All HMC Faculty Publications and Research Copyright (c) 2013 Claremont Colleges All rights reserved. http://scholarship.claremont.edu/hmc_fac_pub Recent documents in All HMC Faculty Publications and Research en-us Sun, 12 May 2013 01:35:21 PDT 3600 Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media http://scholarship.claremont.edu/hmc_fac_pub/422 http://scholarship.claremont.edu/hmc_fac_pub/422 Fri, 10 May 2013 14:40:26 PDT The one-dimensional elastic wave equations for compressional waves have the form (1)

\hfill∈t(x,t)−ux(x,t)=0\hfill(ρ(x)u(x,t))t−σ(∈(x,t),x)x=0

where ε(x, t) is the strain and u(x, t) the velocity. We consider a heterogeneous material with the density specified by ρ(x) and a nonlinear constitutive relation for the stress given by a function σ(∈, x) that also varies explicitly with x. This is a hyperbolic system of conservation laws with a spatially-varying flux function, q t + f(q, x) x = 0.

]]> Darryl H. Yong et al. Xantusia Vigilis (Desert Night Lizard) and Sceloporus Magister (Desert Spiny Lizard). Predation and Diet. http://scholarship.claremont.edu/hmc_fac_pub/421 http://scholarship.claremont.edu/hmc_fac_pub/421 Fri, 19 Apr 2013 16:49:12 PDT Here, we report evidence of predation on Xantusia vigilis by Sceloporus magister. We collected a yearling female S. magister (71 mm SVL, mass = 13.6 g) on 24 July 1996, 5 km SE of Llano, Los Angeles County, California, USA (34°29'N, 117°46'W, elevation 1120 m). In the laboratory, on 29 July, the S. magister deposited a fecal pellet that contained part of a Xantusia vigilis body, including sections of dorsal and ventral integument and both hind limbs.

]]> Stephen C. Adolph et al. Gambelia Wislizenii (Long-nosed Leopard Lizard). Arboreal behavior. http://scholarship.claremont.edu/hmc_fac_pub/420 http://scholarship.claremont.edu/hmc_fac_pub/420 Fri, 19 Apr 2013 16:49:10 PDT In the North American southwest, leopard lizards (genus Gambelia) are characteristically ground dwelling (Stebbins 2003. A Field Guide to Western Reptiles and Amphibians, 3rd ed., Houghton-Mifflin, New York. 533 pp.; Smith 1946. Handbook of Lizards, Comstock Publishing Co., Ithaca, New York. 557 pp.). In G. wislizenii, climbing is not mentioned in several substantive ecological studies of this species (Parker and Pianka 1976. Herpetologica 32:95-114; Tanner and Krogh 1974. Herpetologica 30:63-72), and to our knowledge, only a few seconds exist of climbing in this species. Clark (1974. Trans. Kansas Acad. Sci. 77:68) observed a G. wislizenii perched 30 cm off the ground in a shrub, and Miller and Stebbins (1964. The Lives of Desert Animals in Joshua Tree National Monument,. University of California Press, Berkeley. 452 pp.) mentioned collecting an individual on top of a "massive rock 30 feet from the ground." Crowley and Pietruszka (1983. Anim. Behav. 31:1055-1060) commented that this species often climbs into shrubs or onto rocks, but did not provide additional information. For this reason, we augment the limited data on climbing in G. wislizenii with an observation from the Mojave Desert of California (USA).

]]> Stephen C. Adolph et al. Methods for Estimating Peak Physiological Performance and Correlating Performance Measures http://scholarship.claremont.edu/hmc_fac_pub/419 http://scholarship.claremont.edu/hmc_fac_pub/419 Fri, 19 Apr 2013 16:49:08 PDT Estimates of animal performance often use the maximum of a small number of laboratory trials, a method which has several statistical disadvantages. Sample maxima always underestimate the true maximum performance, and the degree of the bias depends on sample size. Here, we suggest an alternative approach that involves estimating a specific performance quantile (e.g., the 0.90 quantile). We use the information on within-individual variation in performance to obtain a sampling distribution for the residual performance measures; we use this distribution to estimate a desired performance quantile for each individual. We illustrate our approach using simulations and with data on sprint speed in lizards. The quantile method has several advantages over the sample maximum: it reduces or eliminates bias, it uses all of the data from each individual, and its accuracy is independent of sample size. Additionally, we address the estimation of correlations between two different performance measures, such as sample maxima, quantiles, or means. In particular, because of sampling variability, we propose that the correlation of sample means does a better job estimating the correlation of population maxima than the estimator which is the correlation of sample maxima.

