[{"date_updated":"2021-01-12T08:19:47Z","abstract":[{"text":"In this paper, using the ideas of Bessi and Mather, we present a simple mechanical system exhibiting Arnold diffusion. This system of a particle in a small periodic potential can be also interpreted as ray propagation in a periodic optical medium with a near-constant index of refraction. Arnold diffusion in this context manifests itself as an arbitrary finite change of direction for nearly constant index of refraction.","lang":"eng"}],"publication_status":"published","issue":"3","status":"public","citation":{"mla":"Kaloshin, Vadim, and Mark Levi. “An Example of Arnold Diffusion for Near-Integrable Hamiltonians.” <i>Bulletin of the American Mathematical Society</i>, vol. 45, no. 3, American Mathematical Society, 2008, pp. 409–27, doi:<a href=\"https://doi.org/10.1090/s0273-0979-08-01211-1\">10.1090/s0273-0979-08-01211-1</a>.","ama":"Kaloshin V, Levi M. An example of Arnold diffusion for near-integrable Hamiltonians. <i>Bulletin of the American Mathematical Society</i>. 2008;45(3):409-427. doi:<a href=\"https://doi.org/10.1090/s0273-0979-08-01211-1\">10.1090/s0273-0979-08-01211-1</a>","ista":"Kaloshin V, Levi M. 2008. An example of Arnold diffusion for near-integrable Hamiltonians. Bulletin of the American Mathematical Society. 45(3), 409–427.","ieee":"V. Kaloshin and M. Levi, “An example of Arnold diffusion for near-integrable Hamiltonians,” <i>Bulletin of the American Mathematical Society</i>, vol. 45, no. 3. American Mathematical Society, pp. 409–427, 2008.","apa":"Kaloshin, V., &#38; Levi, M. (2008). An example of Arnold diffusion for near-integrable Hamiltonians. <i>Bulletin of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/s0273-0979-08-01211-1\">https://doi.org/10.1090/s0273-0979-08-01211-1</a>","chicago":"Kaloshin, Vadim, and Mark Levi. “An Example of Arnold Diffusion for Near-Integrable Hamiltonians.” <i>Bulletin of the American Mathematical Society</i>. American Mathematical Society, 2008. <a href=\"https://doi.org/10.1090/s0273-0979-08-01211-1\">https://doi.org/10.1090/s0273-0979-08-01211-1</a>.","short":"V. Kaloshin, M. Levi, Bulletin of the American Mathematical Society 45 (2008) 409–427."},"doi":"10.1090/s0273-0979-08-01211-1","publication":"Bulletin of the American Mathematical Society","intvolume":"        45","publication_identifier":{"issn":["0273-0979"]},"date_published":"2008-07-01T00:00:00Z","_id":"8510","publisher":"American Mathematical Society","language":[{"iso":"eng"}],"article_processing_charge":"No","title":"An example of Arnold diffusion for near-integrable Hamiltonians","volume":45,"year":"2008","keyword":["Applied Mathematics","General Mathematics"],"day":"01","article_type":"original","oa_version":"None","date_created":"2020-09-18T10:48:20Z","type":"journal_article","author":[{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","first_name":"Vadim"},{"full_name":"Levi, Mark","last_name":"Levi","first_name":"Mark"}],"page":"409-427","quality_controlled":"1","month":"07","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"type":"journal_article","date_created":"2018-12-11T11:49:04Z","day":"01","year":"2008","volume":8,"title":"Evolution of a behavior-linked microsatellite-containing element in the 5′ flanking region of the primate AVPR1A gene","month":"01","extern":1,"quality_controlled":0,"author":[{"last_name":"Donaldson","first_name":"Zoe","full_name":"Donaldson, Zoe R"},{"first_name":"Fyodor","last_name":"Kondrashov","orcid":"0000-0001-8243-4694","id":"44FDEF62-F248-11E8-B48F-1D18A9856A87","full_name":"Fyodor Kondrashov"},{"full_name":"Putnam, Andrea S","last_name":"Putnam","first_name":"Andrea"},{"last_name":"Bai","first_name":"Yaohui","full_name":"Bai, Yaohui"},{"last_name":"Stoinski","first_name":"Tara","full_name":"Stoinski, Tara S"},{"full_name":"Hammock, Elizabeth A","last_name":"Hammock","first_name":"Elizabeth"},{"last_name":"Young","first_name":"Larry","full_name":"Young, Larry"}],"license":"https://creativecommons.org/licenses/by/4.0/","intvolume":"         8","publication":"BMC Evolutionary Biology","doi":"10.1186/1471-2148-8-180","citation":{"ieee":"Z. Donaldson <i>et al.</i>, “Evolution of a behavior-linked microsatellite-containing element in the 5′ flanking region of the primate AVPR1A gene,” <i>BMC Evolutionary Biology</i>, vol. 8, no. 1. BioMed Central, 2008.","short":"Z. Donaldson, F. Kondrashov, A. Putnam, Y. Bai, T. Stoinski, E. Hammock, L. Young, BMC Evolutionary Biology 8 (2008).","chicago":"Donaldson, Zoe, Fyodor Kondrashov, Andrea Putnam, Yaohui Bai, Tara Stoinski, Elizabeth Hammock, and Larry Young. “Evolution of a Behavior-Linked Microsatellite-Containing Element in the 5′ Flanking Region of the Primate AVPR1A Gene.” <i>BMC Evolutionary Biology</i>. BioMed Central, 2008. <a href=\"https://doi.org/10.1186/1471-2148-8-180\">https://doi.org/10.1186/1471-2148-8-180</a>.","apa":"Donaldson, Z., Kondrashov, F., Putnam, A., Bai, Y., Stoinski, T., Hammock, E., &#38; Young, L. (2008). Evolution of a behavior-linked microsatellite-containing element in the 5′ flanking region of the primate AVPR1A gene. <i>BMC Evolutionary Biology</i>. BioMed Central. <a href=\"https://doi.org/10.1186/1471-2148-8-180\">https://doi.org/10.1186/1471-2148-8-180</a>","ama":"Donaldson Z, Kondrashov F, Putnam A, et al. Evolution of a behavior-linked microsatellite-containing element in the 5′ flanking region of the primate AVPR1A gene. <i>BMC Evolutionary Biology</i>. 2008;8(1). doi:<a href=\"https://doi.org/10.1186/1471-2148-8-180\">10.1186/1471-2148-8-180</a>","mla":"Donaldson, Zoe, et al. “Evolution of a Behavior-Linked Microsatellite-Containing Element in the 5′ Flanking Region of the Primate AVPR1A Gene.” <i>BMC Evolutionary Biology</i>, vol. 8, no. 1, BioMed Central, 2008, doi:<a href=\"https://doi.org/10.1186/1471-2148-8-180\">10.1186/1471-2148-8-180</a>.","ista":"Donaldson Z, Kondrashov F, Putnam A, Bai Y, Stoinski T, Hammock E, Young L. 2008. Evolution of a behavior-linked microsatellite-containing element in the 5′ flanking region of the primate AVPR1A gene. BMC Evolutionary Biology. 8(1)."},"status":"public","publication_status":"published","issue":"1","abstract":[{"lang":"eng","text":"Background. The arginine vasopressin V1a receptor (V1aR) modulates social cognition and behavior in a wide variety of species. Variation in a repetitive microsatellite element in the 5′ flanking region of the V1aR gene (AVPR1A) in rodents has been associated with variation in brain V1aR expression and in social behavior. In humans, the 5′ flanking region of AVPR1A contains a tandem duplication of two ∼350 bp, microsatellite-containing elements located approximately 3.5 kb upstream of the transcription start site. The first block, referred to as DupA, contains a polymorphic (GT) 25microsatellite; the second block, DupB, has a complex (CT) 4-(TT)-(CT)8-(GT)24polymorphic motif, known as RS3. Polymorphisms in RS3 have been associated with variation in sociobehavioral traits in humans, including autism spectrum disorders. Thus, evolution of these regions may have contributed to variation in social behavior in primates. We examined the structure of these regions in six ape, six monkey, and one prosimian species. Results. Both tandem repeat blocks are present upstream of the AVPR1A coding region in five of the ape species we investigated, while monkeys have only one copy of this region. As in humans, the microsatellites within DupA and DupB are polymorphic in many primate species. Furthermore, both single (lacking DupB) and duplicated alleles (containing both DupA and DupB) are present in chimpanzee (Pan troglodytes) populations with allele frequencies of 0.795 and 0.205 for the single and duplicated alleles, respectively, based on the analysis of 47 wild-caught individuals. Finally, a phylogenetic reconstruction suggests two alternate evolutionary histories for this locus. Conclusion. There is no obvious relationship between the presence of the RS3 duplication and social organization in primates. However, polymorphisms identified in some species may be useful in future genetic association studies. In particular, the presence of both single and duplicated alleles in chimpanzees provides a unique opportunity to assess the functional role of this duplication in contributing to variation in social behavior in primates. While our initial studies show no signs of directional selection on this locus in chimps, pharmacological and genetic association studies support a potential role for this region in influencing V1aR expression and social behavior."