Some explicit badly approximable pairs

I consider the Diophantine approximation problem of sup-norm simultaneous rational approximation with common denominator of a pair of irrational numbers, and compute explicitly some pairs with large approximation constant. One of these pairs is the most badly approximable pair yet computed.Comment: 2 figure

Simulation of phosphorus implantation into silicon with a single-parameter electronic stopping power model

We simulate dopant profiles for phosphorus implantation into silicon using a new model for electronic stopping power. In this model, the electronic stopping power is factorized into a globally averaged effective charge Z1*, and a local charge density dependent electronic stopping power for a proton. There is only a single adjustable parameter in the model, namely the one electron radius rs0 which controls Z1*. By fine tuning this parameter, we obtain excellent agreement between simulated dopant profiles and the SIMS data over a wide range of energies for the channeling case. Our work provides a further example of implant species, in addition to boron and arsenic, to verify the validity of the electronic stopping power model and to illustrate its generality for studies of physical processes involving electronic stopping.Comment: 11 pages, 7 figures. See http://bifrost.lanl.gov/~reed

The Generation of Badly Approximable Pairs for Communications via Real Interference Alignment

Certain proposed coding schemes require sets of irrational numbers (a1,a2,...,an) which generate linear forms. It is conjectured that the more badly approximable these linear forms, meaning the greater the positive lower bound of qn|q+p1a1+...+pnan| for any choice of integers (q,p1, ..., pn), the better the coding scheme, thus the lower the error rate. In contrast to classical one-dimensional Diophantine approximation theory (n=1), the situation for n>1 is full of unsolved problems, and it is not even known what the worst approximable pair is. The aim of this paper will be to present some purely numerical results which suggest some good candidates for bad pairs, and to demonstrate the performance of these pairs in a transmission protocol. For this we use an algorithm due to Vaughan Clarkson, but the software implementation requires some very delicate treatment of floating-point arithmetic. This results in the first fully-rigorous implementation of an algorithm for finding the sequence of best approximants for a linear form q+p1a1+p2a2, and for the simultaneous rational approximation of two irrationals, and we demonstrate the effect of using such linear forms on the error rate of our coding scheme

Single-cell transcriptomic analysis of bloodstream Trypanosoma brucei reconstructs cell cycle progression and developmental quorum sensing

Developmental steps in the trypanosome life-cycle involve transition between replicative and non-replicative forms specialised for survival in, and transmission between, mammalian and tsetse fly hosts. Here, using oligopeptide-induced differentiation in vitro, we model the progressive development of replicative ‘slender’ to transmissible ‘stumpy’ bloodstream form Trypanosoma brucei and capture the transcriptomes of 8,599 parasites using single cell transcriptomics (scRNA-seq). Using this framework, we detail the relative order of biological events during asynchronous development, profile dynamic gene expression patterns and identify putative regulators. We additionally map the cell cycle of proliferating parasites and position stumpy cell-cycle exit at early G1 before progression to a distinct G0 state. A null mutant for one transiently elevated developmental regulator, ZC3H20 is further analysed by scRNA-seq, identifying its point of failure in the developmental atlas. This approach provides a paradigm for the dissection of differentiation events in parasites, relevant to diverse transitions in pathogen biology

Modelling train delays with q-exponential functions

We demonstrate that the distribution of train delays on the British railway network is accurately described by q-exponential functions. We explain this by constructing an underlying superstatistical model.Comment: 12 pages, 5 figure

Fractional flow reserve versus angiography in guiding management to optimize outcomes in non–ST-elevation myocardial infarction (FAMOUS-NSTEMI): rationale and design of a randomized controlled clinical trial

<p>Background: In patients with acute non–ST-elevation myocardial infarction (NSTEMI), coronary arteriography is usually recommended; but visual interpretation of the angiogram is subjective. We hypothesized that functional assessment of coronary stenosis severity with a pressure-sensitive guide wire (fractional flow reserve [FFR]) would have additive diagnostic, clinical, and health economic utility as compared with angiography-guided standard care.</p> <p>Methods and design: A prospective multicenter parallel-group 1:1 randomized controlled superiority trial in 350 NSTEMI patients with ≥1 coronary stenosis ≥30% severity (threshold for FFR measurement) will be conducted. Patients will be randomized immediately after coronary angiography to the FFR-guided group or angiography-guided group. All patients will then undergo FFR measurement in all vessels with a coronary stenosis ≥30% severity including culprit and nonculprit lesions. Fractional flow reserve will be disclosed to guide treatment in the FFR-guided group but not disclosed in the “angiography-guided” group. In the FFR-guided group, an FFR ≤0.80 will be an indication for revascularization by percutaneous coronary intervention or coronary artery bypass surgery, as appropriate. The primary outcome is the between-group difference in the proportion of patients allocated to medical management only compared with revascularization. Secondary outcomes include the occurrence of cardiac death or hospitalization for myocardial infarction or heart failure, quality of life, and health care costs. The minimum and average follow-up periods for the primary analysis are 6 and 18 months, respectively.</p> <p>Conclusions: Our developmental clinical trial will address the feasibility of FFR measurement in NSTEMI and the influence of FFR disclosure on treatment decisions and health and economic outcomes.</p&gt