Small-world MCMC and convergence to multi-modal distributions: From slow mixing to fast mixing

We compare convergence rates of Metropolis--Hastings chains to multi-modal target distributions when the proposal distributions can be of ``local'' and ``small world'' type. In particular, we show that by adding occasional long-range jumps to a given local proposal distribution, one can turn a chain that is ``slowly mixing'' (in the complexity of the problem) into a chain that is ``rapidly mixing.'' To do this, we obtain spectral gap estimates via a new state decomposition theorem and apply an isoperimetric inequality for log-concave probability measures. We discuss potential applicability of our result to Metropolis-coupled Markov chain Monte Carlo schemes.Comment: Published at http://dx.doi.org/10.1214/105051606000000772 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Opinion strength influences the spatial dynamics of opinion formation

Opinions are rarely binary; they can be held with different degrees of conviction, and this expanded attitude spectrum can affect the influence one opinion has on others. Our goal is to understand how different aspects of influence lead to recognizable spatio-temporal patterns of opinions and their strengths. To do this, we introduce a stochastic spatial agent-based model of opinion dynamics that includes a spectrum of opinion strengths and various possible rules for how the opinion strength of one individual affects the influence that this individual has on others. Through simulations, we find that even a small amount of amplification of opinion strength through interaction with like-minded neighbors can tip the scales in favor of polarization and deadlock

Spatial opinion dynamics and the effects of two types of mixing

Spatially situated opinions that can be held with different degrees of conviction lead to spatiotemporal patterns such as clustering (homophily), polarization, and deadlock. Our goal is to understand how sensitive these patterns are to changes in the local nature of interactions. We introduce two different mixing mechanisms, spatial relocation and nonlocal interaction (“telephoning”), to an earlier fully spatial model (no mixing). Interestingly, the mechanisms that create deadlock in the fully spatial model have the opposite effect when there is a sufficient amount of mixing. With telephoning, not only is polarization and deadlock broken up, but consensus is hastened. The effects of mixing by relocation are even more pronounced. Further insight into these dynamics is obtained for selected parameter regimes via comparison to the mean-field differential equations

Application of Ecological Network Theory to the Human Microbiome

In healthy humans, many microbial consortia constitute rich ecosystems with dozens to hundreds of species, finely tuned to functions relevant to human health. Medical interventions, lifestyle changes, and the normal rhythms of life sometimes upset the balance in microbial ecosystems, facilitating pathogen invasions or causing other clinically relevant problems. Some diseases, such as bacterial vaginosis, have exactly this sort of community etiology. Mathematical network theory is ideal for studying the ecological networks of interacting species that comprise the human microbiome. Theoretical networks require little consortia specific data to provide insight into both normal and disturbed microbial community functions, but it is easy to incorporate additional empirical data as it becomes available. We argue that understanding some diseases, such as bacterial vaginosis, requires a shift of focus from individual bacteria to (mathematical) networks of interacting populations, and that known emergent properties of these networks will provide insights that would be otherwise elusive

Risk of Major Complications From Coronary Angioplasty Performed Immediately After Diagnostic Coronary Angiography: Results From the Registry of the Society for Cardiac Angiography and Interventions

AbstractObjectives. This study was designed to determine the risk of performing percutaneous transluminal coronary angioplasty (PTCA) at the time of diagnostic catheterization (“combined procedures”).Background. Health care providers are under increasing pressure to combine diagnostic and interventional coronary procedures to reduce costs. However, the risk associated with combined procedures has not been rigorously assessed.Methods. A multicenter cohort study of 35,700 patients undergoing elective PTCA from 1992 through 1995 was performed to determine the risk of major complications (myocardial infarction, emergency coronary artery bypass graft surgery or death) from combined relative to staged procedures (i.e., performing PTCA at a session subsequent to diagnostic catheterization).Results. The risks of major complications from combined and staged procedures were 2.0% and 1.6%, respectively (unadjusted odds ratio [OR] 1.28, 95% confidence interval [CI] 1.05 to 1.57). After adjusting for clinical and angiographic differences and clustering by laboratory, the risk from combined procedures was not significantly elevated (multivariable OR 1.18, 95% CI 0.89 to 1.55). However, several subgroups of patients did have an increased risk from combined procedures: patients with multivessel disease (multivariable OR 1.64, 95% CI 1.13 to 2.39); women (multivariable OR 1.64, 95% CI 1.05 to 2.55); patients >65 years old (multivariable OR 1.40, 95% CI 1.02 to 1.93); and patients undergoing multilesion PTCA (multivariable OR 1.53, 95% CI 1.06 to 2.21). The risk of combined relative to staged procedures decreased over the 4-year period (multivariable p = 0.029).Conclusions. Combining PTCA with diagnostic catheterization appears to be safe in many patients. However, several subgroups of patients may be at increased risk. Careful patient selection will most likely remain critical to ensuring the safety of combined procedures.(J Am Coll Cardiol 1997;30:193–200

