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

Electron Tomography of HIV-1 Infection in Gut-Associated Lymphoid Tissue

Critical aspects of HIV-1 infection occur in mucosal tissues, particularly in the gut, which contains large numbers of HIV-1 target cells that are depleted early in infection. We used electron tomography (ET) to image HIV-1 in gut-associated lymphoid tissue (GALT) of HIV-1–infected humanized mice, the first three-dimensional ultrastructural examination of HIV-1 infection in vivo. Human immune cells were successfully engrafted in the mice, and following infection with HIV-1, human T cells were reduced in GALT. Virions were found by ET at all stages of egress, including budding immature virions and free mature and immature viruses. Immuno-electron microscopy verified the virions were HIV-1 and showed CD4 sequestration in the endoplasmic reticulum of infected cells. Observation of HIV-1 in infected GALT tissue revealed that most HIV-1–infected cells, identified by immunolabeling and/or the presence of budding virions, were localized to intestinal crypts with pools of free virions concentrated in spaces between cells. Fewer infected cells were found in mucosal regions and the lamina propria. The preservation quality of reconstructed tissue volumes allowed details of budding virions, including structures interpreted as host-encoded scission machinery, to be resolved. Although HIV-1 virions released from infected cultured cells have been described as exclusively mature, we found pools of both immature and mature free virions within infected tissue. The pools could be classified as containing either mostly mature or mostly immature particles, and analyses of their proximities to the cell of origin supported a model of semi-synchronous waves of virion release. In addition to HIV-1 transmission by pools of free virus, we found evidence of transmission via virological synapses. Three-dimensional EM imaging of an active infection within tissue revealed important differences between cultured cell and tissue infection models and furthered the ultrastructural understanding of HIV-1 transmission within lymphoid tissue

Bugs, drugs, and HIV : the role of the vaginal microbiome in HIV risk and antiretroviral efficacy for HIV prevention.

CAPRISA, 2017.Abstract available in pdf

Gli1 enhances migration and invasion via up-regulation of MMP-11 and promotes metastasis in ERα negative breast cancer cell lines

Gli1 is an established oncogene and its expression in Estrogen Receptor (ER) α negative and triple negative breast cancers is predictive of a poor prognosis; however, the biological functions regulated by Gli1 in breast cancer have not been extensively evaluated. Herein, Gli1 was over-expressed or down-regulated (by RNA interference and by expression of the repressor form of Gli3) in the ERα negative, human breast cancer cell lines MDA-MB-231 and SUM1315. Reduced expression of Gli1 in these two cell lines resulted in a decrease in migration and invasion. Gli1 over-expression increased the migration and invasion of MDA-MB-231 cells with a corresponding increase in expression of MMP-11. Silencing MMP-11 in MDA-MB-231 cells that over-expressed Gli1 abrogated the Gli1-induced enhancement of migration and invasion. Sustained suppression of Gli1 expression decreased growth of MDA-MB-231 in vitro by increasing apoptosis and decreasing proliferation. In addition, silencing of Gli1 reduced the numbers and sizes of pulmonary metastases of MDA-MB-231 in an in vivo experimental metastasis assay. In summary, Gli1 promotes the growth, survival, migration, invasion and metastasis of ERα negative breast cancer. Additionally, MMP-11 is up-regulated by Gli1 and mediates the migration and invasion induced by Gli1 in MDA-MB-231

Winding Strings and Decay of D-Branes with Flux

We study the boundary state associated with the decay of an unstable D-brane with uniform electric field, 1>e>0 in the string units. Compactifying the D-brane along the direction of the electric field, we find that the decay process is dominated by production of closed strings with some winding numbers; closed strings produced are such that the winding mode carries precisely the fraction $e$ of the individual string energy. This supports the conjecture that the final state at tree level is composed of winding strings with heavy oscillations turned on. As a corollary, we argue that the closed strings disperse into spacetime at a much slower rate than the case without electric field.Comment: 14 pages, harvmac, minor changes, clarified gauge choice, version to appear in JHE

HIV-associated changes in the enteric microbial community: potential role in loss of homeostasis and development of systemic inflammation

