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Inverse problems are often marked by highly dimensional state vectors. The high dimension affects the quality of the estimation result as well as the computational complexity of the estimation problem. This paper aims to present a state reduction technique based on prior knowledge.

Ill-posed inverse problems require prior knowledge to find a stable solution. The prior distribution is constructed for the high-dimensional data space. The authors use the prior distribution to construct a reduced state description based on a lower-dimensional basis, which they derive from the prior distribution. The approach is tested for the inverse problem of electrical capacitance tomography.

Based on a singular value decomposition of a sample-based prior distribution, a reduced state model can be constructed, which is based on principal components of the prior distribution. The approximation error of the reduced basis is evaluated, showing good behavior with respect to the achievable data reduction. Owing to the structure, the reduced state representation can be applied within existing algorithms.

The full state description is a linear function of the reduced state description. The reduced basis can be used within any existing reconstruction algorithm. Increased noise robustness has been found for the application of the reduced state description in a back projection-type reconstruction algorithm.

The paper presents the construction of a prior-based state reduction technique. Several applications of the reduced state description are discussed, reaching from the use in deterministic reconstruction methods up to proposal generation for computational Bayesian inference, e.g. Markov chain Monte Carlo techniques.

The application of statistical inversion theory provides a powerful approach for solving estimation problems including the ability for uncertainty quantification (UQ) by means of Markov chain Monte Carlo (MCMC) methods and Monte Carlo integration. This paper aims to analyze the application of a state reduction technique within different MCMC techniques to improve the computational efficiency and the tuning process of these algorithms.

A reduced state representation is constructed from a general prior distribution. For sampling the Metropolis Hastings (MH) Algorithm and the Gibbs sampler are used. Efficient proposal generation techniques and techniques for conditional sampling are proposed and evaluated for an exemplary inverse problem.

For the MH-algorithm, high acceptance rates can be obtained with a simple proposal kernel. For the Gibbs sampler, an efficient technique for conditional sampling was found. The state reduction scheme stabilizes the ill-posed inverse problem, allowing a solution without a dedicated prior distribution. The state reduction is suitable to represent general material distributions.

The state reduction scheme and the MCMC techniques can be applied in different imaging problems. The stabilizing nature of the state reduction improves the solution of ill-posed problems. The tuning of the MCMC methods is simplified.

The paper presents a method to improve the solution process of inverse problems within the Bayesian framework. The stabilization of the inverse problem due to the state reduction improves the solution. The approach simplifies the tuning of MCMC methods.

The purpose of this paper is to establish a cheap but accurate approximation of the forward map in electrical capacitance tomography in order to approach robust real‐time inversion in the framework of Bayesian statistics based on Markov chain Monte Carlo (MCMC) sampling.

Existing formulations and methods to reduce the order of the forward model with focus on electrical tomography are reviewed and compared. In this work, the problem of fast and robust estimation of shape and position of non‐conducting inclusions in an otherwise uniform background is considered. The boundary of the inclusion is represented implicitly using an appropriate interpolation strategy based on radial basis functions. The inverse problem is formulated as Bayesian inference, with MCMC sampling used to efficiently explore the posterior distribution. An affine approximation to the forward map built over the state space is introduced to significantly reduce the reconstruction time, while maintaining spatial accuracy. It is shown that the proposed approximation is unbiased and the variance of the introduced additional model error is even smaller than the measurement error of the tomography instrumentation. Numerical examples are presented, avoiding all inverse crimes.

Provides a consistent formulation of the affine approximation with application to imaging of binary mixtures in electrical tomography using MCMC sampling with Metropolis‐Hastings‐Green dynamics.

The proposed cheap approximation indicates that accurate real‐time inversion of capacitance data using statistical inversion is possible.

The proposed approach demonstrates that a tolerably small increase in posterior uncertainty of relevant parameters, e.g. inclusion area and contour shape, is traded for a huge reduction in computing time without introducing bias in estimates. Furthermore, the proposed framework – approximated forward map combined with statistical inversion – can be applied to all kinds of soft‐field tomography problems.

The purpose of this paper is to demonstrate an inverse problem approach for the determination of stress zones in steel plates of electrical machines. Steel plates of electrical machines suffer large mechanical stress by processes like cutting or punching during the fabrication. The mechanical stress has effects on the electrical properties of the steel, and thus on the losses of the machine.

In this paper, the authors present a sensor arrangement and an appropriate algorithm for determining the spatial permeability distribution in steel plates. The forward problem for stress zone imaging is explained and an appropriate numerical solution technique is proposed. Then an inverse problem formulation is introduced and the nature of the problem is analyzed.

