@article{8198, abstract = {We investigate how the critical driving amplitude at the Floquet many-body localized (MBL) to ergodic phase transition differs between smooth and nonsmooth drives. To this end, we numerically study a disordered spin-1/2 chain which is periodically driven by a sine or square-wave drive over a wide range of driving frequencies. In both cases the critical driving amplitude increases monotonically with the frequency, and at large frequencies it is identical for the two drives. However, at low and intermediate frequencies the critical amplitude of the square-wave drive depends strongly on the frequency, while that of the sinusoidal drive is almost constant over a wide frequency range. By analyzing the density of drive-induced resonances we conclude that this difference is due to resonances induced by the higher harmonics which are present (absent) in the Fourier spectrum of the square-wave (sine) drive. Furthermore, we suggest a numerically efficient method for estimating the frequency dependence of the critical driving amplitudes for different drives which is based on calculating the density of drive-induced resonances. We conclude that delocalization occurs once the density of drive-induced resonances reaches a critical value determined only by the static system.}, author = {Diringer, Asaf A. and Gulden, Tobias}, issn = {24699969}, journal = {Physical Review B}, number = {21}, publisher = {American Physical Society}, title = {{Impact of drive harmonics on the stability of Floquet many-body localization}}, doi = {10.1103/PhysRevB.103.214204}, volume = {103}, 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{8286, abstract = {We consider the following dynamic load-balancing process: given an underlying graph G with n nodes, in each step t≥ 0, one unit of load is created, and placed at a randomly chosen graph node. In the same step, the chosen node picks a random neighbor, and the two nodes balance their loads by averaging them. We are interested in the expected gap between the minimum and maximum loads at nodes as the process progresses, and its dependence on n and on the graph structure. Variants of the above graphical balanced allocation process have been studied previously by Peres, Talwar, and Wieder [Peres et al., 2015], and by Sauerwald and Sun [Sauerwald and Sun, 2015]. These authors left as open the question of characterizing the gap in the case of cycle graphs in the dynamic case, where weights are created during the algorithm’s execution. For this case, the only known upper bound is of 𝒪(n log n), following from a majorization argument due to [Peres et al., 2015], which analyzes a related graphical allocation process. In this paper, we provide an upper bound of 𝒪 (√n log n) on the expected gap of the above process for cycles of length n. We introduce a new potential analysis technique, which enables us to bound the difference in load between k-hop neighbors on the cycle, for any k ≤ n/2. We complement this with a "gap covering" argument, which bounds the maximum value of the gap by bounding its value across all possible subsets of a certain structure, and recursively bounding the gaps within each subset. We provide analytical and experimental evidence that our upper bound on the gap is tight up to a logarithmic factor. }, author = {Alistarh, Dan-Adrian and Nadiradze, Giorgi and Sabour, Amirmojtaba}, issn = {1432-0541}, journal = {Algorithmica}, location = {Virtual, Online; Germany}, publisher = {Springer Nature}, title = {{Dynamic averaging load balancing on cycles}}, doi = {10.1007/s00453-021-00905-9}, year = {2021}, } @article{8317, abstract = {When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.