Purpose of review Despite HIV therapy advances, average life expectancy in HIV-infected individuals on effective treatment is significantly decreased relative to uninfected persons, largely because of increased incidence of inflammation-related diseases, such as cardiovascular disease and renal dysfunction. The enteric microbial community could potentially cause this inflammation, as HIV-driven destruction of gastrointestinal CD4+ T cells may disturb the microbiota–mucosal immune system balance, disrupting the stable gut microbiome and leading to further deleterious host outcomes. Recent findings Varied enteric microbiome changes have been reported during HIV infection, but unifying patterns have emerged. Community diversity is decreased, similar to pathologies such as inflammatory bowel disease, obesity, and Clostridium difficile infection. Many taxa frequently enriched in HIV-infected individuals, such as Enterobacteriaceae and Erysipelotrichaceae, have pathogenic potential, whereas depleted taxa, such as Bacteroidaceae and Ruminococcaceae, are more linked with anti-inflammatory properties and maintenance of gut homeostasis. The gut viral community in HIV has been found to contain a greater abundance of pathogenesis-associated Adenoviridae and Anelloviridae. These bacterial and viral changes correlate with increased systemic inflammatory markers, such as serum sCD14, sCD163, and IL-6. Summary Enteric microbial community changes may contribute to chronic HIV pathogenesis, but more investigation is necessary, especially in the developing world population with the greatest HIV burden (Video, Supplemental Digital Content 1, which includes the authors’ summary of the importance of the work)

Rapid, efficient functional characterization and recovery of HIV-specific human CD8+ T cells using microengraving

The nature of certain clinical samples (tissue biopsies, fluids) or the subjects themselves (pediatric subjects, neonates) often constrain the number of cells available to evaluate the breadth of functional T-cell responses to infections or therapeutic interventions. The methods most commonly used to assess this functional diversity ex vivo and to recover specific cells to expand in vitro usually require more than 106 cells. Here we present a process to identify antigen-specific responses efficiently ex vivo from 104–105 single cells from blood or mucosal tissues using dense arrays of subnanoliter wells. The approach combines on-chip imaging cytometry with a technique for capturing secreted proteins—called “microengraving”—to enumerate antigenspecific responses by single T cells in a manner comparable to conventional assays such as ELISpot and intracellular cytokine staining. Unlike those assays, however, the individual cells identified can be recovered readily by micromanipulation for further characterization in vitro. Applying this method to assess HIV-specific T cell responses demonstrates that it is possible to establish clonal CD8+ T-cell lines that represent the most abundant specificities present in circulation using 100- to 1,000-fold fewer cells than traditional approaches require and without extensive genotypic analysis a priori. This rapid (<24 h), efficient, and inexpensive process should improve the comparative study of human T-cell immunology across ages and anatomic compartments

Coupling between M2-branes and Form Fields

In the context of low-energy effective theory of multiple M2-branes, we construct the interaction terms between the world-volume fields of M2-branes and the antisymmetric tensor fields of three- and six-forms. By utilizing the compactification procedure, we show coincidence between the dimensionally reduced coupling and the R-R coupling to D-branes in type II string theory. We also discuss that a cubic term proportional to six-form field reproduces the quartic mass-deformation term in the world-volume theory of multiple M2-branes.Comment: 18 page

Profiling Human Antibody Responses by Integrated Single-Cell Analysis

Comprehensive characterization of the antigen-specific B cells induced during infections or following vaccination would facilitate the discovery of novel antibodies and inform how interventions shape protective humoral responses. The analysis of human B cells and their antibodies has been performed using flow cytometry to evaluate memory B cells and expanded plasmablasts, while microtechnologies have also provided a useful tool to examine plasmablasts/plasma cells after vaccination. Here we present an integrated analytical platform, using arrays of subnanoliter wells (nanowells), for constructing detailed profiles for human B cells comprising the immunophenotypes of these cells, the distribution of isotypes of the secreted antibodies, the specificity and relative affinity for defined antigens, and for a subset of cells, the genes encoding the heavy and light chains. The approach combines on-chip image cytometry, microengraving, and single-cell RT-PCR. Using clinical samples from HIV-infected subjects, we demonstrate that the method can identify antigen-specific neutralizing antibodies, is compatible with both plasmablasts/plasma cells and activated memory B cells, and is well-suited for characterizing the limited numbers of B cells isolated from tissue biopsies (e.g., colon biopsies). The technology should facilitate detailed analyses of human humoral responses for evaluating vaccines and their ability to raise protective antibody responses across multiple anatomical compartments

Modeling the temporal dynamics of cervicovaginal microbiota identifies targets that may promote reproductive health (vol 9, 163, 2021)

Following the publication of the original article [1], the authors noticed a misspelling on the name of one of the co-authors. “Musie S. Ghebermichael” should read “Musie S. Ghebremichael” The original article has been updated