}],"date_updated":"2021-01-12T08:21:29Z","publisher":"BioMed Central","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"_id":"895","date_published":"2008-01-01T00:00:00Z","acknowledgement":"We thank the caretakers at Zoo Atlanta and Yerkes National Primate Center for help with procuring specimens. Additional DNA samples were supplied by Bill Hopkins, Emory University (chimpanzee), Allyson Bennet, Wake Forest University (chimpanzee, rhesus macaque, bonnet macaque), Mar Sanchez, Emory University (rhesus macaque), and Anne Yoder, Duke University (galago). Susan Lambeth, M.D. Anderson Cancer Center, and Katie Chace, Yerkes National Primate Center, helped provide records regarding the origins of wild born chimps at these centers. We would like to thank Dr Lisa McGraw and two anonymous reviewers for their com- ments on this manuscript. This work was supported by NSF IBN-9876754, NIH RR00165, NIMH56897 (LJY), MH64692 (LJY) and a Howard Hughes Predoctoral Fellowship (ZRD).\n","publist_id":"6753"},{"publist_id":"6743","date_published":"2008-10-01T00:00:00Z","_id":"907","publisher":"Elsevier","date_updated":"2021-01-12T08:21:49Z","abstract":[{"lang":"eng","text":"The most common form of protein-coding gene overlap in eukaryotes is a simple nested structure, whereby one gene is embedded in an intron of another. Analysis of nested protein-coding genes in vertebrates, fruit flies and nematodes revealed substantially higher rates of evolutionary gains than losses. The accumulation of nested gene structures could not be attributed to any obvious functional relationships between the genes involved and represents an increase of the organizational complexity of animal genomes via a neutral process."}],"publication_status":"published","issue":"10","citation":{"ista":"Assis R, Kondrashov A, Koonin E, Kondrashov F. 2008. Nested genes and increasing organizational complexity of metazoan genomes. Trends in Genetics. 24(10), 475–478.","mla":"Assis, Raquel, et al. “Nested Genes and Increasing Organizational Complexity of Metazoan Genomes.” <i>Trends in Genetics</i>, vol. 24, no. 10, Elsevier, 2008, pp. 475–78, doi:<a href=\"https://doi.org/10.1016/j.tig.2008.08.003\">10.1016/j.tig.2008.08.003</a>.","ama":"Assis R, Kondrashov A, Koonin E, Kondrashov F. Nested genes and increasing organizational complexity of metazoan genomes. <i>Trends in Genetics</i>. 2008;24(10):475-478. doi:<a href=\"https://doi.org/10.1016/j.tig.2008.08.003\">10.1016/j.tig.2008.08.003</a>","apa":"Assis, R., Kondrashov, A., Koonin, E., &#38; Kondrashov, F. (2008). Nested genes and increasing organizational complexity of metazoan genomes. <i>Trends in Genetics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.tig.2008.08.003\">https://doi.org/10.1016/j.tig.2008.08.003</a>","short":"R. Assis, A. Kondrashov, E. Koonin, F. Kondrashov, Trends in Genetics 24 (2008) 475–478.","chicago":"Assis, Raquel, Alexey Kondrashov, Eugene Koonin, and Fyodor Kondrashov. “Nested Genes and Increasing Organizational Complexity of Metazoan Genomes.” <i>Trends in Genetics</i>. Elsevier, 2008. <a href=\"https://doi.org/10.1016/j.tig.2008.08.003\">https://doi.org/10.1016/j.tig.2008.08.003</a>.","ieee":"R. Assis, A. Kondrashov, E. Koonin, and F. Kondrashov, “Nested genes and increasing organizational complexity of metazoan genomes,” <i>Trends in Genetics</i>, vol. 24, no. 10. Elsevier, pp. 475–478, 2008."},"status":"public","doi":"10.1016/j.tig.2008.08.003","publication":"Trends in Genetics","intvolume":"        24","page":"475 - 478","author":[{"full_name":"Assis, Raquel","last_name":"Assis","first_name":"Raquel"},{"first_name":"Alexey","last_name":"Kondrashov","full_name":"Kondrashov, Alexey S"},{"full_name":"Koonin, Eugene V","first_name":"Eugene","last_name":"Koonin"},{"last_name":"Kondrashov","first_name":"Fyodor","orcid":"0000-0001-8243-4694","id":"44FDEF62-F248-11E8-B48F-1D18A9856A87","full_name":"Fyodor Kondrashov"}],"quality_controlled":0,"extern":1,"month":"10","title":"Nested genes and increasing organizational complexity of metazoan genomes","volume":24,"year":"2008","day":"01","date_created":"2018-12-11T11:49:08Z","type":"journal_article"},{"_id":"9457","article_processing_charge":"No","language":[{"iso":"eng"}],"doi":"10.1038/nature07324","scopus_import":"1","intvolume":"       456","date_updated":"2021-12-14T08:54:36Z","publication_status":"published","issue":"7218","status":"public","page":"125-129","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","extern":"1","keyword":["Multidisciplinary"],"article_type":"letter_note","oa_version":"Submitted Version","type":"journal_article","department":[{"_id":"DaZi"}],"title":"Histone H2A.Z and DNA methylation are mutually antagonistic chromatin marks","publisher":"Springer Nature","pmid":1,"publication_identifier":{"issn":["0028-0836"],"eissn":["1476-4687"]},"date_published":"2008-11-06T00:00:00Z","external_id":{"pmid":["18815594"]},"publication":"Nature","main_file_link":[{"url":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2877514/","open_access":"1"}],"abstract":[{"text":"Eukaryotic chromatin is separated into functional domains differentiated by posttranslational histone modifications, histone variants, and DNA methylation1–6. Methylation is associated with repression of transcriptional initiation in plants and animals, and is frequently found in transposable elements. Proper methylation patterns are critical for eukaryotic development4,5, and aberrant methylation-induced silencing of tumor suppressor genes is a common feature of human cancer7. In contrast to methylation, the histone variant H2A.Z is preferentially deposited by the Swr1 ATPase complex near 5′ ends of genes where it promotes transcriptional competence8–20. How DNA methylation and H2A.Z influence transcription remains largely unknown. Here we show that in the plant Arabidopsis thaliana, regions of DNA methylation are quantitatively deficient in H2A.Z. Exclusion of H2A.Z is seen at sites of DNA methylation in the bodies of actively transcribed genes and in methylated transposons. Mutation of the MET1 DNA methyltransferase, which causes both losses and gains of DNA methylation4,5, engenders opposite changes in H2A.Z deposition, while mutation of the PIE1 subunit of the Swr1 complex that deposits H2A.Z17 leads to genome-wide hypermethylation. Our findings indicate that DNA methylation can influence chromatin structure and effect gene silencing by excluding H2A.Z, and that H2A.Z protects genes from DNA methylation.","lang":"eng"}],"citation":{"ieee":"D. Zilberman, D. Coleman-Derr, T. Ballinger, and S. Henikoff, “Histone H2A.Z and DNA methylation are mutually antagonistic chromatin marks,” <i>Nature</i>, vol. 456, no. 7218. Springer Nature, pp. 125–129, 2008.","apa":"Zilberman, D., Coleman-Derr, D., Ballinger, T., &#38; Henikoff, S. (2008). Histone H2A.Z and DNA methylation are mutually antagonistic chromatin marks. <i>Nature</i>. Springer Nature. <a href=\"https://doi.org/10.1038/nature07324\">https://doi.org/10.1038/nature07324</a>","chicago":"Zilberman, Daniel, Devin Coleman-Derr, Tracy Ballinger, and Steven Henikoff. “Histone H2A.Z and DNA Methylation Are Mutually Antagonistic Chromatin Marks.” <i>Nature</i>. Springer Nature, 2008. <a href=\"https://doi.org/10.1038/nature07324\">https://doi.org/10.1038/nature07324</a>.","short":"D. Zilberman, D. Coleman-Derr, T. Ballinger, S. Henikoff, Nature 456 (2008) 125–129.","mla":"Zilberman, Daniel, et al. “Histone H2A.Z and DNA Methylation Are Mutually Antagonistic Chromatin Marks.” <i>Nature</i>, vol. 456, no. 7218, Springer Nature, 2008, pp. 125–29, doi:<a href=\"https://doi.org/10.1038/nature07324\">10.1038/nature07324</a>.","ama":"Zilberman D, Coleman-Derr D, Ballinger T, Henikoff S. Histone H2A.Z and DNA methylation are mutually antagonistic chromatin marks. <i>Nature</i>. 2008;456(7218):125-129. doi:<a href=\"https://doi.org/10.1038/nature07324\">10.1038/nature07324</a>","ista":"Zilberman D, Coleman-Derr D, Ballinger T, Henikoff S. 2008. Histone H2A.Z and DNA methylation are mutually antagonistic chromatin marks. Nature. 