The research in my lab focuses on sensory signal processing, particularly in cases where sensory systems perform at or near the limits imposed by physics. Photon counting in the visual system is a beautiful example. At its peak sensitivity, the performance of the visual system is limited largely by the division of light into discrete photons. This observation has several implications for phototransduction and signal processing in the retina: rod photoreceptors must transduce single photon absorptions with high fidelity, single photon signals in photoreceptors, which are only 0.03 – 0.1 mV, must be reliably transmitted to second-order cells in the retina, and absorption of a single photon by a single rod must produce a noticeable change in the pattern of action potentials sent from the eye to the brain. My approach is to combine quantitative physiological experiments and theory to understand photon counting in terms of basic biophysical mechanisms. Fortunately there is more to visual perception than counting photons. The visual system is very adept at operating over a wide range of light intensities (about 12 orders of magnitude). Over most of this range, vision is mediated by cone photoreceptors. Thus adaptation is paramount to cone vision. Again one would like to understand quantitatively how the biophysical mechanisms involved in phototransduction, synaptic transmission, and neural coding contribute to adaptation.

Although animals can estimate numerical quantities, true counting and arithmetic abilities are unique to humans and are inextricably linked to symbolic competence. However, our unprecedented numerical skills are deeply rooted in our neuronal heritage as primates and vertebrates. I argue that numerical competence in humans is the result of three neural constraints. First, I propose that the neuronal mechanisms of quantity estimation are part of our evolutionary heritage and can be witnessed across primate and vertebrate phylogeny. Second, I suggest that a basic understanding of number, what numerical quantity means, is innately wired into the brain and gives rise to an intuitive number sense, or number instinct. Third and finally, I argue that symbolic counting and arithmetic in humans is rooted in an evolutionarily and ontogenetically primeval neural system for non-symbolic number representations. These three neural constraints jointly determine the basic processing of number concepts in the human mind.

The Neural Engineering Framework has been used to create a wide variety of biologically realistic brain simulations that are capable of performing simple cognitive tasks (remembering a list, counting, etc.). This includes the largest existing functional brain model. This talk will describe this method, and show some examples of using it to take high-level cognitive algorithms and convert them into a neural network that implements those algorithms. Overall, this approach gives us new ways of thinking about how the brain works and what sorts of algorithms it is capable of performing.