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Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra.

Since their discovery, SOCS have been characterised as regulatory cornerstones of intracellular signalling. While classically controlling the JAK/STAT pathway, their inhibitory effects are documented across several cascades, underpinning their essential role in homeostatic maintenance and disease. After 20 years of extensive research, SOCS3 has emerged as arguably the most important family member, through its regulation of both cytokine- and pathogen-induced cascades. In fact, low expression of SOCS3 is associated with autoimmunity and oncogenesis, while high expression is linked to diabetes and pathogenic immune evasion. The induction of SOCS3 by both viruses and bacteria and its impact upon inflammatory disorders, underscores this protein’s increasing clinical potential. Therefore, with the aim of highlighting SOCS3 as a therapeutic target for future development, this review revisits its multi-faceted immune regulatory functions and summarises its role in a broad ranges of diseases.

Climate change can drive local climates outside the range of their historical year-to-year variability, straining the adaptive capacity of ecological and human communities. We demonstrate that dependencies between climate variables can produce larger and earlier departures from natural variability than is detectable in individual variables. Using the example of summer temperature (Tx) and precipitation (Pr), we show that this departure intensification effect occurs when the bivariate climate change trajectory is misaligned with the dominant mode of joint historical variability. Departure intensification is evident in all six CMIP5 models that we examined: 23% (9–34%) of the global land area of each model exhibits a pronounced increase in 2 σ anomalies in the Tx-Pr regime relative to Tx or Pr alone. Observational data suggest that summer Tx-Pr correlations in distinct regions on all continents are sufficient to produce departure intensification. Precipitation can be an important driver of multivariate climate change signals relative to natural variability, despite typically having a much weaker univariate signal than temperature. Climate change can drive local climates outside the range of their historical variability, straining the adaptive capacity of ecological communities. Here the authors show dependencies between climate variables can produce larger and earlier departures from natural variability than is detectable in individual variables.

Objective To determine if a low glycaemic index diet in pregnancy could reduce the incidence of macrosomia in an at risk group.Design Randomised controlled trial.Setting Maternity hospital in Dublin, Ireland.Participants 800 women without diabetes, all in their second pregnancy between January 2007 to January 2011, having previously delivered an infant weighing greater than 4 kg. Intervention Women were randomised to receive no dietary intervention or start on a low glycaemic index diet from early pregnancy.Main outcomes The primary outcome measure was difference in birth weight. The secondary outcome measure was difference in gestational weight gain.Results No significant difference was seen between the two groups in absolute birth weight, birthweight centile, or ponderal index. Significantly less gestational weight gain occurred in women in the intervention arm (12.2 v 13.7 kg; mean difference −1.3, 95% confidence interval −2.4 to −0.2; P=0.01). The rate of glucose intolerance was also lower in the intervention arm: 21% (67/320) compared with 28% (100/352) of controls had a fasting glucose of 5.1 mmol/L or greater or a 1 hour glucose challenge test result of greater than 7.8 mmol/L (P=0.02).Conclusion A low glycaemic index diet in pregnancy did not reduce the incidence of large for gestational age infants in a group at risk of fetal macrosomia. It did, however, have a significant positive effect on gestational weight gain and maternal glucose intolerance.Trial registration Current Controlled Trials ISRCTN54392969.

The velocity of climate change, which estimates the migration speed necessary to maintain constant climatic conditions, is increasingly used to map climate‐related threats to biodiversity. Using newly developed climate velocity data for North America to 2100 based on an ensemble of current‐generation climate projections, we asked how important differing sources of uncertainty from global climate model projections are, how the magnitude of this uncertainty compares with the internal variability of the climate system, and what aspects of climate velocity are robust to such uncertainty. We found that most variation was due to contrasts among global climate models, followed by variation among alternative emissions pathways. However, correlation was great enough (0.817) to allow application of velocity to inform conservation and management. In contrast, internal variability (i.e., weather at multidecadal timescales) resulted in low correlation between simulated and observed velocity for the 2001–2020 period. A null model using current baseline climate data and assumed uniform 2° heating was moderately correlated with velocity from ensemble future projections, helping to identify model‐independent velocity patterns difficult to capture via rules such as protection of elevational gradients. Such uncertainty analyses are essential for informed application of velocity and other climate exposure metrics. The velocity of climate change, the migration speed necessary to maintain constant climatic conditions, is widely used to map climate‐related threats to biodiversity. We analyzed the importance of differing sources of uncertainty in estimating velocity and what aspects of climate velocity are robust to such uncertainty. Such uncertainty analyses are essential for informed application of velocity and other climate exposure metrics to ecology and conservation.

