Dissertations / Theses on the topic 'Longitudinal'
To see the other types of publications on this topic, follow the link: Longitudinal.
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Longitudinal.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Petzold, Max. "Evaluation of information in longitudinal data." Göteborg : Statistical Research Unit, Göteborg University, 2003. http://catalog.hathitrust.org/api/volumes/oclc/52551306.html.
Full text
2
Arnal, Mathieu. "Développement d'une évaluation génomique pour l'analyse de données longitudinales : application aux contrôles élémentaires chez les caprins laitiers." Thesis, Toulouse, INPT, 2019. http://www.theses.fr/2019INPT0124.
Full textAbstract:
L’amélioration génétique des caprins laitiers est basée, à ce jour, sur la mesure de la quantité et de la qualité de la production laitière des femelles en ferme, à intervalles de 4 à 5 semaines au cours de la lactation, selon des protocoles stricts. L’évaluation génétique de la quantité de lait repose sur l’estimation de la quantité de lait totale produite par lactation. Cette sélection à partir de la quantité totale de lait à la lactation a tendance à sélectionner des animaux avec une production au pic de lactation de plus en plus élevée. Une production importante en début de lactation peut être à l’origine, pour les femelles, de problèmes métaboliques. De plus, en caprins laitiers, dans un contexte de production saisonnée, une production laitière qui se maintient après le pic, i.e. persistante, permettrait une production laitière plus étalée, en lien avec les attentes du marché. Il y a donc un intérêt zootechnique et économique de vouloir sélectionner des chèvres laitières plus persistantes. Dans notre étude, l’approche consiste à modéliser la forme de la courbe de lactation à partir des informations recueillies lors de chaque contrôle en ferme. Les modèles permettant l’analyse de telles données longitudinales sont généralement appelés modèles de contrôles élémentaires. L’un des principaux intérêts, est une meilleure prise en compte d’effets d’environnement, affectant la production le jour du contrôle, avec un effet troupeau-jour de contrôle ne dépendant que des animaux présents lors du contrôle. Le deuxième avantage de ce type de modèle réside dans la modélisation de la plupart des effets génétiques et d’environnement sous forme de courbes ; il serait donc possible de sélectionner les animaux avec la meilleure valeur génétique pour la persistance. La mise au point de ces modèles nécessite l’étude préalable des effets d’environnement affectant la production laitière au cours du temps. Suite à une analyse descriptive détaillée des courbes de lactation des deux principales races caprines françaises (Alpine et Saanen), nous avons montré qu’il existait une variabilité de la forme de courbes de lactation, et en particulier que le mois de mise bas était impliqué dans les différentes formes de courbe. Nous avons ensuite proposé un modèle de régression aléatoire, proche de celui développé chez les bovins laitiers français. La modélisation proposée permet d’obtenir directement deux index génétiques : un premier correspondant à la valeur génétique de l’animal pour la quantité totale de lait au cours de la lactation et un deuxième correspondant à une valeur génétique de la persistance laitière de l’animal, et cela sans corrélation entre les deux. Le modèle développé permet de prendre en compte de façon disjointe les chèvres en primipares et les chèvres en multipares. Nous avons également étudié les corrélations entre index de différents caractères, au cours de la lactation ainsi que les corrélations entre persistance et fertilité à l’IA ou entre persistance et longévité. Dans une dernière partie, nous avons étendu le modèle d’évaluation génétique des contrôles élémentaires à un modèle d’évaluation génomique (Singlestep GBLUP) permettant d’exploiter l’ensemble des informations moléculaires disponibles (génotypages SNP 50K). Une validation de ce modèle et une comparaison au modèle actuel ont été réalisées. Les différences de moyennes des index estimés par année de naissance des boucs constituaient la principale différence entre le modèle Single-step GBLUP RRM et le Single-step GBLUP modèle à la lactation utilisé actuellement. Enfin, à partir du modèle Single-step GBLUP nous avons mis en évidence quelques régions du génome intéressantes liées à la persistance laitièreGenetic improvement of dairy goats is based on the measurement of the quantity and quality of milk production of females on farms, at intervals of 4 to 5 weeks during lactation, according to strict protocols. The genetic evaluation of the quantity of milk is based on the estimation of the total quantity of milk produced per lactation. This selection based on the total quantity of milk in lactation tends to select animals with increasingly high peak lactation production. High production at the beginning of lactation can cause metabolic problems for females. In addition, in the case of dairy goats, in a context of seasonal production, a milk production that is maintained after the peak, i.e. persistent, would allow a more spread out milk production, in line with market expectations. There is therefore a zootechnical and economic interest in wanting to select more persistent dairy goats. In our study, the approach consists in modelling the shape of the lactation curve based on the information collected during each farm test. Models allowing the analysis of such longitudinal data are generally called test-day models. One of the main interests is to take better account of environmental effects, affecting production on test-day, with a herd-test-day effect depending only on the animals present during the test. The second advantage of this type of model is that most genetic and environmental effects are modelled as curves, so it would be possible to select animals with the best genetic value for persistence. The development of these models requires the prior study of the environmental effects affecting milk production over time. Following a detailed descriptive analysis of the lactation curves of the two main French goat breeds (Alpine and Saanen), we showed that there was a variability in the shape of the lactation curves, and in particular the month of calving was involved in the different curve shapes. Then we proposed a random regression model, similar to that developed in French dairy cattle. The proposed modeling makes it possible to obtain two genetic indexes directly: one corresponding to the genetic value of the animal for the total quantity of milk during lactation and a second corresponding to a genetic value of the animal's milk persistency, without correlation between the two. The model proposed is more relevant than the current one because it takes into account, in a disjointed way, the goats in primiparous and the goats in multiparous. We also studied correlations between indexes of different traits during lactation and correlations between persistence and AI fertility or between persistence and longevity. In the last part of the thesis, we extended the genetic evaluation of test-day to a genomic evaluation model (Single-step GBLUP) allowing to exploit all available molecular information (genotyping SNP 50K). A validation of this model and a comparison with the current model was carried out. The main difference between the Single-step GBLUP RRM and the Single-step GBLUP lactation model currently in use was the differences in the averages of the estimated indexes per year of birth of the bucks. Finally, from the Single-step GBLUP model we have identified some interested regions of the genome linked to milk persistence
3
Metzger, Nikolaus K. "Longitudinal optical binding." Thesis, St Andrews, 2008. http://hdl.handle.net/10023/519.
