Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.

Deep learning review and its applications

Deep neural networks have recently gained popularity for improv- ing state-of-the-art machine learning algorithms in diverse areas such as speech recognition, computer vision and bioinformatics. Convolutional networks especially have shown prowess in visual recognition tasks such as object recognition and detection in which this work is focused on. Mod- ern award-winning architectures have systematically surpassed previous attempts at tackling computer vision problems and keep winning most current competitions. After a brief study of deep learning architectures and readily available frameworks and libraries, the LeNet handwriting digit recognition network study case is developed, and lastly a deep learn- ing network for playing simple videogames is reviewed.