Rubber Bands, Pursuit Games and Shy Couplings

In this paper, we consider pursuit-evasion and probabilistic consequences of some geometric notions for bounded and suitably regular domains in Euclidean space that are CAT(kappa) for some kappa > 0. These geometric notions are useful for analyzing the related problems of (a) existence/nonexistence of successful evasion strategies for the Man in Lion and Man problems, and (b) existence/nonexistence of shy couplings for reflected Brownian motions. They involve properties of rubber bands and the extent to which a loop in the domain in question can be deformed to a point without, in between, increasing its loop length. The existence of a stable rubber band will imply the existence of a successful evasion strategy but, if all loops in the domain are well-contractible, then no successful evasion strategy will exist and there can be no co-adapted shy coupling. For example, there can be no shy couplings in bounded and suitably regular star-shaped domains and so, in this setting, any two reflected Brownian motions must almost surely make arbitrarily close encounters as t tends to infinity.Comment: 48 pages, 8 figure

New string vacua from twistor spaces

We find a new family of AdS_4 vacua in IIA string theory. The internal space is topologically either the complex projective space CP^3 or the "flag manifold" SU(3)/(U(1)xU(1)), but the metric is in general neither Einstein nor Kaehler. All known moduli are stabilized by fluxes, without using quantum effects or orientifold planes. The analysis is completely ten--dimensional and does not rely on assumptions about Kaluza--Klein reduction.Comment: 19 pages. v3: published version, further minor correction

A Mass Bound for Spherically Symmetric Black Hole Spacetimes

Requiring that the matter fields are subject to the dominant energy condition, we establish the lower bound $(4\pi)^{-1} \kappa {\cal A}$ for the total mass $M$ of a static, spherically symmetric black hole spacetime. (${\cal A}$ and $\kappa$ denote the area and the surface gravity of the horizon, respectively.) Together with the fact that the Komar integral provides a simple relation between $M - (4\pi)^{-1} \kappa A$ and the strong energy condition, this enables us to prove that the Schwarzschild metric represents the only static, spherically symmetric black hole solution of a selfgravitating matter model satisfying the dominant, but violating the strong energy condition for the timelike Killing field $K$ at every point, that is, $R(K,K) \leq 0$. Applying this result to scalar fields, we recover the fact that the only black hole configuration of the spherically symmetric Einstein-Higgs model with arbitrary non-negative potential is the Schwarzschild spacetime with constant Higgs field. In the presence of electromagnetic fields, we also derive a stronger bound for the total mass, involving the electromagnetic potentials and charges. Again, this estimate provides a simple tool to prove a ``no-hair'' theorem for matter fields violating the strong energy condition.Comment: 16 pages, LATEX, no figure

Body site colonization in patients with community-associated methicillin-resistant Staphylococcus aureus and other types of S. aureus skin infections

AbstractEfforts to control spread of community-associated methicillin-resistant Staphylococcus aureus (CA-MRSA) are often based on eradication of colonization. However, the role of nasal and non-nasal colonization in the pathogenesis of these infections remains poorly understood. Patients with acute S. aureus skin and soft tissue infection (SSTI) were prospectively enrolled. Each subject's nasal, axillary, inguinal and rectal areas were swabbed for S. aureus and epidemiological risk factors were surveyed. Among the 117 patients enrolled, there were 99 patients who had an SSTI and for whom data could be analysed. Sixty-five patients had a CA-MRSA SSTI. Among these patients, MRSA colonization in the nares, axilla, inguinal area and rectum was 25, 6, 11 and 13%, respectively, and 37% overall were MRSA colonized. Most (96%) MRSA colonization was detected using nose and inguinal screening alone. Non-nasal colonization was 25% among CA-MRSA patients, but only 6% among patients with CA-methicillin-susceptible S. aureus (MSSA) or healthcare-associated MRSA or MSSA. These findings suggest that colonization patterns in CA-MRSA infection are distinct from those in non-CA-MRSA S. aureus infections. The relatively high prevalence of non-nasal colonization may play a key role in CA-MRSA transmission and acquisition of infection

Sequences of Willmore surfaces

In this paper we develop the theory of Willmore sequences for Willmore surfaces in the 4-sphere. We show that under appropriate conditions this sequence has to terminate. In this case the Willmore surface either is the twistor projection of a holomorphic curve into complex projective space or the inversion of a minimal surface with planar ends in 4-space. These results give a unified explanation of previous work on the characterization of Willmore spheres and Willmore tori with non-trivial normal bundles by various authors.Comment: 10 page

Is diagnosis enough to guide interventions in mental health? Using case formulation in clinical practice

While diagnosis has traditionally been viewed as an essential concept in medicine, particularly when selecting treatments, we suggest that the use of diagnosis alone may be limited, particularly within mental health. The concept of clinical case formulation advocates for collaboratively working with patients to identify idiosyncratic aspects of their presentation and select interventions on this basis. Identifying individualized contributing factors, and how these could influence the person\u27s presentation, in addition to attending to personal strengths, may allow the clinician a deeper understanding of a patient, result in a more personalized treatment approach, and potentially provide a better clinical outcome.<br /

