@article{8163, abstract = {Fejes Tóth [3] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the square of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We refute this claim, and show that the asymptotic behavior of the Hausdorff distance is linear, that is the same as for convex surfaces.}, author = {Vegter, Gert and Wintraecken, Mathijs}, issn = {1588-2896}, journal = {Studia Scientiarum Mathematicarum Hungarica}, number = {2}, pages = {193--199}, publisher = {Akadémiai Kiadó}, title = {{Refutation of a claim made by Fejes Tóth on the accuracy of surface meshes}}, doi = {10.1556/012.2020.57.2.1454}, volume = {57}, year = {2020}, } @article{8671, abstract = {We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempsterchr('39')s multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory. We also demonstrate that one can induce a natural belief structure on one set, given a belief structure on another set, if the two sets are related by a partial monotone S-approximation space. }, author = {Shakiba, A. and Goharshady, Amir Kafshdar and Hooshmandasl, M.R. and Alambardar Meybodi, M.}, issn = {2008-9473}, journal = {Iranian Journal of Mathematical Sciences and Informatics}, number = {2}, pages = {117--128}, publisher = {Iranian Academic Center for Education, Culture and Research}, title = {{A note on belief structures and s-approximation spaces}}, doi = {10.29252/ijmsi.15.2.117}, volume = {15}, year = {2020}, } @article{6359, abstract = {The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of α-Hölder drift in the recent literature the rate α/2 was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to 1/2 for all α>0. The result extends to Dini continuous coefficients, while in d=1 also to all bounded measurable coefficients.}, author = {Dareiotis, Konstantinos and Gerencser, Mate}, issn = {1083-6489}, journal = {Electronic Journal of Probability}, publisher = {Institute of Mathematical Statistics}, title = {{On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift}}, doi = {10.1214/20-EJP479}, volume = {25}, year = {2020}, } @phdthesis{8390, abstract = {Deep neural networks have established a new standard for data-dependent feature extraction pipelines in the Computer Vision literature. Despite their remarkable performance in the standard supervised learning scenario, i.e. when models are trained with labeled data and tested on samples that follow a similar distribution, neural networks have been shown to struggle with more advanced generalization abilities, such as transferring knowledge across visually different domains, or generalizing to new unseen combinations of known concepts. In this thesis we argue that, in contrast to the usual black-box behavior of neural networks, leveraging more structured internal representations is a promising direction for tackling such problems. In particular, we focus on two forms of structure. First, we tackle modularity: We show that (i) compositional architectures are a natural tool for modeling reasoning tasks, in that they efficiently capture their combinatorial nature, which is key for generalizing beyond the compositions seen during training. We investigate how to to learn such models, both formally and experimentally, for the task of abstract visual reasoning. Then, we show that (ii) in some settings, modularity allows us to efficiently break down complex tasks into smaller, easier, modules, thereby improving computational efficiency; We study this behavior in the context of generative models for colorization, as well as for small objects detection. Secondly, we investigate the inherently layered structure of representations learned by neural networks, and analyze its role in the context of transfer learning and domain adaptation across visually dissimilar domains. }, author = {Royer, Amélie}, isbn = {978-3-99078-007-7}, issn = {2663-337X}, pages = {197}, publisher = {Institute of Science and Technology Austria}, title = {{Leveraging structure in Computer Vision tasks for flexible Deep Learning models}}, doi = {10.15479/AT:ISTA:8390}, year = {2020}, } @inproceedings{8186, abstract = {Numerous methods have been proposed for probabilistic generative modelling of 3D objects. However, none of these is able to produce textured objects, which renders them of limited use for practical tasks. In this work, we present the first generative model of textured 3D meshes. Training such a model would traditionally require a large dataset of textured meshes, but unfortunately, existing datasets of meshes lack detailed