On distinguishing trees by their chromatic symmetric functions

Let $T$ be an unrooted tree. The \emph{chromatic symmetric function} $X_T$, introduced by Stanley, is a sum of monomial symmetric functions corresponding to proper colorings of $T$. The \emph{subtree polynomial} $S_T$, first considered under a different name by Chaudhary and Gordon, is the bivariate generating function for subtrees of $T$ by their numbers of edges and leaves. We prove that $S_T =$, where $$ is the Hall inner product on symmetric functions and $\Phi$ is a certain symmetric function that does not depend on $T$. Thus the chromatic symmetric function is a stronger isomorphism invariant than the subtree polynomial. As a corollary, the path and degree sequences of a tree can be obtained from its chromatic symmetric function. As another application, we exhibit two infinite families of trees (\emph{spiders} and some \emph{caterpillars}), and one family of unicyclic graphs (\emph{squids}) whose members are determined completely by their chromatic symmetric functions.Comment: 16 pages, 3 figures. Added references [2], [13], and [15

Elective Course Choice as a Factor in K12 Graduation Rates

This paper explores the relationship that elective course offerings and requirements have on student success through graduation rates. The purpose of this study is to better understand the effect that elective courses have on a student’s academic success. This research focused on the Big 9 conference of southeastern Minnesota Public High Schools, which consisted of nine different school districts. These districts paralleled the makeup and diversity of districts around the state. All data reviewed was public information and included resources such as the Minnesota Department of Education’s Report Card database, and course catalogs from each district in the study. Graduation rates from 2017-19 were compared to the amount of elective courses required to graduate, as well as the amount of elective courses offered in each district. Data was compared through the Pearson correlation coefficient. Results indicated little to no correlation between the number of elective courses offered and graduation rates. A moderate positive correlation was seen between the required number of elective credits to graduate in comparison to graduation rates. This research has concluded that increasing the number of electives required for graduation would have a positive relationship to student success through improved graduation rates. The number of elective courses to select from however does not strongly influence student success. Implications for school leaders and state legislators include the importance of a stronger consideration of elective courses for future cohorts of Minnesota High School students through improved funding and graduation requirements

The Dynamics of Vote Buying in Developing Democracies: Party Attachment and Party Competition in Southeast Asia

Broadly defined, what factors explain changes in party competition in developing democracies? The dominant theoretical paradigm used to explain changes in party competition in established democracies does not offer much leverage in emerging ones. The literature argues that linkages between voting blocs and parties erode and cleavages shift, allowing for new voter blocs or even new parties. However, if social groups, parties, and party systems are different in emerging democracies than in established ones, does this mean the dynamics of party competition are also different? Also, what does is the role of voters in these systems? My dissertation outlines a theory for how changes in competition occur. Over time, voters form partisan attachments to parties based upon what parties say and do. Using extensive fieldwork my dissertation maps the broad contours of clientelism in Malaysia. I demonstrate that clientelism, as part of the party brand, has been a significant part of the electoral strategy for Malaysia’s longstanding dominant coalition. Nonetheless, in recent years programmatic platforms of opposition parties have become more popular, culminating in a substantial decline of Malaysia’s longstanding ruling coalition in the 2018 elections. This finding challenges much of the existing literature, which treats Malaysia as a case where ethnic political parties are the driving force behind electoral politics. However, in failing to account for clientelism and the way it is changing, this literature misses a major factor driving party competition. This has broad implications for democracy in Malaysia

Using WebCT as a course supplement to facilitate a learner-centered environment : a case study of a communication technology course

Although online technologies are often seen as channels through which entire courses could be delivered, in fact online technologies are more commonly used as supplements to the classroom. This study examined this supplementary use of one online technology-WebCT, in a manner consistent with the learner-centered principles. Pre- and post-surveys were administered to students in a communication technology class in fall, 2001, to measure comfort with online technologies, attitudes toward traditional and online learning and motivation. In addition, the relationship between the course instructor and instructional designer was examined. Using the discussion tool, students took ownership of their learning, selecting topics for study and team presentations. The post-class survey indicated that students felt very positive about this learner-centered approach. Survey results showed that most students in the class were already comfortable with use of computers for learning. However, many had not used the communication tools such as chat and discussion in a classroom environment. Student enjoyment with using online technologies increased significantly after using these technologies. Results also indicate that students in general like both online and traditional classroom learning approaches, rather than having a strong preference for one or the other. Interviews with the instructor and instructional designer indicate that to be effective, early course assignments should require use of online tools rather than assuming that students will use them automatically. In addition, the instructor should clearly indicate how both face-to-face and online supplements should be used and how they fit into the overall course plan

