Geometric construction of spinors in orthogonal modular categories

A geometric construction of Z_2-graded orthogonal modular categories is given. Their 0-graded parts coincide with categories previously obtained by Blanchet and the author from the category of tangles modulo the Kauffman skein relations. Quantum dimensions and twist coefficients for 1-graded simple objects (spinors) are calculated. We show that our even orthogonal modular categories admit cohomological refinements and the odd orthogonal ones lead to spin refinements. The relation with the quantum group approach is discussed.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-32.abs.htm

On the triplet anti-triplet symmetry in 3-3-1 models

We present a detailed discussion of the triplet anti-triplet symmetry in 3-3-1 models. The full set of conditions to realize this symmetry is provided, which includes in particular the requirement that the two vacuum expectation values of the two scalar triplets responsible for making the W and Z bosons massive must be interchanged. We apply this new understanding to the calculation of processes that have a Z-Z' mixing.Comment: 14 page

Unpacking the Imposter Syndrome and Mental Health as a Person of Color First Generation College Student within Institutions of Higher Education

Extant literature on Imposter syndrome primarily focuses on Asian Americans. This current review of literature seeks to make a comparison of Imposter syndrome between two marginalized communities – Asian Americans and African Americans. Imposter syndrome, also referred to as the imposter phenomenon, refers to an individual who doubts their own skills, abilities, successes, and overall capabilities in their life (Parkman, 2016). Asian American students are stereotyped as the model minority and are believed to be intelligent, hardworking, high achieving, and academic and seen to be free from any emotional or adaptive problems. Although these stereotypes are perceived to be positive, they also place a great deal of pressure on Asian American students to excel in school and this can produce increased anxiety and distress. Among African-Americans, shame-proneness manifests differently. It is directly related to a fear of intimacy and self-deprecation (Austin, 2009). Researchers looking at the relationship between Imposter syndrome and mental health among student populations have found it to be a predictor of mental health, it has been found to be positively correlated with anxiety, depression, psychological distress, and minority student status stress (Parkman, 2016). This review will seek to answer which of the two aforesaid stated student populations of first-generation students, Asian American and African American experience a greater detriment in mental health and if there are any specific patterns of mental symptoms of psychological distress that are found among each of these student populations

Riemannian Median and Its Estimation

In this paper, we define the geometric median of a probability measure on a Riemannian manifold, give its characterization and a natural condition to ensure its uniqueness. In order to calculate the median in practical cases, we also propose a subgradient algorithm and prove its convergence as well as estimating the error of approximation and the rate of convergence. The convergence property of this subgradient algorithm, which is a generalization of the classical Weiszfeld algorithm in Euclidean spaces to the context of Riemannian manifolds, also answers a recent question in P. T. Fletcher et al. [13