Blaschke Decompositions on Weighted Hardy Spaces and the Unwinding Series

Recently, several authors have considered a nonlinear analogue of Fourier series in signal analysis, referred to as either the unwinding series or adaptive Fourier decomposition. In these processes, a signal is represented as the real component of the boundary value of an analytic function F : ∂D → C, and by performing an iterative method to obtain a sequence of Blaschke decompositions, the signal can be efficiently approximated using only a few terms. To better understand the convergence of these methods, the study of Blaschke decompositions on weighted Hardy spaces was initiated by Coifman and Steinerberger, under the assumption that the complex valued function F has an analytic extension to D_1+ε for some ε \u3e 0. This provided bounds on weighted Hardy norms involving a single zero, α ∈ D, of F and its Blaschke decomposition. That work also noted that in many specific examples, the unwinding series of F converges at an exponential rate to F, which when coupled with an efficient algorithm to compute a Blaschke decomposition, has led to the hope that this process will provide a new and efficient way to approximate signals. In this work, we accomplish three things. Firstly, we continue the study of Blaschke decompositions on weighted Hardy Spaces for functions in the larger space H^2(D) under the assumption that the function has finitely many roots in D. This is meaningful, since there are many functions that meet this criterion but do not extend analytically to D_1+ε for any ε \u3e 0, for example F(z) = log(1−z). By studying the growth rate of the weights, we improve the bounds provided by Coifman and Steinerberger to obtain new estimates containing all roots of F in D. This provides us with new insights into Blaschke decompositions on classical function spaces including the Hardy-Sobolev spaces and weighted Bergman spaces, which correspond to making specific choices for the aforementioned weights. Further, we state a sufficient condition on the weights for our improved bounds to hold for any function in the Hardy space, H^2(D), in particular functions with an infinite number of roots in D. Second, we compare the Fourier series and the unwinding series: we show that there are many examples of functions whose unwinding series converges much faster than the Fourier series, but there are also functions for which the Fourier and unwinding series are term wise equal. From the latter, we show the existence of functions that have unwinding series that do not converge exponentially. Lastly, we discuss an efficient algorithm for computing Blaschke decompositions, and apply this algorithm to verify our theoretical results and to gain a better understanding of the underlying mechanics of the unwinding series

The Evolving Activity of the Dynamically Young Comet C/2009 P1 (Garradd)

We used the UltraViolet-Optical Telescope on board Swift to observe the dynamically young comet C/2009 P1 (Garradd) from a heliocentric distance of 3.5 AU pre-perihelion until 4.0 AU outbound. At 3.5 AU pre-perihelion, comet Garradd had one of the highest dust-to-gas ratios ever observed, matched only by comet Hale-Bopp. The evolving morphology of the dust in its coma suggests an outburst that ended around 2.2 AU pre-perihelion. Comparing slit-based measurements and observations acquired with larger fields of view indicated that between 3 AU and 2 AU pre-perihelion a significant extended source started producing water in the coma. We demonstrate that this source, which could be due to icy grains, disappeared quickly around perihelion. Water production by the nucleus may be attributed to a constantly active source of at least 75 km$^2$, estimated to be more than 20 percent of the surface. Based on our measurements, the comet lost $4x10^{11}$ kg of ice and dust during this apparition, corresponding to at most a few meters of its surface.Even though this was likely not Garradd's first passage through the inner solar system, the activity of the comet was complex and changed significantly during the time it was observed

Quantification of annual settlement growth in rural mining areas using machine learning

