@article{9383,
  abstract     = {A primary roadblock to our understanding of speciation is that it usually occurs over a timeframe that is too long to study from start to finish. The idea of a speciation continuum provides something of a solution to this problem; rather than observing the entire process, we can simply reconstruct it from the multitude of speciation events that surround us. But what do we really mean when we talk about the speciation continuum, and can it really help us understand speciation? We explored these questions using a literature review and online survey of speciation researchers. Although most researchers were familiar with the concept and thought it was useful, our survey revealed extensive disagreement about what the speciation continuum actually tells us. This is due partly to the lack of a clear definition. Here, we provide an explicit definition that is compatible with the Biological Species Concept. That is, the speciation continuum is a continuum of reproductive isolation. After outlining the logic of the definition in light of alternatives, we explain why attempts to reconstruct the speciation process from present‐day populations will ultimately fail. We then outline how we think the speciation continuum concept can continue to act as a foundation for understanding the continuum of reproductive isolation that surrounds us.},
  author       = {Stankowski, Sean and Ravinet, Mark},
  issn         = {1558-5646},
  journal      = {Evolution},
  number       = {6},
  pages        = {1256--1273},
  publisher    = {Oxford University Press},
  title        = {{Defining the speciation continuum}},
  doi          = {10.1111/evo.14215},
  volume       = {75},
  year         = {2021},
}

@misc{9389,
  abstract     = {This .zip File contains the transport data for  "Non-topological zero bias peaks in full-shell nanowires induced by flux tunable Andreev states" by M. Valentini, et. al.  
The measurements were done using Labber Software and the data is stored in the hdf5 file format.
Instructions of how to read the data are in "Notebook_Valentini.pdf".},
  author       = {Valentini, Marco},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Research data for "Non-topological zero bias peaks in full-shell nanowires induced by flux tunable Andreev states"}},
  doi          = {10.15479/AT:ISTA:9389},
  year         = {2021},
}

@article{9392,
  abstract     = {Humans conceptualize the diversity of life by classifying individuals into types we call ‘species’1. The species we recognize influence political and financial decisions and guide our understanding of how units of diversity evolve and interact. Although the idea of species may seem intuitive, a debate about the best way to define them has raged even before Darwin2. So much energy has been devoted to the so-called ‘species problem’ that no amount of discourse will ever likely solve it2,3. Dozens of species concepts are currently recognized3, but we lack a concrete understanding of how much researchers actually disagree and the factors that cause them to think differently1,2. To address this, we used a survey to quantify the species problem for the first time. The results indicate that the disagreement is extensive: two randomly chosen respondents will most likely disagree on the nature of species. The probability of disagreement is not predicted by researcher experience or broad study system, but tended to be lower among researchers with similar focus, training and who study the same organism. Should we see this diversity of perspectives as a problem? We argue that we should not.},
  author       = {Stankowski, Sean and Ravinet, Mark},
  issn         = {1879-0445},
  journal      = {Current Biology},
  number       = {9},
  pages        = {R428--R429},
  publisher    = {Cell Press},
  title        = {{Quantifying the use of species concepts}},
  doi          = {10.1016/j.cub.2021.03.060},
  volume       = {31},
  year         = {2021},
}

@article{9393,
  abstract     = {We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff, the ratio, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with bounded treewidth—a class that contains the control flow graphs of most programs. Let n denote the number of nodes of a graph, m the number of edges (for bounded treewidth 𝑚=𝑂(𝑛)) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for the minimum initial credit problem we show that (1) for general graphs the problem can be solved in 𝑂(𝑛2⋅𝑚) time and the associated decision problem in 𝑂(𝑛⋅𝑚) time, improving the previous known 𝑂(𝑛3⋅𝑚⋅log(𝑛⋅𝑊)) and 𝑂(𝑛2⋅𝑚) bounds, respectively; and (2) for bounded treewidth graphs we present an algorithm that requires 𝑂(𝑛⋅log𝑛) time. Second, for bounded treewidth graphs we present an algorithm that approximates the mean-payoff value within a factor of 1+𝜖 in time 𝑂(𝑛⋅log(𝑛/𝜖)) as compared to the classical exact algorithms on general graphs that require quadratic time. Third, for the ratio property we present an algorithm that for bounded treewidth graphs works in time 𝑂(𝑛⋅log(|𝑎⋅𝑏|))=𝑂(𝑛⋅log(𝑛⋅𝑊)), when the output is 𝑎𝑏, as compared to the previously best known algorithm on general graphs with running time 𝑂(𝑛2⋅log(𝑛⋅𝑊)). We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.},
  author       = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
  issn         = {1572-8102},
  journal      = {Formal Methods in System Design},
  pages        = {401--428},
  publisher    = {Springer},
  title        = {{Faster algorithms for quantitative verification in bounded treewidth graphs}},
  doi          = {10.1007/s10703-021-00373-5},
  volume       = {57},
  year         = {2021},
}

