--- _id: '9196' abstract: - lang: eng text: In order to provide a local description of a regular function in a small neighbourhood of a point x, it is sufficient by Taylor’s theorem to know the value of the function as well as all of its derivatives up to the required order at the point x itself. In other words, one could say that a regular function is locally modelled by the set of polynomials. The theory of regularity structures due to Hairer generalizes this observation and provides an abstract setup, which in the application to singular SPDE extends the set of polynomials by functionals constructed from, e.g., white noise. In this context, the notion of Taylor polynomials is lifted to the notion of so-called modelled distributions. The celebrated reconstruction theorem, which in turn was inspired by Gubinelli’s \textit {sewing lemma}, is of paramount importance for the theory. It enables one to reconstruct a modelled distribution as a true distribution on Rd which is locally approximated by this extended set of models or “monomials”. In the original work of Hairer, the error is measured by means of Hölder norms. This was then generalized to the whole scale of Besov spaces by Hairer and Labbé. It is the aim of this work to adapt the analytic part of the theory of regularity structures to the scale of Triebel–Lizorkin spaces. article_processing_charge: No article_type: original author: - first_name: Sebastian full_name: Hensel, Sebastian id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87 last_name: Hensel orcid: 0000-0001-7252-8072 - first_name: Tommaso full_name: Rosati, Tommaso last_name: Rosati citation: ama: Hensel S, Rosati T. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 2020;252(3):251-297. doi:10.4064/sm180411-11-2 apa: Hensel, S., & Rosati, T. (2020). Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. Instytut Matematyczny. https://doi.org/10.4064/sm180411-11-2 chicago: Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” Studia Mathematica. Instytut Matematyczny, 2020. https://doi.org/10.4064/sm180411-11-2. ieee: S. Hensel and T. Rosati, “Modelled distributions of Triebel–Lizorkin type,” Studia Mathematica, vol. 252, no. 3. Instytut Matematyczny, pp. 251–297, 2020. ista: Hensel S, Rosati T. 2020. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 252(3), 251–297. mla: Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” Studia Mathematica, vol. 252, no. 3, Instytut Matematyczny, 2020, pp. 251–97, doi:10.4064/sm180411-11-2. short: S. Hensel, T. Rosati, Studia Mathematica 252 (2020) 251–297. date_created: 2021-02-25T08:55:03Z date_published: 2020-03-01T00:00:00Z date_updated: 2023-10-17T09:15:53Z day: '01' department: - _id: JuFi - _id: GradSch doi: 10.4064/sm180411-11-2 external_id: arxiv: - '1709.05202' isi: - '000558100500002' intvolume: ' 252' isi: 1 issue: '3' keyword: - General Mathematics language: - iso: eng month: '03' oa_version: Preprint page: 251-297 publication: Studia Mathematica publication_identifier: eissn: - 1730-6337 issn: - 0039-3223 publication_status: published publisher: Instytut Matematyczny quality_controlled: '1' scopus_import: '1' status: public title: Modelled distributions of Triebel–Lizorkin type type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 252 year: '2020' ... --- _id: '7464' abstract: - lang: eng text: 'Retrovirus assembly is driven by the multidomain structural protein Gag. Interactions between the capsid domains (CA) of Gag result in Gag multimerization, leading to an immature virus particle that is formed by a protein lattice based on dimeric, trimeric, and hexameric protein contacts. Among retroviruses the inter- and intra-hexamer contacts differ, especially in the N-terminal sub-domain of CA (CANTD). For HIV-1 the cellular molecule inositol hexakisphosphate (IP6) interacts with and stabilizes the immature hexamer, and is required for production of infectious virus particles. We have used in vitro assembly, cryo-electron tomography and subtomogram averaging, atomistic molecular dynamics simulations and mutational analyses to study the HIV-related lentivirus equine infectious anemia virus (EIAV). In particular, we sought to understand the structural conservation of the immature lentivirus lattice and the role of IP6 in EIAV assembly. Similar to HIV-1, IP6 strongly promoted in vitro assembly of EIAV Gag proteins into virus-like particles (VLPs), which