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Although a number of above-knee amputees have expressed a desire to participate in recreational activities involving running, no currently available lower limb prosthesis has proven adequate in allowing amputees to achieve a natural, efficient, one-to-one running gait. Until recently, amputee runners such as Terry Fox and Steve Fonyo have adopted a variety of asymmetrical gaits, although the Terry Fox Jogging Prosthesis has allowed some amputees to achieve an inefficient one-to-one running pattern. The objective is to design a conservative running prosthesis which will functionally imitate the intact limb during running activities. The prosthesis performance criteria were established for both stance and swing, based on an examination of non-amputee running biomechanics. The prosthesis incorporates a shank unit assembly which linearly compresses upon heel-strike, absorbing the impact energies in a helical coil compression spring, and then uses a ratchet device to store these impact energies throughout the stance phase. In late stance, the natural dorsi flexion of the prosthetic foot initiates the release of the stored energies, propelling the amputee upward and forward into the swing phase. It is recommended that a comprehensive biomechanical gait analysis be performed on the prosthesis' operation to allow for optimization of its configuration and performance. In conclusion, the features of this prosthesis will allow above-knee amputees to achieve a more natural, one-to-one running gait and participate more actively in activities involving running. / Thesis / Master of Engineering (ME)

In recent years, the accumulation of space debris has become an increasingly pressing issue, and adequately monitoring it is a formidable task for designated ground-based sensors. Supplementing the capabilities of these ground-based networks with orbiting sensing platforms would dramatically enhance the ability of such systems to detect, track, identify, and characterize resident space objects -- the primary goals of modern space situational awareness (SSA). Space-based space situational awareness (SBSSA), then, is concerned with achieving the stated SSA goals through coordinated orbiting sensing platforms. To facilitate the design of satellite constellations that promote SSA goals, an optimization approach is selected, which inherently requires a pre-defined mathematical representation of a cost index or measure of merit. Such representations are often analytically available, but when considering optimal constellation design for SBSSA applications, a closed-form expression for the cost index is only available under certain assumptions. The present study focuses on a subset of cases that admit exact representations. In this case, geometrical arguments are employed to establish an analytical formulation for the coverage area provided as well as for the coverage multiplicity. These analytical results are essential in validating numerical approximations that are able to simulate more complex configurations. / text

A comparison of above ground forest metrics with below ground soil CO₂ respiration was carried out in an attempt to reveal if any correlations exist. Above ground measurements of 2720 clonally propagated trees were taken assessing the silvicultural treatments of stocking, herbicide and fertiliser. These were compared to 480 below ground soil CO₂ respiration measurements. Using measurements of mean height, mean dbh and basal area the data was analysed and returned significant results for mean dbh and the interactions of herbicide and clones, and stocking and herbicide. Mean height returned a significant result for the interaction of stocking and herbicide. Below ground measurements showed an interaction between ripping and stocking; however these results were not ratified by the above ground results. Overall the results were encouraging and should aid in future experiments that seek to understand what effect above ground treatments have on below ground CO₂ activity.

