All roots of unity are detected by the A-polynomial

For an arbitrary positive integer n, we construct infinitely many one-cusped hyperbolic 3-manifolds where each manifold's A-polynomial detects every n-th root of unity. This answers a question of Cooper, Culler, Gillet, Long, and Shalen as to which roots of unity arise in this manner.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-11.abs.htm

Algebraic invariants, mutation, and commensurability of link complements

We construct a family of hyperbolic link complements by gluing tangles along totally geodesic four-punctured spheres, then investigate the commensurability relation among its members. Those with different volume are incommensurable, distinguished by their scissors congruence classes. Mutation produces arbitrarily large finite subfamilies of nonisometric manifolds with the same volume and scissors congruence class. Depending on the choice of mutation, these manifolds may be commensurable or incommensurable, distinguished in the latter case by cusp parameters. All have trace field Q(i,\sqrt{2}), but some have integral traces while others do not.Comment: Minor changes following referee's suggestion

Online Dating Profile Analysis: The Intersection of Identity, Gender & Religion

According to standpoint theory, individuals experience the world based on the social groups that they belong to. Using this theoretical lens, my content analysis compared how gender and religion were conveyed on the user profiles of three online dating sites: JDate.com, ChristianMingle.com and OkCupid.com. In my initial reading of data, I used inductive thematic analysis to distinguish 7 categories of words and 7 categories of photographs that were relevant to portrayals of gender and religion. These categories were then analyzed through frequency counts by adding the total number of word types and photograph types used by men and women on each site. Findings showed an emphasis on religious cultural background on ChristianMingle.com. Gender roles were supported overall with male emphasis on career and sports and female emphasis on attractiveness and care

Closed surfaces and character varieties

The powerful character variety techniques of Culler and Shalen can be used to find essential surfaces in knot manifolds. We show that module structures on the coordinate ring of the character variety can be used to identify detected boundary slopes as well as when closed surfaces are detected. This approach also yields new number theoretic invariants for the character varieties of knot manifolds.Comment: 28 pages, 1 figur

Targeting of the prion protein to the cytosol: mechanisms and consequences

Prion diseases are characterized by the conformational transition of the cellular prion protein (PrPC) into an aberrant protein conformer, designated scrapie-prion protein (PrPSc). A causal link between protein misfolding and neurodegeneration has been established for a variety of neurodegenerative disease, such as Alzheimer's disease, Parkinson's disease and polyglutamine diseases, but there is an ongoing debate about the nature of the neurotoxic species and how non-native conformers can damage neuronal populations. PrP is normally imported into the endoplasmic reticulum (ER) and targeted to the outer leaflet of the plasma membrane via a glycosylphosphatidylinositol (GPI) anchor. However, several conditions, such as ER stress or some pathogenic mutations in the PrP gene, can induce the mislocalization of PrP in the cytosol, where it has a neurotoxic potential as demonstrated in cell culture and transgenic mouse models. In this review we focus on intrinsic factors and cellular pathways implicated in the import of PrP into the ER and its mistargeting to the cytosol. The findings summarized here not only reveal a complex regulation of the biogenesis of PrP, but also provide interesting new insight into toxic activities of pathogenic protein conformers and quality control pathways of ER-targeted proteins

Endogenous Viral Etiology of Prion Diseases

Transmissible spongiform encephalopathies (TSEs), or prion diseases, are a group of incurable neurodegenerative disorders, including Kuru and Creutzfeldt-Jakob disease in humans, “mad cow” disease in cattle, and scrapie in sheep. This paper presents structural, genetic, and evolutionary evidence supporting an endogenous TSE virus model that integrates the three major traditional views on the nature of TSE pathogens, the conventional virus view, the prion hypothesis, and the virino concept, into a novel conceptual and evolutionary framework. According to this model, the TSE pathogens are symbiotic endogenous viruses that inadvertently produce transmissible viral particles that lack the viral genome and are composed primarily of the viral prion protein (PrP). Production of defective viral particles that contain a partial genome or lack the viral genome entirely is a relatively common event in the life cycle of many viruses. Similar to the normal viral particles, which contain a genome, these defective viral particles can be transmitted to new host cells. Obviously, in the absence of viral genome, these protein-only viral particles cannot establish a productive infection. However, if these viral particles enter a host cell that carries the parental or a related virus and induce the production of similar protein-only particles, then they would appear as self-replicating, protein-only infectious pathogens if mistakenly taken out from the context of the viral life cycle. This misconception, which is rooted into the current dogma of viruses as viral particles, led to the development of the prion theory. The endogenous TSE virus model is consistent with the TSE data and offers solutions to many enigmatic features associated with TSE, including the function of PrP that, despite more than two decades of TSE research conducted primarily within the framework of the prion hypothesis, is still not known. According to the TSE endogenous virus model, PrP is the protein of an endogenous virus that has co-evolved with their vertebrate hosts by providing a protective function against pathogenic viruses. The evidence for the endogenous TSE virus model and for the antiviral protective function of PrP is strong, and they are fully open to additional experimental testing. The endogenous virus model opens the TSE research field to new interpretations and directions, both in basic research and in associated biomedical and public health fields, and could lead to development of new diagnostic and therapeutic approaches

A novel, resistance-linked ovine PrP variant and its equivalent mouse variant modulate the in vitro cell-free conversion of rPrP to PrPres

Prion diseases are associated with the conversion of the normal cellular prion protein, PrPc, to the abnormal, disease-associated form, PrPSc. This conversion can be mimicked in vitro by using a cell-free conversion assay. It has recently been shown that this assay can be modified to use bacterial recombinant PrP as substrate and mimic the in vivo transmission characteristics of rodent scrapie. Here, it is demonstrated that the assay replicates the ovine polymorphism barriers of scrapie transmission. In addition, the recently identified ovine PrP variant ARL168Q, which is associated with resistance of sheep to experimental BSE, modulates the cell-free conversion of ovine recombinant PrP to PrPres by three different types of PrPSc, reducing conversion efficiencies to levels similar to those of the ovine resistance-associated ARR variant. Also, the equivalent variant in mice (L164) is resistant to conversion by 87V scrapie. Together, these results suggest a significant role for this position and/or amino acid in conversion

Factorial growth rates for the number of hyperbolic 3-manifolds of a given volume

The work of J{\o}rgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. In this paper, we construct examples showing that the number of hyperbolic knot complements with a given volume v can grow at least factorially fast with v. A similar statement holds for closed hyperbolic 3-manifolds, obtained via Dehn surgery. Furthermore, we give explicit estimates for lower bounds of N(v) in terms of v for these examples. These results improve upon the work of Hodgson and Masai, which describes examples that grow exponentially fast with v. Our constructions rely on performing volume preserving mutations along Conway spheres and on the classification of Montesinos knots.Comment: 13 pages, 6 figure