Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

Changes in fire regimes since the Last Glacial Maximum: an assessment based on a global synthesis and analysis of charcoal data

Fire activity has varied globally and continuously since the last glacial maximum (LGM) in response to long-term changes in global climate and shorter-term regional changes in climate, vegetation, and human land use. We have synthesized sedimentary charcoal records of biomass burning since the LGM and present global maps showing changes in fire activity for time slices during the past 21,000 years (as differences in charcoal accumulation values compared to pre-industrial). There is strong broad-scale coherence in fire activity after the LGM, but spatial heterogeneity in the signals increases thereafter. In North America, Europe and southern South America, charcoal records indicate less-than-present fire activity during the deglacial period, from 21,000 to ∼11,000 cal yr BP. In contrast, the tropical latitudes of South America and Africa show greater-than-present fire activity from ∼19,000 to ∼17,000 cal yr BP and most sites from Indochina and Australia show greater-than-present fire activity from 16,000 to ∼13,000 cal yr BP. Many sites indicate greater-than-present or near-present activity during the Holocene with the exception of eastern North America and eastern Asia from 8,000 to ∼3,000 cal yr BP, Indonesia and Australia from 11,000 to 4,000 cal yr BP, and southern South America from 6,000 to 3,000 cal yr BP where fire activity was less than present. Regional coherence in the patterns of change in fire activity was evident throughout the post-glacial period. These complex patterns can largely be explained in terms of large-scale climate controls modulated by local changes in vegetation and fuel load

Engineering the electronic bandgaps and band edge positions in carbon-substituted 2D boron nitride: a first-principles investigation

Modification of graphene to open a robust gap in its electronic spectrum is essential for its use in field effect transistors and photochemistry applications. Inspired by recent experimental success in the preparation of homogeneous alloys of graphene and boron nitride (BN), we consider here engineering the electronic structure and bandgap of C2xB1−xN1−x alloys via both compositional and configurational modification. We start from the BN end-member, which already has a large bandgap, and then show that (a) the bandgap can in principle be reduced to about 2 eV with moderate substitution of C (x < 0.25); and (b) the electronic structure of C2xB1−xN1−x can be further tuned not only with composition x, but also with the configuration adopted by C substituents in the BN matrix. Our analysis, based on accurate screened hybrid functional calculations, provides a clear understanding of the correlation found between the bandgap and the level of aggregation of C atoms: the bandgap decreases most when the C atoms are maximally isolated, and increases with aggregation of C atoms due to the formation of bonding and anti-bonding bands associated with hybridization of occupied and empty defect states. We determine the location of valence and conduction band edges relative to vacuum and discuss the implications on the potential use of 2D C2xB1−xN1−x alloys in photocatalytic applications. Finally, we assess the thermodynamic limitations on the formation of these alloys using a cluster expansion model derived from first-principles.

Towards more precise sugar beet management based on geostatistical analysis of spatial variability within fields

Within-field variation in sugar beet yield and quality was investigated in three commercial sugar beet fields in the east of England to identify the main associated variables and to examine the possibility of predicting yield early in the season with a view to spatially variable management of sugar beet crops. Irregular grid sampling with some purposively-located nested samples was applied. It revealed the spatial variability in each sugar beet field efficiently. In geostatistical analyses, most variograms were isotropic with moderate to strong spatial dependency indicating a significant spatial variation in sugar beet yield and associated growth and environmental variables in all directions within each field. The Kriged maps showed spatial patterns of yield variability within each field and visual association with the maps of other variables. This was confirmed by redundancy analyses and Pearson correlation coefficients. The main variables associated with yield variability were soil type, organic matter, soil moisture, weed density and canopy temperature. Kriged maps of final yield variability were strongly related to that in crop canopy cover, LAI and intercepted solar radiation early in the growing season, and the yield maps of previous crops. Therefore, yield maps of previous crops together with early assessment of sugar beet growth may make an early prediction of within-field variability in sugar beet yield possible. The Broom’s Barn sugar beet model failed to account for the spatial variability in sugar yield, but the simulation was greatly improved when corrected for early canopy development cover and when the simulated yield was adjusted for weeds and plant population. Further research to optimize inputs to maximise sugar yield should target the irrigation and fertilizing of areas within fields with low canopy cover early in the season.

