On the robustness of the h-index

The h-index (Hirsch, 2005) is robust, remaining relatively unaffected by errors in the long tails of the citations-rank distribution, such as typographic errors that short-change frequently-cited papers and create bogus additional records. This robustness, and the ease with which h-indices can be verified, support the use of a Hirsch-type index over alternatives such as the journal impact factor. These merits of the h-index apply to both individuals and to journals.Comment: 10 pages, 4 tables, 1 figur

On the Robustness of the h-index: a mathematical approach

The h-index is an index recently proposed by Hirsch (2005) to measure scientific achievement by individual scholars. It is a compound measure of publications and citations. We show the robustness of this index. This means that h-index increases with both the number of publications and the number of citations only when these numbers are significant.

On the Robustness of the h-index: a mathematical approach

International audienceThe h-index is an index recently proposed by Hirsch (2005) to measure scientific achievement by individual scholars. It is a compound measure of publications and citations. We show the robustness of this index. This means that h-index increases with both the number of publications and the number of citations only when these numbers are significant

On the robustness of the Hβ\beta Lick index as a cosmic clock in passive early-type galaxies

We examine the H$\beta$ Lick index in a sample of $\sim 24000$ massive ($\rm log(M/M_{\odot})>10.75$) and passive early-type galaxies extracted from SDSS at z<0.3, in order to assess the reliability of this index to constrain the epoch of formation and age evolution of these systems. We further investigate the possibility of exploiting this index as "cosmic chronometer", i.e. to derive the Hubble parameter from its differential evolution with redshift, hence constraining cosmological models independently of other probes. We find that the H$\beta$ strength increases with redshift as expected in passive evolution models, and shows at each redshift weaker values in more massive galaxies. However, a detailed comparison of the observed index with the predictions of stellar population synthesis models highlights a significant tension, with the observed index being systematically lower than expected. By analyzing the stacked spectra, we find a weak [NII]$\lambda6584$ emission line (not detectable in the single spectra) which anti-correlates with the mass, that can be interpreted as a hint of the presence of ionized gas. We estimated the correction of the H$\beta$ index by the residual emission component exploiting different approaches, but find it very uncertain and model-dependent. We conclude that, while the qualitative trends of the observed H$\beta$-z relations are consistent with the expected passive and downsizing scenario, the possible presence of ionized gas even in the most massive and passive galaxies prevents to use this index for a quantitative estimate of the age evolution and for cosmological applications.Comment: 20 pages, 11 figures, 1 table. Accepted for publication in MNRAS Main Journa

Robust control of systems with real parameter uncertainty and unmodelled dynamics

During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value

National Scientific Facilities and Their Science Impact on Non-Biomedical Research

H-index, proposed by Hirsch is a good indicator of the impact of a scientist's research. When evaluating departments, institutions or labs, the importance of h-index can be further enhanced when properly calibrated for size. Particularly acute is the issue of federally funded facilities whose number of actively publishing scientists frequently dwarfs that of academic departments. Recently Molinari and Molinari developed a methodology that shows the h-index has a universal growth rate for large numbers of papers, allowing for meaningful comparisons between institutions. An additional challenge when comparing large institutions is that fields have distinct internal cultures, with different typical rates of publication and citation; biology is more highly cited than physics, which is more highly cited than engineering. For this reason, this study has focused on the physical sciences, engineering, and technology, and has excluded bio-medical research. Comparisons between individual disciplines are reported here to provide contextual framework. Generally, it was found that the universal growth rate of Molinari and Molinari holds well across all the categories considered, testifying to the robustness of both their growth law and our results. The overall goal here is to set the highest standard of comparison for federal investment in science; comparisons are made with the nations preeminent private and public institutions. We find that many among the national facilities compare favorably in research impact with the nations leading universities.Comment: 22 pages, 7 figure

INTEGRATED BEAM ORIENTATION OPTIMIZATION FOR ROBUST INTENSITY-MODULATED PROTON THERAPY

Methods The unified framework is formulated to include a dose fidelity term, a heterogeneity-weighted group sparsity term, and a sensitivity regularization term. The dose fidelity term encourages less physical dose deviation from ideal distribution. The L2,1/2-norm group sparsity is used to reduce the number of active beams from the initial 1162 evenly distributed non-coplanar candidate beams, to between 2 and 4. A heterogeneity index, which evaluates the lateral tissue heterogeneity of a beam, is used to weigh the group sparsity term. With this index, beams more resilient to setup uncertainties are encouraged. There is a symbiotic relationship between the heterogeneity index and the sensitivity regularization; the integrated optimization framework further improves beam robustness against both range and setup uncertainties. This Sensitivity regularization and Heterogeneity weighting based BOO and FMO framework (SHBOO-FMO) was tested on two skull-base tumor (SBT) patients and two bilateral head-and-neck (H&amp;N) patients. The conventional CTV-based optimized plans (Conv) with SHBOO-FMO beams (SHBOO-Conv) and manual beams (MAN-Conv) were compared to investigate the beam robustness of the proposed method. The dosimetry and robustness of SHBOO-FMO plan were compared against the manual beam plan with CTV-based voxel-wise worst-case scenario approach (MAN-WC).Results With SHBOO-FMO method, the beams with superior range robustness over manual beams were selected while the setup robustness was maintained or improved. On average, the lowest [D95%, V95%, V100%] of CTV were increased from [93.8%, 91.0%, 70.6%] in MAN-Conv plans, to [98.6%, 98.6%, 96.1%] in SHBOO-Conv plans with range uncertainties. With setup uncertainties, the average lowest [D98%, D95%, V95%, V100%] of CTV were increased from [92.0%, 94.8%, 94.3%, 78.9%] in MAN-Conv plans, to [93.5%, 96.6%, 97.0%, 91.9%] in SHBOO-Conv plans. Compared with the MAN-WC plans, the final SHBOO-FMO plans achieved comparable plan robustness and better OAR sparing, with an average reduction of [Dmean, Dmax] of [6.3, 6.6] GyRBE for the SBT cases and [1.9, 5.1] GyRBE for the H&amp;N cases from the MAN-WC plans. Conclusions A novel robust optimization method was developed for IMPT. It integrates robust BOO and robust FMO into a unified framework, and the resulting optimization problem can be solved efficiently. Compared with the current clinical practice, where beam angles are manually selected and fluence map is optimized by worst-case method, the planning efficiency is improved, and it generates plans with superior dosimetry and good robustness