Enhanced magnetic fields within a stratified layer

Mounting evidence from both seismology and numerical experiments on core composition suggests the existence of a layer of stably stratified fluid at the top of Earth’s outer core. In such a layer, a magnetostrophic force balance and suppressed radial motion lead to stringent constraints on the magnetic field, named Malkus constraints, which are a much more restrictive extension of the well known Taylor constraints. Here, we explore the consequences of such constraints for the structure of the core’s internal magnetic field. We provide a new simple derivation of these Malkus constraints, and show solutions exist which can be matched to any external potential field with arbitrary depth of stratified layer. From considerations of these magnetostatic Malkus constraints alone, it is therefore not possible to uniquely infer the depth of the stratified layer from external geomagnetic observations. We examine two models of the geomagnetic field defined within a spherical core, which obey the Taylor constraints in an inner convective region and the Malkus constraints in an outer stratified layer. When matched to a single-epoch geomagnetic potential field model, both models show that the toroidal magnetic field within the outer layer is about 100 times stronger compared to that in the inner region, taking a maximum value of 8 mT at a depth of 70 km. The dynamic regime of such a layer, modulated by suppressed radial motion but also a locally enhanced magnetic field, may therefore be quite distinct from that of any interior dynamo

The inherent instability of axisymmetric magnetostrophic dynamo models

Recent studies have demonstrated the possibility of constructing magnetostrophic dynamo models, which describe the slowly evolving background state of Earth's magnetic field when inertia and viscosity are negligible. Here we explore the properties of steady, stable magnetostrophic states as a leading order approximation to the slow dynamics within Earth's core. For the case of an axisymmetric magnetostrophic system driven by a prescribed α-effect, we confirmed the existence of four known steady states: ±Bd, ±Bq, where Bd is purely dipolar and Bq is purely quadrupolar. Importantly, here we show that in all but the most weakly driven cases, an initial magnetic field that is not purely dipolar or quadrapolar never converges to these states. Despite this instability, we also show that there are a plethora of instantaneous solutions that are quasi-steady, but nevertheless unstable. If the dynamics in Earth's core are reasonably modelled by a strongly driven α-effect, this work suggests that the background state can never be steady. We discuss the difficulties in comparing our magnetostrophic models with geomagnetic timeseries

Relative blocking in posets

Poset-theoretic generalizations of set-theoretic committee constructions are presented. The structure of the corresponding subposets is described. Sequences of irreducible fractions associated to the principal order ideals of finite bounded posets are considered and those related to the Boolean lattices are explored; it is shown that such sequences inherit all the familiar properties of the Farey sequences.Comment: 29 pages. Corrected version of original publication which is available at http://www.springerlink.com, see Corrigendu

Association of dementia with mortality among adults with down syndrome older than 35 years

Importance: This work quantifies the fatal burden of dementia associated with Alzheimer disease in individuals with Down syndrome (DS). Objective: To explore the association of dementia associated with Alzheimer disease with mortality and examine factors associated with dementia in adults with DS. Design, Settings and Participants: Prospective longitudinal study in a community setting in England. Data collection began March 29, 2012. Cases were censored on December 13, 2017. The potential sample consisted of all adults 36 years and older from the London Down Syndrome Consortium cohort with 2 data times and dementia status recorded (N = 300); 6 withdrew from study, 28 were lost to follow-up, and 55 had a single data collection point at time of analysis. The final sample consisted of 211 participants, with 503.92 person-years' follow-up. Exposures: Dementia status, age, sex, APOE genotype, level of intellectual disability, health variables, and living situation. Main Outcomes and Measures: Crude mortality rates, time to death, and time to dementia diagnosis with proportional hazards of predictors. Results: Of the 211 participants, 96 were women (45.5%) and 66 (31.3%) had a clinical dementia diagnosis. Twenty-seven participants (11 female; mean age at death, 56.74 years) died during the study period. Seventy percent had dementia. Crude mortality rates for individuals with dementia (1191.85 deaths per 10 000 person-years; 95% CI, 1168.49-1215.21) were 5 times higher than for those without (232.22 deaths per 10 000 person-years; 95% CI, 227.67-236.77). For those with dementia, APOE ε4 carriers had a 7-fold increased risk of death (hazard ratio [HR], 6.91; 95% CI, 1.756-27.195). For those without dementia, epilepsy with onset after age 36 years was associated with mortality (HR, 9.66; 95% CI, 1.59-58.56). APOE ε4 carriers (HR, 4.91; 95% CI, 2.53-9.56), adults with early-onset epilepsy (HR, 3.61; 95% CI, 1.12-11.60), multiple health comorbidities (HR, 1.956; 95% CI, 1.087-3.519), and those living with family (HR, 2.14; 95% CI, 1.08-4.20) received significantly earlier dementia diagnoses. Conclusions and Relevance: Dementia was associated with mortality in 70% of older adults with DS. APOE ε4 carriers and/or people with multiple comorbid health conditions were at increased risk of dementia and death, highlighting the need for good health care. For those who died without a dementia diagnosis, late-onset epilepsy was the only significant factor associated with death, raising questions about potentially undiagnosed dementia cases in this group

