The stability of the h -index

Over the last years the h-index has gained popularity as a measure for comparing the impact of scientists. We investigate if ranking according to the h-index is stable with respect to (i) different choices of citation databases, (ii) normalizing citation counts by the number of authors or by removing self-citations, (iii) small amounts of noise created by randomly removing citations or publications and (iv) small changes in the definition of the index. In experiments for 5,283 computer scientists and 1,354 physicists we show that although the ranking of the h-index is stable under most of these changes, it is unstable when different databases are used. Therefore, comparisons based on the h-index should only be trusted when the rankings of multiple citation databases agre

Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in (1/2,1)(1/2,1)

This paper addresses the exponential stability of the trivial solution of some types of evolution equations driven by H\"older continuous functions with H\"older index greater than $1/2$. The results can be applied to the case of equations whose noisy inputs are given by a fractional Brownian motion $B^H$ with covariance operator $Q$, provided that $H\in (1/2,1)$ and ${\rm tr}(Q)$ is sufficiently small.Comment: 19 page

Divide and color representations for threshold Gaussian and stable vectors

We study the question of when a (\{0,1\})-valued threshold process associated to a mean zero Gaussian or a symmetric stable vector corresponds to a {\it divide and color (DC) process}. This means that the process corresponding to fixing a threshold level $h$ and letting a 1 correspond to the variable being larger than $h$ arises from a random partition of the index set followed by coloring {\it all} elements in each partition element 1 or 0 with probabilities $p$ and $1-p$, independently for different partition elements. While it turns out that all discrete Gaussian free fields yield a DC process when the threshold is zero, for general $n$-dimensional mean zero, variance one Gaussian vectors with nonnegative covariances, this is true in general when $n=3$ but is false for $n=4$. The behavior is quite different depending on whether the threshold level $h$ is zero or not and we show that there is no general monotonicity in $h$ in either direction. We also show that all constant variance discrete Gaussian free fields with a finite number of variables yield DC processes for large thresholds. In the stable case, for the simplest nontrivial symmetric stable vector with three variables, we obtain a phase transition in the stability exponent $\alpha$ at the surprising value of $1/2$; if the index of stability is larger than $1/2$, then the process yields a DC process for large $h$ while if the index of stability is smaller than $1/2$, then this is not the case.Comment: 51 pages, 6 figures This paper together with arXiv:1911.00513, arXiv:1910.09813 and arXiv:1909.11322 replace the first version of this pape

The Z-index: A geometric representation of productivity and impact which accounts for information in the entire rank-citation profile

We present a simple generalization of Hirsch's h-index, Z = \sqrt{h^{2}+C}/\sqrt{5}, where C is the total number of citations. Z is aimed at correcting the potentially excessive penalty made by h on a scientist's highly cited papers, because for the majority of scientists analyzed, we find the excess citation fraction (C-h^{2})/C to be distributed closely around the value 0.75, meaning that 75 percent of the author's impact is neglected. Additionally, Z is less sensitive to local changes in a scientist's citation profile, namely perturbations which increase h while only marginally affecting C. Using real career data for 476 physicists careers and 488 biologist careers, we analyze both the distribution of $Z$ and the rank stability of Z with respect to the Hirsch index h and the Egghe index g. We analyze careers distributed across a wide range of total impact, including top-cited physicists and biologists for benchmark comparison. In practice, the Z-index requires the same information needed to calculate h and could be effortlessly incorporated within career profile databases, such as Google Scholar and ResearcherID. Because Z incorporates information from the entire publication profile while being more robust than h and g to local perturbations, we argue that Z is better suited for ranking comparisons in academic decision-making scenarios comprising a large number of scientists.Comment: 9 pages, 5 figure

The stability of the h-index

Over the last years the h-index has gained popularity as a measure for comparing the impact of scientists. We investigate if ranking according to the h-index is stable with respect to (i) different choices of citation databases, (ii) normalizing citation counts by the number of authors or by removing self-citations, (iii) small amounts of noise created by randomly removing citations or publications and (iv) small changes in the definition of the index. In experiments for 5,283 computer scientists and 1,354 physicists we show that although the ranking of the h-index is stable under most of these changes, it is unstable when different databases are used. Therefore, comparisons based on the h-index should only be trusted when the rankings of multiple citation databases agree

Human Disturbance Reduces Plant Species Diversity and Stability of Phyllostachys pubescens Forests

Plant species diversity is an important index reflecting the functional complexity and stability of ecosystems. Human activity can completely alter plant species diversity and cause serious degradation of ecosystems but its impact on bamboo forest still lacks of systematic evaluation. In this study, we performed a field investigation to reveal the influences of human disturbances on the plant diversity and stability of Moso bamboo forests at Southern China. The selected bamboo fields contained different intensities of human activities that could be classified as slight, moderate and severe disturbance level. Species richness index S, Shannon-Wienner index H, Simpson index D, Pielou index Jsw, community similarity index IS and community stability index were employed to quantitatively evaluate the plant species diversity and stability. The survey revealed that there were 203 species belonging to 83 families and 108 genera in Moso bamboo forests. The number of plant species in the Moso bamboo forests decreased with the increasing of disturbance intensity. The species diversity indexes generally followed the order of slight > moderate > severe disturbance, as well as the richness index S, Shannon-Wienner index H and Pielou index Jsw. The similarity and species stability of the bamboo forest communities also decreased with the increase of the disturbance intensity. Under the severe disturbance, plant species replacement occurred strongly. The obtained results provide some a guideline for the sustainable management of bamboo forest