29,057 research outputs found
Angle Tree: Nearest Neighbor Search in High Dimensions with Low Intrinsic Dimensionality
We propose an extension of tree-based space-partitioning indexing structures
for data with low intrinsic dimensionality embedded in a high dimensional
space. We call this extension an Angle Tree. Our extension can be applied to
both classical kd-trees as well as the more recent rp-trees. The key idea of
our approach is to store the angle (the "dihedral angle") between the data
region (which is a low dimensional manifold) and the random hyperplane that
splits the region (the "splitter"). We show that the dihedral angle can be used
to obtain a tight lower bound on the distance between the query point and any
point on the opposite side of the splitter. This in turn can be used to
efficiently prune the search space. We introduce a novel randomized strategy to
efficiently calculate the dihedral angle with a high degree of accuracy.
Experiments and analysis on real and synthetic data sets shows that the Angle
Tree is the most efficient known indexing structure for nearest neighbor
queries in terms of preprocessing and space usage while achieving high accuracy
and fast search time.Comment: To be submitted to IEEE Transactions on Pattern Analysis and Machine
Intelligenc
Magnetism of CuX2 frustrated chains (X = F, Cl, Br): the role of covalency
Periodic and cluster density-functional theory (DFT) calculations, including
DFT+U and hybrid functionals, are applied to study magnetostructural
correlations in spin-1/2 frustrated chain compounds CuX2: CuCl2, CuBr2, and a
fictitious chain structure of CuF2. The nearest-neighbor and second-neighbor
exchange integrals, J1 and J2, are evaluated as a function of the Cu-X-Cu
bridging angle, theta, in the physically relevant range 80-110deg. In the ionic
CuF2, J1 is ferromagnetic for theta smaller 100deg. For larger angles, the
antiferromagnetic superexchange contribution becomes dominant, in accord with
the Goodenough-Kanamori-Anderson rules. However, both CuCl2 and CuBr2 feature
ferromagnetic J1 in the whole angular range studied. This surprising behavior
is ascribed to the increased covalency in the Cl and Br compounds, which
amplifies the contribution from Hund's exchange on the ligand atoms and renders
J1 ferromagnetic. At the same time, the larger spatial extent of X orbitals
enhances the antiferromagnetic J2, which is realized via the long-range
Cu-X-X-Cu paths. Both, periodic and cluster approaches supply a consistent
description of the magnetic behavior which is in good agreement with the
experimental data for CuCl2 and CuBr2. Thus, owing to their simplicity, cluster
calculations have excellent potential to study magnetic correlations in more
involved spin lattices and facilitate application of quantum-chemical methods
A 3D radiative transfer framework: I. non-local operator splitting and continuum scattering problems
We describe a highly flexible framework to solve 3D radiation transfer
problems in scattering dominated environments based on a long characteristics
piece-wise parabolic formal solution and an operator splitting method. We find
that the linear systems are efficiently solved with iterative solvers such as
Gauss-Seidel and Jordan techniques. We use a sphere-in-a-box test model to
compare the 3D results to 1D solutions in order to assess the accuracy of the
method. We have implemented the method for static media, however, it can be
used to solve problems in the Eulerian-frame for media with low velocity
fields.Comment: A&A, in press. 14 pages, 19 figures. Full resolution figures
available at ftp://phoenix.hs.uni-hamburg.de/preprints/3DRT_paper1.pdf HTML
version (low res figures) at
http://hobbes.hs.uni-hamburg.de/~yeti/PAPERS/3drt_paper1/index.htm
Exact one- and two-particle excitation spectra of acute-angle helimagnets above their saturation magnetic field
The two-magnon problem for the frustrated XXZ spin-1/2 Heisenberg Hamiltonian
and external magnetic fields exceeding the saturation field Bs is considered.
