Towards gravitationally assisted negative refraction of light by vacuum

Propagation of electromagnetic plane waves in some directions in gravitationally affected vacuum over limited ranges of spacetime can be such that the phase velocity vector casts a negative projection on the time-averaged Poynting vector. This conclusion suggests, inter alia, gravitationally assisted negative refraction by vacuum.Comment: 6 page

Breathers in the weakly coupled topological discrete sine-Gordon system

Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems previously considered in studies of discrete breathers, the TDSG system does not decouple into independent oscillator units in the weak coupling limit. The results of a systematic numerical study of these breathers are presented, including breather initial profiles and a portrait of their domain of existence in the frequency-coupling parameter space. It is found that the breathers are uniformly qualitatively different from those found in conventional spatially discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely rewritte

Community Detection as an Inference Problem

We express community detection as an inference problem of determining the most likely arrangement of communities. We then apply belief propagation and mean-field theory to this problem, and show that this leads to fast, accurate algorithms for community detection.Comment: 4 pages, 2 figure

Very small deletions within the NESP55 gene in pseudohypoparathyroidism type 1b

Pseudohypoparathyroidism (PHP) is caused by reduced expression of genes within the GNAS cluster, resulting in parathormone resistance. The cluster contains multiple imprinted transcripts, including the stimulatory G protein α subunit (Gs-α) and NESP55 transcript preferentially expressed from the maternal allele, and the paternally expressed XLas, A/B and antisense transcripts. PHP1b can be caused by loss of imprinting affecting GNAS A/B alone (associated with STX16 deletion), or the entire GNAS cluster (associated with deletions of NESP55 in a minority of cases). We performed targeted genomic next-generation sequencing (NGS) of the GNAS cluster to seek variants and indels underlying PHP1b. Seven patients were sequenced by hybridisation-based capture and fourteen more by long-range PCR and transposon-mediated insertion and sequencing. A bioinformatic pipeline was developed for variant and indel detection. In one family with two affected siblings, and in a second family with a single affected individual, we detected maternally inherited deletions of 40 and 33 bp, respectively, within the deletion previously reported in rare families with PHP1b. All three affected individuals presented with atypically severe PHP1b; interestingly, the unaffected mother in one family had the detected deletion on her maternally inherited allele. Targeted NGS can reveal sequence changes undetectable by current diagnostic methods. Identification of genetic mutations underlying epigenetic changes can facilitate accurate diagnosis and counselling, and potentially highlight genetic elements critical for normal imprint settin

Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential

Coupled-mode systems are used in physical literature to simplify the nonlinear Maxwell and Gross-Pitaevskii equations with a small periodic potential and to approximate localized solutions called gap solitons by analytical expressions involving hyperbolic functions. We justify the use of the one-dimensional stationary coupled-mode system for a relevant elliptic problem by employing the method of Lyapunov--Schmidt reductions in Fourier space. In particular, existence of periodic/anti-periodic and decaying solutions is proved and the error terms are controlled in suitable norms. The use of multi-dimensional stationary coupled-mode systems is justified for analysis of bifurcations of periodic/anti-periodic solutions in a small multi-dimensional periodic potential.Comment: 18 pages, no figure