Jonas A. Actor

Ph.D. Candidate, Rice University

I am currently a Ph.D. candidate in the Department of Computational and Applied Mathematics (CAAM) at Rice University in Houston, Texas. My current research, with Dr. Beatrice Riviere (CAAM) and Dr. David Fuentes (MD Anderson), focuses on automated detection and measurement of liver cancer from medical imaging data. For these tasks, I am developing novel image segmentation techniques that combine partial differential equations and neural networks.

I am a predoctoral fellow of the Gulf Coast Consortia, as part of the Keck Center's National Library of Medicine Training Grant in Biomedical Informatics and Data Science.

In addition to my studies, I serve as a Graduate Writing Consultant at the Center for Academic and Professional Communication . In this position, I advise undergraduate and graduate students on their academic writing and presentations. I have also served two years on the Rice University SIAM Student Chapter executive board, first as secretary and more recently as president, and also on the CAAM department's graduate student advisory board.

I am currently looking for academic positions, for start in summer or fall 2021.

My CV contains more information about me and my research background. I can be reached at jonasactor@rice.edu.  CV

Education
  • Ph.D., Computational and Applied Mathematics, Rice University, May 2021 (expected)
  • M.A., Computational and Applied Mathematics, Rice University, August 2018
  • B.S., Mathematics, University of Chicago, June 2016
Experience
  • Student Assistant, Lawrence Berkeley National Laboratory, May - August 2018
  • Consultant, NanoEar Technologies, September 2017 - May 2018
Teaching
  • Instructor, UNIV 105, Intro to Coding in Python, Rice Emerging Scholars Program, Summer 2020
  • Instructor, UNIV 105, Intro to Coding in Python, Rice Emerging Scholars Program, Summer 2019
  • Guest Lecturer, COMP 543, Data Science Tools and Models, Fall 2019
  • Grader, CAAM 520, Computational Science II, Spring 2020
  • Grader, CAAM 519, Computational Science I, Fall 2019
  • Grader, CAAM 336, Differential equations in Science and Engineering, Spring 2019
  • Grader, CAAM 336, Differential Equations in Science and Engineering, Fall 2018
  • Course Assistant, CAAM 536, Numerical Methods for PDE's, Spring 2018
  • Grader, CAAM 453/550, Numerical Analysis, Fall 2017
  • Grader, CAAM 335, Matrix Analysis, Spring 2017
  • Grader, CAAM 335, Matrix Analysis, Fall 2016
Awards
  • Keck Fellowship, Gulf Coast Consortia, August 2018 - June 2021 (subject to renewal)
  • NSF GRFP, Honorable Mention, April 2018
  • SIAM IS20 Student Travel Award, Travel to SIAM Imaging Sciences 2020, Toronto ON, July 2020
  • Alan Weiser Travel Award, Travel to SGA 2018, TU Munich, July 23-28 2018
  • Computer Science and Engineering Enhancement Fellowship,
       Ken Kennedy Institute for Information Technology, August 2016 - May 2020

Research Interests

  • Scientific machine learning
  • Functional analysis for neural networks
  • Numerical methods for PDE's
  • Image segmentation
  • Biomedical informatics
  • Nonlinear approximation theory
  • Matrix factorization and numerical (multi)linear algebra

Current Research Topics

Differential Equations and Machine Learning for Image Segmentation

Image segmentation is a difficult outstanding task; while classically done using variational methods using partial differential equations, recent advances in machine learning and neural networks have been able to achieve significant improvements in accuracy. My research explores ways to improve deep learning methods for medical image segmentation by exploiting similarities between convolutional neural networks and numerical discretizations for solving partial differential equations.

Specifically, two common techniques for image segmentation, level set methods and convolutional neural networks (CNN), rely on alternating convolutions with nonlinearities to describe image features: neural networks with mean-zero convolution kernels can be viewed as upwind finite difference discretizations of differential equations. Such a comparison provides a well-established framework for proving properties of CNNs, such as stability and approximation accuracy. Using this comparison, I construct a level set network, a CNN whose structure is determined by an upwind discretization of the level set equation, so that by construction, each layer of the network becomes a timestep in our discretization. In this sense, forward propagation through the CNN is equivalent to solving the level set equation. The level set network achieves comparable segmentation accuracy to solving the level set equation, while requiring substantially fewer parameters than conventional CNN architectures.

With Dr. Beatrice Riviere, Rice University, and Dr. David Fuentes, MD Anderson Cancer Center.

