The Critical Exponent is Computable for Automatic Sequences

The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. Our results also apply to variants of the critical exponent, such as the initial critical exponent of Berthe, Holton, and Zamboni and the Diophantine exponent of Adamczewski and Bugeaud. Our work generalizes or recovers previous results of Krieger and others, and is applicable to other situations; e.g., the computation of the optimal recurrence constant for a linearly recurrent k-automatic sequence.Comment: In Proceedings WORDS 2011, arXiv:1108.341

A new code for Fourier-Legendre analysis of large datasets: first results and a comparison with ring-diagram analysis

Fourier-Legendre decomposition (FLD) of solar Doppler imaging data is a promising method to estimate the sub-surface solar meridional flow. FLD is sensible to low-degree oscillation modes and thus has the potential to probe the deep meridional flow. We present a newly developed code to be used for large scale FLD analysis of helioseismic data as provided by the Global Oscillation Network Group (GONG), the Michelson Doppler Imager (MDI) instrument, and the upcoming Helioseismic and Magnetic Imager (HMI) instrument. First results obtained with the new code are qualitatively comparable to those obtained from ring-diagram analyis of the same time series.Comment: 4 pages, 2 figures, 4th HELAS International Conference "Seismological Challenges for Stellar Structure", 1-5 February 2010, Arrecife, Lanzarote (Canary Islands

Defamation Per Se Cases Should Include Guaranteed Minimum Presumed Damage Awards to Private Plaintiffs

To combat the reputational harm associated with defamatory comments, forty states allow plaintiffs to recover presumed damages for reputational harm for defamatory statements considered “per se” defamation without having to prove the exact dollar figure associated with their reputational damages. While damages are presumed to a plaintiff’s reputation in a successful defamation per se lawsuit, the spectrum of presumed damages is so wide that there is almost no practical way for a plaintiff to reliably know the size of a presumed damages award, especially a lower-income plaintiff. Plaintiffs cannot evaluate the financial merit of a defamation lawsuit, which removes the primary benefit of presumed damages. This is especially problematic for plaintiffs relying on presumed damages to their reputations to justify the costs of litigation for defamation per se cases, which are the most egregious types of defamation, and why reputational damages are presumed. Without some assurance that a defamed plaintiff will be awarded damages to compensate them for the harm to their reputation, presumed damages have insufficient practical value—lower income plaintiffs who are defamed and later struggle to find employment or who live with tarnished reputations will not pursue litigation while their defamers face no repercussions and no fear of repeating that behavior. Instead of abolishing the doctrine of presumed damages, which some states have done because presumed damages are difficult to quantify, a better approach is to set a guaranteed minimum damages floor associated with presumed damages for plaintiffs who are successful in a per se defamation claim