Topic
Harmonic mean
About: Harmonic mean is a research topic. Over the lifetime, 794 publications have been published within this topic receiving 12913 citations. The topic is also known as: subcontrary mean & HM.
Papers published on a yearly basis
Papers
More filters
TL;DR: The present article proposes to employ another method, based on an analogy with statistical physics, called thermodynamic integration, which is applied to the comparison of several alternative models of amino-acid replacement, indicating that modeling pattern heterogeneity across sites tends to yield better models than standard empirical matrices.
Abstract: 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 statistical physics, called thermodynamic integration. We describe the method, propose an implementation, and show on two analytical examples that this numerical method yields reliable estimates. In contrast, the harmonic mean estimator leads to a strong overestimation of the marginal likelihood, which is all the more pronounced as the model is higher dimensional. As a result, the harmonic mean estimator systematically favors more parameter-rich models, an artefact that might explain some recent puzzling observations, based on harmonic mean estimates, suggesting that Bayes factors tend to overscore complex models. Finally, we apply our method to the comparison of several alternative models of amino-acid replacement. We confirm our previous observations, indicating that modeling pattern heterogeneity across sites tends to yield better models than standard empirical matrices.
618 citations
TL;DR: Comparisons between regenerative and nonregenerative systems show that the former systems clearly outperform the latter ones for low average signal-to-noise ratios (SNRs) and that the two systems have similar performance at high average SNRs.
Abstract: Closed-form expressions for the statistics of the harmonic mean of two independent and identically distributed gamma variates are presented. The probability density function of the harmonic mean of two F variates is also derived. These statistical results are then applied to study the performance of wireless communication systems with nonregenerative relays over flat Nakagami fading channels. More specifically, outage probability formulas for noise-limited systems as well as systems affected by interference are obtained. Furthermore, general expressions for average bit-error rates are also derived. Finally, comparisons between regenerative and nonregenerative systems are presented. Numerical results show that the former systems clearly outperform the latter ones for low average signal-to-noise ratios (SNRs). They also show that the two systems have similar performance at high average SNRs.
509 citations
TL;DR: This paper gives precise definitions of different, properly invariant notions of mean or average rotation and shows that the Riemannian mean rotation shares many common features with the geometricmean of positive numbers and the geometric mean of positive Hermitian operators.
Abstract: In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to the usual arithmetic mean of the given rotation matrices. The mean rotation associated with the intrinsic metric on SO(3) is the Riemannian center of mass of the given rotation matrices. We show that the Riemannian mean rotation shares many common features with the geometric mean of positive numbers and the geometric mean of positive Hermitian operators. We give some examples with closed-form solutions of both notions of mean.
464 citations
TL;DR: This analysis suggested that the gas conductance of the barrier is nearly optimal if one considers the mass of tissue and the minimal barrier thickness as fixed properties which are determined by other functional requirements on the alveolo-capillary membrane.
Abstract: A reliable knowledge of the thickness of the alveolo-capillary "membrane" or air-blood barrier is of physiologic interest since it is intimately related to a quantitative estimation of such functional events as gas diffusion or tissue metabolism in the lung. The characteristic thickness of the air-blood barrier with respect to gas diffusion is its harmonic mean thickness, while the arithmetic mean thickness is related to the mass of tissue building the barrier and consuming oxygen in the lung. Two morphometric methods are proposed by which these two dimensions can be estimated from random measurements in the electron microscope in a reliable, simple, and efficient manner. By applying these methods to three rat lungs the arithmetic mean thickness of the barrier was found to measure 1.25 µ, the harmonic mean thickness, 0.57 µ. On the basis of these measurements a geometric model of the barrier in the form of a corrugated membrane was derived. Its dimensions showed close similarity to those of the natural barrier. This analysis suggested furthermore that the gas conductance of the barrier is nearly optimal if one considers the mass of tissue and the minimal barrier thickness as fixed properties which are determined by other functional requirements on the alveolo-capillary membrane.
368 citations
TL;DR: In this article, a benchmark comparison between various numerical codes (Eulerian and Lagrangian, Finite Element and Finite Difference, with and without markers) as well as a laboratory experiment is presented.
365 citations