Results

Evolving Gene Networks During Drosophila Development

We applied TESLA to estimate the latent sequence of temporal rewiring gene network during the life cycle of Drosophila Melanogaster from a microarray time course. Our results offer the first glimpse into the temporal evolution of gene networks in a living organism during its full developmental course. Below we show a “movie” of the Drosophila developmental gene network as the organism ages using a circular layout and a scatter plot of the network adjacency. In the circular layout, genes are ordered according to their top level biological function. The dynamic networks appear to rewire over time in response to the developmental requirement of the organism. For instance, in the middle of embryonic stage, most of genes selectively interact with other genes which results in a sparse network consisting mainly of paths. In contrast, near the end of the adulthood stage, genes are more active and each gene interacts with many other genes which leads to visible clusters of gene interactions.

Moreover, we used the recovered networks by TESLA to pinpoint the temporal on-and-off sequence for previously verified known gene interactions in Flybase and visually display them in the following figure. The activation of each gene interaction over time is represented as one column. Within each column, if a gene interaction is active a blue dot is drawn otherwise the space is left blank. To ease visualization, hierarchical clustering is performed on these set of recovered gene interactions based on their activation patterns. It can be seen that all these interactions are transient and very specific to a certain stage of the life cycle of the Drosophila Melanogaster. The specific names of the genes involved in the interactions are not shown to avoid over-crowding the figure

US Senate Network

We used TESLA to analyze the voting record of 642 bills brought to U.S. Senate of the 109th Congress (2005 – 2006). Each of the 100 senators can be regarded as a node in a latent evolving social network in the senate. Our goal was to discover how the relationships between senators change over time. Below we depict three estimated networks at March 2005, Jan 2006, and Aug 2006, respectively. In this figure rectangular, ellipsoid, and diamond nodes denote Democrats, Republicans and Independents, respectively. Democratic and Republican senators tended to bunch together (with then-Sen. Barack Obama always connected only to other Democrats) in their voting, though there were anomalies. For instance, Sen. James Jeffords, then an independent senator from Vermont, had a voting record that was closely tied to Democrats, though around January 2006 his voting began to reflect slightly more connections with the Republicans, his original party. The votes of then-Sen. Lincoln Chafee (R-R.I.) can be seen to progressively change toward the Democrats; he subsequently became an Independent after losing re-election in 2006.

Author-Keyword Academic Social Network

We used TESLA to reverse engineer and analyze the dynamics of the academic social network over authors and keywords in the proceeding of NIPS, a machine learning conference, from the years of 1987-1999. To visualize the result, we select 6 keyword nodes:`Gaussian’, `classifier’ , `likelihood’, `approximation’, `error’ and `variational’ (highlighted in the following figure), and track their subnetworks containing neighboring authors and keywords up to the first neighbors to avoid over-crowding the display. The following figure shows the NIPS networks corresponding to the first and last two epochs. Looking at this figure, first, one should observe the smooth transition between the networks from 1987 to 1988 and from 1998 to 1999. Second, the size of the neighborhood of a word is a good indication of the contextual diversity of the usage of this word. For instances, in early years, the word `likelihood’ had a limited context in `Gaussian’ settings; however, over the years, this behavior changed and at the year 1998 and 1999 `likelihood’ started to appear in different contexts like `speech’, `Bayesian’, `mixture’, etc., thus its neighborhood expanded over the years. On the other hand, words like `Gaussian’ were always popular in different settings and get more popular over the years and as such the model smoothly expanded its neighborhood as well. Also, note how `Hinton’ (a famous machine learning researcher) was always connected to terms related to Boltzmann machines like `distribution’ and `field’ in the 1980s and `weights’ on 1998, and how the work ‘variational’ was dominated in recent years of the conference by `Jordan’ and `Ghahramani’ who werevery active researchers in this area at this time