A one-sided Prime Ideal Principle for noncommutative rings

Completely prime right ideals are introduced as a one-sided generalization of the concept of a prime ideal in a commutative ring. Some of their basic properties are investigated, pointing out both similarities and differences between these right ideals and their commutative counterparts. We prove the Completely Prime Ideal Principle, a theorem stating that right ideals that are maximal in a specific sense must be completely prime. We offer a number of applications of the Completely Prime Ideal Principle arising from many diverse concepts in rings and modules. These applications show how completely prime right ideals control the one-sided structure of a ring, and they recover earlier theorems stating that certain noncommutative rings are domains (namely, proper right PCI rings and rings with the right restricted minimum condition that are not right artinian). In order to provide a deeper understanding of the set of completely prime right ideals in a general ring, we study the special subset of comonoform right ideals.Comment: 38 page

Noncommutative generalizations of theorems of Cohen and Kaplansky

This paper investigates situations where a property of a ring can be tested on a set of "prime right ideals." Generalizing theorems of Cohen and Kaplansky, we show that every right ideal of a ring is finitely generated (resp. principal) iff every "prime right ideal" is finitely generated (resp. principal), where the phrase "prime right ideal" can be interpreted in one of many different ways. We also use our methods to show that other properties can be tested on special sets of right ideals, such as the right artinian property and various homological properties. Applying these methods, we prove the following noncommutative generalization of a result of Kaplansky: a (left and right) noetherian ring is a principal right ideal ring iff all of its maximal right ideals are principal. A counterexample shows that the left noetherian hypothesis cannot be dropped. Finally, we compare our results to earlier generalizations of Cohen's and Kaplansky's theorems in the literature.Comment: 41 pages. To appear in Algebras and Representation Theory. Minor changes were made to the numbering system, in order to remain consistent with the published versio

Obstructing extensions of the functor Spec to noncommutative rings

In this paper we study contravariant functors from the category of rings to the category of sets whose restriction to the full subcategory of commutative rings is isomorphic to the prime spectrum functor Spec. The main result reveals a common characteristic of these functors: every such functor assigns the empty set to M_n(C) for n >= 3. The proof relies, in part, on the Kochen-Specker Theorem of quantum mechanics. The analogous result for noncommutative extensions of the Gelfand spectrum functor for C*-algebras is also proved.Comment: 23 pages. To appear in Israel J. Math. Title was changed; introduction was rewritten; old Section 2 was removed to streamline the exposition; final section was rewritten to omit an error in the earlier proof of Theorem 1.

Racial Disparities in Quality-Adjusted Life-Years Associated With Diabetes and Visual Impairment

OBJECTIVE Compare differences in health-related quality of life among blacks and whites to examine if race, diabetes, and visual impairment (VI) present a triple disadvantage in terms of quality-adjusted life expectancy. RESEARCH DESIGN AND METHODS Data were analyzed from the 2000–2003 Medical Expenditure Panel Survey, a nationally representative survey that contains the EuroQol 5D (EQ-5D). The EQ-5D generates health utility values that provide a measure of the morbidity associated with various health states, such as having moderate or severe problems with mobility. The EQ-5D score can be linked with life expectancy data to calculate quality-adjusted life-years (QALYs), the number of years of optimal health an individual is expected to live. Multivariate analyses were conducted to estimate and compare differences in QALYs by diabetes status, VI status, and race. RESULTS Whites had a higher quality-adjusted life expectancy across all diabetes/VI comparisons. Overall, blacks with diabetes and VI had the fewest number of QALYs remaining (19.6 years), and whites with no impairment had the greatest number of QALYs remaining (31.6 years). Blacks with diabetes only had 1.7 fewer years of optimal health (fewer QALYs) than whites with diabetes. Within individuals with both diabetes and VI, however, this gap more than doubled, with blacks experiencing 3.5 fewer QALYs than whites. CONCLUSIONS Although efforts to target and reduce racial health disparities associated with diabetes appear to be effective, black communities may be contributing to a greater overall burden of illness given poorer infrastructure and less accommodation for disabilities such as VI

