Background Rising atmospheric carbon dioxide concentrations are anticipated to decrease the zinc and iron concentrations of crops. The associated disease burden and optimal mitigation strate- gies remain unknown. We sought to understand where and to what extent increasing carbon dioxide concentrations may increase the global burden of nutritional deficiencies through changes in crop nutrient concentrations, and the effects of potential mitigation strategies. Methods and findings For each of 137 countries, we incorporated estimates of climate change, crop nutrient con- centrations, dietary patterns, and disease risk into a microsimulation model of zinc and iron deficiency. These estimates were obtained from the Intergovernmental Panel on Climate Change, US Department of Agriculture, Statistics Division of the Food and Agriculture Orga- nization of the United Nations, and Global Burden of Disease Project, respectively. In the absence of increasing carbon dioxide concentrations, we estimated that zinc and iron defi- ciencies would induce 1,072.9 million disability-adjusted life years (DALYs) globally over the period 2015 to 2050 (95% credible interval [CrI]: 971.1–1,167.7). In the presence of increas- ing carbon dioxide concentrations, we estimated that decreasing zinc and iron concentra- tions of crops would induce an additional 125.8 million DALYs globally over the same period (95% CrI: 113.6–138.9). This carbon-dioxide-induced disease burden is projected to dispro- portionately affect nations in the World Health Organization’s South-East Asia and African Regions (44.0 and 28.5 million DALYs, respectively), which already have high existing dis- ease burdens from zinc and iron deficiencies (364.3 and 299.5 million DALYs, respectively), increasing global nutritional inequalities. A climate mitigation strategy such as the Paris Agreement (an international agreement to keep global temperatures within 2 ̊C of pre-indus- trial levels) would be expected to avert 48.2% of this burden (95% CrI: 47.8%–48.5%), while traditional public health interventions including nutrient supplementation and disease control programs would be expected to avert 26.6% of the burden (95% CrI: 23.8%–29.6%). Of the traditional public health interventions, zinc supplementation would be expected to avert 5.5%, iron supplementation 15.7%, malaria mitigation 3.2%, pneumonia mitigation 1.6%, and diarrhea mitigation 0.5%. The primary limitations of the analysis include uncertainty regarding how food consumption patterns may change with climate, how disease mortality rates will change over time, and how crop zinc and iron concentrations will decline from those at present to those in 2050. Conclusions Effects of increased carbon dioxide on crop nutrient concentrations are anticipated to exac- erbate inequalities in zinc and iron deficiencies by 2050. Proposed Paris Agreement strate- gies are expected to be more effective than traditional public health measures to avert the increased inequality.
Background Rising atmospheric carbon dioxide concentrations are anticipated to decrease the zinc and iron concentrations of crops. The associated disease burden and optimal mitigation strate- gies remain unknown. We sought to understand where and to what extent increasing carbon dioxide concentrations may increase the global burden of nutritional deficiencies through changes in crop nutrient concentrations, and the effects of potential mitigation strategies. Methods and findings For each of 137 countries, we incorporated estimates of climate change, crop nutrient con- centrations, dietary patterns, and disease risk into a microsimulation model of zinc and iron deficiency. These estimates were obtained from the Intergovernmental Panel on Climate Change, US Department of Agriculture, Statistics Division of the Food and Agriculture Orga- nization of the United Nations, and Global Burden of Disease Project, respectively. In the absence of increasing carbon dioxide concentrations, we estimated that zinc and iron defi- ciencies would induce 1,072.9 million disability-adjusted life years (DALYs) globally over the period 2015 to 2050 (95% credible interval [CrI]: 971.1–1,167.7). In the presence of increas- ing carbon dioxide concentrations, we estimated that decreasing zinc and iron concentra- tions of crops would induce an additional 125.8 million DALYs globally over the same period (95% CrI: 113.6–138.9). This carbon-dioxide-induced disease burden is projected to dispro- portionately affect nations in the World Health Organization’s South-East Asia and African Regions (44.0 and 28.5 million DALYs, respectively), which already have high existing dis- ease burdens from zinc and iron deficiencies (364.3 and 299.5 million DALYs, respectively), increasing global nutritional inequalities. A climate mitigation strategy such as the Paris Agreement (an international agreement to keep global temperatures within 2 ̊C of pre-indus- trial levels) would be expected to avert 48.2% of this burden (95% CrI: 47.8%–48.5%), while traditional public health interventions including nutrient supplementation and disease control programs would be expected to avert 26.6% of the burden (95% CrI: 23.8%–29.6%). Of the traditional public health interventions, zinc supplementation would be expected to avert 5.5%, iron supplementation 15.7%, malaria mitigation 3.2%, pneumonia mitigation 1.6%, and diarrhea mitigation 0.5%. The primary limitations of the analysis include uncertainty regarding how food consumption patterns may change with climate, how disease mortality rates will change over time, and how crop zinc and iron concentrations will decline from those at present to those in 2050. Conclusions Effects of increased carbon dioxide on crop nutrient concentrations are anticipated to exac- erbate inequalities in zinc and iron deficiencies by 2050. Proposed Paris Agreement strate- gies are expected to be more effective than traditional public health measures to avert the increased inequality.

