[{"quality_controlled":"1","publisher":"Elsevier","oa":1,"date_published":"2019-01-02T00:00:00Z","doi":"10.1016/j.neuron.2018.11.015","date_created":"2019-01-13T22:59:10Z","page":"119-132.e4","day":"02","publication":"Neuron","isi":1,"year":"2019","project":[{"grant_number":"281511","name":"Memory-related information processing in neuronal circuits of the hippocampus and entorhinal cortex","_id":"257A4776-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"title":"Assembly responses of hippocampal CA1 place cells predict learned behavior in goal-directed spatial tasks on the radial eight-arm maze","author":[{"id":"310349D0-F248-11E8-B48F-1D18A9856A87","first_name":"Haibing","full_name":"Xu, Haibing","last_name":"Xu"},{"last_name":"Baracskay","full_name":"Baracskay, Peter","id":"361CC00E-F248-11E8-B48F-1D18A9856A87","first_name":"Peter"},{"last_name":"O'Neill","full_name":"O'Neill, Joseph","id":"426376DC-F248-11E8-B48F-1D18A9856A87","first_name":"Joseph"},{"first_name":"Jozsef L","id":"3FA14672-F248-11E8-B48F-1D18A9856A87","last_name":"Csicsvari","orcid":"0000-0002-5193-4036","full_name":"Csicsvari, Jozsef L"}],"article_processing_charge":"No","external_id":{"isi":["000454791500014"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Xu, Haibing, et al. “Assembly Responses of Hippocampal CA1 Place Cells Predict Learned Behavior in Goal-Directed Spatial Tasks on the Radial Eight-Arm Maze.” Neuron, vol. 101, no. 1, Elsevier, 2019, p. 119–132.e4, doi:10.1016/j.neuron.2018.11.015.","ieee":"H. Xu, P. Baracskay, J. O’Neill, and J. L. Csicsvari, “Assembly responses of hippocampal CA1 place cells predict learned behavior in goal-directed spatial tasks on the radial eight-arm maze,” Neuron, vol. 101, no. 1. Elsevier, p. 119–132.e4, 2019.","short":"H. Xu, P. Baracskay, J. O’Neill, J.L. Csicsvari, Neuron 101 (2019) 119–132.e4.","apa":"Xu, H., Baracskay, P., O’Neill, J., & Csicsvari, J. L. (2019). Assembly responses of hippocampal CA1 place cells predict learned behavior in goal-directed spatial tasks on the radial eight-arm maze. Neuron. Elsevier. https://doi.org/10.1016/j.neuron.2018.11.015","ama":"Xu H, Baracskay P, O’Neill J, Csicsvari JL. Assembly responses of hippocampal CA1 place cells predict learned behavior in goal-directed spatial tasks on the radial eight-arm maze. Neuron. 2019;101(1):119-132.e4. doi:10.1016/j.neuron.2018.11.015","chicago":"Xu, Haibing, Peter Baracskay, Joseph O’Neill, and Jozsef L Csicsvari. “Assembly Responses of Hippocampal CA1 Place Cells Predict Learned Behavior in Goal-Directed Spatial Tasks on the Radial Eight-Arm Maze.” Neuron. Elsevier, 2019. https://doi.org/10.1016/j.neuron.2018.11.015.","ista":"Xu H, Baracskay P, O’Neill J, Csicsvari JL. 2019. Assembly responses of hippocampal CA1 place cells predict learned behavior in goal-directed spatial tasks on the radial eight-arm maze. Neuron. 101(1), 119–132.e4."},"month":"01","intvolume":" 101","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://www.doi.org/10.1016/j.neuron.2018.11.015"}],"oa_version":"Published Version","abstract":[{"text":"Hippocampus is needed for both spatial working and reference memories. Here, using a radial eight-arm maze, we examined how the combined demand on these memories influenced CA1 place cell assemblies while reference memories were partially updated. This was contrasted with control tasks requiring only working memory or the update of reference memory. Reference memory update led to the reward-directed place field shifts at newly rewarded arms and to the gradual strengthening of firing in passes between newly rewarded arms but not between those passes that included a familiar-rewarded arm. At the maze center, transient network synchronization periods preferentially replayed trajectories of the next chosen arm in reference memory tasks but the previously visited arm in the working memory task. Hence, reference memory demand was uniquely associated with a gradual, goal novelty-related reorganization of place cell assemblies and with trajectory replay that reflected the animal's decision of which arm to visit next.","lang":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"837","status":"public"}],"link":[{"relation":"press_release","url":"https://ist.ac.at/en/news/reading-rats-minds/","description":"News on IST Homepage"}]},"volume":101,"issue":"1","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["10974199"]},"publication_status":"published","status":"public","article_type":"original","type":"journal_article","_id":"5828","department":[{"_id":"JoCs"}],"date_updated":"2023-09-07T12:06:37Z"},{"issue":"4","volume":20,"related_material":{"record":[{"id":"52","status":"public","relation":"dissertation_contains"}]},"license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"file":[{"date_updated":"2020-07-14T12:47:12Z","file_size":859846,"creator":"dernst","date_created":"2019-01-28T15:27:17Z","file_name":"2019_Annales_Moser.