Stable Medical Image Segmentation in the Presence of Noise

Over the last decade, deep learning for medical imaging has rapidly become a valuable tool to gather quantitative data in devising better treatments and in improving clinical care. Despite many high-profile successes, there are concerns about the viability of deep learning methods, since many promising results on specific datasets have not been replicable, due to subtle differences in image properties such as noise or image acquisition parameters. In this sense, deep learning methods are unstable: small noise in input can cause drastically different segmentation results. As a result of this instability, deep learning segmentation methods are viewed as “brittle black boxes”, raising questions of reliability and clinical liability. My work address these concerns by improving the stability of deep learning methods. To do so, we propose a novel method that incorporates into the training process a notion of how much each convolution layer can be distorted due to noise. In this approach, Holder’s Inequality bounds the spectral norm of the convolution linear operators, as this norm measures the possible distortion at each layer. Our bound applies to a broader class of convolutions than previous methods, is fast to compute, and requires no additional implementation beyond the tools available in current deep learning toolkits. This bound is incorporated as a regularization term in training as part of this method. We evaluate the effectiveness of our method on models for liver segmentation from CT image data, and we demonstrate that our method helps to stabilize segmentation output in the presence of noise.

With Dr. Beatrice Riviere, Rice University, and Dr. David Fuentes, MD Anderson Cancer Center.

Previous Research Topics

Kolmogorov Superposition Theorem

The Kolmogorov Superposition Theorem (KST) states that any multivariate continuous function can be represented using a small number of superpositions of continuous univariate functions. Specifically, for every continuous function $\,f: [0,1]^n \rightarrow \mathbb{R}$, there exists univariate functions $\,\chi: \mathbb{R} \rightarrow \mathbb{R}$ and $\,\psi_{p,q}: [0,1] \rightarrow \mathbb{R}$ such that $$f(x_1,\dots,x_n) = \sum_{q=0}^{2n} \chi \left( \sum_{p=1}^n \psi_{p,q}(x_p) \right).$$ In this representation, the functions $\,\psi_{p,q}$ do not depend on the function $\,f$ in question. Therefore, we can associate $\,f$ with its corresponding univariate function $\,\chi$, i.e. the function that enables representation via KST. Using this theorem, we effectively trade the number of variables for smoothness: the functions $\,\psi$ and $\,\chi$ are inherently nonsmooth. My research explores how to computationally represent multivariate functions using KST while maintaining the best possible smoothness of these functions.

With Dr. Matthew Knepley, University at Buffalo.

Inertia for Hierarchical Semiseparable (HSS) Matrices

HSS matrix factorization exploits a hierarchical low-rank off-diagonal structure to make the solution of large linear algebra problems feasible. The software package STRUMPACK computes such factorizations for both dense and sparse matrices, making use of multithreading and distributed memory to enable peak performance. However, recent versions of STRUMPACK do not have the capability of finding the inertia of a matrix. This limitation prevents STRUMPACK from being used as a direct solver for optimization problems, where the inertia is needed to evaluate the optimality of a solution. My contributions to STRUMPACK involve adding routines to find the inertia for both dense and sparse HSS matrices. Future work will extend my routines for the distributed memory case.

With Dr. Xiaoye (Sherry) Li and Dr. Pieter Ghysels, Lawrence Berkeley National Laboratory.

Publications and Presentations

Here are materials from recent (and not-so-recent) research I have done. Please see my CV for a full list of publications and presentations.

CV

Publications

Fully Implicit DG Formulations for Time-Dependent Coupled Darcy - Navier-Stokes Equations
Actor, J.A. and B. Riviere.
In preparation, December 2020.
Depthwise Convolution Factorization for Network Compression
Actor, J.A., S. Escobar, and B. Riviere.
In preparation, November 2020.
Effects of CT Scanner Type on Deep Learning Segmentation Algorithms
Actor, J.A., B. Riviere, K. Elsayes, and D. Fuentes.
Submitted, IEEE Internationa Symposium of Biomedical Imaging 2021.
Bridging the Gaps: Adapting a Deep Learning Module for a Mixed Audience
Actor, J.A. and R. Myers
Submitted, ACM TOCE, June 2020.
Robust Regularized Neural Networks in the Presence of Noise
In revision, Med Im Analysis, March 2020.
Identification of Kernels in a Convolutional Neural Network:
Connections Between Level Set Equation and Deep Learning for Image Segmentation.

Actor, J. A., Fuentes, D.T., and B. Riviere.
Proceedings of SPIE Medical Imaging: Image Processing 2020.
Computation for the Kolmogorov Superposition Theorem.
Actor, J. A.
Rice University, Thesis, Master of Arts (2018).
An Algorithm for Computing Lipschitz Inner Functions in Kolmogorov's Superposition Theorem.
Actor, J. A. and M. G. Knepley.
ArXiv (2018).
Break-off Model for $CaCO_3$ Fouling in Heat Exchangers.
Babuska, I., Silva, R. S., and Actor, J. A.
International Journal of Heat and Mass Transfer 116 (2018), 104–114.

