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.

Stabilization of Juxta-Physeal Distal Tibial and Fibular Fractures in a Juvenile Tiger Using a Hybrid Circular-Linear External Fixator

OBJECTIVE: To report stabilization of closed, comminuted distal metaphyseal transverse fractures of the left tibia and fibula in a tiger using a hybrid circular-linear external skeletal fixator. STUDY DESIGN: Clinical report. ANIMAL: Juvenile tiger (15 months, 90 kg). METHODS: From imaging studies, the tiger had comminuted distal metaphyseal transverse fractures of the left tibia and fibula, with mild caudolateral displacement and moderate compression. Multiple fissures extended from the fractures through the distal metaphyses, extending toward, but not involving the distal tibial and fibular physes. A hybrid circular-linear external skeletal fixator was applied by closed reduction, to stabilize the fractures. RESULTS: The fractures healed and the fixator was removed 5 weeks after stabilization. Limb length and alignment were similar to the normal contralateral limb at hospital discharge, 8 weeks after surgery. Two weeks later, the tiger had fractures of the right tibia and fibula and was euthanatized. Necropsy confirmed pathologic fractures ascribed to copper deficiency. CONCLUSION: Closed application of the hybrid construct provided sufficient stability to allow this 90 kg tiger's juxta-articular fractures to heal with minimal complications and without disrupting growth from the adjacent physes.

Temporal trends of extended-spectrum cephalosporin-resistant Escherichia coli and Klebsiella pneumoniae isolates in in- and outpatients in Switzerland, 2004 to 2011

Increasing trends for invasive infections with extended-spectrum cephalosporin-resistant (ESC-R) Enterobacteriaceae have been described in many countries worldwide. However, data on the rates of ESC-R isolates in non-invasive infections and in the outpatient setting are scarce. We used a laboratory-based nationwide surveillance system to compare temporal trends of ESC-R rates in Escherichia coli and Klebsiella pneumoniae for in- and outpatients in Switzerland. Our data showed a significant increase in ESC-R rates from 1% to 5.8% in E. coli (p<0.001) and from 1.1% to 4.4% in K. pneumoniae (p=0.002) during an eight-year period (2004–2011). For E. coli, the increase was significantly higher in inpatients (from 1.2% to 6.6%), in patients residing in eastern Switzerland (from 1.0% to 6.2%), in patients older than 45 years (from 1.2% to 6.7%), and in male patients (from 1.2% to 8.1%). While the increase in inpatients was linear (p<0.001) for E. coli, the increase of ESC R K. pneumoniae isolates was the result of multiple outbreaks in several institutions. Notably, an increasing proportion of ESC-R E. coli was co-resistant to both trimethoprim-sulfamethoxazole and quinolones (42% in 2004 to 49.1% in 2011, p=0.009), further limiting the available oral therapeutic options.

NLCHECK: Stata module to check linearity assumption after model estimation

nlcheck is a simple diagnostic tool that can be used after fitting a model to quickly check the linearity assumption for a given predictor. nlcheck categorizes the predictor into bins, refits the model including dummy variables for the bins, and then performs a joint Wald test for the added parameters. Alternative, nlcheck uses linear splines for the adaptive model. Support for discrete variables is also provided. Optionally, nlcheck also displays a graph of the adjusted linear predictions from the original model and the adaptive model

Corpus callosum index and long-term disability in multiple sclerosis patients

Prediction of long-term disability in patients with multiple sclerosis (MS) is essential. Magnetic resonance imaging (MRI) measurement of brain volume may be of predictive value but sophisticated MRI techniques are often inaccessible in clinical practice. The corpus callosum index (CCI) is a normalized measurement that reflects changes of brain volume. We investigated medical records and 533 MRI scans at diagnosis and during clinical follow-up of 169 MS patients (mean age 42 +/- 11 years, 86% relapsing-remitting MS, time since first relapse 11 +/- 9 years). CCI at diagnosis was 0.345 +/- 0.04 and correlated with duration of disease (p = 0.002; r = -0.234) and expanded disability status scale (EDSS) score at diagnosis (r = -0.428; p < 0.001). Linear regression analyses identified age, duration of disease, relapse rate and EDSS at diagnosis as independent predictors for disability after mean of 7.1 years (Nagelkerkes' R:0.56). Annual CCI decrease was 0.01 +/- 0.02 (annual tissue loss: 1.3%). In secondary progressive MS patients, CCI decrease was double compared to that in relapsing-remitting MS patients (p = 0.04). There was a trend of greater CCI decrease in untreated patients compared to those who received disease modifying drugs (p = 0.2). CCI is an easy to use MRI marker for estimating brain atrophy in patients with MS. Brain atrophy as measured with CCI was associated with disability progression but it was not an independent predictor of long-term disability.

