@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}, } @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 = {1469-8137}, 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{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 = {1097-0312}, 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 = {1467-7652}, 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 = {1745-2481}, 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 = {1420-9101}, 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}, } @article{8723, abstract = {Deep learning at scale is dominated by communication time. Distributing samples across nodes usually yields the best performance, but poses scaling challenges due to global information dissemination and load imbalance across uneven sample lengths. State-of-the-art decentralized optimizers mitigate the problem, but require more iterations to achieve the same accuracy as their globally-communicating counterparts. We present Wait-Avoiding Group Model Averaging (WAGMA) SGD, a wait-avoiding stochastic optimizer that reduces global communication via subgroup weight exchange. The key insight is a combination of algorithmic changes to the averaging scheme and the use of a group allreduce operation. We prove the convergence of WAGMA-SGD, and empirically show that it retains convergence rates similar to Allreduce-SGD. For evaluation, we train ResNet-50 on ImageNet; Transformer for machine translation; and deep reinforcement learning for navigation at scale. Compared with state-of-the-art decentralized SGD variants, WAGMA-SGD significantly improves training throughput (e.g., 2.1× on 1,024 GPUs for reinforcement learning), and achieves the fastest time-to-solution (e.g., the highest score using the shortest training time for Transformer).}, author = {Li, Shigang and Tal Ben-Nun, Tal Ben-Nun and Nadiradze, Giorgi and Girolamo, Salvatore Di and Dryden, Nikoli and Alistarh, Dan-Adrian and Hoefler, Torsten}, issn = {1045-9219}, journal = {IEEE Transactions on Parallel and Distributed Systems}, number = {7}, publisher = {IEEE}, title = {{Breaking (global) barriers in parallel stochastic optimization with wait-avoiding group averaging}}, doi = {10.1109/TPDS.2020.3040606}, volume = {32}, year = {2021}, } @article{8730, abstract = {P-glycoprotein (ABCB1) and breast cancer resistance protein (ABCG2) restrict at the blood–brain barrier (BBB) the brain distribution of the majority of currently known molecularly targeted anticancer drugs. To improve brain delivery of dual ABCB1/ABCG2 substrates, both ABCB1 and ABCG2 need to be inhibited simultaneously at the BBB. We examined the feasibility of simultaneous ABCB1/ABCG2 inhibition with i.v. co-infusion of erlotinib and tariquidar by studying brain distribution of the model ABCB1/ABCG2 substrate [11C]erlotinib in mice and rhesus macaques with PET. Tolerability of the erlotinib/tariquidar combination was assessed in human embryonic stem cell-derived cerebral organoids. In mice and macaques, baseline brain distribution of [11C]erlotinib was low (brain distribution volume, VT,brain < 0.3 mL/cm3). Co-infusion of erlotinib and tariquidar increased VT,brain in mice by 3.0-fold and in macaques by 3.4- to 5.0-fold, while infusion of erlotinib alone or tariquidar alone led to less pronounced VT,brain increases in both species. Treatment of cerebral organoids with erlotinib/tariquidar led to an induction of Caspase-3-dependent apoptosis. Co-infusion of erlotinib/tariquidar may potentially allow for complete ABCB1/ABCG2 inhibition at the BBB, while simultaneously achieving brain-targeted EGFR inhibition. Our protocol may be applicable to enhance brain delivery of molecularly targeted anticancer drugs for a more effective treatment of brain tumors.}, author = {Tournier, N and Goutal, S and Mairinger, S and Lozano, IH and Filip, T and Sauberer, M and Caillé, F and Breuil, L and Stanek, J and Freeman, AF and Novarino, Gaia and Truillet, C and Wanek, T and Langer, O}, issn = {1559-7016}, journal = {Journal of Cerebral Blood Flow and Metabolism}, number = {7}, pages = {1634--1646}, publisher = {SAGE Publications}, title = {{Complete inhibition of ABCB1 and ABCG2 at the blood-brain barrier by co-infusion of erlotinib and tariquidar to improve brain delivery of the model ABCB1/ABCG2 substrate [11C]erlotinib}}, doi = {10.1177/0271678X20965500}, volume = {41}, year = {2021}, } @article{8742, abstract = {We develop a version of Ekedahl’s geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to compute the density of coprime values of polynomials, and furthermore, to address a question about local solubility in families of varieties parameterised by the zeros.