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Giorgos Kotsovolis - One of the best experts on this subject based on the ideXlab platform.

  • Partially smooth universal Taylor series on products of simply connected domains
    Monatshefte für Mathematik, 2020
    Co-Authors: Giorgos Kotsovolis
    Abstract:

    Using a recent Mergelyan type theorem, we show the existence of universal Taylor series on products of planar simply connected domains $$\Omega _i$$ Ω i that extend continuously on $$\prod \nolimits _{i=1}^{d}(\Omega _i \cup S_i)$$ ∏ i = 1 d ( Ω i ∪ S i ) , where $$S_i$$ S i are subsets of $$\partial \,\Omega _i$$ ∂ Ω i , open in the Relative Topology. The universal approximation occurs on every product of compact sets $$K_i$$ K i such that $$C-K_i$$ C - K i are connected and for some $$i_0$$ i 0 it holds $$K_{i_0}\cap (\Omega _{i_0}\cup \overline{S_{i_0}})=\varnothing $$ K i 0 ∩ ( Ω i 0 ∪ S i 0 ¯ ) = ∅ .

  • Partially Smooth Universal Taylor Series on products of simply connected domains
    arXiv: Complex Variables, 2019
    Co-Authors: Giorgos Kotsovolis
    Abstract:

    Using a recent Mergelyan type theorem, we show the existence of universal Taylor series on products of planar simply connected domains Oi that extend continuously on the product of the union of Oi with Si , where Si are subsets of the boundary of Oi, open in the Relative Topology. The universal approximation occurs on every product of compact sets Ki such that C - Ki are connected and for some i0 it holds that Ki0 is contained in the complement of the union of Oi0 with the closure of Si0. Furthermore,we introduce some topological properties of universal Taylor series that lead to the voidance of some families of functions.

Helene Conjeaud - One of the best experts on this subject based on the ideXlab platform.

  • structure of the tetraspanin main extracellular domain a partially conserved fold with a structurally variable domain insertion
    Journal of Biological Chemistry, 2001
    Co-Authors: Michel Seigneuret, Alix Delaguillaumie, Cecile Lagaudrieregesbert, Helene Conjeaud
    Abstract:

    Abstract The tetraspanin family of membrane glycoproteins is involved in the regulation of cellular development, proliferation, activation, and mobility. We have attempted to predict the structural features of the large extracellular domain of tetraspanins (EC2), which is very important in determining their functional specificity. The tetraspanin EC2 is composed of two subdomains: a conserved three-helix subdomain and a variable secondary structure subdomain inserted within the conserved subdomain. The occurrence of key disulphide bridges and other invariant residues leads to a conserved Relative Topology of both subdomains and also suggests a structural classification of tetraspanins. Using the CD81 EC2 structure as a template, the structures of two other EC2s were predicted by homology modeling and indicate a conserved shape, in which the variable subdomain is located at one side of the structure. The conserved and variable subdomains might contain sites that correspond, respectively, to common and specific interactions of tetraspanins. The tetraspanin EC2 seems to correspond to a new scheme of fold conservation/variability among proteins, namely the insertion of a structurally variable subdomain within an otherwise conserved fold.

Michel Seigneuret - One of the best experts on this subject based on the ideXlab platform.

  • structure of the tetraspanin main extracellular domain a partially conserved fold with a structurally variable domain insertion
    Journal of Biological Chemistry, 2001
    Co-Authors: Michel Seigneuret, Alix Delaguillaumie, Cecile Lagaudrieregesbert, Helene Conjeaud
    Abstract:

    Abstract The tetraspanin family of membrane glycoproteins is involved in the regulation of cellular development, proliferation, activation, and mobility. We have attempted to predict the structural features of the large extracellular domain of tetraspanins (EC2), which is very important in determining their functional specificity. The tetraspanin EC2 is composed of two subdomains: a conserved three-helix subdomain and a variable secondary structure subdomain inserted within the conserved subdomain. The occurrence of key disulphide bridges and other invariant residues leads to a conserved Relative Topology of both subdomains and also suggests a structural classification of tetraspanins. Using the CD81 EC2 structure as a template, the structures of two other EC2s were predicted by homology modeling and indicate a conserved shape, in which the variable subdomain is located at one side of the structure. The conserved and variable subdomains might contain sites that correspond, respectively, to common and specific interactions of tetraspanins. The tetraspanin EC2 seems to correspond to a new scheme of fold conservation/variability among proteins, namely the insertion of a structurally variable subdomain within an otherwise conserved fold.

Tong Zhang - One of the best experts on this subject based on the ideXlab platform.

  • NIPS - Spectral Methods for Learning Multivariate Latent Tree Structure
    2011
    Co-Authors: Animashree Anandkumar, Kamalika Chaudhuri, Sham M Kakade, Le Song, Daniel Hsu, Tong Zhang
    Abstract:

    This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models, hidden Markov models, Gaussian mixture models, and Markov evolutionary trees. The setting is one where we only have samples from certain observed variables in the tree, and our goal is to estimate the tree structure (i.e., the graph of how the underlying hidden variables are connected to each other and to the observed variables). We propose the Spectral Recursive Grouping algorithm, an efficient and simple bottom-up procedure for recovering the tree structure from independent samples of the observed variables. Our finite sample size bounds for exact recovery of the tree structure reveal certain natural dependencies on underlying statistical and structural properties of the underlying joint distribution. Furthermore, our sample complexity guarantees have no explicit dependence on the dimensionality of the observed variables, making the algorithm applicable to many high-dimensional settings. At the heart of our algorithm is a spectral quartet test for determining the Relative Topology of a quartet of variables from second-order statistics.

  • spectral methods for learning multivariate latent tree structure
    arXiv: Learning, 2011
    Co-Authors: Animashree Anandkumar, Kamalika Chaudhuri, Sham M Kakade, Le Song, Tong Zhang
    Abstract:

    This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models, hidden Markov models, Gaussian mixture models, and Markov evolutionary trees. The setting is one where we only have samples from certain observed variables in the tree, and our goal is to estimate the tree structure (i.e., the graph of how the underlying hidden variables are connected to each other and to the observed variables). We propose the Spectral Recursive Grouping algorithm, an efficient and simple bottom-up procedure for recovering the tree structure from independent samples of the observed variables. Our finite sample size bounds for exact recovery of the tree structure reveal certain natural dependencies on underlying statistical and structural properties of the underlying joint distribution. Furthermore, our sample complexity guarantees have no explicit dependence on the dimensionality of the observed variables, making the algorithm applicable to many high-dimensional settings. At the heart of our algorithm is a spectral quartet test for determining the Relative Topology of a quartet of variables from second-order statistics.

Zhang Guo-fang - One of the best experts on this subject based on the ideXlab platform.