Based on sensitivity analysis, different measurement procedures are compared and a measurement setup is suggested. Further the ill‐posed nature of the inverse problem is analyzed by the Picard condition.

Because of the increased losses due to stress zones, the quantification of stress effects is of interest to adjust the production process. Stress zone imaging is a first approach for the application of an imaging system to quantify these material defects.

This paper presents a simulation study about the applicability of an inverse problem for stress zone imaging and presents first reconstruction results. Further, the paper discusses several issues about stress zone imaging for the ongoing research.

The purpose of this paper is to analyze the relationship between host country (HC) language skills, fear of terror, and cross-cultural adjustment (CCA) of expatriates based in host countries with different terrorist threat levels.

Integrating the expatriate adjustment framework by Black et al. (1991) with social identity theory-based literature, this study first, theorizes about the effects of both fear of terror and HC language proficiency on CCA and, second, puts forward the moderating effect of the actual terrorist threat level on the relationship between HC language proficiency and fear of terror. Hypotheses are tested using survey data of 116 expatriates based in host countries with different threat levels.

HC language proficiency is positively associated with CCA. Yet, it is also positively associated with fear of terror, which is, in turn, negatively related to CCA. Consequently, the beneficial effect of HC language skills on CCA is reduced in environments where expatriates experience significant fear of terror. While the actual threat level has a direct positive effect on fear of terror, it also positively moderates the relationship between HC language proficiency and fear of terror.

This study extends prior literature on expatriation to dangerous environments by zooming in on a specific type of risk factor associated with international assignments, i.e., terrorism, and by integrating HC language proficiency and fear of terror as important factors, which may influence CCA in contexts in which expatriates experience significant fear of terror.

This paper has two main purposes. First, it considers the detrimental effects of four politically‐salient asymmetries on the policy choices of liberal democracies when dealing with the problem of human‐induced climate change. Second, it outlines and evaluates possible solutions for reducing or countering these asymmetries.

The approach involves an analysis and evaluation of policy options based on a survey of the relevant literature.

The paper highlights the serious mismatch between the magnitude and urgency of the climate change problem and the current political will to overcome or mitigate the problem. Although four categories of potential solutions, and the various mechanisms through which they might operate, are discussed, it is recognized that all the available options have significant drawbacks, not least limited political feasibility and doubtful effectiveness. In short, action within liberal democracies to mitigate climate change is likely to remain seriously constrained by the four asymmetries discussed, thus increasing the risk of dangerous climate change.

The paper highlights the complexities, both international and national, of confronting human‐induced climate change. In particular, it identifies four systemic reasons, in the form of politically‐salient asymmetries, why liberal democracies have struggled to take effective measures to reduce greenhouse gas emissions and provides a systematic assessment of possible solutions to these asymmetries. These include changes to accounting frameworks to ensure that the impact of humanity on the environment and future generations is more transparent.

An unconscious concern regarding one’s inevitable death, known as mortality salience, may affect consumers’ brand choices in the aftermath of disastrous events, such as earthquakes. The purpose of this paper is to examine the role of self-identification with global consumer culture (IDGCC) in global brand purchase intention in response to disasters that heighten mortality salience. The roles of materialism, consumer ethnocentrism, cosmopolitanism and hope in this this process are also explored.

An online experiment was conducted with a large sample of Japanese consumers. Japan was selected because it had recently suffered from a series of devastating earthquakes. Participants’ mortality salience was primed with an earthquake scenario. All measures were adapted from prior research. The authors used structural equation modeling to test the hypotheses and validate the model.

The results reveal that IDGCC is a direct predictor of global brand purchase intention when mortality salience is high. It appears that identifying with global consumer culture and buying global brands enhances self-esteem and reduces anxiety for those with high IDGCC. As predicted, materialism and cosmopolitanism positively influence IDGCC, whereas consumer ethnocentrism does not impede IDGCC. Hope directly and positively affects global brand purchase intention.

Some consumers who experience traumatic events may resist mortality salience and experience a heightened sense of global citizenship. Meanwhile, those with lower IDGCC may revert to in-group favoritism, whereas those with higher IDGCC tend to purchase global brands. Using a scenario to simulate the mental state evoked by a disaster limits generalizability.

The findings illuminate how firms should modify their international marketing strategies in the face of traumatic global events when targeting consumers with high vs low IDGCC in terms of framing messages about global brands. Additionally, using global brands that emphasize an optimistic outlook may help global marketers capture attention from consumers high in IDGCC.

This study is one of the first to address traumatic events and hope, relating these concepts to IDGCC and global brand purchase intention in an international marketing context.