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This note explores the extension of D-stability to non-square matrices, applicable to distributed/decentralized controllability analysis. We first present a definition of D-stability for non-square matrices, directly extending from square matrices. We propose sufficient conditions for specific configurations of non-square matrices. Finally, we consider the selection of configurations to ensure the D-stability of a given non-square system., Comment: arXiv admin note: text overlap with arXiv:2401.00367

The calibration of MEMS triaxial gyroscopes is crucial for achieving precise attitude estimation for various wearable health monitoring applications. However, gyroscope calibration poses greater challenges compared to accelerometers and magnetometers. This paper introduces an efficient method for calibrating MEMS triaxial gyroscopes via only a servo motor, making it well-suited for field environments. The core strategy of the method involves utilizing the fact that the dot product of the measured gravity and the rotational speed in a fixed frame remains constant. To eliminate the influence of rotating centrifugal force on the accelerometer, the accelerometer data is measured while stationary. The proposed calibration experiment scheme, which allows gyroscopic measurements when operating each axis at a specific rotation speed, making it easier to evaluate the linearity across a related speed range constituted by a series of rotation speeds. Moreover, solely the classical least squares algorithm proves adequate for estimating the scale factor, notably streamlining the analysis of the calibration process. Extensive numerical simulations were conducted to analyze the proposed method's performance in calibrating a triaxial gyroscope model. Experimental validation was also carried out using a commercially available MEMS inertial measurement unit (LSM9DS1 from Arduino nano 33 BLE SENSE) and a servo motor capable of controlling precise speed. The experimental results effectively demonstrate the efficacy of the proposed calibration approach.

Brain-Computer Interfaces (BCIs) rely on accurately decoding electroencephalography (EEG) motor imagery (MI) signals for effective device control. Graph Neural Networks (GNNs) outperform Convolutional Neural Networks (CNNs) in this regard, by leveraging the spatial relationships between EEG electrodes through adjacency matrices. The EEG_GLT-Net framework, featuring the state-of-the-art EEG_GLT adjacency matrix method, has notably enhanced EEG MI signal classification, evidenced by an average accuracy of 83.95% across 20 subjects on the PhysioNet dataset. This significantly exceeds the 76.10% accuracy rate achieved using the Pearson Correlation Coefficient (PCC) method within the same framework. In this research, we advance the field by applying a Reinforcement Learning (RL) approach to the classification of EEG MI signals. Our innovative method empowers the RL agent, enabling not only the classification of EEG MI data points with higher accuracy, but effective identification of EEG MI data points that are less distinct. We present the EEG_RL-Net, an enhancement of the EEG_GLT-Net framework, which incorporates the trained EEG GCN Block from EEG_GLT-Net at an adjacency matrix density of 13.39% alongside the RL-centric Dueling Deep Q Network (Dueling DQN) block. The EEG_RL-Net model showcases exceptional classification performance, achieving an unprecedented average accuracy of 96.40% across 20 subjects within 25 milliseconds. This model illustrates the transformative effect of the RL in EEG MI time point classification.

Brain-Computer Interfaces connect the brain to external control devices, necessitating the accurate translation of brain signals such as from electroencephalography (EEG) into executable commands. Graph Neural Networks (GCN) have been increasingly applied for classifying EEG Motor Imagery signals, primarily because they incorporates the spatial relationships among EEG channels, resulting in improved accuracy over traditional convolutional methods. Recent advances by GCNs-Net in real-time EEG MI signal classification utilised Pearson Coefficient Correlation (PCC) for constructing adjacency matrices, yielding significant results on the PhysioNet dataset. Our paper introduces the EEG Graph Lottery Ticket (EEG_GLT) algorithm, an innovative technique for constructing adjacency matrices for EEG channels. It does not require pre-existing knowledge of inter-channel relationships, and it can be tailored to suit both individual subjects and GCN model architectures. Our findings demonstrated that the PCC method outperformed the Geodesic approach by 9.65% in mean accuracy, while our EEG_GLT matrix consistently exceeded the performance of the PCC method by a mean accuracy of 13.39%. Also, we found that the construction of the adjacency matrix significantly influenced accuracy, to a greater extent than GCN model configurations. A basic GCN configuration utilising our EEG_GLT matrix exceeded the performance of even the most complex GCN setup with a PCC matrix in average accuracy. Our EEG_GLT method also reduced MACs by up to 97% compared to the PCC method, while maintaining or enhancing accuracy. In conclusion, the EEG_GLT algorithm marks a breakthrough in the development of optimal adjacency matrices, effectively boosting both computational accuracy and efficiency, making it well-suited for real-time classification of EEG MI signals that demand intensive computational resources.