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"5894","checksum":"255e42f957a8e2b10aad2499c750a8d6"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["14240637"]},"publication_status":"published","month":"04","intvolume":" 20","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"We give a bound on the ground-state energy of a system of N non-interacting fermions in a three-dimensional cubic box interacting with an impurity particle via point interactions. We show that the change in energy compared to the system in the absence of the impurity is bounded in terms of the gas density and the scattering length of the interaction, independently of N. Our bound holds as long as the ratio of the mass of the impurity to the one of the gas particles is larger than a critical value m∗ ∗≈ 0.36 , which is the same regime for which we recently showed stability of the system.","lang":"eng"}],"file_date_updated":"2020-07-14T12:47:12Z","department":[{"_id":"RoSe"}],"ddc":["530"],"date_updated":"2023-09-07T12:37:42Z","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"5856","doi":"10.1007/s00023-018-00757-0","date_published":"2019-04-01T00:00:00Z","date_created":"2019-01-20T22:59:17Z","page":"1325–1365","day":"01","publication":"Annales Henri Poincare","isi":1,"has_accepted_license":"1","year":"2019","publisher":"Springer","quality_controlled":"1","oa":1,"title":"Energy contribution of a point-interacting impurity in a Fermi gas","author":[{"id":"2B5FC9A4-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas","full_name":"Moser, Thomas","last_name":"Moser"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"external_id":{"isi":["000462444300008"],"arxiv":["1807.00739"]},"article_processing_charge":"Yes (via OA deal)","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Moser T, Seiringer R. 2019. Energy contribution of a point-interacting impurity in a Fermi gas. Annales Henri Poincare. 20(4), 1325–1365.","chicago":"Moser, Thomas, and Robert Seiringer. “Energy Contribution of a Point-Interacting Impurity in a Fermi Gas.” Annales Henri Poincare. Springer, 2019. https://doi.org/10.1007/s00023-018-00757-0.","apa":"Moser, T., & Seiringer, R. (2019). Energy contribution of a point-interacting impurity in a Fermi gas. Annales Henri Poincare. Springer. https://doi.org/10.1007/s00023-018-00757-0","ama":"Moser T, Seiringer R. Energy contribution of a point-interacting impurity in a Fermi gas. Annales Henri Poincare. 2019;20(4):1325–1365. doi:10.1007/s00023-018-00757-0","short":"T. Moser, R. Seiringer, Annales Henri Poincare 20 (2019) 1325–1365.","ieee":"T. Moser and R. Seiringer, “Energy contribution of a point-interacting impurity in a Fermi gas,” Annales Henri Poincare, vol. 20, no. 4. Springer, pp. 1325–1365, 2019.","mla":"Moser, Thomas, and Robert Seiringer. “Energy Contribution of a Point-Interacting Impurity in a Fermi Gas.” Annales Henri Poincare, vol. 20, no. 4, Springer, 2019, pp. 1325–1365, doi:10.1007/s00023-018-00757-0."},"project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"P27533_N27","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}]},{"oa_version":"Published Version","abstract":[{"text":"In many shear flows like pipe flow, plane Couette flow, plane Poiseuille flow, etc. turbulence emerges subcritically. Here, when subjected to strong enough perturbations, the flow becomes turbulent in spite of the laminar base flow being linearly stable. The nature of this instability has puzzled the scientific community for decades. At onset, turbulence appears in localized patches and flows are spatio-temporally intermittent. In pipe flow the localized turbulent structures are referred to as puffs and in planar flows like plane Couette and channel flow, patches arise in the form of localized oblique bands. In this thesis, we study the onset of turbulence in channel flow in direct numerical simulations from a dynamical system theory perspective, as well as by performing experiments in a large aspect ratio channel.\r\n\r\nThe aim of the experimental work is to determine the critical Reynolds number where turbulence first becomes sustained. Recently, the onset of turbulence has been described in analogy to absorbing state phase transition (i.e. directed percolation). In particular, it has been shown that the critical point can be estimated from the competition between spreading and decay processes. Here, by performing experiments, we identify the mechanisms underlying turbulence proliferation in channel flow and find the critical Reynolds number, above which turbulence becomes sustained. Above the critical point, the continuous growth at the tip of the stripes outweighs the stochastic shedding of turbulent patches at the tail and the stripes expand. For growing stripes, the probability to decay decreases while the probability of stripe splitting increases. Consequently, and unlike for the puffs in pipe flow, neither of these two processes is time-independent i.e. memoryless. Coupling between stripe expansion and creation of new stripes via splitting leads to a significantly lower critical point ($Re_c=670+/-10$) than most earlier studies suggest. \r\n\r\nWhile the above approach sheds light on how turbulence first becomes sustained, it provides no insight into the origin of the stripes themselves. In the numerical part of the thesis we investigate how turbulent stripes form from invariant solutions of the Navier-Stokes equations. The origin of these turbulent stripes can be identified by applying concepts from the