Conformal Invariance in Percolation, Self-Avoiding Walks and Related Problems

Over the years, problems like percolation and self-avoiding walks have provided important testing grounds for our understanding of the nature of the critical state. I describe some very recent ideas, as well as some older ones, which cast light both on these problems themselves and on the quantum field theories to which they correspond. These ideas come from conformal field theory, Coulomb gas mappings, and stochastic Loewner evolution.Comment: Plenary talk given at TH-2002, Paris. 21 pages, 9 figure

The extreme vulnerability of interdependent spatially embedded networks

Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abruptly fragment the system, while below this "critical dependency" (CD) a failure of few nodes leads only to small damage to the system. So far, the research has been focused on interdependent random networks without space limitations. However, many real systems, such as power grids and the Internet, are not random but are spatially embedded. Here we analytically and numerically analyze the stability of systems consisting of interdependent spatially embedded networks modeled as lattice networks. Surprisingly, we find that in lattice systems, in contrast to non-embedded systems, there is no CD and \textit{any} small fraction of interdependent nodes leads to an abrupt collapse. We show that this extreme vulnerability of very weakly coupled lattices is a consequence of the critical exponent describing the percolation transition of a single lattice. Our results are important for understanding the vulnerabilities and for designing robust interdependent spatial embedded networks.Comment: 13 pages, 5 figure

Full quantum distribution of contrast in interference experiments between interacting one dimensional Bose liquids

We analyze interference experiments for a pair of independent one dimensional condensates of interacting bosonic atoms at zero temperature. We show that the distribution function of fringe amplitudes contains non-trivial information about non-local correlations within individual condensates and can be calculated explicitly using methods of conformal field theory. We point out interesting relations between these distribution functions, the partition function for a quantum impurity in a one-dimensional Luttinger liquid, and transfer matrices of conformal field theories. We demonstrate the connection between interference experiments in cold atoms and a variety of statistical models ranging from stochastic growth models to two dimensional quantum gravity. Such connection can be used to design a quantum simulator of unusual two-dimensional models described by nonunitary conformal field theories with negative central charges.Comment: 9 pages, 5 figures; Accepted for publication in Nature Physic

Scale invariance and universality of force networks in static granular matter

Force networks form the skeleton of static granular matter. They are the key ingredient to mechanical properties, such as stability, elasticity and sound transmission, which are of utmost importance for civil engineering and industrial processing. Previous studies have focused on the global structure of external forces (the boundary condition), and on the probability distribution of individual contact forces. The disordered spatial structure of the force network, however, has remained elusive so far. Here we report evidence for scale invariance of clusters of particles that interact via relatively strong forces. We analyzed granular packings generated by molecular dynamics simulations mimicking real granular matter; despite the visual variation, force networks for various values of the confining pressure and other parameters have identical scaling exponents and scaling function, and thus determine a universality class. Remarkably, the flat ensemble of force configurations--a simple generalization of equilibrium statistical mechanics--belongs to the same universality class, while some widely studied simplified models do not.Comment: 15 pages, 4 figures; to appear in Natur

Calibration of myocardial T2 and T1 against iron concentration.

BACKGROUND: The assessment of myocardial iron using T2* cardiovascular magnetic resonance (CMR) has been validated and calibrated, and is in clinical use. However, there is very limited data assessing the relaxation parameters T1 and T2 for measurement of human myocardial iron. METHODS: Twelve hearts were examined from transfusion-dependent patients: 11 with end-stage heart failure, either following death (n=7) or cardiac transplantation (n=4), and 1 heart from a patient who died from a stroke with no cardiac iron loading. Ex-vivo R1 and R2 measurements (R1=1/T1 and R2=1/T2) at 1.5 Tesla were compared with myocardial iron concentration measured using inductively coupled plasma atomic emission spectroscopy. RESULTS: From a single myocardial slice in formalin which was repeatedly examined, a modest decrease in T2 was observed with time, from mean (± SD) 23.7 ± 0.93 ms at baseline (13 days after death and formalin fixation) to 18.5 ± 1.41 ms at day 566 (p<0.001). Raw T2 values were therefore adjusted to correct for this fall over time. Myocardial R2 was correlated with iron concentration [Fe] (R2 0.566, p<0.001), but the correlation was stronger between LnR2 and Ln[Fe] (R2 0.790, p<0.001). The relation was [Fe] = 5081•(T2)-2.22 between T2 (ms) and myocardial iron (mg/g dry weight). Analysis of T1 proved challenging with a dichotomous distribution of T1, with very short T1 (mean 72.3 ± 25.8 ms) that was independent of iron concentration in all hearts stored in formalin for greater than 12 months. In the remaining hearts stored for <10 weeks prior to scanning, LnR1 and iron concentration were correlated but with marked scatter (R2 0.517, p<0.001). A linear relationship was present between T1 and T2 in the hearts stored for a short period (R2 0.657, p<0.001). CONCLUSION: Myocardial T2 correlates well with myocardial iron concentration, which raises the possibility that T2 may provide additive information to T2* for patients with myocardial siderosis. However, ex-vivo T1 measurements are less reliable due to the severe chemical effects of formalin on T1 shortening, and therefore T1 calibration may only be practical from in-vivo human studies