In this note, we discuss the extension of several important stable square matrices, e.g., D-stable matrices, diagonal dominance matrices, Volterra-Lyapunov stable matrices, to their corresponding non-square matrices. The extension is motivated by some distributed control-related problems, such as decentralized unconditional stability and decentralized integral controllability for non-square processes. We will provide the connections of conditions between these special square matrices and their associated non-square counterparts. Some conjectures for these special matrices are proposed for future research., Comment: 7 pages; no figure

This paper aims to develop a new human-machine interface to improve rehabilitation performance from the perspective of both the user (patient) and the machine (robot) by introducing the co-adaption techniques via model-based reinforcement learning. Previous studies focus more on robot assistance, i.e., to improve the control strategy so as to fulfill the objective of Assist-As-Needed. In this study, we treat the full process of robot-assisted rehabilitation as a co-adaptive or mutual learning process and emphasize the adaptation of the user to the machine. To this end, we proposed a Co-adaptive MDPs (CaMDPs) model to quantify the learning rates based on cooperative multi-agent reinforcement learning (MARL) in the high abstraction layer of the systems. We proposed several approaches to cooperatively adjust the Policy Improvement among the two agents in the framework of Policy Iteration. Based on the proposed co-adaptive MDPs, the simulation study indicates the non-stationary problem can be mitigated using various proposed Policy Improvement approaches., Comment: 11 pages; 4 figures

This paper focuses on the task of survival time analysis for lung cancer. Although much progress has been made in this problem in recent years, the performance of existing methods is still far from satisfactory. Traditional and some deep learning-based survival time analyses for lung cancer are mostly based on textual clinical information such as staging, age, histology, etc. Unlike existing methods that predicting on the single modality, we observe that a human clinician usually takes multimodal data such as text clinical data and visual scans to estimate survival time. Motivated by this, in this work, we contribute a smart cross-modality network for survival analysis network named Lite-ProSENet that simulates a human's manner of decision making. Extensive experiments were conducted using data from 422 NSCLC patients from The Cancer Imaging Archive (TCIA). The results show that our Lite-ProSENet outperforms favorably again all comparison methods and achieves the new state of the art with the 89.3% on concordance. The code will be made publicly available., Comment: 11 pages, 6 figures, Multimodal learning, NSCLC, Survival analysis, Transformer

Differentiable Architecture Search (DARTS) has received massive attention in recent years, mainly because it significantly reduces the computational cost through weight sharing and continuous relaxation. However, more recent works find that existing differentiable NAS techniques struggle to outperform naive baselines, yielding deteriorative architectures as the search proceeds. Rather than directly optimizing the architecture parameters, this paper formulates the neural architecture search as a distribution learning problem through relaxing the architecture weights into Gaussian distributions. By leveraging the natural-gradient variational inference (NGVI), the architecture distribution can be easily optimized based on existing codebases without incurring more memory and computational consumption. We demonstrate how the differentiable NAS benefits from Bayesian principles, enhancing exploration and improving stability. The experimental results on NAS-Bench-201 and NAS-Bench-1shot1 benchmark datasets confirm the significant improvements the proposed framework can make. In addition, instead of simply applying the argmax on the learned parameters, we further leverage the recently-proposed training-free proxies in NAS to select the optimal architecture from a group architectures drawn from the optimized distribution, where we achieve state-of-the-art results on the NAS-Bench-201 and NAS-Bench-1shot1 benchmarks. Our best architecture in the DARTS search space also obtains competitive test errors with 2.37\%, 15.72\%, and 24.2\% on CIFAR-10, CIFAR-100, and ImageNet datasets, respectively.

