31,364 research outputs found
Vector cross product in n-dimensional vector space
The definition of vector cross product (VCP) introduced by Eckmann only
exists in thethree- and the seven- dimensional vector space. In this paper,
according to the orthogonal completeness, magnitude of basis vector cross
product and all kinds of combinations of basis vector , the
generalized definition of VCP in the odd n-dimensional vector space is given by
introducing a cross term . In addition, the definition is validated by
reducing the generalization definition to the fundamental three- and
seven-dimensional vector space.Comment: 9 pages, 1 figure, comments are welcom
Letter to the Editor
The paper by Alfons, Croux and Gelper (2013), Sparse least trimmed squares
regression for analyzing high-dimensional large data sets, considered a
combination of least trimmed squares (LTS) and lasso penalty for robust and
sparse high-dimensional regression. In a recent paper [She and Owen (2011)], a
method for outlier detection based on a sparsity penalty on the mean shift
parameter was proposed (designated by "SO" in the following). This work is
mentioned in Alfons et al. as being an "entirely different approach." Certainly
the problem studied by Alfons et al. is novel and interesting.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS640 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Universal Quantum Degeneracy Point for Superconducting Qubits
The quantum degeneracy point approach [D. Vion et al., Science 296, 886
(2002)] effectively protects superconducting qubits from low-frequency noise
that couples with the qubits as transverse noise. However, low-frequency noise
in superconducting qubits can originate from various mechanisms and can couple
with the qubits either as transverse or as longitudinal noise. Here, we present
a quantum circuit containing a universal quantum degeneracy point that protects
an encoded qubit from arbitrary low-frequency noise. We further show that
universal quantum logic gates can be performed on the encoded qubit with high
gate fidelity. The proposed scheme is robust against small parameter spreads
due to fabrication errors in the superconducting qubits.Comment: 7 pages, 4 figure
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