Hundsdorfer, Willem; Mozartova, Anna; Savcenco, Valeriu(Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws, Springer Nature, 2013)[Book Chapter]
Multirate schemes for conservation laws or convection-dominated problems seem to come in two flavors: schemes that are locally inconsistent, and schemes that lack mass-conservation. In this paper these two defects are discussed for one-dimensional conservation laws. Particular attention will be given to monotonicity properties of the multirate schemes, such as maximum principles and the total variation diminishing (TVD) property. The study of these properties will be done within the framework of partitioned Runge-Kutta methods. It will also be seen that the incompatibility of consistency and mass-conservation holds for ‘genuine’ multirate schemes, but not for general partitioned methods.
Tan, Cheston; Leibo, Joel Z.; Poggio, Tomaso(Studies in Computational Intelligence, Springer Nature, 2013)[Book Chapter]
In recent years, scientific and technological advances have produced artificial systems that have matched or surpassed human capabilities in narrow domains such as face detection and optical character recognition. However, the problem of producing truly intelligent machines still remains far from being solved. In this chapter, we first describe some of these recent advances, and then review one approach to moving beyond these limited successes – the neuromorphic approach of studying and reverse-engineering the networks of neurons in the human brain (specifically, the visual system). Finally, we discuss several possible future directions in the quest for visual intelligence.
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