If you're tiling a circular room with square tiles, how many do you need? What if your tiles are parallelograms? As the circle gets larger, is there a pattern? Mathematically, this can be framed as counting integer points in a large circle. We're interested in how this count changes as you change the shape of the tiles, and to understand this better, we started by counting the number of integer vector pairs within a ball of radius R so that the parallelogram they make has a fixed area (determinant). We created a Python program that would generate all of the primitive points out to radius R, which we then extended to count the number of vector pairs with a certain determinant k. We were able to compute the limiting density of this count, extending known results for the case of determinant 1. We are now studying other discrete sets, such as ones generated by objects from hyperbolic geometry, known as Hecke triangle groups. In the future, we plan to use our research for counting pairs of vectors in different spaces and generalize it for counts of k-tuple vectors. Come for floor tilings, stay for beautiful pictures!

Hybrid dynamical systems (HDS) are time dependent systems that have both discrete and continuous behavior, such as a bouncing ball or jumping leg. The BioRobotics Lab studies HDS in order to better understand locomotion and develop controls for robotics. As controllers are developed, they need to be tested in the hybrid dynamical system (HDS) either through simulation or implementing in physical robotics. While simulated system environments are useful in early controller development, they are unable to capture all the intricacies of a physical system. Thus, testing controllers in a physical system can provide better insights for future development. We developed a hopping robot for the purpose of easily implementing controllers through software. The hopping robot is designed to be modular and easily configured for different dynamics. Simulations of the robot were also developed so that researchers can use both simulated and physical environments. This tool will help researchers develop new controllers and could bring new insights to studying hybrid dynamical systems.

The physics behind wave-driven mixing of river and ocean waters and current-driven wave breaking are not well understood. The current body of work surrounding river-ocean interactions focuses on large rivers. However, small rivers, which are much more strongly influenced by waves, make up the majority of such systems, and contribute significantly to global riverine discharge. Examining the momentum balance of river flow in opposition to wave-driven forcing from the ocean is necessary to understand how waves influence the travel and mixing of river water. One way to measure this interaction is using instrumental drifting buoys that follow the path of the river water and take temporal measurements of water properties. These leave gaps in our knowledge, as such buoys do not provide a description of the entire system, only specific points. To fill in these gaps, Unmanned Aerial Vehicle (UAV) footage was used to understand broader wave-current interactions at the Quinault River mouth, a small river that feeds directly into the Pacific Ocean. The town of Taholah, WA, is on its banks, and faces challenges due to wave-driven flooding. The size of the surf zone, the nearshore region where waves break at high frequency, was mapped with UAV footage, and related back to local environmental conditions, such as tidal phase. At low water, the momentum from the river is maximized, and so is the cross-shore extent of the surf zone. This decreases salinity around the river mouth, as freshwater is trapped by the surf zone. At high tide, these conditions are reversed, and fresh water streams can be detected past the surf zone, suggesting the river water has escaped from this region of high turbulence. The conditions under which these escapes occur are to be understood by combining analyses of UAV footage with drifter and tidal data.

Genetic diversity and gene flow are important to long-term viability in wild populations. In migratory species, gene flow (i.e. dispersal between disparate populations) is inherently influenced by the spatial and temporal components of their migrations. Recent findings have revealed the importance of fine-scale population structure in both space and time in Sockeye Salmon (O. nerka). However, the fitness consequences of this fine-scale structure are unclear. Here we evaluate the biological relevance of fine-scale spatial and temporal homing by examining their effects on a quantitative trait, individual lifetime reproductive success. Salmonids are well-known for their extensive journey from the freshwater stream where they hatch, to the ocean, and back to their home stream (i.e. ‘homing’). Homing behavior is associated with individual fitness; individuals are locally adapted to their natal streams, and dispersers between non-natal streams can have reduced reproductive success. Population structure within individual streams is generally assumed to be random (panmictic). However, individuals may be locally adapted on a finer scale than previously known, both in space (homing within their natal stream) and return timing. Fine-scale spatial and temporal homing may play a role in individual fitness; therefore, it is important to investigate this relationship. We used zero-inflated negative binomial models and a multi-generation pedigree, reconstructed from two populations of Alaskan Sockeye Salmon, to estimate the impact of homing on individual reproductive success (number of offspring per fish). Our results suggest that fine-scale dispersal in both space and time may reduce lifetime fitness. These results have broad implications for fisheries management and habitat conservation: recognizing the connection between reproductive success and return timing could inform within-season fisheries management, helping maintain the genetic diversity associated with local adaptation; likewise, recognizing the connection between individual salmon success and their habitat may promote maintaining natural heterogeneity in salmon streams.

