Visibility properties of polygons

Two problems dealing with visibility in the interior of a polygon are investigated. We present a linear time algorithm for computing the stair-case visibility polygon from a point inside a simple polygon, which is optimal within a constant factor. We show that the problem of locating the minimum number of 90{dollar}\sp\circ{dollar}-flood-lights to illuminate the interior of a simple polygon is NP-complete. We also discuss the generalization of the above results

Mapping human cortical areas in vivo based on myelin content as revealed by t1- and t2-weighted MRI

Non-invasively mapping the layout of cortical areas in humans is a continuing challenge for neuroscience. We present a new method of mapping cortical areas based on myelin content as revealed by T1-weighted (T1w) and T2-weighted (T2w) MRI. The method is generalizable across different 3T scanners and pulse sequences. We use the ratio of T1w/T2w image intensities to eliminate the MR-related image intensity bias and enhance the contrast to noise ratio for myelin. Data from each subject was mapped to the cortical surface and aligned across individuals using surface-based registration. The spatial gradient of the group average myelin map provides an observer-independent measure of sharp transitions in myelin content across the surface—i.e. putative cortical areal borders. We found excellent agreement between the gradients of the myelin maps and the gradients of published probabilistic cytoarchitectonically defined cortical areas that were registered to the same surface-based atlas. For other cortical regions, we used published anatomical and functional information to make putative identifications of dozens of cortical areas or candidate areas. In general, primary and early unimodal association cortices are heavily myelinated and higher, multi-modal, association cortices are more lightly myelinated, but there are notable exceptions in the literature that are confirmed by our results. The overall pattern in the myelin maps also has important correlations with the developmental onset of subcortical white matter myelination, evolutionary cortical areal expansion in humans compared to macaques, postnatal cortical expansion in humans, and maps of neuronal density in non-human primates

Rapid thinning of the Welsh Ice Cap at 20–19 ka based on 10Be ages

New 10Be ages from the summits of three mountain areas of North Wales reveal a very similar exposure timing as the Welsh Ice Cap thinned after the global Last Glacial Maximum. Eight bedrock and one boulder sample gave a combined arithmetic mean exposure age of 19.08 ± 0.80 ka (4.2%, 1σ). Similar exposure ages over a 320 m vertical range (824 to 581 m altitude) show that ice cap thinning was very rapid and spatially uniform. Using the same production rate and scaling scheme, we recalculated six published 10Be exposure ages from the nearby Arans, which also covered a similar elevation range from 608 to 901 m and obtained an arithmetic mean of 19.41 ± 1.45 ka (7.5%, 1σ). The average exposure age of all 15 accepted deglaciation ages is 19.21 ± 1.07 (5.6%, 1σ). The complete dataset from North Wales provides very strong evidence indicating that these summits became exposed as nunataks at 20–19 ka. This result provides important insight to the magnitude of ice surface lowering and behavior of the Welsh Ice Cap during the last deglaciation that can be compared to other ice masses that made up the British-Irish Ice Sheet.</jats:p

Quantitative assessment of prefrontal cortex in humans relative to nonhuman primates

Significance A longstanding controversy in neuroscience pertains to differences in human prefrontal cortex (PFC) compared with other primate species; specifically, is human PFC disproportionately large? Distinctively human behavioral capacities related to higher cognition and affect presumably arose from evolutionary modifications since humans and great apes diverged from a common ancestor about 6–8 Mya. Accurate determination of regional differences in the amount of cortical gray and subcortical white matter content in humans, great apes, and Old World monkeys can further our understanding of the link between structure and function of the human brain. Using tissue volume analyses, we show a disproportionately large amount of gray and white matter corresponding to PFC in humans compared with nonhuman primates.</jats:p

Neurite imaging reveals microstructural variations in human cerebral cortical gray matter

We present distinct patterns of neurite distribution in the human cerebral cortex using diffusion magnetic resonance imaging (MRI). We analyzed both high-resolution structural (T1w and T2w images) and diffusion MRI data in 505 subjects from the Human Connectome Project. Neurite distributions were evaluated using the neurite orientation dispersion and density imaging (NODDI) model, optimized for gray matter, and mapped onto the cortical surface using a method weighted towards the cortical mid-thickness to reduce partial volume effects. The estimated neurite density was high in both somatosensory and motor areas, early visual and auditory areas, and middle temporal area (MT), showing a strikingly similar distribution to myelin maps estimated from the T1w/T2w ratio. The estimated neurite orientation dispersion was particularly high in early sensory areas, which are known for dense tangential fibers and are classified as granular cortex by classical anatomists. Spatial gradients of these cortical neurite properties revealed transitions that colocalize with some areal boundaries in a recent multi-modal parcellation of the human cerebral cortex, providing mutually supportive evidence. Our findings indicate that analyzing the cortical gray matter neurite morphology using diffusion MRI and NODDI provides valuable information regarding cortical microstructure that is related to but complementary to myeloarchitecture