@article{106,
  abstract     = {The goal of this article is to introduce the reader to the theory of intrinsic geometry of convex surfaces. We illustrate the power of the tools by proving a theorem on convex surfaces containing an arbitrarily long closed simple geodesic. Let us remind ourselves that a curve in a surface is called geodesic if every sufficiently short arc of the curve is length minimizing; if, in addition, it has no self-intersections, we call it simple geodesic. A tetrahedron with equal opposite edges is called isosceles. The axiomatic method of Alexandrov geometry allows us to work with the metrics of convex surfaces directly, without approximating it first by a smooth or polyhedral metric. Such approximations destroy the closed geodesics on the surface; therefore it is difficult (if at all possible) to apply approximations in the proof of our theorem. On the other hand, a proof in the smooth or polyhedral case usually admits a translation into Alexandrov’s language; such translation makes the result more general. In fact, our proof resembles a translation of the proof given by Protasov. Note that the main theorem implies in particular that a smooth convex surface does not have arbitrarily long simple closed geodesics. However we do not know a proof of this corollary that is essentially simpler than the one presented below.},
  author       = {Akopyan, Arseniy and Petrunin, Anton},
  journal      = {Mathematical Intelligencer},
  number       = {3},
  pages        = {26 -- 31},
  publisher    = {Springer},
  title        = {{Long geodesics on convex surfaces}},
  doi          = {10.1007/s00283-018-9795-5},
  volume       = {40},
  year         = {2018},
}

@article{10626,
  abstract     = {Owing to their wide tunability, multiple internal degrees of freedom, and low disorder, graphene heterostructures are emerging as a promising experimental platform for fractional quantum Hall (FQH) studies. Here, we report FQH thermal activation gap measurements in dual graphite-gated monolayer graphene devices fabricated in an edgeless Corbino geometry. In devices with substrate-induced sublattice splitting, we find a tunable crossover between single- and multicomponent FQH states in the zero energy Landau level. Activation gaps in the single-component regime show excellent agreement with numerical calculations using a single broadening parameter 
Γ≈7.2K. In the first excited Landau level, in contrast, FQH gaps are strongly influenced by Landau level mixing, and we observe an unexpected valley-ordered state at integer filling ν=−4.},
  author       = {Polshyn, Hryhoriy and Zhou, H. and Spanton, E. M. and Taniguchi, T. and Watanabe, K. and Young, A. F.},
  issn         = {1079-7114},
  journal      = {Physical Review Letters},
  keywords     = {general physics and astronomy},
  number       = {22},
  publisher    = {American Physical Society},
  title        = {{Quantitative transport measurements of fractional quantum Hall energy gaps in edgeless graphene devices}},
  doi          = {10.1103/physrevlett.121.226801},
  volume       = {121},
  year         = {2018},
}

@article{10627,
  abstract     = {We present a scanning probe technique for measuring the dynamics of individual fluxoid transitions in multiply connected superconducting structures. In these measurements, a small magnetic particle attached to the tip of a silicon cantilever is scanned over a micron-size superconducting ring fabricated from a thin aluminum film. We find that near the superconducting transition temperature of the aluminum, the dissipation and frequency of the cantilever changes significantly at particular locations where the tip-induced magnetic flux penetrating the ring causes the two lowest-energy fluxoid states to become nearly degenerate. In this regime, we show that changes in the cantilever frequency and dissipation are well-described by a stochastic resonance (SR) process, wherein small oscillations of the cantilever in the presence of thermally activated phase slips (TAPS) in the ring give rise to a dynamical force that modifies the mechanical properties of the cantilever. Using the SR model, we calculate the average fluctuation rate of the TAPS as a function of temperature over a 32-dB range in frequency, and we compare it to the Langer-Ambegaokar-McCumber-Halperin theory for TAPS in one-dimensional superconducting structures.},
  author       = {Polshyn, Hryhoriy and Naibert, Tyler R. and Budakian, Raffi},
  issn         = {2469-9969},
  journal      = {Physical Review B},
  number       = {18},
  publisher    = {American Physical Society},
  title        = {{Imaging phase slip dynamics in micron-size superconducting rings}},
  doi          = {10.1103/physrevb.97.184501},
  volume       = {97},
  year         = {2018},
}

