Automated Water Management

Conservation of water resources is critical in many places of the world, including the American West. Current technologies enabling flow instrumentation and the remote control of automated gates and release mechanisms at dams facilitate our systematic modeling and control of complex river systems. Real-time flow data related to our work for the modeling and control of the Piute Reservoir and the Sevier River in Central Utah can be found at www.sevierriver.org.

Coalition Robustness of Multiagent Systems

This research explores the interplay of cooperation and competition in multiagent dynamics. Our study begins with the stability robustness of multiagent systems with respect to uncertain coalition structure. Such systems arise naturally from a variety of compartmental models, including those used in security analysis, economics, ecology, etc. Moreover, coalition robustness becomes significant when conducting organizational analysis, such as in merger simulation, market structure analysis, or in other areas of industrial organization.

Papers: CDC07, Thesis07.

Demand Forecasting

Predictive modeling is essential for rational decision making, since understanding the consequences of various options is the first step toward choosing between them. Merchants need such models to understand how pricing and other decisions will impact revenue generated in their respective markets. This project details known algorithms for using a finite record of sales data to generate predictive models and forecast demand.

Dynamic Pricing

Changing prices of a good or service allows a firm to gather information about the market demand for the product, but knowledge of market demand motivates fixing the price at its profit-maximizing value. This project explores tradeoffs in exploration versus exploitation of market information and helps a firm understand how the dynamic, feedback structure of economic interaction influences effective pricing decisions. This work has included collaboration with the Applied Machine Learning Laboratory at BYU.

Ellipsometry-Driven Feedback Control of Epitaxial Processes

Epitaxy is a process for depositing atomic-scale films of a specified composition on a wafer substrate. Meticulously growing a particular 'sandwich' of nanofilms is a critical step in the production of many semiconductor devices. Nevertheless, one often does not know if the deposited film has the right properties, such as thickness and material composition, until growth is completed. This work uses in-situ ellipsometry, an optical device for probing film-growth as it occurs, to adjust epitaxy process parameters in real-time to guarantee that the actual film grows as planned.

Factory Optimization

Flexible production systems use the same sequence of machines to produce different products. The recipe for making each product, however, may tie up each machine differently, skip some machines, or require reprocessing on certain machines. Moreover, the factory may contain multiple copies of a given machine that operate in parallel (to speed up that stage of production), different machines may process different batch sizes of different products, and there may or may not be temporary storage facilities between machines. Scheduling the optimal production sequence to manufacture a specified quota for each type of product is computationally difficult; we explore efficient approximations for this and related problems. This includes how to best invest resources for additional machines, or how to determine how operational constraints on the duration of the workday and workweek affect the optimal schedule and the associated return on investment of the capital equipment in the factory.

Federal Reserve Policy

Good monetary policy is crucial to low inflation, high employment, and stable economic growth. The Federal Reserve puts its policy into effect on a daily basis through the use of Open Market Operations, which indirectly controls our nation's money supply through the buying and selling of securities in our nation's banking system. The purpose of this project is to model this process as a dynamical system and then explore how to control our monetary policies algorithmically.

Geometric Limits of Performance for Path Control

Tracking problems use feedback control to drive a system to follow a specified time trajectory. Sometimes, however, one is only interested in how well the system stayed on the specified path, and not necessarily when it transversed each point along the path. If we allow a tracking system to speed up or slow down, as necessary, to transverse a given curve within a fixed completion time, we find a trade off between the geometric shape of the curve and the path error incurred by the system. This work investigates this tradeoff and defines fundamental limits of performance.

Inventory Management

The purpose of this project is to connect inventory management problems to those of mathematical finance. For example, there are close similarities between the classical Newsvendor Problem in operations research and that of pricing a European put option in math finance. The goal of this project is to rigorously connect inventory management problems in operations research to portfolio management problems in math finance, and explore the use of traditional and exotic investment vehicles as way to manage inventories and hedge the risks associated with selling and distributing real goods in the market.