\textit{Differentiable ARchiTecture Search} (DARTS) has recently become the mainstream of neural architecture search (NAS) due to its efficiency and simplicity. With a gradient-based bi-level optimization, DARTS alternately optimizes the inner model weights and the outer architecture parameter in a weight-sharing supernet. A key challenge to the scalability and quality of the learned architectures is the need for differentiating through the inner-loop optimisation. While much has been discussed about several potentially fatal factors in DARTS, the architecture gradient, a.k.a. hypergradient, has received less attention. In this paper, we tackle the hypergradient computation in DARTS based on the implicit function theorem, making it only depends on the obtained solution to the inner-loop optimization and agnostic to the optimization path. To further reduce the computational requirements, we formulate a stochastic hypergradient approximation for differentiable NAS, and theoretically show that the architecture optimization with the proposed method, named iDARTS, is expected to converge to a stationary point. Comprehensive experiments on two NAS benchmark search spaces and the common NAS search space verify the effectiveness of our proposed method. It leads to architectures outperforming, with large margins, those learned by the baseline methods., Comment: ICML2021

Lung cancer is the leading cause of cancer death worldwide. The critical reason for the deaths is delayed diagnosis and poor prognosis. With the accelerated development of deep learning techniques, it has been successfully applied extensively in many real-world applications, including health sectors such as medical image interpretation and disease diagnosis. By combining more modalities that being engaged in the processing of information, multimodal learning can extract better features and improve predictive ability. The conventional methods for lung cancer survival analysis normally utilize clinical data and only provide a statistical probability. To improve the survival prediction accuracy and help prognostic decision-making in clinical practice for medical experts, we for the first time propose a multimodal deep learning method for non-small cell lung cancer (NSCLC) survival analysis, named DeepMMSA. This method leverages CT images in combination with clinical data, enabling the abundant information hold within medical images to be associate with lung cancer survival information. We validate our method on the data of 422 NSCLC patients from The Cancer Imaging Archive (TCIA). Experimental results support our hypothesis that there is an underlying relationship between prognostic information and radiomic images. Besides, quantitative results showing that the established multimodal model can be applied to traditional method and has the potential to break bottleneck of existing methods and increase the the percentage of concordant pairs(right predicted pairs) in overall population by 4%., Comment: 7 Submitted to IEEE TBME

This paper presents an efficient in-field calibration method tailored for low-cost triaxial MEMS gyroscopes often used in healthcare applications. Traditional calibration techniques are challenging to implement in clinical settings due to the unavailability of high-precision equipment. Unlike the auto-calibration approaches used for triaxial MEMS accelerometers, which rely on local gravity, gyroscopes lack a reliable reference since the Earth's self-rotation speed is insufficient for accurate calibration. To address this limitation, we propose a novel method that uses manual rotation of the MEMS gyroscope to a specific angle (360{\deg}) as the calibration reference. This approach iteratively estimates the sensor's attitude without requiring any external equipment. Numerical simulations and empirical tests validate that the calibration error is low and that parameter estimation is unbiased. The method can be implemented in real-time on a low-energy microcontroller and completed in under 30 seconds. Comparative results demonstrate that the proposed technique outperforms existing state-of-the-art methods, achieving scale factor and bias errors of less than $2.5\times10^{-2}$ for LSM9DS1 and less than $1\times10^{-2}$ for ICM20948.

This paper presents an efficient servomotor-aided calibration method for the triaxial gyroscope. The entire calibration process only requires approximately one minute, and does not require high-precision equipment. This method is based on the idea that the measurement of the gyroscope should be equal to the rotation speed of the servomotor. A six-observation experimental design is proposed to minimize the maximum variance of the estimated scale factors and biases. In addition, a fast converging recursive linear least square estimation method is presented to reduce computational complexity. The simulation results reflect the robustness of the calibration method under normal and extreme conditions. We experimentally demonstrate the feasibility of the proposed method on a robot arm, and implement the method on a microcontroller. We verify the calibration results of the proposed method by comparing with a traditional turntable approach, and the experiment indicates that the results of these two methods are comparable. By comparing the calibrated low-cost gyroscope reading with the reading from a high-precision gyroscope, we can conclude that our method significantly increases the gyroscope's accuracy.

