Cyclically five-connected cubic graphs

A cubic graph $G$ is cyclically 5-connected if $G$ is simple, 3-connected, has at least 10 vertices and for every set $F$ of edges of size at most four, at most one component of $G\backslash F$ contains circuits. We prove that if $G$ and $H$ are cyclically 5-connected cubic graphs and $H$ topologically contains $G$, then either $G$ and $H$ are isomorphic, or (modulo well-described exceptions) there exists a cyclically 5-connected cubic graph $G'$ such that $H$ topologically contains $G'$ and $G'$ is obtained from $G$ in one of the following two ways. Either $G'$ is obtained from $G$ by subdividing two distinct edges of $G$ and joining the two new vertices by an edge, or $G'$ is obtained from $G$ by subdividing each edge of a circuit of length five and joining the new vertices by a matching to a new circuit of length five disjoint from $G$ in such a way that the cyclic orders of the two circuits agree. We prove a companion result, where by slightly increasing the connectivity of $H$ we are able to eliminate the second construction. We also prove versions of both of these results when $G$ is almost cyclically 5-connected in the sense that it satisfies the definition except for 4-edge cuts such that one side is a circuit of length four. In this case $G'$ is required to be almost cyclically 5-connected and to have fewer circuits of length four than $G$. In particular, if $G$ has at most one circuit of length four, then $G'$ is required to be cyclically 5-connected. However, in this more general setting the operations describing the possible graphs $G'$ are more complicated.Comment: 47 pages, 5 figures. Revised according to referee's comments. To appear in J. Combin. Theory Ser.

Connectivity of pseudomanifold graphs from an algebraic point of view

The connectivity of graphs of simplicial and polytopal complexes is a classical subject going back at least to Steinitz, and the topic has since been studied by many authors, including Balinski, Barnette, Athanasiadis and Bjorner. In this note, we provide a unifying approach which allows us to obtain more general results. Moreover, we provide a relation to commutative algebra by relating connectivity problems to graded Betti numbers of the associated Stanley--Reisner rings.Comment: 4 pages, minor change

The width of 5-dimensional prismatoids

Santos' construction of counter-examples to the Hirsch Conjecture (2012) is based on the existence of prismatoids of dimension d of width greater than d. Santos, Stephen and Thomas (2012) have shown that this cannot occur in $d \le 4$. Motivated by this we here study the width of 5-dimensional prismatoids, obtaining the following results: - There are 5-prismatoids of width six with only 25 vertices, versus the 48 vertices in Santos' original construction. This leads to non-Hirsch polytopes of dimension 20, rather than the original dimension 43. - There are 5-prismatoids with $n$ vertices and width $\Omega(\sqrt{n})$ for arbitrarily large $n$. Hence, the width of 5-prismatoids is unbounded.Comment: 31 pages, 10 figures. Changes from v1: the introduction has been edited, and a minor correction made in the statement of Proposition 1.

Untangling polygons and graphs

Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C_n while keeping at least \Omega(n^{2/3}) vertices fixed. For any graph G, we also present an upper bound on the number of fixed vertices in the worst case. The bound is a function of the number of vertices, maximum degree and diameter of G. One of its consequences is the upper bound O((n log n)^{2/3}) for all 3-vertex-connected planar graphs.Comment: 11 pages, 3 figure

Type I Error Of Four Pairwise Mean Comparison Procedures Conducted As Protected And Unprotected Tests

Type I error control accuracy of four commonly used pairwise mean comparison procedures, conducted as protected or unprotected tests, is examined. If error control philosophy is experimentwise, Tukey’s HSD, as an unprotected test, is most accurate and if philosophy is per-experiment, Dunn-Bonferroni, conducted as an unprotected test, is most accurate

Irreducible triangulations of surfaces with boundary

A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of vertices of an irreducible triangulation of a (possibly non-orientable) surface of genus g>=0 with b>=0 boundaries is O(g+b). So far, the result was known only for surfaces without boundary (b=0). While our technique yields a worse constant in the O(.) notation, the present proof is elementary, and simpler than the previous ones in the case of surfaces without boundary

Designing an Evidence Based Medicine Resource Page to Help Student Pharmacists

This is an unpublished manuscript of the background research for a poster presented at the 2015 ACCP Global Conference on Clinical Pharmacy.Objectives: Develop an online Evidence Based Medicine (EBM) resource page to improve student utilization of EBM. Evaluate potential clinical and educational benefit of resource page by college faculty. Identify perceptions of P4 student EBM skill level. Methods: EBM related literature and resources were reviewed to create an online resource page. Surveys were distributed to pharmacy faculty assessing perceptions of EBM knowledge and skill of P4 students, overall usefulness of the resource page, and demographics. Constructs were evaluated using a 5-point Likert scale. Results: The EBM resource page was available university wide summer 2015. The resource page was viewed positively by all respondents (n=12) for its overall description of EBM principles, identification of useful resources, potential clinical and educational value. Only 17% of faculty respondents agreed that students were familiar with EBM focused resources. The majority (10 of 11, 83%) of faculty agreed or strongly agreed that students could benefit from more training in applying EBM to patient care. Conclusions: The development of an EBM resource page is an initial step to improve the knowledge and utilization of EBM by pharmacy students by providing a place to search EBM focused resources

A Prospective Analysis of Pharmacists Integration in the Patient-Centered Medical Home: Preparing for Value-Based Care

This is an unpublished manuscript of research completed in several patient centered medical homes that provide pharmacy services; presented at the 2016 American Pharmacists Association annual meeting in Baltimore, MD.Objective: The purpose of this project was to describe pharmacy services in a patient-centered medical home to demonstrate pharmacists’ involvement in the evolving delivery of primary care. Design: This was a prospective, qualitative study. Setting and Participants: This project analyzed the work of eight pharmacists employed at a National Committee for Quality Assurance tier III patient-centered medical home associated with a large, academic medical center. Outcome Measures: The primary outcome was to identify and quantify the types of services completed by pharmacists in a patient-centered medical home. Secondary outcomes included determining the percentage of pharmacist recommendations accepted by providers and patients, the percentage of pharmacist interventions submitted for third-party reimbursement, and the average time spent per encounter. Results: Eight pharmacists (representing 4.0 full-time equivalents) facilitated 581 encounters over 20 days. Mean time spent per encounter was 20 minutes (± 19). The most common types of encounters were interdisciplinary visits (31.8%) and phone/secure portal communication (30.0%). Of 918 pharmacist recommendations made to providers, 830 (90.4%) were accepted and implemented. Of 412 pharmacist recommendations made to patients, 393 (95.4%) were verbally accepted. Thirty-nine percent of encounters were eligible for direct payor billing. Conclusion: Our data show that pharmacists working in a patient-centered medical home are effectively integrated within the evolving delivery of primary care. Consistent inclusion of pharmacy services should be readily supported in future models of health care reform