Analytic perturbation theory in QCD and Schwinger's connection between the beta-function and the spectral density

We argue that a technique called analytic perturbation theory leads to a well-defined method for analytically continuing the running coupling constant from the spacelike to the timelike region, which allows us to give a self-consistent definition of the running coupling constant for timelike momentum. The corresponding $\beta$-function is proportional to the spectral density, which confirms a hypothesis due to Schwinger.Comment: 11 pages, 2 figure

Investigating the linkage between mesopic spatial summation and variations in retinal ganglion cell density across the central visual field

PURPOSE: The relationship between perimetric stimulus area and Ricco's area (RA) determines measured thresholds and the sensitivity of perimetry to retinal disease. The nature of this relationship, in addition to effect of retinal ganglion cell (RGC) number on this, is currently unknown for the adaptation conditions of mesopic microperimetry. In this study, achromatic mesopic spatial summation was measured across the central visual field to estimate RA with the number of RGCs underlying RA also being established. METHODS: Achromatic luminance thresholds were measured for six incremental spot stimuli (0.009-2.07 deg2 ) and 190.4 ms duration, at four locations, each at 2.5°, 5° and 10° eccentricity in five healthy observers (mean age 61.4 years) under mesopic conditions (background 1.58 cd/m2 ). RA was estimated using two-phase regression analysis with the number of RGCs underlying RA being calculated using normative histological RGC counts. RESULTS: Ricco's area exhibited a small but statistically insignificant increase between 2.5° and 10° eccentricity. Compared with photopic conditions, RA was larger, with the difference between RA and the Goldmann III stimulus (0.43°) being minimised. RGC number underlying RA was also higher than reported for photopic conditions (median 70 cells, IQR 36-93), with no significant difference being observed across test locations. CONCLUSIONS: Ricco's area and the number of RGCs underlying RA do not vary significantly across the central visual field in mesopic conditions. However, RA is larger and more similar to the standard perimetric Goldmann III stimulus under mesopic compared with photopic adaptation conditions. Further work is required to determine if compensatory enlargements in RA occur in age-related macular degeneration, to establish the optimal stimulus parameters for AMD-specific microperimetry

Estimating the Critical Duration for Temporal Summation of Standard Achromatic Perimetric Stimuli

Purpose: To estimate the critical duration of temporal summation for achromatic Goldmann III stimuli under the conditions of standard automated perimetry (SAP) and quantify response variability for short duration stimuli. Methods: Contrast thresholds were gathered using the method of constant stimuli for seven circular (0.48° diameter) incremental stimuli of varying duration (sum-of-frames equivalent: 8.3-198.3 msec), at an eccentricity of 8.8° along the four principal meridians of the visual field in two healthy, psychophysically experienced observers. Stimuli were presented on a high-resolution CRT display with a background luminance of 10 cd/m2. Psychometric functions were fitted using a probit model and non-parametric local linear analysis. The critical duration was estimated using iterative two-phase regression analysis, the results also being compared with values produced using previously published methods of analysis. Results: The median critical duration estimated using iterative two-phase regression analysis was 27.7 msec (IQR 22.5-29.8). A slight steepening of the psychometric function slope (lower variability) was observed for longer stimulus durations, using both probit and local-linear analysis techniques, but this was not statistically significant. Conclusions: Critical duration estimates in this study are substantially shorter than those previously reported for a Goldmann III stimulus under the conditions of SAP. Further work is required to firmly establish the relationship between measurement variability and the degree of local temporal and spatial summation

The relative importance of electron-electron interactions compared to disorder in the two-dimensional "metallic" state

The effect of substrate bias and surface gate voltage on the low temperature resistivity of a Si-MOSFET is studied for electron concentrations where the resistivity increases with increasing temperature. This technique offers two degrees of freedom for controlling the electron concentration and the device mobility, thereby providing a means to evaluate the relative importance of electron-electron interactions and disorder in this so-called ``metallic'' regime. For temperatures well below the Fermi temperature, the data obey a scaling law where the disorder parameter ($k_{\rm{F}}l$), and not the concentration, appears explicitly. This suggests that interactions, although present, do not alter the Fermi-liquid properties of the system fundamentally. Furthermore, this experimental observation is reproduced in results of calculations based on temperature-dependent screening, in the context of Drude-Boltzmann theory.Comment: 5 pages, 6 figure

Driving precision policy responses to child health and developmental inequities

The growing evidence base on the extent of and opportunities to reduce inequities in children’s health and development still lacks the specificity to inform clear policy decisions. A new phase of research is needed that builds on contemporary directions in precision medicine to develop precision policy making; with the aim to redress child inequities. This would include identifying effective interventions and their ideal time point(s), duration, and intensity to maximise impact. Drawing on existing data sources and innovations in epidemiology and biostatistics would be key. The economic and social gains that could be achieved from reducing child inequities are immense. <br

The effect of age on the area of complete spatial summation for chromatic and achromatic stimuli

