The dimension of the range of a transient random walk

We find formulas for the macroscopic Minkowski and Hausdorff dimensions of the range of an arbitrary transient walk in Z^d. This endeavor solves a problem of Barlow and Taylor (1991).Comment: 37 pages, 5 figure

Ethnographic perspectives on global mental health

The field of Global Mental Health (GMH) aims to influence mental health policy and practice worldwide, with a focus on human rights and access to care. There have been important achievements, but GMH has also been the focus of scholarly controversies arising from political, cultural and pragmatic critiques. These debates have become increasingly polarized, giving rise to a need for more dialogue and experience-near research to inform theorizing. Ethnography has much to offer in this respect. This paper frames and introduces five articles in the issue of Transcultural Psychiatry that illustrate the role of ethnographic methods in understanding the effects and implications of the field of global mental health on mental health policy and practice. The papers include ethnographies from South Africa, India and Tonga, that show the potential for ethnographic evidence to inform GMH projects. These studies provide nuanced conceptualizations of GMH’s varied manifestations across different settings, the diverse ways that GMH’s achievements can be evaluated, and the connections that can be drawn between locally observed experiences and wider historical, political and social phenomena. Ethnography can provide a basis for constructive dialogue between those engaged in developing and implementing GMH interventions and those critical of some of its approaches

Dynamical percolation on general trees

H\"aggstr\"om, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph $G$. When $G$ is a tree they derived a necessary and sufficient condition for percolation to exist at some time $t$. In the case that $G$ is a spherically symmetric tree, H\"aggstr\"om, Peres, and Steif (1997) derived a necessary and sufficient condition for percolation to exist at some time $t$ in a given target set $D$. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time $t\in D$, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation.Comment: 24 pages; to appear in Probability Theory and Related Field

A macroscopic multifractal analysis of parabolic stochastic PDEs

It is generally argued that the solution to a stochastic PDE with multiplicative noise---such as $\dot{u}=\frac12 u"+u\xi$, where $\xi$ denotes space-time white noise---routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (2005), Gibbon and Titi (2005), and Zimmermann et al (2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (1989; 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE.Comment: 41 page

Near complete response after single dose of nivolumab in patient with advanced heavily pre-treated KRAS mutant pulmonary adenocarcinoma

The programmed death 1 (PD-1) receptor is expressed by activated T-cells and engaged by ligands PD-L1 and PD-L2 normally expressed by infiltrating immune cells in response to viral infection. The PD-1/PD-L1 axis is a negative inhibitory pathway that down-regulates T-cells but is also used by tumors to evade anti-tumor immunity. Antibodies targeting PD-1/PD-L1 axis are capable of restoring functional anti-tumor immunity and have demonstrated efficacy in a broad range of tumor types including non-small cell lung cancer in both squamous and adenocarcinoma histologies. Ongoing issues affecting clinical development of these agents include assessment of response, optimal duration of therapy in excellent responders, predictive biomarkers and mechanisms of resistance. In this report, we describe a patient with advanced KRAS mutant heavily pretreated pulmonary adenocarcinoma who developed an excellent response after a single-dose of nivolumab. Pre-treatment tumor was found to have moderate CD3 and PD-L1 positivity by immunohistochemical staining. Evaluation of exceptional responders and non-responders are critical to furthering our understanding of the mechanisms of action (and resistance) to these agents

A workflow for patient-specific fluid-structure interaction analysis of the mitral valve: A proof of concept on a mitral regurgitation case

The mechanics of the mitral valve (MV) are the result of the interaction of different anatomical structures complexly arranged within the left heart (LH), with the blood flow. MV structure abnormalities might cause valve regurgitation which in turn can lead to heart failure. Patient-specific computational models of the MV could provide a personalised understanding of MV mechanics, dysfunctions and possible interventions. In this study, we propose a semi-automatic pipeline for MV modelling based on the integration of state-of-the-art medical imaging, i.e. cardiac magnetic resonance (CMR) and 3D transoesophageal-echocardiogram (TOE) with fluid-structure interaction (FSI) simulations. An FSI model of a patient with MV regurgitation was implemented using the finite element (FE) method and smoothed particle hydrodynamics (SPH). Our study showed the feasibility of combining image information and computer simulations to reproduce patient-specific MV mechanics as seen on medical images, and the potential for efficient in-silico studies of MV disease, personalised treatments and device design