@article{6366, abstract = {Plants have a remarkable capacity to adjust their growth and development to elevated ambient temperatures. Increased elongation growth of roots, hypocotyls and petioles in warm temperatures are hallmarks of seedling thermomorphogenesis. In the last decade, significant progress has been made to identify the molecular signaling components regulating these growth responses. Increased ambient temperature utilizes diverse components of the light sensing and signal transduction network to trigger growth adjustments. However, it remains unknown whether temperature sensing and responses are universal processes that occur uniformly in all plant organs. Alternatively, temperature sensing may be confined to specific tissues or organs, which would require a systemic signal that mediates responses in distal parts of the plant. Here we show that Arabidopsis (Arabidopsis thaliana) seedlings show organ-specific transcriptome responses to elevated temperatures, and that thermomorphogenesis involves both autonomous and organ-interdependent temperature sensing and signaling. Seedling roots can sense and respond to temperature in a shoot-independent manner, whereas shoot temperature responses require both local and systemic processes. The induction of cell elongation in hypocotyls requires temperature sensing in cotyledons, followed by generation of a mobile auxin signal. Subsequently, auxin travels to the hypocotyl where it triggers local brassinosteroid-induced cell elongation in seedling stems, which depends upon a distinct, permissive temperature sensor in the hypocotyl.}, author = {Bellstaedt, Julia and Trenner, Jana and Lippmann, Rebecca and Poeschl, Yvonne and Zhang, Xixi and Friml, Jiří and Quint, Marcel and Delker, Carolin}, issn = {1532-2548}, journal = {Plant Physiology}, number = {2}, pages = {757--766}, publisher = {ASPB}, title = {{A mobile auxin signal connects temperature sensing in cotyledons with growth responses in hypocotyls}}, doi = {10.1104/pp.18.01377}, volume = {180}, year = {2019}, } @article{6377, abstract = {Clathrin-mediated endocytosis (CME) is a highly conserved and essential cellular process in eukaryotic cells, but its dynamic and vital nature makes it challenging to study using classical genetics tools. In contrast, although small molecules can acutely and reversibly perturb CME, the few chemical CME inhibitors that have been applied to plants are either ineffective or show undesirable side effects. Here, we identify the previously described endosidin9 (ES9) as an inhibitor of clathrin heavy chain (CHC) function in both Arabidopsis and human cells through affinity-based target isolation, in vitro binding studies and X-ray crystallography. Moreover, we present a chemically improved ES9 analog, ES9-17, which lacks the undesirable side effects of ES9 while retaining the ability to target CHC. ES9 and ES9-17 have expanded the chemical toolbox used to probe CHC function, and present chemical scaffolds for further design of more specific and potent CHC inhibitors across different systems.}, author = {Dejonghe, Wim and Sharma, Isha and Denoo, Bram and De Munck, Steven and Lu, Qing and Mishev, Kiril and Bulut, Haydar and Mylle, Evelien and De Rycke, Riet and Vasileva, Mina K and Savatin, Daniel V. and Nerinckx, Wim and Staes, An and Drozdzecki, Andrzej and Audenaert, Dominique and Yperman, Klaas and Madder, Annemieke and Friml, Jiří and Van Damme, Daniël and Gevaert, Kris and Haucke, Volker and Savvides, Savvas N. and Winne, Johan and Russinova, Eugenia}, issn = {1552-4469}, journal = {Nature Chemical Biology}, number = {6}, pages = {641–649}, publisher = {Springer Nature}, title = {{Disruption of endocytosis through chemical inhibition of clathrin heavy chain function}}, doi = {10.1038/s41589-019-0262-1}, volume = {15}, year = {2019}, } @article{6412, abstract = {Polycomb group (PcG) proteins play critical roles in the epigenetic inheritance of cell fate. The Polycomb Repressive Complexes PRC1 and PRC2 catalyse distinct chromatin modifications to enforce gene silencing, but how transcriptional repression is propagated through mitotic cell divisions remains a key unresolved question. Using reversible tethering of PcG proteins to ectopic sites in mouse embryonic stem cells, here we show that PRC1 can trigger transcriptional repression and Polycomb-dependent chromatin modifications. We find that canonical PRC1 (cPRC1), but not variant PRC1, maintains gene silencing through cell division upon reversal of tethering. Propagation of gene repression is sustained by cis-acting histone modifications, PRC2-mediated H3K27me3 and cPRC1-mediated H2AK119ub1, promoting a sequence-independent feedback mechanism for PcG protein recruitment. Thus, the distinct PRC1 complexes present in vertebrates can differentially regulate epigenetic maintenance of gene silencing, potentially enabling dynamic heritable responses to complex stimuli. Our findings reveal how PcG repression is potentially inherited in vertebrates.