Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root is either the central vertex or, in the more challenging problem, a pendant vertex of the star graph. At all other pendant vertices Dirichlet conditions are imposed; at the central vertex, at which a mass may be placed, continuity and Kirchhoff conditions are assumed. We derive conditions on two sets of real numbers to be the spectra of the above Dirichlet and Neumann problems. Our solution for the inverse problems is constructive: we establish algorithms to recover the mass distribution on the star graph (i.e. the point masses and lengths of subintervals between them) from these two spectra and from the lengths of the separate strings. If the root is a pendant vertex, the two spectra uniquely determine the parameters on the main string (i.e. the string incident to the root) if the length of the main string is known. The mass distribution on the other edges need not be unique; the reason for this is the non-uniqueness caused by the non-strict interlacing of the given data in the case when the root is the central vertex. Finally, we relate of our results to tree-patterned matrix inverse problems.

Multinomial goodness-of-fit: large sample tests with survey design correction and exact tests for small samples

I introduce the new mgof command to compute distributional tests for discrete (categorical, multinomial) variables. The command supports largesample tests for complex survey designs and exact tests for small samples as well as classic large-sample x2-approximation tests based on Pearson’s X2, the likelihood ratio, or any other statistic from the power-divergence family (Cressie and Read, 1984, Journal of the Royal Statistical Society, Series B (Methodological) 46: 440–464). The complex survey correction is based on the approach by Rao and Scott (1981, Journal of the American Statistical Association 76: 221–230) and parallels the survey design correction used for independence tests in svy: tabulate. mgof computes the exact tests by using Monte Carlo methods or exhaustive enumeration. mgof also provides an exact one-sample Kolmogorov–Smirnov test for discrete data.

MGOF: Stata module to perform goodness-of-fit tests for multinomial data

mgof computes goodness-of-fit tests for the distribution of a discrete (categorical, multinomial) variable. The default is to perform classical large sample chi-squared approximation tests based on Pearson's X2 statistic and the log likelihood ratio (G2) statistic or a statistic from the Cressie-Read family. Alternatively, mgof computes exact tests using Monte Carlo methods or exhaustive enumeration. A Kolmogorov-Smirnov test for discrete data is also provided. The moremata package, also available from SSC, is required.

Multinomial goodness-of-fit: large sample tests with survey design correction and exact tests for small samples

A new Stata command called -mgof- is introduced. The command is used to compute distributional tests for discrete (categorical, multinomial) variables. Apart from classic large sample $\chi^2$-approximation tests based on Pearson's $X^2$, the likelihood ratio, or any other statistic from the power-divergence family (Cressie and Read 1984), large sample tests for complex survey designs and exact tests for small samples are supported. The complex survey correction is based on the approach by Rao and Scott (1981) and parallels the survey design correction used for independence tests in -svy:tabulate-. The exact tests are computed using Monte Carlo methods or exhaustive enumeration. An exact Kolmogorov-Smirnov test for discrete data is also provided.

Renal insufficiency is independently associated with a distal distribution pattern of symptomatic lower-limb atherosclerosis

Objectives The purpose of this study was to assess the impact of renal insufficiency (RI) on the distribution pattern of peripheral arterial disease (PAD). We hypothesised that RI is associated with a distally accentuated involvement of the peripheral arterial tree. Design This is a retrospective analysis. Materials and Methods Analysis was based on a consecutive series of 2709 patients with chronic PAD of atherosclerotic origin undergoing primary endovascular treatment of lower-extremity arteries. Atherosclerotic pattern was grouped into femoropopliteal (n = 2085) and infragenicular (n = 892) disease according to target lesions treated while using iliac disease (n = 1133) as reference. Univariable and multivariable multinomial regression analyses were performed to assess relation with RI. Results are shown as relative risk ratio (RRRs) with 95% confidence intervals (95% CIs). A p < 0.05 was considered statistically significant. RI was defined as glomerular filtration rate (GFR) < 60 ml min−1 1.73 m−2. Results Presence of RI was an independent risk factor for a centrifugal lesion pattern (RRR 1.48, 95% CI: 1.17–1.86, p = 0.001). Moreover, a decrease in GFR by 10 ml min−1 1.73 m−2 was associated with an RRR of 1.08 for below-the-knee arterial disease (95% CI: 1.03–1.13, p = 0.003). Conclusion Presence and severity of RI are independent predictors of a distal obstructive pattern in patients with symptomatic PAD.

