On Ptolemaic metric simplicial complexes

We show that under certain mild conditions, a metric simplicial complex which satisfies the Ptolemy inequality is a CAT(0) space. Ptolemy's inequality is closely related to inversions of metric spaces. For a large class of metric simplicial complexes, we characterize those which are isometric to Euclidean space in terms of metric inversions.Comment: 13 page

Reflections on Litigating Holocaust Stolen Art Cases

In this Article we have attempted to provide an overview of the Nazi-looted art cases in their historical context. We have based the discussion on our knowledge and experience in litigating art law cases, particularly cases involving Nazi art looting, post-war restitution, and recent developments in art law. Any discussion of the legal implications of crimes committed by Nazi authorities during the Holocaust must begin with an obvious disclaimer. While bringing cases to recover artwork stolen by Nazi authorities is self-evidently a worthy pursuit, and while our firm is very proud to be intensively involved in this effort, we cannot even imagine the extent of the atrocities suffered by our clients\u27 ancestors (and our own) as a result of the high crimes committed against them. It is nonetheless humbly gratifying to work in this area of the law and to think that, in some small way, we are bringing comfort to the victims and their families. In the case of Mrs. Altmann, a vibrant and fascinating 89-year-old woman who vividly recalls the specific location in her uncle and aunt\u27s residence of each Klimt masterpiece she is seeking to recover, this sense of personal gratification is particularly high

Coexistence of two- and three-dimensional Shubnikov-de Haas oscillations in Ar^+ -irradiated KTaO_3

We report the electron doping in the surface vicinity of KTaO_3 by inducing oxygen-vacancies via Ar^+ -irradiation. The doped electrons have high mobility (> 10^4 cm^2/Vs) at low temperatures, and exhibit Shubnikov-de Haas oscillations with both two- and three-dimensional components. A disparity of the extracted in-plane effective mass, compared to the bulk values, suggests mixing of the orbital characters. Our observations demonstrate that Ar^+ -irradiation serves as a flexible tool to study low dimensional quantum transport in 5d semiconducting oxides

Magnetic quantum oscillations in nanowires

Analytical expressions for the magnetization and the longitudinal conductivity of nanowires are derived in a magnetic field, B. We show that the interplay between size and magnetic field energy-level quantizations manifests itself through novel magnetic quantum oscillations in metallic nanowires. There are three characteristic frequencies of de Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillations, F=F_0,F_1, and F_2 in contrast with a single frequency F'_0 in simple bulk metals. The amplitude of oscillations is strongly enhanced in some "magic" magnetic fields. The wire cross-section S can be measured along with the Fermi surface cross-section, S_F

Combination quantum oscillations in canonical single-band Fermi liquids

Chemical potential oscillations mix individual-band frequencies of the de Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) magneto-oscillations in canonical low-dimensional multi-band Fermi liquids. We predict a similar mixing in canonical single-band Fermi liquids, which Fermi-surfaces have two or more extremal cross-sections. Combination harmonics are analysed using a single-band almost two-dimensional energy spectrum. We outline some experimental conditions allowing for resolution of combination harmonics

Fitting Voronoi Diagrams to Planar Tesselations

Given a tesselation of the plane, defined by a planar straight-line graph $G$, we want to find a minimal set $S$ of points in the plane, such that the Voronoi diagram associated with $S$ "fits" \ $G$. This is the Generalized Inverse Voronoi Problem (GIVP), defined in \cite{Trin07} and rediscovered recently in \cite{Baner12}. Here we give an algorithm that solves this problem with a number of points that is linear in the size of $G$, assuming that the smallest angle in $G$ is constant.Comment: 14 pages, 8 figures, 1 table. Presented at IWOCA 2013 (Int. Workshop on Combinatorial Algorithms), Rouen, France, July 201

Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability distributions. The JSD has several interesting properties. It arises in information theory and, unlike the Kullback-Leibler divergence, it is symmetric, always well defined and bounded. We show that the quantum JSD (QJSD) shares with the relative entropy most of the physically relevant properties, in particular those required for a "good" quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.Comment: 14 pages, corrected equation 1

Poroelastic modeling of seismic boundary conditions across afracture

A fracture within a porous background is modeled as a thin porous layer with increased compliance and finite permeability. For small layer thickness, a set of boundary conditions can be derived that relate particle velocity and stress across a fracture, induced by incident poroelastic waves. These boundary conditions are given via phenomenological parameters that can be used to examine and characterize the seismic response of a fracture. One of these parameters, here it is called membrane permeability, is shown through several examples to control the scattering amplitude of the slow P waves for very low-permeability fractures, which in turn controls the intrinsic attenuation of the waves

Size and composition of consumer saving

Saving and investment ; Consumer behavior

On the Schoenberg Transformations in Data Analysis: Theory and Illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A simple distance-based discriminant algorithm illustrates the theory, intimately connected to the Gaussian kernels of Machine Learning