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2001

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Articles 1261 - 1290 of 3030

Full-Text Articles in Physical Sciences and Mathematics

Idmp-Based Fast Handoffs And Paging In Ip-Based Cellular Networks, Archan Misra, Subir Das, Ashutosh Dutta, Sajal K. Das May 2001

Idmp-Based Fast Handoffs And Paging In Ip-Based Cellular Networks, Archan Misra, Subir Das, Ashutosh Dutta, Sajal K. Das

Research Collection School Of Computing and Information Systems

We consider the use of our previously proposed Intra-Domain Mobility Management Protocol (IDMP) in fourth-generation mobile networks. On evaluating the heterogeneous access technologies, cellular layouts, and application characteristics of 4G environments, we realize a need to reduce both handoff latency and the frequency of mobility-related signaling. We first present IDMP's fast intradomain handoff mechanism that uses a duration-limited proactive packet multicasting solution. We quantify the expected buffering requirements of our proposed multicasting scheme for typical 4G network characteristics and compare it with alternative IP-based fast handoff solutions. We also present a paging scheme under IDMP that replicates the current cellular …


Discrete Spring Solitons, Donald Greenspan May 2001

Discrete Spring Solitons, Donald Greenspan

Mathematics Technical Papers

A soliton is a local, traveling wave pulse. It is significant in a variety of unrelated areas, like studies of water waves, acoustic waves, electron transfer, gravity waves, plasmas, optics and condensed matter (Miura [4], Newell [5]). In this paper we will generate and study solitons in a new context, that is, from the point of view of discrete string motion in the XY plane. Our approach enables one to elucidate the complexities of soliton interactions easily using only a scientific personal computer and velocity profiles. Detailed examples are presented and displayed graphically.


Generalizations Of The Zero-Divisor Graph Of A Ring, Shane Patrick Redmond May 2001

Generalizations Of The Zero-Divisor Graph Of A Ring, Shane Patrick Redmond

Doctoral Dissertations

Let R be a commutative ring with 1, and let Z(R) denote the set of zero­divisors of R. We define an undirected graph Γ(R) with vertices Z(R)* = Z(R) - {0}, where distinct vertices x and y of R are connected if and only if xy = 0. This graph is called the zero-divisor graph of R. We extend the definition of the zero-divisor graph to a noncommutative ring in several ways. Next, given a commutative ring R and ideal Ι of R, we introduce the notion of an …


Seasonal Patterns Of Photosynthesis In Douglas Fir Seedlings During The Third And Fourth Year Of Exposure To Elevated Co2 And Temperature, James D. Lewis, Melissa S. Lucash, David M. Olszyk, David T. Tingey May 2001

Seasonal Patterns Of Photosynthesis In Douglas Fir Seedlings During The Third And Fourth Year Of Exposure To Elevated Co2 And Temperature, James D. Lewis, Melissa S. Lucash, David M. Olszyk, David T. Tingey

Environmental Science and Management Faculty Publications and Presentations

The interactive effects of elevated atmospheric CO2 and temperature on seasonal patterns of photosynthesis in Douglas fir (Psuedotsuga menziesii (Mirb.) Franco) seedlings were examined. Seedlings were grown in sunlit chambers controlled to track either ambient (~400 p.p.m.) CO2 or ambient +200 p.p.m. CO2, and either ambient temperature or ambient +4 °C. Light-saturated net photosynthetic rates were measured approximately monthly over a 21 month period. Elevated CO2 increased net photosynthetic rates by an average of 21% across temperature treatments during both the 1996 hydrologic year, the third year of exposure, and the 1997 hydrologic year. Elevated …


Status Of The Major Oyster Diseases In Virginia 2000 A Summary Of The Annual Monitoring Program, Lisa M. Ragone Calvo, Eugene M. Burreson May 2001

Status Of The Major Oyster Diseases In Virginia 2000 A Summary Of The Annual Monitoring Program, Lisa M. Ragone Calvo, Eugene M. Burreson

Reports

As a consequence of the relatively warm temperatures, high salinities, and high oyster parasite abundances in the fall of 1999, both P. marinus and H. nelsoni were widely distributed throughout oyster populations in Virginia in 2000. Fortunately, however, we did not see severe epizootics of the diseases as observed in some areas in 1999.


