This thesis focuses on control and inverse problems for the wave equation on finite metric graphs. The first part deals with the control problem for the wave equation on tree graphs. We propose new constructive algorithms for solving initial boundary value problems on general graphs and boundary control problems on tree graphs. We demonstrate that the wave equation on a tree is exactly controllable if and only if controls are applied at all or all but one of the boundary vertices. We find the minimal controllability time and prove that our result is optimal in the general case. The second part deals with the inverse problem for the wave equation on tree graphs. We describe the dynamical Leaf Peeling (LP) method. The main step of the method is recalculating the response operator from the original tree to a peeled tree. The LP method allows us to recover the connectivity, potential function on a tree graph and the lengths of its edges from the response operator given on a finite time interval. In the third part we consider the control problem for the wave equation on graphs with cycles. Among all vertices and edges we choose certain active vertices and edges, and give a constructive proof that the wave equation on the graph is exactly controllable if Neumann controllers are placed at the active vertices and Dirichlet controllers are placed at the active edges. The control time for this construction is determined by the chosen orientation and path decomposition of the graph. We indicate the optimal time that guarantees the exact controllability for all systems of a described class on a given graph. While the choice of the active vertices and edges is not unique, we find the minimum number of controllers to guarantee the exact controllability as a graph invariant.

The Chukchi and Beaufort seas benthic habitats are home to a multitude of ecologically and commercially important organisms that are subject to ongoing environmental changes, including the impacts of climate change and increased exposure to contaminants. Benthic bacteria and archaea can be considered biogeochemical engineers. They play a major role in organic matter (OM) degradation and nutrient cycling and their community structure can reflect changes in environmental conditions such as OM composition and quantity, nutrient availability, redox conditions, and natural/anthropogenic contaminants (e.g. petroleum hydrocarbons). Yet, sediment microbial communities have rarely been examined in these marginal seas of North American Arctic. In this dissertation, I characterized marine sediment microbial communities along environmental gradients in the Beaufort (Chapter 2) and Chukchi seas (Chapter 3) and assess Arctic benthic microbial community response to oil exposure (Chapter 4). I assessed diversity, community structure, and environmental correlates of prokaryotic communities via 16S rRNA amplicon sequencing in surface sediments (upper 1 cm) from the Northern Bering Sea to the Amundsen Gulf in the southern Beaufort Sea. On a broad spatial scale encompassing the whole study area, I observed three distinct microbial assemblages. One assemblage was characteristic of the Northern Bering-Chukchi seas shelf, and two distinguished nearshore and offshore sediments in the Beaufort Sea. Within the Beaufort Sea, four assemblages were identified, reflecting habitat heterogeneity with respect to OM loading, water depth, and nearshore/riverine input, including a major influence of the Mackenzie River. Two assemblages were distinguished within the Bering-Chukchi region, including one representative of suboxic sediments and one suggesting influence of phytodetrital OM input as evidenced by the abundance of diatom/particle-associated microbes. These two assemblages may also reflect differences between local versus advective OM inputs. Incubation experiments exposing Arctic marine sediments to fresh and weathered crude oil under anaerobic and aerobic conditions were performed to assess oil biodegradation potential and identify putative oil-degrading microbes in the benthos. Molecular analyses revealed that significant community shifts occurred in the oiled treatments, with distinct communities emerging following exposure to fresh versus weathered oil, and in oxic versus anoxic conditions. The work presented here constitutes the first large-scale survey of benthic microbes in this region of the North American Arctic, including their response to petroleum contamination, generating valuable baseline data for the changes to come.

