On positive solutions and the Omega limit set for a class of delay differential equations

This paper studies the positive solutions of a class of delay differential equations with two delays. These equations originate from the modeling of hematopoietic cell populations. We give a sufficient condition on the initial function for $t\leq 0$ such that the solution is positive for all time $t>0$. The condition is "optimal". We also discuss the long time behavior of these positive solutions through a dynamical system on the space of continuous functions. We give a characteristic description of the $\omega$ limit set of this dynamical system, which can provide informations about the long time behavior of positive solutions of the delay differential equation.Comment: 15 pages, 2 figure

Species Composition of Benthic Diatoms and Distribution of Chlorophyll a on an Intertidal Flat in the Dutch Wadden Sea

A linear transect with 12 sampling points was sampled in a tidal estuarine environment during 1973 for chlorophyll a and pheophytin, and for species composition of epipelic diatoms. A gradual pattern in sediment from coarse to fine was found from the most seaward station towards the most landward station of the transect. Differences in station level gave emersion times of 37 to 67 % of the tidal cycle. In the course of the year, fluctuations in chlorophyll a content (mg chlorophyll a m-* in the top 2 cm of the sediment) appeared to be distinctly parallel at all stations. However, mean yearly values differed widely from station to station, ranging between 20 and 100mg chlorophyll a m-2. Chlorophyll a concentration was positively related to the amount of particles < 16 pm in the sediment; this proportion was considered to relate negatively to the degree of exposure to currents and wave action. It is likely that low daily winter irradiances limited diatom growth. Heavy rain and strong wave action during storms suddenly reduced the chlorophyll a content considerably. Species composition of epipelic benthic diatoms could partly be related to the sediment gradient and time of year. It seems that high biomass values are formed almost exclusively by single species which are indifferent in their spatial distribution

On the uniqueness of paths for spin-0 and spin-1 quantum mechanics

The uniqueness of the Bohmian particle interpretation of the Kemmer equation, which describes massive spin-0 and spin-1 particles, is discussed. Recently the same problem for spin-1/2 was dealt with by Holland. It appears that the uniqueness of boson paths can be enforced under well determined conditions. This in turn fixes the nonrelativistic particle equations of the nonrelativistic Schrodinger equation, which appear to correspond with the original definitions given by de Broglie and Bohm only in the spin-0 case. Similar to the spin-1/2 case, there appears an additional spin-dependent term in the guidance equation in the spin-1 case. We also discuss the ambiguity associated with the introduction of an electromagnetic coupling in the Kemmer theory. We argue that when the minimal coupling is correctly introduced, then the current constructed from the energy-momentum tensor is no longer conserved. Hence this current can not serve as a particle probability four-vector.Comment: 19 pages, no figures, LaTex, shortened version for Phys. Lett.

Analysis of complex metabolic behavior through pathway decomposition

<p>Abstract</p> <p>Background</p> <p>Understanding complex systems through decomposition into simple interacting components is a pervasive paradigm throughout modern science and engineering. For cellular metabolism, complexity can be reduced by decomposition into pathways with particular biochemical functions, and the concept of elementary flux modes provides a systematic way for organizing metabolic networks into such pathways. While decomposition using elementary flux modes has proven to be a powerful tool for understanding and manipulating cellular metabolism, its utility, however, is severely limited since the number of modes in a network increases exponentially with its size.</p> <p>Results</p> <p>Here, we present a new method for decomposition of metabolic flux distributions into elementary flux modes. Our method can easily operate on large, genome-scale networks since it does not require all relevant modes of the metabolic network to be generated. We illustrate the utility of our method for metabolic engineering of <it>Escherichia coli </it>and for understanding the survival of <it>Mycobacterium tuberculosis </it>(MTB) during infection.</p> <p>Conclusions</p> <p>Our method can achieve computational time improvements exceeding 2000-fold and requires only several seconds to generate elementary mode decompositions on genome-scale networks. These improvements arise from not having to generate all relevant elementary modes prior to initiating the decomposition. The decompositions from our method are useful for understanding complex flux distributions and debugging genome-scale models.</p

Monte Carlo Simulation Variance Reduction Techniques for Photon Transport in Liquid Xenon Detectors

