Critical properties of loop percolation models with optimization constraints

We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple cubic lattice by elementary loops leads to a percolation transition that is in the same universality class as the conventional bond percolation. In contrast to this an optimization constraint for the loop configurations, which then have to minimize a particular generic energy function, leads to a percolation transition that constitutes a new universality class, for which we report the critical exponents. Implication for the physics of solid-on-solid and vortex glass models are discussed.Comment: 8 pages, 8 figure

Definitions, methods, and applications in interpretable machine learning.

Machine-learning models have demonstrated great success in learning complex patterns that enable them to make predictions about unobserved data. In addition to using models for prediction, the ability to interpret what a model has learned is receiving an increasing amount of attention. However, this increased focus has led to considerable confusion about the notion of interpretability. In particular, it is unclear how the wide array of proposed interpretation methods are related and what common concepts can be used to evaluate them. We aim to address these concerns by defining interpretability in the context of machine learning and introducing the predictive, descriptive, relevant (PDR) framework for discussing interpretations. The PDR framework provides 3 overarching desiderata for evaluation: predictive accuracy, descriptive accuracy, and relevancy, with relevancy judged relative to a human audience. Moreover, to help manage the deluge of interpretation methods, we introduce a categorization of existing techniques into model-based and post hoc categories, with subgroups including sparsity, modularity, and simulatability. To demonstrate how practitioners can use the PDR framework to evaluate and understand interpretations, we provide numerous real-world examples. These examples highlight the often underappreciated role played by human audiences in discussions of interpretability. Finally, based on our framework, we discuss limitations of existing methods and directions for future work. We hope that this work will provide a common vocabulary that will make it easier for both practitioners and researchers to discuss and choose from the full range of interpretation methods

Prevalence, Determinants, and Consequences of Vestibular Hypofunction. Results From the KORA-FF4 Survey

Objective: Uni- or bilateral vestibular hypofunction (VH) impairs balance and mobility, and may specifically lead to injury from falls and to disability. The extent of this problem in the general population is still unknown and most likely to be underestimated. Objective of this study was to determine the prevalence, determinants, and consequences of VH in the general population.Methods: Data originates from the cross-sectional second follow-up (FF4) in 2013/14 of the KORA (Cooperative Health Research in the Region of Augsburg)-S4 study (1999–2001) from Southern Germany. This was a random sample of the target population consisting of all residents of the region aged 25–74 years in 1999. We included all participants who reported moderate or severe vertigo or dizziness during the last 12 months and a random sub-sample of participants representative for the general population without vertigo or dizziness during the last 12 months were tested. VH was assessed with the Video-Head Impulse Test (vHIT). Trained examiners applied high-acceleration, small-amplitude passive head rotations (“head impulses”) to the left and right in the plane of the horizontal semicircular canals while participants fixated a target straight ahead. During head impulses, head movements were measured with inertial sensors, eye movements with video-oculography (EyeSeeCam vHIT).Results: A total of 2,279 participants were included (mean age 60.8 years, 51.6% female), 570 (25.0%) with moderate or severe vertigo or dizziness during the last 12 months. Of these, 450 were assessed with vHIT where 26 (5.8%) had unilateral VH, and 16 (3.6%) had bilateral VH. Likewise, 190 asymptomatic participants were tested. Of these 5 (2.6%) had unilateral VH, and 2 (1.1%) had bilateral VH. Prevalence of uni- or bilateral VH among tested symptomatic participants was 2.4% in those < 48 years, and 32.1% in individuals aged 79 and over. Age-adjusted prevalence was 6.7% (95% CI 4.8%; 8.6%). VH was associated with worse health, falls, hearing loss, hearing impairment, and ear pressure.Conclusion: VH may affect between 53 and 95 million adults in Europe and the US. While not all affected persons will experience the full spectrum of symptoms and consequences, adequate diagnostic and therapeutic measures should become standard of care to decrease the burden of disease

Der Weismannstadel in Hemau

Bei dem im Jahre 1824 erbauten Weismannstadel in der Dietfurter Straße 16 in Hemau handelt es sich um einen Jurastadel, also um eine Scheune mit Kalkplattendach. Bis in die Mitte des 20. Jahrhunderts haben Gebäude mit einer solchen Dachdeckung das Altmühlgebiet und damit auch die südwestliche Oberpfalz geprägt. Heute gibt es jedoch nur noch wenige Beispiele dieser einzigartigen ländlichen Baukultur. Auch der Weismannstadel sollte nach langem Leerstand abgerissen und durch eine Wohnanlage oder Parkplätze ersetzt werden. Die Familie Semmler aus Hemau hat ihn buchstäblich in letzter Minute vor diesem Schicksal bewahrt und zwischen 2011 und 2013 vorbildlich saniert. Der Band informiert über die Geschichte und Bedeutung des Stadels und dokumentiert seine denkmalgerechte Instandsetzung. Gedruckte Exemplare (Hardcover, 72 S., 21 x 27 cm) können für 11,80 € (zzgl. Porto) direkt beim Verlag Th. Feuerer bezogen werden

Universality and Critical Phenomena in String Defect Statistics

The idea of biased symmetries to avoid or alleviate cosmological problems caused by the appearance of some topological defects is familiar in the context of domain walls, where the defect statistics lend themselves naturally to a percolation theory description, and for cosmic strings, where the proportion of infinite strings can be varied or disappear entirely depending on the bias in the symmetry. In this paper we measure the initial configurational statistics of a network of string defects after a symmetry-breaking phase transition with initial bias in the symmetry of the ground state. Using an improved algorithm, which is useful for a more general class of self-interacting walks on an infinite lattice, we extend the work in \cite{MHKS} to better statistics and a different ground state manifold, namely $\R P^2$, and explore various different discretisations. Within the statistical errors, the critical exponents of the Hagedorn transition are found to be quite possibly universal and identical to the critical exponents of three-dimensional bond or site percolation. This improves our understanding of the percolation theory description of defect statistics after a biased phase transition, as proposed in \cite{MHKS}. We also find strong evidence that the existence of infinite strings in the Vachaspati Vilenkin algorithm is generic to all (string-bearing) vacuum manifolds, all discretisations thereof, and all regular three-dimensional lattices.Comment: 62 pages, plain LaTeX, macro mathsymb.sty included, figures included. also available on http://starsky.pcss.maps.susx.ac.uk/groups/pt/preprints/96/96011.ps.g