Causal decomposition depicts a cause-effect relationship that is not based on the concept of prediction, but based on the phase dependence of time series. It has been validated in both stochastic and deterministic systems and is now anticipated for its application in the complex dynamic process. Here, we present an extension of causal decomposition in the mutual complex dynamic process: cause and effect of time series are inherited in the decomposition of intrinsic components in a similar time scale. Furthermore, we illustrate comparative studies with predominate methods used in neuroscience, and show the applicability of the method particularly to physiological time series in brain-muscle interactions, implying the potential to the causality analysis in the complex physiological process., Comment: 18 pages, 4 figures

One-Shot Neural architecture search (NAS) attracts broad attention recently due to its capacity to reduce the computational hours through weight sharing. However, extensive experiments on several recent works show that there is no positive correlation between the validation accuracy with inherited weights from the supernet and the test accuracy after re-training for One-Shot NAS. Different from devising a controller to find the best performing architecture with inherited weights, this paper focuses on how to sample architectures to train the supernet to make it more predictive. A single-path supernet is adopted, where only a small part of weights are optimized in each step, to reduce the memory demand greatly. Furthermore, we abandon devising complicated reward based architecture sampling controller, and sample architectures to train supernet based on novelty search. An efficient novelty search method for NAS is devised in this paper, and extensive experiments demonstrate the effectiveness and efficiency of our novelty search based architecture sampling method. The best architecture obtained by our algorithm with the same search space achieves the state-of-the-art test error rate of 2.51\% on CIFAR-10 with only 7.5 hours search time in a single GPU, and a validation perplexity of 60.02 and a test perplexity of 57.36 on PTB. We also transfer these search cell structures to larger datasets ImageNet and WikiText-2, respectively., Comment: 10 pages, 2 figures

Bayesian optimization (BO) has been broadly applied to computational expensive problems, but it is still challenging to extend BO to high dimensions. Existing works are usually under strict assumption of an additive or a linear embedding structure for objective functions. This paper directly introduces a supervised dimension reduction method, Sliced Inverse Regression (SIR), to high dimensional Bayesian optimization, which could effectively learn the intrinsic sub-structure of objective function during the optimization. Furthermore, a kernel trick is developed to reduce computational complexity and learn nonlinear subset of the unknowing function when applying SIR to extremely high dimensional BO. We present several computational benefits and derive theoretical regret bounds of our algorithm. Extensive experiments on synthetic examples and two real applications demonstrate the superiority of our algorithms for high dimensional Bayesian optimization., Comment: 7 pages, 3 figures, IJCAI 2019 accepted paper

This paper investigates lung nodule classification by using deep neural networks (DNNs). Hyperparameter optimization in DNNs is a computationally expensive problem, where evaluating a hyperparameter configuration may take several hours or even days. Bayesian optimization has been recently introduced for the automatically searching of optimal hyperparameter configurations of DNNs. It applies probabilistic surrogate models to approximate the validation error function of hyperparameter configurations, such as Gaussian processes, and reduce the computational complexity to a large extent. However, most existing surrogate models adopt stationary covariance functions to measure the difference between hyperparameter points based on spatial distance without considering its spatial locations. This distance-based assumption together with the condition of constant smoothness throughout the whole hyperparameter search space clearly violates the property that the points far away from optimal points usually get similarly poor performance even though each two of them have huge spatial distance between them. In this paper, a non-stationary kernel is proposed which allows the surrogate model to adapt to functions whose smoothness varies with the spatial location of inputs, and a multi-level convolutional neural network (ML-CNN) is built for lung nodule classification whose hyperparameter configuration is optimized by using the proposed non-stationary kernel based Gaussian surrogate model. Our algorithm searches the surrogate for optimal setting via hyperparameter importance based evolutionary strategy, and the experiments demonstrate our algorithm outperforms manual tuning and well-established hyperparameter optimization methods such as Random search, Gaussian processes with stationary kernels, and recently proposed Hyperparameter Optimization via RBF and Dynamic coordinate search.

This note investigates the stability of both linear and nonlinear switched systems with average dwell time. Two new analysis methods are proposed. Different from existing approaches, the proposed methods take into account the sequence in which the subsystems are switched. Depending on the predecessor or successor subsystems to be considered, sequence-based average preceding dwell time (SBAPDT) and sequence-based average subsequence dwell time (SBASDT) approaches are proposed and discussed for both continuous and discrete time systems. These proposed methods, when considering the switch sequence, have the potential to further reduce the conservativeness of the existing approaches. A comparative numerical example is also given to demonstrate the advantages of the proposed approaches.