}, author = {Aichholzer, Oswin and Akitaya, Hugo A. and Cheung, Kenneth C. and Demaine, Erik D. and Demaine, Martin L. and Fekete, Sándor P. and Kleist, Linda and Kostitsyna, Irina and Löffler, Maarten and Masárová, Zuzana and Mundilova, Klara and Schmidt, Christiane}, issn = {09257721}, journal = {Computational Geometry: Theory and Applications}, publisher = {Elsevier}, title = {{Folding polyominoes with holes into a cube}}, doi = {10.1016/j.comgeo.2020.101700}, volume = {93}, 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{8430, abstract = {While recent advancements in computation and modelling have improved the analysis of complex traits, our understanding of the genetic basis of the time at symptom onset remains limited. Here, we develop a Bayesian approach (BayesW) that provides probabilistic inference of the genetic architecture of age-at-onset phenotypes in a sampling scheme that facilitates biobank-scale time-to-event analyses. We show in extensive simulation work the benefits BayesW provides in terms of number of discoveries, model performance and genomic prediction. In the UK Biobank, we find many thousands of common genomic regions underlying the age-at-onset of high blood pressure (HBP), cardiac disease (CAD), and type-2 diabetes (T2D), and for the genetic basis of onset reflecting the underlying genetic liability to disease. Age-at-menopause and age-at-menarche are also highly polygenic, but with higher variance contributed by low frequency variants. Genomic prediction into the Estonian Biobank data shows that BayesW gives higher prediction accuracy than other approaches.}, author = {Ojavee, Sven E and Kousathanas, Athanasios and Trejo Banos, Daniel and Orliac, Etienne J and Patxot, Marion and Lall, Kristi and Magi, Reedik and Fischer, Krista and Kutalik, Zoltan and Robinson, Matthew Richard}, issn = {20411723}, journal = {Nature Communications}, number = {1}, publisher = {Nature Research}, title = {{Genomic architecture and prediction of censored time-to-event phenotypes with a Bayesian genome-wide analysis}}, doi = {10.1038/s41467-021-22538-w}, 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}, } @article{8546, abstract = {Brain neurons arise from relatively few progenitors generating an enormous diversity of neuronal types. Nonetheless, a cardinal feature of mammalian brain neurogenesis is thought to be that excitatory and inhibitory neurons derive from separate, spatially segregated progenitors. Whether bi-potential progenitors with an intrinsic capacity to generate both lineages exist and how such a fate decision may be regulated are unknown. Using cerebellar development as a model, we discover that individual progenitors can give rise to both inhibitory and excitatory lineages. Gradations of Notch activity determine the fates of the progenitors and their daughters. Daughters with the highest levels of Notch activity retain the progenitor fate, while intermediate levels of Notch activity generate inhibitory neurons, and daughters with very low levels of Notch signaling adopt the excitatory fate. Therefore, Notch-mediated binary cell fate choice is a mechanism for regulating the ratio of excitatory to inhibitory neurons from common progenitors.}, author = {Zhang, Tingting and Liu, Tengyuan and Mora, Natalia and Guegan, Justine and Bertrand, Mathilde and Contreras, Ximena and Hansen, Andi H and Streicher, Carmen and Anderle, Marica and Danda, Natasha and Tiberi, Luca and Hippenmeyer, Simon and Hassan, Bassem A.}, issn = { 22111247}, journal = {Cell Reports}, number = {10}, publisher = {Elsevier}, title = {{Generation of excitatory and inhibitory neurons from common progenitors via Notch signaling in the cerebellum}}, doi = {10.1016/j.celrep.2021.109208}, volume = {35}, year = {2021}, } @article{8582, abstract = {Cell and tissue polarization is fundamental for plant growth and morphogenesis. The polar, cellular localization of Arabidopsis PIN‐FORMED (PIN) proteins is crucial for their function in directional auxin transport. The clustering of PIN polar cargoes within the plasma membrane has been proposed to be important for the maintenance of their polar distribution. However, the more detailed features of PIN clusters and the cellular requirements of cargo clustering remain unclear. Here, we characterized PIN clusters in detail by means of multiple advanced microscopy and quantification methods, such as 3D quantitative imaging or freeze‐fracture replica labeling. The size and aggregation types of PIN clusters were determined by electron microscopy at the nanometer level at different polar domains and at different developmental stages, revealing a strong preference for clustering at the polar domains. Pharmacological and genetic studies revealed that PIN clusters depend on phosphoinositol pathways, cytoskeletal structures and specific cell‐wall components as well as connections between the cell wall and the plasma membrane. This study identifies the role of different cellular processes and structures in polar cargo clustering and provides initial mechanistic insight into the maintenance of polarity in plants and other systems.