}, author = {Moussa, Hagar F. and Bsteh, Daniel and Yelagandula, Ramesh and Pribitzer, Carina and Stecher, Karin and Bartalska, Katarina and Michetti, Luca and Wang, Jingkui and Zepeda-Martinez, Jorge A. and Elling, Ulrich and Stuckey, Jacob I. and James, Lindsey I. and Frye, Stephen V. and Bell, Oliver}, issn = {2041-1723}, journal = {Nature Communications}, number = {1}, publisher = {Springer Nature}, title = {{Canonical PRC1 controls sequence-independent propagation of Polycomb-mediated gene silencing}}, doi = {10.1038/s41467-019-09628-6}, volume = {10}, year = {2019}, } @article{6413, abstract = {Phase-field methods have long been used to model the flow of immiscible fluids. Their ability to naturally capture interface topological changes is widely recognized, but their accuracy in simulating flows of real fluids in practical geometries is not established. We here quantitatively investigate the convergence of the phase-field method to the sharp-interface limit with simulations of two-phase pipe flow. We focus on core-annular flows, in which a highly viscous fluid is lubricated by a less viscous fluid, and validate our simulations with an analytic laminar solution, a formal linear stability analysis and also in the fully nonlinear regime. We demonstrate the ability of the phase-field method to accurately deal with non-rectangular geometry, strong advection, unsteady fluctuations and large viscosity contrast. We argue that phase-field methods are very promising for quantitatively studying moderately turbulent flows, especially at high concentrations of the disperse phase.}, author = {Song, Baofang and Plana, Carlos and Lopez Alonso, Jose M and Avila, Marc}, issn = {0301-9322}, journal = {International Journal of Multiphase Flow}, pages = {14--24}, publisher = {Elsevier}, title = {{Phase-field simulation of core-annular pipe flow}}, doi = {10.1016/j.ijmultiphaseflow.2019.04.027}, volume = {117}, year = {2019}, } @article{6415, abstract = {Ant invasions are often harmful to native species communities. Their pathogens and host disease defense mechanisms may be one component of their devastating success. First, they can introduce harmful diseases to their competitors in the introduced range, to which they themselves are tolerant. Second, their supercolonial social structure of huge multi-queen nest networks means that they will harbor a broad pathogen spectrum and high pathogen load while remaining resilient, unlike the smaller, territorial colonies of the native species. Thus, it is likely that invasive ants act as a disease reservoir, promoting their competitive advantage and invasive success.}, author = {Cremer, Sylvia}, issn = {2214-5753}, journal = {Current Opinion in Insect Science}, pages = {63--68}, publisher = {Elsevier}, title = {{Pathogens and disease defense of invasive ants}}, doi = {10.1016/j.cois.2019.03.011}, volume = {33}, year = {2019}, } @article{6418, abstract = {Males and females of Artemia franciscana, a crustacean commonly used in the aquarium trade, are highly dimorphic. Sex is determined by a pair of ZW chromosomes, but the nature and extent of differentiation of these chromosomes is unknown. Here, we characterize the Z chromosome by detecting genomic regions that show lower genomic coverage in female than in male samples, and regions that harbor an excess of female-specific SNPs. We detect many Z-specific genes, which no longer have homologs on the W, but also Z-linked genes that appear to have diverged very recently from their existing W-linked homolog. We assess patterns of male and female expression in two tissues with extensive morphological dimorphism, gonads, and heads. In agreement with their morphology, sex-biased expression is common in both tissues. Interestingly, the Z chromosome is not enriched for sex-biased genes, and seems to in fact have a mechanism of dosage compensation that leads to equal expression in males and in females. Both of these patterns are contrary to most ZW systems studied so far, making A. franciscana an excellent model for investigating the interplay between the evolution of sexual dimorphism and dosage compensation, as well as Z chromosome evolution in general.