textures. We instead propose a new training methodology that allows learning from collections of 2D images without any 3D information. To do so, we train our model to explain a distribution of images by modelling each image as a 3D foreground object placed in front of a 2D background. Thus, it learns to generate meshes that when rendered, produce images similar to those in its training set. A well-known problem when generating meshes with deep networks is the emergence of self-intersections, which are problematic for many use-cases. As a second contribution we therefore introduce a new generation process for 3D meshes that guarantees no self-intersections arise, based on the physical intuition that faces should push one another out of the way as they move. We conduct extensive experiments on our approach, reporting quantitative and qualitative results on both synthetic data and natural images. These show our method successfully learns to generate plausible and diverse textured 3D samples for five challenging object classes.}, author = {Henderson, Paul M and Tsiminaki, Vagia and Lampert, Christoph}, booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition}, issn = {2575-7075}, location = {Virtual}, pages = {7498--7507}, publisher = {IEEE}, title = {{Leveraging 2D data to learn textured 3D mesh generation}}, doi = {10.1109/CVPR42600.2020.00752}, year = {2020}, } @article{7416, abstract = {Earlier, we demonstrated that transcript levels of METAL TOLERANCE PROTEIN2 (MTP2) and of HEAVY METAL ATPase2 (HMA2) increase strongly in roots of Arabidopsis upon prolonged zinc (Zn) deficiency and respond to shoot physiological Zn status, and not to the local Zn status in roots. This provided evidence for shoot-to-root communication in the acclimation of plants to Zn deficiency. Zn-deficient soils limit both the yield and quality of agricultural crops and can result in clinically relevant nutritional Zn deficiency in human populations. Implementing Zn deficiency during cultivation of the model plant Arabidopsis thaliana on agar-solidified media is difficult because trace element contaminations are present in almost all commercially available agars. Here, we demonstrate root morphological acclimations to Zn deficiency on agar-solidified medium following the effective removal of contaminants. These advancements allow reproducible phenotyping toward understanding fundamental plant responses to deficiencies of Zn and other essential trace elements.}, author = {Sinclair, Scott A and Krämer, U.}, issn = {1559-2324}, journal = {Plant Signaling & Behavior}, number = {1}, publisher = {Taylor & Francis}, title = {{Generation of effective zinc-deficient agar-solidified media allows identification of root morphology changes in response to zinc limitation}}, doi = {10.1080/15592324.2019.1687175}, volume = {15}, year = {2020}, } @article{7464, abstract = {Retrovirus assembly is driven by the multidomain structural protein Gag. Interactions between the capsid domains (CA) of Gag result in Gag multimerization, leading to an immature virus particle that is formed by a protein lattice based on dimeric, trimeric, and hexameric protein contacts. Among retroviruses the inter- and intra-hexamer contacts differ, especially in the N-terminal sub-domain of CA (CANTD). For HIV-1 the cellular molecule inositol hexakisphosphate (IP6) interacts with and stabilizes the immature hexamer, and is required for production of infectious virus particles. We have used in vitro assembly, cryo-electron tomography and subtomogram averaging, atomistic molecular dynamics simulations and mutational analyses to study the HIV-related lentivirus equine infectious anemia virus (EIAV). In particular, we sought to understand the structural conservation of the immature lentivirus lattice and the role of IP6 in EIAV assembly. Similar to HIV-1, IP6 strongly promoted in vitro assembly of EIAV Gag proteins into virus-like particles (VLPs), which took three morphologically highly distinct forms: narrow tubes, wide tubes, and spheres. Structural characterization of these VLPs to sub-4Å resolution unexpectedly showed that all three morphologies are based on an immature lattice with preserved key structural components, highlighting the structural versatility of CA to form immature assemblies. A direct comparison between EIAV and HIV revealed that both lentiviruses maintain similar immature interfaces, which are established by both conserved and non-conserved residues. In both EIAV and HIV-1, IP6 regulates immature assembly via conserved lysine residues within the CACTD and SP. Lastly, we demonstrate that IP6 stimulates in vitro assembly of immature particles of several other retroviruses in the lentivirus genus, suggesting a conserved role for IP6 in lentiviral assembly.