On the ideals of equivariant tree models

We introduce equivariant tree models in algebraic statistics, which unify and generalise existing tree models such as the general Markov model, the strand symmetric model, and group based models. We focus on the ideals of such models. We show how the ideals for general trees can be determined from the ideals for stars. The main novelty is our proof that this procedure yields the entire ideal, not just an ideal defining the model set-theoretically. A corollary of theoretical importance is that the ideal for a general tree is generated by the ideals of its flattenings at vertices.Comment: 23 pages. Greatly improved exposition, in part following suggestions by a referee--thanks! Also added exampl

Four lectures on secant varieties

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhause

The parent?infant dyad and the construction of the subjective self

Developmental psychology and psychopathology has in the past been more concerned with the quality of self-representation than with the development of the subjective agency which underpins our experience of feeling, thought and action, a key function of mentalisation. This review begins by contrasting a Cartesian view of pre-wired introspective subjectivity with a constructionist model based on the assumption of an innate contingency detector which orients the infant towards aspects of the social world that react congruently and in a specifically cued informative manner that expresses and facilitates the assimilation of cultural knowledge. Research on the neural mechanisms associated with mentalisation and social influences on its development are reviewed. It is suggested that the infant focuses on the attachment figure as a source of reliable information about the world. The construction of the sense of a subjective self is then an aspect of acquiring knowledge about the world through the caregiver's pedagogical communicative displays which in this context focuses on the child's thoughts and feelings. We argue that a number of possible mechanisms, including complementary activation of attachment and mentalisation, the disruptive effect of maltreatment on parent-child communication, the biobehavioural overlap of cues for learning and cues for attachment, may have a role in ensuring that the quality of relationship with the caregiver influences the development of the child's experience of thoughts and feelings

Rapid estimation of bacterial antibiotic susceptibility with flow cytometry

Bacterial antibiotic susceptibility was rapidly estimated for Escherichia coli and Staphylococcus spp. by flow cytometry. This was achieved by measuring the uptake of a negatively charged membrane potential sensitive dye bis‐(1,3‐dibutylbarbituric acid) trimethine oxonol and observing changes in low‐angle light scatter (excitation light scattered by up to 15°). Estimations of ampicillin, gentamicin and ciprofloxacin susceptibilities were possible within 2–5 h from a plate culture, depending on the species and antibiotic used. This includes the time necessary to establish steady‐state growth in liquid culture

A volumetric comparison of the insular cortex and its subregions in primates

The neuronal composition of the insula in primates displays a gradient, transitioning from granular neocortex in the posterior-dorsal insula to agranular neocortex in the anterior-ventral insula with an intermediate zone of dysgranularity. Additionally, apes and humans exhibit a distinctive subdomain in the agranular insula, the frontoinsular cortex (FI), defined by the presence of clusters of von Economo neurons (VENs). Studies in humans indicate that the ventral anterior insula, including agranular insular cortex and FI, is involved in social awareness, and that the posterodorsal insula, including granular and dysgranular cortices, produces an internal representation of the body's homeostatic state. We examined the volumes of these cytoarchitectural areas of insular cortex in 30 primate species, including the volume of FI in apes and humans. Results indicate that the whole insula scales hyperallometrically (exponent = 1.13) relative to total brain mass, and the agranular insula (including FI) scales against total brain mass with even greater positive allometry (exponent = 1.23), providing a potential neural basis for enhancement of social cognition in association with increased brain size. The relative volumes of the subdivisions of the insular cortex, after controlling for total brain volume, are not correlated with species typical social group size. Although its size is predicted by primate-wide allometric scaling patterns, we found that the absolute volume of the left and right agranular insula and left FI are among the most differentially expanded of the human cerebral cortex compared to our closest living relative, the chimpanzee