Full text
4
Lin, Ying-Tsair. "Ship longitudinal strength modelling." Thesis, University of Glasgow, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320513.
Full text
5
Moroder, Daniel. "Longitudinal bar buckling behavior." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2008. http://amslaurea.unibo.it/94/.
Full textAbstract:
Reinforced concrete columns might fail because of buckling of the longitudinal reinforcing bar when exposed to earthquake motions. Depending on the hoop stiffness and the length-over-diameter ratio, the instability can be local (in between two subsequent hoops) or global (the buckling length comprises several hoop spacings).
To get insight into the topic, an extensive literary research of 19 existing models has been carried out including different approaches and assumptions which yield different results. Finite element fiberanalysis was carried out to study the local buckling behavior with varying length-over-diameter and initial imperfection-over-diameter ratios. The comparison of the analytical results with some experimental results shows good agreement before the post buckling behavior undergoes large deformation. Furthermore, different global buckling analysis cases were run considering the influence of different parameters; for certain hoop stiffnesses and length-over-diameter ratios local buckling was encountered. A parametric study yields an adimensional critical stress in function of a stiffness ratio characterized by the reinforcement configuration.
Colonne in cemento armato possono collassare per via dell’instabilità dell’armatura longitudinale se sottoposte all’azione di un sisma. In funzione della rigidezza dei ferri trasversali e del rapporto lunghezza d’inflessione-diametro, l’instabilità può essere locale (fra due staffe adiacenti) o globale (la lunghezza d’instabilità comprende alcune staffe).
Per introdurre alla materia, è proposta un’esauriente ricerca bibliografica di 19 modelli esistenti che include approcci e ipotesi differenti che portano a risultati distinti. Tramite un’analisi a fibre e elementi finiti si è studiata l’instabilità locale con vari rapporti lunghezza d’inflessione-diametro e imperfezione iniziale-diametro. Il confronto dei risultati analitici con quelli sperimentali mostra una buona coincidenza fino al raggiungimento di grandi spostamenti. Inoltre, il caso d’instabilità globale è stato simulato valutando l’influenza di vari parametri; per certe configurazioni di rigidezza delle staffe e lunghezza d’inflessione-diametro si hanno ottenuto casi di instabilità locale. Uno studio parametrico ha permesso di ottenere un carico critico adimensionale in funzione del rapporto di rigidezza dato dalle caratteristiche dell’armatura.
6
Ettinger, Ronald L. "Overdentures : a longitudinal perspective." Thesis, The University of Sydney, 1992. http://hdl.handle.net/2123/4645.
Full text
7
Mandele, L. Martin van der. "Leadership and the inflection point : a longitudinal perspective = Leiderschap en het inflectiepunt : een longitudinaal perspectief /." Rotterdam : Erasmus Research Institute of Management, 2004. http://hdl.handle.net/1765/1302.
Full text
8
Sieber, Jan. "Longitudinal dynamics of semiconductor lasers." Doctoral thesis, [S.l. : s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=963267795.
Full text
9
Husain, Syeda Tasmine. "Bayesian analysis of longitudinal models /." Internet access available to MUN users only, 2003. http://collections.mun.ca/u?/theses,163598.
Full text
10
Ju, Hyunsu. "Topics in analyzing longitudinal data." Texas A&M University, 2004. http://hdl.handle.net/1969.1/1565.
Full textAbstract:
We propose methods for analyzing longitudinal data, obtained in clinical trials
and other applications with repeated measures of responses taken over time. Common
characteristics of longitudinal studies are correlated responses and observations taken
at unequal points in time. The first part of this dissertation examines the justification
of a block bootstrap procedure for the repeated measurement designs, which takes
into account the dependence structure of the data by resampling blocks of adjacent
observations rather than individual data points. In the case of dependent stationary
data, under regular conditions, the approximately studentized or standardized block
bootstrap possesses a higher order of accuracy. With longitudinal data, the second
part of this dissertation shows that the diagonal optimal weights for unbalanced
designs can be made to improve the efficiency of the estimators in terms of mean
squared error criterion. Simulation study is conducted for each of the longitudinal
designs. We will also analyze repeated measurement data set concerning nursing home
residents with multiple sclerosis, which is obtained from a large database termed the
minimum data set (MDS).
11
Ryu, Duchwan. "Regression analysis with longitudinal measurements." Texas A&M University, 2005. http://hdl.handle.net/1969.1/2398.
Full textAbstract:
Bayesian approaches to the regression analysis for longitudinal measurements are
considered. The history of measurements from a subject may convey characteristics
of the subject. Hence, in a regression analysis with longitudinal measurements, the
characteristics of each subject can be served as covariates, in addition to possible other
covariates. Also, the longitudinal measurements may lead to complicated covariance
structures within each subject and they should be modeled properly.
When covariates are some unobservable characteristics of each subject, Bayesian
parametric and nonparametric regressions have been considered. Although covariates
are not observable directly, by virtue of longitudinal measurements, the covariates
can be estimated. In this case, the measurement error problem is inevitable. Hence,
a classical measurement error model is established. In the Bayesian framework, the
regression function as well as all the unobservable covariates and nuisance parameters
are estimated. As multiple covariates are involved, a generalized additive model is
adopted, and the Bayesian backfitting algorithm is utilized for each component of the
additive model. For the binary response, the logistic regression has been proposed,
where the link function is estimated by the Bayesian parametric and nonparametric
regressions. For the link function, introduction of latent variables make the computing
fast.
