38,506 research outputs found
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 , in which
tree has 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 in the
number of taxa . 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 taxa,
increasing a previous bound of
to . 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
Photometric catalog of nearby globular clusters (I)
We present the first part of the first large and homogeneous CCD
color-magnitude diagram (CMD) data base, comprising 52 nearby Galactic globular
clusters (GGC) imaged in the V and I bands using only two telescopes (one for
each hemisphere). The observed clusters represent 75% of the known Galactic
globulars with (m-M)v<=16.15 mag, cover most of the globular cluster
metallicity range (-2.2 <= [Fe/H] <= -0.4), and span Galactocentric distances
from ~1.2 to ~18.5 kpc.
In this paper, the CMDs for the 39 GGCs observed in the southern hemisphere
are presented. The remaining 13 northern hemisphere clusters of the catalog are
presented in a companion paper. For four clusters (NGC 4833, NGC 5986, NGC
6543, and NGC 6638) we present for the first time a CMD from CCD data. The
typical CMD spans from the 22nd V magnitude to the tip of the red giant branch.
Based on a large number of standard stars, the absolute photometric calibration
is reliable to the ~0.02 mag level in both filters.
This catalog, because of its homogeneity, is expected to represent a useful
data base for the measurement of the main absolute and relative parameters
characterizing the CMD of GGCs.Comment: 34 pages, 108 figures, Astronomy & Astrophysics Supplement Series, in
press. Full resolution figures can be obtained from the authors upon reques
- …