[{"language":[{"iso":"eng"}],"title":"A mutation in the Gsk3-binding domain of zebrafish Masterblind/Axin1 leads to a fate transformation of telencephalon and eyes to diencephalon","type":"journal_article","author":[{"first_name":"Carl-Philipp J","orcid":"0000-0002-0912-4566","id":"39427864-F248-11E8-B48F-1D18A9856A87","last_name":"Heisenberg","full_name":"Heisenberg, Carl-Philipp J"},{"full_name":"Houart, Corinne","last_name":"Houart","first_name":"Corinne"},{"first_name":"Masaya","full_name":"Take Uchi, Masaya","last_name":"Take Uchi"},{"last_name":"Rauch","full_name":"Rauch, Gerd","first_name":"Gerd"},{"last_name":"Young","full_name":"Young, Neville","first_name":"Neville"},{"first_name":"Pedro","last_name":"Coutinho","full_name":"Coutinho, Pedro"},{"first_name":"Ichiro","last_name":"Masai","full_name":"Masai, Ichiro"},{"first_name":"Luca","last_name":"Caneparo","full_name":"Caneparo, Luca"},{"full_name":"Concha, Miguel","last_name":"Concha","first_name":"Miguel"},{"first_name":"Robert","full_name":"Geisler, Robert","last_name":"Geisler"},{"full_name":"Dale, Trevor","last_name":"Dale","first_name":"Trevor"},{"full_name":"Wilson, Stephen","last_name":"Wilson","first_name":"Stephen"},{"full_name":"Stemple, Derek","last_name":"Stemple","first_name":"Derek"}],"publist_id":"1916","date_created":"2018-12-11T12:07:33Z","citation":{"short":"C.-P.J. Heisenberg, C. Houart, M. Take Uchi, G. Rauch, N. Young, P. Coutinho, I. Masai, L. Caneparo, M. Concha, R. Geisler, T. Dale, S. Wilson, D. Stemple, Genes and Development 15 (2001) 1427–1434.","ama":"Heisenberg C-PJ, Houart C, Take Uchi M, et al. A mutation in the Gsk3-binding domain of zebrafish Masterblind/Axin1 leads to a fate transformation of telencephalon and eyes to diencephalon. *Genes and Development*. 2001;15(11):1427-1434. doi:10.1101/gad.194301","ista":"Heisenberg C-PJ, Houart C, Take Uchi M, Rauch G, Young N, Coutinho P, Masai I, Caneparo L, Concha M, Geisler R, Dale T, Wilson S, Stemple D. 2001. A mutation in the Gsk3-binding domain of zebrafish Masterblind/Axin1 leads to a fate transformation of telencephalon and eyes to diencephalon. Genes and Development. 15(11), 1427–1434.","mla":"Heisenberg, Carl-Philipp J., et al. “A Mutation in the Gsk3-Binding Domain of Zebrafish Masterblind/Axin1 Leads to a Fate Transformation of Telencephalon and Eyes to Diencephalon.” *Genes and Development*, vol. 15, no. 11, Cold Spring Harbor Laboratory Press, 2001, pp. 1427–34, doi:10.1101/gad.194301.","ieee":"C.-P. J. Heisenberg *et al.*, “A mutation in the Gsk3-binding domain of zebrafish Masterblind/Axin1 leads to a fate transformation of telencephalon and eyes to diencephalon,” *Genes and Development*, vol. 15, no. 11, pp. 1427–1434, 2001.","apa":"Heisenberg, C.-P. J., Houart, C., Take Uchi, M., Rauch, G., Young, N., Coutinho, P., … Stemple, D. (2001). A mutation in the Gsk3-binding domain of zebrafish Masterblind/Axin1 leads to a fate transformation of telencephalon and eyes to diencephalon. *Genes and Development*, *15*(11), 1427–1434. https://doi.org/10.1101/gad.194301","chicago":"Heisenberg, Carl-Philipp J, Corinne Houart, Masaya Take Uchi, Gerd Rauch, Neville Young, Pedro Coutinho, Ichiro Masai, et al. “A Mutation in the Gsk3-Binding Domain of Zebrafish Masterblind/Axin1 Leads to a Fate Transformation of Telencephalon and Eyes to Diencephalon.” *Genes and Development* 15, no. 11 (2001): 1427–34. https://doi.org/10.1101/gad.194301."