[{"date_published":"2023-02-27T00:00:00Z","citation":{"apa":"Mckerral, J. C., Kleshnina, M., Ejov, V., Bartle, L., Mitchell, J. G., & Filar, J. A. (2023). Empirical parameterisation and dynamical analysis of the allometric Rosenzweig-MacArthur equations. PLoS One. Public Library of Science. https://doi.org/10.1371/journal.pone.0279838","ieee":"J. C. Mckerral, M. Kleshnina, V. Ejov, L. Bartle, J. G. Mitchell, and J. A. Filar, “Empirical parameterisation and dynamical analysis of the allometric Rosenzweig-MacArthur equations,” PLoS One, vol. 18, no. 2. Public Library of Science, p. e0279838, 2023.","ista":"Mckerral JC, Kleshnina M, Ejov V, Bartle L, Mitchell JG, Filar JA. 2023. Empirical parameterisation and dynamical analysis of the allometric Rosenzweig-MacArthur equations. PLoS One. 18(2), e0279838.","ama":"Mckerral JC, Kleshnina M, Ejov V, Bartle L, Mitchell JG, Filar JA. Empirical parameterisation and dynamical analysis of the allometric Rosenzweig-MacArthur equations. PLoS One. 2023;18(2):e0279838. doi:10.1371/journal.pone.0279838","chicago":"Mckerral, Jody C., Maria Kleshnina, Vladimir Ejov, Louise Bartle, James G. Mitchell, and Jerzy A. Filar. “Empirical Parameterisation and Dynamical Analysis of the Allometric Rosenzweig-MacArthur Equations.” PLoS One. Public Library of Science, 2023. https://doi.org/10.1371/journal.pone.0279838.","short":"J.C. Mckerral, M. Kleshnina, V. Ejov, L. Bartle, J.G. Mitchell, J.A. Filar, PLoS One 18 (2023) e0279838.","mla":"Mckerral, Jody C., et al. “Empirical Parameterisation and Dynamical Analysis of the Allometric Rosenzweig-MacArthur Equations.” PLoS One, vol. 18, no. 2, Public Library of Science, 2023, p. e0279838, doi:10.1371/journal.pone.0279838."},"publication":"PLoS One","page":"e0279838","article_type":"original","has_accepted_license":"1","article_processing_charge":"No","day":"27","scopus_import":"1","oa_version":"Published Version","file":[{"creator":"cchlebak","content_type":"application/pdf","file_size":1257003,"file_name":"2023_PLOSOne_Mckerral.pdf","access_level":"open_access","date_updated":"2023-03-07T10:26:45Z","date_created":"2023-03-07T10:26:45Z","success":1,"checksum":"798ed5739a4117b03173e5d56e0534c9","file_id":"12712","relation":"main_file"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12706","intvolume":" 18","status":"public","ddc":["000"],"title":"Empirical parameterisation and dynamical analysis of the allometric Rosenzweig-MacArthur equations","issue":"2","abstract":[{"lang":"eng","text":"Allometric settings of population dynamics models are appealing due to their parsimonious nature and broad utility when studying system level effects. Here, we parameterise the size-scaled Rosenzweig-MacArthur differential equations to eliminate prey-mass dependency, facilitating an in depth analytic study of the equations which incorporates scaling parameters’ contributions to coexistence. We define the functional response term to match empirical findings, and examine situations where metabolic theory derivations and observation diverge. The dynamical properties of the Rosenzweig-MacArthur system, encompassing the distribution of size-abundance equilibria, the scaling of period and amplitude of population cycling, and relationships between predator and prey abundances, are consistent with empirical observation. Our parameterisation is an accurate minimal model across 15+ orders of mass magnitude."}],"type":"journal_article","doi":"10.1371/journal.pone.0279838","language":[{"iso":"eng"}],"external_id":{"isi":["000996122900022"],"pmid":["36848357"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"isi":1,"quality_controlled":"1","publication_identifier":{"eissn":["1932-6203"]},"month":"02","author":[{"first_name":"Jody C.","last_name":"Mckerral","full_name":"Mckerral, Jody C."},{"full_name":"Kleshnina, Maria","id":"4E21749C-F248-11E8-B48F-1D18A9856A87","last_name":"Kleshnina","first_name":"Maria"},{"full_name":"Ejov, Vladimir","first_name":"Vladimir","last_name":"Ejov"},{"full_name":"Bartle, Louise","last_name":"Bartle","first_name":"Louise"},{"full_name":"Mitchell, James G.","first_name":"James G.","last_name":"Mitchell"},{"last_name":"Filar","first_name":"Jerzy A.","full_name":"Filar, Jerzy A."