6,019 research outputs found
Pattern Matching in Multiple Streams
We investigate the problem of deterministic pattern matching in multiple
streams. In this model, one symbol arrives at a time and is associated with one
of s streaming texts. The task at each time step is to report if there is a new
match between a fixed pattern of length m and a newly updated stream. As is
usual in the streaming context, the goal is to use as little space as possible
while still reporting matches quickly. We give almost matching upper and lower
space bounds for three distinct pattern matching problems. For exact matching
we show that the problem can be solved in constant time per arriving symbol and
O(m+s) words of space. For the k-mismatch and k-difference problems we give
O(k) time solutions that require O(m+ks) words of space. In all three cases we
also give space lower bounds which show our methods are optimal up to a single
logarithmic factor. Finally we set out a number of open problems related to
this new model for pattern matching.Comment: 13 pages, 1 figur
Non-equilibrium microtubule fluctuations in a model cytoskeleton
Biological activity gives rise to non-equilibrium fluctuations in the
cytoplasm of cells; however, there are few methods to directly measure these
fluctuations. Using a reconstituted actin cytoskeleton, we show that the
bending dynamics of embedded microtubules can be used to probe local stress
fluctuations. We add myosin motors that drive the network out of equilibrium,
resulting in an increased amplitude and modified time-dependence of microtubule
bending fluctuations. We show that this behavior results from step-like forces
on the order of 10 pN driven by collective motor dynamics
On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA
Newly formed black holes are expected to emit characteristic radiation in the
form of quasi-normal modes, called ringdown waves, with discrete frequencies.
LISA should be able to detect the ringdown waves emitted by oscillating
supermassive black holes throughout the observable Universe. We develop a
multi-mode formalism, applicable to any interferometric detectors, for
detecting ringdown signals, for estimating black hole parameters from those
signals, and for testing the no-hair theorem of general relativity. Focusing on
LISA, we use current models of its sensitivity to compute the expected
signal-to-noise ratio for ringdown events, the relative parameter estimation
accuracy, and the resolvability of different modes. We also discuss the extent
to which uncertainties on physical parameters, such as the black hole spin and
the energy emitted in each mode, will affect our ability to do black hole
spectroscopy.Comment: 44 pages, 21 figures, 10 tables. Minor changes to match version in
press in Phys. Rev.
Stellar Dynamics of Extreme-Mass-Ratio Inspirals
Inspiral of compact stellar remnants into massive black holes (MBHs) is
accompanied by the emission of gravitational waves at frequencies that are
potentially detectable by space-based interferometers. Event rates computed
from statistical (Fokker-Planck, Monte-Carlo) approaches span a wide range due
to uncertaintities about the rate coefficients. Here we present results from
direct integration of the post-Newtonian N-body equations of motion descrbing
dense clusters of compact stars around Schwarzschild MBHs. These simulations
embody an essentially exact (at the post-Newtonian level) treatment of the
interplay between stellar dynamical relaxation, relativistic precession, and
gravitational-wave energy loss. The rate of capture of stars by the MBH is
found to be greatly reduced by relativistic precession, which limits the
ability of torques from the stellar potential to change orbital angular
momenta. Penetration of this "Schwarzschild barrier" does occasionally occur,
resulting in capture of stars onto orbits that gradually inspiral due to
gravitational wave emission; we discuss two mechanisms for barrier penetration
and find evidence for both in the simulations. We derive an approximate formula
for the capture rate, which predicts that captures would be strongly disfavored
from orbits with semi-major axes below a certain value; this prediction, as
well as the predicted rate, are verified in the N-body integrations. We discuss
the implications of our results for the detection of extreme-mass-ratio
inspirals from galactic nuclei with a range of physical properties.Comment: 28 pages, 16 figures. Version 2 is significantly revised to reflect
new insights into J and Q effects, to be published late
Towards predictive modelling of near-edge structures in electron energy loss spectra of AlN based ternary alloys
Although electron energy loss near edge structure analysis provides a tool
for experimentally probing unoccupied density of states, a detailed comparison
with simulations is necessary in order to understand the origin of individual
peaks. This paper presents a density functional theory based technique for
predicting the N K-edge for ternary (quasi-binary) nitrogen alloys by adopting
a core hole approach, a methodology that has been successful for binary nitride
compounds. It is demonstrated that using the spectra of binary compounds for
optimising the core hole charge ( for cubic TiAlN
and for wurtzite AlGaN), the predicted spectra
evolutions of the ternary alloys agree well with the experiments. The spectral
features are subsequently discussed in terms of the electronic structure and
bonding of the alloys.Comment: 11 pages, 9 figures, 1 tabl
Differential Calculus on -Deformed Light-Cone
We propose the ``short'' version of q-deformed differential calculus on the
light-cone using twistor representation. The commutation relations between
coordinates and momenta are obtained. The quasi-classical limit introduced
gives an exact shape of the off-shell shifting.Comment: 11 pages, Standard LaTeX 2.0
Holographic Aspects of Fermi Liquids in a Background Magnetic Field
We study the effects of an external magnetic field on the properties of the
quasiparticle spectrum of the class of 2+1 dimensional strongly coupled
theories holographically dual to charged AdS black holes at zero
temperature. We uncover several interesting features. At certain values of the
magnetic field, there are multiple quasiparticle peaks representing a novel
level structure of the associated Fermi surfaces. Furthermore, increasing
magnetic field deforms the dispersion characteristics of the quasiparticle
peaks from non-Landau toward Landau behaviour. At a certain value of the
magnetic field, just at the onset of Landau-like behaviour of the Fermi liquid,
the quasiparticles and Fermi surface disappear.Comment: 18 pages, 10 figures. Revised some of the terminology: changed
non-separable solutions to infinite-sum solution
- …