},"doi":"10.1101/gad.194301","date_published":"2001-06-01T00:00:00Z","extern":"1","_id":"4200","page":"1427 - 1434","publication_status":"published","year":"2001","publication":"Genes and Development","publisher":"Cold Spring Harbor Laboratory Press","status":"public","issue":"11","month":"06","article_processing_charge":"No","abstract":[{"lang":"eng","text":"Zebrafish embryos homozygous for the masterblind (mb1) mutation exhibit a striking phenotype in which the eyes and telencephalon are reduced or absent and diencephalic fates expand to the front of the brain. Here we show that mb1(-/-) embryos carry an amino-acid change at a conserved site in the Wnt pathway scaffolding protein, Axin1. The amino-acid substitution present in the mbl allele abolishes the binding of Axin to Gsk3 and affects Tcf-dependent transcription. Therefore, Gsk3 activity may be decreased in mbl(-/-) embryos and in support of this possibility, overexpression of either wild-type Axin1 or Gsk3 beta can restore eye and telencephalic fates to mb1(-/-) embryos. Our data reveal a crucial role for Axin1-dependent inhibition of the Wnt pathway in the early regional subdivision of the anterior neural plate into telencephalic, diencephalic, and eye-forming territories."}],"day":"01","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2020-10-07T07:09:14Z","intvolume":" 15","volume":15},{"title":"A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I","article_type":"original","language":[{"iso":"eng"}],"author":[{"full_name":"Kaloshin, Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim"},{"first_name":"Brian R.","full_name":"Hunt, Brian R.","last_name":"Hunt"}],"type":"journal_article","date_created":"2020-09-18T10:49:56Z","citation":{"ista":"Kaloshin V, Hunt BR. 2001. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I. Electronic Research Announcements of the American Mathematical Society. 7(4), 17–27.","ama":"Kaloshin V, Hunt BR. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I. *Electronic Research Announcements of the American Mathematical Society*. 2001;7(4):17-27. doi:10.1090/s1079-6762-01-00090-7","short":"V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American Mathematical Society 7 (2001) 17–27.","chicago":"Kaloshin, Vadim, and Brian R. Hunt. “A Stretched Exponential Bound on the Rate of Growth of the Number of Periodic Points for Prevalent Diffeomorphisms I.” *Electronic Research Announcements of the American Mathematical Society* 7, no. 4 (2001): 17–27. https://doi.org/10.1090/s1079-6762-01-00090-7.","apa":"Kaloshin, V., & Hunt, B. R. (2001). A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I. *Electronic Research Announcements of the American Mathematical Society*, *7*(4), 17–27. https://doi.org/10.1090/s1079-6762-01-00090-7","ieee":"V. Kaloshin and B. R. Hunt, “A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I,” *Electronic Research Announcements of the American Mathematical Society*, vol. 7, no. 4, pp. 17–27, 2001.","mla":"Kaloshin, Vadim, and Brian R. Hunt. “A Stretched Exponential Bound on the Rate of Growth of the Number of Periodic Points for Prevalent Diffeomorphisms I.” *Electronic Research Announcements of the American Mathematical Society*, vol. 7, no. 4, American Mathematical Society, 2001, pp. 17–27, doi:10.1090/s1079-6762-01-00090-7."},"_id":"8522","page":"17-27","doi":"10.1090/s1079-6762-01-00090-7","quality_controlled":"1","extern":"1","date_published":"2001-04-18T00:00:00Z","year":"2001","publication_status":"published","publisher":"American Mathematical Society","publication":"Electronic Research Announcements of the American Mathematical Society","issue":"4","status":"public","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","keyword":["General Mathematics"],"month":"04","article_processing_charge":"No","abstract":[{"text":"For diffeomorphisms of smooth compact manifolds, we consider the problem of how fast the number of periodic points with period $n$grows as a function of $n$. In many familiar cases (e.g., Anosov systems) the growth is exponential, but arbitrarily fast growth is possible; in fact, the first author has