dynamical system theory. In doing so, we identify the exact coherent structures underlying stripes and their bifurcations and how they give rise to the turbulent attractor in phase space. We first report a family of localized nonlinear traveling wave solutions of the Navier-Stokes equations in channel flow. These solutions show structural similarities with turbulent stripes in experiments like obliqueness, quasi-streamwise streaks and vortices, etc. A parametric study of these traveling wave solution is performed, with parameters like Reynolds number, stripe tilt angle and domain size, including the stability of the solutions. These solutions emerge through saddle-node bifurcations and form a phase space skeleton for the turbulent stripes observed in the experiments. The lower branches of these TW solutions at different tilt angles undergo Hopf bifurcation and new solutions branches of relative periodic orbits emerge. These RPO solutions do not belong to the same family and therefore the routes to chaos for different angles are different. \r\n\r\nIn shear flows, turbulence at onset is transient in nature. Consequently,turbulence can not be tracked to lower Reynolds numbers, where the dynamics may simplify. Before this happens, turbulence becomes short-lived and laminarizes. In the last part of the thesis, we show that using numerical simulations we can continue turbulent stripes in channel flow past the 'relaminarization barrier' all the way to their origin. Here, turbulent stripe dynamics simplifies and the fluctuations are no longer stochastic and the stripe settles down to a relative periodic orbit. This relative periodic orbit originates from the aforementioned traveling wave solutions. Starting from the relative periodic orbit, a small increase in speed i.e. Reynolds number gives rise to chaos and the attractor dimension sharply increases in contrast to the classical transition scenario where the instabilities affect the flow globally and give rise to much more gradual route to turbulence.","lang":"eng"}],"month":"10","alternative_title":["ISTA Thesis"],"file":[{"relation":"source_file","access_level":"closed","content_type":"application/zip","checksum":"7ba298ba0ce7e1d11691af6b8eaf0a0a","file_id":"6962","creator":"cparanjape","file_size":45828099,"date_updated":"2020-07-14T12:47:46Z","file_name":"Chaitanya_Paranjape_source_files_tex_figures.zip","date_created":"2019-10-23T09:54:43Z"},{"date_created":"2019-10-23T10:37:09Z","file_name":"Chaitanya_Paranjape_Thesis.pdf","date_updated":"2020-07-14T12:47:46Z","file_size":19504197,"creator":"cparanjape","checksum":"642697618314e31ac31392da7909c2d9","file_id":"6963","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","_id":"6957","status":"public","keyword":["Instabilities","Turbulence","Nonlinear dynamics"],"type":"dissertation","ddc":["532"],"supervisor":[{"last_name":"Hof","full_name":"Hof, Björn","orcid":"0000-0003-2057-2754","first_name":"Björn","id":"3A374330-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2023-09-07T12:53:25Z","department":[{"_id":"BjHo"}],"file_date_updated":"2020-07-14T12:47:46Z","publisher":"Institute of Science and Technology Austria","oa":1,"day":"24","has_accepted_license":"1","year":"2019","date_published":"2019-10-24T00:00:00Z","doi":"10.15479/AT:ISTA:6957","date_created":"2019-10-22T12:08:43Z","page":"138","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Paranjape, Chaitanya S. Onset of Turbulence in Plane Poiseuille Flow. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:6957.","apa":"Paranjape, C. S. (2019). Onset of turbulence in plane Poiseuille flow. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:6957","ama":"Paranjape CS. Onset of turbulence in plane Poiseuille flow. 2019. doi:10.15479/AT:ISTA:6957","short":"C.S. Paranjape, Onset of Turbulence in Plane Poiseuille Flow, Institute of Science and Technology Austria, 2019.","ieee":"C. S. Paranjape, “Onset of turbulence in plane Poiseuille flow,” Institute of Science and Technology Austria, 2019.","chicago":"Paranjape, Chaitanya S. “Onset of Turbulence in Plane Poiseuille Flow.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:6957.","ista":"Paranjape CS. 2019. Onset of turbulence in plane Poiseuille flow. Institute of Science and Technology Austria."},"title":"Onset of turbulence in plane Poiseuille flow","author":[{"last_name":"Paranjape","full_name":"Paranjape, Chaitanya S","id":"3D85B7C4-F248-11E8-B48F-1D18A9856A87","first_name":"Chaitanya S"}],"article_processing_charge":"No"},{"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_number":"e8","article_processing_charge":"No","external_id":{"arxiv":["1705.10661"],"isi":["000488847100001"]},"author":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"title":"Random matrices with slow correlation decay","citation":{"chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma. Cambridge University Press, 2019. https://doi.org/10.1017/fms.2019.2.","ista":"Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8.","mla":"Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma, vol. 7, e8, Cambridge University Press, 2019, doi:10.1017/fms.2019.2.","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press, 2019.