Active Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models

Segmentation is a fundamental task for extracting semantically meaningful regions from an image. The goal of segmentation algorithms is to accurately assign object labels to each image location. However, image-noise, shortcomings of algorithms, and image ambiguities cause uncertainty in label assignment. Estimating the uncertainty in label assignment is important in multiple application domains, such as segmenting tumors from medical images for radiation treatment planning. One way to estimate these uncertainties is through the computation of posteriors of Bayesian models, which is computationally prohibitive for many practical applications. On the other hand, most computationally efficient methods fail to estimate label uncertainty. We therefore propose in this paper the Active Mean Fields (AMF) approach, a technique based on Bayesian modeling that uses a mean-field approximation to efficiently compute a segmentation and its corresponding uncertainty. Based on a variational formulation, the resulting convex model combines any label-likelihood measure with a prior on the length of the segmentation boundary. A specific implementation of that model is the Chan-Vese segmentation model (CV), in which the binary segmentation task is defined by a Gaussian likelihood and a prior regularizing the length of the segmentation boundary. Furthermore, the Euler-Lagrange equations derived from the AMF model are equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image denoising. Solutions to the AMF model can thus be implemented by directly utilizing highly-efficient ROF solvers on log-likelihood ratio fields. We qualitatively assess the approach on synthetic data as well as on real natural and medical images. For a quantitative evaluation, we apply our approach to the icgbench dataset

Theory of the n=2 levels in muonic deuterium

The present knowledge of Lamb shift, fine- and hyperfine structure of the $\mathrm{2S}$ and $\mathrm{2P}$ states in muonic deuterium is reviewed in anticipation of the results of a first measurement of several $\mathrm{2S-2P}$ transition frequencies in muonic deuterium ($\mu\mathrm{d}$). A term-by-term comparison of all available sources reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift, which are essential for a determination of the deuteron rms charge radius from $\mu\mathrm{d}$. Apparent discrepancies between different sources are resolved, in particular for the difficult two-photon exchange contributions. Problematic single-sourced terms are identified which require independent recalculation.Comment: 26 pages, add missing feynman diagrams (Fig. 3), renumber items (Tab. IV), correct a sum (column 5, Tab. IV

Equidistribution of cusp points of Hecke triangle groups

In the framework of infinite ergodic theory, we derive equidistribution results for suitable weighted sequences of cusp points of Hecke triangle groups encoded by group elements of constant word length with respect to a set of natural generators. This is a generalization of the corresponding results for the modular group, for which we rely on advanced results from infinite ergodic theory and transfer operator techniques developed for AFN-maps.Comment: 29 pages, 2 figure

When Leader-member exchanges make workers happy and innovative: do efforts and rewards act as mediators?

Today innovation is considered to be essential for organizational development, and organizations depend increasingly on employees’ efforts to innovate. Drawing on the eudemonic theory of well-being based on the idea of optimal functioning, we look at whether rewards and efforts act as mediators between leader-member exchange (LMX) and two dependent variables: well-being at work and innovative work behaviors (IWB). We examine how LMX is linked to IWB and well-being at work, and we test the mediating effects of workload and rewards in these links. A sample of 179 French workers responded to an online questionnaire. The results indicated that LMX was significantly linked to IWB and psychological well-being at work. The study also found an indirect effect of work rewards between LMX and psychological well-being at work. This mediating role was not found in the relationship between LMX and IWB.Hoy en día se considera que la innovación es esencial para el desarrollo organizativo, y las organizaciones dependen cada vez más de los esfuerzos de los empleados por innovar. Partiendo de la teoría eudemónica del bienestar basada en la idea del funcionamiento óptimo, examinamos si las recompensas y los esfuerzos actúan como mediadores entre el intercambio líder-miembro (LMX) y dos variables dependientes: el bienestar en el trabajo y los comportamientos laborales innovadores (IWB). Examinamos cómo el LMX está vinculado al IWB y al bienestar en el trabajo, y comprobamos los efectos mediadores de la carga de trabajo y las recompensas en estos vínculos. Una muestra de 179 trabajadores franceses respondió a un cuestionario en línea. Los resultados indicaron que la LMX estaba significativamente vinculada a la IWB y al bienestar psicológico en el trabajo. El estudio también encontró un efecto indirecto de las recompensas laborales entre la LMX y el bienestar psicológico en el trabajo. Este papel mediador no se encontró en la relación entre LMX y IWB

Asymmetric Rydberg blockade of giant excitons in cuprous oxide

The ability to generate and control strong long-range interactions via highly excited electronic states has been the foundation for recent breakthroughs in a host of areas, from atomic and molecular physics to quantum optics and technology. Rydberg excitons provide a promising solid-state realization of such highly excited states, for which record-breaking orbital sizes of up to a micrometer have indeed been observed in cuprous oxide semiconductors. Here, we demonstrate the generation and control of strong exciton interactions in this material by optically producing two distinct quantum states of Rydberg excitons. This is made possible by two-color pump-probe experiments that allow for a detailed probing of the interactions. Our experiments reveal the emergence of strong spatial correlations and an inter-state Rydberg blockade that extends over remarkably large distances of several micrometers. The generated many-body states of semiconductor excitons exhibit universal properties that only depend on the shape of the interaction potential and yield clear evidence for its vastly extended-range and power-law character

