152,113 research outputs found
A computational approach to the Thompson group
Let denote the Thompson group with standard generators , .
It is a long standing open problem whether is an amenable group. By a
result of Kesten from 1959, amenability of is equivalent to and to where in both
cases the norm of an element in the group ring is computed in
via the regular representation of . By extensive numerical
computations, we obtain precise lower bounds for the norms in and ,
as well as good estimates of the spectral distributions of
and of with respect to the tracial state on the
group von Neumann Algebra . Our computational results suggest, that
It is
however hard to obtain precise upper bounds for the norms, and our methods
cannot be used to prove non-amenability of .Comment: appears in International Journal of Algebra and Computation (2015
Soliton Dynamics in Computational Anatomy
Computational anatomy (CA) has introduced the idea of anatomical structures
being transformed by geodesic deformations on groups of diffeomorphisms. Among
these geometric structures, landmarks and image outlines in CA are shown to be
singular solutions of a partial differential equation that is called the
geodesic EPDiff equation. A recently discovered momentum map for singular
solutions of EPDiff yields their canonical Hamiltonian formulation, which in
turn provides a complete parameterization of the landmarks by their canonical
positions and momenta. The momentum map provides an isomorphism between
landmarks (and outlines) for images and singular soliton solutions of the
EPDiff equation. This isomorphism suggests a new dynamical paradigm for CA, as
well as new data representation.Comment: published in NeuroImag
CASTRO: A New Compressible Astrophysical Solver. III. Multigroup Radiation Hydrodynamics
We present a formulation for multigroup radiation hydrodynamics that is
correct to order using the comoving-frame approach and the
flux-limited diffusion approximation. We describe a numerical algorithm for
solving the system, implemented in the compressible astrophysics code, CASTRO.
CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement
based on a nested hierarchy of logically-rectangular variable-sized grids with
simultaneous refinement in both space and time. In our multigroup radiation
solver, the system is split into three parts, one part that couples the
radiation and fluid in a hyperbolic subsystem, another part that advects the
radiation in frequency space, and a parabolic part that evolves radiation
diffusion and source-sink terms. The hyperbolic subsystem and the frequency
space advection are solved explicitly with high-order Godunov schemes, whereas
the parabolic part is solved implicitly with a first-order backward Euler
method. Our multigroup radiation solver works for both neutrino and photon
radiation.Comment: accepted by ApJS, 27 pages, 20 figures, high-resolution version
available at https://ccse.lbl.gov/Publications/wqzhang/castro3.pd
A Personalized System for Conversational Recommendations
Searching for and making decisions about information is becoming increasingly
difficult as the amount of information and number of choices increases.
Recommendation systems help users find items of interest of a particular type,
such as movies or restaurants, but are still somewhat awkward to use. Our
solution is to take advantage of the complementary strengths of personalized
recommendation systems and dialogue systems, creating personalized aides. We
present a system -- the Adaptive Place Advisor -- that treats item selection as
an interactive, conversational process, with the program inquiring about item
attributes and the user responding. Individual, long-term user preferences are
unobtrusively obtained in the course of normal recommendation dialogues and
used to direct future conversations with the same user. We present a novel user
model that influences both item search and the questions asked during a
conversation. We demonstrate the effectiveness of our system in significantly
reducing the time and number of interactions required to find a satisfactory
item, as compared to a control group of users interacting with a non-adaptive
version of the system
Two-dimensional, Time-dependent, Multi-group, Multi-angle Radiation Hydrodynamics Test Simulation in the Core-Collapse Supernova Context
We have developed a time-dependent, multi-energy-group, and multi-angle
(S) Boltzmann transport scheme for radiation hydrodynamics simulations, in
one and two spatial dimensions. The implicit transport is coupled to both 1D
(spherically-symmetric) and 2D (axially-symmetric) versions of the explicit
Newtonian hydrodynamics code VULCAN. The 2D variant, VULCAN/2D, can be operated
in general structured or unstructured grids and though the code can address
many problems in astrophysics it was constructed specifically to study the
core-collapse supernova problem. Furthermore, VULCAN/2D can simulate the
radiation/hydrodynamic evolution of differentially rotating bodies. We
summarize the equations solved and methods incorporated into the algorithm and
present results of a time-dependent 2D test calculation. A more complete
description of the algorithm is postponed to another paper. We highlight a 2D
test run that follows for 22 milliseconds the immediate post-bounce evolution
of a collapsed core. We present the relationship between the anisotropies of
the overturning matter field and the distribution of the corresponding flux
vectors, as a function of energy group. This is the first 2D multi-group,
multi-angle, time-dependent radiation/hydro calculation ever performed in core
collapse studies. Though the transport module of the code is not gray and does
not use flux limiters (however, there is a flux-limited variant of VULCAN/2D),
it still does not include energy redistribution and most velocity-dependent
terms.Comment: 19 pages, plus 13 figures in JPEG format. Submitted to the
Astrophysical Journa
Observation of large-scale multi-agent based simulations
The computational cost of large-scale multi-agent based simulations (MABS)
can be extremely important, especially if simulations have to be monitored for
validation purposes. In this paper, two methods, based on self-observation and
statistical survey theory, are introduced in order to optimize the computation
of observations in MABS. An empirical comparison of the computational cost of
these methods is performed on a toy problem
All mixed up? Finding the optimal feature set for general readability prediction and its application to English and Dutch
Readability research has a long and rich tradition, but there has been too little focus on general readability prediction without targeting a specific audience or text genre. Moreover, though NLP-inspired research has focused on adding more complex readability features there is still no consensus on which features contribute most to the prediction. In this article, we investigate in close detail the feasibility of constructing a readability prediction system for English and Dutch generic text using supervised machine learning. Based on readability assessments by both experts
and a crowd, we implement different types of text characteristics ranging from easy-to-compute superficial text characteristics to features requiring a deep linguistic processing, resulting in ten
different feature groups. Both a regression and classification setup are investigated reflecting the two possible readability prediction tasks: scoring individual texts or comparing two texts. We show that going beyond correlation calculations for readability optimization using a wrapper-based genetic algorithm optimization approach is a promising task which provides considerable insights in which feature combinations contribute to the overall readability prediction. Since we also have gold standard information available for those features requiring deep processing we are able to investigate the true upper bound of our Dutch system. Interestingly, we will observe that the performance of our fully-automatic readability prediction pipeline is on par with the pipeline using golden deep syntactic and semantic information
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