Total mercury (THg) concentrations exceed thresholds of concern in some Steller sea lion (Eumetopias jubatus; SSL) tissues from certain portions of the Aleutian Islands, Alaska. Here, compound-specific stable isotope analyses (CSIA) of carbon in essential amino acids ([delta]¹³CEAA values) and nitrogen in AAs ([delta]¹⁵NAA values) in fish muscle tissue was applied to quantify the proportional contributions of primary production sources and trophic positions of eight prey species (n = 474 total) that are part of SSL diets. Previous THg analyses of fish muscle, coupled with additional monomethylmercury (MMHg) analyses of a subset of samples, substantiated previous findings that fishes from the west of Amchitka Pass, a discrete oceanographic boundary of the Aleutian Archipelago, have higher muscle THg concentrations relative to fishes from east of the pass. All fish muscle samples were analyzed separately for, both, CSIA-AA of carbon and nitrogen. The [delta]¹³CEAA values in fish muscle demonstrated that although most fishes obtained their EAAs primarily from algae, some species varied in the extent to which they relied on this primary production source. Certain [delta]¹⁵NAA values of the same fish samples indicated that trophic positions of fishes were higher from the west relative to the east of the pass for some species. Total Hg was positively correlated with bulk [delta]¹⁵N values, [delta]¹⁵N values of glutamic acid ([delta]¹⁵NGlu), and trophic positions. However, only trophic magnification slopes using [delta]¹⁵NGlu values indicated a higher rate of Hg biomagnification to the west of Amchitka Pass. Broad and species-level multiple linear regression models revealed that trophic position was the most important driver of fish muscle THg with a smaller amount of variation explained by other parameters, such as proportional contributions of primary production sources, fish body condition, and catch location. Collectively, results indicate that differences in fish trophic positions were the most consistent determinants of the higher fish THg concentrations to the west of Amchitka Pass. However, a higher rate of THg biomagnification to the west of Amchitka Pass may also play a role in the regional differences in fish muscle THg.

Bismuth (Bi) and tellurium (Te) are technologically critical elements (TCEs), also known as critical minerals, primarily recovered as byproducts in the extraction of lead (Pb) and copper (Cu), respectively. Global demand for Bi and Te is expected to rise signicantly in the coming decades as energy production becomes carbon neutral. In order to meet this demand, alternative sources of Bi and Te must be identifed. Bismuth and Te are commonly enriched in granitoid-related gold (Au) deposits and epithermal Au-Ag-Te deposits but are not presently recovered. Identifying which Bi and Te minerals are present throughout the Au extraction process is essential to determining where these elements might be recovered and in what quantities. Concurrent with the need to identify potential sources of TCEs is the need to validate advancements in analytical geochemical methods. Energy Dispersive Spectrometry (EDS) methods have become a go-to mineralogical identication tool in the mineral exploration and mining industries due to their rapid automated analysis. However, little cross-validation has been done to verify the results and determine the limitations of these tools. Here I present the results of three studies: 1) an EDS bulk mineralogy phase mapping method validation study on Au and Cu mill processing samples; 2) a detailed elemental composition and mineralogical analysis of samples from the Pogo Mine Mill (Interior Alaska, USA) identifying potential annual byproduct recovery of 13.5 and 7.5 metric tonnes of Bi and Te, respectively; and 3) a detailed elemental composition and mineralogical analysis of mill samples from the Golden Sunlight Mine Mill (Whitehall, Montana, USA) identifying Te primarily hosted in pyrite. Using this approach for similar metallurgical studies at other Au mines with known signicant Bi and Te could yield additional targets for recovery and provide a framework for identifying other potential TCEs/critical minerals in other deposits.

