Jason K. Eshraghian

Signal Flow Platform for Mapping and Simulation of Vertebrate Retina for Sensor Systems

Our visual processing system is remarkably good; the retina is nothing like the CMOS image sensor, or for that matter, any of the vision processing architectures that have driven vision systems research for over three decades. Therefore, before embarking upon the complex task of architectural mapping of the retina into hardware, it is essential to gain a realistic insight into the theoretical functions of the retina. In addition, an understanding of the kinds of chemical/electrical interactions taking place must be ascertained in order to venture into the next insurmountable task - the simulation platform. This paper presents a generic signal flow architecture for the mapping of the vertebrate retina derived from ionic current movements and interactions. The approach pursued is focused on the functional behavior of the signal that traverses from the photoreceptor to the ganglion cell in the architecture through transforming the system of nonlinear ordinary differential equations (ODEs) into an equivalent set of non-linear integral equations to cope with the singularity characteristic of retinal systems, providing an increase in the computational speed of ~36 % when compared with the conventional ODE methods, thus enhancing the realization of a functional retina as part of future hardware-based sensor systems.

Modelling and characterization of dynamic behavior of coupled memristor circuits

This paper explores the dynamic behavior of dual flux coupled memristor circuits in order to further ascertain fundamental theory of memristor circuits. Different cases of flux coupling are mathematically modelled where two memristors are connected in both series and parallel, with consideration given to the polarity of each device. The dynamic behavior is characterized based on the constitutive relations, with a variation of memductance represented in terms of flux, charge, voltage and current. The agreement between theoretical and simulation analyses affirm the memristor closure theorem with coupled memristor circuits behaving as a different type of memristor with higher complexity.

Analysis and generation of chaos using compositely connected coupled memristors.

In large-scale high-density integrated circuits, memristors in close proximity to one another both influence, and are influenced by, the behavior of nearby memristors. However, the previous analyses of memristors-based circuit applications have seldom considered the possibility of coupling effects between memristors which invariably influences the response of all memristors, thus rendering much previous research as incomplete. In this paper, the circuit dynamics of memristive Chuas circuits are systematically analyzed based on a pair of compositely connected flux-controlled memristors characterized by cubic nonlinearity as a typical example. A theoretical analysis is undertaken and verified via MATLAB. While tuning the coupling strength, variations in circuit dynamics are characterized by phase portraits, bifurcation diagrams, and Lyapunov exponents. A new floating memristor emulator with coupling ports, described by cubic nonlinearity, is designed using off-the-shelf circuit devices and is shown to be successfully used in building chaotic circuits in hardware experiments, verifying theoretical results in simulations. This paper provides a new way through which memristors-based circuit dynamics can be influenced by tuning the coupling strength between memristors without changing other circuit parameters. It is further highlighted that when designing future memristors-based circuits, the coupling action between memristors should be considered if necessary and compensated when causing undesired circuit responses.

Modelling and analysis of signal flow platform implementation into retinal cell pathway

This paper implements an established signal flow platform with its foundation derived from a system of nonlinear integral equations, characterizing the functional behavior of the signal that traverses from the photoreceptor to the ganglion cell in the vision processing architecture. While an increase in computational speed over the conventional method of solving a system of nonlinear ordinary differential equations (ODEs) has been confirmed for a single ganglion cell, the notion is extended to a retinal dual-pathway simulation which provides for a significantly improved adoption for organic mechanisms. There are various numerical methods in solving such a system which all have a bearing on both speed and error, and as such, systematic analyses using two common forms of integral solving methods are shown to improve the overall performance of simulating the extended pathway of the retinal model.

Biological modeling of vertebrate retina: Rod cell to bipolar cell

Advances in retinal research has recently enabled significant development in the arena of biomedical prostheses, thus enhancing the quality of therapeutic healthcare for patients suffering from retinal disorders. All vertebrates have complex vision systems, and mapping these neuroanatomical processes into a hardware platform to mimic retinal functionality is yet to be successful. A thorough understanding of the multifaceted cellular system and the neurons within the retina is a key requirement for implementation as a hardware device. Instead of modeling the full signal flow pathway of undetermined retinal features which remain to be experimentally validated, this paper hones in specifically on the known interactions between the retinal rod cells and bipolar cells. This is performed by introducing biochemical theory, dynamical analysis and presenting a biological signal flow architecture of the outer layer of the retina, from the photoreceptor to the bipolar cell through chemical synapses. The model is comprised of a numerical system based on the Hodgkin Huxley equations. This approach provides an acceptable replication of the dynamics of action potentials within the neuron. Numerical simulations for the signal flow model, represented by a system of nonlinear differential equations, are performed in order to provide a detailed analysis for a neurons response under varying light conditions.

Maximization of Crossbar Array Memory Using Fundamental Memristor Theory

The packing density associated with crossbar arrays offers important architectural solutions to numerous forms of computational engines. Mitigation of sneak paths in the crossbar array, however, requires additional layers in fabrication technology to impede current flow in order to avoid undesired changes to the state when reading and writing to and from the array. This results in an unavoidable increase in the vertical stacking dimension of the array. With the recent emergence of bistable memristors under both dc and ac, by adopting their asymptotic dynamics, we realize a significant improvement in memory construct and spatial constraints of memristor crossbar arrays. In this brief, we formalize a method of configuring a whole array architecture to any permutation of states without sacrificing array density by using a rigorous theoretical analysis, and confirmed via simulation.

Live demonstration: Signal flow platform implementation into retinal cell pathway

This live demonstration implements an established signal flow platform with its foundation derived from a system of nonlinear integral equations in a MATLAB simulation environment, characterizing the functional behavior of the signal that traverses from the photoreceptor to the ganglion cell in the vision processing architecture. While an increase in computational speed over the conventional method of solving a system of nonlinear ordinary differential equations (ODEs) has been confirmed for a single ganglion cell, the notion is extended to a retinal dual-pathway simulation which provides for a significantly improved adoption for organic mechanisms. There are various numerical methods in solving such a system which all have a bearing on both speed and error, and as such, systematic analyses using two common forms of integral solving methods are shown to improve the overall performance of simulating the extended pathway of the retinal model.