Jonas A. Actor

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

Research Interests

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

Current and Previous Research Topics

Differential Equations and Machine Learning for Image Segmentation

Medical 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.

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

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

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

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