Uniform convergence of conditional distributions for one-dimensional diffusion processes

In this paper, we study the quasi-stationary behavior of the one-dimensional diffusion process with a regular or exit boundary at 0 and an entrance boundary at $\infty$. By using the Doob's $h$-transform, we show that the conditional distribution of the process converges to its unique quasi-stationary distribution exponentially fast in the total variation norm, uniformly with respect to the initial distribution. Moreover, we also use the same method to show that the conditional distribution of the process converges exponentially fast in the $\psi$-norm to the unique quasi-stationary distribution.Comment: 15 page

Kernel Exponential Family Estimation via Doubly Dual Embedding

We investigate penalized maximum log-likelihood estimation for exponential family distributions whose natural parameter resides in a reproducing kernel Hilbert space. Key to our approach is a novel technique, doubly dual embedding, that avoids computation of the partition function. This technique also allows the development of a flexible sampling strategy that amortizes the cost of Monte-Carlo sampling in the inference stage. The resulting estimator can be easily generalized to kernel conditional exponential families. We establish a connection between kernel exponential family estimation and MMD-GANs, revealing a new perspective for understanding GANs. Compared to the score matching based estimators, the proposed method improves both memory and time efficiency while enjoying stronger statistical properties, such as fully capturing smoothness in its statistical convergence rate while the score matching estimator appears to saturate. Finally, we show that the proposed estimator empirically outperforms state-of-the-artComment: 22 pages, 20 figures; AISTATS 201

CELLULASE6 and MANNANASE7 affect cell differentiation and silique dehiscence in Arabidopsis

Cellulases, hemicellulases and pectinases play important roles in fruit development and maturation, but mutants with defects in the fruit have not been reported for cellulase or hemicellulase genes. Here we report the functional characterization of cellulase gene CEL6 and hemicellulase gene MAN7 in silique development and dehiscence in Arabidopsis. These genes were found to be expressed in vegetative and reproductive organs, and their expression in the silique partially depended on the IND and ALC transcriptional factors. Mutant alleles of cel6 and man7 exhibited delayed secondary cell wall thickening and altered cell morphology in the valve margin and impaired silique dehiscence. Cells in the separation layer in nearly mature siliques of the single mutants and the cel6-1 man7-3 double mutant remained intact whereas they degenerated in the wild-type control. Phenotypic studies of single, double, triple and quadruple mutants revealed that the higher-order mutant combinations of the cel6-1, man7-3, and pectinase adpg1-1 and adpg2- 1 mutations produced more severe silique indehiscent phenotypes than the corresponding lower-order mutant combinations, except for some combinations involving cel6-1, man7-3, and adpg2-1. Our results demonstrate that the ability of the silique to dehisce can be manipulated to different degrees by altering the activities of proteins of different types.Plant Biology, Ecology and Evolutio

The More the Worse? Mining Valuable Ideas with Sentiment Analysis for Idea Recommendation

Many firms have an interest in an open innovation community, recognizing its business value. They can collect and analyze the ideas of their customers from the community to get valuable ideas which can lead to innovation such as a new product or service. However, such a community overloaded with too many ideas from customers cannot make use of them at the right time because of the limited time and human resources to deal with them. Therefore, it would be a great help to those firms if they have a recommendation system which recommends top n ideas for innovation. MyStarbucksIdea (MSI) is such an open community, created by Starbucks. To build such an innovative idea recommendation system for Starbucks, we analyzed a dataset collected from MSI, utilizing data mining and sentiment analysis techniques. Experimental results show that our recommendation system can help firms identify prospective ideas which can be valuable enough for their innovation among a large amount of ideas, efficiently