6,913 research outputs found
Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes
In diffusion MRI (dMRI), a good sampling scheme is important for efficient
acquisition and robust reconstruction. Diffusion weighted signal is normally
acquired on single or multiple shells in q-space. Signal samples are typically
distributed uniformly on different shells to make them invariant to the
orientation of structures within tissue, or the laboratory coordinate frame.
The Electrostatic Energy Minimization (EEM) method, originally proposed for
single shell sampling scheme in dMRI, was recently generalized to multi-shell
schemes, called Generalized EEM (GEEM). GEEM has been successfully used in the
Human Connectome Project (HCP). However, EEM does not directly address the goal
of optimal sampling, i.e., achieving large angular separation between sampling
points. In this paper, we propose a more natural formulation, called Spherical
Code (SC), to directly maximize the minimal angle between different samples in
single or multiple shells. We consider not only continuous problems to design
single or multiple shell sampling schemes, but also discrete problems to
uniformly extract sub-sampled schemes from an existing single or multiple shell
scheme, and to order samples in an existing scheme. We propose five algorithms
to solve the above problems, including an incremental SC (ISC), a sophisticated
greedy algorithm called Iterative Maximum Overlap Construction (IMOC), an 1-Opt
greedy method, a Mixed Integer Linear Programming (MILP) method, and a
Constrained Non-Linear Optimization (CNLO) method. To our knowledge, this is
the first work to use the SC formulation for single or multiple shell sampling
schemes in dMRI. Experimental results indicate that SC methods obtain larger
angular separation and better rotational invariance than the state-of-the-art
EEM and GEEM. The related codes and a tutorial have been released in DMRITool.Comment: Accepted by IEEE transactions on Medical Imaging. Codes have been
released in dmritool
https://diffusionmritool.github.io/tutorial_qspacesampling.htm
Catch me if you can: is there a runaway-mass black hole in the Orion Nebula Cluster?
We investigate the dynamical evolution of the Orion Nebula Cluster (ONC) by
means of direct N-body integrations. A large fraction of residual gas was
probably expelled when the ONC formed, so we assume that the ONC was much more
compact when it formed compared to its current size, in agreement with the
embedded cluster radius-mass relation from Marks & Kroupa (2012). Hence, we
assume that few-body relaxation played an important role during the initial
phase of evolution of the ONC. In particular, three body interactions among OB
stars likely led to their ejection from the cluster and, at the same time, to
the formation of a massive object via runaway physical stellar collisions. The
resulting depletion of the high mass end of the stellar mass function in the
cluster is one of the important points where our models fit the observational
data. We speculate that the runaway-mass star may have collapsed directly into
a massive black hole (Mbh > 100Msun). Such a dark object could explain the
large velocity dispersion of the four Trapezium stars observed in the ONC core.
We further show that the putative massive black hole is likely to be a member
of a binary system with appr. 70 per cent probability. In such a case, it could
be detected either due to short periods of enhanced accretion of stellar winds
from the secondary star during pericentre passages, or through a measurement of
the motion of the secondary whose velocity would exceed 10 km/s along the whole
orbit.Comment: 10 pages, 6 figures, accepted by Ap
Post-Newtonian Dynamics in Dense Star Clusters: Highly-Eccentric, Highly-Spinning, and Repeated Binary Black Hole Mergers
We present models of realistic globular clusters with post-Newtonian dynamics
for black holes. By modeling the relativistic accelerations and
gravitational-wave emission in isolated binaries and during three- and
four-body encounters, we find that nearly half of all binary black hole mergers
occur inside the cluster, with about 10% of those mergers entering the
LIGO/Virgo band with eccentricities greater than 0.1. In-cluster mergers lead
to the birth of a second generation of black holes with larger masses and high
spins, which, depending on the black hole natal spins, can sometimes be
retained in the cluster and merge again. As a result, globular clusters can
produce merging binaries with detectable spins regardless of the birth spins of
black holes formed from massive stars. These second-generation black holes
would also populate any upper mass gap created by pair-instability supernovae.Comment: 9 pages, 3 figures, 2 appendices. To appear in Physical Review
Letter
A new code for orbit analysis and Schwarzschild modelling of triaxial stellar systems
We review the methods used to study the orbital structure and chaotic
properties of various galactic models and to construct self-consistent
equilibrium solutions by Schwarzschild's orbit superposition technique. These
methods are implemented in a new publicly available software tool, SMILE, which
is intended to be a convenient and interactive instrument for studying a
variety of 2D and 3D models, including arbitrary potentials represented by a
basis-set expansion, a spherical-harmonic expansion with coefficients being
smooth functions of radius (splines), or a set of fixed point masses. We also
propose two new variants of Schwarzschild modelling, in which the density of
each orbit is represented by the coefficients of the basis-set or spline
spherical-harmonic expansion, and the orbit weights are assigned in such a way
as to reproduce the coefficients of the underlying density model. We explore
the accuracy of these general-purpose potential expansions and show that they
may be efficiently used to approximate a wide range of analytic density models
and serve as smooth representations of discrete particle sets (e.g. snapshots
from an N-body simulation), for instance, for the purpose of orbit analysis of
the snapshot. For the variants of Schwarzschild modelling, we use two test
cases - a triaxial Dehnen model containing a central black hole, and a model
re-created from an N-body snapshot obtained by a cold collapse. These tests
demonstrate that all modelling approaches are capable of creating equilibrium
models.Comment: MNRAS, 24 pages, 18 figures. Software is available at
http://td.lpi.ru/~eugvas/smile
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