{"title":"Categorical Torelli theorems: results and open problems.","authors":"Laura Pertusi, Paolo Stellari","doi":"10.1007/s12215-022-00796-x","DOIUrl":"10.1007/s12215-022-00796-x","url":null,"abstract":"<p><p>We survey some recent results concerning the so called Categorical Torelli problem. This is to say how one can reconstruct a smooth projective variety up to isomorphism, by using the homological properties of special admissible subcategories of the bounded derived category of coherent sheaves of such a variety. The focus is on Enriques surfaces, prime Fano threefolds and cubic fourfolds.</p>","PeriodicalId":46620,"journal":{"name":"Rendiconti del Circolo Matematico di Palermo","volume":"72 5","pages":"2949-3011"},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10326895/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9810139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
David Hoffman, Irena Dragojević, Jeremy Hoisak, David Hoopes, Ryan Manger
{"title":"Lung Stereotactic Body Radiation Therapy (SBRT) dose gradient and PTV volume: a retrospective multi-center analysis.","authors":"David Hoffman, Irena Dragojević, Jeremy Hoisak, David Hoopes, Ryan Manger","doi":"10.1186/s13014-019-1334-9","DOIUrl":"10.1186/s13014-019-1334-9","url":null,"abstract":"<p><strong>Background: </strong>The treatment of lung lesions with stereotactic body radiation therapy calls for highly conformal dose, which is evaluated by a number of metrics. Lung stereotactic body radiation therapy clinical trials constrain a plans gradient index. The purpose of this work is to describe the dependence of clinically achievable dose gradient on planning target volume.</p><p><strong>Methods: </strong>Three hundred seventy-four lung stereotactic body radiation therapy treatment plans were retrospectively reviewed and selected for this study. The relationship between R50% and planning target volume size was observed and compared against the RTOG 0915 and 0813 constraints noting minor and major deviations. Then a least squares regression was used to determine the coefficients for a power functional form of the dependence of gradient measure (GM) on planning target volume size.</p><p><strong>Results: </strong>Of the 317 peripheral lung SBRT plans, 142 exhibited no deviation, 135 exhibited a minor deviation, and 40 exhibited a major deviation according to the RTOG 0915 dosimetric. conformality and dose fall-off constraints. A plot of gradient measure versus planning target volume size for peripheral lesions, excluding RTOG 0915 major deviations, is fit with an power function of GM = 0.564 V<sup>0.215</sup>.</p><p><strong>Conclusions: </strong>Using the PTV size and GM relationship we have characterized, treatment plans with PTV < 85 cm<sup>3</sup> can be evaluated subjectively to our previously plans, and given a percentile GM. This relationship and evaluation is useful for volumetric modulated arc therapy lung stereotactic body radiation therapy treatment planning and quality control.</p>","PeriodicalId":46620,"journal":{"name":"Rendiconti del Circolo Matematico di Palermo","volume":"16 1","pages":"162"},"PeriodicalIF":3.3,"publicationDate":"2019-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6724320/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74123609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Functional derivatives","authors":"E. Allgower","doi":"10.1007/BF02844029","DOIUrl":"https://doi.org/10.1007/BF02844029","url":null,"abstract":"","PeriodicalId":46620,"journal":{"name":"Rendiconti del Circolo Matematico di Palermo","volume":"14 1","pages":"267-277"},"PeriodicalIF":1.0,"publicationDate":"2019-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/BF02844029","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47772374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The locus of curves with $$D_n$$Dn-symmetry inside $$mathfrak M_g$$Mg","authors":"Binru Li, Sascha Weigl","doi":"10.1007/S12215-015-0216-8","DOIUrl":"https://doi.org/10.1007/S12215-015-0216-8","url":null,"abstract":"","PeriodicalId":46620,"journal":{"name":"Rendiconti del Circolo Matematico di Palermo","volume":"2014 1","pages":"33-45"},"PeriodicalIF":1.0,"publicationDate":"2016-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86648158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A procedure for the construction of non-stationary Riccati-type flows for incompressible 3D Navier–Stokes equations","authors":"S. Ershkov","doi":"10.1007/s12215-015-0219-5","DOIUrl":"https://doi.org/10.1007/s12215-015-0219-5","url":null,"abstract":"","PeriodicalId":46620,"journal":{"name":"Rendiconti del Circolo Matematico di Palermo","volume":"5 1","pages":"73 - 85"},"PeriodicalIF":1.0,"publicationDate":"2016-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78615758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Local MV -Algebras","authors":"A. Nola, R. Grigolia, E. Turunen","doi":"10.1007/978-3-319-30406-9_5","DOIUrl":"https://doi.org/10.1007/978-3-319-30406-9_5","url":null,"abstract":"","PeriodicalId":46620,"journal":{"name":"Rendiconti del Circolo Matematico di Palermo","volume":"41 10","pages":"33-36"},"PeriodicalIF":1.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51014524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Torsion units for a Ree group, Tits group and a Steinberg triality group","authors":"J. Gildea","doi":"10.1007/s12215-015-0225-7","DOIUrl":"https://doi.org/10.1007/s12215-015-0225-7","url":null,"abstract":"","PeriodicalId":46620,"journal":{"name":"Rendiconti del Circolo Matematico di Palermo","volume":"148 1","pages":"139 - 157"},"PeriodicalIF":1.0,"publicationDate":"2015-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76449484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Logarithmic Bloch spaces and their weighted composition operators","authors":"J. Ramos-Fernández","doi":"10.1007/s12215-015-0226-6","DOIUrl":"https://doi.org/10.1007/s12215-015-0226-6","url":null,"abstract":"","PeriodicalId":46620,"journal":{"name":"Rendiconti del Circolo Matematico di Palermo","volume":"69 1","pages":"159 - 174"},"PeriodicalIF":1.0,"publicationDate":"2015-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73441515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Second order monotonicities and second order variational-like inequality problems","authors":"Sarita Choudhury, Anurag Jayswal, I. Ahmad","doi":"10.1007/s12215-015-0224-8","DOIUrl":"https://doi.org/10.1007/s12215-015-0224-8","url":null,"abstract":"","PeriodicalId":46620,"journal":{"name":"Rendiconti del Circolo Matematico di Palermo","volume":"137 3","pages":"123 - 137"},"PeriodicalIF":1.0,"publicationDate":"2015-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12215-015-0224-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72444181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}