Secure blockchains for cyber-physical systems

“Blockchains are a data structure used to perform state agreement in a distributed system across an entire network. One unique trait of blockchains is the lack of a centralized trusted third-party to control the system. This prevents a corrupted trusted third party from being able to control the entire blockchain. All nodes can reach agreement in an untrusted network where nodes do not need to trust one another to believe the accuracy of the information stored. Two main issues occur when trying to apply this technology to other applications: verifiability and scalability. In previous blockchain architectures, there is no way to validate off-chain data i.e. sensor reading. Some have purposed the use of a trusted third-party. Unfortunately, using a trusted third-party undoes a main advantage of blockchains and allows corruption to become a concerning possibility. Other challenges to applying blockchains to cyber-physical systems include keeping a single ledger up-to-date in real-time. The drawbacks of Bitcoin, a popular application of blockchains, have been very well documented in terms of speed. The main purpose of this work is to address the verifiability and scalability issues of blockchains for cyber-physical systems. It proposes a solution that expands the application of blockchains to cyber-physical systems while maintaining the benefits. If the use of blockchains is to be expanded to off-chain data, they need to have the capability to securely encapsulate the physical world in a verifiable way. The following is a list of major contributions by the work: 1) propose a framework for verifying physical transactions in a blockchain, 2) propose a method to increase scalability and allow the use of blockchains in a disconnected network, 3) propose a truncation mechanism for cyber-physical transactions that allow for real-time speed. With these three contributions, this work introduces some additional ideas to blockchains and expands their applications”--Abstract, page iii

Controlled topological transitions in thin film phase separation

In this paper the evolution of a binary mixture in a thin-film geometry with a wall at the top and bottom is considered. By bringing the mixture into its miscibility gap so that no spinodal decomposition occurs in the bulk, a slight energetic bias of the walls towards each one of the constituents ensures the nucleation of thin boundary layers that grow until the constituents have moved into one of the two layers. These layers are separated by an interfacial region where the composition changes rapidly. Conditions that ensure the separation into two layers with a thin interfacial region are investigated based on a phase-field model. Using matched asymptotic expansions a corresponding sharp-interface problem for the location of the interface is established. It is then argued that this newly created two-layer system is not at its energetic minimum but destabilizes into a controlled self-replicating pattern of trapezoidal vertical stripes by minimizing the interfacial energy between the phases while conserving their area. A quantitative analysis of this mechanism is carried out via a thin-film model for the free interfaces, which is derived asymptotically from the sharp-interface model.Comment: Submitted 23/12/201

Search for Gamma-ray Emission from Dark Matter Annihilation in the Small Magellanic Cloud with the Fermi Large Area Telescope

The Small Magellanic Cloud (SMC) is the second-largest satellite galaxy of the Milky Way and is only 60 kpc away. As a nearby, massive, and dense object with relatively low astrophysical backgrounds, it is a natural target for dark matter indirect detection searches. In this work, we use six years of Pass 8 data from the Fermi Large Area Telescope to search for gamma-ray signals of dark matter annihilation in the SMC. Using data-driven fits to the gamma-ray backgrounds, and a combination of N-body simulations and direct measurements of rotation curves to estimate the SMC DM density profile, we found that the SMC was well described by standard astrophysical sources, and no signal from dark matter annihilation was detected. We set conservative upper limits on the dark matter annihilation cross section. These constraints are in agreement with stronger constraints set by searches in the Large Magellanic Cloud and approach the canonical thermal relic cross section at dark matter masses lower than 10 GeV in the $b\bar{b}$ and $\tau^+\tau^-$ channels.Comment: 17 pages, 11 figures. Accepted by PR