]]> Austen Head '08 et al. The Contributions of Evolutionary Divergence and Phenotypic Plasticity to Geographic Variation in the Western Fence Lizard, Sceloporus Occidentalis http://scholarship.claremont.edu/hmc_fac_pub/418 http://scholarship.claremont.edu/hmc_fac_pub/418 Fri, 19 Apr 2013 16:49:05 PDT Local genetic adaptation and phenotypic plasticity are two mechanisms that can have marked effects on the morphology, performance, and behaviour of animals, producing geographic variation among populations. However, few studies have examined how these mechanisms interact during ontogeny to shape organismal phenotypes. We incubated eggs of the western fence lizard, Sceloporus occidentalis, from four populations (representing two latitudes and altitudes) in either a warm or cool environment in the laboratory. We then raised the hatchlings under common laboratory conditions, measured morphological and performance traits until 5 weeks of age, and compared juvenile morphology with that of field-caught adults from each population. The results obtained indicate that some phenotypic traits that contribute to performance (body size, hindlimb length, head shape) were relatively canalized in juveniles and differed among populations in a way that was consistent with adults from their population of origin. However, other traits (forelimb length, inter-limb length, mass, tail length), showed significant effects of incubation temperature, and this environmentally induced variation persisted throughout the experiment. Although selection pressure may be stronger for traits that are integral to survival, developmental effects might still have a lasting impact on traits less important to organismal fitness. We discuss the results obtained in the present study the context of the life history of these animals.

]]> Christine R. Buckley et al. Latitudinal and Climatic Variation in Body Size and Dorsal Scale Counts in Sceloporus Lizards: A Phylogenetic Perspective http://scholarship.claremont.edu/hmc_fac_pub/417 http://scholarship.claremont.edu/hmc_fac_pub/417 Fri, 19 Apr 2013 16:49:02 PDT Squamates often follow an inverse Bergmann's rule, with larger-bodied animals occurring in warmer areas or at lower latitudes. The size of dorsal scales in lizards has also been proposed to vary along climatic gradients, with species in warmer areas exhibiting larger scales, putatively to reduce heat load. We tested for these patterns in the diverse and widespread lizard genus Sceloporus. Among 106 species or populations, body size was associated positively with maximum temperature (consistent with the inverse of Bergmann's rule) and aridity, but did not covary with latitude. Scale size (inferred from the inverse relation with numbers of scales) was positively related to body size. Controlling for body size via multiple regression, scale size was associated negatively with latitude (best predictor), positively with minimum temperature, and negatively with aridity (similar results were obtained using scores from a principal components analysis of latitude and climatic indicators). Thus, lizards with larger scales are not necessarily found in areas with higher temperatures. Univariate analyses indicated phylogenetic signal for body size, scale counts, latitude, and all climate indicators. In all cases, phylogenetic regression models fit the data significantly better than nonphylogenetic models; thus, residuals for log10 number of dorsal scale rows exhibited phylogenetic signal.

