--- _id: '1451' abstract: - lang: eng text: Extending work of Bielawski-Dancer 3 and Konno 14, we develop a theory of toric hyperkähler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework is a detailed study of semi-projective toric varieties, meaning GIT quotients of affine spaces by torus actions, and specifically, of Lawrence toric varieties, meaning GIT quotients of even-dimensional affine spaces by symplectic torus actions. A toric hyperkähler variety is a complete intersection in a Lawrence toric variety. Both varieties are non-compact, and they share the same cohomology ring, namely, the Stanley-Reisner ring of a matroid modulo a linear system of parameters. Familiar applications of toric geometry to combinatorics, including the Hard Lefschetz Theorem and the volume polynomials of Khovanskii-Pukhlikov 11, are extended to the hyperkähler setting. When the matroid is graphic, our construction gives the toric quiver varieties, in the sense of Nakajima 17. acknowledgement: "Both authors were supported by the Miller Institute for Basic Research in Science, in the form of a Miller Research Fellowship (1999-2002) for the first author and a Miller Professorship (2000-2001) for the second author. The second author was also supported by the National Science\r\nFoundation (DMS-9970254)." article_processing_charge: No article_type: original author: - first_name: Tamas full_name: Hausel, Tamas id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel - first_name: Bernd full_name: Sturmfels, Bernd last_name: Sturmfels citation: ama: Hausel T, Sturmfels B. Toric hyperkähler varieties. Documenta Mathematica. 2002;7(1):495-534. doi:10.4171/DM/130 apa: Hausel, T., & Sturmfels, B. (2002). Toric hyperkähler varieties. Documenta Mathematica. Deutsche Mathematiker Vereinigung. https://doi.org/10.4171/DM/130 chicago: Hausel, Tamás, and Bernd Sturmfels. “Toric Hyperkähler Varieties.” Documenta Mathematica. Deutsche Mathematiker Vereinigung, 2002. https://doi.org/10.4171/DM/130. ieee: T. Hausel and B. Sturmfels, “Toric hyperkähler varieties,” Documenta Mathematica, vol. 7, no. 1. Deutsche Mathematiker Vereinigung, pp. 495–534, 2002. ista: Hausel T, Sturmfels B. 2002. Toric hyperkähler varieties. Documenta Mathematica. 7(1), 495–534. mla: Hausel, Tamás, and Bernd Sturmfels. “Toric Hyperkähler Varieties.” Documenta Mathematica, vol. 7, no. 1, Deutsche Mathematiker Vereinigung, 2002, pp. 495–534, doi:10.4171/DM/130. short: T. Hausel, B. Sturmfels, Documenta Mathematica 7 (2002) 495–534. date_created: 2018-12-11T11:52:06Z date_published: 2002-01-01T00:00:00Z date_updated: 2023-07-26T09:16:33Z day: '01' doi: 10.4171/DM/130 extern: '1' external_id: arxiv: - math/0203096 intvolume: ' 7' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://ems.press/journals/dm/articles/8965058 month: '01' oa: 1 oa_version: Published Version page: 495 - 534 publication: Documenta Mathematica publication_identifier: issn: - 1431-0635 publication_status: published publisher: Deutsche Mathematiker Vereinigung publist_id: '5741' quality_controlled: '1' scopus_import: '1' status: public title: Toric hyperkähler varieties type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 7 year: '2002' ... --- _id: '897' abstract: - lang: eng text: "Transcription is a slow and expensive process: in eukaryotes, approximately 20 nucleotides can be transcribed per second at the expense of at least two ATP molecules per nucleotide. Thus, at least for highly expressed genes, transcription of long introns, which are particularly common in mammals, is costly. Using data on the expression of genes that encode proteins in Caenorhabditis elegans and Homo sapiens, we show that introns in highly expressed genes are substantially shorter than those in genes that are expressed at low levels. This difference is greater in humans, such that introns are, on average, 14 times shorter in highly expressed genes than in genes with low expression, whereas in C. Elegans the difference in intron length is only twofold. In contrast, the density of introns in a gene does not strongly depend on the level of gene expression. Thus, natural selection appears to favor short introns in highly expressed genes to minimize the cost of transcription and other molecular processes, such as splicing.