Derivative observations in Gaussian Process models of dynamic systems

Gaussian processes provide an approach to nonparametric modelling which allows a straightforward combination of function and derivative observations in an empirical model. This is of particular importance in identification of nonlinear dynamic systems from experimental data. 1)It allows us to combine derivative information, and associated uncertainty with normal function observations into the learning and inference process. This derivative information can be in the form of priors specified by an expert or identified from perturbation data close to equilibrium. 2) It allows a seamless fusion of multiple local linear models in a consistent manner, inferring consistent models and ensuring that integrability constraints are met. 3) It improves dramatically the computational efficiency of Gaussian process models for dynamic system identification, by summarising large quantities of near-equilibrium data by a handful of linearisations, reducing the training size - traditionally a problem for Gaussian process models

A survey of low-velocity collisional features in Saturn's F ring

Small (~50km scale), irregular features seen in Cassini images to be emanating from Saturn's F ring have been termed mini-jets by Attree et al. (2012). One particular mini-jet was tracked over half an orbital period, revealing its evolution with time and suggesting a collision with a local moonlet as its origin. In addition to these data we present here a much more detailed analysis of the full catalogue of over 800 F ring mini-jets, examining their distribution, morphology and lifetimes in order to place constraints on the underlying moonlet population. We find mini-jets randomly located in longitude around the ring, with little correlation to the moon Prometheus, and randomly distributed in time, over the full Cassini tour to date. They have a tendency to cluster together, forming complicated `multiple' structures, and have typical lifetimes of ~1d. Repeated observations of some features show significant evolution, including the creation of new mini-jets, implying repeated collisions by the same object. This suggests a population of <~1km radius objects with some internal strength and orbits spread over 100km in semi-major axis relative to the F ring but with the majority within 20km. These objects likely formed in the ring under, and were subsequently scattered onto differing orbits by, the perturbing action of Prometheus. This reinforces the idea of the F ring as a region with a complex balance between collisions, disruption and accretion.Comment: 21 pages, 12 figures. Accepted for publication in Icarus. Supplementary information available at http://www.maths.qmul.ac.uk/~attree/mini-jets

An Appraisal of the United States—Philippines\u27 Special Relationship

Since 1898, when the United States acquired possession of the Philippines from Spain, both sides have characterized relations with the other as special. As with other characterizations of this type, special relationship has meant different things at different times. This article will attempt to chip away some of the encrustation that has accumulated upon this term over the years, at least in the economic sphere, and to see what this special economic relationship should mean in the world of the mid-1960\u27s. In the early period of United States administration of the Philippines, the special relationship could perhaps be said to have been motivated by a paternal instinct and an inarticulated but real sense of national mission. While at the outset, the stated intention was to prepare the country for independence, progress along this road was slow in the early years. After World War I, empires began to go out of style, and American attitudes began to be shaped by Wilsonian principles of self-determination. This new philosophy prodded the national conscience further into taking steps to make the Philippines independent. Japanese occupation of the islands during World War II and the joint American-Filipino efforts to win them back added a new facet to the special relationship-a spirit of allied partnership striving for a common goal. Upon independence, the Philippines, responding to assurances given by the United States during the war, looked to Washington for assistance in rebuilding its devastated economy. This search for help was again to shape the relationship. Today, the character of the special relationship, at least from the United States\u27 point of view, is probably a potpourri of all American earlier attitudes towards the Philippines-paternal feelings, conscience, gratitude and moral obligations

Modelling and experimental investigation of carangiform locomotion for control

We propose a model for planar carangiform swimming based on conservative equations for the interaction of a rigid body and an incompressible fluid. We account for the generation of thrust due to vortex shedding through controlled coupling terms. We investigate the correct form of this coupling experimentally with a robotic propulsor, comparing its observed behavior to that predicted by unsteady hydrodynamics. Our analysis of thrust generation by an oscillating hydrofoil allows us to characterize and evaluate certain families of gaits. Our final swimming model takes the form of a control-affine nonlinear system