Automated digital watermarking is an excellent technique for prevention of online digital data from theft and piracy. With current advances in internet, network and social media technologies, protecting online data theft and piracy to preserve brand ownership remains a top priority. A watermark is a pattern inserted into a digital image, audio or video file which identifies a file’s copyright information. Common types of signals to watermark are text, digital images, audio music clips and videos. Digital images are stored as arrays/matrices on computers which allows matrix-algebra based methods for image processing. We have applied mathematical modeling techniques using singular value decomposition (SVD) for digital watermarking of visual data. We wrote Python-based codes to digitize images and embedded copyright information into visual images using SVD based methods. We find that the embedded watermark is tamper resistant and the watermark could be retrieved from manipulated greyscale images subject to rotation and compression distortions. Our preliminary studies using greyscale images suggest that SVD based digital watermarking methods are robust and can be used to verify and authenticate data ownership. Digital watermarking can be used to prevent copyright infringement and data theft online. This project integrates advanced application of linear-algebra based mathematical methods with Python based programming to provide solutions to real-world problems of current interest.

 Nano-devices, nanoscale metals, and other molecular-scale electronics are key components in most modern electronics, and the semiconductor industry is continuously looking for ways to improve on existing technology. Innovation of this kind can be aided by computer simulations, such as electronic conductance simulations, which can be used to predict the performance of prospective devices without manufacturing a prototype, or for explanatory modeling of existing devices. To simulate open boundary conditions in a finite space, one such electronic conductance code, TRANSEC, uses complex absorbing potentials (CAPs) to keep electrons that interact with the simulation boundaries from reflecting and interfering with results. These CAPs take the form of complex-valued functions placed at the boundaries of the simulation, and must be tuned to successfully absorb electrons. The larger the CAP width is, the more space needs to be simulated to accommodate it, which increases computing time. The goal of our research has been to optimize the CAP form and volume so as to reduce the CAP’s impact on computing time. To do this, we have used a simplified tight-binding model of an electronic transport calculation, allowing us to efficiently perform evaluations of CAP accuracy for numerous CAP forms and widths. Our results thus far indicate that the gaussian CAP form performs at least as well as monomial forms of order 1 through 5, and that CAP width can be decreased significantly by increasing the CAP height parameter. This research pertains particularly to the existing electronic transport code, TRANSEC, as well as to other approaches that make use of CAPs.

Mathematical modeling and simulations of the gait and pose of mobile robots find important applications for mobile robot design for process automation, industrial applications, and deriving algorithms for walking styles. Here, we have used Webot robotic simulations and mathematical modeling methods to study, analyze and interpret the gait and pose of six-legged (hexapod) and four-legged (quadruped) robots that mimic dog-like movements. Hexapod and quadruped mobile robots are perfect for deployment for outer space exploration as these mobile robots can traverse uneven terrain and use artificial intelligence to plan their safe foothold positions to navigate their environment. We have analyzed the simulated gait and pose of the hexapod robot using rigid body inverse kinematics and symmetry analysis. The hexapod mantis insect-shaped robot motion in the simulations can be expressed as linear combinations of rigid translational and rotational motion. The hexapod robot moves using an alternating tripod-like gait wherein three legs move at a time while the other three remain stationary. The hexapod robot has greater dynamic stability for uneven terrain and can move more legs as compared to a quadruped robot. This research project serves as an elegant platform for applications of simulations and mathematical methods for studying the gait and stability of legged mobile robots that are relevant for the safety design of computer-controlled walking robots for radioactive waste management, space exploration, and for the design of mobile robots working in nuclear power stations and finding other industrial applications.