456(7218), 125–129."},"author":[{"full_name":"Zilberman, Daniel","orcid":"0000-0002-0123-8649","id":"6973db13-dd5f-11ea-814e-b3e5455e9ed1","last_name":"Zilberman","first_name":"Daniel"},{"full_name":"Coleman-Derr, Devin","last_name":"Coleman-Derr","first_name":"Devin"},{"full_name":"Ballinger, Tracy","last_name":"Ballinger","first_name":"Tracy"},{"full_name":"Henikoff, Steven","last_name":"Henikoff","first_name":"Steven"}],"quality_controlled":"1","month":"11","oa":1,"year":"2008","day":"06","date_created":"2021-06-04T11:49:32Z","volume":456},{"volume":11,"date_created":"2021-06-08T13:13:37Z","year":"2008","month":"10","quality_controlled":"1","author":[{"first_name":"Daniel","last_name":"Zilberman","id":"6973db13-dd5f-11ea-814e-b3e5455e9ed1","orcid":"0000-0002-0123-8649","full_name":"Zilberman, Daniel"}],"citation":{"short":"D. Zilberman, Current Opinion in Plant Biology 11 (2008) 554–559.","chicago":"Zilberman, Daniel. “The Evolving Functions of DNA Methylation.” <i>Current Opinion in Plant Biology</i>. Elsevier , 2008. <a href=\"https://doi.org/10.1016/j.pbi.2008.07.004\">https://doi.org/10.1016/j.pbi.2008.07.004</a>.","apa":"Zilberman, D. (2008). The evolving functions of DNA methylation. <i>Current Opinion in Plant Biology</i>. Elsevier . <a href=\"https://doi.org/10.1016/j.pbi.2008.07.004\">https://doi.org/10.1016/j.pbi.2008.07.004</a>","ieee":"D. Zilberman, “The evolving functions of DNA methylation,” <i>Current Opinion in Plant Biology</i>, vol. 11, no. 5. Elsevier , pp. 554–559, 2008.","ista":"Zilberman D. 2008. The evolving functions of DNA methylation. Current Opinion in Plant Biology. 11(5), 554–559.","ama":"Zilberman D. The evolving functions of DNA methylation. <i>Current Opinion in Plant Biology</i>. 2008;11(5):554-559. doi:<a href=\"https://doi.org/10.1016/j.pbi.2008.07.004\">10.1016/j.pbi.2008.07.004</a>","mla":"Zilberman, Daniel. “The Evolving Functions of DNA Methylation.” <i>Current Opinion in Plant Biology</i>, vol. 11, no. 5, Elsevier , 2008, pp. 554–59, doi:<a href=\"https://doi.org/10.1016/j.pbi.2008.07.004\">10.1016/j.pbi.2008.07.004</a>."},"abstract":[{"lang":"eng","text":"DNA methylation is an ancient process found in all domains of life. Although the enzymes that mediate methylation have remained highly conserved, DNA methylation has been adapted for a variety of uses throughout evolution, including defense against transposable elements and control of gene expression. Defects in DNA methylation are linked to human diseases, including cancer. Methylation has been lost several times in the course of animal and fungal evolution, thus limiting the opportunity for study in common model organisms. In the past decade, plants have emerged as a premier model system for genetic dissection of DNA methylation. A recent combination of plant genetics with powerful genomic approaches has led to a number of exciting discoveries and promises many more."}],"publication":"Current Opinion in Plant Biology","date_published":"2008-10-01T00:00:00Z","external_id":{"pmid":["18774331"]},"publication_identifier":{"issn":["1369-5266"]},"pmid":1,"publisher":"Elsevier ","title":"The evolving functions of DNA methylation","department":[{"_id":"DaZi"}],"type":"journal_article","oa_version":"None","article_type":"review","extern":"1","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","page":"554-559","status":"public","issue":"5","publication_status":"published","date_updated":"2021-12-14T08:54:07Z","intvolume":"        11","scopus_import":"1","doi":"10.1016/j.pbi.2008.07.004","language":[{"iso":"eng"}],"article_processing_charge":"No","_id":"9537"},{"oa":1,"month":"01","extern":1,"page":"270 - 293","author":[{"full_name":"Morozov, Alexei Y","first_name":"Alexei","last_name":"Morozov"},{"full_name":"Maksym Serbyn","first_name":"Maksym","last_name":"Serbyn","orcid":"0000-0002-2399-5827","id":"47809E7E-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":0,"title":"Nonlinear algebra and Bogoliubov's recursion","volume":154,"date_created":"2018-12-11T11:49:26Z","type":"journal_article","year":"2008","day":"01","acknowledgement":"This work is supported in part by the Dynasty Foundation (M. N. S.),  the\nRussian Foundation for Basic Research (Grant No\ns. 07-02-00878 and 07-02-00645), a joint grant (Grant\nNo. 06-01-92059-CE), the NWO (Project No. 047.011.2004.026), INTAS (Grant No. 05-1000008-7865), the\nProgram for Supporting Leading Scientific School\ns (Grant No. NSh-8004.2006.2), and also by a project\n(Project No. ANR-05-BLAN-0029-01, A. Yu. M.).","date_published":"2008-01-01T00:00:00Z","publist_id":"6437","_id":"965","publisher":"Elsevier","issue":"2","publication_status":"published","citation":{"apa":"Morozov, A., &#38; Serbyn, M. (2008). Nonlinear algebra and Bogoliubov’s recursion. <i>Theoretical and Mathematical Physics</i>. Elsevier. <a href=\"https://doi.org/10.1007/s11232-008-0026-7\">https://doi.org/10.1007/s11232-008-0026-7</a>","short":"A. Morozov, M. Serbyn, Theoretical and Mathematical Physics 154 (2008) 270–293.","chicago":"Morozov, Alexei, and Maksym Serbyn. “Nonlinear Algebra and Bogoliubov’s Recursion.” <i>Theoretical and Mathematical Physics</i>. Elsevier, 2008. <a href=\"https://doi.org/10.1007/s11232-008-0026-7\">https://doi.org/10.1007/s11232-008-0026-7</a>.","ieee":"A. Morozov and M. Serbyn, “Nonlinear algebra and Bogoliubov’s recursion,” <i>Theoretical and Mathematical Physics</i>, vol. 154, no. 2. Elsevier, pp. 270–293, 2008.","ista":"Morozov A, Serbyn M. 2008. Nonlinear algebra and Bogoliubov’s recursion. Theoretical and Mathematical Physics. 154(2), 270–293.","mla":"Morozov, Alexei, and Maksym Serbyn. “Nonlinear Algebra and Bogoliubov’s Recursion.” <i>Theoretical and Mathematical Physics</i>, vol. 154, no. 2, Elsevier, 2008, pp. 270–93, doi:<a href=\"https://doi.org/10.1007/s11232-008-0026-7\">10.1007/s11232-008-0026-7</a>.","ama":"Morozov A, Serbyn M. Nonlinear algebra and Bogoliubov’s recursion. <i>Theoretical and Mathematical Physics</i>. 2008;154(2):270-293. doi:<a href=\"https://doi.org/10.1007/s11232-008-0026-7\">10.1007/s11232-008-0026-7</a>"},"status":"public","date_updated":"2021-01-12T08:22:17Z","abstract":[{"lang":"eng","text":"We give many examples of applying Bogoliubov's forest formula to iterative solutions of various nonlinear equations. The same formula describes an extremely wide class of objects, from an ordinary quadratic equation to renormalization in quantum field theory."}],"intvolume":"       154","publication":"Theoretical and Mathematical Physics","doi":"10.1007/s11232-008-0026-7","main_file_link":[{"url":"https://arxiv.org/abs/hep-th/0703258","open_access":"1"}]},{"article_processing_charge":"No","language":[{"iso":"eng"}],"_id":"7320","publisher":"Elsevier","publication_identifier":{"issn":["0013-4686"]},"date_published":"2008-12-30T00:00:00Z","intvolume":"        54","publication":"Electrochimica Acta","doi":"10.1016/j.electacta.2008.07.034","issue":"2","publication_status":"published","citation":{"ieee":"R. Flückiger, S. A. Freunberger, D. Kramer, A. Wokaun, G. G. Scherer, and F. N. Büchi, “Anisotropic, effective diffusivity of porous gas diffusion layer materials for PEFC,” <i>Electrochimica Acta</i>, vol. 54, no. 2. Elsevier, pp. 551–559, 2008.","chicago":"Flückiger, Reto, Stefan Alexander Freunberger, Denis Kramer, Alexander Wokaun, Günther G. Scherer, and Felix N. Büchi. “Anisotropic, Effective Diffusivity of Porous Gas Diffusion Layer Materials for PEFC.” <i>Electrochimica Acta</i>. Elsevier, 2008. <a href=\"https://doi.org/10.1016/j.electacta.2008.07.034\">https://doi.org/10.1016/j.electacta.2008.07.034</a>.","short":"R. Flückiger, S.A. Freunberger, D. Kramer, A. Wokaun, G.G. Scherer, F.N. Büchi, Electrochimica Acta 54 (2008) 551–559.","apa":"Flückiger, R., Freunberger, S. A., Kramer, D., Wokaun, A., Scherer, G. G., &#38; Büchi, F. N. (2008). Anisotropic, effective diffusivity of porous gas diffusion layer materials for PEFC. <i>Electrochimica Acta</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.electacta.2008.07.034\">https://doi.org/10.1016/j.electacta.2008.07.034</a>","ama":"Flückiger R, Freunberger SA, Kramer D, Wokaun A, Scherer GG, Büchi FN. Anisotropic, effective diffusivity of porous gas diffusion layer materials for PEFC. <i>Electrochimica Acta</i>. 