Hip Hop Hermeneutics: How the Culture Influences Preachers

Hip Hop Hermeneutics essay lays out findings of current research into how Hip Hop culture has been formational for African American preachers, and how that culture informs their preaching. There is a generation of preachers leading congregations today that have grown up with Hip Hop. Hip Hop culture has left an indelible mark upon them; just as the church has. How does the cultural influence of Hip Hop affect their preaching? Hip Hop hermeneutics is the response put forth by this article. This article traces the practice and theology of early African American preachers, the work of James Cone in Black Liberation theology, and Womanist theologians to demonstrate how Black theology has always included the Black experience as part of its theological norm. The article then posits that the next generation of Black theology must take into account that Hip Hop is also part of that Black experience, before going on to delineate a Hip Hop hermeneutic. A Hip Hop hermeneutic is a particular way of reading scripture that embraces the honest and raw fullness of the Black experience

Minimizing the number of independent sets in triangle-free regular graphs

Recently, Davies, Jenssen, Perkins, and Roberts gave a very nice proof of the result (due, in various parts, to Kahn, Galvin-Tetali, and Zhao) that the independence polynomial of a $d$-regular graph is maximized by disjoint copies of $K_{d,d}$. Their proof uses linear programming bounds on the distribution of a cleverly chosen random variable. In this paper, we use this method to give lower bounds on the independence polynomial of regular graphs. We also give new bounds on the number of independent sets in triangle-free regular graphs

Counting dominating sets and related structures in graphs

We consider some problems concerning the maximum number of (strong) dominating sets in a regular graph, and their weighted analogues. Our primary tool is Shearer's entropy lemma. These techniques extend to a reasonably broad class of graph parameters enumerating vertex colorings satisfying conditions on the multiset of colors appearing in (closed) neighborhoods. We also generalize further to enumeration problems for what we call existence homomorphisms. Here our results are substantially less complete, though we do solve some natural problems

Vertex Isoperimetric Inequalities for a Family of Graphs on Z^k

We consider the family of graphs whose vertex set is Z^k where two vertices are connected by an edge when their l\infty-distance is 1. We prove the optimal vertex isoperimetric inequality for this family of graphs. That is, given a positive integer n, we find a set A \subset Z^k of size n such that the number of vertices who share an edge with some vertex in A is minimized. These sets of minimal boundary are nested, and the proof uses the technique of compression. We also show a method of calculating the vertex boundary for certain subsets in this family of graphs. This calculation and the isoperimetric inequality allow us to indirectly find the sets which minimize the function calculating the boundary.Comment: 19 pages, 2 figure

Natural Enemies of Alfalfa Weevil, \u3ci\u3eHypera Postica\u3c/i\u3e (Coleoptera: Curculionidae), in Minnesota

Alfalfa weevil, Hypera postica, is present throughout Minnesota. How- ever, economically damaging populations seldom occur, due to a combination of natural enemies and adverse climatic conditions. Five natural enemies of alfalfa weevil were found in Minnesota. Microctonus aethiopoides (Hymenoptera: Braconidae), a parasitoid of adults, was recovered from 43 of 65 counties surveyed during 1984 and 1985. Tetrastichus incertus (Hymenoptera: Eulophidae) and Bathyplectes curculionis (Hymenoptera: Ichneumonidae), para­sitoids of larvae, were each recovered from 13 of 15 counties surveyed during 1991-1993. Bathyplectes anurus, another parasitoid of larvae, was recovered from one county In 1991, four counties in 1992, and six counties in 1993. Zoophthora phytonomi (Entomophthora: Entomophthoraceae), a pathogen of larvae, was recovered from 14 of 15 counties surveyed in 1991-1993. Winters with low minimum temperatures and little snow cover were detrimental to the weevil. Usually, southeastern Minnesota has milder winters and higher alfalfa weevil populations than other areas of the State. However, even here, because of natural enemies, weevil populations seldom reach economically damaging levels

Supersaturation for subgraph counts

The classic extremal problem is that of computing the maximum number of edges in an $F$-free graph. In the case where $F=K_{r+1}$, the extremal number was determined by Tur\'an. Later results, known as supersaturation theorems, proved that in a graph containing more edges than the extremal number, there must also be many copies of $K_{r+1}$. Alon and Shikhelman introduced a broader class of problems asking for the maximum number of copies of a graph $T$ in an $F$-free graph. In this paper, we determine some of these generalized extremal numbers and prove supersaturation results for them