A new invention, the cellular neural network (CNN) universal machine and supercomputer, is presented. This is the first algorithmically programmable analog array computer having real-time and supercomputer power on a single chip. The CNN universal machine is described, emphasizing its programmability as well as global and distributed analog memory and logic, high throughput via electromagnetic waves, and complex cells that may be used also for simulating a broad class of PDEs. Its implementation, the CNN universal chip, is also described, along with its use of a multichip supercomputer. Other types of hardware implementations are also briefly discussed. Details of the algorithmic aspects of the new type of analogic (analog logic) algorithms, as well as the analogic software (language, compiler, machine code, etc.) are explained, along with a brief description of the available CNN workstation for implementing and simulating these new concepts. A broad range of applications is reviewed, including neuromorphic computing, programmable physics, programmable chemistry, and programmable bionics. >

The CNN universal machine: an analogic array computer

How reliably do action potentials in cortical neurons encode information about a visual stimulus? Most physiological studies do not weigh the occurrences of particular action potentials as significant but treat them only as reflections of average neuronal excitation. We report that single neurons recorded in a previous study by Newsome et al. (1989; see also Britten et al. 1992) from cortical area MT in the behaving monkey respond to dynamic and unpredictable motion stimuli with a markedly reproducible temporal modulation that is precise to a few milliseconds. This temporal modulation is stimulus dependent, being present for highly dynamic random motion but absent when the stimulus translates rigidly.

/pdf/temporal-precision-of-spike-trains-in-extrastriate-cortex-of-3n2vbdzlbl.pdf

Temporal precision of spike trains in extrastriate cortex of the behaving macaque monkey

CNN is an acronym for either Cellular Neural Network when used in the context of brain science, or Cellular Nonlinear Network when used in the context of coupled dynamical systems. A CNN is defined by two mathematical constructs: 1. A spatially discrete collection of continuous nonlinear dynamical systems called cells, where information can be encrypted into each cell via three independent variables called input, threshold, and initial state. 2. A coupling law relating one or more relevant variables of each cell Cij to all neighbor cells Ckl located within a prescribed sphere of influence Sij(r) of radius r, centered at Cij. In the special case where the CNN consists of a homogeneous array, and where its cells have no inputs, no thresholds, and no outputs, and where the sphere of influence extends only to the nearest neighbors (i.e. r = 1), the CNN reduces to the familiar concept of a nonlinear lattice. The bulk of this three-part exposition is devoted to the standard CNN equation where xij, yij, uij and zij are scalars called state, output, input, and threshold of cell Cij; akl and bkl are scalars called synaptic weights, and Sij(r) is the sphere of influence of radius r. In the special case where r = 1, a standard CNN is uniquely defined by a string of "19" real numbers (a uniform thresholdzkl = z, nine feedback synaptic weights akl, and nine control synaptic weights bkl) called a CNN gene because it completely determines the properties of the CNN. The universe of all CNN genes is called the CNN genome. Many applications from image processing, pattern recognition, and brain science can be easily implemented by a CNN "program" defined by a string of CNN genes called a CNN chromosome. The first new result presented in this exposition asserts that every Boolean function of the neighboring-cell inputs can be explicitly synthesized by a CNN chromosome. This general theorem implies that every cellular automata (with binary states) is a CNN chromosome. In particular, a constructive proof is given which shows that the game-of-life cellular automata can be realized by a CNN chromosome made of only three CNN genes. Consequently, this "game-of-life" CNN chromosome is a universal Turing machine, and is capable of self-replication in the Von Neumann sense [Berlekamp et al., 1982]. One of the new concepts presented in this exposition is that of a generalized cellular automata (GCA), which is outside the framework of classic cellular (Von Neumann) automata because it cannot be defined by local rules: It is simply defined by iterating a CNN gene, or chromosome, in a "CNN DO LOOP". This new class of generalized cellular automata includes not only global Boolean maps, but also continuum-state cellular automata where the initial state configuration and its iterates are real numbers, not just a finite number of states as in classical (von Neumann) cellular automata. Another new result reported in this exposition is the successful implementation of an analog input analog output CNN universal machine, called a CNN universal chip, on a single silicon chip. This chip is a complete dynamic array stored-program computer where a CNN chromosome (i.e. a CNN algorithm or flow chart) can be programmed and executed on the chip at an extremely high speed of 1 Tera (1012) analog instructions per second (based on a 100 × 100 chip). The CNN universal chip is based entirely on nonlinear dynamics and therefore differs from a digital computer in its fundamental operating principles. Part II of this exposition is devoted to the important subclass of autonomous CNNs where the cells have no inputs. This class of CNNs can exhibit a great variety of complex phenomena, including pattern formation, Turing patterns, knots, auto waves, spiral waves, scroll waves, and spatiotemporal chaos. It provides a unified paradigm for complexity, as well as an alternative paradigm for simulating nonlinear partial differential equations (PDE's). In this context, rather than regarding the autonomous CNN as an approximation of nonlinear PDE's, we advocate the more provocative point of view that nonlinear PDE's are merely idealizations of CNNs, because while nonlinear PDE's can be regarded as a limiting form of autonomous CNNs, only a small class of CNNs has a limiting PDE representation. Part III of this exposition is rather short but no less significant. It contains in fact the potentially most important original results of this exposition. In particular, it asserts that all of the phenomena described in the complexity literature under various names and headings (e.g. synergetics, dissipative structures, self-organization, cooperative and competitive phenomena, far-from-thermodynamic equilibrium phenomena, edge of chaos, etc.) are merely qualitative manifestations of a more fundamental and quantitative principle called the local activity dogma. It is quantitative in the sense that it not only has a precise definition but can also be explicitly tested by computing whether a certain explicitly defined expression derived from the CNN paradigm can assume a negative value or not. Stated in words, the local activity dogma asserts that in order for a system or model to exhibit any form of complexity, such as those cited above, the associated CNN parameters must be chosen so that either the cells or their couplings are locally active.