@article{1064,
  abstract     = {In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot be separated into two subfamilies by a straight line disjoint from the disks. In this note we show that essentially the same idea may work for different analogues and generalizations of their result. In particular, we prove the following: Given a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane disjoint from the homothets.},
  author       = {Akopyan, Arseniy and Balitskiy, Alexey and Grigorev, Mikhail},
  issn         = {1432-0444},
  journal      = {Discrete & Computational Geometry},
  number       = {4},
  pages        = {1001--1009},
  publisher    = {Springer},
  title        = {{On the circle covering theorem by A.W. Goodman and R.E. Goodman}},
  doi          = {10.1007/s00454-017-9883-x},
  volume       = {59},
  year         = {2018},
}

@article{107,
  abstract     = {We introduce the notion of “non-malleable codes” which relaxes the notion of error correction and error detection. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message, or a completely unrelated value. In contrast to error correction and error detection, non-malleability can be achieved for very rich classes of modifications. We construct an efficient code that is non-malleable with respect to modifications that affect each bit of the codeword arbitrarily (i.e., leave it untouched, flip it, or set it to either 0 or 1), but independently of the value of the other bits of the codeword. Using the probabilistic method, we also show a very strong and general statement: there exists a non-malleable code for every “small enough” family F of functions via which codewords can be modified. Although this probabilistic method argument does not directly yield efficient constructions, it gives us efficient non-malleable codes in the random-oracle model for very general classes of tampering functions—e.g., functions where every bit in the tampered codeword can depend arbitrarily on any 99% of the bits in the original codeword. As an application of non-malleable codes, we show that they provide an elegant algorithmic solution to the task of protecting functionalities implemented in hardware (e.g., signature cards) against “tampering attacks.” In such attacks, the secret state of a physical system is tampered, in the hopes that future interaction with the modified system will reveal some secret information. This problem was previously studied in the work of Gennaro et al. in 2004 under the name “algorithmic tamper proof security” (ATP). We show that non-malleable codes can be used to achieve important improvements over the prior work. In particular, we show that any functionality can be made secure against a large class of tampering attacks, simply by encoding the secret state with a non-malleable code while it is stored in memory.},
  author       = {Dziembowski, Stefan and Pietrzak, Krzysztof Z and Wichs, Daniel},
  journal      = {Journal of the ACM},
  number       = {4},
  publisher    = {ACM},
  title        = {{Non-malleable codes}},
  doi          = {10.1145/3178432},
  volume       = {65},
  year         = {2018},
}

@inproceedings{108,
  abstract     = {Universal hashing found a lot of applications in computer science. In cryptography the most important fact about universal families is the so called Leftover Hash Lemma, proved by Impagliazzo, Levin and Luby. In the language of modern cryptography it states that almost universal families are good extractors. In this work we provide a somewhat surprising characterization in the opposite direction. Namely, every extractor with sufficiently good parameters yields a universal family on a noticeable fraction of its inputs. Our proof technique is based on tools from extremal graph theory applied to the \'collision graph\' induced by the extractor, and may be of independent interest. We discuss possible applications to the theory of randomness extractors and non-malleable codes.},
  author       = {Obremski, Marciej and Skorski, Maciej},
  location     = {Vail, CO, USA},
  publisher    = {IEEE},
  title        = {{Inverted leftover hash lemma}},
  doi          = {10.1109/ISIT.2018.8437654},
  volume       = {2018},
  year         = {2018},
}

@article{76,
  abstract     = {Consider a fully-connected synchronous distributed system consisting of n nodes, where up to f nodes may be faulty and every node starts in an arbitrary initial state. In the synchronous C-counting problem, all nodes need to eventually agree on a counter that is increased by one modulo C in each round for given C>1. In the self-stabilising firing squad problem, the task is to eventually guarantee that all non-faulty nodes have simultaneous responses to external inputs: if a subset of the correct nodes receive an external “go” signal as input, then all correct nodes should agree on a round (in the not-too-distant future) in which to jointly output a “fire” signal. Moreover, no node should generate a “fire” signal without some correct node having previously received a “go” signal as input. We present a framework reducing both tasks to binary consensus at very small cost. For example, we obtain a deterministic algorithm for self-stabilising Byzantine firing squads with optimal resilience f<n/3, asymptotically optimal stabilisation and response time O(f), and message size O(log f). As our framework does not restrict the type of consensus routines used, we also obtain efficient randomised solutions.},
  author       = {Lenzen, Christoph and Rybicki, Joel},
  journal      = {Distributed Computing},
  publisher    = {Springer},
  title        = {{Near-optimal self-stabilising counting and firing squads}},
  doi          = {10.1007/s00446-018-0342-6},
  year         = {2018},
}