took three morphologically highly distinct forms: narrow tubes, wide tubes, and spheres. Structural characterization of these VLPs to sub-4Å resolution unexpectedly showed that all three morphologies are based on an immature lattice with preserved key structural components, highlighting the structural versatility of CA to form immature assemblies. A direct comparison between EIAV and HIV revealed that both lentiviruses maintain similar immature interfaces, which are established by both conserved and non-conserved residues. In both EIAV and HIV-1, IP6 regulates immature assembly via conserved lysine residues within the CACTD and SP. Lastly, we demonstrate that IP6 stimulates in vitro assembly of immature particles of several other retroviruses in the lentivirus genus, suggesting a conserved role for IP6 in lentiviral assembly.' acknowledged_ssus: - _id: ScienComp article_number: e1008277 article_processing_charge: No article_type: original author: - first_name: Robert A. full_name: Dick, Robert A. last_name: Dick - first_name: Chaoyi full_name: Xu, Chaoyi last_name: Xu - first_name: Dustin R. full_name: Morado, Dustin R. last_name: Morado - first_name: Vladyslav full_name: Kravchuk, Vladyslav id: 4D62F2A6-F248-11E8-B48F-1D18A9856A87 last_name: Kravchuk orcid: 0000-0001-9523-9089 - first_name: Clifton L. full_name: Ricana, Clifton L. last_name: Ricana - first_name: Terri D. full_name: Lyddon, Terri D. last_name: Lyddon - first_name: Arianna M. full_name: Broad, Arianna M. last_name: Broad - first_name: J. Ryan full_name: Feathers, J. Ryan last_name: Feathers - first_name: Marc C. full_name: Johnson, Marc C. last_name: Johnson - first_name: Volker M. full_name: Vogt, Volker M. last_name: Vogt - first_name: Juan R. full_name: Perilla, Juan R. last_name: Perilla - first_name: John A. G. full_name: Briggs, John A. G. last_name: Briggs - first_name: Florian KM full_name: Schur, Florian KM id: 48AD8942-F248-11E8-B48F-1D18A9856A87 last_name: Schur orcid: 0000-0003-4790-8078 citation: ama: Dick RA, Xu C, Morado DR, et al. Structures of immature EIAV Gag lattices reveal a conserved role for IP6 in lentivirus assembly. PLOS Pathogens. 2020;16(1). doi:10.1371/journal.ppat.1008277 apa: Dick, R. A., Xu, C., Morado, D. R., Kravchuk, V., Ricana, C. L., Lyddon, T. D., … Schur, F. K. (2020). Structures of immature EIAV Gag lattices reveal a conserved role for IP6 in lentivirus assembly. PLOS Pathogens. Public Library of Science. https://doi.org/10.1371/journal.ppat.1008277 chicago: Dick, Robert A., Chaoyi Xu, Dustin R. Morado, Vladyslav Kravchuk, Clifton L. Ricana, Terri D. Lyddon, Arianna M. Broad, et al. “Structures of Immature EIAV Gag Lattices Reveal a Conserved Role for IP6 in Lentivirus Assembly.” PLOS Pathogens. Public Library of Science, 2020. https://doi.org/10.1371/journal.ppat.1008277. ieee: R. A. Dick et al., “Structures of immature EIAV Gag lattices reveal a conserved role for IP6 in lentivirus assembly,” PLOS Pathogens, vol. 16, no. 1. Public Library of Science, 2020. ista: Dick RA, Xu C, Morado DR, Kravchuk V, Ricana CL, Lyddon TD, Broad AM, Feathers JR, Johnson MC, Vogt VM, Perilla JR, Briggs JAG, Schur FK. 2020. Structures of immature EIAV Gag lattices reveal a conserved role for IP6 in lentivirus assembly. PLOS Pathogens. 16(1), e1008277. mla: Dick, Robert A., et al. “Structures of Immature EIAV Gag Lattices Reveal a Conserved Role for IP6 in Lentivirus Assembly.” PLOS Pathogens, vol. 16, no. 1, e1008277, Public Library of Science, 2020, doi:10.1371/journal.ppat.1008277. short: R.A. Dick, C. Xu, D.R. Morado, V. Kravchuk, C.L. Ricana, T.D. Lyddon, A.M. Broad, J.R. Feathers, M.C. Johnson, V.M. Vogt, J.R. Perilla, J.A.G. Briggs, F.K. Schur, PLOS Pathogens 16 (2020). date_created: 2020-02-06T18:47:17Z date_published: 2020-01-27T00:00:00Z date_updated: 2023-10-17T12:29:34Z day: '27' ddc: - '570' department: - _id: FlSc doi: 10.1371/journal.ppat.1008277 external_id: isi: - '000510746400010' pmid: - '31986188' file: - access_level: open_access checksum: a297f54d1fef0efe4789ca00f37f241e content_type: application/pdf creator: dernst date_created: 2020-02-11T10:07:28Z date_updated: 2020-07-14T12:47:59Z file_id: '7484' file_name: 2020_PLOSPatho_Dick.pdf file_size: 4551246 relation: main_file file_date_updated: 2020-07-14T12:47:59Z has_accepted_license: '1' intvolume: ' 16' isi: 1 issue: '1' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '01' oa: 