An additional k-means clustering step improves the biological features of WGCNA gene co-expression networks

Background: Weighted Gene Co-expression Network Analysis (WGCNA) is a widely used R software package for the generation of gene co-expression networks (GCN). WGCNA generates both a GCN and a derived partitioning of clusters of genes (modules). We propose k-means clustering as an additional processing step to conventional WGCNA, which we have implemented in the R package km2gcn (k-means to gene co-expression network, https://github.com/juanbot/km2gcn). Results: We assessed our method on networks created from UKBEC data (10 different human brain tissues), on networks created from GTEx data (42 human tissues, including 13 brain tissues), and on simulated networks derived from GTEx data. We observed substantially improved module properties, including: (1) few or zero misplaced genes; (2) increased counts of replicable clusters in alternate tissues (x3.1 on average); (3) improved enrichment of Gene Ontology terms (seen in 48/52 GCNs) (4) improved cell type enrichment signals (seen in 21/23 brain GCNs); and (5) more accurate partitions in simulated data according to a range of similarity indices. Conclusions: The results obtained from our investigations indicate that our k-means method, applied as an adjunct to standard WGCNA, results in better network partitions. These improved partitions enable more fruitful downstream analyses, as gene modules are more biologically meaningful

Differential Associations of Apolipoprotein E ε4 Genotype With Attentional Abilities Across the Life Span of Individuals With Down Syndrome

Importance: Risk of Alzheimer disease (AD) is particularly high for individuals with Down syndrome (DS). The ε4 allele of the apolipoprotein E gene (APOE ε4) is associated with an additional risk for AD. In typical development, there is evidence that the APOE ε4 genotype is associated with an early cognitive advantage. Here we investigate associations of APOE ε4 with attention across the life span of individuals with DS. Objective: To investigate associations between APOE ε4 and attentional abilities in young children and in adults with DS. Design, Settings, and Participants: In this cross-sectional study, data were collected from 80 young children with DS (8-62 months of age) and 240 adults with DS (16-71 years of age) during the period from 2013 to 2018 at a research center to examine the association between APOE status (ε4 carrier vs ε4 noncarrier) and attentional abilities. Exposure: APOE status (ε4 carrier vs ε4 noncarrier). Main Outcomes and Measures: For the children, attentional ability was assessed using an eye-tracking paradigm, the gap-overlap task; the size of the gap effect was the primary outcome. For the adults, attentional ability was assessed using the CANTAB simple reaction time task; the standard deviation of response time latencies was the primary outcome. Cross-sectional developmental trajectories were constructed linking attentional ability with age in ε4 carriers and ε4 noncarriers for children and adults separately. Results: The child sample comprised 23 ε4 carriers and 57 ε4 noncarriers. The adult sample comprised 61 ε4 carriers and 179 ε4 noncarriers. For the children, a significant difference between trajectory intercepts (ηp2 = 0.14) indicated that ε4 carriers (B = 100.24 [95% CI, 18.52-181.96]) exhibited an attentional advantage over ε4 noncarriers (B = 314.78 [95% CI, 252.17-377.39]). There was an interaction between APOE status and age (ηp2 = 0.10); while the gap effect decreased with age for ε4 noncarriers (B = -4.58 [95% CI, -6.67 to -2.48]), reflecting the development of the attention system, there was no change across age in ε4 carriers (B = 0.77 [95% CI, -1.57 to 3.12]). For the adults, there was no main effect of ε4 carrier status, but there was an interaction between APOE status and age (B = 0.02 [95% CI, 0.004-0.07]), so that ε4 carriers had poorer attentional ability than ε4 noncarriers at older ages. Conclusions and Relevance: APOE ε4 is associated with an attentional advantage early in development and a disadvantage later in life for individuals with DS, similar to the pattern reported in typical development. Understanding the differential role of APOE across the life span is an important step toward future interventions

