Rayleigh’s monotonicity principle states that if the resistances of a circuit of resistors are increased, the effective resistance between any two points can only increase. If they are decreased, they can only decrease. You can find a short proof in the Doyle-Snell book right here. One can use this intuitive principle to prove classic and […]
Few days ago I presented my recent paper on opinion dynamics and the wisdom of crowds at ECML-PKDD, joint work with two excellent PhD students at BU, Fabian Spaeh and Dragos Ristache. Wisdom of Crowds In 1906, approximately about 800 villagers participated in an event where they estimated the weight of an ox. Sir Francis […]
Let given points have the property that the line joining any two of them passes through a third point of the set. Must the points all lie on one line? This question was posed by Sylvester in his article “Mathematical question 11851” in 1893. The answer is no in general (complex projective plane), but on […]
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