}, author = {Huylmans, Ann K and Toups, Melissa A and Macon, Ariana and Gammerdinger, William J and Vicoso, Beatriz}, issn = {1759-6653}, journal = {Genome biology and evolution}, number = {4}, pages = {1033--1044}, publisher = {Oxford University Press}, title = {{Sex-biased gene expression and dosage compensation on the Artemia franciscana Z-chromosome}}, doi = {10.1093/gbe/evz053}, volume = {11}, year = {2019}, } @inbook{19987, abstract = {These lecture notes are based on Yang’s talk at the MATRIX program Geometric R-Matrices: from Geometry to Probability, at the University of Melbourne, Dec. 18–22, 2017, and Zhao’s talk at Perimeter Institute for Theoretical Physics in January 2018. We give an introductory survey of the results in Yang and Zhao (Quiver varieties and elliptic quantum groups, 2017. arxiv1708.01418). We discuss a sheafified elliptic quantum group associated to any symmetric Kac-Moody Lie algebra. The sheafification is obtained by applying the equivariant elliptic cohomological theory to the moduli space of representations of a preprojective algebra. By construction, the elliptic quantum group naturally acts on the equivariant elliptic cohomology of Nakajima quiver varieties. As an application, we obtain a relation between the sheafified elliptic quantum group and the global affine Grassmannian over an elliptic curve.}, author = {Yang, Yaping and Zhao, Gufang}, booktitle = {2017 MATRIX Annals}, isbn = {9783030041601}, issn = {2523-305X}, pages = {675--691}, publisher = {Springer International Publishing}, title = {{How to Sheafify an Elliptic Quantum Group}}, doi = {10.1007/978-3-030-04161-8_54}, volume = {2}, year = {2019}, } @inbook{19988, abstract = {Quantitative studies of cell metabolism are often based on large chemical reaction network models. A steady-state approach is suited to analyze phenomena on the timescale of cell growth and circumvents the problem of incomplete experimental knowledge on kinetic laws and parameters, but it should be supported by a correct implementation of thermodynamic constraints. In this chapter, we review the latter aspect, highlighting its computational challenges and physical insights. The simple introduction of Gibbs inequalities avoids the presence of unfeasible loops allowing for correct timescale analysis, but leads to possibly non-convex feasible flux spaces whose exploration needs efficient algorithms. We briefly review the implementation of thermodynamics through variational principles in constraint-based models of metabolic networks.}, author = {De Martino, A and De Martino, Daniele and Marinari, E}, booktitle = {Chemical Kinetics}, isbn = {9781786347008}, pages = {455--471}, publisher = {World Scientific Publishing}, title = {{The Essential Role of Thermodynamics in Metabolic Network Modeling: Physical Insights and Computational Challenges}}, doi = {10.1142/9781786347015_0018}, year = {2019}, } @inbook{19989, abstract = {Neurone empfangen Eingangssignale, konvertieren diese in Aktionspotenziale und generieren schließlich Ausgangssignale auf ihren Zielzellen. Dabei sind die zu überwindenden räumlichen Distanzen oft groß. Daher ist entscheidend, dass elektrische Signale in Nervenzellen schnell von einem zum anderen Ort geleitet werden können. Diese wichtige Aufgabe erfüllt das Axon, der „Ausgangsfortsatz“ der Nervenzelle. Für die schnelle Leitung des Aktionspotenzials sind sowohl die passiven Eigenschaften des axonalen Kabels als auch die aktiven Eigenschaften der Zellmembran von entscheidender Bedeutung. Die Evolution bedient sich zweier Tricks, um die Leitungsgeschwindigkeit des Aktionspotenzials zu maximieren. Der eine Trick ist die Zunahme des Axondurchmessers. Der andere Trick ist die Ausbildung von Markscheiden. Dies führt bei nahezu gleichem Platzbedarf zu einer Zunahme der Leistungsgeschwindigkeit um fast zwei Größenordnungen. Die Aktionspotenzialleitung an myelinisierten Axonen erfolgt „saltatorisch“.