Thirring Solitons in the presence of dispersion

The effect of dispersion or diffraction on zero-velocity solitons is studied for the generalized massive Thirring model describing a nonlinear optical fiber with grating or parallel-coupled planar waveguides with misaligned axes. The Thirring solitons existing at zero dispersion/diffraction are shown numerically to be separated by a finite gap from three isolated soliton branches. Inside the gap, there is an infinity of multi-soliton branches. Thus, the Thirring solitons are structurally unstable. In another parameter region (far from the Thirring limit), solitons exist everywhere.Comment: 12 pages, Latex. To appear in Phys. Rev. Let

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem

The variable relationship between arm and hand use: a rationale for using finger magnetometry to complement wrist accelerometry when measuring daily use of the upper extremity.

Wrist-worn accelerometers are becoming more prevalent as a means to assess use of the impaired upper extremity in daily life after stroke. However, wrist accelerometry does not measure joint movements of the hand, which are integral to functional use of the upper extremity. In this study, we used a custom-built, non-obtrusive device called the manumeter to measure both arm use (via wrist accelerometry) and hand use (via finger magnetometry) of a group of unimpaired subjects while they performed twelve motor tasks at three intensities. We also gave the devices to four stroke subjects and asked them to wear them for six hours a day for one month. From the in-lab testing we found that arm use was a strong predictor of hand use for individual tasks, but that the slope of the relationship varied by up to a factor of ~12 depending on the task being performed. Consistent with this, in the daily use data collected from stroke subjects we found a broad spread in the relationship between arm and hand use. These results suggest that analyzing the spread of the relationship between daily hand and arm use will give more insight into upper extremity recovery than wrist accelerometry or finger magnetometry alone, because the spread reflects the nature of the daily tasks performed as well as the amount of upper extremity use

Donor-Acceptor Oligorotaxanes Made to Order

Five donor–acceptor oligorotaxanes made up of dumbbells composed of tetraethylene glycol chains, interspersed with three and five 1,5-dioxynaphthalene units, and terminated by 2,6-diisopropylphenoxy stoppers, have been prepared by the threading of discrete numbers of cyclobis(paraquat-p-phenylene) rings, followed by a kinetically controlled stoppering protocol that relies on click chemistry. The well-known copper(I)-catalyzed alkyne–azide cycloaddition between azide functions placed at the ends of the polyether chains and alkyne-bearing stopper precursors was employed during the final kinetically controlled template-directed synthesis of the five oligorotaxanes, which were characterized subsequently by ^1H NMR spectroscopy at low temperature (233 K) in deuterated acetonitrile. The secondary structures, as well as the conformations, of the five oligorotaxanes were unraveled by spectroscopic comparison with the dumbbell and ring components. By focusing attention on the changes in chemical shifts of some key probe protons, obtained from a wide range of low-temperature spectra, a picture emerges of a high degree of folding within the thread protons of the dumbbells of four of the five oligorotaxanes—the fifth oligorotaxane represents a control compound in effect— brought about by a combination of C-H···O and π–π stacking interactions between the p-electron-deficient bipyridinium units in the rings and the π-electron-rich 1,5-dioxynaphthalene units and polyether chains in the dumbbells. The secondary structures of a foldamer-like nature have received further support from a solid-state superstructure of a related [3]pseudorotaxane and density functional calculations performed thereon

Impact of Atrial Fibrillation on Stroke‐Related Healthcare Costs

Background: Limited data exist on the economic implications of stroke among patients with atrial fibrillation (AF). This study assesses the impact of AF on healthcare costs associated with ischemic stroke (IS), hemorrhagic stroke (HS), or transient ischemic attack (TIA). Methods and Results: A retrospective analysis of MarketScan claims data (2005‐2011) for AF patients ≥18 years old with ≥1 inpatient claim for stroke, or ≥1 ED or inpatient claim for TIA as identified by ICD‐9‐CM codes who had ≥12 months continuous enrollment prior to initial stroke. Initial event‐ and stroke‐related costs 12 months post‐index were compared among patients with AF and without AF. Adjusted costs were estimated, controlling for demographics, comorbidities, anticoagulant use, and baseline resource use. Data from 23 807 AF patients and 136 649 patients without AF were analyzed. Unadjusted mean cost of the index event was $20 933 for IS,$59 054 for HS, $8616 for TIA hospitalization, and$3395 for TIA ED visit. After controlling for potential confounders, adjusted mean incremental costs (index plus 12‐month post‐index) for AF patients were higher than those for non‐AF patients by: $4726,$7824, and $1890 for index IS, HS, TIA (identified by hospitalization), respectively, and$1700 for TIA (identified by ED) (all P<0.01). In multivariate regression analysis, AF was associated with a 20% (IS), 13% (HS), and 18% (TIA) increase in total stroke‐related costs. Conclusion: Stroke‐related care for IS, HS, and TIA is costly, especially among individuals with AF. Reducing the risk of AF‐related stroke is important from both clinical and economic standpoints

Expert-augmented machine learning.

Machine learning is proving invaluable across disciplines. However, its success is often limited by the quality and quantity of available data, while its adoption is limited by the level of trust afforded by given models. Human vs. machine performance is commonly compared empirically to decide whether a certain task should be performed by a computer or an expert. In reality, the optimal learning strategy may involve combining the complementary strengths of humans and machines. Here, we present expert-augmented machine learning (EAML), an automated method that guides the extraction of expert knowledge and its integration into machine-learned models. We used a large dataset of intensive-care patient data to derive 126 decision rules that predict hospital mortality. Using an online platform, we asked 15 clinicians to assess the relative risk of the subpopulation defined by each rule compared to the total sample. We compared the clinician-assessed risk to the empirical risk and found that, while clinicians agreed with the data in most cases, there were notable exceptions where they overestimated or underestimated the true risk. Studying the rules with greatest disagreement, we identified problems with the training data, including one miscoded variable and one hidden confounder. Filtering the rules based on the extent of disagreement between clinician-assessed risk and empirical risk, we improved performance on out-of-sample data and were able to train with less data. EAML provides a platform for automated creation of problem-specific priors, which help build robust and dependable machine-learning models in critical applications

Magnetic ordering, electronic structure and magnetic anisotropy energy in the high-spin Mn10_{10} single molecule magnet

We report the electronic structure and magnetic ordering of the single molecule magnet [Mn$_{10}$O$_{4}$(2,2'-biphenoxide)$_{4}$Br$_{12}$]$^{4-}$ based on first-principles all-electron density-functional calculations. We find that two of the ten core Mn atoms are coupled antiferromagnetically to the remaining eight, resulting in a ferrimagnetic ground state with total spin S=13. The calculated magnetic anisotropy barrier is found to be 9 K in good agreement with experiment. The presence of the Br anions impact the electronic structure and therefore the magnetic properties of the 10 Mn atoms. However, the electric field due to the negative charges has no significant effect on the magnetic anisotropy.Comment: 4 pages, submitted to PR