From First Lyapunov Coefficients to Maximal Canards

Hopf bifurcations in fast-slow systems of ordinary differential equations can be associated with surprising rapid growth of periodic orbits. This process is referred to as canard explosion. The key step in locating a canard explosion is to calculate the location of a special trajectory, called a maximal canard, in parameter space. A first-order asymptotic expansion of this location was found by Krupa and Szmolyan in the framework of a "canard point"-normal-form for systems with one fast and one slow variable. We show how to compute the coefficient in this expansion using the first Lyapunov coefficient at the Hopf bifurcation thereby avoiding use of this normal form. Our results connect the theory of canard explosions with existing numerical software, enabling easier calculations of where canard explosions occur.Comment: preprint version - for final version see journal referenc

Severely Deformed Extraarticular Fractures of the Scapula: A Review

Nonoperative treatment of severely deformed fractures of the scapula was historically common. However, the findings of newer research have challenged the notion that conservatively managing these fractures results in the most successful outcomes. In an attempt to possibly reveal important indicators for surgical treatment, I reviewed studies on scapula fractures involving scapular anatomy; associated injuries; technological advances that have helped with fracture evaluation; and treatment outcomes between nonsurgical and surgical methods. Although a universally accepted classification scheme of scapula fractures does not exist, use of 3D reconstruction with computed tomography can help define the level and category of fracture deformity. Most fractures heal predictably well with nonoperative management, yet fixation techniques should at least be considered for treating severely deformed scapula fractures. Individualized factors such as patient characteristics, measurable fracture type, and associated injuries may help in determining possible indicators for surgical treatment

Identification of three high molecular mass cysteine proteinases from rat skeletal muscle

AbstractThree cysteine proteinases were isolated from the post-myofibrillar fraction of rat skeletal muscle. Proteinase I preferentially hydrolyzes Z-Phe—Arg-NMec with pH optimum at 8–9. The enzyme activity is stabilized by ATP against thermal inactivation. Proteinase II and III were not resolved by anion-exchange chromatography, by affinity chromatography on Arginine—Sepharose or by gel filtration. Proteinase II, splitting Bz-ValGlyArg-NMec optimally at pH 10–10.5, is inactivated by ATP, whereas Proteinase III, hydrolyzing Suc-AlaAlaPhe-NMec at pH 7–7.5 is not affected by the nucleotide. The molecular mass of proteinase I is about 750 000 and that of proteinase II and III is about 650 000, as determined by gel filtration

Archeological and Geoarcheological Survey of State Highway 35 between Angleton and Old Ocean, Brazoria County, Texas

During March through July 2003, The Center for Archaeological Research of The University of Texas at San Antonio conducted a cultural resources survey, including geoarcheological studies, along portions of State Highway 35 from Angleton to Old Ocean in Brazoria County, Texas. This survey was conducted under Texas Antiquities Permit No. 3091 and was performed for the Texas Department of Transportation, Environmental Affairs Division. During the early phases of the survey, a Historic Context for the project was developed by Hardy-Heck-Moore, Inc. of Austin, Texas. This Historic Context was used to guide the latter phases of the survey, and is reproduced in this document. The project area consisted of a 15-mile-long discontinuous portion of the highway, with variable widths and eight separate detention ponds, varying in area from 2–12 acres each. Nearly 600 auger borings, here substituted for shovel tests, and 176 backhoe trenches were excavated, encountering no significant cultural deposits or features. The artifacts uncovered during these investigations were of recent origin and, therefore, none were collected for analysis and curation. With the exception of testing at site 41BO184, this project completes the cultural resources inventory of the State Highway 35 corridor between Angleton and Old Ocean

Computing Slow Manifolds of Saddle Type

Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for computing trajectories on slow manifolds that are normally hyperbolic with both stable and unstable fast manifolds. We present two examples of bifurcation problems where these manifolds play a key role and a third example in which saddle-type slow manifolds are part of a traveling wave profile of a partial differential equation. Initial value solvers are incapable of computing trajectories on saddle-type slow manifolds, so the slow manifold of saddle type (SMST) algorithm presented here is formulated as a boundary value method. We take an empirical approach here to assessing the accuracy and effectiveness of the algorithm.Comment: preprint version - for final version see journal referenc

Post-polyploidisation morphotype diversification associates with gene copy number variation

Genetic models for polyploid crop adaptation provide important information relevant for future breeding prospects. A well-suited model is Brassica napus, a recent allopolyploid closely related to Arabidopsis thaliana. Flowering time is a major adaptation trait determining life cycle synchronization with the environment. Here we unravel natural genetic variation in B. napus flowering time regulators and investigate associations with evolutionary diversification into different life cycle morphotypes. Deep sequencing of 35 flowering regulators was performed in 280 diverse B. napus genotypes. High sequencing depth enabled high-quality calling of single-nucleotide polymorphisms (SNPs), insertion-deletions (InDels) and copy number variants (CNVs). By combining these data with genotyping data from the Brassica 60 K Illumina® Infinium SNP array, we performed a genome-wide marker distribution analysis across the 4 ecogeographical morphotypes. Twelve haplotypes, including Bna.FLC.A10, Bna.VIN3.A02 and the Bna.FT promoter on C02_random, were diagnostic for the diversification of winter and spring types. The subspecies split between oilseed/kale (B. napus ssp. napus) and swedes/rutabagas (B. napus ssp. napobrassica) was defined by 13 haplotypes, including genomic rearrangements encompassing copies of Bna.FLC, Bna.PHYA and Bna.GA3ox1. De novo variation in copies of important flowering-time genes in B. napus arose during allopolyploidisation, enabling sub-functionalisation that allowed different morphotypes to appropriately fine-tune their lifecycle

Targeted deep sequencing of flowering regulators in Brassica napus reveals extensive copy number variation

Gene copy number variation (CNV) is increasingly implicated in control of complex trait networks, particularly in polyploid plants like rapeseed (Brassica napus L.) with an evolutionary history of genome restructuring. Here we performed sequence capture to assay nucleotide variation and CNV in a panel of central flowering time regulatory genes across a species-wide diversity set of 280 B. napus accessions. The genes were chosen based on prior knowledge from Arabidopsis thaliana and related Brassica species. Target enrichment was performed using the Agilent SureSelect technology, followed by Illumina sequencing. A bait (probe) pool was developed based on results of a preliminary experiment with representatives from different B. napus morphotypes. A very high mean target coverage of ~670x allowed reliable calling of CNV, single nucleotide polymorphisms (SNPs) and insertion-deletion (InDel) polymorphisms. No accession exhibited no CNV, and at least one homolog of every gene we investigated showed CNV in some accessions. Some CNV appear more often in specific morphotypes, indicating a role in diversification