In the next part, each subject is assumed to be observed not at the prespecifiedtime-points. Furthermore, the time of next measurement from a subject is supposed to
be dependent on the previous measurement history of the subject. For this outcome-
dependent follow-up times, various modeling options and the associated analyses
have been examined to investigate how outcome-dependent follow-up times affect
the estimation, within the frameworks of Bayesian parametric and nonparametric
regressions. Correlation structures of outcomes are based on different correlation
coefficients for different subjects. First, by assuming a Poisson process for the follow-
up times, regression models have been constructed. To interpret the subject-specific
random effects, more flexible models are considered by introducing a latent variable
for the subject-specific random effect and a survival distribution for the follow-up
times. The performance of each model has been evaluated by utilizing Bayesian
model assessments.
12
Sampson, Elizabeth Lesley. "Longitudinal studies in frontotemporal dementia." Thesis, University College London (University of London), 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.406422.
Full text
13
Mills, Joanna E. "The analysis longitudinal binary data." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ57350.pdf.
Full text
14
Kliment, Linda K. "Dynamics of longitudinal wake vortices." Diss., Wichita State University, 2009. http://hdl.handle.net/10057/2554.
Full textAbstract:
In the present study, the mid-field vortex wake is investigated. For the most part, the results focus on the motion of a pair of co-rotating vortices prior to merger, both in and out of ground effect. However, in order to verify the experimental and computational methods, results for single vortices, counter-rotating pairs, and complex wakes are also presented. A method is presented which allows measurement of the time dependent motion of vortex filaments. This optical method interferes minimally with the wake and allows recording of vortex location and time-dependent motion. From the position and time information recorded, extraction of the amplitudes of motion, core motion, spiraling behavior, vortex strengths, and the principal planes of motion is possible.
First, a single vortex is studied in order to establish a basis for comparison. The dye remains in the core and the motion of a single vortex is shown to exhibit a growth in amplitude with increasing downstream distance and strength. The core motion is shown to be minimal, remaining smaller that one core diameter. In addition, when the single vortex is forced to oscillate at a given frequency, the dye still remains in the core, even though the amplitudes of motion are large. The forcing frequency is identified easily against the background noise. Two four-vortex cases are then presented. The first case consists of filaments that spiral while in the second they scatter. These results are consistent with those shown in literature and show that the experimental method can be used for analyzing complex wakes. Pairs of unforced, co-rotating filaments are studied outside of ground effect. Many cases are presented, some for nearly equal strengths and others in which one vortex is much stronger than the other. As in the single-vortex case, the amplitudes of motion are shown to increase as the downstream distance becomes greater. The constant rate of spiraling is shown to increase as the vortex strength increases and vortex span decreases. Vortex span either remains constant or decreases with downstream distance depending on the vortex separation distance. The motion of the center of spiraling is shown to be minimal, similar to the motion of the vortex core in the single-vortex cases. The filaments are shown to sometimes oscillate along preferred directions, which is inconsistent with a theoretical model developed in 1975. A few cases are also presented in which the merger location is analyzed. However, these are visual investigations only, since it is not possible to obtain quantitative data for such cases with the experimental method available. The behavior of co-rotating vortices in the presence of forcing functions is then presented. The results are compared to the theoretical model developed in 1975 and those published after 2002. However, a direct comparison with analytical results is not possible due to the large scatter in the experimental data. Regardless, the experimental results show that the forced corotating vortices do have an unstable oscillatory motion with growing amplitude. The preferred direction of motion implies the presence of stationary waves. These results contradict those of the analytical model developed in 1975 but agree in nature with those published more recently. Ground effect is then considered for counter-rotating vortices, because there is a wealth of information on this topic in the literature. When counter-rotating vortices are near a ground plane, a lateral drift as well as a rebounding behavior is present. The counter-rotating vortices are shown to have a preferred direction of motion which tends to become parallel to the ground plane. The motion is also shown to have increasing amplitude, although this quantity is slightly reduced by the presence of the ground plane. In addition, ground roughness in the form of streamwise ridges has no affect on the vortex trajectories, within the range of downstream distances observable in these experiments. After comparing the results to those in literature, it is concluded that the experimental method is valid and can be used to study co-rotating vortices in ground effect.
Literature lacks information on co-rotating vortices in ground effect. The results in this document show that co-rotating vortices in ground effect have a lateral drift as well as a rebound similar to those of counter-rotating pairs. The resulting motion is similar to that of leapfrogging vortex rings. Preferred directions of motion are present, although no trend can be established. In addition, the amplitudes of motion are reduced slightly by the presence of the ground, just as they are for the counter-rotating vortices. Due to the lack of information on co-rotating vortices in ground effect in the current literature, a comparison is impossible. Therefore, two simple computation efforts are undertaken in order to verify some of the flow features. Using a two-dimensional viscous analysis, limited to laminar flow, it is shown that when co-rotating vortices are placed near a stationary wall, a boundary layer forms on the surface and separates. The secondary vortex released by boundary layer separation leads to rebounding of the primary vortices. In addition to affecting the trajectory, the no-slip boundary also affects the time to vortex merger as well as leading to an elongation of the vorticity contours. Furthermore, this analysis demonstrates that making the strengths of the two vortices differ slightly does not affect the spiraling rate, surface boundary layer separation, or rebound. A second inviscid model is also used to study cases consisting of two vortices of unequal strengths. Having unequal strengths does affect the lateral drift of corotating vortices in ground effect. Also, the center of spiraling shifts towards the stronger vortex. However, the inviscid model shows that the vortex span is unaffected by difference in strengths.Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of Aerospace Engineering
15
Zhou, Wei 1968 Jan 17. "Longitudinal data with change-points." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=98532.
