Efficient Learning of a One-dimensional Density Functional Theory

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In addition, the computational result---energy and charge density distribution of the ground state---is useful for electronic properties of solids mostly when reduced to a band structure interpretation based on the Kohn-Sham approach. Here, we demonstrate how machine learning algorithms can help to free density functional theory from these limitations. We study a theory of spinless fermions on a one-dimensional lattice. The density functional is implicitly represented by a neural network, which predicts, besides the ground-state energy and density distribution, density-density correlation functions. At no point do we require a band structure interpretation. The training data, obtained via exact diagonalization, feeds into a learning scheme inspired by active learning, which minimizes the computational costs for data generation. We show that the network results are of high quantitative accuracy and, despite learning on random potentials, capture both symmetry-breaking and topological phase transitions correctly.Comment: 5 pages, 3 figures; 4+ pages appendi

The Mechanics of Embodiment: A Dialogue on Embodiment and Computational Modeling

Embodied theories are increasingly challenging traditional views of cognition by arguing that conceptual representations that constitute our knowledge are grounded in sensory and motor experiences, and processed at this sensorimotor level, rather than being represented and processed abstractly in an amodal conceptual system. Given the established empirical foundation, and the relatively underspecified theories to date, many researchers are extremely interested in embodied cognition but are clamouring for more mechanistic implementations. What is needed at this stage is a push toward explicit computational models that implement sensory-motor grounding as intrinsic to cognitive processes. In this article, six authors from varying backgrounds and approaches address issues concerning the construction of embodied computational models, and illustrate what they view as the critical current and next steps toward mechanistic theories of embodiment. The first part has the form of a dialogue between two fictional characters: Ernest, the �experimenter�, and Mary, the �computational modeller�. The dialogue consists of an interactive sequence of questions, requests for clarification, challenges, and (tentative) answers, and touches the most important aspects of grounded theories that should inform computational modeling and, conversely, the impact that computational modeling could have on embodied theories. The second part of the article discusses the most important open challenges for embodied computational modelling

Cooperative core competencies in tourism: Combining resource-based and relational approaches in destination governance

Community-based tourist destinations can be understood as networks of tourism service providers, which need to combine their resources and competencies to generate the overall holiday experience. Building on strategic management theories, the study aims at exploring the relationship between the destinations management’s reflexive capabilities and the cooperative core competencies of a tourist destination. By means of reflexive capabilities, destination management is suggested to be able to induce a high level of network quality, which in turn may be a pre-condition for the interlacing of the service providers’ competencies and resources, i.e. for the development of cooperative core competencies. Based on a quantitative survey in Bavaria, the results support these assumptions and indicate that reflexive capabilities may promote the development of cooperative core competencies in tourist destinations. The paper advances tourism literature by introducing, operationalizing and testing the idea of cooperative core competencies in the context of tourist destinations

Observation of many-body localization of interacting fermions in a quasi-random optical lattice

We experimentally observe many-body localization of interacting fermions in a one-dimensional quasi-random optical lattice. We identify the many-body localization transition through the relaxation dynamics of an initially-prepared charge density wave. For sufficiently weak disorder the time evolution appears ergodic and thermalizing, erasing all remnants of the initial order. In contrast, above a critical disorder strength a significant portion of the initial ordering persists, thereby serving as an effective order parameter for localization. The stationary density wave order and the critical disorder value show a distinctive dependence on the interaction strength, in agreement with numerical simulations. We connect this dependence to the ubiquitous logarithmic growth of entanglement entropy characterizing the generic many-body localized phase.Comment: 6 pages, 6 figures + supplementary informatio