Studies on annual settlement growth have mainly focused on larger cities or incorporated data rarely available in, or applicable to, sparsely populated areas in sub-Saharan Africa, such as aerial photography or night-time light data. The aim of the present study is to quantify settlement growth in rural communities in Burkina Faso affected by industrial mining, which often experience substantial in-migration. A multi-annual training dataset was created using historic Google Earth imagery. Support vector machine classifiers were fitted on Landsat scenes to produce annual land use classification maps. Post-classification steps included visual quality assessments, majority voting of scenes of the same year and temporal consistency correction. Overall accuracy in the four studied scenes ranged between 58.5% and 95.1%. Arid conditions and limited availability of Google Earth imagery negatively affected classification accuracy. Humid study sites, where training data could be generated in proximity to the areas of interest, showed the highest classification accuracies. Overall, by relying solely on freely and globally available imagery, the proposed methodology is a promising approach for tracking fast-paced population dynamics in rural areas where population data is scarce. With the growing availability of longitudinal high-resolution imagery, including data from the Sentinel satellites, the potential applications of the methodology presented will further increase in the futur

Industrial mining and HIV risk: evidence from 39 mine openings across 16 countries in sub-Saharan Africa

OBJECTIVES: The aim of this study was to assess the impact of natural resource extraction projects on HIV transmission risks in local communities in sub-Saharan Africa. DESIGN: Difference-in-differences design using repeated cross-sectional data from around newly opened mines. METHODS: We combined data on mine openings with HIV data from the Demographic and Health Surveys (DHS). Using logistic regression models, we compared HIV related indicators between mining (i.e. up to 10 km distance from the mine) and comparison (i.e. 10-50 km) areas before and after mine opening to identify their impact on HIV prevalence, sexual behavior and HIV knowledge. RESULTS: A total of 33,086 individuals across 39 mine openings were analyzed. Adjusting for baseline differences and temporal trends in the study regions, mine opening increased the odds of HIV infection almost two-fold (odds ratio (OR): 1.93, 95% confidence interval (CI): 1.19-3.14). Strongest effects were seen in high-prevalence countries and in the 20-29 years age group. In mining communities around operational mines there was a tendency towards lower HIV knowledge (OR: 0.81, 95% CI: 0.63-1.04). New mine openings increased the odds of risky sexual behaviors, such as having multiple sex partners (OR: 1.61, 95% CI: 1.02-2.55), high-risk sexual partners (OR: 1.45, 95% CI: 1.03-2.05) and unprotected sex with high-risk partners (OR: 1.77, 95% CI: 1.18-2.67). CONCLUSION: The findings suggest that in our sample of households surrounding industrial mines, HIV infection risks substantially increase upon mine opening. Existing strategies for addressing mining-related risks for HIV transmission seem to be insufficient. Further efforts for mitigating and monitoring impacts of mines are needed. Video Abstract: http://links.lww.com/QAD/C557

Impact of mining projects on water and sanitation infrastructures and associated child health outcomes: a multi-country analysis of Demographic and Health Surveys (DHS) in sub-Saharan Africa

BACKGROUND: Access to improved water and sanitation infrastructures are key determinants of health. The sub-Saharan African region in particular is lagging behind the ambitious goal of the 2030 Agenda for Sustainable Development to ensure universal access to improved and reliable water and sanitation for all (Sustainable Development Goal (SDG) 6). Large mining projects can promote economic growth and hence investments in water and sanitation infrastructures, but at the same time lead to rapid population growth and environmental degradation. In turn, these changes can pose risks and opportunities for child health (SDG 3). In this study we aim to quantify the impacts of mining projects on access to water and sanitation infrastructure as well as diarrhea and malnutrition among children using data from 131 Demographic and Health Surveys from sub-Saharan Africa. RESULTS: From a sample of around 1.2 million households, data within the proximity of 52 mine-panels were selected for longitudinal analyses, resulting in 41,896 households and 32,112 children. Improvements in access to modern water and sanitation infrastructures after mine opening were much larger in households near mining sites than in comparison areas located further away (adjusted relative risk ratio (aRRR) water: 18.60, 95 % confidence interval (CI): 13.08-26.46 and aRRR sanitation: 2.56, 95 % CI: 1.32-4.99). However, these associations were weaker among poorer households. In areas close to the mining sites, stunting and underweight prevalence decreased more strongly upon mine opening (adjusted odds ratio (aOR) stunting: 0.62, 95 % CI: 0.43-0.90; aOR underweight: 0.55, 95 % CI: 0.36-0.84). No differential changes were seen for wasting and diarrhea. Large impact heterogeneity was observed both within and across countries. CONCLUSIONS: Our results suggest that the opening of mines is associated with improvements in access to modern water and sanitation infrastructures (SDG 6) as well as in some health outcomes (SDG 3). However, the large impact heterogeneity suggests that the assessment and management of mining-related impacts on communities should have an increased equity-focus, in order to "leave no one behind" in the work towards the 2030 Agenda for Sustainable Development. Overall, the findings of this study underscore that the resource extraction sector has the potential to make positive and substantial contributions towards achieving the SDGs

