Joint denoising and distortion correction of atomic scale scanning transmission electron microscopy images

Nowadays, modern electron microscopes deliver images at atomic scale. The precise atomic structure encodes information about material properties. Thus, an important ingredient in the image analysis is to locate the centers of the atoms shown in micrographs as precisely as possible. Here, we consider scanning transmission electron microscopy (STEM), which acquires data in a rastering pattern, pixel by pixel. Due to this rastering combined with the magnification to atomic scale, movements of the specimen even at the nanometer scale lead to random image distortions that make precise atom localization difficult. Given a series of STEM images, we derive a Bayesian method that jointly estimates the distortion in each image and reconstructs the underlying atomic grid of the material by fitting the atom bumps with suitable bump functions. The resulting highly non-convex minimization problems are solved numerically with a trust region approach. Well-posedness of the reconstruction method and the model behavior for faster and faster rastering are investigated using variational techniques. The performance of the method is finally evaluated on both synthetic and real experimental data

Dynamic Models of Wasserstein-1-Type Unbalanced Transport

We consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which transport costs are proportional to transport distance. For those models we derive an equivalent, computationally more efficient static formulation, we perform a detailed analysis of the model optimizers and the associated optimal mass change and transport, and we examine which static models are generated by a corresponding equivalent dynamic one. Alongside we discuss thoroughly how the employed model formulations relate to other formulations found in the literature.Comment: to appear in ESAIM: Control, Optimisation and Calculus of Variation

A non-standard approach to a market with boundedly rational consumers and strategic firms. Part I: A microfoundation for the evolution of sales

In our model, individual consumers follow simple behavioral decision rules based on imitation and habit as suggested in consumer research, social learning, and related fields. Demand can be viewed as the outcome of a population game whose revision protocol is determined by the consumers' behavioral rules. The consumer dynamics are then analyzed in order to explore the demand side and first implications for a strategic supply side.bounded rationality, social learning, population game, mean dynamic

Product Pricing when Demand Follows a Rule of Thumb

We analyze the strategic behavior of firms when demand is determined by a rule of thumb behavior of consumers. We assume consumer dynamics where individual consumers follow simple behavioral decision rules governed by imitation and habit as suggested in consumer research. On this basis, we investigate monopoly and competition between firms, described via an open-loop differential game which in this setting is equivalent to but analytically more convenient than a closed-loop system. We derive a Nash equilibrium and examine the influence of advertising. We show for the monopoly case that a reduction of the space of all price paths in time to the space of time-constant prices is sensible since the latter in general contains Nash equilibria. We prove that the equilibrium price of the weakest active firm tends to marginal cost as the number of (non-identical) firms grows. Our model is consistent with observed market behavior such as product life cycles.bounded rationality, social learning, population game, differential game, product life cycle, monopoly, competition, pricing, advertising