Global Bifurcation of Rotating Vortex Patches

We rigorously construct continuous curves of rotating vortex patch solutions to the two-dimensional Euler equations. The curves are large in that, as the parameter tends to infinity, the minimum along the interface of the angular fluid velocity in the rotating frame becomes arbitrarily small. This is consistent with the conjectured existence [30, 38] of singular limiting patches with 90 corners at which the relative fluid velocity vanishes. For solutions close to the disk, we prove that there are “cat's-eyes”-type structures in the flow, and provide numerical evidence that these structures persist along the entire solution curves and are related to the formation of corners. We also show, for any rotating vortex patch, that the boundary is analytic as soon as it is sufficiently regular.</p

The Unified Method: I Non-Linearizable Problems on the Half-Line

Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the complex $k$-plane (the Fourier plane), which has a jump matrix with explicit $(x,t)$-dependence involving four scalar functions of $k$, called spectral functions. Two of these functions depend on the initial data, whereas the other two depend on all boundary values. The most difficult step of the new method is the characterization of the latter two spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. For certain boundary conditions, called linearizable, this can be achieved simply using algebraic manipulations. Here, we present an effective characterization of the spectral functions in terms of the given initial and boundary data for the general case of non-linearizable boundary conditions. This characterization is based on the analysis of the so-called global relation, on the analysis of the equations obtained from the global relation via certain transformations leaving the dispersion relation of the associated linearized PDE invariant, and on the computation of the large $k$ asymptotics of the eigenfunctions defining the relevant spectral functions.Comment: 39 page

Estimation of Breast Cancer Incident Cases and Medical Care Costs Attributable to Alcohol Consumption Among Insured Women Aged <45 Years in the U.S.

This study estimated the percentage of breast cancer cases, total number of incident cases, and total annual medical care costs attributable to alcohol consumption among insured younger women (aged 18–44 years) by type of insurance and stage at diagnosis

Medical costs associated with metastatic breast cancer in younger, midlife, and older women

Purpose: We estimated average medical costs due to metastatic breast cancer (mBC) among younger (aged 18–44), midlife (aged 45–64), and older women (aged 65 and older) by phase of care: initial, continuing, and terminal. Methods: We used 2003–2014 North Carolina cancer registry data linked with administrative claims from public and private payers. We developed a claims-based algorithm to identify breast cancer patients who progressed to metastatic disease. We matched breast cancer patients (mBC and earlier stage) to non-cancer patients on age group, county of residence, and insurance plan. Outcomes were average monthly medical expenditures and expected medical expenditures by phase. We used regression to estimate excess costs attributed to mBC as the difference in mean payments between patients with mBC (N = 4806) and patients with each earlier-stage breast cancer (stage 1, stage 2, stage 3, and unknown stage; N = 21,772) and non-cancer controls (N = 109,631) by treatment phase and age group. Results: Adjusted monthly costs for women with mBC were significantly higher than for women with earlier-stage breast cancer and non-cancer controls for all age groups and treatment phases except the initial treatment among women with stage 3 breast cancer at diagnosis. The largest expected total costs were for women aged 18–44 with mBC during the continuing phase ($209,961 95$165,736–254,186). Conclusions: We found substantial excess costs for mBC among younger women and during the continuing and terminal phases of survivorship. It is important to assess whether this care is high value for these women

Juvenile obesity and its association with utilisation and costs of pharmaceuticals - results from the KiGGS study

<p>Abstract</p> <p>Background</p> <p>According to a national reference, 15% of German children and adolescents are overweight (including obese) and 6.3% are obese. An earlier study analysed the impact of childhood overweight and obesity on different components of direct medical costs (physician, hospital and therapists). To complement the existing literature for Germany, this study aims to explore the association of body mass index (BMI) with utilisation of pharmaceuticals and related costs in German children and adolescents.</p> <p>Methods</p> <p>Based on data from 14, 836 respondents aged 3-17 years in the German Interview and Examination Survey for Children and Adolescents (KiGGS), drug intake and associated costs were estimated using a bottom-up approach. To investigate the association of BMI with utilisation and costs, univariate analyses and multivariate generalised mixed models were conducted.</p> <p>Results</p> <p>There was no significant difference between BMI groups regarding the probability of drug utilisation. However, the number of pharmaceuticals used was significantly higher (14%) for obese children than for normal weight children. Furthermore, there was a trend for more physician-prescribed medication in obese children and adolescents. Among children with pharmaceutical intake, estimated costs were 24% higher for obese children compared with the normal weight group.</p> <p>Conclusions</p> <p>This is the first study to estimate excess drug costs for obesity based on a representative cross-sectional sample of the child and adolescent population in Germany. The results suggest that obese children should be classified as a priority group for prevention. This study complements the existing literature and provides important information concerning the relevance of childhood obesity as a health problem.</p