1 oa_version: Published Version pmid: 1 project: - _id: 26736D6A-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31445 name: Structural conservation and diversity in retroviral capsid publication: PLOS Pathogens publication_identifier: issn: - 1553-7374 publication_status: published publisher: Public Library of Science quality_controlled: '1' related_material: record: - id: '9723' relation: research_data status: deleted scopus_import: '1' status: public title: Structures of immature EIAV Gag lattices reveal a conserved role for IP6 in lentivirus assembly 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2020' ... --- _id: '7212' abstract: - lang: eng text: The fixation probability of a single mutant invading a population of residents is among the most widely-studied quantities in evolutionary dynamics. Amplifiers of natural selection are population structures that increase the fixation probability of advantageous mutants, compared to well-mixed populations. Extensive studies have shown that many amplifiers exist for the Birth-death Moran process, some of them substantially increasing the fixation probability or even guaranteeing fixation in the limit of large population size. On the other hand, no amplifiers are known for the death-Birth Moran process, and computer-assisted exhaustive searches have failed to discover amplification. In this work we resolve this disparity, by showing that any amplification under death-Birth updating is necessarily bounded and transient. Our boundedness result states that even if a population structure does amplify selection, the resulting fixation probability is close to that of the well-mixed population. Our transience result states that for any population structure there exists a threshold r⋆ such that the population structure ceases to amplify selection if the mutant fitness advantage r is larger than r⋆. Finally, we also extend the above results to δ-death-Birth updating, which is a combination of Birth-death and death-Birth updating. On the positive side, we identify population structures that maintain amplification for a wide range of values r and δ. These results demonstrate that amplification of natural selection depends on the specific mechanisms of the evolutionary process. article_number: e1007494 article_processing_charge: No article_type: original author: - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 - first_name: Andreas full_name: Pavlogiannis, Andreas id: 49704004-F248-11E8-B48F-1D18A9856A87 last_name: Pavlogiannis orcid: 0000-0002-8943-0722 - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Martin A. full_name: Nowak, Martin A. last_name: Nowak citation: ama: Tkadlec J, Pavlogiannis A, Chatterjee K, Nowak MA. Limits on amplifiers of natural selection under death-Birth updating. PLoS computational biology. 2020;16. doi:10.1371/journal.pcbi.1007494 apa: Tkadlec, J., Pavlogiannis, A., Chatterjee, K., & Nowak, M. A. (2020). Limits on amplifiers of natural selection under death-Birth updating. PLoS Computational Biology. Public Library of Science. https://doi.org/10.1371/journal.pcbi.1007494 chicago: Tkadlec, Josef, Andreas Pavlogiannis, Krishnendu Chatterjee, and Martin A. Nowak. “Limits on Amplifiers of Natural Selection under Death-Birth Updating.” PLoS Computational Biology. Public Library of Science, 2020. https://doi.org/10.1371/journal.pcbi.1007494. ieee: J. Tkadlec, A. Pavlogiannis, K. Chatterjee, and M. A. Nowak, “Limits on amplifiers of natural selection under death-Birth updating,” PLoS computational biology, vol. 16. Public Library of Science, 2020. ista: Tkadlec J, Pavlogiannis A, Chatterjee K, Nowak MA. 2020. Limits on amplifiers of natural selection under death-Birth updating. PLoS computational biology. 