An extension of the Kreiss stability theorem to families of matrices of unbounded order

AbstractThe Kreiss matrix theorem asserts three necessary and sufficient conditions for a family of matrices of fixed finite order to be L2-stable: a resolvent condition (R), a triangularization condition (S) and a Hermitian norm condition (H). We extend the Kreiss theorem to families of matrices of finite but unbounded order with the restriction that the degrees of the minimal polynomials of all matrices in the family are less than a fixed constant. For such matrix families, we show that (R) and (H) remain necessary and sufficient for L2-stability, while (S) must be replaced by a somewhat stronger “block triangularization” condition (S′). This extended Kreiss theorem permits a corresponding extension of the Buchanan stability theorem

Trade-offs between cost and accuracy in active case-finding for tuberculosis: a dynamic modelling analysis

Background Active case-finding (ACF) may be valuable in tuberculosis (TB) control, but questions remain about its optimum implementation in different settings. For example, smear microscopy misses up to half of TB cases, yet is cheap, and detects the most infectious TB cases. What, then, is the incremental value of using more sensitive and specific, yet more costly, tests such as Xpert MTB/RIF, in ACF in a high burden setting? Methods and Findings We constructed a dynamic transmission model of TB, calibrated to be consistent with an urban slum population in India. We applied this model to compare the potential cost and impact of two hypothetical approaches, following initial symptom screening: (i) ‘moderate accuracy’ testing employing a microscopy-like test (that is, lower cost but also lower accuracy) for bacteriological confirmation and (ii) ‘high accuracy’ testing employing an Xpert-like test (higher-cost but also higher accuracy, while also detecting rifampicin resistance). Results suggest that ACF using a moderate-accuracy test could in fact cost more overall than using a high-accuracy test. Under an illustrative budget of USD 20 million in a slum population of 2 million, high-accuracy testing would avert 1·14 (95% Bayesian credible intervals 0·75 – 1·99, with p = 0.28) cases relative to each case averted by moderate-accuracy testing. Test specificity is a key driver: high-accuracy testing would be significantly more impactful at the 5% significance level, as long as the high-accuracy test has specificity at least 3 percentage points greater than the moderate-accuracy test. Additional factors promoting the impact of a high-accuracy are that: its ability to detect rifampicin resistance can lead to long-term cost savings in second-line treatment; and its higher sensitivity contributes to the overall cases averted by ACF. Amongst limitations of this study, our cost model has a narrow focus on the commodity costs of testing and treatment; our estimates should not be taken as indicative of the overall cost of ACF. There remains uncertainty about the true specificity of tests such as smear and Xpert-like tests in ACF, including variations in the accuracy of the reference standard under such conditions. Conclusions Our results suggest that cheaper diagnostics do not necessarily translate to less costly ACF, as any savings from the test cost can be strongly outweighed by factors including false-positive TB treatment, reduced sensitivity, and foregone savings in second-line treatment. In resource-limited settings, it is therefore important to take all of these factors into account, when designing cost-effective strategies for ACF

Characterization of the PTB ultra-high pulse dose rate reference electron beam

: Purpose. This investigation aims to present the characterisation and optimisation of an ultra-high pulse dose rate (UHPDR) electron beam at the PTB facility in Germany. A Monte Carlo beam model has been developed for dosimetry study for future investigation in FLASH radiotherapy and will be presented.Material and methods. The 20 MeV electron beams generated by the research linear accelerator has been characterised both in-beamline with profile monitors and magnet spectrometer, and in-water with a diamond detector prototype. The Monte Carlo model has been used to investigate six different setups to enable different dose per pulse (DPP) ranges and beam sizes in water. The properties of the electron radiation field in water have also been characterised in terms of beam size, quality specifierR50and flatness. The beam stability has also been studied.Results. The difference between the Monte-Carlo simulated and measuredR50was smaller than 0.5 mm. The simulated beam sizes agreed with the measured ones within 2 mm. Two suitable setups have been identified for delivering reference UHPDR electron beams. The first one is characterised by a SSD of 70 cm, while in the second one an SSD of 90 cm is used in combination with a 2 mm aluminium scattering plates. The two set-ups are quick and simple to install and enable an expected overall DPP range from 0.13 Gy up to 6.7 Gy per pulse.Conclusion. The electron beams generated by the PTB research accelerator have shown to be stable throughout the four-months length of this investigation. The Monte Carlo models have shown to be in good agreement for beam size and depth dose and within 1% for the beam flatness. The diamond detector prototype has shown to be a promising tool to be used for relative measurements in UHPDR electron beams

