TY - GEN AB - The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1, L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses. The problem of computing edit distance to a pushdown automaton is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k. AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A AU - Ibsen-Jensen, Rasmus AU - Otop, Jan ID - 5438 SN - 2664-1690 TI - Edit distance for pushdown automata ER - TY - GEN AB - Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom for payoff in the context of evolution. The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. The fitness (or the reproductive rate) is a non-negative number, and depends on the payoff. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are as follows: First, we consider a special case of the general problem, where the residents do not reproduce. We show that the qualitative question is NP-complete, and the quantitative approximation question is #P-complete, and the hardness results hold even in the special case where the interaction and the replacement graphs coincide. Second, we show that in general both the qualitative and the quantitative approximation questions are PSPACE-complete. The PSPACE-hardness result for quantitative approximation holds even when the fitness is always positive. AU - Chatterjee, Krishnendu AU - Ibsen-Jensen, Rasmus AU - Nowak, Martin ID - 5440 SN - 2664-1690 TI - The complexity of evolutionary games on graphs ER - TY - GEN AB - Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom in the context of evolution.The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are: (1) We show that the qualitative question is NP-complete and the quantitative approximation question is #P-hard in the special case when the interaction and the replacement graphs coincide and even with the restriction that the resident individuals do not reproduce (which corresponds to an invading population taking over an empty structure). (2) We show that in general the qualitative question is PSPACE-complete and the quantitative approximation question is PSPACE-hard and can be solved in exponential time. AU - Chatterjee, Krishnendu AU - Ibsen-Jensen, Rasmus AU - Nowak, Martin ID - 5432 SN - 2664-1690 TI - The complexity of evolutionary games on graphs ER - TY - GEN AB - A comprehensive understanding of the clonal evolution of cancer is critical for understanding neoplasia. Genome-wide sequencing data enables evolutionary studies at unprecedented depth. However, classical phylogenetic methods often struggle with noisy sequencing data of impure DNA samples and fail to detect subclones that have different evolutionary trajectories. We have developed a tool, called Treeomics, that allows us to reconstruct the phylogeny of a cancer with commonly available sequencing technologies. Using Bayesian inference and Integer Linear Programming, robust phylogenies consistent with the biological processes underlying cancer evolution were obtained for pancreatic, ovarian, and prostate cancers. Furthermore, Treeomics correctly identified sequencing artifacts such as those resulting from low statistical power; nearly 7% of variants were misclassified by conventional statistical methods. These artifacts can skew phylogenies by creating illusory tumor heterogeneity among distinct samples. Importantly, we show that the evolutionary trees generated with Treeomics are mathematically optimal. AU - Reiter, Johannes AU - Makohon-Moore, Alvin AU - Gerold, Jeffrey AU - Bozic, Ivana AU - Chatterjee, Krishnendu AU - Iacobuzio-Donahue, Christine AU - Vogelstein, Bert AU - Nowak, Martin ID - 5444 SN - 2664-1690 TI - Reconstructing robust phylogenies of metastatic cancers ER - TY - GEN AB - POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIME-complete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach. AU - Chatterjee, Krishnendu AU - Chmelik, Martin AU - Davies, Jessica ID - 5443 SN - 2664-1690 TI - A symbolic SAT-based algorithm for almost-sure reachability with small strategies in POMDPs ER - TY - JOUR AB - We present here the first integer-based algorithm for constructing a well-defined lattice sphere specified by integer radius and integer center. The algorithm evolves from a unique correspondence between the lattice points comprising the sphere and the distribution of sum of three square numbers in integer intervals. We characterize