The Alexander-Orbach conjecture holds in high dimensions

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.Comment: 25 pages, 2 figures. To appear in Inventiones Mathematica

The utility of hand-held mobile spirometer technology in a resource-constrained setting

CITATION: Du Plessis, E., et al. 2019. The utility of hand-held mobile spirometer technology in a resource-constrained setting. South African Medical Journal, 109(4):219-222, doi:10.7196/SAMJ.2019.v109i4.13845.The original publication is available at http://www.samj.org.zaBackground. Mobile phone-linked spirometry technology has been designed specifically for evaluating lung function at primary care level. The Air-Smart Spirometer is the first mobile spirometer accepted in Europe for the screening of patients with chronic respiratory diseases. Objectives. To prospectively assess the accuracy of the device in measuring forced expiratory volume in the first second (FEV1) and forced vital capacity (FVC) in a South African population, and to investigate the ability of the device to detect obstructive ventilatory impairment. Methods. A total of 200 participants were randomly assigned to perform spirometry with either the mobile spirometer connected to a smartphone or the desktop spirometer first, followed by the other. The FEV1/FVC ratio as well as the absolute FEV1 and FVC measurements were compared, using each participant as their own control. A Pearson correlation and Bland-Altman analysis were performed to measure the agreement between the two devices. We defined obstructive ventilatory impairment as FEV1/FVC <0.7 measured by desktop spirometry in order to calculate the sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) of the Air-Smart Spirometer. Results. There was a strong correlation between the absolute FEV1 and FVC values and FEV1/FVC ratio measured with the mobile Air-Smart Spirometer and more conventional pulmonary function testing, with r=0.951, r=0.955 and r=0.898, respectively. The Air-Smart Spirometer had a sensitivity of 97.6%, specificity of 74.4%, PPV of 73.0% and NPV of 97.8% for obstructive ventilatory impairment. Conclusions. The mobile Air-Smart Spirometer compared well with conventional spirometry, making it an attractive and potentially affordable tool for screening purposes in a primary care setting. Moreover, it had a high sensitivity and NPV for obstructive ventilatory impairment.http://www.samj.org.za/index.php/samj/article/view/12582Publisher's versio

Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk

We consider self-avoiding walk, percolation and the Ising model with long and finite range. By means of the lace expansion we prove mean-field behavior for these models if $d>2(\alpha\wedge2)$ for self-avoiding walk and the Ising model, and $d>3(\alpha\wedge2)$ for percolation, where $d$ denotes the dimension and $\alpha$ the power-law decay exponent of the coupling function. We provide a simplified analysis of the lace expansion based on the trigonometric approach in Borgs et al. (2007)Comment: 43 pages, many figures. Version v2 with various (minor) changes (in particular in Sections 1.4 and A.1), and Sect. 4 is shortened. Journal of Statistical Physics (to appear

Decentralized subcontractor scheduling with divisible jobs

Subcontracting allows manufacturer agents to reduce completion times of their jobs and thus obtain savings. This paper addresses the coordination of decentralized scheduling systems with a single subcontractor and several agents having divisible jobs. Assuming complete information, we design parametric pricing schemes that strongly coordinate this decentralized system, i.e., the agents’ choices of subcontracting intervals always result in efficient schedules. The subcontractor’s revenue under the pricing schemes depends on a single parameter which can be chosen to make the revenue as close to the total savings as required. Also, we give a lower bound on the subcontractor’s revenue for any coordinating pricing scheme. Allowing private information about processing times, we prove that the pivotal mechanism is coordinating, i.e., agents are better off by reporting their true processing times, and by participating in the subcontracting. We show that the subcontractor’s maximum revenue with any coordinating mechanism under private information equals the lower bound of that with coordinating pricing schemes under complete information. Finally, we address the asymmetric case where agents obtain savings at different rates per unit reduction in completion times. We show that coordinating pricing schemes do not always exist in this case

Risk measures for direct real estate investments with non-normal or unknown return distributions

The volatility of returns is probably the most widely used risk measure for real estate. This is rather surprising since a number of studies have cast doubts on the view that volatility can capture the manifold risks attached to properties and corresponds to the risk attitude of investors. A central issue in this discussion is the statistical properties of real estate returns—in contrast to neoclassical capital market theory they are mostly non-normal and often unknown, which render many statistical measures useless. Based on a literature review and an analysis of data from Germany we provide evidence that volatility alone is inappropriate for measuring the risk of direct real estate. We use a unique data sample by IPD, which includes the total returns of 939 properties across different usage types (56% office, 20% retail, 8% others and 16% residential properties) from 1996 to 2009, the German IPD Index, and the German Property Index. The analysis of the distributional characteristics shows that German real estate returns in this period were not normally distributed and that a logistic distribution would have been a better fit. This is in line with most of the current literature on this subject and leads to the question which indicators are more appropriate to measure real estate risks. We suggest that a combination of quantitative and qualitative risk measures more adequately captures real estate risks and conforms better with investor attitudes to risk. Furthermore, we present criteria for the purpose of risk classification

Euclid Preparation. XXVIII. Forecasts for ten different higher-order weak lensing statistics

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set of $Euclid$-like mocks, derived from N-body simulations. In this first paper of the HOWLS series, we computed the nontomographic ($\Omega_{\rm m}$, $\sigma_8$) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a $4.5$ times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses with $Euclid$. The data used in this analysis are publicly released with the paper

Current challenges facing the assessment of the allergenic capacity of food allergens in animal models

Food allergy is a major health problem of increasing concern. The insufficiency of protein sources for human nutrition in a world with a growing population is also a significant problem. The introduction of new protein sources into the diet, such as newly developed innovative foods or foods produced using new technologies and production processes, insects, algae, duckweed, or agricultural products from third countries, creates the opportunity for development of new food allergies, and this in turn has driven the need to develop test methods capable of characterizing the allergenic potential of novel food proteins. There is no doubt that robust and reliable animal models for the identification and characterization of food allergens would be valuable tools for safety assessment. However, although various animal models have been proposed for this purpose, to date, none have been formally validated as predictive and none are currently suitable to test the allergenic potential of new foods. Here, the design of various animal models are reviewed, including among others considerations of species and strain, diet, route of administration, dose and formulation of the test protein, relevant controls and endpoints measured