@article{14039, abstract = {Membranes are essential for life. They act as semi-permeable boundaries that define cells and organelles. In addition, their surfaces actively participate in biochemical reaction networks, where they confine proteins, align reaction partners, and directly control enzymatic activities. Membrane-localized reactions shape cellular membranes, define the identity of organelles, compartmentalize biochemical processes, and can even be the source of signaling gradients that originate at the plasma membrane and reach into the cytoplasm and nucleus. The membrane surface is, therefore, an essential platform upon which myriad cellular processes are scaffolded. In this review, we summarize our current understanding of the biophysics and biochemistry of membrane-localized reactions with particular focus on insights derived from reconstituted and cellular systems. We discuss how the interplay of cellular factors results in their self-organization, condensation, assembly, and activity, and the emergent properties derived from them.}, author = {Leonard, Thomas A. and Loose, Martin and Martens, Sascha}, issn = {1878-1551}, journal = {Developmental Cell}, number = {15}, pages = {1315--1332}, publisher = {Elsevier}, title = {{The membrane surface as a platform that organizes cellular and biochemical processes}}, doi = {10.1016/j.devcel.2023.06.001}, volume = {58}, year = {2023}, } @article{14040, abstract = {Robust oxygenic photosynthesis requires a suite of accessory factors to ensure efficient assembly and repair of the oxygen-evolving photosystem two (PSII) complex. The highly conserved Ycf48 assembly factor binds to the newly synthesized D1 reaction center polypeptide and promotes the initial steps of PSII assembly, but its binding site is unclear. Here we use cryo-electron microscopy to determine the structure of a cyanobacterial PSII D1/D2 reaction center assembly complex with Ycf48 attached. Ycf48, a 7-bladed beta propeller, binds to the amino-acid residues of D1 that ultimately ligate the water-oxidising Mn4CaO5 cluster, thereby preventing the premature binding of Mn2+ and Ca2+ ions and protecting the site from damage. Interactions with D2 help explain how Ycf48 promotes assembly of the D1/D2 complex. Overall, our work provides valuable insights into the early stages of PSII assembly and the structural changes that create the binding site for the Mn4CaO5 cluster.}, author = {Zhao, Ziyu and Vercellino, Irene and Knoppová, Jana and Sobotka, Roman and Murray, James W. and Nixon, Peter J. and Sazanov, Leonid A and Komenda, Josef}, issn = {2041-1723}, journal = {Nature Communications}, publisher = {Springer Nature}, title = {{The Ycf48 accessory factor occupies the site of the oxygen-evolving manganese cluster during photosystem II biogenesis}}, doi = {10.1038/s41467-023-40388-6}, volume = {14}, year = {2023}, } @inproceedings{13967, abstract = {A classic solution technique for Markov decision processes (MDP) and stochastic games (SG) is value iteration (VI). Due to its good practical performance, this approximative approach is typically preferred over exact techniques, even though no practical bounds on the imprecision of the result could be given until recently. As a consequence, even the most used model checkers could return arbitrarily wrong results. Over the past decade, different works derived stopping criteria, indicating when the precision reaches the desired level, for various settings, in particular MDP with reachability, total reward, and mean payoff, and SG with reachability.In this paper, we provide the first stopping criteria for VI on SG with total reward and mean payoff, yielding the first anytime algorithms in these settings. To this end, we provide the solution in two flavours: First through a reduction to the MDP case and second directly on SG. The former is simpler and automatically utilizes any advances on MDP. The latter allows for more local computations, heading towards better practical efficiency.Our solution unifies the previously mentioned approaches for MDP and SG and their underlying ideas. To achieve this, we isolate objective-specific subroutines as well as identify objective-independent concepts. These structural concepts, while surprisingly simple, form the very essence of the unified solution.