George B. Davis

Clearing the FOG: Fuzzy, overlapping groups for social networks

Humans are well known to belong to many associative groups simultaneously, with various levels of affiliation. However, most group detection algorithms for social networks impose a strict partitioning on nodes, forcing entities to belong to a single group. Link analysis research has produced several methods which detect multiple memberships but force equal membership. This paper extends these approaches by introducing the FOG framework, a stochastic model and group detection algorithm for fuzzy, overlapping groups. We apply our algorithm to both link data and network data, where we use a random walk approach to generate rich links from networks. The results demonstrate that not only can fuzzy groups be located, but also that the strength of membership in a group and the fraction of individuals with exclusive membership are highly informative of emerging group dynamics.

Sequence Similarity Network Reveals Common Ancestry of Multidomain Proteins

We address the problem of homology identification in complex multidomain families with varied domain architectures. The challenge is to distinguish sequence pairs that share common ancestry from pairs that share an inserted domain but are otherwise unrelated. This distinction is essential for accuracy in gene annotation, function prediction, and comparative genomics. There are two major obstacles to multidomain homology identification: lack of a formal definition and lack of curated benchmarks for evaluating the performance of new methods. We offer preliminary solutions to both problems: 1) an extension of the traditional model of homology to include domain insertions; and 2) a manually curated benchmark of well-studied families in mouse and human. We further present Neighborhood Correlation, a novel method that exploits the local structure of the sequence similarity network to identify homologs with great accuracy based on the observation that gene duplication and domain shuffling leave distinct patterns in the sequence similarity network. In a rigorous, empirical comparison using our curated data, Neighborhood Correlation outperforms sequence similarity, alignment length, and domain architecture comparison. Neighborhood Correlation is well suited for automated, genome-scale analyses. It is easy to compute, does not require explicit knowledge of domain architecture, and classifies both single and multidomain homologs with high accuracy. Homolog predictions obtained with our method, as well as our manually curated benchmark and a web-based visualization tool for exploratory analysis of the network neighborhood structure, are available at http://www.neighborhoodcorrelation.org. Our work represents a departure from the prevailing view that the concept of homology cannot be applied to genes that have undergone domain shuffling. In contrast to current approaches that either focus on the homology of individual domains or consider only families with identical domain architectures, we show that homology can be rationally defined for multidomain families with diverse architectures by considering the genomic context of the genes that encode them. Our study demonstrates the utility of mining network structure for evolutionary information, suggesting this is a fertile approach for investigating evolutionary processes in the post-genomic era.

Graph theoretical insights into evolution of multidomain proteins

We study properties of multidomain proteins from a graph theoretical perspective. In particular, we demonstrate connections between properties of the domain overlap graph and certain variants of Dollo parsimony models. We apply our graph theoretical results to address several interrelated questions: do proteins acquire new domains infrequently, or often enough that the same combinations of domains will be created repeatedly through independent events? Once domain architectures are created, do they persist? In other words, is the existence of ancestral proteins with domain compositions not observed in contemporary proteins unlikely? Our experimental results indicate that independent merges of domain pairs are not uncommon in large superfamilies.

Graph theoretical insights into evolution of multidomain proteins.

We study properties of multidomain proteins from a graph theoretical perspective. In particular, we demonstrate connections between properties of the domain overlap graph and certain variants of Dollo parsimony models. We apply our graph theoretical results to address several interrelated questions: do proteins acquire new domains infrequently, or often enough that the same combinations of domains will be created repeatedly through independent events? Once domain architectures are created do they persist? In other words, is the existence of ancestral proteins with domain compositions not observed in contemporary proteins unlikely? Our experimental results indicate that independent merges of domain pairs are not uncommon in large superfamilies.

Algorithms for closed under rational behavior (CURB) sets

We provide a series of algorithms demonstrating that solutions according to the fundamental game-theoretic solution concept of closed under rational behavior (CURB) sets in two-player, normal-form games can be computed in polynomial time (we also discuss extensions to n-player games). First, we describe an algorithm that identifies all of a players best responses conditioned on the belief that the other player will play from within a given subset of its strategy space. This algorithm serves as a subroutine in a series of polynomial-time algorithms for finding all minimal CURB sets, one minimal CURB set, and the smallest minimal CURB set in a game. We then show that the complexity of finding a Nash equilibrium can be exponential only in the size of a games smallest CURB set. Related to this, we show that the smallest CURB set can be an arbitrarily small portion of the game, but it can also be arbitrarily larger than the supports of its only enclosed Nash equilibrium. We test our algorithms empirically and find that most commonly studied academic games tend to have either very large or very small minimal CURB sets.

Unsupervised plan detection with factor graphs

Recognizing plans of moving agents is a natural goal for many sensor systems, with applications including robotic pathfinding, traffic control, and detection of anomalous behavior. This paper considers plan recognition complicated by the absence of contextual information such as labeled plans and relevant locations. Instead, we introduce 2 unsupervised methods to simultaneously estimate model parameters and hidden values within a Factor graph representing agent transitions over time. We evaluate our approach by applying it to goal prediction in a GPS dataset tracking 1074 ships over 5 days in the English channel.