}],"volume":18,"date_updated":"2023-10-17T12:53:30Z","date_created":"2023-03-05T23:01:05Z","pmid":1,"acknowledgement":"This research was supported by an Australian Government Research Training Program\r\n(RTP) Scholarship to JCM (https://www.dese.gov.au), and LB is supported by the Centre de\r\nrecherche sur le vieillissement Fellowship Program. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.","year":"2023","publisher":"Public Library of Science","department":[{"_id":"KrCh"}],"publication_status":"published","file_date_updated":"2023-03-07T10:26:45Z"},{"day":"07","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1","date_published":"2023-06-07T00:00:00Z","publication":"The Journal of Neuroscience","citation":{"ama":"Eguchi K, Le Monnier E, Shigemoto R. Nanoscale phosphoinositide distribution on cell membranes of mouse cerebellar neurons. The Journal of Neuroscience. 2023;43(23):4197-4216. doi:10.1523/JNEUROSCI.1514-22.2023","ista":"Eguchi K, Le Monnier E, Shigemoto R. 2023. Nanoscale phosphoinositide distribution on cell membranes of mouse cerebellar neurons. The Journal of Neuroscience. 43(23), 4197–4216.","ieee":"K. Eguchi, E. Le Monnier, and R. Shigemoto, “Nanoscale phosphoinositide distribution on cell membranes of mouse cerebellar neurons,” The Journal of Neuroscience, vol. 43, no. 23. Society for Neuroscience, pp. 4197–4216, 2023.","apa":"Eguchi, K., Le Monnier, E., & Shigemoto, R. (2023). Nanoscale phosphoinositide distribution on cell membranes of mouse cerebellar neurons. The Journal of Neuroscience. Society for Neuroscience. https://doi.org/10.1523/JNEUROSCI.1514-22.2023","mla":"Eguchi, Kohgaku, et al. “Nanoscale Phosphoinositide Distribution on Cell Membranes of Mouse Cerebellar Neurons.” The Journal of Neuroscience, vol. 43, no. 23, Society for Neuroscience, 2023, pp. 4197–216, doi:10.1523/JNEUROSCI.1514-22.2023.","short":"K. Eguchi, E. Le Monnier, R. Shigemoto, The Journal of Neuroscience 43 (2023) 4197–4216.","chicago":"Eguchi, Kohgaku, Elodie Le Monnier, and Ryuichi Shigemoto. “Nanoscale Phosphoinositide Distribution on Cell Membranes of Mouse Cerebellar Neurons.” The Journal of Neuroscience. Society for Neuroscience, 2023. https://doi.org/10.1523/JNEUROSCI.1514-22.2023."},"article_type":"original","page":"4197-4216","abstract":[{"lang":"eng","text":"Phosphatidylinositol-4,5-bisphosphate (PI(4,5)P2) plays an essential role in neuronal activities through interaction with various proteins involved in signaling at membranes. However, the distribution pattern of PI(4,5)P2 and the association with these proteins on the neuronal cell membranes remain elusive. In this study, we established a method for visualizing PI(4,5)P2 by SDS-digested freeze-fracture replica labeling (SDS-FRL) to investigate the quantitative nanoscale distribution of PI(4,5)P2 in cryo-fixed brain. We demonstrate that PI(4,5)P2 forms tiny clusters with a mean size of ∼1000 nm2 rather than randomly distributed in cerebellar neuronal membranes in male C57BL/6J mice. These clusters show preferential accumulation in specific membrane compartments of different cell types, in particular, in Purkinje cell (PC) spines and granule cell (GC) presynaptic active zones. Furthermore, we revealed extensive association of PI(4,5)P2 with CaV2.1 and GIRK3 across different membrane compartments, whereas its association with mGluR1α was compartment specific. These results suggest that our SDS-FRL method provides valuable insights into the physiological functions of PI(4,5)P2 in neurons."