23,195 research outputs found
Dancing with black holes
We describe efforts over the last six years to implement regularization
methods suitable for studying one or more interacting black holes by direct
N-body simulations. Three different methods have been adapted to large-N
systems: (i) Time-Transformed Leapfrog, (ii) Wheel-Spoke, and (iii) Algorithmic
Regularization. These methods have been tried out with some success on
GRAPE-type computers. Special emphasis has also been devoted to including
post-Newtonian terms, with application to moderately massive black holes in
stellar clusters. Some examples of simulations leading to coalescence by
gravitational radiation will be presented to illustrate the practical
usefulness of such methods.Comment: 8 figures, 10 pages, to appear in "Dynamical Evolution of Dense
Stellar Systems", ed. E. Vesperin
Stepping Stones to Inductive Synthesis of Low-Level Looping Programs
Inductive program synthesis, from input/output examples, can provide an
opportunity to automatically create programs from scratch without presupposing
the algorithmic form of the solution. For induction of general programs with
loops (as opposed to loop-free programs, or synthesis for domain-specific
languages), the state of the art is at the level of introductory programming
assignments. Most problems that require algorithmic subtlety, such as fast
sorting, have remained out of reach without the benefit of significant
problem-specific background knowledge. A key challenge is to identify cues that
are available to guide search towards correct looping programs. We present
MAKESPEARE, a simple delayed-acceptance hillclimbing method that synthesizes
low-level looping programs from input/output examples. During search, delayed
acceptance bypasses small gains to identify significantly-improved stepping
stone programs that tend to generalize and enable further progress. The method
performs well on a set of established benchmarks, and succeeds on the
previously unsolved "Collatz Numbers" program synthesis problem. Additional
benchmarks include the problem of rapidly sorting integer arrays, in which we
observe the emergence of comb sort (a Shell sort variant that is empirically
fast). MAKESPEARE has also synthesized a record-setting program on one of the
puzzles from the TIS-100 assembly language programming game.Comment: AAAI 201
Probing quantum-classical boundary with compression software
We experimentally demonstrate that it is impossible to simulate quantum
bipartite correlations with a deterministic universal Turing machine. Our
approach is based on the Normalized Information Distance (NID) that allows the
comparison of two pieces of data without detailed knowledge about their origin.
Using NID, we derive an inequality for output of two local deterministic
universal Turing machines with correlated inputs. This inequality is violated
by correlations generated by a maximally entangled polarization state of two
photons. The violation is shown using a freely available lossless compression
program. The presented technique may allow to complement the common statistical
interpretation of quantum physics by an algorithmic one.Comment: 7 pages, 6 figure
Algorithmic complexity for psychology: A user-friendly implementation of the coding theorem method
Kolmogorov-Chaitin complexity has long been believed to be impossible to
approximate when it comes to short sequences (e.g. of length 5-50). However,
with the newly developed \emph{coding theorem method} the complexity of strings
of length 2-11 can now be numerically estimated. We present the theoretical
basis of algorithmic complexity for short strings (ACSS) and describe an
R-package providing functions based on ACSS that will cover psychologists'
needs and improve upon previous methods in three ways: (1) ACSS is now
available not only for binary strings, but for strings based on up to 9
different symbols, (2) ACSS no longer requires time-consuming computing, and
(3) a new approach based on ACSS gives access to an estimation of the
complexity of strings of any length. Finally, three illustrative examples show
how these tools can be applied to psychology.Comment: to appear in "Behavioral Research Methods", 14 pages in journal
format, R package at http://cran.r-project.org/web/packages/acss/index.htm
Application of block Krylov subspace algorithms to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD
It is well known that the block Krylov subspace solvers work efficiently for
some cases of the solution of differential equations with multiple right-hand
sides. In lattice QCD calculation of physical quantities on a given
configuration demands us to solve the Dirac equation with multiple sources. We
show that a new block Krylov subspace algorithm recently proposed by the
authors reduces the computational cost significantly without loosing numerical
accuracy for the solution of the O(a)-improved Wilson-Dirac equation.Comment: 12 pages, 5 figure
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