The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful abstraction, algorithms for computing a finite automaton for the downward closure of a given language have been established only for few language classes. This wo...

Just as classical knots and links can be represented by the closures of braids, so can virtual knots and links be represented by the closures of virtual braids [16]. Virtual braids have a group structure that can be described by generators and relations, generalizing the generators and relations of the classical braid group. This structure of virtual braids is worth study for its own sake. The ...

Pandemic and seasonal infectious diseases such as influenza may have serious negative health and economic consequences. Certain non-pharmaceutical intervention strategies--including school closures--can be implemented rapidly as a first line of defense against spread. Such interventions attempt to reduce the effective number of contacts between individuals within a community; yet the efficacy o...

Optimal boundary closures are derived for first derivative, finite difference operators of order 2, 4, 6 and 8. The closures are based on a diagonal-norm summation-by-parts (SBP) framework, thereby guaranteeing linear stability on piecewise curvilinear multi-block grids and entropy stability for nonlinear equations that support a convex extension. The new closures are developed by enriching con...

Periareolar closure in augmentation, mastopexy, and breast reduction has evolved dramatically over the past 10 years with changes in technique and technology. Plastic surgeons have tried many techniques from simple purse string closures using permanent sutures to interlocking purse string closures with GORE-TEX (Gore Medical, Newark, DE) or absorbable sutures. Running and interrupted suture tec...

BACKGROUND During the 2009 H1N1 influenza pandemic, Australian public health officials closed schools as a strategy to mitigate the spread of the infection. This article examines school communities' understanding of, and participation in, school closures and the beliefs and values which underpinned school responses to the closures. METHODS We interviewed four school principals, 25 staff, 14 p...

Aim: The primary author previously described his technique for periareolar closure in mastopexy using a pinwheel interlocking purse string with absorbable barbed suture and now reports the results of a retrospective photometric analysis comparing this technique with the same closure using Gortex® suture. This study is designed to compare the degree of areolar widening and safety profile of usin...

Moment closures of gaskinetic theory offer a method for the prediction of non-equilibrium flows which have a wider range of validity than standard continuum methods, such as solution of the Navier-Stokes equations, and can be much more computationally efficient than particle-based techniques, such as Direct Simulation Monte Carlo (DSMC). Moment methods yield systems of first-order partial diffe...

BACKGROUND Proximity is an important component of access to healthcare services. Recent changes in generic pricing in Ontario have caused speculation about pharmacy closures. However, there is little information on the current geographic accessibility of pharmacies. Therefore, we studied geographic access to pharmacies and modelled the impact of possible closures. METHODS We used location dat...