Scholarship on American Buddhism has, from its beginnings, struggled with defining “who” and “what” makes an American Buddhist. American Buddhism has thus been split off into two branches: one “ethnic,” which is defined as being practiced by Buddhist immigrants and their descendants, the other “convert,” which makes up Americans of all races and ethnicities who decide to convert to Buddhism. However, temples like the Tacoma Buddhist Temple, a Jodo Shinshu temple located in downtown Tacoma, is one of these many communities with varied membership that falls outside of the two-branch model and is thus why scholars have disputed the model for its inability to fully describe American Buddhists. The dualism of these the two terms create a divide within the American Buddhist community and also racializes the two categories since the term “ethnic Buddhist” is highly associated with the Asian community. As a result, the two terms fail to recognize many of those who fall outside the model, such as non-Asian Buddhists whose parents were convert Buddhists themselves and Asian Buddhists who grew up in a non-Buddhist household and chose to convert to Buddhism later on in their lives. The terms also have a tendency to polarize communities, making it seem as if “ethnic” communities and “convert” communities and thus “ethnic” and “convert” Buddhists have little interaction. The Tacoma Buddhist temple, however, is a community of not only “ethnic” and “convert” Buddhists practicing Buddhism side by side, but also those who the model fails to recognize. Therefore, through the research gathered at the Tacoma Buddhist Temple, it becomes evident that the two-branch model fails to capture the diversity of American Buddhism.

In cystic fibrosis (CF), a genetic defect in the CFTR anion channel compromises host defenses and causes chronic lung infections with organisms like Staphylococcus aureus. Our lab has been studying the effects of combining ivacaftor, a CFTR modulator which increases CFTR channel activity, with a period of intensive antibiotic treatment. We found that S. aureus lung infections generally persisted despite this aggressive treatment. However, most subjects undergoing treatment were found to be infected by different S. aureus strains one year after treatment than were present before treatment was initiated. Understanding the dynamics of strain switching provide new knowledge about the natural history of chronic CF infections, help define the effects of CFTR modulators and antibiotics, and inform new approaches that might produce infection eradication. We hypothesize that (1) strain switching is most likely to occur during the period of combined ivacaftor and antibiotic treatment, as sputum bacterial burdens were lowest during combined treatment; and that (2) strain switching is rare in the absence of combined treatment. To test this, we used a new population-based multilocus sequence typing (PopMLST) method we developed to perform strain-level genotyping on S. aureus. PopMLST uses PCR amplification and next generation sequencing of housekeeping genes from bacterial isolate pools cultured from sputum. Sequencing determines the number and relative abundance of unique sequence types present, and the data can be used to infer the number of strains present. This analysis was performed on samples obtained before treatment, during treatment with ivacaftor alone, and during combined treatment. We also examined a cohort of subjects receiving usual care. These data improve understanding of strain dynamics during CF infections and suggest new strategies to eliminate infection.

Intracranial aneurysms can rupture, leading to hemorrhagic stroke, a devastating and deadly disease. The geometry of vessels plays a crucial role in the onset and molecular pathophysiology of intracranial aneurysm formation. Notably, regions of bifurcation tend to be more susceptible to aneurysm formation. Numerous studies focus solely on the interactions between hemodynamics and vascular geometry or those between hemodynamics and molecular expression changes. Despite the significant relationship between the structure of vessels and the endothelial cell (EC) molecular expression, there has been few investigations tying the relationship between how vascular geometry affects the EC expression, particularly genes known to be related to EC pathological response: ADAMTS-1, VCAM-1, MCP-1, PDGF-B. These genes are implicated in endothelial dysfunction and aneurysm pathophysiology. Here, we aim to see how the geometry of the parent vessel affects endothelial gene expression, using 3D-printed, endothelialized, idealized bifurcation aneurysm models of varying degrees of parent vessel curvature. We then quantify the mRNA and protein expression for the genes associated with endothelial response. By elucidating the relationship between the vessel geometry and EC expression, we hope to contribute in further advancing the modeling of aneurysm pathology.

Roborun is a simulation game that utilizes crowdsourcing to identify legged movement patterns for land-based robotic movement. By using a game controller, keyboard, or by providing a set of instructions to execute in order (e.g. “rotate front leg X degrees”, “move back leg forward Y meters”, etc.), players can control joint torques and leg movements in order to navigate a virtual two-legged robot through several 2D obstacle courses that contain varied terrain and movable boxes. The game can be played through a web browser on either a computer or smartphone, making the game accessible to players across multiple platforms. In future development, we intend to implement a scoring system based on efficiency and speed of course solutions and will replicate the best scoring solutions from players on a commercially-available robot in our testing laboratory. It is our hope that their solutions will help develop reliable robotic movement algorithms and shed some insight into the dynamics of land-based movement.

