It is well known that the thermal noise behavior at the terminals of any LTI RLC circuit can be predicted from knowledge of the driving-point impedance and temperature alone. This paper offers the conjecture that similar results hold if the capacitors and inductors are nonlinear. We refine the conjecture by analyzing the behavior of an RLC bridge circuit with the nonlinear inductor and capacitor carefully matched so the terminal behavior reduces to that of a linear resistor R. We show that the terminal noise current is precisely that predicted by the Nyquist-Johnson model for R if the driving voltage is zero or constant, but not if the driving voltage is time-dependent or the inductor and capacitor are time-varying. This paper makes exact calculations using techniques from stochastic differential equations and using reversibility arguments.

This paper builds on previous results by incorporating both the shot-noise model and the standard Nyquist-Johnson model for linear resistors in one general multiport configuration. The differential equations for circuits driven by Nyquist-Johnson models can be solved via the Fokker-Planck equation; for circuits driven by Poisson, or shot-noise, models, the Master equation is used. A circuit driven by both types of noise requires a hybrid differential equation called the "differential Chapman-Kolmogorov equation." Under the same constraint on the two Poisson process rates found in our previous work, the shot-noise model continues to satisfy thermodynamic requirements when connected to fairly general networks also containing standard Nyquist-Johnson noise models. A specific example is developed, consisting of the parallel combination of a shot-noise device, a linear resistor, an inductor, and a capacitor.

Oja's equations describe a well-studied system for unsupervised Hebbian learning of principal components. This paper derives the explicit time-domain solution of Oja's equations for the single-neuron case. It also shows that, under a linear change of coordinates, these equations are a gradient system in the general multi-neuron case. This latter result leads to a new Lyapunov-like function for Oja's equations.

The goal of the MIT Vision Chip Project is to design and build prototype analog early vision systems that are remarkably low-power, small, and fast. The typical system will perform one or more computation-intensive image-processing tasks at hundreds to thousands of frames per second using only tens to hundreds of milliwatts. The entire system with lens, imager, power supply and support circuitry can fit inside a cigar box. The authors briefly outline the overall project and describe two tested chips in some detail. Particular attention is given to a fast imager and processor chip for object position and orientation, and to an integrated ccd (charge-coupled device) imager and processors for edge detection.>

In the analog VLSI implementation of neural systems, it is sometimes convenient to build lateral inhibition networks by using a locally connected on-chip resistive grid to interconnect active elements. A serious problem of unwanted spontaneous oscillation often arises with these circuits and renders them unusable in practice. This paper reports on criteria that guarantee these and certain other systems will be stable, even though the values of designed elements in the resistive grid may be imprecise and the location and values of parasitic elements may be unknown. The method is based on a rigorous, somewhat novel mathematical analysis using Tellegen's theorem (Penfield et al. 1970) from electrical circuits and the idea of a Popov multiplier (Vidyasagar 1978; Desoer and Vidya sagar 1975) from control theory. The criteria are local in that no overall analysis of the interconnected system is required for their use, empirical in that they involve only measurable frequency response data on the individual cells, and robust in that they are insensitive to network topology and to unmodelled parasitic resistances and capacitances in the interconnect network. Certain results are robust in the additional sense that specified nonlinear elements in the grid do not affect the stability criteria. The results are designed to be applicable, with further development, to complex and incompletely modeled living neural systems.