197,321 research outputs found
Two binary Darboux transformations for the KdV hierarchy with self-consistent sources
Two binary (integral type) Darboux transformations for the KdV hierarchy with
self-consistent sources are proposed. In contrast with the Darboux
transformation for the KdV hierarchy, one of the two binary Darboux
transformations provides non auto-B\"{a}cklund transformation between two n-th
KdV equations with self-consistent sources with different degrees. The formula
for the m-times repeated binary Darboux transformations are presented. This
enables us to construct the N-soliton solution for the KdV hierarchy with
self-consistent sources.Comment: 19 pages, LaTeX, no figures, to be published in Journal of
Mathematical Physic
A Topic Modeling Toolbox Using Belief Propagation
Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model
for probabilistic topic modeling, which attracts worldwide interests and
touches on many important applications in text mining, computer vision and
computational biology. This paper introduces a topic modeling toolbox (TMBP)
based on the belief propagation (BP) algorithms. TMBP toolbox is implemented by
MEX C++/Matlab/Octave for either Windows 7 or Linux. Compared with existing
topic modeling packages, the novelty of this toolbox lies in the BP algorithms
for learning LDA-based topic models. The current version includes BP algorithms
for latent Dirichlet allocation (LDA), author-topic models (ATM), relational
topic models (RTM), and labeled LDA (LaLDA). This toolbox is an ongoing project
and more BP-based algorithms for various topic models will be added in the near
future. Interested users may also extend BP algorithms for learning more
complicated topic models. The source codes are freely available under the GNU
General Public Licence, Version 1.0 at https://mloss.org/software/view/399/.Comment: 4 page
Second-order Stable Finite Difference Schemes for the Time-fractional Diffusion-wave Equation
We propose two stable and one conditionally stable finite difference schemes
of second-order in both time and space for the time-fractional diffusion-wave
equation. In the first scheme, we apply the fractional trapezoidal rule in time
and the central difference in space. We use the generalized Newton-Gregory
formula in time for the second scheme and its modification for the third
scheme. While the second scheme is conditionally stable, the first and the
third schemes are stable. We apply the methodology to the considered equation
with also linear advection-reaction terms and also obtain second-order schemes
both in time and space. Numerical examples with comparisons among the proposed
schemes and the existing ones verify the theoretical analysis and show that the
present schemes exhibit better performances than the known ones
Likelihood approach for marginal proportional hazards regression in the presence of dependent censoring
In many public health problems, an important goal is to identify the effect
of some treatment/intervention on the risk of failure for the whole population.
A marginal proportional hazards regression model is often used to analyze such
an effect. When dependent censoring is explained by many auxiliary covariates,
we utilize two working models to condense high-dimensional covariates to
achieve dimension reduction. Then the estimator of the treatment effect is
obtained by maximizing a pseudo-likelihood function over a sieve space. Such an
estimator is shown to be consistent and asymptotically normal when either of
the two working models is correct; additionally, when both working models are
correct, its asymptotic variance is the same as the semiparametric efficiency
bound.Comment: Published at http://dx.doi.org/10.1214/009053604000001291 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
How Vertex reinforced jump process arises naturally
We prove that the only nearest neighbor jump process with local dependence on
the occupation times satisfying the partial exchangeability property is the
vertex reinforced jump process, under some technical conditions. This result
gives a counterpart to the characterization of edge reinforced random walk
given by Rolles.Comment: 14 pages, 3 figures, version
Kolmogorov's law of the iterated logarithm for noncommutative martingales
We prove Kolmogorov's law of the iterated logarithm for noncommutative
martingales. The commutative case was due to Stout. The key ingredient is an
exponential inequality proved recently by Junge and the author.Comment: Revise
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