Full textAbstract:
Longitudinal data often consist of a set of covariates and repeated measurements of an outcome over time. In clinical and health studies, a main concern is often the time that a treatment takes into effect, which is referred to as the change-point in this thesis. Modeling and measuring impact of a change in longitudinal data has not been thoroughly explored in the statistical literature. Viewing longitudinal data from the perspective of change-point analysis, we have a data structure that statisticians sometimes refer to as a multi-path change-point problem.In multipath change-point problems, it is often of interest to assess the impact of covariates on the change-point. We model the effect of covariates through hazard of the change using Cox's proportional odds model. We take a maximum quasi-likelihood (MqL) approach in estimation and statistical inference. To find the MqL estimators of the unknown parameters in our model, we have used a variant of simulated annealing. By the means of simulation we compare our model with a model suggested by Diggle et al. for analyzing a set of longitudinal observations on the body weights of 27 cows.
16
Fullwood, Catherine Lee. "Longitudinal analysis of anticoagulent data." Thesis, Lancaster University, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.431469.
Full text
17
Bai, Yang, and 柏楊. "Statistical analysis for longitudinal data." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B42841756.
Full text
18
Sacker, Amanda. "Longitudinal models of maladaptive behaviour." Thesis, University of Hertfordshire, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.361262.
Full text
19
Glowinkowski, S. P. "Managerial stress : A longitudinal study." Thesis, University of Manchester, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373224.
Full text
20
Vieira, Marcel de Toledo. "Modelling complex longitudinal survey data." Thesis, University of Southampton, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.423245.
Full text
21
Allison, Duncan. "Longitudinal vibration of road vehicles." Thesis, Cranfield University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.284907.
Full text
22
Murphy, Enda. "Longitudinal dispersion in vegetated flow." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/34603.
Full textAbstract:
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2006.Includes bibliographical references (p. 171-183).
Vegetation is ubiquitous in rivers, estuaries and wetlands, strongly influencing both water conveyance and mass transport. The plant canopy affects both mean and turbulent flow structure, and thus both advection and dispersion. Accurate prediction of the fate and transport of nutrients, microbes, dissolved oxygen and other scalars depends on our ability to quantify vegetative impacts. In this thesis, the focus is on longitudinal dispersion, which traditionally has been modeled by drawing analogy to rough boundary layers. This approach is inappropriate in many cases, as the vegetation provides a significant dead zone, which may trap scalars and augment dispersion. The dead zone process is not captured in the rough boundary model. This thesis describes a new theoretical model for longitudinal dispersion in a vegetated channel, which isolates three separate contributory processes. To evaluate the performance of the model, tracer experiments and velocity measurements were conducted in a laboratory flume. Results show that the mechanism of exchange between the free stream and the vegetated region is critical to the overall dispersion, and is primarily controlled by the canopy density.
(cont.) A numerical random walk particle-tracking model was developed to assess the uncertainty associated with the experimental data. Results suggest that the time scale required to obtain sound experimental data in tracer studies is longer than the commonly used Fickian time scale.
by Enda Murphy.
S.M.
23
Andrews, Jeffrey Pratt. "Longitudinal misalignment based strain sensor." Thesis, Virginia Tech, 1989. http://hdl.handle.net/10919/43283.
Full textAbstract:
A practical fiber optic strain sensor has been developed to measure strains in the range of 0.0 to 2.0 percent strain with a resolution ranging between 10 and 100 microstrain depending on sensor design choices. This intensity based sensor measures strain by monitoring strain induced longitudinal misalignment in a novel fiber interconnection. This interconnection is created by aligning fibers within a segment of hollow core fiber. Related splice loss mechanisms are investigated for their effect on resolution. The effect of gauge length and launch conditions are also investigated.
Master of Science
24
Dufour, Alyssa Beth. "Cluster analysis of longitudinal trajectories." Thesis, Boston University, 2013. https://hdl.handle.net/2144/12751.
Full textAbstract:
Thesis (Ph.D.)--Boston UniversityCluster analysis is widely used in many disciplines including biology, psychology, archaeology, geography, and marketing. Methods have been developed to extend cluster analysis to longitudinal data, clustering subject trajectories rather than single time points. Here, I examine 2 methods of longitudinal cluster analysis: k-means and model-based (implemented using FlexMix in R) cluster analysis. I compare these two methods based on the Correct Classification Rate, the ability of the method to correctly classify subject trajectories into groups, using a simulation study. Both methods are found to perform well under most circumstances, but in 64% of the scenarios examined, the model-based method out-performs the k-means approach. Next, I examine three criteria that have been used to determine how many groups exist in the data: the Akaike's Information Criteria (AIC), the Davies-Bouldin Index (DB), and the Calinski-Harabasz pseudo F-statistic (CH). The latter two were developed specifically for choosing the number of groups in a cluster analysis with a single observation per person, while the AIC was developed as a general model fit statistic. Few studies have used these criteria in the context of longitudinal data and no study has compared their efficacy. We found that the DB and CH fail to correctly identify the number of groups in the majority cases, while the AIC was better able to determine the correct number. Finally, as no study has examined the addition of a covariate to cluster analysis, we compare results of a cluster analysis when a covariate was taken into account to when it is ignored. When a covariate is both time-dependent and associated with the outcome, regardless of the magnitude of the association, it is important to take this variable into account in the analysis. If the covariate is associated only with the outcome and not time-dependent, depending on the magnitude of the association, it may be necessary to account for the covariate. In summary, we present methods for clustering trajectories, evaluate methods for determining the number of groups and determine the importance of adjusting for covariates in the cluster analysis of longitudinal data.
25
Sandy, Megan Elizabeth. "Longitudinal Study of Adjustable Workstations." Scholar Commons, 2016. http://scholarcommons.usf.edu/etd/6378.
