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.

Food Security and Agri-Foreign Direct Investment in Weak States: Finding the Governance Gap to Avoid ‘Land Grab’

Food security is important. A rising world population coupled with climate change creates growing pressure on global world food supplies. States alleviate this pressure domestically by attracting agri-foreign direct investment (agri-FDI). This is a high-risk strategy for weak states: the state may gain valuable foreign currency, technology and debt-free growth; but equally, investors may fail to deliver on their commitments and exploit weak domestic legal infrastructure to ‘grab’ large areas of prime agricultural land, leaving only marginal land for domestic production. A net loss to local food security and to the national economy results. This is problematic because the state must continue to guarantee its citizens’ right to food and property. Agri-FDI needs close regulation to maximise its benefit. This article maps the multilevel system of governance covering agri-FDI. We show how this system creates asymmetric rights in favour of the investor to the detriment of the host state’s food security and how these problems might be alleviated.

Validation and reclassification of MGAP and GAP in hospital settings using data from the Trauma Audit and Research Network.

BACKGROUND Recently, two simple clinical scores were published to predict survival in trauma patients. Both scores may successfully guide major trauma triage, but neither has been independently validated in a hospital setting. METHODS This is a cohort study with 30-day mortality as the primary outcome to validate two new trauma scores-Mechanism, Glasgow Coma Scale (GCS), Age, and Pressure (MGAP) score and GCS, Age and Pressure (GAP) score-using data from the UK Trauma Audit and Research Network. First, an assessment of discrimination, using the area under the receiver operating characteristic (ROC) curve, and calibration, comparing mortality rates with those originally published, were performed. Second, we calculated sensitivity, specificity, predictive values, and likelihood ratios for prognostic score performance. Third, we propose new cutoffs for the risk categories. RESULTS A total of 79,807 adult (≥16 years) major trauma patients (2000-2010) were included; 5,474 (6.9%) died. Mean (SD) age was 51.5 (22.4) years, median GCS score was 15 (interquartile range, 15-15), and median Injury Severity Score (ISS) was 9 (interquartile range, 9-16). More than 50% of the patients had a low-risk GAP or MGAP score (1% mortality). With regard to discrimination, areas under the ROC curve were 87.2% for GAP score (95% confidence interval, 86.7-87.7) and 86.8% for MGAP score (95% confidence interval, 86.2-87.3). With regard to calibration, 2,390 (3.3%), 1,900 (28.5%), and 1,184 (72.2%) patients died in the low, medium, and high GAP risk categories, respectively. In the low- and medium-risk groups, these were almost double the previously published rates. For MGAP, 1,861 (2.8%), 1,455 (15.2%), and 2,158 (58.6%) patients died in the low-, medium-, and high-risk categories, consonant with results originally published. Reclassifying score point cutoffs improved likelihood ratios, sensitivity and specificity, as well as areas under the ROC curve. CONCLUSION We found both scores to be valid triage tools to stratify emergency department patients, according to their risk of death. MGAP calibrated better, but GAP slightly improved discrimination. The newly proposed cutoffs better differentiate risk classification and may therefore facilitate hospital resource allocation. LEVEL OF EVIDENCE Prognostic study, level II.

Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R n , with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from [6], and provide a numerical comparison of the two time discretization methods.