these intervals to derive a useful set of recurrences, which, in turn, aids in efficient computation. Each point of the lattice sphere is determined by resorting to only a few primitive operations in the integer domain. The symmetry of its quadraginta octants provides an added advantage by confining the computation to its prima quadraginta octant. Detailed theoretical analysis and experimental results have been furnished to demonstrate its simplicity and elegance. AU - Biswas, Ranita AU - Bhowmick, Partha ID - 5804 IS - 4 JF - Theoretical Computer Science SN - 0304-3975 TI - From prima quadraginta octant to lattice sphere through primitive integer operations VL - 624 ER - TY - JOUR AU - Biswas, Ranita AU - Bhowmick, Partha ID - 5807 IS - 11 JF - Theoretical Computer Science SN - 0304-3975 TI - On different topological classes of spherical geodesic paths and circles inZ3 VL - 605 ER - TY - JOUR AU - Biswas, Ranita AU - Bhowmick, Partha ID - 5808 IS - 6-8 JF - The Visual Computer SN - 0178-2789 TI - Layer the sphere VL - 31 ER - TY - JOUR AB - Transcription of eukaryotic protein-coding genes commences with the assembly of a conserved initiation complex, which consists of RNA polymerase II (Pol II) and the general transcription factors, at promoter DNA. After two decades of research, the structural basis of transcription initiation is emerging. Crystal structures of many components of the initiation complex have been resolved, and structural information on Pol II complexes with general transcription factors has recently been obtained. Although mechanistic details await elucidation, available data outline how Pol II cooperates with the general transcription factors to bind to and open promoter DNA, and how Pol II directs RNA synthesis and escapes from the promoter. AU - Sainsbury, Sarah AU - Bernecky, Carrie A AU - Cramer, Patrick ID - 594 IS - 3 JF - Nature Reviews Molecular Cell Biology TI - Structural basis of transcription initiation by RNA polymerase II VL - 16 ER - TY - CONF AB - The fact that the complete graph K_5 does not embed in the plane has been generalized in two independent directions. On the one hand, the solution of the classical Heawood problem for graphs on surfaces established that the complete graph K_n embeds in a closed surface M if and only if (n-3)(n-4) is at most 6b_1(M), where b_1(M) is the first Z_2-Betti number of M. On the other hand, Van Kampen and Flores proved that the k-skeleton of the n-dimensional simplex (the higher-dimensional analogue of K_{n+1}) embeds in R^{2k} if and only if n is less or equal to 2k+2. Two decades ago, Kuhnel conjectured that the k-skeleton of the n-simplex embeds in a compact, (k-1)-connected 2k-manifold with kth Z_2-Betti number b_k only if the following generalized Heawood inequality holds: binom{n-k-1}{k+1} is at most binom{2k+1}{k+1} b_k. This is a common generalization of the case of graphs on surfaces as well as the Van Kampen--Flores theorem. In the spirit of Kuhnel's conjecture, we prove that if the k-skeleton of the n-simplex embeds in a 2k-manifold with kth Z_2-Betti number b_k, then n is at most 2b_k binom{2k+2}{k} + 2k + 5. This bound is weaker than the generalized Heawood inequality, but does not require the assumption that M is (k-1)-connected. Our proof uses a result of Volovikov about maps that satisfy a certain homological triviality condition. AU - Goaoc, Xavier AU - Mabillard, Isaac AU - Paták, Pavel AU - Patakova, Zuzana AU - Tancer, Martin AU - Wagner, Uli ID - 1511 TI - On generalized Heawood inequalities for manifolds: A Van Kampen–Flores-type nonembeddability result VL - 34 ER - TY - JOUR AB - Carbon dioxide (CO2) gradients are ubiquitous and provide animals with information about their environment, such as the potential presence of prey or predators. The nematode Caenorhabditis elegans avoids elevated CO2, and previous work identified three neuron pairs called “BAG,” “AFD,” and “ASE” that respond to CO2 stimuli. Using in vivo Ca2+ imaging and behavioral analysis, we show that C. elegans can detect CO2 independently of these sensory pathways. Many of the C. elegans sensory neurons we examined, including the AWC olfactory neurons, the ASJ and ASK gustatory neurons, and the ASH and ADL nociceptors, respond to a rise in CO2 with a rise in Ca2+. In contrast, glial sheath cells harboring the sensory endings of C. elegans’ major chemosensory neurons exhibit strong and sustained decreases in Ca2+ in response to high CO2. Some of these CO2 responses appear to be cell intrinsic. Worms therefore may couple detection of CO2 to that of other cues at the earliest stages of sensory processing. We show that C. elegans persistently suppresses oviposition at high CO2. Hermaphrodite-specific neurons (HSNs), the executive neurons driving egg-laying, are tonically inhibited when CO2 is elevated. CO2 modulates the egg-laying system partly through the AWC olfactory neurons: High CO2 tonically activates AWC by a cGMP-dependent mechanism, and AWC output inhibits the HSNs. Our work shows that CO2 is a more complex sensory cue for C. elegans than previously thought, both in terms of behavior and neural circuitry. AU - Fenk, Lorenz A. AU - de Bono, Mario ID - 6118 IS - 27 JF - Proceedings of the National Academy of Sciences SN - 0027-8424 TI - Environmental CO2 inhibits Caenorhabditis elegans egg-laying by modulating olfactory neurons and evokes widespread changes in neural activity VL - 112 ER - TY - JOUR AB - Brains organize behavior and physiology to optimize the response to threats or opportunities. We dissect how 21% O2, an indicator of surface exposure, reprograms C. elegans' global state, inducing sustained locomotory arousal and altering expression of neuropeptides, metabolic enzymes, and other non-neural genes. The URX O2-sensing neurons drive arousal at 21% O2 by tonically activating the RMG interneurons. Stimulating RMG is sufficient to switch behavioral state. Ablating the ASH, ADL, or ASK sensory neurons connected to RMG by gap junctions does not disrupt arousal. However, disrupting cation currents in these neurons curtails RMG neurosecretion and arousal. RMG signals high O2 by peptidergic secretion. Neuropeptide reporters reveal neural circuit state, as neurosecretion stimulates neuropeptide expression. Neural imaging in unrestrained animals shows that URX and RMG encode O2 concentration rather than behavior, while the activity of downstream interneurons such as AVB and AIY reflect both O2 levels and the behavior being executed. AU - Laurent, Patrick AU - Soltesz, Zoltan AU - Nelson, Geoffrey M AU - Chen, Changchun AU - Arellano-Carbajal, Fausto AU - Levy, Emmanuel AU - de Bono, Mario ID - 6120 JF - eLife SN - 2050-084X TI - Decoding a neural circuit controlling global animal state in C. elegans VL - 4 ER - TY - CONF AB - An instance of the Valued Constraint Satisfaction Problem (VCSP) is given by a finite set of variables, a finite domain of labels, and a sum of functions, each function depending on a subset of the variables. Each function can take finite values specifying costs of assignments of labels to its variables or the infinite value, which indicates an infeasible assignment. The goal is to find an assignment of labels to the variables that minimizes the sum. We study, assuming that P ≠ NP, how the complexity of this very general problem depends on the set of functions allowed in the instances, the so-called constraint language. The case when all allowed functions take values in {0, ∞} corresponds to ordinary CSPs, where one deals only with the feasibility issue and there is no optimization. This case is the subject of the Algebraic CSP Dichotomy Conjecture predicting for which constraint languages CSPs are tractable (i.e. solvable in polynomial time) and for which NP-hard. The case when all allowed functions take only finite values corresponds to finite-valued CSP, where the feasibility aspect is trivial and one deals only with the optimization issue. The complexity of finite-valued CSPs was fully classified by Thapper and Zivny. An algebraic necessary condition for tractability of a general-valued CSP with a fixed constraint language was recently given by Kozik and Ochremiak. As our main result, we prove that if a constraint language satisfies this algebraic necessary condition, and the feasibility CSP (i.e. the problem of deciding whether a given instance has a feasible solution) corresponding to the VCSP with this language is tractable, then the VCSP is tractable. The algorithm is a simple combination of the assumed algorithm for the feasibility CSP and the standard LP relaxation. As a corollary, we obtain that a dichotomy for ordinary CSPs would imply a dichotomy for general-valued CSPs. AU - Kolmogorov, Vladimir