On Conditions for Uniqueness in Sparse Phase Retrieval

The phase retrieval problem has a long history and is an important problem in many areas of optics. Theoretical understanding of phase retrieval is still limited and fundamental questions such as uniqueness and stability of the recovered solution are not yet fully understood. This paper provides several additions to the theoretical understanding of sparse phase retrieval. In particular we show that if the measurement ensemble can be chosen freely, as few as 4k-1 phaseless measurements suffice to guarantee uniqueness of a k-sparse M-dimensional real solution. We also prove that 2(k^2-k+1) Fourier magnitude measurements are sufficient under rather general conditions

Magnon dispersion to four loops in the ABJM and ABJ models

The ABJM model is a superconformal Chern-Simons theory with N=6 supersymmetry which is believed to be integrable in the planar limit. However, there is a coupling dependent function that appears in the magnon dispersion relation and the asymptotic Bethe ansatz that is only known to leading order at strong and weak coupling. We compute this function to four loops in perturbation theory by an explicit Feynman diagram calculation for both the ABJM model and the ABJ extension. We find that all coefficients have maximal transcendentality. We then compute the four-loop wrapping correction for a scalar operator in the 20 of SU(4) and find that it agrees with a recent prediction from the ABJM Y-system of Gromov, Kazakov and Vieira. We also propose a limit of the ABJ model that might be perturbatively integrable at all loop orders but has a short range Hamiltonian.Comment: LaTeX, feynmp, 17 pages; v2: coupling factor in one Feynman diagram corrected: modified result in the ABJ case only, formulations improved, typos fixed, references added; v3: signs of three diagrams corrected, modifying the final resul

Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J

This paper studies giant magnons in AdS_4 x CP^3 using both the string sigma-model and the algebraic curve. We complete the dictionary of solutions by finding the dyonic generalisation of the CP^1 string solution, which matches the `small' giant magnon in the algebraic curve, and by pointing out that the solution recently constructed by the dressing method is the `big' giant magnon. We then use the curve to compute finite-J corrections to all cases, which for the non-dyonic cases always match the AFZ result. For the dyonic RP^3 magnon we recover the S^5 answer, but for the `small' and `big' giant magnons we obtain new corrections.Comment: 22 pages, 3 figures, 2 tables. v2 adds note on breather solution, and minor clarification

Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories

Using N=2 superspace techniques we compute the four-loop spectrum of single trace operators in the SU(2) x SU(2) sector of ABJM and ABJ supersymmetric Chern-Simons theories. Our computation yields a four-loop contribution to the function h^2(\lambda) (and its ABJ generalization) in the magnon dispersion relation which has fixed maximum transcendentality and coincides with the findings in components given in the revised versions of arXiv:0908.2463 and arXiv:0912.3460. We also discuss possible scenarios for an all-loop function h^2(\lambda) that interpolates between weak and strong couplings.Comment: LaTeX, feynmp, 34 pages; v2: typos corrected, formulations improved, references adde

Secretory leukocyte protease inhibitor in punch biopsies from human colonic mucosa.

Secretory leukocyte protease inhibitor (SLPI) is a well-known protease inhibitor. Its function is thought to be protease/protease-inhibitor balance. Free proteolytic activity, mainly pancreatic elastase, anionic trypsin and granulocytic elastase, has been demonstrated in faecal extracts from patients with ulcerative colitis. We wanted to verify that SLPI is actually secreted from normal human colonic mucosa. Also, we wanted to ascertain whether studies of SLPI secretion based on punch biopsies were dependent on biopsy area or on biopsy circumference. Normal colonic mucosa was sampled during surgery for colonic cancer. A total of 36 samples from four patients were used. Mucosa preparation was carried out using a punch biopsy technique, and samples of 3, 4 and 6 mm diameter were used. All media contained SLPI at varying concentrations. When expressed in terms of the sample area, the secretion per millimetre-squared seemed to decrease with increasing area. When calculated as secretion per circumference, secretion seemed to be constant. In conclusion, SLPI was secreted from normal human colonic mucosa. The SLPI secretion seemed dependent on the circumference of the biopsy rather than on the area of the biopsy

Fungal foraging behaviour and hyphal space exploration in micro-structured Soil Chips

How do fungi navigate through the complex microscopic maze-like structures found in the soil? Fungal behaviour, especially at the hyphal scale, is largely unknown and challenging to study in natural habitats such as the opaque soil matrix. We monitored hyphal growth behaviour and strategies of seven Basidiomycete litter decomposing species in a micro-fabricated "Soil Chip" system that simulates principal aspects of the soil pore space and its micro-spatial heterogeneity. The hyphae were faced with micrometre constrictions, sharp turns and protruding obstacles, and the species examined were found to have profoundly different responses in terms of foraging range and persistence, spatial exploration and ability to pass obstacles. Hyphal behaviour was not predictable solely based on ecological assumptions, and our results obtained a level of trait information at the hyphal scale that cannot be fully explained using classical concepts of space exploration and exploitation such as the phalanx/guerrilla strategies. Instead, we propose a multivariate trait analysis, acknowledging the complex trade-offs and microscale strategies that fungal mycelia exhibit. Our results provide novel insights about hyphal behaviour, as well as an additional understanding of fungal habitat colonisation, their foraging strategies and niche partitioning in the soil environment