]]> Christopher E. Oufiero et al. Estimating Maximum Performance: Effects of Intraindividual Variation http://scholarship.claremont.edu/hmc_fac_pub/416 http://scholarship.claremont.edu/hmc_fac_pub/416 Fri, 19 Apr 2013 16:48:58 PDT Researchers often estimate the performance capabilities of animals using a small number of trials per individual. This procedure inevitably underestimates maximum performance, but few studies have examined the magnitude of this effect. In this study we explored the effects of intraindividual variation and individual sample size on the estimation of locomotor performance parameters. We measured sprint speed of the lizard Sceloporus occidentalis at two temperatures (20 degrees C and 35 degrees C), obtaining 20 measurements per individual. Speed did not vary temporally, indicating no training or fatigue effects. About 50% of the overall variation in speed at each temperature was due to intraindividual variation. While speed was repeatable, repeatability decreased slightly with increasing separation between trials. Speeds at 20 degrees C and 35 degrees C were positively correlated, indicating repeatability across temperatures as well. We performed statistical sampling experiments in which we randomly drew a subset of each individual's full set of 20 trials. As expected, the sample's maximum speed increased with the number of trials per individual; for example, five trials yielded an estimate averaging 89% of the true maximum. The number of trials also influenced the sample correlation between mean speeds at 20 degrees C and 35 degrees C; for example, five trials yielded a correlation coefficient averaging 90% of the true correlation. Therefore, intraindividual variation caused underestimation of maximal speed and the correlation between speeds across temperatures. These biases declined as the number of trials per individual increased, and depended on the magnitude of intraindividual variation, as illustrated by running sampling experiments that used modified data sets.

]]> Stephen C. Adolph et al. Mathematical Biology at an Undergraduate Liberal Arts College http://scholarship.claremont.edu/hmc_fac_pub/415 http://scholarship.claremont.edu/hmc_fac_pub/415 Fri, 19 Apr 2013 16:48:56 PDT Since 2002 we have offered an undergraduate major in Mathematical Biology at Harvey Mudd College. The major was developed and is administered jointly by the mathematics and biology faculty. In this paper we describe the major, courses, and faculty and student research and discuss some of the challenges and opportunities we have experienced.

]]> Stephen C. Adolph et al. Flight Delays at RegionEx http://scholarship.claremont.edu/hmc_fac_pub/414 http://scholarship.claremont.edu/hmc_fac_pub/414 Fri, 19 Apr 2013 16:48:55 PDT In this case about two fictitious airlines, RegionEx, a small regional airline, is a contracted regional carrier for Mississippi Delta Airlines (MDA), a major U.S. airline. In September, RegionEx exhibited a worse flight delay record than MDA, and is now at risk of losing its contract. The flight operations manager at RegionEx is tasked with analyzing the flight delay records and explaining RegionEx's seemingly poor performance to RegionEx's chief operations officer. Reflecting the recommendations of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) published by the American Statistical Association, this case emphasizes statistical literacy and conceptual understanding of data analysis rather than rote procedures. Undergraduate and MBA students will use basic data analysis techniques, such as graphical analysis, descriptive statistics, and two-sample hypothesis testing and correlation, to discover important paradoxes in the flight delay data. They will learn that subtle differences in the definition of business performance metrics can radically change their interpretation; graphical analysis of data can provide information about distributions that are masked by summary statistics; aggregating data across disparate sample sizes can skew means (Simpson's paradox); and correlation does not imply causation.

]]> Susan E. Martonosi et al. Methods for Estimating Peak Physiological Performance and Correlating Performance Measures http://scholarship.claremont.edu/hmc_fac_pub/413 http://scholarship.claremont.edu/hmc_fac_pub/413 Fri, 19 Apr 2013 14:04:23 PDT Estimates of animal performance often use the maximum of a small number of laboratory trials, a method which has several statistical disadvantages. Sample maxima always underestimate the true maximum performance, and the degree of the bias depends on sample size. Here, we suggest an alternative approach that involves estimating a specific performance quantile (e.g., the 0.90 quantile). We use the information on within-individual variation in performance to obtain a sampling distribution for the residual performance measures; we use this distribution to estimate a desired performance quantile for each individual. We illustrate our approach using simulations and with data on sprint speed in lizards. The quantile method has several advantages over the sample maximum: it reduces or eliminates bias, it uses all of the data from each individual, and its accuracy is independent of sample size. Additionally, we address the estimation of correlations between two different performance measures, such as sample maxima, quantiles, or means. In particular, because of sampling variability, we propose that the correlation of sample means does a better job estimating the correlation of population maxima than the estimator which is the correlation of sample maxima.

