Unitary null energy condition violation in P(X)P(X) cosmologies

A non-singular cosmological bounce in the Einstein frame can only take place if the Null Energy Condition (NEC) is violated. We explore situations where a single scalar field drives the NEC violation and derive the constraints imposed by demanding tree level unitarity on a cosmological background. We then focus on the explicit constraints that arise in P(X) theories and show that constraints from perturbative unitarity make it impossible for the NEC violation to occur within the region of validity of the effective field theory without also involving irrelevant operators that arise at a higher scale that would enter from integrating out more massive degrees of freedom. Within the context of P(X) theories we show that including such operators allows for a bounce that does not manifestly violate tree level unitarity, but at the price of either imposing a shift symmetry or involving technically unnatural small operator coefficients within the low-energy effective field theory.Comment: 35 pages, 1 figur

Metrics for generalized persistence modules

We consider the question of defining interleaving metrics on generalized persistence modules over arbitrary preordered sets. Our constructions are functorial, which implies a form of stability for these metrics. We describe a large class of examples, inverse-image persistence modules, which occur whenever a topological space is mapped to a metric space. Several standard theories of persistence and their stability can be described in this framework. This includes the classical case of sublevelset persistent homology. We introduce a distinction between `soft' and `hard' stability theorems. While our treatment is direct and elementary, the approach can be explained abstractly in terms of monoidal functors.Comment: Final version; no changes from previous version. Published online Oct 2014 in Foundations of Computational Mathematics. Print version to appea

Null boundary controllability of a 1-dimensional heat equation with an internal point mass

We consider a linear hybrid system composed by two rods of equal length connected by a point mass. We show that the system is null controllable with Dirichlet and Neumann controls. The results are based on a careful spectral spectral analysis together with the moment method.Comment: 12 pages, typos corrected, added references, matches version to be submitted to Systems and Control Letter

Reconciling the Returns to Education in Off-FarmWage Employment in Rural China

Previous studies have found that the returns to education in rural China are far lower than estimates for other developing economies. In this paper, we seek to determine why previous estimates are so low and provide estimates of what we believe are more accurate measures of the returns. Whereas estimates for the early 1990s average 2.3 percent, we find an average return of 6.4 percent. Furthermore, we find even higher returns among younger people, migrants,and for post-primary education. The paper demonstrates that, although part of the difference between our estimate and previous estimates can be attributed to increasing returns during the 1990s, a larger part of the difference is due to the nature of the data and the methodological approaches used by other authors.

Household Investment through migration in Rural China

In this paper, we strive to better understand how household investment is affected by participation in migration in rural China. After we describe investment patterns across different regions of rural China, we use a theoretical model to describe a relationship between migration and investment and to generate hypotheses about the relationship consistent with our descriptive findings. We test the hypotheses using household data collected in rural China in 2000 and find that in poorer areas migration increases consumptive investment by nearly 20 percent. We find no evidence of a link between migration and productive investment.China, migration, development, household investment, dynamic panel data