Convergence rate of numerical solutions to SFDEs with jumps

In this paper, we are interested in numerical solutions of stochastic functional differential equations with jumps. Under a global Lipschitz condition, we show that the pth-moment convergence of Euler–Maruyama numerical solutions to stochastic functional differential equations with jumps has order 1/p for any p ≥ 2. This is significantly different from the case of stochastic functional differential equations without jumps, where the order is 1/2 for any p ≥ 2. It is therefore best to use the mean-square convergence for stochastic functional differential equations with jumps. Moreover, under a local Lipschitz condition, we reveal that the order of mean-square convergence is close to 1/2, provided that local Lipschitz constants, valid on balls of radius j, do not grow faster than log j

Comparison theorem of one-dimensional stochastic hybrid delay systems

The comparison theorem of stochastic differential equations has been investigated by many authors. However, little research is available on the comparison theorem of stochastic hybrid systems, which is the topic of this paper. The systems discussed is stochastic delay differential equations with Markovian switching. It is an important class of hybrid systems

Efficient Genomic Interval Queries Using Augmented Range Trees

Efficient large-scale annotation of genomic intervals is essential for personal genome interpretation in the realm of precision medicine. There are 13 possible relations between two intervals according to Allen's interval algebra. Conventional interval trees are routinely used to identify the genomic intervals satisfying a coarse relation with a query interval, but cannot support efficient query for more refined relations such as all Allen's relations. We design and implement a novel approach to address this unmet need. Through rewriting Allen's interval relations, we transform an interval query to a range query, then adapt and utilize the range trees for querying. We implement two types of range trees: a basic 2-dimensional range tree (2D-RT) and an augmented range tree with fractional cascading (RTFC) and compare them with the conventional interval tree (IT). Theoretical analysis shows that RTFC can achieve the best time complexity for interval queries regarding all Allen's relations among the three trees. We also perform comparative experiments on the efficiency of RTFC, 2D-RT and IT in querying noncoding element annotations in a large collection of personal genomes. Our experimental results show that 2D-RT is more efficient than IT for interval queries regarding most of Allen's relations, RTFC is even more efficient than 2D-RT. The results demonstrate that RTFC is an efficient data structure for querying large-scale datasets regarding Allen's relations between genomic intervals, such as those required by interpreting genome-wide variation in large populations.Comment: 4 figures, 4 table

Graph Convolutional Networks for Text Classification

Text classification is an important and classical problem in natural language processing. There have been a number of studies that applied convolutional neural networks (convolution on regular grid, e.g., sequence) to classification. However, only a limited number of studies have explored the more flexible graph convolutional neural networks (convolution on non-grid, e.g., arbitrary graph) for the task. In this work, we propose to use graph convolutional networks for text classification. We build a single text graph for a corpus based on word co-occurrence and document word relations, then learn a Text Graph Convolutional Network (Text GCN) for the corpus. Our Text GCN is initialized with one-hot representation for word and document, it then jointly learns the embeddings for both words and documents, as supervised by the known class labels for documents. Our experimental results on multiple benchmark datasets demonstrate that a vanilla Text GCN without any external word embeddings or knowledge outperforms state-of-the-art methods for text classification. On the other hand, Text GCN also learns predictive word and document embeddings. In addition, experimental results show that the improvement of Text GCN over state-of-the-art comparison methods become more prominent as we lower the percentage of training data, suggesting the robustness of Text GCN to less training data in text classification.Comment: Accepted by 33rd AAAI Conference on Artificial Intelligence (AAAI 2019

Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching

The main aim of this paper is to discuss the almost surely asymptotic stability of the neutral stochastic differential delay equations (NSDDEs) with Markovian switching. Linear NSDDEs with Markovian switching and nonlinear examples will be discussed to illustrate the theory