8,870 research outputs found
Computing the smallest k-enclosing circle and related problems
AbstractWe present an efficient algorithm for solving the “smallest k-enclosing circle” (kSC) problem: Given a set of n points in the plane and an integer k ⩽ n, find the smallest disk containing k of the points. We present two solutions. When using O(nk) storage, the problem can be solved in time O(nk log2 n). When only O(n log n) storage is allowed, the running time is O(nk log2 n log n/k). We also extend our technique to obtain efficient solutions of several related problems (with similar time and storage bounds). These related problems include: finding the smallest homothetic copy of a given convex polygon P which contains k points from a given planar set, and finding the smallest disk intersecting k segments from a given planar set of non-intersecting segments
Design study of a device to simulate the dynamic environment encountered under condi- tions of reduced or zero gravity final report
Design study of reduced or zero gravity environment simulation devic
Edge pinch instability of oblate liquid metal drops in a transverse AC magnetic field
This paper considers the stability of liquid metal drops subject to a
high-frequency AC magnetic field. An energy variation principle is derived in
terms of the surface integral of the scalar magnetic potential. This principle
is applied to a thin perfectly conducting liquid disk, which is used to model
the drops constrained in a horizontal gap between two parallel insulating
plates. Firstly, the stability of a circular disk is analysed with respect to
small-amplitude harmonic edge perturbations. Analytical solution shows that the
edge deformations with the azimuthal wavenumbers m=2,3,4... start to develop as
the magnetic Bond number exceeds the critical threshold Bm_c=3pi(m+1)/2. The
most unstable is m=2 mode, which corresponds to an elliptical deformation.
Secondly, strongly deformed equilibrium shapes are modelled numerically by
minimising the associated energy in combination with the solution of a surface
integral equation for the scalar magnetic potential on an unstructured
triangular mesh. The edge instability is found to result in the equilibrium
shapes of either two- or threefold rotational symmetry depending on the
magnetic field strength and the initial perturbation. The shapes of higher
rotational symmetries are unstable and fall back to one of these two basic
states. The developed method is both efficient and accurate enough for
modelling of strongly deformed drop shapes.Comment: 18 pages, 11 figures, corrected final revision, to appear in J. Fluid
Mec
Grounding semantics in robots for Visual Question Answering
In this thesis I describe an operational implementation of an object detection and description system that incorporates in an end-to-end Visual Question Answering system and evaluated it on two visual question answering datasets for compositional language and elementary visual reasoning
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