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).","apa":"Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with slow correlation decay. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2019.2","ama":"Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 2019;7. doi:10.1017/fms.2019.2"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"publisher":"Cambridge University Press","quality_controlled":"1","date_created":"2019-03-28T09:05:23Z","date_published":"2019-03-26T00:00:00Z","doi":"10.1017/fms.2019.2","year":"2019","isi":1,"has_accepted_license":"1","publication":"Forum of Mathematics, Sigma","day":"26","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","_id":"6182","file_date_updated":"2020-07-14T12:47:22Z","department":[{"_id":"LaEr"}],"date_updated":"2023-09-07T12:54:12Z","ddc":["510"],"scopus_import":"1","intvolume":" 7","month":"03","abstract":[{"text":"We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion.","lang":"eng"}],"oa_version":"Published Version","ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6179"}]},"volume":7,"publication_status":"published","publication_identifier":{"eissn":["20505094"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"6883","checksum":"933a472568221c73b2c3ce8c87bf6d15","date_updated":"2020-07-14T12:47:22Z","file_size":1520344,"creator":"dernst","date_created":"2019-09-17T14:24:13Z","file_name":"2019_Forum_Erdoes.pdf"}]},{"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385"}],"article_processing_charge":"No","external_id":{"arxiv":["1811.04055"]},"author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"title":"Cusp universality for random matrices, II: The real symmetric case","citation":{"ista":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4), 615–707.","chicago":"Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis . MSP, 2019. https://doi.org/10.2140/paa.2019.1.615.","short":"G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis 1 (2019) 615–707.","ieee":"G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” Pure and Applied Analysis , vol. 1, no. 4. MSP, pp. 615–707, 2019.","ama":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 2019;1(4):615–707. doi:10.2140/paa.2019.1.615","apa":"Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . MSP. https://doi.org/10.2140/paa.2019.1.615","mla":"Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis , vol. 1, no. 4, MSP, 2019, pp. 615–707, doi:10.2140/paa.2019.1.615."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"publisher":"MSP","quality_controlled":"1","page":"615–707","date_created":"2019-03-28T10:21:17Z","doi":"10.2140/paa.2019.1.615","date_published":"2019-10-12T00:00:00Z","year":"2019","publication":"Pure and Applied Analysis ","day":"12","type":"journal_article","article_type":"original","status":"public","_id":"6186","department":[{"_id":"LaEr"}],"date_updated":"2023-09-07T12:54:12Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.04055"}],"intvolume":" 1","month":"10","abstract":[{"lang":"eng","text":"We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices near the cusp points of the eigenvalue density are universal. Together\r\nwith the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe complex Hermitian symmetry class, this completes the last remaining case of\r\nthe Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities have been established in the last years. We extend the recent\r\nDyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum principle of the heat flow related to the Dyson\r\nBrownian motion."}],"oa_version":"Preprint","ec_funded":1,"volume":1,"issue":"4","related_material":{"record":[{"status":"public","id":"6179","relation":"dissertation_contains"}]},"publication_status":"published","publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"file":[{"file_id":"6925","checksum":"81bdce1361c9aa8395d6fa635fb6ab47","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2019-10-01T10:53:45Z","file_name":"2019_PLoS_Cepeda-Humerez.pdf","creator":"kschuh","date_updated":"2020-07-14T12:47:44Z","file_size":3081855}],"publication_status":"published","publication_identifier":{"eissn":["15537358"]},"volume":15,"issue":"9","related_material":{"record":[{"status":"public","id":"6473","relation":"part_of_dissertation"}]},"pmid":1,"oa_version":"Published Version","abstract":[{"lang":"eng","text":"Across diverse biological systems—ranging from neural networks to intracellular signaling and genetic regulatory networks—the information about changes in the environment is frequently encoded in the full temporal dynamics of the network nodes. A pressing data-analysis challenge has thus been to efficiently estimate the amount of information that these dynamics convey from experimental data. Here we develop and evaluate decoding-based estimation methods to lower bound the mutual information about a finite set of inputs, encoded in single-cell high-dimensional time series data. For biological reaction networks governed by the chemical Master equation, we derive model-based information approximations and analytical upper bounds, against which we benchmark our proposed model-free decoding estimators. In contrast to the frequently-used k-nearest-neighbor estimator, decoding-based estimators robustly extract a large fraction of the available information from high-dimensional trajectories with a realistic number of data samples. We apply these estimators to previously published data on Erk and Ca2+ signaling in mammalian cells and to yeast stress-response, and find that substantial amount of information about environmental state can be encoded by non-trivial response statistics even in stationary signals. We argue that these single-cell, decoding-based information estimates, rather than the commonly-used tests for significant differences between selected population response statistics, provide a proper and unbiased measure for the performance of biological signaling networks."