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Volume 41 - Issue 2 - December 2016
• Telescoping sums, permutations, and first occurrence distributions
Anant Godbole, Jie Hao
Telescoping sums very naturally lead to probability distributions on Z+. But are these distributions typically cosmetic and devoid of motivation? In this paper we give three examples of `first occurrence' distributions, each defined by telescoping sums, and each arising from concrete questions about the structure of permutations.
• Examples of zero correlation not implying independence
S. Nadarajah, Y. Zhang
A review of known distributions of (X, Y) is given, where the zero correlation between X and Y does not imply independence. The review may be helpful for teachers and students.
• Settling the waters: exploring an iterative integration technique
Kristin Dettmers, Jennifer Switkes
We explore an iterative integration technique called sledge-hammer integration. This method, first introduced in Ahner (2009), repeatedly `flattens' the integrand in an area-preserving way. We expand upon Ahner's work by extending the method to double integrals and investigate two specific examples.
• Balls in cells and Markov chains
In this paper we are concerned with the relationship between occupancy problems and the Poisson distribution with reference to Markov chains. A Markov chain for an occupancy problem arising in statistical physics is modified for application to a problem in demography with reference to the distribution of household size. A possible application of the original chain from physics to Markov chain Monte Carlo simulation of households is proposed.
• Combinatorial models for tribonacci polynomials
We present two combinatorial models for tribonacci polynomials, and use one of them to extract some tribonacci delights. We then exhibit a bijection between the two models.
• Kolmogorov equations applied to an SIS-coupled epidemiological
Mayteé Cruz-Aponte, Stephen Wirkus
Mathematical modeling of infectious diseases is necessary to study patterns of transmission and propagation that can potentially help public health officials to make better decisions to mitigate epidemic outbreaks. Both discrete and continuous population models can give insight into the approximations of the modeling approaches we implement. Metapopulation models in which we examine disease dynamics on separate patches and allow movement of the population between the patches have become increasingly popular to model the spread of diseases over geographically distinct regions. We use the forward Kolmogorov equations and present a formal proof that states that the deterministic model is in fact the expected value of the continuous-time Markov chain stochastic model trials. We show the connection between both modeling approaches in an SIS metapopulation model. We present the results of simulations to illustrate the results for different values of R0 , the basic reproductive number.
• Density-dependent Leslie matrix modeling for logistic populations with
steady-state distribution control
Andrew Davis, Bruce Kessler
The Leslie matrix model allows for the discrete modeling of population age groups whose total population grows exponentially. Many attempts have been made to adapt this model to a logistic model with a carrying capacity (see Allen (1989), Jensen (1995), Leslie (1948), (1959), and Liu and Cohen (1987)), with mixed results. In this paper we provide a new model for logistic populations that tracks age-group populations with repeated multiplication of a density-dependent matrix constructed from an original Leslie matrix, the chosen carrying capacity of the model, and the desired steady-state age-group distribution. The total populations from the model converge to a discrete logistic model with the same initial population and carrying capacity, and growth rate equal to the dominant eigenvalue of the Leslie matrix minus 1.
• Models for the spread of Chlamydia
J. Gani, R. J. Swift
We consider deterministic and stochastic models for the spread of Chlamydia in a closed population. Explicit solutions for an approximate model, as well in terms of Laplace transforms for the exact model are presented.
• Letter to the Editor: An identity involving the fourth central moment
R. Sharma, R. Saini
• Index to Volume 41