Quantum Hall transitions: An exact theory based on conformal restriction

We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, based on the theory of conformal restriction. This is a mathematical theory that was recently developed within the context of the Schramm-Loewner evolution which describes the stochastic geometry of fractal curves and other stochastic geometrical fractal objects in 2D space. Observables elucidating the connection with the plateau transition include the so-called point-contact conductances (PCCs) between points on the boundary of the sample, described within the language of the Chalker-Coddington network model. We show that the disorder-averaged PCCs are characterized by classical probabilities for certain geometric objects in the plane (pictures), occurring with positive statistical weights, that satisfy the crucial restriction property with respect to changes in the shape of the sample with absorbing boundaries. Upon combining this restriction property with the expected conformal invariance at the transition point, we employ the mathematical theory of conformal restriction measures to relate the disorder-averaged PCCs to correlation functions of primary operators in a conformal field theory (of central charge $c=0$). We show how this can be used to calculate these functions in a number of geometries with various boundary conditions. Since our results employ only the conformal restriction property, they are equally applicable to a number of other critical disordered electronic systems in 2D. For most of these systems, we also predict exact values of critical exponents related to the spatial behavior of various disorder-averaged PCCs.Comment: Published versio

Evaluation of two interaction techniques for visualization of dynamic graphs

Several techniques for visualization of dynamic graphs are based on different spatial arrangements of a temporal sequence of node-link diagrams. Many studies in the literature have investigated the importance of maintaining the user's mental map across this temporal sequence, but usually each layout is considered as a static graph drawing and the effect of user interaction is disregarded. We conducted a task-based controlled experiment to assess the effectiveness of two basic interaction techniques: the adjustment of the layout stability and the highlighting of adjacent nodes and edges. We found that generally both interaction techniques increase accuracy, sometimes at the cost of longer completion times, and that the highlighting outclasses the stability adjustment for many tasks except the most complex ones.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Circulating complement component 4d (C4d) correlates with tumor volume, chemotherapeutic response and survival in patients with malignant pleural mesothelioma

Only limited information is available on the role of complement activation in malignant pleural mesothelioma (MPM). Thus, we investigated the circulating and tissue levels of the complement component 4d (C4d) in MPM. Plasma samples from 55 MPM patients, 21 healthy volunteers (HV) and 14 patients with non-malignant pleural diseases (NMPD) were measured by ELISA for C4d levels. Tissue specimens from 32 patients were analyzed by C4d immunohistochemistry. Tumor volumetry was measured in 20 patients. We found no C4d labeling on tumor cells, but on ectopic lymphoid structures within the tumor stroma. Plasma C4d levels did not significantly differ between MPM, HV or NMPD. Late-stage MPM patients had higher plasma C4d levels compared to early-stage (p = 0.079). High circulating C4d was associated with a higher tumor volume (p = 0.047). Plasma C4d levels following induction chemotherapy were significantly higher in patients with stable/progressive disease compared to those with partial/major response (p = 0.005). Strikingly, patients with low C4d levels at diagnosis had a significantly better overall survival, confirmed in a multivariate cox regression model (hazard ratio 0.263, p = 0.01). Our findings suggest that circulating plasma C4d is a promising new prognostic biomarker in patients with MPM and, moreover, helps to select patients for surgery following induction chemotherapy

The strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

Visualisation of Integrated Patient-Centric Data as Pathways: Enhancing Electronic Medical Records in Clinical Practice

Routinely collected data in hospital Electronic Medical Records (EMR) is rich and abundant but often not linked or analysed for purposes other than direct patient care. We have created a methodology to integrate patient-centric data from different EMR systems into clinical pathways that represent the history of all patient interactions with the hospital during the course of a disease and beyond. In this paper, the literature in the area of data visualisation in healthcare is reviewed and a method for visualising the journeys that patients take through care is discussed. Examples of the hidden knowledge that could be discovered using this approach are explored and the main application areas of visualisation tools are identified. This paper also highlights the challenges of collecting and analysing such data and making the visualisations extensively used in the medical domain. This paper starts by presenting the state-of-the-art in visualisation of clinical and other health related data. Then, it describes an example clinical problem and discusses the visualisation tools and techniques created for the utilisation of these data by clinicians and researchers. Finally, we look at the open problems in this area of research and discuss future challenges

Atom chip based generation of entanglement for quantum metrology

Atom chips provide a versatile `quantum laboratory on a microchip' for experiments with ultracold atomic gases. They have been used in experiments on diverse topics such as low-dimensional quantum gases, cavity quantum electrodynamics, atom-surface interactions, and chip-based atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. Such techniques enable chip-based studies of entangled many-body systems and are a key prerequisite for atom chip applications in quantum simulations, quantum information processing, and quantum metrology. Here we report experiments where we generate multi-particle entanglement on an atom chip by controlling elastic collisional interactions with a state-dependent potential. We employ this technique to generate spin-squeezed states of a two-component Bose-Einstein condensate and show that they are useful for quantum metrology. The observed 3.7 dB reduction in spin noise combined with the spin coherence imply four-partite entanglement between the condensate atoms and could be used to improve an interferometric measurement by 2.5 dB over the standard quantum limit. Our data show good agreement with a dynamical multi-mode simulation and allow us to reconstruct the Wigner function of the spin-squeezed condensate. The techniques demonstrated here could be directly applied in chip-based atomic clocks which are currently being set up

Mean-field phase diagram of disordered bosons in a lattice at non-zero temperature

Bosons in a periodic lattice with on-site disorder at low but non-zero temperature are considered within a mean-field theory. The criteria used for the definition of the superfluid, Mott insulator and Bose glass are analysed. Since the compressibility does never vanish at non-zero temperature, it can not be used as a general criterium. We show that the phases are unambiguously distinguished by the superfluid density and the density of states of the low-energy exitations. The phase diagram of the system is calculated. It is shown that even a tiny temperature leads to a significant shift of the boundary between the Bose glass and superfluid

On the Estimation Stability of Efficiency and Economies of Scale in Microfinance Institutions

This paper uses a panel data set of microfinance institutions (MFI) across the world to compare several identification strategies of cost efficiency and economies of scale. Concretely, we contrast the non-parametric Data Envelopment Analysis (DEA) with the Stochastic Frontier Analysis (SFA) and a distribution-free identification based on time-invariant heterogeneity estimates. Furthermore, we analyze differences of production functions across regions and investigate the relevance of accounting for unobserved heterogeneity across countries. The results suggest that efficiency rankings of MFIs are robust across identification strategies, but highlight the relevance of accounting for unobserved heterogeneity. We further find substantial economies of scale for a pure financial production process. However, accounting for the multi-dimensional production process of MFIs by including a measure of outreach lowers the estimated extent of economies of scale for the parametric estimations, suggesting that producing outreach creates high transaction costs and requires exploitation of local knowledge