11,532 research outputs found
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Truncated Moment Problem for Dirac Mixture Densities with Entropy Regularization
We assume that a finite set of moments of a random vector is given. Its
underlying density is unknown. An algorithm is proposed for efficiently
calculating Dirac mixture densities maintaining these moments while providing a
homogeneous coverage of the state space.Comment: 18 pages, 6 figure
Algorithms and Data Structures for Multi-Adaptive Time-Stepping
Multi-adaptive Galerkin methods are extensions of the standard continuous and
discontinuous Galerkin methods for the numerical solution of initial value
problems for ordinary or partial differential equations. In particular, the
multi-adaptive methods allow individual and adaptive time steps to be used for
different components or in different regions of space. We present algorithms
for efficient multi-adaptive time-stepping, including the recursive
construction of time slabs and adaptive time step selection. We also present
data structures for efficient storage and interpolation of the multi-adaptive
solution. The efficiency of the proposed algorithms and data structures is
demonstrated for a series of benchmark problems.Comment: ACM Transactions on Mathematical Software 35(3), 24 pages (2008
Better estimates from binned income data: Interpolated CDFs and mean-matching
Researchers often estimate income statistics from summaries that report the
number of incomes in bins such as \$0-10,000, \$10,001-20,000,...,\$200,000+.
Some analysts assign incomes to bin midpoints, but this treats income as
discrete. Other analysts fit a continuous parametric distribution, but the
distribution may not fit well.
We fit nonparametric continuous distributions that reproduce the bin counts
perfectly by interpolating the cumulative distribution function (CDF). We also
show how both midpoints and interpolated CDFs can be constrained to reproduce
the mean of income when it is known.
We compare the methods' accuracy in estimating the Gini coefficients of all
3,221 US counties. Fitting parametric distributions is very slow. Fitting
interpolated CDFs is much faster and slightly more accurate. Both interpolated
CDFs and midpoints give dramatically better estimates if constrained to match a
known mean.
We have implemented interpolated CDFs in the binsmooth package for R. We have
implemented the midpoint method in the rpme command for Stata. Both
implementations can be constrained to match a known mean.Comment: 20 pages (including Appendix), 3 tables, 2 figures (+2 in Appendix
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