Reporting of research quality characteristics of studies published in 6 major clinical dental specialty journals

The objective of this article was to record reporting characteristics related to study quality of research published in major specialty dental journals with the highest impact factor (Journal of Endodontics, Journal of Oral and Maxillofacial Surgery, American Journal of Orthodontics and Dentofacial Orthopedics; Pediatric Dentistry, Journal of Clinical Periodontology, and International Journal of Prosthetic Dentistry). The included articles were classified into the following 3 broad subject categories: (1) cross-sectional (snap-shot), (2) observational, and (3) interventional. Multinomial logistic regression was conducted for effect estimation using the journal as the response and randomization, sample calculation, confounding discussed, multivariate analysis, effect measurement, and confidence intervals as the explanatory variables. The results showed that cross-sectional studies were the dominant design (55%), whereas observational investigations accounted for 13%, and interventions/clinical trials for 32%. Reporting on quality characteristics was low for all variables: random allocation (15%), sample size calculation (7%), confounding issues/possible confounders (38%), effect measurements (16%), and multivariate analysis (21%). Eighty-four percent of the published articles reported a statistically significant main finding and only 13% presented confidence intervals. The Journal of Clinical Periodontology showed the highest probability of including quality characteristics in reporting results among all dental journals.

Association of cardiovascular risk factors with pattern of lower limb atherosclerosis in 2659 patients undergoing angioplasty

OBJECTIVES: Aim of this study is to correlate distribution pattern of lower limb atherosclerosis with cardiovascular risk factor profile of patients with peripheral arterial occlusive disease (PAD). PATIENTS AND METHODS: Analysis is based on a consecutive series of 2659 patients (1583 men, 1076 women, 70+/-11 years) with chronic PAD of atherosclerotic origin undergoing primary endovascular treatment of lower extremity arteries. Pattern of atherosclerosis was grouped into iliac (n=1166), femoropopliteal (n=2151) and infrageniculate (n=888) disease defined according to target lesions treated. A multivariable multinomial logistic regression analysis was performed to assess relation with age, gender and classical cardiovascular risk factors (diabetes mellitus, arterial hypertension, hypercholesterolemia, cigarette smoking) using femoropopliteal disease as reference. RESULTS: Iliac disease was associated with younger age (RRR 0.95 per year of age, 95%-CI 0.94-0.96, p<0.001), male gender (RRR 1.32, 95%-CI 1.09-1.59, p=0.004) and cigarette smoking (RRR 2.02, 95%-CI 1.68-2.42, p<0.001). Infrageniculate disease was associated with higher age (RRR 1.02, 95%-CI 1.01-1.02, p<0.001), male gender (RRR 1.23, 95%-CI 1.06-1.41, p=0.005) and diabetes mellitus (RRR 1.68, 95%-CI 1.47-1.92, p<0.001). Hypercholesterolemia was less prevalent in patients with lesions below the knee (RRR 0.82, 95%-CI 0.71-0.94, p=0.006), whereas no distinct pattern was apparent related to arterial hypertension. CONCLUSION: Clinical phenotype of peripheral atherosclerosis varies with prevalence of cardiovascular risk factors suggesting differences in mechanisms involved in iliac as compared with infrageniculate lesions. Identification of molecular mechanism might have influence on future therapeutic strategies in PAD patients.