}, author = {Jonas, Peter M}, booktitle = {Physiologie des Menschen}, isbn = {9783662564677}, issn = {2512-5214}, pages = {72--82}, publisher = {Springer Nature}, title = {{Aktionspotenzial: Fortleitung im Axon}}, doi = {10.1007/978-3-662-56468-4_7}, year = {2019}, } @inproceedings{10190, abstract = {The verification of concurrent programs remains an open challenge, as thread interaction has to be accounted for, which leads to state-space explosion. Stateless model checking battles this problem by exploring traces rather than states of the program. As there are exponentially many traces, dynamic partial-order reduction (DPOR) techniques are used to partition the trace space into equivalence classes, and explore a few representatives from each class. The standard equivalence that underlies most DPOR techniques is the happens-before equivalence, however recent works have spawned a vivid interest towards coarser equivalences. The efficiency of such approaches is a product of two parameters: (i) the size of the partitioning induced by the equivalence, and (ii) the time spent by the exploration algorithm in each class of the partitioning. In this work, we present a new equivalence, called value-happens-before and show that it has two appealing features. First, value-happens-before is always at least as coarse as the happens-before equivalence, and can be even exponentially coarser. Second, the value-happens-before partitioning is efficiently explorable when the number of threads is bounded. We present an algorithm called value-centric DPOR (VCDPOR), which explores the underlying partitioning using polynomial time per class. Finally, we perform an experimental evaluation of VCDPOR on various benchmarks, and compare it against other state-of-the-art approaches. Our results show that value-happens-before typically induces a significant reduction in the size of the underlying partitioning, which leads to a considerable reduction in the running time for exploring the whole partitioning.}, author = {Chatterjee, Krishnendu and Pavlogiannis, Andreas and Toman, Viktor}, booktitle = {Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications}, issn = {2475-1421}, keywords = {safety, risk, reliability and quality, software}, location = {Athens, Greece}, publisher = {ACM}, title = {{Value-centric dynamic partial order reduction}}, doi = {10.1145/3360550}, volume = {3}, year = {2019}, } @article{105, abstract = {Clinical Utility Gene Card. 1. Name of Disease (Synonyms): Pontocerebellar hypoplasia type 9 (PCH9) and spastic paraplegia-63 (SPG63). 2. OMIM# of the Disease: 615809 and 615686. 3. Name of the Analysed Genes or DNA/Chromosome Segments: AMPD2 at 1p13.3. 4. OMIM# of the Gene(s): 102771.}, author = {Marsh, Ashley and Novarino, Gaia and Lockhart, Paul and Leventer, Richard}, journal = {European Journal of Human Genetics}, pages = {161--166}, publisher = {Springer Nature}, title = {{CUGC for pontocerebellar hypoplasia type 9 and spastic paraplegia-63}}, doi = {10.1038/s41431-018-0231-2}, volume = {27}, year = {2019}, } @inproceedings{7576, abstract = {We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2019. In this year, 6 tools Ariadne, CORA, DynIbex, Flow*, Isabelle/HOL, and JuliaReach (in alphabetic order) participated. They are applied to solve reachability analysis problems on four benchmark problems, one of them with hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tools.}, author = {Immler, Fabian and Althoff, Matthias and Benet, Luis and Chapoutot, Alexandre and Chen, Xin and Forets, Marcelo and Geretti, Luca and Kochdumper, Niklas and Sanders, David P. and Schilling, Christian}, booktitle = {EPiC Series in Computing}, issn = {2398-7340}, location = {Montreal, Canada}, pages = {41--61}, publisher = {EasyChair}, title = {{ARCH-COMP19 Category Report: Continuous and hybrid systems with nonlinear dynamics}}, doi = {10.29007/m75b}, volume = {61}, year = {2019}, } @inproceedings{7606, abstract = {We derive a tight lower bound on equivocation (conditional entropy), or equivalently a tight upper bound on mutual information between a signal variable and channel outputs. The bound is in terms of the joint distribution of the signals and maximum a posteriori decodes (most probable signals given channel output). As part of our derivation, we describe the key properties of the distribution of signals, channel outputs and decodes, that minimizes equivocation and maximizes mutual information. This work addresses a problem in data analysis, where mutual information between signals and decodes is sometimes used to lower bound the mutual information between signals and channel outputs. Our result provides a corresponding upper bound.