2008;54(2):551-559. doi:<a href=\"https://doi.org/10.1016/j.electacta.2008.07.034\">10.1016/j.electacta.2008.07.034</a>","mla":"Flückiger, Reto, et al. “Anisotropic, Effective Diffusivity of Porous Gas Diffusion Layer Materials for PEFC.” <i>Electrochimica Acta</i>, vol. 54, no. 2, Elsevier, 2008, pp. 551–59, doi:<a href=\"https://doi.org/10.1016/j.electacta.2008.07.034\">10.1016/j.electacta.2008.07.034</a>.","ista":"Flückiger R, Freunberger SA, Kramer D, Wokaun A, Scherer GG, Büchi FN. 2008. Anisotropic, effective diffusivity of porous gas diffusion layer materials for PEFC. Electrochimica Acta. 54(2), 551–559."},"status":"public","date_updated":"2021-01-12T08:13:02Z","abstract":[{"text":"A comparative, experimental diffusivity study of gas diffusion layer (GDL) materials for polymer electrolyte fuel cells (PEFC) is presented for the first time. The GDL plays an important role for electrochemical losses due to gas transport limitations at high current densities. Characterization and optimization of these layers is therefore essential to improve power density. A recently developed method which allows for fast diffusimetry is applied and data compared to the literature values. Measurements are made as a function of direction and compression and the effect of different binder structures and hydrophobic treatments on effective diffusivities are discussed. A better understanding of the results is gained by including novel GDL cross-section images and a meaningful unit cell model for the interpretation of the data. The diffusivity data is valuable for GDL manufacturers and future PEFC models. The study reveals that a binder–fiber ratio larger than 50% has a negative impact on the effective diffusion properties. The hydrophobic treatment which is necessary to improve the water management can impede diffusion and thus reduce the power density. Furthermore binder has an isotropic effect while compression pronounces the in-plane orientation of the fibers.","lang":"eng"}],"extern":"1","month":"12","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"551-559","author":[{"full_name":"Flückiger, Reto","first_name":"Reto","last_name":"Flückiger"},{"full_name":"Freunberger, Stefan Alexander","last_name":"Freunberger","first_name":"Stefan Alexander","id":"A8CA28E6-CE23-11E9-AD2D-EC27E6697425","orcid":"0000-0003-2902-5319"},{"first_name":"Denis","last_name":"Kramer","full_name":"Kramer, Denis"},{"full_name":"Wokaun, Alexander","last_name":"Wokaun","first_name":"Alexander"},{"full_name":"Scherer, Günther G.","last_name":"Scherer","first_name":"Günther G."},{"full_name":"Büchi, Felix N.","last_name":"Büchi","first_name":"Felix N."}],"quality_controlled":"1","oa_version":"None","date_created":"2020-01-15T12:21:36Z","type":"journal_article","year":"2008","day":"30","article_type":"original","title":"Anisotropic, effective diffusivity of porous gas diffusion layer materials for PEFC","volume":54},{"year":"2008","article_type":"original","article_number":"B704","day":"08","date_created":"2020-01-15T12:21:47Z","oa_version":"None","type":"journal_article","title":"Cell interaction phenomena in polymer electrolyte fuel cell stacks","volume":155,"author":[{"id":"A8CA28E6-CE23-11E9-AD2D-EC27E6697425","orcid":"0000-0003-2902-5319","last_name":"Freunberger","first_name":"Stefan Alexander","full_name":"Freunberger, Stefan Alexander"},{"full_name":"Schneider, Ingo A.","last_name":"Schneider","first_name":"Ingo A."},{"first_name":"Pang-Chieh","last_name":"Sui","full_name":"Sui, Pang-Chieh"},{"full_name":"Wokaun, Alexander","last_name":"Wokaun","first_name":"Alexander"},{"full_name":"Djilali, Nedjib","first_name":"Nedjib","last_name":"Djilali"},{"full_name":"Büchi, Felix N.","last_name":"Büchi","first_name":"Felix N."}],"quality_controlled":"1","month":"05","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1149/1.2913095","publication":"Journal of The Electrochemical Society","intvolume":"       155","date_updated":"2021-01-12T08:13:03Z","abstract":[{"text":"Cell interaction phenomena in polymer electrolyte fuel cell stacks that arise from imbalance between adjacent cells are investigated in detail experimentally and theoretically. A specialized two-cell stack with advanced localized diagnostics was developed and used to analyze the mechanism and effect of cell-to-cell coupling as a result of operationally relevant variations in reactant feed flow. Contributions to overall and local voltage changes with respect to uniformly operated cells are scrutinized. Unequal operation of the cells causes in-plane current in the bipolar plate to redistribute current and result in inhomogeneous polarization. Both increasing and decreasing polarization along the air-flow path reduces cell power as compared to isopotential operation. A two-dimensional model based on a commercial computational fluid dynamics code is used to back and extend the experimental results to more general cases. Furthermore, the experimental setup presented allowed for the first time to perform simultaneous localized electrochemical impedance spectroscopy beyond the single-cell level. The mechanism of mutual cell interaction on local and integral spectra is revealed. Results show that virtually identical operation of the cells is essential to obtain meaningful integral spectra.","lang":"eng"}],"publication_status":"published","issue":"7","status":"public","citation":{"ama":"Freunberger SA, Schneider IA, Sui P-C, Wokaun A, Djilali N, Büchi FN. Cell interaction phenomena in polymer electrolyte fuel cell stacks. <i>Journal of The Electrochemical Society</i>. 2008;155(7). doi:<a href=\"https://doi.org/10.1149/1.2913095\">10.1149/1.2913095</a>","mla":"Freunberger, Stefan Alexander, et al. “Cell Interaction Phenomena in Polymer Electrolyte Fuel Cell Stacks.” <i>Journal of The Electrochemical Society</i>, vol. 155, no. 7, B704, The Electrochemical Society, 2008, doi:<a href=\"https://doi.org/10.1149/1.2913095\">10.1149/1.2913095</a>.","ista":"Freunberger SA, Schneider IA, Sui P-C, Wokaun A, Djilali N, Büchi FN. 2008. Cell interaction phenomena in polymer electrolyte fuel cell stacks. Journal of The Electrochemical Society. 155(7), B704.","ieee":"S. A. Freunberger, I. A. Schneider, P.-C. Sui, A. Wokaun, N. Djilali, and F. N. Büchi, “Cell interaction phenomena in polymer electrolyte fuel cell stacks,” <i>Journal of The Electrochemical Society</i>, vol. 155, no. 7. The Electrochemical Society, 2008.","short":"S.A. Freunberger, I.A. Schneider, P.-C. Sui, A. Wokaun, N. Djilali, F.N. Büchi, Journal of The Electrochemical Society 155 (2008).","chicago":"Freunberger, Stefan Alexander, Ingo A. Schneider, Pang-Chieh Sui, Alexander Wokaun, Nedjib Djilali, and Felix N. Büchi. “Cell Interaction Phenomena in Polymer Electrolyte Fuel Cell Stacks.” <i>Journal of The Electrochemical Society</i>. The Electrochemical Society, 2008. <a href=\"https://doi.org/10.1149/1.2913095\">https://doi.org/10.1149/1.2913095</a>.","apa":"Freunberger, S. A., Schneider, I. A., Sui, P.-C., Wokaun, A., Djilali, N., &#38; Büchi, F. N. (2008). Cell interaction phenomena in polymer electrolyte fuel cell stacks. <i>Journal of The Electrochemical Society</i>. The Electrochemical Society. <a href=\"https://doi.org/10.1149/1.2913095\">https://doi.org/10.1149/1.2913095</a>"},"_id":"7321","publisher":"The Electrochemical Society","article_processing_charge":"No","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0013-4651"]},"date_published":"2008-05-08T00:00:00Z"},{"month":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","quality_controlled":"1","page":"63-77","author":[{"first_name":"Denis","last_name":"Kramer","full_name":"Kramer, Denis"},{"full_name":"Freunberger, Stefan Alexander","id":"A8CA28E6-CE23-11E9-AD2D-EC27E6697425","orcid":"0000-0003-2902-5319","first_name":"Stefan Alexander","last_name":"Freunberger"},{"last_name":"Flückiger","first_name":"Reto","full_name":"Flückiger, Reto"},{"full_name":"Schneider, Ingo A.","first_name":"Ingo A.","last_name":"Schneider"},{"full_name":"Wokaun, Alexander","first_name":"Alexander","last_name":"Wokaun"},{"first_name":"Felix N.","last_name":"Büchi","full_name":"Büchi, Felix N."