Full textAbstract:
Workplace interventions to reduce discomfort and sedentary time have been studied in a variety of settings. Adjustable workstations are one type of ergonomic intervention that is used to potentially reduce occupational sitting time, negative health impacts, and to increase productivity. This investigation compared two types of ergonomic interventions, as well as contrasting behavioral interventions among workers with and without adjustable workstations. Seventy-two sedentary office workers were selected to participate in a longitudinal study to evaluate interventions for a reduction in occupational sitting time, to understand the effect on productivity and to evaluate musculoskeletal pain and behaviors. Workers were randomly placed into four different intervention groups and observed over 14 weeks. Group assignments were: control group, employees trained on behavioral interventions, employees given adjustable workstations and the final group had both ergonomic and behavioral interventions. During the study, there was a decrease in discomfort scores and fatigue for the adjustable workstation users. Standing time was increased in groups that had the adjustable workstations and frequency of workstation use remained constant throughout the 14 weeks. There was sufficient evidence to suggest that adjustable workstations will decrease sitting time and decease all over body discomfort in occupations that typically involve long hours of sitting. More research is needed to determine the health benefits of less occupational sitting.
26
Ridderbusch, Heiko. "Longitudinal angeregte passiv gütegeschaltete Laserzündkerze." München Utz, 2008. http://d-nb.info/990564088/04.
Full text
27
Staud, Benjamin T. "Seepage through longitudinal drainage trenches." Morgantown, W. Va. : [West Virginia University Libraries], 2000. http://etd.wvu.edu/templates/showETD.cfm?recnum=1405.
Full textAbstract:
Thesis (M.S.)--West Virginia University, 2000.Title from document title page. Document formatted into pages; contains xiv, 134 p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references (p. 75).
28
Bai, Yang. "Statistical analysis for longitudinal data." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B42841756.
Full text
29
Dong, Lei. "Nonparametric tests for longitudinal data." Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/2295.
Full text
30
Kim, Yangjin. "Statistical analysis of longitudinal data /." free to MU campus, to others for purchase, 2003. http://wwwlib.umi.com/cr/mo/fullcit?p3100054.
Full text
31
Khatiwada, Aastha. "Multilevel Models for Longitudinal Data." Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etd/3090.
Full textAbstract:
Longitudinal data arise when individuals are measured several times during an ob- servation period and thus the data for each individual are not independent. There are several ways of analyzing longitudinal data when different treatments are com- pared. Multilevel models are used to analyze data that are clustered in some way. In this work, multilevel models are used to analyze longitudinal data from a case study. Results from other more commonly used methods are compared to multilevel models. Also, comparison in output between two software, SAS and R, is done. Finally a method consisting of fitting individual models for each individual and then doing ANOVA type analysis on the estimated parameters of the individual models is proposed and its power for different sample sizes and effect sizes is studied by simulation.
32
Rolfe, Margaret Irene. "Bayesian models for longitudinal data." Thesis, Queensland University of Technology, 2010. https://eprints.qut.edu.au/34435/1/Margaret_Rolfe_Thesis.pdf.
Full textAbstract:
Longitudinal data, where data are repeatedly observed or measured on a temporal basis of time or age provides the foundation of the analysis of processes which evolve over time, and these can be referred to as growth or trajectory models. One of the traditional ways of looking at growth models is to employ either linear or polynomial functional forms to model trajectory shape, and account for variation around an overall mean trend with the inclusion of random eects or individual variation on the functional shape parameters. The identification of distinct subgroups or sub-classes (latent classes) within these trajectory models which are not based on some pre-existing individual classification provides an important methodology with substantive implications. The identification of subgroups or classes has a wide application in the medical arena where responder/non-responder identification based on distinctly diering trajectories delivers further information for clinical processes. This thesis develops Bayesian statistical models and techniques for the identification of subgroups in the analysis of longitudinal data where the number of time intervals is limited. These models are then applied to a single case study which investigates the neuropsychological cognition for early stage breast cancer patients undergoing adjuvant chemotherapy treatment from the Cognition in Breast Cancer Study undertaken by the Wesley Research Institute of Brisbane, Queensland. Alternative formulations to the linear or polynomial approach are taken which use piecewise linear models with a single turning point, change-point or knot at a known time point and latent basis models for the non-linear trajectories found for the verbal memory domain of cognitive function before and after chemotherapy treatment. Hierarchical Bayesian random eects models are used as a starting point for the latent class modelling process and are extended with the incorporation of covariates in the trajectory profiles and as predictors of class membership. The Bayesian latent basis models enable the degree of recovery post-chemotherapy to be estimated for short and long-term followup occasions, and the distinct class trajectories assist in the identification of breast cancer patients who maybe at risk of long-term verbal memory impairment.
33
Schiratti, Jean-Baptiste. "Methods and algorithms to learn spatio-temporal changes from longitudinal manifold-valued observations." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX009/document.
Full textAbstract:
Dans ce manuscrit, nous présentons un modèle à effets mixtes, présenté dans un cadre Bayésien, permettant d'estimer la progression temporelle d'un phénomène biologique à partir d'observations répétées, à valeurs dans une variété Riemannienne, et obtenues pour un individu ou groupe d'individus. La progression est modélisée par des trajectoires continues dans l'espace des observations, que l'on suppose être une variété Riemannienne. La trajectoire moyenne est définie par les effets mixtes du modèle. Pour définir les trajectoires de progression individuelles, nous avons introduit la notion de variation parallèle d'une courbe sur une variété Riemannienne. Pour chaque individu, une trajectoire individuelle est construite en considérant une variation parallèle de la trajectoire moyenne et en reparamétrisant en temps cette parallèle. Les transformations spatio-temporelles sujet-spécifiques, que sont la variation parallèle et la reparamétrisation temporelle sont définnies par les effets aléatoires du modèle et permettent de quantifier les changements de direction et vitesse à laquelle les trajectoires sont parcourues. Le cadre de la géométrie Riemannienne permet d'utiliser ce modèle générique avec n'importe quel type de données définies par des contraintes lisses. Une version stochastique de l'algorithme EM, le Monte Carlo Markov Chains Stochastic Approximation EM (MCMC-SAEM), est utilisé pour estimer les paramètres du modèle au sens du maximum a posteriori. L'utilisation du MCMC-SAEM avec un schéma numérique permettant de calculer le transport parallèle est discutée dans ce manuscrit. De plus, le modèle et le MCMC-SAEM sont validés sur des données synthétiques, ainsi qu'en grande dimension. Enfin, nous des résultats obtenus sur différents jeux de données liés à la santéWe propose a generic Bayesian mixed-effects model to estimate the temporal progression of a biological phenomenon from manifold-valued observations obtained at multiple time points for an individual or group of individuals. The progression is modeled by continuous trajectories in the space of measurements, which is assumed to be a Riemannian manifold. The group-average trajectory is defined by the fixed effects of the model. To define the individual trajectories, we introduced the notion of « parallel variations » of a curve on a Riemannian manifold. For each individual, the individual trajectory is constructed by considering a parallel variation of the average trajectory and reparametrizing this parallel in time. The subject specific spatiotemporal transformations, namely parallel variation and time reparametrization, are defined by the individual random effects and allow to quantify the changes in direction and pace at which the trajectories are followed. The framework of Riemannian geometry allows the model to be used with any kind of measurements with smooth constraints. A stochastic version of the Expectation-Maximization algorithm, the Monte Carlo Markov Chains Stochastic Approximation EM algorithm (MCMC-SAEM), is used to produce produce maximum a posteriori estimates of the parameters. The use of the MCMC-SAEM together with a numerical scheme for the approximation of parallel transport is discussed. In addition to this, the method is validated on synthetic data and in high-dimensional settings. We also provide experimental results obtained on health data
34
Levillain, Maxime. "Double longitudinal spin asymmetries in single hadron photoproduction at high pT at COMPASS." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLS059/document.