shown that arbitrarily fast growth is topologically (Baire) generic for $C^2$ or smoother diffeomorphisms. In the present work we show that, by contrast, for a measure-theoretic notion of genericity we call ``prevalence'', the growth is not much faster than exponential. Specifically, we show that for each $\\delta > 0$, there is a prevalent set of ( $C^{1+\\rho}$ or smoother) diffeomorphisms for which the number of period $n$ points is bounded above by $\\operatorname{exp}(C n^{1+\\delta})$ for some $C$ independent of $n$. We also obtain a related bound on the decay of the hyperbolicity of the periodic points as a function of $n$. The contrast between topologically generic and measure-theoretically generic behavior for the growth of the number of periodic points and the decay of their hyperbolicity shows this to be a subtle and complex phenomenon, reminiscent of KAM theory.","lang":"eng"}],"day":"18","intvolume":" 7","publication_identifier":{"issn":["1079-6762"]},"volume":7,"date_updated":"2020-10-12T13:26:39Z"},{"type":"journal_article","author":[{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","full_name":"Kaloshin, Vadim","last_name":"Kaloshin"},{"first_name":"I.","full_name":"Rodnianski, I.","last_name":"Rodnianski"}],"language":[{"iso":"eng"}],"article_type":"original","title":"Diophantine properties of elements of SO(3)","doi":"10.1007/s00039-001-8222-8","quality_controlled":"1","date_published":"2001-12-01T00:00:00Z","extern":"1","_id":"8524","page":"953-970","date_created":"2020-09-18T10:50:11Z","citation":{"apa":"Kaloshin, V., & Rodnianski, I. (2001). Diophantine properties of elements of SO(3). *Geometric And Functional Analysis*, *11*(5), 953–970. https://doi.org/10.1007/s00039-001-8222-8","chicago":"Kaloshin, Vadim, and I. Rodnianski. “Diophantine Properties of Elements of SO(3).” *Geometric And Functional Analysis* 11, no. 5 (2001): 953–70. https://doi.org/10.1007/s00039-001-8222-8.","ieee":"V. Kaloshin and I. Rodnianski, “Diophantine properties of elements of SO(3),” *Geometric And Functional Analysis*, vol. 11, no. 5, pp. 953–970, 2001.","mla":"Kaloshin, Vadim, and I. Rodnianski. “Diophantine Properties of Elements of SO(3).” *Geometric And Functional Analysis*, vol. 11, no. 5, Springer Nature, 2001, pp. 953–70, doi:10.1007/s00039-001-8222-8.","ama":"Kaloshin V, Rodnianski I. Diophantine properties of elements of SO(3). *Geometric And Functional Analysis*. 2001;11(5):953-970. doi:10.1007/s00039-001-8222-8","ista":"Kaloshin V, Rodnianski I. 2001. Diophantine properties of elements of SO(3). Geometric And Functional Analysis. 11(5), 953–970.","short":"V. Kaloshin, I. Rodnianski, Geometric And Functional Analysis 11 (2001) 953–970."},"issue":"5","status":"public","year":"2001","publication_status":"published","publication":"Geometric And Functional Analysis","publisher":"Springer Nature","date_updated":"2020-10-12T13:24:12Z","intvolume":" 11","volume":11,"publication_identifier":{"issn":["1016-443X","1420-8970"]},"month":"12","article_processing_charge":"No","abstract":[{"lang":"eng","text":"A number α∈R is diophantine if it is not well approximable by rationals, i.e. for some C,ε>0 and any relatively prime p,q∈Z we have |αq−p|>Cq−1−ε. It is well-known and is easy to prove that almost every α in R is diophantine. In this paper we address a noncommutative version of the diophantine properties. Consider a pair A,B∈SO(3) and for each n∈Z+ take all possible words in A, A -1, B, and B - 1 of length n, i.e. for a multiindex I=(i1,i1,…,im,jm) define |I|=∑mk=1(|ik|+|jk|)=n and \\( W_n(A,B ) = \\{W_{\\cal I}(A,B) = A^{i_1} B^{j_1} \\dots A^{i_m} B^{j_m}\\}_{|{\\cal I|}=n \\).