Every generic linear functional (Formula presented.) on a convex polytope (Formula presented.) induces an orientation on the graph of (Formula presented.). From the resulting directed graph one can define a notion of (Formula presented.) -arborescence and (Formula presented.) -monotone path on (Formula presented.), as well as a natural graph structure on the vertex set of (Formula presented.) -monotone paths. These concepts are important in geometric combinatorics and optimization. This paper bounds the number of (Formula presented.) -arborescences, the number of (Formula presented.) -monotone paths, and the diameter of the graph of (Formula presented.) -monotone paths for polytopes (Formula presented.) in terms of their dimension and number of vertices or facets.

Organic aerosol particles (OA) play major roles in atmospheric chemistry, climate, and public health. Aerosol particle viscosity is highly important since it can determine the ability of chemical species such as oxidants, organics or water to diffuse into the particle bulk. Recent measurements indicate that OA may be present in highly viscous states, however, diffusion rates of small molecules such as water are not limited by these high viscosities. Direct observational evidence of kinetic barriers caused by high viscosity and low diffusivity in aerosol particles were not available until recently; and techniques that are able to dynamically quantify and track viscosity changes during atmospherically relevant processes are still unavailable for atmospheric aerosols. Here we report quantitative, real-time, online observations of microscopic viscosity changes in aerosol particles of atmospherically relevant composition, using fluorescence lifetime imaging (FLIM) of viscosity. We show that microviscosity in ozonated oleic acid droplets and secondary organic aerosol (SOA) particles formed by ozonolysis of myrcene increases substantially with decreasing humidity and atmospheric oxidative aging processes. Furthermore, we found unexpected heterogeneities of microviscosity inside individual aerosol particles. The results of this study enhance our understanding of organic aerosol processes on microscopic scales and may have important implications for the modeling of atmospheric aerosol growth, composition and interactions with trace gases and clouds.

For more than half a century, Denmark has maintained population-wide demographic, health care, and socioeconomic registers that provide detailed information on the interaction between all residents and the extensive national social services system. We leverage this resource to reconstruct the genealogy of the entire nation based on all individuals legally residing in Denmark since 1968. We cross-reference 6,691,426 individuals with nationwide health care registers to estimate heritability and genetic correlations of 10 broad diagnostic categories involving all major organs and systems. Heritability estimates for mental disorders were consistently the highest across demographic cohorts (average h2 = 0.406, 95% CI = [0.403, 0.408]), whereas estimates for cancers were the lowest (average h2 = 0.130, 95% CI = [0.125, 0.134]). The average genetic correlation of each of the 10 diagnostic categories with the other nine was highest for gastrointestinal conditions (average rg = 0.567, 95% CI = [0.566, 0.567]) and lowest for urogenital conditions (average rg = 0.386, 95% CI = [0.385, 0.388]). Mental, pulmonary, gastrointestinal, and neurological conditions had similar genetic correlation profiles.

The observation of genetic correlations between disparate human traits has been interpreted as evidence of widespread pleiotropy. Here, we introduce cross-trait assortative mating (xAM) as an alternative explanation. We observe that xAM affects many phenotypes and that phenotypic cross-mate correlation estimates are strongly associated with genetic correlation estimates (R²=74%). We demonstrate that existing xAM plausibly accounts for substantial fractions of genetic correlation estimates and that previously reported genetic correlation estimates between some pairs of psychiatric disorders are congruent with xAM alone. Finally, we provide evidence for a history of xAM at the genetic level using cross-trait even/odd chromosome polygenic score correlations. Together, our results demonstrate that previous reports have likely overestimated the true genetic similarity between many phenotypes.

Recent studies suggest that closely related species can accumulate substantial genetic and phenotypic differences despite ongoing gene flow, thus challenging traditional ideas regarding the genetics of speciation. Baboons (genus Papio) are Old World monkeys consisting of six readily distinguishable species. Baboon species hybridize in the wild, and prior data imply a complex history of differentiation and introgression. We produced a reference genome assembly for the olive baboon (Papio anubis) and whole-genome sequence data for all six extant species. We document multiple episodes of admixture and introgression during the radiation of Papio baboons, thus demonstrating their value as a model of complex evolutionary divergence, hybridization, and reticulation. These results help inform our understanding of similar cases, including modern humans, Neanderthals, Denisovans, and other ancient hominins.

Attention-deficit hyperactivity disorder (ADHD) is a prevalent neurodevelopmental disorder with a major genetic component. Here, we present a genome-wide association study meta-analysis of ADHD comprising 38,691 individuals with ADHD and 186,843 controls. We identified 27 genome-wide significant loci, highlighting 76 potential risk genes enriched among genes expressed particularly in early brain development. Overall, ADHD genetic risk was associated with several brain-specific neuronal subtypes and midbrain dopaminergic neurons. In exome-sequencing data from 17,896 individuals, we identified an increased load of rare protein-truncating variants in ADHD for a set of risk genes enriched with probable causal common variants, potentially implicating SORCS3 in ADHD by both common and rare variants. Bivariate Gaussian mixture modeling estimated that 84-98% of ADHD-influencing variants are shared with other psychiatric disorders. In addition, common-variant ADHD risk was associated with impaired complex cognition such as verbal reasoning and a range of executive functions, including attention.

Depression is a common psychiatric disorder and a leading cause of disability worldwide. Here we conducted a genome-wide association study meta-analysis of six datasets, including >1.3 million individuals (371,184 with depression) and identified 243 risk loci. Overall, 64 loci were new, including genes encoding glutamate and GABA receptors, which are targets for antidepressant drugs. Intersection with functional genomics data prioritized likely causal genes and revealed new enrichment of prenatal GABAergic neurons, astrocytes and oligodendrocyte lineages. We found depression to be highly polygenic, with ~11,700 variants explaining 90% of the single-nucleotide polymorphism heritability, estimating that >95% of risk variants for other psychiatric disorders (anxiety, schizophrenia, bipolar disorder and attention deficit hyperactivity disorder) were influencing depression risk when both concordant and discordant variants were considered, and nearly all depression risk variants influenced educational attainment. Additionally, depression genetic risk was associated with impaired complex cognition domains. We dissected the genetic and clinical heterogeneity, revealing distinct polygenic architectures across subgroups of depression and demonstrating significantly increased absolute risks for recurrence and psychiatric comorbidity among cases of depression with the highest polygenic burden, with considerable sex differences. The risks were up to 5- and 32-fold higher than cases with the lowest polygenic burden and the background population, respectively. These results deepen the understanding of the biology underlying depression, its disease progression and inform precision medicine approaches to treatment.

The population history of Aboriginal Australians remains largely uncharacterized. Here we generate high-coverage genomes for 83 Aboriginal Australians (speakers of Pama-Nyungan languages) and 25 Papuans from the New Guinea Highlands. We find that Papuan and Aboriginal Australian ancestors diversified 25-40 thousand years ago (kya), suggesting pre-Holocene population structure in the ancient continent of Sahul (Australia, New Guinea and Tasmania). However, all of the studied Aboriginal Australians descend from a single founding population that differentiated ~10-32 kya. We infer a population expansion in northeast Australia during the Holocene epoch (past 10,000 years) associated with limited gene flow from this region to the rest of Australia, consistent with the spread of the Pama-Nyungan languages. We estimate that Aboriginal Australians and Papuans diverged from Eurasians 51-72 kya, following a single out-of-Africa dispersal, and subsequently admixed with archaic populations. Finally, we report evidence of selection in Aboriginal Australians potentially associated with living in the desert.