@article{17585, abstract = {Recent gravitational wave (GW) observations by LIGO/Virgo show evidence for hierarchical mergers, where the merging BHs are the remnants of previous BH merger events. These events may carry important clues about the astrophysical host environments of the GW sources. In this paper, we present the distributions of the effective spin parameter (χeff), the precession spin parameter (χp), and the chirp mass (mchirp) expected in hierarchical mergers. Under a wide range of assumptions, hierarchical mergers produce (i) a monotonic increase of the average of the typical total spin for merging binaries, which we characterize with χ¯typ≡(χ2eff+χ2p)1/2¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯, up to roughly the maximum mchirp among first-generation (1g) BHs, and (ii) a plateau at χ¯typ∼0.6 at higher mchirp. We suggest that the maximum mass and typical spin magnitudes for 1g BHs can be estimated from χ¯typ as a function of mchirp. The GW data observed in LIGO/Virgo O1--O3a prefers an increase in χ¯typ at low mchirp, which is consistent with the growth of the BH spin magnitude by hierarchical mergers, at ∼2σ confidence. A Bayesian analysis suggests that 1g BHs have the maximum mass of ∼15--30M⊙ if the majority of mergers are of high-generation BHs (not among 1g-1g BHs), which is consistent with mergers in active galactic nucleus disks and/or nuclear star clusters, while if mergers mainly originate from globular clusters, 1g BHs are favored to have non-zero spin magnitudes of ∼0.3. We also forecast that signatures for hierarchical mergers in the χ¯typ distribution can be confidently recovered once the number of GW events increases to ≳O(100).}, author = {Tagawa, Hiromichi and Haiman, Zoltán and Bartos, Imre and Kocsis, Bence and Omukai, Kazuyuki}, issn = {0035-8711}, journal = {Monthly Notices of the Royal Astronomical Society}, number = {3}, pages = {3362--3380}, publisher = {Oxford University Press}, title = {{Signatures of hierarchical mergers in black hole spin and mass distribution}}, doi = {10.1093/mnras/stab2315}, volume = {507}, year = {2021}, } @article{17586, abstract = {Variable active galactic nuclei showing periodic light curves have been proposed as massive black hole binary (MBHB) candidates. In such scenarios, the periodicity can be due to relativistic Doppler-boosting of the emitted light. This hypothesis can be tested through the timing of scattered polarized light. Following the results of polarization studies in type I nuclei and of dynamical studies of MBHBs with circumbinary discs, we assume a coplanar equatorial scattering ring, whose elements contribute differently to the total polarized flux, due to different scattering angles, levels of Doppler boost, and line-of-sight time delays. We find that in the presence of an MBHB, both the degree of polarization and the polarization position angle have periodic modulations. The polarization angle oscillates around the semiminor axis of the projected MBHB orbital ellipse, with a frequency equal either to the binary’s orbital frequency (for large scattering screen radii), or twice this value (for smaller scattering structures). These distinctive features can be used to probe the nature of periodic MBHB candidates and to compile catalogues of the most promising sub-pc MBHBs. The identification of such polarization features in gravitational-wave (GW) detected MBHBs would enormously increase the amount of physical information about the sources, allowing the measurement of the individual masses of the binary components, and the orientation of the line of nodes on the sky, even for monochromatic GW signals.}, author = {Dotti, Massimo and Bonetti, Matteo and D’Orazio, Daniel J and Haiman, Zoltán and Ho, Luis C}, issn = {0035-8711}, journal = {Monthly Notices of the Royal Astronomical Society}, number = {1}, pages = {212--223}, publisher = {Oxford University Press}, title = {{Binary black hole signatures in polarized light curves}}, doi = {10.1093/mnras/stab2893}, volume = {509}, year = {2021}, } @article{17589, abstract = {The origin of the black hole mergers detected by LIGO and Virgo remains an open question. While the unusual mass and spin of a few events constrain their possible astrophysical formation mechanisms, it is difficult to classify the bulk of the observed mergers. Here we consider the distribution of masses and spins in LIGO/Virgo's first and second observing catalogs, and find that for a significant fraction (25%) of these detected events, an AGN-disk origin model is preferred over a parametric mass-spin model fit to the full GWTC-2 merger sample (Bayes factor B>10). We use this to estimate the black hole merger rate in AGNs to be about 2.8±1.8\, Gpc−3yr−1, comparable to theoretical expectations. We find that AGNs can explain the rate and mass distribution of the observed events with primary black hole mass in the pair-instability mass gap (M≳50\, M⊙).