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Recent Submissions
Learning the Quantum, Scrambling the Universe
(University of Waterloo, 2025-07-10) Liu, Shuwei
This thesis explores how quantum information behaves in extreme physical settings, from black hole interiors to noisy quantum devices.
First, we derive a thermodynamic relation linking gravitational shockwaves to microscopic deformations of the black hole horizon, illuminating the connection between quantum chaos and horizon area deformation.
Next, we explore the black hole information problem through the lens of holography, demonstrating how scrambling and recoverability emerge from gravitational backreaction in shockwave geometries.
Finally, we shift to quantum technologies, introducing noise-strength-adapted (NSA) quantum error-correcting codes discovered via hybrid machine learning. These non-stabilizer codes outperform conventional designs under amplitude damping and generalize to larger systems.
Together, these works reveal how quantum information unifies seemingly disparate domains, offering both conceptual insights into spacetime and practical tools for building resilient quantum systems.
A University-Landscape Architect Collaboration to Develop an Augmentative and Alternative Communication (AAC) Board for a City Park Playground: A Full Report of its Design
(2025-07-05) O'Neill, Daniela K.; Vento, Olivia; Aurini, Maia; Ritchie, Catelyn; Landry, Aimee
In this report, we detail the development of an AAC board for a community playground situated in a large park in the heart of Waterloo, Ontario, Canada. AAC boards for community locations have received much less attention and study than AAC tools intended for individual use at home and/or in schools, or by children on school playgrounds. This AAC board was developed through an ongoing collaboration between the landscape architect redeveloping the playground for the city and a professor of developmental psychology with expertise in children’s early social pragmatic communication, along with her students at the University of Waterloo. For this AAC board, we prioritized practical communication in a playground context by adopting an activity-focused approach. We describe the major steps taken in developing the AAC board and explain the reasoning and empirical support that guided our content and design decisions. These included choices about the vocabulary included, the symbols used and developed, and the positioning of all components on the board. We also considered symbol and border colours to support accessibility and ease of use. In this process, we sourced empirical evidence from many domains, including speech-language pathology, AAC, and language and cognitive development within developmental psychology. We also trialled a draft version of the AAC board in the park and made revisions based on feedback from children and their parents. We considered novel factors our expertise suggested would be relevant, such as the age and height of children and the vertical position of symbols on the board, and we introduced some novel elements such as a colour wheel. We conclude by outlining limitations and recent developments by manufacturers that may improve the design and use of playground AAC boards. We also highlight areas for further research that might be particularly helpful. We have prioritized sharing all aspects of our work openly so that it can be easily accessed, used, and shared by others without restrictions.
Bending the curve of biodiversity loss: Identifying barriers and opportunities to accelerate endangered species recovery in Canada
(University of Waterloo, 2025-07-09) Kraus, Daniel
The decline of wild species represents one of the most urgent crises of our time, with significant ecological, cultural, and economic implications. Understanding the barriers and opportunities to accelerate wildlife recovery is essential to inform effective conservation planning, policymaking, and action, and ultimately to halt and reverse the loss of nature. Research for this thesis was guided by three interconnected objectives: 1) identify the patterns and processes of wildlife extinction and recovery in Canada, with a detailed examination of nationally endemic species, 2) compare and examine the effectiveness of national approaches to endangered species assessment, listing and recovery, thereby identifying bridges and barriers to recovery, and 3) develop and advance new approaches to planning and implementation that will accelerate endangered species recovery in Canada. These objectives are intended to provide novel contributions that fill key knowledge gaps to support the practice of endangered species conservation.
This research describes over 200 species ‘missing’ from Canada since European settlement, revealing significantly more extinctions and extirpations than reported under the Species at Risk Act. These losses are concentrated in Ontario, BC, and Quebec, with unsustainable harvesting historically driving extinctions, and habitat degradation emerging as the dominant contemporary threat. In contrast, the research also identifies 49 species with genuine improvements in conservation status, as well as over 50 species that began to recover before formal national assessments began. Key drivers of recovery include harvest management, pollution abatement, with more contemporary recoveries resulting from translocations, stewardship, and protected areas. The research also highlights that most improvements in the conservation status of species at risk are the result of discovering new populations and cautions against misclassifying these as conservation successes.