}, author = {Kretinsky, Jan and Meggendorfer, Tobias and Weininger, Maximilian}, booktitle = {38th Annual ACM/IEEE Symposium on Logic in Computer Science}, isbn = {9798350335873}, issn = {1043-6871}, location = {Boston, MA, United States}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Stopping criteria for value iteration on stochastic games with quantitative objectives}}, doi = {10.1109/LICS56636.2023.10175771}, volume = {2023}, year = {2023}, } @article{13965, abstract = {Many modes and mechanisms of epigenetic inheritance have been elucidated in eukaryotes. Most of them are relatively short-term, generally not exceeding one or a few organismal generations. However, emerging evidence indicates that one mechanism, cytosine DNA methylation, can mediate epigenetic inheritance over much longer timescales, which are mostly or completely inaccessible in the laboratory. Here we discuss the evidence for, and mechanisms and implications of, such long-term epigenetic inheritance. We argue that compelling evidence supports the long-term epigenetic inheritance of gene body methylation, at least in the model angiosperm Arabidopsis thaliana, and that variation in such methylation can therefore serve as an epigenetic basis for phenotypic variation in natural populations.}, author = {Hollwey, Elizabeth and Briffa, Amy and Howard, Martin and Zilberman, Daniel}, issn = {1879-0380}, journal = {Current Opinion in Genetics and Development}, number = {8}, publisher = {Elsevier}, title = {{Concepts, mechanisms and implications of long-term epigenetic inheritance}}, doi = {10.1016/j.gde.2023.102087}, volume = {81}, year = {2023}, } @phdthesis{14058, abstract = {Females and males across species are subject to divergent selective pressures arising from di↵erent reproductive interests and ecological niches. This often translates into a intricate array of sex-specific natural and sexual selection on traits that have a shared genetic basis between both sexes, causing a genetic sexual conflict. The resolution of this conflict mostly relies on the evolution of sex-specific expression of the shared genes, leading to phenotypic sexual dimorphism. Such sex-specific gene expression is thought to evolve via modifications of the genetic networks ultimately linked to sex-determining transcription factors. Although much empirical and theoretical evidence supports this standard picture of the molecular basis of sexual conflict resolution, there still are a few open questions regarding the complex array of selective forces driving phenotypic di↵erentiation between the sexes, as well as the molecular mechanisms underlying sexspecific adaptation. I address some of these open questions in my PhD thesis. First, how do patterns of phenotypic sexual dimorphism vary within populations, as a response to the temporal and spatial changes in sex-specific selective forces? To tackle this question, I analyze the patterns of sex-specific phenotypic variation along three life stages and across populations spanning the whole geographical range of Rumex hastatulus, a wind-pollinated angiosperm, in the first Chapter of the thesis. Second, how do gene expression patterns lead to phenotypic dimorphism, and what are the molecular mechanisms underlying the observed transcriptomic variation? I address this question by examining the sex- and tissue-specific expression variation in newly-generated datasets of sex-specific expression in heads and gonads of Drosophila melanogaster. I additionally used two complementary approaches for the study of the genetic basis of sex di↵erences in gene expression in the second and third Chapters of the thesis. Third, how does intersex correlation, thought to be one of the main aspects constraining the ability for the two sexes to decouple, interact with the evolution of sexual dimorphism? I develop models of sex-specific stabilizing selection, mutation and drift to formalize common intuition regarding the patterns of covariation between intersex correlation and sexual dimorphism in the fourth Chapter of the thesis. Alltogether, the work described in this PhD thesis provides useful insights into the links between genetic, transcriptomic and phenotypic layers of sex-specific variation, and contributes to our general understanding of the dynamics of sexual dimorphism evolution.}, author = {Puixeu Sala, Gemma}, isbn = {978-3-99078-035-0}, issn = {2663-337X}, pages = {230}, publisher = {Institute of Science and Technology Austria}, title = {{The molecular basis of sexual dimorphism: Experimental and theoretical characterization of phenotypic, transcriptomic and genetic patterns of sex-specific adaptation}}, doi = {10.15479/at:ista:14058}, year = {2023}, } @article{14077, abstract = {The regulatory architecture of gene expression is known to differ substantially between sexes in Drosophila, but most studies performed so far used whole-body data and only single crosses, which may have limited their scope to detect patterns that are robust across tissues and biological replicates. Here, we use allele-specific gene expression of parental and reciprocal hybrid crosses between 6 Drosophila melanogaster inbred lines to quantify cis- and trans-regulatory variation in heads and gonads of both sexes separately across 3 replicate crosses. Our results suggest that female and male heads, as well as ovaries, have