[{"type":"journal_article","abstract":[{"lang":"eng","text":"The evolution of finitely many particles obeying Langevin dynamics is described by Dean–Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative noise in divergence form. We derive a regularised Dean–Kawasaki model based on second order Langevin dynamics by analysing a system of particles interacting via a pairwise potential. Key tools of our analysis are the propagation of chaos and Simon's compactness criterion. The model we obtain is a small-noise stochastic perturbation of the undamped McKean–Vlasov equation. We also provide a high-probability result for existence and uniqueness for our model."}],"issue":"2","status":"public","title":"From weakly interacting particles to a regularised Dean-Kawasaki model","intvolume":" 33","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7637","oa_version":"Preprint","scopus_import":"1","day":"10","article_processing_charge":"No","article_type":"original","page":"864-891","publication":"Nonlinearity","citation":{"ieee":"F. Cornalba, T. Shardlow, and J. Zimmer, “From weakly interacting particles to a regularised Dean-Kawasaki model,” Nonlinearity, vol. 33, no. 2. IOP Publishing, pp. 864–891, 2020.","apa":"Cornalba, F., Shardlow, T., & Zimmer, J. (2020). From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/ab5174","ista":"Cornalba F, Shardlow T, Zimmer J. 2020. From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity. 33(2), 864–891.","ama":"Cornalba F, Shardlow T, Zimmer J. From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity. 2020;33(2):864-891. doi:10.1088/1361-6544/ab5174","chicago":"Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “From Weakly Interacting Particles to a Regularised Dean-Kawasaki Model.” Nonlinearity. IOP Publishing, 2020. https://doi.org/10.1088/1361-6544/ab5174.","short":"F. Cornalba, T. Shardlow, J. Zimmer, Nonlinearity 33 (2020) 864–891.","mla":"Cornalba, Federico, et al. “From Weakly Interacting Particles to a Regularised Dean-Kawasaki Model.” Nonlinearity, vol. 33, no. 2, IOP Publishing, 2020, pp. 864–91, doi:10.1088/1361-6544/ab5174."},"date_published":"2020-01-10T00:00:00Z","publication_status":"published","department":[{"_id":"JuFi"}],"publisher":"IOP Publishing","year":"2020","date_created":"2020-04-05T22:00:49Z","date_updated":"2023-08-18T10:26:07Z","volume":33,"author":[{"orcid":"0000-0002-6269-5149","id":"2CEB641C-A400-11E9-A717-D712E6697425","last_name":"Cornalba","first_name":"Federico","full_name":"Cornalba, Federico"},{"last_name":"Shardlow","first_name":"Tony","full_name":"Shardlow, Tony"},{"last_name":"Zimmer","first_name":"Johannes","full_name":"Zimmer, Johannes"}],"month":"01","publication_identifier":{"eissn":["13616544"],"issn":["09517715"]},"quality_controlled":"1","isi":1,"main_file_link":[{"url":"https://arxiv.org/abs/1811.06448","open_access":"1"}],"oa":1,"external_id":{"arxiv":["1811.06448"],"isi":["000508175400001"]},"language":[{"iso":"eng"}],"doi":"10.1088/1361-6544/ab5174"},{"file_date_updated":"2020-07-14T12:48:01Z","article_number":"2459","author":[{"last_name":"Martín-Belmonte","first_name":"Alejandro","full_name":"Martín-Belmonte, Alejandro"},{"first_name":"Carolina","last_name":"Aguado","full_name":"Aguado, Carolina"},{"last_name":"Alfaro-Ruíz","first_name":"Rocío","full_name":"Alfaro-Ruíz, Rocío"},{"last_name":"Moreno-Martínez","first_name":"Ana Esther","full_name":"Moreno-Martínez, Ana Esther"},{"last_name":"De La Ossa","first_name":"Luis","full_name":"De La Ossa, Luis"},{"first_name":"José","last_name":"Martínez-Hernández","full_name":"Martínez-Hernández, José"},{"full_name":"Buisson, Alain","last_name":"Buisson","first_name":"Alain"},{"full_name":"Shigemoto, Ryuichi","last_name":"Shigemoto","first_name":"Ryuichi","orcid":"0000-0001-8761-9444","id":"499F3ABC-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Yugo","last_name":"Fukazawa","full_name":"Fukazawa, Yugo"},{"last_name":"Luján","first_name":"Rafael","full_name":"Luján, Rafael"}],"volume":21,"date_updated":"2023-08-21T06:13:19Z","date_created":"2020-04-19T22:00:55Z","pmid":1,"year":"2020","publisher":"MDPI","department":[{"_id":"RySh"}],"publication_status":"published","publication_identifier":{"eissn":["14220067"]},"month":"04","doi":"10.3390/ijms21072459","language":[{"iso":"eng"}],"external_id":{"pmid":["32252271"],"isi":["000535574200201"]},"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","issue":"7","abstract":[{"text":"Metabotropic