}, author = {Li, Hongjiang and von Wangenheim, Daniel and Zhang, Xixi and Tan, Shutang and Darwish-Miranda, Nasser and Naramoto, Satoshi and Wabnik, Krzysztof T and de Rycke, Riet and Kaufmann, Walter and Gütl, Daniel J and Tejos, Ricardo and Grones, Peter and Ke, Meiyu and Chen, Xu and Dettmer, Jan and Friml, Jiří}, issn = {14698137}, journal = {New Phytologist}, number = {1}, pages = {351--369}, publisher = {Wiley}, title = {{Cellular requirements for PIN polar cargo clustering in Arabidopsis thaliana}}, doi = {10.1111/nph.16887}, volume = {229}, year = {2021}, } @article{8601, abstract = {We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble.}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {14322064}, journal = {Probability Theory and Related Fields}, publisher = {Springer Nature}, title = {{Edge universality for non-Hermitian random matrices}}, doi = {10.1007/s00440-020-01003-7}, year = {2021}, } @article{8602, abstract = {Collective cell migration offers a rich field of study for non-equilibrium physics and cellular biology, revealing phenomena such as glassy dynamics, pattern formation and active turbulence. However, how mechanical and chemical signalling are integrated at the cellular level to give rise to such collective behaviours remains unclear. We address this by focusing on the highly conserved phenomenon of spatiotemporal waves of density and extracellular signal-regulated kinase (ERK) activation, which appear both in vitro and in vivo during collective cell migration and wound healing. First, we propose a biophysical theory, backed by mechanical and optogenetic perturbation experiments, showing that patterns can be quantitatively explained by a mechanochemical coupling between active cellular tensions and the mechanosensitive ERK pathway. Next, we demonstrate how this biophysical mechanism can robustly induce long-ranged order and migration in a desired orientation, and we determine the theoretically optimal wavelength and period for inducing maximal migration towards free edges, which fits well with experimentally observed dynamics. We thereby provide a bridge between the biophysical origin of spatiotemporal instabilities and the design principles of robust and efficient long-ranged migration.}, author = {Boocock, Daniel R and Hino, Naoya and Ruzickova, Natalia and Hirashima, Tsuyoshi and Hannezo, Edouard B}, issn = {17452481}, journal = {Nature Physics}, pages = {267--274}, publisher = {Springer Nature}, title = {{Theory of mechanochemical patterning and optimal migration in cell monolayers}}, doi = {10.1038/s41567-020-01037-7}, volume = {17}, year = {2021}, } @article{8603, abstract = {We consider the Fröhlich polaron model in the strong coupling limit. It is well‐known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we establish the subleading correction, describing quantum fluctuation about the classical limit. Our proof applies to a model of a confined polaron, where both the electron and the polarization field are restricted to a set of finite volume, with linear size determined by the natural length scale of the Pekar problem.}, author = {Frank, Rupert and Seiringer, Robert}, issn = {10970312}, journal = {Communications on Pure and Applied Mathematics}, number = {3}, pages = {544--588}, publisher = {Wiley}, title = {{Quantum corrections to the Pekar asymptotics of a strongly coupled polaron}}, doi = {10.1002/cpa.21944}, volume = {74}, year = {2021}, } @article{8606, abstract = {The leaf is a crucial organ evolved with remarkable morphological diversity to maximize plant photosynthesis. The leaf shape is a key trait that affects photosynthesis, flowering rates, disease resistance, and yield. Although many genes regulating leaf development have been identified in the past years, the precise regulatory architecture underlying the generation