}, author = {Gayathri, V. and Yang, Y. and Tagawa, H. and Haiman, Zoltán and Bartos, I.}, issn = {2041-8205}, journal = {The Astrophysical Journal Letters}, number = {2}, publisher = {American Astronomical Society}, title = {{Black hole mergers of AGN origin in LIGO–Virgo’s O1–O3a observing periods}}, doi = {10.3847/2041-8213/ac2cc1}, volume = {920}, year = {2021}, } @article{17592, abstract = {Using high-resolution hydrodynamics simulations, we show that equal-mass binaries accreting from a circumbinary disk evolve toward an orbital eccentricity of e ≃ 0.45, unless they are initialized on a nearly circular orbit with e ≲ 0.08, in which case they further circularize. The implied bi-modal eccentricity distribution resembles that seen in post-AGB stellar binaries. Large accretion spikes around periapse impart a tell-tale, quasiperiodic, bursty signature on the light curves of eccentric binaries. We predict that intermediate-mass and massive black hole binaries at z ≲ 10 entering the LISA band will have measurable eccentricities in the range of e ≃ 10−3 − 10−2, if they have experienced a gas-driven phase. On the other hand, GW190521 would have entered the LIGO/Virgo band with undetectable eccentricity ∼10−6 if it had been driven into the gravitational-wave regime by a gas disk.}, author = {Zrake, Jonathan and Tiede, Christopher and MacFadyen, Andrew and Haiman, Zoltán}, issn = {2041-8213}, journal = {The Astrophysical Journal Letters}, number = {1}, publisher = {American Astronomical Society}, title = {{Equilibrium eccentricity of accreting binaries}}, doi = {10.3847/2041-8213/abdd1c}, volume = {909}, year = {2021}, } @article{17593, abstract = {The science objectives of the LISA mission have been defined under the implicit assumption of a 4-years continuous data stream. Based on the performance of LISA Pathfinder, it is now expected that LISA will have a duty cycle of ≈0.75 , which would reduce the effective span of usable data to 3 years. This paper reports the results of a study by the LISA Science Group, which was charged with assessing the additional science return of increasing the mission lifetime. We explore various observational scenarios to assess the impact of mission duration on the main science objectives of the mission. We find that the science investigations most affected by mission duration concern the search for seed black holes at cosmic dawn, as well as the study of stellar-origin black holes and of their formation channels via multi-band and multi-messenger observations. We conclude that an extension to 6 years of mission operations is recommended.}, author = {Amaro Seoane, Pau and Arca Sedda, Manuel and Babak, Stanislav and Berry, Christopher P. L. and Berti, Emanuele and Bertone, Gianfranco and Blas, Diego and Bogdanović, Tamara and Bonetti, Matteo and Breivik, Katelyn and Brito, Richard and Caldwell, Robert and Capelo, Pedro R. and Caprini, Chiara and Cardoso, Vitor and Carson, Zack and Chen, Hsin-Yu and Chua, Alvin J. K. and Dvorkin, Irina and Haiman, Zoltán and Heisenberg, Lavinia and Isi, Maximiliano and Karnesis, Nikolaos and Kavanagh, Bradley J. and Littenberg, Tyson B. and Mangiagli, Alberto and Marcoccia, Paolo and Maselli, Andrea and Nardini, Germano and Pani, Paolo and Peloso, Marco and Pieroni, Mauro and Ricciardone, Angelo and Sesana, Alberto and Tamanini, Nicola and Toubiana, Alexandre and Valiante, Rosa and Vretinaris, Stamatis and Weir, David J. and Yagi, Kent and Zimmerman, Aaron}, issn = {0001-7701}, journal = {General Relativity and Gravitation}, number = {1}, publisher = {Springer Science and Business Media LLC}, title = {{The effect of mission duration on LISA science objectives}}, doi = {10.1007/s10714-021-02889-x}, volume = {54}, year = {2021}, } @article{17598, abstract = {The successive discoveries of binary merger events by Advanced LIGO-Virgo have been revealing the statistical properties of binary black hole (BBH) populations. A stochastic gravitational wave background (GWB) is a useful tool to probe the cosmological evolution