Thesis (M.S.)--Boston University

Robust estimates of forest above-ground biomass (AGB) are needed in order to constrain the uncertainty in regional and global carbon budgets, predictions of global climate change and remote sensing efforts to monitor large scale changes in forest cover and biomass. Estimates of AGB and their associated uncertainty are also essential for international forest-based climate change mitigation strategies such as REDD+. Mangrove forests are widely recognised as globally important carbon stores. Continuing high rates of global mangrove deforestation represent a loss of future carbon sequestration potential and could result in significant release into the atmosphere of the carbon currently being stored within mangroves. The main aims of this thesis are 1) to provide information on the current AGB stocks of mangrove forests in Kenya at spatial scales relevant for climate change research, forest management and REDD+ and 2) to evaluate and constrain the uncertainty associated with these AGB estimates. This thesis adopted both a ground-based statistical approach and a remote sensing based approach to estimating mangrove AGB in Kenya. Allometric equations were developed for Kenyan mangroves using mixed-effects regression analysis and uncertainties were fully propagated (using a Monte Carlo based approach) to estimates of AGB at all spatial scales (tree, plot, region and landscape). In this study, species and site effects accounted for a large proportion (41%) of the total variability in mangrove AGB. The generic biomass equation produced for Kenyan mangroves has the potential for broad application as it can be used to estimate the AGB of new trees where there is no pre-existing knowledge of the specific species-site allometric relationship. The 95% prediction intervals for landscape scale estimates of total AGB suggest that between 5.4 and 7.2 megatonnes (Mt) of AGB is currently held in Kenyan mangrove forests. An in-depth evaluation of the relative contribution of various components of uncertainty (measurement, parameter and residual uncertainty) to the magnitude of the total uncertainty of AGB estimates was carried out. This evaluation was undertaken using both the mixed-effects regression model and a standard ordinary least squares (OLS) regression model. The exclusion of measurement uncertainty during the biomass estimation process had negligible impact on the magnitude of the uncertainty regardless of spatial scale or tree size. Excluding the uncertainty due to species and site effects (from the mixed-effects model) consistently resulted in a large reduction (~ 70%) in the overall uncertainty. Estimates of the uncertainty produced by the OLS model were unrealistically low which is illustrative of the general need to account for group effects in biomass regression models. L-band Synthetic Aperture Radar (SAR) was used to estimate the AGB of Kenyan mangroves. There was an observable relationship (R2 = 0.45) between L-band HH and AGB with HH backscatter found to decrease as a function of increasing AGB. There was no significant relationship found between L-band HV and AGB. The negative relationship between HH and AGB in this study can possibly be attributed to enhanced backscatter at lower AGB due to strong double-bounce and direct surface scattering from short stature/open forests and attenuation of the SAR signal at higher AGB. The SAR-derived estimate of total AGB for Kenyan mangroves was 5.32 Mt ± 18.6%. However, due to the unexpected nature of the HH-AGB relationship found in this study the SAR-derived estimates of mangrove AGB in this study should be considered with caution.

The motivation of this thesis is to understand how nodes can cooperate in a particular relay channel, say a relay channel with orthogonal link between relay and destination. We are especially interested in the scenario where relay cannot decode the message sent because the coding rate is too large vis-a-vis what it can handle, and try to investigate the optimality of compress-and-forward strategy for this scenario. Specifically, noting that relay's compression is based on the unconditional distribution of its observation, it is natural to ask if relay can do better if it utilizes the source's codebook information, such that the performance of the relay network is improved? To answer this key question, we need to find the posterior Conditional Distribution of channel Output given Codebook Information (namely CDOCI) for the channel between source and relay. Firstly, we model it as Binary Symmetric Channel (BSC) and show that under the now standard random coding framework, if the input distribution is uniform, then with high probability, the CDOCI is asymptotically uniform when coding rate is greater than the channel capacity and the block length is sufficiently large. Then it is shown that under the discrete memoryless channel (DMC), for those strongly typical output sequences, with high probability, the CDOCI is also asymptotically uniform and close to the unconditional distribution, for rate above capacity and sufficiently large block length. These results implicate that relay can hardly do better with codebook information used. To confirm this implication, we show that for sufficiently large block length, the rate needed for relay to forward its observation when the codebook information is utilized approaches the rate needed when the relay simply ignore the codebook information, if the coding rate at source is larger than channel capacity. Now the answer to the above key question is apparent: in the cases of BSC and DMC, even if the relay tries to utilize the information obtained by knowing the codebook used at the source, it can hardly do better than simply ignore the codebook information. Therefore, the compress-and-forward strategy is kind of optimal in this sense, under the random coding framework.