Fish species found in high latitude waters are especially vulnerable to climatic changes due to their inability to regulate body temperature and long evolution in cold, oxygen-rich aquatic environments. Antarctic notothenioid fishes have evolved to thrive in an extremely stable, cold, oxygen-rich environment. Likewise, lake trout live in a cold, oxygen-rich environment, but commonly experience a wider range of temperatures than notothenioids. Millions of years of evolution in the cold have shaped the genetics of these fishes, but the effects on their biology remain largely unexplored. This dissertation seeks to learn from the past evolution of these two evolutionarily distant types of high latitude fishes to enhance predictions for how these animals can cope with future environmental changes. Specifically, this dissertation examines the genetics of fishes with limited thermal tolerance from the population level down to a single gene. These studies relied on DNA sequence evidence produced with two different technologies and analyzed under functional, phylogenetic, and population genetic frameworks. In the first study, mitochondrial DNA (mtDNA) variation is examined to determine ancestral affinities and geographic distribution of mtDNA variants in lake trout across Alaska. Lake trout in Alaska descend from two distinct mtDNA lineages. One mtDNA lineage is restricted to Arctic Alaska, north of the Brooks Range, while the other lineage is found across Alaska. Lake trout likely dispersed from glacial refugia in western Canada to recolonize Alaska and the movement patterns from recolonization assist in determining how lake trout are likely to move across the landscape in the future. In the second study, genome wide genetic diversity of lake trout in seven Alaskan lakes is explored to determine ancestral affinities and colonization pathways. Despite past movement, the lake trout population currently found in each of the sampled lakes is genetically distinct from all other sampled populations and no migration currently seems to be occurring, even between lakes less than 20 km from each other. This research shows lake trout in Alaska are genetically diverse, but with little gene flow, genetic rescue and transfer of genetic variation between populations is unlikely to occur. In the third component of this dissertation, the evolution of the critical hypoxia transcription factor is examined in Antarctic notothenioids. The hypoxia-inducible factor-1alpha (HIF-1alpha) of Antarctic notothenioids contains a polyglutamine/glutamic acid insert that may impact the function of this key transcription factor. Thus, Antarctic notothenioids may have difficulties in responding to climate change induced hypoxia. Overall, the adaptive consequences of evolution in high latitude aquatic environments may be detrimental to fishes as they face climate changes. Other high latitude freshwater fishes like lake trout may have limited gene flow among populations, reducing potential for adaptation and genetic rescue in response to climate change. More research into the evolution and functional implications of different natural genetic variants is needed to protect these unique high latitude species.

In this dissertation, we first consider the problem of exact controllability of a system of N one-dimensional coupled wave equations when the control is exerted on a part of the boundary by means of one control. We provide a Kalman condition (necessary and sufficient) and give a description of the attainable set. The second problem we consider is the inverse problem for the vector Schrödinger equation on the interval with a non-self-adjoint matrix potential. In doing so, we prove controllability of the system and develop a method to recover spectral data from the system. Then, we solve the inverse problem using techniques of the Boundary Control method. The final problem is that of internal null controllability of a beam equation on an interval. We provide a partial characterization for controllability for arbitrary open subsets where the control is applied.

This qualitative single case study examined the phenomenon of cultural identity development from the perspective of young Indigenous children situated within the context of their southeast Alaskan community. Decades of assimilationist policies have eroded cultural identity among many Indigenous Alaskans, yet a strong cultural identity is known to be a protective factor for Indigenous peoples. Building on Indigenous identity development theory, the study sought to answer the research questions: (1) How do young children demonstrate their cultural identity through interactions on the Land? (2) How do community organizations support cultural identity development (CID) in young Indigenous children? (3) What role do peers play in nurturing cultural identity development (CID)? And (4) How do teachers and families nurture CID? The primary data source was video collected by children wearing forehead cameras as they engaged in semi-structured activities on the Land; video data were augmented by surveys, interviews, children's drawings, and careful observations. These methods allowed the researcher to examine the child's lived experiences to begin to untangle the rich interactions between children, the Land, parents, and educators, and to describe CID nurturing factors. Reflexive thematic analysis was employed to discover themes and patterns in the data. Findings reveal that children demonstrate their Indigenous identity by learning and exhibiting traditional ecological knowledge, which includes intricate knowledge of the Land, subsistence practices, and core cultural values. The process of cultural identity development was supported by the community through vision and funding for cultural initiatives. Peers, parents, and educators contributed to the cultural identity development of the young participants by enacting moves to increase confidence and competence on the Land. This study has implications for policymakers, educators, families, and others interested in nurturing healthy identity development among young Indigenous children.

