Ongoing Work and Research Opportunities
I currently supervise one Ph.D. student and two undergraduate research students, but I have some projects where I have opportunities for students to study, so I have summarized the state of my open projects (as of Nov 2020).
Statistical Models with Applications to Geoscience REU Program
During the summers of 2021-2023, FIT is hosting an NSF-supported research experience for undergraduates (REU) program involving projects in climate science and marine biology. It's a great opportunity for aspiring scientists to participate in a funded program, get some training, and gain research experience.
This is a relatively new research area for me that has consumed much of my interest in the past couple of years, through teaching, research, and industrial work.
Document Classification: Large-scale machine learning project with a global development company aimed at classifying and categorizing unlabeled documents to facilitate effective knowledge management.
This project is in the early stages, involves several terabytes of documents, and currently focuses on data cleaning and feature extraction. As more features are extracted, they will be used in labeling and organization and feed a document clustering procedure to learn more exploitable structure. As the data becomes structured enough to offer a robust enough labeled dataset, we can pursue a supervised classification approach to the remainder of the unlabeled documents.
Intrusion Detection: I am interested in pushing the boundary of the sorts of intrusions we can detect by taking known attack signatures attempting to learn novel vulnerabilities by generating variations of known signatures via convolutional autoencoders and generative adversarial networks. This work is in its infancy.
I am also open to supervising reasonable machine learning projects proposed by students under certain circumstances, especially those involving neural methods.
Most of my published academic work is in the area of stochastic analysis and probability theory. I have many projects ongoing in this area, which I have broken into several categories, although the categories have some overlapping content.
Reliability of Stochastic Networks: I'm studying another random process taking place on large weighted graphs (networks) where, at random times, random batches of nodes get incapacitated, each with a random number of edges with random weights. I'm interested in finding how long it takes for the sum of nodes or edges or weights lost to surpass some given thresholds.
I have mathematical results, but the next step is to simplify the results to more practical situations, which involves finding the inverses of certain operators, probably via numerical approximations, to confirm they are easy enough to compute to be useful. Then, simulations are needed to confirm the formulas match empirical results.
R. T. White (2015). Random Walks on Random Lattices and Their Applications. PhD thesis, Florida Institute of Technology. [slides] [fulltext]
J. H. Dshalalow and R. T. White (2014). On Strategic Defense in Stochastic Networks. Stochastic Analysis and Applications, 32:3, 365-396. [arXiv preprint]
R. T. White (2013). Stochastic Analysis of Strategic Networks. 38th Annual SIAM Southeastern Atlantic Section Conference. Melbourne, FL. [slides]
J. H. Dshalalow and R. T. White (2013). On Reliability of Stochastic Networks. Neural, Parallel, and Scientific Computations, 21, 141-160 [arXiv preprint]
Random walks: these are points moving around in n-dimensional space by making random jumps at random times. I study the dynamics of these processes when they exit from a fixed set in the space.
Existing models have trouble being applied to fully empirical distributions, although it is, in principle, almost certainly possible, so this is a top priority here.
Mathematical: we need to generalize existing results to higher dimensions and derive similar results for non-monotone processes.
R. T. White & J. H. Dshalalow (2020). Characterizations of random walks on random lattices and their ramifications, Stochastic Analysis and Applications, 38:2, 307-342.
R. T. White (2018). On Exits of Oscillating Random Walks Under Delayed Observation. AMS/MAA Joint Mathematical Meetings. San Diego, CA. [slides]
R. T. White (2017). Time Sensitive Analysis of d-dimensional Independent and Stationary Increment Processes. AMS Fall Southeastern Sectional Meeting. University of Central Florida [slides]
J. H. Dshalalow and R. T. White (2016). Time Sensitive Analysis of Independent and Stationary Increment Processes. Journal of Mathematical Analysis and Applications. 443:2. [arXiv preprint]
R. T. White (2015). Time Sensitive Analysis of Multivariate Marked Random Walks. SIAM Conference on Computational Science and Engineering. Salt Lake City, UT. [slides]
Applied: the models are useful in modeling queuing systems that efficiently order tasks for a processor to do (well-established area) and possibly intrusion detection systems for networks (some new ideas).
J. H. Dshalalow, A. Merie, and R. T. White (2020). Fluctuation Analysis in Parallel Queues with Hysteretic Control. Methodology and Computing in Applied Probability, 22: 295–327.
R. T. White (2019). Fluctuation Analysis in Parallel Queues with Hysteretic Control. AMS Fall Southeastern Sectional Meeting. University of Florida [slides]
J. H. Dshalalow and A. Merie (2018). Fluctuation Analysis in Queues with Several Operational Modes and Priority Customers, TOP, 26: 309-333.
J. H. Dshalalow, K. Iwezulu, and R. T. White (2016). Discrete Operational Calculus in Delayed Stochastic Games. Neural, Parallel, and Scientific Computations, 24: 55-64. [arXiv preprint]
Numerical/Complex Analysis: Current capabilities for computing the inverse Laplace transforms we need are not sufficient for higher-dimensional problems. There are many algorithms in use, none of which are especially good at doing more than two transforms sequentially. There is room for improvement and I have some ideas.
Minimal Sufficient-Probability Sets: I am studying the evolution of small high-probability sets for the location of a stochastic process. We study how these sets change over time by watching how probability density flows through the boundary of the sets from the previous moment in time. I aim to continuously deform the sets over time by analyzing the flux across their boundaries. Much mathematical and applied work is needed.
Mathematical: expand beyond toy examples to determine more general conditions under which it can be done and to find closed-form solutions in these settings, if possible. (It should heavily relate to PDEs, but I have not investigated the link well.)
Applied: implement mathematical results in practical problems, write efficient algorithms to compute similar results for simulated processes where closed-form solutions are elusive, and ensure acceptable error bounds.
R. T. White (2020). On the Evolution of Minimal-Volume, Sufficient-Probability Sets for Stochastic Paths. 14th International Conference in Monte Carlo & Quasi-Monte Carlo Methods in Scientific Computing, Oxford University. [slides]
Students: please feel free to get in touch!