Equivariant configuration spaces

The compression theorem is used to prove results for equivariant configuration spaces that are analogous to the well-known non-equivariant results of May, Milgram and Segal

James bundles

We study cubical sets without degeneracies, which we call {square}-sets. These sets arise naturally in a number of settings and they have a beautiful intrinsic geometry; in particular a {square}-set C has an infinite family of associated {square}-sets Ji(C), for i = 1, 2, ..., which we call James complexes. There are mock bundle projections pi: |Ji(C)| -> |C| (which we call James bundles) defining classes in unstable cohomotopy which generalise the classical James–Hopf invariants of {Omega}(S2). The algebra of these classes mimics the algebra of the cohomotopy of {Omega}(S2) and the reduction to cohomology defines a sequence of natural characteristic classes for a {square}-set. An associated map to BO leads to a generalised cohomology theory with geometric interpretation similar to that for Mahowald orientation

Unified Interacting Quark Stars in Regularized 4D Einstein Gauss-Bonnet Gravity

Since the derivation of a well-defined $D\rightarrow 4$ limit for 4D Einstein Gauss-Bonnet (4DEGB) gravity coupled to a scalar field, there has been interest in testing it as an alternative to Einstein's general theory of relativity. Using the Tolman-Oppenheimer-Volkoff (TOV) equations modified for 4DEGB gravity, we model the stellar structure of quark stars using a novel interacting quark matter equation of state. We find that increasing the Gauss-Bonnet coupling constant $\alpha$ or the interaction parameter $\lambda$ both tend to increase the mass-radius profiles of quark stars described by this theory, allowing a given central pressure to support larger quark stars in general. These results logically extend to cases where $\lambda < 0$, in which increasing the magnitude of the interaction effects instead diminishes masses and radii. We also analytically identify a critical central pressure in both regimes, below which no quark star solutions exist due to the pressure function having no roots. Most interestingly, we find that quark stars can exist below the general relativistic Buchdahl bound and Schwarzschild radius $R=2M$, due to the lack of a mass gap between black holes and compact stars in 4DEGB. Even for small $\alpha$ well within current observational constraints, we find that quark star solutions in this theory can describe Extreme Compact Objects (ECOs), objects whose radii are smaller than what is allowed by general relativity

On the Expansions in Spin Foam Cosmology

We discuss the expansions used in spin foam cosmology. We point out that already at the one vertex level arbitrarily complicated amplitudes contribute, and discuss the geometric asymptotics of the five simplest ones. We discuss what type of consistency conditions would be required to control the expansion. We show that the factorisation of the amplitude originally considered is best interpreted in topological terms. We then consider the next higher term in the graph expansion. We demonstrate the tension between the truncation to small graphs and going to the homogeneous sector, and conclude that it is necessary to truncate the dynamics as well.Comment: 17 pages, 4 figures, published versio

Strategies Employed by Community-Based Service Providers to Address HIV-Associated Neurocognitive Challenges: A Qualitative Study

Background: HIV-associated neurocognitive disorders and other causes of neurocognitive challenges experienced by people living with HIV (PLWH) persist as public health concerns in developed countries. Consequently, PLWH who experience neurocognitive challenges increasingly require social support and mental health services from community-based providers in the HIV sector. Methods: Thirty-three providers from 22 AIDS service organizations across Ontario, Canada, were interviewed to determine the strategies they used to support PLWH experiencing neurocognitive difficulties. Thematic analysis was conducted to determine key themes from the interview data. Results: Three types of strategies were identified: (a) intrapersonal, (b) interpersonal, and (c) organizational. Intrapersonal strategies involved learning and staying informed about causes of neurocognitive challenges. Interpersonal strategies included providing practical assistance, information, counseling, and/or referrals to PLWH. Organizational strategies included creating dedicated support groups for PLWH experiencing neurocognitive challenges, partnering with other organizations with services not available within their own organization, and advocating for greater access to services with expertise and experience working with PLWH. Conclusion: Through concerted efforts in the future, it is likely that empirically investigating, developing, and customizing these strategies specifically to address HIV-associated neurocognitive challenges will yield improved social support and mental health outcomes for PLWH

Implementation of the Backlund transformations for the Ablowitz-Ladik hierarchy

The derivation of the Backlund transformations (BTs) is a standard problem of the theory of the integrable systems. Here, I discuss the equations describing the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already obtained by several authors. The main aim of this work is to solve these equations. This can be done in the framework of the so-called functional representation of the ALH, when an infinite number of the evolutionary equations are replaced, using the Miwa's shifts, with a few equations linking tau-functions with different arguments. It is shown that starting from these equations it is possible to obtain explicit solutions of the BT equations. In other words, the main result of this work is a presentation of the discrete BTs as a superposition of an infinite number of evolutionary flows of the hierarchy. These results are used to derive the superposition formulae for the BTs as well as pure soliton solutions.Comment: 20 page

Imaginative Representations of Two- and Three-Dimensional Matrices in Children with Nonverbal Learning Disabilities

Children with non-verbal learning disabilities (NLD) are characterized by high verbal and poor non-verbal intelligence, poor cognitive abilities, school difficulties, and—sometimes—depressive symptoms. NLD children lack visuospatial working memory, but it is not clear whether they encounter difficulties in mental imagery tasks. In the present study, NLD adolescents without depressive symptoms, depressed adolescents without NLD symptoms, and a control group were administered a mental imagery task requiring them to imagine to move along the cells of a 2-D (5 × 5) or 3-D (3 × 3 × 3) matrix. Results showed that NLD adolescents had difficulty at performing the imagery task when a 3-D pattern was involved. It is suggested that 3-D mental imagery tasks tap visuospatial processes which are weak in NLD individuals. In addition, their poor cognitive performance cannot be attributed to a depressive state, as the depressed group had a performance similar to that of controls

Affirmative Action Bans and Health Risk Behaviors

College affirmative action bans were associated with higher rates of smoking and drinking in underrepresented minority 11th and 12th graders, and these students continued to smoke at higher rates into young adulthood. Policymakers should consider unintended public health consequences of proposals, such as affirmative action bans, that may limit socioeconomic opportunities

The Fermi surface and f-valence electron count of UPt3

Combining old and new de Haas-van Alphen (dHvA) and magnetoresistance data, we arrive at a detailed picture of the Fermi surface of the heavy fermion superconductor UPt3. Our work was partially motivated by a new proposal that two 5f valence electrons per formula unit in UPt3 are localized by correlation effects -- agreement with previous dHvA measurements of the Fermi surface was invoked in its support. Comprehensive comparison with our new observations shows that this 'partially localized' model fails to predict the existence of a major sheet of the Fermi surface, and is therefore less compatible with experiment than the originally proposed 'fully itinerant' model of the electronic structure of UPt3. In support of this conclusion, we offer a more complete analysis of the fully itinerant band structure calculation, where we find a number of previously unrecognized extremal orbits on the Fermi surface.Comment: 23 pages, 12 figures, latex, iopart clas