Learning low-rank latent mesoscale structures in networks.

Researchers in many fields use networks to represent interactions between entities in complex systems. To study the large-scale behavior of complex systems, it is useful to examine mesoscale structures in networks as building blocks that influence such behavior. In this paper, we present an approach to describe low-rank mesoscale structures in networks. We find that many real-world networks possess a small set of latent motifs that effectively approximate most subgraphs at a fixed mesoscale. Such low-rank mesoscale structures allow one to reconstruct networks by approximating subgraphs of a network using combinations of latent motifs. Employing subgraph sampling and nonnegative matrix factorization enables the discovery of these latent motifs. The ability to encode and reconstruct networks using a small set of latent motifs has many applications in network analysis, including network comparison, network denoising, and edge inference.

Learning to predict synchronization of coupled oscillators on randomly generated graphs.

Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph structure, this is an important yet analytically intractable question in general. In this work, we take an alternative approach to the synchronization prediction problem by viewing it as a classification problem based on the fact that any given system will eventually synchronize or converge to a non-synchronizing limit cycle. By only using some basic statistics of the underlying graphs such as edge density and diameter, our method can achieve perfect accuracy when there is a significant difference in the topology of the underlying graphs between the synchronizing and the non-synchronizing examples. However, in the problem setting where these graph statistics cannot distinguish the two classes very well (e.g., when the graphs are generated from the same random graph model), we find that pairing a few iterations of the initial dynamics along with the graph statistics as the input to our classification algorithms can lead to significant improvement in accuracy; far exceeding what is known by the classical oscillator theory. More surprisingly, we find that in almost all such settings, dropping out the basic graph statistics and training our algorithms with only initial dynamics achieves nearly the same accuracy. We demonstrate our method on three models of continuous and discrete coupled oscillators-the Kuramoto model, Firefly Cellular Automata, and Greenberg-Hastings model. Finally, we also propose an "ensemble prediction" algorithm that successfully scales our method to large graphs by training on dynamics observed from multiple random subgraphs.

On the relation of gene essentiality to intron structure: a computational and deep learning approach.

Essential genes have been studied by copy number variants and deletions, both associated with introns. The premise of our work is that introns of essential genes have distinct characteristic properties. We provide support for this by training a deep learning model and demonstrating that introns alone can be used to classify essentiality. The model, limited to first introns, performs at an increased level, implicating first introns in essentiality. We identify unique properties of introns of essential genes, finding that their structure protects against deletion and intron-loss events, especially centered on the first intron. We show that GC density is increased in the first introns of essential genes, allowing for increased enhancer activity, protection against deletions, and improved splice site recognition. We find that first introns of essential genes are of remarkably smaller size than their nonessential counterparts, and to protect against common 3' end deletion events, essential genes carry an increased number of (smaller) introns. To demonstrate the importance of the seven features we identified, we train a feature-based model using only these features and achieve high performance.

Antibiotic Treatment Response in Chronic Lyme Disease: Why Do Some Patients Improve While Others Do Not?

There is considerable uncertainty regarding treatment of Lyme disease patients who do not respond fully to initial short-term antibiotic therapy. Choosing the best treatment approach and duration remains challenging because treatment response among these patients varies: some patients improve with treatment while others do not. A previous study examined treatment response variation in a sample of over 3500 patients enrolled in the MyLymeData patient registry developed by LymeDisease.org (San Ramon, CA, USA). That study used a validated Global Rating of Change (GROC) scale to identify three treatment response subgroups among Lyme disease patients who remained ill: nonresponders, low responders, and high responders. The present study first characterizes the health status, symptom severity, and percentage of treatment response across these three patient subgroups together with a fourth subgroup, patients who identify as well. We then employed machine learning techniques across these subgroups to determine features most closely associated with improved patient outcomes, and we used traditional statistical techniques to examine how these features relate to treatment response of the four groups. High treatment response was most closely associated with (1) the use of antibiotics or a combination of antibiotics and alternative treatments, (2) longer duration of treatment, and (3) oversight by a clinician whose practice focused on the treatment of tick-borne diseases.