@article{7698,
  abstract     = {Motor output varies along the rostro-caudal axis of the tetrapod spinal cord. At limb levels, ∼60 motor pools control the alternation of flexor and extensor muscles about each joint, whereas at thoracic levels as few as 10 motor pools supply muscle groups that support posture, inspiration, and expiration. Whether such differences in motor neuron identity and muscle number are associated with segmental distinctions in interneuron diversity has not been resolved. We show that select combinations of nineteen transcription factors that specify lumbar V1 inhibitory interneurons generate subpopulations enriched at limb and thoracic levels. Specification of limb and thoracic V1 interneurons involves the Hox gene Hoxc9 independently of motor neurons. Thus, early Hox patterning of the spinal cord determines the identity of V1 interneurons and motor neurons. These studies reveal a developmental program of V1 interneuron diversity, providing insight into the organization of inhibitory interneurons associated with differential motor output.},
  author       = {Sweeney, Lora Beatrice Jaeger and Bikoff, Jay B. and Gabitto, Mariano I. and Brenner-Morton, Susan and Baek, Myungin and Yang, Jerry H. and Tabak, Esteban G. and Dasen, Jeremy S. and Kintner, Christopher R. and Jessell, Thomas M.},
  issn         = {0896-6273},
  journal      = {Neuron},
  number       = {2},
  pages        = {341--355.e3},
  publisher    = {Elsevier},
  title        = {{Origin and segmental diversity of spinal inhibitory interneurons}},
  doi          = {10.1016/j.neuron.2017.12.029},
  volume       = {97},
  year         = {2018},
}

@article{77,
  abstract     = {Holes confined in quantum dots have gained considerable interest in the past few years due to their potential as spin qubits. Here we demonstrate two-axis control of a spin 3/2 qubit in natural Ge. The qubit is formed in a hut wire double quantum dot device. The Pauli spin blockade principle allowed us to demonstrate electric dipole spin resonance by applying a radio frequency electric field to one of the electrodes defining the double quantum dot. Coherent hole spin oscillations with Rabi frequencies reaching 140 MHz are demonstrated and dephasing times of 130 ns are measured. The reported results emphasize the potential of Ge as a platform for fast and electrically tunable hole spin qubit devices.},
  author       = {Watzinger, Hannes and Kukucka, Josip and Vukusic, Lada and Gao, Fei and Wang, Ting and Schäffler, Friedrich and Zhang, Jian and Katsaros, Georgios},
  journal      = {Nature Communications},
  number       = {3902 },
  publisher    = {Nature Publishing Group},
  title        = {{A germanium hole spin qubit}},
  doi          = {10.1038/s41467-018-06418-4},
  volume       = {9},
  year         = {2018},
}

@article{7712,
  abstract     = {Male pattern baldness (MPB) is a sex-limited, age-related, complex trait. We study MPB genetics in 205,327 European males from the UK Biobank. Here we show that MPB is strongly heritable and polygenic, with pedigree-heritability of 0.62 (SE = 0.03) estimated from close relatives, and SNP-heritability of 0.39 (SE = 0.01) from conventionally-unrelated males. We detect 624 near-independent genome-wide loci, contributing SNP-heritability of 0.25 (SE = 0.01), of which 26 X-chromosome loci explain 11.6%. Autosomal genetic variance is enriched for common variants and regions of lower linkage disequilibrium. We identify plausible genetic correlations between MPB and multiple sex-limited markers of earlier puberty, increased bone mineral density (rg = 0.15) and pancreatic β-cell function (rg = 0.12). Correlations with reproductive traits imply an effect on fitness, consistent with an estimated linear selection gradient of -0.018 per MPB standard deviation. Overall, we provide genetic insights into MPB: a phenotype of interest in its own right, with value as a model sex-limited, complex trait.},
  author       = {Yap, Chloe X. and Sidorenko, Julia and Wu, Yang and Kemper, Kathryn E. and Yang, Jian and Wray, Naomi R. and Robinson, Matthew Richard and Visscher, Peter M.},
  issn         = {2041-1723},
  journal      = {Nature Communications},
  publisher    = {Springer Nature},
  title        = {{Dissection of genetic variation and evidence for pleiotropy in male pattern baldness}},
  doi          = {10.1038/s41467-018-07862-y},
  volume       = {9},
  year         = {2018},
}

