597,996 research outputs found
Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization
Principal component analysis (PCA) is widely used for dimensionality
reduction, with well-documented merits in various applications involving
high-dimensional data, including computer vision, preference measurement, and
bioinformatics. In this context, the fresh look advocated here permeates
benefits from variable selection and compressive sampling, to robustify PCA
against outliers. A least-trimmed squares estimator of a low-rank bilinear
factor analysis model is shown closely related to that obtained from an
-(pseudo)norm-regularized criterion encouraging sparsity in a matrix
explicitly modeling the outliers. This connection suggests robust PCA schemes
based on convex relaxation, which lead naturally to a family of robust
estimators encompassing Huber's optimal M-class as a special case. Outliers are
identified by tuning a regularization parameter, which amounts to controlling
sparsity of the outlier matrix along the whole robustification path of (group)
least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its
neat ties to robust statistics, the developed outlier-aware PCA framework is
versatile to accommodate novel and scalable algorithms to: i) track the
low-rank signal subspace robustly, as new data are acquired in real time; and
ii) determine principal components robustly in (possibly) infinite-dimensional
feature spaces. Synthetic and real data tests corroborate the effectiveness of
the proposed robust PCA schemes, when used to identify aberrant responses in
personality assessment surveys, as well as unveil communities in social
networks, and intruders from video surveillance data.Comment: 30 pages, submitted to IEEE Transactions on Signal Processin
Faithful qubit distribution assisted by one additional qubit against collective noise
We propose a distribution scheme of polarization states of a single photon
over collective-noise channel. By adding one extra photon with a fixed
polarization, we can protect the state against collective noise via a
parity-check measurement and post-selection. While the scheme succeeds only
probabilistically, it is simpler and more flexible than the schemes utilizing
decoherence-free subspace. An application to BB84 protocol through collective
noise channel, which is robust to the Trojan horse attack, is also given.Comment: 4 pages, 3 figures; published version in Phys. Rev. Let
Classical Field Approach to Quantum Weak Measurements
By generalizing the quantum weak measurement protocol to the case of quantum
fields, we show that weak measurements probe an effective classical background
field that describes the average field configuration in the spacetime region
between pre- and post-selection boundary conditions. The classical field is
itself a weak value of the corresponding quantum field operator and satisfies
equations of motion that extremize an effective action. Weak measurements
perturb this effective action, producing measurable changes to the classical
field dynamics. As such, weakly measured effects always correspond to an
effective classical field. This general result explains why these effects
appear to be robust for pre- and post-selected ensembles, and why they can also
be measured using classical field techniques that are not weak for individual
excitations of the field.Comment: 6 pages, 2 figures, published versio
A high-flux BEC source for mobile atom interferometers
Quantum sensors based on coherent matter-waves are precise measurement
devices whose ultimate accuracy is achieved with Bose-Einstein condensates
(BEC) in extended free fall. This is ideally realized in microgravity
environments such as drop towers, ballistic rockets and space platforms.
However, the transition from lab-based BEC machines to robust and mobile
sources with comparable performance is a challenging endeavor. Here we report
on the realization of a miniaturized setup, generating a flux of quantum degenerate Rb atoms every 1.6s. Ensembles of atoms can be produced at a 1Hz rate. This is achieved by loading a
cold atomic beam directly into a multi-layer atom chip that is designed for
efficient transfer from laser-cooled to magnetically trapped clouds. The
attained flux of degenerate atoms is on par with current lab-based BEC
experiments while offering significantly higher repetition rates. Additionally,
the flux is approaching those of current interferometers employing Raman-type
velocity selection of laser-cooled atoms. The compact and robust design allows
for mobile operation in a variety of demanding environments and paves the way
for transportable high-precision quantum sensors.Comment: 22 pages, 6 figure
Can fuzzy Multi-Criteria Decision Making improve Strategic planning by balanced scorecard?
Strategic management is momentous for organizational success and competitive advantage in an increasingly turbulent business environment. Balanced scorecard (BSC) is a framework for evaluating strategic management performance which translates strategy into action via various sets of performance measurement indicators. The main objective of this research is to develop a new fuzzy group Multi-Criteria Decision Making (MCDM) model for strategic plans selection process in the BSC. For this to happen, the current study has implemented linguistic extension of MCDM model for robust selection of strategic plans. The new linguistic reasoning for group decision making is able to aggregate subjective evaluation of the decision makers and hence create an opportunity to perform more robust strategic plans, despite of the vagueness and uncertainty of strategic plans selection process. A numerical example demonstrates possibilities for the improvement of BSC through applying the proposed model
- …