Purpose. Previously, an association between the area of complete spatial summation (Ricco's area) and age under scotopic conditions had been found. The authors sought to determine whether Ricco's area is similarly associated with age under photopic achromatic and selective S-cone conditions in peripheral vision and whether any association relates to a loss of ganglion cell density as determined by measurements of peripheral grating resolution acuity. Methods. Achromatic spatial summation functions were plotted for 68 healthy subjects (aged 20–77 years) in four oblique meridians on a gray background field of 10 cd/m2. Similar functions were generated for the S-cone pathway (isolated using Stiles' two-color threshold method) for the same locations. Ricco's area was determined using two-phase regression analysis. Achromatic peripheral grating resolution acuity was measured at the same locations using high-contrast Gabor stimuli, as an estimate of localized functional ganglion cell density. Results. There was a notable decrease in overall contrast sensitivity with age for all stimulus sizes. However, there was no evidence of age-related change in Ricco's area for either achromatic (superior field, r2 = 0.05; inferior field, r2 = 0.0007; all P > 0.05) or chromatic (superior field, r2 = 0.01; inferior field, r2 = 0.006; all P > 0.05) stimuli, despite a significant decrease in peripheral grating resolution acuity with age (superior field, r2 = 0.15; inferior field, r2 = 0.17; both P < 0.05). Conclusions. An age-related decline in functional ganglion cell density is not accompanied by a significant change in Ricco's area for achromatic or chromatic stimuli

Sensitivity loss in early glaucoma can be mapped to an enlargement of the area of complete spatial summation

Purpose. The area of complete spatial summation (Ricco's area) is the largest stimulus size for which area × intensity is constant at threshold. The authors sought to investigate whether Ricco's area changes in early glaucoma to account for the decreased visual signal/noise ratio that may accompany retinal ganglion cell loss. Methods. Spatial summation functions were measured, and Ricco's area was determined at four 10° retinal locations in 24 patients with early glaucoma (total deviation at test locations, mean, −1.3 dB; range, +2 dB to −8 dB) and 26 age-similar healthy subjects under achromatic and S-cone isolation conditions. Achromatic grating resolution acuity was measured at the same locations to estimate functional ganglion cell density. Results. Ricco's area was enlarged in patients compared with controls for both achromatic (enlarged by: superior field, 0.57 log units, P < 0.01; inferior field, 0.72 log units, P < 0.01) and chromatic (enlarged by: superior field, 0.26 log units, P < 0.01; inferior field, 0.25 log units, P = 0.065) stimuli, with negligible vertical summation curve shifts along the intensity axis. Resolution acuity was significantly reduced in glaucoma patients in both hemifields (P < 0.001). There was a weak, but significant, relationship between Ricco's area and resolution acuity. Conclusions. Enlargement of Ricco's area completely compensates for reduced perimetric sensitivity in early glaucoma to maintain constant threshold at Ricco's area, suggesting an increase in signal pooling in response to ganglion cell loss. The rightward displacement of the spatial summation curve indicates that perimetric stimuli should be capable of modulating in size as well as/instead of contrast, which may boost the glaucoma signal within measurement noise

Relating retinal nerve fiber layer thickness and functional estimates of ganglion cell sampling density in healthy eyes and in early glaucoma

Purpose. To investigate the relationship between retinal nerve fiber layer (RNFL) thickness and peripheral grating resolution acuity (PGRA) as well as differential light sensitivity (DLS) in healthy subjects and patients with early glaucoma. The agreement between estimates of retinal ganglion cell (GC) density from each functional test is explored. Methods. PGRA was measured in 24 patients with early glaucoma (mean deviation [MD] > −8 dB) and 26 healthy subjects using achromatic Gabor stimuli in 4 diagonal visual field locations at 10° eccentricity. DLS for a Goldmann size III equivalent was obtained from individual spatial summation functions and expressed in Humphrey Field Analyzer-equivalent decibel values. RNFL thickness was measured around the optic nerve head using Zeiss Stratus optical coherence tomography and related to functional measures using a retinotopic map. Functional GC density was estimated using structure/function models for both tests. Passing-Bablok regression was used to investigate the structure/function relationships. Results. A positive and statistically significant association was found between PGRA and RNFL thickness, and separately between DLS and RNFL thickness, for combined glaucoma and healthy data (both P 0.05). Agreement between estimates of GC density from psychophysical data was moderate. Conclusions. The relationship between PGRA and RNFL thickness is at least as great in magnitude as that between DLS and RNFL thickness; a significant structure/function association is also observed in healthy subjects alone

Two-Loop Calculations with Vertex Corrections in the Walecka Model

Two-loop corrections with scalar and vector form factors are calculated for nuclear matter in the Walecka model. The on-shell form factors are derived from vertex corrections within the framework of the model and are highly damped at large spacelike momenta. The two-loop corrections are evaluated first by using the one-loop parameters and mean fields and then by refitting the total energy/baryon to empirical nuclear matter saturation properties. The modified two-loop corrections are significantly smaller than those computed with bare vertices. Contributions from the anomalous isoscalar form factor of the nucleon are included for the first time. The effects of the implicit density dependence of the form factors, which arise from the shift in the baryon mass, are also considered. Finally, necessary extensions of these calculations are discussed.Comment: 29 pages in REVTeX, 18 figures, preprint IU/NTC 94-02 //OSU--94-11