8,875 research outputs found
TMB: Automatic Differentiation and Laplace Approximation
TMB is an open source R package that enables quick implementation of complex
nonlinear random effect (latent variable) models in a manner similar to the
established AD Model Builder package (ADMB, admb-project.org). In addition, it
offers easy access to parallel computations. The user defines the joint
likelihood for the data and the random effects as a C++ template function,
while all the other operations are done in R; e.g., reading in the data. The
package evaluates and maximizes the Laplace approximation of the marginal
likelihood where the random effects are automatically integrated out. This
approximation, and its derivatives, are obtained using automatic
differentiation (up to order three) of the joint likelihood. The computations
are designed to be fast for problems with many random effects (~10^6) and
parameters (~10^3). Computation times using ADMB and TMB are compared on a
suite of examples ranging from simple models to large spatial models where the
random effects are a Gaussian random field. Speedups ranging from 1.5 to about
100 are obtained with increasing gains for large problems. The package and
examples are available at http://tmb-project.org
Asymptotics of Relativistic Spin Networks
The stationary phase technique is used to calculate asymptotic formulae for
SO(4) Relativistic Spin Networks. For the tetrahedral spin network this gives
the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j symbol. For
the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical
calculations of the Spin Network evaluation. Finally we discuss the asymptotics
of the SO(3,1) 10j-symbol.Comment: 31 pages, latex. v3: minor clarification
Implementation of the "hyperdynamics of infrequent events" method for acceleration of thermal switching dynamics of magnetic moments
For acceleration of the calculations of thermal magnetic switching, we report the use of the Voter method, recently proposed in chemical physics (also called "hyperdynamics of the infrequent events"). The method consists of modification of the magnetic potential so that the transition state remains unchanged. We have found that the method correctly describes the mean first passage time even in the case of small damping (precessional case) and for an oblique angle between the anisotropy and the field directions. Due to the costly evaluation of the lowest energy eigenvalue, the actual acceleration depends on its fast computation. In the current implementation, it is limited to intermediate time scale and to small system size
Distributed-memory large deformation diffeomorphic 3D image registration
We present a parallel distributed-memory algorithm for large deformation
diffeomorphic registration of volumetric images that produces large isochoric
deformations (locally volume preserving). Image registration is a key
technology in medical image analysis. Our algorithm uses a partial differential
equation constrained optimal control formulation. Finding the optimal
deformation map requires the solution of a highly nonlinear problem that
involves pseudo-differential operators, biharmonic operators, and pure
advection operators both forward and back- ward in time. A key issue is the
time to solution, which poses the demand for efficient optimization methods as
well as an effective utilization of high performance computing resources. To
address this problem we use a preconditioned, inexact, Gauss-Newton- Krylov
solver. Our algorithm integrates several components: a spectral discretization
in space, a semi-Lagrangian formulation in time, analytic adjoints, different
regularization functionals (including volume-preserving ones), a spectral
preconditioner, a highly optimized distributed Fast Fourier Transform, and a
cubic interpolation scheme for the semi-Lagrangian time-stepping. We
demonstrate the scalability of our algorithm on images with resolution of up to
on the "Maverick" and "Stampede" systems at the Texas Advanced
Computing Center (TACC). The critical problem in the medical imaging
application domain is strong scaling, that is, solving registration problems of
a moderate size of ---a typical resolution for medical images. We are
able to solve the registration problem for images of this size in less than
five seconds on 64 x86 nodes of TACC's "Maverick" system.Comment: accepted for publication at SC16 in Salt Lake City, Utah, USA;
November 201
The phonon drag force acting on a mobile crystal defect: full treatment of discreteness and non-linearity
Phonon scattering calculations predict the drag force acting on defects and
dislocations rises linearly with temperature, in direct contradiction with
molecular dynamics simulations that often finds the drag force to be
independent of temperature. Using the Mori-Zwanzig projection technique, with
no recourse to elasticity or scattering theories, we derive a general Langevin
equation for a crystal defect, with full treatment of discreteness and
non-linearity in the defect core. We obtain an analytical expression for the
drag force that is evaluated in molecular statics and molecular dynamics,
extracting the force on a defect directly from the inter-atomic forces. Our
results show that a temperature independent drag force arises because
vibrations in a discrete crystal are never independent of the defect motion, an
implicit assumption in any phonon-based approach. This effect remains even when
the Peierls barrier is effectively zero, invalidating qualitative explanations
involving the radiation of phonons. We apply our methods to an interstitial
defect in tungsten and solitons in the Frenkel-Kontorova model, finding very
good agreement with trajectory-based estimations of the thermal drag force.Comment: 20 pages, 8 figure
Power of unentangled measurements on two antiparallel spins
We consider a pair of antiparallel spins polarized in a random direction to
encode quantum information. We wish to extract as much information as possible
on the polarization direction attainable by an unentangled measurement, i.e.,
by a measurement, whose outcomes are associated with product states. We develop
analytically the upper bound 0.7935 bits to the Shannon mutual information
obtainable by an unentangled measurement, which is definitely less than the
value 0.8664 bits attained by an entangled measurement. This proves our main
result, that not every ensemble of product states can be optimally
distinguished by an unentangled measurement, if the measure of
distinguishability is defined in the sense of Shannon. We also present results
from numerical calculations and discuss briefly the case of parallel spins.Comment: Latex file, 18 pages, 1 figure; published versio
- …