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Understanding temporal dependencies of videos is fundamental for vision problems, but deep learning–based models are still insufficient in this field. In this article, we propose a novel deep multiplicative neural network (DMNN) for learning hierarchical long-term representations from video. The DMNN is built upon the multiplicative block that remembers the pairwise transformations between consecutive frames using multiplicative interactions rather than the regular weighted-sum ones. The block is slided over the timesteps to update the memory of the networks on the frame pairs. Deep architecture can be implemented by stacking multiple layers of the sliding blocks. The multiplicative interactions lead to exact, rather than approximate, modeling of temporal dependencies. The memory mechanism can remember the temporal dependencies for an arbitrary length of time. The multiple layers output multiple-level representations that reflect the multi-timescale structure of video. Moreover, to address the difficulty of training DMNNs, we derive a theoretically sound convergent method, which leads to a fast and stable convergence. We demonstrate a new state-of-the-art classification performance with proposed networks on the UCF101 dataset and the effectiveness of capturing complicate temporal dependencies on a variety of synthetic datasets.

Cluster analysis of power loads can not only accurately extract the commonalities and characteristics of the loads, but also help to understand the users’ habits and patterns of electricity consumption, so as to optimize the power dispatching and regulate the operation of the entire power grid. Based on the traditional clustering methods, this paper proposes a clustering algorithm that can automatically determine the optimal cluster number. Firstly, Fast-DTW algorithm is used as the similarity measuring function to calculate the similar matrix between two time series, and then Spectral Clustering and Affinity Propagation (AP) algorithm are used for clustering. It is combined with Euclidean distance, DTW and Fast-DTW algorithms to evaluate the algorithm effect. By analyzing the actual power data, our results show that the improved external performance evaluation index ARI, AMI and internal performance evaluation index SSE are significantly improved and have better time series similarity and accuracy. Applying the algorithm to more than six thousands of users, twelve kinds of typical power load patterns can be obtained. For any other load curve, it can be mapped to a standard load by feature extraction. The corresponding prediction model is adopted, which is of great significance to reduce the peak power consumption, adjust the electricity price appropriately and solve the problem of system balance.

This paper presents a new approach to generate inequalities invariants of hybrid system based on template and quantifier elimination. The main idea is to introduce a candidate parametric invariant as template and then reduce the verification condition into a quantifier elimination problem. The challenge is to deal with the continuous consecution condition of hybrid system because of the existence of differential equation. From the preliminary experiment results, we demonstrate the feasibility of our approach.

We present a mechanical algorithm for proving a geometric theorem involving inequality. The main idea is to convert the geometric theorem into a polynomial problem and then use polynomial solver to resolve it. We first eliminate quantifier of prenex formula via software package QEPCAD, and prove the inequality based on the extreme value theory.

Proving termination of program loops is necessary in many applications, especially those safety critical software. Discovering ranking function is a classical method to prove the termination, but the existence of ranking function is a sufficient condition on the termination of a loop program. In this paper, we present an algorithm to remedy the limitation of ranking function for analyzing the termination of linear programs with conditionals. We transform the linear loop programs with conditionals into the nested linear loop programs, and then check whether the inner loop terminates or not by positive eigenvalues and their corresponding eigenvectors. If one of the inner loop in the nested linear loop is nonterminating, then the linear loop is nonterminating. Otherwise, we use discovering ranking functions based on qualifier elimination to analyze the termination of the linear loop. To illustrate the main idea of the algorithm, we perform it on some examples.

Non-termination analysis of loop programs plays a central role in many applications, especially in the field of safety critical softwares. This paper presents a method to analyze non-termination of linear programs with conditionals. We transform the linear loop programs with conditionals into the nested linear loop programs, and then check whether the inner loop terminates or not by the positive eigenvalues and their corresponding eigenvectors. If one of the inner loop in the nested linear loop is non-terminating, then the linear loop is non-terminating. Otherwise, we need to use ranking function or finite differences of expressions over transition systems to analyze the termination of the outer loop.

The verification of termination is a difficult problem. While most of the recent work on automated termination proofs focuses on the construction of linear ranking functions for unnested loops, we present an algorithm based on region graphs to prove termination of nested loops. The method can prove the termination of terminating nested loops that may not have linear ranking function. For the programs we have considered, this approach converges faster and sufficiently.