@article{7713,
  abstract     = {There are mean differences in complex traits among global human populations. We hypothesize that part of the phenotypic differentiation is due to natural selection. To address this hypothesis, we assess the differentiation in allele frequencies of trait-associated SNPs among African, Eastern Asian, and European populations for ten complex traits using data of large sample size (up to ~405,000). We show that SNPs associated with height (P=2.46×10−5), waist-to-hip ratio (P=2.77×10−4), and schizophrenia (P=3.96×10−5) are significantly more differentiated among populations than matched “control” SNPs, suggesting that these trait-associated SNPs have undergone natural selection. We further find that SNPs associated with height (P=2.01×10−6) and schizophrenia (P=5.16×10−18) show significantly higher variance in linkage disequilibrium (LD) scores across populations than control SNPs. Our results support the hypothesis that natural selection has shaped the genetic differentiation of complex traits, such as height and schizophrenia, among worldwide populations.},
  author       = {Guo, Jing and Wu, Yang and Zhu, Zhihong and Zheng, Zhili and Trzaskowski, Maciej and Zeng, Jian and Robinson, Matthew Richard and Visscher, Peter M. and Yang, Jian},
  issn         = {2041-1723},
  journal      = {Nature Communications},
  publisher    = {Springer Nature},
  title        = {{Global genetic differentiation of complex traits shaped by natural selection in humans}},
  doi          = {10.1038/s41467-018-04191-y},
  volume       = {9},
  year         = {2018},
}

@article{7714,
  abstract     = {Health risk factors such as body mass index (BMI) and serum cholesterol are associated with many common diseases. It often remains unclear whether the risk factors are cause or consequence of disease, or whether the associations are the result of confounding. We develop and apply a method (called GSMR) that performs a multi-SNP Mendelian randomization analysis using summary-level data from genome-wide association studies to test the causal associations of BMI, waist-to-hip ratio, serum cholesterols, blood pressures, height, and years of schooling (EduYears) with common diseases (sample sizes of up to 405,072). We identify a number of causal associations including a protective effect of LDL-cholesterol against type-2 diabetes (T2D) that might explain the side effects of statins on T2D, a protective effect of EduYears against Alzheimer’s disease, and bidirectional associations with opposite effects (e.g., higher BMI increases the risk of T2D but the effect of T2D on BMI is negative).},
  author       = {Zhu, Zhihong and Zheng, Zhili and Zhang, Futao and Wu, Yang and Trzaskowski, Maciej and Maier, Robert and Robinson, Matthew Richard and McGrath, John J. and Visscher, Peter M. and Wray, Naomi R. and Yang, Jian},
  issn         = {2041-1723},
  journal      = {Nature Communications},
  publisher    = {Springer Nature},
  title        = {{Causal associations between risk factors and common diseases inferred from GWAS summary data}},
  doi          = {10.1038/s41467-017-02317-2},
  volume       = {9},
  year         = {2018},
}