For investigations into nanoscopic properties of matter, computational simulation is a key tool. In particular, simulations of the electronic configuration and conductance of nanoscale devices facilitate the continued miniaturization of semiconductor devices used in integrated circuits and computer processors. However, due to the importance of quantum mechanics at these scales, accurate calculations can be highly costly. In our research we consider improvements to one such parallelizable electronic transport code, TRANSEC. We seek to better understand how a Monte Carlo technique, combined with a special polynomial expansion, may improve the scaling of TRANSEC’s computing time with the size of the simulation. We apply the Monte Carlo technique within a simplified tight-binding model of a TRANSEC calculation. We test how the Monte Carlo technique facilitates the calculation of the electronic transmission probability, given an initial Hamiltonian energy matrix along with absorbing boundary conditions (referred to as complex absorbing potentials, or CAPs). We expect that the results of this study may provide algorithms which allow for faster calculation times when integrated at scale into TRANSEC. Improvements to computing time for determining parameters such as nanoscopic conduction helps to advance computer modeling of nanoscopic structures (such as transistors, interconnect, or molecular electronics), which could benefit semiconductor technology.

Fused Deposition Modeling (FDM), typical for thermoplastic polymer fabrication, has become the most accessible technique among all 3D printing methods for both non-professional users and engineers. However, one primary consideration of FDM prototype application is the high directional dependency of material-structural properties due to its inherent additive building process. This includes, but is not limited to, mechanical strength, thermal conductivity, and porosity. On behalf of the Boeing Advanced Research Center at UW, I am leading The Boeing Company's Additively Manufactured Polymer Structure project series and studying the characteristics of FDM PEEK prototypes. My work focused on the relationship between meso-level porosity and macro mechanical behaviors on FDM parts with multiphysics & multiscale analysis. This study attempts to validate the accuracy of closed-form equation approximations by correlating the models' numerical analysis results with mechanical testing measurements. The study result is envisioned to simplify the analytical modeling process of generic FDM products while also defining the credible region & potential influence of relevant parameters, adding confidence to all-leveled FDM parts applications.

Approximate computing provides benefits with respect to logic area, latency, and/or power consumption without significantly affecting the outputs of some applications. Various approximate computing techniques have been applied for floating-point (FP) dividers, as division is resource-expensive compared to other FP operations. Since the accuracy requirement may vary depending on the application, this project uses an accuracy-configurable FP divider design. My design first computes the approximate reciprocal of a divisor in a hardware-friendly way. To compensate for errors, I calculated multiple error biases based on error analyses of possible input value ranges. A specific error correction is then applied using a lookup table to select the correct value from the table as determined by the divisor input. The calculated reciprocal is then multiplied by a dividend using an iterative logarithmic FP multiplier, which features accuracy-configurability. This allows applications to determine the desired level of accuracy, versus latency and power consumption, by selecting the number of iterations the multiplier will use. My FP divider design greatly improves the accuracy of previous approximate logarithmic FP divider designs by only adding a small number of hardware resources to our existing FP multiplier. Compared to the state-of-the-art design, the proposed design reduces the amount of required lookup table logic blocks by 53%, and the number of flip-flops by 90%, in a hardware implementation. As the prevalence of division and multiplication-intensive applications, such as artificial neural networks, continues to increase, improving the efficiency of these operations is becoming more critical. This research demonstrates that approximate computing can be a viable approach for many applications and provides a benchmark for future researchers working on methods to streamline division and multiplication operations.

In face-to-face surveys containing sensitive questions, Social Desirability Bias (SDB), respondent’s tendency to provide socially acceptable responses rather than truthful ones, can compromise data accuracy. Randomized response techniques (RRT) are survey models that allow respondents to provide scrambled responses, thereby circumventing SDB. In this study, we introduce a mixture optional quantitative RRT model that combines the elements of both the Pollock and Bek (1976) additive RRT model and the Greenberg et al. (1971) unrelated question quantitative RRT model. We examine the utility of the proposed mixture model using a unified measure of efficiency and privacy introduced by Gupta et al. (2018) that provides a metric of both predictive accuracy and respondent privacy. We also account for the lack of trust in RRT models. Both empirical and theoretical results show that the mixture model outperforms the two component models. The proposed optional quantitative mixture RRT model provides a survey technique that can account for not only SDB but also respondent lack of trust, leading to more accurate and interpretable data used to inform decision making that does not compromise the privacy of respondents.