239,515 research outputs found
Sweeping an oval to a vanishing point
Given a convex region in the plane, and a sweep-line as a tool, what is best
way to reduce the region to a single point by a sequence of sweeps? The problem
of sweeping points by orthogonal sweeps was first studied in [2]. Here we
consider the following \emph{slanted} variant of sweeping recently introduced
in [1]: In a single sweep, the sweep-line is placed at a start position
somewhere in the plane, then moved continuously according to a sweep vector
(not necessarily orthogonal to the sweep-line) to another parallel end
position, and then lifted from the plane. The cost of a sequence of sweeps is
the sum of the lengths of the sweep vectors. The (optimal) sweeping cost of a
region is the infimum of the costs over all finite sweeping sequences for that
region. An optimal sweeping sequence for a region is one with a minimum total
cost, if it exists. Another parameter of interest is the number of sweeps.
We show that there exist convex regions for which the optimal sweeping cost
cannot be attained by two sweeps. This disproves a conjecture of Bousany,
Karker, O'Rourke, and Sparaco stating that two sweeps (with vectors along the
two adjacent sides of a minimum-perimeter enclosing parallelogram) always
suffice [1]. Moreover, we conjecture that for some convex regions, no finite
sweeping sequence is optimal. On the other hand, we show that both the 2-sweep
algorithm based on minimum-perimeter enclosing rectangle and the 2-sweep
algorithm based on minimum-perimeter enclosing parallelogram achieve a approximation in this sweeping model.Comment: 9 pages, 4 figure
Computing the minimum distance between two Bézier curves
International audienceA sweeping sphere clipping method is presented for computing the minimum distance between two Bézier curves. The sweeping sphere is constructed by rolling a sphere with its center point along a curve. The initial radius of the sweeping sphere can be set as the minimum distance between an end point and the other curve. The nearest point on a curve must be contained in the sweeping sphere along the other curve, and all of the parts outside the sweeping sphere can be eliminated. A simple sufficient condition when the nearest point is one of the two end points of a curve is provided, which turns the curve/curve case into a point/curve case and leads to higher efficiency. Examples are shown to illustrate efficiency and robustness of the new method
Interest on Bank Reserves and Optimal Sweeping
This paper utilizes a profit maximizing banking model to analyze sweeping behavior. Comparative statics results indicate that sweeping responds positively to increases in bank loan rates and reserve ratios and negatively to increases in the interest rate on reserves or to exogenous increases in bank deposits or equity. Sweeping generates greater responsiveness in lending to changes in loan rates or the interest rate on reserves and lower responsiveness to exogenous changes in reserve ratios or equity. Empirical analysis of an explicit condition that we derive relating sweeping to the interest rate on reserves suggests with an unchanged reserve requirement, the Fed could eliminate sweeping by setting the interest rate on reserves to no less than 3.67 percentage points below the market loan rate. The range of interest rates on reserves that lead to zero sweeping increases sharply, however, as the required reserve ratio is reduced
Detecting all regular polygons in a point set
In this paper, we analyze the time complexity of finding regular polygons in
a set of n points. We combine two different approaches to find regular
polygons, depending on their number of edges. Our result depends on the
parameter alpha, which has been used to bound the maximum number of isosceles
triangles that can be formed by n points. This bound has been expressed as
O(n^{2+2alpha+epsilon}), and the current best value for alpha is ~0.068.
Our algorithm finds polygons with O(n^alpha) edges by sweeping a line through
the set of points, while larger polygons are found by random sampling. We can
find all regular polygons with high probability in O(n^{2+alpha+epsilon})
expected time for every positive epsilon. This compares well to the
O(n^{2+2alpha+epsilon}) deterministic algorithm of Brass.Comment: 11 pages, 4 figure
Selective coupling of superconducting qubits via tunable stripline cavity
We theoretically investigate selective coupling of superconducting charge
qubits mediated by a superconducting stripline cavity with a tunable resonance
frequency. The frequency control is provided by a flux biased dc-SQUID attached
to the cavity. Selective entanglement of the qubit states is achieved by
sweeping the cavity frequency through the qubit-cavity resonances. The circuit
is scalable, and allows to keep the qubits at their optimal points with respect
to decoherence during the whole operation. We derive an effective quantum
Hamiltonian for the basic, two-qubit-cavity system, and analyze appropriate
circuit parameters. We present a protocol for performing Bell inequality
measurements, and discuss a composite pulse sequence generating a universal
control-phase gate
Making Octants Colorful and Related Covering Decomposition Problems
We give new positive results on the long-standing open problem of geometric
covering decomposition for homothetic polygons. In particular, we prove that
for any positive integer k, every finite set of points in R^3 can be colored
with k colors so that every translate of the negative octant containing at
least k^6 points contains at least one of each color. The best previously known
bound was doubly exponential in k. This yields, among other corollaries, the
first polynomial bound for the decomposability of multiple coverings by
homothetic triangles. We also investigate related decomposition problems
involving intervals appearing on a line. We prove that no algorithm can
dynamically maintain a decomposition of a multiple covering by intervals under
insertion of new intervals, even in a semi-online model, in which some coloring
decisions can be delayed. This implies that a wide range of sweeping plane
algorithms cannot guarantee any bound even for special cases of the octant
problem.Comment: version after revision process; minor changes in the expositio
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