Full textAbstract:
Cette thèse présente une nouvelle étude ayant pour but de contraindre la contribution du gluon au spin 1/2 du nucléon. Cette analyse se place dans le cadre théorique de la pQCD colinéaire pour calculer des asymétries de section efficaces pour des hadrons inclusifs à grande impulsion transverse (pT>1 GeV/c) dans le régime de photoproduction quasi-réel (Q^2<1 GeV^2). Ces calculs sont réalisés jusqu'à NLO (Next-to-Leading Order) avec une inclusion prévue de resommation des gluons au seuil jusqu'à NLL (texit{Next-to-Leading Logarithm}), qui n'est pour l'instant fait que pour le cas non-polarisé. Cela rend les asymétries sensibles non seulement à la fusion photon-gluon ("gamma^* g") mais aussi à des processus de photon résolu tel que "q g" ou "g g".La mesure des asymétries est réalisée pour toutes les données de COMPASS de 2002 à 2011 avec un faisceau de muons polarisés à 160-200 GeV diffusé sur une cible de deuterium (LiD de 2002 à 2006) ou de proton (NH3 pour 2007 et 2011). Ces asymétries sont présentées en fonction de pT et de la pseudorapidité eta (pT dans [1,4] avec = 3 (GeV/c)^2, et eta dans [-0.1,2.4]).Les calculs de resommation n'étant pas terminés pour le cas polarisé, les mesures sont seulement comparés aux calculs théoriques en utilisant différents jeux de parametrisations de fonctions de distribution de parton polarisées ayant des valeurs de DeltaG assez étendues. Ces comparaisons sont ensuite utilisées pour évaluer le DeltaG des mesures.De façon complémentaire à cette analyse, une étude sur de nouveaux détecteurs, les pixel Micromegas, servant à pister le passage des particules, a été réalisée. Après certaines calibrations, ces détecteurs montrent des résultats prometteurs aussi bien en terme d'éfficacité qu'en terme de résolution temporelle et spatialeThis thesis presents a new study aiming at constraining the gluon contribution DeltaG to the 1/2 nucleon spin. The collinear pQCD theoretical framework, on which it is based, deals with asymmetries calculated from cross-sections for single inclusive hadron in the regime of quasi-real photoproduction (Q^2<1 GeV^2) at high hadron transverse momentum (pT>1 GeV/c). These calculations are done up to Next-to-Leading order with a foreseen inclusion of Next-to-Leading logarithm threshold gluon resummation, only performed for the unpolarised cross-sections yet. This makes the asymmetries sensitive to the gluon polarisation not only through Photon Gluon Fusion ("gamma^* g") but also through resolved photon processes such as "q g" or "g g".The measurement of the asymmetries is performed for all the COMPASS data available from 2002 to 2011 with a polarised muon beam at 160-200 GeV scattered off a longitudinally polarised target of deuteron (LiD for 2002-2006) or proton (NH3 for 2007 and 2011). The asymmetries are presented in bins of pT and of pseudorapidity eta (p_T in [1,4]$ with = 3 (GeV/c)^2, and eta in [-0.1,2.4]).Since the resummation calculations are not completed yet for the polarised case, the measurements are only compared with theoretical calculations using different parametrisation sets of polarised Parton Distribution Functions with a large range of different DeltaG. This comparison is then used to evaluate the DeltaG of these measurements.Complementary to this analysis, a study of new tracking detectors, the pixelised Micromegas, is performed. After calibration, it shows promising efficiencies and time and spatial resolutions
35
McFarland, Martha. "Full day kindergarten : a longitudinal perspective of perceived benefit." Virtual Press, 2007. http://liblink.bsu.edu/uhtbin/catkey/1364937.
