Sufficient dimension reduction has been extensively explored in the context of independent and identically distributed data. In this article we generalize sufficient dimension reduction to longitudinal data and propose an estimating equation approach to estimating the central mean subspace. The proposed method accounts for the covariance structure within each subject and improves estimation eff...

A new set of amino acid descriptors, SZOTT (Scores of Zero dimension, One dimension, Two dimension, Three dimension) was derived from principal component analysis on a matrix of 1369 descriptors including 0D, 1D, 2D and 3D information of 20 coded amino acids. SZOTT scales were then employed to represent structures of HLA-A*0201 restrictive CTL epitopes, and further, quantitative sequence-activi...

We present a method for reliability assessment in extreme conditions from numerical simulator through surrogate based importance sampling. As proposed recent works the literature, Kriging is used to build an approximation of limit state function and optimal density. Our contribution then use sufficient dimension reduction which enables construction metamodel lower dimension. The so called augme...

Large database schemata can be drastically simplified if techniques of modular and structural modeling are used. Applications and thus schemata have an inner meta-structure. The explicit treatment of the inner structuring may be used during development of large database schemata and may ease the development to a large extent. It is surprising that dimensions and internal separations have not be...

We show that recent results on randomized dimension reduction schemes that exploit structural properties of data can be applied in the context of persistent homology. In the spirit of compressed sensing, the dimension reduction is determined by the Gaussian width of a structure associated to the data set, rather than its size, and such a reduction can be computed efficiently. We further relate ...