Related papers: The Retina as a Dynamical System
With a kind of magnetism, the human retina draws the eye of neuroscientist and physicist alike. It is attractive as a self-organizing system, which forms as a part of the central nervous system via biochemical and mechanical cues. The…
Neural circuits in the retina divide the incoming visual scene into more than a dozen distinct representations that are sent on to central brain areas, such as the lateral geniculate nucleus and the superior colliculus. The retina can be…
We present a detailed physiological model of the retina that includes the biochemistry and electrophysiology of phototransduction, neuronal electrical coupling, and the spherical geometry of the eye. The model is a parabolic-elliptic system…
The retina is the entrance of the visual system. Although based on common biophysical principles the dynamics of retinal neurons is quite different from their cortical counterparts, raising interesting problems for modellers. In this paper…
Beings, animate or inanimate, are dynamical systems which continuously interact with the (external and /or internal) environment through the physical or physiologic interfaces of their Kantian (representational) realities. And the nature of…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
The concept of a cell$'$s receptive field is a bedrock in systems neuroscience, and the classical static description of the receptive field has had enormous success in explaining the fundamental mechanisms underlying visual processing.…
This paper is an introduction to the membrane potential equation for neurons. Its properties are described, as well as sample applications. Networks of these equations can be used for modeling neuronal systems, which also process images and…
Visual information determines majority of our spatial behavior. The eye projects a 2-D image of the world on the retina. We demonstrate that when a monocular-like imaging system operates entirely with optically dense fluids, an increase in…
Mathematical modelling of the microcirculatory hemodynamics in the retina is an essential tool for understanding various diseases of the retina, yet remains challenging due to the multiscale nature of the retinal vasculature and its…
We consider neural networks from the point of view of dynamical systems theory. In this spirit we review recent results dealing with the following questions, adressed in the context of specific models. 1. Characterizing the collective…
Vital to primary visual processing, retinal circuitry shows many similar structures across a very broad array of species, both vertebrate and non-vertebrate, especially functional components such as lateral inhibition. This surprisingly…
We consider a class of multi-layer interacting particle systems and characterize the set of ergodic measures with finite moments. The main technical tool is duality combined with successful coupling.
The nervous system displays a variety of rhythms in both waking and sleep. These rhythms have been closely associated with different behavioral and cognitive states, but it is still unknown how the nervous system makes use of these rhythms…
There is perceptual and physiological evidence that the retina registers and signals luminance and luminance contrast using dual-channel mechanisms. This process begins in the retina, wherein the luminance of a uniform zone and…
Recent experimental results based on multi-electrode and imaging techniques have reinvigorated the idea that large neural networks operate near a critical point, between order and disorder. However, evidence for criticality has relied on…
Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main…
The design of deep neural networks remains somewhat of an art rather than precise science. By tentatively adopting ergodic theory considerations on top of viewing the network as the time evolution of a dynamical system, with each layer…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) the system of planets orbiting the sun or any other classical…