One of the closest exoplanet pairs to the 3:2 Mean Motion Resonance: K2-19b \& c

The K2 mission has recently begun to discover new and diverse planetary systems. In December 2014 Campaign 1 data from the mission was released, providing high-precision photometry for ~22000 objects over an 80 day timespan. We searched these data with the aim of detecting further important new objects. Our search through two separate pipelines led to the independent discovery of K2-19b \& c, a two-planet system of Neptune sized objects (4.2 and 7.2 $R_\oplus$), orbiting a K dwarf extremely close to the 3:2 mean motion resonance. The two planets each show transits, sometimes simultaneously due to their proximity to resonance and alignment of conjunctions. We obtain further ground based photometry of the larger planet with the NITES telescope, demonstrating the presence of large transit timing variations (TTVs), and use the observed TTVs to place mass constraints on the transiting objects under the hypothesis that the objects are near but not in resonance. We then statistically validate the planets through the \texttt{PASTIS} tool, independently of the TTV analysis.Comment: 18 pages, 10 figures, accepted to A&A, updated to match published versio

Reaction rates and transport in neutron stars

Understanding signals from neutron stars requires knowledge about the transport inside the star. We review the transport properties and the underlying reaction rates of dense hadronic and quark matter in the crust and the core of neutron stars and point out open problems and future directions.Comment: 74 pages; commissioned for the book "Physics and Astrophysics of Neutron Stars", NewCompStar COST Action MP1304; version 3: minor changes, references updated, overview graphic added in the introduction, improvements in Sec IV.A.

Dynamic Mechanisms of Cell Rigidity Sensing: Insights from a Computational Model of Actomyosin Networks

Cells modulate themselves in response to the surrounding environment like substrate elasticity, exhibiting structural reorganization driven by the contractility of cytoskeleton. The cytoskeleton is the scaffolding structure of eukaryotic cells, playing a central role in many mechanical and biological functions. It is composed of a network of actins, actin cross-linking proteins (ACPs), and molecular motors. The motors generate contractile forces by sliding couples of actin filaments in a polar fashion, and the contractile response of the cytoskeleton network is known to be modulated also by external stimuli, such as substrate stiffness. This implies an important role of actomyosin contractility in the cell mechano-sensing. However, how cells sense matrix stiffness via the contractility remains an open question. Here, we present a 3-D Brownian dynamics computational model of a cross-linked actin network including the dynamics of molecular motors and ACPs. The mechano-sensing properties of this active network are investigated by evaluating contraction and stress in response to different substrate stiffness. Results demonstrate two mechanisms that act to limit internal stress: (i) In stiff substrates, motors walk until they exert their maximum force, leading to a plateau stress that is independent of substrate stiffness, whereas (ii) in soft substrates, motors walk until they become blocked by other motors or ACPs, leading to submaximal stress levels. Therefore, this study provides new insights into the role of molecular motors in the contraction and rigidity sensing of cells

Erratum: Sequence data and association statistics from 12,940 type 2 diabetes cases and controls.

This corrects the article DOI: 10.1038/sdata.2017.179

Efficacy of rifabutin-based triple therapy as second-line treatment to eradicate helicobacter pylori infection

<p>Abstract</p> <p>Background</p> <p>Rifabutin has been found to be effective in multi-resistant patients after various treatment cycles for Helicobacter pylori (HP) infection, but it has not been analysed as a second-line treatment. Therefore, we seek to compare the effectiveness of a treatment regimen including rifabutin versus conventional quadruple therapy (QT).</p> <p>Methods</p> <p>Open clinical trial, randomised and multi-centre, of two treatment protocols: A) Conventional regime -QT- (omeprazole 20 mg bid, bismuth citrate 120 mg qid, tetracycline 500 mg qid and metronidazole 500 mg tid); B) Experimental one -OAR- (omeprazole 20 mg bid, amoxicillin 1 gr bid, and rifabutin 150 mg bid), both taken orally for 7 days, in patients with HP infection for whom first-line treatment had failed. Eradication was determined by Urea Breath Test (UBT). Safety was determined by the adverse events.</p> <p>Results</p> <p>99 patients were randomised, QT, n = 54; OAR, n = 45. The two groups were homogeneous. In 8 cases, treatment was suspended (6 in QT and 2 in OAR). The eradication achieved, analysed by ITT, was for QT, 38 cases (70.4%), and for OAR, 20 cases (44.4%); p = 0.009, OR = 1.58. Of the cases analysed PP, QT were 77.1%; OAR, 46.5%; p = 0.002. Adverse effects were described in 64% of the QT patients and in 44% of the OAR patients (p = 0.04).</p> <p>Conclusion</p> <p>A 7-day rifabutin-based triple therapy associated to amoxicillin and omeprazole at standard dose was not found to be effective as a second-line rescue therapy. The problem with quadruple therapy lies in the adverse side effects it provokes. We believe the search should continue for alternatives that are more comfortably administered and that are at least as effective, but with fewer adverse side effects.</p> <p>Trial Registration</p> <p>Current Controlled Trials ISRCTN81058036</p