}, author = {Hledik, Michal and Sokolowski, Thomas R and Tkačik, Gašper}, booktitle = {IEEE Information Theory Workshop, ITW 2019}, isbn = {9781538669006}, location = {Visby, Sweden}, publisher = {IEEE}, title = {{A tight upper bound on mutual information}}, doi = {10.1109/ITW44776.2019.8989292}, year = {2019}, } @inproceedings{7639, abstract = {Deep neural networks (DNNs) have become increasingly important due to their excellent empirical performance on a wide range of problems. However, regularization is generally achieved by indirect means, largely due to the complex set of functions defined by a network and the difficulty in measuring function complexity. There exists no method in the literature for additive regularization based on a norm of the function, as is classically considered in statistical learning theory. In this work, we study the tractability of function norms for deep neural networks with ReLU activations. We provide, to the best of our knowledge, the first proof in the literature of the NP-hardness of computing function norms of DNNs of 3 or more layers. We also highlight a fundamental difference between shallow and deep networks. In the light on these results, we propose a new regularization strategy based on approximate function norms, and show its efficiency on a segmentation task with a DNN.}, author = {Rannen-Triki, Amal and Berman, Maxim and Kolmogorov, Vladimir and Blaschko, Matthew B.}, booktitle = {Proceedings of the 2019 International Conference on Computer Vision Workshop}, isbn = {9781728150239}, location = {Seoul, South Korea}, publisher = {IEEE}, title = {{Function norms for neural networks}}, doi = {10.1109/ICCVW.2019.00097}, year = {2019}, } @inproceedings{7640, abstract = {We propose a new model for detecting visual relationships, such as "person riding motorcycle" or "bottle on table". This task is an important step towards comprehensive structured mage understanding, going beyond detecting individual objects. Our main novelty is a Box Attention mechanism that allows to model pairwise interactions between objects using standard object detection pipelines. The resulting model is conceptually clean, expressive and relies on well-justified training and prediction procedures. Moreover, unlike previously proposed approaches, our model does not introduce any additional complex components or hyperparameters on top of those already required by the underlying detection model. We conduct an experimental evaluation on two datasets, V-COCO and Open Images, demonstrating strong quantitative and qualitative results.}, author = {Kolesnikov, Alexander and Kuznetsova, Alina and Lampert, Christoph and Ferrari, Vittorio}, booktitle = {Proceedings of the 2019 International Conference on Computer Vision Workshop}, isbn = {9781728150239}, location = {Seoul, South Korea}, publisher = {IEEE}, title = {{Detecting visual relationships using box attention}}, doi = {10.1109/ICCVW.2019.00217}, year = {2019}, } @unpublished{7950, abstract = {The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results: 1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.}, author = {Biniaz, Ahmad and Jain, Kshitij and Lubiw, Anna and Masárová, Zuzana and Miltzow, Tillmann and Mondal, Debajyoti and Naredla, Anurag Murty and Tkadlec, Josef and Turcotte, Alexi}, booktitle = {arXiv}, title = {{Token swapping on trees}}, doi = {10.48550/arXiv.1903.06981}, year = {2019}, } @article{8, abstract = {Despite their different origins, Drosophila glia and hemocytes are related cell populations that provide an immune function. Drosophila hemocytes patrol the body cavity and act as macrophages outside the nervous system whereas glia originate from the neuroepithelium and provide the scavenger population of the nervous system. Drosophila glia are hence the functional orthologs of vertebrate microglia, even though the latter are cells of immune origin that subsequently move into the brain during development. Interestingly, the Drosophila immune cells within (glia) and outside the nervous system (hemocytes) require the same transcription factor Glide/Gcm for their development. This raises the issue of how do glia specifically differentiate in the nervous system and hemocytes in the procephalic mesoderm. The Repo homeodomain transcription factor and pan-glial direct target of Glide/Gcm is known to ensure glial terminal differentiation. Here we show that Repo also takes center stage in the process that discriminates between glia and hemocytes. First, Repo expression is repressed in the hemocyte anlagen by mesoderm-specific factors. Second, Repo ectopic activation in the procephalic mesoderm is sufficient to repress the expression of hemocyte-specific genes. Third, the lack of Repo triggers the expression of hemocyte markers in glia. Thus, a complex network of tissue-specific cues biases the potential of Glide/Gcm. These data allow us to revise the concept of fate determinants and help us understand the bases of cell specification. Both sexes were analyzed.SIGNIFICANCE