\r\n" acknowledgement: We are grateful to A. Kondrashov, I. Rogozin and A. Feldman for reading the manuscript and P. Bouman, J. Cherry, J. Blumensteil and T. Kim for discussion. article_processing_charge: No article_type: original author: - first_name: Cristian full_name: Castillo Davis, Cristian last_name: Castillo Davis - first_name: Sergei full_name: Mekhedov, Sergei last_name: Mekhedov - first_name: Daniel full_name: Hartl, Daniel last_name: Hartl - first_name: Eugene full_name: Koonin, Eugene last_name: Koonin - first_name: Fyodor full_name: Kondrashov, Fyodor id: 44FDEF62-F248-11E8-B48F-1D18A9856A87 last_name: Kondrashov orcid: 0000-0001-8243-4694 citation: ama: Castillo Davis C, Mekhedov S, Hartl D, Koonin E, Kondrashov F. Selection for short introns in highly expressed genes. Nature Genetics. 2002;31(4):415-418. doi:10.1038/ng940 apa: Castillo Davis, C., Mekhedov, S., Hartl, D., Koonin, E., & Kondrashov, F. (2002). Selection for short introns in highly expressed genes. Nature Genetics. Nature Publishing Group. https://doi.org/10.1038/ng940 chicago: Castillo Davis, Cristian, Sergei Mekhedov, Daniel Hartl, Eugene Koonin, and Fyodor Kondrashov. “Selection for Short Introns in Highly Expressed Genes.” Nature Genetics. Nature Publishing Group, 2002. https://doi.org/10.1038/ng940. ieee: C. Castillo Davis, S. Mekhedov, D. Hartl, E. Koonin, and F. Kondrashov, “Selection for short introns in highly expressed genes,” Nature Genetics, vol. 31, no. 4. Nature Publishing Group, pp. 415–418, 2002. ista: Castillo Davis C, Mekhedov S, Hartl D, Koonin E, Kondrashov F. 2002. Selection for short introns in highly expressed genes. Nature Genetics. 31(4), 415–418. mla: Castillo Davis, Cristian, et al. “Selection for Short Introns in Highly Expressed Genes.” Nature Genetics, vol. 31, no. 4, Nature Publishing Group, 2002, pp. 415–18, doi:10.1038/ng940. short: C. Castillo Davis, S. Mekhedov, D. Hartl, E. Koonin, F. Kondrashov, Nature Genetics 31 (2002) 415–418. date_created: 2018-12-11T11:49:05Z date_published: 2002-08-01T00:00:00Z date_updated: 2023-07-26T09:45:30Z day: '01' doi: 10.1038/ng940 extern: '1' external_id: pmid: - '12134150' intvolume: ' 31' issue: '4' language: - iso: eng month: '08' oa_version: None page: 415 - 418 pmid: 1 publication: Nature Genetics publication_status: published publisher: Nature Publishing Group publist_id: '6751' quality_controlled: '1' scopus_import: '1' status: public title: Selection for short introns in highly expressed genes type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 31 year: '2002' ... --- _id: '871' abstract: - lang: eng text: 'BACKGROUND: Gene duplications have a major role in the evolution of new biological functions. Theoretical studies often assume that a duplication per se is selectively neutral and that, following a duplication, one of the gene copies is freed from purifying (stabilizing) selection, which creates the potential for evolution of a new function. RESULTS: In search of systematic evidence of accelerated evolution after duplication, we used data from 26 bacterial, six archaeal, and seven eukaryotic genomes to compare the mode and strength of selection acting on recently duplicated genes (paralogs) and on similarly diverged, unduplicated orthologous genes in different species. We find that the ratio of nonsynonymous to synonymous substitutions (Kn/Ks) in most paralogous pairs is <<1 and that paralogs typically evolve at similar rates, without significant asymmetry, indicating that both paralogs produced by a duplication are subject to purifying selection. This selection is, however, substantially weaker than the purifying selection affecting unduplicated orthologs that have diverged to the same extent as the analyzed paralogs. Most of the recently duplicated genes appear to be involved in various forms of environmental response; in particular, many of them encode membrane and secreted proteins. CONCLUSIONS: The results of this analysis indicate that recently duplicated paralogs evolve faster than orthologs with the same level of divergence and similar functions, but apparently do not experience a phase of neutral evolution. We