2D, 2.5D, or 3D? An Exploratory Study on Multilayer Network Visualisations in Virtual Reality

Relational information between different types of entities is often modelled by a multilayer network (MLN) -- a network with subnetworks represented by layers. The layers of an MLN can be arranged in different ways in a visual representation, however, the impact of the arrangement on the readability of the network is an open question. Therefore, we studied this impact for several commonly occurring tasks related to MLN analysis. Additionally, layer arrangements with a dimensionality beyond 2D, which are common in this scenario, motivate the use of stereoscopic displays. We ran a human subject study utilising a Virtual Reality headset to evaluate 2D, 2.5D, and 3D layer arrangements. The study employs six analysis tasks that cover the spectrum of an MLN task taxonomy, from path finding and pattern identification to comparisons between and across layers. We found no clear overall winner. However, we explore the task-to-arrangement space and derive empirical-based recommendations on the effective use of 2D, 2.5D, and 3D layer arrangements for MLNs.Comment: IEEE Transactions on Visualization and Computer Graphics, In press, To appear. Accepted to IEEE VIS 202

All-Sky Near Infrared Space Astrometry

Gaia is currently revolutionizing modern astronomy. However, much of the Galactic plane, center and the spiral arm regions are obscured by interstellar extinction, rendering them inaccessible because Gaia is an optical instrument. An all-sky near infrared (NIR) space observatory operating in the optical NIR, separated in time from the original Gaia would provide microarcsecond NIR astrometry and millimag photometry to penetrate obscured regions unraveling the internal dynamics of the Galaxy.Comment: 7 page

Pubertal presentation in seven patients with congenital adrenal hyperplasia due to P450 Oxidoreductase deficiency

Context: P450 oxidoreductase (POR) is a crucial electron donor to all microsomal P450 cytochrome (CYP) enzymes including 17α-hydroxylase (CYP17A1), 21-hydroxylase (CYP21A2) and P450 aromatase. Mutant POR causes congenital adrenal hyperplasia with combined glucocorticoid and sex steroid deficiency. P450 oxidoreductase deficiency (ORD) commonly presents neonatally, with disordered sex development in both sexes, skeletal malformations, and glucocorticoid deficiency. \ud \ud Objective: The aim of the study was to describe the clinical and biochemical characteristics of ORD during puberty. \ud \ud Design: Clinical, biochemical, and genetic assessment of seven ORD patients (five females, two males) presenting during puberty was conducted. \ud \ud Results: Predominant findings in females were incomplete pubertal development (four of five) and large ovarian cysts (five of five) prone to spontaneous rupture, in some only resolving after combined treatment with estrogen/progestin, GnRH superagonists, and glucocorticoids. Pubertal development in the two boys was more mildly affected, with some spontaneous progression. Urinary steroid profiling revealed combined CYP17A1 and CYP21A2 deficiencies indicative of ORD in all patients; all but one failed to mount an appropriate cortisol response to ACTH stimulation indicative of adrenal insufficiency. Diagnosis of ORD was confirmed by direct sequencing, demonstrating disease-causing POR mutations. \ud \ud Conclusion: Delayed and disordered puberty can be the first sign leading to a diagnosis of ORD. Appropriate testosterone production during puberty in affected boys but manifest primary hypogonadism in girls with ORD may indicate that testicular steroidogenesis is less dependent on POR than adrenal and ovarian steroidogenesis. Ovarian cysts in pubertal girls may be driven not only by high gonadotropins but possibly also by impaired CYP51A1-mediated production of meiosis-activating sterols due to mutant POR

2D, 2.5D, or 3D? An Exploratory Study on Multilayer Network Visualisations in Virtual Reality

Relational information between different types of entities is often modelled by a multilayer network (MLN) – a network with subnetworks represented by layers. The layers of an MLN can be arranged in different ways in a visual representation, however, the impact of the arrangement on the readability of the network is an open question. Therefore, we studied this impact for several commonly occurring tasks related to MLN analysis. Additionally, layer arrangements with a dimensionality beyond 2D, which are common in this scenario, motivate the use of stereoscopic displays. We ran a human subject study utilising a Virtual Reality headset to evaluate 2D, 2.5D, and 3D layer arrangements. The study employs six analysis tasks that cover the spectrum of an MLN task taxonomy, from path finding and pattern identification to comparisons between and across layers. We found no clear overall winner. However, we explore the task-to-arrangement space and derive empirical-based recommendations on the effective use of 2D, 2.5D, and 3D layer arrangements for MLNs