STATEMENTDistinct cell types often require the same pioneer transcription factor, raising the issue of how does one factor trigger different fates. In Drosophila, glia and hemocytes provide a scavenger activity within and outside the nervous system, respectively. While they both require the Glide/Gcm transcription factor, glia originate from the ectoderm, hemocytes from the mesoderm. Here we show that tissue-specific factors inhibit the gliogenic potential of Glide/Gcm in the mesoderm by repressing the expression of the homeodomain protein Repo, a major glial-specific target of Glide/Gcm. Repo expression in turn inhibits the expression of hemocyte-specific genes in the nervous system. These cell-specific networks secure the establishment of the glial fate only in the nervous system and allow cell diversification.}, author = {Trébuchet, Guillaume and Cattenoz, Pierre B and Zsámboki, János and Mazaud, David and Siekhaus, Daria E and Fanto, Manolis and Giangrande, Angela}, journal = {Journal of Neuroscience}, number = {2}, pages = {238--255}, publisher = {Society for Neuroscience}, title = {{The Repo homeodomain transcription factor suppresses hematopoiesis in Drosophila and preserves the glial fate}}, doi = {10.1523/JNEUROSCI.1059-18.2018}, volume = {39}, year = {2019}, } @article{80, abstract = {We consider an interacting, dilute Bose gas trapped in a harmonic potential at a positive temperature. The system is analyzed in a combination of a thermodynamic and a Gross–Pitaevskii (GP) limit where the trap frequency ω, the temperature T, and the particle number N are related by N∼ (T/ ω) 3→ ∞ while the scattering length is so small that the interaction energy per particle around the center of the trap is of the same order of magnitude as the spectral gap in the trap. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Bose–Einstein condensation in the following sense: The one-particle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer.}, author = {Deuchert, Andreas and Seiringer, Robert and Yngvason, Jakob}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {723--776}, publisher = {Springer}, title = {{Bose–Einstein condensation in a dilute, trapped gas at positive temperature}}, doi = {10.1007/s00220-018-3239-0}, volume = {368}, year = {2019}, } @inproceedings{8175, abstract = {We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's problem on longest increasing subsequences of random permutations and the last passage percolation (corner growth) discrete versions thereof. Moreover they interpolate between said measures and the uniform measure on partitions. In the new KPZ-like 1/3 exponent edge scaling limit with logarithmic corrections, we find new probability distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions from the theory of random matrices.}, author = {Betea, Dan and Bouttier, Jérémie and Nejjar, Peter and Vuletíc, Mirjana}, booktitle = {Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics}, location = {Ljubljana, Slovenia}, publisher = {Formal Power Series and Algebraic Combinatorics}, title = {{New edge asymptotics of skew Young diagrams via free boundaries}}, year = {2019}, } @unpublished{8182, abstract = {Suppose that $n\neq p^k$ and $n\neq 2p^k$ for all $k$ and all primes $p$. We prove that for any Hausdorff compactum $X$ with a free action of the symmetric group $\mathfrak S_n$ there exists an $\mathfrak S_n$-equivariant map $X \to {\mathbb R}^n$ whose image avoids the diagonal $\{(x,x\dots,x)\in {\mathbb R}^n|x\in {\mathbb R}\}$. Previously, the special cases of this statement for certain $X$ were usually proved using the equivartiant obstruction theory. Such calculations are difficult and may become infeasible past the first (primary) obstruction. We take a different approach which allows us to prove the vanishing of all obstructions simultaneously. The essential step in the proof is classifying the possible degrees of $\mathfrak S_n$-equivariant maps from the boundary $\partial\Delta^{n-1}$ of $(n-1)$-simplex to itself. Existence of equivariant maps between spaces is important for many questions arising from discrete mathematics and geometry, such as Kneser's conjecture, the Square Peg conjecture, the Splitting Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate the utility of our result applying it to one such question, a specific instance of envy-free division problem.}, author = {Avvakumov, Sergey and Kudrya, Sergey}, booktitle = {arXiv}, title = {{Vanishing of all equivariant obstructions and the mapping degree}}, doi = {10.48550/arXiv.1910.12628}, year = {2019}, }