I discuss a formula decomposing the integral of time-ordered products of operators into sums of products of integrals of time-ordered commutators. The resulting factorization enables summation of an infinite series to be carried out to yield an explicit formula for the time-ordered exponentials. The Campbell-Baker-Hausdorff formula and the nonabelian eikonal formula obtained previously are both...

In constancy experiments, humans report very small changes in appearance with substantial illumination changes. Hermann von Helmholtz introduced the term “discounting the illuminant” to describe 19th century thinking about underlying mechanisms of constancy. It uses an indirect approach. Since observers see objects as constant, observers “must” be able to detect the spatial and spectral changes...

We present a decomposition formula for Un, an integral of time-ordered products of operators, in terms of sums of products of the more primitive quantities Cm, which are the integrals of time-ordered commutators of the same operators. The resulting factorization enables a summation over n to be carried out to yield an explicit expression for the time-ordered exponential, an expression which tur...

1Department of Human Communication Science, University Correspondence to: Ruth Campbell, Department of Human College London,UK, 2Max Planck Institut für Psychiatrie, Communication Studies, University College London, Klinisches Institut, München, Germany, 3Program in Chandler House, Wakefield Street, London WC1N 1PG, UK Experimental Psychology, University of Southern California, Santa Cruz, Cali...

This master thesis examines the impact of the New Cooperative Medical Scheme (NCMS) on rural residents' out-of-pocket medical expenses (OOP) in China. The thesis first uses quantitative methods to identify the statistical relationships between NCMS and rural OOP and finds that enrolling in NCMS is associated with higher OOP. Then, using the 2009 reform, also known as Healthy China 2020, as a st...

The research discussed in this paper is the result of the work of a research team organized by the Centre for Schooling and Learning Technologies at Edith Cowan University (http://csalt.education.ecu.edu. au/). The team was led by Paul Newhouse and John Williams and includes senior researchers Dawn Penney, Cher Ping Lim, Jeremy Pagram, Andrew Jones, Martin Cooper, Alistair Campbell, and many re...

In this paper we examine heterogeneity in the simultaneous space-time impact of foreclosures on neighborhood property values. The heterogeneity arises from foreclosed properties that experienced different types of foreclosure outcomes. We find that for foreclosures that are not observed to have concluded with a market sale, the negative price impacts begin while the foreclosing household still ...

This paper characterizes the labor supply and borrowing of a household facing collateral requirements that limit its debt and compel it to accumulate equity in its durable goods stock. The household's discount rate exceeds the market rate of interest, so it would otherwise finance increased current consumption by borrowing against future wages. Collateral constraints generate a positive comovem...

iii Acknowledgments I would like to thank Professor Roy H. Campbell for his considerable assistance in providing direction and helping me successfully achieve my goals for this project. Special thanks to Fabio Kon for providing support in many ways, the answers to many questions, and for performing an excellent review of this thesis. I also want to thank the other members of the 2K project team...

For each automatic monoid the word problem can be solved in quadratic time (Campbell et al 1996), and hence, the Dehn function of a nitely presented automatic monoid is recursive. Here we show that this result on the Dehn function cannot be improved in general by presenting nitely presented bi-automatic monoids the Dehn functions of which realize arbitrary complexity classes that are suuciently...