Portrait of Professor Breidenbaugh

People often do not see what is right in front of them; objects that are passed by everyday are often unnoticed. People are not necessarily unobservant, but are probably more absorbed with their own activities. One object that is hidden in plain sight on the Gettysburg College campus is the portrait of Professor Edward S. Breidenbaugh that hangs in the Science Center. The name Breidenbaugh is commonly known amongst the students at Gettysburg because of the building in his name, Breidenbaugh Hall. However, the history behind Breidenbaugh and his portrait is not as commonly known as the name, but is important in understanding his influence at Gettysburg College. [excerpt] Course Information: Course Title: HIST 300: Historical Method Academic Term: Fall 2006 Course Instructor: Dr. Michael J. Birkner \u2772 Hidden in Plain Sight is a collection of student papers on objects that are hidden in plain sight around the Gettysburg College campus. Topics range from the Glatfelter Hall gargoyles to the statue of Eisenhower and from historical markers to athletic accomplishments. You can download the paper in pdf format and click View Photo to see the image in greater detail.https://cupola.gettysburg.edu/hiddenpapers/1013/thumbnail.jp

The hitting time of rainbow connection number two

In a graph $G$ with a given edge colouring, a rainbow path is a path all of whose edges have distinct colours. The minimum number of colours required to colour the edges of $G$ so that every pair of vertices is joined by at least one rainbow path is called the rainbow connection number $rc(G)$ of the graph $G$. For any graph $G$, $rc(G) \ge diam(G)$. We will show that for the Erd\H{o}s-R\'enyi random graph $G(n,p)$ close to the diameter 2 threshold, with high probability if $diam(G)=2$ then $rc(G)=2$. In fact, further strengthening this result, we will show that in the random graph process, with high probability the hitting times of diameter 2 and of rainbow connection number 2 coincide.Comment: 16 pages, 2 figure

On the threshold for rainbow connection number r in random graphs

We call an edge colouring of a graph G a rainbow colouring if every pair of vertices is joined by a rainbow path, i.e., a path where no two edges have the same colour. The minimum number of colours required for a rainbow colouring of the edges of G is called the rainbow connection number (or rainbow connectivity) rc(G) of G. We investigate sharp thresholds in the Erd\H{o}s-R\'enyi random graph for the property "rc(G) <= r" where r is a fixed integer. It is known that for r=2, rainbow connection number 2 and diameter 2 happen essentially at the same time in random graphs. For r >= 3, we conjecture that this is not the case, propose an alternative threshold, and prove that this is an upper bound for the threshold for rainbow connection number r.Comment: 16 pages, 2 figure

Detecting and Refactoring Operational Smells within the Domain Name System

The Domain Name System (DNS) is one of the most important components of the Internet infrastructure. DNS relies on a delegation-based architecture, where resolution of names to their IP addresses requires resolving the names of the servers responsible for those names. The recursive structures of the inter dependencies that exist between name servers associated with each zone are called dependency graphs. System administrators' operational decisions have far reaching effects on the DNSs qualities. They need to be soundly made to create a balance between the availability, security and resilience of the system. We utilize dependency graphs to identify, detect and catalogue operational bad smells. Our method deals with smells on a high-level of abstraction using a consistent taxonomy and reusable vocabulary, defined by a DNS Operational Model. The method will be used to build a diagnostic advisory tool that will detect configuration changes that might decrease the robustness or security posture of domain names before they become into production.Comment: In Proceedings GaM 2015, arXiv:1504.0244