Geometric invariant theory of syzygies, with applications to moduli spaces

We define syzygy points of projective schemes, and introduce a program of studying their GIT stability. Then we describe two cases where we have managed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, and a new construction in the Hassett-Keel program for the moduli space of genus six curves.Comment: v1: 23 pages, submitted to the Proceedings of the Abel Symposium 2017, v2: final version, corrects a sign error and resulting divisor class calculations on the moduli space of K3 surfaces in Section 5, other minor changes, In: Christophersen J., Ranestad K. (eds) Geometry of Moduli. Abelsymposium 2017. Abel Symposia, vol 14. Springer, Cha

Design principles for riboswitch function

Scientific and technological advances that enable the tuning of integrated regulatory components to match network and system requirements are critical to reliably control the function of biological systems. RNA provides a promising building block for the construction of tunable regulatory components based on its rich regulatory capacity and our current understanding of the sequence–function relationship. One prominent example of RNA-based regulatory components is riboswitches, genetic elements that mediate ligand control of gene expression through diverse regulatory mechanisms. While characterization of natural and synthetic riboswitches has revealed that riboswitch function can be modulated through sequence alteration, no quantitative frameworks exist to investigate or guide riboswitch tuning. Here, we combined mathematical modeling and experimental approaches to investigate the relationship between riboswitch function and performance. Model results demonstrated that the competition between reversible and irreversible rate constants dictates performance for different regulatory mechanisms. We also found that practical system restrictions, such as an upper limit on ligand concentration, can significantly alter the requirements for riboswitch performance, necessitating alternative tuning strategies. Previous experimental data for natural and synthetic riboswitches as well as experiments conducted in this work support model predictions. From our results, we developed a set of general design principles for synthetic riboswitches. Our results also provide a foundation from which to investigate how natural riboswitches are tuned to meet systems-level regulatory demands

The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds

We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian threefold. Our proof includes the following essential steps: 1. We simultaneously strengthen a conjecture by the first two authors and Toda, and prove that it follows from a more natural and seemingly weaker statement. This conjecture is a Bogomolov-Gieseker type inequality involving the third Chern character of "tilt-stable" two-term complexes on smooth projective threefolds; we extend it from complexes of tilt-slope zero to arbitrary tilt-slope. 2. We show that this stronger conjecture implies the so-called support property of Bridgeland stability conditions, and the existence of an explicit open subset of the space of stability conditions. 3. We prove our conjecture for abelian threefolds, thereby giving reproving and generalizing a result by Maciocia and Piyaratne. Important in our approach is a more systematic understanding on the behaviour of quadratic inequalities for semistable objects under wall-crossing, closely related to the support property.Comment: 45 pages, 1 figure. v2: addressed referee comments. To appear in Inventiones Mat

Deep-Sea Origin and In-Situ Diversification of Chrysogorgiid Octocorals

The diversity, ubiquity and prevalence in deep waters of the octocoral family Chrysogorgiidae Verrill, 1883 make it noteworthy as a model system to study radiation and diversification in the deep sea. Here we provide the first comprehensive phylogenetic analysis of the Chrysogorgiidae, and compare phylogeny and depth distribution. Phylogenetic relationships among 10 of 14 currently-described Chrysogorgiidae genera were inferred based on mitochondrial (mtMutS, cox1) and nuclear (18S) markers. Bathymetric distribution was estimated from multiple sources, including museum records, a literature review, and our own sampling records (985 stations, 2345 specimens). Genetic analyses suggest that the Chrysogorgiidae as currently described is a polyphyletic family. Shallow-water genera, and two of eight deep-water genera, appear more closely related to other octocoral families than to the remainder of the monophyletic, deep-water chrysogorgiid genera. Monophyletic chrysogorgiids are composed of strictly (Iridogorgia Verrill, 1883, Metallogorgia Versluys, 1902, Radicipes Stearns, 1883, Pseudochrysogorgia Pante & France, 2010) and predominantly (Chrysogorgia Duchassaing & Michelotti, 1864) deep-sea genera that diversified in situ. This group is sister to gold corals (Primnoidae Milne Edwards, 1857) and deep-sea bamboo corals (Keratoisidinae Gray, 1870), whose diversity also peaks in the deep sea. Nine species of Chrysogorgia that were described from depths shallower than 200 m, and mtMutS haplotypes sequenced from specimens sampled as shallow as 101 m, suggest a shallow-water emergence of some Chrysogorgia species

An investigation of causes of false positive single nucleotide polymorphisms using simulated reads from a small eukaryote genome

