Finding Tractable Formulas in NNF

Many applications in Computer Science require to represent knowledge and to reason with non normal form formulas. However, most of the advances in tractable reasoning are applied only to CNF formulas. In this paper, we extend tractability to several classes of non normal formulas which are of high practical interest. Thus, we first define three non normal Horn-like classes of formulas F1 F2 : : : Fn where each F i is constituted by a disjunction of two optional terms F i = NNF \Gamma i C + i : the first one is in Negation Normal Form (NNF) composed exclusively with negative literals and the second one is a conjunction of positive propositions. These formulas codify the same problems that the Horn formulas but with significantly, even exponentially, less propositional symbols. Second, we define sound and refutational complete inference rule sets for each class. Our third contribution consists in the design of a sound, complete and strictly linear running time algorit..

Calcitonin Gene-Related Peptide (CGRP) Receptors Are Important to Maintain Cerebrovascular Reactivity in Chronic Hypertension

Cerebral blood flow autoregulation (CA) shifts to higher blood pressures in chronic hypertensive patients, which increases their risk for brain damage. Although cerebral vascular smooth muscle cells express the potent vasodilatatory peptides calcitonin gene-related peptide (CGRP) and adrenomedullin (AM) and their receptors (calcitonin receptor-like receptor (Calclr), receptor-modifying proteins (RAMP) 1 and 2), their contribution to CA during chronic hypertension is poorly understood. Here we report that chronic (10 weeks) hypertensive (one-kidney-one-clip-method) mice overexpressing the Calclr in smooth muscle cells (CLR-tg), which increases the natural sensitivity of the brain vasculature to CGRP and AM show significantly better blood pressure drop-induced cerebrovascular reactivity than wt controls. Compared to sham mice, this was paralleled by increased cerebral CGRP-binding sites (receptor autoradiography), significantly in CLR-tg but not wt mice. AM-binding sites remained unchanged. Whereas hypertension did not alter RAMP-1 expression (droplet digital (dd) PCR) in either mouse line, RAMP-2 expression dropped significantly in both mouse lines by about 65%. Moreover, in wt only Calclr expression was reduced by about 70% parallel to an increase of smooth muscle actin (Acta2) expression. Thus, chronic hypertension induces a stoichiometric shift between CGRP and AM receptors in favor of the CGRP receptor. However, the parallel reduction of Calclr expression observed in wt mice but not CLR-tg mice appears to be a key mechanism in chronic hypertension impairing cerebrovascular reactivity