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In the bioinformatics field, there has been a growing interest in modelling dihedral angles of amino acids by viewing them as data on the torus.
Stereochemistry of polypeptide chain configurations
Ramachandran, G. N. (1963) · 1963
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Statistics of directional data
Mardia, K. V. (1975) · 1975
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Measures and models for angular correlation and angular-linear correlation
Johnson, R. A. and T. E. Wehrly (1977) · 1977
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Bivariate models for dependence of angular observations and a related Markov process
Wehrly, T. E. and R. A. Johnson (1980) · 1980
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A correlation coefficient for circular data
Fisher, N. I. and A. J. Lee (1983) · 1983
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A class of distributions which includes the normal ones
Azzalini, A. (1985) · 1985
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Interior algorithms for linear, quadratic, and linearly constrained non-linear programming
Ye, Y. (1987) · 1987
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A distribution for dependent unit vectors
Rivest, L.-P. (1988) · 1988
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The multivariate skew-normal distribution
Azzalini, A. and A. Dalla Valle (1996) · 1996
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A decentred predictor for circular-circular regression
Rivest, L.-P. (1997) · 1997
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Directional Statistics
Mardia, K. V. and P. E. Jupp (2000) · 2000
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Asymptotic Statistics
Van der Vaart, A. W. (2000) · 2000
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Circular regression
Downs, T. D. and K. V. Mardia (2002) · 2002
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Probabilistic model for two dependent circular variables
Singh, H., V. Hnizdo, and E. Demchuk (2002) · 2002
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A skew-symmetric representation of multivariate distribution
Wang, J., J. Boyer, and M. G. Genton (2004) · 2004
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Directions and projective shapes
Mardia, K. V. and V. Patrangenaru (2005) · 2005
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Models for circular-linear and circular-circular data constructed from circular distributions based on nonnegative trigonometric sums
Fernández-Duran, J. J. (2007) · 2007
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Protein bioinformatics and mixtures of bivariate von Mises distributions for angular data
Mardia, K. V., C. C. Taylor, and G. K. Subramaniam (2007) · 2007
Beyond rotamers: a generative, probabilistic model of side chains in proteins
Harder, T., W. Boomsma, M. Paluszewski, J. Frellsen, K. E. Johansson, and T. Hamelryck (2010) · 2010
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Sine-skewed circular distributions
Abe, T. and A. Pewsey (2011) · 2011
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Modeling and comparing the organization of circular genomes
Shieh, G. S., S. Zheng, R. A. Johnson, Y. F. Chang, K. Shimizu, C. C. Wang, and S. L. Tang (2011) · 2011
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Bayesian Methods in Structural Bioinformatics
Hamelryck, T., K. V. Mardia, and J. Ferkinghoff-Borg (Eds.) (2012) · 2012
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Statistical approaches to three key challenges in protein structural bioinformatics
Mardia, K. V. (2013) · 2013
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Rsolnp: General Non-linear Optimization Using Augmented Lagrange Multiplier Method
Ghalanos, A. and S. Theussl (2015) · 2015
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A generative, probabilistic model of local protein structure
Boomsma, W., K. V. Mardia, C. C. Taylor, J. Ferkinghoff-Borg, A. Krogh, and T. Hamelryck (2008) · 2008
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A circular–circular regression model
Kato, S., K. Shimizu, and G. S. Shieh (2008) · 2008
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Modelling strategies for bivariate circular data
Kent, J. T., K. V. Mardia, and C. C. Taylor (2008) · 2008
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A multivariate von Mises distribution with applications to bioinformatics
Mardia, K. V., G. Hughes, C. C. Taylor, and H. Singh (2008) · 2008
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A distribution for a pair of unit vectors generated by Brownian motion
Kato, S. (2009) · 2009
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Building asymmetry into circular distributions
Umbach, D. and S. R. Jammalamadaka (2009) · 2009
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On a class of circulas: copulas for circular distributions
Jones, M. C., A. Pewsey, and S. Kato (2015) · 2015
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A Möbius transformation-induced distribution on the torus
Kato, S. and A. Pewsey (2015) · 2015
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A general setting for symmetric distributions and their relationship to general distributions
Jupp, P. E., G. Regoli, and A. Azzalini (2016) · 2016
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Applied Directional Statistics: Modern Methods and Case Studies
Mardia, K. V., J. I. Foldager, and J. Frellsen (2018) · 2018
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Langevin diffusions on the torus: estimation and applications
García-Portugués, E., M. Sörensen, K. V. Mardia, and T. Hamelryck (2019) · 2019
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Applied Directional Statistics: Modern Methods and Case Studies
Ley, C. and T. Verdebout (Eds.) (2019) · 2019
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