On covers of cyclic acts over monoids

In (Bull. Lond. Math. Soc. 33:385–390, 2001) Bican, Bashir and Enochs finally solved a long standing conjecture in module theory that all modules over a unitary ring have a flat cover. The only substantial work on covers of acts over monoids seems to be that of Isbell (Semigroup Forum 2:95–118, 1971), Fountain (Proc. Edinb. Math. Soc. (2) 20:87–93, 1976) and Kilp (Semigroup Forum 53:225–229, 1996) who only consider projective covers. To our knowledge the situation for flat covers of acts has not been addressed and this paper is an attempt to initiate such a study. We consider almost exclusively covers of cyclic acts and restrict our attention to strongly flat and condition (P) covers. We give a necessary and sufficient condition for the existence of such covers and for a monoid to have the property that all its cyclic right acts have a strongly flat cover (resp. (P)-cover). We give numerous classes of monoids that satisfy these conditions and we also show that there are monoids that do not satisfy this condition in the strongly flat case. We give a new necessary and sufficient condition for a cyclic act to have a projective cover and provide a new proof of one of Isbell’s classic results concerning projective covers. We show also that condition (P) covers are not unique, unlike the situation for projective covers

2010), “Control and estimation through cognitive radio with distributed and dynamic spectral activity,” ACC

Abstract-Cognitive radio systems are currently a popular topic and are a good prospect for research when combined with control technology. In this paper, we consider the control and estimation via a two switch model which can represent a cognitive radio system. We provide an optimal estimator for this model and demonstrate that the optimal LQG controller is not a linear gain of the estimate of the states, as well as showing how the separation principle does not hold. Several conditions of stability are also discussed. Numerical examples are provided to verify the results

Nitric oxide synthase (nNOS) gene transfer modifies venous bypass graft remodeling: effects on vascular smooth muscle cell differentiation and superoxide production

Background: Pathological vascular remodeling in venous bypass grafts (VGs) results in smooth muscle cell (SMC) intimal hyperplasia and provides the substrate for progressive atherosclerosis, the principal cause of late VG failure. Nitric oxide (NO) bioactivity is reduced in VGs, in association with increased vascular superoxide production, but how these features relate to pathological VG remodeling remains unclear. We used gene transfer of the neuronal isoform of nitric oxide synthase (nNOS) to investigate how increased NO production modulates vascular remodeling in VGs and determined the effects on late VG phenotype. Methods and Results: New Zealand White rabbits (n=60) underwent jugular-carotid interposition bypass graft surgery with intraoperative adenoviral gene transfer of nNOS or β-galactosidase. Vessels were analyzed after 3 days (early, to investigate acute injury/inflammation) or 28 days (late, to investigate SMC intimal hyperplasia). In early VGs, nNOS gene transfer significantly increased NOS activity and substantially reduced adhesion molecule expression and inflammatory cell infiltration. In late VGs, recombinant nNOS protein was no longer evident, but there were sustained effects on VG remodeling, resulting in a striking reduction in SMC intimal hyperplasia, a more differentiated intimal SMC phenotype, and reduced vascular superoxide production. Conclusions: Intraoperative nNOS gene transfer has sustained favorable effects on VG remodeling and on the vascular phenotype of mature VGs. These findings suggest that early, transient modification of the response to vascular injury is a powerful approach to modulate VG biology and highlight the potential utility of NOS gene transfer as a therapeutic strategy in VGs

Divide activity of the model.

<p>Divide activity of the model.</p

Cell position validation.

<p>Stages of AB32 and AB64 mean when the AB lineage divides into 32 and 64 cells. Color-coded rule is the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0166551#pone.0166551.g006" target="_blank">Fig 6</a>. Dots represent the exact cell positions in a specific simulation/observational case, and ellipses represent the average position of each coresponding cell (with one standard deviation).</p