Physical Sciences and Mathematics Commons^™

An Efficient And Robust Computational Framework For Studying Lifetime And Information Capacity In Sensor Networks, Enrique J. Duarte-Melo, Mingyan Liu, Archan Misra

Research Collection School Of Computing and Information Systems

In this paper we investigate the expected lifetime and information capacity, defined as the maximum amount of data (bits) transferred before the first sensor node death due to energy depletion, of a data-gathering wireless sensor network. We develop a fluid-flow based computational framework that extends the existing approach, which requires precise knowledge of the layout/deployment of the network, i.e., exact sensor positions. Our method, on the other hand, views a specific network deployment as a particular instance (sample path) from an underlying distribution of sensor node layouts and sensor data rates. To compute the expected information capacity under this distribution-based …

Spatial Sampling Design For Parameter Estimation Of The Covariance Function, Zhengyuan Zhu, Michael L. Stein

Zhengyuan Zhu

Phase-Matching Optimization Of Laser High-Order Harmonics Generated In A Gas Cell, Julia Robin Miller Sutherland

Theses and Dissertations

Ten-millijoule, thirty-five femtosecond, 800 nm (~40 nm bandwidth) laser pulses are used to study high-order harmonic generation in helium- and neon-filled gas cells of various lengths. Harmonic orders in the range of 50 to 100 are investigated. A semi-infinite cell geometry produces brighter harmonics than cells of sub-centimeter length. In the semi-infinite geometry, the gas occupies the region from the focusing lens to a thin exit foil near the laser focus. Counter-propagating light is used to directly probe where the high harmonics are generated within the laser focus and to investigate phase matching. The phase matching under optimized harmonic generation …

Order Scheduling In Dedicated And Flexible Machine Environments, Haibing Li

Dissertations

Order scheduling models are relatively new in the field of scheduling. Consider a facility with m parallel machines that can process k different products (job types). Each machine can process a given subset of different product types. There are n orders from n different clients. Each order requests specific quantities of the various different products that can be produced concurrently on their given subsets of machines; it may have a release date, a weight and a due date. Preemptions may be allowed. An order can not be shipped until the processing of all the products for the order has been …

Optimizing Allocation Of Monitoring Effort Under Economic And Observational Constraints, Scott A. Field, Andrew J. Tyre, Hugh P. Possingham

School of Natural Resources: Faculty Publications

Efforts to design monitoring regimes capable of detecting population trends can be thwarted by observational and economic constraints inherent to most biological surveys. Ensuring that limited resources are allocated efficiently requires evaluation of statistical power for alternative survey designs. We simulated the process of data collection on a landscape, where we initiated declines over 3 sample periods in species of varying prevalence and detectability. Changing occupancy levels were estimated using a technique that accounted for effects of false-negative errors on survey data. Declines were identified within a frequentist statistical framework, but the significance level was set at an optimal level …

Modeling Basketball Free Throws, Andrew Lang, Joerg M. Gablonsky

College of Science and Engineering Faculty Research and Scholarship

This paper presents a mathematical model for basketball free throws. It is intended to be a supplement to an existing calculus course and could easily be used as a basis for a calculus project. Students will learn how to apply calculus to model an interesting real-world problem, from problem identification all the way through to interpretation and verification. Along the way we will introduce topics such as optimization (univariate and multiobjective), numerical methods, and differential equations.

On Optimizing Multi-Level Designs: Power Under Budget Constraints, Todd C. Headrick, Bruno D. Zumbo

Todd Christopher Headrick

This paper derives a procedure for efficiently allocating the number of units in multi-level designs given prespecified power levels. The derivation of the procedure is based on a constrained optimization problem that maximizes a general form of a ratio of expected mean squares subject to a budget constraint. The procedure makes use of variance component estimates to optimize designs during the budget formulating stages. The method provides more general closed form solutions than other currently available formulae. As such, the proposed procedure allows for the determination of the optimal numbers of units for studies that involve more complex designs. A …

A Tutorial On Radiation Oncology And Optimization, Allen G. Holder, Bill Salter

Mathematics Faculty Research

Designing radiotherapy treatments is a complicated and important task that affects patient care, and modern delivery systems enable a physician more flexibility than can be considered. Consequently, treatment design is increasingly automated by techniques of optimization, and many of the advances in the design process are accomplished by a collaboration among medical physicists, radiation oncologists, and experts in optimization. This tutorial is meant to aid those with a background in optimization in learning about treatment design. Besides discussing several optimization models, we include a clinical perspective so that readers understand the clinical issues that are often ignored in the optimization …