of those compact mergers. In this paper, we study the upper bound on a GWB produced by BBH mergers, whose stellar progenitors dominate the reionization process at the cosmic dawn. Since early reionization by those progenitors yields a high optical depth of the universe inconsistent with the {\it Planck} measurements, the cumulative mass density is limited to ρ⋆≲107 M⊙ Mpc−3. Even with this upper bound, the amplitude of a GWB owing to the high-z BBH mergers is expected to be as high as Ωgw≃1.48+1.80−1.27×10−9 at f≃25 Hz, while their merger rate at the present-day is consistent or lower than the observed GW event rate. This level of GWB is detectable at the design sensitivity of Advanced LIGO-Virgo and would indicate a major contribution of the high-z BBH population to the local GW events. The spectral index is expected to be substantially flatter than the canonical value of ≃2/3 generically produced by lower-redshift and less massive BBHs. Moreover, if their mass function is more top-heavy than in the local universe, the GWB spectrum is even more skewed toward lower frequencies, which would allow us to extract information on the mass function of merging BBHs at high redshifts.}, author = {Inayoshi, Kohei and Kashiyama, Kazumi and Visbal, Eli and Haiman, Zoltán}, issn = {0004-637X}, journal = {The Astrophysical Journal}, number = {1}, publisher = {American Astronomical Society}, title = {{Gravitational wave backgrounds from coalescing black hole binaries at cosmic dawn: An upper bound}}, doi = {10.3847/1538-4357/ac106d}, volume = {919}, year = {2021}, } @article{17610, abstract = {The presence of massive black holes (BHs) with masses of order 109M⊙, powering bright quasars when the Universe was less than 1 Gyr old, poses strong constraints on their formation mechanism. Several scenarios have been proposed to date to explain massive BH formation, from the low-mass seed BH remnants of the first generation of stars to the massive seed BHs resulting from the rapid collapse of massive gas clouds. However, the plausibility of some of these scenarios to occur within the progenitors of high-z quasars has not yet been thoroughly explored. In this work, we investigate, by combining dark-matter only N-body simulations with a semi-analytic framework, whether the conditions for the formation of massive seed BHs from synchronised atomic-cooling halo pairs and/or dynamically-heated mini-haloes are fulfilled in the overdense regions where the progenitors of a typical high-redshift quasar host form and evolve. Our analysis shows that the peculiar conditions in such regions, i.e. strong halo clustering and high star formation rates, are crucial to produce a non-negligible number of massive seed BH host candidates: we find ≈1400 dynamically heated metal-free mini-haloes, including one of these which evolves to a synchronised pair and ends up in the massive quasar-host halo by z=6. This demonstrates that the progenitors of high-redshift quasar host haloes can harbour early massive seed BHs. Our results further suggest that multiple massive seed BHs may form in or near the quasar host's progenitors, potentially merging at lower redshifts and yielding gravitational wave events.}, author = {Lupi, Alessandro and Haiman, Zoltán and Volonteri, Marta}, issn = {0035-8711}, journal = {Monthly Notices of the Royal Astronomical Society}, number = {4}, pages = {5046--5060}, publisher = {Oxford University Press}, title = {{Forming massive seed black holes in high-redshift quasar host progenitors}}, doi = {10.1093/mnras/stab692}, volume = {503}, year = {2021}, } @article{7685, abstract = {We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.}, author = {Boccato, Chiara}, issn = {0129-055X}, journal = {Reviews in Mathematical Physics}, number = {1}, publisher = {World Scientific Publishing}, title = {{The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime}}, doi = {10.1142/S0129055X20600065}, volume = {33}, year = {2021}, } @article{7900, abstract = {Hartree–Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic approximation, deriving an effective Hamiltonian. We then show that for systems with Coulomb interaction this effective theory predicts collective excitations (plasmons) in accordance with the random phase approximation of Bohm and Pines, and with experimental observation.