On the complexity of strongly connected components in directed hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which do not reach any components but themselves). "Almost linear" here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor alpha(n), where alpha is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all SCCs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the SCCs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure

Caribou, Petroleum, and the Limits of Locality in the Canada–US Borderlands

his article discusses Karsten Heuer’s 2006 book Being Caribou in light of debates in ecocriticism and border studies about how to define the local in the context of environmental problems of vast range and uncertain temporality. It explores how Heuer’s book about following the Porcupine Caribou herd’s migration engages in multiple forms of boundary crossing—between countries, between hemispheric locations, and between species—and shows how insights from Indigenous storytelling complicate the book’s appeal to environmentalist readers by asserting a prior, transnational Indigenous presence in the transboundary landscapes of present-day Alaska and the Yukon

Bedmap2: improved ice bed, surface and thickness datasets for Antarctica

We present Bedmap2, a new suite of gridded products describing surface elevation, ice-thickness and the seafloor and subglacial bed elevation of the Antarctic south of 60° S. We derived these products using data from a variety of sources, including many substantial surveys completed since the original Bedmap compilation (Bedmap1) in 2001. In particular, the Bedmap2 ice thickness grid is made from 25 million measurements, over two orders of magnitude more than were used in Bedmap1. In most parts of Antarctica the subglacial landscape is visible in much greater detail than was previously available and the improved data-coverage has in many areas revealed the full scale of mountain ranges, valleys, basins and troughs, only fragments of which were previously indicated in local surveys. The derived statistics for Bedmap2 show that the volume of ice contained in the Antarctic ice sheet (27 million km3) and its potential contribution to sea-level rise (58 m) are similar to those of Bedmap1, but the mean thickness of the ice sheet is 4.6% greater, the mean depth of the bed beneath the grounded ice sheet is 72 m lower and the area of ice sheet grounded on bed below sea level is increased by 10%. The Bedmap2 compilation highlights several areas beneath the ice sheet where the bed elevation is substantially lower than the deepest bed indicated by Bedmap1. These products, along with grids of data coverage and uncertainty, provide new opportunities for detailed modelling of the past and future evolution of the Antarctic ice sheets

Effects of sleep deprivation on neural functioning: an integrative review

Sleep deprivation has a broad variety of effects on human performance and neural functioning that manifest themselves at different levels of description. On a macroscopic level, sleep deprivation mainly affects executive functions, especially in novel tasks. Macroscopic and mesoscopic effects of sleep deprivation on brain activity include reduced cortical responsiveness to incoming stimuli, reflecting reduced attention. On a microscopic level, sleep deprivation is associated with increased levels of adenosine, a neuromodulator that has a general inhibitory effect on neural activity. The inhibition of cholinergic nuclei appears particularly relevant, as the associated decrease in cortical acetylcholine seems to cause effects of sleep deprivation on macroscopic brain activity. In general, however, the relationships between the neural effects of sleep deprivation across observation scales are poorly understood and uncovering these relationships should be a primary target in future research

Bedmap2: improved ice bed, surface and thickness datasets for Antarctica

We present Bedmap2, a new suite of gridded products describing surface elevation, ice-thickness and the seafloor and subglacial bed elevation of the Antarctic south of 60° S. We derived these products using data from a variety of sources, including many substantial surveys completed since the original Bedmap compilation (Bedmap1) in 2001. In particular, the Bedmap2 ice thickness grid is made from 25 million measurements, over two orders of magnitude more than were used in Bedmap1. In most parts of Antarctica the subglacial landscape is visible in much greater detail than was previously available and the improved data-coverage has in many areas revealed the full scale of mountain ranges, valleys, basins and troughs, only fragments of which were previously indicated in local surveys. The derived statistics for Bedmap2 show that the volume of ice contained in the Antarctic ice sheet (27 million km3) and its potential contribution to sea-level rise (58 m) are similar to those of Bedmap1, but the mean thickness of the ice sheet is 4.6% greater, the mean depth of the bed beneath the grounded ice sheet is 72 m lower and the area of ice sheet grounded on bed below sea level is increased by 10%. The Bedmap2 compilation highlights several areas beneath the ice sheet where the bed elevation is substantially lower than the deepest bed indicated by Bedmap1. These products, along with grids of data coverage and uncertainty, provide new opportunities for detailed modelling of the past and future evolution of the Antarctic ice sheets