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We give an introduction to seriation techniques and apply such techniques to the North American folklore tale known as the Star Husband Tale. In particular, a spectral algorithm with imposed clustering is applied, with significant results that support the algorithm’s effectiveness.
Malaria, an infectious disease prevalent in sub-Saharan Africa, is transmitted to humans through mosquito bites, and ordinary differential equation models have often been used to describe the spread of the disease. A basic agent-based model (ABM) of malaria transmission is established and compared to an ODE model of the disease in order to ascertain the similarity of the ABM to typical modeling approaches. Additionally, the ABM is described using protocol from current literature. In order to illustrate the flexibility of the ABM, the basic ABM is modified to incorporate the use of insecticide-treated bed nets (ITNs) and the effect of acquired immunity. The simulations incorporating acquired immunity and the use of ITNs show a decrease in the prevalence of the disease due to these factors. Additionally, the ABM can easily be modified to account for other complicated issues affecting malaria spread.
We present a simple tile-sliding game that can be played on any 3-regular graph, generating a permutation group on the vertices. We classify the resulting permutation groups and obtain a novel presentation for the simple group of 168 elements.
We consider the difference between the definite integral , where is a real parameter, and the approximating sum . We use properties of Bernoulli numbers to show that this difference is unbounded and has infinitely many zeros. We also conjecture that the sign of the difference at any positive integer is determined by the sign of .
Let be positive integers with . For nonsymmetric, we give an alternative description, using elementary techniques, of a minimal presentation of its homogenization . As a consequence, we show that this minimal presentation is unique. We recover Bresinsky’s characterization of the Cohen–Macaulay property of and present a procedure to compute all possible catenary degrees of the elements of .
We introduce the epidemic quasimetric on graphs and study its behavior with respect to clustering techniques. In particular we compare its behavior to known objects such as the graph distance, effective resistance, and modulus of curve families.