--- _id: '5678' abstract: - lang: eng text: "The order-k Voronoi tessellation of a locally finite set \U0001D44B⊆ℝ\U0001D45B decomposes ℝ\U0001D45B into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Anton full_name: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko orcid: 0000-0002-0659-3201 citation: ama: Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2 apa: Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2 chicago: Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2. ieee: H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019. ista: Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878. mla: Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:10.1007/s00454-018-0049-2. short: H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878. date_created: 2018-12-16T22:59:20Z date_published: 2019-12-01T00:00:00Z date_updated: 2023-09-07T12:07:12Z day: '01' ddc: - '516' department: - _id: HeEd doi: 10.1007/s00454-018-0049-2 ec_funded: 1 external_id: arxiv: - '1709.09380' isi: - '000494042900008' file: - access_level: open_access checksum: f9d00e166efaccb5a76bbcbb4dcea3b4 content_type: application/pdf creator: dernst date_created: 2019-02-06T10:10:46Z date_updated: 2020-07-14T12:47:10Z file_id: '5932' file_name: 2018_DiscreteCompGeometry_Edelsbrunner.pdf file_size: 599339 relation: main_file file_date_updated: 2020-07-14T12:47:10Z has_accepted_license: '1' intvolume: ' 62' isi: 1 issue: '4' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 865–878 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Discrete and Computational Geometry publication_identifier: eissn: - '14320444' issn: - '01795376' publication_status: published publisher: Springer quality_controlled: '1' related_material: record: - id: '6287' relation: dissertation_contains status: public scopus_import: '1' status: public title: Poisson–Delaunay Mosaics of Order k tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 62 year: '2019' ... --- _id: '5828' abstract: - lang: eng 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. article_processing_charge: No article_type: original author: - first_name: Haibing full_name: Xu, Haibing id: 310349D0-F248-11E8-B48F-1D18A9856A87 last_name: Xu - first_name: Peter full_name: Baracskay, Peter id: 361CC00E-F248-11E8-B48F-1D18A9856A87 last_name: Baracskay - first_name: Joseph full_name: O'Neill, Joseph id: 426376DC-F248-11E8-B48F-1D18A9856A87 last_name: O'Neill - first_name: Jozsef L full_name: Csicsvari, Jozsef L id: 3FA14672-F248-11E8-B48F-1D18A9856A87 last_name: Csicsvari orcid: 0000-0002-5193-4036 citation: 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 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 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. 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. 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. 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. short: H. Xu, P. Baracskay, J. O’Neill, J.L. Csicsvari, Neuron 101 (2019) 119–132.e4. date_created: 2019-01-13T22:59:10Z date_published: 2019-01-02T00:00:00Z date_updated: 2023-09-07T12:06:37Z day: '02' department: - _id: JoCs doi: 10.1016/j.neuron.2018.11.015 ec_funded: 1 external_id: isi: - '000454791500014' intvolume: ' 101' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://www.doi.org/10.1016/j.neuron.2018.11.015 month: '01' oa: 1 oa_version: Published Version page: 119-132.e4 project: - _id: 257A4776-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '281511' name: Memory-related information processing in neuronal circuits of the hippocampus and entorhinal cortex publication: Neuron publication_identifier: issn: - '10974199' publication_status: published publisher: Elsevier quality_controlled: '1' related_material: link: - description: News on IST Homepage relation: press_release url: https://ist.ac.at/en/news/reading-rats-minds/ record: - id: '837' relation: dissertation_contains status: public scopus_import: '1' status: public title: Assembly responses of hippocampal CA1 place cells predict learned behavior in goal-directed spatial tasks on the radial eight-arm maze type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 101 year: '2019' ... --- _id: '5856' abstract: - lang: eng 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. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Thomas full_name: Moser, Thomas id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87 last_name: Moser - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: 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 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 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. 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. ista: Moser T, Seiringer R. 2019. Energy contribution of a point-interacting impurity in a Fermi gas. Annales Henri Poincare. 20(4), 1325–1365. 