The role of mentorship in protege performance

The role of mentorship on protege performance is a matter of importance to academic, business, and governmental organizations. While the benefits of mentorship for proteges, mentors and their organizations are apparent, the extent to which proteges mimic their mentors' career choices and acquire their mentorship skills is unclear. Here, we investigate one aspect of mentor emulation by studying mentorship fecundity---the number of proteges a mentor trains---with data from the Mathematics Genealogy Project, which tracks the mentorship record of thousands of mathematicians over several centuries. We demonstrate that fecundity among academic mathematicians is correlated with other measures of academic success. We also find that the average fecundity of mentors remains stable over 60 years of recorded mentorship. We further uncover three significant correlations in mentorship fecundity. First, mentors with small mentorship fecundity train proteges that go on to have a 37% larger than expected mentorship fecundity. Second, in the first third of their career, mentors with large fecundity train proteges that go on to have a 29% larger than expected fecundity. Finally, in the last third of their career, mentors with large fecundity train proteges that go on to have a 31% smaller than expected fecundity.Comment: 23 pages double-spaced, 4 figure

Should physical activity recommendations be ethnicity-specific? Evidence from a cross-sectional study of south Asian and European men

Background Expert bodies and health organisations recommend that adults undertake at least 150 min.week−1 of moderate-intensity physical activity (MPA). However, the underpinning data largely emanate from studies of populations of European descent. It is unclear whether this level of activity is appropriate for other ethnic groups, particularly South Asians, who have increased cardio-metabolic disease risk compared to Europeans. The aim of this study was to explore the level of MPA required in South Asians to confer a similar cardio-metabolic risk profile to that observed in Europeans undertaking the currently recommended MPA level of 150 min.week−1.<p></p> Methods Seventy-five South Asian and 83 European men, aged 40–70, without cardiovascular disease or diabetes had fasted blood taken, blood pressure measured, physical activity assessed objectively (using accelerometry), and anthropometric measures made. Factor analysis was used to summarise measured risk biomarkers into underlying latent ‘factors’ for glycaemia, insulin resistance, lipid metabolism, blood pressure, and overall cardio-metabolic risk. Age-adjusted regression models were used to determine the equivalent level of MPA (in bouts of ≥10 minutes) in South Asians needed to elicit the same value in each factor as Europeans undertaking 150 min.week−1 MPA.<p></p> Findings For all factors, except blood pressure, equivalent MPA values in South Asians were significantly higher than 150 min.week−1; the equivalent MPA value for the overall cardio-metabolic risk factor was 266 (95% CI 185-347) min.week−1.<p></p> Conclusions South Asian men may need to undertake greater levels of MPA than Europeans to exhibit a similar cardio-metabolic risk profile, suggesting that a conceptual case can be made for ethnicity-specific physical activity guidance. Further study is needed to extend these findings to women and to replicate them prospectively in a larger cohort.<p></p&gt