a similar regulatory architecture. On the other hand, testes display more and substantially different cis-regulatory effects, suggesting that sex differences in the regulatory architecture that have been previously observed may largely derive from testis-specific effects. We also examine the difference in cis-regulatory variation of genes across different levels of sex bias in gonads and heads. Consistent with the idea that intersex correlations constrain expression and can lead to sexual antagonism, we find more cis variation in unbiased and moderately biased genes in heads. In ovaries, reduced cis variation is observed for male-biased genes, suggesting that cis variants acting on these genes in males do not lead to changes in ovary expression. Finally, we examine the dominance patterns of gene expression and find that sex- and tissue-specific patterns of inheritance as well as trans-regulatory variation are highly variable across biological crosses, although these were performed in highly controlled experimental conditions. This highlights the importance of using various genetic backgrounds to infer generalizable patterns.}, author = {Puixeu Sala, Gemma and Macon, Ariana and Vicoso, Beatriz}, issn = {2160-1836}, journal = {G3: Genes, Genomes, Genetics}, keywords = {Genetics (clinical), Genetics, Molecular Biology}, number = {8}, publisher = {Oxford University Press}, title = {{Sex-specific estimation of cis and trans regulation of gene expression in heads and gonads of Drosophila melanogaster}}, doi = {10.1093/g3journal/jkad121}, volume = {13}, year = {2023}, } @article{14082, abstract = {Epithelial barrier function is commonly analyzed using transepithelial electrical resistance, which measures ion flux across a monolayer, or by adding traceable macromolecules and monitoring their passage across the monolayer. Although these methods measure changes in global barrier function, they lack the sensitivity needed to detect local or transient barrier breaches, and they do not reveal the location of barrier leaks. Therefore, we previously developed a method that we named the zinc-based ultrasensitive microscopic barrier assay (ZnUMBA), which overcomes these limitations, allowing for detection of local tight junction leaks with high spatiotemporal resolution. Here, we present expanded applications for ZnUMBA. ZnUMBA can be used in Xenopus embryos to measure the dynamics of barrier restoration and actin accumulation following laser injury. ZnUMBA can also be effectively utilized in developing zebrafish embryos as well as cultured monolayers of Madin–Darby canine kidney (MDCK) II epithelial cells. ZnUMBA is a powerful and flexible method that, with minimal optimization, can be applied to multiple systems to measure dynamic changes in barrier function with spatiotemporal precision.}, author = {Higashi, Tomohito and Stephenson, Rachel E. and Schwayer, Cornelia and Huljev, Karla and Higashi, Atsuko Y. and Heisenberg, Carl-Philipp J and Chiba, Hideki and Miller, Ann L.}, issn = {1477-9137}, journal = {Journal of Cell Science}, number = {15}, publisher = {The Company of Biologists}, title = {{ZnUMBA - a live imaging method to detect local barrier breaches}}, doi = {10.1242/jcs.260668}, volume = {136}, year = {2023}, } @article{13988, abstract = {Most permissionless blockchains inherently suffer from throughput limitations. Layer-2 systems, such as side-chains or Rollups, have been proposed as a possible strategy to overcome this limitation. Layer-2 systems interact with the main-chain in two ways. First, users can move funds from/to the main-chain to/from the layer-2. Second, layer-2 systems periodically synchronize with the main-chain to keep some form of log of their activity on the main-chain - this log is key for security. Due to this interaction with the main-chain, which is necessary and recurrent, layer-2 systems impose some load on the main-chain. The impact of such load on the main-chain has been, so far, poorly understood. In addition to that, layer-2 approaches typically sacrifice decentralization and security in favor of higher throughput. This paper presents an experimental study that analyzes the current state of Ethereum layer-2 projects. Our goal is to assess the load they impose on Ethereum and to understand their scalability potential in the long-run. Our analysis shows that the impact of any given layer-2 on the main-chain is the result of both technical aspects (how state is logged on the main-chain) and user behavior (how often users decide to transfer funds between the layer-2 and the main-chain). Based on our observations, we infer that without efficient mechanisms that allow users to transfer funds in a secure and fast manner directly from one layer-2 project to another, current layer-2 systems will not be able to scale Ethereum effectively, regardless of their technical solutions. Furthermore, from our results, we conclude that the layer-2 systems that offer similar security guarantees as Ethereum have limited scalability potential, while approaches that offer better performance, sacrifice security and lead to an increase in centralization which runs against the end-goals of permissionless blockchains.