This thesis develops a novel training dataset with patch-pairs of co-located thermal (70 m) and RGB imagery (3 m). Using this novel dataset, this thesis assesses whether a pansharpening model (PanColorGAN) trained on RGB and panchromatic imagery can be successfully applied to the thermal-optical patch-pairs to solve the thermal pansharpening problem. In addition, this thesis will determine if a pansharpening model (pix2pix) trained on the thermal-optical patch-pairs produces higher quality results than the model with pre-trained weights (PanColorGAN). This approach will be applied to five cities with variable climate-urban environments across the United States: Austin, TX, Boulder, CO, Chicago, IL, Los Angeles, CA, and Washington, D.C. The visual and quantitative results indicated that the PanColorGAN framework with pre-trained weights produced higher quality thermal images than the pix2pix framework trained on the thermal-optical patch-pair dataset. While thermal-optical pansharpening successfully recovered many of the spatial details of the high-resolution RGB imagery, it failed to fully retain the valuable spectral information from the thermal imagery.

]]>industry, they are still underrepresented at the highest levels of leadership.

Two factors that may contribute to this leaky pipeline are gender bias,

the tendency to treat individuals differently based on the person’s gender

identity, and homophily, the tendency of people to want to be around those

who are similar to themselves. Here, we present a multilayer network model

of gender representation in professional hierarchies that incorporates these

two factors. This model builds on previous work by Clifton et al. (2019), but

the multilayer network framework allows us to track individual progression

through the hierarchy and relationships at the level of individual agents.

We use this model to investigate how the network structure and location of

female and male nodes within a given network affect gender representation

throughout the hierarchy. ]]>

Among this family, there exists a Randomized Kaczmarz variant called Randomized

Extended Kaczmarz which solves for least squares solutions in inconsistent linear systems.

Among Kaczmarz variants, Randomized Extended Kaczmarz is unique in that it modifies input system in a special way to solve for the least squares solution. In this work we unpack the geometry underlying Randomized Extended Kaczmarz

(REK) by uniting proofs by Zouzias and Freris (2013) and Du (2018), leading to more insight about why REK works. We also provide novel proofs showing: that REK will converge with an alternative sequence of z updates, and giving a closed form for REK’s original z updates. Lastly we have done some work generalizing the ideas behind REK and QuantileRK (Haddock et al., 2020) to lay foundations for a new Randomized Kaczmarz variant called Weighted Randomized Extended Kaczmarz (WREK) which aim to solve weighted least squares problems with dynamic reweightings. ]]>

of information in a population evolves, such as the classical Hegselmann–

Krause model (Hegselmann and Krause, 2002). One extension of the model

has been used to study the impact of media ideology on social media

networks (Brooks and Porter, 2020). In this thesis, we explore various

models of opinions and propose our own model, which is an adaptive

version of the Hegselmann–Krause model. The adaptive version implements

the social phenomenon of

associate together. This is done by having agents dissolve connections if their

opinions are too different from one another and establish new connections

probabilistically, with it being more likely to establish a connection with an

agent with a similar opinion to theirs. We study how our model changes

with various values of the parameters in the model, namely the confidence

parameter and homophily parameter, as well as different initial graph

topologies and varying the number of nodes in the graph. ]]>

We analyze the effect of 𝛾 and 𝛿 on some of the stationary states of the smoothed bounded-confidence model on the complete graph. In particular, we analyze the stationary states with consensus and those with two distinct opinions. ]]>

This thesis also breifly looks into Niebrzydowski Tribrackets which are a different algebraic structure which, in future work, may have interesting behavior on knot diagrams in arbitrary surfaces.

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