},{"full_name":"Scherer, Günther G.","first_name":"Günther G.","last_name":"Scherer"}],"type":"journal_article","oa_version":"None","date_created":"2020-01-15T12:21:57Z","day":"01","article_type":"original","year":"2008","volume":612,"title":"Electrochemical diffusimetry of fuel cell gas diffusion layers","language":[{"iso":"eng"}],"article_processing_charge":"No","publisher":"Elsevier","_id":"7322","date_published":"2008-01-01T00:00:00Z","publication_identifier":{"issn":["1572-6657"]},"intvolume":"       612","doi":"10.1016/j.jelechem.2007.09.014","publication":"Journal of Electroanalytical Chemistry","citation":{"apa":"Kramer, D., Freunberger, S. A., Flückiger, R., Schneider, I. A., Wokaun, A., Büchi, F. N., &#38; Scherer, G. G. (2008). Electrochemical diffusimetry of fuel cell gas diffusion layers. <i>Journal of Electroanalytical Chemistry</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jelechem.2007.09.014\">https://doi.org/10.1016/j.jelechem.2007.09.014</a>","chicago":"Kramer, Denis, Stefan Alexander Freunberger, Reto Flückiger, Ingo A. Schneider, Alexander Wokaun, Felix N. Büchi, and Günther G. Scherer. “Electrochemical Diffusimetry of Fuel Cell Gas Diffusion Layers.” <i>Journal of Electroanalytical Chemistry</i>. Elsevier, 2008. <a href=\"https://doi.org/10.1016/j.jelechem.2007.09.014\">https://doi.org/10.1016/j.jelechem.2007.09.014</a>.","short":"D. Kramer, S.A. Freunberger, R. Flückiger, I.A. Schneider, A. Wokaun, F.N. Büchi, G.G. Scherer, Journal of Electroanalytical Chemistry 612 (2008) 63–77.","ieee":"D. Kramer <i>et al.</i>, “Electrochemical diffusimetry of fuel cell gas diffusion layers,” <i>Journal of Electroanalytical Chemistry</i>, vol. 612, no. 1. Elsevier, pp. 63–77, 2008.","ista":"Kramer D, Freunberger SA, Flückiger R, Schneider IA, Wokaun A, Büchi FN, Scherer GG. 2008. Electrochemical diffusimetry of fuel cell gas diffusion layers. Journal of Electroanalytical Chemistry. 612(1), 63–77.","mla":"Kramer, Denis, et al. “Electrochemical Diffusimetry of Fuel Cell Gas Diffusion Layers.” <i>Journal of Electroanalytical Chemistry</i>, vol. 612, no. 1, Elsevier, 2008, pp. 63–77, doi:<a href=\"https://doi.org/10.1016/j.jelechem.2007.09.014\">10.1016/j.jelechem.2007.09.014</a>.","ama":"Kramer D, Freunberger SA, Flückiger R, et al. Electrochemical diffusimetry of fuel cell gas diffusion layers. <i>Journal of Electroanalytical Chemistry</i>. 2008;612(1):63-77. doi:<a href=\"https://doi.org/10.1016/j.jelechem.2007.09.014\">10.1016/j.jelechem.2007.09.014</a>"},"status":"public","issue":"1","publication_status":"published","abstract":[{"text":"The gas diffusion layers (GDLs) of a membrane electrode assembly (MEA) serve as link between flow field and porous electrode within a polymer electrolyte fuel cell. Beside ensuring sufficient electrical and thermal contact between the whole electrode area and the flow field, these typically 200–400 μm thick porous structures enable the access of educts to the electrode area which would be occluded by the flow field lands if the flow field is directly attached to the electrode. Hence, the characterisation of properties pertaining to mass transport of educts and products through these structures is indispensable whilst examining the contribution of the GDLs to the overall electrochemical characteristics of a MEA. A fast and cost effective method to measure the effective diffusivity of a GDL is presented. Electrochemical impedance spectroscopy is applied to measure the effective ionic conductivity of an electrolyte-soaked GDL. Taking advantage of the analogy between Ficks and Ohms law, this provides a measure for the effective diffusivity. The method is described in detail, including experimental as well as theoretical aspects, and selected results, highlighting the anisotropy and dependence on the degree of compression, are shown. Moreover, a two-dimensional model consisting of regularly spaced ellipses is developed to represent the porous structure of the GDL, and by using conformal maps, the agreement between this model and experiment with respect to the sensitivity of the effective diffusivity towards compression is shown.","lang":"eng"}],"date_updated":"2021-01-12T08:13:03Z"},{"date_created":"2020-01-31T10:14:45Z","oa_version":"None","type":"conference","year":"2008","day":"13","title":"Experimental investigation of the propagation of local current density variations to adjacent cells in PEFC stacks","month":"10","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","author":[{"first_name":"Marco","last_name":"Santis","full_name":"Santis, Marco"},{"full_name":"Freunberger, Stefan Alexander","last_name":"Freunberger","first_name":"Stefan Alexander","orcid":"0000-0003-2902-5319","id":"A8CA28E6-CE23-11E9-AD2D-EC27E6697425"},{"full_name":"Papra, Matthias","last_name":"Papra","first_name":"Matthias"},{"first_name":"Felix N.","last_name":"Büchi","full_name":"Büchi, Felix N."}],"page":"763-765","quality_controlled":"1","publication":"3rd International Conference on Fuel Cell Science, Engineering and Technology","doi":"10.1115/fuelcell2005-74116","publication_status":"published","citation":{"mla":"Santis, Marco, et al. “Experimental Investigation of the Propagation of Local Current Density Variations to Adjacent Cells in PEFC Stacks.” <i>3rd International Conference on Fuel Cell Science, Engineering and Technology</i>, ASMEDC, 2008, pp. 763–65, doi:<a href=\"https://doi.org/10.1115/fuelcell2005-74116\">10.1115/fuelcell2005-74116</a>.","ama":"Santis M, Freunberger SA, Papra M, Büchi FN. Experimental investigation of the propagation of local current density variations to adjacent cells in PEFC stacks. In: <i>3rd International Conference on Fuel Cell Science, Engineering and Technology</i>. ASMEDC; 2008:763-765. doi:<a href=\"https://doi.org/10.1115/fuelcell2005-74116\">10.1115/fuelcell2005-74116</a>","ista":"Santis M, Freunberger SA, Papra M, Büchi FN. 2008. Experimental investigation of the propagation of local current density variations to adjacent cells in PEFC stacks. 3rd International Conference on Fuel Cell Science, Engineering and Technology. International conference on fuel cell science, engineering and technology, 763–765.","ieee":"M. Santis, S. A. Freunberger, M. Papra, and F. N. Büchi, “Experimental investigation of the propagation of local current density variations to adjacent cells in PEFC stacks,” in <i>3rd International Conference on Fuel Cell Science, Engineering and Technology</i>, Ypsilanti, MI, United States, 2008, pp. 763–765.","apa":"Santis, M., Freunberger, S. A., Papra, M., &#38; Büchi, F. N. (2008). Experimental investigation of the propagation of local current density variations to adjacent cells in PEFC stacks. In <i>3rd International Conference on Fuel Cell Science, Engineering and Technology</i> (pp. 763–765). Ypsilanti, MI, United States: ASMEDC. <a href=\"https://doi.org/10.1115/fuelcell2005-74116\">https://doi.org/10.1115/fuelcell2005-74116</a>","short":"M. Santis, S.A. Freunberger, M. Papra, F.N. Büchi, in:, 3rd International Conference on Fuel Cell Science, Engineering and Technology, ASMEDC, 2008, pp. 763–765.","chicago":"Santis, Marco, Stefan Alexander Freunberger, Matthias Papra, and Felix N. Büchi. “Experimental Investigation of the Propagation of Local Current Density Variations to Adjacent Cells in PEFC Stacks.” In <i>3rd International Conference on Fuel Cell Science, Engineering and Technology</i>, 763–65. ASMEDC, 2008. <a href=\"https://doi.org/10.1115/fuelcell2005-74116\">https://doi.org/10.1115/fuelcell2005-74116</a>."},"status":"public","date_updated":"2021-01-12T08:13:33Z","abstract":[{"lang":"eng","text":"The propagation of single cell performance losses to adjacent cells in a polymer electrolyte fuel cell stack is studied by means of local current density measurements in a two cell stack. In this stack, the working conditions of adjacent cells can be controlled independently in order to deliberately change the performance of one cell (inducing cell) and study the coupling effects to the adjacent cell (response cell), while keeping the working conditions of the later one unchanged. The experiments have shown that changes in the current density distribution caused by lowering of the air stoichiometry in the inducing cell cause changes in the current density distribution of the response cell in the order of 60% of the change of the inducing cell, even when the air stoichiometry of the response cell is kept constant. The losses in cell voltage of the inducing cell cause losses in cell voltage of the response cell in a magnitude between 30 and 50%."