HomologyBasis: Fast Computation of Persistent Homology

Simplicial complexes are used in topological data analysis (TDA) to extract topological features of the data. The HomologyBasis algorithm is proposed as an efficient method for the computation of the topological features of a finite filtered simplicial complex. We build up the implementation and intuition of this algorithm from its theoretical foundation ensuring this schema produces the desired simplicial homlogy groups as claimed. HomlogyBasis implemented and compared with the GUHDI algorithm to determine the HomologyBasis' efficiency at computing persistence pairs for finite filtered simplicial complexes. We find the HomologyBasis algorithm performs much better than GUHDI on large low-dimensional simplicial complexes but needs further refinement before it can more efficiently work with high-dimensional complexes.Master's Thesis in MathematicsMAT399MAMN-MA

Ground-Penetrating Radar and Thermal Modeling of Active Layer Thaw Beneath Arctic Streams

Seasonal thaw depth beneath arctic streams significantly impacts physical and biological processes within arctic stream environments. The impact of greater seasonal thaw for extended periods of time can alter ecosystems that have, in the past, resulted from more prevalent permafrost environments. Effects of climatic change on arctic stream environments necessitate the need for more information on characteristics of seasonal thaw and processes that occur within the thawed layer. Multiple ground-penetrating radar (GPR) methods and one-dimensional (1D) thermal modeling were used to investigate seasonal thaw beneath arctic streams and determine the dominant thermal process. Study sites were selected to include stream reaches that span a range of geomorphologic conditions in rivers and streams on Alaska’s North Slope. Results from seasonal time-lapse common-offset GPR transects, gathered throughout the summer season of 2004, illustrated that low-energy stream environments react slowly to seasonal solar input and maintain thaw thicknesses longer throughout the late season. Thaw depths beneath high-energy streams respond quickly in the beginning of the season and appear to decrease just as quickly over the late season period. Continuous multi-offset (CMO) GPR method improves the quality of subsurface images through stacking and velocity filtering and provides measurements of vertical and lateral velocity distributions. Detailed velocities were estimated from CMO transects, gathered in August 2005, using reflection tomography processing methods. Resulting velocity tomograms were then used to estimate water content and porosity using the Topp equation. Porosity estimates were then used to help constrain a 1D finite-difference thermal model. Within the high-energy stream environments three-dimensional (3D) GPR data illustrate greater thaw depths beneath riffle and gravel bar features relative to the neighboring pool features. Due to differences in thermal properties the low-energy stream sites indicate the opposite: greater thaw depths beneath pools and thinner thaws beneath the connecting runs. Results provide detailed 3D geometry of active layer thaw depths that can greatly improve hydrological studies seeking to quantify transport and biogeochemical processes that occur within the hyporheic zone. Using the finite-difference approach a 1D heat transport model with phase change was developed to estimate seasonal temperatures beneath two arctic streams to determine the dominant thermal process occurring beneath the stream sites. The model was driven by stream water or near-surface temperature data recorded at select stream sites near Toolik Field Station, AK, for the summer months of 2004 and 2005. Model temperatures were calibrated to measured temperatures at corresponding depths and evaluated against interpreted thaw depths from cross-sectional GPR images gathered over the 2004 summer season. Results are in reasonable agreement with observed temperatures and GPR thaw depth estimates and imply thaw processes dominated by thermal conduction. Discrepancies between model and observed values are likely due to homogenous soil property assumptions, oversimplified convection influence assumptions, and deviations from the 1D model

Imaging Thermal Stratigraphy in Freshwater Lakes Using Georadar

Thermal stratification exerts significant control over biogeochemical processing in freshwater lakes. Thus, the temporal and spatial distribution of the thermal structure is an important component in understanding lake ecosystems. We present the first reported observations of lake thermal stratification from surface based georadar measurements acquired over two small freshwater lakes. This method is very useful because it can provide rapid acquisition of 2D or 3D lotic stratification