This research also provides the first comprehensive inventory of Canada’s 308 nationally endemic species, approximately 90% of which are of global conservation concern. The analysis identifies 27 spatial concentrations of endemic species, many of which are associated with glacial refugia, islands, coasts, and unique habitats. Despite their significance, nationally endemic species have not been prioritized in national conservation efforts, but their conservation will play an essential role in Canada’s contribution to preventing global extinctions.
Drawing on comparisons with the US and Australia, the thesis identifies systemic barriers to endangered species recovery and offers ten strategic "bridges" to overcome them. These include ecosystem-based recovery, community co-governance, linking wildlife recovery to ecosystem services, and improving public narratives around wildlife loss and recovery. Insights from a survey of 136 Canadian recovery planning practitioners further highlighted that effective implementation of SARA remains illusive, with respondents emphasizing the need for improved consultations, co-production with Indigenous communities, streamlined processes, and knowledge sharing.
The thesis concludes by proposing pathways to reduce extinction risks and accelerate recoveries that are based on the relationships between processes, places and peoples. These include approaches to increase proactive conservation, supporting community-based recovery planning and action, and improving knowledge mobilization. These recommendations aim to strengthen Canada’s capacity to meet its national and global biodiversity commitments and bending the curve of biodiversity loss.
On the distributions of prime divisor counting functions
(University of Waterloo, 2025-07-09) Das, Sourabhashis
Let k and n be natural numbers. Let ω(n) denote the number of distinct prime factors of n, Ω(n) denote the total number of prime factors of n counted with multiplicity, and ω_k(n) denote the number of distinct prime factors of n that occur with multiplicity exactly k.
Let h ≥ 2 be a natural number. We say that n is h-free if every prime factor of n has multiplicity less than h, and h-full if all prime factors of n have multiplicity at least h.
In 1917, Hardy and Ramanujan proved that both ω(n) and Ω(n) have normal order log log n over the natural numbers. In this thesis, using a new counting argument, we establish the first and second moments of all these arithmetic functions over the sets of h-free and h-full numbers. We show that the normal order of ω(n) is log log n for both h-free and h-full numbers. For Ω(n), the normal order is log log n over h-free numbers and h log log n over h-full numbers. We also show that ω_1(n) has normal order log log n over h-free numbers, and ω_h(n) has normal order log log n over h-full numbers. Moreover, we prove that the functions ω_k(n) with 1 < k < h do not have a normal order over h-free numbers, and that the functions ω_k(n) with k > h do not have a normal order over h-full numbers.
In their seminal work, Erdős and Kac showed that ω(n) is normally distributed over the natural numbers. Later, Liu extended this result by proving a subset generalization of the Erdős–Kac theorem. In this thesis, we leverage Liu’s framework to establish the Erdős–Kac theorem for both h-free and h-full numbers. Additionally, we show that ω_1(n) satisfies the Erdős–Kac theorem over h-free numbers, while ω_h(n) satisfies it over h-full numbers.
Development of Ecohydrological Processes on a Partially Removed Well Pad Undergoing Restoration to a Peatland on the Western Boreal Plain, Alberta, Canada
(University of Waterloo, 2025-07-09) McKinnon, Murdoch
Peatlands on the Western Boreal Plain have been disturbed at a landscape scale by industrial developments including those associated with the oil and gas industry. Among these disturbances are in-situ well pads, which are constructed to provide a stable base for oil and gas drilling and extraction infrastructure. In the province of Alberta, Canada, well pads must legally be returned to a state of ‘equivalent land capability’ after decommissioning. For well pads constructed in peatlands, equivalent land capability has recently been defined as including the reestablishment of a self-sustaining and peat accumulating vegetation community. One method proposed to reintroduce peatland vegetation (including peatland mosses) onto decommissioned well pads involves the partial removal of the mineral fill used to construct a well pad. Termed the ‘Partial Removal Technique,’ this approach aligns the reprofiled surface elevation of a pad with that of the water table in the surrounding peatland. Peatland vegetation propagules are then introduced onto the residual mineral substrate using a modified version of the established Moss Layer Transfer Technique. However, considerable uncertainty has remained surrounding the efficacy of the technique as a form of peatland restoration, as it had not yet been applied at the scale of a full-size well pad.