Subaerial Paleokarst In The Upper Pennington Formation (Upper Mississippian) Limestones At Leatherwood Ford, Big South Fork, Tennessee, Sara Elizabeth Humbert May 2001

Subaerial Paleokarst In The Upper Pennington Formation (Upper Mississippian) Limestones At Leatherwood Ford, Big South Fork, Tennessee, Sara Elizabeth Humbert

Masters Theses

The uppermost Pennington Formation (Mississippian - latest Chesterian) consists of limestone deposits, which, in some areas, contain evidence of paleokarst. A 100 m long continuous outcrop of the upper Pennington Formation was studied at Big South Fork National River and Recreation Area, in Scott County, Tennessee, using both field and petrographic methods, in order to test the hypothesis that the paleokarst is of subaerial origin.

The upper Pennington limestone section was subdivided into 4 depositional units, interpreted as recording sea-level change through the end of the Mississippian. Although there was an overall regression toward the end of the Mississippian, changes …


Ontology-Driven Geographic Information Systems, Frederico Torres Fonseca May 2001

Ontology-Driven Geographic Information Systems, Frederico Torres Fonseca

Electronic Theses and Dissertations

Information integration is the combination of different types of information in a framework so that it can be queried, retrieved, and manipulated. Integration of geographic data has gained in importance because of the new possibilities arising from the interconnected world and the increasing availability of geographic information. Many times the need for information is so pressing that it does not matter if some details are lost, as long as integration is achieved. To integrate information across computerized information systems it is necessary first to have explicit formalizations of the mental concepts that people have about the real world. Furthermore, these …


The Foraging And Habitat Ecology Of Black Terns In Maine, Andrew Gilbert May 2001

The Foraging And Habitat Ecology Of Black Terns In Maine, Andrew Gilbert

Electronic Theses and Dissertations

The population of Black Terns in Maine is small and factors related to the ecology of this species’ foraging and habitat ecology might limit population growth and recovery. The objectives were to (1) determine if diet and provisioning rates are limiting chick growth, (2) identify and rank suitable habitat in Maine, and (3) determine if precipitation patterns and water level dynamics are limiting in Maine. I compared growth rates of chicks in 1998-2000 in Maine to rates from other studies, determined the influence of colony, year, and diet on growth rates and food deliveries and used an energetics model to …


Synthesis And Reactivity Of Gold Thiolate Cluster Complexes, Hanan Abdou May 2001

Synthesis And Reactivity Of Gold Thiolate Cluster Complexes, Hanan Abdou

Electronic Theses and Dissertations

Chemical oxidation of dinuclear gold(I) thiolates of the formula LLAu2(SC6H4CH3)2 [LL= dppp, bis(dipheny1phosphine)propane and dppb, bis(dipheny1phosphine)butane] and dinuclear gold(I) thiolate complexes with bridging a propane dithiolate ligand of the formula LLAu2(SC3H6S) [LL = dppp and dppb] was carried out using the mild oxidizing agent, ferrocenium, [Cp2Fe]PF6). Spectroscopic studies and elemental analysis showed the formation of gold(I) clusters, disulfide, and ferrocene as products of this oxidation reaction. The clusters, [(dppp)AU2(SC6H4CH3)](PF6) and [(dppb)Au2(SC …


Radiometric Cross-Calibration Of The Landsat-7 Etm+ And Landsat-5 Tm Sensors Based On Tandem Data Sets, P.M. Teillet, J. L. Barker, B. L. Markham, R. R. Irish, G. Fedosejevs, J.C. Storey Apr 2001

Radiometric Cross-Calibration Of The Landsat-7 Etm+ And Landsat-5 Tm Sensors Based On Tandem Data Sets, P.M. Teillet, J. L. Barker, B. L. Markham, R. R. Irish, G. Fedosejevs, J.C. Storey

United States National Aeronautics and Space Administration: Publications

Early in its mission, the Landsat-7 spacecraft was temporarily placed in a ‘‘tandem’’ orbit very close to that of the Landsat-5 spacecraft in order to facilitate the establishment of sensor calibration continuity between the Landsat-7 Enhanced Thematic Mapper Plus (ETM+) and Landsat-5 Thematic Mapper (TM) sensors. The key period for the tandem configuration was June 1–4, 1999, during which hundreds of nearly coincident matching scenes were recorded by both the Landsat-7 ETM+ and, in cooperation with Space Imaging/EOSAT and international ground stations, the Landsat-5 TM as well. The paper presents a methodology for radiometric cross-calibration of the solar reflective spectral …


