Minimally unstable Pareto improvements over deferred acceptance

We investigate efficient and minimally unstable Pareto improvements over the deferred acceptance (DA) mechanism—a popular school choice mechanism that is stable but not efficient. We show that there is no Pareto improvement over the DA mechanism that is minimally unstable among efficient assignments when the stability comparison is based on counting the number of blocking pairs. Our main result characterizes the priority profiles for which there exists a Pareto improvement over the DA assignment that is minimally unstable among efficient assignments. We further consider an alternative natural stability comparison based on the set of blocking students who are involved in at least one blocking pair, show that the impossibilities remain, and characterize the possibility domain of priority profiles.

(Il)legal Assignments in School Choice

In public school choice, students with strict preferences are assigned to schools. Schools are endowed with priorities over students. Incorporating constraints from different applications, priorities are often modelled as choice functions over sets of students. It has been argued that the most desirable criterion for an assignment is stability; there should not exist any blocking pair: no student shall prefer some school to her assigned school and have higher priority than some student who got into that school or the school has an empty seat. We propose a blocking notion where in addition it must be possible to assign the student to her preferred school. We then define the following stability criterion for a set of assignments: a set of assignments is legal if and only if any assignment outside the set is blocked with some assignment in the set and no two assignments inside the set block each other. We show that under very basic conditions on priorities, there always exists a unique legal set of assignments, and that this set has a structure common to the set of stable assignments: (i) it is a lattice and (ii) it satisfies the rural hospitals theorem. The student-optimal legal assignment is efficient and provides a solution for the conflict between stability and efficiency.

Phosphorylation of linker histone is associated with transcriptional activation in a normally silent nucleus.

Previous studies have suggested that micronuclear linker histones are phosphorylated by cAMP-dependent protein kinase (PKA) in Tetrahymena (Sweet, M.T., and C.D. Allis. 1993. Chromosoma. 102: 637-647). In this study, we report that a rapid and dramatic phosphorylation of the micronuclear linker histone, delta, occurs early in the sexual pathway, conjugation. Phosphorylated isoforms of delta are detected as early as 30 min after mixing cells of different mating types; blocking pair formation abolishes this induction completely. Phosphorylation of delta is stimulated by the addition of N6-benzoyladenosine 3':5' cyclic monophosphate to starved (nonmating) cells, suggesting that a PKA/cAMP signal transduction pathway is involved. Maximal phosphorylation of delta is observed during meiotic prophase, a period when micronuclei become transcriptionally active. In situ staining, using phospho-delta-specific antibodies combined with [3H]uridine autoradiography, shows that decondensed micronuclear chromatin undergoing active transcription is enriched in phosphorylated delta isoforms. In contrast, condensed inactive micronuclear chromatin is enriched in dephosphorylated delta. These results strongly suggest that phosphorylation of linker histone plays an important and previously unsuspected role in establishing transcriptional competence in micronuclei.