On mixture failure rate ordering

Mixtures of increasing failure rate distributions (IFR) can decrease at least in some intervals of time. Usually this property can be observed asymptotically as time tends to infinity. This is due to the fact that the mixture failure rate is ‘bent down’ compared with the corresponding unconditional expectation of the baseline failure rate, which was proved previously for some specific cases. We generalize this result and discuss the “weakest populations are dying first” property, which leads to the change in the failure rate shape. We also consider the problem of mixture failure rate ordering for the ordered mixing distributions. Two types of stochastic ordering are analyzed: ordering in the likelihood ratio sense and ordering in variances when the means are equal.

Asymptotic behavior of mixture failure rates

Mixtures of increasing failure rate distributions (IFR) can decrease at least in some intervals of time. Usually this property is observed asymptotically as time tends to infinity , which is due to the fact that a mixture failure rate is ‘bent down’, as the weakest populations are dying out first. We consider a survival model, generalizing a very well known in reliability and survival analysis additive hazards, proportional hazards and accelerated life models. We obtain new explicit asymptotic relations for a general setting and study specific cases. Under reasonable assumptions we prove that asymptotic behavior of the mixture failure rate depends only on the behavior of the mixing distri-bution in the neighborhood of the left end point of its support and not on the whole mixing distribution.

On asymptotic failure rates in bivariate frailty competing risks models

A bivariate competing risks problem is considered for a rather general class of survival models. The lifetime distribution of each component is indexed by a frailty parameter. Under the assumption of conditional independence of components the correlated frailty model is considered. The explicit asymptotic formula for the mixture failure rate of a system is derived. It is proved that asymptotically the remaining lifetimes of components tend to be independent in the defined sense. Some simple examples are discussed.

Supporting children and young people to assume responsibility from their parents for the self-management of their long-term condition: An integrative review

© 2019 John Wiley & Sons Ltd Background: Children and young people with long-term conditions (LTCs) are usually dependent on, or share management with, their families and are expected to develop self-management skills as they mature. However, during adolescence, young people can find it challenging to follow prescribed treatment regimens resulting in poor clinical outcomes. Though reviews have looked at children's and parents' experiences of self-management, none have explicitly examined the parent-to-child transfer of self-management responsibility. Methods: An integrative review was conducted with the aim of exploring the parent-to-child transfer of LTC self-management responsibility, through addressing two questions: (a) How do children assume responsibility from their parents for self-management of their LTC? (b) What influences the parent-to-child transfer of this responsibility? Eight databases were searched for papers published from 1995 to 2017. Methodological quality was assessed; included papers were synthesized to identify themes. Results: Twenty-nine papers were identified. Most papers used qualitative designs and focused on children with diabetes. Participants were predominantly children and/or parents; only two studies included health professionals. Assuming self-management responsibility was viewed as part of normal development but was rarely explored within the context of the child gaining independence in other areas of their life. Children and parents adopted strategies to help the transfer, but there was limited evidence around health professionals' roles and ambivalence around what was helpful. There was a lack of clarity over whether children and parents were aiming for shared management, or self-management, and whether this was a realistic or desired goal for families. Multiple factors such as the child, family, social networks, health professional, and LTC influenced how a child assumed responsibility. Conclusions: Evidence suggests that the parent-to-child transfer of self-management responsibility is a complex, individualized process. Further research across childhood LTCs is needed to explore children's, parents', and professionals' views on this process and what support families require as responsibilities change

A Short Wavelength GigaHertz Clocked Fiber-Optic Quantum Key Distribution System

A quantum key distribution system has been developed, using standard telecommunications optical fiber, which is capable of operating at clock rates of greater than 1 GHz. The quantum key distribution system implements a polarization encoded version of the B92 protocol. The system employs vertical-cavity surface-emitting lasers with emission wavelengths of 850 nm as weak coherent light sources, and silicon single photon avalanche diodes as the single photon detectors. A distributed feedback laser of emission wavelength 1.3 micro-metres, and a linear gain germanium avalanche photodiode was used to optically synchronize individual photons over the standard telecommunications fiber. The quantum key distribution system exhibited a quantum bit error rate of 1.4%, and an estimated net bit rate greater than 100,000 bits-per-second for a 4.2 km transmission range. For a 10 km fiber range a quantum bit error rate of 2.1%, and estimated net bit rate of greater than 7,000 bits-per-second was achieved.Comment: Pre-press versio

Kinetic Study and Characterization of 1,4-β-Endoglucanase of Aspergillus niger ANL301

Submerged fermentation of Aspergillus niger ANL 301 in basal medium containing cellulose as sole carbon source, yielded crude extracellular proteins with 0.54 ± 0.02 units mg protein-1 of 1,4-β-endoglucanase activity. Partial purification by ammonium sulphate precipitation (80% saturation) and gel filtration on Sephadex 25-300 gave two active fractions of 1,4-β-endoglucanase, which exhibited close activity towards carboxymethyl-cellulose (CMC). The pH profile of the pooled enzyme fractions showed three activity peaks at pH 3.5, 5.5 and 7.0. The enzyme was most active at pH 5.5 and showed optimal activity at 50°C. Vmax of 4.4 ± 0.4 µmol min-1 mg protein-1 and Km of 12.5 ± 0.4 gL-1 was obtained with CMC for the enzyme. Different divalent metal ions and EDTA affected the enzyme activity at 2.0 mM concentrations in different ways. Mn2+ and Fe2+ exhibited 253.4 and 24.0% stimulatory effects, respectively on the enzyme activity. Mg2+, Ca2+, Cu2+, and Zn2+ inhibited the enzyme by between 22.3 and 29.4%, whereas 75.0 and 71.3% inhibition were obtained with Hg2+ and EDTA, respectively. Manganese ion showed an exceptional activation of the 1,4-β-endoglucanase. The organism produced two types of 1,4-β-endoglucanase with different molecular weights

Evaluating Spatial Normalization Methods for the Human Brain

Cortical stimulation mapping (CSM) studies have shown cortical locations for language function are highly variable from one subject to the next. Because no two cortical surfaces are alike and language is a higher order cognitive function, observed variability is attributable to a combination of functional and anatomical variation. If individual variation can be normalized, patterns of language organization may emerge that were heretofore hidden. In order to discover whether or not such patterns exist, computer-aided spatial normalization is required. Because CSM data has been collected on the cortical surface, we believe that a surface-based normalization method will provide more accurate results than will a volume-based method. To investigate this hypothesis, we evaluate a surface-based (Caret) and volume-based method (SPM2). For our application, the "ideal" method would i) minimize variation as measured by spread reduction between cortical language sites across subjects while also ii) preserving anatomical localization of sites. Evaluation technique: Eleven MR image volumes and corresponding CSM site coordinates were selected. Images were segmented to create left hemisphere surface reconstruction for each patient. Individual surfaces were registered to the colin27 human brain atlas using each method. Deformation parameters from each method were applied to CSM coordinates to obtain post-normalization coordinates in 2D space and 3D ICBM152 space. Accuracy metrics were calculated i) as mean distance between language sites across subjects in both 2D and 3D space and ii) by visual inspection of post-normalization site locations on a 2D map. Results: Globally, we found no statistically significant difference between CARET (surface-based method) and SPM2 (volume-based method) as measured by both spread reduction and anatomical localization. Local analysis showed that more than twenty percent of total mapping errors were mapped incorrectly by both methods. There was a statistically significant difference between Caret and SPM2 mapping of type 2 errors