Automated computation of robust normal forms of planar analytic vector fields

We construct an auto-validated algorithm that calculates a close to identity change of variables which brings a general saddle point into a normal form. The transformation is robust in the underlying vector field, and is analytic on a computable neighborhood of the saddle point. The normal form is suitable for computations aimed at enclosing the flow close to the saddle, and the time it takes a trajectory to pass it. Several examples illustrate the usefulness of this method

Price Pooling and the Gains from Hedging: Application to a Swedish Grain Cooperative

Optimal hedging strategies are analyzed for a cooperative operating a price pooling system in the presence of price and quantity risk. A three-period model, accounting for default risk and storage, is developed. Hedging allows the cooperative to increase the pool price offered to farmers by 2.8 - 4% for moderate risk parameters.Agribusiness, Marketing,

Rigidity for infinitely renormalizable area-preserving maps

The period doubling Cantor sets of strongly dissipative Henon-like maps with different average Jacobian are not smoothly conjugated. The Jacobian Rigidity Conjecture says that the period doubling Cantor sets of two-dimensional Henon-like maps with the same average Jacobian are smoothly conjugated. This conjecture is true for average Jacobian zero, e.g. the one-dimensional case. The other extreme case is when the maps preserve area, e.g. the average Jacobian is one. Indeed, the period doubling Cantor set of area-preserving maps in the universality class of the Eckmann-Koch-Wittwer renormalization fixed point are smoothly conjugated.Comment: 55 pages, incl. references; 2 figure

Urine Complement Proteins and the Risk of Kidney Disease Progression and Mortality in Type 2 Diabetes.

ObjectiveWe examined the association of urine complement proteins with progression to end-stage renal disease (ESRD) or death in people with type 2 diabetes and proteinuric diabetic kidney disease (DKD).Research design and methodsUsing targeted mass spectrometry, we quantified urinary abundance of 12 complement proteins in a predominantly Mexican American cohort with type 2 diabetes and proteinuric DKD (n = 141). The association of urine complement proteins with progression to ESRD or death was evaluated using time-to-event analyses.ResultsAt baseline, median estimated glomerular filtration rate (eGFR) was 54 mL/min/1.73 m2 and urine protein-to-creatinine ratio 2.6 g/g. Sixty-seven participants developed ESRD or died, of whom 39 progressed to ESRD over a median of 3.1 years and 40 died over a median 3.6 years. Higher urine CD59, an inhibitor of terminal complement complex formation, was associated with a lower risk of ESRD (hazard ratio [HR] [95% CI per doubling] 0.50 [0.29-0.87]) and death (HR [95% CI] 0.56 [0.34-0.93]), after adjustment for demographic and clinical covariates, including baseline eGFR and proteinuria. Higher urine complement components 4 and 8 were associated with lower risk of death (HR [95% CI] 0.57 [0.41-0.79] and 0.66 [0.44-0.97], respectively); higher urine factor H-related protein 2, a positive regulator of the alternative complement pathway, was associated with greater risk of death (HR [95% CI] 1.61 [1.05-2.48]) in fully adjusted models.ConclusionsIn a largely Mexican American cohort with type 2 diabetes and proteinuric DKD, urine abundance of several complement and complement regulatory proteins was strongly associated with progression to ESRD and death

Clinical Experience with Radioisotopic Powered Cardiac Pacemakers

Significant increase in the useful lifetime of the implantable cardiac pacemaker has been made possible by the development of a radioisotope power source. This paper reports experience with two models, the AEC-ARCO Nu-5 (fixed rate) and the Medtronic Model 9000 (ventricular inhibited demand). Five of the former models were implanted in 1973, and six of the latter more recently. Both types of units have functioned well

Rapid mapping of chromosomal breakpoints: from blood to BAC in 20 days

Structural chromosome aberrations and associated segmental or chromosomal aneusomies are major causes of reproductive failure in humans. Despite the fact that carriers of reciprocal balanced translocation often have no other clinical symptoms or disease, impaired chromosome homologue pairing in meiosis and karyokinesis errors lead to over-representation of translocations carriers in the infertile population and in recurrent pregnancy loss patients. At present, clinicians have no means to select healthy germ cells or balanced zygotes in vivo, but in vitro fertilization (IVF) followed by preimplantation genetic diagnosis (PGD) offers translocation carriers a chance to select balanced or normal embryos for transfer. Although a combination of telomeric and centromeric probes can differentiate embryos that are unbalanced from normal or unbalanced ones, a seemingly random position of breakpoints in these IVF-patients poses a serious obstacle to differentiating between normal and balanced embryos, which for most translocation couples, is desirable. Using a carrier with reciprocal translocation t(4;13) as an example, we describe our state-of-the-art approach to the preparation of patient-specific DNA probes that span or 'extent' the breakpoints. With the techniques and resources described here, most breakpoints can be accurately mapped in a matter of days using carrier lymphocytes, and a few extra days are allowed for PGD-probe optimization. The optimized probes will then be suitable for interphase cell analysis, a prerequisite for PGD since blastomeres are biopsied from normally growing day 3 – embryos regardless of their position in the mitotic cell cycle. Furthermore, routine application of these rapid methods should make PGD even more affordable for translocation carriers enrolled in IVF programs

Peak systolic velocity using color-coded tissue Doppler imaging, a strong and independent predictor of outcome in acute coronary syndrome patients

BACKGROUND: Traditional echocardiographic methods like left ventricular ejection fraction(EF) and wall motion scoring (WMS) and new methods like speckle tracking (ST) based 2D strain carry important prognostic information in acute coronary syndrome (ACS) patients. Parameters from tissue Doppler imaging (TDI), with its high time resolution, may further increase the prognostic value. Peak systolic velocity (PSV) of the basal segments of the left ventricle from TDI is a robust and user independent parameter. The aim was to investigate the prognostic value of PSV compared to EF, WMS, 2D strain and E/e'. METHODS: Echocardiographic images were collected and post processed in 227 ACS patients. Additional clinical data was prospectively gathered and patients were followed for 3-5 years regarding the combined endpoint of death or re-admission due to ACS or heart failure. RESULTS: The combined endpoint occurred in 85 (37%) patients. Those with an event had lower median PSV than those without (4,4 cm/s) vs. (5,3 cm/s), (p<0.001). In a ROC analysis, the AUC was larger for PSV (0.75) than for EF (0.68), WMS (0.63), 2D strain (0.67) and E/e'(0.70). The combined endpoint increased with decreasing PSV. When adjusting for differences in baseline characteristics in a COX-regression model, PSV remained independently associated with outcome where the others did not. PSV was also less sensitive to image quality with fewer values missing or unacceptable for analysis. CONCLUSION: Peak systolic velocity (PSV) is a robust measurement that seems to have a strong and independent association with outcome compared to traditional echocardiographic measurements in ACS patients

Rigorous Enclosures of a Slow Manifold

Slow-fast dynamical systems have two time scales and an explicit parameter representing the ratio of these time scales. Locally invariant slow manifolds along which motion occurs on the slow time scale are a prominent feature of slow-fast systems. This paper introduces a rigorous numerical method to compute enclosures of the slow manifold of a slow-fast system with one fast and two slow variables. A triangulated first order approximation to the two dimensional invariant manifold is computed "algebraically". Two translations of the computed manifold in the fast direction that are transverse to the vector field are computed as the boundaries of an initial enclosure. The enclosures are refined to bring them closer to each other by moving vertices of the enclosure boundaries one at a time. As an application we use it to prove the existence of tangencies of invariant manifolds in the problem of singular Hopf bifurcation and to give bounds on the location of one such tangency