AU - Krokhin, Andrei AU - Rolinek, Michal ID - 1637 TI - The complexity of general-valued CSPs ER - TY - JOUR AB - The osteoclast-associated receptor (OSCAR) is a collagen-binding immune receptor with important roles in dendritic cell maturation and activation of inflammatory monocytes as well as in osteoclastogenesis. The crystal structure of the OSCAR ectodomain is presented, both free and in complex with a consensus triple-helical peptide (THP). The structures revealed a collagen-binding site in each immunoglobulin-like domain (D1 and D2). The THP binds near a predicted collagen-binding groove in D1, but a more extensive interaction with D2 is facilitated by the unusually wide D1-D2 interdomain angle in OSCAR. Direct binding assays, combined with site-directed mutagenesis, confirm that the primary collagen-binding site in OSCAR resides in D2, in marked contrast to the related collagen receptors, glycoprotein VI (GPVI) and leukocyte-associated immunoglobulin-like receptor-1 (LAIR-1). Monomeric OSCAR D1D2 binds to the consensus THP with a KD of 28 µM measured in solution, but shows a higher affinity (KD 1.5 μM) when binding to a solid-phase THP, most likely due to an avidity effect. These data suggest a 2-stage model for the interaction of OSCAR with a collagen fibril, with transient, low-affinity interactions initiated by the membrane-distal D1, followed by firm adhesion to the primary binding site in D2. AU - Zhou, Long AU - Hinerman, J. M. AU - Blaszczyk, M. AU - Miller, J. L. C. AU - Conrady, D. G. AU - Barrow, A. D. AU - Chirgadze, D. Y. AU - Bihan, D. AU - Farndale, R. W. AU - Herr, A. B. ID - 6507 IS - 5 JF - Blood SN - 0006-4971 TI - Structural basis for collagen recognition by the immune receptor OSCAR VL - 127 ER - TY - JOUR AB - This paper presents polar coding schemes for the two-user discrete memoryless broadcast channel (DM-BC) which achieve Marton's region with both common and private messages. This is the best achievable rate region known to date, and it is tight for all classes of two-user DM-BCs whose capacity regions are known. To accomplish this task, we first construct polar codes for both the superposition as well as binning strategy. By combining these two schemes, we obtain Marton's region with private messages only. Finally, we show how to handle the case of common information. The proposed coding schemes possess the usual advantages of polar codes, i.e., they have low encoding and decoding complexity and a superpolynomial decay rate of the error probability. We follow the lead of Goela, Abbe, and Gastpar, who recently introduced polar codes emulating the superposition and binning schemes. To align the polar indices, for both schemes, their solution involves some degradedness constraints that are assumed to hold between the auxiliary random variables and channel outputs. To remove these constraints, we consider the transmission of k blocks and employ a chaining construction that guarantees the proper alignment of the polarized indices. The techniques described in this paper are quite general, and they can be adopted to many other multiterminal scenarios whenever there polar indices need to be aligned. AU - Mondelli, Marco AU - Hassani, Hamed AU - Sason, Igal AU - Urbanke, Rudiger ID - 6737 IS - 2 JF - IEEE Transactions on Information Theory TI - Achieving Marton’s region for broadcast channels using polar codes VL - 61 ER - TY - JOUR AB - Motivated by the significant performance gains which polar codes experience under successive cancellation list decoding, their scaling exponent is studied as a function of the list size. In particular, the error probability is fixed, and the tradeoff between the block length and back-off from capacity is analyzed. A lower bound is provided on the error probability under MAP decoding with list size L for any binary-input memoryless output-symmetric channel and for any class of linear codes such that their minimum distance is unbounded as the block length grows large. Then, it is shown that under MAP decoding, although the introduction of a list can significantly improve the involved constants, the scaling exponent itself, i.e., the speed at which capacity is approached, stays unaffected for any finite list size. In particular, this result applies to polar codes, since their minimum distance tends to infinity as the block length