Gaudin subalgebras and wonderful models

Gaudin hamiltonians form families of r-dimensional abelian Lie subalgebras of the holonomy Lie algebra of the arrangement of reflection hyperplanes of a Coxeter group of rank r. We consider the set of principal Gaudin subalgebras, which is the closure in the appropriate Grassmannian of the set of spans of Gaudin hamiltonians. We show that principal Gaudin subalgebras form a smooth projective variety isomorphic to the De Concini-Procesi compactification of the projectivized complement of the arrangement of reflection hyperplanes.Comment: 13 pages, 2 figures; added detailed description of the B_2 and B_3 cases in the new versio

The Philippines in 2018: A year of disruption and consolidation

2018 is a year of so much uneasiness and tension in Philippine politics. It saw one of the greatest crises in the Supreme Court, the bloodiest period in local politics of late, and successive attempts to silence critics of the president and the government. This year also witnessed major political alignments in the Duterte administration: a change in the leadership of the Senate, the election of Gloria Macapagal Arroyo as Speaker of the House, the rivalry between Hugpong ng Pagbabago and Partido Demokratiko ng Pilipinas-Lakas ng Bayan, and the eventual termination of the alliance with the radical left. This review aims to understand these developments in Philippine politics. It seeks to know why are there so many rifts and shifts in the political rule of Duterte. These changes can be interpreted as part of an ongoing transition toward democratic regression under the Duterte regime. The disruptive events that ensued throughout the year should be understood as the offshoot of the extant efforts to alter the political status quo since the election of Duterte in 2016. The administration uses these events to consolidate its power by rallying its supporters for the 2019 midterm elections and reconfiguring the alignments within the Duterte bloc

High-precision abundances of elements in Kepler LEGACY stars. Verification of trends with stellar age

HARPS-N spectra with S/N > 250 and MARCS model atmospheres were used to derive abundances of C, O, Na, Mg, Al, Si, Ca, Ti, Cr, Fe, Ni, Zn, and Y in ten stars from the Kepler LEGACY sample (including the binary pair 16 Cyg A and B) selected to have metallicities in the range -0.15 < [Fe/H] < +0.15 and ages between 1 and 7 Gyr. Stellar gravities were obtained from seismic data and effective temperatures were determined by comparing non-LTE iron abundances derived from FeI and FeII lines. Available non-LTE corrections were also applied when deriving abundances of the other elements. The results support the [X/Fe]-age relations previously found for solar twins. [Mg/Fe], [Al/Fe], and [Zn/Fe] decrease by ~0.1 dex over the lifetime of the Galactic thin disk due to delayed contribution of iron from Type Ia supernovae relative to prompt production of Mg, Al, and Zn in Type II supernovae. [Y/Mg] and [Y/Al], on the other hand, increase by ~0.3 dex, which can be explained by an increasing contribution of s-process elements from low-mass AGB stars as time goes on. The trends of [C/Fe] and [O/Fe] are more complicated due to variations of the ratio between refractory and volatile elements among stars of similar age. Two stars with about the same age as the Sun show very different trends of [X/H] as a function of elemental condensation temperature Tc and for 16 Cyg, the two components have an abundance difference, which increases with Tc. These anomalies may be connected to planet-star interactions.Comment: 13 pages with 7 figures. Accepted for publication in A&

Suicide Within United States Jails: A Qualitative Interpretive Meta-synthesis

Suicide was the leading cause of unnatural deaths in local jails, accounting for 29% of all jail deaths between 2000 and 2007. Though much literature exists on suicide in jails, very little is qualitative. Additionally, little attention has been focused on how the Interpersonal Theory of Suicide applies to the jail environment. To gain a better understanding of suicide in jails, an interpretive meta-synthesis of three qualitative articles was conducted. The combined sample included thirty-four individuals from three jails. These three articles were analyzed to identify common themes that led inmates to suicide. Three broad categories were identified through constant comparison of the data. These categories are: mental health factors, environmental conditions, and relationship issues. These three broad categories are discussed in relation to the Interpersonal Theory of Suicide, demonstrating its application in the jail setting. This information is essential for correctional facilities and staff for use in their day-to-day interactions with inmates. Future research is needed to identify and examine current suicide prevention programs in the United States penal system

Gaudin subalgebras and stable rational curves

Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned by generators of the Kohno-Drinfeld Lie algebra \Xmathfrak {t}_{\hspace *{.3pt}n}. We show that Gaudin subalgebras form a variety isomorphic to the moduli space $\bar M_{0,n+1}$ of stable curves of genus zero with n+1 marked points. In particular, this gives an embedding of $\bar M_{0,n+1}$ in a Grassmannian of (n−1)-planes in an n(n−1)/2-dimensional space. We show that the sheaf of Gaudin subalgebras over $\bar M_{0,n+1}$ is isomorphic to a sheaf of twisted first-order differential operators. For each representation of the Kohno-Drinfeld Lie algebra with fixed central character, we obtain a sheaf of commutative algebras whose spectrum is a coisotropic subscheme of a twisted version of the logarithmic cotangent bundle of $\bar M_{0,n+1}

Testing the asymptotic relation for period spacings from mixed modes of red giants observed with the Kepler mission

Dipole mixed pulsation modes of consecutive radial order have been detected for thousands of low-mass red-giant stars with the NASA space telescope Kepler. Such modes have the potential to reveal information on the physics of the deep stellar interior. Different methods have been proposed to derive an observed value for the gravity-mode period spacing, the most prominent one relying on a relation derived from asymptotic pulsation theory applied to the gravity-mode character of the mixed modes. Our aim is to compare results based on this asymptotic relation with those derived from an empirical approach for three pulsating red-giant stars. We developed a data-driven method to perform frequency extraction and mode identification. Next, we used the identified dipole mixed modes to determine the gravity-mode period spacing by means of an empirical method and by means of the asymptotic relation. In our methodology, we consider the phase offset, $\epsilon_{\mathrm{g}}$, of the asymptotic relation as a free parameter. Using the frequencies of the identified dipole mixed modes for each star in the sample, we derived a value for the gravity-mode period spacing using the two different methods. These differ by less than 5%. The average precision we achieved for the period spacing derived from the asymptotic relation is better than 1%, while that of our data-driven approach is 3%. Good agreement is found between values for the period spacing derived from the asymptotic relation and from the empirical method. Full abstract in PDF file.Comment: 14 pages, 13 figures, accepted for publication in A&

cISP: A Speed-of-Light Internet Service Provider

Low latency is a requirement for a variety of interactive network applications. The Internet, however, is not optimized for latency. We thus explore the design of cost-effective wide-area networks that move data over paths very close to great-circle paths, at speeds very close to the speed of light in vacuum. Our cISP design augments the Internet's fiber with free-space wireless connectivity. cISP addresses the fundamental challenge of simultaneously providing low latency and scalable bandwidth, while accounting for numerous practical factors ranging from transmission tower availability to packet queuing. We show that instantiations of cISP across the contiguous United States and Europe would achieve mean latencies within 5% of that achievable using great-circle paths at the speed of light, over medium and long distances. Further, we estimate that the economic value from such networks would substantially exceed their expense