Jonas A. Actor
Ph.D. Student, Rice University
I am currently a Ph.D. student 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.
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
 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
 Alan Weiser Travel Award, Travel to SGA 2018, TU Munich, July 2328 2018
 Computer Science and Engineering Enhancement Fellowship,
Ken Kennedy Institute for Information Technology, August 2016  May 2021
Research Interests
 Nonlinear approximation theory
 Functional analysis for neural networks
 Numerical methods for PDE's
 Image segmentation
 Biomedical informatics
 Matrix factorization and numerical linear algebra
Current and 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 lowrank offdiagonal 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.
Unrolled NN Methods + PDE Functionals for Image Segmentation
More coming soon!
With Dr. Beatrice Riviere, Rice University, and Dr. David Fuentes, MD Anderson Cancer Center.
Publications and Presentations
Here are materials from recent (and notsorecent) research I have done. Please see my CV for a full list of publications and presentations.
Publications 


Construction of Lipschitz Inner Functions via Reparameterization for the Kolmogorov Superposition Theorem. Actor, J. A. and M. G. Knepley. In preparation (2018).  
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. Submitted (2018).  
Breakoff 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.  
Presentations and Posters 


Finding the Inertia of HSS Matrices Presentation, CAAM Graduate Seminar, September 2018. 

Inertia of HSS matrices using STRUMPACK Poster, CSSSP Poster Session, Lawrence Berkeley National Laboratory, August 2018. 

Exploiting Lipschitz Continuity for the Kolmogorov Superposition Theorem Talk, Sparse Grids and Applications 2018, TU Munich, July 2018. 

The Kolmogorov Superposition Theorem: A Framework for Multivariate Computation Thesis Defense, Master of Arts, Rice University, May 2018. 

PhysicsBased Machine Learning for Image Segmentation Presentation and Interview, Gulf Coast Consortium, February 2018. 

A Primer on Image Segmentation Presentation, CAAM Graduate Seminar, February 2018. 

Kolmogorov Superposition Theorem: Univariate Encodings for Multivariate Functions Poster, Rice Data Science Conference, Ken Kennedy Institute for Information Technology, October 2017. 

Lipschitz Inner Functions in Kolmogorov's Superposition Theorem Presentation, CAAM Graduate Seminar, September 2017. 

Serial Block Face SEM Visualization of Tuberculosis Infected Macrophages Poster, 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
 Terence Tao's advice on writing papers
 Colin Purrington's website with tips for writing science papers
Posters and Presentations
 Various thoughts from Paul Halmos, from Notices of the AMS
 Zen Faulkes's Better Posters blog
 Colin Purrington's website with tips for designing conference posters
 Colin Purrington's website with tips for giving science talks
Links and Resources
 CAAM Department at Rice University
 SIAM student chapter at Rice University
 SIAM student membership information (free!)
 Terence Tao's blog, an excellent source of mathematical insight
 Lego Grad Student, a veritable font of academic wisdom
Contact
Office
Duncan Hall 2107
(Google Maps)
(Rice Interactive Map)
Mailing Address
Jonas Actor
Rice University
6100 Main St.
MS 134
Houston, TX 77005