In this article, we consider designs of simple analog artificial neural networks based on adiabatic Josephson cells with a sigmoid activation function. A new approach based on the gradient descent method is developed to adjust the circuit parameters, allowing efficient signal transmission between the network layers. The proposed solution is demonstrated on the example of the system implementing XOR and OR logical operations.

When the history of our time comes to be written, one thing that will amaze historians is how an entire civilisation managed to impale itself on its worship of optimisation and efficiency. This obsession is what underpinned the hubris of globalisation. Apple's famous slogan "Designed by Apple in California, manufactured in China" became its guiding light. So long as products could be made available to consumers everywhere, it no longer mattered where they were made. We first twigged this when the pandemic struck, and we became suddenly aware of how fragile supply chains built to maximise efficiency could be.

After a decade of research, we developed a prototype device and experimentally demonstrated that the direct phi q interaction could be memristive, as predicted by Chua in 1971. With a constant input current to avoid any parasitic inductor effect, our device meets three criteria for an ideal memristor: a single valued, nonlinear, continuously differentiable, and strictly monotonically increasing constitutive phi q curve, a pinched v i hysteresis loop, and a charge only dependent resistance. Our work represents a step forward in terms of experimentally verifying the memristive flux charge interaction but we have not reached the final because this prototype still suffers from two serious limitations: 1, a superficial but dominant inductor effect (behind which the above memristive fingerprints hide) due to its inductor-like core structure, and 2. bistability and dynamic sweep of a continuous resistance range. In this article, we also discuss how to make a fully functioning ideal memristor with multiple or an infinite number of stable states and no parasitic inductance, and give a number of suggestions, such as open structure, nanoscale size, magnetic materials with cubic anisotropy (or even isotropy), and sequential switching of the magnetic domains. Additionally, we respond to a recent challenge from arXiv.org that claims that our device is simply an inductor with memory since our device did not pass their designed capacitor-memristor circuit test. Contrary to their conjecture that an ideal memristor may not exist or may be a purely mathematical concept, we remain optimistic that researchers will discover an ideal memristor in nature or make one in the laboratory based on our current work.

Superconducting electronic circuits have much to offer with regard to neuromorphic hardware. Superconducting quantum interference devices (SQUIDs) can serve as an active element to perform the thresholding operation of a neuron's soma. However, a SQUID has a response function that is periodic in the applied signal. We show theoretically that if one restricts the total input to a SQUID to maintain a monotonically increasing response, a large fraction of synapses must be active to drive a neuron to threshold. We then demonstrate that an active dendritic tree (also based on SQUIDs) can significantly reduce the fraction of synapses that must be active to drive the neuron to threshold. In this context, the inclusion of a dendritic tree provides the dual benefits of enhancing the computational abilities of each neuron and allowing the neuron to spike with sparse input activity.