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The Manifestation and Mitigation of Cognitive Bias in the User-Centered Design Process
No full textUsability or safety issues result when products are not designed with a diverse range of end users in mind. As the majority of engineering degree recipients are men, products designed by engineers are often inadequate for women users. One example of this is the higher fatality rate for women in car accidents when compared to men, due to safety systems in cars being designed by and for men. The field of engineering design lacks formal investigation into how cognitive bias manifests in a way that negatively impacts design outcomes, and particularly how these negative impacts may be inequitably distributed among stakeholders. Thus, the goal of this work is to contribute to the understanding of how cognitive bias influences the early stages of the design process.
To fulfill this primary goal, the proposed research was divided into three parts, each fulfilling a more specific research objective. Study I explored the usage of makerspaces, a common site for gender inequity in engineering, through observation and ethnographic interviews with makerspace users. Makerspaces have been identified as an environment where gender impacts user experience, both because makerspaces are typically men-dominated and because different areas of makerspaces have strong stereotypes attached. Findings from Study I were used to develop study materials for Study II, which examined how the stereotyping of a design problem, a user’s gender, and information presentation modality influence the designer’s interpretation of customer problems and needs. Finally, Study III built upon the previous work to develop and test a bias mitigation intervention for design problems. The ability of this intervention to mitigate availability bias was validated in a design activity with professional engineers and designers. This work’s main contributions to the field of engineering design include (1) an exploration into the concrete effects of cognitive bias in the design process and (2) a validated process for reducing the harmful effects of designers’ cognitive bias.Ph.D.Mechanical Engineerin
Concussions and CTE
No full textThis short documentary was created as a course requirement in HTS 3086 – Sociology of Medicine and Health under the supervision of Dr. Jennifer Singh.Runtime: 08:45 minutesThis documentary explores the illness experience of concussion experienced during college and professional football
On probabilistic, planar, and descriptive graph coloring problems
No full textWe investigate graph coloring problems from the perspective of three different types of graphs: graphs with forbidden bipartite subgraphs; planar graphs; and Borel graphs that are line graphs.
We start with studying graph with forbidden bipartite subgraphs. We say a graph is -free if it contains no subgraph (not necessarily induced) isomorphic to graph . It follows from recent work by Davies, Kang, Pirot, and Sereni that if is -free, then as . We improve this bound to , making the constant factor independent of . We further extend our result to the correspondence coloring setting.
Next we study defective coloring of planar graphs. For , a coloring of a graph is \textit{-defective} if every vertex is colored the same as at most of its neighbors. We investigate defective coloring of planar graphs in the context of correspondence coloring. First we show there exist planar graphs that are not -defective -correspondable, strengthening a recent result of Cho, Choi, Kim, Park, Shan, and Zhu. Then we construct a planar graph that is -defective -correspondable but not -correspondable, thereby extending a recent result of Ma, Xu, and Zhu from list coloring to correspondence coloring. Finally we show all outerplanar graphs are -defective 2-correspondence colorable, with defects being best possible.
Finally, we study Borel graphs. We characterize Borel line graphs in terms of 10 forbidden induced subgraphs, namely the 9 finite graphs from the classical result of Beineke together with a 10th infinite graph associated to the equivalence relation on the Cantor space. As a corollary, we prove a partial converse to the Feldman--Moore theorem, which allows us to characterize all locally countable Borel line graphs in terms of their Borel chromatic numbers.Ph.D.Mathematic
Assessing Affordable Housing Adequacy on the Atlanta Beltline
No full textThe Atlanta BeltLine has attracted public concern over gentrification. The City of Atlanta plans to mitigate gentrification and displacement of low-income population with affordable housing. One of Atlanta’s policies is an inclusionary zoning ordinance. This study aims to identify the adequacy of inclusionary zoning to add new affordable housing in Atlanta. The study is based on the proposition that it is preferable for affordable housing to be located near neighborhoods that are gentrifying or vulnerable to gentrification to reduce the social cost of relocation. To understand the relationship between gentrification and affordable housing in Atlanta, we developed a system to identify the gentrification stage using the ordinary least squares regression analysis. The results showed that the number of census tracts under influence of gentrification increased over time. This aligned with results of previous studies and the public concern over the expansion and intensification of gentrification in Atlanta in recent years. The BeltLine has played a critical role for this change. Moreover, the location of city’s affordable housing did not show any significant relationship with neighborhoods that are gentrifying or vulnerable to gentrification, demonstrating in turn that Atlanta’s policy to add new affordable housing fails to pursue the public good and mitigate gentrification by reducing the cost of relocation for displaced populations. The study concludes that supplementary policies are required to protect susceptible populations from gentrification
Reproducing Pairs and Gabor Systems
No full textThis thesis can be summarized as follows. Chapter 1 establishes the foundational concepts and definitions, ensuring the work is largely self-contained. It introduces normed linear spaces, including Banach and Hilbert spaces, with examples like ℓ2(ℤ) and L2(E) for measurable sets E. It covers key notions such as convergence, Cauchy sequences, and orthogonality, with the use of an inner product. The chapter also covers operator theory, including linear and antilinear operators, boundedness, continuity, and the extension of bounded operators from dense subsets. The dual and anti-dual spaces are introduced, culminating in an antilinear version of the Riesz representation theorem.
