Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy

Gapped domain walls, as topological line defects between 2+1D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological orders. Our criteria also determine which 2+1D topological orders must have gapless edge modes, namely which 1+1D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, the tunneling matrix $\mathcal W$, whose entries are the fusion-space dimensions $\mathcal W_{ia}$, to label different types of gapped domain walls. By studying many examples, we find evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls. Since a gapped boundary is a gapped domain wall between a bulk topological order and the vacuum, regarded as the trivial topological order, our theory of gapped domain walls inclusively contains the theory of gapped boundaries. In addition, we derive a topological ground state degeneracy formula, applied to arbitrary orientable spatial 2-manifolds with gapped domain walls, including closed 2-manifolds and open 2-manifolds with gapped boundaries.Comment: 5+9 pages, 3 figures, updated references, fixed typos and refinements, added proof for equivalence to Lagrangian subgroups in Abelian case

Unusual Compression Behavior of Columbite TiO2 via First-Principles Calculations

The physical mechanisms behind the reduction of the bulk modulus of a high-pressure cubic TiO2 phase are confirmed by first-principles calculations. An unusual and abrupt change occurs in the dependence of energy on pressure at 43 GPa, indicating a pressure-induced phase transition from columbite TiO2 to a newly-identified modified fluorite TiO2 with a Pca21 symmetry. Oxygen atom displacement in Pca21 TiO2 unexpectedly reduces the bulk modulus by 34% relative to fluorite TiO2. This discovering provides a direct evidence for understanding the compressive properties of such groups of homologous materialsComment: [email protected] or [email protected]

Resource Signaling via Blood Glucose in Embodied Decision Making

Food, money, and time are exchangeable resources essential for survival and reproduction. Individuals live within finite budgets of these resources and make tradeoffs between money and time when making intertemporal choices between an immediate smaller reward and a delayed lager reward. In this paper, I examine signaling functions of blood glucose in regulating behaviors related to resource regulations beyond caloric metabolisms. These behavioral regulations include choices between energy expenditure and energy conservation, monetary intertemporal choices, and self-control in overcoming temptations. I begin by comparing potential embodied signals for resource forecasting and proactive decision making in terms of their pros and cons as a signal for regulating both metabolism and behavioral decision making and self-control. Based on this analysis, circulating glucose emerges as not only the designated fuel for brain metabolism but also a privileged resource forecasting signal for regulating immediate, short-term, and long-term behavioral adaptations to the resource budget of the decision maker. In the context of an on-going debate between the limited resource model and the motivation accounts of behavioral effects of blood glucose, I propose a dual functions (caloric provision and resource forecasting) and dual signaling (glucose taste and ingestion) hypothesis of circulating glucose in resource management, and provide behavioral and neurophysiological evidence of the separate effects of glucose taste to motivate effort for resource acquisition and glucose ingestion to promote resource conservation and future orientation. Accumulating evidence indicates that the body is able to detect fake signals of non-caloric sweeteners and react to such “caloric crisis” with an enhanced preference for immediate rewards over future rewards, revealing the wisdom of the body