}],"issue":"23","type":"journal_article","file":[{"file_name":"2023_JN_Eguchi.pdf","access_level":"open_access","file_size":7794425,"content_type":"application/pdf","creator":"alisjak","relation":"main_file","file_id":"13205","date_updated":"2023-07-10T09:04:58Z","date_created":"2023-07-10T09:04:58Z","checksum":"70b2141870e0bf1c94fd343e18fdbc32","success":1}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"13202","ddc":["570"],"status":"public","title":"Nanoscale phosphoinositide distribution on cell membranes of mouse cerebellar neurons","intvolume":" 43","month":"06","publication_identifier":{"eissn":["1529-2401"],"issn":["0270-6474"]},"doi":"10.1523/JNEUROSCI.1514-22.2023","acknowledged_ssus":[{"_id":"EM-Fac"}],"language":[{"iso":"eng"}],"external_id":{"isi":["001020132100005"],"pmid":["37160366"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","isi":1,"project":[{"grant_number":"793482","_id":"2659CC84-B435-11E9-9278-68D0E5697425","name":"Ultrastructural analysis of phosphoinositides in nerve terminals: distribution, dynamics and physiological roles in synaptic transmission","call_identifier":"H2020"},{"call_identifier":"H2020","name":"In situ analysis of single channel subunit composition in neurons: physiological implication in synaptic plasticity and behaviour","_id":"25CA28EA-B435-11E9-9278-68D0E5697425","grant_number":"694539"}],"file_date_updated":"2023-07-10T09:04:58Z","ec_funded":1,"author":[{"orcid":"0000-0002-6170-2546","id":"2B7846DC-F248-11E8-B48F-1D18A9856A87","last_name":"Eguchi","first_name":"Kohgaku","full_name":"Eguchi, Kohgaku"},{"last_name":"Le Monnier","first_name":"Elodie","id":"3B59276A-F248-11E8-B48F-1D18A9856A87","full_name":"Le Monnier, Elodie"},{"full_name":"Shigemoto, Ryuichi","id":"499F3ABC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8761-9444","first_name":"Ryuichi","last_name":"Shigemoto"}],"date_created":"2023-07-09T22:01:12Z","date_updated":"2023-10-18T07:12:47Z","volume":43,"year":"2023","acknowledgement":"This work was supported by The Institute of Science and Technology (IST) Austria, the European Union's Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie Grant Agreement No. 793482 (to K.E.) and by the European Research Council (ERC) Grant Agreement No. 694539 (to R.S.). We thank Nicoleta Condruz (IST Austria, Klosterneuburg, Austria) for technical assistance with sample preparation, the Electron Microscopy Facility of IST Austria (Klosterneuburg, Austria) for technical support with EM works, Natalia Baranova (University of Vienna, Vienna, Austria) and Martin Loose (IST Austria, Klosterneuburg, Austria) for advice on liposome preparation, and Yugo Fukazawa (University of Fukui, Fukui, Japan) for comments.","pmid":1,"publication_status":"published","department":[{"_id":"RySh"}],"publisher":"Society for Neuroscience"},{"type":"journal_article","abstract":[{"lang":"eng","text":"We apply a variant of the square-sieve to produce an upper bound for the number of rational points of bounded height on a family of surfaces that admit a fibration over P1 whose general fibre is a hyperelliptic curve. The implied constant does not depend on the coefficients of the polynomial defining the surface.\r\n"}],"issue":"1","status":"public","title":"Uniform bounds for rational points on hyperelliptic fibrations","intvolume":" 24","_id":"12916","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","scopus_import":"1","day":"16","article_processing_charge":"No","article_type":"original","page":"173-204","publication":"Annali della Scuola Normale Superiore di Pisa - Classe di Scienze","citation":{"short":"D. Bonolis, T.D. Browning, Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze 24 (2023) 173–204.","mla":"Bonolis, Dante, and Timothy D. Browning. “Uniform Bounds for Rational Points on Hyperelliptic Fibrations.” Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze, vol. 24, no. 1, Scuola Normale Superiore - Edizioni della Normale, 2023, pp. 173–204, doi:10.2422/2036-2145.202010_018.","chicago":"Bonolis, Dante, and Timothy D Browning. “Uniform Bounds for Rational Points on Hyperelliptic Fibrations.” Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale, 2023. https://doi.org/10.2422/2036-2145.202010_018.","ama":"Bonolis D, Browning TD. Uniform bounds for rational points on hyperelliptic fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 2023;24(1):173-204. doi:10.2422/2036-2145.202010_018","ieee":"D. Bonolis and T. D. Browning, “Uniform bounds for rational points on hyperelliptic fibrations,” Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, vol. 24, no. 1. Scuola Normale Superiore - Edizioni della Normale, pp. 173–204, 2023.","apa":"Bonolis, D., & Browning, T. D. (2023). Uniform bounds for rational points on hyperelliptic fibrations. Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale. https://doi.org/10.2422/2036-2145.202010_018","ista":"Bonolis D, Browning TD. 2023. Uniform bounds for rational points on hyperelliptic fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 24(1), 173–204."},"date_published":"2023-02-16T00:00:00Z","publication_status":"published","publisher":"Scuola Normale Superiore - Edizioni della Normale","department":[{"_id":"TiBr"}],"year":"2023","date_created":"2023-05-07T22:01:04Z","date_updated":"2023-10-18T06:54:30Z","volume":24,"author":[{"id":"6A459894-5FDD-11E9-AF35-BB24E6697425","last_name":"Bonolis","first_name":"Dante","full_name":"Bonolis, Dante"},{"first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D"}],"month":"02","publication_identifier":{"issn":["0391-173X"],"eissn":["2036-2145"]},"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2007.14182"}],"external_id":{"arxiv":["2007.14182"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.2422/2036-2145.202010_018"},{"doi":"10.15479/at:ista:14422","degree_awarded":"PhD","supervisor":[{"full_name":"Vogels, Tim P","first_name":"Tim P","last_name":"Vogels","id":"CB6FF8D2-008F-11EA-8E08-2637E6697425","orcid":"0000-0003-3295-6181"}],"language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"project":[{"name":"Learning the shape of synaptic plasticity rules for neuronal architectures and function through machine learning.","call_identifier":"H2020","grant_number":"819603","_id":"0aacfa84-070f-11eb-9043-d7eb2c709234"}],"month":"10","publication_identifier":{"issn":["2663 - 337X"]},"author":[{"id":"C7610134-B532-11EA-BD9F-F5753DDC885E","first_name":"Basile J","last_name":"Confavreux","full_name":"Confavreux, Basile J"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"9633"}]},"date_updated":"2023-10-18T09:20:56Z","date_created":"2023-10-12T14:13:25Z","year":"2023","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"TiVo"}],"publisher":"Institute of Science and Technology Austria","file_date_updated":"2023-10-18T07:56:08Z","ec_funded":1,"date_published":"2023-10-12T00:00:00Z","citation":{"ama":"Confavreux BJ. Synapseek: Meta-learning synaptic plasticity rules. 2023. doi:10.15479/at:ista:14422","ieee":"B. J. Confavreux, “Synapseek: Meta-learning synaptic plasticity rules,” Institute of Science and Technology Austria, 2023.","apa":"Confavreux, B. J. (2023). Synapseek: Meta-learning synaptic plasticity rules. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14422","ista":"Confavreux BJ. 2023. Synapseek: Meta-learning synaptic plasticity rules. Institute of Science and Technology Austria.","short":"B.J. Confavreux, Synapseek: Meta-Learning Synaptic Plasticity Rules, Institute of Science and Technology Austria, 2023.","mla":"Confavreux, Basile J. Synapseek: Meta-Learning Synaptic Plasticity Rules. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14422.","chicago":"Confavreux, Basile J. “Synapseek: Meta-Learning Synaptic Plasticity Rules.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14422."},"page":"148","day":"12","has_accepted_license":"1","article_processing_charge":"No","file":[{"creator":"cchlebak","file_size":30599717,"content_type":"application/pdf","access_level":"closed","file_name":"Confavreux_Thesis_2A.pdf","embargo_to":"open_access","checksum":"7f636555eae7803323df287672fd13ed","date_updated":"2023-10-12T14:54:52Z","date_created":"2023-10-12T14:53:50Z","file_id":"14424","embargo":"2024-10-12","relation":"main_file"},{"file_name":"Confavreux Thesis.zip","access_level":"closed","creator":"cchlebak","content_type":"application/x-zip-compressed","file_size":68406739,"file_id":"14440","relation":"source_file","date_updated":"2023-10-18T07:56:08Z","date_created":"2023-10-18T07:38:34Z","checksum":"725e85946db92290a4583a0de9779e1b"}],"oa_version":"Published Version","_id":"14422","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","ddc":["610"],"status":"public","title":"Synapseek: Meta-learning synaptic plasticity rules","abstract":[{"text":"Animals exhibit a remarkable ability to learn and remember new behaviors, skills, and