Discordant responses to potent antiretroviral treatment in previously naive HIV-1-infected adults initiating treatment in resource-constrained countries: the antiretroviral therapy in low-income countries (ART-LINC) collaboration

OBJECTIVES: To assess the frequency of and risk factors for discordant responses at 6 months on highly active antiretroviral therapy (HAART) in previously treatment-naive HIV patients from resource-limited countries. METHODS: The Antiretroviral Therapy in Low-Income Countries Collaboration is a network of clinics providing care and treatment to HIV-infected patients in Africa, Latin America, and Asia. Patients who initiated therapy between 1996 and 2004, were aged 16 years or older, and had a baseline CD4 cell count were included in this analysis. Responses were defined based on plasma viral load (PVL) and CD4 cell count at 6 months as complete virologic and immunologic (VR(+)IR(+)), virologic only (VR(+)IR(-)), immunologic only (VR(-)IR(+)), and nonresponse (VR(-)IR(-)). Multinomial logistic regression was used to assess the association between therapy responses and clinical and demographic variables. RESULTS: Of the 3111 patients eligible for analysis, 1914 had available information at 6 months of therapy: 1074 (56.1%) were VR(+)IR(+), 364 (19.0%) were VR(+)IR(-), 283 (14.8%) were (VR(-)IR(+)), and 193 (10.1%) were VR(-)IR(-). OF THE 3111 patients eligible for analysis, 1914 had available information at 6 months of therapy: 1074 (56.1%) were VRIR, 364 (19.0%) were VRIR, 283 (14.8%) were (VRIR), and 193 (10.1%) were VRIR. Compared with complete responders, virologic-only responders were older, had a higher baseline CD4 cell count, had a lower baseline PVL, and were more likely to have received a nonstandard HAART regimen; immunologic-only responders were younger, had a lower baseline CD4 cell count, had a higher baseline PVL, and were more likely to have received a protease inhibitor-based regimen. CONCLUSIONS: The frequency of and risk factors for discordant responses were comparable to those observed in developed countries. Longer follow-up is needed to assess the long-term impact of discordant responses on mortality in these resource-limited settings.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

Exploring the periodicity of cardiovascular events in Switzerland: Variation in deaths and hospitalizations across seasons, day of the week and hour of the day

Purpose The purpose of this study is to explore the periodical patterns of events and deaths related to cardiovascular disease (CVD), acute myocardial infarction (AMI) and stroke in Swiss adults (≥18years). Methods Mortality data for period 1969–2007 (N=869,863 CVD events) and hospitalization data for period 1997–2008 (N=959,990 CVD events) were used. The annual, weekly and circadian distribution of CVD-related deaths and events were assessed. Multivariate analysis was conducted using multinomial logistic regression adjusting for age, gender and calendar year and considering deaths from respiratory diseases, accidents or other causes as competitive events. Results CVD deaths and hospitalizations occurred less frequently in the summer months. Similar patterns were found for AMI and stroke. No significant weekly variation for CVD deaths was found. Stratification by age and gender showed subjects aged <65years to present a higher probability of dying on Mondays and Saturday, only for men. This finding was confirmed after multivariate adjustment. Finally, a circadian variation in CVD mortality was observed, with a first peak in the morning (8–12am) and a smaller second peak in the late afternoon (2–6pm). This pattern persisted after multivariate adjustment and was more pronounced for AMI than for stroke. Conclusion There is a periodicity of hospitalizations and deaths related to CVD, AMI and stroke in Switzerland. This pattern changes slightly according to the age and sex of the subjects. Although the underlying mechanisms are not fully identified, preventive measures should take into account these aspects to develop better strategies of prevention and management of CVD.

Adult parent-child relationships: Relationship quality, support, and reciprocity

In accordance with Bengtson's model of intergenerational solidarity (e.g. Bengtson & Roberts, 1991), the interrelations between adult daughters' family values, their perception of the relationship quality with their parents, the support they reported to give to and to receive from their parents, and their perception of reciprocity in intergenerational support exchange were investigated for N = 265 middle-aged women in Germany. It was also asked whether the support given to parents and perceived reciprocity are related to daughters' felt burden as a result of their support. Cross-sectional, self-report data were examined with multiple and multinomial logistic regression analyses. The analyses revealed positive relations between family values, relationship quality, and support to parents. Perceived reciprocity was associated with the exchange of intergenerational support and imbalance in support had negative effects on the relationship quality. Felt burden was predicted by the extent of support and the perceived reciprocity. However, specific correlational patterns depending on the kind of support as well as differences in the importance of mother and father occurred. The findings are discussed against the background of the meaning of family obligations and reciprocity in a Western culture.