This dissertation is a collection of papers on anomalous phenomena in physics, biology, and sociology. These phenomena are primarily analyzed in terms of their temporal and spatiotemporal statistical properties. The analysis is based on both numerical simulations and, in some cases, real-world physiological and sociological data. The primary methods of analysis are diffusion entropy analysis, power spectral analysis, multifractal analysis, and survival (or waiting-time) analysis.

This research provides a proof of concept and background theory for the physics behind the state-of-the-art ultra-fast plasmonic spiking neurons (PSN), which can serve as a primary synaptic device for developing a platform for fast neural computing. Such a plasmonic-powered computing system allows localized AI with ultra-fast operation speed. The designed architecture for a plasmonic spiking neuron (PSN) presented in this thesis is a photonic integrated nanodevice consisting of two electro-optic and optoelectronic active components and works based on their coupling. The electro-optic active structure incorporated a periodic array of seeded quantum nanorods sandwiched between two electrodes and positioned at a near-field distance from the topmost metal layer of a sub-wavelength metal-oxide multilayer metamaterial. Three of the metal layers of the metamaterials form the active optoelectronic component. The device operates based on the coupling of the two active components through optical complex modes supported by the multilayer and switching between two of them. Both action and resting potentials occur through subsequent quantum and extraordinary photonics phenomena. These phenomena include the generation of plasmonic high-k complex modes, switching between the modes by enhanced quantum-confined stark effect, decay of the plasmonic excitations in each metal layer into hot-electrons, and collecting hot-electrons by …