This conference included the Student Symposium on Computations in Astronomy, Space, and Earth sciences (CASE'96). We were lucky to have as a keynote speaker France Cordova who has recently finished her tenure as NASA's Chief Scientist to join the University of California at Santa Barbara as Vice Chancellor of Research. Dr. Cordova gave an exciting overview of the major directions of NASA research, including Exobiology (search for life and intelligence outside Earth), Mission to Planet Earth (use of spaceships to monitor processes on Earth), and Cosmology. Her emphasis on the need for new computational techniques was emphasized by another keynote talk, by Dr. Scott Starks, the Director of the NASA PACES Center, who said that only 1 to 10% of the data collected from the space missions are actually processed. This is partly caused by the fact that most of the collected bits are useless, because they represent the measurement results below the noise level. From this viewpoint, interval methods, that can automatically filter such useless measurements, can be of great help.

The talk was followed by a demonstration of the new algorithm. When we moved around a robot, it desperately (and, most often, successfully) avoided the obstacles (i.e., us) and continued moving. When we stood motionless around it, the robot sensed being stalled and stopped "to think" (the robot was only once cheated by the steep surface).

Several techniques can be used to trace these periodicities. The main computational problem is: if we apply these techniques to the measured signal and they uncover some periodicities, we would like to know whether these periodicities are real, or whether they are noise-related artifacts on top of non-periodic real signals. For interval-valued errors, this problems becomes interval-related. The easiest thing is to show that some periodicities are not for real: for that, it is sufficient to show that within the error-induced intervals [x](t)=[X(t)-D,X(t)+D] there are signals x(t) that have no periodic component with the supposedly observed frequency. This was actually shown for the 1993 data. For the 1988 data, so far, all attempts to find such aperiodic functions $x(t)$ have failed, which may be an indication that these periodicities are real (although their amplitudes and frequency exclude the possibility of them being caused by gravitational waves).

This is still work in progress, made extremely complicated by the fact that part of the noise is of a clearly statistical nature.

Unfortunately, checking whether two given graphs are isomorphic is known to be a hard problem (conjectured to be NP-hard, i.e., computationally intractable). To solve this problem, the authors use a result (based on a theorem proven by S. Ulam's) according to which two graphs are isomorphic if and only if certain real numbers constructed from these graphs coincide. If we have to compute these numbers with unlimited accuracy, then we run into the same computational problems as before. If we use standard (approximate) computer arithmetic to compute these numbers, then sometimes two different graphs will be assigned the same number, and sometimes, due to computer roundings, two isomorphic graphs can be assigned different numbers. The authors' algorithm uses the appropriate directed roundings and thus (as the authors claim), eliminates the second problem. The first problem remains, but intensive computer simulation shows that for graphs of reasonable size (with 30 to 40 atoms) only 1/100,000 of all possible graphs have non-isomorphic ``twins'' with the same values of the index. Hence, the rounding-spoiled fast identification algorithm works correctly in 99.999% of all cases.

Reported by Ann Q. Gates, Chenyi Hu, and Vladik Kreinovich.