The Cube Recurrence

We construct a combinatorial model that is described by the cube recurrence, a nonlinear recurrence relation introduced by Propp, which generates families of Laurent polynomials indexed by points in $\mathbb{Z}^3$. In the process, we prove several conjectures of Propp and of Fomin and Zelevinsky, and we obtain a combinatorial interpretation for the terms of Gale-Robinson sequences. We also indicate how the model might be used to obtain some interesting results about perfect matchings of certain bipartite planar graphs

Optimal Defaults and Active Decisions

Defaults can have a dramatic influence on consumer decisions. We identify an overlooked but practical alternative to defaults: requiring individuals to make an explicit choice for themselves. We study such "active decisions" in the context of 401(k) saving. We find that compelling new hires to make active decisions about 401(k) enrollment raises the initial fraction that enroll by 28 percentage points relative to a standard opt-in enrollment procedure, producing a savings distribution three months after hire that would take three years to achieve under standard enrollment. We also present a model of 401(k) enrollment and characterize the optimal enrollment regime. Active decisions are optimal when consumers have a strong propensity to procrastinate and savings preferences that are highly heterogeneous. Naive beliefs about future time-inconsistency strengthen the normative appeal of the active-decision enrollment regime. However, financial illiteracy favors default enrollment over active decision enrollment.

Approaches to mechanism design with boundedly rational agents

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Economics, 2012.Cataloged from PDF version of thesis.Includes bibliographical references.This dissertation ties together three papers on mechanism design with boundedly rational agents. These papers explore theoretically whether, and to what extent, limitations on agents' ability to strategically misrepresent their preferences can help a mechanism designer achieve outcomes that she could not achieve with perfectly rational agents. The first chapter investigates whether local incentive constraints are sufficient to logically imply full incentive-compatibility, in a variety of mechanism design settings. This can be motivated by a boundedly rational model in which agents cannot contemplate all possible misrepresentations, but can consider those that are close to their true preferences. This chapter offers a unified approach that covers both continuous and discrete type spaces, showing that in many commonly studied cases, local incentive-compatibility (suitably defined) implies full incentive-compatibility. The second chapter advances the methodology of looking quantitatively at incentives for strategic behavior, motivated by the premise that agents will be truthful if the incentive to be strategic is small enough. This chapter defines a mechanism's susceptibility to manipulation as the maximum amount of expected utility any agent can ever gain from strategic misrepresntation. This measure of susceptibility is then applied to anonymous voting rules. One set of results estimates the susceptibility of specific voting rules; an important finding is that several voting systems previously identified as resistant to manipulation are actually more susceptible than simple plurality rule, by the measure proposed here. A second set of results gives asymptotic lower bounds on susceptibility for any possible voting rule, under various combinations of efficiency, regularity, and informational conditions. These results illustrate how one can quantitatively explore the tradeoffs between susceptibility and other properties of the voting rule. The third chapter carries the methodology of the second chapter to a market environment: unit-demand, private-value double auction markets. This chapter quantitatively studies the tradeoff between inefficiency and susceptibility to manipulation, among all possible mechanisms for such markets. The main result approximately locates the possibility frontier, pinning it down within a factor that is logarithmic in the size of the market.by Gabriel D. Carroll.Ph.D

A New Test of the Einstein Equivalence Principle and the Isotropy of Space

Recent research has established that nonsymmetric gravitation theories like Moffat's NGT predict that a gravitational field singles out an orthogonal pair of polarization states of light that propagate with different phase velocities. We show that a much wider class of nonmetric theories encompassed by the $\chi g$ formalism predict such violations of the Einstein equivalence principle. This gravity-induced birefringence of space implies that propagation through a gravitational field can alter the polarization of light. We use data from polarization measurements of extragalactic sources to constrain birefringence induced by the field of the Galaxy. Our new constraint is $10^8$ times sharper than previous ones.Comment: 21 pages, Latex, 3 Postscript figure

Altered spring phenology of North American freshwater turtles and the importance of representative populations

Globally, populations of diverse taxa have altered phenology in response to climate change. However, most research has focused on a single population of a given taxon, which may be unrepresentative for comparative analyses, and few long-term studies of phenology in ectothermic amniotes have been published. We test for climate- altered phenology using long-term studies (10–36 years) of nesting behavior in 14 populations representing six genera of freshwater turtles (Chelydra, Chrysemys, Kinosternon, Malaclemys, Sternotherus, and Trachemys). Nesting season initiation oc- curs earlier in more recent years, with 11 of the populations advancing phenology. The onset of nesting for nearly all populations correlated well with temperatures during the month preceding nesting. Still, certain populations of some species have not advanced phenology as might be expected from global patterns of climate change. This collection of findings suggests a proximate link between local climate and reproduction that is potentially caused by variation in spring emergence from hibernation, ability to process food, and thermoregulatory opportunities prior to nesting. However, even though all species had populations with at least some evi- dence of phenological advancement, geographic variation in phenology within and among turtle species underscores the critical importance of representative data for accurate comprehensive assessments of the biotic impacts of climate change

Signals for Lorentz Violation in Electrodynamics

An investigation is performed of the Lorentz-violating electrodynamics extracted from the renormalizable sector of the general Lorentz- and CPT-violating standard-model extension. Among the unconventional properties of radiation arising from Lorentz violation is birefringence of the vacuum. Limits on the dispersion of light produced by galactic and extragalactic objects provide bounds of 3 x 10^{-16} on certain coefficients for Lorentz violation in the photon sector. The comparative spectral polarimetry of light from cosmologically distant sources yields stringent constraints of 2 x 10^{-32}. All remaining coefficients in the photon sector are measurable in high-sensitivity tests involving cavity-stabilized oscillators. Experimental configurations in Earth- and space-based laboratories are considered that involve optical or microwave cavities and that could be implemented using existing technology.Comment: 23 pages REVTe

Effective dissipative dynamics for polarized photons

In the framework of open quantum systems, the propagation of polarized photons can be effectively described using quantum dynamical semigroups. These extended time-evolutions induce irreversibility and dissipation. Planned, high sensitive experiments, both in the laboratory and in space, will be able to put stringent bounds on these non-standard effects.Comment: 15 pages, plain-TeX, no figure

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types