The Detectability of Transit Depth Variations due to Exoplanetary Oblateness and Spin Precession

Knowledge of an exoplanet's oblateness and obliquity would give clues about its formation and internal structure. In principle, a light curve of a transiting planet bears information about the planet's shape, but previous work has shown that the oblateness-induced signal will be extremely difficult to detect. Here we investigate the potentially larger signals due to planetary spin precession. The most readily detectable effects are transit depth variations (T$\delta$V) in a sequence of light curves. For a planet as oblate as Jupiter or Saturn, the transit depth will undergo fractional variations of order 1%. The most promising systems are those with orbital periods of approximately 15--30 days, which is short enough for the precession period to be less than about 40 years, and long enough to avoid spin-down due to tidal friction. The detectability of the T$\delta$V signal would be enhanced by moons (which would decrease the precession period) or planetary rings (which would increase the amplitude). The Kepler mission should find several planets for which precession-induced T$\delta$V signals will be detectable. Due to modeling degeneracies, Kepler photometry would yield only a lower bound on oblateness. The degeneracy could be lifted by observing the oblateness-induced asymmetry in at least one transit light curve, or by making assumptions about the planetary interior.Comment: Accepted for publication in The Astrophysical Journa

Promoting Progress with Fair Use

The Intellectual Property (IP) Clause provides that Congress has the power to promote the Progress of Science and useful Arts by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries. In the realm of copyright, Congress and the courts have interpreted the clause as granting Congress a power not to promote progress but to establish limited IP monopolies. To return to an understanding of the IP power better grounded in the constitutional text, Congress and the courts should ensure that any IP enactment promote[s] ... Progress by considering whether it improves the quality or quantity of knowledge and aids the dissemination of knowledge, and whether it does so better than prior IP enactments. The courts can exercise the fair-use doctrine to aid in this re-constitutionalization of IP law by applying a fifth fair-use factor. This proposed fifth factor would balance the progress-promoting value of the alleged infringer\u27s use against the progress-promoting value of enforcing the copyright holder\u27s rights. Reviewing courts should presume that any alleged infringement is fair if it promotes progress better than the enforcement of the copyright

Quasirandom Permutations

Chung and Graham define quasirandom subsets of $\mathbb{Z}_n$ to be those with any one of a large collection of equivalent random-like properties. We weaken their definition and call a subset of $\mathbb{Z}_n$ $\epsilon$-balanced if its discrepancy on each interval is bounded by $\epsilon n$. A quasirandom permutation, then, is one which maps each interval to a highly balanced set. In the spirit of previous studies of quasirandomness, we exhibit several random-like properties which are equivalent to this one, including the property of containing (approximately) the expected number of subsequences of each order-type. We provide a few applications of these results, present a construction for a family of strongly quasirandom permutations, and prove that this construction is essentially optimal, using a result of W. Schmidt on the discrepancy of sequences of real numbers.Comment: 30 pages, 2 figures, submitted to JCT

A comparison of parameter covariance estimation methods for item response models in an expectation-maximization framework

The Expectation-Maximization (EM) algorithm is a method for finding the maximum likelihood estimate of a model in the presence of missing data. Unfortunately, EM does not produce a parameter covariance matrix for standard errors. Both Oakes and Supplemented EM are methods for obtaining the parameter covariance matrix. SEM was discovered in 1991 and is implemented in both opensource and commercial item response model estimation software. Oakes, a more recent method discovered in 1999, had not been implemented in item response model software until now. Convergence properties, accuracy, and elapsed time of Oakes and Supplemental EM family algorithms are compared for a diverse selection IFA models. Oakes exhibits the best accuracy and elapsed time among algorithms compared. We recommend that Oakes be made available in item response model estimation software

Sound the Alarm: Limitations of Liability in Alarm Service Contracts

Home and business owners increasingly rely on alarm systems to protect against theft and property damage. When a burglary or fire occurs and an alarm service customer discovers that the alarm company negligently failed to call the police or fire department, the customer understandably would expect redress for the company’s failure to provide its service. Many customers would be surprised, though, to discover that an alarm company’s liability is often contractually limited to a relatively token amount unrelated to the cost of the service, even when the alarm company is negligent. Some states view these limitations of liability as exculpatory clauses and determine their enforceability based on whether they are unconscionable or violate public policy. Other states view them as liquidated damages and apply a penalty test to determine their enforceability. This Note addresses the differences between these two approaches in the context of the unique remedy difficulties inherent in alarm service contracts. This Note then argues that the prevailing policy rationales for enforcing alarm service provisions that limit a party’s liability for its own negligence are misguided and advocates that these provisions should not be enforced as a matter of public policy