Stabilization of Unstable Procedures: The Recursive Projection Method

Fixed-point iterative procedures for solving nonlinear parameter dependent problems can converge for some interval of parameter values and diverge as the parameter changes. The Recursive Projection Method (RPM), which stabilizes such procedures by computing a projection onto the unstable subspace is presented. On this subspace a Newton or special Newton iteration is performed, and the fixed-point iteration is used on the complement. As continuation in the parameter proceeds, the projection is efficiently updated, possibly increasing or decreasing the dimension of the unstable subspace. The method is extremely effective when the dimension of the unstable subspace is small compared to the dimension of the system. Convergence proofs are given and pseudo-arclength continuation on the unstable subspace is introduced to allow continuation past folds. Examples are presented for an important application of the RPM in which a “black-box” time integration scheme is stabilized, enabling it to compute unstable steady states. The RPM can also be used to accelerate iterative procedures when slow convergence is due to a few slowly decaying modes

Age-Optimal Information Updates in Multihop Networks

The problem of reducing the age-of-information has been extensively studied in the single-hop networks. In this paper, we minimize the age-of-information in general multihop networks. If the packet transmission times over the network links are exponentially distributed, we prove that a preemptive Last Generated First Served (LGFS) policy results in smaller age processes at all nodes of the network (in a stochastic ordering sense) than any other causal policy. In addition, for arbitrary general distributions of packet transmission times, the non-preemptive LGFS policy is shown to minimize the age processes at all nodes of the network among all non-preemptive work-conserving policies (again in a stochastic ordering sense). It is surprising that such simple policies can achieve optimality of the joint distribution of the age processes at all nodes even under arbitrary network topologies, as well as arbitrary packet generation and arrival times. These optimality results not only hold for the age processes, but also for any non-decreasing functional of the age processes.Comment: arXiv admin note: text overlap with arXiv:1603.0618

The Joyous \u3cem\u3eYoni\u3c/em\u3e: An Exploration of Yogic Perspectives Toward Sexual Empowerment for Women

This paper explores yogic approaches to women’s sexuality. Acknowledging that sexualized violence against women is a harsh and pernicious reality for women all over the world, the paper adopts an inclusive perspective on women’s sexuality that focuses on pleasure. A basic introduction to yoga prefaces a discussion of prana (life force) and concepts of unity and oneness. These concepts provide a framework for yogic concepts of the body, with an emphasis on sexuality. Specific breathing exercises, meditations, poses, locks and seals are mentioned. The experience of one of Canada’s most accomplished yoga teachers is also depicted. The paper concludes by affirming that women’s positive experiences of sexuality may be heightened through yogic practices that assist in living in the body more fully. Given the vacuum of scholarly work in this area, this paper is a small step toward understanding the common ground between the vast subjects of yoga and women’s sexual empowerment