5,925 research outputs found
Exact and fixed-parameter algorithms for metro-line crossing minimization problems
A metro-line crossing minimization problem is to draw multiple lines on an
underlying graph that models stations and rail tracks so that the number of
crossings of lines becomes minimum. It has several variations by adding
restrictions on how lines are drawn. Among those, there is one with a
restriction that line terminals have to be drawn at a verge of a station, and
it is known to be NP-hard even when underlying graphs are paths. This paper
studies the problem in this setting, and propose new exact algorithms. We first
show that a problem to decide if lines can be drawn without crossings is solved
in polynomial time, and propose a fast exponential algorithm to solve a
crossing minimization problem. We then propose a fixed-parameter algorithm with
respect to the multiplicity of lines, which implies that the problem is FPT.Comment: 19 pages, 15 figure
Coverage, Continuity and Visual Cortical Architecture
The primary visual cortex of many mammals contains a continuous
representation of visual space, with a roughly repetitive aperiodic map of
orientation preferences superimposed. It was recently found that orientation
preference maps (OPMs) obey statistical laws which are apparently invariant
among species widely separated in eutherian evolution. Here, we examine whether
one of the most prominent models for the optimization of cortical maps, the
elastic net (EN) model, can reproduce this common design. The EN model
generates representations which optimally trade of stimulus space coverage and
map continuity. While this model has been used in numerous studies, no
analytical results about the precise layout of the predicted OPMs have been
obtained so far. We present a mathematical approach to analytically calculate
the cortical representations predicted by the EN model for the joint mapping of
stimulus position and orientation. We find that in all previously studied
regimes, predicted OPM layouts are perfectly periodic. An unbiased search
through the EN parameter space identifies a novel regime of aperiodic OPMs with
pinwheel densities lower than found in experiments. In an extreme limit,
aperiodic OPMs quantitatively resembling experimental observations emerge.
Stabilization of these layouts results from strong nonlocal interactions rather
than from a coverage-continuity-compromise. Our results demonstrate that
optimization models for stimulus representations dominated by nonlocal
suppressive interactions are in principle capable of correctly predicting the
common OPM design. They question that visual cortical feature representations
can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure
Order independent structural alignment of circularly permuted proteins
Circular permutation connects the N and C termini of a protein and
concurrently cleaves elsewhere in the chain, providing an important mechanism
for generating novel protein fold and functions. However, their in genomes is
unknown because current detection methods can miss many occurances, mistaking
random repeats as circular permutation. Here we develop a method for detecting
circularly permuted proteins from structural comparison. Sequence order
independent alignment of protein structures can be regarded as a special case
of the maximum-weight independent set problem, which is known to be
computationally hard. We develop an efficient approximation algorithm by
repeatedly solving relaxations of an appropriate intermediate integer
programming formulation, we show that the approximation ratio is much better
then the theoretical worst case ratio of . Circularly permuted
proteins reported in literature can be identified rapidly with our method,
while they escape the detection by publicly available servers for structural
alignment.Comment: 5 pages, 3 figures, Accepted by IEEE-EMBS 2004 Conference Proceeding
Complexity Analysis of Balloon Drawing for Rooted Trees
In a balloon drawing of a tree, all the children under the same parent are
placed on the circumference of the circle centered at their parent, and the
radius of the circle centered at each node along any path from the root
reflects the number of descendants associated with the node. Among various
styles of tree drawings reported in the literature, the balloon drawing enjoys
a desirable feature of displaying tree structures in a rather balanced fashion.
For each internal node in a balloon drawing, the ray from the node to each of
its children divides the wedge accommodating the subtree rooted at the child
into two sub-wedges. Depending on whether the two sub-wedge angles are required
to be identical or not, a balloon drawing can further be divided into two
types: even sub-wedge and uneven sub-wedge types. In the most general case, for
any internal node in the tree there are two dimensions of freedom that affect
the quality of a balloon drawing: (1) altering the order in which the children
of the node appear in the drawing, and (2) for the subtree rooted at each child
of the node, flipping the two sub-wedges of the subtree. In this paper, we give
a comprehensive complexity analysis for optimizing balloon drawings of rooted
trees with respect to angular resolution, aspect ratio and standard deviation
of angles under various drawing cases depending on whether the tree is of even
or uneven sub-wedge type and whether (1) and (2) above are allowed. It turns
out that some are NP-complete while others can be solved in polynomial time. We
also derive approximation algorithms for those that are intractable in general
On chip interconnects for multiprocessor turbo decoding architectures
International audienc
Modeling and manufacturability assessment of bistable quantum-dot cells
We have investigated the behavior of bistable cells made up of four quantum
dots and occupied by two electrons, in the presence of realistic confinement
potentials produced by depletion gates on top of a GaAs/AlGaAs heterostructure.
Such a cell represents the basic building block for logic architectures based
on the concept of Quantum Cellular Automata (QCA) and of ground state
computation, which have been proposed as an alternative to traditional
transistor-based logic circuits. We have focused on the robustness of the
operation of such cells with respect to asymmetries deriving from fabrication
tolerances. We have developed a 2-D model for the calculation of the electron
density in a driven cell in response to the polarization state of a driver
cell. Our method is based on the one-shot Configuration-Interaction technique,
adapted from molecular chemistry. From the results of our simulations, we
conclude that an implementation of QCA logic based on simple ``hole-arrays'' is
not feasible, because of the extreme sensitivity to fabrication tolerances. As
an alternative, we propose cells defined by multiple gates, where geometrical
asymmetries can be compensated for by adjusting the bias voltages. Even though
not immediately applicable to the implementation of logic gates and not
suitable for large scale integration, the proposed cell layout should allow an
experimental demonstration of a chain of QCA cells.Comment: 26 pages, Revtex, 13 figures, title and some figures changed and
minor revision
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