Characterization of functioning in multiple sclerosis using the ICF

The objective of this study was to explore whether it is possible to describe based on the International Classification of Functioning, Disability and Health (ICF) relevant aspects of functioning and disability affected in multiple sclerosis (MS) as well as environmental factors relevant to persons with MS. The specific aim was to identify most relevant 'Body functions', 'Body structures', 'Activities and participation', as well as 'Environmental factors' in patients with MS using the ICF. Additionally, different MS forms were compared with respect to the identified problems. A multi-centre study was conducted in an empirical cross-sectional design. Data from 205 individuals with MS were collected in rehabilitation centres: disease related data, socio-demographic data, single interviews based on the Extended ICF Checklist and a patient questionnaire including ratings on general health and functioning status, Beck Depression Inventory II (BDI-II) and Comorbidity Questionnaire (SCQ). The 129 ICF categories identified represent a comprehensive classification of functioning in MS from the clinical perspective. Differences between MS forms were observed for several ICF categories, EDSS, general health and functioning status, but not for BDI and SCQ. The study showed that it is possible to describe based on the ICF the spectrum in functioning and disability affected in MS as well as environmental factors relevant to persons with MS.

Review of Lodox Statscan in the detection of peripheral skeletal fractures in multiple injury patients

As part of the primary survey, polytrauma patients in our emergency department are examined using the new 'Lodox Statscan' (LS) digital low-radiation imaging device. The LS provides full-body anterior and lateral views based on enhanced linear slot-scanning technology, in accordance with the recommended Advanced Trauma Life Support (ATLS) Guidelines. This study's objectives were to establish whether LS appropriately rules out peripheral bone injuries and to examine whether LS imaging provides adequate information for the preoperative planning of such lesions.

Monte Carlo simulation of a dynamic MLC based on a multiple source model

Detailed knowledge of the characteristics of the radiation field shaped by a multileaf collimator (MLC) is essential in intensity modulated radiotherapy (IMRT). A previously developed multiple source model (MSM) for a 6 MV beam was extended to a 15 MV beam and supplemented with an accurate model of an 80-leaf dynamic MLC. Using the supplemented MSM and the MC code GEANT, lateral dose distributions were calculated in a water phantom and a portal water phantom. A field which is normally used for the validation of the step and shoot technique and a field from a realistic IMRT treatment plan delivered with dynamic MLC are investigated. To assess possible spectral changes caused by the modulation of beam intensity by an MLC, the energy spectra in five portal planes were calculated for moving slits of different widths. The extension of the MSM to 15 MV was validated by analysing energy fluences, depth doses and dose profiles. In addition, the MC-calculated primary energy spectrum was verified with an energy spectrum which was reconstructed from transmission measurements. MC-calculated dose profiles using the MSM for the step and shoot case and for the dynamic MLC case are in very good agreement with the measured data from film dosimetry. The investigation of a 13 cm wide field shows an increase in mean photon energy of up to 16% for the 0.25 cm slit compared to the open beam for 6 MV and of up to 6% for 15 MV, respectively. In conclusion, the MSM supplemented with the dynamic MLC has proven to be a powerful tool for investigational and benchmarking purposes or even for dose calculations in IMRT.

An integral conservative gridding--algorithm using Hermitian curve interpolation

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).

Mapping Individual Variation in Male Mating Preference Space: Multiple Choice in a Color Polymorphic Cichlid Fish

Sexual selection theory largely rests on the assumption that populations contain individual variation in mating preferences and that individuals are consistent in their preferences. However, there are few empirical studies of within-population variation and even fewer have examined individual male mating preferences. Here, we studied a color polymorphic population of the Lake Victoria cichlid fish Neochromis omnicaeruleus, a species in which color morphs are associated with different sex-determining factors. Wild-caught males were tested in three-way choice trials with multiple combinations of different females belonging to the three color morphs. Compositional log-ratio techniques were applied to analyze individual male mating preferences. Large individual variation in consistency, strength, and direction of male mating preferences for female color morphs was found and hierarchical clustering of the compositional data revealed the presence of four distinct preference groups corresponding to the three color morphs in addition to a no-preference class. Consistency of individual male mating preferences was higher in males with strongest preferences. We discuss the implications of these findings for our understanding of the mechanisms underlying polymorphism in mating preferences.

An insulin infusion advisory system for type 1 diabetes patients based on non-linear model predictive control methods

In this paper, an Insulin Infusion Advisory System (IIAS) for Type 1 diabetes patients, which use insulin pumps for the Continuous Subcutaneous Insulin Infusion (CSII) is presented. The purpose of the system is to estimate the appropriate insulin infusion rates. The system is based on a Non-Linear Model Predictive Controller (NMPC) which uses a hybrid model. The model comprises a Compartmental Model (CM), which simulates the absorption of the glucose to the blood due to meal intakes, and a Neural Network (NN), which simulates the glucose-insulin kinetics. The NN is a Recurrent NN (RNN) trained with the Real Time Recurrent Learning (RTRL) algorithm. The output of the model consists of short term glucose predictions and provides input to the NMPC, in order for the latter to estimate the optimum insulin infusion rates. For the development and the evaluation of the IIAS, data generated from a Mathematical Model (MM) of a Type 1 diabetes patient have been used. The proposed control strategy is evaluated at multiple meal disturbances, various noise levels and additional time delays. The results indicate that the implemented IIAS is capable of handling multiple meals, which correspond to realistic meal profiles, large noise levels and time delays.

