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Nonlinear monotone transformations are used extensively in normalizing flows to construct invertible triangular mappings from simple distributions to complex ones. In existing literature, monotonicity is usually enforced by restricting function classes or model parameters and the inverse transformation is often approximated by root-finding algorithms as a closed-form inverse is unavailable. In this paper, we introduce a new integral-based approach termed: Atomic Unrestricted Time Machine (AUTM), equipped with unrestricted integrands and easy-to-compute explicit inverse. AUTM offers a versatile and efficient way to the design of normalizing flows with explicit inverse and unrestricted function classes or parameters. Theoretically, we present a constructive proof that AUTM is universal: all monotonic normalizing flows can be viewed as limits of AUTM flows. We provide a concrete example to show how to approximate any given monotonic normalizing flow using AUTM flows with guaranteed convergence. Our result implies that AUTM can be used to transform an existing flow into a new one equipped with explicit inverse and unrestricted parameters. The performance of the new approach is evaluated on high dimensional density estimation, variational inference and image generation. 

reveal the mechanism of intermittent coupling, where the nodes are connected merely in discontinuous time durations. Instead of the common weighted average technique, by proposing a direct error method and constructing piecewise Lyapunov functions, several intermittently adaptive designs are developed to update the complex-valued coupling weights. Especially, an adaptive pinning protocol is designed for ICCVNs with heterogeneous coupling weights and the synchronization is ensured by piecewise adjusting the complex-valued weights of edges within a spanning tree. For ICCVNs with homogeneous coupling weights, based on a connected dominating set, an intermittently adaptive algorithm is developed which just depends on the information of the dominating set with their neighbors. At the end, the established theoretical results are verified by providing two numerical examples. 

In this paper, we introduce a deep spiking delayed feedback reservoir (DFR) model to combine DFR with spiking neuros: DFRs are a new type of recurrent neural networks (RNNs) that are able to capture the temporal correlations in time series while spiking neurons are energy-efficient and biologically plausible neurons models. The introduced deep spiking DFR model is energy-efficient and has the capability of analyzing time series signals. The corresponding field programmable gate arrays (FPGA)-based hardware implementation of such deep spiking DFR model is introduced and the underlying energy-efficiency and recourse utilization are evaluated. Various spike encoding schemes are explored and the optimal spike encoding scheme to analyze the time series has been identified. To be specific, we evaluate the performance of the introduced model using the spectrum occupancy time series data in MIMO-OFDM based cognitive radio (CR) in dynamic spectrum sharing (DSS) networks. In a MIMO-OFDM DSS system, available spectrum is very scarce and efficient utilization of spectrum is very essential. To improve the spectrum efficiency, the first step is to identify the frequency bands that are not utilized by the existing users so that a secondary user (SU) can use them for transmission. Due to the channel correlation as well as users' activities, there is a significant temporal correlation in the spectrum occupancy behavior of the frequency bands in different time slots. The introduced deep spiking DFR model is used to capture the temporal correlation of the spectrum occupancy time series and predict the idle/busy subcarriers in future time slots for potential spectrum access. Evaluation results suggest that our introduced model achieves higher area under curve (AUC) in the receiver operating characteristic (ROC) curve compared with the traditional energy detection-based strategies and the learning-based support vector machines (SVMs).