A Primal-Dual Augmented Lagrangian

Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to both the primal and the dual variables simultaneously. A benefit of this approach is that the quality of the dual variables is monitored explicitly during the solution of the subproblem. Moreover, each subproblem may be regularized by imposing explicit bounds on the dual variables. Two primal-dual variants of conventional primal methods are proposed: a primal-dual bound constrained Lagrangian (pdBCL) method and a primal-dual $\ell$1 linearly constrained Lagrangian (pd$\ell$1-LCL) method

Renal Function in Suckling and Fasting Pups of the Northern Elephant Seal

Elephant seals fast for prolonged periods without access to water. This is made possible, in part, by reductions in urine production. However, the mechanisms involved in reducing urine production are not understood. In this study, glomerular filtration rate (GFR) was measured in five northern elephant seal pups (Mirounga angustirostris) via the inulin clearance technique. Measurements were made during day 9 and day 18–22 of nursing and the second and eighth week of the postweaning fast. Plasma aldosterone and cortisol concentrations, quantified by radioimmunoassay, were measured in eight other weanlings during the second and eighth week of the fast. Mean GFR was 79.3±29.3 ml/min during the early suckling period and 78.2±17.1, 89.8±52.7, and 80.4±12.2 ml/min during the late suckling, early fasting and late fasting periods, respectively. Differences between nursing and fasting were insignificant, possibly because reduced protein oxidation during suckling and rapid recruitment of protein for tissue synthesis obviated the need for postprandial hyperfiltration. Alternatively, maintenance of GFR during fasting may facilitate urea concentration by compensating for reductions in the fractional excretion of urea. It is further hypothesized that aldosterone is primarily responsible for mediating renal water reabsorption in this system

Feynman path-integral approach to the QED3 theory of the pseudogap

In this work the connection between vortex condensation in a d-wave superconductor and the QED$_3$ gauge theory of the pseudogap is elucidated. The approach taken circumvents the use of the standard Franz-Tesanovic gauge transformation, borrowing ideas from the path-integral analysis of the Aharonov-Bohm problem. An essential feature of this approach is that gauge-transformations which are prohibited on a particular multiply-connected manifold (e.g. a superconductor with vortices) can be successfully performed on the universal covering space associated with that manifold.Comment: 15 pages, 1 Figure. Int. J. Mod. Phys. B 17, 4509 (2003). Minor changes from previous versio

The Political Economy of Fiscal Policy

If there has been a dominant trend in the evolution of the modern industrial societies of this century it has been the growing importance of government in the allocation of social resources. It is important that we appreciate the fundamentally political nature of the formation of government economic policy. This survey reviews and assesses our present understanding of how the political system might shape a nation's fiscal policy. Our approach is eclectic, drawing both from economics and political science, and decidedly micro-analytic in its orientation. From economics we adopt the perspective of utility maximizing agents and the analytics of trade, agreement, and market failure. From political science we learn just how and when these individual agents might act collectively to provide public goods, redistribute income, or issue government debt. Together the micro-analytics of economics and political science form the core theory of the 'new' political economy and provide a framework for understanding the emergence, and the performance, of governments. There is no more important test for the new discipline than providing a compelling explanation for the formation of fiscal policy in democratic societies.

Coordinated Robot Navigation via Hierarchical Clustering

We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the continuous space of configurations to the combinatorial space of trees. We formalize and exploit this relation, developing computationally effective reactive algorithms for navigating through the combinatorial space in concert with geometric realizations for a particular choice of hierarchical clustering method. These constructions yield computationally effective vector field planners for both hierarchically invariant as well as transitional navigation in the configuration space. We apply these methods to the centralized coordination and control of $n$ perfectly sensed and actuated Euclidean spheres in a $d$-dimensional ambient space (for arbitrary $n$ and $d$). Given a desired configuration supporting a desired hierarchy, we construct a hybrid controller which is quadratic in $n$ and algebraic in $d$ and prove that its execution brings all but a measure zero set of initial configurations to the desired goal with the guarantee of no collisions along the way.Comment: 29 pages, 13 figures, 8 tables, extended version of a paper in preparation for submission to a journa