increases. A similar result is proved for genie-aided successive cancellation decoding when transmission takes place over the binary erasure channel, namely, the scaling exponent remains constant for any fixed number of helps from the genie. Note that since genie-aided successive cancellation decoding might be strictly worse than successive cancellation list decoding, the problem of establishing the scaling exponent of the latter remains open. AU - Mondelli, Marco AU - Hassani, Hamed AU - Urbanke, Rudiger ID - 6736 IS - 9 JF - IEEE Transactions on Information Theory TI - Scaling exponent of list decoders with applications to polar codes VL - 61 ER - TY - JOUR AB - Torque magnetization measurements on YBa2Cu3Oy (YBCO) at doping y=6.67 (p=0.12), in dc fields (B) up to 33 T and temperatures down to 4.5 K, show that weak diamagnetism persists above the extrapolated irreversibility field Hirr(T=0)≈24 T. The differential susceptibility dM/dB, however, is more rapidly suppressed for B≳16 T than expected from the properties of the low field superconducting state, and saturates at a low value for fields B≳24 T. In addition, torque measurements on a p=0.11 YBCO crystal in pulsed field up to 65 T and temperatures down to 8 K show similar behavior, with no additional features at higher fields. We offer two candidate scenarios to explain these observations: (a) superconductivity survives but is heavily suppressed at high field by competition with charge-density-wave (CDW) order; (b) static superconductivity disappears near 24 T and is followed by a region of fluctuating superconductivity, which causes dM/dB to saturate at high field. The diamagnetic signal observed above 50 T for the p=0.11 crystal at 40 K and below may be caused by changes in the normal state susceptibility rather than bulk or fluctuating superconductivity. There will be orbital (Landau) diamagnetism from electron pockets and possibly a reduction in spin susceptibility caused by the stronger three-dimensional ordered CDW. AU - Yu, Jing Fei AU - Ramshaw, B. J. AU - Kokanović, I. AU - Modic, Kimberly A AU - Harrison, N. AU - Day, James AU - Liang, Ruixing AU - Hardy, W. N. AU - Bonn, D. A. AU - McCollam, A. AU - Julian, S. R. AU - Cooper, J. R. ID - 7070 IS - 18 JF - Physical Review B SN - 1098-0121 TI - Magnetization of underdoped YBa2Cu3Oy above the irreversibility field VL - 92 ER - TY - JOUR AB - The rational design of monodisperse ferroelectric nanocrystals with controlled size and shape and their organization into hierarchical structures has been a critical step for understanding the polar ordering in nanoscale ferroelectrics, as well as the design of nanocrystal-based functional materials which harness the properties of individual nanoparticles and the collective interactions between them. We report here on the synthesis and self-assembly of aggregate-free, single-crystalline titanium-based perovskite nanoparticles with controlled morphology and surface composition by using a simple, easily scalable and highly versatile colloidal route. Single-crystalline, non-aggregated BaTiO3 colloidal nanocrystals, used as a model system, have been prepared under solvothermal conditions at temperatures as low as 180 °C. The shape of the nanocrystals was tuned from spheroidal to cubic upon changing the polarity of the solvent, whereas their size was varied from 16 to 30 nm for spheres and 5 to 78 nm for cubes by changing the concentration of the precursors and the reaction time, respectively. The hydrophobic, oleic acid-passivated nanoparticles exhibit very good solubility in non-polar solvents and can be rendered dispersible in polar solvents by a simple process involving the oxidative cleavage of the double bond upon treating the nanopowders with the Lemieux–von Rudloff reagent. Lattice dynamic analysis indicated that regardless of their size, BaTiO3 nanocrystals present local disorder within the perovskite unit cell, associated with the existence of polar ordering. We also demonstrate for the first time that, in addition to being used for fabricating large area, crack-free, highly uniform films, BaTiO3 nanocubes can serve as building blocks for the design of 2D and 3D mesoscale structures, such as superlattices and superparticles. Interestingly, the type of superlattice structure (simple cubic or face centered cubic) appears to be determined by the