Transgenic Maize Hybrid Crop Residues: Nutritive Value and Their Effects on Performance of Grazing Beef Cows

Several maize (Zea mays) hybrids, including three transgenic hybrids containing Bacillus thuringiensis (Bt) enzymes (Bt-maize hybrids), were planted in a field study. Mature, midgestation, beef cows (Bos tarus) strip-grazed post-harvest residues as paddocks over 126 days. Body condition-scores and weights were monitored. Forage yield, weathering losses and forage composition were monitored on grazed and ungrazed areas. Forage selection and intake were estimated. Grain yields, dropped grain, initial crop residue concentrations of dry matter (DM), organic matter (OM) and in vitro digestible organic matter (IVDOM) yields were similar among hybrids. Hybrids varied in infestation of maize borers, initial amounts of residue DM, acid detergent fiber (ADF) and acid detergent lignin (ADL) and IVDOM. Mean rates of change in forage and concentration of IVDOM selected by steers was similar between hybrids. Cows grazing residues required 50% less supplemental hay to retain the same body condition as cows consuming hay in drylot

Ezh2-dCas9 and KRAB-dCas9 enable engineering of epigenetic memory in a context-dependent manner.

BackgroundRewriting of the epigenome has risen as a promising alternative to gene editing for precision medicine. In nature, epigenetic silencing can result in complete attenuation of target gene expression over multiple mitotic divisions. However, persistent repression has been difficult to achieve in a predictable manner using targeted systems.ResultsHere, we report that persistent epigenetic memory required both a DNA methyltransferase (DNMT3A-dCas9) and a histone methyltransferase (Ezh2-dCas9 or KRAB-dCas9). We demonstrate that the histone methyltransferase requirement can be locus specific. Co-targeting Ezh2-dCas9, but not KRAB-dCas9, with DNMT3A-dCas9 and DNMT3L induced long-term HER2 repression over at least 50 days (approximately 57 cell divisions) and triggered an epigenetic switch to a heterochromatic environment. An increase in H3K27 trimethylation and DNA methylation was stably maintained and accompanied by a sustained loss of H3K27 acetylation. Interestingly, substitution of Ezh2-dCas9 with KRAB-dCas9 enabled long-term repression at some target genes (e.g., SNURF) but not at HER2, at which H3K9me3 and DNA methylation were transiently acquired and subsequently lost. Off-target DNA hypermethylation occurred at many individual CpG sites but rarely at multiple CpGs in a single promoter, consistent with no detectable effect on transcription at the off-target loci tested. Conversely, robust hypermethylation was observed at HER2. We further demonstrated that Ezh2-dCas9 required full-length DNMT3L for maximal activity and that co-targeting DNMT3L was sufficient for persistent repression by Ezh2-dCas9 or KRAB-dCas9.ConclusionsThese data demonstrate that targeting different combinations of histone and DNA methyltransferases is required to achieve maximal repression at different loci. Fine-tuning of targeting tools is a necessity to engineer epigenetic memory at any given locus in any given cell type