Algebraic Torsion in Contact Manifolds

We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic fillings and exact symplectic cobordisms. A contact manifold has algebraic torsion of order zero if and only if it is algebraically overtwisted (i.e. has trivial contact homology), and any contact 3-manifold with positive Giroux torsion has algebraic torsion of order one (though the converse is not true). We also construct examples for each nonnegative k of contact 3-manifolds that have algebraic torsion of order k but not k - 1, and derive consequences for contact surgeries on such manifolds. The appendix by Michael Hutchings gives an alternative proof of our cobordism obstructions in dimension three using a refinement of the contact invariant in Embedded Contact Homology.Comment: 53 pages, 4 figures, with an appendix by Michael Hutchings; v.3 is a final update to agree with the published paper, and also corrects a minor error that appeared in the published version of the appendi

Occupancy Modeling, Maximum Contig Size Probabilities and Designing Metagenomics Experiments

Mathematical aspects of coverage and gaps in genome assembly have received substantial attention by bioinformaticians. Typical problems under consideration suppose that reads can be experimentally obtained from a single genome and that the number of reads will be set to cover a large percentage of that genome at a desired depth. In metagenomics experiments genomes from multiple species are simultaneously analyzed and obtaining large numbers of reads per genome is unlikely. We propose the probability of obtaining at least one contig of a desired minimum size from each novel genome in the pool without restriction based on depth of coverage as a metric for metagenomic experimental design. We derive an approximation to the distribution of maximum contig size for single genome assemblies using relatively few reads. This approximation is verified in simulation studies and applied to a number of different metagenomic experimental design problems, ranging in difficulty from detecting a single novel genome in a pool of known species to detecting each of a random number of novel genomes collectively sized and with abundances corresponding to given distributions in a single pool

Diffusion-weighted imaging in oral squamous cell carcinoma using 3 Tesla MRI: is there a chance for preoperative discrimination between benign and malignant lymph nodes in daily clinical routine?

Background Preoperative staging of cervical lymph nodes is important to determine the extent of neck dissection in patients with oral squamous cell carcinoma (OSCC). Purpose To evaluate whether a preoperative discrimination of benign and malignant cervical lymph nodes with diffusion-weighted imaging (DWI) (3T) is feasible for clinical application. Material and Methods Forty-five patients with histological proven OSCC underwent preoperative 3T-MRI. DWI (b=0, 500, and 1000s/mm(2)) was added to the standard magnetic resonance imaging (MRI) protocol. Mean apparent diffusion coefficients (ADC(mean)) were measured for lymph nodes with 3mm or more in short axis by two independent readers. Finally, these results were matched with histology. Results Mean ADC was significantly higher for malignant than for benign nodes (1.1430.188 * 10(-3) mm(2)/s vs. 0.987 +/- 0.215 * 10(-3) mm(2)/s). Using an ADC value of 0.994 * 10(-3) mm(2)/s as threshold results in a sensitivity of 80%, specificity of 65%, positive predictive value of 31%, and negative predictive value of 93%. Conclusion Due to a limited sensitivity and specificity DWI alone is not suitable to reliably discriminate benign from malignant cervical lymph nodes in daily clinical routine. Hence, the preoperative determination of the extent of neck dissection on the basis of ADC measurements is not meaningful

Optimized method for black carbon analysis in ice and snow using the Single Particle Soot Photometer

In this study we attempt to optimize the method for measuring black carbon (BC) in snow and ice using a Single Particle Soot Photometer (SP2). Beside the previously applied ultrasonic (CETAC) and Collison-type nebulizers we introduce a jet (Apex Q) nebulizer to aerosolize the aqueous sample for SP2 analysis. Both CETAC and Apex Q require small sample volumes (a few milliliters) which makes them suitable for ice core analysis. The Apex Q shows the least size-dependent nebulizing efficiency in the BC particle diameter range of 100–1000 nm. The CETAC has the advantage that air and liquid flows can be monitored continuously. All nebulizer-types require a calibration with BC standards for the determination of the BC mass concentration in unknown aqueous samples. We found Aquadag to be a suitable material for preparing calibration standards. Further, we studied the influence of different treatments for fresh discrete snow and ice samples as well as the effect of storage. The results show that samples are best kept frozen until analysis. Once melted, they should be sonicated for 25 min, immediately analyzed while being stirred and not be refrozen