Background: Single Nucleotide Polymorphisms (SNPs) are widely used molecular markers, and their use has increased massively since the inception of Next Generation Sequencing (NGS) technologies, which allow detection of large numbers of SNPs at low cost. However, both NGS data and their analysis are error-prone, which can lead to the generation of false positive (FP) SNPs. We explored the relationship between FP SNPs and seven factors involved in mapping-based variant calling - quality of the reference sequence, read length, choice of mapper and variant caller, mapping stringency and filtering of SNPs by read mapping quality and read depth. This resulted in 576 possible factor level combinations. We used error- and variant-free simulated reads to ensure that every SNP found was indeed a false positive. Results: The variation in the number of FP SNPs generated ranged from 0 to 36,621 for the 120 million base pairs (Mbp) genome. All of the experimental factors tested had statistically significant effects on the number of FP SNPs generated and there was a considerable amount of interaction between the different factors. Using a fragmented reference sequence led to a dramatic increase in the number of FP SNPs generated, as did relaxed read mapping and a lack of SNP filtering. The choice of reference assembler, mapper and variant caller also significantly affected the outcome. The effect of read length was more complex and suggests a possible interaction between mapping specificity and the potential for contributing more false positives as read length increases. Conclusions: The choice of tools and parameters involved in variant calling can have a dramatic effect on the number of FP SNPs produced, with particularly poor combinations of software and/or parameter settings yielding tens of thousands in this experiment. Between-factor interactions make simple recommendations difficult for a SNP discovery pipeline but the quality of the reference sequence is clearly of paramount importance. Our findings are also a stark reminder that it can be unwise to use the relaxed mismatch settings provided as defaults by some read mappers when reads are being mapped to a relatively unfinished reference sequence from e.g. a non-model organism in its early stages of genomic exploration

Implementing Routine HIV Testing: The Role of State Law

In September 2006, the Centers for Disease Control and Prevention (CDC) recommended routine HIV testing for all Americans aged 13–64, which would eliminate requirements for written consent and pretest counseling as previously required. However, this approach may conflict with state requirements concerning pretest counseling and informed consent for HIV testing. Our survey of state HIV testing laws demonstrates that the majority of states have HIV testing requirements that are inconsistent with the CDC's recommendations. Moreover, states that have recently amended their laws have not eased the requirements for pretest counseling and informed consent. The reasons for the persistence of these legal requirements must be understood to effect policy changes to increase HIV testing

Nocturia, Sleep-Disordered Breathing, and Cardiovascular Morbidity in a Community-Based Cohort

Background: Nocturia has been independently associated with cardiovascular morbidity and all-cause mortality, but such studies did not adjust for sleep-disordered breathing (SDB), which may have mediated such a relationship. Our aims were to determine whether an association between nocturia and cardiovascular morbidity exists that is independent of SDB. We also determined whether nocturia is independently associated with SDB. Methodology/Principal Findings: In order to accomplish these aims we performed a cross-sectional analysis of the Sleep Heart Health Study that contained information regarding SDB, nocturia, and cardiovascular morbidity in a middle-age to elderly community-based population. In 6342 participants (age 63±11 [SD] years, 53% women), after adjusting for known confounders such as age, body mass index, diuretic use, diabetes mellitus, alpha-blocker use, nocturia was independently associated with SDB (measured as Apnea Hypopnea index >15 per hour; OR 1.3; 95%CI, 1.2-1.5). After adjusting for SDB and other known confounders, nocturia was independently associated with prevalent hypertension (OR 1.23; 95%CI 1.08-1.40; P = 0.002), cardiovascular disease (OR 1.26; 95%CI 1.05-1.52; P = 0.02) and stroke (OR 1.62; 95%CI 1.14-2.30; P = 0.007). Moreover, nocturia was also associated with adverse objective alterations of sleep as measured by polysomnography and self-reported excessive daytime sleepiness (P<0.05). Conclusions/Significance: Nocturia is independently associated with sleep-disordered breathing. After adjusting for SDB, there remained an association between nocturia and cardiovascular morbidity. Such results support screening for SDB in patients with nocturia, but the mechanisms underlying the relationship between nocturia and cardiovascular morbidity requires further study. MeSH terms: Nocturia, sleep-disordered breathing, obstructive sleep apnea, sleep apnea, polysomnography, hypertension

Differential cell line susceptibility to the emerging Zika virus: implications for disease pathogenesis, non-vector-borne human transmission and animal reservoirs

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