Production Of Χ C1 And Χ C2 In Pp̅ Collisions At √S= 1.8 Tev, T. Affolder, Kenneth A. Bloom, Collider Detector At Fermilab Collaboration Apr 2001

Production Of Χ C1 And Χ C2 In Pp̅ Collisions At √S= 1.8 Tev, T. Affolder, Kenneth A. Bloom, Collider Detector At Fermilab Collaboration

Kenneth Bloom Publications

We have measured the ratio of prompt production rates of the charmonium states χ c1 and χ c2 in 110 pb-1 of pp̅ collisions at √s= 1.8 TeV. The photon from their decay into J/ψγ is reconstructed through conversion into e+e- pairs. The energy resolution this technique provides makes the resolution of the two states possible. We find the ratio of production cross sections (σ χ c2/ σ χ c1=0.96 ± 0.27(stat) ± 0.11(syst) for events with pT(J/ψ)> 4.0 GeV/c, |η(J/ψ)|, 0.6, and pT …


Ecotones: The Heartbeat Of Huxley, 2001, Spring, Issue 04, Kate Koch, Huxley College Of The Environment, Western Washington University Apr 2001

Ecotones: The Heartbeat Of Huxley, 2001, Spring, Issue 04, Kate Koch, Huxley College Of The Environment, Western Washington University

Historical Collection of Huxley Newsletters

No abstract provided.


Asymmetric Nanoscale Switching In Ferroelectric Thin Films By Scanning Force Microscopy, Alexei Gruverman, A. Kholkin, A. I. Kingon, H. Tokumoto Apr 2001

Asymmetric Nanoscale Switching In Ferroelectric Thin Films By Scanning Force Microscopy, Alexei Gruverman, A. Kholkin, A. I. Kingon, H. Tokumoto

Alexei Gruverman Publications

Scanning force microscopy (SFM) has been used to perform nanoscale studies of the switching behavior of Pb(Zr, Ti)O3 thin films via the direct observation of their domain structures. The study revealed a significant asymmetry of a switching pattern which is a function of the voltage polarity and original domain structure of individual grains. The phenomenon of asymmetric switching is attributed (1) to the presence of an internal built-in electric field at the bottom interface and (2) to the mechanical stress exerted by the SFM tip. The former effect results in incomplete 180° switching, while the latter effect leads to …


Design And Analysis For Melt Casting Metallic Fuel Pins Incorporating Volatile Actinides, Yitung Chen, Darrell Pepper, Randy Clarksean Apr 2001

Design And Analysis For Melt Casting Metallic Fuel Pins Incorporating Volatile Actinides, Yitung Chen, Darrell Pepper, Randy Clarksean

Fuels Campaign (TRP)

UNLV investigators will evaluate and select a process for the melt casting of metallic fuel pins that contain volatile actinides. This work will be performed with the guidance of Argonne National Laboratory (ANL) engineers to insure that their knowledge and experience benefits the project. The research to be conducted during year one will center on selecting, evaluating, and modeling potential alternatives to the traditional injection casting process used at ANL. Processing conditions will be analyzed, basic models utilized, and detailed heat and mass transfer models will be developed to analyze the most promising processes. The goal of the first year …


Another Look At Clark's Adit-Silver Series, David W. Meek Apr 2001

Another Look At Clark's Adit-Silver Series, David W. Meek

Conference on Applied Statistics in Agriculture

The empirical semivariogram for Clark's adit-silver series has been the subject of several publications. Its use in the literature along with some other discussed considerations makes this series a suitable selection for a classroom or workshop semivariogram modeling exercise. My emphasis in this exercise is on estimating the scale of fluctuation (8). Alternative unbounded, bounded asymptotic, and bounded transitional models are developed via weighted least-squares estimation for both regular and integral semivariogram parameterizations (ISV). Results are compared with Clark's recommendation along with some other traditional models, nonparametric models, and ad hoc numerical methods. When a given model fits well using …


An Uncertainty Analysis Procedure For Spatially Joint Simulations Of Multiple Attributes, Shoufan Fang, Guangxing Wang, George Z. Gertner, Alan Anderson Apr 2001