Asymmetric Rydberg blockade of giant excitons in Cuprous Oxide

The ability to generate and control strong long-range interactions via highly excited electronic states has been the foundation for recent breakthroughs in a host of areas, from atomic and molecular physics [1, 2] to quantum optics [3, 4] and technology [5-7]. Rydberg excitons provide a promising solid-state realization of such highly excited states, for which record-breaking orbital sizes of up to a micrometer have indeed been observed in cuprous oxide semiconductors [8]. Here, we demonstrate the generation and control of strong exciton interactions in this material by optically producing two distinct quantum states of Rydberg excitons. This makes two-color pump-probe experiments possible that allow for a detailed probing of the interactions. Our experiments reveal the emergence of strong spatial correlations and an inter-state Rydberg blockade that extends over remarkably large distances of several micrometers. The generated many-body states of semiconductor excitons exhibit universal properties that only depend on the shape of the interaction potential and yield clear evidence for its vastly extended-range and power-law character.Comment: Main script: 7 pages, 3 figures. Supplementary file 15 pages, 5 figure

Industrie 4.0 und die Folgen für Arbeitsmarkt und Wirtschaft: Szenario-Rechnungen im Rahmen der BIBB-IAB-Qualifikations- und Berufsfeldprojektionen

Mit diesem Forschungsbericht liegt die erste modellbasierte Wirkungsabschätzung von Industrie 4.0 auf Arbeitsmarkt und Wirtschaft in Deutschland vor. In einer 5-stufigen Szenario-Analyse werden zunächst die Auswirkungen von erhöhten Investitionen in Ausrüstungen (1) und Bau für ein schnelles Internet (2) auf die Gesamtwirtschaft und den Arbeitsmarkt dargestellt. Darauf aufbauend modellieren wir den daraus folgenden Personal- und Materialaufwand der Unternehmen (3) und eine veränderte Nachfragestruktur nach Berufen und Qualifikationen (4). Die kumulativen Effekte der vier Teil-Szenarien werden mit einem Referenz-Szenario, das keinen fortgeschrittenen Entwicklungspfad zu Industrie 4.0 enthält, verglichen. Darüber hinaus werden in einem weiteren Teil-Szenario Arbeitsmarkteffekte einer möglicherweise steigenden Nachfrage nach Gütern (5) in den Blick genommen und ebenfalls am Referenz-Szenario gespiegelt.Im Ergebnis zeigt sich, dass Industrie 4.0 den Strukturwandel hin zu mehr Dienstleistungen beschleunigen wird. Dabei sind Arbeitskräftebewegungen zwischen Branchen und Berufen weitaus größer als die Veränderung der Anzahl der Erwerbstätigen insgesamt. Mit den Umwälzungen auf dem Arbeitsmarkt geht eine zunehmende Wertschöpfung einher, die nicht nur zu mehr volkswirtschaftlichen Gewinnen sondern - aufgrund höherer Anforderungen an die Arbeitskräfte - auch zu höheren Lohnsummen führt. Die getroffenen Annahmen wirken zu Gunsten der ökonomischen Entwicklung. Das bedeutet aber auch, dass bei einer verzögerten oder gar verschleppten Umsetzung, die Annahmen sich gegen den Wirtschaftsstandort Deutschlands wenden: Wir werden weniger exportieren und mehr "neue" Güter im Ausland nachfragen. Um ökonomische Erkenntnisse zu den Wirkungen der Digitalisierung weiter zu verbessern, ist eine Fortentwicklung des QuBe-I4.0-Projekts geplant.This study focuses on the economic effects of the phenomenon of "industry 4.0", the digitalisation of the production processes. These developments involve considerable challenges at enterprise and political level. The five-step scenario analysis begins with the impacts of increased investments of enterprises in equipment (1) and of the state in the network infrastructure (2) on the overall economy and the labour market. On this basis we further model the consequent personnel and material costs of the enterprises (3) and a changed pattern of demand for occupations and skills (4). The cumulative effects of these four partial scenarios are compared with a baseline scenario which contains no advanced development path to industry 4.0. In a further scenario the effects on the labour market of a potentially increasing demand for goods (5) are taken into consideration and also contrasted with the baseline scenario. The results show that industry 4.0 will accelerate the structural change towards more services. In this process labour force movements between branches and occupations are much larger than the change of the number of employees in total. The turnover on the labour market are accompanied by an increasing value added which is leading not only to more economic assets but also - due to higher requirements for the labour force - to higher aggregate wages. The underlying assumptions have a positive effect on the economic development. But this also means that, given a delayed realization, the assumptions are turning against the business location Germany: We will export less and demand more "new" goods from abroad. In order to improve the economic findings on the effects of digitization, a further development of QUBE-I4.0-project is planned

Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas

The ability to control and tune interactions in ultracold atomic gases has paved the way towards the realization of new phases of matter. Whereas experiments have so far achieved a high degree of control over short-ranged interactions, the realization of long-range interactions would open up a whole new realm of many-body physics and has become a central focus of research. Rydberg atoms are very well-suited to achieve this goal, as the van der Waals forces between them are many orders of magnitude larger than for ground state atoms. Consequently, the mere laser excitation of ultracold gases can cause strongly correlated many-body states to emerge directly when atoms are transferred to Rydberg states. A key example are quantum crystals, composed of coherent superpositions of different spatially ordered configurations of collective excitations. Here we report on the direct measurement of strong correlations in a laser excited two-dimensional atomic Mott insulator using high-resolution, in-situ Rydberg atom imaging. The observations reveal the emergence of spatially ordered excitation patterns in the high-density components of the prepared many-body state. They have random orientation, but well defined geometry, forming mesoscopic crystals of collective excitations delocalised throughout the gas. Our experiment demonstrates the potential of Rydberg gases to realise exotic phases of matter, thereby laying the basis for quantum simulations of long-range interacting quantum magnets.Comment: 10 pages, 7 figure