230,497 research outputs found
Classification of Arbitrary Multipartite Entangled States under Local Unitary Equivalence
We propose a practical method for finding the canonical forms of arbitrary
dimensional multipartite entangled states, either pure or mixed. By extending
the technique developed in one of our recent works, the canonical forms for the
mixed -partite entangled states are constructed where they have inherited
local unitary symmetries from their corresponding pure state
counterparts. A systematic scheme to express the local symmetries of the
canonical form is also presented, which provides a feasible way of verifying
the local unitary equivalence for two multipartite entangled states.Comment: 22 pages; published in J. Phys. A: Math. Theo
Safe Learning of Quadrotor Dynamics Using Barrier Certificates
To effectively control complex dynamical systems, accurate nonlinear models
are typically needed. However, these models are not always known. In this
paper, we present a data-driven approach based on Gaussian processes that
learns models of quadrotors operating in partially unknown environments. What
makes this challenging is that if the learning process is not carefully
controlled, the system will go unstable, i.e., the quadcopter will crash. To
this end, barrier certificates are employed for safe learning. The barrier
certificates establish a non-conservative forward invariant safe region, in
which high probability safety guarantees are provided based on the statistics
of the Gaussian Process. A learning controller is designed to efficiently
explore those uncertain states and expand the barrier certified safe region
based on an adaptive sampling scheme. In addition, a recursive Gaussian Process
prediction method is developed to learn the complex quadrotor dynamics in
real-time. Simulation results are provided to demonstrate the effectiveness of
the proposed approach.Comment: Submitted to ICRA 2018, 8 page
Non-Gaussianity, Isocurvature Perturbation, Gravitational Waves and a No-Go Theorem for Isocurvaton
We investigate the isocurvaton model, in which the isocurvature perturbation
plays a role in suppressing the curvature perturbation, and large
non-Gaussianity and gravitational waves can be produced with no isocurvature
perturbation for dark matter. We show that in the slow roll non-interacting
multi-field theory, the isocurvaton mechanism can not be realized. This result
can also be generalized to most of the studied models with generalized kinetic
terms. We also study the implications for the curvaton model. We show that
there is a combined constraint for curvaton on non-Gaussianity, gravitational
waves and isocurvature perturbation. The technique used in this paper can also
help to simplify some calculations in the mixed inflaton and curvaton models.
We also investigate possibilities to produce large negative non-Gaussianity and
nonlocal non-Gaussianity in the curvaton model.Comment: 23 pages, 1 figur
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