--- _id: '8514' abstract: - lang: eng text: We study the extent to which the Hausdorff dimension of a compact subset of an infinite-dimensional Banach space is affected by a typical mapping into a finite-dimensional space. It is possible that the dimension drops under all such mappings, but the amount by which it typically drops is controlled by the ‘thickness exponent’ of the set, which was defined by Hunt and Kaloshin (Nonlinearity12 (1999), 1263–1275). More precisely, let $X$ be a compact subset of a Banach space $B$ with thickness exponent $\tau$ and Hausdorff dimension $d$. Let $M$ be any subspace of the (locally) Lipschitz functions from $B$ to $\mathbb{R}^{m}$ that contains the space of bounded linear functions. We prove that for almost every (in the sense of prevalence) function $f \in M$, the Hausdorff dimension of $f(X)$ is at least $\min\{ m, d / (1 + \tau) \}$. We also prove an analogous result for a certain part of the dimension spectra of Borel probability measures supported on $X$. The factor $1 / (1 + \tau)$ can be improved to $1 / (1 + \tau / 2)$ if $B$ is a Hilbert space. Since dimension cannot increase under a (locally) Lipschitz function, these theorems become dimension preservation results when $\tau = 0$. We conjecture that many of the attractors associated with the evolution equations of mathematical physics have thickness exponent zero. We also discuss the sharpness of our results in the case $\tau > 0$. article_processing_charge: No article_type: original author: - first_name: WILLIAM full_name: OTT, WILLIAM last_name: OTT - first_name: BRIAN full_name: HUNT, BRIAN last_name: HUNT - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 citation: ama: OTT W, HUNT B, Kaloshin V. The effect of projections on fractal sets and measures in Banach spaces. Ergodic Theory and Dynamical Systems. 2006;26(3):869-891. doi:10.1017/s0143385705000714 apa: OTT, W., HUNT, B., & Kaloshin, V. (2006). The effect of projections on fractal sets and measures in Banach spaces. Ergodic Theory and Dynamical Systems. Cambridge University Press. https://doi.org/10.1017/s0143385705000714 chicago: OTT, WILLIAM, BRIAN HUNT, and Vadim Kaloshin. “The Effect of Projections on Fractal Sets and Measures in Banach Spaces.” Ergodic Theory and Dynamical Systems. Cambridge University Press, 2006. https://doi.org/10.1017/s0143385705000714. ieee: W. OTT, B. HUNT, and V. Kaloshin, “The effect of projections on fractal sets and measures in Banach spaces,” Ergodic Theory and Dynamical Systems, vol. 26, no. 3. Cambridge University Press, pp. 869–891, 2006. ista: OTT W, HUNT B, Kaloshin V. 2006. The effect of projections on fractal sets and measures in Banach spaces. Ergodic Theory and Dynamical Systems. 26(3), 869–891. mla: OTT, WILLIAM, et al. “The Effect of Projections on Fractal Sets and Measures in Banach Spaces.” Ergodic Theory and Dynamical Systems, vol. 26, no. 3, Cambridge University Press, 2006, pp. 869–91, doi:10.1017/s0143385705000714. short: W. OTT, B. HUNT, V. Kaloshin, Ergodic Theory and Dynamical Systems 26 (2006) 869–891. date_created: 2020-09-18T10:48:52Z date_published: 2006-06-01T00:00:00Z date_updated: 2021-01-12T08:19:48Z day: '01' doi: 10.1017/s0143385705000714 extern: '1' intvolume: ' 26' issue: '3' language: - iso: eng month: '06' oa_version: None page: 869-891 publication: Ergodic Theory and Dynamical Systems publication_identifier: issn: - 0143-3857 - 1469-4417 publication_status: published publisher: Cambridge University Press quality_controlled: '1' status: public title: The effect of projections on fractal sets and measures in Banach spaces type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 26 year: '2006' ... --- _id: '8515' abstract: - lang: eng text: "We consider the evolution