Doping-dependent study of the periodic Anderson model in three dimensions

We study a simple model for $f$-electron systems, the three-dimensional periodic Anderson model, in which localized $f$ states hybridize with neighboring $d$ states. The $f$ states have a strong on-site repulsion which suppresses the double occupancy and can lead to the formation of a Mott-Hubbard insulator. When the hybridization between the $f$ and $d$ states increases, the effects of these strong electron correlations gradually diminish, giving rise to interesting phenomena on the way. We use the exact quantum Monte-Carlo, approximate diagrammatic fluctuation-exchange approximation, and mean-field Hartree-Fock methods to calculate the local moment, entropy, antiferromagnetic structure factor, singlet-correlator, and internal energy as a function of the $f-d$ hybridization for various dopings. Finally, we discuss the relevance of this work to the volume-collapse phenomenon experimentally observed in f-electron systems.Comment: 12 pages, 8 figure

Applications of Hilbert Module Approach to Multivariable Operator Theory

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space \clh associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: $$\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h,$$where $p \in \mathbb{C}[z_1, \ldots, z_n]$ and $h \in \mathcal{H}$. A companion survey provides an introduction to the theory of Hilbert modules and some (Hilbert) module point of view to multivariable operator theory. The purpose of this survey is to emphasize algebraic and geometric aspects of Hilbert module approach to operator theory and to survey several applications of the theory of Hilbert modules in multivariable operator theory. The topics which are studied include: generalized canonical models and Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert spaces, a class of simple submodules and quotient modules of the Hardy modules over polydisc, commutant lifting theorem, similarity and free Hilbert modules, left invertible multipliers, inner resolutions, essentially normal Hilbert modules, localizations of free resolutions and rigidity phenomenon. This article is a companion paper to "An Introduction to Hilbert Module Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in Handbook of Operator Theory, Springe

Resilience and HIV: a review of the definition and study of resilience

We use a socioecological model of health to define resilience, review the definition and study of resilience among persons living with human immunodeficiency virus (PLWH) in the existing peer-reviewed literature, and discuss the strengths and limitations of how resilience is defined and studied in HIV research. We conducted a review of resilience research for HIV-related behaviors/outcomes of antiretroviral therapy (ART) adherence, clinic attendance, CD4 cell count, viral load, viral suppression, and/or immune functioning among PLWH. We performed searches using PubMed, PsycINFO and Google Scholar databases. The initial search generated 14,296 articles across the three databases, but based on our screening of these articles and inclusion criteria, n = 54 articles were included for review. The majority of HIV resilience research defines resilience only at the individual (i.e., psychological) level or studies individual and limited interpersonal resilience (e.g., social support). Furthermore, the preponderance of HIV resilience research uses general measures of resilience; these measures have not been developed with or tailored to the needs of PLWH. Our review suggests that a socioecological model of health approach can more fully represent the construct of resilience. Furthermore, measures specific to PLWH that capture individual, interpersonal, and neighborhood resilience are needed

Multilevel Resilience and HIV Virologic Suppression Among African American/Black Adults in the Southeastern United States

Objective: To assess overall and by neighborhood risk environments whether multilevel resilience resources were associated with HIV virologic suppression among African American/Black adults in the Southeastern United States. Setting and Methods: This clinical cohort sub-study included 436 African American/Black participants enrolled in two parent HIV clinical cohorts. Resilience was assessed using the Multilevel Resilience Resource Measure (MRM) for African American/Black adults living with HIV, where endorsement of a MRM statement indicated agreement that a resilience resource helped a participant continue HIV care despite challenges or was present in a participant’s neighborhood. Modified Poisson regression models estimated adjusted prevalence ratios (aPRs) for virologic suppression as a function of categorical MRM scores, controlling for demographic, clinical, and behavioral characteristics at or prior to sub-study enrollment. We assessed for effect measure modification (EMM) by neighborhood risk environments. Results: Compared to participants with lesser endorsement of multilevel resilience resources, aPRs for virologic suppression among those with greater or moderate endorsement were 1.03 (95% confidence interval: 0.96–1.11) and 1.03 (0.96–1.11), respectively. Regarding multilevel resilience resource endorsement, there was no strong evidence for EMM by levels of neighborhood risk environments. Conclusions: Modest positive associations between higher multilevel resilience resource endorsement and virologic suppression were at times most compatible with the data. However, null findings were also compatible. There was no strong evidence for EMM concerning multilevel resilience resource endorsement, which could have been due to random error. Prospective studies assessing EMM by levels of the neighborhood risk environment with larger sample sizes are needed