γ-aminobutyric acid (GABAB) receptors contribute to the control of network activity and information processing in hippocampal circuits by regulating neuronal excitability and synaptic transmission. The dysfunction in the dentate gyrus (DG) has been implicated in Alzheimer´s disease (AD). Given the involvement of GABAB receptors in AD, to determine their subcellular localisation and possible alteration in granule cells of the DG in a mouse model of AD at 12 months of age, we used high-resolution immunoelectron microscopic analysis. Immunohistochemistry at the light microscopic level showed that the regional and cellular expression pattern of GABAB1 was similar in an AD model mouse expressing mutated human amyloid precursor protein and presenilin1 (APP/PS1) and in age-matched wild type mice. High-resolution immunoelectron microscopy revealed a distance-dependent gradient of immunolabelling for GABAB receptors, increasing from proximal to distal dendrites in both wild type and APP/PS1 mice. However, the overall density of GABAB receptors at the neuronal surface of these postsynaptic compartments of granule cells was significantly reduced in APP/PS1 mice. Parallel to this reduction in surface receptors, we found a significant increase in GABAB1 at cytoplasmic sites. GABAB receptors were also detected at presynaptic sites in the molecular layer of the DG. We also found a decrease in plasma membrane GABAB receptors in axon terminals contacting dendritic spines of granule cells, which was more pronounced in the outer than in the inner molecular layer. Altogether, our data showing post- and presynaptic reduction in surface GABAB receptors in the DG suggest the alteration of the GABAB-mediated modulation of excitability and synaptic transmission in granule cells, which may contribute to the cognitive dysfunctions in the APP/PS1 model of AD","lang":"eng"}],"type":"journal_article","file":[{"checksum":"b9d2f1657d8c4a74b01a62b474d009b0","date_created":"2020-04-20T11:43:18Z","date_updated":"2020-07-14T12:48:01Z","relation":"main_file","file_id":"7669","file_size":2941197,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2020_JournMolecSciences_Martin_Belmonte.pdf"}],"oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7664","intvolume":" 21","title":"Density of GABAB receptors is reduced in granule cells of the hippocampus in a mouse model of Alzheimer's disease","ddc":["570"],"status":"public","has_accepted_license":"1","article_processing_charge":"No","day":"02","scopus_import":"1","date_published":"2020-04-02T00:00:00Z","citation":{"chicago":"Martín-Belmonte, Alejandro, Carolina Aguado, Rocío Alfaro-Ruíz, Ana Esther Moreno-Martínez, Luis De La Ossa, José Martínez-Hernández, Alain Buisson, Ryuichi Shigemoto, Yugo Fukazawa, and Rafael Luján. “Density of GABAB Receptors Is Reduced in Granule Cells of the Hippocampus in a Mouse Model of Alzheimer’s Disease.” International Journal of Molecular Sciences. MDPI, 2020. https://doi.org/10.3390/ijms21072459.","short":"A. Martín-Belmonte, C. Aguado, R. Alfaro-Ruíz, A.E. Moreno-Martínez, L. De La Ossa, J. Martínez-Hernández, A. Buisson, R. Shigemoto, Y. Fukazawa, R. Luján, International Journal of Molecular Sciences 21 (2020).","mla":"Martín-Belmonte, Alejandro, et al. “Density of GABAB Receptors Is Reduced in Granule Cells of the Hippocampus in a Mouse Model of Alzheimer’s Disease.” International Journal of Molecular Sciences, vol. 21, no. 7, 2459, MDPI, 2020, doi:10.3390/ijms21072459.","ieee":"A. Martín-Belmonte et al., “Density of GABAB receptors is reduced in granule cells of the hippocampus in a mouse model of Alzheimer’s disease,” International journal of molecular sciences, vol. 21, no. 7. MDPI, 2020.","apa":"Martín-Belmonte, A., Aguado, C., Alfaro-Ruíz, R., Moreno-Martínez, A. E., De La Ossa, L., Martínez-Hernández, J., … Luján, R. (2020). Density of GABAB receptors is reduced in granule cells of the hippocampus in a mouse model of Alzheimer’s disease. International Journal of Molecular Sciences. MDPI. https://doi.org/10.3390/ijms21072459","ista":"Martín-Belmonte A, Aguado C, Alfaro-Ruíz R, Moreno-Martínez AE, De La Ossa L, Martínez-Hernández J, Buisson A, Shigemoto R, Fukazawa Y, Luján R. 2020. Density of GABAB receptors is reduced in granule cells of the hippocampus in a mouse model of Alzheimer’s disease. International journal of molecular sciences. 