The motivation of this thesis is to understand how nodes can cooperate in a particular relay channel, say a relay channel with orthogonal link between relay and destination. We are especially interested in the scenario where relay cannot decode the message sent because the coding rate is too large vis-a-vis what it can handle, and try to investigate the optimality of compress-and-forward strategy for this scenario. Specifically, noting that relay's compression is based on the unconditional distribution of its observation, it is natural to ask if relay can do better if it utilizes the source's codebook information, such that the performance of the relay network is improved? To answer this key question, we need to find the posterior Conditional Distribution of channel Output given Codebook Information (namely CDOCI) for the channel between source and relay. Firstly, we model it as Binary Symmetric Channel (BSC) and show that under the now standard random coding framework, if the input distribution is uniform, then with high probability, the CDOCI is asymptotically uniform when coding rate is greater than the channel capacity and the block length is sufficiently large. Then it is shown that under the discrete memoryless channel (DMC), for those strongly typical output sequences, with high probability, the CDOCI is also asymptotically uniform and close to the unconditional distribution, for rate above capacity and sufficiently large block length. These results implicate that relay can hardly do better with codebook information used. To confirm this implication, we show that for sufficiently large block length, the rate needed for relay to forward its observation when the codebook information is utilized approaches the rate needed when the relay simply ignore the codebook information, if the coding rate at source is larger than channel capacity. Now the answer to the above key question is apparent: in the cases of BSC and DMC, even if the relay tries to utilize the information obtained by knowing the codebook used at the source, it can hardly do better than simply ignore the codebook information. Therefore, the compress-and-forward strategy is kind of optimal in this sense, under the random coding framework.

As near-Earth space becomes increasingly crowded with spacecraft and debris, the need for improved space situational awareness has become paramount. Contemporary ground-based systems are limited in the detection of very small or dim targets. In contrast, space-based systems, above most atmospheric interference, can achieve significant improvements in dim target detection by observing targets against a clutter-free space background, i.e. targets above the horizon (ATH). In this study, numerical methods for the evaluation of ATH coverage provided by constellations of satellites are developed. Analysis of ATH coverage volume is reduced to a planar analysis of cross-sectional coverage area in the orbit plane. The coverage model performs sequences of boolean operations between polygons representing cross-sections of satellite sensor coverage regions and regions of interest, returning the coverage area at the desired multiplicity. This methodology allows investigation of any coverage multiplicity for planar constellations of any size, and use of arbitrary sensor profiles and regions of interest. The implementation is applied to several constellation design problems demonstrating the utility of the numerical ATH coverage model in a constellation design process. / text

Monitoring the dynamics of the productivity of ocean water and how it affects fisheries is essential for management. It requires data on proper spatial/temporal scales, which can be provided by operational ocean colour satellites. However, accurate productivity data from ocean colour imagery is only possible with proper validation of, for instance, the atmospheric correction applied to the images. In situ water reflectance data is of great value due to the requirements for validation and it is traditionally measured with the Surface Acquisition System (SAS) solar tracker system. Recently, an application, 'HydroColor', was developed for mobile devices to acquire water reflectance data. We examine the accuracy of the water reflectance acquired by HydroColor with the help of trained and untrained citizens under different environmental conditions. We used water reflectance data acquired by SAS solar tracker and HydroColor onboard the BC ferry Queen of Oak Bay from July to September 2016. Monte Carlo permutation F-tests were used to assess whether the differences between measurements collected by SAS solar tracker and HydroColor with citizens were significant. Results showed that the HydroColor measurements collected by 447 citizens were accurate in red, green, and blue bands, as well as red/green and red/blue ratios under different environmental conditions. Piecewise models were developed for correcting HydroColor blue/green water reflectance ratios based on the SAS solar tracker measurements. In addition, we found that training and environmental conditions had impacts on the data quality. A trained citizen obtained higher quality HydroColor data especially under clear skies at noon run (12:50-2:30 pm). / Graduate