We propose a nonparametric method for estimating the pricing formula of a derivative asset using learning networks. Although not a substitute for the more traditional arbitrage-based pricing fomiulas, network pricing formulas may be more accurate and computationaily more efficient alternatives when the underlying asset's price dynamics are unknown, or when the pricing equation associated with no-arbiaage condition cannot be solved analytically. To assess the potential value of network pricing formulas, we simulate Black-Scholes option prices and show that learning networks can recover the Black-Scholes fonnula from a two-year training set of daily options prices, and that the resulting network fonnula can be used successfully to both price and delta-hedge options out-of-sample. For comparison, we estimate models using four popular methods: ordinary least squares, radial basis function networks, multilayer peivepfln networks, and projection pursuit To illustrate the practical relevance of our network pricing approach, we apply it to the pricing and delta-hedging of S&P 500 fuwres options from 1987 to 1991.

Our study confirms the strong age association with infection due to the NAP1 strain and severe CDI. In addition, patients 60-90 years of age infected with NAP1 are approximately twice as likely to die or to experience a severe CDI-related outcome, compared with those with non-NAP1 infections. Patients >90 years of age experience high rates of severe CDI, regardless of strain type.

The rates are remarkably similar to those found in our previous study; although we found wide variations in HA CDI among the participating hospitals. However, the attributable mortality increased almost 4-fold (5.7% vs. 1.5%; P<.001).

We propose a nonparametric method for estimating the pricing formula of a derivative asset using learning networks. Although not a substitute for the more traditional arbitrage-based pricing formulas, network pricing formulas may be more accurate and computationally more e cient alternatives when the underlying asset's price dynamics are unknown, or when the pricing equation associated with no-arbitrage condition cannot be solved analytically. T o assess the potential value of network pricing formulas, we simulate Black-Scholes option prices and show that learning networks can recover the Black-Scholes formula from a two-year training set of daily options prices, and that the resulting network formula can be used successfully to both price and delta-hedge options out-of-sample. For comparison, we estimate models using four popular methods: ordinary least squares, radial basis function networks, multilayer perceptron networks, and projection pursuit. To illustrate the practical relevance of our network pricing approach, we apply it to the pricing and delta-hedging of S&P 500 futures options from 1987 to 1991.

o us, and to other biological organisms, vision seems effortless. We open our eyes and we "see" the world in all its color, brightness, and movement. Flies, frogs, cats, and humans can all equally well perceive a rapidly changing environment and act on it. Yet, we havegreat difficulties when trying to endow our machines with similar abilities. In this article, we describe recent developments in the theory of early vision that led from the formulation of the motion problem as an ill-posed one to its solution by minimizing certain "cost" functions. These cost or energy functions can be mapped onto simple analog and digital resistive networks. Thus, we can compute the optical flow by injecting currents into resistive networks and recording the resulting stationary voltage distribution at each node. These networks, which we implemented in complementary metal oxide semiconductor (CMOS) very large scale integrated (VLSI) circuits, represent plausible candidates for biological vision systems. MotionThe movement of objects relative to eyes or cameras serves as an important k We can compute optical flow by injecting currents into resistive networks and recording the stationary voltage distribution at each node.source of information for many tasks. We need motion to track objects and to determine whether an object is approaching or receding. Relative motion contains information regarding the three-dimensional structure of objects and allows biological organisms to navigate quickly and efficiently through the environment. There exist two basic methods for computing motion. Intensity-based schemes *Hutchinson is now with Thinking Machines Corprely on spatial and temporal gradients of the image intensity to compute the speed and the direction in which each point in the image moves. The output is a velocity or motion vector field covering the entire image. The second method is based on the identification of special features in the image, called tokens, which are then matched from image to image. This method relies on the unambiguous identification of the tokens-for instance, corners-in each image frame before the matching occurs and only yields a velocity vector at the sparse token locations. Psychophysical evidence suggests that both systems coexist in humans. ' The principal drawback of all intensitybased schemes lies in the data usedtemporal variations in brightness patterns-which give rise to the perceived motion field, the optical flow. In general, the optical flow and the underlying velocity field, a purely geometrical concept, differ.' For example, a featureless rotating sphere will not give rise to any optical flow, because the brightness does not appear to change even though the velocity field is non-zero. Conversely, if a shadow moves across the same featureless but now stationary sphere, the optical flow is non-zero although the velocity field is zero. Apart from such situations, the estimated opti-