hypothesize that gene duplications that persist in an evolving lineage are beneficial from the time of their origin, due primarily to a protein dosage effect in response to variable environmental conditions; duplications are likely to give rise to new functions at a later phase of their evolution once a higher level of divergence is reached.' acknowledgement: We are grateful to A.S. Kondrashov for numerous helpful suggestions, to I. King Jordan, M.A. Roytberg, J.L. Spouge and D.A. Kondrashov for useful discussions and to A.S. Kondrashov, I. King Jordan and D.J. Lipman for critical reading of the manuscript. article_processing_charge: No article_type: original author: - first_name: Fyodor full_name: Kondrashov, Fyodor id: 44FDEF62-F248-11E8-B48F-1D18A9856A87 last_name: Kondrashov orcid: 0000-0001-8243-4694 - first_name: Igor full_name: Rogozin, Igor last_name: Rogozin - first_name: Yuri full_name: Wolf, Yuri last_name: Wolf - first_name: Eugene full_name: Koonin, Eugene last_name: Koonin citation: ama: Kondrashov F, Rogozin I, Wolf Y, Koonin E. Selection in the evolution of gene duplications . Genome Biology. 2002;3(2). doi:10.1186/gb-2002-3-2-research0008 apa: Kondrashov, F., Rogozin, I., Wolf, Y., & Koonin, E. (2002). Selection in the evolution of gene duplications . Genome Biology. BioMed Central. https://doi.org/10.1186/gb-2002-3-2-research0008 chicago: Kondrashov, Fyodor, Igor Rogozin, Yuri Wolf, and Eugene Koonin. “Selection in the Evolution of Gene Duplications .” Genome Biology. BioMed Central, 2002. https://doi.org/10.1186/gb-2002-3-2-research0008. ieee: F. Kondrashov, I. Rogozin, Y. Wolf, and E. Koonin, “Selection in the evolution of gene duplications ,” Genome Biology, vol. 3, no. 2. BioMed Central, 2002. ista: Kondrashov F, Rogozin I, Wolf Y, Koonin E. 2002. Selection in the evolution of gene duplications . Genome Biology. 3(2). mla: Kondrashov, Fyodor, et al. “Selection in the Evolution of Gene Duplications .” Genome Biology, vol. 3, no. 2, BioMed Central, 2002, doi:10.1186/gb-2002-3-2-research0008. short: F. Kondrashov, I. Rogozin, Y. Wolf, E. Koonin, Genome Biology 3 (2002). date_created: 2018-12-11T11:48:57Z date_published: 2002-01-01T00:00:00Z date_updated: 2023-07-26T11:48:27Z day: '01' doi: 10.1186/gb-2002-3-2-research0008 extern: '1' external_id: pmid: - '11864370' intvolume: ' 3' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC65685/ month: '01' oa: 1 oa_version: Published Version pmid: 1 publication: Genome Biology publication_identifier: issn: - 1465-6906 publication_status: published publisher: BioMed Central publist_id: '6781' quality_controlled: '1' scopus_import: '1' status: public title: 'Selection in the evolution of gene duplications ' type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 3 year: '2002' ... --- _id: '859' abstract: - lang: eng text: The polymeric ubiquitin (poly-u) genes are composed of tandem 228-bp repeats with no spacer sequences between individual monomer units. Ubiquitin is one of the most conserved proteins known to date, and the individual units within a number of poly-u genes are significantly more similar to each other than would be expected if each unit evolved independently. It has been proposed that the rather striking similarity among poly-u monomers in some lineages is caused by a series of homogenization events. Here we report the sequences of the polyubiquitin-C (Ubc) genes in two mouse strains. Analysis of these sequences, as well as those of the previously reported Chinese hamster and rat poly-u genes, supports the assertion that the homogenization of the ubiquitin-C gene in rodents is due to unequal crossing-over events. The sequence divergence of noncoding DNA was used to estimate the frequency of unequal crossing-over events (6.3 x 10-5 events per generation) in the Ubc gene, as well as to provide evidence of apparent selection in the poly-u gene. acknowledgement: We are thankful to J.A. Southerland and P.L. Jiang for technical assistance in DNA sequencing, as well as to Y.I. Pavlov for helpful discussions. This work was supported by public Health Service Research Grant AI45135 from the Institute of Allergy and Infectious Diseases, National Institutes of Health. article_processing_charge: No article_type: original author: - first_name: Andrey full_name: Perelygin, Andrey last_name: Perelygin - first_name: Fyodor full_name: Kondrashov, Fyodor id: 44FDEF62-F248-11E8-B48F-1D18A9856A87 last_name: Kondrashov orcid: 0000-0001-8243-4694 - first_name: Igor full_name: Rogozin, Igor last_name: Rogozin - first_name: Margo full_name: Brinton, Margo last_name: Brinton citation: ama: Perelygin A, Kondrashov F, Rogozin I, Brinton M. Evolution of the mouse polyubiquitin C gene. Journal of Molecular Evolution. 