Accordingly, a five-year ecohydrological study was undertaken following the first full-scale implementation of the Partial Removal Technique on a well pad. The subject well pad was located in a fen complex on the Western Boreal Plain near the town of Slave Lake, Alberta, Canada. A series of field studies were undertaken to assess the extent to which the residual mineral substrate would support environmental conditions requisite for the initiation and establishment of a peatland vegetation community. Specific objectives addressed included characterization of the hydrophysical properties of the residual mineral fill and their effect on hydrological connectivity with an adjacent fen, and assessment of whether hydrological connectivity was sufficient to maintain a near-surface water table and optimal moisture availability to mosses across the entire site. The role of additional water balance terms in supporting near-surface water tables and water availability was also assessed, including quantification of snowmelt, vertical groundwater exchange, and evapotranspiration. Additionally, monitoring of the development of biogeochemical processes in the first five years post-partial removal was undertaken, including quantification of the rates of nutrient cycling and supply. The effects of microtopography and application of straw mulch and rock phosphate fertilizer on moisture and nutrient dynamics were also assessed.
Results indicate that hydrological connectivity between the residual well pad and the adjacent fen was limited by the low hydraulic conductivity of the mineral fill and the compacted peat underlying it. Combined with rapid drainage from the mineral fill into the underlying peat following rainfall, this resulted in the water table being poorly regulated across just over half of the pad’s surface area. The deeper water tables observed in those areas were associated with non-optimal moisture availability to mosses (i.e., exceedance of literature desiccation thresholds), particularly in the late growing season when rainfall inputs were infrequent. Combined with high rates of water loss through evapotranspiration, it appears that much of the pad’s surface area is likely to be favourable for the establishment of only those mosses with a high desiccation tolerance. The establishment of a vegetation community characteristic of swamps may thus occur over the long term in areas that are hydrologically disconnected from the fen. Nonetheless, hydrological connectivity with the adjacent fen was sufficient to maintain a water table within 6 cm of the surface in areas located within approximately 20 to 30 metres of the upgradient pad edges. This water table depth was associated with optimal water supply at the surface for moss survival and growth. As such, the establishment of a peatland true moss community is likely to be supported across just under half of the pad’s surface area. Snowmelt may also have provided a large source of water in the early season, although additional study is required to determine the extent to which snowmelt may be lost from the pad as overland flow. Surface runoff from an upland feature constructed out of the excess mineral fill produced during the partial removal process did not constitute an appreciable source of water to the pad.
Nutrient cycling and availability demonstrated limited spatial variability across the residual well pad. Owing to the high cation content of the calcareous residual mineral fill, cation supply rates were sufficiently high to further increase the likelihood of peatland true moss establishment in areas with optimal substrate moisture availability. However, low rates of nitrogen production and a low ratio of nitrogen to phosphorus supply rates indicate that productivity of the vegetation community on the residual pad may be nitrogen limited. This may change over time, as a layer of organic litter was observed to accumulate on the surface of the residual well pad during the study. This is likely to result in increased rates of decomposition, and thus also of nutrient mineralization over time.
Combined, the results of this thesis indicate that there is a need to increase horizontal hydrological connectivity with adjacent peatlands in future implementations of the Partial Removal Technique. This may improve the availability of moisture across a greater proportion of the surface area of residual well pads, while also ensuring the long-term development of anaerobic biogeochemical processes. Additional work is also required to reduce water losses in the form of both vertical drainage from residual mineral substrates and evapotranspiration from the surfaces of residual well pads. Overall, the Partial Removal Technique appears to have promise as a strategy to create favourable environmental conditions for the initiation and establishment of peatland mosses on decommissioned well pads.