]]> Austen Head '08 et al. Mathematics of Voting http://scholarship.claremont.edu/hmc_fac_pub/412 http://scholarship.claremont.edu/hmc_fac_pub/412 Fri, 19 Apr 2013 14:04:22 PDT Voting theory is a fascinating area of research involving mathematics, political scientists, and economists. The American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics chose mathematics and voting as the theme for Mathematics Awareness Month 2008. There is more information on mathematics and voting at www.mathaware.org/mam/08/. It is a mathematical topic that is rich yet accessible to students, pertinent to their lives, especially during this election year, and has the potential to draw students who may not have a strong affinity for mathematics to become interested in mathematics.

]]> Darryl H. Yong A Space-Filling, Nonregular Tetrahedron http://scholarship.claremont.edu/hmc_fac_pub/411 http://scholarship.claremont.edu/hmc_fac_pub/411 Fri, 19 Apr 2013 14:04:20 PDT This activity is an investigation of a special nonregular tetrahedron that can be arranged to fill space without leaving any internal gaps in the same way that certain planar figures tessellate the plane. These tetrahedra can be connected together with hinges to make fun and interesting puzzles. More background information can be found in the paper "An Amazing, Space-Filling, Non-Regular Tetrahedron" by Joyce Frost and Peg Cagle, published by the IAS/Park City Mathematics Institute (available at mathforum.org/pcmi/hstp/resources/dodeca/).

]]> Margaret Cagle et al. Flat Plate Solar Collector Materials (and Designs with an Economic Methodology for Optimizing Collector Design) http://scholarship.claremont.edu/hmc_fac_pub/410 http://scholarship.claremont.edu/hmc_fac_pub/410 Fri, 19 Apr 2013 14:04:18 PDT The desirability of specific materials and designs for conventional flat-plate solar collector components is considered. Then a methodology for choosing the most economic component is presented, consisting of a computer simulation and a rate-of-return analysis. The effect of rising conventional fuel costs is examined. Examples of using the methodology are given, based on Southern California climatic and user-demand conditions. Selective absorber-plate coatings and film inner glazing are shown to be economic, yielding a rate-of-return of 23 percent and 29 percent, respectively.

]]> Donald S. Remer et al. Design and Development of a Photodegradable Bottle Cap http://scholarship.claremont.edu/hmc_fac_pub/409 http://scholarship.claremont.edu/hmc_fac_pub/409 Fri, 19 Apr 2013 14:04:17 PDT The first photodegradable plastic cap for a glass beer bottle was developed and tested. The cap's design is the same as the current plastic, screw-on cap for soda bottles. A photodegradable resin was added to the soda cap plastic to make it photodegradable. Caps with 0%, 10%, and 25% photodegradable additive were made. Tests show that the photodegradable cap meets most of the physical properties required for a beer or a soda cap. A photodegradable cap with 10% degradable additive will cost about three times more than current metal crowns, but only about 10% more than current plastic soda caps. The photodegradable caps can be made on a large scale using the same process as for regular soda caps. 10,000 caps were made for testing.

]]> Kenneth S. Chon '87 et al. Adventures in Teaching: A Professor Goes to High School to Learn about Teaching Math http://scholarship.claremont.edu/hmc_fac_pub/408 http://scholarship.claremont.edu/hmc_fac_pub/408 Fri, 19 Apr 2013 14:04:15 PDT During the 2009–2010 academic year I did something unusual for a university mathematician on sabbatical: I taught high school mathematics in a large urban school district. This might not be so strange except that my school does not have a teacher preparation program and only graduates a few students per year who intend to be teachers. Why did I do this? I, like many of you, am deeply concerned about mathematics education and I wanted to see what a typical high school in my city is like. Because I regularly work with high school mathematics teachers, I wanted to experience the life of a high school teacher for myself. I had neither a research project nor an agenda for changing schools or teachers.

]]> Darryl H. Yong The Cost of Doing a Cost Estimate http://scholarship.claremont.edu/hmc_fac_pub/407 http://scholarship.claremont.edu/hmc_fac_pub/407 Mon, 15 Apr 2013 11:04:50 PDT There are many reasons for cost overruns, but one of the key factors it the lack of resources (time, money, and staffing) spent to do proper up-front cost estimates. Another major reason is that the implements were not involved in the estimating. The purpose of this article is to address the issue of the cost to do a cost estimate [8]. We will report on how others handle this issue and make suggestions on how the Deep Space Network (DSN) should estimate the amount to spend on a cost estimate and its impact on reducing the probability of a cost overrun.