21(7), 2459.","ama":"Martín-Belmonte A, Aguado C, Alfaro-Ruíz R, et al. Density of GABAB receptors is reduced in granule cells of the hippocampus in a mouse model of Alzheimer’s disease. International journal of molecular sciences. 2020;21(7). doi:10.3390/ijms21072459"},"publication":"International journal of molecular sciences","article_type":"original"},{"article_type":"original","citation":{"ama":"Eguchi K, Velicky P, Saeckl E, et al. Advantages of acute brain slices prepared at physiological temperature in the characterization of synaptic functions. Frontiers in Cellular Neuroscience. 2020;14. doi:10.3389/fncel.2020.00063","ieee":"K. Eguchi et al., “Advantages of acute brain slices prepared at physiological temperature in the characterization of synaptic functions,” Frontiers in Cellular Neuroscience, vol. 14. Frontiers Media, 2020.","apa":"Eguchi, K., Velicky, P., Saeckl, E., Itakura, M., Fukazawa, Y., Danzl, J. G., & Shigemoto, R. (2020). Advantages of acute brain slices prepared at physiological temperature in the characterization of synaptic functions. Frontiers in Cellular Neuroscience. Frontiers Media. https://doi.org/10.3389/fncel.2020.00063","ista":"Eguchi K, Velicky P, Saeckl E, Itakura M, Fukazawa Y, Danzl JG, Shigemoto R. 2020. Advantages of acute brain slices prepared at physiological temperature in the characterization of synaptic functions. Frontiers in Cellular Neuroscience. 14, 63.","short":"K. Eguchi, P. Velicky, E. Saeckl, M. Itakura, Y. Fukazawa, J.G. Danzl, R. Shigemoto, Frontiers in Cellular Neuroscience 14 (2020).","mla":"Eguchi, Kohgaku, et al. “Advantages of Acute Brain Slices Prepared at Physiological Temperature in the Characterization of Synaptic Functions.” Frontiers in Cellular Neuroscience, vol. 14, 63, Frontiers Media, 2020, doi:10.3389/fncel.2020.00063.","chicago":"Eguchi, Kohgaku, Philipp Velicky, Elena Saeckl, Makoto Itakura, Yugo Fukazawa, Johann G Danzl, and Ryuichi Shigemoto. “Advantages of Acute Brain Slices Prepared at Physiological Temperature in the Characterization of Synaptic Functions.” Frontiers in Cellular Neuroscience. Frontiers Media, 2020. https://doi.org/10.3389/fncel.2020.00063."},"publication":"Frontiers in Cellular Neuroscience","date_published":"2020-03-19T00:00:00Z","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"19","intvolume":" 14","status":"public","ddc":["570"],"title":"Advantages of acute brain slices prepared at physiological temperature in the characterization of synaptic functions","_id":"7665","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2020_FrontiersCellularNeurosc_Eguchi.pdf","creator":"dernst","content_type":"application/pdf","file_size":9227283,"file_id":"7668","relation":"main_file","checksum":"1c145123c6f8dc3e2e4bd5a66a1ad60e","date_created":"2020-04-20T10:59:49Z","date_updated":"2020-07-14T12:48:01Z"}],"type":"journal_article","abstract":[{"lang":"eng","text":"Acute brain slice preparation is a powerful experimental model for investigating the characteristics of synaptic function in the brain. Although brain tissue is usually cut at ice-cold temperature (CT) to facilitate slicing and avoid neuronal damage, exposure to CT causes molecular and architectural changes of synapses. To address these issues, we investigated ultrastructural and electrophysiological features of synapses in mouse acute cerebellar slices prepared at ice-cold and physiological temperature (PT). In the slices prepared at CT, we found significant spine loss and reconstruction, synaptic vesicle rearrangement and decrease in synaptic proteins, all of which were not detected in slices prepared at PT. Consistent with these structural findings, slices prepared at PT showed higher release probability. Furthermore, preparation at PT allows electrophysiological recording immediately after slicing resulting in higher detectability of long-term depression (LTD) after motor learning compared with that at CT. These results indicate substantial advantages of the slice preparation at PT for investigating synaptic functions in different physiological conditions."