Sticky central limit theorems on open books

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fréchet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine.We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky). © Institute of Mathematical Statistics, 2013.

Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

Hepcidin as a therapeutic tool to limit iron overload and improve anemia in β-thalassemic mice.

Excessive iron absorption is one of the main features of β-thalassemia and can lead to severe morbidity and mortality. Serial analyses of β-thalassemic mice indicate that while hemoglobin levels decrease over time, the concentration of iron in the liver, spleen, and kidneys markedly increases. Iron overload is associated with low levels of hepcidin, a peptide that regulates iron metabolism by triggering degradation of ferroportin, an iron-transport protein localized on absorptive enterocytes as well as hepatocytes and macrophages. Patients with β-thalassemia also have low hepcidin levels. These observations led us to hypothesize that more iron is absorbed in β-thalassemia than is required for erythropoiesis and that increasing the concentration of hepcidin in the body of such patients might be therapeutic, limiting iron overload. Here we demonstrate that a moderate increase in expression of hepcidin in β-thalassemic mice limits iron overload, decreases formation of insoluble membrane-bound globins and reactive oxygen species, and improves anemia. Mice with increased hepcidin expression also demonstrated an increase in the lifespan of their red cells, reversal of ineffective erythropoiesis and splenomegaly, and an increase in total hemoglobin levels. These data led us to suggest that therapeutics that could increase hepcidin levels or act as hepcidin agonists might help treat the abnormal iron absorption in individuals with β-thalassemia and related disorders.

Targeting Gbeta gamma signaling in arterial vascular smooth muscle proliferation: a novel strategy to limit restenosis.

Restenosis continues to be a major problem limiting the effectiveness of revascularization procedures. To date, the roles of heterotrimeric G proteins in the triggering of pathological vascular smooth muscle (VSM) cell proliferation have not been elucidated. betagamma subunits of heterotrimeric G proteins (Gbetagamma) are known to activate mitogen-activated protein (MAP) kinases after stimulation of certain G protein-coupled receptors; however, their relevance in VSM mitogenesis in vitro or in vivo is not known. Using adenoviral-mediated transfer of a transgene encoding a peptide inhibitor of Gbetagamma signaling (betaARKct), we evaluated the role of Gbetagamma in MAP kinase activation and proliferation in response to several mitogens, including serum, in cultured rat VSM cells. Our results include the striking finding that serum-induced proliferation of VSM cells in vitro is mediated largely via Gbetagamma. Furthermore, we studied the effects of in vivo adenoviral-mediated betaARKct gene transfer on VSM intimal hyperplasia in a rat carotid artery restenosis model. Our in vivo results demonstrated that the presence of the betaARKct in injured rat carotid arteries significantly reduced VSM intimal hyperplasia by 70%. Thus, Gbetagamma plays a critical role in physiological VSM proliferation, and targeted Gbetagamma inhibition represents a novel approach for the treatment of pathological conditions such as restenosis.

Human Non-neutralizing HIV-1 Envelope Monoclonal Antibodies Limit the Number of Founder Viruses during SHIV Mucosal Infection in Rhesus Macaques.

HIV-1 mucosal transmission begins with virus or virus-infected cells moving through mucus across mucosal epithelium to infect CD4+ T cells. Although broadly neutralizing antibodies (bnAbs) are the type of HIV-1 antibodies that are most likely protective, they are not induced with current vaccine candidates. In contrast, antibodies that do not neutralize primary HIV-1 strains in the TZM-bl infection assay are readily induced by current vaccine candidates and have also been implicated as secondary correlates of decreased HIV-1 risk in the RV144 vaccine efficacy trial. Here, we have studied the capacity of anti-Env monoclonal antibodies (mAbs) against either the immunodominant region of gp41 (7B2 IgG1), the first constant region of gp120 (A32 IgG1), or the third variable loop (V3) of gp120 (CH22 IgG1) to modulate in vivo rectal mucosal transmission of a high-dose simian-human immunodeficiency virus (SHIV-BaL) in rhesus macaques. 7B2 IgG1 or A32 IgG1, each containing mutations to enhance Fc function, was administered passively to rhesus macaques but afforded no protection against productive clinical infection while the positive control antibody CH22 IgG1 prevented infection in 4 of 6 animals. Enumeration of transmitted/founder (T/F) viruses revealed that passive infusion of each of the three antibodies significantly reduced the number of T/F genomes. Thus, some antibodies that bind HIV-1 Env but fail to neutralize virus in traditional neutralization assays may limit the number of T/F viruses involved in transmission without leading to enhancement of viral infection. For one of these mAbs, gp41 mAb 7B2, we provide the first co-crystal structure in complex with a common cyclical loop motif demonstrated to be critical for infection by other retroviruses.

Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes

Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.