of diverse leaf shapes remains to be elucidated. We used cotton as a reference model to probe the genetic framework underlying divergent leaf forms. Comparative transcriptome analysis revealed that the GhARF16‐1 and GhKNOX2‐1 genes might be potential regulators of leaf shape. We functionally characterized the auxin‐responsive factor ARF16‐1 acting upstream of GhKNOX2‐1 to determine leaf morphology in cotton. The transcription of GhARF16‐1 was significantly higher in lobed‐leaved cotton than in smooth‐leaved cotton. Furthermore, the overexpression of GhARF16‐1 led to the upregulation of GhKNOX2‐1 and resulted in more and deeper serrations in cotton leaves, similar to the leaf shape of cotton plants overexpressing GhKNOX2‐1. We found that GhARF16‐1 specifically bound to the promoter of GhKNOX2‐1 to induce its expression. The heterologous expression of GhARF16‐1 and GhKNOX2‐1 in Arabidopsis led to lobed and curly leaves, and a genetic analysis revealed that GhKNOX2‐1 is epistatic to GhARF16‐1 in Arabidopsis, suggesting that the GhARF16‐1 and GhKNOX2‐1 interaction paradigm also functions to regulate leaf shape in Arabidopsis. To our knowledge, our results uncover a novel mechanism by which auxin, through the key component ARF16‐1 and its downstream‐activated gene KNOX2‐1, determines leaf morphology in eudicots.}, author = {He, P and Zhang, Yuzhou and Li, H and Fu, X and Shang, H and Zou, C and Friml, Jiří and Xiao, G}, issn = {1467-7644}, journal = {Plant Biotechnology Journal}, number = {3}, pages = {548--562}, publisher = {Wiley}, title = {{GhARF16-1 modulates leaf development by transcriptionally regulating the GhKNOX2-1 gene in cotton}}, doi = {10.1111/pbi.13484}, volume = {19}, year = {2021}, } @article{8608, abstract = {To adapt to the diverse array of biotic and abiotic cues, plants have evolved sophisticated mechanisms to sense changes in environmental conditions and modulate their growth. Growth-promoting hormones and defence signalling fine tune plant development antagonistically. During host-pathogen interactions, this defence-growth trade-off is mediated by the counteractive effects of the defence hormone salicylic acid (SA) and the growth hormone auxin. Here we revealed an underlying mechanism of SA regulating auxin signalling by constraining the plasma membrane dynamics of PIN2 auxin efflux transporter in Arabidopsis thaliana roots. The lateral diffusion of PIN2 proteins is constrained by SA signalling, during which PIN2 proteins are condensed into hyperclusters depending on REM1.2-mediated nanodomain compartmentalisation. Furthermore, membrane nanodomain compartmentalisation by SA or Remorin (REM) assembly significantly suppressed clathrin-mediated endocytosis. Consequently, SA-induced heterogeneous surface condensation disrupted asymmetric auxin distribution and the resultant gravitropic response. Our results demonstrated a defence-growth trade-off mechanism by which SA signalling crosstalked with auxin transport by concentrating membrane-resident PIN2 into heterogeneous compartments.}, author = {Ke, M and Ma, Z and Wang, D and Sun, Y and Wen, C and Huang, D and Chen, Z and Yang, L and Tan, Shutang and Li, R and Friml, Jiří and Miao, Y and Chen, X}, issn = {1469-8137}, journal = {New Phytologist}, number = {2}, pages = {963--978}, publisher = {Wiley}, title = {{Salicylic acid regulates PIN2 auxin transporter hyper-clustering and root gravitropic growth via Remorin-dependent lipid nanodomain organization in Arabidopsis thaliana}}, doi = {10.1111/nph.16915}, volume = {229}, year = {2021}, } @article{8673, abstract = {In RuCl3, inelastic neutron scattering and Raman spectroscopy reveal a continuum of non-spin-wave excitations that persists to high temperature, suggesting the presence of a spin liquid state on a honeycomb lattice. In the context of the Kitaev model, finite magnetic fields introduce interactions between the elementary excitations, and thus the effects of high magnetic fields that are comparable to the spin-exchange energy scale must be explored. Here, we report measurements of the magnetotropic coefficient—the thermodynamic coefficient associated with magnetic anisotropy—over a wide range of magnetic fields and temperatures. We find that magnetic field and temperature compete to determine the magnetic response in a way that is independent of the large intrinsic exchange-interaction energy. This emergent scale-invariant magnetic anisotropy provides evidence for a high degree of exchange frustration that favours the formation of a spin liquid state in RuCl3.