Biochar is used as a soil amendment and is created from plant biomass through pyrolysis. Biochar is thought to help plants grow by increasing the fertility of soil as well as impacting water retention in soils. This led to the question: Does biochar increase the water retention of soils found in the Lower Yakima Valley, allowing for a reduction in the amount of water that is needed to grow bell pepper plants in this water-stressed region? This research delves into the effectiveness of biochar by testing water level usage in real world plants grown in two concentrations of biochar (0.5% and 1%) applied to soils trial plots located in the Heritage University Research Farm. A random generator was used to create a split-plot design with three concentrations of biochar (0% or control, 0.5%, 1%) each with three replicates. The spilt-plot contained two different watering schemes. A total of 576 greenhouse grown Capsicum annum plants were transplanted to 18 plots, each plot containing 32 plants. To test the efficiency of biochar in soil water retention, soil moisture data, plant height, dry weight of the plants, and yield abundance were measured. Results indicate that the presence of biochar in soil can lead to increases in biomass of up to 100% in certain conditions. However, there were irrigation engineering complications that led the inability to reliably control the irrigation rates in the two split plots (originally planned for 100% in section 1, 80% reduced flow in section 2). The soil moisture data were inconsistent and highly variable reflecting potential instrument calibration issues, multiple instances of damage to the drip tape leading to water leaks, and persistent problems with the timing mechanisms for watering lines. This experiment led to significant improvement our methods for the following bell pepper research for the following year.

"The Prisoner's Dilemma" (PD) is a Game Theory activity in which a group of individuals simultaneously decide between two choices without knowledge of each other's selection and where individual profit depends on the responses of all participants. PD, when graphed, is often used to mathematically model human cooperation and social interaction. This research delves into the game played repetitively while looking to determine interactions between cooperation and defection in terms of maximal profit. The game was coded using C++ to visually and analytically depict cooperation and defection. A simple lattice structure graph with periodic boundary conditions was used, thus each node had four connections. When running the model, it became evident that defection dominated the game. For cooperation to remain in the game, very strict conditions must be met. As PD in game theory is very basic but structured, it has been used to model a wide range of phenomena in a multitude of disciplines such as stock market changes, bacteria growth, and the decision making of world leaders. The model created in this research is very simple, but with more parameters and variations to the model, we hope to create a more complex system that is capable of modeling such things as social networks as well as take into account socioeconomic factors to model true human cooperation statistics.

In classical electrodynamics, accelerated charges emit electromagnetic radiation. The associated energy loss of the particle can be modeled as a radiation reaction force, proportional to the change in acceleration. Including this force in the usual dynamical equation for a charged particle yields the Abraham-Lorentz-Dirac (ALD) equation. For point particles, solutions to the ALD equation are problematic. First, they require additional initial conditions beyond those needed in regular Newtonian dynamics, but more concerning are the presence of unphysical run-away solutions and acausal trajectories. These problems arise in the point-like limit of the theory, so it is possible that quantum mechanics is the more appropriate framework with which to address the problem. In order to explore the similarities and differences of the classical and quantum frameworks, we compute classical trajectories of charged particles in the presence of a Coulomb field, including radiation reaction. We compare the associated classical cross-section with the quantum field-theoretic cross-section for Coulombic scattering, including radiative corrections. With these calculations, we will be able to assess when the field theoretic formulation of single-photon emission can approximate the classical radiation reaction.

State-Owned Enterprises (SOE) are legal entities either partially or fully owned by the government that undertake commercial activities on behalf of the state. Their legal status, purpose of establishment and missions vary across countries with some becoming tools for countries to better position themselves in the competitive global economy and some to provide public services and ensure distribution of social welfare. In Malaysia, these SOEs are called Government-Linked Companies (GLCs) where the government owns 20% or more of issued or paid-up capital. GLCs not only account for 54% of market capitalization of the Kuala Lumpur Composite Index but also remain as main service providers to the nation in key strategic utilities and services. In 2004, the government of Malaysia introduced the Government-Linked Transformation Program (GLCTP) in response to observing the poor performance of GLCs relative to the broader market on all key financial indicators. It is a 10-year program consisting of 10 Initiatives, most of which aim to elicit better and effective governance through imposition of guidelines and standards supervised and enforced by the Putrajaya Committee on Government-Linked Companies, PCG. With GLCs presence being so abundant and influential, we question the effectiveness of the program which concerns the future of GLCs and non-GLCs in Malaysia. Thus, this paper aims to measure the impact of GLCTP on the financial performance of GLCs (and non-GLCs) by panel data estimation technique. In particular, this project examines the difference in the financial performances of GLCs relative to non-GLCs pre- and post the program after controlling for other confounding variables. Improvements in performances of GLCs compared to that of non-GLCs is expected. If results show statistically significant, the next interesting discussion would then be corporatization over privatization or divestment.