We will report on our literature search and actual data from JPL procurement on what others charge JPL for a cost estimate. Our goal is to come up with guidelines with a methodology for estimating how much to spend on a cost estimate to achieve a desired accuracy. We think that many companies and government agencies typically underallocate resources for producing a cost estimate and, as a result, do not take the time to include all the necessary cost elements. This leads to cost overruns and/or de-scoping of the functional requirements of projects.

]]> Donald S. Remer et al. Determining Maintenance Cost Ratios http://scholarship.claremont.edu/hmc_fac_pub/406 http://scholarship.claremont.edu/hmc_fac_pub/406 Mon, 15 Apr 2013 11:04:48 PDT Maintenance is a necessary (and usually burdensome) function for practically all natural and man-made elements. Simply defined, maintenance is the effort to keep a device or system working. The amount of funding allocated for maintenance by an organization is necessarily a compromise, possibly viewed as too much by management and too little by the operators/maintainers. The objective of our study was to report on the wide range of costs involved in maintaining equipment. We discuss some methods that different industries use to measure and report their maintenance costs; we summarize the results of a literature search on the range of maintenance costs for several industries; and we report on our own study of maintenance costs in the National Aeronautics and Space Administration (NASA) Deep Space Network (DSN) and how these maintenance costs compare to the other reported results.

]]> Donald S. Remer et al. Cost Scale-Up Factors for Airport Construction http://scholarship.claremont.edu/hmc_fac_pub/405 http://scholarship.claremont.edu/hmc_fac_pub/405 Mon, 15 Apr 2013 11:04:47 PDT Engineers must often make a quick "ballpark" cost estimate of a new plant, facility, or piece of equipment before the detailed design phase. One easy way to obtain such an estimate is to base the cost on a known cost for a similar plant, facility, or piece of equipment by using the ratio of the capacities or sizes of the known and proposed item raised to an exponent R. This predesign cost-estimating approach is especially useful for doing sensitivity analyses and feasibility studies for which a high degree of accuracy is not required. This cost-capacity or power-factor model was first developed by Williams in 1947 for equipment costs [7] and by Chilton in 1950 for plant costs [1]. In this article, we present scale-up factors for estimating the costs of terminal expansions to existing airports in the United States and the costs of constructing new international airports.

]]> Donald S. Remer et al. New Perspectives on the Materials Interface with the Three E's -- Energy, Environment and Economics http://scholarship.claremont.edu/hmc_fac_pub/404 http://scholarship.claremont.edu/hmc_fac_pub/404 Mon, 15 Apr 2013 11:04:45 PDT New perspectives are presented on the material interface with the three E's -- Energy, Environment, and Economics. The past, present, and future energy picture is described from 1850 through the year 2030. The major energy sources such as oil, natural gas, coal, nuclear, and several new emerging energy options are compared and contrasted. The lead time, capital, and materials required for bringing on-stream new energy sources is described. Previous U.S. energy forecasts are reviewed and are found to be too optimistic. The U.S. materials situation is outlined with an emphasis on per capita materials use and the critical role that foreign sources play in our materials supply. The interrelationship between energy and materials production is considered for three areas: (1) industrial processing, (2) construction and buildings, and (3) the automobile.

]]> Donald S. Remer Aquatic Photovoltaic Facility http://scholarship.claremont.edu/hmc_fac_pub/403 http://scholarship.claremont.edu/hmc_fac_pub/403 Mon, 15 Apr 2013 11:04:44 PDT A feasibility design and cost estimate was completed for a 1 megawatt photovoltaic (PV) facility which would float on an island reservoir at Catalina Island off the coast the coast of Southern California. If built, this project would be one of the largest PV operating facilities to date and also the first floating PV system. The modular facility consists of 250 floating platforms each supporting 430 square feet of flat panel PV cells. This facility would provide 25% of Catalina's yearly peak energy demand and reduce the amount of diesel fuel used.

]]> Donald S. Remer et al.