}, author = {Benedikter, Niels P}, issn = {1793-6659}, journal = {Reviews in Mathematical Physics}, number = {1}, publisher = {World Scientific Publishing}, title = {{Bosonic collective excitations in Fermi gases}}, doi = {10.1142/s0129055x20600090}, volume = {33}, year = {2021}, } @article{7901, abstract = {We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree–Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.}, author = {Benedikter, Niels P and Nam, Phan Thành and Porta, Marcello and Schlein, Benjamin and Seiringer, Robert}, issn = {1432-1297}, journal = {Inventiones Mathematicae}, pages = {885--979}, publisher = {Springer}, title = {{Correlation energy of a weakly interacting Fermi gas}}, doi = {10.1007/s00222-021-01041-5}, volume = {225}, year = {2021}, } @article{7905, abstract = {We investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a partially ordered set with the Alexandroff topology. We prove that the resulting decomposition is the unique minimal stratification for which the strata are homogeneous and the given sheaf is constructible. In particular, when we choose to work with the local homology sheaf, our algorithm gives an alternative to the local homology transfer algorithm given in Bendich et al. (Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1355–1370, ACM, New York, 2012), and the cohomology stratification algorithm given in Nanda (Found. Comput. Math. 20(2), 195–222, 2020). Additionally, we give examples of stratifications based on the geometric techniques of Breiding et al. (Rev. Mat. Complut. 31(3), 545–593, 2018), illustrating how the sheaf-theoretic approach can be used to study stratifications from both topological and geometric perspectives. This approach also points toward future applications of sheaf theory in the study of topological data analysis by illustrating the utility of the language of sheaf theory in generalizing existing algorithms.}, author = {Brown, Adam and Wang, Bei}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {1166--1198}, publisher = {Springer Nature}, title = {{Sheaf-theoretic stratification learning from geometric and topological perspectives}}, doi = {10.1007/s00454-020-00206-y}, volume = {65}, year = {2021}, } @article{7925, abstract = {In this paper, we introduce a relaxed CQ method with alternated inertial step for solving split feasibility problems. We give convergence of the sequence generated by our method under some suitable assumptions. Some numerical implementations from sparse signal and image deblurring are reported to show the efficiency of our method.}, author = {Shehu, Yekini and Gibali, Aviv}, issn = {1862-4480}, journal = {Optimization Letters}, pages = {2109--2126}, publisher = {Springer Nature}, title = {{New inertial relaxed method for solving split feasibilities}}, doi = {10.1007/s11590-020-01603-1}, volume = {15}, year = {2021}, } @inbook{7941, abstract = {Expansion microscopy is a recently developed super-resolution imaging technique, which provides an alternative to optics-based methods such as deterministic approaches (e.g. STED) or stochastic approaches (e.g. PALM/STORM). The idea behind expansion microscopy is to embed the biological sample in a swellable gel, and then to expand it isotropically, thereby increasing the distance between the fluorophores. This approach breaks the diffraction barrier by simply separating the emission point-spread-functions of the fluorophores. The resolution attainable in expansion microscopy is thus directly dependent on the separation that can be achieved, i.e. on the expansion factor. The original implementation of the technique achieved an expansion factor of fourfold, for a resolution of 70–80 nm. The subsequently developed X10 method achieves an expansion factor of 10-fold, for a resolution of 25–30 nm. This technique can be implemented with minimal technical requirements on any standard fluorescence microscope, and is more easily applied for multi-color imaging than either deterministic or stochastic super-resolution approaches. This renders X10 expansion microscopy a highly promising tool for new biological discoveries, as discussed here, and as demonstrated by several recent applications.}, author = {Truckenbrodt, Sven M and Rizzoli, Silvio O.