Convergent Calculation of the Asymptotic Dimension of Diffusion Limited Aggregates: Scaling and Renormalization of Small Clusters

Diffusion Limited Aggregation (DLA) is a model of fractal growth that had attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. We present a convergent calculation of the fractal dimension D of DLA based on a renormalization scheme for the first Laurent coefficient of the conformal map from the unit circle to the expanding boundary of the fractal cluster. The theory is applicable from very small (2-3 particles) to asymptotically large (n \to \infty) clusters. The computed dimension is D=1.713\pm 0.003

Diffusion Limited Aggregation with Power-Law Pinning

Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth $R_N^{-\gamma}$ (where $R_N$ is the radius of the $N-$ particle cluster). For $\gamma > 1$ the growth pattern is in the same universality class as diffusion limited aggregation (DLA) growth, while for $\gamma < 1$ the resulting patterns have a lower fractal dimension $D(\gamma)$ than a DLA cluster due to the enhancement of growth at the hot tips of the developing pattern. Our results indicate that a pinning transition occurs at $\gamma = 1/2$, significantly smaller than might be expected from the lower bound $\alpha_{min} \simeq 0.67$ of multifractal spectrum of DLA. This limiting case shows that the most singular tips in the pruned cluster now correspond to those expected for a purely one-dimensional line. Using multifractal analysis, analytic expressions are established for $D(\gamma)$ both close to the breakdown of DLA universality class, i.e., $\gamma \lesssim 1$, and close to the pinning transition, i.e., $\gamma \gtrsim 1/2$.Comment: 5 pages, e figures, submitted to Phys. Rev.

Soap Bubbles in Outer Space: Interaction of a Domain Wall with a Black Hole

We discuss the generalized Plateau problem in the 3+1 dimensional Schwarzschild background. This represents the physical situation, which could for instance have appeared in the early universe, where a cosmic membrane (thin domain wall) is located near a black hole. Considering stationary axially symmetric membranes, three different membrane-topologies are possible depending on the boundary conditions at infinity: 2+1 Minkowski topology, 2+1 wormhole topology and 2+1 black hole topology. Interestingly, we find that the different membrane-topologies are connected via phase transitions of the form first discussed by Choptuik in investigations of scalar field collapse. More precisely, we find a first order phase transition (finite mass gap) between wormhole topology and black hole topology; the intermediate membrane being an unstable wormhole collapsing to a black hole. Moreover, we find a second order phase transition (no mass gap) between Minkowski topology and black hole topology; the intermediate membrane being a naked singularity. For the membranes of black hole topology, we find a mass scaling relation analogous to that originally found by Choptuik. However, in our case the parameter $p$ is replaced by a 2-vector $\vec{p}$ parametrizing the solutions. We find that $Mass\propto|\vec{p}-\vec{p}_*|^\gamma$ where $\gamma\approx 0.66$. We also find a periodic wiggle in the scaling relation. Our results show that black hole formation as a critical phenomenon is far more general than expected.Comment: 15 pages, Latex, 4 figures include

TIME-SYMMETRIC INITIAL DATA SETS IN 4--D DILATON GRAVITY

I study the time--symmetric initial--data problem in theories with a massless scalar field (dilaton), free or coupled to a Maxwell field in the stringy way, finding different initial--data sets describing an arbitrary number of black holes with arbitrary masses, charges and asymptotic value of the dilaton. The presence of the scalar field gives rise to a number of interesting effects. The mass and charges of a single black hole are different in its two asymptotically flat regions across the Einstein--Rosen bridge. The same happens to the value of the dilaton at infinity. This forbids the identification of these asymptotic regions in order to build (Misner) wormholes in the most naive way. Using different techniques, I find regular initial data for stringy wormholes. The price payed is the existence singularities in the dilaton field. The presence of a single--valued scalar seems to constrain strongly the allowed topologies of the initial space--like surface. Other kinds of scalar fields (taking values on a circle or being defined up to an additive constant) are also briefly considered.Comment: latex file, 38 pages

Non-linear instability of Kerr-type Cauchy horizons

Using the general solution to the Einstein equations on intersecting null surfaces developed by Hayward, we investigate the non-linear instability of the Cauchy horizon inside a realistic black hole. Making a minimal assumption about the free gravitational data allows us to solve the field equations along a null surface crossing the Cauchy Horizon. As in the spherical case, the results indicate that a diverging influx of gravitational energy, in concert with an outflux across the CH, is responsible for the singularity. The spacetime is asymptotically Petrov type N, the same algebraic type as a gravitational shock wave. Implications for the continuation of spacetime through the singularity are briefly discussed.Comment: 11 pages RevTeX, two postscript figures included using epsf.st

Charged AdS Black Holes and Catastrophic Holography

We compute the properties of a class of charged black holes in anti-de Sitter space-time, in diverse dimensions. These black holes are solutions of consistent Einstein-Maxwell truncations of gauged supergravities, which are shown to arise from the inclusion of rotation in the transverse space. We uncover rich thermodynamic phase structures for these systems, which display classic critical phenomena, including structures isomorphic to the van der Waals-Maxwell liquid-gas system. In that case, the phases are controlled by the universal `cusp' and `swallowtail' shapes familiar from catastrophe theory. All of the thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can sometimes be found on the world volumes of coincident rotating branes.Comment: 19 pages, revtex, psfig, 6 multicomponent figures, typos, references and a few remarks have been repaired, and adde

A phase 2, randomized, double-blind, placebo- controlled study of chemo-immunotherapy combination using motolimod with pegylated liposomal doxorubicin in recurrent or persistent ovarian cancer: a Gynecologic Oncology Group partners study.

