A semismooth newton method for the nearest Euclidean distance matrix problem

The Nearest Euclidean distance matrix problem (NEDM) is a fundamentalcomputational problem in applications such asmultidimensional scaling and molecularconformation from nuclear magnetic resonance data in computational chemistry.Especially in the latter application, the problem is often large scale with the number ofatoms ranging from a few hundreds to a few thousands.In this paper, we introduce asemismooth Newton method that solves the dual problem of (NEDM). We prove that themethod is quadratically convergent.We then present an application of the Newton method to NEDM with $H$-weights.We demonstrate the superior performance of the Newton method over existing methodsincluding the latest quadratic semi-definite programming solver.This research also opens a new avenue towards efficient solution methods for the molecularembedding problem

Topological change of the Fermi surface in ternary iron-pnictides with reduced c/a ratio: A dHvA study of CaFe2P2

We report a de Haas-van Alphen effect study of the Fermi surface of CaFe2P2 using low temperature torque magnetometry up to 45 T. This system is a close structural analogue of the collapsed tetragonal non-magnetic phase of CaFe2As2. We find the Fermi surface of CaFe2P2 to differ from other related ternary phosphides in that its topology is highly dispersive in the c-axis, being three-dimensional in character and with identical mass enhancement on both electron and hole pockets (~1.5). The dramatic change in topology of the Fermi surface suggests that in a state with reduced (c/a) ratio, when bonding between pnictogen layers becomes important, the Fermi surface sheets are unlikely to be nested

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

Assessment of the kidneys: magnetic resonance angiography, perfusion and diffusion

Renal magnetic resonance (MR) imaging has undergone major improvements in the past several years. This review focuses on the technical basics and clinical applications of MR angiography (MRA) with the goal of enabling readers to acquire high-resolution, high quality renal artery MRA. The current role of contrast agents and their safe use in patients with renal impairment is discussed. In addition, an overview of promising techniques on the horizon for renal MR is provided. The clinical value and specific applications of renal MR are critically discussed

Spectral properties of distance matrices

Distance matrices are matrices whose elements are the relative distances between points located on a certain manifold. In all cases considered here all their eigenvalues except one are non-positive. When the points are uncorrelated and randomly distributed we investigate the average density of their eigenvalues and the structure of their eigenfunctions. The spectrum exhibits delocalized and strongly localized states which possess different power-law average behaviour. The exponents depend only on the dimensionality of the manifold.Comment: 31 pages, 9 figure

Metric trees of generalized roundness one

Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is to identify some large classes of countable metric trees that have generalized roundness precisely one. At the outset we consider spherically symmetric trees endowed with the usual combinatorial metric (SSTs). Using a simple geometric argument we show how to determine decent upper bounds on the generalized roundness of finite SSTs that depend only on the downward degree sequence of the tree in question. By considering limits it follows that if the downward degree sequence $(d_{0}, d_{1}, d_{2}...)$ of a SST $(T,\rho)$ satisfies $|\{j \, | \, d_{j} > 1 \}| = \aleph_{0}$, then $(T,\rho)$ has generalized roundness one. Included among the trees that satisfy this condition are all complete $n$-ary trees of depth $\infty$ ($n \geq 2$), all $k$-regular trees ($k \geq 3$) and inductive limits of Cantor trees. The remainder of the paper deals with two classes of countable metric trees of generalized roundness one whose members are not, in general, spherically symmetric. The first such class of trees are merely required to spread out at a sufficient rate (with a restriction on the number of leaves) and the second such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table

Heavy quasiparticles in the ferromagnetic superconductor ZrZn2

We report a study of the de Haas-van Alphen effect in the normal state of the ferromagnetic superconductor ZrZn2. Our results are generally consistent with an LMTO band structure calculation which predicts four exchange-split Fermi surface sheets. Quasiparticle effective masses are enhanced by a factor of about 4.9 implying a strong coupling to magnetic excitations or phonons. Our measurements provide insight in to the mechanism for superconductivity and unusual thermodynamic properties of ZrZn2.Comment: 5 pages, 2 figures (one color

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

Full oxide heterostructure combining a high-Tc diluted ferromagnet with a high-mobility conductor

We report on the growth of heterostructures composed of layers of the high-Curie temperature ferromagnet Co-doped (La,Sr)TiO3 (Co-LSTO) with high-mobility SrTiO3 (STO) substrates processed at low oxygen pressure. While perpendicular spin-dependent transport measurements in STO//Co-LSTO/LAO/Co tunnel junctions demonstrate the existence of a large spin polarization in Co-LSTO, planar magnetotransport experiments on STO//Co-LSTO samples evidence electronic mobilities as high as 10000 cm2/Vs at T = 10 K. At high enough applied fields and low enough temperatures (H < 60 kOe, T < 4 K) Shubnikov-de Haas oscillations are also observed. We present an extensive analysis of these quantum oscillations and relate them with the electronic properties of STO, for which we find large scattering rates up to ~ 10 ps. Thus, this work opens up the possibility to inject a spin-polarized current from a high-Curie temperature diluted oxide into an isostructural system with high-mobility and a large spin diffusion length.Comment: to appear in Phys. Rev.

Interplay of size and Landau quantizations in the de Haas-van Alphen oscillations of metallic nanowires

We examine the interplay between size quantization and Landau quantization in the De Haas-Van Alphen oscillations of clean, metallic nanowires in a longitudinal magnetic field for `hard' boundary conditions, i.e. those of an infinite round well, as opposed to the `soft' parabolically confined boundary conditions previously treated in Alexandrov and Kabanov (Phys. Rev. Lett. {\bf 95}, 076601 (2005) (AK)). We find that there exist {\em two} fundamental frequencies as opposed to the one found in bulk systems and the three frequencies found by AK with soft boundary counditions. In addition, we find that the additional `magic resonances' of AK may be also observed in the infinite well case, though they are now damped. We also compare the numerically generated energy spectrum of the infinite well potential with that of our analytic approximation, and compare calculations of the oscillatory portions of the thermodynamic quantities for both models.Comment: Title changed, paper streamlined on suggestion of referrees, typos corrected, numerical error in figs 2 and 3 corrected and final result simplified -- two not three frequencies (as in the previous version) are observed. Abstract altered accordingly. Submitted to Physical Review