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

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

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