DISCUSSION: A PRODUCER PERSPECTIVE ON THE FUTURE OF DOMESTIC AND TRADE DAIRY POLICY IN CANADA

Agricultural and Food Policy,

An Optimal Control Theory for the Traveling Salesman Problem and Its Variants

We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space of measurable functions to the field of real numbers. Many variants of the TSP, such as those with neighborhoods, with forbidden neighborhoods, with time-windows and with profits, can all be framed under this construct. In sharp contrast to their discrete-optimization counterparts, the modeling constructs presented in this paper represent a fundamentally new domain of analysis and computation for TSPs and their variants. Beyond its apparent mathematical unification of a class of problems in graph theory, the main advantage of the new approach is that it facilitates the modeling of certain application-specific problems in their home space of measurable functions. Consequently, certain elements of economic system theory such as dynamical models and continuous-time cost/profit functionals can be directly incorporated in the new optimization problem formulation. Furthermore, subtour elimination constraints, prevalent in discrete optimization formulations, are naturally enforced through continuity requirements. The price for the new modeling framework is nonsmooth functionals. Although a number of theoretical issues remain open in the proposed mathematical framework, we demonstrate the computational viability of the new modeling constructs over a sample set of problems to illustrate the rapid production of end-to-end TSP solutions to extensively-constrained practical problems.Comment: 24 pages, 8 figure

Polarimetric modeling of corotating interaction regions (CIRs) threading massive-star winds

Massive star winds are complex radiation-hydrodynamic (sometimes magnetohydrodynamic) outflows that are propelled by their enormously strong luminosities. The winds are often found to be structured and variable, but can also display periodic or quasi-periodic behavior in a variety of wind diagnostics. The regular variations observed in putatively single stars, especially in UV wind lines, have often been attributed to corotating interaction regions (CIRs) like those seen in the solar wind. We present light curves for variable polarization from winds with CIR structures. We develop a model for a time-independent CIR based on a kinematical description. Assuming optically thin electron scattering, we explore the range of polarimetric light curves that result as the curvature, latitude, and number of CIRs are varied. We find that a diverse array of variable polarizations result from an exploration of cases. The net polarization from an unresolved source is weighted more toward the inner radii of the wind. Given that most massive stars have relatively fast winds compared to their rotation speeds, CIRs tend to be conical at inner radii, transitioning to a spiral shape at a few to several stellar radii in the wind. Winds with a single CIR structure lead to easily identifiable polarization signatures. By contrast allowing for multiple CIRs, all emerging from a range of azimuth and latitude positions at the star, can yield complex polarimetric behavior. Although our model is based on some simplifying assumptions, it produces qualitative behavior that we expect to be robust, and this has allowed us to explore a wide range of CIR configurations that will prove useful for interpreting polarimetric data.Comment: accepted to A&

L'objet des droits constitutionnels à l'égalité

This article is exclusively devoted to enquiring into the purpose of equality rights guaranteed by sections 15 and 28 of the Canadian Charter of Rights and Freedoms. By first retracing the concept of equality from both a legal and philosophical perspective, the author comes to the conclusion that the juxtaposition of values of human dignity and social justice has brought on the most powerful change in the concept of equality. By invoking these two values in unison, authoritative writings, legislators and the courts have on the one hand, come to recognize the insufficiency of formal legal equality and thereby integrate the principle of substantial equality and have, on the other, conceived equality not merely with regard to individuals alone, but also by taking into account groups that society tends to neglect or dominate due to the existence of tenacious prejudices. The author then specifically examines the Canadian legal and socioeconomic context in search of the purpose of equality rights enshrined in the Charter of rights and shows that the addition of section 28 and the enumeration of grounds of discrimination to equality rights in s.s. 15(1) has as its purpose to provide additional protection to women and members of certain underprivileged groups. This special protection is indicative, in the author's view, of a clear constitutional choice in favour of a substantial conception of equality taking into account the collective dimension of discrimination