George Mathew

Andrzej Banaszuk, Vladimir A. Fonoberov, Thomas A. Frewen et al.

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks.

George Mathew, Tim Menzies, Jairus Hihn

Context: Early size predictions (ESP) can lead to errors in effort predictions for software projects. This problem is particular acute in parametric effort models that give extra weight to size factors (for example, the COCOMO model assumes that effort is exponentially proportional to project size). Objective: To test if effort estimates are crippled by bad ESP. Method: Document inaccuracies in early size estimates. Use those error sizes to determine the implications of those inaccuracies via a Monte Carlo perturbation analysis of effort models and an analysis of the equations used in those effort models. Results: While many projects have errors in ESP of up to +/- 100%, those errors add very little to the overall effort estimate error. Specifically, we find no statistically significant difference in the estimation errors seen after increasing ESP errors from 0 to +/- 100%. An analysis of effort estimation models explains why this is so: the net additional impact of ESP error is relatively small compared to the other sources of error associated with in estimation models. Conclusion: ESP errors effect effort estimates by a relatively minor amount. As soon as a model uses a size estimate and other factors to predict project effort, then ESP errors are not crippling to the process of estimation

Tuhin Sahai, George Mathew, Amit Surana

Can a dynamical system paint masterpieces such as Da Vinci's Mona Lisa or Monet's Water Lilies? Moreover, can this dynamical system be chaotic in the sense that although the trajectories are sensitive to initial conditions, the same painting is created every time? Setting aside the creative aspect of painting a picture, in this work, we develop a novel algorithm to reproduce paintings and photographs. Combining ideas from ergodic theory and control theory, we construct a chaotic dynamical system with predetermined statistical properties. If one makes the spatial distribution of colors in the picture the target distribution, akin to a human, the algorithm first captures large scale features and then goes on to refine small scale features. Beyond reproducing paintings, this approach is expected to have a wide variety of applications such as uncertainty quantification, sampling for efficient inference in scalable machine learning for big data, and developing effective strategies for search and rescue. In particular, our preliminary studies demonstrate that this algorithm provides significant acceleration and higher accuracy than competing methods for Markov Chain Monte Carlo (MCMC).