@article{9394,
  abstract     = {Chromosomal inversions have long been recognized for their role in local adaptation. By suppressing recombination in heterozygous individuals, they can maintain coadapted gene complexes and protect them from homogenizing effects of gene flow. However, to fully understand their importance for local adaptation we need to know their influence on phenotypes under divergent selection. For this, the marine snail Littorina saxatilis provides an ideal study system. Divergent ecotypes adapted to wave action and crab predation occur in close proximity on intertidal shores with gene flow between them. Here, we used F2 individuals obtained from crosses between the ecotypes to test for associations between genomic regions and traits distinguishing the Crab‐/Wave‐adapted ecotypes including size, shape, shell thickness, and behavior. We show that most of these traits are influenced by two previously detected inversion regions that are divergent between ecotypes. We thus gain a better understanding of one important underlying mechanism responsible for the rapid and repeated formation of ecotypes: divergent selection acting on inversions. We also found that some inversions contributed to more than one trait suggesting that they may contain several loci involved in adaptation, consistent with the hypothesis that suppression of recombination within inversions facilitates differentiation in the presence of gene flow.},
  author       = {Koch, Eva L. and Morales, Hernán E. and Larsson, Jenny and Westram, Anja M and Faria, Rui and Lemmon, Alan R. and Lemmon, E. Moriarty and Johannesson, Kerstin and Butlin, Roger K.},
  issn         = {2056-3744},
  journal      = {Evolution Letters},
  number       = {3},
  pages        = {196--213},
  publisher    = {Wiley},
  title        = {{Genetic variation for adaptive traits is associated with polymorphic inversions in Littorina saxatilis}},
  doi          = {10.1002/evl3.227},
  volume       = {5},
  year         = {2021},
}

@inbook{9403,
  abstract     = {Optimal decision making requires individuals to know their available options and to anticipate correctly what consequences these options have. In many social interactions, however, we refrain from gathering all relevant information, even if this information would help us make better decisions and is costless to obtain. This chapter examines several examples of “deliberate ignorance.” Two simple models are proposed to illustrate how ignorance can evolve among self-interested and payoff - maximizing individuals, and open problems are highlighted that lie ahead for future research to explore.},
  author       = {Schmid, Laura and Hilbe, Christian},
  booktitle    = {Deliberate Ignorance: Choosing Not To Know},
  editor       = {Hertwig, Ralph and Engel, Christoph},
  isbn         = {978-0-262-04559-9},
  pages        = {139--152},
  publisher    = {MIT Press},
  title        = {{The evolution of strategic ignorance in strategic interaction}},
  volume       = {29},
  year         = {2021},
}

@article{9407,
  abstract     = {High impact epidemics constitute one of the largest threats humanity is facing in the 21st century. In the absence of pharmaceutical interventions, physical distancing together with testing, contact tracing and quarantining are crucial in slowing down epidemic dynamics. Yet, here we show that if testing capacities are limited, containment may fail dramatically because such combined countermeasures drastically change the rules of the epidemic transition: Instead of continuous, the response to countermeasures becomes discontinuous. Rather than following the conventional exponential growth, the outbreak that is initially strongly suppressed eventually accelerates and scales faster than exponential during an explosive growth period. As a consequence, containment measures either suffice to stop the outbreak at low total case numbers or fail catastrophically if marginally too weak, thus implying large uncertainties in reliably estimating overall epidemic dynamics, both during initial phases and during second wave scenarios.},
  author       = {Scarselli, Davide and Budanur, Nazmi B and Timme, Marc and Hof, Björn},
  issn         = {2041-1723},
  journal      = {Nature Communications},
  number       = {1},
  publisher    = {Springer Nature},
  title        = {{Discontinuous epidemic transition due to limited testing}},
  doi          = {10.1038/s41467-021-22725-9},
  volume       = {12},
  year         = {2021},
}