}, author = {Dick, Robert A. and Xu, Chaoyi and Morado, Dustin R. and Kravchuk, Vladyslav and Ricana, Clifton L. and Lyddon, Terri D. and Broad, Arianna M. and Feathers, J. Ryan and Johnson, Marc C. and Vogt, Volker M. and Perilla, Juan R. and Briggs, John A. G. and Schur, Florian KM}, issn = {1553-7374}, journal = {PLOS Pathogens}, number = {1}, publisher = {Public Library of Science}, title = {{Structures of immature EIAV Gag lattices reveal a conserved role for IP6 in lentivirus assembly}}, doi = {10.1371/journal.ppat.1008277}, volume = {16}, year = {2020}, } @article{7212, abstract = {The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation probability of advantageous mutants, compared to well-mixed populations. Extensive studies have shown that many amplifiers exist for the Birth-death Moran process, some of them substantially increasing the fixation probability or even guaranteeing fixation in the limit of large population size. On the other hand, no amplifiers are known for the death-Birth Moran process, and computer-assisted exhaustive searches have failed to discover amplification. In this work we resolve this disparity, by showing that any amplification under death-Birth updating is necessarily bounded and transient. Our boundedness result states that even if a population structure does amplify selection, the resulting fixation probability is close to that of the well-mixed population. Our transience result states that for any population structure there exists a threshold r⋆ such that the population structure ceases to amplify selection if the mutant fitness advantage r is larger than r⋆. Finally, we also extend the above results to δ-death-Birth updating, which is a combination of Birth-death and death-Birth updating. On the positive side, we identify population structures that maintain amplification for a wide range of values r and δ. These results demonstrate that amplification of natural selection depends on the specific mechanisms of the evolutionary process.}, author = {Tkadlec, Josef and Pavlogiannis, Andreas and Chatterjee, Krishnendu and Nowak, Martin A.}, issn = {15537358}, journal = {PLoS computational biology}, publisher = {Public Library of Science}, title = {{Limits on amplifiers of natural selection under death-Birth updating}}, doi = {10.1371/journal.pcbi.1007494}, volume = {16}, year = {2020}, } @phdthesis{7196, abstract = {In this thesis we study certain mathematical aspects of evolution. The two primary forces that drive an evolutionary process are mutation and selection. Mutation generates new variants in a population. Selection chooses among the variants depending on the reproductive rates of individuals. Evolutionary processes are intrinsically random – a new mutation that is initially present in the population at low frequency can go extinct, even if it confers a reproductive advantage. The overall rate of evolution is largely determined by two quantities: the probability that an invading advantageous mutation spreads through the population (called fixation probability) and the time until it does so (called fixation time). Both those quantities crucially depend not only on the strength of the invading mutation but also on the population structure. In this thesis, we aim to understand how the underlying population structure affects the overall rate of evolution. Specifically, we study population structures that increase the fixation probability of advantageous mutants (called amplifiers of selection). Broadly speaking, our results are of three different types: We present various strong amplifiers, we identify regimes under which only limited amplification is feasible, and we propose population structures that provide different tradeoffs between high fixation probability and short fixation time.