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Highly-interconnected networks of nonlinear analog neurons are shown to be extremely effective in computing. The networks can rapidly provide a collectively-computed solution (a digital output) to a problem on the basis of analog input information. The problems to be solved must be formulated in terms of desired optima, often subject to constraints. The(More)
Paramagnetic deoxyhemoglobin in venous blood is a naturally occurring contrast agent for magnetic resonance imaging (MRI). By accentuating the effects of this agent through the use of gradient-echo techniques in high fields, we demonstrate in vivo images of brain microvasculature with image contrast reflecting the blood oxygen level. This blood oxygenation(More)
We report that visual stimulation produces an easily detectable (5-20%) transient increase in the intensity of water proton magnetic resonance signals in human primary visual cortex in gradient echo images at 4-T magnetic-field strength. The observed changes predominantly occur in areas containing gray matter and can be used to produce(More)
It recently has been demonstrated that magnetic resonance imaging can be used to map changes in brain hemodynamics produced by human mental operations. One method under development relies on blood oxygenation level-dependent (BOLD) contrast: a change in the signal strength of brain water protons produced by the paramagnetic effects of venous blood(More)
We report a technique for two-photon fluorescence imaging with cellular resolution in awake, behaving mice with minimal motion artifact. The apparatus combines an upright, table-mounted two-photon microscope with a spherical treadmill consisting of a large, air-supported Styrofoam ball. Mice, with implanted cranial windows, are head restrained under the(More)
We describe how several optimization problems can be rapidly solved by highly interconnected networks of simple analog processors. Analog-to-digital (A/D) conversion was considered as a simple optimization problem, and an A/D converter of novel architecture was designed. A/D conversion is a simple example of a more general class of signal-decision problems(More)
Patterning in multicellular organisms results from spatial gradients in morphogen concentration, but the dynamics of these gradients remain largely unexplored. We characterize, through in vivo optical imaging, the development and stability of the Bicoid morphogen gradient in Drosophila embryos that express a Bicoid-eGFP fusion protein. The gradient is(More)
Hippocampal place cells encode spatial information in rate and temporal codes. To examine the mechanisms underlying hippocampal coding, here we measured the intracellular dynamics of place cells by combining in vivo whole-cell recordings with a virtual-reality system. Head-restrained mice, running on a spherical treadmill, interacted with a(More)
A new conceptual framework and a minimization principle together provide an understanding of computation in model neural circuits. The circuits consist of nonlinear graded-response model neurons organized into networks with effectively symmetric synaptic connections. The neurons represent an approximation to biological neurons in which a simplified set of(More)
The reproducibility and precision of biological patterning is limited by the accuracy with which concentration profiles of morphogen molecules can be established and read out by their targets. We consider four measures of precision for the Bicoid morphogen in the Drosophila embryo: the concentration differences that distinguish neighboring cells, the limits(More)