Conservation is a pressing and widely discussed topic. There are many people and organizations involved in the issue, meaning there are many different perspectives and opinions. In his paper “Conservation in the Anthropocene,” Peter Kareiva presents controversial ideas about modern day conservation. Based on my rhetorical analysis of his paper, I argue that he takes advantage of the controversy by presenting his ideas in a purposefully more provocative way than he needs to. In this paper we see him attacking conservation icons and ideals as well as putting forward arguments against currently held ideas in the conservation movement and directly attacking traditional environmentalists. This enrages much of his audience, and through that controversy he brings more attention to his paper and his ideas. This paper analyzes how he uses rhetoric to emphasize the controversial aspect of the ideas he presents in this paper to attract more attention to his argument and to open up a discussion about the issues he presents.

Single electron devices (SEDs) are devices that can isolate individual electrons along a conducting path. SEDs have many proposed applications including their use in metrology, and quantum information science. However, there are many barriers that must be overcome before these applications are realized beyond the proof of concept experiments currently being performed in academic research labs. Our group’s work focuses on pathways to overcoming some of these barriers including the issues with material properties and device stability. My contribution focuses on data analysis of SED transport measurements. These analyses produce various metrics for both the SEDs under test as well as the measurement system probing them. They include determinations of charge offset drift, a metric for long term device stability, as well as electron temperature a limiting factor in magneto spectroscopy measurements.

Every non-negative integer can be written using what is known as the factorial base representation. We define this notion and explore certain combinatorial structures arising from the arithmetic of these representations. In particular, we investigate the sum-of-digits function, carry sequences, and a partial order referred to as digital dominance. Finally, we describe an analog of a classical theorem due to Kummer that relates the combinatorial objects of interest by constructing a variety of new integer sequences. Many of the combinatorial objects we describe are of interest in their own right and provide interesting avenues for future discoveries. For instance, the carry sequences we describe correspond to a new family of integer partitions that are analogous to hyper-binary partitions, which have been extensively studied. Moreover, the digital dominance order most likely contains interesting combinatorial information about the integers as represented in the factorial base. Finally, our analog of Kummer's theorem has helped to explain how the classical version of Kummer's theorem can be altered to fit with almost any positional numeration system.

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!

This research focuses on the mathematics of gerrymandering. Gerrymandering refers to how political parties draw district boundaries to give them better odds at receiving a majority during congressional elections. Every 10 years district boundaries in the United States are redrawn for congressional elections by the current majority party. With such change in political cartography, redrawing district boundaries not only affects who wins but also the people who live within them. Given the loosely defined criteria for redistricting, we seek to quantify the process of redrawing district lines to determine when this partisan process becomes an act of manipulation and exclusion. We will be use The Metropolis Hastings (M.H.) Algorithm to produce a random walk that has a stationary distribution that will be the probability distribution of all possible districting plans for a given U.S state. By collecting congressional maps and election results, we implemented the M.H. algorithm in python to produce sample spaces for Washington State and Iowa. We will simulate local and federal redistricting requirements using self-defined parameters which measure: compactness of districts, population division, division of counties, and minority voter populations. We simulated election results with respect to our sample districts and compared the simulated outcomes with actual district maps and their election results. This study helps to determine if current redrawn maps legitimately reflect the people they purport to represent or if they are manipulations and subversions of our democratic process.

Diophantine equations are polynomial equations with integer coefficients. In 1970, Matiyasevich proved that an algorithm to decide whether a given Diophantine equation has a solution does not exist. We investigated some such equations including Pell and Thue equations, that have an infinite and finite number of solutions, respectively. Geometrically the solution set of Diophantine equations in 2 variables corresponds to plane curves, e.g. elliptic or hyperelliptic curves, and the number of rational solutions is related to the genus of the corresponding curve. We gathered statistics on the size of the solution sets in an attempt to address an important unsolved problem in arithmetic geometry, known as Uniformity Conjecture of Caporaso, Harris and Mazur. Our project involved an analysis of Python and C code, specifically through the CoCalc development platform, utilizing data from the L-functions and Modular Forms Database (LMFDB). Currently our results agree with the current known data on the sizes of solution sets, and we hope to extend our results to gather data on curves not currently in the LMFDB. This will serve as a testing ground for the Uniformity Conjecture.