of a set carried by a space periodic incompressible stochastic flow in a Euclidean space. We\r\nreport on three main results obtained in [8, 9, 10] concerning long time behaviour for a typical realization of the stochastic flow. First, at time t most of the particles are at a distance of order √t away from the origin. Moreover, we prove a Central Limit Theorem for the evolution of a measure carried by the flow, which holds for almost every realization of the flow. Second, we show the existence of a zero measure full Hausdorff dimension set of points, which\r\nescape to infinity at a linear rate. Third, in the 2-dimensional case, we study the set of points visited by the original set by time t. Such a set, when scaled down by the factor of t, has a limiting non random shape." article_processing_charge: No author: - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: D. full_name: DOLGOPYAT, D. last_name: DOLGOPYAT - first_name: L. full_name: KORALOV, L. last_name: KORALOV citation: ama: 'Kaloshin V, DOLGOPYAT D, KORALOV L. Long time behaviour of periodic stochastic flows. In: XIVth International Congress on Mathematical Physics. World Scientific; 2006:290-295. doi:10.1142/9789812704016_0026' apa: 'Kaloshin, V., DOLGOPYAT, D., & KORALOV, L. (2006). Long time behaviour of periodic stochastic flows. In XIVth International Congress on Mathematical Physics (pp. 290–295). Lisbon, Portugal: World Scientific. https://doi.org/10.1142/9789812704016_0026' chicago: Kaloshin, Vadim, D. DOLGOPYAT, and L. KORALOV. “Long Time Behaviour of Periodic Stochastic Flows.” In XIVth International Congress on Mathematical Physics, 290–95. World Scientific, 2006. https://doi.org/10.1142/9789812704016_0026. ieee: V. Kaloshin, D. DOLGOPYAT, and L. KORALOV, “Long time behaviour of periodic stochastic flows,” in XIVth International Congress on Mathematical Physics, Lisbon, Portugal, 2006, pp. 290–295. ista: Kaloshin V, DOLGOPYAT D, KORALOV L. 2006. Long time behaviour of periodic stochastic flows. XIVth International Congress on Mathematical Physics. International Congress on Mathematical Physics, 290–295. mla: Kaloshin, Vadim, et al. “Long Time Behaviour of Periodic Stochastic Flows.” XIVth International Congress on Mathematical Physics, World Scientific, 2006, pp. 290–95, doi:10.1142/9789812704016_0026. short: V. Kaloshin, D. DOLGOPYAT, L. KORALOV, in:, XIVth International Congress on Mathematical Physics, World Scientific, 2006, pp. 290–295. conference: end_date: 2003-08-02 location: Lisbon, Portugal name: International Congress on Mathematical Physics start_date: 2003-07-28 date_created: 2020-09-18T10:48:59Z date_published: 2006-03-01T00:00:00Z date_updated: 2021-01-12T08:19:49Z day: '01' doi: 10.1142/9789812704016_0026 extern: '1' language: - iso: eng month: '03' oa_version: None page: 290-295 publication: XIVth International Congress on Mathematical Physics publication_identifier: isbn: - '9789812562012' - '9789812704016' publication_status: published publisher: World Scientific quality_controlled: '1' status: public title: Long time behaviour of periodic stochastic flows type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2006' ... --- _id: '8513' article_processing_charge: No article_type: original author: - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: Maria full_name: Saprykina, Maria last_name: Saprykina citation: ama: Kaloshin V, Saprykina M. Generic 3-dimensional volume-preserving diffeomorphisms with superexponential growth of number of periodic orbits. Discrete & Continuous Dynamical Systems - A. 2006;15(2):611-640. doi:10.3934/dcds.2006.15.611 apa: Kaloshin, V., & Saprykina, M. (2006). Generic 3-dimensional volume-preserving diffeomorphisms with superexponential growth of number of periodic