earlbellinger

7 năm trướcdiscuss

This is very exciting. I worked on these kinds of technologies a bit in graduate school (before switching gears completely and getting a PhD in astrophysics). In the coming decades, we will be able to detect who is on the path to disease before they ever begin showing any symptoms at all. Granted, curing these diseases post-detection is a whole different matter.

earlbellinger

7 năm trướcdiscuss

For problem (b), this is the standard case for inverse problems, which are almost always ill-posed / ill-conditioned. There is now a vast literature on this subject, including many algorithms for solving them robustly.

"...incorrectly posed problems were considered ‘taboo’ for generations of mathematicians, until comparatively recently it became clear that there are a number of quite meaningful problems, the so-called ‘inverse problems,’ which are nearly always unstable with respect to fluctuations of input data." — H. Allison, Inverse Unstable Problems and Some of Their Applications (1979)

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