Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

Genetic and genomic analysis of hyperlipidemia, obesity and diabetes using (C57BL/6J × TALLYHO/JngJ) F2 mice

<p>Abstract</p> <p>Background</p> <p>Type 2 diabetes (T2D) is the most common form of diabetes in humans and is closely associated with dyslipidemia and obesity that magnifies the mortality and morbidity related to T2D. The genetic contribution to human T2D and related metabolic disorders is evident, and mostly follows polygenic inheritance. The TALLYHO/JngJ (TH) mice are a polygenic model for T2D characterized by obesity, hyperinsulinemia, impaired glucose uptake and tolerance, hyperlipidemia, and hyperglycemia.</p> <p>Results</p> <p>In order to determine the genetic factors that contribute to these T2D related characteristics in TH mice, we interbred TH mice with C57BL/6J (B6) mice. The parental, F1, and F2 mice were phenotyped at 8, 12, 16, 20, and 24 weeks of age for 4-hour fasting plasma triglyceride, cholesterol, insulin, and glucose levels and body, fat pad and carcass weights. The F2 mice were genotyped genome-wide and used for quantitative trait locus (QTL) mapping. We also applied a genetical genomic approach using a subset of the F2 mice to seek candidate genes underlying the QTLs. Major QTLs were detected on chromosomes (Chrs) 1, 11, 4, and 8 for hypertriglyceridemia, 1 and 3 for hypercholesterolemia, 4 for hyperglycemia, 11 and 1 for body weight, 1 for fat pad weight, and 11 and 14 for carcass weight. Most alleles, except for Chr 3 and 14 QTLs, increased phenotypic values when contributed by the TH strain. Fourteen pairs of interacting loci were detected, none of which overlapped the major QTLs. The QTL interval linked to hypercholesterolemia and hypertriglyceridemia on distal Chr 1 contains <it>Apoa2 </it>gene. Sequencing analysis revealed polymorphisms of <it>Apoa2 </it>in TH mice, suggesting <it>Apoa2 </it>as the candidate gene for the hyperlipidemia QTL. Gene expression analysis added novel information and aided in selection of candidates underlying the QTLs.</p> <p>Conclusions</p> <p>We identified several genetic loci that affect the quantitative variations of plasma lipid and glucose levels and obesity traits in a TH × B6 intercross. Polymorphisms in <it>Apoa2 </it>gene are suggested to be responsible for the Chr 1 QTL linked to hypercholesterolemia and hypertriglyceridemia. Further, genetical genomic analysis led to potential candidate genes for the QTLs.</p

Convergence Without Hard Criteria: Does EU Soft Law Affect Domestic Unemployment Protection Schemes?

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Tbx2 and Tbx3 induce atrioventricular myocardial development and endocardial cushion formation

A key step in heart development is the coordinated development of the atrioventricular canal (AVC), the constriction between the atria and ventricles that electrically and physically separates the chambers, and the development of the atrioventricular valves that ensure unidirectional blood flow. Using knock-out and inducible overexpression mouse models, we provide evidence that the developmentally important T-box factors Tbx2 and Tbx3, in a functionally redundant manner, maintain the AVC myocardium phenotype during the process of chamber differentiation. Expression profiling and ChIP-sequencing analysis of Tbx3 revealed that it directly interacts with and represses chamber myocardial genes, and induces the atrioventricular pacemaker-like phenotype by activating relevant genes. Moreover, mutant mice lacking 3 or 4 functional alleles of Tbx2 and Tbx3 failed to form atrioventricular cushions, precursors of the valves and septa. Tbx2 and Tbx3 trigger development of the cushions through a regulatory feed-forward loop with Bmp2, thus providing a mechanism for the co-localization and coordination of these important processes in heart development

Association studies of up to 1.2 million individuals yield new insights into the genetic etiology of tobacco and alcohol use

Tobacco and alcohol use are leading causes of mortality that influence risk for many complex diseases and disorders 1 . They are heritable 2,3 and etiologically related 4,5 behaviors that have been resistant to gene discovery efforts 6–11 . In sample sizes up to 1.2 million individuals, we discovered 566 genetic variants in 406 loci associated with multiple stages of tobacco use (initiation, cessation, and heaviness) as well as alcohol use, with 150 loci evidencing pleiotropic association. Smoking phenotypes were positively genetically correlated with many health conditions, whereas alcohol use was negatively correlated with these conditions, such that increased genetic risk for alcohol use is associated with lower disease risk. We report evidence for the involvement of many systems in tobacco and alcohol use, including genes involved in nicotinic, dopaminergic, and glutamatergic neurotransmission. The results provide a solid starting point to evaluate the effects of these loci in model organisms and more precise substance use measures

