**1. Community Detection and Detectability in Multilayer Networks**

**Collaborators: Saray Shai, Dane Taylor, Peter Mucha**

Multilayer networks refer to a collection of networks, where each ‘layer’ encodes one type of interaction. For example, a temporal network can be considered a multilayer network where each layer encodes a network at a particular time. In an effort to understand how community structure can be detected and understood in multilayer networks, we have developed strata multilayer stochastic block model, which is a stochastic block model for multilayer networks. Since community structure can be difficult to detect when networks are sparse, we explored limits of detectability in this model.

**2. Network Compression**

**Collaborators: Roland Kwitt, Marc Niethammer, Peter Mucha**

Community detection becomes challenging in large networks. To facilitate these tasks, we are investigating effective ways to initially compress the network by combining individual nodes into ‘super nodes’ in a principled way. This approach is analogous to and inspired by superpixels in the image segmentation literature, which aims to pre-process images before applying image segmentation.

**3. Classification of the Urinary Metabolome **

**Collaborators: Jeff Henderson, Lindsey Steinberg , Peter Mucha**

We focus on how to profile and understand differences in the urinary metabolomes of different groups of patients.

**4. Understanding Microbial Interactions in the Lung Microbiome**

**Collaborators: Dana Walsh**

From metagenomic sequence data in a collection of burn patients with injury to the lungs/airways, we focus on how to study changes in the microbiome composition of certain subsets of patients. Specifically, we have been studying changes in species co-occurence and microbial interaction networks in groups of patients.

**5. Attributed Stochastic Block Model**

**Collaborators: (See #2)**

We extend the stochastic block model to a setting where nodes have a vector of continuous attributes. To find communities, we use leverage both sources of information in the inference of the stochastic block model parameters.

**6. Longitudinal Network Analysis Applied to Brain Connectivity Data**

**Collaborators: (See #2,6)**

I am applying a variety of machine learning techniques to understand similarities between brain connectivity networks across subjects and how they change over time.** **