On the nature of the torus in the complex Lorenz equations.

The complex Lorenz equations are a nonlinear fifth-order set of physically derived differential equations which exhibit an exact analytic limit cycle which subsequently bifurcates to a torus. In this paper we build upon previously derived results to examine a connection between this torus at high and low r1 bifurcation parameter) and between zero and nonzero r2(complexity parameter); in so doing, we are able to gain insight on the effect of the rotational invariance of the system, and on how extra weak dispersion (r2 ≠ 0) affects the chaotic behavior of the real Lorenz system (which describes a weakly dissipative, dispersive instability)

A delay recruitment model of the cardiovascular control system.

Copyright will be owned by Springer. We develop a nonlinear delay-differential equation for the human cardiovascular control system, and use it to explore blood pressure and heart rate variability under short-term baroreflex control. The model incorporates an intrinsically stable heart rate in the absence of nervous control, and features baroreflex influence on both heart rate and peripheral resistance. Analytical simplifications of the model allow a general investigation of the rôles played by gain and delay, and the effects of ageing.

A Dichotomy Theorem for Circular Colouring Reconfiguration

The "reconfiguration problem" for circular colourings asks, given two $(p,q)$-colourings $f$ and $g$ of a graph $G$, is it possible to transform $f$ into $g$ by changing the colour of one vertex at a time such that every intermediate mapping is a $(p,q)$-colouring? We show that this problem can be solved in polynomial time for $2\leq p/q <4$ and is PSPACE-complete for $p/q\geq 4$. This generalizes a known dichotomy theorem for reconfiguring classical graph colourings.Comment: 22 pages, 5 figure

Time to Cut the Fat: The Case for Government Anti-Obesity Legislation

This Article examines—and ultimately rejects—this anti-paternalism argument against government anti-obesity policies. It argues that government intervention in the food industry for the purpose of stemming the American obesity epidemic is justified and survives paternalistic objections to the contrary. This Article begins by briefly outlining the nature, severity, and causes of the obesity epidemic. It considers what can be done about the problem, finding that only government intervention is capable of effectively combating the crisis. It also outlines several types of potentially successful government anti-obesity strategies. Finally, it considers the primary topic of this Article: whether government anti-obesity policies constitute unjustified government paternalism