}, author = {Neiheiser, Ray and Inacio, Gustavo and Rech, Luciana and Montez, Carlos and Matos, Miguel and Rodrigues, Luis}, issn = {2169-3536}, journal = {IEEE Access}, keywords = {General Engineering, General Materials Science, General Computer Science, Electrical and Electronic Engineering}, pages = {8651--8662}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Practical limitations of Ethereum’s layer-2}}, doi = {10.1109/access.2023.3237897}, volume = {11}, year = {2023}, } @misc{12933, abstract = {Datasets of the publication "Sex-specific estimation of cis and trans regulation of gene expression in heads and gonads of Drosophila melanogaster".}, author = {Puixeu Sala, Gemma}, publisher = {Institute of Science and Technology Austria}, title = {{Data from: Sex-specific estimation of cis and trans regulation of gene expression in heads and gonads of Drosophila melanogaster}}, doi = {10.15479/AT:ISTA:12933}, year = {2023}, } @article{14245, abstract = {We establish effective counting results for lattice points in families of domains in real, complex and quaternionic hyperbolic spaces of any dimension. The domains we focus on are defined as product sets with respect to an Iwasawa decomposition. Several natural diophantine problems can be reduced to counting lattice points in such domains. These include equidistribution of the ratio of the length of the shortest solution (x,y) to the gcd equation bx−ay=1 relative to the length of (a,b), where (a,b) ranges over primitive vectors in a disc whose radius increases, the natural analog of this problem in imaginary quadratic number fields, as well as equidistribution of integral solutions to the diophantine equation defined by an integral Lorentz form in three or more variables. We establish an effective rate of convergence for these equidistribution problems, depending on the size of the spectral gap associated with a suitable lattice subgroup in the isometry group of the relevant hyperbolic space. The main result underlying our discussion amounts to establishing effective joint equidistribution for the horospherical component and the radial component in the Iwasawa decomposition of lattice elements.}, author = {Horesh, Tal and Nevo, Amos}, issn = {1945-5844}, journal = {Pacific Journal of Mathematics}, number = {2}, pages = {265--294}, publisher = {Mathematical Sciences Publishers}, title = {{Horospherical coordinates of lattice points in hyperbolic spaces: Effective counting and equidistribution}}, doi = {10.2140/pjm.2023.324.265}, volume = {324}, year = {2023}, } @article{14246, abstract = {The model of a ring threaded by the Aharonov-Bohm flux underlies our understanding of a coupling between gauge potentials and matter. The typical formulation of the model is based upon a single particle picture, and should be extended when interactions with other particles become relevant. Here, we illustrate such an extension for a particle in an Aharonov-Bohm ring subject to interactions with a weakly interacting Bose gas. We show that the ground state of the system can be described using the Bose-polaron concept—a particle dressed by interactions with a bosonic environment. We connect the energy spectrum to the effective mass of the polaron, and demonstrate how to change currents in the system by tuning boson-particle interactions. Our results suggest the Aharonov-Bohm ring as a platform for studying coherence and few- to many-body crossover of quasi-particles that arise from an impurity immersed in a medium.}, author = {Brauneis, Fabian and Ghazaryan, Areg and Hammer, Hans-Werner and Volosniev, Artem}, issn = {2399-3650}, journal = {Communications Physics}, keywords = {General Physics and Astronomy}, publisher = {Springer Nature}, title = {{Emergence of a Bose polaron in a small ring threaded by the Aharonov-Bohm flux}}, doi = {10.1038/s42005-023-01281-2}, volume = {6}, year = {2023}, } @article{14239, abstract = {Given a resolution of rational singularities π:X~→X over a field of characteristic zero, we use a Hodge-theoretic argument to prove that the image of the functor Rπ∗:Db(X~)→Db(X) between bounded derived categories of coherent sheaves generates Db(X) as a triangulated category. This gives a weak version of the Bondal–Orlov localization conjecture [BO02], answering a question from [PS21]. The same result is established more generally for proper (not necessarily birational) morphisms π:X~→X , with X~ smooth, satisfying Rπ∗(OX~)=OX .