A chain theorem for internally 4-connected binary matroids

This is the post-print version of the Article - Copyright @ 2011 ElsevierLet M be a matroid. When M is 3-connected, Tutte’s Wheels-and-Whirls Theorem proves that M has a 3-connected proper minor N with |E(M) − E(N)| = 1 unless M is a wheel or a whirl. This paper establishes a corresponding result for internally 4-connected binary matroids. In particular, we prove that if M is such a matroid, then M has an internally 4-connected proper minor N with |E(M) − E(N)| at most 3 unless M or its dual is the cycle matroid of a planar or Möbius quartic ladder, or a 16-element variant of such a planar ladder.This study was partially supported by the National Security Agency

Towards a splitter theorem for internally 4-connected binary matroids

This is the post-print version of the Article - Copyright @ 2012 ElsevierWe prove that if M is a 4-connected binary matroid and N is an internally 4-connected proper minor of M with at least 7 elements, then, unless M is a certain 16-element matroid, there is an element e of E(M) such that either M\e or M/e is internally 4-connected having an N-minor. This strengthens a result of Zhou and is a first step towards obtaining a splitter theorem for internally 4-connected binary matroids.This study is partially funded by Marsden Fund of New Zealand and the National Security Agency

Feynman graph polynomials

The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.Comment: 35 pages, references adde

Nonpolar resistance switching of metal/binary-transition-metal oxides/metal sandwiches: homogeneous/inhomogeneous transition of current distribution

Exotic features of a metal/oxide/metal (MOM) sandwich, which will be the basis for a drastically innovative nonvolatile memory device, is brought to light from a physical point of view. Here the insulator is one of the ubiquitous and classic binary-transition-metal oxides (TMO), such as Fe2O3, NiO, and CoO. The sandwich exhibits a resistance that reversibly switches between two states: one is a highly resistive off-state and the other is a conductive on-state. Several distinct features were universally observed in these binary TMO sandwiches: namely, nonpolar switching, non-volatile threshold switching, and current--voltage duality. From the systematic sample-size dependence of the resistance in on- and off-states, we conclude that the resistance switching is due to the homogeneous/inhomogeneous transition of the current distribution at the interface.Comment: 7 pages, 5 figures, REVTeX4, submitted to Phys. Rev. B (Feb. 23, 2007). If you can't download a PDF file of this manscript, an alternative one can be found on the author's website: http://staff.aist.go.jp/i.inoue

Micro-cooler Enhancements by Barrier Interface Analysis

Peer reviewedPublisher PD

Historical wealth accounts for Britain : progress and puzzles in measuring the sustainability of economic growth

We thank the Leverhulme Trust for funding this research under the project ‘History and the Future’.Estimates of Britain's comprehensive wealth are reported for the period 1760-2000. They include measures of produced, natural, and human capital, and illustrate the changing composition of Britain's assets over this time period. We show how genuine savings, GS (a year-on-year measure of the change in total capital and a claimed indicator of sustainable development) has evolved over time. Changes in total wealth are compared to alternative, investment-based measures of GS, including variants augmented with the value of exogenous technology. Additionally, the possible effects of population change on wealth, and the implications of including carbon-dioxide emissions in natural capital are considered.PostprintPeer reviewe

Spectroscopic imaging of single atoms within a bulk solid

The ability to localize, identify and measure the electronic environment of individual atoms will provide fundamental insights into many issues in materials science, physics and nanotechnology. We demonstrate, using an aberration-corrected scanning transmission microscope, the spectroscopic imaging of single La atoms inside CaTiO3. Dynamical simulations confirm that the spectroscopic information is spatially confined around the scattering atom. Furthermore we show how the depth of the atom within the crystal may be estimated.Comment: 4 pages and 3 figures. Accepted in Phys.Rev.Let

Suppression of Octahedral Tilts and Associated Changes of Electronic Properties at Epitaxial Oxide Heterostructure Interfaces

Epitaxial oxide interfaces with broken translational symmetry have emerged as a central paradigm behind the novel behaviors of oxide superlattices. Here, we use scanning transmission electron microscopy to demonstrate a direct, quantitative unit-cell-by-unit-cell mapping of lattice parameters and oxygen octahedral rotations across the BiFeO3-La0.7Sr0.3MnO3 interface to elucidate how the change of crystal symmetry is accommodated. Combined with low-loss electron energy loss spectroscopy imaging, we demonstrate a mesoscopic antiferrodistortive phase transition and elucidate associated changes in electronic properties in a thin layer directly adjacent to the interface