Organic solar cells (OSCs), particularly all-polymer solar cells, have risen as an exciting alternative to standard inorganic solar cells. Their low-cost synthesis, easily tunable properties, and solution-processable fabrication enable facile scale-up for high-throughput production. For commercial viability OSCs will need to have power conversion efficiency (PCE), which is determined by the material characteristics and energetic properties, comparable to their inorganic counterparts (>20%). The question this research aimed to address is: How do processing conditions govern the electronic properties of the photovoltaic layer? Two primary methods were used to evaluate the energy levels: Cyclic Voltammetry (CV) for the highest and lowest occupied molecular orbitals (HOMO/LUMO) and Ultraviolet-Visible Spectroscopy (UV-Vis) for the optical bandgap. A binary blend comprised of a polymer donor, known as PSEHTT, and a polymer acceptor, N2200, was used as a proxy model. Blends of compositions ranging from 0 to 100 weight % PSEHTT were coated on platinum wires for CV and glass substrates for UV-Vis measurements. The collected data behaved as expected, exhibiting a decreasing trend in HOMO level from -5.29 eV to -4.94 eV as the weight % PSEHTT increased. The evolution of the LUMO level with blend compositions was rather challenging to obtain due to possible photoexcitation in the blend leading to free charge available for continuous current extraction. To verify, the samples were isolated from light over the course of the CV measurements to prevent interference. This should result in more accurate LUMO level approximations which are expected to display a similar trend to the HOMO level. Elucidating the relationship between blend composition and blend electronic properties enables a precise and facile device optimization process for highly efficient OSCs.

Cerebral palsy is a congenital disorder which impacts movement, muscle tone, and cognitive ability. This disorder affects 2-3 people per 1,000 births annually. My lab is currently developing a technology to assess motor learning. We’re working on quantifying motor planning deficits in cerebral palsy to aid in targeted therapy. However, the small test population combined with the nature of cerebral palsy means it can be difficult to bring these subjects into the lab to verify our technology. I developed a “simulation” of the controller we use to interface with our technology that can be downloaded onto android devices and can connect to a subject’s bluetooth enabled computer wirelessly. This allows subjects to test our technology remotely in a setting which best suits their needs. Upon testing this virtual controller against the currently used controller, the virtual controller offered a lower mean-squared error to the normal controller, and was proved a viable option for remote testing. This development allows us to expand our testing pool to those who may not be able to physically come to the laboratory for testing, and can be expanded to future developments which require unique controllers.

The study of the behavior of multiple agents, specifically human and machine, in a dynamic environment is challenging due to the unpredictable individual behaviors. Humans will naturally formulate beliefs about the machine’s behavior, which would directly affect their future decisions. Our research aims to develop a framework for the study of human-machine dynamic interactions. With the imperfect information humans and machines have about each other and their environment, a game-theoretic approach was done to study the natural model of their interactions. We derive theoretical models for steady-state (i.e. equilibrium) and transient (i.e. learning) behaviors of humans interacting with other agents (humans and machines). We also design experiments to validate our theory. A haptic testbench, in the shape of a robotic arm, is used as a dynamic simulation platform for studying the trajectories of the human/machine interaction, allowing us to study both theoretically and experimentally. The robotic arm has a position control system that supports a wide variety of human/machine experiments. The user is provided with visual and haptic feedback, which allows for experiments to be designed to study the sensorimotor learning processes. The robotic arm is built using direct-drive brushless motors, force sensors, an open-source ODrive motor controller, and an arm lever. The motor firmware is designed in C/C++, and integrated with a user-interface in Python. With the wide variety of potential applications, we hope our research will give insights into the different natures of human motion and be a fundamental platform for technological breakthroughs in the medical field.

 In vivo animal models are an advanced tool for testing complex biological phenomena and functions in humans, yet are difficult to adapt due to high cost, biological and anatomical differences, and ethical concerns. As an alternative to in vivo models, in vitro organotypic models have been created that can accurately and efficiently reproduce biological processes, allowing researchers to probe specific factors without the difficulties associated with in vivo models. We present further development of a novel microfluidic platform, called Stacks, which uses open and suspended microfluidic principles to enable spatial and temporal manipulation of 3D cultures in suspended collagen plugs. We are developing the Stacks platform to accurately reflect morphology exhibited in the air-liquid interface (ALI) of the epithelial layer of the lung and allow analysis of lung pathophysiology, cell signaling, and immune responses of the lung in both monoculture and coculture. Furthermore, using the flat faces of the device that allow for stacking, we have connected a layer of human lung endothelial cells, representing a model vascular system, with a second layer of immune cells and mycobacterium, representing a model infection system, to study soluble factor signaling in granulomatous infections. Through the modification of the Stacks device, we can achieve granuloma formation and utilize soluble factor analyses (e.g., immunoassay) to observe and characterize infection-dependent changes in vasculature resulting from the exchange of chemical signals generated by the infection model. Future development of the platform will build on these newly developed lung models to combine them for studies involving signaling and disease mechanisms between the lung ALI and the underlying tissue layers.