@article{9408,
  abstract     = {We present a computational design system that assists users to model, optimize, and fabricate quad-robots with soft skins. Our system addresses the challenging task of predicting their physical behavior by fully integrating the multibody dynamics of the mechanical skeleton and the elastic behavior of the soft skin. The developed motion control strategy uses an alternating optimization scheme to avoid expensive full space time-optimization, interleaving space-time optimization for the skeleton, and frame-by-frame optimization for the full dynamics. The output are motor torques to drive the robot to achieve a user prescribed motion trajectory. We also provide a collection of convenient engineering tools and empirical manufacturing guidance to support the fabrication of the designed quad-robot. We validate the feasibility of designs generated with our system through physics simulations and with a physically-fabricated prototype.},
  author       = {Feng, Xudong and Liu, Jiafeng and Wang, Huamin and Yang, Yin and Bao, Hujun and Bickel, Bernd and Xu, Weiwei},
  issn         = {1077-2626},
  journal      = {IEEE Transactions on Visualization and Computer Graphics},
  number       = {6},
  publisher    = {IEEE},
  title        = {{Computational design of skinned Quad-Robots}},
  doi          = {10.1109/TVCG.2019.2957218},
  volume       = {27},
  year         = {2021},
}

@article{9410,
  abstract     = {Antibiotic concentrations vary dramatically in the body and the environment. Hence, understanding the dynamics of resistance evolution along antibiotic concentration gradients is critical for predicting and slowing the emergence and spread of resistance. While it has been shown that increasing the concentration of an antibiotic slows resistance evolution, how adaptation to one antibiotic concentration correlates with fitness at other points along the gradient has not received much attention. Here, we selected populations of Escherichia coli at several points along a concentration gradient for three different antibiotics, asking how rapidly resistance evolved and whether populations became specialized to the antibiotic concentration they were selected on. Populations selected at higher concentrations evolved resistance more slowly but exhibited equal or higher fitness across the whole gradient. Populations selected at lower concentrations evolved resistance rapidly, but overall fitness in the presence of antibiotics was lower. However, these populations readily adapted to higher concentrations upon subsequent selection. Our results indicate that resistance management strategies must account not only for the rates of resistance evolution but also for the fitness of evolved strains.},
  author       = {Lagator, Mato and Uecker, Hildegard and Neve, Paul},
  issn         = {1744-957X},
  journal      = {Biology letters},
  number       = {5},
  publisher    = {Royal Society of London},
  title        = {{Adaptation at different points along antibiotic concentration gradients}},
  doi          = {10.1098/rsbl.2020.0913},
  volume       = {17},
  year         = {2021},
}

@article{9411,
  abstract     = {The dynamics of a triangular magnetocapillary swimmer is studied using the lattice Boltzmann method. We extend on our previous work, which deals with the self-assembly and a specific type of the swimmer motion characterized by the swimmer’s maximum velocity centred around the particle’s inverse viscous time. Here, we identify additional regimes of motion. First, modifying the ratio of surface tension and magnetic forces allows to study the swimmer propagation in the regime of significantly lower frequencies mainly defined by the strength of the magnetocapillary potential. Second, introducing a constant magnetic contribution in each of the particles in addition to their magnetic moment induced by external fields leads to another regime characterized by strong in-plane swimmer reorientations that resemble experimental observations.},
  author       = {Sukhov, Alexander and Hubert, Maxime and Grosjean, Galien M and Trosman, Oleg and Ziegler, Sebastian and Collard, Ylona and Vandewalle, Nicolas and Smith, Ana Sunčana and Harting, Jens},
  issn         = {1292-895X},
  journal      = {European Physical Journal E},
  number       = {4},
  publisher    = {Springer},
  title        = {{Regimes of motion of magnetocapillary swimmers}},
  doi          = {10.1140/epje/s10189-021-00065-2},
  volume       = {44},
  year         = {2021},
}