}],"intvolume":" 15","month":"09","scopus_import":"1","ddc":["570"],"date_updated":"2023-09-07T12:55:21Z","department":[{"_id":"GaTk"}],"file_date_updated":"2020-07-14T12:47:44Z","_id":"6900","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","publication":"PLoS computational biology","day":"03","year":"2019","has_accepted_license":"1","isi":1,"date_created":"2019-09-22T22:00:37Z","doi":"10.1371/journal.pcbi.1007290","date_published":"2019-09-03T00:00:00Z","page":"e1007290","oa":1,"publisher":"Public Library of Science","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Cepeda Humerez SA, Ruess J, Tkačik G. 2019. Estimating information in time-varying signals. PLoS computational biology. 15(9), e1007290.","chicago":"Cepeda Humerez, Sarah A, Jakob Ruess, and Gašper Tkačik. “Estimating Information in Time-Varying Signals.” PLoS Computational Biology. Public Library of Science, 2019. https://doi.org/10.1371/journal.pcbi.1007290.","apa":"Cepeda Humerez, S. A., Ruess, J., & Tkačik, G. (2019). Estimating information in time-varying signals. PLoS Computational Biology. Public Library of Science. https://doi.org/10.1371/journal.pcbi.1007290","ama":"Cepeda Humerez SA, Ruess J, Tkačik G. Estimating information in time-varying signals. PLoS computational biology. 2019;15(9):e1007290. doi:10.1371/journal.pcbi.1007290","ieee":"S. A. Cepeda Humerez, J. Ruess, and G. Tkačik, “Estimating information in time-varying signals,” PLoS computational biology, vol. 15, no. 9. Public Library of Science, p. e1007290, 2019.","short":"S.A. Cepeda Humerez, J. Ruess, G. Tkačik, PLoS Computational Biology 15 (2019) e1007290.","mla":"Cepeda Humerez, Sarah A., et al. “Estimating Information in Time-Varying Signals.” PLoS Computational Biology, vol. 15, no. 9, Public Library of Science, 2019, p. e1007290, doi:10.1371/journal.pcbi.1007290."},"title":"Estimating information in time-varying signals","article_processing_charge":"No","external_id":{"isi":["000489741800021"],"pmid":["31479447"]},"author":[{"full_name":"Cepeda Humerez, Sarah A","last_name":"Cepeda Humerez","id":"3DEE19A4-F248-11E8-B48F-1D18A9856A87","first_name":"Sarah A"},{"last_name":"Ruess","orcid":"0000-0003-1615-3282","full_name":"Ruess, Jakob","first_name":"Jakob"},{"first_name":"Gašper","id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","last_name":"Tkačik","full_name":"Tkačik, Gašper","orcid":"0000-0002-6699-1455"}],"project":[{"name":"Biophysics of information processing in gene regulation","grant_number":"P28844-B27","_id":"254E9036-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}]},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Dejonghe, Wim, et al. “Disruption of Endocytosis through Chemical Inhibition of Clathrin Heavy Chain Function.” Nature Chemical Biology, vol. 15, no. 6, Springer Nature, 2019, pp. 641–649, doi:10.1038/s41589-019-0262-1.","ieee":"W. Dejonghe et al., “Disruption of endocytosis through chemical inhibition of clathrin heavy chain function,” Nature Chemical Biology, vol. 15, no. 6. Springer Nature, pp. 641–649, 2019.","short":"W. Dejonghe, I. Sharma, B. Denoo, S. De Munck, Q. Lu, K. Mishev, H. Bulut, E. Mylle, R. De Rycke, M.K. Vasileva, D.V. Savatin, W. Nerinckx, A. Staes, A. Drozdzecki, D. Audenaert, K. Yperman, A. Madder, J. Friml, D. Van Damme, K. Gevaert, V. Haucke, S.N. Savvides, J. Winne, E. Russinova, Nature Chemical Biology 15 (2019) 641–649.","ama":"Dejonghe W, Sharma I, Denoo B, et al. Disruption of endocytosis through chemical inhibition of clathrin heavy chain function. Nature Chemical Biology. 2019;15(6):641–649. doi:10.1038/s41589-019-0262-1","apa":"Dejonghe, W., Sharma, I., Denoo, B., De Munck, S., Lu, Q., Mishev, K., … Russinova, E. (2019). Disruption of endocytosis through chemical inhibition of clathrin heavy chain function. Nature Chemical Biology. Springer Nature. https://doi.org/10.1038/s41589-019-0262-1","chicago":"Dejonghe, Wim, Isha Sharma, Bram Denoo, Steven De Munck, Qing Lu, Kiril Mishev, Haydar Bulut, et al. “Disruption of Endocytosis through Chemical Inhibition of Clathrin Heavy Chain Function.” Nature Chemical Biology. Springer Nature, 2019. https://doi.org/10.1038/s41589-019-0262-1.","ista":"Dejonghe W, Sharma I, Denoo B, De Munck S, Lu Q, Mishev K, Bulut H, Mylle E, De Rycke R, Vasileva MK, Savatin DV, Nerinckx W, Staes A, Drozdzecki A, Audenaert D, Yperman K, Madder A, Friml J, Van Damme D, Gevaert K, Haucke V, Savvides SN, Winne J, Russinova E. 2019. Disruption of endocytosis through chemical inhibition of clathrin heavy chain function. Nature Chemical Biology. 