9,477 research outputs found
A study of the high-inclination population in the Kuiper belt - II. The Twotinos
As the second part of our study, in this paper we proceed to explore the
dynamics of the high-inclination Twotinos in the 1:2 Neptune mean motion
resonance (NMMR). Depending on the inclination , we show the existence of
two critical eccentricities and , which are lower limits of
the eccentricity for the resonant angle to exhibit libration and
asymmetric libration, respectively. Accordingly, we have determined the
libration centres for inclined orbits, which are strongly dependent
on . With initial on a fine grid of , the
stability of orbits in the 1:2 NMMR is probed by 4-Gyr integrations. It is
shown that symmetric librators are totally unstable for ; while
stable asymmetric librators exist for up to .
We further investigate the 1:2 NMMR capture and retention of planetesimals
with initial inclinations in the planet migration model
using a time-scale of yr. We find that: (1) the capture
efficiency of the 1:2 NMMR decreases drastically with the increase of ,
and it goes to 0 when ; (2) the probability of discovering
Twotinos with , beyond observed values, is roughly estimated to
be per cent; (3) more particles are captured into the leading rather
than the trailing asymmetric resonance for , but this number
difference appears to be the opposite at and is continuously
varying for even larger ; (4) captured Twotinos residing in the trailing
resonance or having are practically outside the Kozai mechanism,
like currently observed samples.Comment: 13 pages, 10 figures, Accepted by MNRAS. Comments welcome
Clustering with diversity
We consider the {\em clustering with diversity} problem: given a set of
colored points in a metric space, partition them into clusters such that each
cluster has at least points, all of which have distinct colors.
We give a 2-approximation to this problem for any when the objective
is to minimize the maximum radius of any cluster. We show that the
approximation ratio is optimal unless , by providing a matching
lower bound. Several extensions to our algorithm have also been developed for
handling outliers. This problem is mainly motivated by applications in
privacy-preserving data publication.Comment: Extended abstract accepted in ICALP 2010. Keywords: Approximation
algorithm, k-center, k-anonymity, l-diversit
Optimal Investment with Stopping in Finite Horizon
In this paper, we investigate dynamic optimization problems featuring both
stochastic control and optimal stopping in a finite time horizon. The paper
aims to develop new methodologies, which are significantly different from those
of mixed dynamic optimal control and stopping problems in the existing
literature, to study a manager's decision. We formulate our model to a free
boundary problem of a fully nonlinear equation. Furthermore, by means of a dual
transformation for the above problem, we convert the above problem to a new
free boundary problem of a linear equation. Finally, we apply the theoretical
results to challenging, yet practically relevant and important, risk-sensitive
problems in wealth management to obtain the properties of the optimal strategy
and the right time to achieve a certain level over a finite time investment
horizon
Conditional Screening for Ultra-high Dimensional Covariates with Survival Outcomes
Identifying important biomarkers that are predictive for cancer patients'
prognosis is key in gaining better insights into the biological influences on
the disease and has become a critical component of precision medicine. The
emergence of large-scale biomedical survival studies, which typically involve
excessive number of biomarkers, has brought high demand in designing efficient
screening tools for selecting predictive biomarkers. The vast amount of
biomarkers defies any existing variable selection methods via regularization.
The recently developed variable screening methods, though powerful in many
practical setting, fail to incorporate prior information on the importance of
each biomarker and are less powerful in detecting marginally weak while jointly
important signals. We propose a new conditional screening method for survival
outcome data by computing the marginal contribution of each biomarker given
priorly known biological information. This is based on the premise that some
biomarkers are known to be associated with disease outcomes a priori. Our
method possesses sure screening properties and a vanishing false selection
rate. The utility of the proposal is further confirmed with extensive
simulation studies and analysis of a Diffuse large B-cell lymphoma (DLBCL)
dataset.Comment: 34 pages, 3 figure
- β¦