}],"conference":{"start_date":"2005-05-23","location":"Ypsilanti, MI, United States","end_date":"2005-05-25","name":"International conference on fuel cell science, engineering and technology"},"article_processing_charge":"No","language":[{"iso":"eng"}],"_id":"7425","publisher":"ASMEDC","publication_identifier":{"isbn":["0791837645","0791837572"]},"date_published":"2008-10-13T00:00:00Z"},{"publist_id":"6904","date_published":"2008-01-01T00:00:00Z","publisher":"Springer","_id":"753","article_processing_charge":"No","language":[{"iso":"eng"}],"conference":{"name":"DISC: Distributed Computing"},"abstract":[{"text":"This paper addresses the following question: what is the minimum-sized synchronous window needed to solve consensus in an otherwise asynchronous system? In answer to this question, we present the first optimally-resilient algorithm ASAP that solves consensus as soon as possible in an eventually synchronous system, i.e., a system that from some time GST onwards, delivers messages in a timely fashion. ASAP guarantees that, in an execution with at most f failures, every process decides no later than round GST + f + 2, which is optimal.","lang":"eng"}],"date_updated":"2023-02-23T13:10:13Z","citation":{"short":"D.-A. Alistarh, S. Gilbert, R. Guerraoui, C. Travers, in:, Springer, 2008, pp. 32–46.","chicago":"Alistarh, Dan-Adrian, Seth Gilbert, Rachid Guerraoui, and Corentin Travers. “How to Solve Consensus in the Smallest Window of Synchrony,” 5218 LNCS:32–46. Springer, 2008. <a href=\"https://doi.org/10.1007/978-3-540-87779-0_3\">https://doi.org/10.1007/978-3-540-87779-0_3</a>.","apa":"Alistarh, D.-A., Gilbert, S., Guerraoui, R., &#38; Travers, C. (2008). How to solve consensus in the smallest window of synchrony (Vol. 5218 LNCS, pp. 32–46). Presented at the DISC: Distributed Computing, Springer. <a href=\"https://doi.org/10.1007/978-3-540-87779-0_3\">https://doi.org/10.1007/978-3-540-87779-0_3</a>","ieee":"D.-A. Alistarh, S. Gilbert, R. Guerraoui, and C. Travers, “How to solve consensus in the smallest window of synchrony,” presented at the DISC: Distributed Computing, 2008, vol. 5218 LNCS, pp. 32–46.","ista":"Alistarh D-A, Gilbert S, Guerraoui R, Travers C. 2008. How to solve consensus in the smallest window of synchrony. DISC: Distributed Computing, LNCS, vol. 5218 LNCS, 32–46.","ama":"Alistarh D-A, Gilbert S, Guerraoui R, Travers C. How to solve consensus in the smallest window of synchrony. In: Vol 5218 LNCS. Springer; 2008:32-46. doi:<a href=\"https://doi.org/10.1007/978-3-540-87779-0_3\">10.1007/978-3-540-87779-0_3</a>","mla":"Alistarh, Dan-Adrian, et al. <i>How to Solve Consensus in the Smallest Window of Synchrony</i>. Vol. 5218 LNCS, Springer, 2008, pp. 32–46, doi:<a href=\"https://doi.org/10.1007/978-3-540-87779-0_3\">10.1007/978-3-540-87779-0_3</a>."},"status":"public","publication_status":"published","doi":"10.1007/978-3-540-87779-0_3","author":[{"full_name":"Alistarh, Dan-Adrian","id":"4A899BFC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3650-940X","first_name":"Dan-Adrian","last_name":"Alistarh"},{"first_name":"Seth","last_name":"Gilbert","full_name":"Gilbert, Seth"},{"first_name":"Rachid","last_name":"Guerraoui","full_name":"Guerraoui, Rachid"},{"last_name":"Travers","first_name":"Corentin","full_name":"Travers, Corentin"}],"page":"32 - 46","month":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","title":"How to solve consensus in the smallest window of synchrony","volume":"5218 LNCS","day":"01","year":"2008","type":"conference","alternative_title":["LNCS"],"oa_version":"None","date_created":"2018-12-11T11:48:19Z"},{"page":"881-919","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","arxiv":1,"article_type":"original","oa_version":"Preprint","type":"journal_article","title":"Minimal-mass blowup solutions of the mass-critical NLS","_id":"22049","mathsc":["35Q55"],"language":[{"iso":"eng"}],"OA_type":"green","article_processing_charge":"No","scopus_import":"1","doi":"10.1515/forum.2008.042","intvolume":"        20","date_updated":"2026-06-25T08:15:22Z","publication_status":"published","issue":"5","status":"public","author":[{"full_name":"Tao, Terence","last_name":"Tao","first_name":"Terence"},{"full_name":"Visan, Monica","first_name":"Monica","last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"},{"first_name":"Xiaoyi","last_name":"Zhang","full_name":"Zhang, Xiaoyi"}],"quality_controlled":"1","month":"11","oa":1,"year":"2008","day":"03","date_created":"2026-06-19T07:53:12Z","volume":20,"publisher":"De Gruyter","das_tickbox":"1","publication_identifier":{"issn":["0933-7741"],"eissn":["1435-5337"]},"OA_place":"repository","date_published":"2008-11-03T00:00:00Z","external_id":{"arxiv":["math/0609690"]},"publication":"Forum Mathematicum","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.math/0609690"}],"abstract":[{"text":"We consider the minimal mass m0 required for solutions to the mass-critical nonlinear Schrödinger (NLS) equation iut + Δu = μ|u|^4/d u to blow up. If m0 is finite, we show that there exists a minimal-mass solution blowing up (in the sense of an infinite spacetime norm) in both time directions, whose orbit in  is compact after quotienting out by the symmetries of the equation. A similar result is obtained for spherically symmetric solutions. Similar results were previously obtained by Keraani, [Keraani S.: On the blow-up phenomenon of the critical nonlinear Schrödinger equation. J. Funct. Anal. 235 (2006), 171–192], in dimensions 1, 2 and Begout and Vargas, [Begout P., Vargas A.: Mass concentration phenomena for the L2-critical nonlinear Schrödinger equation, preprint], in dimensions d ≥ 3 for the mass-critical NLS and by Kenig and Merle, [Kenig C., Merle F.: Global well-posedness, scattering, and blowup for the energy-critical, focusing, non-linear Schrödinger equation in the radial case, preprint], in the energy-critical case. In a subsequent paper we shall use this compactness result to establish global existence and scattering in  for the defocusing NLS in three and higher dimensions with spherically symmetric data.","lang":"eng"}],"citation":{"ista":"Tao T, Vişan M, Zhang X. 2008. Minimal-mass blowup solutions of the mass-critical NLS. Forum Mathematicum. 20(5), 881–919.","ama":"Tao T, Vişan M, Zhang X. Minimal-mass blowup solutions of the mass-critical NLS. <i>Forum Mathematicum</i>. 2008;20(5):881-919. doi:<a href=\"https://doi.org/10.1515/forum.2008.042\">10.1515/forum.2008.042</a>","mla":"Tao, Terence, et al. “Minimal-Mass Blowup Solutions of the Mass-Critical NLS.” <i>Forum Mathematicum</i>, vol. 20, no. 5, De Gruyter, 2008, pp. 881–919, doi:<a href=\"https://doi.org/10.1515/forum.2008.042\">10.1515/forum.2008.042</a>.","chicago":"Tao, Terence, Monica Vişan, and Xiaoyi Zhang. “Minimal-Mass Blowup Solutions of the Mass-Critical NLS.” <i>Forum Mathematicum</i>. De Gruyter, 2008. <a href=\"https://doi.org/10.1515/forum.2008.042\">https://doi.org/10.1515/forum.2008.042</a>.","short":"T. Tao, M. Vişan, X. Zhang, Forum Mathematicum 20 (2008) 881–919.","apa":"Tao, T., Vişan, M., &#38; Zhang, X. (2008). Minimal-mass blowup solutions of the mass-critical NLS. <i>Forum Mathematicum</i>. De Gruyter. <a href=\"https://doi.org/10.1515/forum.2008.042\">https://doi.org/10.1515/forum.2008.042</a>","ieee":"T. Tao, M. Vişan, and X. Zhang, “Minimal-mass blowup solutions of the mass-critical NLS,” <i>Forum Mathematicum</i>, vol. 20, no. 5. De Gruyter, pp. 881–919, 2008."}},{"month":"03","author":[{"first_name":"J.","last_name":"Colliander","full_name":"Colliander, J."