Moving lattice kinks and pulses: an inverse method

We develop a general mapping from given kink or pulse shaped travelling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping - by definition an inverse method - to acoustic solitons in chains with nonlinear intersite interactions, to nonlinear Klein-Gordon chains, to reaction-diffusion equations and to discrete nonlinear Schr\"odinger systems. Potential functions can be found in at least a unique way provided the pulse shape is reflection symmetric and pulse and kink shapes are at least $C^2$ functions. For kinks we discuss the relation of our results to the problem of a Peierls-Nabarro potential and continuous symmetries. We then generalize our method to higher dimensional lattices for reaction-diffusion systems. We find that increasing also the number of components easily allows for moving solutions.Comment: 15 pages, 5 figure

Non-ideality of quantum operations with the electron spin of a 31P donor in a Si crystal due to interaction with a nuclear spin system

We examine a 31P donor electron spin in a Si crystal to be used for the purposes of quantum computation. The interaction with an uncontrolled system of 29Si nuclear spins influences the electron spin dynamics appreciably. The hyperfine field at the 29Si nuclei positions is non-collinear with the external magnetic field. Quantum operations with the electron wave function, i.e. using magnetic field pulses or electrical gates, change the orientation of hyperfine field and disturb the nuclear spin system. This disturbance produces a deviation of the electron spin qubit from an ideal state, at a short time scale in comparison with the nuclear spin diffusion time. For H_ext=9 T, the estimated error rate is comparable to the threshold value required by the quantum error correction algorithms. The rate is lower at higher external magnetic fields.Comment: 11 pages, 2 figure

Stochastic attractors for shell phenomenological models of turbulence

Recently, it has been proposed that the Navier-Stokes equations and a relevant linear advection model have the same long-time statistical properties, in particular, they have the same scaling exponents of their structure functions. This assertion has been investigate rigorously in the context of certain nonlinear deterministic phenomenological shell model, the Sabra shell model, of turbulence and its corresponding linear advection counterpart model. This relationship has been established through a "homotopy-like" coefficient $\lambda$ which bridges continuously between the two systems. That is, for $\lambda=1$ one obtains the full nonlinear model, and the corresponding linear advection model is achieved for $\lambda=0$. In this paper, we investigate the validity of this assertion for certain stochastic phenomenological shell models of turbulence driven by an additive noise. We prove the continuous dependence of the solutions with respect to the parameter $\lambda$. Moreover, we show the existence of a finite-dimensional random attractor for each value of $\lambda$ and establish the upper semicontinuity property of this random attractors, with respect to the parameter $\lambda$. This property is proved by a pathwise argument. Our study aims toward the development of basic results and techniques that may contribute to the understanding of the relation between the long-time statistical properties of the nonlinear and linear models

Minimal to no transfer of certolizumab pegol into breast milk: Results from CRADLE, a prospective, postmarketing, multicentre, pharmacokinetic study

Background Women with chronic inflammatory diseases face uncertainty regarding the safety of biologics during breast feeding. CRADLE was the first industry-sponsored study to evaluate certolizumab pegol (CZP) concentrations in human breast milk and estimate average daily infant dose (ADID) of maternal CZP. Methods CRADLE (NCT02154425) was a pharmacokinetic study of lactating mothers receiving CZP. After ≥3 CZP doses, breast milk samples were collected across one dosing period (14 days for 200 mg every 2 weeks [Q2W]; 28 days for 400 mg every 4 weeks [Q4W]). Optimal analytical methods were developed to determine CZP and polyethylene glycol (PEG) levels in breast milk. ADID and relative infant dose (RID) were estimated. Safety events in mothers and infants were assessed. Results 19 CZP-Treated mothers were screened; 17 entered the sampling period: 16 on 200 mg Q2W, 1 on 400 mg Q4W. 77/137 (56%) breast milk samples had no measurable CZP. For 4/17 mothers, all samples were below the lower limit of quantification (LLOQ). Estimated ADID was 0-0.0104 mg/kg/day; median RID: 0.15%. PEG was undetectable in 134/137 samples (results could not be determined in three samples). Infants of CZP-exposed mothers had a safety profile consistent with that of unexposed similar-Age infants. Conclusion When quantifiable, CZP concentrations were <3× LLOQ (<1% plasma concentration observed with therapeutic dose), indicating no/minimal CZP transfer from plasma to breast milk. RID was 0.15% of maternal dose; <10% is considered unlikely to be of clinical concern. No PEG transfer was observed. CZP absorption by infants via breast milk is unlikely due to its low oral bioavailability and Fc-Â-free molecular structure. These findings are reassuring and support continuation of CZP treatment during breast feeding. Trial registration number NCT02154425; Results

Genomic and phenotypic insights from an atlas of genetic effects on DNA methylation

DNA methylation quantitative trait locus (mQTL) analyses on 32,851 participants identify genetic variants associated with DNA methylation at 420,509 sites in blood, resulting in a database of >270,000 independent mQTLs.Characterizing genetic influences on DNA methylation (DNAm) provides an opportunity to understand mechanisms underpinning gene regulation and disease. In the present study, we describe results of DNAm quantitative trait locus (mQTL) analyses on 32,851 participants, identifying genetic variants associated with DNAm at 420,509 DNAm sites in blood. We present a database of >270,000 independent mQTLs, of which 8.5% comprise long-range (trans) associations. Identified mQTL associations explain 15-17% of the additive genetic variance of DNAm. We show that the genetic architecture of DNAm levels is highly polygenic. Using shared genetic control between distal DNAm sites, we constructed networks, identifying 405 discrete genomic communities enriched for genomic annotations and complex traits. Shared genetic variants are associated with both DNAm levels and complex diseases, but only in a minority of cases do these associations reflect causal relationships from DNAm to trait or vice versa, indicating a more complex genotype-phenotype map than previously anticipated.Molecular Epidemiolog