On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automata in two bases that do not share the same set of prime factors are exactly those that are definable in the first order additive theory of real and integer numbers. This result extends Cobham's theorem, which characterizes the sets of integer numbers that are recognizable by finite automata in multiple bases. In this article, we first generalize this result to multiplicatively independent bases, which brings it closer to the original statement of Cobham's theorem. Then, we study the sets of reals recognizable by Muller automata in two bases. We show with a counterexample that, in this setting, Cobham's theorem does not generalize to multiplicatively independent bases. Finally, we prove that the sets of reals that are recognizable by Muller automata in two bases that do not share the same set of prime factors are exactly those definable in the first order additive theory of real and integer numbers. These sets are thus also recognizable by weak deterministic automata. This result leads to a precise characterization of the sets of real numbers that are recognizable in multiple bases, and provides a theoretical justification to the use of weak automata as symbolic representations of sets.Comment: 17 page

Mask formulas for cograssmannian Kazhdan-Lusztig polynomials

We give two contructions of sets of masks on cograssmannian permutations that can be used in Deodhar's formula for Kazhdan-Lusztig basis elements of the Iwahori-Hecke algebra. The constructions are respectively based on a formula of Lascoux-Schutzenberger and its geometric interpretation by Zelevinsky. The first construction relies on a basis of the Hecke algebra constructed from principal lower order ideals in Bruhat order and a translation of this basis into sets of masks. The second construction relies on an interpretation of masks as cells of the Bott-Samelson resolution. These constructions give distinct answers to a question of Deodhar.Comment: 43 page

Associations between subjective social status and physical and mental health functioning among patients with hypertension

We examine the cross-sectional association between subjective social status and self-rated physical and mental health functioning in 518 Black and White patients enrolled in a community-based hypertension control research study. We found that (1) subjective social status, measured using both a proximal and distal referent group, was positively associated with physical and mental health functioning scores independent of educational level, household income, or both; (2) the effect of subjective social status on physical and mental health functioning differed significantly by race when using the distal, not the proximal, referent group. When the associations differed, they were stronger for Whites than Blacks

High-contrast imaging constraints on gas giant planet formation - The Herbig Ae/Be star opportunity

Planet formation studies are often focused on solar-type stars, implicitly considering our Sun as reference point. This approach overlooks, however, that Herbig Ae/Be stars are in some sense much better targets to study planet formation processes empirically, with their disks generally being larger, brighter and simply easier to observe across a large wavelength range. In addition, massive gas giant planets have been found on wide orbits around early type stars, triggering the question if these objects did indeed form there and, if so, by what process. In the following I briefly review what we currently know about the occurrence rate of planets around intermediate mass stars, before discussing recent results from Herbig Ae/Be stars in the context of planet formation. The main emphasis is put on spatially resolved polarized light images of potentially planet forming disks and how these images - in combination with other data - can be used to empirically constrain (parts of) the planet formation process. Of particular interest are two objects, HD100546 and HD169142, where, in addition to intriguing morphological structures in the disks, direct observational evidence for (very) young planets has been reported. I conclude with an outlook, what further progress we can expect in the very near future with the next generation of high-contrast imagers at 8-m class telescopes and their synergies with ALMA.Comment: Accepted by Astrophysics and Space Science as invited short review in special issue about Herbig Ae/Be stars; 12 pages incl. 5 figures, 2 tables and reference

Understanding Hawking radiation from simple models of atomic Bose-Einstein condensates

This chapter is an introduction to the Bogoliubov theory of dilute Bose condensates as applied to the study of the spontaneous emission of phonons in a stationary condensate flowing at supersonic speeds. This emission process is a condensed-matter analog of Hawking radiation from astrophysical black holes but is derived here from a microscopic quantum theory of the condensate without any use of the analogy with gravitational systems. To facilitate physical understanding of the basic concepts, a simple one-dimensional geometry with a stepwise homogenous flow is considered which allows for a fully analytical treatment.Comment: 41 pages. to appear in the proceedings of the IX SIGRAV School on 'Analogue Gravity', Como (Italy), May 201

Genetic effects on liver chromatin accessibility identify disease regulatory variants

Identifying the molecular mechanisms by which genome-wide association study (GWAS) loci influence traits remains challenging. Chromatin accessibility quantitative trait loci (caQTLs) help identify GWAS loci that may alter GWAS traits by modulating chromatin structure, but caQTLs have been identified in a limited set of human tissues. Here we mapped caQTLs in human liver tissue in 20 liver samples and identified 3,123 caQTLs. The caQTL variants are enriched in liver tissue promoter and enhancer states and frequently disrupt binding motifs of transcription factors expressed in liver. We predicted target genes for 861 caQTL peaks using proximity, chromatin interactions, correlation with promoter accessibility or gene expression, and colocalization with expression QTLs. Using GWAS signals for 19 liver function and/or cardiometabolic traits, we identified 110 colocalized caQTLs and GWAS signals, 56 of which contained a predicted caPeak target gene. At the LITAF LDL-cholesterol GWAS locus, we validated that a caQTL variant showed allelic differences in protein binding and transcriptional activity. These caQTLs contribute to the epigenomic characterization of human liver and help identify molecular mechanisms and genes at GWAS loci