Links to some hardware and software developed by myself for the purpose of individual research and professional development, and released as Supplementary Material to publications, are provided below. None of these products are commercial, and requests for access to hardware for further research will be very welcome.Transistor-based oscillators including fractal resonators
The boards shown below implement a single-transistor chaotic oscillator (left), wherein two inductors have been replaced by Feynman-Sierpinski LC networks with up to 2 levels, and its Foster approximation (right) and its Foster approximation (right). Effects reminiscent of biological observations have been recorded as regards the consequences of non-ideal behaviours and topological imperfections. High-dimensional dynamics are generated despite the elementary nature of the system. The board fabrication files and some experimental time-series and S-parameter measurements can be downloaded here and the corresponding publication can be found here.
LYAPUNOV-1 is a flexible advanced experimental platform for the study of chaotic networks, comprising 32 field-programmable analog arrays, digital-to-analog and analog-to-digital converters and all logic allowing fast reconfiguration and data acquisition on a PCI board. This board has been used to demonstrate the emergence of small-world functional connectivity from a ring via remote synchronization. This finding has relevance to understanding how functional connectivity emerges from structural links in the brain. The board fabrication files, software and example circuits can be downloaded from here, and a large collection of experimental time-series can be found here; the corresponding publication is available here. Remote access can be arranged.
In a more recent study, available here, the mechanism underlying remote synchronization in this system has finally been elucidated through novel experiments and simulations. It has been found that the effect reflects an interference phenomenon, which is more closely related to “local” interactions than to the collective behavior of the network as a whole. The effect arises in a scenario reminiscent of amplitude modulation (AM), wherein the system non-linearity demodulates an envelope signal, that spectrally overlaps a sideband, and interference thereafter occurs due to an unstable phase relationship. The system response to noise and external perturbations is also studied in detail and the corresponding experimental time-series can be downloaded from here.
HISENKEI ARI-1 (非線形蟻-1, meaning non-linear ant-1) is an 18 degrees-of-freedom hexapod robot driven by a hierarchical pattern generator realized with the same reconfigurable non-linear oscillators introduced below in the context of remote synchronization, and implemented on the LYAPUNOV-1 circuit board. The pattern generator is biologically inspired, consisting at the top level of a central pattern generator (CPG) controlling the phase relationships between the legs and at the bottom level of six local pattern generators (LPGs) controlling the trajectories of the individual legs. Based on five control parameters, a considerable variety of gaits and postures can be generated, demonstrating several emergent phenomena observed in living insects. The full source code, some system diagrams and datasets can be downloaded here. The corresponding publication can be found here. A video demonstration can be found here. The press release can be found here.
Based on the initial work on atypical chaotic circuits described below, the largest known collection of novel transistor-based chaotic oscillators was obtained, through describing each circuit with a bit string and performing a random search on a super-computer. It is found that chaos is actually a rather common occurrence in these circuits. One hundred circuits were realized experimentally, and despite their small size and simple structure yielded a remarkable variety of attractors, including the double-scroll attractor. An oscillator generating all-or-nothing spikes and bursts resembling neural discharge was also obtained. Coupling these circuits uncovered the ability to generate complex relationships such as generalized synchronization. The full circuit diagrams and datasets can be downloaded here. The corresponding publication can be found here. The press release can be found here.
ALAN-2, which is an evolution of ALAN-1, is a 6 degrees-of-freedom robotic arm driven by a stereoscopic vision system, which can perform simple operations with coloured bricks driven directly by bio-signals, namely electrooculogram (EOG), electromyogram (EMG) and electroencephalogram (EEG), recorded via a low-cost, commercially-available wearable device. It embodies a tailored hybrid control approach, according to which some operations are controlled proportionally by the user and some are performed automatically. It is meant mainly as proof-of-concept for a meal aid system. The full source code, some system diagrams and datasets can be downloaded here. The corresponding publication can be found here.