CNN: A Vision of Complexity

An analysis of behavioral, neurological, and biochemical research indicates that the sensory systems of the avian embryo become functional in the following order: (1) non-visual photic sensitivity; (2) tactile sensitivity; (3) vestibular sensitivity; (4) proprioception; (5) audition; (6) vision. There is no firm information about the onset of gustation and olfaction in the avian embryo. With the possible exception of vision, there would appear to be adequate stimulation during the normal course of incubation to excite all the sensory systems. Whether such stimulation actually plays a role in regulating species-typical sensory and perceptual development is not known. While it seems doubtful that depriving the embryo of relevant stimulation, or prematurely exposing it to such stimulation, would alter the absolute sequence in which the sensory systems develop, such a manipulation might exert some effect on the relative time of onset of the particular sensory system involved, and a major effect on the develop...

Prenatal behavior of birds.

On the Global Convergence of a Class of Functional Differential Equations with Applications in Neural Network Theory

The equivalent notions of neuroanatomy and the cellular neural network (CNN) model are discussed with a view toward studying the visual system. Various mainly subcortical phenomena are studied and simple effects like directional sensitivity and length tuning are modeled. A more accurate retina model has been developed, taking into account some effects of amacrine cells. It is shown that the standard errors occurring in simple models of retinal illusions can be eliminated by using the more accurate models including delays. Lateral geniculate nucleus (LGN) effects with and without cortical feedback are modeled as well; their CNN models are simple. Simple texture detection effects and motion illusions are explained by neuromorphic CNN models. The goal is to translate known effects into CNN models and to provide a framework for further studies. >

The use of CNN models in the subcortical visual pathway. (Reseach report of the Dual and Neural Computing Systems Laboratory DNS-16-1992)

THE formation of charge-transfer complex between flavin mononucleotide (FMN) and serotonin has been examined in detail1, as a good example for a complex of biochemical interest and of characteristic colour change. Chlorpromazine can also form complexes with FMN and rhodamine B11,12.

Evidence of Complex Formation between Chlorpromazine and Different Xanthene Dyes

Effect of serotonin and other bioactive agents on the rhythmic activity in the glochidia on fresh-water mussel (Anodonta cygnea L.)

Using internal negations acting on Boolean functions, the notion of Boolean–Lie algebra is introduced. The underlying Lie product is the Boolean analogue of the Poisson bracket. The structure of a Boolean–Lie algebra is determined; it turns out to be solvable, but not nilpotent. We prove that the adjoint representation of an element of the Boolean–Lie algebra acts as a derivative operator on the space of Boolean functions. The adjoint representation is related to the previously known concept of the sensitivity function. Using the notion of adjoint representation we give the definition of a temporal derivative applicable to iterative dynamics of Boolean mappings.

https://iopscience.iop.org/article/10.1088/0305-4470/39/22/005/pdf

Boolean–Lie algebras and the Leibniz rule

The use of CNN models in the visual parthway. Part II: The amacrine cell in the modified retina model, simple LGN effects and motion related illusions. (Reseach report of the Dual and Neural Computing Systems Laboratory DNS-9-1992.)

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