Dimensional-invariance principles in coupled dynamical systems-- A unified analysis and applications

In this paper we study coupled dynamical systems and investigate dimension properties of the subspace spanned by solutions of each individual system. Relevant problems on \textit{collinear dynamical systems} and their variations are discussed recently by Montenbruck et. al. in \cite{collinear2017SCL}, while in this paper we aim to provide a unified analysis to derive the dimensional-invariance principles for networked coupled systems, and to generalize the invariance principles for networked systems with more general forms of coupling terms. To be specific, we consider two types of coupled systems, one with scalar couplings and the other with matrix couplings. Via the \textit{rank-preserving flow theory}, we show that any scalar-coupled dynamical system (with constant, time-varying or state-dependent couplings) possesses the dimensional-invariance principles, in that the dimension of the subspace spanned by the individual systems' solutions remains invariant. For coupled dynamical systems with matrix coefficients/couplings, necessary and sufficient conditions (for constant, time-varying and state-dependent couplings) are given to characterize dimensional-invariance principles. The proofs via a rank-preserving matrix flow theory in this paper simplify the analysis in \cite{collinear2017SCL}, and we also extend the invariance principles to the cases of time-varying couplings and state-dependent couplings. Furthermore, subspace-preserving property and signature-preserving flows are also developed for coupled networked systems with particular coupling terms. These invariance principles provide insightful characterizations to analyze transient behaviors and solution evolutions for a large family of coupled systems, such as multi-agent consensus dynamics, distributed coordination systems, formation control systems, among others.Comment: Single column, 15 pages, 2 figures, and 2 table

Partial Sliced Inverse Regression for Quality-Relevant Multivariate Statistical Process Monitoring

This paper introduces a popular dimension reduction method, sliced inverse regression (SIR), into multivariate statistical process monitoring. Provides an extension of SIR for the single-index model by adopting the idea from partial least squares (PLS). Our partial sliced inverse regression (PSIR) method has the merit of incorporating information from both predictors (x) and responses (y), and it has capability of handling large, nonlinear, or "n<p" dataset. Two statistics with their corresponding distributions and control limits are given based on the X-space decomposition of PSIR for the purpose of fault detection in process monitoring. Simulations showed PSIR outperformed over PLS and SIR for both linear and nonlinear model

Investigating Prior Knowledge for Challenging Chinese Machine Reading Comprehension

Machine reading comprehension tasks require a machine reader to answer questions relevant to the given document. In this paper, we present the first free-form multiple-Choice Chinese machine reading Comprehension dataset (C^3), containing 13,369 documents (dialogues or more formally written mixed-genre texts) and their associated 19,577 multiple-choice free-form questions collected from Chinese-as-a-second-language examinations. We present a comprehensive analysis of the prior knowledge (i.e., linguistic, domain-specific, and general world knowledge) needed for these real-world problems. We implement rule-based and popular neural methods and find that there is still a significant performance gap between the best performing model (68.5%) and human readers (96.0%), especially on problems that require prior knowledge. We further study the effects of distractor plausibility and data augmentation based on translated relevant datasets for English on model performance. We expect C^3 to present great challenges to existing systems as answering 86.8% of questions requires both knowledge within and beyond the accompanying document, and we hope that C^3 can serve as a platform to study how to leverage various kinds of prior knowledge to better understand a given written or orally oriented text. C^3 is available at https://dataset.org/c3/.Comment: To appear in TAC

Recurrent Meta-Structure for Robust Similarity Measure in Heterogeneous Information Networks

Similarity measure as a fundamental task in heterogeneous information network analysis has been applied to many areas, e.g., product recommendation, clustering and Web search. Most of the existing metrics depend on the meta-path or meta-structure specified by users in advance. These metrics are thus sensitive to the pre-specified meta-path or meta-structure. In this paper, a novel similarity measure in heterogeneous information networks, called Recurrent Meta-Structure-based Similarity (RMSS), is proposed. The recurrent meta-structure as a schematic structure in heterogeneous information networks provides a unified framework to integrate all of the meta-paths and meta-structures. Therefore, RMSS is robust to the meta-paths and meta-structures. We devise an approach to automatically constructing the recurrent meta-structure. In order to formalize the semantics, the recurrent meta-structure is decomposed into several recurrent meta-paths and recurrent meta-trees, and we then define the commuting matrices of the recurrent meta-paths and meta-trees. All of the commuting matrices of the recurrent meta-paths and meta-trees are combined according to different weights. Note that the weights can be determined by two kinds of weighting strategies: local weighting strategy and global weighting strategy. As a result, RMSS is defined by virtue of the final commuting matrix. Experimental evaluations show that the existing metrics are sensitive to different meta-paths or meta-structures and that the proposed RMSS outperforms the existing metrics in terms of ranking and clustering tasks