}],"project":[{"grant_number":"793482","_id":"2659CC84-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Ultrastructural analysis of phosphoinositides in nerve terminals: distribution, dynamics and physiological roles in synaptic transmission"},{"_id":"25CA28EA-B435-11E9-9278-68D0E5697425","grant_number":"694539","name":"In situ analysis of single channel subunit composition in neurons: physiological implication in synaptic plasticity and behaviour","call_identifier":"H2020"},{"name":"Optical control of synaptic function via adhesion molecules","call_identifier":"FWF","_id":"265CB4D0-B435-11E9-9278-68D0E5697425","grant_number":"I03600"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","isi":1,"external_id":{"isi":["000525582200001"]},"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,"language":[{"iso":"eng"}],"doi":"10.3389/fncel.2020.00063","publication_identifier":{"issn":["16625102"]},"month":"03","publisher":"Frontiers Media","department":[{"_id":"JoDa"},{"_id":"RySh"}],"publication_status":"published","year":"2020","volume":14,"date_updated":"2023-08-21T06:12:48Z","date_created":"2020-04-19T22:00:55Z","author":[{"first_name":"Kohgaku","last_name":"Eguchi","id":"2B7846DC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6170-2546","full_name":"Eguchi, Kohgaku"},{"orcid":"0000-0002-2340-7431","id":"39BDC62C-F248-11E8-B48F-1D18A9856A87","last_name":"Velicky","first_name":"Philipp","full_name":"Velicky, Philipp"},{"full_name":"Hollergschwandtner, Elena","first_name":"Elena","last_name":"Hollergschwandtner","id":"3C054040-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Itakura","first_name":"Makoto","full_name":"Itakura, Makoto"},{"full_name":"Fukazawa, Yugo","first_name":"Yugo","last_name":"Fukazawa"},{"id":"42EFD3B6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8559-3973","first_name":"Johann G","last_name":"Danzl","full_name":"Danzl, Johann G"},{"full_name":"Shigemoto, Ryuichi","first_name":"Ryuichi","last_name":"Shigemoto","id":"499F3ABC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8761-9444"}],"article_number":"63","ec_funded":1,"file_date_updated":"2020-07-14T12:48:01Z"},{"isi":1,"quality_controlled":"1","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,"external_id":{"isi":["000526413400055"],"pmid":["32196350"]},"language":[{"iso":"eng"}],"doi":"10.1021/acs.nanolett.0c00205","publication_identifier":{"eissn":["15306992"]},"month":"04","department":[{"_id":"MaLo"}],"publisher":"American Chemical Society","publication_status":"published","pmid":1,"year":"2020","volume":20,"date_updated":"2023-08-21T06:12:09Z","date_created":"2020-04-19T22:00:54Z","author":[{"last_name":"Felhofer","first_name":"Martin","full_name":"Felhofer, Martin"},{"full_name":"Bock, Peter","first_name":"Peter","last_name":"Bock"},{"first_name":"Adya","last_name":"Singh","full_name":"Singh, Adya"},{"last_name":"Prats Mateu","first_name":"Batirtze","id":"299FE892-F248-11E8-B48F-1D18A9856A87","full_name":"Prats Mateu, Batirtze"},{"first_name":"Ronald","last_name":"Zirbs","full_name":"Zirbs, Ronald"},{"full_name":"Gierlinger, Notburga","first_name":"Notburga","last_name":"Gierlinger"}],"file_date_updated":"2020-07-14T12:48:01Z","page":"2647-2653","article_type":"original","citation":{"short":"M. Felhofer, P. Bock, A. Singh, B. Prats Mateu, R. Zirbs, N. Gierlinger, Nano Letters 20 (2020) 2647–2653.","mla":"Felhofer, Martin, et al. “Wood Deformation Leads to Rearrangement of Molecules at the Nanoscale.” Nano Letters, vol. 20, no. 4, American Chemical Society, 2020, pp. 2647–53, doi:10.1021/acs.nanolett.0c00205.","chicago":"Felhofer, Martin, Peter Bock, Adya Singh, Batirtze Prats Mateu, Ronald Zirbs, and Notburga Gierlinger. “Wood Deformation Leads to Rearrangement of Molecules at the Nanoscale.” Nano Letters. American Chemical Society, 2020. https://doi.org/10.1021/acs.nanolett.0c00205.","ama":"Felhofer M, Bock P, Singh A, Prats Mateu B, Zirbs R, Gierlinger N. Wood deformation leads to rearrangement of molecules at the nanoscale. Nano Letters. 2020;20(4):2647-2653. doi:10.1021/acs.nanolett.0c00205","apa":"Felhofer, M., Bock, P., Singh, A., Prats Mateu, B., Zirbs, R., & Gierlinger, N. (2020). Wood deformation leads to rearrangement of molecules at the nanoscale. Nano Letters. American Chemical Society. https://doi.org/10.1021/acs.nanolett.0c00205","ieee":"M. Felhofer, P. Bock, A. Singh, B. Prats Mateu, R. Zirbs, and N. Gierlinger, “Wood deformation leads to rearrangement of molecules at the nanoscale,” Nano Letters, vol. 20, no. 4. American Chemical Society, pp. 2647–2653, 2020.","ista":"Felhofer M, Bock P, Singh A, Prats Mateu B, Zirbs R, Gierlinger N. 2020. Wood deformation leads to rearrangement of molecules at the nanoscale. Nano Letters. 