Pre-Columbian and contemporary Indigenous Nations of North and South America (hereafter referred to as Turtle Island and Abya Yala) have managed ecosystems extensively to produce prolific and predictable food systems for themselves and non-humans, whom they often view as relatives. The elements of earth, water, fire, and air are explored to analyze Indigenous soil management, Indigenous aquaculture, Indigenous pyrogenic land management, and Indigenous oral histories, respectively. First, a review of four Indigenous societies and their soil management techniques revealed that none of these systems require outside fertilizer or irrigation to sustain ecocentric food systems on millennial scales. Second, a comparative analysis of six Indigenous fisheries showed how these communities operate on regional-scales, manually augment habitat for key species, are thousands of years old, and are driven by value systems rooted in reciprocity, reverence, respect, restraint, and responsibility to homeland. Third, an in-depth analysis of fire regime data from a variety of sources indicates that Diné and Pueblo Ancestors did indeed manage the Ch'ooshgai (Chuska) Mountain Range with routine burning during the Holocene epoch and negates theories that these fire regimes were due to lightning ignition. Fourth, a synthesis of interviews with four contemporary Indigenous land managers confirms that these cultural groups were and are active managers of local ecosystems. Despite coming from different places, all interviewees are driven by a similar set of principles: reverence for the sacredness of life, non-humans are the equal and sacred relatives of humans, and a belief that human groups are divinely assigned to care for their respective homelands. The next chapter offers an articulation of a theory of Indigenous Regenerative Ecosystem Design (IRED) to support the field and outline potential avenues for future research. The eighth chapter offers policy recommendations based on successful Indigenous food systems for federal, tribal, and nongovernmental agencies to help us effectively address the social and environmental challenges of our times. The ninth chapter proposes that the extent and sophistication of Indigenous food systems were minimized in the historical record precisely because they are living contradictions to the narratives used to legitimize land seizure and attempted genocide. Overall, it was found that most traditional Indigenous communities are not passive observers of nature but are instead influential facilitators of landscape scale abundance, rooted in an ethic of kinship and reverence.

Volcanic eruptions of any size can pose a significant risk to the life and livelihood of humans, as well as to infrastructure and the economy. Understanding the dynamics of an eruption is crucial to providing timely and accurate assessments of the eruption and associated hazard. Ideally the monitoring of volcanic unrest and eruption dynamics is done remotely to minimize exposure to volcanologists and maximize the spatial monitoring coverage of instruments. Another important factor is to have real-time data to facilitate rapid analysis and interpretation. Seismic and acoustic (infrasound) waves have proven useful in terms of remote real-time volcano monitoring. However, accurate interpretation of these signals is a challenge due to the complexity of each volcano and each eruption. In this dissertation I present three projects that aim to improve the interpretation of seismic and acoustic signals, specifically their spectral properties, generated by multiphase flow during an eruption. In Chapter 2 we derive a seismic tremor model for a source underground but above the fragmentation level where the gas and particles rush through the volcanic conduit. This physical model assumes ash particles and gas turbulence impact the conduit wall and exert a force that generates seismic waves and is recorded as eruption tremor. We show that it is possible to model the seismic spectral amplitude and shape of a large sustained volcanic eruption, the eruption of Pavlof Volcano in 2016, with particle impacts and turbulence as seismic sources. Our modeling provides a framework to 1) narrow down the parameters associated with eruption dynamics and source processes, and 2) highlight that seismic amplitude and mass eruption rate are not necessarily correlated. Both findings are crucial for the successful interpretation of seismic data during a sustained eruption. In Chapter 3 we move further up above the vent to investigate the acoustic expression of sustained eruptions. The rapid discharge of the multiphase flow through the relatively small vent has been successfully compared to jetting in the past. We develop an algorithm to automatically fit laboratory-derived jet noise spectral shapes (similarity spectra) to the spectrum of three volcanic eruptions: Mount St. Helens 2005, Tungurahua 2006 and Kīlauea 2018. Our quantitative analysis of the misfit between the jet noise spectra and volcanic eruption shows that: 1) the jet noise spectra show a very good fit during the eruption, so we can assume it produces a volcanic form of jet noise, 2) we can distinguish between non-eruptive noise and eruption by the higher misfit of the former and the lower misfit of the latter, and 3) changes in spectral shape correspond to changes in eruption dynamics, which are highlighted by changes in the misfit in time and frequency space. To further look into how changes in spectral properties correspond to changes in eruption dynamics, Chapter 4 focuses in detail on the eruption of fissure 8 on Kilauea volcano in 2018. With the knowledge that the eruption produced jet noise (Chapter 3) we apply jet noise scaling laws and develop a model that relates the changes in infrasound amplitude and peak frequency to changes in jet velocity and diameter. Our analysis shows that in mid-June the infrasound amplitude peaks and the peak frequency decreases. Our jet noise scaling model explains this change through a decrease in jet velocity and increase in jet diameter. This interpretation fits video observations that show a decrease in lava fountain height and a widening of the fountain base around the same time. Our work demonstrates the potential to estimate lava fountain dimensions from infrasound recordings that could be useful for real-time, remote monitoring.

