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

The Bubonic Plague

The bubonic plague is a very serious infectious disease caused by the bacterium Yersinia pestis. The plague is a zoonotic disease, which means it is usually transmitted to humans by animals. It is commonly transmitted through the bites of infected fleas or coming in direct contact with infected animal tissue (Schoenstadt, 2006). The bacterium can be found in fleas or small rodents such as chipmunks, squirrels, rats, or prairie dogs. The symptoms, including fever, chills, headache, and hemorrhages under the skin causing discoloration, are very harsh and unpleasant. This disease is infectious and extremely severe, and it is deadly if not treated properly and promptly (CDC, 2012)

On distinguishing trees by their chromatic symmetric functions

This is the author's accepted manuscript

Software Verification of Orion Cockpit Displays

NASA's latest spacecraft Orion is in the development process of taking humans deeper into space. Orion is equipped with three main displays to monitor and control the spacecraft. To ensure the software behind the glass displays operates without faults, rigorous testing is needed. To conduct such testing, the Rapid Prototyping Lab at NASA's Johnson Space Center along with the University of Texas at Tyler employed a software verification tool, EggPlant Functional by TestPlant. It is an image based test automation tool that allows users to create scripts to verify the functionality within a program. A set of edge key framework and Common EggPlant Functions were developed to enable creation of scripts in an efficient fashion. This framework standardized the way to code and to simulate user inputs in the verification process. Moreover, the Common EggPlant Functions can be used repeatedly in verification of different displays