Transferability of Regional Permafrost Disturbance Susceptibility Modelling Using Generalized Linear and Generalized Additive Models

To effectively assess and mitigate risk of permafrost disturbance, disturbance-p rone areas can be predicted through the application of susceptibility models. In this study we developed regional susceptibility models for permafrost disturbances using a field disturbance inventory to test the transferability of the model to a broader region in the Canadian High Arctic. Resulting maps of susceptibility were then used to explore the effect of terrain variables on the occurrence of disturbances within this region. To account for a large range of landscape charac- teristics, the model was calibrated using two locations: Sabine Peninsula, Melville Island, NU, and Fosheim Pen- insula, Ellesmere Island, NU. Spatial patterns of disturbance were predicted with a generalized linear model (GLM) and generalized additive model (GAM), each calibrated using disturbed and randomized undisturbed lo- cations from both locations and GIS-derived terrain predictor variables including slope, potential incoming solar radiation, wetness index, topographic position index, elevation, and distance to water. Each model was validated for the Sabine and Fosheim Peninsulas using independent data sets while the transferability of the model to an independent site was assessed at Cape Bounty, Melville Island, NU. The regional GLM and GAM validated well for both calibration sites (Sabine and Fosheim) with the area under the receiver operating curves (AUROC) N 0.79. Both models were applied directly to Cape Bounty without calibration and validated equally with AUROC's of 0.76; however, each model predicted disturbed and undisturbed samples differently. Addition- ally, the sensitivity of the transferred model was assessed using data sets with different sample sizes. Results in- dicated that models based on larger sample sizes transferred more consistently and captured the variability within the terrain attributes in the respective study areas. Terrain attributes associated with the initiation of dis- turbances were similar regardless of the location. Disturbances commonly occurred on slopes between 4 and 15°, below Holocene marine limit, and in areas with low potential incoming solar radiation

Detection and Grading of Prostate Cancer in Temporal Enhanced Ultrasound using Convolutional Neural Networks

Prostate cancer is the most common non-dermatological cancer amongst men in the developed world. The current definitive diagnosis is core needle biopsy guided by transrectal ultrasound. However, this method suffers from low sensitivity and specificity in detecting cancer. Recently, a new ultrasound based tissue typing approach has been proposed, known as temporal enhanced ultrasound (TeUS). In this approach, a set of temporal ultrasound frames is collected from a stationary tissue location without any intentional mechanical excitation. The main aim of this thesis is to implement a deep learning-based solution for prostate cancer detection and grading using TeUS data. In the proposed solution, convolutional neural networks are trained to extract high-level features from time domain TeUS data in temporally and spatially adjacent frames in nine in vivo prostatectomy cases. This approach avoids information loss due to feature extraction and also improves cancer detection rate. The output likelihoods of two TeUS arrangements are then combined to form our novel decision support system. This deep learning-based approach results in the area under the receiver operating characteristic curve (AUC) of 0.80 and 0.73 for prostate cancer detection and grading, respectively, in leave-one-patient-out cross-validation. Recently, multi-parametric magnetic resonance imaging (mp-MRI) has been utilized to improve detection rate of aggressive prostate cancer. In this thesis, for the first time, we present the fusion of mp-MRI and TeUS for characterization of prostate cancer to compensates the deficiencies of each image modalities and improve cancer detection rate. The results obtained using TeUS are fused with those attained using consolidated mp-MRI maps from multiple MR modalities and cancer delineations on those by multiple clinicians. The proposed fusion approach yields the AUC of 0.86 in prostate cancer detection. The outcomes of this thesis emphasize the viable potential of TeUS as a tissue typing method. Employing this ultrasound-based intervention, which is non-invasive and inexpensive, can be a valuable and practical addition to enhance the current prostate cancer detection.

New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.