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

Evaluation of phylogenetic reconstruction methods using bacterial whole genomes: a simulation based study

Background: Phylogenetic reconstruction is a necessary first step in many analyses which use whole genome sequence data from bacterial populations. There are many available methods to infer phylogenies, and these have various advantages and disadvantages, but few unbiased comparisons of the range of approaches have been made. Methods: We simulated data from a defined "true tree" using a realistic evolutionary model. We built phylogenies from this data using a range of methods, and compared reconstructed trees to the true tree using two measures, noting the computational time needed for different phylogenetic reconstructions. We also used real data from Streptococcus pneumoniae alignments to compare individual core gene trees to a core genome tree. Results: We found that, as expected, maximum likelihood trees from good quality alignments were the most accurate, but also the most computationally intensive. Using less accurate phylogenetic reconstruction methods, we were able to obtain results of comparable accuracy; we found that approximate results can rapidly be obtained using genetic distance based methods. In real data we found that highly conserved core genes, such as those involved in translation, gave an inaccurate tree topology, whereas genes involved in recombination events gave inaccurate branch lengths. We also show a tree-of-trees, relating the results of different phylogenetic reconstructions to each other. Conclusions: We recommend three approaches, depending on requirements for accuracy and computational time. Quicker approaches that do not perform full maximum likelihood optimisation may be useful for many analyses requiring a phylogeny, as generating a high quality input alignment is likely to be the major limiting factor of accurate tree topology. We have publicly released our simulated data and code to enable further comparisons

Complementarity of direct detection experiments in search of light Dark Matter

Dark Matter experiments searching for Weakly interacting massive particles (WIMPs) primarily use nuclear recoils (NRs) in their attempt to detect WIMPs. Migdal-induced electronic recoils (ERs) provide additional sensitivity to light Dark Matter with $\mathcal{O}(\text{GeV}/c^2)$ masses. In this work, we use Bayesian inference to find the parameter space where future detectors like XENONnT and SuperCDMS SNOLAB will be able to detect WIMP Dark Matter through NRs, Migdal-induced ERs or a combination thereof. We identify regions where each detector is best at constraining the Dark Matter mass and spin independent cross-section and infer where two or more detection configurations are complementary to constraining these Dark Matter parameters through a combined analysis.Comment: 19 pages, 7 figure

The detection of single electrons by means of a Micromegas-covered MediPix2 pixel CMOS readout circuit

A small drift chamber was read out by means of a MediPix2 readout chip as direct anode. A Micromegas foil was placed 50 $\mu$m above the chip, and electron multiplication occurred in the gap. With a He/Isobutane 80/20 mixture, gas multiplication factors up to tens of thousands were achieved, resulting in an efficiency for detecting single electrons of better than 90% . We recorded many frames containing 2D images with tracks from cosmic muons. Along these tracks, electron clusters were observed, as well as delta-rays.Comment: 15 pages, 9 included postscript figures, 5 separate jpeg figures, submitted to Nucl. Instr. and Meth. A. A complete postscript version with high resolution figures 1, 3, 11, 12 and 14 can be found at http://www.nikhef.nl/~i06/RandD/final/letter4.p

Precision measurements of the scintillation pulse shape for low-energy recoils in liquid xenon

We present measurements of the scintillation pulse shape in liquid xenon for nuclear recoils (NR) and electronic recoils (ER) at electric fields of 0 to 0.5 kV/cm for energies $<$ 15 keV and $<$ 70 keV electron-equivalent, respectively. The average pulse shapes are well-described by an effective model with two exponential decay components, where both decay times are fit parameters. We find significant broadening of the pulse for ER due to delayed luminescence from the recombination process. In addition to the effective model, we fit a model describing the recombination luminescence for ER at zero field and obtain good agreement. We estimate the best performance of a combined S2/S1 and pulse shape ER/NR discrimination and show that even with 2 ns time resolution, the improvement over S2/S1 discrimination alone is marginal, so that pulse shape discrimination will likely not be useful for future dual-phase liquid xenon experiments looking for elastic dark matter recoil interactions

Implications of Lorentz covariance for the guidance equation in two-slit quantum interference

It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin particles. In the non-relativistic domain this implies a guidance law for the electron which differs by an additional spin-dependent term from that originally proposed by de Broglie and Bohm. In this paper we explore some of the implications of the modified guidance law. We bring out a property of mutual dependence in the particle coordinates that arises in product states, and show that the quantum potential has scalar and vector components which implies the particle is subject to a Lorentz-like force. The conditions for the classical limit and the limit of negligible spin are given, and the empirical sufficiency of the model is demonstrated. We then present a series of calculations of the trajectories based on two-dimensional Gaussian wave packets which illustrate how the additional spin-dependent term plays a significant role in structuring both the individual trajectories and the ensemble. The single packet corresponds to quantum inertial motion. The distinct features encountered when the wavefunction is a product or a superposition are explored, and the trajectories that model the two-slit experiment are given. The latter paths exhibit several new characteristics compared with the original de Broglie-Bohm ones, such as crossing of the axis of symmetry.Comment: 27 pages including 6 pages of figure

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

The evaluation of an intervention based on the application of patient self-completion concordance forms in Dutch community pharmacies and the effect on adherence to chronic medication

Objective: To evaluate the use of patient self-completion concordance forms and to determine the effect of patient counselling by using concordance forms on adherence to chronic medication. Methods: Patients with a prescription for new chronic treatment were randomised in an intervention or control group. The intervention group received a concordance form to fill in at home and to discuss during a consultation 2 weeks later in the pharmacy. The control group received the Usual information and instruction on how to use the medicine. Afterwards, all patients were asked to fill in a questionnaire about their use of medicines and contact with the pharmacy employees. Adherence to the medicine was determined using rates of prescription refills after 6 months of use. Results: The questionnaires showed that patients were satisfied about the concordance model. After 6 months of use, 79% of the patients from both intervention and control group were defined as adherent. Conclusions: There was no significant difference found in adherence between intervention and control group. Practice implications: Use five selected questions from the concordance form which provided most answers. Focus on one drug group and have more consultation moments. (C) 2009 Elsevier Ireland Ltd. All rights reserved