Laser Stabilization

Diode lasers typically suffer from wavelength drift and exhibit a line width that is too broad to drive the atomic transitions in an atom interferometer. This project, in collaboration with Professor Dallin Durfee of BYU's Physics Department, uses feedback control to stabilize the wavelength and narrow the line width of a side-emitting Grating-Stabilized External-Cavity Diode Laser.

Market Making as a Dynamical System

In the capital markets, financial intermediaries such as market specialists, banks, and other financial services companies provide both a bid price and an ask price on the securities that they broker. The difference between these two prices is called the bid-ask spread; it essentially represents fees that are passed on to the buyers and sellers to account for the intermediaries' market risk, transaction costs and inventory costs. The purpose of this project is to model the market making problem as a dynamical system and then to explore how to automate the clearing of markets as an Algorithmic Decision Process.

Market Structure Analysis

The market power a firm exerts depends on both the way consumer demand links various products together and on the industrial organization of other businesses that control strongly linked products to those of the firm. This project explores the extent that a measure of market power is computable from a single firm's transactions data. This analysis is useful both for anti-trust activities of the Department of Justice as well as for corporate management.

Markov Approximation

Hidden Markov Models are a powerful tool for describing the behavior of many autonomous systems, including speech, internet traffic, and microbiological mechanisms such as protein structure or DNA sequence patterns. While asymptotically consistent algorithms exist for estimating the parameters of an HMM from data, such algorithms demand that the true system generating the data is in the class of models being explored. Typically, however, mathematical models are necessarily simplifications of the true system. This work investigates the nature of low order Hidden Markov Models that approximate the behavior of higher-order HMMs, and the impact of such approximations on the performance of the associated learning algorithms.

Network Reconstruction

One of the key problems in analyzing complex systems is estimating a system’s network structure given only input/output data. This problem arises in a variety of applications, but especially in systems biology where scientists want to understand how various protein interactions and signaling “pathways” result in particular cellular dynamics. This project, in collaboration with Professor Jorge Goncalves and the Control Systems Group at Cambridge University, explores implications of the graphical structure of a decision processes on the achievable dynamics of the entire system.

Papers: CDC07, TAC07.

Retail Instrumentation: Design of a Loyalty Program

Although virtually every merchant collects and warehouses sales data, often such data is not informative enough to guide merchandising and marketing decisions. The missing link is knowing who is buying what. Loyalty programs offer incentives to customers in exchange for exactly this kind of information. This project explores the design of such incentives to minimize the corporate cost of fully instrumenting their operations.

Retail Laboratory

Laboratories are widely available for biology, chemistry, and physics. This project develops the blueprints for, and implements, the first-of-its-kind economic laboratory for retail. We begin by making the subtle but important distinction between a laboratory, that uses controlled experimentation to generate new data about a phenomenon, and data processing algorithms that mine warehoused data for understanding. Every merchandising and marketing decision is based explicitly or implicitly on a model, or expectations, of how the market will react; the purpose of a laboratory is to verify that this model is good enough to make the proposed decisions worthwhile. We draw on the feedback structure of retail, between a firm and its market, to develop a concrete invalidation protocol, or marketing process, that allows decision makers to implement their ideas in a way that ensures errors in judgment become clear before they damage the enterprise. A prototype of these ideas is then executed at the on-campus retailer, the BYU Bookstore, to demonstrate their utility on a live retail operation; our retail laboratory is a real, functioning venture. Partners on the project include the Data Mining Laboratory at BYU.

Verification that software works as designed to control external devices is critical in a variety of settings. Yet the complexity and shear size of software applications today make such verification very difficult. It is especially important to ensure that errors in interactive software designed to control something, such as an airplane or a power plant or the brakes on a car, does not induce catastrophic failure. This project explores how the feedback structure of such software systems affects our approach to the verification problem. This work has been conducted in collaboration with BYU's Verification & Validation Laboratory.

The three-dimensional structure of biological complexes can beobtained from two-dimensional images taken from an electronmicroscope. However, electron images are very noisy, and thusthere are challenges involved in getting high resolution images of the resulting reconstruction. We are exploring mathematical and computational methods to improve the resolution of these images. This project is a collaboration with David M. Belnap in the Department of Chemistry and Biochemistry at BYU.