@article{7715,
  abstract     = {Preference for mates with similar phenotypes; that is, assortative mating, is widely observed in humans1,2,3,4,5 and has evolutionary consequences6,7,8. Under Fisher's classical theory6, assortative mating is predicted to induce a signature in the genome at trait-associated loci that can be detected and quantified. Here, we develop and apply a method to quantify assortative mating on a specific trait by estimating the correlation (θ) between genetic predictors of the trait from single nucleotide polymorphisms on odd- versus even-numbered chromosomes. We show by theory and simulation that the effect of assortative mating can be quantified in the presence of population stratification. We applied this approach to 32 complex traits and diseases using single nucleotide polymorphism data from ~400,000 unrelated individuals of European ancestry. We found significant evidence of assortative mating for height (θ = 3.2%) and educational attainment (θ = 2.7%), both of which were consistent with theoretical predictions. Overall, our results imply that assortative mating involves multiple traits and affects the genomic architecture of loci that are associated with these traits, and that the consequence of mate choice can be detected from a random sample of genomes.},
  author       = {Yengo, Loic and Robinson, Matthew Richard and Keller, Matthew C. and Kemper, Kathryn E. and Yang, Yuanhao and Trzaskowski, Maciej and Gratten, Jacob and Turley, Patrick and Cesarini, David and Benjamin, Daniel J. and Wray, Naomi R. and Goddard, Michael E. and Yang, Jian and Visscher, Peter M.},
  issn         = {2397-3374},
  journal      = {Nature Human Behaviour},
  number       = {12},
  pages        = {948--954},
  publisher    = {Springer Nature},
  title        = {{Imprint of assortative mating on the human genome}},
  doi          = {10.1038/s41562-018-0476-3},
  volume       = {2},
  year         = {2018},
}

@article{7716,
  abstract     = {Genomic prediction has the potential to contribute to precision medicine. However, to date, the utility of such predictors is limited due to low accuracy for most traits. Here theory and simulation study are used to demonstrate that widespread pleiotropy among phenotypes can be utilised to improve genomic risk prediction. We show how a genetic predictor can be created as a weighted index that combines published genome-wide association study (GWAS) summary statistics across many different traits. We apply this framework to predict risk of schizophrenia and bipolar disorder in the Psychiatric Genomics consortium data, finding substantial heterogeneity in prediction accuracy increases across cohorts. For six additional phenotypes in the UK Biobank data, we find increases in prediction accuracy ranging from 0.7% for height to 47% for type 2 diabetes, when using a multi-trait predictor that combines published summary statistics from multiple traits, as compared to a predictor based only on one trait.},
  author       = {Maier, Robert M. and Zhu, Zhihong and Lee, Sang Hong and Trzaskowski, Maciej and Ruderfer, Douglas M. and Stahl, Eli A. and Ripke, Stephan and Wray, Naomi R. and Yang, Jian and Visscher, Peter M. and Robinson, Matthew Richard},
  issn         = {2041-1723},
  journal      = {Nature Communications},
  publisher    = {Springer Nature},
  title        = {{Improving genetic prediction by leveraging genetic correlations among human diseases and traits}},
  doi          = {10.1038/s41467-017-02769-6},
  volume       = {9},
  year         = {2018},
}

@article{7717,
  abstract     = {Background: DNA methylation levels change along with age, but few studies have examined the variation in the rate of such changes between individuals.
Methods: We performed a longitudinal analysis to quantify the variation in the rate of change of DNA methylation between individuals using whole blood DNA methylation array profiles collected at 2–4 time points (N = 2894) in 954 individuals (67–90 years).
Results: After stringent quality control, we identified 1507 DNA methylation CpG sites (rsCpGs) with statistically significant variation in the rate of change (random slope) of DNA methylation among individuals in a mixed linear model analysis. Genes in the vicinity of these rsCpGs were found to be enriched in Homeobox transcription factors and the Wnt signalling pathway, both of which are related to ageing processes. Furthermore, we investigated the SNP effect on the random slope. We found that 4 out of 1507 rsCpGs had one significant (P < 5 × 10−8/1507) SNP effect and 343 rsCpGs had at least one SNP effect (436 SNP-probe pairs) reaching genome-wide significance (P < 5 × 10−8). Ninety-five percent of the significant (P < 5 × 10−8) SNPs are on different chromosomes from their corresponding probes.
Conclusions: We identified CpG sites that have variability in the rate of change of DNA methylation between individuals, and our results suggest a genetic basis of this variation. Genes around these CpG sites have been reported to be involved in the ageing process.},
  author       = {Zhang, Qian and Marioni, Riccardo E and Robinson, Matthew Richard and Higham, Jon and Sproul, Duncan and Wray, Naomi R and Deary, Ian J and McRae, Allan F and Visscher, Peter M},
  issn         = {1756-994X},
  journal      = {Genome Medicine},
  number       = {1},
  publisher    = {Springer Nature},
  title        = {{Genotype effects contribute to variation in longitudinal methylome patterns in older people}},
  doi          = {10.1186/s13073-018-0585-7},
  volume       = {10},
  year         = {2018},
}

