The amalgamation operation is frequently used to reduce the number of parts of compositional data but it is a non-linear operation in the simplex with the usual geometry, the Aitchison geometry. The concept of balances between groups, a particular coordinate system designed over binary partitions of the parts, could be an alternative to the amalgamation in some cases. In this work we discuss th...

We consider the nonsmooth convex composition optimization problem where the objective isa composition of two finite-sum functions and analyze stochastic compositional variance reducedgradient (SCVRG) methods for them. SCVRG and its variants have recently drawn much atten-tion given their edge over stochastic compositional gradient descent (SCGD); but the theoreticalanalysis ...

Compositional genomics is an approach to the problem of the organization of eukaryotic genomes. Initially this approach consisted of analysing the base composition of complex eukaryotic genomes (such as the nuclear genomes of vertebrates) by using density gradient centrifugation in the presence of sequence-specific ligands. This approach revealed that vertebrate genomes are mosaics of very long...

Stochastic compositional optimization generalizes classic (non-compositional) stochastic to the minimization of compositions functions. Each composition may introduce an additional expectation. The series expectations be nested. is gaining popularity in applications such as reinforcement learning and meta learning. This paper presents a new Stochastically Corrected Compositional gradient method...

Ni-implantation has been conducted for sputter deposited Zr alloy films to investigate compositional dependent amorphization behavior in proportion to Ni in Zr alloys. As-deposited Zr and Zr–Cu with thickness of 200 nm shows columnar hcp-Zr and nano-crystalline hcp-Zr(Cu), respectively. Implantation of 150 keV Niþ with the amount of 1 10 ions/cm induces amorphization of Zr and Zr(Cu) with 100 n...

The past decade has brought major improvements in large-scale asteroid discovery and characterization with over half a million known asteroids and over 100,000 with some measurement of physical characterization. This explosion of data has allowed us to create a new global picture of the Main Asteroid Belt. Put in context with meteorite measurements and dynamical models, a new and more complete ...