Chapter 2 explores reproducing pairs in Hilbert spaces, focusing on the discrete case. Reproducing pairs are a generalization of frames. They consist of two sequences ψ and Φ and an induced bounded invertible operator Sψ,Φ: ℋ ⟶ ℋ, defined weakly by
⟨S,f , h⟩ = iJ⟨f , ψᵢ⟩ ⟨φᵢ , h⟩ , f, h ∈ ℋ
In the context of reproducing pairs, we study sequences that are overcomplete by one element—those that become exact upon removal of a single element. Theorem 2.2.2 shows that if such a sequence has a reproducing partner, the resulting subsequence must be a Schauder basis. This is applied to weighted exponential systems and the Gaussian Gabor system at critical density, both of which lack Schauder bases and hence cannot admit reproducing partners. Theorem 2.5.3 generalizes this result to sequences overcomplete by finitely many elements, with applications to weighted exponential systems.
The chapter concludes by introducing exponential reproducing pairs, where the sequences are weighted exponentials. The weak operator Sgɣ is defined by
⟨Sgf , h⟩ = nℤ⟨f ,gen⟩ ⟨en , h⟩ , f, h ∈ ℋ
where en = e2πint and the inner product is on L2([0,1]). Theorem2.6.4 shows that Sgɣ acts as a multiplication operator: Sgɣf = f g̅ɣ for f ∈ L2([0,1]). Theorem 2.6.6 gives necessary and sufficient conditions for (g,ɣ) to form an exponential reproducing pair, with further refinements in Section 2.7 under weakened assumptions.
In Chapter~3, we extend a 2012 result of Heil and Yoon, on exact weighted exponential sequences to two dimensions. We first characterize when the weighted double exponential system ℰ(d_{x₀,ξ₀}(x, ξ)ⁿ, ℤ² \ F), with F ⊆ ℤ² finite and
d_{x₀, ξ₀}(x, ξ) = √((x - x₀)² + (ξ - ξ₀)²)
is minimal and complete, culminating in Theorem 3.2.18. We then analyze when the weighted system ℰ(g, ℤ² \ F) is exact for arbitrary g ∈ L²(Q), obtaining sufficient and necessary conditions (Theorems 3.4.4 and Theorem 3.5).
Finally, Chapter 4 presents a minor result in frame theory: Theorem 4.3.2 proves that no frame exists whose every infinite subset is also a frame.Ph.D.Mathematic
Automorphisms of Smooth Fine Curve Graphs
No full textIn this work, we consider the automorphisms of fine curve graphs where the vertices are restricted to continuously k-differentiable curves. We show that for closed surfaces with genus at least 2, they are all induced by homeomorphisms of the surface. Specifically, we show that the automorphisms of these graphs are naturally isomorphic to Homeo^k(S), the subgroup of homeomorphisms that preserve the set of one-dimensional C^k submanifolds of the surface. This result extends analogous work of Farb--Margalit and Long--Margalit--Pham--Verberne--Yao.
In addition, we study in further depth the particular case when k=1 and provide local conditions that characterize Homeo^1(S). We show that there exists a collection of conditions that are both necessary and sufficient for a homeomorphism of the surface to be an element of this group. These conditions primarily depend upon the structure of the induced map on the projective tangent bundle.