15(6), 641–649."},"title":"Disruption of endocytosis through chemical inhibition of clathrin heavy chain function","author":[{"last_name":"Dejonghe","full_name":"Dejonghe, Wim","first_name":"Wim"},{"last_name":"Sharma","full_name":"Sharma, Isha","first_name":"Isha"},{"full_name":"Denoo, Bram","last_name":"Denoo","first_name":"Bram"},{"last_name":"De Munck","full_name":"De Munck, Steven","first_name":"Steven"},{"first_name":"Qing","full_name":"Lu, Qing","last_name":"Lu"},{"first_name":"Kiril","full_name":"Mishev, Kiril","last_name":"Mishev"},{"last_name":"Bulut","full_name":"Bulut, Haydar","first_name":"Haydar"},{"first_name":"Evelien","last_name":"Mylle","full_name":"Mylle, Evelien"},{"first_name":"Riet","full_name":"De Rycke, Riet","last_name":"De Rycke"},{"id":"3407EB18-F248-11E8-B48F-1D18A9856A87","first_name":"Mina K","full_name":"Vasileva, Mina K","last_name":"Vasileva"},{"first_name":"Daniel V.","full_name":"Savatin, Daniel V.","last_name":"Savatin"},{"last_name":"Nerinckx","full_name":"Nerinckx, Wim","first_name":"Wim"},{"last_name":"Staes","full_name":"Staes, An","first_name":"An"},{"first_name":"Andrzej","full_name":"Drozdzecki, Andrzej","last_name":"Drozdzecki"},{"first_name":"Dominique","full_name":"Audenaert, Dominique","last_name":"Audenaert"},{"first_name":"Klaas","last_name":"Yperman","full_name":"Yperman, Klaas"},{"full_name":"Madder, Annemieke","last_name":"Madder","first_name":"Annemieke"},{"orcid":"0000-0002-8302-7596","full_name":"Friml, Jiří","last_name":"Friml","id":"4159519E-F248-11E8-B48F-1D18A9856A87","first_name":"Jiří"},{"first_name":"Daniël","full_name":"Van Damme, Daniël","last_name":"Van Damme"},{"full_name":"Gevaert, Kris","last_name":"Gevaert","first_name":"Kris"},{"last_name":"Haucke","full_name":"Haucke, Volker","first_name":"Volker"},{"last_name":"Savvides","full_name":"Savvides, Savvas N.","first_name":"Savvas N."},{"last_name":"Winne","full_name":"Winne, Johan","first_name":"Johan"},{"first_name":"Eugenia","last_name":"Russinova","full_name":"Russinova, Eugenia"}],"external_id":{"isi":["000468195600018"]},"article_processing_charge":"No","day":"01","publication":"Nature Chemical Biology","isi":1,"year":"2019","date_published":"2019-06-01T00:00:00Z","doi":"10.1038/s41589-019-0262-1","date_created":"2019-05-05T21:59:11Z","page":"641–649","publisher":"Springer Nature","quality_controlled":"1","date_updated":"2023-09-07T12:54:35Z","department":[{"_id":"JiFr"}],"_id":"6377","status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["15524469"],"issn":["15524450"]},"publication_status":"published","volume":15,"issue":"6","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"7172"}]},"oa_version":"None","abstract":[{"lang":"eng","text":"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."}],"month":"06","intvolume":" 15","scopus_import":"1"},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Schwayer C. 2019. Mechanosensation of tight junctions depends on ZO-1 phase separation and flow. Institute of Science and Technology Austria.","chicago":"Schwayer, Cornelia. “Mechanosensation of Tight Junctions Depends on ZO-1 Phase Separation and Flow.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:7186.","ieee":"C. Schwayer, “Mechanosensation of tight junctions depends on ZO-1 phase separation and flow,” Institute of Science and Technology Austria, 2019.","short":"C. Schwayer, Mechanosensation of Tight Junctions Depends on ZO-1 Phase Separation and Flow, Institute of Science and Technology Austria, 2019.","ama":"Schwayer C. Mechanosensation of tight junctions depends on ZO-1 phase separation and flow. 2019. doi:10.15479/AT:ISTA:7186","apa":"Schwayer, C. (2019). Mechanosensation of tight junctions depends on ZO-1 phase separation and flow. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7186","mla":"Schwayer, Cornelia. Mechanosensation of Tight Junctions Depends on ZO-1 Phase Separation and Flow. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:7186."},"title":"Mechanosensation of tight junctions depends on ZO-1 phase separation and flow","article_processing_charge":"No","author":[{"id":"3436488C-F248-11E8-B48F-1D18A9856A87","first_name":"Cornelia","orcid":"0000-0001-5130-2226","full_name":"Schwayer, Cornelia","last_name":"Schwayer"}],"oa":1,"publisher":"Institute of Science and Technology Austria","day":"16","year":"2019","has_accepted_license":"1","date_created":"2019-12-16T14:26:14Z","date_published":"2019-12-16T00:00:00Z","doi":"10.15479/AT:ISTA:7186","page":"107","_id":"7186","status":"public","type":"dissertation","ddc":["570"],"date_updated":"2023-09-07T12:56:42Z","supervisor":[{"first_name":"Carl-Philipp J","id":"39427864-F248-11E8-B48F-1D18A9856A87","full_name":"Heisenberg, Carl-Philipp J","orcid":"0000-0002-0912-4566","last_name":"Heisenberg"}],"file_date_updated":"2020-07-14T12:47:52Z","department":[{"_id":"CaHe"}],"oa_version":"Published Version","abstract":[{"lang":"eng","text":"Tissue morphogenesis in developmental or physiological processes is regulated by molecular\r\nand mechanical signals. While the molecular signaling cascades are increasingly well\r\ndescribed, the mechanical signals affecting tissue shape changes have