¶Gamburd—Jakobson—Sarnak [GJS] raised the problem: prove that for Haar almost every pair A,B∈SO(3) the closest distance of words of length n to the identity, i.e. sA,B(n)=min|I|=n∥WI(A,B)−E∥, is bounded from below by an exponential function in n. This is the analog of the diophantine property for elements of SO(3). In this paper we prove that s A,B (n) is bounded from below by an exponential function in n 2. We also exhibit obstructions to a “simple” proof of the exponential estimate in n."}],"day":"01","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"date_created":"2020-09-18T10:49:43Z","citation":{"mla":"Kaloshin, Vadim, and Brian R. Hunt. “A Stretched Exponential Bound on the Rate of Growth of the Number of Periodic Points for Prevalent Diffeomorphisms II.” *Electronic Research Announcements of the American Mathematical Society*, vol. 7, no. 5, American Mathematical Society, 2001, pp. 28–36, doi:10.1090/s1079-6762-01-00091-9.","ieee":"V. Kaloshin and B. R. Hunt, “A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II,” *Electronic Research Announcements of the American Mathematical Society*, vol. 7, no. 5, pp. 28–36, 2001.","chicago":"Kaloshin, Vadim, and Brian R. Hunt. “A Stretched Exponential Bound on the Rate of Growth of the Number of Periodic Points for Prevalent Diffeomorphisms II.” *Electronic Research Announcements of the American Mathematical Society* 7, no. 5 (2001): 28–36. https://doi.org/10.1090/s1079-6762-01-00091-9.","apa":"Kaloshin, V., & Hunt, B. R. (2001). A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II. *Electronic Research Announcements of the American Mathematical Society*, *7*(5), 28–36. https://doi.org/10.1090/s1079-6762-01-00091-9","short":"V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American Mathematical Society 7 (2001) 28–36.","ista":"Kaloshin V, Hunt BR. 2001. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II. Electronic Research Announcements of the American Mathematical Society. 7(5), 28–36.","ama":"Kaloshin V, Hunt BR. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II. *Electronic Research Announcements of the American Mathematical Society*. 2001;7(5):28-36. doi:10.1090/s1079-6762-01-00091-9"},"page":"28-36","_id":"8521","date_published":"2001-04-24T00:00:00Z","extern":"1","quality_controlled":"1","doi":"10.1090/s1079-6762-01-00091-9","title":"A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II","article_type":"original","language":[{"iso":"eng"}],"author":[{"first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","full_name":"Kaloshin, Vadim"},{"first_name":"Brian R.","last_name":"Hunt","full_name":"Hunt, Brian R."}],"type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","day":"24","abstract":[{"lang":"eng","text":"We continue the previous article's discussion of bounds, for prevalent diffeomorphisms of smooth compact manifolds, on the growth of the number of periodic points and the decay of their hyperbolicity as a function of their period $n$. In that article we reduced the main results to a problem, for certain families of diffeomorphisms, of bounding the measure of parameter values for which the diffeomorphism has (for a given period $n$) an almost periodic point that is almost nonhyperbolic. We also formulated our results for $1$-dimensional endomorphisms on a compact interval. In this article we describe some of the main techniques involved and outline the rest of the proof. To simplify notation, we concentrate primarily on the $1$-dimensional case."}],"month":"04","keyword":["General Mathematics"],"article_processing_charge":"No","publication_identifier":{"issn":["1079-6762"]},"volume":7,"intvolume":" 7","date_updated":"2020-10-12T13:28:17Z","publication":"Electronic Research Announcements of the American Mathematical Society","publisher":"American Mathematical Society","year":"2001","publication_status":"published","issue":"5","status":"public"}]