},{"full_name":"Holmer, Justin","first_name":"Justin","last_name":"Holmer"},{"full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan","first_name":"Monica"},{"last_name":"Zhang","first_name":"Xiaoyi","full_name":"Zhang, Xiaoyi"}],"quality_controlled":"1","oa":1,"date_created":"2026-06-19T08:27:11Z","year":"2008","day":"01","volume":7,"das_tickbox":"1","publisher":"American Institute of Mathematical Sciences","OA_place":"repository","publication_identifier":{"eissn":["1553-5258"],"issn":["1534-0392"]},"external_id":{"arxiv":["math/0612452"]},"date_published":"2008-03-01T00:00:00Z","publication":"Communications on Pure and Applied Analysis","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.math/0612452","open_access":"1"}],"citation":{"short":"J. Colliander, J. Holmer, M. Vişan, X. Zhang, Communications on Pure and Applied Analysis 7 (2008) 467–489.","chicago":"Colliander, J., Justin Holmer, Monica Vişan, and Xiaoyi Zhang. “Global Existence and Scattering for Rough Solutions to Generalized Nonlinear Schrödinger Equations on $R$.” <i>Communications on Pure and Applied Analysis</i>. American Institute of Mathematical Sciences, 2008. <a href=\"https://doi.org/10.3934/cpaa.2008.7.467\">https://doi.org/10.3934/cpaa.2008.7.467</a>.","apa":"Colliander, J., Holmer, J., Vişan, M., &#38; Zhang, X. (2008). Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. <i>Communications on Pure and Applied Analysis</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/cpaa.2008.7.467\">https://doi.org/10.3934/cpaa.2008.7.467</a>","ieee":"J. Colliander, J. Holmer, M. Vişan, and X. Zhang, “Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$,” <i>Communications on Pure and Applied Analysis</i>, vol. 7, no. 3. American Institute of Mathematical Sciences, pp. 467–489, 2008.","ista":"Colliander J, Holmer J, Vişan M, Zhang X. 2008. Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. Communications on Pure and Applied Analysis. 7(3), 467–489.","ama":"Colliander J, Holmer J, Vişan M, Zhang X. Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. <i>Communications on Pure and Applied Analysis</i>. 2008;7(3):467-489. doi:<a href=\"https://doi.org/10.3934/cpaa.2008.7.467\">10.3934/cpaa.2008.7.467</a>","mla":"Colliander, J., et al. “Global Existence and Scattering for Rough Solutions to Generalized Nonlinear Schrödinger Equations on $R$.” <i>Communications on Pure and Applied Analysis</i>, vol. 7, no. 3, American Institute of Mathematical Sciences, 2008, pp. 467–89, doi:<a href=\"https://doi.org/10.3934/cpaa.2008.7.467\">10.3934/cpaa.2008.7.467</a>."},"abstract":[{"text":"We consider the Cauchy problem for a family of semilinear defocusing Schrödinger equations with monomial nonlinearities in one space dimension. We establish global well-posedness and scattering. Our analysis is based on a four-particle interaction Morawetz estimate giving a priori $L_{t,x}^8$ spacetime control on solutions.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","arxiv":1,"page":"467-489","oa_version":"Preprint","type":"journal_article","article_type":"original","title":"Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$","language":[{"iso":"eng"}],"article_processing_charge":"No","OA_type":"green","_id":"22081","mathsc":["35Q55"],"intvolume":"         7","doi":"10.3934/cpaa.2008.7.467","scopus_import":"1","issue":"3","publication_status":"published","status":"public","date_updated":"2026-07-01T07:05:55Z"},{"title":"The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher","article_type":"original","oa_version":"Preprint","type":"journal_article","page":"229-266","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","arxiv":1,"date_updated":"2026-07-01T07:15:15Z","issue":"2","publication_status":"published","status":"public","scopus_import":"1","doi":"10.2140/apde.2008.1.229","intvolume":"         1","_id":"22082","language":[{"iso":"eng"}],"OA_type":"green","article_processing_charge":"No","volume":1,"year":"2008","day":"01","date_created":"2026-06-19T08:27:33Z","oa":1,"author":[{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"full_name":"Visan, Monica","first_name":"Monica","last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"},{"first_name":"Xiaoyi","last_name":"Zhang","full_name":"Zhang, Xiaoyi"}],"quality_controlled":"1","month":"06","abstract":[{"lang":"eng","text":"We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation (mathematical formular)  for large spherically symmetric L2/x(R^d) initial data in dimensions d >= 3.\r\nIn the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time."}],"citation":{"apa":"Killip, R., Vişan, M., &#38; Zhang, X. (2008). The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher. <i>Analysis &#38; PDE</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/apde.2008.1.229\">https://doi.org/10.2140/apde.2008.1.229</a>","chicago":"Killip, Rowan, Monica Vişan, and Xiaoyi Zhang. “The Mass-Critical Nonlinear Schrödinger Equation with Radial Data in Dimensions Three and Higher.” <i>Analysis &#38; PDE</i>. Mathematical Sciences Publishers, 2008. <a href=\"https://doi.org/10.2140/apde.2008.1.229\">https://doi.org/10.2140/apde.2008.1.229</a>.","short":"R. Killip, M. Vişan, X. Zhang, Analysis &#38; PDE 1 (2008) 229–266.","ieee":"R. Killip, M. Vişan, and X. Zhang, “The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher,” <i>Analysis &#38; PDE</i>, vol. 1, no. 2. Mathematical Sciences Publishers, pp. 229–266, 2008.","ista":"Killip R, Vişan M, Zhang X. 2008. The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher. Analysis &#38; PDE. 1(2), 229–266.","mla":"Killip, Rowan, et al. “The Mass-Critical Nonlinear Schrödinger Equation with Radial Data in Dimensions Three and Higher.” <i>Analysis &#38; PDE</i>, vol. 1, no. 2, Mathematical Sciences Publishers, 2008, pp. 229–66, doi:<a href=\"https://doi.org/10.2140/apde.2008.1.229\">10.2140/apde.2008.1.229</a>.","ama":"Killip R, Vişan M, Zhang X. The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher. <i>Analysis &#38; PDE</i>. 2008;1(2):229-266. doi:<a href=\"https://doi.org/10.2140/apde.2008.1.229\">10.2140/apde.2008.1.229</a>"},"publication":"Analysis & PDE","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.0708.0849"}],"OA_place":"repository","publication_identifier":{"eissn":["1948-206X"],"issn":["2157-5045"]},"external_id":{"arxiv":["0708.0849"]},"date_published":"2008-06-01T00:00:00Z","publisher":"Mathematical Sciences Publishers","das_tickbox":"1"},{"citation":{"ieee":"K. Chatterjee, L. De Alfaro, R. Majumdar, and V. Raman, “Algorithms for game metrics,” presented at the FSTTCS: Foundations of Software Technology and Theoretical Computer Science, 2008, vol. 2, pp. 107–118.","apa":"Chatterjee, K., De Alfaro, L., Majumdar, R., &#38; Raman, V. (2008). Algorithms for game metrics (Vol. 2, pp. 107–118). Presented at the FSTTCS: Foundations of Software Technology and Theoretical Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1745\">https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1745</a>","short":"K. Chatterjee, L. De Alfaro, R. Majumdar, V. Raman, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2008, pp. 107–118.","chicago":"Chatterjee, Krishnendu, Luca De Alfaro, Ritankar Majumdar, and Vishwanath Raman. “Algorithms for Game Metrics,” 2:107–18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2008. <a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1745\">https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1745</a>.","mla":"Chatterjee, Krishnendu, et al. <i>Algorithms for Game Metrics</i>. Vol. 2, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2008, pp. 107–18, doi:<a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1745\">10.4230/LIPIcs.FSTTCS.2008.1745</a>.","ama":"Chatterjee K, De Alfaro L, Majumdar R, Raman V. Algorithms for game metrics. In: Vol 2. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2008:107-118. doi:<a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2008.1745\">10.4230/LIPIcs.FSTTCS.2008.1745</a>","ista":"Chatterjee K, De Alfaro L, Majumdar R, Raman V. 2008. Algorithms for game metrics. FSTTCS: Foundations of Software Technology and Theoretical Computer Science, LIPIcs, vol. 2, 107–118."},"abstract":[{"text":"Simulation and bisimulation metrics for stochastic systems provide a quantitative gen- eralization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative specifications written in the quantitative μ-calculus and related probabilistic logics.