Neutrino tomography - Learning about the Earth's interior using the propagation of neutrinos

Because the propagation of neutrinos is affected by the presence of Earth matter, it opens new possibilities to probe the Earth's interior. Different approaches range from techniques based upon the interaction of high energy (above TeV) neutrinos with Earth matter, to methods using the MSW effect on the neutrino oscillations of low energy (MeV to GeV) neutrinos. In principle, neutrinos from many different sources (sun, atmosphere, supernovae, beams etc.) can be used. In this talk, we summarize and compare different approaches with an emphasis on more recent developments. In addition, we point out other geophysical aspects relevant for neutrino oscillations.Comment: 22 pages, 9 figures. Proceedings of ``Neutrino sciences 2005: Neutrino geophysics'', December 14-16, 2005, Honolulu, USA. Minor changes, some references added. Final version to appear in Earth, Moon, and Planet

Advancing maternal age is associated with lower bone mineral density in young adult male offspring

Summary Advancing maternal age has been related to increased risk of fetal death and morbidity, as well as higher fracture risk during childhood, in the offspring. In the present study, we demonstrate that advancing maternal age is independently associated with reduced bone mass in the young adult male offspring. Introduction In Sweden the maternal age in both primi- and multipara mothers has steadily increased during the last three decades. It has been previously reported that advancing maternal age increases the risk of fetal death, but also of morbidity in the offspring, such as chromosome abnormalities, leukemia, diabetes mellitus type 1, and schizophrenia. Whether or not maternal age influences peak bone mass has not been reported. The aim of the present study was to investigate whether a high maternal age was associated with lower peak bone mass, as measured using DXA in a large cohort of male offspring [the Gothenburg Osteoporosis and Obesity Determinants study (GOOD)]. Methods Through the Swedish multi-generation register, we identified the mothers of 1,009 GOOD study subjects. From the Swedish medical birth register detailed information about the medical circumstances at the time of child birth were obtained, including maternal and offspring anthropometrics (birth height and weight), maternal age, and smoking habits, parity and length of pregnancy. Results Maternal age was inversely correlated to areal BMD (aBMD) at the total body (r =−0.07, p = 0.03) and the lumbar spine (r =−0.09, p < 0.01). Using a linear regression model (with covariates including current physical activity, smoking, calcium intake, weight, present height and birth height, total body lean and fat mass in the offspring, and length of pregnancy), we found that maternal age negatively independently predicted lumbar spine aBMD (β =−0.08, p < 0.01) in the male offspring. Conclusions In conclusion, our results suggest that advancing maternal age could negatively affect bone mass in young adult men

Sperm microRNA content is altered in a mouse model of male obesity, but the same suite of microRNAs are not altered in offspring's sperm

The prevalence of obesity is increasing worldwide and has tripled in men of reproductive age since the 1970s. Concerningly, obesity is not only comorbid with other chronic diseases, but there is mounting evidence that it increases the non-communicable disease load in their children (eg mortality, obesity, autism). Animal studies have demonstrated that paternal obesity increases the risk of metabolic (eg glucose metabolism defects, obesity) and reproductive disorders in offspring. Epigenetic changes within sperm are clear mechanistic candidates that are associated with both changes to the father’s environment and offspring phenotype. Specifically there is emerging evidence that a father’s sperm microRNA content both responds to paternal environmental cues and alters the gene expression profile and subsequent development of the early embryo. We used a mouse model of high fat diet (HFD) induced obesity to investigate whether male obesity could modulate sperm microRNA content. We also investigated whether this alteration to a father’s sperm microRNA content lead to a similar change in the sperm of male offspring. Our investigations were initially guided by a Taqman PCR array, which indicated the differential abundance of 28 sperm borne microRNAs in HFD mice. qPCR confirmation in a much larger cohort of founder males demonstrated that 13 of these microRNAs were differentially abundant (11 up-regulated; 2 down-regulated) due to HFD feeding. Despite metabolic and reproductive phenotypes also being observed in grand-offspring fathered via the male offspring lineage, there was no evidence that any of the 13 microRNAs were also dysregulated in male offspring sperm. This was presumably due to the variation seen within both groups of offspring and suggests other mechanisms might act between offspring and grand-offspring. Thus 13 sperm borne microRNAs are modulated by a father’s HFD and the presumed transfer of this altered microRNA payload to the embryo at fertilisation potentially acts to alter the embryonic molecular makeup post-fertilisation, altering its growth trajectory, ultimately affecting adult offspring phenotype and may contribute to paternal programming.Tod Fullston, E. Maria C. Ohlsson-Teague, Cristin G. Print, Lauren Y. Sandeman, Michelle Lan