A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem

A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows to compute appropriate homoclinic orbits to the NHIM from which we can infer the existence a chaotic saddle. NHIMs control the phase space transport across an equilibrium point of saddle-centre-...-centre stability type, which is a fundamental mechanism for chemical reactions, capture and escape, scattering, and, more generally, ``transformation'' in many different areas of physics. Consequently, the presented methods and results are of broad interest. The procedure is illustrated for the spatial Hill's problem which is a well known model in celestial mechanics and which gained much interest e.g. in the study of the formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys

Some Empirical Criteria for Attributing Creativity to a Computer Program

Peer reviewedPostprin

Efficient Inflation Estimation

This paper investigates the use of trimmed means as high-frequency estimators of" inflation. The known characteristics of price change distributions, specifically the observation" that they generally exhibit high levels of kurtosis, imply that simple averages of price data are" unlikely to produce efficient estimates of inflation. Trimmed means produce superior estimates" of core inflation,' which we define as a long-run centered moving average of CPI and PPI" inflation. We find that trimming 9% from each tail of the CPI price-change distribution from the tails of the PPI price-change distribution, yields an efficient estimator of core inflation" for these two series, although lesser trims also produce substantial efficiency gains. Historically the optimal trimmed estimators are found to be nearly 23% more efficient (in terms of root-mean-square error) than the standard mean CPI Moreover, the efficient estimators are robust to sample period and to the definition of the" presumed underlying long-run trend in inflation.

Look! It's moving! Is it alive? How movement affects humans' affinity to living and non-living entities

CCBY This article is about the relation between human observers and various human and non-human entities. Our focus is on humans & #x0027; perception of movement. In particular how it affects the relationship to entities. We explore the way the movement of natural entities, locomoting animals and robots or the expressivity of dancers, play a vital part in our perception of these things. Humans & #x0027; intuitive process of categorizing and attributing characteristics as a dialog and understanding of things, as found in the concept of metaphor, is central to our method

New tests of the pp-wave correspondence.

The pp-wave/SYM correspondence is an equivalence relation, H string = Δ-J , between the hamiltonian H string of string field theory in the pp-wave background and the dilatation operator Δ in = 4 Super Yang-Mills in the double scaling limit. We calculate matrix elements of these operators in string field theory and in gauge theory. In the string theory Hilbert space we use the natural string basis, and in the gauge theory we use the basis which is isomorphic to it. States in this basis are specific linear combinations of the original BMN operators, and were constructed previously for the case of two scalar impurities. We extend this construction to incorporate BMN operators with vector and mixed impurities. This enables us to verify from the gauge theory perspective two key properties of the three-string interaction vertex of Spradlin and Volovich: (1) the vanishing of the three-string amplitude for string states with one vector and one scalar impurity; and (2) the relative minus sign in the string amplitude involving states with two vector impurities compared to that with two scalar impurities. This implies a spontaneous breaking of the 2 symmetry of the string field theory in the pp-wave background. Furthermore, we calculate the gauge theory matrix elements of Δ-J for states with an arbitrary number of scalar impurities. In all cases we find perfect agreement with the corresponding string amplitudes derived from the three-string vertex

Harnessing Phenotypic Diversity towards Multiple Independent Objectives

This work was funded by EPSRC through the Media and Arts Technology Programme, an RCUK Doctoral Training Centre EP/G03723X/1. Computational facilities were provided by the MidPlus Regional Centre of Excellence for Computational Science, Engineering and Mathematics, under EPSRC grant EP/K000128/1