orbits. Discrete & Continuous Dynamical Systems - A. American Institute of Mathematical Sciences (AIMS). https://doi.org/10.3934/dcds.2006.15.611 chicago: Kaloshin, Vadim, and Maria Saprykina. “Generic 3-Dimensional Volume-Preserving Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” Discrete & Continuous Dynamical Systems - A. American Institute of Mathematical Sciences (AIMS), 2006. https://doi.org/10.3934/dcds.2006.15.611. ieee: V. Kaloshin and M. Saprykina, “Generic 3-dimensional volume-preserving diffeomorphisms with superexponential growth of number of periodic orbits,” Discrete & Continuous Dynamical Systems - A, vol. 15, no. 2. American Institute of Mathematical Sciences (AIMS), pp. 611–640, 2006. ista: Kaloshin V, Saprykina M. 2006. Generic 3-dimensional volume-preserving diffeomorphisms with superexponential growth of number of periodic orbits. Discrete & Continuous Dynamical Systems - A. 15(2), 611–640. mla: Kaloshin, Vadim, and Maria Saprykina. “Generic 3-Dimensional Volume-Preserving Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” Discrete & Continuous Dynamical Systems - A, vol. 15, no. 2, American Institute of Mathematical Sciences (AIMS), 2006, pp. 611–40, doi:10.3934/dcds.2006.15.611. short: V. Kaloshin, M. Saprykina, Discrete & Continuous Dynamical Systems - A 15 (2006) 611–640. date_created: 2020-09-18T10:48:43Z date_published: 2006-05-01T00:00:00Z date_updated: 2021-01-12T08:19:48Z day: '01' doi: 10.3934/dcds.2006.15.611 extern: '1' intvolume: ' 15' issue: '2' language: - iso: eng month: '05' oa_version: None page: 611-640 publication: Discrete & Continuous Dynamical Systems - A publication_identifier: issn: - 1553-5231 publication_status: published publisher: American Institute of Mathematical Sciences (AIMS) quality_controlled: '1' status: public title: Generic 3-dimensional volume-preserving diffeomorphisms with superexponential growth of number of periodic orbits type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 15 year: '2006' ... --- _id: '869' abstract: - lang: eng text: The impact of synonymous nucleotide substitutions on fitness in mammals remains controversial. Despite some indications of selective constraint, synonymous sites are often assumed to be neutral, and the rate of their evolution is used as a proxy for mutation rate. We subdivide all sites into four classes in terms of the mutable CpG context, nonCpG, postC, preG, and postCpreG, and compare four-fold synonymous sites and intron sites residing outside transposable elements. The distribution of the rate of evolution across all synonymous sites is trimodal. Rate of evolution at nonCpG synonymous sites, not preceded by C and not followed by G, is ∼10% below that at such intron sites. In contrast, rate of evolution at postCpreG synonymous sites is ∼30% above that at such intron sites. Finally, synonymous and intron postC and preG sites evolve at similar rates. The relationship between the levels of polymorphism at the corresponding synonymous and intron sites is very similar to that between their rates of evolution. Within every class, synonymous sites are occupied by G or C much more often than intron sites, whose nucleotide composition is consistent with neutral mutation-drift equilibrium. These patterns suggest that synonymous sites are under weak selection in favor of G and C, with the average coefficient s∼0.25/Ne∼10-5, where Ne is the effective population size. Such selection decelerates evolution and reduces variability at sites with symmetric mutation, but has the opposite effects at sites where the favored nucleotides are more mutable. The amino-acid composition of proteins dictates that many synonymous sites are CpGprone, which causes them, on average, to evolve faster and to be