only recently been\r\nstudied in greater detail. To gain more insight into the mechanochemical and biophysical\r\nbasis of an epithelial spreading process (epiboly) in early zebrafish development, we studied\r\ncell-cell junction formation and actomyosin network dynamics at the boundary between\r\nsurface layer epithelial cells (EVL) and the yolk syncytial layer (YSL). During zebrafish epiboly,\r\nthe cell mass sitting on top of the yolk cell spreads to engulf the yolk cell by the end of\r\ngastrulation. It has been previously shown that an actomyosin ring residing within the YSL\r\npulls on the EVL tissue through a cable-constriction and a flow-friction motor, thereby\r\ndragging the tissue vegetal wards. Pulling forces are likely transmitted from the YSL\r\nactomyosin ring to EVL cells; however, the nature and formation of the junctional structure\r\nmediating this process has not been well described so far. Therefore, our main aim was to\r\ndetermine the nature, dynamics and potential function of the EVL-YSL junction during this\r\nepithelial tissue spreading. Specifically, we show that the EVL-YSL junction is a\r\nmechanosensitive structure, predominantly made of tight junction (TJ) proteins. The process\r\nof TJ mechanosensation depends on the retrograde flow of non-junctional, phase-separated\r\nZonula Occludens-1 (ZO-1) protein clusters towards the EVL-YSL boundary. Interestingly, we\r\ncould demonstrate that ZO-1 is present in a non-junctional pool on the surface of the yolk\r\ncell, and ZO-1 undergoes a phase separation process that likely renders the protein\r\nresponsive to flows. These flows are directed towards the junction and mediate proper\r\ntension-dependent recruitment of ZO-1. Upon reaching the EVL-YSL junction ZO-1 gets\r\nincorporated into the junctional pool mediated through its direct actin-binding domain.\r\nWhen the non-junctional pool and/or ZO-1 direct actin binding is absent, TJs fail in their\r\nproper mechanosensitive responses resulting in slower tissue spreading. We could further\r\ndemonstrate that depletion of ZO proteins within the YSL results in diminished actomyosin\r\nring formation. This suggests that a mechanochemical feedback loop is at work during\r\nzebrafish epiboly: ZO proteins help in proper actomyosin ring formation and actomyosin\r\ncontractility and flows positively influence ZO-1 junctional recruitment. Finally, such a\r\nmesoscale polarization process mediated through the flow of phase-separated protein\r\nclusters might have implications for other processes such as immunological synapse\r\nformation, C. elegans zygote polarization and wound healing."}],"acknowledged_ssus":[{"_id":"Bio"},{"_id":"LifeSc"},{"_id":"EM-Fac"},{"_id":"SSU"}],"month":"12","alternative_title":["ISTA Thesis"],"language":[{"iso":"eng"}],"file":[{"file_id":"7194","checksum":"585583c1c875c5d9525703a539668a7c","access_level":"closed","relation":"source_file","content_type":"application/zip","date_created":"2019-12-19T15:18:11Z","file_name":"DocumentSourceFiles.zip","creator":"cschwayer","date_updated":"2020-07-14T12:47:52Z","file_size":19431292},{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"7195","checksum":"9b9b24351514948d27cec659e632e2cd","date_updated":"2020-07-14T12:47:52Z","file_size":19226428,"creator":"cschwayer","date_created":"2019-12-19T15:19:21Z","file_name":"Thesis_CS_final.pdf"}],"publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"related_material":{"record":[{"relation":"dissertation_contains","id":"1096","status":"public"},{"relation":"part_of_dissertation","id":"7001","status":"public"}]}},{"publisher":"Institute of Science and Technology Austria","oa":1,"doi":"10.15479/AT:ISTA:6681","date_published":"2019-08-08T00:00:00Z","date_created":"2019-07-26T11:14:34Z","page":"104","day":"08","has_accepted_license":"1","year":"2019","title":"Algorithmic aspects of homotopy theory and embeddability","author":[{"first_name":"Stephan Y","id":"3AA52972-F248-11E8-B48F-1D18A9856A87","full_name":"Zhechev, Stephan Y","last_name":"Zhechev"}],"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ama":"Zhechev SY. Algorithmic aspects of homotopy theory and embeddability. 2019. doi:10.15479/AT:ISTA:6681","apa":"Zhechev, S. Y. (2019). Algorithmic aspects of homotopy theory and embeddability. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:6681","short":"S.Y. Zhechev, Algorithmic Aspects of Homotopy Theory and Embeddability, Institute of Science and Technology Austria, 2019.","ieee":"S. Y. Zhechev, “Algorithmic aspects of homotopy theory and embeddability,” Institute of Science and Technology Austria, 2019.","mla":"Zhechev, Stephan Y. Algorithmic Aspects of Homotopy Theory and Embeddability. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:6681.","ista":"Zhechev SY. 2019. Algorithmic aspects of homotopy theory and embeddability. Institute of Science and Technology Austria.","chicago":"Zhechev, Stephan Y. “Algorithmic Aspects of Homotopy Theory and Embeddability.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:6681."