A Web Aggregation Approach for Distributed Randomized PageRank Algorithms

The PageRank algorithm employed at Google assigns a measure of importance to each web page for rankings in search results. In our recent papers, we have proposed a distributed randomized approach for this algorithm, where web pages are treated as agents computing their own PageRank by communicating with linked pages. This paper builds upon this approach to reduce the computation and communication loads for the algorithms. In particular, we develop a method to systematically aggregate the web pages into groups by exploiting the sparsity inherent in the web. For each group, an aggregated PageRank value is computed, which can then be distributed among the group members. We provide a distributed update scheme for the aggregated PageRank along with an analysis on its convergence properties. The method is especially motivated by results on singular perturbation techniques for large-scale Markov chains and multi-agent consensus.Comment: To appear in the IEEE Transactions on Automatic Control, 201

Stochastic Constrained DRO with a Complexity Independent of Sample Size

Distributionally Robust Optimization (DRO), as a popular method to train robust models against distribution shift between training and test sets, has received tremendous attention in recent years. In this paper, we propose and analyze stochastic algorithms that apply to both non-convex and convex losses for solving Kullback Leibler divergence constrained DRO problem. Compared with existing methods solving this problem, our stochastic algorithms not only enjoy competitive if not better complexity independent of sample size but also just require a constant batch size at every iteration, which is more practical for broad applications. We establish a nearly optimal complexity bound for finding an $\epsilon$ stationary solution for non-convex losses and an optimal complexity for finding an $\epsilon$ optimal solution for convex losses. Empirical studies demonstrate the effectiveness of the proposed algorithms for solving non-convex and convex constrained DRO problems.Comment: 37 pages, 16 figure

Subtle mutations in the SMN1 gene in Chinese patients with SMA: p.Arg288Met mutation causing SMN1 transcript exclusion of exon7

BACKGROUND: Proximal spinal muscular atrophy (SMA) is a common neuromuscular disorder resulting in death during childhood. Around 81 ~ 95% of SMA cases are a result of homozygous deletions of survival motor neuron gene 1 (SMN1) gene or gene conversions from SMN1 to SMN2. Less than 5% of cases showed rare subtle mutations in SMN1. Our aim was to identify subtle mutations in Chinese SMA patients carrying a single SMN1 copy. METHODS: We examined 14 patients from 13 unrelated families. Multiplex ligation-dependent probe amplification analysis was carried out to determine the copy numbers of SMN1 and SMN2. Reverse transcription polymerase chain reaction (RT-PCR) and clone sequencing were used to detect subtle mutations in SMN1. SMN transcript levels were determined using quantitative RT-PCR. RESULTS: Six subtle mutations (p.Ser8LysfsX23, p.Glu134Lys, p.Leu228X, p.Ser230Leu, p.Tyr277Cys, and p.Arg288Met) were identified in 12 patients. The p.Tyr277Cys mutation has not been reported previously. The p.Ser8LysfsX23, p.Leu228X, and p.Tyr277Cys mutations have only been reported in Chinese SMA patients and the first two mutations seem to be the common ones. Levels of full length SMN1 (fl-SMN1) transcripts were very low in patients carrying p.Ser8LysfsX23, p.Leu228X or p.Arg288Met compared with healthy carriers. In patients carrying p.Glu134Lys or p.Ser230Leu, levels of fl-SMN1 transcripts were reduced but not significant. The SMN1 transcript almost skipped exon 7 entirely in patients with the p.Arg288Met mutation. CONCLUSIONS: Our study reveals a distinct spectrum of subtle mutations in SMN1 of Chinese SMA patients from that of other ethnicities. The p.Arg288Met missense mutation possibly influences the correct splicing of exon 7 in SMN1. Mutation analysis of the SMN1 gene in Chinese patients may contribute to the identification of potential ethnic differences and enrich the SMN1 subtle mutation database

A globally consistent nonlinear least squares estimator for identification of nonlinear rational systems

© 2016 Elsevier Ltd This paper considers identification of nonlinear rational systems defined as the ratio of two nonlinear functions of past inputs and outputs. Despite its long history, a globally consistent identification algorithm remains illusive. This paper proposes a globally convergent identification algorithm for such nonlinear rational systems. To the best of our knowledge, this is the first globally convergent algorithm for the nonlinear rational systems. The technique employed is a two-step estimator. Though two-step estimators are known to produce consistent nonlinear least squares estimates if a N consistent estimate can be determined in the first step, how to find such a N consistent estimate in the first step for nonlinear rational systems is nontrivial and is not answered by any two-step estimators. The technical contribution of the paper is to develop a globally consistent estimator for nonlinear rational systems in the first step. This is achieved by involving model transformation, bias analysis, noise variance estimation, and bias compensation in the paper. Two simulation examples and a practical example are provided to verify the good performance of the proposed two-step estimator

Bolus characteristics based on Magnetic Resonance Angiography

BACKGROUND: A detailed contrast bolus propagation model is essential for optimizing bolus-chasing Computed Tomography Angiography (CTA). Bolus characteristics were studied using bolus-timing datasets from Magnetic Resonance Angiography (MRA) for adaptive controller design and validation. METHODS: MRA bolus-timing datasets of the aorta in thirty patients were analyzed by a program developed with MATLAB. Bolus characteristics, such as peak position, dispersion and bolus velocity, were studied. The bolus profile was fit to a convolution function, which would serve as a mathematical model of bolus propagation in future controller design. RESULTS: The maximum speed of the bolus in the aorta ranged from 5–13 cm/s and the dwell time ranged from 7–13 seconds. Bolus characteristics were well described by the proposed propagation model, which included the exact functional relationships between the parameters and aortic location. CONCLUSION: The convolution function describes bolus dynamics reasonably well and could be used to implement the adaptive controller design