Let X1, · · · , Xn and Y1, · · · , Yn be independent heterogeneous geometric random variables with parameters p1 ≤ · · · ≤ pn and q1 ≤ · · · ≤ qn, respectively. We prove that ∑k i=1Xi is larger than ∑k i=1 Yi, for k = 1, · · · , n, in mean residual life order if, and only if, the harmonic mean of p1, · · · , pk is smaller than the harmonic mean of q1, · · · , qk, for k = 1, · · · , n. In this w...

Abstract. The exact evolution of a system coupled to a complex environment can be described by a stochastic mean-field evolution of the reduced system density. The formalism developed in Ref. [1] is illustrated in the Caldeira-Leggett model where a harmonic oscillator is coupled to a bath of harmonic oscillators. Similar exact reformulation could be used to extend mean-field transport theories ...

Using the Crank-Nicholson method, we study the evolution of a Bose-Einstein condensate in an optical lattice and harmonic trap. The condensate is excited by displacing it from the center of the harmonic trap. The mean field plays an important role in the Bloch-like oscillations that occur after sufficiently large initial displacement. We find that a moderate mean field significantly suppresses ...

In the Bayesian paradigm, a common method for comparing two models is to compute the Bayes factor, defined as the ratio of their respective marginal likelihoods. In recent phylogenetic works, the numerical evaluation of marginal likelihoods has often been performed using the harmonic mean estimation procedure. In the present article, we propose to employ another method, based on an analogy with...