Geodesics on Lie groups: Euler equations and totally geodesic subgroup

The geodesic motion on a Lie group equipped with a left or right invariant Riemannian metric is governed by the Euler-Arnold equation. This paper investigates conditions on the metric in order for a given subgroup to be totally geodesic. Results on the construction and characterisation of such metrics are given. The setting works both in the classical nite dimensional case, and in the category of in nite dimensional Fr echet Lie groups, in which di eomorphism groups are included. Using the framework we give new examples of both nite and in nite dimensional totally geodesic subgroups. In particular, based on the cross helicity, we construct right invariant metrics such that a given subgroup of exact volume preserving di eomorphisms is totally geodesic. The paper also gives a general framework for the representation of Euler-Arnold equations in arbitrary choice of dual pairing

Antarctic Circumpolar Modes in a Coupled Ocean-Atmosphere Model

Eastward-propagating patterns in anomalous potential temperature and salinity of the Southern Ocean are analyzed in the output of a 1000-year simulation of the global coupled atmosphere–ocean GCM ECHO-G. Such features can be associated with the so-called Antarctic Circumpolar Wave (ACW). It is found that time–longitude diagrams that have traditionally been used to aid the visualization of the ACW are strongly influenced by the width of the bandpass time filtering. This is due to the masking of considerable low-frequency variability that occurs over a broad range of time scales. Frequency–wavenumber analysis of the ACW shows that the eastward-propagating waves do have preferred spectral peaks, but that both the period and wavenumber change erratically when comparing different centuries throughout the simulation. The variability of the ACW on a variety of time scales from interannual to centennial suggests that the waiting time for a sufficient observational record to determine the time scale of variability of the real world ACW (and the associated decadal time scale predictability of climate for southern landmasses) will be a very long one

K-Bit-Swap: a new operator for real-coded evolutionary algorithms

There have been a variety of crossover operators proposed for real-coded genetic algorithms (RCGAs). Such operators recombine values from pairs of strings to generate new solutions. In this article, we present a recombination operator for RCGAs that selects the string locations for change separately randomly in the parent and offspring, enabling solution parts to move within a string, and compare it to mainstream crossover operators in a set of experiments on a range of standard multidimensional optimization problems and a real-world clustering problem. We present two variants of the operator, either selecting bits uniformly at random in both strings or sampling the second bit from a normal distribution centered at the selected location in the first string. While the operator is biased toward exploitation of fitness space, the random selection of the second bit for swapping reduces this bias slightly. Statistical analysis of the experimental results using a nonparametric test shows the advantage of the new recombination operators on our test optimization functions

Learning globally consistent maps by relaxation

Mobile robots require the ability to build their own maps to operate in unknown environments. A fundamental problem is that odometry-based dead reckoning cannot be used to assign accurate global position information to a map because of drift errors caused by wheel slippage. The paper introduces a fast, online method of learning globally consistent maps, using only local metric information. The approach differs from previous work in that it is computationally cheap, easy to implement and is guaranteed to find a globally optimal solution. Experiments are presented in which large, complex environments were successfully mapped by a real robot, and quantitative performance measures are used to assess the quality of the maps obtained

Self-Healing Partial Reconfiguration of an FPGA

The goal of this project, sponsored by General Dynamics, is to create an FPGA-based system capable of detecting and gracefully recovering from errors without compromising system functionality. Previous research developed a prototype for partial reconfiguration, but a major limitation was the need for a PC to partially reprogram the FPGA. By implementing a method of self-reconfiguration and developing a system using triple module redundancy, the FPGA can locate errors and partially self-reconfigure the corrupted areas while maintaining valid system outputs

Geodesic Warps by Conformal Mappings

In recent years there has been considerable interest in methods for diffeomorphic warping of images, with applications e.g.\ in medical imaging and evolutionary biology. The original work generally cited is that of the evolutionary biologist D'Arcy Wentworth Thompson, who demonstrated warps to deform images of one species into another. However, unlike the deformations in modern methods, which are drawn from the full set of diffeomorphism, he deliberately chose lower-dimensional sets of transformations, such as planar conformal mappings. In this paper we study warps of such conformal mappings. The approach is to equip the infinite dimensional manifold of conformal embeddings with a Riemannian metric, and then use the corresponding geodesic equation in order to obtain diffeomorphic warps. After deriving the geodesic equation, a numerical discretisation method is developed. Several examples of geodesic warps are then given. We also show that the equation admits totally geodesic solutions corresponding to scaling and translation, but not to affine transformations

A Multi-signal Variant for the GPU-based Parallelization of Growing Self-Organizing Networks

Among the many possible approaches for the parallelization of self-organizing networks, and in particular of growing self-organizing networks, perhaps the most common one is producing an optimized, parallel implementation of the standard sequential algorithms reported in the literature. In this paper we explore an alternative approach, based on a new algorithm variant specifically designed to match the features of the large-scale, fine-grained parallelism of GPUs, in which multiple input signals are processed at once. Comparative tests have been performed, using both parallel and sequential implementations of the new algorithm variant, in particular for a growing self-organizing network that reconstructs surfaces from point clouds. The experimental results show that this approach allows harnessing in a more effective way the intrinsic parallelism that the self-organizing networks algorithms seem intuitively to suggest, obtaining better performances even with networks of smaller size.Comment: 17 page

On the superposition of mean advective and eddy-induced transports in global ocean heat and salt budgets

Ocean thermal expansion is a large contributor to observed sea level rise, which is expected to continue into the future. However, large uncertainties exist in sea level projections among climate models, partially due to intermodel differences in ocean heat uptake and redistribution of buoyancy. Here, the mechanisms of vertical ocean heat and salt transport are investigated in quasi-steady-state model simulations using the Australian Community Climate and Earth-System Simulator Ocean Model (ACCESS-OM2). New insights into the net effect of key physical processes are gained within the superresidual transport (SRT) framework. In this framework, vertical tracer transport is dominated by downward fluxes associated with the large-scale ocean circulation and upward fluxes induced by mesoscale eddies, with two distinct physical regimes. In the upper ocean, where high-latitude water masses are formed by mixed layer processes, through cooling or salinification, the SRT counteracts those processes by transporting heat and salt downward. In contrast, in the ocean interior, the SRT opposes dianeutral diffusion via upward fluxes of heat and salt, with about 60% of the vertical heat transport occurring in the Southern Ocean. Overall, the SRT is largely responsible for removing newly formed water masses from the mixed layer into the ocean interior, where they are eroded by dianeutral diffusion. Unlike the classical advective–diffusive balance, dianeutral diffusion is bottom intensified above rough bottom topography, allowing an overturning cell to develop in alignment with recent theories. Implications are discussed for understanding the role of vertical tracer transport on the simulation of ocean climate and sea level

Developments in the field of allergy in 2017 through the eyes of Clinical and Experimental Allergy

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146621/1/cea13318.pd