The Assessment of Multiple Processes Underlying the Attentional Blink: A Fixed - links Modeling Approach based on Behavioral and Electrophysiological Data

When observers are presented with two visual targets appearing in the same position in close temporal proximity, a marked reduction in detection performance of the second target has often been reported, the so-called attentional blink phenomenon. Several studies found a similar decrement of P300 amplitudes during the attentional blink period as observed with detection performances of the second target. However, whether the parallel courses of second target performances and corresponding P300 amplitudes resulted from the same underlying mechanisms remained unclear. The aim of our study was therefore to investigate whether the mechanisms underlying the AB can be assessed by fixed-links modeling and whether this kind of assessment would reveal the same or at least related processes in the behavioral and electrophysiological data. On both levels of observation three highly similar processes could be identified: an increasing, a decreasing and a u-shaped trend. Corresponding processes from the behavioral and electrophysiological data were substantially correlated, with the two u-shaped trends showing the strongest association with each other. Our results provide evidence for the assumption that the same mechanisms underlie attentional blink task performance at the electrophysiological and behavioral levels as assessed by fixed-links models.

Monitoring Programmes, Multiple Stress Analysis and Decision Support for River Basin Management

The identification of plausible causes for water body status deterioration will be much easier if it can build on available, reliable, extensive and comprehensive biogeochemical monitoring data (preferably aggregated in a database). A plausible identification of such causes is a prerequisite for well-informed decisions on which mitigation or remediation measures to take. In this chapter, first a rationale for an extended monitoring programme is provided; it is then compared to the one required by the Water Framework Directive (WFD). This proposal includes a list of relevant parameters that are needed for an integrated, a priori status assessment. Secondly, a few sophisticated statistical tools are described that subsequently allow for the estiation of the magnitude of impairment as well as the likely relative importance of different stressors in a multiple stressed environment. The advantages and restrictions of these rather complicated analytical methods are discussed. Finally, the use of Decision Support Systems (DSS) is advocated with regard to the specific WFD implementation requirements.

Groundwater age distributions at a public drinking water supply well field derived from multiple age tracers (⁸⁵Kr, ³H/³He, and ³⁹Ar)

Groundwater age is a key aspect of production well vulnerability. Public drinking water supply wells typically have long screens and are expected to produce a mixture of groundwater ages. The groundwater age distributions of seven production wells of the Holten well field (Netherlands) were estimated from tritium-helium (3H/3He), krypton-85 (85Kr), and argon-39 (39Ar), using a new application of a discrete age distribution model and existing mathematical models, by minimizing the uncertainty-weighted squared differences of modeled and measured tracer concentrations. The observed tracer concentrations fitted well to a 4-bin discrete age distribution model or a dispersion model with a fraction of old groundwater. Our results show that more than 75 of the water pumped by four shallow production wells has a groundwater age of less than 20 years and these wells are very vulnerable to recent surface contamination. More than 50 of the water pumped by three deep production wells is older than 60 years. 3H/3He samples from short screened monitoring wells surrounding the well field constrained the age stratification in the aquifer. The discrepancy between the age stratification with depth and the groundwater age distribution of the production wells showed that the well field preferentially pumps from the shallow part of the aquifer. The discrete groundwater age distribution model appears to be a suitable approach in settings where the shape of the age distribution cannot be assumed to follow a simple mathematical model, such as a production well field where wells compete for capture area.

Discrete Improvement in Racial Disparity in Survival among Patients with Stage IV Colorectal Cancer: a 21-Year Population-Based Analysis

Purpose Recently, multiple clinical trials have demonstrated improved outcomes in patients with metastatic colorectal cancer. This study investigated if the improved survival is race dependent. Patients and Methods Overall and cancer-specific survival of 77,490 White and Black patients with metastatic colorectal cancer from the 1988–2008 Surveillance Epidemiology and End Results registry were compared using unadjusted and multivariable adjusted Cox proportional hazard regression as well as competing risk analyses. Results Median age was 69 years, 47.4 % were female and 86.0 % White. Median survival was 11 months overall, with an overall increase from 8 to 14 months between 1988 and 2008. Overall survival increased from 8 to 14 months for White, and from 6 to 13 months for Black patients. After multivariable adjustment, the following parameters were associated with better survival: White, female, younger, better educated and married patients, patients with higher income and living in urban areas, patients with rectosigmoid junction and rectal cancer, undergoing cancer-directed surgery, having well/moderately differentiated, and N0 tumors (p<0.05 for all covariates). Discrepancies in overall survival based on race did not change significantly over time; however, there was a significant decrease of cancer-specific survival discrepancies over time between White and Black patients with a hazard ratio of 0.995 (95 % confidence interval 0.991–1.000) per year (p=0.03). Conclusion A clinically relevant overall survival increase was found from 1988 to 2008 in this population-based analysis for both White and Black patients with metastatic colorectal cancer. Although both White and Black patients benefitted from this improvement, a slight discrepancy between the two groups remained.