}, author = {Browning, Timothy D and Heath-Brown, Roger}, issn = {1435-5337}, journal = {Forum Mathematicum}, number = {1}, pages = {147--165}, publisher = {De Gruyter}, title = {{The geometric sieve for quadrics}}, doi = {10.1515/forum-2020-0074}, volume = {33}, year = {2021}, } @article{8743, abstract = {Montane cloud forests are areas of high endemism, and are one of the more vulnerable terrestrial ecosystems to climate change. Thus, understanding how they both contribute to the generation of biodiversity, and will respond to ongoing climate change, are important and related challenges. The widely accepted model for montane cloud forest dynamics involves upslope forcing of their range limits with global climate warming. However, limited climate data provides some support for an alternative model, where range limits are forced downslope with climate warming. Testing between these two models is challenging, due to the inherent limitations of climate and pollen records. We overcome this with an alternative source of historical information, testing between competing model predictions using genomic data and demographic analyses for a species of beetle tightly associated to an oceanic island cloud forest. Results unequivocally support the alternative model: populations that were isolated at higher elevation peaks during the Last Glacial Maximum are now in contact and hybridizing at lower elevations. Our results suggest that genomic data are a rich source of information to further understand how montane cloud forest biodiversity originates, and how it is likely to be impacted by ongoing climate change.}, author = {Salces-Castellano, Antonia and Stankowski, Sean and Arribas, Paula and Patino, Jairo and Karger, Dirk N. and Butlin, Roger and Emerson, Brent C.}, issn = {1558-5646}, journal = {Evolution}, number = {2}, pages = {231--244}, publisher = {Wiley}, title = {{Long-term cloud forest response to climate warming revealed by insect speciation history}}, doi = {10.1111/evo.14111}, volume = {75}, year = {2021}, } @article{8757, abstract = {Traditional scientific conferences and seminar events have been hugely disrupted by the COVID-19 pandemic, paving the way for virtual forms of scientific communication to take hold and be put to the test.}, author = {Bozelos, Panagiotis and Vogels, Tim P}, issn = {1471-0048}, journal = {Nature Reviews Neuroscience}, number = {1}, pages = {1--2}, publisher = {Springer Nature}, title = {{Talking science, online}}, doi = {10.1038/s41583-020-00408-6}, volume = {22}, year = {2021}, } @article{8773, abstract = {Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell.}, author = {Brown, Adam and Romanov, Anna}, issn = {1088-6826}, journal = {Proceedings of the American Mathematical Society}, keywords = {Applied Mathematics, General Mathematics}, number = {1}, pages = {37--52}, publisher = {American Mathematical Society}, title = {{Contravariant forms on Whittaker modules}}, doi = {10.1090/proc/15205}, volume = {149}, year = {2021}, } @article{8792, abstract = {This paper is concerned with a non-isothermal Cahn-Hilliard model based on a microforce balance. The model was derived by A. Miranville and G. Schimperna starting from the two fundamental laws of Thermodynamics, following M. Gurtin's two-scale approach. The main working assumptions are made on the behaviour of the heat flux as the absolute temperature tends to zero and to infinity. A suitable Ginzburg-Landau free energy is considered. Global-in-time existence for the initial-boundary value problem associated to the entropy formulation and, in a subcase, also to the weak formulation of the model is proved by deriving suitable a priori estimates and by showing weak sequential stability of families of approximating solutions. At last, some highlights are given regarding a possible approximation scheme compatible with the a-priori estimates available for the system.}, author = {Marveggio, Alice and Schimperna, Giulio}, issn = {1090-2732}, journal = {Journal of Differential Equations}, number = {2}, pages = {924--970}, publisher = {Elsevier}, title = {{On a non-isothermal Cahn-Hilliard model based on a microforce balance}}, doi = {10.1016/j.jde.2020.10.030}, volume = {274}, year = {2021}, } @article{8816, abstract = {Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.}, author = {Runkel, Ingo and Szegedy, Lorant}, issn = {1432-0916}, journal = {Communications in Mathematical Physics}, number = {1}, pages = {83–117}, publisher = {Springer Nature}, title = {{Area-dependent quantum field theory}}, doi = {10.1007/s00220-020-03902-1}, volume = {381}, year = {2021}, }