New obstructions to symplectic embeddings

In this paper we establish new restrictions on symplectic embeddings of certain convex domains into symplectic vector spaces. These restrictions are stronger than those implied by the Ekeland-Hofer capacities. By refining an embedding technique due to Guth, we also show that they are sharp.Comment: 80 pages, 3 figures, v2: improved exposition and minor corrections, v3: Final version, expanded and improved exposition and minor corrections. The final publication is available at link.springer.co

An 800-year high-resolution black carbon ice core record from Lomonosovfonna, Svalbard

Produced by the incomplete combustion of fossil fuel and biomass, black carbon (BC) contributes to Arctic warming by reducing snow albedo and thus triggering a snow-albedo feedback leading to increased snowmelt. Therefore, it is of high importance to assess past BC emissions to better understand and constrain their role. However, only a few long-term BC records are available from the Arctic, mainly originating from Greenland ice cores. Here, we present the first long-term and high-resolution refractory black carbon (rBC) record from Svalbard, derived from the analysis of two ice cores drilled at the Lomonosovfonna ice field in 2009 (LF-09) and 2011 (LF-11) and covering 800 years of atmospheric emissions. Our results show that rBC concentrations strongly increased from 1860 on due to anthropogenic emissions and reached two maxima, at the end of the 19th century and in the middle of the 20th century. No increase in rBC concentrations during the last decades was observed, which is corroborated by atmospheric measurements elsewhere in the Arctic but contradicts a previous study from another ice core from Svalbard. While melting may affect BC concentrations during periods of high temperatures, rBC concentrations remain well preserved prior to the 20th century due to lower temperatures inducing little melt. Therefore, the preindustrial rBC record (before 1800), along with ammonium (NH4+), formate (HCOO−) and specific organic markers (vanillic acid, VA, and p-hydroxybenzoic acid, p-HBA), was used as a proxy for biomass burning. Despite numerous single events, no long-term trend was observed over the time period 1222–1800 for rBC and NH4+. In contrast, formate, VA, and p-HBA experience multi-decadal peaks reflecting periods of enhanced biomass burning. Most of the background variations and single peak events are corroborated by other ice core records from Greenland and Siberia. We suggest that the paleofire record from the LF ice core primarily reflects biomass burning episodes from northern Eurasia, induced by decadal-scale climatic variations.</p

Aspects of coverage in medical DNA sequencing

<p>Abstract</p> <p>Background</p> <p>DNA sequencing is now emerging as an important component in biomedical studies of diseases like cancer. Short-read, highly parallel sequencing instruments are expected to be used heavily for such projects, but many design specifications have yet to be conclusively established. Perhaps the most fundamental of these is the redundancy required to detect sequence variations, which bears directly upon genomic coverage and the consequent resolving power for discerning somatic mutations.</p> <p>Results</p> <p>We address the medical sequencing coverage problem via an extension of the standard mathematical theory of haploid coverage. The expected diploid multi-fold coverage, as well as its generalization for aneuploidy are derived and these expressions can be readily evaluated for any project. The resulting theory is used as a scaling law to calibrate performance to that of standard BAC sequencing at 8× to 10× redundancy, i.e. for expected coverages that exceed 99% of the unique sequence. A differential strategy is formalized for tumor/normal studies wherein tumor samples are sequenced more deeply than normal ones. In particular, both tumor alleles should be detected at least twice, while both normal alleles are detected at least once. Our theory predicts these requirements can be met for tumor and normal redundancies of approximately 26× and 21×, respectively. We explain why these values do not differ by a factor of 2, as might intuitively be expected. Future technology developments should prompt even deeper sequencing of tumors, but the 21× value for normal samples is essentially a constant.</p> <p>Conclusion</p> <p>Given the assumptions of standard coverage theory, our model gives pragmatic estimates for required redundancy. The differential strategy should be an efficient means of identifying potential somatic mutations for further study.</p

Weak and strong fillability of higher dimensional contact manifolds

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five),while also being obstructed by all known manifestations of "overtwistedness". We also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense. These depend on a higher-dimensional analogue of Giroux torsion, which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary.Comment: 68 pages, 5 figures. v2: Some attributions clarified, and other minor edits. v3: exposition improved using referee's comments. Published by Invent. Mat

Numerical and Experimental Investigation of Circulation in Short Cylinders

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. Simulations show that endcaps corotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted azimuthal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at $Re\le 3200$ agrees remarkably well with experiment at $Re\sim 10^6$. This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps. After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings