@article{568, abstract = {We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r > 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C).}, author = {Franek, Peter and Krcál, Marek}, issn = {15320073}, journal = {Homology, Homotopy and Applications}, number = {2}, pages = {313 -- 342}, publisher = {International Press}, title = {{Persistence of zero sets}}, doi = {10.4310/HHA.2017.v19.n2.a16}, volume = {19}, year = {2017}, } @article{569, abstract = {The actomyosin ring generates force to ingress the cytokinetic cleavage furrow in animal cells, yet its filament organization and the mechanism of contractility is not well understood. We quantified actin filament order in human cells using fluorescence polarization microscopy and found that cleavage furrow ingression initiates by contraction of an equatorial actin network with randomly oriented filaments. The network subsequently gradually reoriented actin filaments along the cell equator. This strictly depended on myosin II activity, suggesting local network reorganization by mechanical forces. Cortical laser microsurgery revealed that during cytokinesis progression, mechanical tension increased substantially along the direction of the cell equator, while the network contracted laterally along the pole-to-pole axis without a detectable increase in tension. Our data suggest that an asymmetric increase in cortical tension promotes filament reorientation along the cytokinetic cleavage furrow, which might have implications for diverse other biological processes involving actomyosin rings.}, author = {Spira, Felix and Cuylen Haering, Sara and Mehta, Shalin and Samwer, Matthias and Reversat, Anne and Verma, Amitabh and Oldenbourg, Rudolf and Sixt, Michael K and Gerlich, Daniel}, issn = {2050084X}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{Cytokinesis in vertebrate cells initiates by contraction of an equatorial actomyosin network composed of randomly oriented filaments}}, doi = {10.7554/eLife.30867}, volume = {6}, year = {2017}, } @article{570, abstract = {Most phenotypes are determined by molecular systems composed of specifically interacting molecules. However, unlike for individual components, little is known about the distributions of mutational effects of molecular systems as a whole. We ask how the distribution of mutational effects of a transcriptional regulatory system differs from the distributions of its components, by first independently, and then simultaneously, mutating a transcription factor and the associated promoter it represses. We find that the system distribution exhibits increased phenotypic variation compared to individual component distributions - an effect arising from intermolecular epistasis between the transcription factor and its DNA-binding site. In large part, this epistasis can be qualitatively attributed to the structure of the transcriptional regulatory system and could therefore be a common feature in prokaryotes. Counter-intuitively, intermolecular epistasis can alleviate the constraints of individual components, thereby increasing phenotypic variation that selection could act on and facilitating adaptive evolution. }, author = {Lagator, Mato and Sarikas, Srdjan and Acar, Hande and Bollback, Jonathan P and Guet, Calin C}, issn = {2050084X}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{Regulatory network structure determines patterns of intermolecular epistasis}}, doi = {10.7554/eLife.28921}, volume = {6}, year = {2017}, } @article{571, abstract = {Blood platelets are critical for hemostasis and thrombosis and play diverse roles during immune responses. Despite these versatile tasks in mammalian biology, their skills on a cellular level are deemed limited, mainly consisting in rolling, adhesion, and aggregate formation. Here, we identify an unappreciated asset of platelets and show that adherent platelets use adhesion receptors to mechanically probe the adhesive substrate in their local microenvironment. When actomyosin-dependent traction forces overcome substrate resistance, platelets migrate and pile up the adhesive substrate together with any bound particulate material. They use this ability to act as cellular scavengers, scanning the vascular surface for potential invaders and collecting deposited bacteria. Microbe collection by migrating platelets boosts the activity of professional phagocytes, exacerbating inflammatory tissue injury in sepsis. This assigns platelets a central role in innate immune responses and identifies them as potential targets to dampen inflammatory tissue damage in clinical scenarios of severe systemic infection. In addition to their role in thrombosis and hemostasis, platelets can also migrate to sites of infection to help trap bacteria and clear the vascular surface.}, author = {Gärtner, Florian R and Ahmad, Zerkah and Rosenberger, Gerhild and Fan, Shuxia and Nicolai, Leo and Busch, Benjamin and Yavuz, Gökce and Luckner, Manja and Ishikawa Ankerhold, Hellen and Hennel, Roman and Benechet, Alexandre and Lorenz, Michael and Chandraratne, Sue and Schubert, Irene and Helmer, Sebastian and Striednig, Bianca and Stark, Konstantin and Janko, Marek and Böttcher, Ralph and Verschoor, Admar and Leon, Catherine and Gachet, Christian and Gudermann, Thomas and Mederos Y Schnitzler, Michael and Pincus, Zachary and Iannacone, Matteo and Haas, Rainer and Wanner, Gerhard and Lauber, Kirsten and Sixt, Michael K and Massberg, Steffen}, issn = {00928674}, journal = {Cell Press}, number = {6}, pages = {1368 -- 1382}, publisher = {Cell Press}, title = {{Migrating platelets are mechano scavengers that collect and bundle bacteria}}, doi = {10.1016/j.cell.2017.11.001}, volume = {171}, year = {2017}, } @article{572, abstract = {In this review, we summarize the different biosynthesis-related pathways that contribute to the regulation of endogenous auxin in plants. We demonstrate that all known genes involved in auxin biosynthesis also have a role in root formation, from the initiation of a root meristem during embryogenesis to the generation of a functional root system with a primary root, secondary lateral root branches and adventitious roots. Furthermore, the versatile adaptation of root development in response to environmental challenges is mediated by both local and distant control of auxin biosynthesis. In conclusion, auxin homeostasis mediated by spatial and temporal regulation of auxin biosynthesis plays a central role in determining root architecture.}, author = {Olatunji, Damilola and Geelen, Danny and Verstraeten, Inge}, journal = {International Journal of Molecular Sciences}, number = {12}, publisher = {MDPI}, title = {{Control of endogenous auxin levels in plant root development}}, doi = {10.3390/ijms18122587}, volume = {18}, year = {2017}, } @article{5799, abstract = {We construct a polyhedral surface called a graceful surface, which provides best possible approximation to a given sphere regarding certain criteria. In digital geometry terms, the graceful surface is uniquely characterized by its minimality while guaranteeing the connectivity of certain discrete (polyhedral) curves defined on it. The notion of “gracefulness” was first proposed in Brimkov and Barneva (1999) and shown to be useful for triangular mesh discretization through graceful planes and graceful lines. In this paper we extend the considerations to a nonlinear object such as a sphere. In particular, we investigate the properties of a discrete geodesic path between two voxels and show that discrete 3D circles, circular arcs, and Mobius triangles are all constructible on a graceful sphere, with guaranteed minimum thickness and the desired connectivity in the discrete topological space.}, author = {Biswas, Ranita and Bhowmick, Partha and Brimkov, Valentin E.}, issn = {0166-218X}, journal = {Discrete Applied Mathematics}, pages = {362--375}, publisher = {Elsevier}, title = {{On the polyhedra of graceful spheres and circular geodesics}}, doi = {10.1016/j.dam.2015.11.017}, volume = {216}, year = {2017}, } @article{5800, abstract = {This paper presents a novel study on the functional gradation of coordinate planes in connection with the thinnest and tunnel-free (i.e., naive) discretization of sphere in the integer space. For each of the 48-symmetric quadraginta octants of naive sphere with integer radius and integer center, we show that the corresponding voxel set forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as its functional plane. We use this fundamental property to prove several other theoretical results for naive sphere. First, the quadraginta octants form symmetry groups and subgroups with certain equivalent topological properties. Second, a naive sphere is always unique and consists of fewest voxels. Third, it is efficiently constructible from its functional-plane projection. And finally, a special class of 4-symmetric discrete 3D circles can be constructed on a naive sphere based on back projection from the functional plane.}, author = {Biswas, Ranita and Bhowmick, Partha}, issn = {09249907}, journal = {Journal of Mathematical Imaging and Vision}, number = {1}, pages = {69--83}, publisher = {Springer Nature}, title = {{On the functionality and usefulness of Quadraginta octants of naive sphere}}, doi = {10.1007/s10851-017-0718-4}, volume = {59}, year = {2017}, } @inproceedings{5801, abstract = {Space filling circles and spheres have various applications in mathematical imaging and physical modeling. In this paper, we first show how the thinnest (i.e., 2-minimal) model of digital sphere can be augmented to a space filling model by fixing certain “simple voxels” and “filler voxels” associated with it. Based on elementary number-theoretic properties of such voxels, we design an efficient incremental algorithm for generation of these space filling spheres with successively increasing radius. The novelty of the proposed technique is established further through circular space filling on 3D digital plane. As evident from a preliminary set of experimental result, this can particularly be useful for parallel computing of 3D Voronoi diagrams in the digital space.}, author = {Dwivedi, Shivam and Gupta, Aniket and Roy, Siddhant and Biswas, Ranita and Bhowmick, Partha}, booktitle = {20th IAPR International Conference}, isbn = {978-3-319-66271-8}, issn = {1611-3349}, location = {Vienna, Austria}, pages = {347--359}, publisher = {Springer Nature}, title = {{Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space}}, doi = {10.1007/978-3-319-66272-5_28}, volume = {10502}, year = {2017}, } @inproceedings{5802, abstract = {This papers introduces a definition of digital primitives based on focal points and weighted distances (with positive weights). The proposed definition is applicable to general dimensions and covers in its gamut various regular curves and surfaces like circles, ellipses, digital spheres and hyperspheres, ellipsoids and k-ellipsoids, Cartesian k-ovals, etc. Several interesting properties are presented for this class of digital primitives such as space partitioning, topological separation, and connectivity properties. To demonstrate further the potential of this new way of defining digital primitives, we propose, as extension, another class of digital conics defined by focus-directrix combination.}, author = {Andres, Eric and Biswas, Ranita and Bhowmick, Partha}, booktitle = {20th IAPR International Conference}, isbn = {978-3-319-66271-8}, issn = {1611-3349}, location = {Vienna, Austria}, pages = {388--398}, publisher = {Springer Nature}, title = {{Digital primitives defined by weighted focal set}}, doi = {10.1007/978-3-319-66272-5_31}, volume = {10502}, year = {2017}, } @inbook{5803, abstract = {Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept.}, author = {Biswas, Ranita and Bhowmick, Partha}, booktitle = {Combinatorial image analysis}, isbn = {978-3-319-59107-0}, issn = {0302-9743}, location = {Plovdiv, Bulgaria}, pages = {93--104}, publisher = {Springer Nature}, title = {{Construction of persistent Voronoi diagram on 3D digital plane}}, doi = {10.1007/978-3-319-59108-7_8}, volume = {10256}, year = {2017}, } @article{593, abstract = {Bell correlations, indicating nonlocality in composite quantum systems, were until recently only seen in small systems. Here, we demonstrate Bell correlations in squeezed states of 5×105 Rb87 atoms. The correlations are inferred using collective measurements as witnesses and are statistically significant to 124 standard deviations. The states are both generated and characterized using optical-cavity aided measurements.}, author = {Engelsen, Nils and Krishnakumar, Rajiv and Hosten, Onur and Kasevich, Mark}, journal = {Physical Review Letters}, number = {14}, publisher = {American Physical Society}, title = {{Bell correlations in spin-squeezed states of 500 000 atoms}}, doi = {10.1103/PhysRevLett.118.140401}, volume = {118}, year = {2017}, } @article{600, abstract = {Transcription initiation at the ribosomal RNA promoter requires RNA polymerase (Pol) I and the initiation factors Rrn3 and core factor (CF). Here, we combine X-ray crystallography and cryo-electron microscopy (cryo-EM) to obtain a molecular model for basal Pol I initiation. The three-subunit CF binds upstream promoter DNA, docks to the Pol I-Rrn3 complex, and loads DNA into the expanded active center cleft of the polymerase. DNA unwinding between the Pol I protrusion and clamp domains enables cleft contraction, resulting in an active Pol I conformation and RNA synthesis. Comparison with the Pol II system suggests that promoter specificity relies on a distinct “bendability” and “meltability” of the promoter sequence that enables contacts between initiation factors, DNA, and polymerase.}, author = {Engel, Christoph and Gubbey, Tobias and Neyer, Simon and Sainsbury, Sarah and Oberthuer, Christiane and Baejen, Carlo and Bernecky, Carrie A and Cramer, Patrick}, issn = {00928674}, journal = {Cell}, number = {1}, pages = {120 -- 131.e22}, publisher = {Cell Press}, title = {{Structural basis of RNA polymerase I transcription initiation}}, doi = {10.1016/j.cell.2017.03.003}, volume = {169}, year = {2017}, } @article{601, abstract = {The conserved polymerase-Associated factor 1 complex (Paf1C) plays multiple roles in chromatin transcription and genomic regulation. Paf1C comprises the five subunits Paf1, Leo1, Ctr9, Cdc73 and Rtf1, and binds to the RNA polymerase II (Pol II) transcription elongation complex (EC). Here we report the reconstitution of Paf1C from Saccharomyces cerevisiae, and a structural analysis of Paf1C bound to a Pol II EC containing the elongation factor TFIIS. Cryo-electron microscopy and crosslinking data reveal that Paf1C is highly mobile and extends over the outer Pol II surface from the Rpb2 to the Rpb3 subunit. The Paf1-Leo1 heterodimer and Cdc73 form opposite ends of Paf1C, whereas Ctr9 bridges between them. Consistent with the structural observations, the initiation factor TFIIF impairs Paf1C binding to Pol II, whereas the elongation factor TFIIS enhances it. We further show that Paf1C is globally required for normal mRNA transcription in yeast. These results provide a three-dimensional framework for further analysis of Paf1C function in transcription through chromatin. }, author = {Xu, Youwei and Bernecky, Carrie A and Lee, Chung and Maier, Kerstin and Schwalb, Björn and Tegunov, Dimitri and Plitzko, Jürgen and Urlaub, Henning and Cramer, Patrick}, issn = {20411723}, journal = {Nature Communications}, publisher = {Nature Publishing Group}, title = {{Architecture of the RNA polymerase II-Paf1C-TFIIS transcription elongation complex}}, doi = {10.1038/ncomms15741}, volume = {8}, year = {2017}, } @article{6013, abstract = {The first hundred attoseconds of the electron dynamics during strong field tunneling ionization are investigated. We quantify theoretically how the electron’s classical trajectories in the continuum emerge from the tunneling process and test the results with those achieved in parallel from attoclock measurements. An especially high sensitivity on the tunneling barrier is accomplished here by comparing the momentum distributions of two atomic species of slightly deviating atomic potentials (argon and krypton) being ionized under absolutely identical conditions with near-infrared laser pulses (1300 nm). The agreement between experiment and theory provides clear evidence for a nonzero tunneling time delay and a nonvanishing longitudinal momentum of the electron at the “tunnel exit.”}, author = {Camus, Nicolas and Yakaboylu, Enderalp and Fechner, Lutz and Klaiber, Michael and Laux, Martin and Mi, Yonghao and Hatsagortsyan, Karen Z. and Pfeifer, Thomas and Keitel, Christoph H. and Moshammer, Robert}, issn = {1079-7114}, journal = {Physical Review Letters}, number = {2}, publisher = {American Physical Society}, title = {{Experimental evidence for quantum tunneling time}}, doi = {10.1103/PhysRevLett.119.023201}, volume = {119}, year = {2017}, } @article{603, abstract = {During transcription, RNA polymerase II (Pol II) associates with the conserved elongation factor DSIF. DSIF renders the elongation complex stable and functions during Pol II pausing and RNA processing. We combined cryo-EM and X-ray crystallography to determine the structure of the mammalian Pol II-DSIF elongation complex at a nominal resolution of 3.4. Human DSIF has a modular structure with two domains forming a DNA clamp, two domains forming an RNA clamp, and one domain buttressing the RNA clamp. The clamps maintain the transcription bubble, position upstream DNA, and retain the RNA transcript in the exit tunnel. The mobile C-terminal region of DSIF is located near exiting RNA, where it can recruit factors for RNA processing. The structure provides insight into the roles of DSIF during mRNA synthesis.}, author = {Bernecky, Carrie A and Plitzko, Jürgen and Cramer, Patrick}, issn = {15459993}, journal = {Nature Structural and Molecular Biology}, number = {10}, pages = {809 -- 815}, publisher = {Nature Publishing Group}, title = {{Structure of a transcribing RNA polymerase II-DSIF complex reveals a multidentate DNA-RNA clamp}}, doi = {10.1038/nsmb.3465}, volume = {24}, year = {2017}, } @inbook{604, abstract = {In several settings of physics and chemistry one has to deal with molecules interacting with some kind of an external environment, be it a gas, a solution, or a crystal surface. Understanding molecular processes in the presence of such a many-particle bath is inherently challenging, and usually requires large-scale numerical computations. Here, we present an alternative approach to the problem, based on the notion of the angulon quasiparticle. We show that molecules rotating inside superfluid helium nanodroplets and Bose–Einstein condensates form angulons, and therefore can be described by straightforward solutions of a simple microscopic Hamiltonian. Casting the problem in the language of angulons allows us not only to greatly simplify it, but also to gain insights into the origins of the observed phenomena and to make predictions for future experimental studies.