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Various coordinate rings of varieties appearing in the theory of Poisson Lie groups and Poisson homogeneous spaces belong to the large, axiomatically defined class of symmetric Poisson nilpotent algebras, e.g. coordinate rings of Schubert cells for symmetrizable Kac–Moody groups, affine charts of Bott-Samelson varieties, coordinate rings of double Bruhat cells (in the last case after a localization). We prove that every symmetric Poisson nilpotent algebra satisfying a mild condition on certain scalars is canonically isomorphic to a cluster algebra which coincides with the corresponding upper cluster algebra, without additional localizations by frozen variables. The constructed cluster structure is compatible with the Poisson structure in the sense of Gekhtman, Shapiro and Vainshtein. All Poisson nilpotent algebras are proved to be equivariant Poisson Unique Factorization Domains. Their seeds are constructed from sequences of Poisson-prime elements for chains of Poisson UFDs; mutation matrices are effectively determined from linear systems in terms of the underlying Poisson structure. Uniqueness, existence, mutation, and other properties are established for these sequences of Poisson-prime elements. 

InAs quantum dots (QDs) embedded into a waveguiding GaAs semiconductor matrix may produce scintillation detectors with exceptional speed and yield, making them valuable for nuclear security, medical imaging, and high energy physics applications. In this work, we developed thick (~25um) epitaxial heterostructres with high luminescence efficiency composed of self-assembled nano-engineered InAs QDs grown by molecular beam epitaxy. The bulk GaAs acts as a stopping material for incident particles and as a waveguide when layer-transferred onto a low-index substrate. Waveguiding and self-absorption (<1cm-1) were studied using photoluminescence with scanning laser excitation and modeled with ray optics approximation and geometrical coupling of high-index waveguide to a collection fiber. Scintillating signals from alpha-particles were analyzed with an external photodiode (PD) and an integrated PD which provided an improved optical coupling. The mean charge collected by the integrated PD corresponded to 5×1e4 photoelectrons per 1 MeV of deposited energy, or ~20% of the theoretically achievable light yield. Combined with the previously measured QD scintillation time of 0.3-0.6 ns, this makes the InAs/GaAs QD heterostructures the fastest high yield scintillation material reported.