The Memory-Conservation Theory of Memristance

The memristor, the recently discovered fundamental circuit element, is of great interest for neuromorphic computing, nonlinear electronics and computer memory. It is usually modelled either using Chua's equations, which lack material device properties, or using Strukov's phenomenological model (or models derived from it), which deviates from Chua's definitions due to the lack of a magnetic flux term. It is shown that by modelling the magnetostatics of the memory-holding ionic current (oxygen vacancies in the Strukov memristor), the memristor's magnetic flux can be identified as the flux arising from the ions. This leads to a novel theory of memristance consisting of two components: 1. A memory function which describes how the memristance, as felt by the ions, affects the conducting electrons located in the `on' part of the device; 2. A conservation function which describes the time-varying resistance in the `off' part of the device. This model allows for a straight-forward incorporation of the ions within the electronic theory and relates Chua's constitutive definition of a memristor with device material properties for the first time.Comment: 11 pages, 4 figures, conference paper accepted to UKSim2014. UKSim2014, March 201

The missing magnetic flux in the HP memristor found

Ever since real-world two terminal memristor devices were created, detractors have derided them as not `true' Chua memristors because there is no magnetic flux in the system. This report shows that the flux is present and equal to the magnetic flux of the oxygen vacancies. This shows that the HP memristor is a `true' Chua memristor. The memristor description has been separated out into the memory function, which is the memrsitance described by Chua in 1971 and the conservation function, which is necessary to describe the whole HP memristor. As the memory function deals with the vacancy mobility and the measurable current is mostly electronic, it is apparent that a description of the HP memristor must include two charge carriers. From analysis of Stan William's model in terms of memory and conservation functions, a direct relation to Chua's original memristance equation and an approximation of magnetic flux have both been identified as being present in the original model. With this, the phenomenological model used by experimentalists and the mathematical model beloved by theoreticians have been combined into one

Spiking memristor logic gates are a type of time-variant perceptron

Memristors are low-power memory-holding resistors thought to be useful for neuromophic computing, which can compute via spike-interactions mediated through the device's short-term memory. Using interacting spikes, it is possible to build an AND gate that computes OR at the same time, similarly a full adder can be built that computes the arithmetical sum of its inputs. Here we show how these gates can be understood by modelling the memristors as a novel type of perceptron: one which is sensitive to input order. The memristor's memory can change the input weights for later inputs, and thus the memristor gates cannot be accurately described by a single perceptron, requiring either a network of time-invarient perceptrons or a complex time-varying self-reprogrammable perceptron. This work demonstrates the high functionality of memristor logic gates, and also that the addition of theasholding could enable the creation of a standard perceptron in hardware, which may have use in building neural net chips.Comment: 8 pages, 3 figures. Poster presentation at a conferenc

My, and others', spiking memristors are true memristors: a response to R.S. Williams' question at the New Memory Paradigms: Memristive Phenomena and Neuromorphic Applications Faraday Discussion

At the Faraday Discussion, in the paper titled `Neuromorphic computation with spiking memristors: habituation, experimental instantiation of logic gates and a novel sequence-sensitive perceptron model' it was demonstrated that a large amount of computation could be done in a sequential way using memristor current spikes (d.c. response). As these spikes are found in many memristors (possibly all), this novel approach could be highly useful for fast and reproducible memristor circuits. However, questions were raised as to whether these spikes were actually due to memristance or merely capacitance in the circuit. In this longer version of the Faraday Discussion response, as much information as is available from both published and unpublished data from my lab is marshalled together. We find that the devices are likely imperfect memristors with some capacitance, and that the spikes are related to the frequency effect seen in memristor hysteresis curves, thus are an integral part of memristance.Comment: Long form of a Faraday Discussions commen

Is Spiking Logic the Route to Memristor-Based Computers?

Memristors have been suggested as a novel route to neuromorphic computing based on the similarity between neurons (synapses and ion pumps) and memristors. The D.C. action of the memristor is a current spike, which we think will be fruitful for building memristor computers. In this paper, we introduce 4 different logical assignations to implement sequential logic in the memristor and introduce the physical rules, summation, `bounce-back', directionality and `diminishing returns', elucidated from our investigations. We then demonstrate how memristor sequential logic works by instantiating a NOT gate, an AND gate and a Full Adder with a single memristor. The Full Adder makes use of the memristor's memory to add three binary values together and outputs the value, the carry digit and even the order they were input in.Comment: Conference paper. Work also reported in US patent: `Logic device and method of performing a logical operation', patent application no. 14/089,191 (November 25, 2013

Connecting Spiking Neurons to a Spiking Memristor Network Changes the Memristor Dynamics

Memristors have been suggested as neuromorphic computing elements. Spike-time dependent plasticity and the Hodgkin-Huxley model of the neuron have both been modelled effectively by memristor theory. The d.c. response of the memristor is a current spike. Based on these three facts we suggest that memristors are well-placed to interface directly with neurons. In this paper we show that connecting a spiking memristor network to spiking neuronal cells causes a change in the memristor network dynamics by: removing the memristor spikes, which we show is due to the effects of connection to aqueous medium; causing a change in current decay rate consistent with a change in memristor state; presenting more-linear $I-t$ dynamics; and increasing the memristor spiking rate, as a consequence of interaction with the spiking neurons. This demonstrates that neurons are capable of communicating directly with memristors, without the need for computer translation.Comment: Conference paper, 4 page