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Abstract-It is well-known that maximum entropy distributions, subject to appropriate moment constraints, arise in physics and mathematics. In an attempt to find a physical reason for the appearance of maximum entropy distributions, the following theorem is offered. The conditional distribution of X, given the empirical observation(1 /n)X:, ,/I ( X,) = (Y, where X, , X2, . are independent identically distributed random variables with common density g converges to fA( x) = e A'h(x)g( x) (suitably normalized), where X is chosen to satisfy jfx( x) h( x) dx = o. Thus the conditional distribution of a given random variable X is the (normalized) product of the maximum entropy distribution and the initial distribution. This distribution is the maximum entropy distribution when g is uniform. The proof of this and related results relies heavily on the work of Zabell and Lanford.

By virtue of their low cost and simplicity, ultrasonic sensors are widely used in time-of-flight ranging systems. Unfortunately, correctly interpreting the readings from such sensors proves to be very difficult. We present a high-resolution sensor composed of three ultrasonic sensors: one transmitterh-eceiver and two extra receivers, which allows a significant improvement in the information-extraction process. With this sensor we can determine the position, both distance and bearing, of all isolated objects in the field of view (E 25") using information contained in one single snapshot of a moderately complex scene. It is further shown that, within limits, the sensor system can also discriminate between different types of reflectors, based on their radius of curvature. In particular, the sensor can discriminate between walls and edges. These results are all based on the determination of the arrival times of the echoes present at the three receivers. In this respect, too, our sensor differs from the conventional ultrasonic sensor, which processes only the first echo to arrive at the receiver. A noise model, explaining the measured variations of the arrival times, is used to derive limits on the resolution of the results provided by the sensor. Furthermore, based on this model it is shown that, to a large extent, the results of the sensor are impervious to measurement variations common to all three receivers. Finally, this sensor is used in a realistic environment and the results are compared with those obtained from a conventional time-of-flight sensor.

We propose photonic reservoir computing as a new approach to optical signal processing in the context of large scale pattern recognition problems. Photonic reservoir computing is a photonic implementation of the recently proposed reservoir computing concept, where the dynamics of a network of nonlinear elements are exploited to perform general signal processing tasks. In our proposed photonic implementation, we employ a network of coupled Semiconductor Optical Amplifiers (SOA) as the basic building blocks for the reservoir. Although they differ in many key respects from traditional software-based hyperbolic tangent reservoirs, we show using simulations that such a photonic reservoir can outperform traditional reservoirs on a benchmark classification task. Moreover, a photonic implementation offers the promise of massively parallel information processing with low power and high speed.

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