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This tutorial describes challenges and possible avenues for the implementation of the components of a solid-state system, which emulates a biological brain. The tutorial is devoted mostly to a charge-based (i.e. electric controlled) implementation using transition metal oxides materials, which exhibit unique properties that emulate key functionalities needed for this application. In the Introduction, we compare the main differences between a conventional computational machine, based on the Turing-von Neumann paradigm, to a Neuromorphic machine, which tries to emulate important functionalities of a biological brain. We also describe the main electrical properties of biological systems, which would be useful to implement in a charge-based system. In Chapter II, we describe the main components of a possible solid-state implementation. In Chapter III, we describe a variety of Resistive Switching phenomena, which may serve as the functional basis for the implementation of key devices for Neuromorphic computing. In Chapter IV we describe why transition metal oxides, are promising materials for future Neuromorphic machines. Theoretical models describing different resistive switching mechanisms are discussed in Chapter V while existing implementations are described in Chapter VI. Chapter VII presents applications to practical problems. We list in Chapter VIII important basic research challenges and open issues. We discuss issues related to specific implementations, novel materials, devices and phenomena. The development of reliable, fault tolerant, energy efficient devices, their scaling and integration into a Neuromorphic computer may bring us closer to the development of a machine that rivals the brain.

Many correlated systems feature an insulator-to-metal transition that can be triggered by an electric field. Although it is known that metallization takes place through filament formation, the details of how this process initiates and evolves remain elusive. We use in-operando optical reflectivity to capture the growth dynamics of the metallic phase with space and time resolution. We demonstrate that filament formation is triggered by nucleation at hotspots, with a subsequent expansion over several decades in time. By comparing three case studies (VO2, V3O5 and V2O3), we identify the resistivity change across the transition as the crucial parameter governing this process. Our results provide a spatiotemporal characterization of volatile resistive switching in Mott insulators, key for emerging technologies such as optoelectronics or neuromorphic computing.