117 research outputs found
Determination of the doubly-symmetric periodic orbits in the restricted three-body problem and Hill's lunar problem
We review some recent progress on the research of the periodic orbits of the
N-body problem,and propose a numerical scheme to determine the spatial
doubly-symmetric periodic orbits (SDSPs for short). Both comet- and lunar-type
SDSPs in the circular restricted three-body problem are computed, as well as
the Hill-type SDSPs in Hill's lunar problem. Doubly symmetries are exploited so
that the SDSPs can be computed efficiently. The monodromy matrix can be
calculated by the information of one fourth period. The periodicity conditions
are solved by Broyden's method with a line-search, and the algorithm is
reviewed. Some numerical examples show that the scheme is very efficient. For a
fixed period ratio and a given acute angle, there exist sixteen cases of
initial values. For the restricted three-body problem, the cases of "Copenhagen
problem" and the Sun-Jupiter-asteroid model are considered. New SDSPs are also
numerically found in Hill's lunar problem. Though the period ratio should be
small theoretically, some new periodic orbits are found when the ratio is not
too small, and most of the searched SDSPs are linearly stable.Comment: 29 pages, 11 figure
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Financial Portfolio Risk Management: Model Risk, Robustness and Rebalancing Error
Risk management has always been in key component of portfolio management. While more and more complicated models are proposed and implemented as research advances, they all inevitably rely on imperfect assumptions and estimates. This dissertation aims to investigate the gap between complicated theoretical modelling and practice. We mainly focus on two directions: model risk and reblancing error. In the first part of the thesis, we develop a framework for quantifying the impact of model error and for measuring and minimizing risk in a way that is robust to model error. This robust approach starts from a baseline model and finds the worst-case error in risk measurement that would be incurred through a deviation from the baseline model, given a precise constraint on the plausibility of the deviation. Using relative entropy to constrain model distance leads to an explicit characterization of worst-case model errors; this characterization lends itself to Monte Carlo simulation, allowing straightforward calculation of bounds on model error with very little computational effort beyond that required to evaluate performance under the baseline nominal model. This approach goes well beyond the effect of errors in parameter estimates to consider errors in the underlying stochastic assumptions of the model and to characterize the greatest vulnerabilities to error in a model. We apply this approach to problems of portfolio risk measurement, credit risk, delta hedging, and counterparty risk measured through credit valuation adjustment. In the second part, we apply this robust approach to a dynamic portfolio control problem. The sources of model error include the evolution of market factors and the influence of these factors on asset returns. We analyze both finite- and infinite-horizon problems in a model in which returns are driven by factors that evolve stochastically. The model incorporates transaction costs and leads to simple and tractable optimal robust controls for multiple assets. We illustrate the performance of the controls on historical data. Robustness does improve performance in out-of-sample tests in which the model is estimated on a rolling window of data and then applied over a subsequent time period. By acknowledging uncertainty in the estimated model, the robust rules lead to less aggressive trading and are less sensitive to sharp moves in underlying prices. In the last part, we analyze the error between a discretely rebalanced portfolio and its continuously rebalanced counterpart in the presence of jumps or mean-reversion in the underlying asset dynamics. With discrete rebalancing, the portfolio's composition is restored to a set of fixed target weights at discrete intervals; with continuous rebalancing, the target weights are maintained at all times. We examine the difference between the two portfolios as the number of discrete rebalancing dates increases. We derive the limiting variance of the relative error between the two portfolios for both the mean-reverting and jump-diffusion cases. For both cases, we derive ``volatility adjustments'' to improve the approximation of the discretely rebalanced portfolio by the continuously rebalanced portfolio, based on on the limiting covariance between the relative rebalancing error and the level of the continuously rebalanced portfolio. These results are based on strong approximation results for jump-diffusion processes
Coherent manipulation of spin wave vector for polarization of photons in an atomic ensemble
We experimentally demonstrate the manipulation of two-orthogonal components
of a spin wave in an atomic ensemble. Based on Raman two-photon transition and
Larmor spin precession induced by magnetic field pulses, the coherent rotations
between the two components of the spin wave is controllably achieved.
Successively, the two manipulated spin-wave components are mapped into two
orthogonal polarized optical emissions, respectively. By measuring Ramsey
fringes of the retrieved optical signals, the \pi/2-pulse fidelity of ~96% is
obtained. The presented manipulation scheme can be used to build an arbitrary
rotation for qubit operations in quantum information processing based on atomic
ensembles
Quantum Interference of Stored Coherent Spin-wave Excitations in a Two-channel Memory
Quantum memories are essential elements in long-distance quantum networks and
quantum computation. Significant advances have been achieved in demonstrating
relative long-lived single-channel memory at single-photon level in cold atomic
media. However, the qubit memory corresponding to store two-channel spin-wave
excitations (SWEs) still faces challenges, including the limitations resulting
from Larmor procession, fluctuating ambient magnetic field, and
manipulation/measurement of the relative phase between the two channels. Here,
we demonstrate a two-channel memory scheme in an ideal tripod atomic system, in
which the total readout signal exhibits either constructive or destructive
interference when the two-channel SWEs are retrieved by two reading beams with
a controllable relative phase. Experimental result indicates quantum coherence
between the stored SWEs. Based on such phase-sensitive storage/retrieval
scheme, measurements of the relative phase between the two SWEs and Rabi
oscillation, as well as elimination of the collapse and revival of the readout
signal, are experimentally demonstrated
Nucleon spin decomposition with one dynamical gluon
We solve for the light-front wave functions of the nucleon from a light-front
quantum chromodynamics (QCD) effective Hamiltonian with three-dimensional
confinement. We obtain solutions using constituent three quarks combined with
three quarks and one gluon Fock components. The resulting light-front wave
functions provide a good quality description of the nucleon's quark
distribution functions following QCD scale evolution. We present the effects
from incorporating a dynamical gluon on the nucleon's gluon densities, helicity
distribution and orbital angular momentum that constitutes the nucleon spin sum
rule
CRISPR/Cas Derivatives as Novel Gene Modulating Tools:Possibilities and In Vivo Applications
The field of genome editing started with the discovery of meganucleases (e.g., the LAGLIDADG family of homing endonucleases) in yeast. After the discovery of transcription activator-like effector nucleases and zinc finger nucleases, the recently discovered clustered regularly interspaced short palindromic repeats (CRISPR)/CRISPR associated proteins (Cas) system has opened a new window of applications in the field of gene editing. Here, we review different Cas proteins and their corresponding features including advantages and disadvantages, and we provide an overview of the different endonuclease-deficient Cas protein (dCas) derivatives. These dCas derivatives consist of an endonuclease-deficient Cas9 which can be fused to different effector domains to perform distinct in vitro applications such as tracking, transcriptional activation and repression, as well as base editing. Finally, we review the in vivo applications of these dCas derivatives and discuss their potential to perform gene activation and repression in vivo, as well as their potential future use in human therapy
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