Reflection positivity and invertible topological phases

We implement an extended version of reflection positivity (Wick-rotated unitarity) for invertible topological quantum field theories and compute the abelian group of deformation classes using stable homotopy theory. We apply these field theory considerations to lattice systems, assuming the existence and validity of low energy effective field theory approximations, and thereby produce a general formula for the group of Symmetry Protected Topological (SPT) phases in terms of Thom's bordism spectra; the only input is the dimension and symmetry group. We provide computations for fermionic systems in physically relevant dimensions. Other topics include symmetry in quantum field theories, a relativistic 10-fold way, the homotopy theory of relativistic free fermions, and a topological spin-statistics theorem.Comment: 136 pages, 16 figures; minor changes/corrections in version 2; v3 major revision; v4 minor revision: corrected proof of Lemma 9.55, many small changes throughout; v5 version for publication in Geometry & Topolog

Density regulation in strictly metric-free swarms

There is now experimental evidence that nearest-neighbour interactions in flocks of birds are metric free, i.e. they have no characteristic interaction length scale. However, models that involve interactions between neighbours that are assigned topologically are naturally invariant under spatial expansion, supporting a continuous reduction in density towards zero, unless additional cohesive interactions are introduced or the density is artificially controlled, e.g. via a finite system size. We propose a solution that involves a metric-free motional bias on those individuals that are topologically identified to be on an edge of the swarm. This model has only two primary control parameters, one controlling the relative strength of stochastic noise to the degree of co-alignment and another controlling the degree of the motional bias for those on the edge, relative to the tendency to co-align. We find a novel power-law scaling of the real-space density with the number of individuals N as well as a familiar order-to-disorder transition

Towards Economic Models for MOOC Pricing Strategy Design

MOOCs have brought unprecedented opportunities of making high-quality courses accessible to everybody. However, from the business point of view, MOOCs are often challenged for lacking of sustainable business models, and academic research for marketing strategies of MOOCs is also a blind spot currently. In this work, we try to formulate the business models and pricing strategies in a structured and scientific way. Based on both theoretical research and real marketing data analysis from a MOOC platform, we present the insights of the pricing strategies for existing MOOC markets. We focus on the pricing strategies for verified certificates in the B2C markets, and also give ideas of modeling the course sub-licensing services in B2B markets

Can Lower Tax Rates be Bought? Business Rent-Seeking and Tax Competition among U.S. States

The standard model of strategic tax competition assumes that government policymakers are perfectly benevolent, acting solely to maximize the utility of the representative resident in their jurisdiction. We depart from this assumption by allowing for the possibility that policymakers also may be influenced by the rent-seeking (lobbying) behavior of businesses. This extension to the standard strategic tax competition model implies that business contributions may affect not only the levels of equilibrium tax rates but also the slope of the tax reaction function between jurisdictions, thus enhancing or retarding the mobility of capital across jurisdictions. The model is estimated with panel data for 48 U.S. states and unique data on business campaign contributions. Among other results, we document a significant direct effect of business contributions on tax policy; the economic value of a $1 business campaign contribution in terms of lower state corporate taxes is approximately$6.65.business campaign contributions, state business tax policy, rent-seeking, capital mobility

Phantom Accretion by Black Holes and the Generalized Second Law of Thermodynamics

The accretion of a phantom fluid with non-zero chemical potential by black holes is discussed with basis on the Generalized Second Law of thermodynamics. For phantom fluids with positive temperature and negative chemical potential we demonstrate that the accretion process is possible, and that the condition guaranteeing the positiveness of the phantom fluid entropy coincides with the one required by Generalized Second Law. In particular, this result provides a complementary confirmation that cosmological phantom fluids do not need to have negative temperatures

Can lower tax rates be bought? Business rent-seeking and tax competition among U.S. states

The standard model of strategic tax competition – the non-cooperative tax-setting behavior of jurisdictions competing for a mobile capital tax base – assumes that government policymakers are perfectly benevolent, acting solely to maximize the utility of the representative resident in their jurisdiction. We depart from this assumption by allowing for the possibility that policymakers, given the political and electoral environments in which they operate, also may be influenced by the rent-seeking (lobbying) behavior of businesses. Firms recognize the factors affecting policymakers’ welfare and may make campaign contributions to influence tax policy. These changes to the standard strategic tax competition model imply that business contributions affect not only the levels of equilibrium tax rates but also the slope of the tax reaction function between jurisdictions. Thus, business campaign contributions may affect tax competition and enhance or retard the mobility of capital across jurisdictions. ; Based on a panel of 48 U.S. states and unique data on business campaign contributions, our empirical work uncovers four key results. First, we document a significant direct effect of business contributions on tax policy. Second, the economic value of a $1 business campaign contribution in terms of lower state corporate taxes is nearly$4. Third, the slope of the reaction function between tax policy in a given state and the tax policies of its competitive states is negative. Fourth, we highlight the sensitivity of the empirical results to state effects.Taxation

The observation of possible reconnection events in the boundary changes of solar coronal holes

Coronal holes are large scale regions of magnetically open fields which are easily observed in solar soft X-ray images. The boundaries of coronal holes are separatrices between large scale regions of open and closed magnetic fields where one might expect to observe evidence of solar magnetic reconnection. Previous studies by Nolte and colleagues using Skylab X-ray images established that large scale (greater than or equal to 9 x 10(4) km) changes in coronal hole boundaries were due to coronal processes, i.e., magnetic reconnection, rather than to photospheric motions. Those studies were limited to time scales of about one day, and no conclusion could be drawn about the size and time scales of the reconnection process at hole boundaries. Sequences of appropriate Skylab X-ray images were used with a time resolution of about 90 min during times of the central meridian passages of the coronal hole labelled Coronal Hole 1 to search for hole boundary changes which can yield the spatial and temporal scales of coronal magnetic reconnection. It was found that 29 of 32 observed boundary changes could be associated with bright points. The appearance of the bright point may be the signature of reconnection between small scale and large scale magnetic fields. The observed boundary changes contributed to the quasi-rigid rotation of Coronal Hole 1