Low-density series expansions for directed percolation I: A new efficient algorithm with applications to the square lattice

A new algorithm for the derivation of low-density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems. Numerical evidence shows that the computational complexity grows exponentially, but with a growth factor \lambda < \protect{\sqrt[8]{2}}, which is much smaller than the growth factor \lambda = \protect{\sqrt[4]{2}} of the previous best algorithm. For bond (site) percolation on the directed square lattice the series has been extended to order 171 (158). Analysis of the series yields sharper estimates of the critical points and exponents.Comment: 20 pages, 8 figures (3 of them > 1Mb

Book Reviews

Book reviews by Leon L. Lancaster, Jr., Jack C. Hynes, James J. Kearney, Joseph F. Nigro, Louis P. Da Pra, and Francis Bright

Phantom investigation of 3D motion-dependent volume aliasing during CT simulation for radiation therapy planning

PURPOSE: To quantify volumetric and positional aliasing during non-gated fast- and slow-scan acquisition CT in the presence of 3D target motion. METHODS: Single-slice fast, single-slice slow, and multi-slice fast scan helical CTs were acquired of dynamic spherical targets (1 and 3.15 cm in diameter), embedded in an anthropomorphic phantom. 3D target motions typical of clinically observed tumor motion parameters were investigated. Motion excursions included ± 5, ± 10, and ± 15 mm displacements in the S-I direction synchronized with constant displacements of ± 5 and ± 2 mm in the A-P and lateral directions, respectively. For each target, scan technique, and motion excursion, eight different initial motion-to-scan phase relationships were investigated. RESULTS: An anticipated general trend of target volume overestimation was observed. The mean percentage overestimation of the true physical target volume typically increased with target motion amplitude and decreasing target diameter. Slow-scan percentage overestimations were larger, and better approximated the time-averaged motion envelope, as opposed to fast-scans. Motion induced centroid misrepresentation was greater in the S-I direction for fast-scan techniques, and transaxial direction for the slow-scan technique. Overestimation is fairly uniform for slice widths < 5 mm, beyond which there is gross overestimation. CONCLUSION: Non-gated CT imaging of targets describing clinically relevant, 3D motion results in aliased overestimation of the target volume and misrepresentation of centroid location, with little or no correlation between the physical target geometry and the CT-generated target geometry. Slow-scan techniques are a practical method for characterizing time-averaged target position. Fast-scan techniques provide a more reliable, albeit still distorted, target margin

ALE Meta-Analysis Workflows Via the Brainmap Database: Progress Towards A Probabilistic Functional Brain Atlas

With the ever-increasing number of studies in human functional brain mapping, an abundance of data has been generated that is ready to be synthesized and modeled on a large scale. The BrainMap database archives peak coordinates from published neuroimaging studies, along with the corresponding metadata that summarize the experimental design. BrainMap was designed to facilitate quantitative meta-analysis of neuroimaging results reported in the literature and supports the use of the activation likelihood estimation (ALE) method. In this paper, we present a discussion of the potential analyses that are possible using the BrainMap database and coordinate-based ALE meta-analyses, along with some examples of how these tools can be applied to create a probabilistic atlas and ontological system of describing function–structure correspondences

Anatomical Global Spatial Normalization

Anatomical global spatial normalization (aGSN) is presented as a method to scale high-resolution brain images to control for variability in brain size without altering the mean size of other brain structures. Two types of mean preserving scaling methods were investigated, “shape preserving” and “shape standardizing”. aGSN was tested by examining 56 brain structures from an adult brain atlas of 40 individuals (LPBA40) before and after normalization, with detailed analyses of cerebral hemispheres, all gyri collectively, cerebellum, brainstem, and left and right caudate, putamen, and hippocampus. Mean sizes of brain structures as measured by volume, distance, and area were preserved and variance reduced for both types of scale factors. An interesting finding was that scale factors derived from each of the ten brain structures were also mean preserving. However, variance was best reduced using whole brain hemispheres as the reference structure, and this reduction was related to its high average correlation with other brain structures. The fractional reduction in variance of structure volumes was directly related to ρ2, the square of the reference-to-structure correlation coefficient. The average reduction in variance in volumes by aGSN with whole brain hemispheres as the reference structure was approximately 32%. An analytical method was provided to directly convert between conventional and aGSN scale factors to support adaptation of aGSN to popular spatial normalization software packages

Association of plasma and cortical beta-amyloid is modulated by APOE ε4 status.

Background: APOE ε4’s role as a modulator of the relationship between soluble plasma beta-amyloid (Aβ) and fibrillar brain Aβ measured by Pittsburgh Compound-B positron emission tomography ([11C]PiB PET) has not been assessed. Methods: Ninety-six Alzheimer’s Disease Neuroimaging Initiative participants with [11C]PiB scans and plasma Aβ1-40 and Aβ1-42 measurements at time of scan were included. Regional and voxel-wise analyses of [11C]PiB data were used to determine the influence of APOE ε4 on association of plasma Aβ1-40, Aβ1-42, and Aβ1-40/Aβ1-42 with [11C]PiB uptake. Results: In APOE ε4− but not ε4+ participants, positive relationships between plasma Aβ1-40/Aβ1-42 and [11C]PiB uptake were observed. Modeling the interaction of APOE and plasma Aβ1-40/Aβ1-42 improved the explained variance in [11C]PiB binding compared to using APOE and plasma Aβ1-40/Aβ1-42 as separate terms. Conclusions: The results suggest that plasma Aβ is a potential Alzheimer’s disease biomarker and highlight the importance of genetic variation in interpretation of plasma Aβ levels