78,044 research outputs found
Optimal Computation of Avoided Words
The deviation of the observed frequency of a word from its expected
frequency in a given sequence is used to determine whether or not the word
is avoided. This concept is particularly useful in DNA linguistic analysis. The
value of the standard deviation of , denoted by , effectively
characterises the extent of a word by its edge contrast in the context in which
it occurs. A word of length is a -avoided word in if
, for a given threshold . Notice that such a word
may be completely absent from . Hence computing all such words na\"{\i}vely
can be a very time-consuming procedure, in particular for large . In this
article, we propose an -time and -space algorithm to compute all
-avoided words of length in a given sequence of length over a
fixed-sized alphabet. We also present a time-optimal -time and
-space algorithm to compute all -avoided words (of any
length) in a sequence of length over an alphabet of size .
Furthermore, we provide a tight asymptotic upper bound for the number of
-avoided words and the expected length of the longest one. We make
available an open-source implementation of our algorithm. Experimental results,
using both real and synthetic data, show the efficiency of our implementation
Fault-Tolerant Error Correction with Efficient Quantum Codes
We exhibit a simple, systematic procedure for detecting and correcting errors
using any of the recently reported quantum error-correcting codes. The
procedure is shown explicitly for a code in which one qubit is mapped into
five. The quantum networks obtained are fault tolerant, that is, they can
function successfully even if errors occur during the error correction. Our
construction is derived using a recently introduced group-theoretic framework
for unifying all known quantum codes.Comment: 12 pages REVTeX, 1 ps figure included. Minor additions and revision
Atomic and molecular complex resonances from real eigenvalues using standard (hermitian) electronic structure calculations
Complex eigenvalues, resonances, play an important role in large variety of
fields in physics and chemistry. For example, in cold molecular collision
experiments and electron scattering experiments, autoionizing and
pre-dissociative metastable resonances are generated. However, the computation
of complex resonance eigenvalues is difficult, since it requires severe
modifications of standard electronic structure codes and methods. Here we show
how resonance eigenvalues, positions and widths, can be calculated using the
standard, widely used, electronic-structure packages. Our method enables the
calculations of the complex resonance eigenvalues by using analytical
continuation procedures (such as Pad\'{e}). The key point in our approach is
the existence of narrow analytical passages from the real axis to the complex
energy plane. In fact, the existence of these analytical passages relies on
using finite basis sets. These passages become narrower as the basis set
becomes more complete, whereas in the exact limit, these passages to the
complex plane are closed.
As illustrative numerical examples we calculated the autoionization
resonances of helium, hydrogen anion and hydrogen molecule. We show that our
results are in an excellent agreement with the results obtained by other
theoretical methods and with available experimental results
Recommended from our members
An improved connectionist activation function for energy minimization
Symmetric networks that are based on energy minimization, such as Boltzmann machines or Hopfield nets, are used extensively for optimization, constraint satisfaction, and approximation of NP-hard problems. Nevertheless, finding a global minimum for the energy function is not guaranteed, and even a local minimum may take an exponential number of steps. We propose an improvement to the standard activation function used for such networks. The improved algorithm guarantees that a global minimum is found in linear time for tree-like subnetworks. The algorithm is uniform and does not assume that the network is a tree. It performs no worse than the standard algorithms for any network topology. In the case where there are trees growing from a cyclic subnetwork, the new algorithm performs better than the standard algorithms by avoiding local minima along the trees and by optimizing the free energy of these trees in linear time. The algorithm is self-stabilizing for trees (cycle-free undirected graphs) and remains correct under various scheduling demons. However, no uniform protocol exists to optimize trees under a pure distributed demon and no such protocol exists for cyclic networks under central demon
Efficient Path Interpolation and Speed Profile Computation for Nonholonomic Mobile Robots
This paper studies path synthesis for nonholonomic mobile robots moving in
two-dimensional space. We first address the problem of interpolating paths
expressed as sequences of straight line segments, such as those produced by
some planning algorithms, into smooth curves that can be followed without
stopping. Our solution has the advantage of being simpler than other existing
approaches, and has a low computational cost that allows a real-time
implementation. It produces discretized paths on which curvature and variation
of curvature are bounded at all points, and preserves obstacle clearance. Then,
we consider the problem of computing a time-optimal speed profile for such
paths. We introduce an algorithm that solves this problem in linear time, and
that is able to take into account a broader class of physical constraints than
other solutions. Our contributions have been implemented and evaluated in the
framework of the Eurobot contest
- …