Full textAbstract:
This study was designed to investigate the sustainable academic benefits of a full time kindergarten experience beyond the kindergarten year with additional consideration of the relationship between productive learning behaviors and ongoing academic advantage. The study was conducted across four elementary schools that housed both alternating full day and daily full day kindergarten programs. The initial sample consisted of 321 students enrolled in either daily full day or alternating full day kindergarten during the 2001-2002 school year, which decreased, through attrition, to a total of 198 students enrolled in fourth grade during the 2005-2006 school year. Student academic achievement was measured using a combination of criterion referenced skill assessments, standardized test measures, and a teacher-rated social behavior scale. Hypotheses were tested at the .05 level of significance using chi square analyses, multivariate and univariate analyses of variance, and correlation and regression analyses.The findings indicated that by the end of the kindergarten year, full day kindergarten students outperformed their alternating day peers in both reading and mathematics. However, as measured at the beginning of the second grade year, the academic gains realized during the kindergarten year had dissipated. By the beginning of the fourth grade year, there was no difference in achievement across program types in mathematics, while a significant achievement difference was found in English/language arts, with alternating full day students outperforming their daily full day peers. Further, during the third and fourth grade years, there was a significant interaction between gender and student achievement for the cohort, with significant differences by gender and the combined effect of gender/kindergarten type on social learning behaviors. While the data established a significant, positive relationship between competent social behavior and academic achievement regardless of gender for students from both program types, boys who attended daily full day kindergarten demonstrated significantly less productive social behavior than did boys from the alternating day program and girls from the daily full day program. For those who attended daily full day kindergarten, lower social behavior ratings predicted depressed academic achievement in English/language arts well beyond the kindergarten year.Department of Educational Leadership
36
Boudreau, Christian. "Duration data analysis in longitudinal surveys." Waterloo, Ont. : University of Waterloo, 2003. http://etd.uwaterloo.ca/etd/cboudrea2003.pdf.
Full textAbstract:
Thesis (Ph.D.)--University of Waterloo, 2003."A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Statistics". Includes bibliographical references. Also available in microfiche format.
37
Wallgren-Pettersson, Carina. "Congenital nemaline myopathy a longitudinal study /." Helsinki, Finland : Finnish Society of Sciences and Letters, 1990. http://catalog.hathitrust.org/api/volumes/oclc/24051855.html.
Full text
38
Rytterstedt, Peter. "Observer for a vehicle longitudinal controller." Thesis, Linköping University, Department of Electrical Engineering, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-8820.
Full textAbstract:
The longitudinal controller at DaimlerChrysler AG consists of two cascade controllers. The outer control loop contains the driver assistance functions such as speed limiter, cruise control, etc. The inner control loop consists of a PID-controller and an observer. The task of the observer is to estimate the part of the vehicle's acceleration caused by large disturbances, for example by a changed vehicle mass or the slope of the road.
As observer the Kalman filter is selected. It is the optimal filter when the process model is linear and the process noise and measurement noise can be modeled as Gaussian noise. In this Master's thesis the theory for the Kalman filter is presented and it is shown how to choose the filter parameters. Simulated annealing is a global optimization technique which can be used when autotuning, i.e., automatically find the optimal parameter settings. To be able to perform autotuning for the longitudinal controller one has to model the environment and driving situations.
In this Master's thesis it is verified that the parameter choice is a compromise between a fast but jerky, or a slow but smooth estimate. As the output from the Kalman filter is directly added to the control value for the engine and brakes, it is important that the output is smooth. It is shown that the Kalman filter implemented in the test vehicles today can be exchanged with a first-order lag function, without loss in performance. This makes the filter tuning easier, as there is only one parameter to choose.
Change detection is a method that can be used to detect large changes in the signal, and react accordingly - for example by making the filter faster. A filter using change detection is implemented and simulations show that it is possible to improve the estimate using this method. It is suggested to implement the change detection algorithm in a test vehicle and evaluate it further.
39
Boudreau, Christian. "Duration Data Analysis in Longitudinal Survey." Thesis, University of Waterloo, 2003. http://hdl.handle.net/10012/1043.
Full textAbstract:
Considerable amounts of event history data are collected through longitudinal surveys. These surveys have many particularities or features that are the results of the dynamic nature of the population under study and of the fact that data collected through longitudinal surveys involve the use of complex survey designs, with clustering and stratification. These particularities include: attrition, seam-effect, censoring, left-truncation and complications in the variance estimation due to the use of complex survey designs. This thesis focuses on the last two points.
Statistical methods based on the stratified Cox proportional hazards model that account for intra-cluster dependence, when the sampling design is uninformative, are proposed. This is achieved using the theory of estimating equations in conjunction with empirical process theory. Issues concerning analytic inference from survey data and the use of weighted versus unweighted procedures are also discussed. The proposed methodology is applied to data from the U. S. Survey of Income and Program Participation (SIPP) and data from the Canadian Survey of Labour and Income Dynamics (SLID).
Finally, different statistical methods for handling left-truncated sojourns are explored and compared. These include the conditional partial likelihood and other methods, based on the Exponential or the Weibull distributions.
40
Hobbs, Marissa. "Sorority Eating Patterns: A Longitudinal Investigation." TopSCHOLAR®, 2006. http://digitalcommons.wku.edu/theses/279.
Full textAbstract:
To date, most research in the area of college women and eating disorders has only been conducted to determine the prevalence of eating disorders among selected college subgroups. Although such research is limited, particularly for those women that choose to join social sororities, it generally indicates that sorority women represent a subgroup with high instances of eating disorders and often presents a conflicting view of these women's eating patterns and beliefs regarding weight loss and food. The present study was designed to continue the investigation of sorority women and their eating patterns by conducting a longitudinal study, consisting of five assessments over the course of one academic year, to assess whether the sorority women who are engaging in maladaptive eating behaviors and thought processes had these problems before joining a sorority or developed them later on as a member of the sorority. Specifically, this study was designed to answer the following research questions: First, do sorority women and nonsorority women differ in regards to weight, self-objectification, eating beliefs, or eating disorder symptoms at the start of or throughout the study? Additionally, do these initial reported weights, self-objectification scores, eating beliefs, or eating disorder symptoms vary over time for either group? Finally, is sorority membership a factor in any of these changes? Participants completed self-report measures of weight, eating beliefs (EBQ), eating disorder symptoms (EDDS), and self-objectification (TSOQ). The effects of time were analyzed for sorority members and non-sorority members using a 2 (sorority membership: sorority vs. non-sorority) x 5 (time: August vs. September vs. November vs. February vs. April) repeated measures analysis of variance (ANOVA) approach for the all of the dependent variables. Additionally, the interactions of sorority membership were analyzed. Results indicated there were no significant differences for self-objectification or the eating beliefs subscales of stereotypes, superstitions, or science. However, significant findings were shown for weight, the salves eating belief subscale, and reported eating disorder symptoms across time. Results are discussed in regards to the overall lack of significant differences between the two groups.
