984 research outputs found
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 -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
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
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
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
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
A Generalization of the Convex Kakeya Problem
Given a set of line segments in the plane, not necessarily finite, what is a
convex region of smallest area that contains a translate of each input segment?
This question can be seen as a generalization of Kakeya's problem of finding a
convex region of smallest area such that a needle can be rotated through 360
degrees within this region. We show that there is always an optimal region that
is a triangle, and we give an optimal \Theta(n log n)-time algorithm to compute
such a triangle for a given set of n segments. We also show that, if the goal
is to minimize the perimeter of the region instead of its area, then placing
the segments with their midpoint at the origin and taking their convex hull
results in an optimal solution. Finally, we show that for any compact convex
figure G, the smallest enclosing disk of G is a smallest-perimeter region
containing a translate of every rotated copy of G.Comment: 14 pages, 9 figure
Selenium isotope evidence for pulsed flow of oxidative slab fluids
Isotope systematics of the redox sensitive and chalcophile element selenium (Se) were investigated on exhumed parts of subducted oceanic lithosphere to provide new constraints on slab dehydration conditions during subduction. The samples c,, show increasing delta(82/76)Se(NIST3149 )with higher abundances of fluid mobile elements, comprising a larger range (-1.89 to +0.48 parts per thousand) than that of mantle (-0.13 +/- 0.12 parts per thousand) and altered ocean crust (-0.35 to -0.07 parts per thousand). Our data point to pronounced, local scale redox variations within the subducting crust, wherein oxidative fluids dissolve sulfides and mobilise oxidised Se species. Subsequently recrystallising sulfides preferentially incorporate isotopically lighter, reduced Se, which shifts evolving fluids and late stage sulfides to higher delta Se-82/76(NIST3149). Redistribution of Se by repeated cydes of sulfide reworking within the subducted crust can be reconciled with episodes of oxidised fluid pulses from underlying slab mantle in modem subduction zones
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.
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 of a SST satisfies , then has generalized roundness one. Included among the
trees that satisfy this condition are all complete -ary trees of depth
(), all -regular trees () 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
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