49,526 research outputs found
Characterising the complexity of tissue P systems with fission rules
We analyse the computational efficiency of tissue P systems, a biologically-inspired computing device modelling the communication between cells. In particular, we focus on tissue P systems with fission rules (cell division and/or cell separation), where the number of cells can increase exponentially during the computation. We prove that the complexity class characterised by these devices in polynomial time is exactly P^#P, the class of problems solved by polynomial-time Turing machines with oracles for counting problems
Computing Aggregate Properties of Preimages for 2D Cellular Automata
Computing properties of the set of precursors of a given configuration is a
common problem underlying many important questions about cellular automata.
Unfortunately, such computations quickly become intractable in dimension
greater than one. This paper presents an algorithm --- incremental aggregation
--- that can compute aggregate properties of the set of precursors
exponentially faster than na{\"i}ve approaches. The incremental aggregation
algorithm is demonstrated on two problems from the two-dimensional binary Game
of Life cellular automaton: precursor count distributions and higher-order mean
field theory coefficients. In both cases, incremental aggregation allows us to
obtain new results that were previously beyond reach
Linear-Space Data Structures for Range Mode Query in Arrays
A mode of a multiset is an element of maximum multiplicity;
that is, occurs at least as frequently as any other element in . Given a
list of items, we consider the problem of constructing a data
structure that efficiently answers range mode queries on . Each query
consists of an input pair of indices for which a mode of must
be returned. We present an -space static data structure
that supports range mode queries in time in the worst case, for
any fixed . When , this corresponds to
the first linear-space data structure to guarantee query time. We
then describe three additional linear-space data structures that provide
, , and query time, respectively, where denotes the
number of distinct elements in and denotes the frequency of the mode of
. Finally, we examine generalizing our data structures to higher dimensions.Comment: 13 pages, 2 figure
The Fractal Density Structure in Supersonic Isothermal Turbulence: Solenoidal versus Compressive Energy Injection
In a systematic study, we compare the density statistics in high resolution
numerical experiments of supersonic isothermal turbulence, driven by the
usually adopted solenoidal (divergence-free) forcing and by compressive
(curl-free) forcing. We find that for the same rms Mach number, compressive
forcing produces much stronger density enhancements and larger voids compared
to solenoidal forcing. Consequently, the Fourier spectra of density
fluctuations are significantly steeper. This result is confirmed using the
Delta-variance analysis, which yields power-law exponents beta~3.4 for
compressive forcing and beta~2.8 for solenoidal forcing. We obtain fractal
dimension estimates from the density spectra and Delta-variance scaling, and by
using the box counting, mass size and perimeter area methods applied to the
volumetric data, projections and slices of our turbulent density fields. Our
results suggest that compressive forcing yields fractal dimensions
significantly smaller compared to solenoidal forcing. However, the actual
values depend sensitively on the adopted method, with the most reliable
estimates based on the Delta-variance, or equivalently, on Fourier spectra.
Using these methods, we obtain D~2.3 for compressive and D~2.6 for solenoidal
forcing, which is within the range of fractal dimension estimates inferred from
observations (D~2.0-2.7). The velocity dispersion to size relations for both
solenoidal and compressive forcing obtained from velocity spectra follow a
power law with exponents in the range 0.4-0.5, in good agreement with previous
studies.Comment: 17 pages, 11 figures, ApJ in press, minor changes to language,
simulation movies available at
http://www.ita.uni-heidelberg.de/~chfeder/videos.shtml?lang=e
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