Finally, we provide examples of several types of elements of Homeo^k(S) that are not diffeomorphisms. These include elements inducing discontinuous maps on the projective tangent bundle and having infinitely many non-differentiable points.Ph.D.Mathematic
Hybrid learning models for statistical continuum mechanics
No full textThis document summarizes my research aimed at creating interpretable and useful machine
learning models to assist efforts in materials design. In particular, I focus on the problem of predict-
ing local response fields (stresses and strains) over heterogeneous structures subjected to boundary
loading conditions, also known as the localization problem. In a sense all of micromechanics con-
sists of elasticity plus defect motion; my doctoral work extensively explores the first half of that
equation in relation to machine learning. This thesis comprises three papers: an exploratory study
applying iterative neural networks to elastic localization, a thermodynamically-informed iterative
neural operator which generalizes these ideas to work over a wider range of microstructure classes
and loading directions, and an extrapolation study which explores how far neural operators can be
taken outside their training distribution by hybridizing them with FFT-based relaxation solvers. All
three papers focus on purely elastic deformations, but keep an eye on the long-term goal of mod-
eling time-dependent, dissipative deformations. These are contextualized as part of the general
stochastic inverse problem known as process-structure-property modeling.
Beyond the localization problem, I have been fortunate to collaborate on a number of works
which build up different parts of the process-structure-property linkage. Most of these efforts have
been published in the theses of Dr. Andreas Robertson and Dr. Adam Generale, so I only pro-
vide brief descriptions and summaries for each paper. In particular, I contextualize these works
as part of the increasing alignment between the fields of deep learning, numerical methods, and
continuum mechanics. The contributions of this thesis are thus twofold: to provide useful deep
learning models which allow exploration of the microstructure space, and to advance a shared lan-
guage bridging the conceptually-isolated fields of data-driven modeling and statistical continuum
mechanics.Ph.D.Computational Science and Engineerin
Targeted gene delivery in brain tumors with microbubble enhanced focused ultrasound
No full textEffective treatment of brain tumors remains an unmet need. While RNA-based therapies offer several advantages over conventional approaches, their effective delivery to brain tumors remains a major challenge due to the vascular, interstitial, and cellular barriers of the brain. Although the incorporation of RNA into a nanoparticle (NP) can prolong circulation time and facilitate cellular uptake, its accumulation in the brain tumor microenvironment (TME) remains particularly poor due to the low NP permeability across the vasculature and limited interstitial transport. Microbubble enhanced focused ultrasound (MB-FUS) provides a physical method to promote the transport of a wide range of anticancer agents across the brain vessels and in the tumor core through the local application of mechanical stress. Although the promising preclinical data have led to Phase I/II clinical trials, the underlying transport dynamics that drive the observed improvement of anti-cancer agent delivery remain poorly understood which may lead to suboptimal operation and ultimately limit outcomes in ongoing clinical trials. This research integrates mathematical modeling with quantitative image analysis to provide mechanistic insights on the MB-FUS mediated mass and drug transport dynamics and identify the optimal microbubble (MB) properties, focused ultrasound (FUS) treatment protocol, and RNA nanocarrier design for effective RNA-based therapeutics delivery in brain tumors. Collectively, this work not only establishes design rules for effective RNA-based therapies against brain tumors with MB-FUS but also provides a platform for developing next-generation tunable delivery systems for RNA-based therapy in brain tumors.Ph.D.Mechanical Engineerin
Thulium Atoms Embedded in a Solid-State System of Neon for Quantum and Sensing Applications
No full textInvestigating the magnetic dipole ²F₅⸝₂ - ²F₇⸝₂ transition of thulium and its interactions with a crystal host matrix, we embed thulium atoms in solid-state neon and conduct a spectrum-wide survey to build upon current literature regarding thulium in solid-state noble gases and evaluate Tm:Ne’s potential as a qubit or quantum sensor. Rather than use prior methods of spectrum-hole burning to examine the structure of the system, we employ spectrum-wide burning with a pump-probe experiment. We found ten of twelve predicted features in a thermally stable complex pumped at 1139.65 nm. The energy spacings of this trapping site follow the interval rule, and its allowed transitions are subject to magnetic dipole and electric quadrupole selection rules.UndergraduatePhysic
Towards Genuine Robot Teammates: Inferring and Applying Cognitive State to Enable Novel Human-Autonomy Teaming Capabilities
No full textWhat makes a teammate? Surprisingly little research has focused on developing robot capabilities that replicate the interactions and inferences commonly observed in human-human teams. This dissertation investigates a broad range of interaction techniques and application domains that leverage personalized information about human users to inform a robot's decision-making and task execution. I model users through two key aspects of cognitive state: their latent cognitive skills and inferred mental models. These models are applied to practical human-robot teaming problems. Additionally, I explore how robot error type impacts user responses and team performance in structured shared decision-making. The findings presented in this dissertation enable novel teaming capabilities that adapt to individuals' prior knowledge and real-time belief states.Ph.D.Robotic