}, author = {Tkadlec, Josef}, issn = {2663-337X}, pages = {144}, publisher = {Institute of Science and Technology Austria}, title = {{A role of graphs in evolutionary processes}}, doi = {10.15479/AT:ISTA:7196}, year = {2020}, } @inproceedings{9198, abstract = {The optimization of multilayer neural networks typically leads to a solution with zero training error, yet the landscape can exhibit spurious local minima and the minima can be disconnected. In this paper, we shed light on this phenomenon: we show that the combination of stochastic gradient descent (SGD) and over-parameterization makes the landscape of multilayer neural networks approximately connected and thus more favorable to optimization. More specifically, we prove that SGD solutions are connected via a piecewise linear path, and the increase in loss along this path vanishes as the number of neurons grows large. This result is a consequence of the fact that the parameters found by SGD are increasingly dropout stable as the network becomes wider. We show that, if we remove part of the neurons (and suitably rescale the remaining ones), the change in loss is independent of the total number of neurons, and it depends only on how many neurons are left. Our results exhibit a mild dependence on the input dimension: they are dimension-free for two-layer networks and depend linearly on the dimension for multilayer networks. We validate our theoretical findings with numerical experiments for different architectures and classification tasks.}, author = {Shevchenko, Alexander and Mondelli, Marco}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {8773--8784}, publisher = {ML Research Press}, title = {{Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks}}, volume = {119}, year = {2020}, } @article{9157, abstract = {Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy.}, author = {Akopyan, Arseniy and Edelsbrunner, Herbert}, issn = {2544-7297}, journal = {Computational and Mathematical Biophysics}, number = {1}, pages = {51--67}, publisher = {De Gruyter}, title = {{The weighted mean curvature derivative of a space-filling diagram}}, doi = {10.1515/cmb-2020-0100}, volume = {8}, year = {2020}, } @article{9156, abstract = {The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.}, author = {Akopyan, Arseniy and Edelsbrunner, Herbert}, issn = {2544-7297}, journal = {Computational and Mathematical Biophysics}, number = {1}, pages = {74--88}, publisher = {De Gruyter}, title = {{The weighted Gaussian curvature derivative of a space-filling diagram}}, doi = {10.1515/cmb-2020-0101}, volume = {8}, year = {2020}, } @article{8973, abstract = {We consider the symmetric simple exclusion process in Zd with quenched bounded dynamic random conductances and prove its hydrodynamic limit in path space. The main tool is the connection, due to the self-duality of the process, between the invariance principle for single particles starting from all points and the macroscopic behavior of the density field. While the hydrodynamic limit at fixed macroscopic times is obtained via a generalization to the time-inhomogeneous context of the strategy introduced in [41], in order to prove tightness for the sequence of empirical density fields we develop a new criterion based on the notion of uniform conditional stochastic continuity, following [50]. In conclusion, we show that uniform elliptic dynamic conductances provide an example of environments in which the so-called arbitrary starting point invariance principle may be derived from the invariance principle of a single particle starting from the origin. Therefore, our hydrodynamics result applies to the examples of quenched environments considered in, e.g., [1], [3], [6] in combination with the hypothesis of uniform ellipticity.}, author = {Redig, Frank and Saada, Ellen and Sau, Federico}, issn = {1083-6489}, journal = {Electronic Journal of Probability}, publisher = { Institute of Mathematical Statistics}, title = {{Symmetric simple exclusion process in dynamic environment: Hydrodynamics}}, doi = {10.1214/20-EJP536}, volume = {25}, year = {2020}, } @article{179, abstract = {An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface x1y21+⋯+x4y24=0 in ℙ3×ℙ3. This confirms the modified Manin conjecture for this variety, in which the removal of a thin set of rational points is allowed.}, author = {Browning, Timothy D and Heath Brown, Roger}, issn = {0012-7094}, journal = {Duke Mathematical Journal}, number = {16}, pages = {3099--3165}, publisher = {Duke University Press}, title = {{Density of rational points on a quadric bundle in ℙ3×ℙ3}}, doi = {10.1215/00127094-2020-0031}, volume = {169}, year = {2020}, } @misc{9814, abstract = {Data and mathematica notebooks for plotting figures from Language learning with communication between learners}, author = {Ibsen-Jensen, Rasmus and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin}, publisher = {Royal Society}, title = {{Data and mathematica notebooks for plotting figures from language learning with communication