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

Recovering holomorphic functions from their real or imaginary parts without the Cauchy-Riemann equations

Students of elementary complex analysis usually begin by seeing the derivation of the Cauchy--Riemann equations. A topic of interest to both the development of the theory and its applications is the reconstruction of a holomorphic function from its real part, or the extraction of the imaginary part from the real part, or vice versa. Usually this takes place by solving the partial differential system embodied by the Cauchy-Riemann equations. Here I show in general how this may be accomplished by purely algebraic means. Several examples are given, for functions with increasing levels of complexity. The development of these ideas within the Mathematica software system is also presented. This approach could easily serve as an alternative in the early development of complex variable theory

Press Release for the Thirteenth Annual John F. Sonnett Memorial Lecture Series: The Supreme Court of the United States

Press release for the Thirteenth Annual John F. Sonnett Memorial Lecture Series, The Supreme Court of the United States, given by William T. Coleman, partner at O\u27Melveny & Myers and former United States Secretary of Transportation (1975-1977).https://ir.lawnet.fordham.edu/events_programs_sonnett_miscellaneous/1017/thumbnail.jp

Rare B Decays and B Decay Dynamics

I present some recent measurements of B meson decay rates to leptonic and charmless hadronic final states, as well as of CP-violation charge asymmetries and other features. I sketch the theoretical frameworks used to predict these, and indicate the level of agreement of the estimates with experiment.Comment: Comments: 10 pages, 13 postscript figues, contributed to the Proceedings of the XXV Physics in Collisio

Constitutional Equity and the Innovative Tradition

It is argued that the court\u27s status as a general equity court with constitutionally vested jurisdiction has benefitted the legal system. The Delaware court of chancery is an example of an equity court that resolves complex disputes expeditiously and lets the litigants move on

\u3ci\u3eTypocerus Deceptus\u3c/i\u3e in Southern Illinois (Coleoptera: Cerambycidae)

The lepturine cerambycid Typocerus deceptus is reported from southern Illinois for the first time. It was collected in association with T. v. velutinus near, or in oak- hickory forest stands on Hydrangea arborescens, a new host plant record