An Uncertainty Analysis Procedure For Spatially Joint Simulations Of Multiple Attributes, Shoufan Fang, Guangxing Wang, George Z. Gertner, Alan Anderson

Conference on Applied Statistics in Agriculture

In this study, an uncertainty analysis procedure for joint sequential simulation of multiple attributes of spatially explicit models was developed based on regression analysis. This procedure utilizes information obtained from joint sequential simulation to establish the relationship between model uncertainty and variation of model inputs. Using this procedure, model variance can be partitioned by model input parameters on a pixel by pixel basis. In the partitioning, the correlation of neighboring pixels is accounted for. With traditional uncertainty analysis methods, this is not possible. In a case study, spatial variation of soil erodibility from a joint sequential simulation of soil properties …


Comparison Of Sas Proc Nlin And Nlmixed For Parameter Estimation In Pet Model, Y. Xie, A. M. Parkhurst, T. L. Mader, J. B. Gaughan Apr 2001

Comparison Of Sas Proc Nlin And Nlmixed For Parameter Estimation In Pet Model, Y. Xie, A. M. Parkhurst, T. L. Mader, J. B. Gaughan

Conference on Applied Statistics in Agriculture

Cattle body temperatures were measured under semi-controlled hot cyclic chamber temperatures. The four-parameter nonlinear PET model, is used to estimate body temperature in cattle challenged by heat stress. For each steer, the parameters can be estimated by the Nlin procedure and the sensitivity of each animal can be studied. It is also desirable to generalize the results by using the Nlmixed procedure to combine both the fixed and random effects. When comparing the results from the two procedures, we found heterogeneity among animals and/or days caused convergence problems for proc Nlmixed. Simulation studies were used to study how deviations from …


Developing System For Auditing The Database Of Agricultural Trial, Olga Susana Filippini De Delfino, Ana Aguua, Hugo Delfino Apr 2001

Developing System For Auditing The Database Of Agricultural Trial, Olga Susana Filippini De Delfino, Ana Aguua, Hugo Delfino

Conference on Applied Statistics in Agriculture

Many steps are involved in getting data from an experimental unit of an agricultural trial into a final report. Each step may introduce a great variety of errors. Building quality into systems is much more productive than building checks onto the end. Poor quality database have effects on final study results in terms of estimation, significance testing and power; but auditing agricultural trial is a complex process designed to ensure that it will provide a reliable answer to the question being posed. By introducing digit errors into database in a tomato assay, with small sample size, we demonstrate that simple …


Assessing Refinements In Modeling Sinusoidal Conditions Used To Drive Cattle Body Temperatures, Sheng Feng, Anne Parkhurst, Kent Eskridge, Daryl Travnicek, Donald Spiers, G. L. Hahn, Terry Mader Apr 2001

Assessing Refinements In Modeling Sinusoidal Conditions Used To Drive Cattle Body Temperatures, Sheng Feng, Anne Parkhurst, Kent Eskridge, Daryl Travnicek, Donald Spiers, G. L. Hahn, Terry Mader

Conference on Applied Statistics in Agriculture

A model, termed the PET model, is used to estimate body temperature in cattle challenged by hot cyclic chamber temperatures. The model is based on Newton's law of cooling, driven by an estimated sinusoidal function. In practice, it is often difficult to maintain hot sinusoidal fluctuations in chamber temperatures. However, it is possible to model cyclic chamber temperatures using a discrete Fourier series. By increasing the precision in estimating the cyclic temperature driving function, we can more precisely estimate the parameters in the PET model. Simulation studies were performed to investigate the effect of under- and over-parameterization on accuracy of …


Predicting Soybean Weight Per Pod, Timothy P. Keller, Michael Schmidt, Catherine Schmidt Apr 2001

Predicting Soybean Weight Per Pod, Timothy P. Keller, Michael Schmidt, Catherine Schmidt

Conference on Applied Statistics in Agriculture

The National Agricultural Statistics Service (NASS) makes predictions of soybean yield at both the state and national level. Experience indicates that the key to improving yield predictions is improving the prediction of soybean weight pod. Towards this end, NASS has entered into a three year cooperative agreement with the Department of Plant, Soil and General Agriculture at Southern lllinois University at Carbondale (SID-C) to investigate predictive models for soybean weight per pod based on a measurement of pod width and a count of the number of seeds per pod. Aside from the scientific issues involved in this effort, the practical …