Monte Carlo simulations are a crucial tool for the analysis and prediction of various background components in liquid xenon (LXe) detectors. With improving shielding in new experiments, the simulation of external backgrounds, such as induced by gamma rays from detector materials, gets more computationally expensive. We introduce and validate an accelerated Monte Carlo simulation technique for photon transport in liquid xenon detectors. The method simulates photon-induced interactions within a defined geometry and energy range with high statistics while interactions outside of the region of interest are not simulated directly but are taken into account by means of probability weights. For a simulation of gamma induced backgrounds in an exemplary detector geometry we achieve a three orders of magnitude acceleration compared to a standard simulation of a current ton-scale LXe dark matter experiment

Selecting likely causal risk factors from high-throughput experiments using multivariable Mendelian randomization

Modern high-throughput experiments provide a rich resource to investigate causal determinants of disease risk. Mendelian randomization (MR) is the use of genetic variants as instrumental variables to infer the causal effect of a specific risk factor on an outcome. Multivariable MR is an extension of the standard MR framework to consider multiple potential risk factors in a single model. However, current implementations of multivariable MR use standard linear regression and hence perform poorly with many risk factors. Here, we propose a two-sample multivariable MR approach based on Bayesian model averaging (MR-BMA) that scales to high-throughput experiments. In a realistic simulation study, we show that MR-BMA can detect true causal risk factors even when the candidate risk factors are highly correlated. We illustrate MR-BMA by analysing publicly-available summarized data on metabolites to prioritise likely causal biomarkers for age-related macular degeneration

A Passive, Adaptive and Autonomous Gas Gap Heat Switch

We report on the development of a heat switch for autonomous temperature control of electronic components in a satellite. A heat switch can modulate when needed between roles of a good thermal conductor and a good thermal insulator. Electronic boxes on a satellite should be maintained within a typical optimum temperature range of 260 to 310 K. The heat sinking is usually by means of a radiator. When the operating temperature of the electronic box increases beyond 310 K, a good contact to the radiator is desired for maximum cooling. On the other hand, when the satellite is in a cold dormant state, the electronics box should be heated by the onboard batteries. In this state a weak thermal contact is desired between the electronic box and the heat sink. In the present study, we are developing a gas gap heat switch in which the sorber material is thermally anchored to the electronic box. A temperature change of the electronic box triggers the (de-)sorption of gas from the sorber material and subsequently the gas pressure in the gas gap. This paper describes the physical principles and the current status of this technology. This approach can be extended to cryogenic temperature rang

Mathematical modelling long-term effects of replacing Prevnar7 with Prevnar13 on invasive pneumococcal diseases in England and Wales

England and Wales recently replaced the 7-valent pneumococcal conjugate vaccine (PCV7) with its 13-valent equivalent (PCV13), partly based on projections from mathematical models of the long-term impact of such a switch compared to ceasing pneumococcal conjugate vaccination altogether. A compartmental deterministic model was used to estimate parameters governing transmission of infection and competition between different groups of pneumococcal serotypes prior to the introduction of PCV13. The best-fitting parameters were used in an individual based model to describe pneumococcal transmission dynamics and effects of various options for the vaccination programme change in England and Wales. A number of scenarios were conducted using (i) different assumptions about the number of invasive pneumococcal disease cases adjusted for the increasing trend in disease incidence prior to PCV7 introduction in England and Wales, and (ii) a range of values representing serotype replacement induced by vaccination of the additional six serotypes in PCV13. Most of the scenarios considered suggest that ceasing pneumococcal conjugate vaccine use would cause an increase in invasive pneumococcal disease incidence, while replacing PCV7 with PCV13 would cause an overall decrease. However, the size of this reduction largely depends on the level of competition induced by the additional serotypes in PCV13. The model estimates that over 20 years of PCV13 vaccination, around 5000–62000 IPD cases could be prevented compared to stopping pneumococcal conjugate vaccination altogether. Despite inevitable uncertainty around serotype replacement effects following introduction of PCV13, the model suggests a reduction in overall invasive pneumococcal disease incidence in all cases. Our results provide useful evidence on the benefits of PCV13 to countries replacing or considering replacing PCV7 with PCV13, as well as data that can be used to evaluate the cost-effectiveness of such a switch