Implicit complexity for coinductive data: a characterization of corecurrence

We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using productivity (fairness) as the fundamental assertion, rather than bi-simulation. The latter is expressible in terms of the former. As an application to this framework, we give an implicit characterization of corecurrence: a function is definable using corecurrence iff its productivity is provable using coinduction for formulas in which data-predicates do not occur negatively. This is an analog, albeit in weaker form, of a characterization of recurrence (i.e. primitive recursion) in [Leivant, Unipolar induction, TCS 318, 2004].Comment: In Proceedings DICE 2011, arXiv:1201.034

Regulation of Mycobacterium-Specific Mononuclear Cell Responses by 25-Hydroxyvitamin D3

The active vitamin D metabolite, 1,25-dihydroxyvitamin D3 (1,25(OH)2D3), has been shown to be an important regulator of innate and adaptive immune function. In addition, synthesis of 1,25(OH)2D3 from 25-hydroxyvitamin D3 (25(OH)D3) by the enzyme 1α-hydroxylase in monocytes upon activation by TLR signaling has been found to regulate innate immune responses of monocytes in an intracrine fashion. In this study we wanted to determine what cells expressed 1α-hydroxylase in stimulated peripheral blood mononuclear cell (PBMC) cultures and if conversion of 25(OH)D3 to 1,25(OH)2D3 in PBMC cultures regulated antigen-specific immune responses. Initially, we found that stimulation of PBMCs from animals vaccinated with Mycobacterium bovis (M. bovis) BCG with purified protein derivative of M. bovis (M. bovis PPD) induced 1α-hydroxylase gene expression and that treatment with a physiological concentration of 25(OH)D3 down-regulated IFN-γ and IL-17F gene expression. Next, we stimulated PBMCs from M. bovis BCG-vaccinated and non-vaccinated cattle with M. bovis PPD and sorted them by FACS according to surface markers for monocytes/macrophages (CD14), B cells (IgM), and T cells (CD3). Sorting the PBMCs revealed that 1α-hydroxylase expression was induced in the monocytes and B cells, but not in the T cells. Furthermore, treatment of stimulated PBMCs with 25(OH)D3 down-regulated antigen-specific IFN-γ and IL-17F responses in the T cells, even though 1α-hydroxylase expression was not induced in the T cells. Based on evidence of no T cell 1α-hydroxylase we hypothesize that activated monocytes and B cells synthesize 1,25(OH)2D3 and that 1,25(OH)2D3 down-regulates antigen-specific expression of IFN-γ and IL-17F in T cells in a paracrine fashion

A Uniform Model Theory for the Specification of Data and Process types

Generalizing products in Lawvere's algebraic theories to projective and injective Kan extensions and their conjunctive combinations one gets a powerful categorical model theory. Based on this categorical model theory the foundations of a uniform axiomatic specification formalism for data and process types is developed