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. short: T. Moser, R. Seiringer, Annales Henri Poincare 20 (2019) 1325–1365. date_created: 2019-01-20T22:59:17Z date_published: 2019-04-01T00:00:00Z date_updated: 2023-09-07T12:37:42Z day: '01' ddc: - '530' department: - _id: RoSe doi: 10.1007/s00023-018-00757-0 ec_funded: 1 external_id: arxiv: - '1807.00739' isi: - '000462444300008' file: - access_level: open_access checksum: 255e42f957a8e2b10aad2499c750a8d6 content_type: application/pdf creator: dernst date_created: 2019-01-28T15:27:17Z date_updated: 2020-07-14T12:47:12Z file_id: '5894' file_name: 2019_Annales_Moser.pdf file_size: 859846 relation: main_file file_date_updated: 2020-07-14T12:47:12Z has_accepted_license: '1' intvolume: ' 20' isi: 1 issue: '4' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 1325–1365 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Annales Henri Poincare publication_identifier: issn: - '14240637' publication_status: published publisher: Springer quality_controlled: '1' related_material: record: - id: '52' relation: dissertation_contains status: public scopus_import: '1' status: public title: Energy contribution of a point-interacting impurity in a Fermi gas tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 20 year: '2019' ... --- _id: '6957' abstract: - lang: eng 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." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Chaitanya S full_name: Paranjape, Chaitanya S id: 3D85B7C4-F248-11E8-B48F-1D18A9856A87 last_name: Paranjape citation: ama: Paranjape CS. Onset of turbulence in plane Poiseuille flow. 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 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. ieee: C. S. Paranjape, “Onset of turbulence in plane Poiseuille flow,” Institute of Science and Technology Austria, 2019. ista: Paranjape CS. 2019. Onset of turbulence in plane Poiseuille flow. Institute of Science and Technology Austria. mla: Paranjape, Chaitanya S. Onset of Turbulence in Plane Poiseuille Flow. Institute of Science and Technology Austria, 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. date_created: 2019-10-22T12:08:43Z date_published: 2019-10-24T00:00:00Z date_updated: 2023-09-07T12:53:25Z day: '24' ddc: - '532' degree_awarded: PhD department: - _id: BjHo doi: 10.15479/AT:ISTA:6957 file: - access_level: closed checksum: 7ba298ba0ce7e1d11691af6b8eaf0a0a content_type: application/zip creator: cparanjape date_created: 2019-10-23T09:54:43Z date_updated: 2020-07-14T12:47:46Z file_id: '6962' file_name: Chaitanya_Paranjape_source_files_tex_figures.zip file_size: 45828099 relation: source_file - access_level: open_access checksum: 642697618314e31ac31392da7909c2d9 content_type: application/pdf creator: cparanjape date_created: 2019-10-23T10:37:09Z date_updated: 2020-07-14T12:47:46Z file_id: '6963' file_name: Chaitanya_Paranjape_Thesis.pdf file_size: 19504197 relation: main_file file_date_updated: 2020-07-14T12:47:46Z has_accepted_license: '1' keyword: - Instabilities - Turbulence - Nonlinear dynamics language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: '138' publication_identifier: eissn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria status: public supervisor: - first_name: Björn full_name: Hof, Björn id: 3A374330-F248-11E8-B48F-1D18A9856A87 last_name: Hof orcid: 0000-0003-2057-2754 title: Onset of turbulence in plane Poiseuille flow type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2019' ... --- _id: '6182' abstract: - lang: eng 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." article_number: e8 article_processing_charge: No article_type: original author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: 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 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 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. 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. 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. short: L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019). date_created: 2019-03-28T09:05:23Z date_published: 2019-03-26T00:00:00Z date_updated: 2023-09-07T12:54:12Z day: '26' ddc: - '510' department: - _id: LaEr doi: 10.1017/fms.2019.2 ec_funded: 1 external_id: arxiv: - '1705.10661' isi: - '000488847100001' file: - access_level: open_access checksum: 933a472568221c73b2c3ce8c87bf6d15 content_type: application/pdf creator: dernst date_created: 2019-09-17T14:24:13Z date_updated: 2020-07-14T12:47:22Z file_id: '6883' file_name: 2019_Forum_Erdoes.pdf file_size: 1520344 relation: main_file file_date_updated: 2020-07-14T12:47:22Z has_accepted_license: '1' intvolume: ' 7' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Forum of Mathematics, Sigma publication_identifier: eissn: - '20505094' publication_status: published publisher: Cambridge University Press quality_controlled: '1' related_material: record: - id: '6179' relation: dissertation_contains status: public scopus_import: '1' status: public title: Random matrices with slow correlation decay tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 7 year: '2019' ...