more polymorphic than intron sites. An average genotype carries ∼107 suboptimal nucleotides at synonymous sites, implying synergistic epistasis in selection against them. acknowledgement: This research was supported in part by the Intramural Research Program of the NIH, National Library of Medicine. author: - first_name: Fyodor full_name: Fyodor Kondrashov id: 44FDEF62-F248-11E8-B48F-1D18A9856A87 last_name: Kondrashov orcid: 0000-0001-8243-4694 - first_name: Aleksey full_name: Ogurtsov, Aleksey Yu last_name: Ogurtsov - first_name: Alexey full_name: Kondrashov, Alexey S last_name: Kondrashov citation: ama: Kondrashov F, Ogurtsov A, Kondrashov A. Selection in favor of nucleotides G and C diversifies evolution rates and levels of polymorphism at mammalian synonymous sites. Journal of Theoretical Biology. 2006;240(4):616-626. doi:10.1016/j.jtbi.2005.10.020 apa: Kondrashov, F., Ogurtsov, A., & Kondrashov, A. (2006). Selection in favor of nucleotides G and C diversifies evolution rates and levels of polymorphism at mammalian synonymous sites. Journal of Theoretical Biology. Elsevier. https://doi.org/10.1016/j.jtbi.2005.10.020 chicago: Kondrashov, Fyodor, Aleksey Ogurtsov, and Alexey Kondrashov. “Selection in Favor of Nucleotides G and C Diversifies Evolution Rates and Levels of Polymorphism at Mammalian Synonymous Sites.” Journal of Theoretical Biology. Elsevier, 2006. https://doi.org/10.1016/j.jtbi.2005.10.020. ieee: F. Kondrashov, A. Ogurtsov, and A. Kondrashov, “Selection in favor of nucleotides G and C diversifies evolution rates and levels of polymorphism at mammalian synonymous sites,” Journal of Theoretical Biology, vol. 240, no. 4. Elsevier, pp. 616–626, 2006. ista: Kondrashov F, Ogurtsov A, Kondrashov A. 2006. Selection in favor of nucleotides G and C diversifies evolution rates and levels of polymorphism at mammalian synonymous sites. Journal of Theoretical Biology. 240(4), 616–626. mla: Kondrashov, Fyodor, et al. “Selection in Favor of Nucleotides G and C Diversifies Evolution Rates and Levels of Polymorphism at Mammalian Synonymous Sites.” Journal of Theoretical Biology, vol. 240, no. 4, Elsevier, 2006, pp. 616–26, doi:10.1016/j.jtbi.2005.10.020. short: F. Kondrashov, A. Ogurtsov, A. Kondrashov, Journal of Theoretical Biology 240 (2006) 616–626. date_created: 2018-12-11T11:48:56Z date_published: 2006-06-21T00:00:00Z date_updated: 2021-01-12T08:20:33Z day: '21' doi: 10.1016/j.jtbi.2005.10.020 extern: 1 intvolume: ' 240' issue: '4' month: '06' page: 616 - 626 publication: Journal of Theoretical Biology publication_status: published publisher: Elsevier publist_id: '6779' quality_controlled: 0 status: public title: Selection in favor of nucleotides G and C diversifies evolution rates and levels of polymorphism at mammalian synonymous sites type: journal_article volume: 240 year: '2006' ... --- _id: '903' abstract: - lang: eng text: 'Background: Carcinogenesis typically involves multiple somatic mutations in caretaker (DNA repair) and gatekeeper (tumor suppressors and oncogenes) genes. Analysis of mutation spectra of the tumor suppressor that is most commonly mutated in human cancers, p53, unexpectedly suggested that somatic evolution of the p53 gene during tumorigenesis is dominated by positive selection for gain of function. This conclusion is supported by accumulating experimental evidence of evolution of new functions of p53 in tumors. These findings prompted a genome-wide analysis of possible positive selection during tumor evolution. Methods: A comprehensive analysis of probable somatic mutations in the sequences of Expressed Sequence Tags (ESTs) from malignant tumors and normal tissues was performed in order to access the prevalence of positive selection in cancer evolution. For each