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This article is concerned with the second-order nonlocal retarded semilinear differential systems with fixed delay in control. Utilizing the theory of fixed point as well as cosine family, we establish the existence and uniqueness of the mild solution of the system. Then a set of new sufficient conditions are established for the controllability of the semilinear system. The theory is illustrated by providing an example. [ABSTRACT FROM AUTHOR]

Human action localization in any long, untrimmed video can be determined from where and what action takes place in a given video segment. The main hurdles in human action localization are the spatiotemporal randomnesses of their happening in a parallel mode which means the location (a particular set of frames containing action instances) and duration of any particular action in real-life video sequences generally are not fixed. At another end, the uncontrolled conditions such as occlusions, viewpoints and motions at the crisp boundary of the action sequences demand to develop a fast deep network which can be easily trained from unlabeled samples of complex video sequences. Motivated from the facts, we proposed a weakly supervised deep network model for human action localization. The model is trained from unlabeled action samples from UCF50 action benchmark. The five-channel data obtained from the concatenation of RGB (three-channel) and optical flow vectors (two-channel) are fed to the proposed convolutional neural network. LSTM network is used to yield the region of action happening area. The performance of the model is tested on UCF-sports dataset. The observation and comparative results reflect that our model can localize any action from annotation-free data samples captured in uncontrolled conditions. [ABSTRACT FROM AUTHOR]