimation is consistent. Examples include shifts of finite type with Gibbs measures and Axiom A attractors with SRB measures.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1259 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The fine-tuning cost of the likelihood in SUSY models

In SUSY models, the fine tuning of the electroweak (EW) scale with respect to their parameters gamma_i={m_0, m_{1/2}, mu_0, A_0, B_0,...} and the maximal likelihood L to fit the experimental data are usually regarded as two different problems. We show that, if one regards the EW minimum conditions as constraints that fix the EW scale, this commonly held view is not correct and that the likelihood contains all the information about fine-tuning. In this case we show that the corrected likelihood is equal to the ratio L/Delta of the usual likelihood L and the traditional fine tuning measure Delta of the EW scale. A similar result is obtained for the integrated likelihood over the set {gamma_i}, that can be written as a surface integral of the ratio L/Delta, with the surface in gamma_i space determined by the EW minimum constraints. As a result, a large likelihood actually demands a large ratio L/Delta or equivalently, a small chi^2_{new}=chi^2_{old}+2*ln(Delta). This shows the fine-tuning cost to the likelihood (chi^2_{new}) of the EW scale stability enforced by SUSY, that is ignored in data fits. A good chi^2_{new}/d.o.f.\approx 1 thus demands SUSY models have a fine tuning amount Delta<<exp(d.o.f./2), which provides a model-independent criterion for acceptable fine-tuning. If this criterion is not met, one can thus rule out SUSY models without a further chi^2/d.o.f. analysis. Numerical methods to fit the data can easily be adapted to account for this effect.Comment: 10 pages (v3: small comment added

Likelihood Adaptively Modified Penalties

A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study stability properties of the penalized maximum likelihood estimator, two types of asymptotic stability are defined. Theoretical properties, including the parameter estimation consistency, model selection consistency, and asymptotic stability, are established under suitable regularity conditions. An efficient coordinate-descent algorithm is proposed. Simulation results and real data analysis show that the proposed method has competitive performance in comparison with existing ones.Comment: 42 pages, 4 figure