Absorbed-dose-to-water measurement using alanine in ultra-high-pulse-dose-rate electron beams

: Objective. The aim of the presented study is to evaluate the dose response of the PTB's secondary standard system, which is based on alanine and electron spin resonance (ESR) spectroscopy measurement, in ultra-high-pulse-dose-rate (UHPDR) electron beams.Approach. The alanine dosimeter system was evaluated in the PTB's UHPDR electron beams (20 MeV) in a range of 0.15-6.2 Gy per pulse. The relationship between the obtained absorbed dose to water per pulse and the in-beamline charge measurement of the electron pulses acquired using an integrating current transformer (ICT) was evaluated. Monte Carlo simulations were used to determine the beam quality conversion and correction factors required to perform alanine dosimetry.Main results. The beam quality conversion factor from the reference quality60Co to 20 MeV obtained by Monte Carlo simulation, 1.010(1), was found to be within the standard uncertainty of the consensus value, 1.014(5). The dose-to-water relative standard uncertainty was determined to be 0.68% in PTB's UHPDR electron beams.Significance. In this investigation, the dose-response of the PTB's alanine dosimeter system was evaluated in a range of dose per pulse between 0.15 Gy and 6.2 Gy and no evidence of dose-response dependency of the PTB's secondary standard system based on alanine was observed. The alanine/ESR system was shown to be a precise dosimetry system for evaluating absorbed dose to water in UHPDR electron beams

Challenges in the estimation of the annual risk of mycobacterium tuberculosis infection in children aged less than 5 years

Accurate estimates of Mycobacterium tuberculosis infection in young children provide a critical indicator of ongoing community transmission of M. tuberculosis. Cross-reactions due to infection with environmental mycobacteria and/or bacille Calmette-Guérin (BCG) vaccination compromise the estimates derived from population-level tuberculin skin-test surveys using traditional cutoff methods. Newer statistical approaches are prone to failure of model convergence, especially in settings where the prevalence of M. tuberculosis infection is low and environmental sensitization is high. We conducted a tuberculin skin-test survey in 5,119 preschool children in the general population and among household contacts of tuberculosis cases in 2012–2014 in a district in northern Malawi where sensitization to environmental mycobacteria is common and almost all children are BCG-vaccinated. We compared different proposed methods of estimating M. tuberculosis prevalence, including a method described by Rust and Thomas more than 40 years ago. With the different methods, estimated prevalence in the general population was 0.7%–11.5% at ages <2 years and 0.8%–3.3% at ages 2–4 years. The Rust and Thomas method was the only method to give a lower estimate in the younger age group (0.7% vs 0.8%), suggesting that it was the only method that adjusted appropriately for the marked effect of BCG-attributable induration in the very young

Risk factors for Mycobacterium tuberculosis infection in 2-4 year olds in a rural HIV-prevalent setting.

BACKGROUND: Mycobacterium tuberculosis infection in children acts as a sentinel for infectious tuberculosis. OBJECTIVE: To assess risk factors associated with tuberculous infection in pre-school children. METHOD: We conducted a population-wide tuberculin skin test (TST) survey from January to December 2012 in Malawi. All children aged 2-4 years residing in a demographic surveillance area were eligible. Detailed demographic data, including adult human immunodeficiency virus (HIV) status, and clinical and sociodemographic data on all diagnosed tuberculosis (TB) patients were available. RESULTS: The prevalence of M. tuberculosis infection was 1.1% using a TST induration cut-off of 15 mm (estimated annual risk of infection of 0.3%). The main identifiable risk factors were maternal HIV infection at birth (adjusted OR [aOR] 3.6, 95%CI 1.1-12.2), having three or more adult members in the household over a lifetime (aOR 2.4, 95%CI 1.2-4.8) and living in close proximity to a known case of infectious TB (aOR 1.6, 95%CI 1.1-2.4), modelled as a linear variable across categories (>200 m, 100-200 m, <100 m, within household). Less than 20% of the infected children lived within 200 m of a known diagnosed case. CONCLUSION: Household and community risk factors identified do not explain the majority of M. tuberculosis infections in children in our setting

Human Immunodeficiency Virus-Associated Chronic Lung Disease in Children and Adolescents in Zimbabwe: Chest Radiographic and High-Resolution Computed Tomographic Findings.

