#### Timeline Labs (TLL) / SeaChange International

At Timeline Labs we designed algorithms and software to facilitate the discovery of trending and breaking news on Twitter in various news verticals (Entertainment, Music, Sports, Crime, Natural Disasters, etc.) at the global, U.S., and local levels. This included development of ranking and scoring algorithms for content, linguistic rules for defining targeted content streams on Twitter, text clustering, and many different approaches for analyzing social media content.

Two of the more interesting projects we tackled included the **prediction of user location **on Twitter and the** identification of eyewitnesses** and eyewitness events on Twitter.

**Location Prediction on Social Networks**

On Twitter, less than 5% of users have GPS tags on their tweets. However, use of social networks is still very localized in terms of who we communicate with on a daily basis. It turns out that for users Tweeting in English, one can easily predict the location of a majority of users on the network (over 85%) with a median error of under 10 km.

We start by identifying users on the network and all communication patterns between those users (retweets, in-replies, @mentions). Each user's location can be represented by a mixture of Gaussians, and we can then seed this graph with users with known location from their GPS coordinates. Performing a label propagation process on the graph then allows us to add locations to other users based on their connections. Full details are available in the conference proceedings.

* **S. Apreleva and A. Cantarero. Predicting the location of users on Twitter from low density graphs. 2015 IEEE International Conference on Big Data, pp. 976-983, **2015. Link. ResearchGate.*

**Identifying Eyewitness Messages on Twitter**

Identifying messages that came from people who witnessed an event on social media is a very challenging problem. Separating Tweets from news outlets, people resharing the news and others accounts, and those who actually witnessed an event is very interesting for companies interested in identifying news content on social networks.

More details on identifying eyewitness messages on social networks can be found in our conference paper.

*E. Doggett and A. Cantarero. Identifying Eyewitness News-worthy Events on Twitter. Proceedings of the 4th International Workshop on Natural Language Processing for Social Media, 2016. ResearchGate.*

Timeline Labs was acquired by SeaChange International in early 2015. At SeaChange, we focused on problems in content marketing, including identifying and building audiences for news content, predicting engagement on Facebook posts, and using targeted advertising to increase broadcast tune-in, drive in market DMA likes for news outlets, and sales conversions for e-commerce companies.

#### HRL Laboratories

#### Ubiquity Broadcasting Corporation

## I worked as a research scientist for Ubiquity Broadcasting Corporation from 2008-2012. The team I worked with developed next generation video compression technologies for mobile devices as well as object and scene recognition tools operating on video streams such as youtube.

#### University of California, Los Angeles

My dissertation research at UCLA was conducted under the direction of Joseph Teran. I have done work on a couple different problems, described below. The title of my dissertation was *Numerical Methods and Inverse Problems in Elliptic PDEs.*

### Multigrid

We have studied methods for efficiently solving the equations of linear elasticity in the near incompressible limit. Special care must be taken to ensure that multigrid methods maintain their convergence properties in that limit. We also have looked at how to handle irregular domains with geometric multigrid methods to produce fast and efficient solvers. We handle this by embedding the domain in a regular cartesian grid.

Y. Zhu, Y. Wang, J. Hellrung, A. Cantarero, E. Sifakis, and J. Teran.

*A second-order virtual node algorithm for nearly incompressible linear elasticity in irregular domains. *Journal of Computational Physics 231 (2012), pp. 7092-7117.

PDF.

### Elliptic Inverse Problems

We are currently working on inverse problems coming from elliptic PDEs. The basic problem formulation we are considering is that we have some given data that were generated by an elliptic PDE that has piecewise constant coefficients. Given these data, we attempt to recover both the interface between the regions as well as the coefficients in each region. We look at specific examples coming from Poisson's equation and linear elasticity.

Below, we show an example of our results, recovering the interface defining the boundary between two different materials. We start with an initial guess on the left, and as the algorithm runs, we recover the three shapes on the right. In the process of recovering the interface, we also find the parameters that define the two different materials.

J. Hegemann, A. Cantarero, C. Richardson, and J. Teran. An Explicit Update Scheme for Inverse Parameter and Interface Estimation of Piecewise Constant, Discontinuous Coefficients in Linear Elliptic PDEs. **Submitted**.

A second, extremely fast approach to this problem allows us to solve at higher resolutions and with more complex geometry. The basic idea is to build functions that are approximately equal to the unknown coefficients and then recover the regions and coefficient values using a piecewise constant segmentation method. Examples in 2d and 3d are shown below. The image on the left is a composite of images used with permission from

http://www.tribalshapes.com.

A. Cantarero and T. Goldstein. A Fast Method for Interface and Parameter Estimation in Linear Elliptic PDEs with Piecewise Constant Coefficients.

**Submitted. **CAM Report.

#### Sandia National Laboratories

In the summer of 2005 I worked as a student intern at Sandia in Livermore, California under the direction of

Jonathan Hu. My project involved comparing the effectiveness of energy minimization versus smoothed aggregation for generating prolongation operators for algebraic multigrid.

#### University of Colorado, Boulder

As an undergraduate at the University of Colorado I conducted research into a number of areas of image processing using linear algebra, wavelets, and PDE methods.

Most of this research was conducted under Kristian Sandberg, currently at

Computational Solutions. As part of my research and undergraduate thesis (completed in the computer science department under the direction of

Henry Tufo), I focused on automatically extracting cellular structures from images generated via electron microscopy, as well as their efficient and parallel implementation. Our images were obtained from

the Boulder Laboratory for 3-D Electron Microscopy of Cells.

These images contain complicated structure and noise that is not easily statistically modeled, resulting in many standard imaging techniques failing to obtain good results. I managed to obtain reasonably good results through a combination of PDE image denoising coupled with a level set segmentation technique. Examples of results are shown below.