16, e1007494. mla: Tkadlec, Josef, et al. “Limits on Amplifiers of Natural Selection under Death-Birth Updating.” PLoS Computational Biology, vol. 16, e1007494, Public Library of Science, 2020, doi:10.1371/journal.pcbi.1007494. short: J. Tkadlec, A. Pavlogiannis, K. Chatterjee, M.A. Nowak, PLoS Computational Biology 16 (2020). date_created: 2019-12-23T13:45:11Z date_published: 2020-01-17T00:00:00Z date_updated: 2023-10-17T12:29:47Z day: '17' ddc: - '000' department: - _id: KrCh doi: 10.1371/journal.pcbi.1007494 ec_funded: 1 external_id: arxiv: - '1906.02785' isi: - '000510916500025' file: - access_level: open_access checksum: ce32ee2d2f53aed832f78bbd47e882df content_type: application/pdf creator: dernst date_created: 2020-02-03T07:32:42Z date_updated: 2020-07-14T12:47:53Z file_id: '7441' file_name: 2020_PlosCompBio_Tkadlec.pdf file_size: 1817531 relation: main_file file_date_updated: 2020-07-14T12:47:53Z has_accepted_license: '1' intvolume: ' 16' isi: 1 language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory publication: PLoS computational biology publication_identifier: eissn: - '15537358' publication_status: published publisher: Public Library of Science quality_controlled: '1' related_material: record: - id: '7196' relation: part_of_dissertation status: public scopus_import: '1' status: public title: Limits on amplifiers of natural selection under death-Birth updating 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2020' ... --- _id: '7196' abstract: - lang: eng text: 'In this thesis we study certain mathematical aspects of evolution. The two primary forces that drive an evolutionary process are mutation and selection. Mutation generates new variants in a population. Selection chooses among the variants depending on the reproductive rates of individuals. Evolutionary processes are intrinsically random – a new mutation that is initially present in the population at low frequency can go extinct, even if it confers a reproductive advantage. The overall rate of evolution is largely determined by two quantities: the probability that an invading advantageous mutation spreads through the population (called fixation probability) and the time until it does so (called fixation time). Both those quantities crucially depend not only on the strength of the invading mutation but also on the population structure. In this thesis, we aim to understand how the underlying population structure affects the overall rate of evolution. Specifically, we study population structures that increase the fixation probability of advantageous mutants (called amplifiers of selection). Broadly speaking, our results are of three different types: We present various strong amplifiers, we identify regimes under which only limited amplification is feasible, and we propose population structures that provide different tradeoffs between high fixation probability and short fixation time.' alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 citation: ama: Tkadlec J. A role of graphs in evolutionary processes. 2020. doi:10.15479/AT:ISTA:7196 apa: Tkadlec, J. (2020). A role of graphs in evolutionary processes. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7196 chicago: Tkadlec, Josef. “A Role of Graphs in Evolutionary Processes.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7196. ieee: J. Tkadlec, “A role of graphs in evolutionary processes,” Institute of Science and Technology Austria, 2020. ista: Tkadlec J. 2020. A role of graphs in evolutionary processes. Institute of Science and Technology Austria. mla: Tkadlec, Josef. A Role of Graphs in Evolutionary Processes. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7196. short: J. Tkadlec, A Role of Graphs in Evolutionary Processes, Institute of Science and Technology Austria, 2020. date_created: 2019-12-20T12:26:36Z date_published: 2020-01-12T00:00:00Z date_updated: 2023-10-17T12:29:46Z day: '12' ddc: - '519' degree_awarded: PhD department: - _id: KrCh - _id: GradSch doi: 10.15479/AT:ISTA:7196 file: - access_level: closed checksum: 451f8e64b0eb26bf297644ac72bfcbe9 content_type: application/zip creator: jtkadlec date_created: 2020-01-12T11:49:49Z date_updated: 2020-07-14T12:47:52Z file_id: '7255' file_name: thesis.zip file_size: 21100497 relation: source_file - access_level: open_access checksum: d8c44cbc4f939c49a8efc9d4b8bb3985 content_type: application/pdf creator: dernst date_created: 2020-01-28T07:32:42Z date_updated: 2020-07-14T12:47:52Z file_id: '7367' file_name: 2020_Tkadlec_Thesis.pdf file_size: 11670983 relation: main_file file_date_updated: 2020-07-14T12:47:52Z has_accepted_license: '1' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: '144' publication_identifier: eissn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '7210' relation: dissertation_contains status: public - id: '5751' relation: dissertation_contains status: public - id: '7212' relation: dissertation_contains status: public status: public supervisor: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X title: A role of graphs in evolutionary