}, author = {Mauri, Mirko and Shinder, Evgeny}, issn = {2050-5094}, journal = {Forum of Mathematics, Sigma}, publisher = {Cambridge University Press}, title = {{Homological Bondal-Orlov localization conjecture for rational singularities}}, doi = {10.1017/fms.2023.65}, volume = {11}, year = {2023}, } @article{14192, abstract = {For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the translation invariant Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling.}, author = {Lampart, Jonas and Mitrouskas, David Johannes and Mysliwy, Krzysztof}, issn = {1572-9656}, journal = {Mathematical Physics, Analysis and Geometry}, keywords = {Geometry and Topology, Mathematical Physics}, number = {3}, publisher = {Springer Nature}, title = {{On the global minimum of the energy–momentum relation for the polaron}}, doi = {10.1007/s11040-023-09460-x}, volume = {26}, year = {2023}, } @article{14238, abstract = {We demonstrate that a sodium dimer, Na2(13Σ+u), residing on the surface of a helium nanodroplet, can be set into rotation by a nonresonant 1.0 ps infrared laser pulse. The time-dependent degree of alignment measured, exhibits a periodic, gradually decreasing structure that deviates qualitatively from that expected for gas-phase dimers. Comparison to alignment dynamics calculated from the time-dependent rotational Schrödinger equation shows that the deviation is due to the alignment dependent interaction between the dimer and the droplet surface. This interaction confines the dimer to the tangential plane of the droplet surface at the point where it resides and is the reason that the observed alignment dynamics is also well described by a 2D quantum rotor model.}, author = {Kranabetter, Lorenz and Kristensen, Henrik H. and Ghazaryan, Areg and Schouder, Constant A. and Chatterley, Adam S. and Janssen, Paul and Jensen, Frank and Zillich, Robert E. and Lemeshko, Mikhail and Stapelfeldt, Henrik}, issn = {1079-7114}, journal = {Physical Review Letters}, number = {5}, publisher = {American Physical Society}, title = {{Nonadiabatic laser-induced alignment dynamics of molecules on a surface}}, doi = {10.1103/PhysRevLett.131.053201}, volume = {131}, year = {2023}, } @article{14255, abstract = {Toscana virus is a major cause of arboviral disease in humans in the Mediterranean basin during summer. However, early virus-host cell interactions and entry mechanisms remain poorly characterized. Investigating iPSC-derived human neurons and cell lines, we found that virus binding to the cell surface was specific, and 50% of bound virions were endocytosed within 10 min. Virions entered Rab5a+ early endosomes and, subsequently, Rab7a+ and LAMP-1+ late endosomal compartments. Penetration required intact late endosomes and occurred within 30 min following internalization. Virus entry relied on vacuolar acidification, with an optimal pH for viral membrane fusion at pH 5.5. The pH threshold increased to 5.8 with longer pre-exposure of virions to the slightly acidic pH in early endosomes. Strikingly, the particles remained infectious after entering late endosomes with a pH below the fusion threshold. Overall, our study establishes Toscana virus as a late-penetrating virus and reveals an atypical use of vacuolar acidity by this virus to enter host cells.}, author = {Koch, Jana and Xin, Qilin and Obr, Martin and Schäfer, Alicia and Rolfs, Nina and Anagho, Holda A. and Kudulyte, Aiste and Woltereck, Lea and Kummer, Susann and Campos, Joaquin and Uckeley, Zina M. and Bell-Sakyi, Lesley and Kräusslich, Hans Georg and Schur, Florian Km and Acuna, Claudio and Lozach, Pierre Yves}, issn = {1553-7374}, journal = {PLoS Pathogens}, number = {8}, publisher = {Public Library of Science}, title = {{The phenuivirus Toscana virus makes an atypical use of vacuolar acidity to enter host cells}}, doi = {10.1371/journal.ppat.1011562}, volume = {19}, year = {2023}, } @article{14339, abstract = {Lateral roots are typically maintained at non-vertical angles with respect to gravity. These gravitropic setpoint angles are intriguing because their maintenance requires that roots are able to effect growth response both with and against the gravity vector, a phenomenon previously attributed to gravitropism acting against an antigravitropic offset mechanism. Here we show how the components mediating gravitropism in the vertical primary root—PINs and phosphatases acting upon them—are reconfigured in their regulation such that lateral root growth at a range of angles can be maintained. We show that the ability of Arabidopsis lateral roots to bend both downward and upward requires the generation of auxin asymmetries and is driven by angle-dependent variation in downward gravitropic auxin flux acting against angle-independent upward, antigravitropic flux. Further, we demonstrate a symmetry in auxin distribution in lateral roots at gravitropic setpoint angle that can be traced back to a net, balanced polarization of PIN3 and PIN7 auxin transporters in the columella. These auxin fluxes are shifted by altering PIN protein phosphoregulation in the columella, either by introducing PIN3 phosphovariant versions or via manipulation of levels of the phosphatase subunit PP2A/RCN1. Finally, we show that auxin, in addition to driving lateral root directional growth, acts within the lateral root columella to induce more vertical growth by increasing RCN1 levels, causing a downward shift in PIN3 localization, thereby diminishing the magnitude of the upward, antigravitropic auxin flux.