Development Of Experiments For The Harvesting And Storing Of Vidalia Sweet Onions, Ben G. Mullinix, Bryan W. Maw, Reid L. Torrance Apr 2001

Development Of Experiments For The Harvesting And Storing Of Vidalia Sweet Onions, Ben G. Mullinix, Bryan W. Maw, Reid L. Torrance

Conference on Applied Statistics in Agriculture

Sweet onions brought in nearly $70 million in 1998. Sweet onions have a soft bulb which makes them susceptible to injury if handled too roughly. Once injured, invasion by pathogens tends to render the bulbs unusable except for quick sale. They were harvested by hand until about ten years ago when efforts were begun to develop a mechanical harvester. Also, at that time, work was underway to develop a way of storing part of the crop so as to extend the market window beyond the traditional 6-8 weeks. Low temperature and low oxygen atmosphere conditions proved to be the most …


Are Spatial Models Needed With Adequately Blocked Field Trials?, Reid D. Landes, Kent M. Eskridge, P. Stephen Baenziger, David B. Marx Apr 2001

Are Spatial Models Needed With Adequately Blocked Field Trials?, Reid D. Landes, Kent M. Eskridge, P. Stephen Baenziger, David B. Marx

Conference on Applied Statistics in Agriculture

The use of nearest neighbors and spatial models (SPAT) to analyze field trial data has become commonplace in recent years. These two types of analyses improve precision compared to ANOVA when trials are poorly blocked, but results are less clear in well-blocked trials. We examined data from wheat trials containing 60 cultivars, conducted at five locations, where each location was set up as an alpha lattice design. We compared the relative efficiency of detecting cultivar differences for spatial models and nearest neighbors analyses (NNA) to ANOVA, fit of the models, and correlations of ranked cultivars. Though the SPAT and NNA …


An Analysis Of Daily Peak Stream Discharge Using A Non-Gaussian Time Series Model, S. Perera Apr 2001

An Analysis Of Daily Peak Stream Discharge Using A Non-Gaussian Time Series Model, S. Perera

Conference on Applied Statistics in Agriculture

Daily peak stream discharge data, collected over time, are typically characterized by a few large peaks separated by runs of small values, where peaks correspond to the occurrence of storms. Furthermore, the peak discharge on the first day of a storm has little or no relationship to the previous day's discharge. These characteristics are not present in standard Gaussian time series models in which a zig-zag behavior not conducive to runs of small values is observed and the present value always depends on the previous value. However, they can be successfully captured with non-Gaussian time series models.

Daily peak stream …


Using Proc Nlmixed To Analyze A Time Of Weed Removal Study, Erin E. Blankenship, Sean Evans, Walter W. Stroup, Stevan Z. Knezevic Apr 2001

Using Proc Nlmixed To Analyze A Time Of Weed Removal Study, Erin E. Blankenship, Sean Evans, Walter W. Stroup, Stevan Z. Knezevic

Conference on Applied Statistics in Agriculture

Many studies in weed science involve fitting a nonlinear model to experimental data. Examples of such studies include dose-response experiments and studies to determine the critical period of weed control. The experiments typically use block designs and often have additional complexity such as split-plot features. However, nonlinear models are typically fit using software such as SAS PROC NLIN that are limited to a single error term and whose ability to account for blocking is either awkward or lacking entirely. For example, Seefeldt et al. (1995) only proceeded in fitting the nonlinear model after establishing that the block effect was negligible. …


Model Building In Multi-Factor Plant Nutrition Experiments, L. M. Olson, W. W. Stroup, E. T. Paparozzi, M. E. Conley Apr 2001

Model Building In Multi-Factor Plant Nutrition Experiments, L. M. Olson, W. W. Stroup, E. T. Paparozzi, M. E. Conley

Conference on Applied Statistics in Agriculture

Often, the goal of plant science experiments is to model plant response as a function of quantitative treatment factors, such as the amount of nutrient applied. As the number of factors increases, modeling the response becomes increasingly challenging, especially since the resources available for such experiments are usually severely limited. Typical methods of analysis, notably second-order response surface regression, often fail to accurately explain the data. Alternatives such as non-linear models and segmented regression have been used successfully with two-factor experiments (Landes, et. aI, 1999). This paper extends previous work to three-and-more factor experiments. Models are assessed to explain the …