between learners from language acquisition with communication between learners}}, doi = {10.6084/m9.figshare.5973013.v1}, year = {2020}, } @article{8285, abstract = {We demonstrate the utility of optical cavity generated spin-squeezed states in free space atomic fountain clocks in ensembles of 390 000 87Rb atoms. Fluorescence imaging, correlated to an initial quantum nondemolition measurement, is used for population spectroscopy after the atoms are released from a confining lattice. For a free fall time of 4 milliseconds, we resolve a single-shot phase sensitivity of 814(61) microradians, which is 5.8(0.6) decibels (dB) below the quantum projection limit. We observe that this squeezing is preserved as the cloud expands to a roughly 200  μm radius and falls roughly 300  μm in free space. Ramsey spectroscopy with 240 000 atoms at a 3.6 ms Ramsey time results in a single-shot fractional frequency stability of 8.4(0.2)×10−12, 3.8(0.2) dB below the quantum projection limit. The sensitivity and stability are limited by the technical noise in the fluorescence detection protocol and the microwave system, respectively.}, author = {Malia, Benjamin K. and Martínez-Rincón, Julián and Wu, Yunfan and Hosten, Onur and Kasevich, Mark A.}, issn = {1079-7114}, journal = {Physical Review Letters}, number = {4}, publisher = {American Physical Society}, title = {{Free space Ramsey spectroscopy in rubidium with noise below the quantum projection limit}}, doi = {10.1103/PhysRevLett.125.043202}, volume = {125}, year = {2020}, } @inproceedings{9633, abstract = {The search for biologically faithful synaptic plasticity rules has resulted in a large body of models. They are usually inspired by – and fitted to – experimental data, but they rarely produce neural dynamics that serve complex functions. These failures suggest that current plasticity models are still under-constrained by existing data. Here, we present an alternative approach that uses meta-learning to discover plausible synaptic plasticity rules. Instead of experimental data, the rules are constrained by the functions they implement and the structure they are meant to produce. Briefly, we parameterize synaptic plasticity rules by a Volterra expansion and then use supervised learning methods (gradient descent or evolutionary strategies) to minimize a problem-dependent loss function that quantifies how effectively a candidate plasticity rule transforms an initially random network into one with the desired function. We first validate our approach by re-discovering previously described plasticity rules, starting at the single-neuron level and “Oja’s rule”, a simple Hebbian plasticity rule that captures the direction of most variability of inputs to a neuron (i.e., the first principal component). We expand the problem to the network level and ask the framework to find Oja’s rule together with an anti-Hebbian rule such that an initially random two-layer firing-rate network will recover several principal components of the input space after learning. Next, we move to networks of integrate-and-fire neurons with plastic inhibitory afferents. We train for rules that achieve a target firing rate by countering tuned excitation. Our algorithm discovers a specific subset of the manifold of rules that can solve this task. Our work is a proof of principle of an automated and unbiased approach to unveil synaptic plasticity rules that obey biological constraints and can solve complex functions.}, author = {Confavreux, Basile J and Zenke, Friedemann and Agnes, Everton J. and Lillicrap, Timothy and Vogels, Tim P}, booktitle = {Advances in Neural Information Processing Systems}, issn = {1049-5258}, location = {Vancouver, Canada}, pages = {16398--16408}, title = {{A meta-learning approach to (re)discover plasticity rules that carve a desired function into a neural network}}, volume = {33}, year = {2020}, } @article{8943, abstract = {The widely used non-steroidal anti-inflammatory drugs (NSAIDs) are derivatives of the phytohormone salicylic acid (SA). SA is well known to regulate plant immunity and development, whereas there have been few reports focusing on the effects of NSAIDs in plants. Our studies here reveal that NSAIDs exhibit largely overlapping physiological activities to SA in the model plant Arabidopsis. NSAID treatments lead to shorter and agravitropic primary roots and inhibited lateral root organogenesis. Notably, in addition to the SA-like action, which in roots involves binding to the protein phosphatase 2A (PP2A), NSAIDs also exhibit PP2A-independent effects. Cell biological and biochemical analyses reveal that many NSAIDs bind directly to and inhibit the chaperone activity of TWISTED DWARF1, thereby regulating actin cytoskeleton dynamics and subsequent endosomal trafficking. Our findings uncover an unexpected bioactivity of human pharmaceuticals in plants and provide insights into the molecular mechanism underlying the cellular action of this class of anti-inflammatory compounds.