@article{7718,
  abstract     = {Flores Island, Indonesia, was inhabited by the small-bodied hominin species Homo floresiensis, which has an unknown evolutionary relationship to modern humans. This island is also home to an extant human pygmy population. Here we describe genome-scale single-nucleotide polymorphism data and whole-genome sequences from a contemporary human pygmy population living on Flores near the cave where H. floresiensis was found. The genomes of Flores pygmies reveal a complex history of admixture with Denisovans and Neanderthals but no evidence for gene flow with other archaic hominins. Modern individuals bear the signatures of recent positive selection encompassing the FADS (fatty acid desaturase) gene cluster, likely related to diet, and polygenic selection acting on standing variation that contributed to their short-stature phenotype. Thus, multiple independent instances of hominin insular dwarfism occurred on Flores.},
  author       = {Tucci, Serena and Vohr, Samuel H. and McCoy, Rajiv C. and Vernot, Benjamin and Robinson, Matthew Richard and Barbieri, Chiara and Nelson, Brad J. and Fu, Wenqing and Purnomo, Gludhug A. and Sudoyo, Herawati and Eichler, Evan E. and Barbujani, Guido and Visscher, Peter M. and Akey, Joshua M. and Green, Richard E.},
  issn         = {0036-8075},
  journal      = {Science},
  number       = {6401},
  pages        = {511--516},
  publisher    = {American Association for the Advancement of Science},
  title        = {{Evolutionary history and adaptation of a human pygmy population of Flores Island, Indonesia}},
  doi          = {10.1126/science.aar8486},
  volume       = {361},
  year         = {2018},
}

@article{7721,
  abstract     = {The availability of genome-wide genetic data on hundreds of thousands of people has led to an equally rapid growth in methodologies available to analyse these data. While the motivation for undertaking genome-wide association studies (GWAS) is identification of genetic markers associated with complex traits, once generated these data can be used for many other analyses. GWAS have demonstrated that complex traits exhibit a highly polygenic genetic architecture, often with shared genetic risk factors across traits. New methods to analyse data from GWAS are increasingly being used to address a diverse set of questions about the aetiology of complex traits and diseases, including psychiatric disorders. Here, we give an overview of some of these methods and present examples of how they have contributed to our understanding of psychiatric disorders. We consider: (i) estimation of the extent of genetic influence on traits, (ii) uncovering of shared genetic control between traits, (iii) predictions of genetic risk for individuals, (iv) uncovering of causal relationships between traits, (v) identifying causal single-nucleotide polymorphisms and genes or (vi) the detection of genetic heterogeneity. This classification helps organise the large number of recently developed methods, although some could be placed in more than one category. While some methods require GWAS data on individual people, others simply use GWAS summary statistics data, allowing novel well-powered analyses to be conducted at a low computational burden.},
  author       = {Maier, R. M. and Visscher, P. M. and Robinson, Matthew Richard and Wray, N. R.},
  issn         = {0033-2917},
  journal      = {Psychological Medicine},
  number       = {7},
  pages        = {1055--1067},
  publisher    = {Cambridge University Press},
  title        = {{Embracing polygenicity: A review of methods and tools for psychiatric genetics research}},
  doi          = {10.1017/s0033291717002318},
  volume       = {48},
  year         = {2018},
}