We show that the problem can be exactly mapped onto an effective tight-binding
impurity problem. It allows to obtain explicit exact expressions for the
two-magnon Green's functions for arbitrary dimension and number of
interactions. We apply this theory to a quasi-one dimensional helimagnet with
ferromagnetic nearest neighbor J1 < 0 and antiferromagnetic next-nearest
neighbor J2 > 0 interactions. An outstanding feature of the excitation spectrum
is the existence of two-magnon bound states. This leads to deviations of the
saturation field Bs from its classical value Bs(classical) which coincides with
the one-magnon instability. For the refined frustration ratio |J2/J1|> 0.374661
the minimum of the two-magnon spectrum occurs at the boundary of the Brillouin
zone. Based on the two-magnon approach, we propose general analytic expressions
for the saturation field Bs, confirming known previous results for
one-dimensional isotropic systems, but explore also the role of interchain and
long-ranged intrachain interactions as well as of the exchange anisotropy.Comment: 21 pages, 6 Figures. submitted to Phys. Rev.
Magnetic and superconducting instabilities of the Hubbard model at the van Hove filling
We use a novel temperature-flow renormalization group technique to analyze
magnetic and superconducting instabilities in the two-dimensional t-t' Hubbard
model for particle densities close to the van Hove filling as a function of the
next-nearest neighbor hopping t'. In the one-loop flow at the van Hove filling,
the characteristic temperature for the flow to strong coupling is suppressed
drastically around t'_c approx. -0.33t, suggesting a quantum critical point
between d-wave pairing at moderate t'>t'_c and ferromagnetism for t'<t'_c. Upon
increasing the particle density in the latter regime the leading instability
occurs in the triplet pairing channel.Comment: 4 pages, to appear in Physical Review Letter
Correlation induced electron-hole asymmetry in quasi-2D iridates
We determine the motion of a charge (hole or electron) added to the Mott
insulating, antiferromagnetic (AF) ground-state of quasi-2D iridates such as Ba
2 IrO 4 or Sr 2 IrO 4 . We show that correlation effects, calculated within the
self-consistent Born approximation, render the hole and electron case very
different. An added electron forms a spin-polaron, which closely resembles the
well-known cuprates, but the situation of a removed electron is far more
complex. Many-body 5d 4 configurations form which can be singlet and triplets
of total angular momentum J and strongly affect the hole motion between AF
sublattices. This not only has important ramifications for the interpretation
of (inverse-)photoemission experiments of quasi-2D iridates but also
demonstrates that the correlation physics in electron- and hole-doped iridates
is fundamentally different.Comment: 11 pages main text, 11 pages supplementary, 10 figure
Maximum Inner-Product Search using Tree Data-structures
The problem of {\em efficiently} finding the best match for a query in a
given set with respect to the Euclidean distance or the cosine similarity has
been extensively studied in literature. However, a closely related problem of
efficiently finding the best match with respect to the inner product has never
been explored in the general setting to the best of our knowledge. In this
paper we consider this general problem and contrast it with the existing
best-match algorithms. First, we propose a general branch-and-bound algorithm
using a tree data structure. Subsequently, we present a dual-tree algorithm for
the case where there are multiple queries. Finally we present a new data
structure for increasing the efficiency of the dual-tree algorithm. These
branch-and-bound algorithms involve novel bounds suited for the purpose of
best-matching with inner products. We evaluate our proposed algorithms on a
variety of data sets from various applications, and exhibit up to five orders
of magnitude improvement in query time over the naive search technique.Comment: Under submission in KDD 201
Space Exploration via Proximity Search
We investigate what computational tasks can be performed on a point set in
, if we are only given black-box access to it via nearest-neighbor
search. This is a reasonable assumption if the underlying point set is either
provided implicitly, or it is stored in a data structure that can answer such
queries. In particular, we show the following: (A) One can compute an
approximate bi-criteria -center clustering of the point set, and more
generally compute a greedy permutation of the point set. (B) One can decide if
a query point is (approximately) inside the convex-hull of the point set.
We also investigate the problem of clustering the given point set, such that
meaningful proximity queries can be carried out on the centers of the clusters,
instead of the whole point set
- …