Improving Machine Reading Comprehension with General Reading Strategies

Reading strategies have been shown to improve comprehension levels, especially for readers lacking adequate prior knowledge. Just as the process of knowledge accumulation is time-consuming for human readers, it is resource-demanding to impart rich general domain knowledge into a deep language model via pre-training. Inspired by reading strategies identified in cognitive science, and given limited computational resources -- just a pre-trained model and a fixed number of training instances -- we propose three general strategies aimed to improve non-extractive machine reading comprehension (MRC): (i) BACK AND FORTH READING that considers both the original and reverse order of an input sequence, (ii) HIGHLIGHTING, which adds a trainable embedding to the text embedding of tokens that are relevant to the question and candidate answers, and (iii) SELF-ASSESSMENT that generates practice questions and candidate answers directly from the text in an unsupervised manner. By fine-tuning a pre-trained language model (Radford et al., 2018) with our proposed strategies on the largest general domain multiple-choice MRC dataset RACE, we obtain a 5.8% absolute increase in accuracy over the previous best result achieved by the same pre-trained model fine-tuned on RACE without the use of strategies. We further fine-tune the resulting model on a target MRC task, leading to an absolute improvement of 6.2% in average accuracy over previous state-of-the-art approaches on six representative non-extractive MRC datasets from different domains (i.e., ARC, OpenBookQA, MCTest, SemEval-2018 Task 11, ROCStories, and MultiRC). These results demonstrate the effectiveness of our proposed strategies and the versatility and general applicability of our fine-tuned models that incorporate these strategies. Core code is available at https://github.com/nlpdata/strategy/.Comment: To appear in NAACL-HLT 201

Joint Object and State Recognition using Language Knowledge

The state of an object is an important piece of knowledge in robotics applications. States and objects are intertwined together, meaning that object information can help recognize the state of an image and vice versa. This paper addresses the state identification problem in cooking related images and uses state and object predictions together to improve the classification accuracy of objects and their states from a single image. The pipeline presented in this paper includes a CNN with a double classification layer and the Concept-Net language knowledge graph on top. The language knowledge creates a semantic likelihood between objects and states. The resulting object and state confidences from the deep architecture are used together with object and state relatedness estimates from a language knowledge graph to produce marginal probabilities for objects and states. The marginal probabilities and confidences of objects (or states) are fused together to improve the final object (or state) classification results. Experiments on a dataset of cooking objects show that using a language knowledge graph on top of a deep neural network effectively enhances object and state classification.Comment: 5 pages, 4 figures, 1 tabl

Note on acoustic black holes from black D3-brane

In this paper, we study the acoustic black hole emerged from the nonextremal black D3-brane, based on the holographic approaches in constructing the acoustic black hole in asymptotically Anti de-Sitter spacetime (AAdS) and the effective hydrodynamic description of the nonextremal black D3-brane. We show that the holographic dual description of the acoustic black hole appeared on the timelike cutoff surface in the nonextremal black D3-brane also exist. The duality includes the dynamical connection between the acoustic black hole and the bulk gravity, a universal equation relating the Hawking-like temperature and the Hawking temperature, and a phonon/scalar channel quasinormal mode correspondence.Comment: 14 pages, no figure

Stability of Scattering Decoder For Nonlinear Diffractive Imaging

The problem of image reconstruction under multiple light scattering is usually formulated as a regularized non-convex optimization. A deep learning architecture, Scattering Decoder (ScaDec), was recently proposed to solve this problem in a purely data-driven fashion. The proposed method was shown to substantially outperform optimization-based baselines and achieve state-of-the-art results. In this paper, we thoroughly test the robustness of ScaDec to different permittivity contrasts, number of transmissions, and input signal-to-noise ratios. The results on high-fidelity simulated datasets show that the performance of ScaDec is stable in different settings.Comment: in Proceedings of iTWIST'18, Paper-ID: 31, Marseille, France, November, 21-23, 201

A note on the sum of reciprocals

For a fixed positive integer $m$ and any partition $m = m_1 + m_2 + \cdots + m_e$ , there exists a sequence $\{n_{i}\}_{i=1}^{k}$ of positive integers such that $$m=\frac{1}{n_{1}}+\frac{1}{n_{2}}+\cdots+\frac{1}{n_{k}},$$ with the property that partial sums of the series $\{\frac{1}{n_i}\}_{i=1}^{k}$ can only represent the integers with the form $\sum_{i\in I}m_i$, where $I\subset\{1,...,e\}$.Comment: This is a very very preliminary draft, which maybe contains some mistake

Quantum searching's underlying SU(2) structure and its quantum decoherence effects

The search operation for a marked state by means of Grover's quantum searching algorithm is shown to be an element of group SU(2) which acts on a 2-dimensional space spanned by the marked state and the unmarked collective state. Based on this underlying structure, those exact bounds of the steps in various quantum search algorithms are obtained in a quite concise way. This reformulation of the quantum searching algorithm also enables a detailed analysis of the decoherence effects caused by its coupling with an environment. It turns out that the environment will not only make the quantum search invalid in case of complete decoherence, where the probability of finding the marked state is unchanged, but also it may make the quantum search algorithm worse than expected: It will decrease this probability when the environment shows its quantum feature.Comment: 11 Pages; RevTe