Pub Date : 2023-06-13eCollection Date: 2023-01-01DOI: 10.3897/zookeys.1166.103247
Rita M Austin, Pia Merete Eriksen, Lutz Bachmann
The endangered Galápagos sea lion (Zalophuswollebaeki) inhabits the Galápagos Islands off the coast of Ecuador. We present a complete mitochondrial genome (16 465 bp) of a female paratype from the collections of the Natural History Museum Oslo, Norway, assembled from next-generation sequencing reads. It contains all canonical protein-coding, rRNA, tRNA genes, and the D-loop region. Sequence similarity is 99.93% to a previously published conspecific mitogenome sequence and 99.37% to the mitogenome sequence of the sister species Z.californianus. Sequence similarity of the D-loop region of the Z.wollebaeki paratype mitogenome is >99%, while the sequence difference to the Z.californianus sequences exceeds 2.5%. The paratype mitogenome sequence supports the taxonomic status of Z.wollebaeki as a separate species.
濒危的加拉帕戈斯海狮（Zalophuswollebaeki）栖息在厄瓜多尔海岸附近的加拉帕戈斯群岛。我们展示了挪威奥斯陆自然历史博物馆收藏的一只雌性副样的完整线粒体基因组（16 465 bp），该基因组由下一代测序读数组装而成。该基因组包含所有典型的蛋白质编码、rRNA、tRNA 基因和 D 环区。它与之前发表的同种有丝分裂基因组序列的相似度为 99.93%，与姊妹种加利福尼亚蛙的有丝分裂基因组序列的相似度为 99.37%。Z.wollebaeki 副样有丝分裂基因组 D 环区的序列相似性大于 99%，而与 Z.californianus 序列的差异超过 2.5%。副样有丝分裂基因组序列支持 Z.wollebaeki 作为一个独立物种的分类地位。
{"title":"Complete mitochondrial genome of the Galápagos sea lion, <i>Zalophuswollebaeki</i> (Carnivora, Otariidae): paratype specimen confirms separate species status.","authors":"Rita M Austin, Pia Merete Eriksen, Lutz Bachmann","doi":"10.3897/zookeys.1166.103247","DOIUrl":"10.3897/zookeys.1166.103247","url":null,"abstract":"<p><p>The endangered Galápagos sea lion (<i>Zalophuswollebaeki</i>) inhabits the Galápagos Islands off the coast of Ecuador. We present a complete mitochondrial genome (16 465 bp) of a female paratype from the collections of the Natural History Museum Oslo, Norway, assembled from next-generation sequencing reads. It contains all canonical protein-coding, rRNA, tRNA genes, and the D-loop region. Sequence similarity is 99.93% to a previously published conspecific mitogenome sequence and 99.37% to the mitogenome sequence of the sister species <i>Z.californianus</i>. Sequence similarity of the D-loop region of the <i>Z.wollebaeki</i> paratype mitogenome is >99%, while the sequence difference to the <i>Z.californianus</i> sequences exceeds 2.5%. The paratype mitogenome sequence supports the taxonomic status of <i>Z.wollebaeki</i> as a separate species.</p>","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":"94 1","pages":"307-313"},"PeriodicalIF":1.3,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10848830/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85501276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Issue Information","authors":"","doi":"10.1111/mbe.12327","DOIUrl":"https://doi.org/10.1111/mbe.12327","url":null,"abstract":"","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48681044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Issue Information","authors":"","doi":"10.1111/1467-9604.12447","DOIUrl":"https://doi.org/10.1111/1467-9604.12447","url":null,"abstract":"","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43455543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Issue Information","authors":"","doi":"10.1112/plms.12453","DOIUrl":"https://doi.org/10.1112/plms.12453","url":null,"abstract":"","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42993493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Issue Information","authors":"","doi":"10.1112/plms.12452","DOIUrl":"https://doi.org/10.1112/plms.12452","url":null,"abstract":"","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42427099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a global version of Heath‐Brown's p‐adic determinant method to study the asymptotic behaviour of the number N(W; B) of rational points of height at most B on certain subvarieties W of Pn defined over Q. The most important application is a proof of the dimension growth conjecture of Heath‐Brown and Serre for all integral projective varieties of degree d ≥ 2 over Q. For projective varieties of degree d ≥ 4, we prove a uniform version N(W; B) = Od,n,ε(Bdim W+ε) of this conjecture. We also use our global determinant method to improve upon previous estimates for quasi‐projective surfaces. If, for example, X́$Xacute{ }$ is the complement of the lines on a non‐singular surface X ⊂ P3 of degree d, then we show that N(X́;B)=Od(B3/√d(logB)4+B)$N(Xacute{ };B) = {O}_d( {{B}^{3/surd d }{{( {log B} )}}^4 + B} )$ . For surfaces defined by forms a0x0d+a1x1d+a2x2d+a3x3d${a}_0x_0^d + {a}_1x_1^d + {a}_2x_2^d + {a}_3x_3^d$ with non‐zero coefficients, then we use a new geometric result for Fermat surfaces to show that N(X́;B)=Od(B3/√d(logB)4)$N( {Xacute{ };B} ) = {O}_d({B}^{3/surd d}{( {log B} )}^4)$ for B ≥ e.