2002;55(2):202-210. doi:10.1007/s00239-002-2318-0 apa: Perelygin, A., Kondrashov, F., Rogozin, I., & Brinton, M. (2002). Evolution of the mouse polyubiquitin C gene. Journal of Molecular Evolution. Springer. https://doi.org/10.1007/s00239-002-2318-0 chicago: Perelygin, Andrey, Fyodor Kondrashov, Igor Rogozin, and Margo Brinton. “Evolution of the Mouse Polyubiquitin C Gene.” Journal of Molecular Evolution. Springer, 2002. https://doi.org/10.1007/s00239-002-2318-0. ieee: A. Perelygin, F. Kondrashov, I. Rogozin, and M. Brinton, “Evolution of the mouse polyubiquitin C gene,” Journal of Molecular Evolution, vol. 55, no. 2. Springer, pp. 202–210, 2002. ista: Perelygin A, Kondrashov F, Rogozin I, Brinton M. 2002. Evolution of the mouse polyubiquitin C gene. Journal of Molecular Evolution. 55(2), 202–210. mla: Perelygin, Andrey, et al. “Evolution of the Mouse Polyubiquitin C Gene.” Journal of Molecular Evolution, vol. 55, no. 2, Springer, 2002, pp. 202–10, doi:10.1007/s00239-002-2318-0. short: A. Perelygin, F. Kondrashov, I. Rogozin, M. Brinton, Journal of Molecular Evolution 55 (2002) 202–210. date_created: 2018-12-11T11:48:53Z date_published: 2002-01-01T00:00:00Z date_updated: 2023-07-26T12:01:34Z day: '01' doi: 10.1007/s00239-002-2318-0 extern: '1' external_id: pmid: - '12107596' intvolume: ' 55' issue: '2' language: - iso: eng month: '01' oa_version: None page: 202 - 210 pmid: 1 publication: Journal of Molecular Evolution publication_identifier: issn: - 0022-2844 publication_status: published publisher: Springer publist_id: '6787' quality_controlled: '1' scopus_import: '1' status: public title: Evolution of the mouse polyubiquitin C gene type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 55 year: '2002' ... --- _id: '204' abstract: - lang: eng text: Let k⩾5 be an integer, and let x⩾1 be an arbitrary real number. We derive a bound[Formula presented] for the number of positive integers less than or equal to x which can be represented as a sum of two non-negative coprime kth powers, in essentially more than one way. article_processing_charge: No article_type: original author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 citation: ama: Browning TD. Equal Sums of Two kth Powers. Journal of Number Theory. 2002;96(2):293-318. doi:10.1006/jnth.2002.2800 apa: Browning, T. D. (2002). Equal Sums of Two kth Powers. Journal of Number Theory. Academic Press. https://doi.org/10.1006/jnth.2002.2800 chicago: Browning, Timothy D. “Equal Sums of Two Kth Powers.” Journal of Number Theory. Academic Press, 2002. https://doi.org/10.1006/jnth.2002.2800. ieee: T. D. Browning, “Equal Sums of Two kth Powers,” Journal of Number Theory, vol. 96, no. 2. Academic Press, pp. 293–318, 2002. ista: Browning TD. 2002. Equal Sums of Two kth Powers. Journal of Number Theory. 96(2), 293–318. mla: Browning, Timothy D. “Equal Sums of Two Kth Powers.” Journal of Number Theory, vol. 96, no. 2, Academic Press, 2002, pp. 293–318, doi:10.1006/jnth.2002.2800. short: T.D. Browning, Journal of Number Theory 96 (2002) 293–318. date_created: 2018-12-11T11:45:11Z date_published: 2002-10-02T00:00:00Z date_updated: 2023-07-26T12:15:14Z day: '02' doi: 10.1006/jnth.2002.2800 extern: '1' intvolume: ' 96' issue: '2' language: - iso: eng month: '10' oa_version: Published Version page: 293 - 318 publication: Journal of Number Theory publication_identifier: issn: - 0022-314X publication_status: published publisher: Academic Press publist_id: '7708' quality_controlled: '1' scopus_import: '1' status: public title: Equal Sums of Two kth Powers 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: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 96 year: '2002' ...