\r\nWe present algorithms for computing the metrics on Markov decision processes (MDPs), turn- based stochastic games, and concurrent games. For turn-based games and MDPs, we provide a polynomial-time algorithm based on linear programming for the computation of the one-step metric distance between states. The algorithm improves on the previously known exponential-time algo- rithm based on a reduction to the theory of reals. We then present PSPACE algorithms for both the decision problem and the problem of approximating the metric distance between two states, matching the best known bound for Markov chains. For the bisimulation kernel of the metric, which corresponds to probabilistic bisimulation, our algorithm works in time O(n4) for both turn-based games and MDPs; improving the previously best known O(n9 · log(n)) time algorithm for MDPs. For a concurrent game G, we show that computing the exact distance between states is at least as hard as computing the value of concurrent reachability games and the square-root-sum problem in computational geometry. We show that checking whether the metric distance is bounded by a rational r, can be accomplished via a reduction to the theory of real closed fields, involving a\r\nformula with three quantifier alternations, yielding O(|G|O(|G|5)) time complexity, improving the previously known reduction with O(|G|O(|G|7)) time complexity. These algorithms can be iterated\r\nto approximate the metrics using binary search.","lang":"eng"}],"has_accepted_license":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"acknowledgement":"This research was supported in part by the NSF grants CCR-0132780 and CNS-0720884.","date_published":"2008-12-05T00:00:00Z","file_date_updated":"2020-07-14T12:46:12Z","publist_id":"2883","alternative_title":["LIPIcs"],"date_created":"2018-12-11T12:03:40Z","day":"05","year":"2008","volume":2,"month":"12","quality_controlled":"1","related_material":{"record":[{"id":"3868","status":"public","relation":"later_version"}]},"author":[{"full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu"},{"last_name":"De Alfaro","first_name":"Luca","full_name":"De Alfaro, Luca"},{"last_name":"Majumdar","first_name":"Ritankar","full_name":"Majumdar, Ritankar"},{"full_name":"Raman, Vishwanath","first_name":"Vishwanath","last_name":"Raman"}],"oa":1,"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","intvolume":"         2","doi":"10.4230/LIPIcs.FSTTCS.2008.1745","status":"public","publication_status":"published","conference":{"name":"FSTTCS: Foundations of Software Technology and Theoretical Computer Science"},"date_updated":"2026-07-06T13:25:11Z","language":[{"iso":"eng"}],"ddc":["000"],"file":[{"access_level":"open_access","date_updated":"2020-07-14T12:46:12Z","file_name":"2008_LIPIcs_Chatterjee.pdf","checksum":"0a447454a24e273f7ddf51dbfe47f877","content_type":"application/pdf","date_created":"2019-05-10T10:01:21Z","file_id":"6398","creator":"dernst","relation":"main_file","file_size":442139}],"_id":"3504","type":"conference","oa_version":"Published Version","title":"Algorithms for game metrics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","page":"107 - 118"},{"article_processing_charge":"No","OA_type":"green","language":[{"iso":"eng"}],"_id":"3876","intvolume":"      5215","doi":"10.1007/978-3-540-85778-5_10","publication_status":"published","status":"public","date_updated":"2026-07-06T13:25:38Z","conference":{"name":"FORMATS: Formal Modeling and Analysis of Timed Systems","end_date":"2008-09-17","location":"Saint Malo, France","start_date":"2008-09-15"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","extern":"1","arxiv":1,"page":"124 - 140","oa_version":"None","type":"conference","title":"Timed parity games: complexity and robustness","publisher":"Springer Nature","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783540857778"],"issn":["0302-9743"]},"OA_place":"repository","acknowledgement":"This research was supported in part by the NSF grants CCR-0132780, CNS-0720884, and CCR-0225610, and by the European COMBEST project.","date_published":"2008-10-01T00:00:00Z","external_id":{"arxiv":["0807.1165"]},"publist_id":"2294","publication":"Proceedings of the 6th international conference on Formal Modeling and Analysis of Timed Systems","citation":{"ista":"Chatterjee K, Henzinger TA, Prabhu V. 2008. Timed parity games: complexity and robustness. Proceedings of the 6th international conference on Formal Modeling and Analysis of Timed Systems. FORMATS: Formal Modeling and Analysis of Timed Systems, LNCS, vol. 5215, 124–140.","ama":"Chatterjee K, Henzinger TA, Prabhu V. Timed parity games: complexity and robustness. In: <i>Proceedings of the 6th International Conference on Formal Modeling and Analysis of Timed Systems</i>. Vol 5215. Springer Nature; 2008:124-140. doi:<a href=\"https://doi.org/10.1007/978-3-540-85778-5_10\">10.1007/978-3-540-85778-5_10</a>","mla":"Chatterjee, Krishnendu, et al. “Timed Parity Games: Complexity and Robustness.” <i>Proceedings of the 6th International Conference on Formal Modeling and Analysis of Timed Systems</i>, vol. 5215, Springer Nature, 2008, pp. 124–40, doi:<a href=\"https://doi.org/10.1007/978-3-540-85778-5_10\">10.1007/978-3-540-85778-5_10</a>.","short":"K. Chatterjee, T.A. Henzinger, V. Prabhu, in:, Proceedings of the 6th International Conference on Formal Modeling and Analysis of Timed Systems, Springer Nature, 2008, pp. 124–140.","chicago":"Chatterjee, Krishnendu, Thomas A Henzinger, and Vinayak Prabhu. “Timed Parity Games: Complexity and Robustness.” In <i>Proceedings of the 6th International Conference on Formal Modeling and Analysis of Timed Systems</i>, 5215:124–40. Springer Nature, 2008. <a href=\"https://doi.org/10.1007/978-3-540-85778-5_10\">https://doi.org/10.1007/978-3-540-85778-5_10</a>.","apa":"Chatterjee, K., Henzinger, T. A., &#38; Prabhu, V. (2008). Timed parity games: complexity and robustness. In <i>Proceedings of the 6th international conference on Formal Modeling and Analysis of Timed Systems</i> (Vol. 5215, pp. 124–140). Saint Malo, France: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-540-85778-5_10\">https://doi.org/10.1007/978-3-540-85778-5_10</a>","ieee":"K. Chatterjee, T. A. Henzinger, and V. Prabhu, “Timed parity games: complexity and robustness,” in <i>Proceedings of the 6th international conference on Formal Modeling and Analysis of Timed Systems</i>, Saint Malo, France, 2008, vol. 5215, pp. 124–140."},"abstract":[{"text":"We consider two-player games played in real time on game structures with clocks and parity objectives. The games are concurrent in that at each turn, both players independently propose a time delay and an action, and the action with the shorter delay is chosen. To prevent a player from winning by blocking time, we restrict each player to strategies that ensure that the player cannot be responsible for causing a zeno run. First, we present an efficient reduction of these games to turn-based (i.e., nonconcurrent) finite-state (i.e., untimed) parity games. The states of the resulting game are pairs of clock regions of the original game. Our reduction improves the best known complexity for solving timed parity games. Moreover, the rich class of algorithms for classical parity games can now be applied to timed parity games. Second, we consider two restricted classes of strategies for the player that represents the controller in a real-time synthesis problem, namely, limit-robust and bounded-robust strategies. Using a limit-robust strategy, the controller cannot choose an exact real-valued time delay but must allow for some nonzero jitter in each of its actions. If there is a given lower bound on the jitter, then the strategy is bounded-robust. We show that exact strategies are more powerful than limit-robust strategies, which are more powerful than bounded-robust strategies for any bound. For both kinds of robust strategies, we present efficient reductions to standard timed automaton games. These reductions provide algorithms for the synthesis of robust real-time controllers.","lang":"eng"}],"month":"10","related_material":{"record":[{"status":"public","id":"3315","relation":"later_version"}]},"author":[{"full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu"},{"full_name":"Henzinger, Thomas A","last_name":"Henzinger","first_name":"Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","orcid":"0000−0002−2985−7724"},{"full_name":"Prabhu, Vinayak","first_name":"Vinayak","last_name":"Prabhu"}],"date_created":"2018-12-11T12:05:39Z","alternative_title":["LNCS"],"year":"2008","day":"01","volume":5215}]