}, author = {Roychoudhry, S and Sageman-Furnas, K and Wolverton, C and Grones, Peter and Tan, Shutang and Molnar, Gergely and De Angelis, M and Goodman, HL and Capstaff, N and JPB, Lloyd and Mullen, J and Hangarter, R and Friml, Jiří and Kepinski, S}, issn = {2055-0278}, journal = {Nature Plants}, pages = {1500--1513}, publisher = {Springer Nature}, title = {{Antigravitropic PIN polarization maintains non-vertical growth in lateral roots}}, doi = {10.1038/s41477-023-01478-x}, volume = {9}, year = {2023}, } @article{14363, abstract = {Mitochondrial networks remodel their connectivity, content, and subcellular localization to support optimized energy production in conditions of increased environmental or cellular stress. Microglia rely on mitochondria to respond to these stressors, however our knowledge about mitochondrial networks and their adaptations in microglia in vivo is limited. Here, we generate a mouse model that selectively labels mitochondria in microglia. We identify that mitochondrial networks are more fragmented with increased content and perinuclear localization in vitro vs. in vivo. Mitochondrial networks adapt similarly in microglia closest to the injury site after optic nerve crush. Preventing microglial UCP2 increase after injury by selective knockout induces cellular stress. This results in mitochondrial hyperfusion in male microglia, a phenotype absent in females due to circulating estrogens. Our results establish the foundation for mitochondrial network analysis of microglia in vivo, emphasizing the importance of mitochondrial-based sex effects of microglia in other pathologies.}, author = {Maes, Margaret E and Colombo, Gloria and Schoot Uiterkamp, Florianne E and Sternberg, Felix and Venturino, Alessandro and Pohl, Elena E. and Siegert, Sandra}, issn = {2589-0042}, journal = {iScience}, number = {10}, publisher = {Elsevier}, title = {{Mitochondrial network adaptations of microglia reveal sex-specific stress response after injury and UCP2 knockout}}, doi = {10.1016/j.isci.2023.107780}, volume = {26}, year = {2023}, } @article{14343, abstract = {The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation.}, author = {Cipolloni, Giorgio and Erdös, László and Henheik, Sven Joscha and Kolupaiev, Oleksii}, issn = {2050-5094}, journal = {Forum of Mathematics, Sigma}, publisher = {Cambridge University Press}, title = {{Gaussian fluctuations in the equipartition principle for Wigner matrices}}, doi = {10.1017/fms.2023.70}, volume = {11}, year = {2023}, } @article{14364, abstract = {We introduce extension-based proofs, a class of impossibility proofs that includes valency arguments. They are modelled as an interaction between a prover and a protocol. Using proofs based on combinatorial topology, it has been shown that it is impossible to deterministically solve -set agreement among processes or approximate agreement on a cycle of length 4 among processes in a wait-free manner in asynchronous models where processes communicate using objects that can be constructed from shared registers. However, it was unknown whether proofs based on simpler techniques were possible. We show that these impossibility results cannot be obtained by extension-based proofs in the iterated snapshot model and, hence, extension-based proofs are limited in power.}, author = {Alistarh, Dan-Adrian and Aspnes, James and Ellen, Faith and Gelashvili, Rati and Zhu, Leqi}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {4}, pages = {913--944}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Why extension-based proofs fail}}, doi = {10.1137/20M1375851}, volume = {52}, year = {2023}, } @article{14345, abstract = {For a locally finite set in R2, the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R2 is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970)).}, author = {Edelsbrunner, Herbert and Garber, Alexey and Ghafari, Mohadese and Heiss, Teresa and Saghafian, Morteza}, issn = {1432-0444}, journal = {Discrete and Computational Geometry}, publisher = {Springer Nature}, title = {{On angles in higher order Brillouin tessellations and related tilings in the plane}}, doi = {10.1007/s00454-023-00566-1}, year = {2023}, }