}, booktitle = {Methods in Cell Biology}, isbn = {978012820807-6}, issn = {0091-679X}, pages = {33--56}, publisher = {Elsevier}, title = {{Simple multi-color super-resolution by X10 microscopy}}, doi = {10.1016/bs.mcb.2020.04.016}, volume = {161}, year = {2021}, } @article{8196, abstract = {This paper aims to obtain a strong convergence result for a Douglas–Rachford splitting method with inertial extrapolation step for finding a zero of the sum of two set-valued maximal monotone operators without any further assumption of uniform monotonicity on any of the involved maximal monotone operators. Furthermore, our proposed method is easy to implement and the inertial factor in our proposed method is a natural choice. Our method of proof is of independent interest. Finally, some numerical implementations are given to confirm the theoretical analysis.}, author = {Shehu, Yekini and Dong, Qiao-Li and Liu, Lu-Lu and Yao, Jen-Chih}, issn = {1573-2924}, journal = {Optimization and Engineering}, pages = {2627--2653}, publisher = {Springer Nature}, title = {{New strong convergence method for the sum of two maximal monotone operators}}, doi = {10.1007/s11081-020-09544-5}, volume = {22}, year = {2021}, } @article{8248, abstract = {We consider the following setting: suppose that we are given a manifold M in Rd with positive reach. Moreover assume that we have an embedded simplical complex A without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in A have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then A is a triangulation of the manifold, that is, they are homeomorphic.}, author = {Boissonnat, Jean-Daniel and Dyer, Ramsay and Ghosh, Arijit and Lieutier, Andre and Wintraecken, Mathijs}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {666--686}, publisher = {Springer Nature}, title = {{Local conditions for triangulating submanifolds of Euclidean space}}, doi = {10.1007/s00454-020-00233-9}, volume = {66}, year = {2021}, } @article{8253, abstract = {Brains process information in spiking neural networks. Their intricate connections shape the diverse functions these networks perform. In comparison, the functional capabilities of models of spiking networks are still rudimentary. This shortcoming is mainly due to the lack of insight and practical algorithms to construct the necessary connectivity. Any such algorithm typically attempts to build networks by iteratively reducing the error compared to a desired output. But assigning credit to hidden units in multi-layered spiking networks has remained challenging due to the non-differentiable nonlinearity of spikes. To avoid this issue, one can employ surrogate gradients to discover the required connectivity in spiking network models. However, the choice of a surrogate is not unique, raising the question of how its implementation influences the effectiveness of the method. Here, we use numerical simulations to systematically study how essential design parameters of surrogate gradients impact learning performance on a range of classification problems. We show that surrogate gradient learning is robust to different shapes of underlying surrogate derivatives, but the choice of the derivative’s scale can substantially affect learning performance. When we combine surrogate gradients with a suitable activity regularization technique, robust information processing can be achieved in spiking networks even at the sparse activity limit. Our study provides a systematic account of the remarkable robustness of surrogate gradient learning and serves as a practical guide to model functional spiking neural networks.}, author = {Zenke, Friedemann and Vogels, Tim P}, issn = {1530-888X}, journal = {Neural Computation}, number = {4}, pages = {899--925}, publisher = {MIT Press}, title = {{The remarkable robustness of surrogate gradient learning for instilling complex function in spiking neural networks}}, doi = {10.1162/neco_a_01367}, volume = {33}, year = {2021}, } @article{8338, abstract = {Canonical parametrisations of classical confocal coordinate systems are introduced and exploited to construct non-planar analogues of incircular (IC) nets on individual quadrics and systems of confocal quadrics. Intimate connections with classical deformations of quadrics that are isometric along asymptotic lines and circular cross-sections of quadrics are revealed. The existence of octahedral webs of surfaces of Blaschke type generated by asymptotic and characteristic lines that are diagonally related to lines of curvature is proved theoretically and established constructively. Appropriate samplings (grids) of these webs lead to three-dimensional extensions of non-planar IC nets. Three-dimensional octahedral grids composed of planes and spatially extending (checkerboard) IC-nets are shown to arise in connection with systems of confocal quadrics in Minkowski space. In this context, the Laguerre geometric notion of conical octahedral grids of planes is introduced. The latter generalise the octahedral grids derived from systems of confocal quadrics in Minkowski space. An explicit construction of conical octahedral grids is presented. The results are accompanied by various illustrations which are based on the explicit formulae provided by the theory.