Commutative unital rings elementarily equivalent to prescribed product rings

The classical work of Feferman Vaught gives a powerful, constructive analysis of definability in (generalized) product structures, and certain associated enriched Boolean structures. %structures in terms of definability in the component structures. Here, by closely related methods, but in the special setting of commutative unital rings, we obtain a kind of converse allowing us to determine in interesting cases, when a commutative unital R is elementarily equivalent to a nontrivial product of a family of commutative unital rings R_i. We use this in the model theoretic analysis of residue rings of models of Peano Arithmetic

The algebraic numbers definable in various exponential fields

We prove the following theorems: Theorem 1: For any E-field with cyclic kernel, in particular $\mathbb C$ or the Zilber fields, all real abelian algebraic numbers are pointwise definable. Theorem 2: For the Zilber fields, the only pointwise definable algebraic numbers are the real abelian numbers

The cytotoxic T cell proteome and its shaping by the kinase mTOR

High-resolution mass spectrometry maps the cytotoxic T lymphocyte (CTL) proteome and the impact of mammalian target of rapamycin complex 1 (mTORC1) on CTLs. The CTL proteome was dominated by metabolic regulators and granzymes and mTORC1 selectively repressed and promoted expression of subset of CTL proteins (~10%). These included key CTL effector molecules, signaling proteins and a subset of metabolic enzymes. Proteomic data highlighted the potential for mTORC1 negative control of phosphatidylinositol (3,4,5)-trisphosphate (PtdIns(3,4,5)P(3)) production in CTL. mTORC1 was shown to repress PtdIns(3,4,5)P(3) production and to determine the mTORC2 requirement for activation of the kinase Akt. Unbiased proteomic analysis thus provides a comprehensive understanding of CTL identity and mTORC1 control of CTL function