7,339 research outputs found
Maximizing the Closed Loop Asymptotic Decay Rate for the Two-Mass-Spring Control Problem
We consider the following problem: find a fixed-order linear controller that
maximizes the closed-loop asymptotic decay rate for the classical
two-mass-spring system. This can be formulated as the problem of minimizing the
abscissa (maximum of the real parts of the roots) of a polynomial whose
coefficients depend linearly on the controller parameters. We show that the
only order for which there is a non-trivial solution is 2. In this case, we
derive a controller that we prove locally maximizes the asymptotic decay rate,
using recently developed techniques from nonsmooth analysis
Leapfrogging vortex rings for the three dimensional Gross-Pitaevskii equation
Leapfrogging motion of vortex rings sharing the same axis of symmetry was
first predicted by Helmholtz in his famous work on the Euler equation for
incompressible fluids. Its justification in that framework remains an open
question to date. In this paper, we rigorously derive the corresponding
leapfrogging motion for the axially symmetric three-dimensional
Gross-Pitaevskii equation.Comment: 39 pages, 2 figure
Multiobjective Robust Control with HIFOO 2.0
Multiobjective control design is known to be a difficult problem both in
theory and practice. Our approach is to search for locally optimal solutions of
a nonsmooth optimization problem that is built to incorporate minimization
objectives and constraints for multiple plants. We report on the success of
this approach using our public-domain Matlab toolbox HIFOO 2.0, comparing our
results with benchmarks in the literature
Fast and High-Fidelity Entangling Gate through Parametrically Modulated Longitudinal Coupling
We investigate an approach to universal quantum computation based on the
modulation of longitudinal qubit-oscillator coupling. We show how to realize a
controlled-phase gate by simultaneously modulating the longitudinal coupling of
two qubits to a common oscillator mode. In contrast to the more familiar
transversal qubit-oscillator coupling, the magnitude of the effective
qubit-qubit interaction does not rely on a small perturbative parameter. As a
result, this effective interaction strength can be made large, leading to short
gate times and high gate fidelities. We moreover show how the gate infidelity
can be exponentially suppressed with squeezing and how the entangling gate can
be generalized to qubits coupled to separate oscillators. Our proposal can be
realized in multiple physical platforms for quantum computing, including
superconducting and spin qubits.Comment: 5 pages, 3 figures, Supplemental Materia
Unexploited gains from international diversification : patterns of portfolio holdings around the world
This paper studies how portfolios with a global investment scope are allocated internationally using a unique micro dataset on U.S. equity mutual funds. While mutual funds have great flexibility to invest globally, they invest in a surprisingly limited number of stocks, around 100. The number of holdings in stocks and countries from a given region declines as the investment scope of funds broadens. This restrictive investment practice has costs. A mean-variance strategy shows unexploited gains from further international diversification. Mutual funds investing globally could achieve better risk-adjusted returns by broadening their asset allocation, including stocks held by more specialized funds within the same mutual fund family (company). This investment pattern is not explained by lack of information or instruments, transaction costs, or a better ability of global funds to minimize negative outcomes. Instead, industry practices related to organizational factors seem to play an important role.Mutual Funds,Debt Markets,Emerging Markets,Rural Development Knowledge&Information Systems,Access to Finance
Confidence regions for the multinomial parameter with small sample size
Consider the observation of n iid realizations of an experiment with d>1
possible outcomes, which corresponds to a single observation of a multinomial
distribution M(n,p) where p is an unknown discrete distribution on {1,...,d}.
In many applications, the construction of a confidence region for p when n is
small is crucial. This concrete challenging problem has a long history. It is
well known that the confidence regions built from asymptotic statistics do not
have good coverage when n is small. On the other hand, most available methods
providing non-asymptotic regions with controlled coverage are limited to the
binomial case d=2. In the present work, we propose a new method valid for any
d>1. This method provides confidence regions with controlled coverage and small
volume, and consists of the inversion of the "covering collection"' associated
with level-sets of the likelihood. The behavior when d/n tends to infinity
remains an interesting open problem beyond the scope of this work.Comment: Accepted for publication in Journal of the American Statistical
Association (JASA
Infinite average lifetime of an unstable bright state in the green fluorescent protein
The time evolution of the fluorescence intensity emitted by well-defined
ensembles of Green Fluorescent Proteins has been studied by using a standard
confocal microscope. In contrast with previous results obtained in single
molecule experiments, the photo-bleaching of the ensemble is well described by
a model based on Levy statistics. Moreover, this simple theoretical model
allows us to obtain information about the energy-scales involved in the aging
process.Comment: 4 pages, 4 figure
The impact of high frequency repetitive transcranial magnetic stimulation on fine motor function in medication resistant major depression
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