type of solvent in which the nanocrystals were dispersed. This approach provides an excellent platform for the synthesis of other titanium-based perovskite colloidal nanocrystals with controlled chemical composition, surface structure and morphology and for their assembly into complex architectures, therefore opening the door for the design of novel mesoscale functional materials/nanocomposites with potential applications in energy conversion, data storage and the biomedical field. AU - Caruntu, Daniela AU - Rostamzadeh, Taha AU - Costanzo, Tommaso AU - Salemizadeh Parizi, Saman AU - Caruntu, Gabriel ID - 7456 IS - 30 JF - Nanoscale SN - 2040-3364 TI - Solvothermal synthesis and controlled self-assembly of monodisperse titanium-based perovskite colloidal nanocrystals VL - 7 ER - TY - JOUR AB - A new organic–inorganic ferroelectric hybrid capacitor designed by uniformly incorporating surface modified monodisperse 15 nm ferroelectric BaTiO3 nanocubes into non-polar polymer blends of poly(methyl methacrylate) (PMMA) polymer and acrylonitrile-butadiene-styrene (ABS) terpolymer is described. The investigation of spatial distribution of nanofillers via a non-distractive thermal pulse method illustrates that the surface functionalization of nanocubes plays a key role in the uniform distribution of charge polarization within the polymer matrix. The discharged energy density of the nanocomposite with 30 vol% BaTiO3 nanocubes is ∼44 × 10−3 J cm−3, which is almost six times higher than that of the neat polymer. The facile processing, along with the superior mechanical and electrical properties of the BaTiO3/PMMA–ABS nanocomposites make them suitable for implementation into capacitive electrical energy storage devices. AU - Parizi, Saman Salemizadeh AU - Conley, Gavin AU - Costanzo, Tommaso AU - Howell, Bob AU - Mellinger, Axel AU - Caruntu, Gabriel ID - 7457 IS - 93 JF - RSC Advances SN - 2046-2069 TI - Fabrication of barium titanate/acrylonitrile-butadiene styrene/poly(methyl methacrylate) nanocomposite films for hybrid ferroelectric capacitors VL - 5 ER - TY - JOUR AB - Across-nation differences in the mean values for complex traits are common1,2,3,4,5,6,7,8, but the reasons for these differences are unknown. Here we find that many independent loci contribute to population genetic differences in height and body mass index (BMI) in 9,416 individuals across 14 European countries. Using discovery data on over 250,000 individuals and unbiased effect size estimates from 17,500 sibling pairs, we estimate that 24% (95% credible interval (CI) = 9%, 41%) and 8% (95% CI = 4%, 16%) of the captured additive genetic variance for height and BMI, respectively, reflect population genetic differences. Population genetic divergence differed significantly from that in a null model (height, P < 3.94 × 10−8; BMI, P < 5.95 × 10−4), and we find an among-population genetic correlation for tall and slender individuals (r = −0.80, 95% CI = −0.95, −0.60), consistent with correlated selection for both phenotypes. Observed differences in height among populations reflected the predicted genetic means (r = 0.51; P < 0.001), but environmental differences across Europe masked genetic differentiation for BMI (P < 0.58). AU - Robinson, Matthew Richard AU - Hemani, Gibran AU - Medina-Gomez, Carolina AU - Mezzavilla, Massimo AU - Esko, Tonu AU - Shakhbazov, Konstantin AU - Powell, Joseph E AU - Vinkhuyzen, Anna AU - Berndt, Sonja I AU - Gustafsson, Stefan AU - Justice, Anne E AU - Kahali, Bratati AU - Locke, Adam E AU - Pers, Tune H AU - Vedantam, Sailaja AU - Wood, Andrew R AU - van Rheenen, Wouter AU - Andreassen, Ole A AU - Gasparini, Paolo AU - Metspalu, Andres AU - Berg, Leonard H van den AU - Veldink, Jan H AU - Rivadeneira, Fernando AU - Werge, Thomas M AU - Abecasis, Goncalo R AU - Boomsma, Dorret I AU - Chasman, Daniel I AU - de Geus, Eco J C AU - Frayling, Timothy M AU - Hirschhorn, Joel N AU - Hottenga, Jouke Jan AU - Ingelsson, Erik AU - Loos, Ruth J F AU - Magnusson, Patrik K E AU - Martin, Nicholas G AU - Montgomery, Grant W AU - North, Kari E AU - Pedersen, Nancy L AU - Spector, Timothy D AU - Speliotes, Elizabeth K AU - Goddard, Michael E AU - Yang, Jian AU - Visscher, Peter M ID - 7742 IS - 11 JF - Nature Genetics SN - 1061-4036 TI - Population genetic differentiation of height and body mass index across Europe VL - 47 ER -