International Water Rights on the White Nile of the New State of South Sudan

The birth of South Sudan falls directly in the demarcation zone of the rivalry between downstream and upstream riparian states on the waters of the Nile River. The downstream states—Egypt and Sudan—stress their “natural and historic” rights to the entire flow of the Nile based on the 1959 Nile Agreement and older colonial treaties, while the upstream African states refuse to be bound by colonial treaties and claim their equitable share of the Nile River by promoting South Sudan’s accession to the Cooperative Framework Agreement (CFA). The Nile River Basin lacks an international binding water agreement that includes and satisfies all the riparian states. This Article analyzes the status quo of South Sudan’s water rights to the Nile River by addressing the following questions: Is the new state bound by any rights and obligations established by the 1959 Nile Agreement? Is it advantageous for South Sudan to accede to the CFA, which provides for modern principles of international water law? The Article applies the customary international law of state succession to South Sudan’s secession from Sudan to determine if the 1959 Nile Agreement is binding between the two states. It concludes that South Sudan succeeded Sudan with regard to territorial rights and obligations established by the 1959 Nile Agreement, as customary international law recognizes that legal obligations of a territorial nature remain unaffected by state succession. South Sudan should enter into negotiations on a binding water agreement to allocate the 18.5 billion cubic meters of water granted to it under the 1959 Nile Agreement. The Article concludes that South Sudan should accede to the CFA within its allotted portion of the Nile waters under the 1959 Nile Agreement

Statistical aspects of discerning indel-type structural variation via DNA sequence alignment

<p>Abstract</p> <p>Background</p> <p>Structural variations in the form of DNA insertions and deletions are an important aspect of human genetics and especially relevant to medical disorders. Investigations have shown that such events can be detected via tell-tale discrepancies in the aligned lengths of paired-end DNA sequencing reads. Quantitative aspects underlying this method remain poorly understood, despite its importance and conceptual simplicity. We report the statistical theory characterizing the length-discrepancy scheme for Gaussian libraries, including coverage-related effects that preceding models are unable to account for.</p> <p>Results</p> <p>Deletion and insertion statistics both depend heavily on physical coverage, but otherwise differ dramatically, refuting a commonly held doctrine of symmetry. Specifically, coverage restrictions render insertions much more difficult to capture. Increased read length has the counterintuitive effect of worsening insertion detection characteristics of short inserts. Variance in library insert length is also a critical factor here and should be minimized to the greatest degree possible. Conversely, no significant improvement would be realized in lowering fosmid variances beyond current levels. Detection power is examined under a straightforward alternative hypothesis and found to be generally acceptable. We also consider the proposition of characterizing variation over the entire spectrum of variant sizes under constant risk of false-positive errors. At 1% risk, many designs will leave a significant gap in the 100 to 200 bp neighborhood, requiring unacceptably high redundancies to compensate. We show that a few modifications largely close this gap and we give a few examples of feasible spectrum-covering designs.</p> <p>Conclusion</p> <p>The theory resolves several outstanding issues and furnishes a general methodology for designing future projects from the standpoint of a spectrum-wide constant risk.</p

The theory of discovering rare variants via DNA sequencing

<p>Abstract</p> <p>Background</p> <p>Rare population variants are known to have important biomedical implications, but their systematic discovery has only recently been enabled by advances in DNA sequencing. The design process of a discovery project remains formidable, being limited to <it>ad hoc </it>mixtures of extensive computer simulation and pilot sequencing. Here, the task is examined from a general mathematical perspective.</p> <p>Results</p> <p>We pose and solve the population sequencing design problem and subsequently apply standard optimization techniques that maximize the discovery probability. Emphasis is placed on cases whose discovery thresholds place them within reach of current technologies. We find that parameter values characteristic of rare-variant projects lead to a general, yet remarkably simple set of optimization rules. Specifically, optimal processing occurs at constant values of the per-sample redundancy, refuting current notions that sample size should be selected outright. Optimal project-wide redundancy and sample size are then shown to be inversely proportional to the desired variant frequency. A second family of constants governs these relationships, permitting one to immediately establish the most efficient settings for a given set of discovery conditions. Our results largely concur with the empirical design of the Thousand Genomes Project, though they furnish some additional refinement.</p> <p>Conclusion</p> <p>The optimization principles reported here dramatically simplify the design process and should be broadly useful as rare-variant projects become both more important and routine in the future.</p

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

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

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

Optimized signal deduction procedure for the MIEZE neutron spectroscopy technique

We report a method to determine the phase and amplitude of sinusoidally modulated event rates, binned into 4 bins per oscillation. The presented algorithm relies on a reconstruction of the unknown parameters. It omits a calculation intensive fitting procedure and avoids contrast reduction due to averaging effects. It allows the current data acquisition bottleneck to be relaxed by a factor of 4. Here, we explain the approach in detail and compare it to the established fitting procedures of time series having 4 and 16 time bins per oscillation. In addition we present the empirical estimates of the errors of the three methods and compare them to each other. We show that the reconstruction is unbiased, asymptotic, and efficient for estimating the phase. Reconstructing the contrast, which corresponds to the amplitude of the modulation, is roughly 10% less efficient than fitting 16 time binned oscillations. Finally, we give analytical equations to estimate the error for phase and contrast as a function of their initial values and counting statistics.Comment: 14 pages, 5 figures, submitted to IOP Measurement Science and Technolog

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

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

Stable Hamiltonian structures in dimension three are supported by open books

We prove that every stable Hamiltonian structure on a closed oriented three-manifold is stably homotopic to one which is supported (with suitable signs) by an open book.Comment: 30 pages, 6 figure