@article{9412,
  abstract     = {We extend our recent result [22] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices X with independent, identically distributed complex entries to the real symmetry class. We find that the expectation and variance substantially differ from their complex counterparts, reflecting (i) the special spectral symmetry of real matrices onto the real axis; and (ii) the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes the previously known special cases where either the test function is analytic [49] or the first four moments of the matrix elements match the real Gaussian [59, 44]. The key element of the proof is the analysis of several weakly dependent Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared with [22] is that the correlation structure of the stochastic differentials in each individual DBM is non-trivial, potentially even jeopardising its well-posedness.},
  author       = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
  issn         = {1083-6489},
  journal      = {Electronic Journal of Probability},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{Fluctuation around the circular law for random matrices with real entries}},
  doi          = {10.1214/21-EJP591},
  volume       = {26},
  year         = {2021},
}

@article{9414,
  abstract     = {Microtubule plus-end depolymerization rate is a potentially important target of physiological regulation, but it has been challenging to measure, so its role in spatial organization is poorly understood. Here we apply a method for tracking plus ends based on time difference imaging to measure depolymerization rates in large interphase asters growing in Xenopus egg extract. We observed strong spatial regulation of depolymerization rates, which were higher in the aster interior compared with the periphery, and much less regulation of polymerization or catastrophe rates. We interpret these data in terms of a limiting component model, where aster growth results in lower levels of soluble tubulin and microtubule-associated proteins (MAPs) in the interior cytosol compared with that at the periphery. The steady-state polymer fraction of tubulin was ∼30%, so tubulin is not strongly depleted in the aster interior. We propose that the limiting component for microtubule assembly is a MAP that inhibits depolymerization, and that egg asters are tuned to low microtubule density.},
  author       = {Ishihara, Keisuke and Decker, Franziska and Dos Santos Caldas, Paulo R and Pelletier, James F. and Loose, Martin and Brugués, Jan and Mitchison, Timothy J.},
  issn         = {1939-4586},
  journal      = {Molecular Biology of the Cell},
  number       = {9},
  pages        = {869--879},
  publisher    = {American Society for Cell Biology},
  title        = {{Spatial variation of microtubule depolymerization in large asters}},
  doi          = {10.1091/MBC.E20-11-0723},
  volume       = {32},
  year         = {2021},
}

@article{9431,
  abstract     = {Inositol hexakisphosphate (IP6) is an assembly cofactor for HIV-1. We report here that IP6 is also used for assembly of Rous sarcoma virus (RSV), a retrovirus from a different genus. IP6 is ~100-fold more potent at promoting RSV mature capsid protein (CA) assembly than observed for HIV-1 and removal of IP6 in cells reduces infectivity by 100-fold. Here, visualized by cryo-electron tomography and subtomogram averaging, mature capsid-like particles show an IP6-like density in the CA hexamer, coordinated by rings of six lysines and six arginines. Phosphate and IP6 have opposing effects on CA in vitro assembly, inducing formation of T = 1 icosahedrons and tubes, respectively, implying that phosphate promotes pentamer and IP6 hexamer formation. Subtomogram averaging and classification optimized for analysis of pleomorphic retrovirus particles reveal that the heterogeneity of mature RSV CA polyhedrons results from an unexpected, intrinsic CA hexamer flexibility. In contrast, the CA pentamer forms rigid units organizing the local architecture. These different features of hexamers and pentamers determine the structural mechanism to form CA polyhedrons of variable shape in mature RSV particles.},
  author       = {Obr, Martin and Ricana, Clifton L. and Nikulin, Nadia and Feathers, Jon-Philip R. and Klanschnig, Marco and Thader, Andreas and Johnson, Marc C. and Vogt, Volker M. and Schur, Florian KM and Dick, Robert A.},
  issn         = {2041-1723},
  journal      = {Nature Communications},
  keywords     = {General Biochemistry, Genetics and Molecular Biology, General Physics and Astronomy, General Chemistry},
  number       = {1},
  publisher    = {Nature Research},
  title        = {{Structure of the mature Rous sarcoma virus lattice reveals a role for IP6 in the formation of the capsid hexamer}},
  doi          = {10.1038/s41467-021-23506-0},
  volume       = {12},
  year         = {2021},
}

