Tom LaGatta

Elections, Protest, and Alternation of Power

Canonical theories of elections assume that rules determining the winner will be followed, which necessitates separate models for democratic and nondemocratic elections. To overcome this bifurcation in the literature, we develop a model where compliance is determined endogenously. Rather than serve as a binding contract, elections are modeled solely as a public signal of the regime’s popularity. However, citizens can protest against leaders who break electoral rules. Compliance is possible when the election is informative enough that citizens can coordinate on either massive protests or supporting the incumbent in the case of close results. Leaders may also step down after performing poorly in a less informative election independent of the rules, but unlike the case of rule-based alternation, this often requires citizens to protest in equilibrium. An extension shows why reports of electoral fraud are often central to post-election protests and thus why international or domestic monitoring may be required for electoral rules to be enforceable.

A shape theorem for Riemannian first-passage percolation

Riemannian first-passage percolation is a continuum model, with a distance function arising from a random Riemannian metric in Rd. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability of 1.

Continuous Disintegrations of Gaussian Processes

The goal of this paper is to understand the conditional law of a stochastic process once it has been observed over an interval. To make this precise, we introduce the notion of a continuous disintegration: a regular conditional probability measure which varies continuously in the conditioned parameter. The conditioning is infinite-dimensional in character, which leads us to consider the general case of probability measures in Banach spaces. Our main result is that for a certain quantity

Geodesics of Random Riemannian Metrics

M

Systems Biology of Cancer: A Challenging Expedition for Clinical and Quantitative Biologists

based on the covariance structure, the finiteness of M is a necessary and sufficient condition for a Gaussian measure to have a continuous disintegration. The condition is quite reasonable: for the familiar case of stationary processes, M = 1.

Geodesics of Random Riemannian Metrics: Supplementary Material

We analyze the disordered Riemannian geometry resulting from random perturbations of the Euclidean metric. We focus on geodesics, the paths traced out by a particle traveling in this quenched random environment. By taking the point of the view of the particle, we show that the law of its observed environment is absolutely continuous with respect to the law of the random metric, and we provide an explicit form for its Radon–Nikodym derivative. We use this result to prove a “local Markov property” along an unbounded geodesic, demonstrating that it eventually encounters any type of geometric phenomenon. We also develop in this paper some general results on conditional Gaussian measures. Our Main Theorem states that a geodesic chosen with random initial conditions (chosen independently of the metric) is almost surely not minimizing. To demonstrate this, we show that a minimizing geodesic is guaranteed to eventually pass over a certain “bump surface,” which locally has constant positive curvature. By using Jacobi fields, we show that this is sufficient to destabilize the minimizing property.

Prizes, Groups and Pivotal Voting in a Poisson Voting Game

A systems-biology approach to complex disease (such as cancer) is now complementing traditional experience-based approaches, which have typically been invasive and expensive. The rapid progress in biomedical knowledge is enabling the targeting of disease with therapies that are precise, proactive, preventive, and personalized. In this paper, we summarize and classify models of systems biology and model checking tools, which have been used to great success in computational biology and related fields. We demonstrate how these models and tools have been used to study some of the twelve biochemical pathways implicated in but not unique to pancreatic cancer, and conclude that the resulting mechanistic models will need to be further enhanced by various abstraction techniques to interpret phenomenological models of cancer progression.