},"month":"08","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","abstract":[{"text":"The first part of the thesis considers the computational aspects of the homotopy groups πd(X) of a topological space X. It is well known that there is no algorithm to decide whether the fundamental group π1(X) of a given finite simplicial complex X is trivial. On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with π1(X) trivial), compute the higher homotopy group πd(X) for any given d ≥ 2.\r\nHowever, these algorithms come with a caveat: They compute the isomorphism type of πd(X), d ≥ 2 as an abstract finitely generated abelian group given by generators and relations, but they work with very implicit representations of the elements of πd(X). We present an algorithm that, given a simply connected space X, computes πd(X) and represents its elements as simplicial maps from suitable triangulations of the d-sphere Sd to X. For fixed d, the algorithm runs in time exponential in size(X), the number of simplices of X. Moreover, we prove that this is optimal: For every fixed d ≥ 2,\r\nwe construct a family of simply connected spaces X such that for any simplicial map representing a generator of πd(X), the size of the triangulation of S d on which the map is defined, is exponential in size(X).\r\nIn the second part of the thesis, we prove that the following question is algorithmically undecidable for d < ⌊3(k+1)/2⌋, k ≥ 5 and (k, d) ̸= (5, 7), which covers essentially everything outside the meta-stable range: Given a finite simplicial complex K of dimension k, decide whether there exists a piecewise-linear (i.e., linear on an arbitrarily fine subdivision of K) embedding f : K ↪→ Rd of K into a d-dimensional Euclidean space.","lang":"eng"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"6774"}]},"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"3231e7cbfca3b5687366f84f0a57a0c0","file_id":"6771","date_updated":"2020-07-14T12:47:37Z","file_size":1464227,"creator":"szhechev","date_created":"2019-08-07T13:02:50Z","file_name":"Stephan_Zhechev_thesis.pdf"},{"relation":"source_file","access_level":"closed","content_type":"application/octet-stream","checksum":"85d65eb27b4377a9e332ee37a70f08b6","file_id":"6772","creator":"szhechev","file_size":303988,"date_updated":"2020-07-14T12:47:37Z","file_name":"Stephan_Zhechev_thesis.tex","date_created":"2019-08-07T13:03:22Z"},{"checksum":"86b374d264ca2dd53e712728e253ee75","file_id":"6773","content_type":"application/zip","relation":"supplementary_material","access_level":"closed","file_name":"supplementary_material.zip","date_created":"2019-08-07T13:03:34Z","file_size":1087004,"date_updated":"2020-07-14T12:47:37Z","creator":"szhechev"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","degree_awarded":"PhD","status":"public","type":"dissertation","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"6681","file_date_updated":"2020-07-14T12:47:37Z","department":[{"_id":"UlWa"}],"ddc":["514"],"supervisor":[{"last_name":"Wagner","full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli"}],"date_updated":"2023-09-07T13:10:36Z"},{"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1910.12628","open_access":"1"}],"publisher":"arXiv","month":"10","abstract":[{"text":"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 $X \\to\r\n{\\mathbb R}^n$ whose image avoids the diagonal $\\{(x,x\\dots,x)\\in {\\mathbb R}^n|x\\in {\\mathbb R}\\}$.\r\n 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\r\ntake 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\r\n$\\partial\\Delta^{n-1}$ 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.","lang":"eng"}],"oa_version":"Preprint","date_created":"2020-07-30T10:45:08Z","related_material":{"record":[{"status":"public","id":"11446","relation":"later_version"},{"relation":"dissertation_contains","status":"public","id":"8156"}]},"date_published":"2019-10-28T00:00:00Z","year":"2019","publication_status":"submitted","publication":"arXiv","language":[{"iso":"eng"}],"day":"28","type":"preprint","project":[{"call_identifier":"FWF","_id":"26611F5C-B435-11E9-9278-68D0E5697425","name":"Algorithms for Embeddings and Homotopy Theory","grant_number":"P31312"}],"status":"public","_id":"8182","article_number":"1910.12628","article_processing_charge":"No","external_id":{"arxiv":["1910.12628"]},"author":[{"full_name":"Avvakumov, Sergey","last_name":"Avvakumov","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey"},{"id":"ecf01965-d252-11ea-95a5-8ada5f6c6a67","first_name":"Sergey","full_name":"Kudrya, Sergey","last_name":"Kudrya"}],"department":[{"_id":"UlWa"}],"title":"Vanishing of all equivariant obstructions and the mapping degree","citation":{"ama":"Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. arXiv.","apa":"Avvakumov, S., & Kudrya, S. (n.d.). Vanishing of all equivariant obstructions and the mapping degree. arXiv. arXiv.","short":"S. Avvakumov, S. Kudrya, ArXiv (n.d.).","ieee":"S. Avvakumov and S. Kudrya, “Vanishing of all equivariant obstructions and the mapping degree,” arXiv. arXiv.","mla":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” ArXiv, 1910.12628, arXiv.","ista":"Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. arXiv, 1910.12628.","chicago":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” ArXiv. arXiv, n.d."},"date_updated":"2023-09-07T13:12:17Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}]