Laboratory diagnosis of Buruli ulcer : challenges and future perspectives

Current options to control Buruli ulcer (BU) are limited, as no effective vaccine is available and knowledge on transmission mechanisms of the causative agent, Mycobacterium ulcerans, is incomplete. Early case detection and rapid initiation of treatment are key elements to prevent the development of large, disfiguring ulcers often associated with permanent physical disability and stigma. BU has been reported from 34 countries, with the greatest disease burden in West Africa and steadily increasing case numbers in south-eastern Australia. The disease can present in a variety of clinical manifestations, including relatively unspecific, painless nodules, plaques, and edema, which may eventually progress to chronic, ulcerative lesions. The clinical diagnosis of BU is therefore complicated by a broad differential diagnosis, particularly in tropical areas, where the prevalence of other skin conditions with a similar appearance is high. With the introduction of combination antibiotic therapy, replacing excision surgery as the standard treatment for BU, pre-treatment confirmation of the clinical diagnosis has further gained in importance to avoid the redundant use of anti-mycobacterial drugs. At present, available confirmatory diagnostic tests either lack sufficient sensitivity/specificity or are centralized and thus often not accessible to patients living in remote, rural areas of Africa. In recognition of this disparity, WHO and other stakeholders have called for new diagnostic tools for BU that can be applied at district hospitals or primary healthcare facilities. This chapter highlights challenges, advances and future prospects for the necessary decentralization of the diagnosis of BU

Risks to pollinators and pollination from invasive alien species

Invasive alien species modify pollinator biodiversity and the services they provide that underpin ecosystem function and human well-being. Building on the Intergovernmental Science-Policy Platform for Biodiversity and Ecosystem Services (IPBES) global assessment of pollinators and pollination, we synthesize current understanding of invasive alien impacts on pollinators and pollination. Invasive alien species create risks and opportunities for pollinator nutrition, re-organize species interactions to affect native pollination and community stability, and spread and select for virulent diseases. Risks are complex but substantial, and depend greatly on the ecological function and evolutionary history of both the invader and the recipient ecosystem. We highlight evolutionary implications for pollination from invasive alien species, and identify future research directions, key messages and options for decision-making

First‐Order River Delta Morphology Is Explained by the Sediment Flux Balance From Rivers, Waves, and Tides

We present a novel quantitative test of a 50-year-old hypothesis which asserts that river delta morphology is determined by the balance between river and marine influence. We define three metrics to capture the first-order morphology of deltas (shoreline roughness, number of distributary channel mouths, and presence/absence of spits), and use a recently developed sediment flux framework to quantify the river-marine influence. Through analysis of simulated and field deltas we quantitatively demonstrate the relationship between sediment flux balance and delta morphology and show that the flux balance accounts for at least 35% of the variance in the number of distributary channel mouths and 42% of the variance in the shoreline roughness for real-world and simulated deltas. We identify a tipping point in the flux balance where wave influence halts distributary channel formation and show how this explains morphological transitions in real world deltas

River Delta Morphotypes Emerge From Multiscale Characterization of Shorelines

Delta shoreline structure has long been hypothesized to encode information on the relative influence of fluvial, wave, and tidal processes on delta formation and evolution. We introduce here a novel multiscale characterization of shorelines by defining three process-informed morphological metrics. We show that this characterization yields self-emerging classes of morphologically similar deltas, that is, delta morphotypes, and also predicts the dominant forcing of each morphotype. Then we show that the dominant forcings inferred from shoreline structure generally align with those estimated via relative sediment fluxes, while positing that misalignments arise from spatiotemporal heterogeneity in deltaic sediment fluxes not captured in their estimates. The proposed framework for shoreline characterization advances our quantitative understanding of how shoreline features reflect delta forcings, and may aid in deciphering paleoclimate from images of ancient deposits and projecting delta morphologic response to changes in sediment fluxes