Addendum to "Amitsur's complex for purely inseparable fields"

We begin this note by pointing out that a few modifications in some of the notations and arguments of C131 will make these fit in more closely with results in the literature. We also complete the results of C131 in several points. In particular we point out that the spectral sequence used in C131 is not quite a genuine generalization of the Hochschild-Serre spectral sequence in Galois cohomology. However with a slightly different spectral sequence the results of C131 can also be obtained and we shall show in section 2 that this is indeed a genuine generalization of the Hochschild-Serre sequence for Galois cohomology. In section 3 we shall use some of the results of [13] to derive an exact sequence complementary to that of Proposition 7.8 of [13] from which we deduce the following result first pointed out to us by S. Shatz: Let C be a field, C, its separable algebraic closure and its algebraic closure. Then if X is the lift map [2, Def. 2. 3.1, we have that X : Hr(C,/C)- . ~ ' ( 6 1is~ ) an isomorphism for r = 1,2, ..

Coalescent histories for lodgepole species trees

Coalescent histories are combinatorial structures that describe for a given gene tree and species tree the possible lists of branches of the species tree on which the gene tree coalescences take place. Properties of the number of coalescent histories for gene trees and species trees affect a variety of probabilistic calculations in mathematical phylogenetics. Exact and asymptotic evaluations of the number of coalescent histories, however, are known only in a limited number of cases. Here we introduce a particular family of species trees, the \emph{lodgepole} species trees $(\lambda_n)_{n\geq 0}$, in which tree $\lambda_n$ has $m=2n+1$ taxa. We determine the number of coalescent histories for the lodgepole species trees, in the case that the gene tree matches the species tree, showing that this number grows with $m!!$ in the number of taxa $m$. This computation demonstrates the existence of tree families in which the growth in the number of coalescent histories is faster than exponential. Further, it provides a substantial improvement on the lower bound for the ratio of the largest number of matching coalescent histories to the smallest number of matching coalescent histories for trees with $m$ taxa, increasing a previous bound of $(\sqrt{\pi} / 32)[(5m-12)/(4m-6)] m \sqrt{m}$ to $[ \sqrt{m-1}/(4 \sqrt{e}) ]^{m}$. We discuss the implications of our enumerative results for phylogenetic computations

On the number of ranked species trees producing anomalous ranked gene trees

Analysis of probability distributions conditional on species trees has demonstrated the existence of anomalous ranked gene trees (ARGTs), ranked gene trees that are more probable than the ranked gene tree that accords with the ranked species tree. Here, to improve the characterization of ARGTs, we study enumerative and probabilistic properties of two classes of ranked labeled species trees, focusing on the presence or avoidance of certain subtree patterns associated with the production of ARGTs. We provide exact enumerations and asymptotic estimates for cardinalities of these sets of trees, showing that as the number of species increases without bound, the fraction of all ranked labeled species trees that are ARGT-producing approaches 1. This result extends beyond earlier existence results to provide a probabilistic claim about the frequency of ARGTs

The Butz Stops Here: Why the Food Movement Needs to Rethink Agricultural History

From the 1890s to the 1930s, rural Americans played a vital role in radical leftist politics. While specialists know this history well, the public tends to know a folk history, written by figures associated with contemporary food movements. This folk history rests on several key myths, which cover different periods of modern history from the New Deal to the present. This essay challenges these myths to reveal the causes and extent of the suffering endured by rural families in the 20th century, which in turn, decimated the populist left. A reconsideration of the history of agricultural policy will help food-system reformers develop a more radical and effective vision for rural Americ

Inverse cascades in turbulence and the case of rotating flows

We first summarize briefly several properties concerning the dynamics of two-dimensional (2D) turbulence, with an emphasis on the inverse cascade of energy to the largest accessible scale of the system. In order to study a similar phenomenon in three-dimensional (3D) turbulence undergoing strong solid-body rotation, we test a previously developed Large Eddy Simulation (LES) model against a high-resolution direct numerical simulation of rotating turbulence on a grid of $3072^3$ points. We then describe new numerical results on the inverse energy cascade in rotating flows using this LES model and contrast the case of 2D versus 3D forcing, as well as non-helical forcing (i.e., with weak overall alignment between velocity and vorticity) versus the fully helical Beltrami case, both for deterministic and random forcing. The different scaling of the inverse energy cascade can be attributed to the dimensionality of the forcing, with, in general, either a $k_{\perp}^{-3}$ or a $k_{\perp}^{-5/3}$ energy spectrum of slow modes at large scales, perpendicular referring to the direction of rotation. We finally invoke the role of shear in the case of a strongly anisotropic deterministic forcing, using the so-called ABC flow.Comment: 10 pages, 3 figure

U.S. NEW ENGLAND GROUNDFISH MANAGEMENT UNDER THE MAGNUSON-STEVENS FISHERY CONSERVATION AND MANAGEMENT ACT

Resource /Energy Economics and Policy,