Analysis of soil carbon transit times and age distributions using network theories

The long-term soil carbon dynamics may be approximated by networks of linear compartments, permitting theoretical analysis of transit time (i.e., the total time spent by a molecule in the system) and age (the time elapsed since the molecule entered the system) distributions. We compute and compare these distributions for different network. configurations, ranging from the simple individual compartment, to series and parallel linear compartments, feedback systems, and models assuming a continuous distribution of decay constants. We also derive the transit time and age distributions of some complex, widely used soil carbon models (the compartmental models CENTURY and Rothamsted, and the continuous-quality Q-Model), and discuss them in the context of long-term carbon sequestration in soils. We show how complex models including feedback loops and slow compartments have distributions with heavier tails than simpler models. Power law tails emerge when using continuous-quality models, indicating long retention times for an important fraction of soil carbon. The responsiveness of the soil system to changes in decay constants due to altered climatic conditions or plant species composition is found to be stronger when all compartments respond equally to the environmental change, and when the slower compartments are more sensitive than the faster ones or lose more carbon through microbial respiration. Copyright 2009 by the American Geophysical Union.

Fermion bag approach to lattice field theories

We propose a new approach to the fermion sign problem in systems where there is a coupling U such that when it is infinite the fermions are paired into bosons, and there is no fermion permutation sign to worry about. We argue that as U becomes finite, fermions are liberated but are naturally confined to regions which we refer to as fermion bags. The fermion sign problem is then confined to these bags and may be solved using the determinantal trick. In the parameter regime where the fermion bags are small and their typical size does not grow with the system size, construction of Monte Carlo methods that are far more efficient than conventional algorithms should be possible. In the region where the fermion bags grow with system size, the fermion bag approach continues to provide an alternative approach to the problem but may lose its main advantage in terms of efficiency. The fermion bag approach also provides new insights and solutions to sign problems. A natural solution to the "silver blaze problem" also emerges. Using the three-dimensional massless lattice Thirring model as an example, we introduce the fermion bag approach and demonstrate some of these features. We compute the critical exponents at the quantum phase transition and find ν=0.87(2) and η=0.62(2). © 2010 The American Physical Society.

Integrating simultaneous prosocial and antisocial behavior into theories of collective action.

Trust and cooperation constitute cornerstones of common-pool resource theory, showing that "prosocial" strategies among resource users can overcome collective action problems and lead to sustainable resource governance. Yet, antisocial behavior and especially the coexistence of prosocial and antisocial behaviors have received less attention. We broaden the analysis to include the effects of both "prosocial" and "antisocial" interactions. We do so in the context of marine protected areas (MPAs), the most prominent form of biodiversity conservation intervention worldwide. Our multimethod approach relied on lab-in-the-field economic experiments (n = 127) in two MPA and two non-MPA communities in Baja California, Mexico. In addition, we deployed a standardized fishers' survey (n = 544) to verify the external validity of our findings and expert informant interviews (n = 77) to develop potential explanatory mechanisms. In MPA sites, prosocial and antisocial behavior is significantly higher, and the presence of antisocial behavior does not seem to have a negative effect on prosocial behavior. We suggest that market integration, economic diversification, and strengthened group identity in MPAs are the main potential mechanisms for the simultaneity of prosocial and antisocial behavior we observed. This study constitutes a first step in better understanding the interaction between prosociality and antisociality as related to natural resources governance and conservation science, integrating literatures from social psychology, evolutionary anthropology, behavioral economics, and ecology.

Do the Messages Matter? An Investigation of Classroom Messages and College Students’ Personal Theories about Education

Students hold a number of personal theories about education that influence motivation and achievement in the classroom: theories about their own abilities, knowledge, and the learning process. Therefore, college instructors have a great interest in helping to develop adaptive personal theories in their students. The current studies investigated whether specific messages that instructors send in college classroom might serve as a mechanism of personal theory development. Across 2 studies, 17 college instructors and 401 students completed surveys assessing their personal theories about education at the beginning and end of college courses. Students and instructors reported hearing and sending many messages in the classroom, including instructor help messages, conciliatory messages, uncertainty in the field messages, differential ability messages and generalized positive and negative feedback. Between-class and within-class differences in message reports were associated with students’ personal theories at the end of their courses, controlling for initial personal theories. Students’ initial personal theories were also related to the messages students reported hearing. The findings demonstrate the utility of assessing non-content messages in college classrooms as potential mechanisms for changing students’ personal theories in college. Implications for research and practice are discussed.

Moduli Space of (0,2) Conformal Field Theories

In this thesis we study aspects of (0,2) superconformal field theories (SCFTs), which are suitable for compactification of the heterotic string. In the first part, we study a class of (2,2) SCFTs obtained by fibering a Landau-Ginzburg (LG) orbifold CFT over a compact K\"ahler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model (GLSM), our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of GLSMs and comparing spectra among the phases. In the second part, we turn to the study of the role of accidental symmetries in two-dimensional (0,2) SCFTs obtained by RG flow from (0,2) LG theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) LG models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. In the final part, we study the stability of heterotic compactifications described by (0,2) GLSMs with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of GLSMs for which a vanishing theorem holds.

Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion

and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.