Sharp Things

Covering Things with Things

An abstract NP-hard covering problem is presented and xed-parameter tractable algorithms for this problem are described. The running times of the algorithms are expressed in terms of three parameters: n, the number of elements to be covered, k, the number of sets allowed in the covering, and d, the combinatorial dimension of the problem. The rst algorithm is deterministic and has running time O...

From little things big things grow: . . .

Sharp Thresholds

The Kolmogorov Zero-One law states that for tail events on infinite-dimensional probability spaces, the probability must be either zero or one. Behavior analogous in a natural sense to this exists on finite-dimensional spaces as well. Events exhibiting this behavior are said to have a sharp threshold. Let Qn = {0, 1}n be the discrete hypercube with the probability measure Pp defined by Pp(ω1, ω...

Talking Things

Have you ever wished to know and actually feel what your friends feel so you could help them better? Or maybe you have wondered how it is to be one of those celebrities you admire? And how about to become an apple for example? To experience lazy days of hanging on a tree enjoying sunshine and being washed by rains? Or maybe it feels the opposite – a hard life of fighting against worms, decay, a...

treatment with muḥarramāt (forbidden things)

the jurists have since early times wondered whether illnesses can be treated with forbidden or ḥarām things and thereby improve the illness and restore the patients to health; or whether it is totally forbidden and impermissible to step into this arena even if motivated by treatment of illness. of course, using the unlawful in treating illnesses where exploitations other than eating and drinkin...