@unpublished{9435,
  abstract     = {For any given positive integer l, we prove that every plane deformation of a circlewhich preserves the 1/2and 1/ (2l + 1) -rational caustics is trivial i.e. the deformationconsists only of similarities (rescalings and isometries).},
  author       = {Kaloshin, Vadim and Koudjinan, Edmond},
  booktitle    = {arXiv},
  title        = {{Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles}},
  doi          = {10.48550/arXiv.2107.03499},
  year         = {2021},
}

@article{9439,
  abstract     = {The ability to adapt to changes in stimulus statistics is a hallmark of sensory systems. Here, we developed a theoretical framework that can account for the dynamics of adaptation from an information processing perspective. We use this framework to optimize and analyze adaptive sensory codes, and we show that codes optimized for stationary environments can suffer from prolonged periods of poor performance when the environment changes. To mitigate the adversarial effects of these environmental changes, sensory systems must navigate tradeoffs between the ability to accurately encode incoming stimuli and the ability to rapidly detect and adapt to changes in the distribution of these stimuli. We derive families of codes that balance these objectives, and we demonstrate their close match to experimentally observed neural dynamics during mean and variance adaptation. Our results provide a unifying perspective on adaptation across a range of sensory systems, environments, and sensory tasks.},
  author       = {Mlynarski, Wiktor F and Hermundstad, Ann M.},
  issn         = {1546-1726},
  journal      = {Nature Neuroscience},
  pages        = {998--1009},
  publisher    = {Springer Nature},
  title        = {{Efficient and adaptive sensory codes}},
  doi          = {10.1038/s41593-021-00846-0},
  volume       = {24},
  year         = {2021},
}

@article{9443,
  abstract     = {Endoplasmic reticulum–plasma membrane contact sites (ER–PM CS) play fundamental roles in all eukaryotic cells. Arabidopsis thaliana mutants lacking the ER–PM protein tether synaptotagmin1 (SYT1) exhibit decreased PM integrity under multiple abiotic stresses, such as freezing, high salt, osmotic stress, and mechanical damage. Here, we show that, together with SYT1, the stress-induced SYT3 is an ER–PM tether that also functions in maintaining PM integrity. The ER–PM CS localization of SYT1 and SYT3 is dependent on PM phosphatidylinositol-4-phosphate and is regulated by abiotic stress. Lipidomic analysis revealed that cold stress increased the accumulation of diacylglycerol at the PM in a syt1/3 double mutant relative to wild-type while the levels of most glycerolipid species remain unchanged. In addition, the SYT1-green fluorescent protein fusion preferentially binds diacylglycerol in vivo with little affinity for polar glycerolipids. Our work uncovers a SYT-dependent mechanism of stress adaptation counteracting the detrimental accumulation of diacylglycerol at the PM produced during episodes of abiotic stress.},
  author       = {Ruiz-Lopez, N and Pérez-Sancho, J and Esteban Del Valle, A and Haslam, RP and Vanneste, S and Catalá, R and Perea-Resa, C and Van Damme, D and García-Hernández, S and Albert, A and Vallarino, J and Lin, J and Friml, Jiří and Macho, AP and Salinas, J and Rosado, A and Napier, JA and Amorim-Silva, V and Botella, MA},
  issn         = {1532-298x},
  journal      = {Plant Cell},
  number       = {7},
  pages        = {2431--2453},
  publisher    = {American Society of Plant Biologists},
  title        = {{Synaptotagmins at the endoplasmic reticulum-plasma membrane contact sites maintain diacylglycerol homeostasis during abiotic stress}},
  doi          = {10.1093/plcell/koab122},
  volume       = {33},
  year         = {2021},
}

