Well-Posedness and a Finite Difference Approximation for a Mathematical Model of HPV-Induced Cervical Cancer

We present a first-order finite difference scheme for approximating solutions of a mathematical model of cervical cancer induced by the human papillomavirus (HPV), which consists of four nonlinear partial differential equations and a nonlinear first-order ordinary differential equation. The scheme is analyzed and used to provide an existence-uniqueness result. Numerical simulations are performed in order to demonstrate the first-order rate of convergence. A sensitivity analysis was done in order to compare the effects of two drug types, those that increase the death rate of HPV-infected cells, and those that increase the death rate of the precancerous cell population. The model predicts that treatments that affect the precancerous cell population by directly increasing the corresponding death rate are far more effective than those that increase the death rate of HPV-infected cells.

Factors Affecting Students’Plans to Take the CPA Examination

Enrollments in accounting programs and the demand for accounting graduates are increasing,but the number of candidates sitting for the CPA exam is decreasing.This study compares characteristics of students at a mid-size regional university who plan to sit for the CPA exam with those who do not.In addition,reasons offered by students for their plans to take or not take the CPA exam are explored.The study finds that a student’s desired career path,as well as their mother’s educational level,is significantly related to their intention to sit for the exam.Career alignment or misalignments were the primary factors shaping a student’s plan to sit for the CPA exam.The proportion of students intending to sit for the CPA exam decreases with class level,and the majority of students intend to work outside of public accounting.This study will be of interest to the profession and public as the decline in CPA examination candidates coincides with a higher than average percentage of CPAs projected to retire in the next three years.

Colorful facial markings are associated with foraging rates and affiliative relationships in a wild group-living cichlid fish

Many animals use color to signal their quality and/or behavioral motivations.Colorful signals have been well studied in the contexts of competi-tion and mate choice;however,the role of these signals in nonsexual,affiliative relationships is not as well understood.Here,we used wild social groups of the cichlid fish Neolamprologus pulcher to investigate whether the size of a brightly colored facial patch was related to 1)individual quality,2)social dominance,and/or 3)affiliative relationships.Individuals with larger patches spent more time foraging and tended to perform more aggressive acts against conspecific territory intruders.We did not find any evidence that the size of these yellow patches was related to social rank or body size,but dominant males tended to have larger patches than dominant females.Additionally,patch size had a rank-specific relationship with the number of affiliative interactions that individuals engaged in.Dominant males with large patches received fewer affiliative acts from their groupmates compared to dominant males with small patches.However,subordinates with large patches tended to receive more affiliative acts from their groupmates while performing fewer affiliative acts themselves.Taken together,our results suggest that patch size reflects interindividual variation in foraging effort in this cichlid fish and offer some of the first evidence that colorful signals may shape affiliative relationships withinwildsocialgroups.

Group Connectivity and Group Colorings of Graphs -- A Survey

In 1950s, Tutte introduced the theory of nowhere-zero flows as a tool to investigate the coloring problem of maps, together with his most fascinating conjectures on nowhere-zero flows. These have been extended by Jaeger et al. in 1992 to group connectivity, the nonhomogeneous form of nowhere-zero flows. Let G be a 2-edge-connected undirected graph, A be an （additive） abelian group and A＊ = A - {0}. The graph G is A-connected if G has an orientation D（G） such that for every map b ： V（G） → A satisfying ∑v∈V（G）b（v） ： 0, there is a function f ： E（G） → A＊ such that for each vertex v ∈ V（G）, the total amount of f-values on the edges directed out from v minus the total amount of f-values on the edges directed into v is equal to b（v）. The group coloring of a graph arises from the dual concept of group connectivity. There have been lots of investigations on these subjects. This survey provides a summary of researches on group connectivity and group colorings of graphs. It contains the following sections. 1. Nowhere-zero Flows and Group Connectivity of Graphs 2. Complete Families and A-reductions 3. Reductions with Edge-deletions, Vertex-deletions and Vertex-splitting 4. Group Colorings as a Dual Concept of Group Connectivity 5. Brooks Theorem, Its Variations and Dual Forms 6. Planar Graphs 7. Group Connectivity of Graphs 7.1 Highly Connected Graphs and Collapsible Graphs 7.2 Degrees Conditions 7.3 Complementary Graphs 7.4 Products of Graphs 7.5 Graphs with Diameter at Most 2 7.6 Line Graphs and Claw-Free Graphs 7.7 Triangular Graphs 7.8 Claw-decompositions and All Tutte-orientations