Previously, we studied a model of an infection's spread through a hospital ward. The ward was small enough that we could track each patient individually, but when population size grows, this kind of ...model becomes impractical; accordingly, we turn our attention in this paper to models that study the population as a whole. As before, we divide the population into three groups: at day t, I(t) is the infected proportion of the population, whereas S(t) is the proportion that has never been infected. These quantities satisfy 0 /spl les/ I(t) /spl les/ 1 and 0 /spl les/ S(t) /spl les/ 1 for t /spl ges/ 0. We derive the third part, R(t) the proportion of the population that was once infected but has now recovered - from the first two: R(t) = I - I(t) - S(t).
The identification of specialized areas in the mammalian neocortex, such as the primary visual or somatosensory cortex, is based on distinctions in architectural and functional features. The extent ...to which certain features that distinguish neocortical areas in rats are prespecified or emerge as a result of epigenetic interactions was investigated. Late embryonic visual cortex transplanted to neonatal somatosensory cortex was later assayed for "barrels," anatomically identified functional units unique to somatosensory cortex, and for boundaries of glycoconjugated molecules associated with barrels. Barrels and boundaries form in transplanted visual cortex and are organized in an array that resembles the pattern in the normal barrelfield. These findings show that different regions of the developing neocortex have similar potentials to differentiate features that distinguish neocortical areas and contribute to their unique functional organizations.
Inverse problems are among the most challenging computations in science and engineering because they involve determining the parameters of a system that is only observed indirectly. For example, we ...might have a spectrum and want to determine the species that produced it as well as their relative proportions, or we may have sonar measurements of a containment tank and want to know whether it has an internal crack. Given a blurred image and a linear model for the blurring, the original image is reconstructed. This linear inverse problem illustrates the impact of ill-conditioning on the choice of algorithms.
Individual neurons in the brain send their axons over considerable distances to multiple targets, but the mechanisms governing this process are unresolved. An amenable system for studying axon ...outgrowth, branching, and target selection is the mammalian corticopontine projection. This major connection develops from parent corticospinal axons that have already grown past the pons, by a delayed interstitial budding of collateral branches that then grow directly into their target, the basilar pons. When cocultured with explants of developing cortex in three-dimensional collagen matrices, the basilar pons elicits the formation and directional growth of cortical axon collaterals across the intervening matrix. This effect appears to be target-specific and selectively influences neurons in the appropriate cortical layer. These in vitro findings provide evidence that the basilar pons becomes innervated by controlling at a distance the budding and directed ingrowth of cortical axon collaterals through the release of a diffusible, chemotropic molecule.
Suppose we have a robot arm with a single joint, simply modeled as a damped driven pendulum. it's amazing how such a trivial system illustrates so many difficult concepts! The authors study the ...stability and behavior of this robot arm and develop a strategy to move the arm from one position to another using minimal energy.
ON 28–29 APRIL 2000, THE BOARD ON MATHEMATICAL SCIENCES AND THE COMPUTER SCIENCE AND TELECOMMUNICATIONS BOARD OF THE NATIONAL RESEARCH COUNCIL COSPONSORED A WORKSHOP ON THE INTERFACE BETWEEN THE ...mathematical sciences and three areas of computer science: network traffic modeling, computer vision, and data mining. The workshop’s goal was to identify some open research questions in the mathematical sciences whose solutions could contribute to important unsolved problems in those computer science disciplines. The 48 participants engaged in lively discussions and identified at least 36 research challenges of a mathematical, statistical, or probabilistic nature.
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