20(4), 2647–2653."},"publication":"Nano Letters","date_published":"2020-04-08T00:00:00Z","scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"08","intvolume":" 20","ddc":["530"],"status":"public","title":"Wood deformation leads to rearrangement of molecules at the nanoscale","_id":"7663","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2020_NanoLetters_Felhofer.pdf","creator":"dernst","content_type":"application/pdf","file_size":7108014,"file_id":"7667","relation":"main_file","checksum":"fe46146a9c4c620592a1932a8599069e","date_created":"2020-04-20T10:43:36Z","date_updated":"2020-07-14T12:48:01Z"}],"type":"journal_article","issue":"4","abstract":[{"lang":"eng","text":"Wood, as the most abundant carbon dioxide storing bioresource, is currently driven beyond its traditional use through creative innovations and nanotechnology. For many properties the micro- and nanostructure plays a crucial role and one key challenge is control and detection of chemical and physical processes in the confined microstructure and nanopores of the wooden cell wall. In this study, correlative Raman and atomic force microscopy show high potential for tracking in situ molecular rearrangement of wood polymers during compression. More water molecules (interpreted as wider cellulose microfibril distances) and disentangling of hemicellulose chains are detected in the opened cell wall regions, whereas an increase of lignin is revealed in the compressed areas. These results support a new more “loose” cell wall model based on flexible lignin nanodomains and advance our knowledge of the molecular reorganization during deformation of wood for optimized processing and utilization."}]},{"publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"month":"03","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"},"external_id":{"isi":["000520918800001"]},"oa":1,"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"quality_controlled":"1","isi":1,"doi":"10.1007/s00454-020-00188-x","language":[{"iso":"eng"}],"ec_funded":1,"file_date_updated":"2020-11-20T13:22:21Z","acknowledgement":"This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF).","year":"2020","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Ölsböck, Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4672-8297","first_name":"Katharina","last_name":"Ölsböck"}],"volume":64,"date_created":"2020-04-19T22:00:56Z","date_updated":"2023-08-21T06:13:48Z","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"20","citation":{"short":"H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry 64 (2020) 759–775.","mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry, vol. 64, Springer Nature, 2020, pp. 759–75, doi:10.1007/s00454-020-00188-x.","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry. Springer Nature, 2020. https://doi.org/10.1007/s00454-020-00188-x.","ama":"Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 2020;64:759-775. doi:10.1007/s00454-020-00188-x","ieee":"H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,” Discrete and Computational Geometry, vol. 64. Springer Nature, pp. 759–775, 2020.","apa":"Edelsbrunner, H., & Ölsböck, K. (2020). Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00188-x","ista":"Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 64, 759–775."},"publication":"Discrete and Computational Geometry","page":"759-775","article_type":"original","date_published":"2020-03-20T00:00:00Z","type":"journal_article","abstract":[{"lang":"eng","text":"Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral complex, K, and every dimension, p, there is a partition of the set of p-cells into a maximal p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition is unique, and it can be computed by a matrix reduction algorithm that also constructs canonical bases of cycle and boundary groups."}],"_id":"7666","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 64","ddc":["510"],"title":"Tri-partitions and bases of an ordered complex","status":"public","file":[{"creator":"dernst","file_size":701673,"content_type":"application/pdf","access_level":"open_access","file_name":"2020_DiscreteCompGeo_Edelsbrunner.pdf","success":1,"checksum":"f8cc96e497f00c38340b5dafe0cb91d7","date_updated":"2020-11-20T13:22:21Z","date_created":"2020-11-20T13:22:21Z","file_id":"8786","relation":"main_file"}],"oa_version":"Published Version"}]