---
_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
license: https://creativecommons.org/licenses/by/4.0/
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'
...