Immunomodulator expression in trophoblasts from the feline immunodeficiency virus (FIV)-infected cat

<p>Abstract</p> <p>Background</p> <p>FIV infection frequently compromises pregnancy under experimental conditions and is accompanied by aberrant expression of some placental cytokines. Trophoblasts produce numerous immunomodulators that play a role in placental development and pregnancy maintenance. We hypothesized that FIV infection may cause dysregulation of trophoblast immunomodulator expression, and aberrant expression of these molecules may potentiate inflammation and compromise pregnancy. The purpose of this project was to evaluate the expression of representative pro-(TNF-α, IFN-γ, IL-1β, IL-2, IL-6, IL-12p35, IL-12p40, IL-18, and GM-CSF) and anti-inflammatory cytokines (IL-4, IL-5, and IL-10); CD134, a secondary co-stimulatory molecule expressed on activated T cells (FIV primary receptor); the chemokine receptor CXCR4 (FIV co-receptor); SDF-1α, the chemokine ligand to CXCR4; and FIV gag in trophoblasts from early-and late-term pregnancy.</p> <p>Methods</p> <p>We used an anti-cytokeratin antibody in immunohistochemistry to identify trophoblasts selectively, collected these cells using laser capture microdissection, and extracted total RNA from the captured cell populations. Real time, reverse transcription-PCR was used to quantify gene expression.</p> <p>Results</p> <p>We detected IL-4, IL-5, IL-6, IL-1β, IL-12p35, IL-12p40, and CXCR4 in trophoblasts from early-and late-term pregnancy. Expression of cytokines increased from early to late pregnancy in normal tissues. A clear, pro-inflammatory microenvironment was not evident in trophoblasts from FIV-infected queens at either stage of pregnancy. Reproductive failure was accompanied by down-regulation of both pro-and anti-inflammatory cytokines. CD134 was not detected in trophoblasts, and FIV gag was detected in only one of ten trophoblast specimens collected from FIV-infected queens.</p> <p>Conclusion</p> <p>Feline trophoblasts express an array of pro-and anti-inflammatory immunomodulators whose expression increases from early to late pregnancy in normal tissues. Non-viable pregnancies were associated with decreased expression of immunomodulators which regulate trophoblast invasion in other species. The detection of FIV RNA in trophoblasts was rare, suggesting that the high rate of reproductive failure in FIV-infected queens was not a direct result of viral replication in trophoblasts. The influence of placental immune cells on trophoblast function and pregnancy maintenance in the FIV-infected cat requires additional study.</p

THE UNIQUENESS THEOREM FOR ROTATING BLACK HOLE SOLUTIONS OF SELF-GRAVITATING HARMONIC MAPPINGS

We consider rotating black hole configurations of self-gravitating maps from spacetime into arbitrary Riemannian manifolds. We first establish the integrability conditions for the Killing fields generating the stationary and the axisymmetric isometry (circularity theorem). Restricting ourselves to mappings with harmonic action, we subsequently prove that the only stationary and axisymmetric, asymptotically flat black hole solution with regular event horizon is the Kerr metric. Together with the uniqueness result for non-rotating configurations and the strong rigidity theorem, this establishes the uniqueness of the Kerr family amongst all stationary black hole solutions of self-gravitating harmonic mappings.Comment: 18 pages, latex, no figure

On the Evolution Equation for Magnetic Geodesics

In this paper we prove the existence of long time solutions for the parabolic equation for closed magnetic geodesics.Comment: In this paper we prove the existence of long time solutions for the parabolic equation for closed magnetic geodesic

Clinical and Experimental Applications of NIR-LED Photobiomodulation

This review presents current research on the use of far-red to near-infrared (NIR) light treatment in various in vitro and in vivo models. Low-intensity light therapy, commonly referred to as “photobiomodulation,” uses light in the far-red to near-infrared region of the spectrum (630–1000 nm) and modulates numerous cellular functions. Positive effects of NIR–light-emitting diode (LED) light treatment include acceleration of wound healing, improved recovery from ischemic injury of the heart, and attenuated degeneration of injured optic nerves by improving mitochondrial energy metabolism and production. Various in vitro and in vivo models of mitochondrial dysfunction were treated with a variety of wavelengths of NIR-LED light. These studies were performed to determine the effect of NIR-LED light treatment on physiologic and pathologic processes. NIRLED light treatment stimulates the photoacceptor cytochrome c oxidase, resulting in increased energy metabolism and production. NIR-LED light treatment accelerates wound healing in ischemic rat and murine diabetic wound healing models, attenuates the retinotoxic effects of methanol-derived formic acid in rat models, and attenuates the developmental toxicity of dioxin in chicken embryos. Furthermore, NIR-LED light treatment prevents the development of oral mucositis in pediatric bone marrow transplant patients. The experimental results demonstrate that NIR-LED light treatment stimulates mitochondrial oxidative metabolism in vitro, and accelerates cell and tissue repair in vivo. NIR-LED light represents a novel, noninvasive, therapeutic intervention for the treatment of numerous diseases linked to mitochondrial dysfunction