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

Mixture of latent trait analyzers for model-based clustering of categorical data

Model-based clustering methods for continuous data are well established and commonly used in a wide range of applications. However, model-based clustering methods for categorical data are less standard. Latent class analysis is a commonly used method for model-based clustering of binary data and/or categorical data, but due to an assumed local independence structure there may not be a correspondence between the estimated latent classes and groups in the population of interest. The mixture of latent trait analyzers model extends latent class analysis by assuming a model for the categorical response variables that depends on both a categorical latent class and a continuous latent trait variable; the discrete latent class accommodates group structure and the continuous latent trait accommodates dependence within these groups. Fitting the mixture of latent trait analyzers model is potentially difficult because the likelihood function involves an integral that cannot be evaluated analytically. We develop a variational approach for fitting the mixture of latent trait models and this provides an efficient model fitting strategy. The mixture of latent trait analyzers model is demonstrated on the analysis of data from the National Long Term Care Survey (NLTCS) and voting in the U.S. Congress. The model is shown to yield intuitive clustering results and it gives a much better fit than either latent class analysis or latent trait analysis alone

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

Track E Implementation Science, Health Systems and Economics

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138412/1/jia218443.pd

Quantifying atmospheric nitrate formation pathways based on a global model of the oxygen isotopic composition (δ17O) of atmospheric nitrate

The oxygen isotopic composition (δ17O) of atmospheric nitrate is a function of the relative abundance of atmospheric oxidants (O 3, ROx=OH+HO2+RO2) and the formation pathway of nitrate from its precursor NOx (=NO+NO2). Coupled observations and modeling of nitrate δ17O can be used to quantify the relative importance of chemical formation pathways leading to nitrate formation and reduce uncertainties in the budget of reactive nitrogen chemistry in the atmosphere. We present the first global model of atmospheric nitrate δ17O and compare with available observations. The largest uncertainty for calculations of nitrate δ17O is the unconstrained variability in the δ17O value of tropospheric ozone. The model shows the best agreement with a global compilation of observations when assuming a δ17O value of tropospheric ozone equal to 35 % and preferential oxidation of NOx by the terminal oxygen atoms of ozone. Calculated values of annual-mean nitrate δ17O in the lowest model layer (0-200m above the surface) vary from 7% in the tropics to 41% in the polar-regions. The global, annual-mean tropospheric inorganic nitrate burden is dominated by nitrate formation via NO2+OH (76%), followed by N5O2 hydrolysis (18%) and NO2+DMS/HC (4%). Calculated nitrate δ17O is sensitive to the relative importance of each nitrate formation pathway, suggesting that observations of nitrate δ17O can be used to quantify the importance of individual reactions (e.g. N2O5 hydrolysis) leading to nitrate formation if the δ17O value of ozone is known. © 2009 Author(s)

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