A Complete and Recursive Feature Theory

Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions considered in this paper are the possibly quantified first-order formulae obtained from a signature of binary and unary predicates called features and sorts, respectively. We establish a first-order theory FT by means of three axiom schemes, show its completeness, and construct three elementarily equivalent models. One of the models consists of so-called feature graphs, a data structure common in computational linguistics. The other two models consist of so-called feature trees, a record-like data structure generalizing the trees corresponding to first-order terms. Our completeness proof exhibits a terminating simplification system deciding validity and satisfiability of possibly quantified feature descriptions.Comment: Short version appeared in the 1992 Annual Meeting of the Association for Computational Linguistic

HIP to be Square: Simplifying Nitridophosphate Synthesis in a Hot Isostatic Press

(Oxo)Nitridophosphates have recently been identified as a promising compound class for application in the field of solid‐state lighting. Especially, the latest medium‐pressure syntheses under ammonothermal conditions draw attention of the semiconductor and lighting industry on nitridophosphates. In this contribution, we introduce hot isostatic presses as a new type of medium‐pressure synthetic tool, further simplifying nitridophosphate synthesis. In a second step, phosphorus nitride was replaced as starting material by red phosphorus, enabling the synthesis of Ca2PN3 as model compound, starting only from readily available compounds. Moreover, first luminescence investigations on Eu2+‐doped samples reveal Ca2PN3:Eu2+ as a promising broad‐band red‐emitter (λem=650 nm; fwhm=1972 cm−1). Besides simple handling, the presented synthetic method offers access to large sample volumes, and the underlying reaction conditions facilitate single‐crystal growth, required for excellent optical properties

Ammonothermal Synthesis of Ba2PO3N – An Oxonitridophosphate with Non‐Condensed PO3N Tetrahedra

The ortho‐oxonitridophosphate Ba2PO3N was synthesized under ammonobasic conditions (T = 1070 K, p = 120 MPa) in custom‐built high‐temperature autoclaves, starting from red phosphorus, BaO, NaN3 and KOH. Thus, single crystals of up to several hundred µm were obtained, which were used for single‐crystal X‐ray diffraction. Ba2PO3N [Pnma (no. 62), a = 7.596(2), b = 5.796(1), c = 10.212(3) Å, Z = 4] crystallizes in the β‐K2SO4 structure type with non‐condensed [PO3N]4– ions and is isotypic to its lighter homologues EA2PO3N (EA = Ca, Sr). Powder X‐ray diffraction, energy dispersive X‐ray and Fourier Transformed Infrared spectroscopy corroborate the crystal structure. The optical band gap was determined by means of diffuse reflectance UV/Vis spectroscopy to be 4.3 eV. Eu2+ doped samples show green luminescence (λem = 534 nm, fwhm = 85 nm/2961 cm–1) when irradiated with UV light (λexc = 420 nm). However, Ba2PO3N:Eu2+ shows strong thermal quenching, even at room temperature

Sr3P3N7: Complementary Approach by Ammonothermal and High‐Pressure Syntheses

Nitridophosphates exhibit an intriguing structural diversity with different structural motifs, for example, chains, layers or frameworks. In this contribution the novel nitridophosphate Sr3P3N7 with unprecedented dreier double chains is presented. Crystalline powders were synthesized using the ammonothermal method, while single crystals were obtained by a high‐pressure multianvil technique. The crystal structure of Sr3P3N7 was solved and refined from single‐crystal X‐ray diffraction and confirmed by powder X‐ray methods. Sr3P3N7 crystallizes in monoclinic space group P 2/c . Energy‐dispersive X‐ray and Fourier‐transformed infrared spectroscopy were conducted to confirm the chemical composition, as well as the absence of NHx functionality. The optical band gap was estimated to be 4.4 eV using diffuse reflectance UV/Vis spectroscopy. Upon doping with Eu2+, Sr3P3N7 shows a broad deep‐red to infrared emission (λem=681 nm, fwhm≈3402 cm−1) with an internal quantum efficiency of 42 %

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

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

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

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

GenomeVIP: A cloud platform for genomic variant discovery and interpretation

Identifying genomic variants is a fundamental first step toward the understanding of the role of inherited and acquired variation in disease. The accelerating growth in the corpus of sequencing data that underpins such analysis is making the data-download bottleneck more evident, placing substantial burdens on the research community to keep pace. As a result, the search for alternative approaches to the traditional “download and analyze” paradigm on local computing resources has led to a rapidly growing demand for cloud-computing solutions for genomics analysis. Here, we introduce the Genome Variant Investigation Platform (GenomeVIP), an open-source framework for performing genomics variant discovery and annotation using cloud- or local high-performance computing infrastructure. GenomeVIP orchestrates the analysis of whole-genome and exome sequence data using a set of robust and popular task-specific tools, including VarScan, GATK, Pindel, BreakDancer, Strelka, and Genome STRiP, through a web interface. GenomeVIP has been used for genomic analysis in large-data projects such as the TCGA PanCanAtlas and in other projects, such as the ICGC Pilots, CPTAC, ICGC-TCGA DREAM Challenges, and the 1000 Genomes SV Project. Here, we demonstrate GenomeVIP's ability to provide high-confidence annotated somatic, germline, and de novo variants of potential biological significance using publicly available data sets.</jats:p