associations throughout their lifetime. These capabilities are made possible thanks to a variety of\r\nchanges in the brain throughout adulthood, regrouped under the term \"plasticity\". Some cells\r\nin the brain —neurons— and specifically changes in the connections between neurons, the\r\nsynapses, were shown to be crucial for the formation, selection, and consolidation of memories\r\nfrom past experiences. These ongoing changes of synapses across time are called synaptic\r\nplasticity. Understanding how a myriad of biochemical processes operating at individual\r\nsynapses can somehow work in concert to give rise to meaningful changes in behavior is a\r\nfascinating problem and an active area of research.\r\nHowever, the experimental search for the precise plasticity mechanisms at play in the brain\r\nis daunting, as it is difficult to control and observe synapses during learning. Theoretical\r\napproaches have thus been the default method to probe the plasticity-behavior connection. Such\r\nstudies attempt to extract unifying principles across synapses and model all observed synaptic\r\nchanges using plasticity rules: equations that govern the evolution of synaptic strengths across\r\ntime in neuronal network models. These rules can use many relevant quantities to determine\r\nthe magnitude of synaptic changes, such as the precise timings of pre- and postsynaptic\r\naction potentials, the recent neuronal activity levels, the state of neighboring synapses, etc.\r\nHowever, analytical studies rely heavily on human intuition and are forced to make simplifying\r\nassumptions about plasticity rules.\r\nIn this thesis, we aim to assist and augment human intuition in this search for plasticity rules.\r\nWe explore whether a numerical approach could automatically discover the plasticity rules\r\nthat elicit desired behaviors in large networks of interconnected neurons. This approach is\r\ndubbed meta-learning synaptic plasticity: learning plasticity rules which themselves will make\r\nneuronal networks learn how to solve a desired task. We first write all the potential plasticity\r\nmechanisms to consider using a single expression with adjustable parameters. We then optimize\r\nthese plasticity parameters using evolutionary strategies or Bayesian inference on tasks known\r\nto involve synaptic plasticity, such as familiarity detection and network stabilization.\r\nWe show that these automated approaches are powerful tools, able to complement established\r\nanalytical methods. By comprehensively screening plasticity rules at all synapse types in\r\nrealistic, spiking neuronal network models, we discover entire sets of degenerate plausible\r\nplasticity rules that reliably elicit memory-related behaviors. Our approaches allow for more\r\nrobust experimental predictions, by abstracting out the idiosyncrasies of individual plasticity\r\nrules, and provide fresh insights on synaptic plasticity in spiking network models.\r\n","lang":"eng"}],"type":"dissertation","alternative_title":["ISTA Thesis"]},{"file_date_updated":"2023-10-06T11:38:01Z","ec_funded":1,"author":[{"full_name":"Roos, Barbara","orcid":"0000-0002-9071-5880","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","last_name":"Roos","first_name":"Barbara"}],"related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"13207"},{"id":"10850","status":"public","relation":"part_of_dissertation"}]},"date_created":"2023-09-28T14:23:04Z","date_updated":"2023-10-27T10:37:30Z","year":"2023","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"publisher":"Institute of Science and Technology Austria","month":"09","publication_identifier":{"issn":["2663 - 337X"]},"doi":"10.15479/at:ista:14374","supervisor":[{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert"}],"degree_awarded":"PhD","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","grant_number":"I06427"}],"abstract":[{"text":"Superconductivity has many important applications ranging from levitating trains over qubits to MRI scanners. The phenomenon is successfully modeled by Bardeen-Cooper-Schrieffer (BCS) theory. From a mathematical perspective, BCS theory has been studied extensively for systems without boundary. However, little is known in the presence of boundaries. With the help of numerical methods physicists observed that the critical temperature may increase in the presence of a boundary. The goal of this thesis is to understand the influence of boundaries on the critical temperature in BCS theory and to give a first rigorous justification of these observations. On the way, we also study two-body Schrödinger operators on domains with boundaries and prove additional results for superconductors without boundary.