Mathematics and Statistics, Department ofQueen's University Informationhttp://hdl.handle.net/1974/62017-09-26T07:11:56Z2017-09-26T07:11:56ZWorking with sophisticated problems in a grade 10 math classroom: The exploration of new experiences on self-efficacyLala, Divyahttp://hdl.handle.net/1974/227442017-09-26T04:46:25Z2017-09-01T00:00:00ZWorking with sophisticated problems in a grade 10 math classroom: The exploration of new experiences on self-efficacy
Lala, Divya
Studies show that self-efficacy is a strong indicator of student math achievement (Kitsantas et al., 2011). It has also been seen that self-efficacy changes based on the situation that one has to face (Bandura, 1997). This study investigated how the implementation of a new project, called Transformations 10, in an Ontario grade 10 mathematics classroom affected the students' self-efficacy. This project implemented new mathematics, a group environment and mentoring into the classes during a two week period. The study used qualitative and quantitative methods to determine what the students and mentors perceived as both positive and negative influences to the students' self-efficacy. Four aspects were found to play a role: the students' peers, the material taught, the extra help given to them and the pace of the project. In general, it was seen that the different aspects played a positive role on student self-efficacy. Overall, this study provided insight for further research and development on the Transformations10 project.
2017-09-01T00:00:00ZEvaluation and Application of a Test for Treatment-Biomarker Interaction Effects Using Probabilistic IndicesHaltner, Anjahttp://hdl.handle.net/1974/227382017-09-26T04:46:16Z2017-08-01T00:00:00ZEvaluation and Application of a Test for Treatment-Biomarker Interaction Effects Using Probabilistic Indices
Haltner, Anja
A predictive biomarker is a patient characteristic which associates with different effects
of the treatment on the patient. In clinical trials, it is often of interest to assess
whether the effects of the treatment differ depending on the level of the biomarker.
A common method to assess the treatment-biomarker interaction effect is to use Cox
proportional hazard model. However, this method might not be appropriate when the
proportional hazard assumption is not satisfied. Jiang, Chen and Tu (2016) developed
a non-parametric test for the treatment-biomarker interaction based on Efron's
estimator of probabilistic indices, which is free of any assumptions. This report is
mainly a review of their proposed method and will focus on determining its test size
on simulated data.
Various simulation studies demonstrated that the method based on Efron's estimator
performs well when the censoring rates are low. That is, the produced test
sizes were closer to the nominal test size. Other findings from the simulation studies
will lead to discussions on why the method performs badly when the censoring rate
is high, and how to dichotomize the biomarker when it is continuous based on some
cut point. The usefulness of these ideas in practice are presented by applying them
to sets of clinical trial data.
2017-08-01T00:00:00ZChannel Optimized Scalar Quantization over Orthogonal Multiple Access Channels with MemoryPreusser, Kiraseyahttp://hdl.handle.net/1974/227012017-09-19T15:53:07ZChannel Optimized Scalar Quantization over Orthogonal Multiple Access Channels with Memory
Preusser, Kiraseya
In this thesis, the joint source-channel coding method, channel optimized scalar quantization, is applied to real-valued, correlated data. The data is sent over the orthogonal multiple access channel, with non-binary noisy discrete channels with memory as the two sub-channels. Three different schemes are compared for this system: in the first scheme encoding and decoding are performed independently, in the second scheme encoding is done independently and joint decoding is carried out, and the third scheme is with jointly optimized encoders and joint decoding. The goal is to derive optimality conditions that will result in a lower end-to-end distortion. To this end, necessary optimality conditions for the two latter schemes are fully derived and implemented for the bivariate Gaussian and bivariate Laplacian distributions of varying correlation.\\
The first and second methods are then further compared, by implementing them for an image transmission system. Here the images are first processed with the 2 dimensional discrete cosine transform, and then encoded using channel optimized scalar quantization. At the decoder, two different methods are used, the independent and joint decoder.\\
In addition to comparing the different coding methods, various channels characteristics are exploited. For example, the non-binary noisy discrete channel can be used to model memory and the $2^q$-ary output allows for performance improvement via soft-decision decoding. It is observed that by taking the source correlation into consideration, significant signal-to-distortion ratio gains can be achieved. For example, the highest gain incurred from the third scheme is when the bivariate Gaussian is compressed at rate 2, where the gain in signal-to-distortion ratio due to source correlation is 10.90 dB.
Ensemble Controllability of Linear Control SystemsAdu, Danielhttp://hdl.handle.net/1974/226512017-09-16T04:46:03Z2017-01-01T00:00:00ZEnsemble Controllability of Linear Control Systems
Adu, Daniel
This thesis is concerned about ensemble controllability. We give an overview of the notions of ensemble controllability, in particular, $L_{2}$-ensemble controllability, and uniform ensemble controllability. We review the results presented in~\cite{UH-MS:14} on uniform ensemble controllability of one-parameter time-invariant linear systems and in~\cite{JSL:11} on $L_{2}$-ensemble controllability. In contrast to the notions in~\cite{UH-MS:14} and~\cite{JSL:11}, we investigate on the possibility to steer an ensemble using constrained control signals in the unit interval, which we call uniform~\emph{null}~ensemble controllability for one-parameter time-invariant linear systems using constrained control signals in the unit interval. We give a necessary as well as a sufficient condition for uniform~\emph{null}~ensemble controllability of one-parameter time-invariant linear systems using constrained control signals in the unit interval. Using tools from complex approximation theory, we show that in the discrete-time scenario, the problem of uniform~\emph{null}~ensemble controllability of one-parameter time-invariant linear systems using control signals in the unit interval is equivalent to polynomial approximation problem.
2017-01-01T00:00:00Z