Guidelines for the use and interpretation of assays for monitoring autophagy (3rd edition)

In 2008 we published the first set of guidelines for standardizing research in autophagy. Since then, research on this topic has continued to accelerate, and many new scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Accordingly, it is important to update these guidelines for monitoring autophagy in different organisms. Various reviews have described the range of assays that have been used for this purpose. Nevertheless, there continues to be confusion regarding acceptable methods to measure autophagy, especially in multicellular eukaryotes. For example, a key point that needs to be emphasized is that there is a difference between measurements that monitor the numbers or volume of autophagic elements (e.g., autophagosomes or autolysosomes) at any stage of the autophagic process versus those that measure fl ux through the autophagy pathway (i.e., the complete process including the amount and rate of cargo sequestered and degraded). In particular, a block in macroautophagy that results in autophagosome accumulation must be differentiated from stimuli that increase autophagic activity, defi ned as increased autophagy induction coupled with increased delivery to, and degradation within, lysosomes (inmost higher eukaryotes and some protists such as Dictyostelium ) or the vacuole (in plants and fungi). In other words, it is especially important that investigators new to the fi eld understand that the appearance of more autophagosomes does not necessarily equate with more autophagy. In fact, in many cases, autophagosomes accumulate because of a block in trafficking to lysosomes without a concomitant change in autophagosome biogenesis, whereas an increase in autolysosomes may reflect a reduction in degradative activity. It is worth emphasizing here that lysosomal digestion is a stage of autophagy and evaluating its competence is a crucial part of the evaluation of autophagic flux, or complete autophagy. Here, we present a set of guidelines for the selection and interpretation of methods for use by investigators who aim to examine macroautophagy and related processes, as well as for reviewers who need to provide realistic and reasonable critiques of papers that are focused on these processes. These guidelines are not meant to be a formulaic set of rules, because the appropriate assays depend in part on the question being asked and the system being used. In addition, we emphasize that no individual assay is guaranteed to be the most appropriate one in every situation, and we strongly recommend the use of multiple assays to monitor autophagy. Along these lines, because of the potential for pleiotropic effects due to blocking autophagy through genetic manipulation it is imperative to delete or knock down more than one autophagy-related gene. In addition, some individual Atg proteins, or groups of proteins, are involved in other cellular pathways so not all Atg proteins can be used as a specific marker for an autophagic process. In these guidelines, we consider these various methods of assessing autophagy and what information can, or cannot, be obtained from them. Finally, by discussing the merits and limits of particular autophagy assays, we hope to encourage technical innovation in the field

Effects of alirocumab on types of myocardial infarction: insights from the ODYSSEY OUTCOMES trial

Aims  The third Universal Definition of Myocardial Infarction (MI) Task Force classified MIs into five types: Type 1, spontaneous; Type 2, related to oxygen supply/demand imbalance; Type 3, fatal without ascertainment of cardiac biomarkers; Type 4, related to percutaneous coronary intervention; and Type 5, related to coronary artery bypass surgery. Low-density lipoprotein cholesterol (LDL-C) reduction with statins and proprotein convertase subtilisin–kexin Type 9 (PCSK9) inhibitors reduces risk of MI, but less is known about effects on types of MI. ODYSSEY OUTCOMES compared the PCSK9 inhibitor alirocumab with placebo in 18 924 patients with recent acute coronary syndrome (ACS) and elevated LDL-C (≥1.8 mmol/L) despite intensive statin therapy. In a pre-specified analysis, we assessed the effects of alirocumab on types of MI. Methods and results  Median follow-up was 2.8 years. Myocardial infarction types were prospectively adjudicated and classified. Of 1860 total MIs, 1223 (65.8%) were adjudicated as Type 1, 386 (20.8%) as Type 2, and 244 (13.1%) as Type 4. Few events were Type 3 (n = 2) or Type 5 (n = 5). Alirocumab reduced first MIs [hazard ratio (HR) 0.85, 95% confidence interval (CI) 0.77–0.95; P = 0.003], with reductions in both Type 1 (HR 0.87, 95% CI 0.77–0.99; P = 0.032) and Type 2 (0.77, 0.61–0.97; P = 0.025), but not Type 4 MI. Conclusion  After ACS, alirocumab added to intensive statin therapy favourably impacted on Type 1 and 2 MIs. The data indicate for the first time that a lipid-lowering therapy can attenuate the risk of Type 2 MI. Low-density lipoprotein cholesterol reduction below levels achievable with statins is an effective preventive strategy for both MI types.For complete list of authors see http://dx.doi.org/10.1093/eurheartj/ehz299</p