Spatial dynamics in fish populations are challenging to identify and incorporate into population dynamics models due to the large amount of data required and the uncertainty associated with spatial processes. However, ignoring spatial dynamics can result in biased population estimates and negatively affect population sustainability or the ability to meet fishery management goals. My research explored implications of spatial dynamics for the assessment and management of Alaska sablefish (Anoplopoma fimbria). Sablefish are highly mobile, targeted in commercial and recreational fisheries, and documented to have spatial variation in population dynamics such as abundance and biomass. However, gaps remain in understanding the drivers of these spatial dynamics and their effects on fishery management. Chapter 1 focused on sablefish population dynamics in Alaska by developing a spatial stock assessment model with movement between modeled areas. Chapters 2 and 3 detail the development (Chapter 2) and application of a simulation and estimation model framework (Chapter 3) to examine alternative management scenarios and inform fisheries management. The spatial stock assessment models developed in Chapter 1 showed that a combination of population processes (movement, recruitment) and fishing have resulted in spatial differences in sablefish spawning biomass and fishing mortality, and some management areas are likely below target biomass levels despite the population as a whole being at or near biomass targets. The implications of this apparent localized depletion are unknown, but could negatively impact recruitment success if depleted areas are crucial to population sustainability. Chapter 1 also highlights the complexity of spatial stock assessment models, which require large quantities of data and pose challenges for parameter estimation. In Chapters 2 and 3, sablefish spatial population processes were simulated based on parameters estimated in the spatial stock assessment developed for Chapter 1 then assessed using a single-area, panmictic stock assessment model. Chapter 2 focuses on the simulation framework development and tests a suite of alternative population assumptions regarding movement and recruitment, which were found to be very influential in preliminary analyses. The analyses also revealed the challenges associated with a simulation framework that relies on a relatively complex stock assessment model and cannot rely on human scientists to monitor and tweak assessment model estimation processes during the automated simulations. In Chapter 3, five alternative methods for apportioning harvest opportunity among management areas were examined through the simulation to understand whether there were unexpected consequences of how catch opportunities were apportioned across space, given the assumed underlying population dynamics. We found that recruitment was poorly estimated by the single-area stock assessment model, and recruitment and movement rates between areas were drivers of population dynamics in each modeled region. We also found that no method for apportioning sablefish resulted in long-term population declines under the simulation and management assumptions, but recommended an apportionment method that used data from an annual survey so that catch opportunities are relational to observed spatial biomass. Each apportionment method resulted in different levels of catch for management areas and different year-to-year stability in catch, and these differences may be meaningful to stakeholders. This research highlights the challenges and benefits of incorporating spatial population dynamics in assessment of a relatively data-rich species with high movement rates. For species with known processes that could create spatial dynamics but insufficient data for development of spatial stock assessment models, the development and implementation of monitoring and research plans to close data gaps could be a long-term strategy for improving understanding of the species' dynamics. However, monitoring can be logistically challenging and economically prohibitive in some situations, so simulation analyses such as those conducted here may help understand which data are most important to collect or inform the development of management procedures which are robust to the most plausible hypothetical population dynamics or future environmental conditions.