Impact of a Fram Strait cyclone on ice edge, drift, divergence, and concentration: Possibilities and limits of an observational analysis

This study aims at the determination of a Fram Strait cyclone track and of the cyclone’s impact on ice edge, drift, divergence, and concentration. A 24 h period on 13–14 March 2002 framed by two RADARSAT images is analyzed. Data are included from autonomous ice buoys, a research vessel, Special Sensor Microwave Imager (SSM/I) and QuikSCAT satellite, and the operational European Centre for Medium-Range Weather Forecasts (ECMWF) model. During this 24 h period the cyclone moved northward along the western ice edge in the Fram Strait, crossed the northern ice edge, made a left-turn loop with 150 km diameter over the sea ice, and returned to the northern ice edge. The ECMWF analysis places the cyclone track 100 km too far west over the sea ice, a deviation which is too large for representative sea ice simulations. On the east side of the northward moving cyclone, the ice edge was pushed northward by 55 km because of strong winds. On the rear side, the ice edge advanced toward the open water but by a smaller distance because of weaker winds there. The ice drift pattern as calculated from the ice buoys and the two RADARSAT images is cyclonically curved around the center of the cyclone loop. Ice drift divergence shows a spatial pattern with divergence in the loop center and a zone of convergence around. Ice concentration changes as retrieved from SSM/I data follow the divergence pattern such that sea ice concentration increased in areas of divergence and decreased in areas of convergence.

Trends in adult body-mass index in 200 countries from 1975 to 2014: a pooled analysis of 1698 population-based measurement studies with 19·2 million participants

Background Underweight and severe and morbid obesity are associated with highly elevated risks of adverse health outcomes. We estimated trends in mean body-mass index (BMI), which characterises its population distribution, and in the prevalences of a complete set of BMI categories for adults in all countries. Methods We analysed, with use of a consistent protocol, population-based studies that had measured height and weight in adults aged 18 years and older. We applied a Bayesian hierarchical model to these data to estimate trends from 1975 to 2014 in mean BMI and in the prevalences of BMI categories (<18·5 kg/m2 [underweight], 18·5 kg/m2 to <20 kg/m2, 20 kg/m2 to <25 kg/m2, 25 kg/m2 to <30 kg/m2, 30 kg/m2 to <35 kg/m2, 35 kg/m2 to <40 kg/m2, ≥40 kg/m2 [morbid obesity]), by sex in 200 countries and territories, organised in 21 regions. We calculated the posterior probability of meeting the target of halting by 2025 the rise in obesity at its 2010 levels, if post-2000 trends continue. Findings We used 1698 population-based data sources, with more than 19·2 million adult participants (9·9 million men and 9·3 million women) in 186 of 200 countries for which estimates were made. Global age-standardised mean BMI increased from 21·7 kg/m2 (95% credible interval 21·3–22·1) in 1975 to 24·2 kg/m2 (24·0–24·4) in 2014 in men, and from 22·1 kg/m2 (21·7–22·5) in 1975 to 24·4 kg/m2 (24·2–24·6) in 2014 in women. Regional mean BMIs in 2014 for men ranged from 21·4 kg/m2 in central Africa and south Asia to 29·2 kg/m2 (28·6–29·8) in Polynesia and Micronesia; for women the range was from 21·8 kg/m2 (21·4–22·3) in south Asia to 32·2 kg/m2 (31·5–32·8) in Polynesia and Micronesia. Over these four decades, age-standardised global prevalence of underweight decreased from 13·8% (10·5–17·4) to 8·8% (7·4–10·3) in men and from 14·6% (11·6–17·9) to 9·7% (8·3–11·1) in women. South Asia had the highest prevalence of underweight in 2014, 23·4% (17·8–29·2) in men and 24·0% (18·9–29·3) in women. Age-standardised prevalence of obesity increased from 3·2% (2·4–4·1) in 1975 to 10·8% (9·7–12·0) in 2014 in men, and from 6·4% (5·1–7·8) to 14·9% (13·6–16·1) in women. 2·3% (2·0–2·7) of the world's men and 5·0% (4·4–5·6) of women were severely obese (ie, have BMI ≥35 kg/m2). Globally, prevalence of morbid obesity was 0·64% (0·46–0·86) in men and 1·6% (1·3–1·9) in women. Interpretation If post-2000 trends continue, the probability of meeting the global obesity target is virtually zero. Rather, if these trends continue, by 2025, global obesity prevalence will reach 18% in men and surpass 21% in women; severe obesity will surpass 6% in men and 9% in women. Nonetheless, underweight remains prevalent in the world's poorest regions, especially in south Asia.