An O(n) method of calculating Kendall correlations of spike trains

The ability to record from increasingly large numbers of neurons, and the increasing attention being paid to large scale neural network simulations, demands computationally fast algorithms to compute relevant statistical measures. We present an O(n) algorithm for calculating the Kendall correlation of spike trains, a correlation measure that is becoming especially recognized as an important tool in neuroscience. We show that our method is around 50 times faster than the O (n ln n) method which is a current standard for quickly computing the Kendall correlation. In addition to providing a faster algorithm, we emphasize the role that taking the specific nature of spike trains had on reducing the run time. We imagine that there are many other useful algorithms that can be even more significantly sped up when taking this into consideration. A MATLAB function executing the method described here has been made freely available on-line.Comment: 7 pages, 1 figure, 1 tabl

Constitutional Law - Eighth Amendment - Capital Punishment - State Death Penalty Statutes - Procedural Safeguards

The Supreme Court of the United States has held that the Alabama death penalty statute which prohibited a jury instruction of lesser included offenses in a capital case is unconstitutional because it diminishes the reliability of the guilt determination process, leading to an arbitrary and irrational imposition of the death penalty. Beck v. Alabama, 447 U.S. 625 (1980)

Development of Future Habitat Suitability Models for the Swift fox (Vulpes velox) in the American Southwest

The Swift fox (Vupes velox) is a habitat specialist species of short or mixed grass prairie. We used bioclimatic envelope models and habitat suitability models under three future climate scenarios (based on CO2 emission rates) from "www.climatewizard.org":http://www.climatewizard.org to fit species distribution models, using the maximum entropy method. Current suitable habitat for the swift fox covers an area of 161,984 km2. Under the future climate scenarios the habitat decreases by 27% in the low emission scenario, 63% for medium emissions, and 53% in the high emissions scenario. This decrease in suitable habitat corresponded to an overall decrease in total grassland landcover. The current total area of grassland is 423,440 km2. Under the future climate scenarios the grassland decreased by 12% in the low emissions scenario, 24% for medium emissions, and 16% in the high emissions scenario

A search for CO+ in planetary nebulae

We have carried out a systematic search for the molecular ion CO+ in a sample of 8 protoplanetary and planetary nebulae in order to determine the origin of the unexpectedly strong HCO+ emission previously detected in these sources. An understanding of the HCO+ chemistry may provide direct clues to the physical and chemical evolution of planetary nebulae. We find that the integrated intensity of the CO+ line may be correlated with that of HCO+, suggesting that the reaction of CO+ with molecular hydrogen may be an important formation route for HCO+ in these planetary nebulae.Comment: 6 pages, 4 figures, accepted for publication in MNRA