@article{9447,
  abstract     = {Lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) based water-in-salt electrolytes (WiSEs) has recently emerged as a new promising class of electrolytes, primarily owing to their wide electrochemical stability windows (~3–4 V), that by far exceed the thermodynamic stability window of water (1.23 V). Upon increasing the salt concentration towards superconcentration the onset of the oxygen evolution reaction (OER) shifts more significantly than the hydrogen evolution reaction (HER) does. The OER shift has been explained by the accumulation of hydrophobic anions blocking water access to the electrode surface, hence by double layer theory. Here we demonstrate that the processes during oxidation are much more complex, involving OER, carbon and salt decomposition by OER intermediates, and salt precipitation upon local oversaturation. The positive shift in the onset potential of oxidation currents was elucidated by combining several advanced analysis techniques: rotating ring-disk electrode voltammetry, online electrochemical mass spectrometry, and X-ray photoelectron spectroscopy, using both dilute and superconcentrated electrolytes. The results demonstrate the importance of reactive OER intermediates and surface films for electrolyte and electrode stability and motivate further studies of the nature of the electrode.},
  author       = {Maffre, Marion and Bouchal, Roza and Freunberger, Stefan Alexander and Lindahl, Niklas and Johansson, Patrik and Favier, Frédéric and Fontaine, Olivier and Bélanger, Daniel},
  issn         = {1945-7111},
  journal      = {Journal of The Electrochemical Society},
  keywords     = {Renewable Energy, Sustainability and the Environment, Electrochemistry, Materials Chemistry, Electronic, Optical and Magnetic Materials, Surfaces, Coatings and Films, Condensed Matter Physics},
  number       = {5},
  publisher    = {IOP Publishing},
  title        = {{Investigation of electrochemical and chemical processes occurring at positive potentials in “Water-in-Salt” electrolytes}},
  doi          = {10.1149/1945-7111/ac0300},
  volume       = {168},
  year         = {2021},
}

@article{9462,
  abstract     = {We consider a system of N trapped bosons with repulsive interactions in a combined semiclassical mean-field limit at positive temperature. We show that the free energy is well approximated by the minimum of the Hartree free energy functional – a natural extension of the Hartree energy functional to positive temperatures. The Hartree free energy functional converges in the same limit to a semiclassical free energy functional, and we show that the system displays Bose–Einstein condensation if and only if it occurs in the semiclassical free energy functional. This allows us to show that for weak coupling the critical temperature decreases due to the repulsive interactions.},
  author       = {Deuchert, Andreas and Seiringer, Robert},
  issn         = {1096-0783},
  journal      = {Journal of Functional Analysis},
  number       = {6},
  publisher    = {Elsevier},
  title        = {{Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons}},
  doi          = {10.1016/j.jfa.2021.109096},
  volume       = {281},
  year         = {2021},
}

@inproceedings{9464,
  abstract     = {We firstly introduce the self-assembled growth of highly uniform Ge quantum wires with controllable position, distance and length on patterned Si (001) substrates. We then present the electrically tunable strong spin-orbit coupling, the first Ge hole spin qubit and ultrafast operation of hole spin qubit in the Ge/Si quantum wires.},
  author       = {Gao, Fei and Zhang, Jie Yin and Wang, Jian Huan and Ming, Ming and Wang, Tina and Zhang, Jian Jun and Watzinger, Hannes and Kukucka, Josip and Vukušić, Lada and Katsaros, Georgios and Wang, Ke and Xu, Gang and Li, Hai Ou and Guo, Guo Ping},
  booktitle    = {2021 5th IEEE Electron Devices Technology and Manufacturing Conference, EDTM 2021},
  isbn         = {9781728181769},
  location     = {Virtual, Online},
  publisher    = {IEEE},
  title        = {{Ge/Si quantum wires for quantum computing}},
  doi          = {10.1109/EDTM50988.2021.9420817},
  year         = {2021},
}

@article{9465,
  abstract     = {Given a locally finite set 𝑋⊆ℝ𝑑 and an integer 𝑘≥0, we consider the function 𝐰𝑘:Del𝑘(𝑋)→ℝ on the dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf Theory IT-29:551–559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett 114:76–83, 2014). While this function is not necessarily generalized discrete Morse, in the sense of Forman (Adv Math 134:90–145, 1998) and Freij (Discrete Math 309:3821–3829, 2009), we prove that it satisfies similar properties so that its increments can be meaningfully classified into critical and non-critical steps. This result extends to the case of weighted points and sheds light on k-fold covers with balls in Euclidean space.},
  author       = {Edelsbrunner, Herbert and Nikitenko, Anton and Osang, Georg F},
  issn         = {1420-8997},
  journal      = {Journal of Geometry},
  number       = {1},
  publisher    = {Springer Nature},
  title        = {{A step in the Delaunay mosaic of order k}},
  doi          = {10.1007/s00022-021-00577-4},
  volume       = {112},
  year         = {2021},
}

