L1TV computes the flat norm for boundaries

We show that the recently introduced L1TV functional can be used to explicitly compute the flat norm for co-dimension one boundaries. While this observation alone is very useful, other important implications for image analysis and shape statistics include a method for denoising sets which are not boundaries or which have higher co-dimension and the fact that using the flat norm to compute distances not only gives a distance, but also an informative decomposition of the distance. This decomposition is made to depend on scale using the "flat norm with scale" which we define in direct analogy to the L1TV functional. We illustrate the results and implications with examples and figures

Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs on the unit sphere $S^2$, in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group $SU(1,1) = Sp(2, R) = SL(2,R)$, the double cover of SO(2,1). The present work develops a theory of turns for $SL(2,C)$, the double and universal cover of SO(3,1) and $SO(3,C)$, rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late

Peres-Horodecki separability criterion for continuous variable systems

The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states. The partial transpose operation admits, in the continuous case, a geometric interpretation as mirror reflection in phase space. This recognition leads to uncertainty principles, stronger than the traditional ones, to be obeyed by all separable states. For all bipartite Gaussian states, the Peres-Horodecki criterion turns out to be necessary and sufficient condition for separability.Comment: 6 pages, no figure

Comment on ``Evidence for Anisotropic State of Two-Dimensional Electrons in High Landau Levels''

In a recent letter M. Lilly et al [PRL 82, 394 (1999)] have shown that a highly anisotropic state can arise in certain two dimensional electron systems. In the large square samples studied, resistances measured in the two perpendicular directions are found to have a ratio that may be 60 or larger at low temperature and at certain magnetic fields. In Hall bar measurements, the anisotropy ratio is found to be much smaller (roughly 5). In this comment we resolve this discrepancy by noting that the anisotropy of the underlying sheet resistivities is correctly represented by Hall bar resistance measurements but shows up exponentially enhanced in resistance measurements on square samples due to simple geometric effects. We note, however, that the origin of this underlying resistivity anisotropy remains unknown, and is not addressed here.Comment: 1 page, minor calculational error repaire

Quantum Computing: Pro and Con

I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; I discuss recently developed fault-tolerant procedures that enable a quantum computer with noisy gates to perform reliably. Quantum computing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantum computation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in high-precision experimental physics. A broad interdisciplinary effort will be needed if quantum computers are to fulfill their destiny as the world's fastest computing devices. (This paper is an expanded version of remarks that were prepared for a panel discussion at the ITP Conference on Quantum Coherence and Decoherence, 17 December 1996.)Comment: 17 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor correction

Contextual and interdependent causes of climate change adaptation barriers: Insights from water management institutions in Himachal Pradesh, India

Research on adaptation barriers is increasing as the need for climate change adaptation becomes evident. However, empirical studies regarding the emergence, causes and sustenance of adaptation barriers remain limited. This research identifies key contextual causes of adaptation barriers in water institutions in the mountainous Himalayan state of Himachal Pradesh in northern India. Semi-structured interviews were carried out with representatives from twenty-six key governmental, non-governmental, academic and research institutions in the State with responsibilities spanning domestic water supply, irrigation and hydropower generation, environmental monitoring and research. It identified low knowledge capacity and resources, policy implementation gaps, normative attitudes, and unavailability and inaccessibility of data and information compounded with weak interinstitutional networks as key adaptation barriers. Although these barriers are similar to those reported elsewhere, they have important locally-contextual root causes. For instance, inadequate resources result from fragmented resources allocation due to competing developmental priorities and the desire of the political leadership to please diverse electors, rather than climate scepticism. The identified individual barriers are found to be highly inter-dependent and closely intertwined which enables the identification of leverage points for interventions to maximise barrier removal. For instance, breaking down key barriers hindering accessibility to data and information, which are shaped by systemic bureaucracies and cultural attitudes, will involve attitudinal change through sensitisation to the importance of accurate and accessible data and information and the building trust between different actors, in addition to institutional structural changes through legislation and inter-institutional agreements. Approaching barriers as a system of contextually interconnected cultural, systemic, geographical and political underlying factors enriches the understanding of adaptation enablers, thereby contributing to achieving a better adapted society

A Matlab Implementation of a Flat Norm Motivated Polygonal Edge Matching Method using a Decomposition of Boundary into Four 1-Dimensional Currents

We describe and provide code and examples for a polygonal edge matching method.Comment: Contains Matlab code and 4 figure

Comparative genome analysis of Wolbachia strain wAu

BACKGROUND: Wolbachia intracellular bacteria can manipulate the reproduction of their arthropod hosts, including inducing sterility between populations known as cytoplasmic incompatibility (CI). Certain strains have been identified that are unable to induce or rescue CI, including wAu from Drosophila. Genome sequencing and comparison with CI-inducing related strain wMel was undertaken in order to better understand the molecular basis of the phenotype. RESULTS: Although the genomes were broadly similar, several rearrangements were identified, particularly in the prophage regions. Many orthologous genes contained single nucleotide polymorphisms (SNPs) between the two strains, but a subset containing major differences that would likely cause inactivation in wAu were identified, including the absence of the wMel ortholog of a gene recently identified as a CI candidate in a proteomic study. The comparative analyses also focused on a family of transcriptional regulator genes implicated in CI in previous work, and revealed numerous differences between the strains, including those that would have major effects on predicted function. CONCLUSIONS: The study provides support for existing candidates and novel genes that may be involved in CI, and provides a basis for further functional studies to examine the molecular basis of the phenotype

Current-induced metallic behavior in Pr0.5_{0.5}Ca0.5_{0.5}MnO3_3 thin films: competition between Joule heating and nonlinear conduction mechanism

Thin films of Pr0.5Ca0.5MnO3 manganites exhibiting charge/orbital-ordered properties with colossal magnetoresistance have been synthesized by the pulsed laser deposition technique on both (100)-SrTiO3 and (100)-LaAlO3 substrates. The effects of current-induced metallic-behavior of the films are investigated as a function of the temperature and the magnetic field. Calculations based on a heat transfer model across the substrate, and our resistivity measurements reveal effects of Joule heating on charge transport over certain ranges of temperatures and magnetic fields. Our results also indicate that a nonlinear conduction, which cannot be explained by homogeneous Joule heating of the film, is observed when the material is less resistive (10-2 W.cm). The origin of this behavior is explained with a model based on local thermal instabilities associated with phase-separation mechanism and a change in the long range charge-ordered state.Comment: To be published in Phys. Rev.