A fault-tolerant controller is a controller that drives the plant to satisfy control specifications under both nominal operation and after the occurrence of faults. This paper introduces a framework that ensures the fault-tolerance of a discrete-event system (DES) plant, which includes: (i) a nominal supervisor with respect to the nominal plant to ensure the control specification that is prior ...

RE EQUATIONS BEAUTIFUL? TO SCIENTISTS, FORMULAS’ ABILITY TO represent fundamental truths or concisely capture complexity is indeed exquisite. To many in the public, though, they can be the opposite of beautiful—intimidating, utilitarian and opaque. Yet for others, the very mystery can be alluring: even when we cannot understand what equations say, we can be moved by knowing they have meanings b...

Elegance is a prized quality in science that is associated with simplicity and explanatory power. This essay considers the qualities that make a scientific model, experiment, method, or theory "elegant," with a focus on the life sciences. We propose a definition of elegance that includes clarity, cleverness, correctness, explanatory power, parsimony, and beauty. The pursuit of elegance can impr...