Complementary Algorithms For Tableaux

We study four operations defined on pairs of tableaux. Algorithms for the first three involve the familiar procedures of jeu de taquin, row insertion, and column insertion. The fourth operation, hopscotch, is new, although specialised versions have appeared previously. Like the other three operations, this new operation may be computed with a set of local rules in a growth diagram, and it preserves Knuth equivalence class. Each of these four operations gives rise to an a priori distinct theory of dual equivalence. We show that these four theories coincide. The four operations are linked via the involutive tableau operations of complementation and conjugation.Comment: 29 pages, 52 .eps files for figures, JCTA, to appea

A personalized support tool for the training of mindful walking: The mobile “MindfulWalk” application

Digital health prevention is a trend that becomes increasingly important in various domains. Health insurers crave for effective methods that can be offered to their customers. Moreover, smart mobile devices pose many advantages as they can be easily used in everyday life without being burdensome. Taking these advantages into account, completely new applications become possible. This thesis presents an application that is intended to support users to walk mindfully. It is a mobile personalized tool that senses the walking speed and provides haptic feedback thereof. The procedure of mindful walking, the technical prototype as well as preliminary study results are presented and discussed. The reported user experience and the study result indicate promising perspectives for a tool that supports a mindful walking behavior. Altogether, the use of modern smart mobile device sensors paves the way for useful mobile application in the context of health prevention in particular and health care in general

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Experimental microbial evolution: History and conceptual underpinnings

We chronicle and dissect the history of the field of Experimental Microbial Evolution, beginning with work by Monod. Early research was largely carried out by microbiologists and biochemists, who used experimental evolutionary change as a tool to understand structure-function relationships. These studies attracted the interest of evolutionary biologists who recognized the power of the approach to address issues such as the tempo of adaptive change, the costs and benefits of sex, parallelism, and the role which contingency plays in the evolutionary process. In the 1980s and 1990s, an ever-expanding body of microbial, physiological and biochemical data, together with new technologies for manipulating microbial genomes, allowed such questions to be addressed in ever-increasing detail. Since then, technological advances leading to low-cost, high-throughput DNA sequencing have made it possible for these and other fundamental questions in evolutionary biology to be addressed at the molecular level

Replacing Neural Networks by Optimal Analytical Predictors for the Detection of Phase Transitions

Identifying phase transitions and classifying phases of matter is central to understanding the properties and behavior of a broad range of material systems. In recent years, machine-learning (ML) techniques have been successfully applied to perform such tasks in a data-driven manner. However, the success of this approach notwithstanding, we still lack a clear understanding of ML methods for detecting phase transitions, particularly of those that utilize neural networks (NNs). In this work, we derive analytical expressions for the optimal output of three widely used NN-based methods for detecting phase transitions. These optimal predictions correspond to the results obtained in the limit of high model capacity. Therefore, in practice, they can, for example, be recovered using sufficiently large, well-trained NNs. The inner workings of the considered methods are revealed through the explicit dependence of the optimal output on the input data. By evaluating the analytical expressions, we can identify phase transitions directly from experimentally accessible data without training NNs, which makes this procedure favorable in terms of computation time. Our theoretical results are supported by extensive numerical simulations covering, e.g., topological, quantum, and many-body localization phase transitions. We expect similar analyses to provide a deeper understanding of other classification tasks in condensed matter physics