Bias-Reduction in Variational Regularization

The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a consecutive debiasing step minimizing the data fidelity on an appropriate set, the so-called model manifold. The latter is defined by Bregman distances or infimal convolutions thereof, using the (uniquely defined) subgradient appearing in the optimality condition of the variational method. For particular settings, such as anisotropic $\ell^1$ and TV-type regularization, previously used debiasing techniques are shown to be special cases. The proposed approach is however easily applicable to a wider range of regularizations. The two-step debiasing is shown to be well-defined and to optimally reduce bias in a certain setting. In addition to visual and PSNR-based evaluations, different notions of bias and variance decompositions are investigated in numerical studies. The improvements offered by the proposed scheme are demonstrated and its performance is shown to be comparable to optimal results obtained with Bregman iterations.Comment: Accepted by JMI

Liquid morphologies and capillary forces between three spherical beads

Equilibrium shapes of coalesced pendular bridges in a static assembly of spherical beads are computed by numerical minimization of the interfacial energy. Our present study focuses on generic bead configurations involving three beads, one of which is in contact to the two others while there is a gap of variable size between the latter. In agreement with previous experimental studies, we find interfacial `trimer' morphologies consisting of three coalesced pendular bridges, and `dimers' of two coalesced bridges. In a certain range of the gap opening we observe a bistability between the dimer and trimer morphology during shrinking and growth. The magnitude of the corresponding capillary forces in presence of a trimer or dimer depends, besides the gap opening only on the volume or Laplace pressure of liquid. For a given Laplace pressure, the capillary forces in presence of a trimer are slightly larger than the force of a single bridges at the same gap opening, which could explain the shallow maximum and plateau of the capillary cohesion of a wetting liquid for saturations in the funicular regime

Developing Strategic Capability through Business Intelligence Applications: A case study from the German Healthcare Insurance Industry

Wynn, M. and Brinkmann, D., (2018), in Yeoh, W. and Miah, S. (eds) Business Intelligence in Organisational Settings, IGI-Global. Company performance can be measured at all levels across an organisation, and in the German healthcare industry, Business Intelligence systems play a crucial role in achieving this. For one major health insurance company (discussed here as an alias - AK Healthcare), the deployment of Business Intelligence applications has supported sustained growth in turnover and market share in the past five years. In this article, these tools are classified within an appropriate conceptual framework which encompasses the organisation’s information infrastructure and associated processes. Different components of the framework are identified and examples are given - systems infrastructure, data provision/access control, the BI tools and technologies, report generation, and information users. The use and integration of Business Intelligence tools in the strategy development process is then analyzed, and the key functions and features of these tools for strategic capability development are discussed. Research findings encompass system access, report characteristics, and end-users capabilities

The Role of Contact Angle Hysteresis for Fluid Transport in Wet Granular Matter

The stability of sand castles is determined by the structure of wet granulates. Experimental data about the size distribution of fluid pockets are ambiguous about their origin. We discovered that contact angle hysteresis plays a fundamental role in the equilibrium distribution of bridge volumes, and not geometrical disorder as commonly conjectured, which has substantial consequences on the mechanical properties of wet granular beds, including a history dependent rheology and lowered strength. Our findings are obtained using a novel model where the Laplace pressures, bridge volumes and contact angles are dynamical variables associated to the contact points. While accounting for contact line pinning, we track the temporal evolution of each bridge. We observe a cross-over to a power-law decay of the variance of capillary pressures at late times and a saturation of the variance of bridge volumes to a finite value connected to contact line pinning. Large scale simulations of liquid transport in the bridge network reveal that the equilibration dynamics at early times is well described by a mean field model. The spread of final bridge volumes can be directly related to the magnitude of contact angle hysteresis