Adaptive Photoreceptor with Wide Dynamic Range

We describe a photoreceptor circuit that can be used in massively parallel analog VLSI silicon chips, in conjunction with other local circuits, to perform initial analog visual information processing. The receptor provides a continuous-time output that has low gain for static signals (including circuit mismatches), and high gain for transient signals that are centered around the adaptation point. The response is logarithmic, which makes the response to a fixed image contrast invariant to absolute light intensity. The 5-transistor receptor can be fabricated in an area of about 70 μm by 70 μm in a 2-μm single-poly CMOS technology. It has a dynamic range of 1-2 decades at a single adaptation level, and a total dynamic range of more than 6 decades. Several technical improvements in the circuit yield an additional 1-2 decades dynamic range over previous designs without sacrificing signal quality. The lower limit of the dynamic range, defined arbitrarily as the illuminance at which the bandwidth of the receptor is 60 Hz, is at approximately 1 lux, which is the border between rod and cone vision and also the limit of current consumer video cameras. The receptor uses an adaptive element that is resistant to excess minority carrier diffusion. The continuous and logarithmic transduction process makes the bandwidth scale with intensity. As a result, the total A.C. RMS receptor noise is constant, independent of intensity. The spectral density of the noise is within a factor of two of pure photon shot noise and varies inversely with intensity. The connection between shot and thermal noise in a system governed by Boltzman statistics is beautifully illustrated

Analog VLSI Phototransduction by continuous-time, adaptive, logarithmic photoreceptor circuits

Over the last few years, we and others have built a number of interesting neuromorphic analog vision chips that do focal-plane time-domain computation. These chips do local, continuous-time, spatiotemporal processing that takes place before any sampling or long-range communication, for example, motion processing, change detection, neuromorphic retinal preprocessing, stereo image matching, and synthesis of auditory images from visual scenes. This processing requires photoreceptor circuits that transduce from light falling on the chip to an electrical signal. If we want to build analog vision chips that do high-quality focal plane processing, then we need good photoreceptors. It's not enough to just demonstrate a concept; ultimate usefulness will be determined by market forces, which, among other factors, depend a lot on raw performance. The receptor circuits we discuss here have not been used in any commercial product, so they have not yet passed that most crucial test, but by every performance metric we can come up with, including successful fabrication and test of demonstration systems, they match performance criteria met by other phototransduction techniques that are used in end-product consumer electronic devices. We hope that this article will serve several purposes: We want people to have a reference where they can look to see the functioning and practical problems of phototransducers built in a typical CMOS or BiCMOS process. We want to inspire people to build low-power, integrated commercial vision devices for practical purposes. We want to provide a photoreceptor that can be used as a front end transducer in more advanced research on neuromorphic systems. The transduction process seems mundane, but it is important --GIGO comes to mind. Subsequent computation relies on the information. We don't know of any contemporary (VLSI-era) literature that comprehensively explore the subject. Previous results are lacking in some aspect, either in the circuit itself, or in the understanding of the physics, or in the realistic measurement of limitations on behavior. We'll focus on one highly-evolved adaptive receptor circuit to understand how it operates, what are the limitations on its dynamic range, and what is the physics of the noise behavior. The receptor has new and previously unpublished technical improvements, and we understand the noise properties and illumination limits much better than we did before. We'll also discuss the practical aspects of the interaction of light with silicon: What are the spectral responses of various devices? How far do light-generated minority carriers diffuse and how do they affect circuit operation? How effective are guard bars to protect against them? Finally, we'll talk about biological receptors: How do their functional characteristics inspire the electronic model? How are the mechanisms of gain and adaptation related

QED Corrections to Planck's Radiation Law and Photon Thermodynamics

Leading corrections to Planck's formula and photon thermodynamics arising from the pair-mediated photon-photon interaction are calculated. This interaction is attractive and causes an increase in occupation number for all modes. Possible consequences, including the role of the cosmic photon gas in structure formation, are considered.Comment: 15 pages, Revtex 3.

Enhancement of vacuum polarization effects in a plasma

The dispersive effects of vacuum polarization on the propagation of a strong circularly polarized electromagnetic wave through a cold collisional plasma are studied analytically. It is found that, due to the singular dielectric features of the plasma, the vacuum effects on the wave propagation in a plasma are qualitatively different and much larger than those in pure vacuum in the regime when the frequency of the propagating wave approaches the plasma frequency. A possible experimental setup to detect these effects in plasma is described.Comment: 33 pages, 3 figure

The Compressibility of Minimal Lattice Knots

The (isothermic) compressibility of lattice knots can be examined as a model of the effects of topology and geometry on the compressibility of ring polymers. In this paper, the compressibility of minimal length lattice knots in the simple cubic, face centered cubic and body centered cubic lattices are determined. Our results show that the compressibility is generally not monotonic, but in some cases increases with pressure. Differences of the compressibility for different knot types show that topology is a factor determining the compressibility of a lattice knot, and differences between the three lattices show that compressibility is also a function of geometry.Comment: Submitted to J. Stat. Mec

Equilibrium shapes of flat knots

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using rigorous scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localised on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.Comment: 4 pages, 3 figure

A Comprehensive Workflow for General-Purpose Neural Modeling with Highly Configurable Neuromorphic Hardware Systems

In this paper we present a methodological framework that meets novel requirements emerging from upcoming types of accelerated and highly configurable neuromorphic hardware systems. We describe in detail a device with 45 million programmable and dynamic synapses that is currently under development, and we sketch the conceptual challenges that arise from taking this platform into operation. More specifically, we aim at the establishment of this neuromorphic system as a flexible and neuroscientifically valuable modeling tool that can be used by non-hardware-experts. We consider various functional aspects to be crucial for this purpose, and we introduce a consistent workflow with detailed descriptions of all involved modules that implement the suggested steps: The integration of the hardware interface into the simulator-independent model description language PyNN; a fully automated translation between the PyNN domain and appropriate hardware configurations; an executable specification of the future neuromorphic system that can be seamlessly integrated into this biology-to-hardware mapping process as a test bench for all software layers and possible hardware design modifications; an evaluation scheme that deploys models from a dedicated benchmark library, compares the results generated by virtual or prototype hardware devices with reference software simulations and analyzes the differences. The integration of these components into one hardware-software workflow provides an ecosystem for ongoing preparative studies that support the hardware design process and represents the basis for the maturity of the model-to-hardware mapping software. The functionality and flexibility of the latter is proven with a variety of experimental results

On the Dominance of Trivial Knots among SAPs on a Cubic Lattice

The knotting probability is defined by the probability with which an $N$-step self-avoiding polygon (SAP) with a fixed type of knot appears in the configuration space. We evaluate these probabilities for some knot types on a simple cubic lattice. For the trivial knot, we find that the knotting probability decays much slower for the SAP on the cubic lattice than for continuum models of the SAP as a function of $N$. In particular the characteristic length of the trivial knot that corresponds to a `half-life' of the knotting probability is estimated to be $2.5 \times 10^5$ on the cubic lattice.Comment: LaTeX2e, 21 pages, 8 figur

Critical exponents for random knots

The size of a zero thickness (no excluded volume) polymer ring is shown to scale with chain length $N$ in the same way as the size of the excluded volume (self-avoiding) linear polymer, as $N^{\nu}$, where $\nu \approx 0.588$. The consequences of that fact are examined, including sizes of trivial and non-trivial knots.Comment: 4 pages, 0 figure