{"title":"Counting rational points on projective varieties","authors":"P. Salberger","doi":"10.1112/plms.12508","DOIUrl":"https://doi.org/10.1112/plms.12508","url":null,"abstract":"We develop a global version of Heath‐Brown's p‐adic determinant method to study the asymptotic behaviour of the number N(W; B) of rational points of height at most B on certain subvarieties W of Pn defined over Q. The most important application is a proof of the dimension growth conjecture of Heath‐Brown and Serre for all integral projective varieties of degree d ≥ 2 over Q. For projective varieties of degree d ≥ 4, we prove a uniform version N(W; B) = Od,n,ε(Bdim W+ε) of this conjecture. We also use our global determinant method to improve upon previous estimates for quasi‐projective surfaces. If, for example, X́$Xacute{ }$ is the complement of the lines on a non‐singular surface X ⊂ P3 of degree d, then we show that N(X́;B)=Od(B3/√d(logB)4+B)$N(Xacute{ };B) = {O}_d( {{B}^{3/surd d }{{( {log B} )}}^4 + B} )$ . For surfaces defined by forms a0x0d+a1x1d+a2x2d+a3x3d${a}_0x_0^d + {a}_1x_1^d + {a}_2x_2^d + {a}_3x_3^d$ with non‐zero coefficients, then we use a new geometric result for Fermat surfaces to show that N(X́;B)=Od(B3/√d(logB)4)$N( {Xacute{ };B} ) = {O}_d({B}^{3/surd d}{( {log B} )}^4)$ for B ≥ e.","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47464432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Issue Information","authors":"","doi":"10.1112/plms.12451","DOIUrl":"https://doi.org/10.1112/plms.12451","url":null,"abstract":"","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48746799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Issue Information","authors":"","doi":"10.1112/plms.12450","DOIUrl":"https://doi.org/10.1112/plms.12450","url":null,"abstract":"","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48375679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maria Chudnovsky, Alex Scott, Paul Seymour, Sophie Spirkl
Abstract The Erdős–Hajnal conjecture says that for every graph there exists such that every graph not containing as an induced subgraph has a clique or stable set of cardinality at least . We prove that this is true when is a cycle of length five. We also prove several further results: for instance, that if is a cycle and is the complement of a forest, there exists such that every graph containing neither of as an induced subgraph has a clique or stable set of cardinality at least .
{"title":"Erdős–Hajnal for graphs with no 5‐hole","authors":"Maria Chudnovsky, Alex Scott, Paul Seymour, Sophie Spirkl","doi":"10.1112/plms.12504","DOIUrl":"https://doi.org/10.1112/plms.12504","url":null,"abstract":"Abstract The Erdős–Hajnal conjecture says that for every graph there exists such that every graph not containing as an induced subgraph has a clique or stable set of cardinality at least . We prove that this is true when is a cycle of length five. We also prove several further results: for instance, that if is a cycle and is the complement of a forest, there exists such that every graph containing neither of as an induced subgraph has a clique or stable set of cardinality at least .","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135200958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We start by identifying a class of pseudo‐differential operators, generated by the set of continuous negative definite functions, that are in the weak similarity (WS) orbit of the self‐adjoint log‐Bessel operator on the Euclidean space. These WS relations turn out to be useful to first characterize a core for each operator in this class, which enables us to show that they generate a class, denoted by P$mathcal {P}$ , of non‐self‐adjoint C0$mathcal {C}_0$ ‐contraction positive semigroups. Up to a homeomorphism, P$mathcal {P}$ includes, as fundamental objects in probability theory, the family of self‐similar Markov semigroups on R+d$mathbb {R}_+^d$ . Relying on the WS orbit, we characterize the nature of the spectrum of each element in P$mathcal {P}$ that is used in their spectral representation which depends on analytical properties of the Bernstein‐gamma functions defined from the associated negative definite functions, and, it is either the point, residual, approximate or continuous spectrum. We proceed by providing a spectral representation of each element in P$mathcal {P}$ which is expressed in terms of Fourier multiplier operators and valid, at least, on a dense domain of a natural weighted L2$mathbf {L}^{2}$ ‐space. Surprisingly, the domain is the full Hilbert space when the spectrum is the residual one, something which seems to be noticed for the first time in the literature. We end up the paper by presenting a series of examples for which all spectral components are computed explicitly in terms of special functions or recently introduced power series.
{"title":"Weak similarity orbit of (log)‐self‐similar Markov semigroups on the Euclidean space","authors":"P. Patie, Rohan Sarkar","doi":"10.1112/plms.12514","DOIUrl":"https://doi.org/10.1112/plms.12514","url":null,"abstract":"We start by identifying a class of pseudo‐differential operators, generated by the set of continuous negative definite functions, that are in the weak similarity (WS) orbit of the self‐adjoint log‐Bessel operator on the Euclidean space. These WS relations turn out to be useful to first characterize a core for each operator in this class, which enables us to show that they generate a class, denoted by P$mathcal {P}$ , of non‐self‐adjoint C0$mathcal {C}_0$ ‐contraction positive semigroups. Up to a homeomorphism, P$mathcal {P}$ includes, as fundamental objects in probability theory, the family of self‐similar Markov semigroups on R+d$mathbb {R}_+^d$ . Relying on the WS orbit, we characterize the nature of the spectrum of each element in P$mathcal {P}$ that is used in their spectral representation which depends on analytical properties of the Bernstein‐gamma functions defined from the associated negative definite functions, and, it is either the point, residual, approximate or continuous spectrum. We proceed by providing a spectral representation of each element in P$mathcal {P}$ which is expressed in terms of Fourier multiplier operators and valid, at least, on a dense domain of a natural weighted L2$mathbf {L}^{2}$ ‐space. Surprisingly, the domain is the full Hilbert space when the spectrum is the residual one, something which seems to be noticed for the first time in the literature. We end up the paper by presenting a series of examples for which all spectral components are computed explicitly in terms of special functions or recently introduced power series.","PeriodicalId":49667,"journal":{"name":"Proceedings of the London Mathematical Society","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42999133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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