41
Skaff, Misty Lynne. "Predicting longitudinal loneliness in older adults." [Ames, Iowa : Iowa State University], 2007.
Find full text
42
Ricci, Peter J. "Some aspects of longitudinal data analysis /." Title page, contents and summary only, 1994. http://web4.library.adelaide.edu.au/theses/09PH/09phr491.pdf.
Full text
43
Spencer, Neil Hardy. "Longitudinal multilevel models in educational research." Thesis, Lancaster University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.306918.
Full text
44
Donald, I. P. "The Gloucestershire longitudinal study of disability." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.598592.
Full text
45
Dittrich, Regina, Brian Francis, and Walter Katzenbeisser. "Temporal dependence in longitudinal paired comparisons." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2008. http://epub.wu.ac.at/1452/1/document.pdf.
Full textAbstract:
This paper develops a new approach to the analysis of longitudinal paired comparison data, where comparisons of the same objects by the same judges are made on more than one occasion. As an alternative to other recent approaches to such data, which are based on Kalman filter- ing, our approach treats the problem as one of multivariate multinomial data, allowing dependence terms between comparisons over time to be incorporated. The resulting model can be fitted as a Poisson log-linear model and has parallels with the quadratic binary exponential distribution of Cox. An example from the British Household Panel Survey illustrates the approach. (author´s abstract)Series: Research Report Series / Department of Statistics and Mathematics
46
Marquez, Edanjarlo Joson. "Longitudinal distribution of radiolarians within Tethys." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B31245845.
Full text
47
Matthews, Cory. "Longitudinal Diet Studies of Arctic Whales." Marine Biological Association of the United Kingdom, 2013. http://hdl.handle.net/1993/30149.
Full textAbstract:
An animal’s foraging ecology can vary over a range of temporal scales, mirroring seasonal and longer term changes in prey availability, as well as ontogenetic shifts in diet and distribution. Obtaining individual-based, longitudinal diet information through direct observation, however, is logistically challenging for marine mammals that pursue and consume prey underwater, and are often widely distributed. Isotopic profiling along continuously growing tissues like teeth and baleen, which archive dietary inputs at the time of growth in their stable isotope composition, allows for chronological dietary reconstructions over multi-year timespans. This thesis reports longitudinal diet studies of three Arctic whale species, killer whales (Orcinus orca), bowhead whales (Balaena mysticetus) and beluga whales (Delphinapterus leucas), derived from serial isotopic measurements along teeth and baleen. Study objectives varied by species, but general goals were to characterize seasonal, ontogenetic, and/or individual diet variation.
Results revealed similar trophic-level diet, but regional spatial separation, among eastern Canadian Arctic/Northwest Atlantic killer whales. However, isotope and tooth wear differences between two individuals and the rest of the sampled whales suggested potential specialisation on sharks, while the other whales likely had diets comprising marine mammals. Cyclic isotopic variation along Eastern Canada-West Greenland bowhead whale baleen was consistent with year-round foraging, although at a reduced rate during winter. Resting zooplankton could be an important food resource outside of periods of peak productivity, and accessibility likely drives winter habitat selection. Isotopic cycling did not differ between female and male bowheads, or among age classes, indicating similar seasonal foraging patterns despite reported spatial segregation throughout their summer range. Individual beluga whales from three eastern Canadian Arctic populations varied in timing of ontogenetic diet shifts (i.e. weaning age), as well as overall trophic position, which could reflect size-specific energetic requirements and foraging capabilities. Population-specific beluga whale diet trends over a period of several decades likely reflected climate-related expansions of southern forage fish. Collectively, findings of seasonal, ontogenetic, and/or individual diet variation contribute a greater understanding of intrapopulation variation in foraging ecology of these species, and of large-scale structuring of Arctic marine ecosystems.
48
Fear, Simon Charles. "The analysis of categorical longitudinal data." Thesis, University of Liverpool, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266052.
Full text
49
Davis, Philip Mark. "Longitudinal dispersion mechanisms in natural channels." Thesis, University of East Anglia, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280921.
Full text
50
Henshaw, Carol Anne. "A longitudinal study of postnatal dysphoria." Thesis, University of Aberdeen, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312368.
Full textAbstract:
Background: Postnatal depression (PND) follows 10-15% of deliveries. Postnatal blues occur in the first postpartum week and are thought to have little significance. Studies report links between them, PND and premenstrual symptomatology but are methodologically flawed. Hypotheses: Women with severe blues are more likely to become depressed in the 6 months after delivery and more likely to experience premenstrual symptomatology when menstruation resumes. Subjects: First-time mothers who were literate, English speaking, had a singleton pregnancy, no current severe mental illness and whose fetus was healthy. Method: Written informed consent was obtained in late pregnancy. Baseline data include the Eysenck Personality Questionnaire, Edinburgh Postnatal Depression Scale (EPDS), sociodemographic and obstetric details. The Blues Questionnaire was completed on postpartum days 3 & 5. Obstetric data were recorded. Subjects (scores >/75th centile on the Blues Questionnaire) and controls (\<25th centile) were matched for age, marital status and social class. All participants completed monthly postal EPDS. When menstruation returned, daily Menstrual Distress Questionnaires and visual analogue scales for premenstrual symptoms were completed for 2 cycles. At 6 months all women with EPDS scores >/9 at any time postpartum were interviewed using the Schedule for Affective Disorder and Schizophrenia (Lifetime version). Research Diagnostic Criteria diagnoses were made for current or past psychiatric disorder. 1 in 5 women with EPDS scores <9 were interviewed to exclude false negatives. Results: Women with severe blues were 3.8 times more likely to become depressed and to have a major rather than minor illness. Their depressions began sooner after delivery and lasted longer than those with no blues. They were more likely to experience premenstrual symptoms. Discussion: Results support the idea that these conditions are variants of affective disorder, severe blues acting as a marker of affective vulnerability. Clinical applications of the results and areas for further research are explored.