Application of Time-Lapse ERT Imaging to Watershed Characterization

Time-lapse electrical resistivity tomography (ERT) has many practical applications to the study of subsurface properties and processes. When inverting time-lapse ERT data, it is useful to proceed beyond straightforward inversion of data differences and take advantage of the time-lapse nature of the data. We assess various approaches for inverting and interpreting time-lapse ERT data and determine that two approaches work well. The first approach is model subtraction after separate inversion of the data from two time periods, and the second approach is to use the inverted model from a base data set as the reference model or prior information for subsequent time periods. We prefer this second approach. Data inversion methodology should be consideredwhen designing data acquisition; i.e., to utilize the second approach, it is important to collect one or more data sets for which the bulk of the subsurface is in a background or relatively unperturbed state. A third and commonly used approach to time-lapse inversion, inverting the difference between two data sets, localizes the regions of the model in which change has occurred; however, varying noise levels between the two data sets can be problematic. To further assess the various time-lapse inversion approaches, we acquired field data from a catchment within the Dry Creek Experimental Watershed near Boise, Idaho, U.S.A. We combined the complimentary information from individual static ERT inversions, time-lapse ERT images, and available hydrologic data in a robust interpretation scheme to aid in quantifying seasonal variations in subsurface moisture content

The MMM Initiative

We’ve determined that information collected and distributed by and on news and social media outlets has manifested in political biases of its users. It is clear that this issue has subsequently led to political polarization and ethnic prejudice. To combat this problem, we have devised an online informational package and an interactive experience to teach people how to use it. Our website provides the resources to check personal biases and recognize ethnic prejudices. The seminar encourages people to apply and spread their newfound knowledge. We conducted interviews with experts, surveys, and an extensive literature review. Through our research and feedback from over 40 partners, we have found that access to social media literacy education is virtually non-existent — hence the need for a comprehensive, easily digestible informational package. It\u27s not enough to create a package, we also need people to see it. Our interviews with experts tell us that the best way to engage students is through interactive experiences. Therefore, we supplemented these educational tools with an experience that consists of a community group and the extensive use of partners to promote our package to their respective networks. Our resources use text, visuals, videos, conversation, and other interactive elements to educate users on how the use of media can exacerbate ethnic prejudices. To measure the attitude change of our viewers, we created a set of surveys concerning media usage and its relationship with bias. We also tracked the attendance of the seminar so that we could understand how widespread our message is. Hundreds of people have accessed our website with an accumulation of over 2,000 views. We expect this to continue growing exponentially as word of its existence continues to spread. Our project has a global reach with at least 15 countries and 25 states reached

Hyporheic Exchange and Water Chemistry of Two Arctic Tundra Streams of Contrasting Geomorphology

The North Slope of Alaska’s Brooks Range is underlain by continuous permafrost, but an active layer of thawed sediments develops at the tundra surface and beneath streambeds during the summer, facilitating hyporheic exchange. Our goal was to understand how active layer extent and stream geomorphology influence hyporheic exchange and nutrient chemistry. We studied two arctic tundra streams of contrasting geomorphology: a high-gradient, alluvial stream with riffle-pool sequences and a low-gradient, peat-bottomed stream with large deep pools connected by deep runs. Hyporheic exchange occurred to ~50 cm beneath the alluvial streambed and to only ~15 cm beneath the peat streambed. The thaw bulb was deeper than the hyporheic exchange zone in both stream types. The hyporheic zone was a net source of ammonium and soluble reactive phosphorus in both stream types. The hyporheic zone was a net source of nitrate in the alluvial stream, but a net nitrate sink in the peat stream. The mass flux of nutrients regenerated from the hyporheic zones in these two streams was a small portion of the surface water mass flux. Although small, hyporheic sources of regenerated nutrients help maintain the in-stream nutrient balance. If future warming in the arctic increases the depth of the thaw bulb, it may not increase the vertical extent of hyporheic exchange. The greater impacts on annual contributions of hyporheic regeneration are likely to be due to longer thawed seasons, increased sediment temperatures or changes in geomorphology

Influence of Morphology and Permafrost Dynamics on Hyporheic Exchange in Arctic Headwater Streams under Warming Climate Conditions