}, author = {Akopyan, Arseniy and Bobenko, Alexander I. and Schief, Wolfgang K. and Techter, Jan}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, pages = {938--976}, publisher = {Springer Nature}, title = {{On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs}}, doi = {10.1007/s00454-020-00240-w}, volume = {66}, year = {2021}, } @article{8373, abstract = {It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted A#H-mean introduced by Kim, Lawson, and Lim.}, author = {Pitrik, József and Virosztek, Daniel}, issn = {0024-3795}, journal = {Linear Algebra and its Applications}, keywords = {Kubo-Ando mean, weighted multivariate mean, barycenter}, pages = {203--217}, publisher = {Elsevier}, title = {{A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means}}, doi = {10.1016/j.laa.2020.09.007}, volume = {609}, year = {2021}, } @article{8429, abstract = {We develop a Bayesian model (BayesRR-RC) that provides robust SNP-heritability estimation, an alternative to marker discovery, and accurate genomic prediction, taking 22 seconds per iteration to estimate 8.4 million SNP-effects and 78 SNP-heritability parameters in the UK Biobank. We find that only ≤10% of the genetic variation captured for height, body mass index, cardiovascular disease, and type 2 diabetes is attributable to proximal regulatory regions within 10kb upstream of genes, while 12-25% is attributed to coding regions, 32–44% to introns, and 22-28% to distal 10-500kb upstream regions. Up to 24% of all cis and coding regions of each chromosome are associated with each trait, with over 3,100 independent exonic and intronic regions and over 5,400 independent regulatory regions having ≥95% probability of contributing ≥0.001% to the genetic variance of these four traits. Our open-source software (GMRM) provides a scalable alternative to current approaches for biobank data.}, author = {Patxot, Marion and Trejo Banos, Daniel and Kousathanas, Athanasios and Orliac, Etienne J and Ojavee, Sven E and Moser, Gerhard and Sidorenko, Julia and Kutalik, Zoltan and Magi, Reedik and Visscher, Peter M and Ronnegard, Lars and Robinson, Matthew Richard}, issn = {2041-1723}, journal = {Nature Communications}, number = {1}, publisher = {Springer Nature}, title = {{Probabilistic inference of the genetic architecture underlying functional enrichment of complex traits}}, doi = {10.1038/s41467-021-27258-9}, volume = {12}, year = {2021}, } @article{8544, abstract = {The synaptotrophic hypothesis posits that synapse formation stabilizes dendritic branches, yet this hypothesis has not been causally tested in vivo in the mammalian brain. Presynaptic ligand cerebellin-1 (Cbln1) and postsynaptic receptor GluD2 mediate synaptogenesis between granule cells and Purkinje cells in the molecular layer of the cerebellar cortex. Here we show that sparse but not global knockout of GluD2 causes under-elaboration of Purkinje cell dendrites in the deep molecular layer and overelaboration in the superficial molecular layer. Developmental, overexpression, structure-function, and genetic epistasis analyses indicate that dendrite morphogenesis defects result from competitive synaptogenesis in a Cbln1/GluD2-dependent manner. A generative model of dendritic growth based on competitive synaptogenesis largely recapitulates GluD2 sparse and global knockout phenotypes. Our results support the synaptotrophic hypothesis at initial stages of dendrite development, suggest a second mode in which cumulative synapse formation inhibits further dendrite growth, and highlight the importance of competition in dendrite morphogenesis.}, author = {Takeo, Yukari H. and Shuster, S. Andrew and Jiang, Linnie and Hu, Miley and Luginbuhl, David J. and Rülicke, Thomas and Contreras, Ximena and Hippenmeyer, Simon and Wagner, Mark J. and Ganguli, Surya and Luo, Liqun}, issn = {1097-4199}, journal = {Neuron}, number = {4}, pages = {P629--644.E8}, publisher = {Elsevier}, title = {{GluD2- and Cbln1-mediated competitive synaptogenesis shapes the dendritic arbors of cerebellar Purkinje cells}}, doi = {10.1016/j.neuron.2020.11.028}, volume = {109}, year = {2021}, }