Designing Microarrays, B. A. Craig, O. Vitek, M. A. Black, M. Tanurdzic, R. W. Doerge Apr 2001

Designing Microarrays, B. A. Craig, O. Vitek, M. A. Black, M. Tanurdzic, R. W. Doerge

Conference on Applied Statistics in Agriculture

Microarrays allow the simultaneous assessment of expression levels for thousands of genes across various treatment conditions and time. It has been shown that in these experiments expression levels can also be affected by factors in the printing of the slide, in the hybridization process, and in the post-hybridization process. Recently, variations of the incomplete block design were proposed as a way to avoid confounding the expression levels of interest with several of these nuisance factors. In this paper, we propose additional design procedures to remove factors that contribute to the spatial variability on a slide. This approach requires the use …


Calculation Of The Minimum Number Of Replicate Spots Required For Detection Of Significant Gene Expression Fold Change In Microarra Y Experiments, Michael A. Black, R. W. Doerge Apr 2001

Calculation Of The Minimum Number Of Replicate Spots Required For Detection Of Significant Gene Expression Fold Change In Microarra Y Experiments, Michael A. Black, R. W. Doerge

Conference on Applied Statistics in Agriculture

Calculations for the number of per gene replicate spots in microarray experiments are presented for the purpose of obtaining estimates of the sampling variability present in microarray data, and for determining the minimum number of replicate spots required to achieve a high probability of detecting a significant fold change in gene expression. Our approach is based on data from control microarrays, and employs standard statistical estimation techniques. We have demonstrated the usefulness of our framework by analyzing two experimental data sets containing control array data. The minimum number of replicate spots required on a treatment array were calculated to achieve …


Statistical Issues In The Analysis Of Microbial Communities In Soil, J. D. Wilbur, C. H. Nakatsu, S. M. Brouder, J. K. Ghosh, R. W. Doerge Apr 2001

Statistical Issues In The Analysis Of Microbial Communities In Soil, J. D. Wilbur, C. H. Nakatsu, S. M. Brouder, J. K. Ghosh, R. W. Doerge

Conference on Applied Statistics in Agriculture

Corn and soybean production dominates the agricultural systems of the mid-western United States. Studies have found that when a single crop species is grown continually, without the rotation of other crops, yield decline occurs. At present, this phenomenon, remains poorly understood, but there are possible links to microbial community dynamics in the associated rhizosphere soil. In this study, corn plants were grown in disturbed and undisturbed soils with a 24 year history of growth as a mono culture crop or two crops grown in annual rotation. Characteristic profiles of the microbial communities were obtained by denaturing gradient gel electrophoresis of …


Another Look At New Gma Orthogonal Arrays, Yingfu Li, Timothy Wittig Apr 2001

Another Look At New Gma Orthogonal Arrays, Yingfu Li, Timothy Wittig

Conference on Applied Statistics in Agriculture

Non-regular factorial designs have not been advocated until last decade clue to their complex aliasing structure. However, some researchers recently found that the complex aliasing structure of non-regular factorial designs is a challenge as well as an opportunity. Li, Deng, and Tang (2000) studied nonl-regular designs and generated a collection of non-equivalent orthogonal arrays using a generalized miniumm aberration criterion, proposed by Deng and Tang (1999). Some new orthogonal arrays they found cannot be embedded into Hadamard matrices. In this paper, we study these orthogonal arrays from the angle of projection. We show that these new GMA orthogonal arrays are …


A Comparison Of Some Methods To Analyze Repeated Measures Ordinal Categorical Data, Yaobing Sui, Walter W. Stroup Apr 2001

A Comparison Of Some Methods To Analyze Repeated Measures Ordinal Categorical Data, Yaobing Sui, Walter W. Stroup

Conference on Applied Statistics in Agriculture

Recent advances in statistical software made possible by the rapid development of computer technology in the past decade have made many new procedures available to data analysts. We focus in this paper on methods for ordinal categorical data with repeated measures that can be implemented using SAS. These procedures are illustrated using data from an animal health experiment. The responses, measured as severity of symptoms on an ordinal scale, are recorded for test animals over time. The experiment was designed to estimate treatment and time effects on the severity of symptoms. The data were analyzed with various approaches using PROC …