Decomposition of Trees and Paths via Correlation

We study the problem of decomposing (clustering) a tree with respect to costs attributed to pairs of nodes, so as to minimize the sum of costs for those pairs of nodes that are in the same component (cluster). For the general case and for the special case of the tree being a star, we show that the problem is NP-hard. For the special case of the tree being a path, this problem is known to be polynomial time solvable. We characterize several classes of facets of the combinatorial polytope associated with a formulation of this clustering problem in terms of lifted multicuts. In particular, our results yield a complete totally dual integral (TDI) description of the lifted multicut polytope for paths, which establishes a connection to the combinatorial properties of alternative formulations such as set partitioning.Comment: v2 is a complete revisio

Combinatorial persistency criteria for multicut and max-cut

In combinatorial optimization, partial variable assignments are called persistent if they agree with some optimal solution. We propose persistency criteria for the multicut and max-cut problem as well as fast combinatorial routines to verify them. The criteria that we derive are based on mappings that improve feasible multicuts, respectively cuts. Our elementary criteria can be checked enumeratively. The more advanced ones rely on fast algorithms for upper and lower bounds for the respective cut problems and max-flow techniques for auxiliary min-cut problems. Our methods can be used as a preprocessing technique for reducing problem sizes or for computing partial optimality guarantees for solutions output by heuristic solvers. We show the efficacy of our methods on instances of both problems from computer vision, biomedical image analysis and statistical physics

Integrating Taxonomies into Theory-Based Digital Health Interventions for Behavior Change: A Holistic Framework

Digital health interventions have been emerging in the last decade. Due to their interdisciplinary nature, digital health interventions are guided and influenced by theories (e.g., behavioral theories, behavior change technologies, persuasive technology) from different research communities. However, digital health interventions are always coded using various taxonomies and reported in insufficient perspectives. The inconsistency and incomprehensiveness will bring difficulty for conducting systematic reviews and sharing contributions among communities. Based on existing related work, therefore, we propose a holistic framework that embeds behavioral theories, behavior change technique (BCT) taxonomy, and persuasive system design (PSD) principles. Including four development steps, two toolboxes, and one workflow, our framework aims to guide digital health intervention developers to design, evaluate, and report their work in a formative and comprehensive way

Bellman filtering for state-space models

This article presents a filter for state-space models based on Bellman's dynamic programming principle applied to the mode estimator. The proposed Bellman filter (BF) generalises the Kalman filter (KF) including its extended and iterated versions, while remaining equally inexpensive computationally. The BF is also (unlike the KF) robust under heavy-tailed observation noise and applicable to a wider range of (nonlinear and non-Gaussian) models, involving e.g. count, intensity, duration, volatility and dependence. (Hyper)parameters are estimated by numerically maximising a BF-implied log-likelihood decomposition, which is an alternative to the classic prediction-error decomposition for linear Gaussian models. Simulation studies reveal that the BF performs on par with (or even outperforms) state-of-the-art importance-sampling techniques, while requiring a fraction of the computational cost, being straightforward to implement and offering full scalability to higher dimensional state spaces.Comment: 24 page

THERE IS, PROBABLY, NO NEED FOR A DESIGN FRAMEWORK

I present my perspective on the design process in this article, arguing for a focus on student learning and "slow design" that stems from knowledge of mathematics and their support system in the learning process. I have a question about the design process academization and task design research direction. Numerous examples from my work at the Freudenthal Institute are used to illustrate this paper

Brownian motion and multidimensional decision making

This thesis consists of three self-contained parts, each with its own abstract, body, references and page numbering. Part I, "Potential theory, path integrals and the Laplacian of the indicator", finds the transition density of absorbed or reflected Brownian motion in a d-dimensional domain as a Feynman-Kac functional involving the Laplacian of the indicator, thereby relating the hitherto unrelated fields of classical potential theory and path integrals. Part II, "The problem of alternatives", considers parallel investment in alternative technologies or drugs developed over time, where there can be only one winner. Parallel investment accelerates the search for the winner, and increases the winner's expected performance, but is also costly. To determine which candidates show sufficient performance and/or promise, we find an integral equation for the boundary of the optimal continuation region. Part III, "Optimal support for renewable deployment", considers the role of government subsidies for renewable technologies. Rapidly diminishing subsidies are cheaper for taxpayers, but could prematurely kill otherwise successful technologies. By contrast, high subsidies are not only expensive but can also prop up uneconomical technologies. To analyse this trade-off we present a new model for technology learning that makes capacity expansion endogenous. There are two reasons for this standalone structure. First, the target readership is divergent. Part I concerns mathematical physics, Part II operations research, and Part III policy. Readers interested in specific parts can thus read these in isolation. Those interested in the thesis as a whole may prefer to read the three introductions first. Second, the separate parts are only partially interconnected. Each uses some theory from the preceding part, but not all of it; e.g. Part II uses only a subset of the theory from Part I. The quickest route to Part III is therefore not through the entirety of the preceding parts. Furthermore, those instances where results from previous parts are used are clearly indicated.Research support from the Electricity Policy Research Group in Cambridge is gratefully acknowledged (http://www.eprg.group.cam.ac.uk)

Towards a Holistic Approach to Designing Theory-based Mobile Health Interventions

Increasing evidence has shown that theory-based health behavior change interventions are more effective than non-theory-based ones. However, only a few segments of relevant studies were theory-based, especially the studies conducted by non-psychology researchers. On the other hand, many mobile health interventions, even those based on the behavioral theories, may still fail in the absence of a user-centered design process. The gap between behavioral theories and user-centered design increases the difficulty of designing and implementing mobile health interventions. To bridge this gap, we propose a holistic approach to designing theory-based mobile health interventions built on the existing theories and frameworks of three categories: (1) behavioral theories (e.g., the Social Cognitive Theory, the Theory of Planned Behavior, and the Health Action Process Approach), (2) the technological models and frameworks (e.g., the Behavior Change Techniques, the Persuasive System Design and Behavior Change Support System, and the Just-in-Time Adaptive Interventions), and (3) the user-centered systematic approaches (e.g., the CeHRes Roadmap, the Wendel's Approach, and the IDEAS Model). This holistic approach provides researchers a lens to see the whole picture for developing mobile health interventions