}, author = {Lemeshko, Mikhail and Schmidt, Richard}, booktitle = {Cold Chemistry: Molecular Scattering and Reactivity Near Absolute Zero }, editor = {Dulieu, Oliver and Osterwalder, Andreas}, issn = {20413181}, pages = {444 -- 495}, publisher = {The Royal Society of Chemistry}, title = {{Molecular impurities interacting with a many-particle environment: From ultracold gases to helium nanodroplets}}, doi = {10.1039/9781782626800-00444}, volume = {11}, year = {2017}, } @inproceedings{605, abstract = {Position based cryptography (PBC), proposed in the seminal work of Chandran, Goyal, Moriarty, and Ostrovsky (SIAM J. Computing, 2014), aims at constructing cryptographic schemes in which the identity of the user is his geographic position. Chandran et al. construct PBC schemes for secure positioning and position-based key agreement in the bounded-storage model (Maurer, J. Cryptology, 1992). Apart from bounded memory, their security proofs need a strong additional restriction on the power of the adversary: he cannot compute joint functions of his inputs. Removing this assumption is left as an open problem. We show that an answer to this question would resolve a long standing open problem in multiparty communication complexity: finding a function that is hard to compute with low communication complexity in the simultaneous message model, but easy to compute in the fully adaptive model. On a more positive side: we also show some implications in the other direction, i.e.: we prove that lower bounds on the communication complexity of certain multiparty problems imply existence of PBC primitives. Using this result we then show two attractive ways to “bypass” our hardness result: the first uses the random oracle model, the second weakens the locality requirement in the bounded-storage model to online computability. The random oracle construction is arguably one of the simplest proposed so far in this area. Our results indicate that constructing improved provably secure protocols for PBC requires a better understanding of multiparty communication complexity. This is yet another example where negative results in one area (in our case: lower bounds in multiparty communication complexity) can be used to construct secure cryptographic schemes.}, author = {Brody, Joshua and Dziembowski, Stefan and Faust, Sebastian and Pietrzak, Krzysztof Z}, editor = {Kalai, Yael and Reyzin, Leonid}, isbn = {978-331970499-9}, location = {Baltimore, MD, United States}, pages = {56 -- 81}, publisher = {Springer}, title = {{Position based cryptography and multiparty communication complexity}}, doi = {10.1007/978-3-319-70500-2_3}, volume = {10677}, year = {2017}, } @article{6059, abstract = {Neutrophils or polymorphonuclear cells (PMN) eliminate bacteria via phagocytosis and/or NETosis. Apartfrom these conventional roles, PMN also have immune-regulatory functions. They can transdifferentiateand upregulate MHCII as well as ligands for costimulatory receptors which enables them to behave asantigen presenting cells (APC). The initial step for activating T-cells is the formation of an immunesynapse between T-cells and antigen-presenting cells. However, the immune synapse that develops atthe PMN/T-cell contact zone is as yet hardly investigated due to the non-availability of methods foranalysis of large number of PMN interactions. In order to overcome these obstacles, we introduce herea workflow to analyse the immune synapse of primary human PMN and T-cells using multispectral imag-ing flow cytometry (InFlow microscopy) and super-resolution microscopy. For that purpose, we used CD3and CD66b as the lineage markers for T-cells and PMN, respectively. Thereafter, we applied and criticallydiscussed various ‘‘masks” for identification of T-cell PMN interactions. Using this approach, we foundthat a small fraction of transdifferentiated PMN (CD66b+CD86high) formed stable PMN/T-cell conjugates.Interestingly, while both CD3 and CD66b accumulation in the immune synapse was dependent on thematuration state of the PMN, only CD3 accumulation was greatly enhanced by the presence of superanti-gen. The actin cytoskeleton was weakly rearranged at the PMN side on the immune synapse upon contactwith a T-cell in the presence of superantigen. A more detailed analysis using super-resolution microscopy(structured-illumination microscopy, SIM) confirmed this finding. Together, we present an InFlow micro-scopy based approach for the large scale analysis of PMN/T-cell interactions and – combined with SIM – apossibility for an in-depth analysis of protein translocation at the site of interactions.}, author = {Balta, Emre and Stopp, Julian A and Castelletti, Laura and Kirchgessner, Henning and Samstag, Yvonne and Wabnitz, Guido H.}, issn = {1046-2023}, journal = {Methods}, number = {1}, pages = {25--38}, publisher = {Elsevier}, title = {{Qualitative and quantitative analysis of PMN/T-cell interactions by InFlow and super-resolution microscopy}}, doi = {10.1016/j.ymeth.2016.09.013}, volume = {112}, year = {2017}, } @inproceedings{609, abstract = {Several cryptographic schemes and applications are based on functions that are both reasonably efficient to compute and moderately hard to invert, including client puzzles for Denial-of-Service protection, password protection via salted hashes, or recent proof-of-work blockchain systems. Despite their wide use, a definition of this concept has not yet been distilled and formalized explicitly. Instead, either the applications are proven directly based on the assumptions underlying the function, or some property of the function is proven, but the security of the application is argued only informally. The goal of this work is to provide a (universal) definition that decouples the efforts of designing new moderately hard functions and of building protocols based on them, serving as an interface between the two. On a technical level, beyond the mentioned definitions, we instantiate the model for four different notions of hardness. We extend the work of Alwen and Serbinenko (STOC 2015) by providing a general tool for proving security for the first notion of memory-hard functions that allows for provably secure applications. The tool allows us to recover all of the graph-theoretic techniques developed for proving security under the older, non-composable, notion of security used by Alwen and Serbinenko. As an application of our definition of moderately hard functions, we prove the security of two different schemes for proofs of effort (PoE). We also formalize and instantiate the concept of a non-interactive proof of effort (niPoE), in which the proof is not bound to a particular communication context but rather any bit-string chosen by the prover.}, author = {Alwen, Joel F and Tackmann, Björn}, editor = {Kalai, Yael and Reyzin, Leonid}, isbn = {978-331970499-9}, location = {Baltimore, MD, United States}, pages = {493 -- 526}, publisher = {Springer}, title = {{Moderately hard functions: Definition, instantiations, and applications}}, doi = {10.1007/978-3-319-70500-2_17}, volume = {10677}, year = {2017}, } @article{610, abstract = {The fact that the complete graph K5 does not embed in the plane has been generalized in two independent directions. On the one hand, the solution of the classical Heawood problem for graphs on surfaces established that the complete graph Kn embeds in a closed surface M (other than the Klein bottle) if and only if (n−3)(n−4) ≤ 6b1(M), where b1(M) is the first Z2-Betti number of M. On the other hand, van Kampen and Flores proved that the k-skeleton of the n-dimensional simplex (the higher-dimensional analogue of Kn+1) embeds in R2k if and only if n ≤ 2k + 1. Two decades ago, Kühnel conjectured that the k-skeleton of the n-simplex embeds in a compact, (k − 1)-connected 2k-manifold with kth Z2-Betti number bk only if the following generalized Heawood inequality holds: (k+1 n−k−1) ≤ (k+1 2k+1)bk. This is a common generalization of the case of graphs on surfaces as well as the van Kampen–Flores theorem. In the spirit of Kühnel’s conjecture, we prove that if the k-skeleton of the n-simplex embeds in a compact 2k-manifold with kth Z2-Betti number bk, then n ≤ 2bk(k 2k+2)+2k+4. This bound is weaker than the generalized Heawood inequality, but does not require the assumption that M is (k−1)-connected. Our results generalize to maps without q-covered points, in the spirit of Tverberg’s theorem, for q a prime power. Our proof uses a result of Volovikov about maps that satisfy a certain homological triviality condition.}, author = {Goaoc, Xavier and Mabillard, Isaac and Paták, Pavel and Patakova, Zuzana and Tancer, Martin and Wagner, Uli}, journal = {Israel Journal of Mathematics}, number = {2}, pages = {841 -- 866}, publisher = {Springer}, title = {{On generalized Heawood inequalities for manifolds: A van Kampen–Flores type nonembeddability result}}, doi = {10.1007/s11856-017-1607-7}, volume = {222}, year = {2017}, }