Augmented reality (AR), which overlays virtual content on top of the user's perception of the real world, is now beginning to enter the consumer market. Besides smartphone platforms, early-stage head-mounted displays such as the Microsoft HoloLens are being actively developed. Many of the most compelling uses of these AR technologies are multi-user: for instance, in-person collaborative tools, multiplayer gaming, and telepresence. Although AR technologies enable new forms of interaction, new security and privacy challenges will also arise when users can augment each other's reality, and it is imperative that these challenges be addressed while the technology is still new and highly malleable. In this work, I explore these emerging challenges in secure and private content sharing for multi-user AR. I systematize design goals for security and functionality that an AR content sharing framework should support, and I design and prototype a framework for the HoloLens that meets these goals. By evaluating my framework against representative application case studies, I show that it meets desired security and functionality goals flexibly across a range of use cases. Preliminary investigations into developer effort suggest that applications' content sharing needs can be achieved in relatively few lines of code. I plan to convert my research prototype into an open-source toolkit so developers can address these challenges in practice. This work opens up directions for future research in how these underlying paradigms should manifest to users in the form of an application's user interface. By building foundations for secure multi-user AR content sharing, my work takes steps toward allowing AR to securely reach its full potential.

 Recently, there seems to be news about blizzards striking East Coast cities nearly every year. However, most reports simply claim that the frequency and intensity of large snowstorms on the East Coast are increasing without providing convincing evidence. Are they telling the truth? We decided to statistically test if the frequency and intensity of large snowstorms in coastal North America have increased in recent years. In our research, we encountered many difficulties during the data collection and cleaning processes. For example, most cities only have records since around 1950 and the Canadian snow data are hard to clean. We first plot frequency of large snowstorms for each city and detected that there is actually a downward trend of snowstorm frequency in coastal North America. To further verify our finding, we also permuted the time-series data and performed permutation tests on the slopes of the linear regression of extreme snowstorm frequencies versus year. In our current progress, the permutation tests suggest that, for all East Coast cities studied, the hypothesized increases in annual frequencies of extreme snowfall are not statistically significant at any reasonable level of significance for looking at exceeding both the 75% and 90% quantiles of annual snowfall. Thus, our current results imply that the frequency of large snowstorms in many East Coast cities has not been increasing in recent years, which is different from the media claims.

Conventional farming techniques involve large quantities of chemical fertilizers, which often leach into bodies of water causing eutrophication. The influx of excess nutrients from fertilizer results in rapid increase of aquatic algal populations followed by dissolved oxygen depletion. This process creates regions of low oxygen that negatively impact the water quality of many major lakes and coastal regions. To address this problem, the sensitivity of plant growth-promoting bacteria (PGPB) to excess fertilizer was investigated. We hypothesize that the addition of high amounts of fertilizer will result in smaller, less productive plants and diminished rhizosphere colonization of the PGPB, Bacillus subtilis. A modified Kirby-Bauer disk diffusion test was performed as an initial assessment of the effect of varied fertilizer concentrations on B. subtilis. Roots of romaine lettuce seedlings were then inoculated with B. subtilis and grown in soil treated with the same range of fertilizer concentrations. The effects of each treatment on plant growth were determined using total leaf area, quantification of the rhizosphere colonization by B. subtilis, and carbon assimilation measured with a LI-6800 Portable Photosynthesis System. These results are an important step towards establishing guidelines for appropriate application of agricultural fertilizer in order to mitigate the frequency and severity of eutrophication events in aquatic systems.

Utilizing protein-based systems, specifically nuclease-dead Cas9 variants, to alter mammalian gene expression is an emergent subfield in synthetic biology. Such methodologies offer means to study a vast diversity of genetic networks including but not limited to cell fate decisions, stem cell differentiation, cell signaling networks, and key genetic players in tumorigenesis. Here, we offer a novel chemical tool for which drug concentration can control gene expression within target cells, by using new chemically induced dimerization systems that can respond to multiple chemical agonists and antagonists. Within our system, we use a protease dead NS3a complex, which functions as a scaffolding complex, and an entirely synthetic protein complex, either a danoprevir-NS3a complex reader (DNCR) or a grazoprevir-NS3a complex reader (GNCR), which specifically bind NS3a only when danoprevir or grazoprevir, respectively, are introduced. Furthermore, nuclease-dead Cas9 offers a means for target sequence specific tethering of nuclear effectors, and may be directed using sgRNAs. The sgRNA sequence may be elongated to allow for a protein specific tethering complex. Here we use an orthogonal scaffold RNA/RNA-binding protein pair (MS2/MCP and PP7/PCP) to localize DNCR (bound to PCP) or GNCR (bound to MCP) to select DNA sequences. The corresponding NS3a complex is fused to enhancer protein VPR, which serves to upregulate gene expression when in sufficiently close proximity. Hence upon drug induction, NS3a-VPR will bind the DNCR-PCP (or GNCR-PCP) complex tethered to dCas9 localized ideally upstream of a target gene, and induce gene expression upon introduction of danoprevir (or grazoprevir). As a direct function of this research, we have demonstrated CID capacity for linearized fold increase of several endogenous and non-endogenous genes in correlation to drug concentration, and now seek to demonstrate the capacity of our tool by studying the concentration-dependence of scaffold function in the JNK pathway.