Hidden heterochromatin: Characterization in the Rodentia species Cricetus cricetus, Peromyscus eremicus (Cricetidae) and Praomys tullbergi (Muridae)

The use of in situ restriction endonuclease (RE) (which cleaves DNA at specific sequences) digestion has proven to be a useful technique in improving the dissection of constitutive heterochromatin (CH), and in the understanding of the CH evolution in different genomes. In the present work we describe in detail the CH of the three Rodentia species, Cricetus cricetus, Peromyscus eremicus (family Cricetidae) and Praomys tullbergi (family Muridae) using a panel of seven REs followed by C-banding. Comparison of the amount, distribution and molecular nature of C-positive heterochromatin revealed molecular heterogeneity in the heterochromatin of the three species. The large number of subclasses of CH identified in Praomys tullbergi chromosomes indicated that the karyotype of this species is the more derived when compared with the other two genomes analyzed, probably originated by a great number of complex chromosomal rearrangements. The high level of sequence heterogeneity identified in the CH of the three genomes suggests the coexistence of different satellite DNA families, or variants of these families in these genomes

Highly symmetric POVMs and their informational power

We discuss the dependence of the Shannon entropy of normalized finite rank-1 POVMs on the choice of the input state, looking for the states that minimize this quantity. To distinguish the class of measurements where the problem can be solved analytically, we introduce the notion of highly symmetric POVMs and classify them in dimension two (for qubits). In this case we prove that the entropy is minimal, and hence the relative entropy (informational power) is maximal, if and only if the input state is orthogonal to one of the states constituting a POVM. The method used in the proof, employing the Michel theory of critical points for group action, the Hermite interpolation and the structure of invariant polynomials for unitary-antiunitary groups, can also be applied in higher dimensions and for other entropy-like functions. The links between entropy minimization and entropic uncertainty relations, the Wehrl entropy and the quantum dynamical entropy are described.Comment: 40 pages, 3 figure