}, author = {Tan, Shutang and Di Donato, Martin and Glanc, Matous and Zhang, Xixi and Klíma, Petr and Liu, Jie and Bailly, Aurélien and Ferro, Noel and Petrášek, Jan and Geisler, Markus and Friml, Jiří}, issn = {22111247}, journal = {Cell Reports}, number = {9}, publisher = {Elsevier}, title = {{Non-steroidal anti-inflammatory drugs target TWISTED DWARF1-regulated actin dynamics and auxin transport-mediated plant development}}, doi = {10.1016/j.celrep.2020.108463}, volume = {33}, year = {2020}, } @article{7932, abstract = {Pulsating flows through tubular geometries are laminar provided that velocities are moderate. This in particular is also believed to apply to cardiovascular flows where inertial forces are typically too low to sustain turbulence. On the other hand, flow instabilities and fluctuating shear stresses are held responsible for a variety of cardiovascular diseases. Here we report a nonlinear instability mechanism for pulsating pipe flow that gives rise to bursts of turbulence at low flow rates. Geometrical distortions of small, yet finite, amplitude are found to excite a state consisting of helical vortices during flow deceleration. The resulting flow pattern grows rapidly in magnitude, breaks down into turbulence, and eventually returns to laminar when the flow accelerates. This scenario causes shear stress fluctuations and flow reversal during each pulsation cycle. Such unsteady conditions can adversely affect blood vessels and have been shown to promote inflammation and dysfunction of the shear stress-sensitive endothelial cell layer.}, author = {Xu, Duo and Varshney, Atul and Ma, Xingyu and Song, Baofang and Riedl, Michael and Avila, Marc and Hof, Björn}, issn = {10916490}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {21}, pages = {11233--11239}, publisher = {National Academy of Sciences}, title = {{Nonlinear hydrodynamic instability and turbulence in pulsatile flow}}, doi = {10.1073/pnas.1913716117}, volume = {117}, year = {2020}, } @article{14694, abstract = {We study the unique solution m of the Dyson equation \( -m(z)^{-1} = z\1 - a + S[m(z)] \) on a von Neumann algebra A with the constraint Imm≥0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of A and S is a positivity-preserving linear operator on A. We show that m is the Stieltjes transform of a compactly supported A-valued measure on R. Under suitable assumptions, we establish that this measure has a uniformly 1/3-Hölder continuous density with respect to the Lebesgue measure, which is supported on finitely many intervals, called bands. In fact, the density is analytic inside the bands with a square-root growth at the edges and internal cubic root cusps whenever the gap between two bands vanishes. The shape of these singularities is universal and no other singularity may occur. We give a precise asymptotic description of m near the singular points. These asymptotics generalize the analysis at the regular edges given in the companion paper on the Tracy-Widom universality for the edge eigenvalue statistics for correlated random matrices [the first author et al., Ann. Probab. 48, No. 2, 963--1001 (2020; Zbl 1434.60017)] and they play a key role in the proof of the Pearcey universality at the cusp for Wigner-type matrices [G. Cipolloni et al., Pure Appl. Anal. 1, No. 4, 615--707 (2019; Zbl 07142203); the second author et al., Commun. Math. Phys. 378, No. 2, 1203--1278 (2020; Zbl 07236118)]. We also extend the finite dimensional band mass formula from [the first author et al., loc. cit.] to the von Neumann algebra setting by showing that the spectral mass of the bands is topologically rigid under deformations and we conclude that these masses are quantized in some important cases.}, author = {Alt, Johannes and Erdös, László and Krüger, Torben H}, issn = {1431-0643}, journal = {Documenta Mathematica}, keywords = {General Mathematics}, pages = {1421--1539}, publisher = {EMS Press}, title = {{The Dyson equation with linear self-energy: Spectral bands, edges and cusps}}, doi = {10.4171/dm/780}, volume = {25}, year = {2020}, }