Wavelet frames to optimally learn functions on diffusion measure spaces.

Based on the theory of wavelets on data defined manifolds we study the Kolmogorov metric entropy and related measures of complexity of certain function spaces. We also develop constructive algorithms to represent those functions within a prescribed accuracy that is asymptotically optimal up to a logarithmic factor

3D genomics across the tree of life reveals condensin II as a determinant of architecture type.

We investigated genome folding across the eukaryotic tree of life. We find two types of three-dimensional (3D) genome architectures at the chromosome scale. Each type appears and disappears repeatedly during eukaryotic evolution. The type of genome architecture that an organism exhibits correlates with the absence of condensin II subunits. Moreover, condensin II depletion converts the architecture of the human genome to a state resembling that seen in organisms such as fungi or mosquitoes. In this state, centromeres cluster together at nucleoli, and heterochromatin domains merge. We propose a physical model in which lengthwise compaction of chromosomes by condensin II during mitosis determines chromosome-scale genome architecture, with effects that are retained during the subsequent interphase. This mechanism likely has been conserved since the last common ancestor of all eukaryotes