An Invitation to Higher Gauge Theory

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group; the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincar\'e 2-group, which leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a 'tangent 2-group', which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an 'inner automorphism 2-group', which serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an 'automorphism 2-group', which plays an important role in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a 'string 2-group'. We also touch upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra that governs 11-dimensional supergravity.Comment: 60 pages, based on lectures at the 2nd School and Workshop on Quantum Gravity and Quantum Geometry at the 2009 Corfu Summer Institut

Clinical Significance of Circulating Tumor Cells in Hormone Receptor–positive Metastatic Breast Cancer Patients who Received Letrozole with or without Bevacizumab

Purpose: We evaluated the prognostic and predictive value of circulating tumor cells (CTCs) hormone receptor–positive (HRþ) metastatic breast cancer (MBC) patients randomized to letrozole alone or letrozole plus bevacizumab in the first-line setting (CALGB 40503). Experimental Design: Blood samples were collected at pretreatment and three additional time points during therapy. The presence of ≥5 CTCs per 7.5 mL of blood was considered CTC positive. Association of CTCs with progression-free survival (PFS) and overall survival (OS) was assessed using Cox regression models. Results: Of 343 patients treated, 294 had CTC data and were included in this analysis. Median follow-up was 39 months. In multivariable analysis, CTC-positive patients at baseline (31%) had significantly reduced PFS [HR, 1.49; 95% confidence interval (CI), 1.12–1.97] and OS (HR, 2.08; 95% CI, 1.49–2.93) compared with CTC negative. Failure to clear CTCs during treatment was associated with significantly increased risk of progression (HR, 2.2; 95% CI, 1.58–3.07) and death (HR, 3.4; 95% CI, 2.36–4.88). CTC-positive patients who received only letrozole had the worse PFS (HR, 2.3; 95% CI, 1.54–3.47) and OS (HR, 2.6; 95% CI, 1.59–4.40). Median PFS in CTC-positive patients was significantly longer (18.0 vs. 7.0 months) in letrozole plus bevacizumab versus letrozole arm (P ¼ 0.0009). Restricted mean survival time analysis further revealed that addition of bevacizumab was associated with PFS benefit in both CTC-positive and CTC-negative patients, but OS benefit was only observed in CTC-positive patients. Conclusions: CTCs were highly prognostic for the addition of bevacizumab to first-line letrozole in patients with HRþ MBC in CALGB 40503. Further research to determine the potential predictive value of CTCs in this setting is warranted

A reconstruction theorem for almost-commutative spectral triples

We propose an expansion of the definition of almost-commutative spectral triple that accommodates non-trivial fibrations and is stable under inner fluctuation of the metric, and then prove a reconstruction theorem for almost-commutative spectral triples under this definition as a simple consequence of Connes's reconstruction theorem for commutative spectral triples. Along the way, we weaken the orientability hypothesis in the reconstruction theorem for commutative spectral triples, and following Chakraborty and Mathai, prove a number of results concerning the stability of properties of spectral triples under suitable perturbation of the Dirac operator.Comment: AMS-LaTeX, 19 pp. V4: Updated version incorporating the erratum of June 2012, correcting the weak orientability axiom in the definition of commutative spectral triple, stengthening Lemma A.10 to cover the odd-dimensional case and the proof of Corollary 2.19 to accommodate the corrected weak orientability axio