We investigated surface-subsurface (hyporheic) exchange in two morphologically distinct arctic headwater streams experiencing warming (thawing) sub-channel conditions. Empirically parameterized and calibrated groundwater flow models were used to assess the influence of sub-channel thaw on hyporheic exchange. Average thaw depths were at least two-fold greater under the higher-energy, alluvial stream than under the lowenergy, peat-lined stream. Alluvial hyporheic exchange had shorter residence times and longer flowpaths that occurred across greater portions of the thawed sediments. For both reaches, the morphologic (longitudinal bed topography) and hydraulic conditions (surface and groundwater flow properties) set the potential for hyporheic flow. Simulations of deeper thaw, as predicted under a warming arctic climate, only influence hyporheic exchange until a threshold depth. This depth is primarily determined by the hydraulic head gradients imposed by the stream morphology. Therefore, arctic hyporheic exchange extent is likely to be independent of greater sub-stream thaw depths

Transient Storage as a Function of Geomorphology, Discharge, and Permafrost Active Layer Conditions in Arctic Tundra Streams

Transient storage of solutes in hyporheic zones or other slow-moving stream waters plays an important role in the biogeochemical processes of streams. While numerous studies have reported a wide range of parameter values from simulations of transient storage, little field work has been done to investigate the correlations between these parameters and shifts in surface and subsurface flow conditions. In this investigation we use the stream properties of the Arctic (namely, highly varied discharges, channel morphologies, and subchannel permafrost conditions) to isolate the effects of discharge, channel morphology, and potential size of the hyporheic zone on transient storage. We repeated stream tracer experiments in five morphologically diverse tundra streams in Arctic Alaska during the thaw season (May–August) of 2004 to assess transient storage and hydrologic characteristics. We compared transient storage model parameters to discharge (Q), the Darcy-Weisbach friction factor (f), and unit stream power (ω). Across all studied streams, permafrost active layer depths (i.e., the potential extent of the hyporheic zone) increased throughout the thaw season, and discharges and velocities varied dramatically with minimum ranges of eight-fold and four-fold, respectively. In all reaches the mean storage residence time (tstor) decreased exponentially with increasing Q, but did not clearly relate to permafrost active layer depths. Furthermore, we found that modeled transient storage metrics (i.e., tstor, storage zone exchange rate (αOTIS), and hydraulic retention (Rh)) correlated better with channel hydraulic descriptors such as f and ω than they did with Q or channel slope. Our results indicate that Q is the first-order control on transient storage dynamics of these streams, and that f and ω are two relatively simple measures of channel hydraulics that may be important metrics for predicting the response of transient storage to perturbations in discharge and morphology in a given stream

Model and Test of an Actively Controlled Cryogenic Micro Valve

Under the supervision of Professor Gregory F. Nellis; 159pp.Future NASA missions require cooling of large optical structures, cryogen storage systems, and instrument chambers and therefore cooling must be applied in a controlled and efficient fashion over a large spatial extent. A cooling system that uses an actively controlled, micro-scale valve may be integrated with heat exchangers and sensors in order to allow the individual branches of a distributed cooling system to be independently controlled in response to local temperature changes. The ability to control the flow area associated with the valve increases the efficiency and flexibility of the distributed cooling system by allowing the cooling to be concentrated according to need. Previous work has selected a suitable micro valve design that addresses the required specifications. However, the precise nature of the flow behavior inside the micro valve was not addressed. Therefore, this thesis focuses on the modeling and test of the pressure-flow behavior of a micro-scale valve over a range of operating conditions. Variable voltage actuation of the PZT actuator within the micro-valve modulates the flow area and therefore the pressure distribution and fluid flow behavior. Fluid-structure models were developed to predict the pressure distribution and flow rates. Experimental data from prototype micro valves was used to validate the analytical predictions

Obtaining the Source Wavefield from Multicomponent Data and its Application in Full Waveform Inversion

In full waveform inversion (FWI) we need to know the seismic source signature. In practice this is generally unknown, and it must be estimated using statistical methods or inversion. However, these methods rely on assumptions that are often false, which results in a poorly estimated source. This can have a crippling effect on FWI, since it is an ill-posed and highly nonlinear problem that is very sensitive to errors in the inputs. Small errors in the source can cause the solution predicted by FWI to deviate significantly from the true solution. To better estimate the source for FWI, we suggest using a method for extracting the source wavefield when given multicomponent data. The method for obtaining the source wavefield derives from the reciprocity theorem, and involves injecting the multicomponent data into an homogeneous model with a finite difference injector. We then use the source wavefield as input for the source in FWI. Numerical examples are presented, and we find that the extracted source field can successfully be used in FWI, although numerical inaccuracies inhibits it from fulfilling its true potential