Background: Chronic respiratory symptoms are common among children living with human immunodeficiency virus (HIV). We investigated the radiological features of chronic lung disease in children aged 6-16 years receiving antiretroviral therapy for ≥6 months in Harare, Zimbabwe. Methods: Consecutive participants from a HIV clinic underwent clinical assessment and chest radiography. Participants with an abnormal chest radiograph (assessed by a clinician) and/or those meeting a clinical case definition for chronic lung disease underwent high-resolution computed tomography (HRCT). Radiological studies were scored independently and blindly by 2 thoracic radiologists. Relationships between radiological abnormalities and lung function were examined. Results: Among 193 participants (46% female; median age, 11.2 years; interquartile range, 9.0-12.8 years), the median CD4 cell count was 720/µL (473-947/µL), and 79% had a human immunodeficiency virus (HIV) load of <400 copies/mL. The most common chest radiographic finding was ring/tramline opacities (55 of 193 participants; 29%). HRCT scans were evaluated in 84 participants (69%); decreased attenuation (present in 43%) was the dominant abnormality seen. The extent of decreased attenuation was strongly correlated with both the severity and extent of bronchiectasis (rs = 0.68 and P < .001 for both). The extent of decreased attenuation was also negatively correlated with forced expiratory volume in first second of expiration (rs = -0.52), forced vital capacity (rs = -0.42), and forced expiratory flow, midexpiratory phase (rs = -0.42) (P < .001 for all). Conclusions: The HRCT findings strongly suggest that obliterative bronchiolitis may be the major cause of chronic lung disease in our cohort. Further studies to understand the pathogenesis and natural history are urgently needed

Delivery of index-linked HIV testing for children: learnings from a qualitative process evaluation of the B-GAP study in Zimbabwe

Background Index-linked HIV testing for children, whereby HIV testing is offered to children of individuals living with HIV, has the potential to identify children living with undiagnosed HIV. The “Bridging the Gap in HIV Testing and Care for Children in Zimbabwe” (B-GAP) study implemented and evaluated the provision of index-linked HIV testing for children aged 2–18 years in Zimbabwe. We conducted a process evaluation to understand the considerations for programmatic delivery and scale-up of this strategy. Methods We used implementation documentation to explore experiences of the field teams and project manager who delivered the index-linked testing program, and to describe barriers and facilitators to index-linked testing from their perspectives. Qualitative data were drawn from weekly logs maintained by the field teams, monthly project meeting minutes, the project coordinator’s incident reports and WhatsApp group chats between the study team and the coordinator. Data from each of the sources was analysed thematically and synthesised to inform the scale-up of this intervention. Results Five main themes were identified related to the implementation of the intervention: (1) there was reduced clinic attendance of potentially eligible indexes due to community-based differentiated HIV care delivery and collection of HIV treatment by proxy individuals; (2) some indexes reported that they did not live in the same household as their children, reflecting the high levels of community mobility; (3) there were also thought to be some instances of ‘soft refusal’; (4) further, delivery of HIV testing was limited by difficulties faced by indexes in attending health facilities with their children for clinic-based testing, stigma around community-based testing, and the lack of familiarity of indexes with caregiver provided oral HIV testing; (5) and finally, test kit stockouts and inadequate staffing also constrained delivery of index-linked HIV testing. Conclusions There was attrition along the index-linked HIV testing cascade of children. While challenges remain at all levels of implementation, programmatic adaptations of index-linked HIV testing approaches to suit patterns of clinic attendance and household structures may strengthen implementation of this strategy. Our findings highlight the need to tailor index-linked HIV testing to subpopulations and contexts to maximise its effectiveness

Observation of Sommerfeld precursors on a fluid surface

We report the observation of two types of Sommerfeld precursors (or forerunners) on the surface of a layer of mercury. When the fluid depth increases, we observe a transition between these two precursor surface waves in good agreement with the predictions of asymptotic analysis. At depths thin enough compared to the capillary length, high frequency precursors propagate ahead of the ''main signal'' and their period and amplitude, measured at a fixed point, increase in time. For larger depths, low frequency ''precursors'' follow the main signal with decreasing period and amplitude. These behaviors are understood in the framework of the analysis first introduced for linear transient electromagnetic waves in a dielectric medium by Sommerfeld and Brillouin [1].Comment: to be published in Physical Review Letter