\r\n\r\nBCS theory is based on a non-linear functional, where the minimizer indicates whether the system is superconducting or in the normal, non-superconducting state. By considering the Hessian of the BCS functional at the normal state, one can analyze whether the normal state is possibly a minimum of the BCS functional and estimate the critical temperature. The Hessian turns out to be a linear operator resembling a Schrödinger operator for two interacting particles, but with more complicated kinetic energy. As a first step, we study the two-body Schrödinger operator in the presence of boundaries.\r\nFor Neumann boundary conditions, we prove that the addition of a boundary can create new eigenvalues, which correspond to the two particles forming a bound state close to the boundary.\r\n\r\nSecond, we need to understand superconductivity in the translation invariant setting. While in three dimensions this has been extensively studied, there is no mathematical literature for the one and two dimensional cases. In dimensions one and two, we compute the weak coupling asymptotics of the critical temperature and the energy gap in the translation invariant setting. We also prove that their ratio is independent of the microscopic details of the model in the weak coupling limit; this property is referred to as universality.\r\n\r\nIn the third part, we study the critical temperature of superconductors in the presence of boundaries. We start by considering the one-dimensional case of a half-line with contact interaction. Then, we generalize the results to generic interactions and half-spaces in one, two and three dimensions. Finally, we compare the critical temperature of a quarter space in two dimensions to the critical temperatures of a half-space and of the full space.","lang":"eng"}],"type":"dissertation","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","file":[{"file_id":"14398","relation":"main_file","checksum":"ef039ffc3de2cb8dee5b14110938e9b6","date_updated":"2023-10-06T11:35:56Z","date_created":"2023-10-06T11:35:56Z","access_level":"open_access","file_name":"phd-thesis-draft_pdfa_acrobat.pdf","creator":"broos","content_type":"application/pdf","file_size":2365702},{"relation":"source_file","file_id":"14399","date_created":"2023-10-06T11:38:01Z","date_updated":"2023-10-06T11:38:01Z","checksum":"81dcac33daeefaf0111db52f41bb1fd0","file_name":"Version5.zip","access_level":"closed","content_type":"application/x-zip-compressed","file_size":4691734,"creator":"broos"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"14374","status":"public","title":"Boundary superconductivity in BCS theory","ddc":["515","539"],"day":"30","article_processing_charge":"No","has_accepted_license":"1","date_published":"2023-09-30T00:00:00Z","citation":{"ieee":"B. Roos, “Boundary superconductivity in BCS theory,” Institute of Science and Technology Austria, 2023.","apa":"Roos, B. (2023). Boundary superconductivity in BCS theory. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14374","ista":"Roos B. 2023. Boundary superconductivity in BCS theory. Institute of Science and Technology Austria.","ama":"Roos B. Boundary superconductivity in BCS theory. 2023. doi:10.15479/at:ista:14374","chicago":"Roos, Barbara. “Boundary Superconductivity in BCS Theory.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14374.","short":"B. Roos, Boundary Superconductivity in BCS Theory, Institute of Science and Technology Austria, 2023.","mla":"Roos, Barbara. Boundary Superconductivity in BCS Theory. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14374."},"page":"206"}]