1. Ella Gale, Ben de Lacy Costello and Andrew Adamatzky Observation and Characterization of Memristor Current Spikes and their Application to Neuromorphic Computation

2. How do Neurons Compute? Competing Models for the Memristor Making Spiking Neural Networks with Memristors The Memristor Acting as a Neuron Characteristics and Properties Where do the Spikes come from? Contents

4. Slow Parallel Processing High degree of interconnectivity Spiking Neural Nets Ionic Analogue How Does the Brain Differ From a Modern-Day Computer?

5. Influx of Ionic I Voltage Spike Axon: Transmission along neuron Synapse: Transmission between neurons How does a Neuron Compute?

6. Memristive Systems to Describe Nerve Axon Membranes

7. Synapse Long-Term Potentiation

8. The Memristor as a Synapse Before learning During learning After learning

9. Process by which synapses are potentiated Related to Hebb’s Rule Possibly a cause of memory and learning Relative timing of spike inputs to a synapse important Spike-Time Dependent Plasticity, STDP Bi and Poo, Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength and Postsynaptic Cell Type, J. Neurosci., 1998

11. Memristor Structure and Function

12. Phenomenological Model Strukov et al, The Missing Memristor Found, Nature, 2008

13. Charge-Controlled Memristor Flux-Controlled Memristor Chua’s Definitions of Types of Memristors L. Chua, Memristor – The Missing Circuit Element, IEEE Trans. Circuit Theory, 1971

14. What the Flux? But, where is the magnetic flux? Chua, 1971Strukov et al, 2008

15. Starting From The Ions…

16. Memristance, as Derived from Ion Flow Gale, The Missing Magnetic Flux in the HP Memristor Found, 2011

17. Mem-Con Theory Gale, The Missing Magnetic Flux in the HP Memristor Found, Submitted, 2011

18. Memristor I-V Behaviour

19. To make a memristor brain & thus a machine intelligence Our Intent:

21. Connecting Memristors with Spiking Neurons to Implement STDP 1. Zamarreno-Ramos et al, On Spike Time Dependent Plasticity, Memristive Devices and Building a Self-Learning Visual Cortex, Frontiers in Neuroscience, 2011 0. Linares-Barranco and Serrano-Gotarredona, Memristance can explain Spike-Time- Dependent-Plasticity in Neural Synapses, Nature Preceedings, 2009 Simulation Results

22. Memristors Spike Naturally! But,

23. Our Memristors Crossed Aluminium electrodes Thin-film (40nm) TiO 2 sol-gel layer 1. Gergel-Hackett et al, A Flexible Solution Processed Memristor, IEEE Elec. Dev. Lett., 2009 2. Gale et al, Aluminium Electrodes Effect the Operation of Titanium Dioxide Sol-Gel Memristors, Submitted 2012

24. Current Spikes Seen in I-t Plots

25. Voltage Square WaveCurrent Spike Response Spikes are Reproducible

26. Voltage Ramp Current Response Spikes are Repeatable

27. Neuron Memristor Memristor Behaviour Looks Similar to Neurons Bal and McCormick, Synchronized Oscilliations in the Inferior Olive are controlled by the Hyperpolarisation-Activated Cation Current I h, J. Neurophysiol, 77, 3145-3156, 1997

28. SPIKES SEEN IN THE LITERATURE

29. Pershin and Di Ventra, Spin Memristive Systems: Spin Memory Effects in Semi-conductor Spintronics, Phys. Rev. B, 2008 Spintronic Memristor Current Spikes

31. Properties of Spikes

32. Pictures Curved (BPS-like) Memristors Triangular (UPS-like) Memristors Two Different Types of Memristor Behaviour Seen in Our Lab

33. Curved (BPS-like) Memristors Triangular (UPS-like) Memristors Two Different Types of Memristor Behaviour Seen in Our Lab

34. Where do the Spikes Come From? Does Current Theory Predict Their Existence?

35. qφ IV qφ VI NeuronsMemristors Mem-Con Model Applied to Memristor Spikes

36. Neuron Voltage SpikesMemristor Current Spikes In Chua’s Model

37. More complex system than a single memristor Short-term memory associated with membrane potential Long term memory associated with the number of synaptic buds What is the Memory Property of Neurons?

38. Sol-Gel Memristor Negative V Sol-Gel Memristor Positive V Memristor Models Fit the Data

39. Memristor Model Fits the PEO-PANI Memristor

40. Al-TiO 2 -Al Sol-Gel Memristor

41. Time & Frequency Dependence of Hysteresis for Al-TiO 2 -Al

42. Au-TiO 2 -Au WORMS Memory

43. I-t Response to Stepped Voltage Time Dependent I-V Au-TiO 2 -Au WORMS Memory

44. Voltage RampCurrent Response Al-TiO 2 -Al Current Response to Voltage Ramp

46. Neurology: Modelling Neurons with the Mem-Con Theory to prove that they are Memristive Investigate the Memory Property for neurons Unconventional Computing: Further Investigation of memristor and ReRAM properties Attempt to build a neuromorphic control system for a navigation robot Further Work

48. Neurons May Be Biological Memristors Neurons Operate via Voltage Spikes Memristors can Operative via Current Spikes Thus, Memristors are Good Candidates for Neuromorphic Computation A Memristor-based Neuromorphic Computer will be Voltage Controlled and transmit data via Current Spikes Summary

49. Ben de Lacy Costello Andrew Adamatzky David Howard Larry Bull With Thanks to Victor Erokhin and his group (University of Parma) Steve Kitson (HP UK) David Pearson (HP UK) Bristol Robotics Laboratory