We evaluate genomic data, relative to phenotypic and climatic data, as a basis for assisted gene flow and genetic conservation. Using a seedling common garden trial of 281 lodgepole pine (Pinus contorta) populations from across western Canada, we compare genomic data to phenotypic and climatic data to assess their effectiveness in characterizing the climatic drivers and spatial scale of local adaptation in this species. We find that phenotype‐associated loci are equivalent or slightly superior to climate data for describing local adaptation in seedling traits, but that climate data are superior to genomic data that have not been selected for phenotypic associations. We also find agreement between the climate variables associated with genomic variation and with 20‐year heights from a long‐term provenance trial, suggesting that genomic data may be a viable option for identifying climatic drivers of local adaptation where phenotypic data are unavailable. Genetic clines associated with the experimental traits occur at broad spatial scales, suggesting that standing variation of adaptive alleles for this and similar species does not require management at scales finer than those indicated by phenotypic data. This study demonstrates that genomic data are most useful when paired with phenotypic data, but can also fill some of the traditional roles of phenotypic data in management of species for which phenotypic trials are not feasible.

This study contributes an accessible, comprehensive database of interpolated climate data for Africa that includes monthly, annual, decadal, and 30-year normal climate data for the last 120 years (1901 to present) as well as multi-model CMIP6 climate change projections for the 21 st century. The database includes variables relevant for ecological research and infrastructure planning, and it comprises more than 25,000 climate grids that can be queried with a provided ClimateAF software package. In addition, 30 arcsecond (~1 km) resolution gridded data are available for download. The climate grids were developed with a three-step approach, using thin-plate spline interpolations of weather station data as a first approximation. Subsequently, a novel deep learning approach is used to model orographic precipitation, rain shadows, lake and coastal effects at moderate resolution. Lastly, lapse-rate based downscaling is applied to generate high-resolution grids. The climate estimates were optimized and cross-validated with a checkerboard approach to ensure that training data was spatially distanced from validation data. We conclude with a discussion of applications and limitations of this database.

In the early eighties Lojasiewicz [in Seminari di Geometria 1982-1983, Universita di Bologna, Istituto di Geometria, Dipartimento di Matematica, 1984, pp. 115--117] proved that a bounded solution of a gradient flow for an analytic cost function converges to a well-defined limit point. In this paper, we show that the iterates of numerical descent algorithms, for an analytic cost function, share this convergence property if they satisfy certain natural descent conditions. The results obtained are applicable to a broad class of optimization schemes and strengthen classical \"weak convergence\" results for descent methods to \"strong limit-point convergence\" for a large class of cost functions of practical interest. The result does not require that the cost has isolated critical points and requires no assumptions on the convexity of the cost nor any nondegeneracy conditions on the Hessian of the cost at critical points.

Objective: To determine the mode of delivery in pregnancies complicated by complex fetal congenital heart disease (CHD). Study Design: Five-year retrospective cohort study at a tertiary fetal medicine center (2007 to 2011). Cases of complex fetal CHD ( n =126) were compared with 45 069 non-anomalous singleton infants ⩾500 g to determine rates of emergency intrapartum cesarean section (CS), preterm delivery and induction of labor. Result: Intrapartum CS is significantly higher in fetal CHD than non-anomalous controls (21% vs 13.5%, odds ratio (OR) 1.7, 95% confidence interval (CI): 1.0 to 2.7; P =0.035), predominantly related to CS for non-reassuring fetal status (OR 2.2, 95% CI: 1.1 to 4.1; P =0.022). Although fetal CHD did not increase emergency CS rates in nulliparous women, CS was significantly increased in multiparous pregnancies (OR 2.4, 95% CI: 1.8 to 4.6; P =0.014). Rates of preterm delivery (OR 3.4, 95% CI: 2.0 to 5.4; P <0.0001) and induction of labor (OR 1.9, 95% CI: 1.3 to 2.9; P =0.001) were higher in the CHD cases. Conclusion: Emergency CS is increased in fetal CHD, attributed to a higher rate of CS for non-reassuring fetal status and seen mostly in multiparous women.

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in Rn. In these formulas, p-planes are represented as the column space of n×p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out.