processes type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2020' ... --- _id: '9198' abstract: - lang: eng text: "The optimization of multilayer neural networks typically leads to a solution\r\nwith zero training error, yet the landscape can exhibit spurious local minima\r\nand the minima can be disconnected. In this paper, we shed light on this\r\nphenomenon: we show that the combination of stochastic gradient descent (SGD)\r\nand over-parameterization makes the landscape of multilayer neural networks\r\napproximately connected and thus more favorable to optimization. More\r\nspecifically, we prove that SGD solutions are connected via a piecewise linear\r\npath, and the increase in loss along this path vanishes as the number of\r\nneurons grows large. This result is a consequence of the fact that the\r\nparameters found by SGD are increasingly dropout stable as the network becomes\r\nwider. We show that, if we remove part of the neurons (and suitably rescale the\r\nremaining ones), the change in loss is independent of the total number of\r\nneurons, and it depends only on how many neurons are left. Our results exhibit\r\na mild dependence on the input dimension: they are dimension-free for two-layer\r\nnetworks and depend linearly on the dimension for multilayer networks. We\r\nvalidate our theoretical findings with numerical experiments for different\r\narchitectures and classification tasks." acknowledgement: M. Mondelli was partially supported by the 2019 LopezLoreta Prize. The authors thank Phan-Minh Nguyen for helpful discussions and the IST Distributed Algorithms and Systems Lab for providing computational resources. article_processing_charge: No author: - first_name: Alexander full_name: Shevchenko, Alexander last_name: Shevchenko - first_name: Marco full_name: Mondelli, Marco id: 27EB676C-8706-11E9-9510-7717E6697425 last_name: Mondelli orcid: 0000-0002-3242-7020 citation: ama: 'Shevchenko A, Mondelli M. Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks. In: Proceedings of the 37th International Conference on Machine Learning. Vol 119. ML Research Press; 2020:8773-8784.' apa: Shevchenko, A., & Mondelli, M. (2020). Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks. In Proceedings of the 37th International Conference on Machine Learning (Vol. 119, pp. 8773–8784). ML Research Press. chicago: Shevchenko, Alexander, and Marco Mondelli. “Landscape Connectivity and Dropout Stability of SGD Solutions for Over-Parameterized Neural Networks.” In Proceedings of the 37th International Conference on Machine Learning, 119:8773–84. ML Research Press, 2020. ieee: A. Shevchenko and M. Mondelli, “Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks,” in Proceedings of the 37th International Conference on Machine Learning, 2020, vol. 119, pp. 8773–8784. ista: Shevchenko A, Mondelli M. 2020. Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks. Proceedings of the 37th International Conference on Machine Learning. vol. 119, 8773–8784. mla: Shevchenko, Alexander, and Marco Mondelli. “Landscape Connectivity and Dropout Stability of SGD Solutions for Over-Parameterized Neural Networks.” Proceedings of the 37th International Conference on Machine Learning, vol. 119, ML Research Press, 2020, pp. 8773–84. short: A. Shevchenko, M. Mondelli, in:, Proceedings of the 37th International Conference on Machine Learning, ML Research Press, 2020, pp. 8773–8784. date_created: 2021-02-25T09:36:22Z date_published: 2020-07-13T00:00:00Z date_updated: 2023-10-17T12:43:19Z day: '13' ddc: - '000' department: - _id: MaMo external_id: arxiv: - '1912.10095' file: - access_level: open_access checksum: f042c8d4316bd87c6361aa76f1fbdbbe content_type: application/pdf creator: dernst date_created: 2021-03-02T15:38:14Z date_updated: 2021-03-02T15:38:14Z file_id: '9217' file_name: 2020_PMLR_Shevchenko.pdf file_size: 5336380 relation: main_file success: 1 file_date_updated: 2021-03-02T15:38:14Z has_accepted_license: '1' intvolume: ' 119' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 8773-8784 project: - _id: 059876FA-7A3F-11EA-A408-12923DDC885E name: Prix Lopez-Loretta 2019 - Marco Mondelli publication: Proceedings of the 37th International Conference on Machine Learning publication_status: published publisher: ML Research Press quality_controlled: '1' status: public title: Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 119 year: '2020' ...