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

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

Can the Future of ID Escape the Inertial Dogma of Its Past? The Exemplars of Shorter Is Better and Oral Is the New IV.

Like all fields of medicine, Infectious Diseases is rife with dogma that underpins much clinical practice. In this study, we discuss 2 specific examples of historical practice that have been overturned recently by numerous prospective studies: traditional durations of antimicrobial therapy and the necessity of intravenous (IV)-only therapy for specific infectious syndromes. These dogmas are based on uncontrolled case series from >50 years ago, amplified by the opinions of eminent experts. In contrast, more than 120 modern, randomized controlled trials have established that shorter durations of therapy are equally effective for many infections. Furthermore, 21 concordant randomized controlled trials have demonstrated that oral antibiotic therapy is at least as effective as IV-only therapy for osteomyelitis, bacteremia, and endocarditis. Nevertheless, practitioners in many clinical settings remain refractory to adopting these changes. It is time for Infectious Diseases to move beyond its history of eminent opinion-based medicine and truly into the era of evidenced-based medicine

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

The (Mis)appropriation of HIV/AIDS advocacy strategies in Global Mental Health: towards a more nuanced approach

Background: Mental health is increasingly finding a place on global health and international development agendas. Advocates for Global Mental Health (GMH), and international organizations such as the World Health Organization (WHO) and the World Bank, argue that treatments available in high-income countries should also be made available in low- and middle-income countries. Such arguments are often made by comparing mental health to infectious diseases, including the relative disease and economic burdens they impose, and pointing to the applicability of the right to access treatment for mental health, not only infectious diseases. HIV/AIDS advocacy in particular has been held up by GMH advocates as offering an appropriate strategy for generating global commitment. Discussion: There is a need to assess how health issues are framed not only in relation to social goods outside of health (such as human rights, security or development), but also in relation to other health or disease models, and how health policy and practice is shaped as a result. The article debates the merits and consequences of likening mental health to HIV/AIDS, and identifies four major problems with the model for GMH advocacy being developed through these analogies: 1. An inappropriately universalizing global approach to context-specific problems; 2. A conception of human rights that focuses on the right to access treatment at the expense of the right to refuse it; 3. A tendency to treat poverty as a psychiatric issue, rather than recognizing that mental distress can be the result of poverty and other forms of inequality; 4. The prioritization of destigmatization of disease over social justice models. Conclusion: There are significant problems with the wholesale adoption of an (often simplified) version of HIV/AIDS advocacy as a model for GMH. Yet critical engagement with the important and nuanced differences between HIV/AIDS and mental health may nevertheless point to some possibilities for productive engagement and cross-fertilisation between advocates, activists and scholars in both fields

Guidelines for the management of gastroenteropancreatic neuroendocrine (including carcinoid) tumours (NETs)

These guidelines update previous guidance published in 2005. They have been revised by a group who are members of the UK and Ireland Neuroendocrine Tumour Society with endorsement from the clinical committees of the British Society of Gastroenterology, the Society for Endocrinology, the Association of Surgeons of Great Britain and Ireland (and its Surgical Specialty Associations), the British Society of Gastrointestinal and Abdominal Radiology and others. The authorship represents leaders of the various groups in the UK and Ireland Neuroendocrine Tumour Society, but a large amount of work has been carried out by other specialists, many of whom attended a guidelines conference in May 2009. We have attempted to represent this work in the acknowledgements section. Over the past few years, there have been advances in the management of neuroendocrine tumours, which have included clearer characterisation, more specific and therapeutically relevant diagnosis, and improved treatments. However, there remain few randomised trials in the field and the disease is uncommon, hence all evidence must be considered weak in comparison with other more common cancers

Use of Novel Strategies to Develop Guidelines for Management of Pyogenic Osteomyelitis in Adults: A WikiGuidelines Group Consensus Statement.

Importance Traditional approaches to practice guidelines frequently result in dissociation between strength of recommendation and quality of evidence. Objective To construct a clinical guideline for pyogenic osteomyelitis management, with a new standard of evidence to resolve the gap between strength of recommendation and quality of evidence, through the use of a novel open access approach utilizing social media tools. Evidence Review This consensus statement and systematic review study used a novel approach from the WikiGuidelines Group, an open access collaborative research project, to construct clinical guidelines for pyogenic osteomyelitis. In June 2021 and February 2022, authors recruited via social media conducted multiple PubMed literature searches, including all years and languages, regarding osteomyelitis management; criteria for article quality and inclusion were specified in the group's charter. The GRADE system for evaluating evidence was not used based on previously published concerns regarding the potential dissociation between strength of recommendation and quality of evidence. Instead, the charter required that clear recommendations be made only when reproducible, prospective, controlled studies provided hypothesis-confirming evidence. In the absence of such data, clinical reviews were drafted to discuss pros and cons of care choices. Both clear recommendations and clinical reviews were planned with the intention to be regularly updated as new data become available. Findings Sixty-three participants with diverse expertise from 8 countries developed the group's charter and its first guideline on pyogenic osteomyelitis. These participants included both nonacademic and academic physicians and pharmacists specializing in general internal medicine or hospital medicine, infectious diseases, orthopedic surgery, pharmacology, and medical microbiology. Of the 7 questions addressed in the guideline, 2 clear recommendations were offered for the use of oral antibiotic therapy and the duration of therapy. In addition, 5 clinical reviews were authored addressing diagnosis, approaches to osteomyelitis underlying a pressure ulcer, timing for the administration of empirical therapy, specific antimicrobial options (including empirical regimens, use of antimicrobials targeting resistant pathogens, the role of bone penetration, and the use of rifampin as adjunctive therapy), and the role of biomarkers and imaging to assess responses to therapy. Conclusions and Relevance The WikiGuidelines approach offers a novel methodology for clinical guideline development that precludes recommendations based on low-quality data or opinion. The primary limitation is the need for more rigorous clinical investigations, enabling additional clear recommendations for clinical questions currently unresolved by high-quality data