Inequalities that sharpen the triangle inequality for sums of NN functions in LpL^p

We study $L^p$ inequalities that sharpen the triangle inequality for sums of $N$ functions in $L^p$

Intergalactic Helium Absorption in Cold Dark Matter Models

Observations from the HUT and the HST have recently detected HeII absorption along the lines of sight to two high redshift quasars. We use cosmological simulations with gas dynamics to investigate HeII absorption in the cold dark matter (CDM) theory of structure formation. We consider two Omega=1 CDM models with different normalizations and one Omega_0=0.4 CDM model, all incorporating the photoionizing UV background spectrum computed by Haardt & Madau (1996). The simulated gas distribution, combined with the H&M spectral shape, accounts for the relative observed values of taubar_HI and taubar_HeII, the effective mean optical depths for HI and HeII absorption. If the background intensity is as high as H&M predict, then matching the absolute values of taubar_HI and taubar_HeII requires a baryon abundance larger (by factors between 1.5 and 3 for the various CDM models) than our assumed value of Omega_b h^2=0.0125. The simulations reproduce the evolution of taubar_heII over the observed redshift range, 2.2 < z < 3.3, if the HeII photoionization rate remains roughly constant. HeII absorption in the CDM simulations is produced by a diffuse, fluctuating, intergalactic medium, which also gives rise to the HI ly-alpha forest. Much of the HeII opacity arises in underdense regions where the HI optical depth is very low. We compute statistical properties of the HeII and HI absorption that can be used to test the CDM models and distinguish them from an alternative scenario in which the HeII absorption is caused by discrete, compact clouds. The CDM scenario predicts that a substantial amount of baryonic material resides in underdense regions at high redshift. HeII absorption is the only sensitive probe of such extremely diffuse, intergalactic gas, so it can provide a vital test of this fundamental prediction.Comment: Accepted for publication in ApJ, 36 pages, LaTeX (aaspp4), 12 figures. Changes include addition of more information on statistical uncertainties and on the adopted UV background. Also available at http://www-astronomy.mps.ohio-state.edu/~racc

Characterization of Lyman Alpha Spectra and Predictions of Structure Formation Models: A Flux Statistics Approach

In gravitational instability models, \lya absorption arises from a continuous fluctuating medium, so that spectra provide a non-linear one-dimensional ``map'' of the underlying density field. We characterise this continuous absorption using statistical measures applied to the distribution of absorbed flux. We describe two simple members of a family of statistics which we apply to simulated spectra in order to show their sensitivity as probes of cosmological parameters (H$_{0}$, $\Omega$, the initial power spectrum of matter fluctuations) and the physical state of the IGM. We make use of SPH simulation results to test the flux statistics, as well as presenting a preliminary application to Keck HIRES data.Comment: Contribution to proceedings of the 18th Texas Symposium on Relativistic Astrophysics (eds A. Olinto, J. Frieman and D. Schramm, World Scientific),Chicago, December 1996, 3 pages, LaTeX (sprocl), 2 figures. Also available at http://www-astronomy.mps.ohio-state.edu/~racc

Inequalities for Lᵖ-Norms that Sharpen the Triangle Inequality and Complement Hanner’s Inequality

In 2006 Carbery raised a question about an improvement on the naïve norm inequality ∥f+g∥^p_p ≤ 2^(p−1)(∥f∥^p_p+∥g∥^p_p) for two functions f and g in Lᵖ of any measure space. When f=g this is an equality, but when the supports of f and g are disjoint the factor 2^(p−1) is not needed. Carbery’s question concerns a proposed interpolation between the two situations for p > 2 with the interpolation parameter measuring the overlap being ∥fg∥_(p/2). Carbery proved that his proposed inequality holds in a special case. Here, we prove the inequality for all functions and, in fact, we prove an inequality of this type that is stronger than the one Carbery proposed. Moreover, our stronger inequalities are valid for all real p ≠ 0

Energy Cost to Make a Hole in the Fermi Sea

The change in energy of an ideal Fermi gas when a local one-body potential is inserted into the system, or when the density is changed locally, are important quantities in condensed matter physics. We show that they can be rigorously bounded from below by a universal constant times the value given by the semiclassical approximation.Comment: 4 pages, final version published in Phys. Rev. Let

Are methodological quality and completeness of reporting associated with citation-based measures of publication impact? A secondary analysis of a systematic review of dementia biomarker studies

Objective: To determine whether methodological and reporting quality are associated with surrogate measures of publication impact in the field of dementia biomarker studies. Methods: We assessed dementia biomarker studies included in a previous systematic review in terms of methodological and reporting quality using the Quality Assessment of Diagnostic Accuracy Studies (QUADAS) and Standards for Reporting of Diagnostic Accuracy (STARD), respectively. We extracted additional study and journal-related data from each publication to account for factors shown to be associated with impact in previous research. We explored associations between potential determinants and measures of publication impact in univariable and stepwise multivariable linear regression analyses. Outcome measures: We aimed to collect data on four measures of publication impact: two traditional measures—average number of citations per year and 5-year impact factor of the publishing journal and two alternative measures—the Altmetric Attention Score and counts of electronic downloads. Results: The systematic review included 142 studies. Due to limited data, Altmetric Attention Scores and electronic downloads were excluded from the analysis, leaving traditional metrics as the only analysed outcome measures. We found no relationship between QUADAS and traditional metrics. Citation rates were independently associated with 5-year journal impact factor (β=0.42; p&lt;0.001), journal subject area (β=0.39; p&lt;0.001), number of years since publication (β=-0.29; p&lt;0.001) and STARD (β=0.13; p&lt;0.05). Independent determinants of 5-year journal impact factor were citation rates (β=0.45; p&lt;0.001), statement on conflict of interest (β=0.22; p&lt;0.01) and baseline sample size (β=0.15; p&lt;0.05). Conclusions: Citation rates and 5-year journal impact factor appear to measure different dimensions of impact. Citation rates were weakly associated with completeness of reporting, while neither traditional metric was related to methodological rigour. Our results suggest that high publication usage and journal outlet is not a guarantee of quality and readers should critically appraise all papers regardless of presumed impact

In Vitro, In Vivo, and In Silico Methods for Assessment of Muscle Size and Muscle Growth Regulation

Trauma, burn injury, sepsis, and ischemia lead to acute and chronic loss of skeletal muscle mass and function. Healthy muscle is essential for eating, posture, respiration, reproduction, and mobility, as well as for appropriate function of the senses including taste, vision, and hearing. Beyond providing support and contraction, skeletal muscle also exerts essential roles in temperature regulation, metabolism, and overall health. As the primary reservoir for amino acids, skeletal muscle regulates whole-body protein and glucose metabolism by providing substrate for protein synthesis and supporting hepatic gluconeogenesis during illness and starvation. Overall, greater muscle mass is linked to greater insulin sensitivity and glucose disposal, strength, power, and longevity. In contrast, low muscle mass correlates with dysmetabolism, dysmobility, and poor survival. Muscle mass is highly plastic, appropriate to its role as reservoir, and subject to striking genetic control. Defining mechanisms of muscle growth regulation holds significant promise to find interventions that promote health and diminish morbidity and mortality after trauma, sepsis, inflammation, and other systemic insults. In this invited review, we summarize techniques and methods to assess and manipulate muscle size and muscle mass in experimental systems, including cell culture and rodent models. These approaches have utility for studies of myopenia, sarcopenia, cachexia, and acute muscle growth or atrophy in the setting of health or injury