@article{7722,
  abstract     = {We develop a Bayesian mixed linear model that simultaneously estimates single-nucleotide polymorphism (SNP)-based heritability, polygenicity (proportion of SNPs with nonzero effects), and the relationship between SNP effect size and minor allele frequency for complex traits in conventionally unrelated individuals using genome-wide SNP data. We apply the method to 28 complex traits in the UK Biobank data (N = 126,752) and show that on average, 6% of SNPs have nonzero effects, which in total explain 22% of phenotypic variance. We detect significant (P < 0.05/28) signatures of natural selection in the genetic architecture of 23 traits, including reproductive, cardiovascular, and anthropometric traits, as well as educational attainment. The significant estimates of the relationship between effect size and minor allele frequency in complex traits are consistent with a model of negative (or purifying) selection, as confirmed by forward simulation. We conclude that negative selection acts pervasively on the genetic variants associated with human complex traits.},
  author       = {Zeng, Jian and de Vlaming, Ronald and Wu, Yang and Robinson, Matthew Richard and Lloyd-Jones, Luke R. and Yengo, Loic and Yap, Chloe X. and Xue, Angli and Sidorenko, Julia and McRae, Allan F. and Powell, Joseph E. and Montgomery, Grant W. and Metspalu, Andres and Esko, Tonu and Gibson, Greg and Wray, Naomi R. and Visscher, Peter M. and Yang, Jian},
  issn         = {1061-4036},
  journal      = {Nature Genetics},
  number       = {5},
  pages        = {746--753},
  publisher    = {Springer Nature},
  title        = {{Signatures of negative selection in the genetic architecture of human complex traits}},
  doi          = {10.1038/s41588-018-0101-4},
  volume       = {50},
  year         = {2018},
}

@article{7723,
  abstract     = {Genome-wide association studies (GWAS) have identified thousands of loci that are robustly associated with complex diseases. The use of linear mixed model (LMM) methodology for GWAS is becoming more prevalent due to its ability to control for population structure and cryptic relatedness and to increase power. The odds ratio (OR) is a common measure of the association of a disease with an exposure (e.g., a genetic variant) and is readably available from logistic regression. However, when the LMM is applied to all-or-none traits it provides estimates of genetic effects on the observed 0–1 scale, a different scale to that in logistic regression. This limits the comparability of results across studies, for example in a meta-analysis, and makes the interpretation of the magnitude of an effect from an LMM GWAS difficult. In this study, we derived transformations from the genetic effects estimated under the LMM to the OR that only rely on summary statistics. To test the proposed transformations, we used real genotypes from two large, publicly available data sets to simulate all-or-none phenotypes for a set of scenarios that differ in underlying model, disease prevalence, and heritability. Furthermore, we applied these transformations to GWAS summary statistics for type 2 diabetes generated from 108,042 individuals in the UK Biobank. In both simulation and real-data application, we observed very high concordance between the transformed OR from the LMM and either the simulated truth or estimates from logistic regression. The transformations derived and validated in this study improve the comparability of results from prospective and already performed LMM GWAS on complex diseases by providing a reliable transformation to a common comparative scale for the genetic effects.},
  author       = {Lloyd-Jones, Luke R. and Robinson, Matthew Richard and Yang, Jian and Visscher, Peter M.},
  issn         = {0016-6731},
  journal      = {Genetics},
  number       = {4},
  pages        = {1397--1408},
  publisher    = {Genetics Society of America},
  title        = {{Transformation of summary statistics from linear mixed model association on all-or-none traits to odds ratio}},
  doi          = {10.1534/genetics.117.300360},
  volume       = {208},
  year         = {2018},
}

@article{7724,
  abstract     = {Modern molecular genetic datasets, primarily collected to study the biology of human health and disease, can be used to directly measure the action of natural selection and reveal important features of contemporary human evolution. Here we leverage the UK Biobank data to test for the presence of linear and nonlinear natural selection in a contemporary population of the United Kingdom. We obtain phenotypic and genetic evidence consistent with the action of linear/directional selection. Phenotypic evidence suggests that stabilizing selection, which acts to reduce variance in the population without necessarily modifying the population mean, is widespread and relatively weak in comparison with estimates from other species.},
  author       = {Sanjak, Jaleal S. and Sidorenko, Julia and Robinson, Matthew Richard and Thornton, Kevin R. and Visscher, Peter M.},
  issn         = {0027-8424},
  journal      = {Proceedings of the National Academy of Sciences},
  number       = {1},
  pages        = {151--156},
  publisher    = {Proceedings of the National Academy of Sciences},
  title        = {{Evidence of directional and stabilizing selection in contemporary humans}},
  doi          = {10.1073/pnas.1707227114},
  volume       = {115},
  year         = {2018},
}