Institutional Repository

: Integrating Ethics Into a Research Experience for Undergraduates; Abstract A Research Experience for Undergraduates (REU) is an extra-curricular opportunity for science or engineering students in the sophomore, junior, or senior year to participate in academic research in much the way graduate students do. It is a way to introduce undergraduates to the excitement of real research. Because it also seems an easy and attractive way to integrate ethics into undergraduate education, working out how professors of engineering or science might actually incorporate professional ethics into an REU seems desirable. This paper describes one effort to do that with engineering students.

: Algorithms for Discrete Data in Statistics and Operations Research; Sponsorship: The Air Force Office of Scientific Research's grant FA9550-14-1-0141 supported Prof. Petrović's and my initial work on this project.

: L-cumulants, L-cumulant embeddings and algebraic statistics; Focusing on the discrete probabilistic setting we generalize the combinatorial definition of cumulants to L-cumulants. This generalization keeps all the desired properties of the classical cumulants like semi-invariance and vanishing for independent blocks of random variables. These properties make L-cumulants useful for the algebraic analysis of statistical models. We illustrate this for general Markov models and hidden Markov processes in the case when the hidden process is binary. The main motivation of this work is to understand cumulant-like coordinates in alge- braic statistics and to give a more insightful explanation why tree cumulants give such an elegant description of binary hidden tree models. Moreover, we argue that L-cumulants can be used in the analysis of certain classical algebraic varieties.

: Hilbert Polynomial of the Kimura 3-Parameter Model; In [2] Buczyn ́ska and Wi ́sniewski showed that the Hilbert polynomial of the algebraic variety associated to the Jukes-Cantor binary model on a trivalent tree depends only on the number of leaves of the tree and not on its shape. We ask if this can be generalized to other group-based models. The Jukes-Cantor binary model has Z2 as the underlying group. We consider the Kimura 3-parameter model with Z2 × Z2 as the underlying group. We show that the generalization of the statement about the Hilbert polynomials to the Kimura 3-parameter model is not possible as the Hilbert polynomial depends on the shape of a trivalent tree.

: Hybrid Surface-Wave Transducer; A transducer for generating and detecting surface elastic waves in a non-piezoelectric material may include an interdigital electrode array coupled to a piezoelectric crystal. The crystal is mechanically coupled to the non-piezoelectric material through an acoustical transmissive medium., Sponsorship: IIT Research Institute, United States Patent

: Recording and Erase Head for Magnetic Recorders; Sponsorship: Armour Research Foundation of Illinois Institute of Technology, United States Patent

: Measuring System Using the Resonant Absorption of Gamma Rays; Sponsorship: IIT Research Institute, United States Patent

: Method of Making Enriched Radioisotopes by Cation Fixation; Sponsorship: IIT Research Institute, United States Patent

: Electrical Musical Instrument; Sponsorship: Armour Research Foundation of Illinois Institute of Technology, United States Patent

: Winding and Reeling Mechanism; Sponsorship: Armour Research Foundation of Illinois Institute of Technology, United States Patent

: Transducer Machine and Spool Construction Therefor; Sponsorship: IIT Research Institute, United States Patent

: Method for Treating Materials; Sponsorship: IIT Research Institute, United States Patent

: Transducer System and Method; Sponsorship: IIT Research Institute, United States Patent

: High Tensile Vanadium Alloys; Sponsorship: Armour Research Foundation of Illinois Institute of Technology, United States Patent

: Hot Forming of Titanium and Titanium Alloys; Sponsorship: IIT Research Institute, United States Patent

: Method of Preparing Rocket Monopropellent Compounds; Sponsorship: IIT Research Institute, United States Patent

: Columbium Base Alloys; Sponsorship: IIT Research Institute, United States Patent

: An Iterative Method Converging to a Positive Solution of Certain Systems of Polynomial Equations; We present a numerical algorithm for finding real non-negative solutions to a certain class of polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find maximum likelihood parameters for certain classes of statistical models. Since our algorithm works by iteratively improving an approximate solution, we find approximate solutions in the cases when there are no exact solutions, such as overconstrained systems.

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