Phase Open Fault Tolerant Control of High Reliability Doubly-Salient Wound-Field Machine

Doubly Salient Wound-Field Machine (DSWFM) can be employed on aeronautics starter-generator because it has good performance on both power generation and starting. To improve the system reliability, a three-phase four bridge legs converter which has fault tolerant capability is proposed to solve one phase open-circuit fault problem of the DSWFM. And the advantage of the proposed converter to the full-bridge converter fault-tolerant mode is analyzed. With the study of DSWFM theory and torque equation, a constant torque fault-tolerant strategy is proposed to keep the performance and reduce the torque ripple. The drive system after fault identification can be reconstructed by the proposed method, and the machine performance can recover quickly. Simulations confirm the feasibility of the proposed fault tolerant system

Low Rank Approximation of Binary Matrices: Column Subset Selection and Generalizations

Low rank matrix approximation is an important tool in machine learning. Given a data matrix, low rank approximation helps to find factors, patterns and provides concise representations for the data. Research on low rank approximation usually focus on real matrices. However, in many applications data are binary (categorical) rather than continuous. This leads to the problem of low rank approximation of binary matrix. Here we are given a $d \times n$ binary matrix $A$ and a small integer $k$. The goal is to find two binary matrices $U$ and $V$ of sizes $d \times k$ and $k \times n$ respectively, so that the Frobenius norm of $A - U V$ is minimized. There are two models of this problem, depending on the definition of the dot product of binary vectors: The $\mathrm{GF}(2)$ model and the Boolean semiring model. Unlike low rank approximation of real matrix which can be efficiently solved by Singular Value Decomposition, approximation of binary matrix is $NP$-hard even for $k=1$. In this paper, we consider the problem of Column Subset Selection (CSS), in which one low rank matrix must be formed by $k$ columns of the data matrix. We characterize the approximation ratio of CSS for binary matrices. For $GF(2)$ model, we show the approximation ratio of CSS is bounded by $\frac{k}{2}+1+\frac{k}{2(2^k-1)}$ and this bound is asymptotically tight. For Boolean model, it turns out that CSS is no longer sufficient to obtain a bound. We then develop a Generalized CSS (GCSS) procedure in which the columns of one low rank matrix are generated from Boolean formulas operating bitwise on columns of the data matrix. We show the approximation ratio of GCSS is bounded by $2^{k-1}+1$, and the exponential dependency on $k$ is inherent.Comment: 38 page

Deep recurrent spiking neural networks capture both static and dynamic representations of the visual cortex under movie stimuli

In the real world, visual stimuli received by the biological visual system are predominantly dynamic rather than static. A better understanding of how the visual cortex represents movie stimuli could provide deeper insight into the information processing mechanisms of the visual system. Although some progress has been made in modeling neural responses to natural movies with deep neural networks, the visual representations of static and dynamic information under such time-series visual stimuli remain to be further explored. In this work, considering abundant recurrent connections in the mouse visual system, we design a recurrent module based on the hierarchy of the mouse cortex and add it into Deep Spiking Neural Networks, which have been demonstrated to be a more compelling computational model for the visual cortex. Using Time-Series Representational Similarity Analysis, we measure the representational similarity between networks and mouse cortical regions under natural movie stimuli. Subsequently, we conduct a comparison of the representational similarity across recurrent/feedforward networks and image/video training tasks. Trained on the video action recognition task, recurrent SNN achieves the highest representational similarity and significantly outperforms feedforward SNN trained on the same task by 15% and the recurrent SNN trained on the image classification task by 8%. We investigate how static and dynamic representations of SNNs influence the similarity, as a way to explain the importance of these two forms of representations in biological neural coding. Taken together, our work is the first to apply deep recurrent SNNs to model the mouse visual cortex under movie stimuli and we establish that these networks are competent to capture both static and dynamic representations and make contributions to understanding the movie information processing mechanisms of the visual cortex

A Validation Approach to Over-parameterized Matrix and Image Recovery

In this paper, we study the problem of recovering a low-rank matrix from a number of noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a prior and use an overspecified factored representation of the matrix variable, where the global optimal solutions overfit and do not correspond to the underlying ground-truth. We then solve the associated nonconvex problem using gradient descent with small random initialization. We show that as long as the measurement operators satisfy the restricted isometry property (RIP) with its rank parameter scaling with the rank of ground-truth matrix rather than scaling with the overspecified matrix variable, gradient descent iterations are on a particular trajectory towards the ground-truth matrix and achieve nearly information-theoretically optimal recovery when stop appropriately. We then propose an efficient early stopping strategy based on the common hold-out method and show that it detects nearly optimal estimator provably. Moreover, experiments show that the proposed validation approach can also be efficiently used for image restoration with deep image prior which over-parameterizes an image with a deep network.Comment: 29 pages and 9 figure