GAGARIN-1 is a general-purpose real-time signal acquisition and processing card, which provides point-to-point fibre optic links to 10 or 20 chaotic circuits via high-speed analog-to-digital (ADC) and digital-to-analog (DAC) converters. It is optimized for chaos control and is being used for experiments in this area. It features a highly flexible design including a field-programmable gate array (FPGA), a digital signal processor (DSP) of the same type used on the QUASAR-1 board (ADSP-21369; Analog Devices, Inc., Norwood, MA, USA) and four pattern-matching coprocessors of the same type used on the HEBB-1 board (CM1K; CogniMem Inc., Folsom CA, USA). Owing to this architecture it enables rapidly reacting to network-wide patterns. The schematics and software will be released at a future date.
VAN DER POL-1 is a 34×34 lattice of neon (glow) lamps, each one independently biased to a globally-applied DC voltage, and capacitively coupled to its four neighbours. As a function of the applied voltage, transition between a high-rate, high-order phase and a low-rate, low-order phase is observed. This transition occurs in proximity of a spinodal point, and simultaneously features metastability, hysteresis, and critical avalanching according to universal exponents identical to those observed for neural activity in-vitro and in-vivo. The design files and the full dataset can be downloaded here. The corresponding publication can be found here.
CHARM-1 is a 0.7 um CMOS ASIC that implements a ring network similar to the one in STRANGE-1 below, importantly without recourse to any discrete reactive components. The chaotic oscillators are implemented as cross-coupled inverter rings of mismatched length. This prototype demonstrates the viability of this approach, which allows realizing very large networks on a single chip. This technology will be used to realize a large-scale network having neuromorphic structural connectivity derived, for example, from human brain connectome data. The corresponding publication is available here. This design also featured in EuroPractice’s 2014 activity report, available here.
STRANGE-1 is a ring of 30 single-transistor chaotic oscillators, each of which is diffusively (resistively) coupled to its neighbours. The operating point and coupling strengths for each oscillator can be independently tuned using trimmers. This board has been used to demonstrate emergence of multi-scale clustering and phase transitions driven by local connectivity, recalling some effects observed macroscopically for the brain. The board fabrication files can be downloaded here and the corresponding publications can be found here and here.
The five small boards shown below are novel single-transistor chaotic oscillators, which were initially obtained via a genetic algorithm. They are deceivingly simple but can generate highly complex time-series. The defining feature of these oscillators, is that they are powered by a DC voltage source with a series resistor. This series resistor (blue trimmer in picture) has a profound effect on the dynamics of the oscillator: tuning it, multiple transitions are observed between chaotic and periodic oscillation modes. This is loosely reminiscent of observations in biological neurons, where depending on many biochemical parameters, a variety of firing patterns can be generated. The simplest of these oscillators (1 BJT, 1 resistor, 2 inductors and 1 capacitor) was used as building block for the STRANGE-1 board, described below. The board fabrication files can be downloaded here and the corresponding publication can be found here.
HEBB-1 is a board dedicated to accelerating voxel-level node degree mapping from functional MRI time-series. It is based on the representative CM1K (CogniMem Inc., Folsom CA, USA) implementation of the zero instruction-set computer (ZISC) concept and replaces multiplication with a large array of L1-norm calculations. The full schematics, board fabrication files and some software can be downloaded here. The corresponding publication can be found here.
DIJKSTRA-1 is a synthesizable, massively parallel implementation of the homonymous algorithm, optimized for use in geodesic mapping of brain and other large networks. The prototype VHDL code can be downloaded here. The corresponding publication can be found here. A dedicated FPGA mini-board has been developed, too.
QUASAR-1 is a Digital Signal Processing (DSP) board optimized for high-speed filtering and analysis of functional MRI and other time-series. It features six ADSP-21369 processors (Analog Devices, Inc., Norwood, MA, USA) running at 480MHz, each with 2MB of SRAM, interfaced via high-speed dual-port SRAM. The full schematics, board fabrication files and some software can be downloaded here. The corresponding publication can be found here.
ALAN-1 is a 6 degrees-of-freedom robotic arm driven by a stereoscopic vision system, which can perform simple operations with coloured bricks driven directly by brain activity decoded from functional MRI time-series via a neural network. It is used to demonstrate the concept of a brain-computer interface operating on “high level” commands. The full source code and some system diagrams can be downloaded here. The corresponding publication can be found here.