48 research outputs found
On Time-optimal Trajectories for a Car-like Robot with One Trailer
In addition to the theoretical value of challenging optimal control problmes,
recent progress in autonomous vehicles mandates further research in optimal
motion planning for wheeled vehicles. Since current numerical optimal control
techniques suffer from either the curse of dimens ionality, e.g. the
Hamilton-Jacobi-Bellman equation, or the curse of complexity, e.g.
pseudospectral optimal control and max-plus methods, analytical
characterization of geodesics for wheeled vehicles becomes important not only
from a theoretical point of view but also from a prac tical one. Such an
analytical characterization provides a fast motion planning algorithm that can
be used in robust feedback loops. In this work, we use the Pontryagin Maximum
Principle to characterize extremal trajectories, i.e. candidate geodesics, for
a car-like robot with one trailer. We use time as the distance function. In
spite of partial progress, this problem has remained open in the past two
decades. Besides straight motion and turn with maximum allowed curvature, we
identify planar elastica as the third piece of motion that occurs along our
extr emals. We give a detailed characterization of such curves, a special case
of which, called \emph{merging curve}, connects maximum curvature turns to
straight line segments. The structure of extremals in our case is revealed
through analytical integration of the system and adjoint equations
An Efficient Algorithm for Upper Bound on the Partition Function of Nucleic Acids
It has been shown that minimum free energy structure for RNAs and RNA-RNA
interaction is often incorrect due to inaccuracies in the energy parameters and
inherent limitations of the energy model. In contrast, ensemble based
quantities such as melting temperature and equilibrium concentrations can be
more reliably predicted. Even structure prediction by sampling from the
ensemble and clustering those structures by Sfold [7] has proven to be more
reliable than minimum free energy structure prediction. The main obstacle for
ensemble based approaches is the computational complexity of the partition
function and base pairing probabilities. For instance, the space complexity of
the partition function for RNA-RNA interaction is and the time
complexity is which are prohibitively large [4,12]. Our goal in this
paper is to give a fast algorithm, based on sparse folding, to calculate an
upper bound on the partition function. Our work is based on the recent
algorithm of Hazan and Jaakkola [10]. The space complexity of our algorithm is
the same as that of sparse folding algorithms, and the time complexity of our
algorithm is for single RNA and for RNA-RNA
interaction in practice, in which is the running time of sparse folding
and () is a sequence dependent parameter
A partition function algorithm for interacting nucleic acid strands
Recent interests, such as RNA interference and antisense RNA regulation, strongly motivate the problem of predicting whether two nucleic acid strands interact