How fast animals move is critical to understanding their energetic requirements, locomotor capacity and foraging performance, yet current methods for measuring speed via animal-attached devices are not universally applicable. Here, we present and evaluate a new method that relates forward speed to the stochastic motion of biologging devices as tag jiggle, the amplitude of the tag vibrations as measured by high sample rate accelerometers, increases exponentially with increasing speed. We successfully tested this method in a flow tank using two types of biologging devices and in situ on wild cetaceans spanning ∼3 to >20 m in length using two types of suction cup-attached tag and two types of dart-attached tag. This technique provides some advantages over other approaches for determining speed as it is device-orientation independent and relies only on a pressure sensor and a high sample rate accelerometer, sensors that are nearly universal across biologging device types.
How fast animals move is critical to understanding their energetic requirements, locomotor capacity and foraging performance, yet current methods for measuring speed via animal-attached devices are not universally applicable. Here, we present and evaluate a new method that relates forward speed to the stochastic motion of biologging devices as tag jiggle, the amplitude of the tag vibrations as measured by high sample rate accelerometers, increases exponentially with increasing speed. We successfully tested this method in a flow tank using two types of biologging devices and in situ on wild cetaceans spanning ∼3 to >20 m in length using two types of suction cup-attached tag and two types of dart-attached tag. This technique provides some advantages over other approaches for determining speed as it is device-orientation independent and relies only on a pressure sensor and a high sample rate accelerometer, sensors that are nearly universal across biologging device types.

Multidimensional Scaling (MDS) is a classical technique for embedding data in low dimensions, still in widespread use today. Originally introduced in the 1950's, MDS was not designed with high-dimensional data in mind; while it remains popular with data analysis practitioners, no doubt it should be adapted to the high-dimensional data regime. In this paper we study MDS under modern setting, and specifically, high dimensions and ambient measurement noise. We show that, as the ambient noise level increase, MDS suffers a sharp breakdown that depends on the data dimension and noise level, and derive an explicit formula for this breakdown point in the case of white noise. We then introduce MDS+, an extremely simple variant of MDS, which applies a carefully derived shrinkage nonlinearity to the eigenvalues of the MDS similarity matrix. Under a loss function measuring the embedding quality, MDS+ is the unique asymptotically optimal shrinkage function. We prove that MDS+ offers improved embedding, sometimes significantly so, compared with classical MDS. Furthermore, MDS+ does not require external estimates of the embedding dimension (a famous difficulty in classical MDS), as it calculates the optimal dimension into which the data should be embedded.
Multidimensional Scaling (MDS) is a classical technique for embedding data in low dimensions, still in widespread use today. Originally introduced in the 1950's, MDS was not designed with high-dimensional data in mind; while it remains popular with data analysis practitioners, no doubt it should be adapted to the high-dimensional data regime. In this paper we study MDS under modern setting, and specifically, high dimensions and ambient measurement noise. We show that, as the ambient noise level increase, MDS suffers a sharp breakdown that depends on the data dimension and noise level, and derive an explicit formula for this breakdown point in the case of white noise. We then introduce MDS+, an extremely simple variant of MDS, which applies a carefully derived shrinkage nonlinearity to the eigenvalues of the MDS similarity matrix. Under a loss function measuring the embedding quality, MDS+ is the unique asymptotically optimal shrinkage function. We prove that MDS+ offers improved embedding, sometimes significantly so, compared with classical MDS. Furthermore, MDS+ does not require external estimates of the embedding dimension (a famous difficulty in classical MDS), as it calculates the optimal dimension into which the data should be embedded.

In Group Synchronization, one attempts to find a collection of unknown group elements from noisy measurements of their pairwise differences. Several important problems in vision and data analysis reduce to group synchronization over various compact groups. Spectral Group Synchronization is a commonly used, robust algorithm for solving group synchronization problems, which relies on diagonalization of a block matrix whose blocks are matrix representations of the measured pairwise differences. Assuming uniformly distributed measurement errors, we present a rigorous analysis of the accuracy and noise sensitivity of spectral group synchronization algorithms over any compact group, up to the rounding error. We identify a Baik-Ben Arous-P\'ech\'e type phase transition in the noise level, beyond which spectral group synchronization necessarily fails. Below the phase transition, spectral group synchronization succeeds in recovering the unknown group elements, but its performance deteriorates with the noise level. We provide asymptotically exact formulas for the accuracy of spectral group synchronization below the phase transition, up to the rounding error. We also provide a consistent risk estimate, allowing practitioners to estimate the method's accuracy from available measurements.
In Group Synchronization, one attempts to find a collection of unknown group elements from noisy measurements of their pairwise differences. Several important problems in vision and data analysis reduce to group synchronization over various compact groups. Spectral Group Synchronization is a commonly used, robust algorithm for solving group synchronization problems, which relies on diagonalization of a block matrix whose blocks are matrix representations of the measured pairwise differences. Assuming uniformly distributed measurement errors, we present a rigorous analysis of the accuracy and noise sensitivity of spectral group synchronization algorithms over any compact group, up to the rounding error. We identify a Baik-Ben Arous-P\'ech\'e type phase transition in the noise level, beyond which spectral group synchronization necessarily fails. Below the phase transition, spectral group synchronization succeeds in recovering the unknown group elements, but its performance deteriorates with the noise level. We provide asymptotically exact formulas for the accuracy of spectral group synchronization below the phase transition, up to the rounding error. We also provide a consistent risk estimate, allowing practitioners to estimate the method's accuracy from available measurements.