A phase 2, randomized, placebo-controlled trial was conducted in women with recurrent epithelial ovarian carcinoma to evaluate the efficacy and safety of motolimod-a Toll-like receptor 8 (TLR8) agonist that stimulates robust innate immune responses-combined with pegylated liposomal doxorubicin (PLD), a chemotherapeutic that induces immunogenic cell death. Women with ovarian, fallopian tube, or primary peritoneal carcinoma were randomized 1 : 1 to receive PLD in combination with blinded motolimod or placebo. Randomization was stratified by platinum-free interval (≤6 versus &gt;6-12 months) and Gynecologic Oncology Group (GOG) performance status (0 versus 1). Treatment cycles were repeated every 28 days until disease progression. The addition of motolimod to PLD did not significantly improve overall survival (OS; log rank one-sided P = 0.923, HR = 1.22) or progression-free survival (PFS; log rank one-sided P = 0.943, HR = 1.21). The combination was well tolerated, with no synergistic or unexpected serious toxicity. Most patients experienced adverse events of fatigue, anemia, nausea, decreased white blood cells, and constipation. In pre-specified subgroup analyses, motolimod-treated patients who experienced injection site reactions (ISR) had a lower risk of death compared with those who did not experience ISR. Additionally, pre-treatment in vitro responses of immune biomarkers to TLR8 stimulation predicted OS outcomes in patients receiving motolimod on study. Immune score (tumor infiltrating lymphocytes; TIL), TLR8 single-nucleotide polymorphisms, mutational status in BRCA and other DNA repair genes, and autoantibody biomarkers did not correlate with OS or PFS. The addition of motolimod to PLD did not improve clinical outcomes compared with placebo. However, subset analyses identified statistically significant differences in the OS of motolimod-treated patients on the basis of ISR and in vitro immune responses. Collectively, these data may provide important clues for identifying patients for treatment with immunomodulatory agents in novel combinations and/or delivery approaches. Clinicaltrials.gov, NCT 01666444

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

HIV-related stigma within communities of gay men: A literature review

While stigma associated with HIV infection is well recognised, there is limited information on the impact of HIV-related stigma between men who have sex with men and within communities of gay men. The consequences of HIV-related stigma can be personal and community-wide, including impacts on mood and emotional well-being, prevention, testing behaviour, and mental and general health. This review of the literature reports a growing division between HIV-positive and HIV-negative gay men, and a fragmentation of gay communities based along lines of perceived or actual HIV status. The literature includes multiple references to HIV stigma and discrimination between gay men, men who have sex with men, and among and between many gay communities. This HIV stigma takes diverse forms and can incorporate aspects of social exclusion, ageism, discrimination based on physical appearance and health status, rejection and violence. By compiling the available information on this understudied form of HIV-related discrimination, we hope to better understand and target research and countermeasures aimed at reducing its impact at multiple levels

Regulation of 5-HT Receptors and the Hypothalamic-Pituitary-Adrenal Axis

Disturbances in the serotonin (5-HT) system is the neurobiological abnormality most consistently associated with suicide. Hyperactivity of the hypothalmic-pituitary-adrenal (HPA) axis is also described in suicide victims. The HPA axis is the classical neuroendocrine system that responds to stress and whose final product, corticosteroids, targets components of the limbic system, particularly the hippocampus. We will review resulsts from animal studies that point to the possibility that many of the 5-HT receptor changes observed in suicide brains may be a result of, or may be worsened by, the HPA overactivity that may be present in some suicide victims. The results of these studies can be summarized as follows: (1) chronic unpredictable stress produces high corticosteroid levels in rats; (2) chronic stress also results in changes in specific 5-HT receptors (increases in cortical 5-HT2A and decreases in hipocampal 5-HT1A and 5-HT1B); (3) chronic antidepressant administration prevents many of the 5-HT receptor changes observed after stress; and (4) chronic antidepressant administration reverses the overactivity of the HPA axis. If indeed 5-HT receptors have a partial role in controlling affective states, then their modulation by corticosteroids provides a potential mechanism by which these hormones may regulate mood. These data may also provide a biological understanding of how stressful events may increase the risk for suicide in vulnerable individuals and may help us elucidate the neurobiological underpinnings of treatment resistance.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73437/1/j.1749-6632.1997.tb52357.x.pd