Equivalent birational embeddings II: divisors

Two divisors in $\P^n$ are said to be Cremona equivalent if there is a Cremona modification sending one to the other. We produce infinitely many non equivalent divisorial embeddings of any variety of dimension at most 14. Then we study the special case of plane curves and rational hypersurfaces. For the latter we characterise surfaces Cremona equivalent to a plane.Comment: v2 Exposition improved, thanks to referee, unconditional characterization of surfaces Cremona equivalent to a plan

Analysis of the superdefomed rotational bands

All available experimental data for the $\Delta I=2$ transition energies in superdeformed bands are analyzed by using a new one-point formula. The existence of deviations from the smooth behavior is confirmed in many bands. However, we stress that one cannot necessarily speak about staggering patterns as they are mostly irregular. Simulations of the experimental data suggest that the irregularities may stem from the presence of irregular kinks in the rotational spectra. This could be a clue but, at the moment, where such kinks come from is an open question.Comment: 6 pages, RevTex, 7 p.s. figures, submitted to P.R.

Lassoing and corraling rooted phylogenetic trees

The construction of a dendogram on a set of individuals is a key component of a genomewide association study. However even with modern sequencing technologies the distances on the individuals required for the construction of such a structure may not always be reliable making it tempting to exclude them from an analysis. This, in turn, results in an input set for dendogram construction that consists of only partial distance information which raises the following fundamental question. For what subset of its leaf set can we reconstruct uniquely the dendogram from the distances that it induces on that subset. By formalizing a dendogram in terms of an edge-weighted, rooted phylogenetic tree on a pre-given finite set X with |X|>2 whose edge-weighting is equidistant and a set of partial distances on X in terms of a set L of 2-subsets of X, we investigate this problem in terms of when such a tree is lassoed, that is, uniquely determined by the elements in L. For this we consider four different formalizations of the idea of "uniquely determining" giving rise to four distinct types of lassos. We present characterizations for all of them in terms of the child-edge graphs of the interior vertices of such a tree. Our characterizations imply in particular that in case the tree in question is binary then all four types of lasso must coincide

Tree-Based Unrooted Phylogenetic Networks

Phylogenetic networks are a generalization of phylogenetic trees that are used to represent non-tree-like evolutionary histories that arise in organisms such as plants and bacteria, or uncertainty in evolutionary histories. An unrooted phylogenetic network on a non-empty, finite set X of taxa, or network, is a connected, simple graph in which every vertex has degree 1 or 3 and whose leaf set is X. It is called a phylogenetic tree if the underlying graph is a tree. In this paper we consider properties of tree-based networks, that is, networks that can be constructed by adding edges into a phylogenetic tree. We show that although they have some properties in common with their rooted analogues which have recently drawn much attention in the literature, they have some striking differences in terms of both their structural and computational properties. We expect that our results could eventually have applications to, for example, detecting horizontal gene transfer or hybridization which are important factors in the evolution of many organisms. Correction available at dx.doi.org/10.1007/s11538-018-0530-

A Note on Encodings of Phylogenetic Networks of Bounded Level

Driven by the need for better models that allow one to shed light into the question how life's diversity has evolved, phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees, clusters, and triplets, respectively. Thus it is not surprising that many network approaches aim to reconstruct a phylogenetic network from such collections. Related to the well-studied perfect phylogeny problem, the following question is of fundamental importance in this context: When does one of the above collections encode (i.e. uniquely describe) the network that induces it? In this note, we present a complete answer to this question for the special case of a level-1 (phylogenetic) network by characterizing those level-1 networks for which an encoding in terms of one (or equivalently all) of the above collections exists. Given that this type of network forms the first layer of the rich hierarchy of level-k networks, k a non-negative integer, it is natural to wonder whether our arguments could be extended to members of that hierarchy for higher values for k. By giving examples, we show that this is not the case

Synaptically-competent neurons derived from canine embryonic stem cells by lineage selection with EGF and noggin

Pluripotent stem cell lines have been generated in several domestic animal species; however, these lines traditionally show poor self-renewal and differentiation. Using canine embryonic stem cell (cESC) lines previously shown to have sufficient self-renewal capacity and potency, we generated and compared canine neural stem cell (cNSC) lines derived by lineage selection with epidermal growth factor (EGF) or Noggin along the neural default differentiation pathway, or by directed differentiation with retinoic acid (RA)-induced floating sphere assay. Lineage selection produced large populations of SOX2+ neural stem/progenitor cell populations and neuronal derivatives while directed differentiation produced few and improper neuronal derivatives. Primary canine neural lines were generated from fetal tissue and used as a positive control for differentiation and electrophysiology. Differentiation of EGF- and Noggin-directed cNSC lines in N2B27 with low-dose growth factors (BDNF/NT-3 or PDGFαα) produced phenotypes equivalent to primary canine neural cells including 3CB2+ radial progenitors, MOSP+ glia restricted precursors, VIM+/GFAP+ astrocytes, and TUBB3+/MAP2+/NFH+/SYN+ neurons. Conversely, induction with RA and neuronal differentiation produced inadequate putative neurons for further study, even though appropriate neuronal gene expression profiles were observed by RT-PCR (including Nestin, TUBB3, PSD95, STX1A, SYNPR, MAP2). Co-culture of cESC-derived neurons with primary canine fetal cells on canine astrocytes was used to test functional maturity of putative neurons. Canine ESC-derived neurons received functional GABAA- and AMPA-receptor mediated synaptic input, but only when co-cultured with primary neurons. This study presents established neural stem/progenitor cell populations and functional neural derivatives in the dog, providing the proof-of-concept required to translate stem cell transplantation strategies into a clinically relevant animal model. © 2011 Wilcox et al

Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary

Consider a finite dimensional (generally reducible) polynomial representation \rho of GL_n. A projective compactification of GL_n is the closure of \rho(GL_n) in the space of all operators defined up to a factor (this class of spaces can be characterized as equivariant projective normal compactifications of GL_n). We give an expicit description for all projective compactifications. We also construct explicitly (in elementary geometrical terms) a universal object for all projective compactifications of GL_n.Comment: 24 pages, corrected varian

On special quadratic birational transformations of a projective space into a hypersurface

We study transformations as in the title with emphasis on those having smooth connected base locus, called "special". In particular, we classify all special quadratic birational maps into a quadric hypersurface whose inverse is given by quadratic forms by showing that there are only four examples having general hyperplane sections of Severi varieties as base loci.Comment: Accepted for publication in Rendiconti del Circolo Matematico di Palerm

Random tree growth by vertex splitting

We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model generalises the preferential attachment model and Ford's $\alpha$-model for phylogenetic trees. We develop a mean field theory for the vertex degree distribution, prove that the mean field theory is exact in some special cases and check that it agrees with numerical simulations in general. We calculate various correlation functions and show that the intrinsic Hausdorff dimension can vary from one to infinity, depending on the parameters of the model.Comment: 47 page