EST, the numbers of synonymous and non-synonymous substitutions were calculated. In order to identify genes with a signature of positive selection in cancers, these numbers were compared to: i) expected numbers and ii) the numbers for the respective genes in the ESTs from normal tissues. Results: We identified 112 genes with a signature of positive selection in cancers, i.e., a significantly elevated ratio of non-synonymous to synonymous substitutions, in tumors as compared to 37 such genes in an approximately equal-sized EST collection from normal tissues. A substantial fraction of the tumor-specific positive-selection candidates have experimentally demonstrated or strongly predicted links to cancer. Conclusion: The results of EST analysis should be interpreted with extreme caution given the noise introduced by sequencing errors and undetected polymorphisms. Furthermore, an inherent limitation of EST analysis is that multiple mutations amenable to statistical analysis can be detected only in relatively highly expressed genes. Nevertheless, the present results suggest that positive selection might affect a substantial number of genes during tumorigenic somatic evolution.' acknowledgement: This work was supported by the Intramural Research Program of the National Library of Medicine at the National Institutes of Health/DHHS. FAK is an NSF Graduate Fellow. We thank Yuri Pavlov for helpful discussions. author: - first_name: Vladimir full_name: Babenko, Vladimir N last_name: Babenko - first_name: Malay full_name: Basu, Malay K last_name: Basu - first_name: Fyodor full_name: Fyodor Kondrashov id: 44FDEF62-F248-11E8-B48F-1D18A9856A87 last_name: Kondrashov orcid: 0000-0001-8243-4694 - first_name: Igor full_name: Rogozin, Igor B last_name: Rogozin - first_name: Eugene full_name: Koonin, Eugene V last_name: Koonin citation: ama: Babenko V, Basu M, Kondrashov F, Rogozin I, Koonin E. Signs of positive selection of somatic mutations in human cancers detected by EST sequence analysis. BMC Cancer. 2006;6. doi:10.1186/1471-2407-6-36 apa: Babenko, V., Basu, M., Kondrashov, F., Rogozin, I., & Koonin, E. (2006). Signs of positive selection of somatic mutations in human cancers detected by EST sequence analysis. BMC Cancer. BioMed Central. https://doi.org/10.1186/1471-2407-6-36 chicago: Babenko, Vladimir, Malay Basu, Fyodor Kondrashov, Igor Rogozin, and Eugene Koonin. “Signs of Positive Selection of Somatic Mutations in Human Cancers Detected by EST Sequence Analysis.” BMC Cancer. BioMed Central, 2006. https://doi.org/10.1186/1471-2407-6-36. ieee: V. Babenko, M. Basu, F. Kondrashov, I. Rogozin, and E. Koonin, “Signs of positive selection of somatic mutations in human cancers detected by EST sequence analysis,” BMC Cancer, vol. 6. BioMed Central, 2006. ista: Babenko V, Basu M, Kondrashov F, Rogozin I, Koonin E. 2006. Signs of positive selection of somatic mutations in human cancers detected by EST sequence analysis. BMC Cancer. 6. mla: Babenko, Vladimir, et al. “Signs of Positive Selection of Somatic Mutations in Human Cancers Detected by EST Sequence Analysis.” BMC Cancer, vol. 6, BioMed Central, 2006, doi:10.1186/1471-2407-6-36. short: V. Babenko, M. Basu, F. Kondrashov, I. Rogozin, E. Koonin, BMC Cancer 6 (2006). date_created: 2018-12-11T11:49:07Z date_published: 2006-02-09T00:00:00Z date_updated: 2021-01-12T08:21:47Z day: '09' doi: 10.1186/1471-2407-6-36 extern: 1 intvolume: ' 6' month: '02' publication: BMC Cancer publication_status: published publisher: BioMed Central publist_id: '6744' quality_controlled: 0 status: public title: Signs of positive selection of somatic mutations in human cancers detected by EST sequence analysis 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 volume: 6 year: '2006' ...