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Under consideration are multicomponent minimization problems in- volving a separable nonsmooth convex function penalizing the com- ponents individually, and nonsmooth convex coupling terms penal- izing linear mixtures of the components. We investigate the appli- cation of block-activated proximal algorithms for solving such prob- lems, i.e., algorithms which, at each iteration, need to use only a block of the underlying functions, as opposed to all of them as in standard methods. For smooth coupling functions, several block- activated algorithms exist and they are well understood. By con- trast, in the fully nonsmooth case, few block-activated methods are available and little effort has been devoted to assessing them. Our goal is to shed more light on the implementation, the features, and the behavior of these algorithms, compare their merits, and provide machine learning and image recovery experiments illustrating their performance.

We show that the weak convergence of the Douglas--Rachford algorithm for finding a zero of the sum of two maximally monotone operators cannot be improved to strong convergence. Likewise, we show that strong convergence can fail for the method of partial inverses.

Histone variants fine-tune transcription, replication, DNA damage repair, and faithful chromosome segregation. Whether and how nucleosome variants encode unique mechanical properties to their cognate chromatin structures remains elusive. Here, using in silico and in vitro nanoindentation methods, extending to in vivo dissections, we report that histone variant nucleosomes are intrinsically more elastic than their canonical counterparts. Furthermore, binding proteins, which discriminate between histone variant nucleosomes, suppress this innate elasticity and also compact chromatin. Interestingly, when we overexpress the binding proteins in vivo, we also observe increased compaction of chromatin enriched for histone variant nucleosomes, correlating with diminished access. Taken together, these data suggest a plausible link between innate mechanical properties possessed by histone variant nucleosomes, the adaptability of chromatin states in vivo, and the epigenetic plasticity of the underlying locus.