}, author = {Modic, Kimberly A and McDonald, Ross D. and Ruff, J.P.C. and Bachmann, Maja D. and Lai, You and Palmstrom, Johanna C. and Graf, David and Chan, Mun K. and Balakirev, F.F. and Betts, J.B. and Boebinger, G.S. and Schmidt, Marcus and Lawler, Michael J. and Sokolov, D.A. and Moll, Philip J.W. and Ramshaw, B.J. and Shekhter, Arkady}, issn = {17452481}, journal = {Nature Physics}, pages = {240--244}, publisher = {Springer Nature}, title = {{Scale-invariant magnetic anisotropy in RuCl3 at high magnetic fields}}, doi = {10.1038/s41567-020-1028-0}, volume = {17}, year = {2021}, } @article{8689, abstract = {This paper continues the discussion started in [CK19] concerning Arnold's legacy on classical KAM theory and (some of) its modern developments. We prove a detailed and explicit `global' Arnold's KAM Theorem, which yields, in particular, the Whitney conjugacy of a non{degenerate, real{analytic, nearly-integrable Hamiltonian system to an integrable system on a closed, nowhere dense, positive measure subset of the phase space. Detailed measure estimates on the Kolmogorov's set are provided in the case the phase space is: (A) a uniform neighbourhood of an arbitrary (bounded) set times the d-torus and (B) a domain with C2 boundary times the d-torus. All constants are explicitly given.}, author = {Chierchia, Luigi and Koudjinan, Edmond}, issn = {1560-3547}, journal = {Regular and Chaotic Dynamics}, keywords = {Nearly{integrable Hamiltonian systems, perturbation theory, KAM Theory, Arnold's scheme, Kolmogorov's set, primary invariant tori, Lagrangian tori, measure estimates, small divisors, integrability on nowhere dense sets, Diophantine frequencies.}, number = {1}, pages = {61--88}, publisher = {Springer Nature}, title = {{V.I. Arnold's ''Global'' KAM theorem and geometric measure estimates}}, doi = {10.1134/S1560354721010044}, volume = {26}, year = {2021}, } @article{8708, abstract = {The Mytilus complex of marine mussel species forms a mosaic of hybrid zones, found across temperate regions of the globe. This allows us to study ‘replicated’ instances of secondary contact between closely related species. Previous work on this complex has shown that local introgression is both widespread and highly heterogeneous, and has identified SNPs that are outliers of differentiation between lineages. Here, we developed an ancestry‐informative panel of such SNPs. We then compared their frequencies in newly sampled populations, including samples from within the hybrid zones, and parental populations at different distances from the contact. Results show that close to the hybrid zones, some outlier loci are near to fixation for the heterospecific allele, suggesting enhanced local introgression, or the local sweep of a shared ancestral allele. Conversely, genomic cline analyses, treating local parental populations as the reference, reveal a globally high concordance among loci, albeit with a few signals of asymmetric introgression. Enhanced local introgression at specific loci is consistent with the early transfer of adaptive variants after contact, possibly including asymmetric bi‐stable variants (Dobzhansky‐Muller incompatibilities), or haplotypes loaded with fewer deleterious mutations. Having escaped one barrier, however, these variants can be trapped or delayed at the next barrier, confining the introgression locally. These results shed light on the decay of species barriers during phases of contact.}, author = {Simon, Alexis and Fraisse, Christelle and El Ayari, Tahani and Liautard‐Haag, Cathy and Strelkov, Petr and Welch, John J and Bierne, Nicolas}, issn = {14209101}, journal = {Journal of Evolutionary Biology}, number = {1}, pages = {208--223}, publisher = {Wiley}, title = {{How do species barriers decay? Concordance and local introgression in mosaic hybrid zones of mussels}}, doi = {10.1111/jeb.13709}, volume = {34}, year = {2021}, }