This research is aimed at improving the functionality and use of multi-robot control through several different aspects. One important aspect of this project is collision avoidance between multiple ASEA Brown Boveri (ABB) industrial robots. The active collision avoidance software is an efficient tool that detects potential collisions between multiple robots working in collaboration and the surrounding cell. The user can specify a safety net around each robot, which notifies the user if one or more robots are on a collision course. Each robot’s position is graphically displayed to the screen with respect to the user-defined world coordinate system, complete with logs of tool center point positions and time stamps, so collisions can be reproduced. This software is intended to be used in conjunction with automated scheduling as an external safety checker. Another important aspect of this research is the end effector, an attachment that is secured onto the end of the ABB robot and used to drill a series of holes in a given surface. The end effector has gone through numerous design improvements through which it became smaller and more cost efficient. The latest design incorporates the addition of a raspberry pi, a small single-board computer, which serves as a failure test. The pi is programmed to generate random failures which notifies the user to take the robot out of the running program. This system will eventually be used to detect real robot failures and alert the user of the malfunction. The end effector also has a separate attachment which is used to hold a camera in order to incorporate machine vision into the multi-robot system. Adding machine vision helps robot position calibration, along with detecting foreign objects other than the moving robots in the robot cell. This addition also improves security and liability of the system.

Malaria is a disease associated with a significant global burden of illness, including hundreds of thousands of deaths every year. Severe malaria is most often due to the Plasmodium Falciparum species of parasite, the pathogenesis of which involves avoidance of host detection through endothelial sequestration. This process allows infected erythrocytes (red blood cells) to adhere to the vessel wall and avoid filtration via the spleen. Severe cases of malaria are often also associated with endothelial activation and release of the adhesive glycoprotein, von Willebrand Factor (VWF). Preliminary data from our laboratory suggests that erythrocytes infected with P. Falciparum may be able to bind to VWF fibers formed under in vitro conditions, and we believe that VWF binding may prove to be a novel mechanism contributing to endothelial sequestration. This study was conducted in order to understand the interactions between plasmodium infected erythrocytes and VWF fibers formed following endothelial activation. Because of the high demand for technical replication for such a project, and the labor and time expenses associated with the lab’s commonly used microvessel system, modifications were made to the geometry and housing to characterize it for the high-throughput platform for the study of VWF’s role in the binding of infected erythrocytes to activated endothelium. By utilizing nanofabrication techniques and soft lithogaphy with Polydimethylsiloxane (PDMS), we have successfully completed design and manufacturing of the novel devices that have allowed an increase in speed and efficiency up to three times that of previous assemblies. In these newly fabricated devices, we saw consistent formation of robust VWF fibers upon activation and aim to continue their use to observe and quantify binding of plasmodium infected erythrocytes in VWF-rich regions within vessels.

Utilizing the Type III Secretion System (T3SS), Shigella spp. uses a cascade of proteins to manipulate, penetrate, and colonize host eukaryotic cells. Inducing epithelial necrosis, Shigella spp. infection is responsible for moderate to severe diarrhea in millions of children and immunocompromised individuals — the majority from low and middle income countries. Previous translational research for Shigella spp. has been limited due to a lack of robust in vitro and in vivo models to screen therapeutic efficacy. Understanding infectivity of Shigella spp. heavily relies on imprecise estimations of intracellular Shigella spp., which ultimately impacts vaccine and antibiotic efforts. This project aims to address this problem by developing a novel red intracellular reporter to quantify successful invasion of Shigella flexneri. By using a series of polymerase chain reaction (PCR) and Gibson assemblies, we have constructed a plasmid with a RFP reporter to be expressed during successful invasion of Shigella spp. The IpaH9.8 MxiE promoter, which has been shown to be expressed upon cell entry, is integrated within the pUltra RFP plasmid and electroporated into a streptomycin-resistant S. flexneri strain. We will test the recombinant strain in vitro by activating ipaH9.8 in broth culture and inoculating a mammalian cell line (HCT-8). RFP expression will be monitored with a BioTek FLX-800 plate reader and visually imaged using a FX-EVOS microscope. The expected outcomes of this project will provide an accurate and efficient method of quantifying invasive S. flexneri. in vitro and in vivo, as well as quantifying pharmacodynamics and pharmacokinetics of new treatment therapies. The implications of this project are crucial to the advancement of shigellosis research and in furthering the efforts of the international community to abate the steadily increasing cases of drug resistant shigellosis cases observed worldwide.