Conference Talks and Presentations

Lipschitz Regularization of Convolution Operators for Stable Image Segmentation
Contributed Talk, SIAM Computational Science and Engineering 2021.
Upwind Schemes and Neural Networks for Image Segmentation
Minisymposium Talk, SIAM TX-LA Meeting, October 2020.
PDF Stabilized Image Segmentation in the Presence of Noise
Open Mic Talk, National Library of Medicine Informatics Training Conference (Virtual), June 2020.
PDF Identification of Kernels in a Convolutional Neural Network
Talk, SPIE Medical Imaging : Image Processing, February 2020.
PDF Understanding Neural Networks for Image Segmentation
Minisypmosium Talk, SIAM TX-LA Meeting, November 2019.
PDF Identification of Kernels in a Convolutional Neural Network
Contributed Talk, Ken Kennedy Institute Rice Data Science Conference, October 2019.
Upwind Schemes and Deep Learning for Image Segmentation
Lightning Talk, Gene Golum SIAM Summer School, June 2019.
PDF Exploiting Lipschitz Continuity for the Kolmogorov Superposition Theorem
Talk, Sparse Grids and Applications 2018, TU Munich, July 2018.
PDF The Kolmogorov Superposition Theorem: A Framework for Multivariate Computation
Thesis Defense, Master of Arts, Rice University, May 2018.
PDF Physics-Based Machine Learning for Image Segmentation
Presentation and Interview, Gulf Coast Consortium, February 2018.

Seminars

Introduction to Determinantal Point Processes
Presentation, CAAM Graduate Seminar, November 2020
Nonnegative Matrix Factorization
Chalk Talk, Rice SIAM Journal Club, October 2020.
Models for Medical Image Segmentation
Presentation, CAAM Graduate Seminar, September 2020.
PDF Medical Image Segmentation
Lightning Talk, CAAM Graduate Recruitment Weekend, February 2020.
PDF Understanding Neural Networks for Image Segmentation
Presentation, CAAM Graduate Student Seminar, November 2019.
Tensor Decompositions
Chalk Talk, Rice SIAM Journal Club, November 2019.
Level Set Networks for Medical Image Segmentation
Chalk Talk, CAAM Graduate Seminar, April 2019.
Fast Marching Methods
Chalk Talk, Rice SIAM Journal Club, February 2019.
PDF Finding the Inertia of HSS Matrices
Presentation, CAAM Graduate Seminar, September 2018.
PDF A Primer on Image Segmentation
Presentation, CAAM Graduate Seminar, February 2018.
PDF Lipschitz Inner Functions in Kolmogorov's Superposition Theorem
Presentation, CAAM Graduate Seminar, September 2017.

Posters

Stabilized Image Segmentation in the Presence of Noise
Gulf Coast Consortia Keck Annual Research Conference, October 2020 (poster as slides).
Effects of Convolution Dimension for Medical Image Segmentation
With S. Escobar
SIAM TX-LA Sectional Meeting 2020, October 2020.
Spectral Norms of Convolution Kernels for Medical Image Segmentation
Contributed Talk / Poster, SIAM Imaging Sciences 2020 (Virtual), July 2020.
PDF Stabilizing Deep Convolutional Neural Networks for Image Segmentation
Rice Oil and Gas HPC Conference, Ken Kennedy Institute for Information Technology, March 2020.
PDF Efficient and Robust CT Image Segmentation with a Level Set Network
AMIA Annual Conference, November 2019.
PDF What Do Neural Networks Learn?
Gulf Coast Consortia Keck Annual Research Confernece, October 2019.
Opening the Black Box of a Convolutional Neural Network Used for Brain Tumor Segmentation
With E. McCollum
CPRIT CURE Summer Undergraduate Research Program, 2019.
PDF A Comparison of Image Segmentation Methods
Rice Oil and Gas HPC Conference, Ken Kennedy Institue for Information Technology, March 2019.
Gene Golub SIAM Summer School, June 2019.
Liver Segmentation via Unrolled Mumford-Shah Neural Network
Gulf Coast Consortia Keck Annual Research Conference, October 2018.
PDF Inertia of HSS matrices using STRUMPACK
CSSSP Poster Session, Lawrence Berkeley National Laboratory, August 2018.
PDF Kolmogorov Superposition Theorem: Univariate Encodings for Multivariate Functions
Rice Data Science Conference, Ken Kennedy Institute for Information Technology, October 2017.
Modeling $CaCO_3$ Fouling in Heat Exchangers
Advances in Mathematics of Finite Elements Conference, 2016.
PDF Serial Block Face SEM Visualization of Tuberculosis Infected Macrophages
Fall Meeting of the American Society for Microbiology, Texas Branch, November 2014.

Mathematical Writing and Academic Presentation

Communicating research is difficult yet necessary. Here are a few of my favorite resources; I reference these almost whenever I have to communicate my research: papers, posters, conference talks, research group meetings, etc.

Style Guides and General Resources
  • Strunk and White, The Elements of Style
  • Steenrod, Halmos, Schiffer, and Dieudonne, How to Write Mathematics
Writing Papers
Posters and Presentations

Contact

Email

jonasactor@rice.edu

Office

Duncan Hall 2107
(Google Maps)
(Rice Interactive Map)

Mailing Address

Jonas Actor
Rice University
6100 Main St.
MS 134
Houston, TX 77005