Drury K.L.S.,Bethel College at North Newton |
Lodge D.M.,University of Notre Dame
Bulletin of Mathematical Biology | Year: 2012
Perturbations are relatively large shocks to state variables that can drive transitions between stable states, while drift in parameter values gradually alters equilibrium magnitudes. This latter effect can lead to equilibrium bifurcation, the generation, or annihilation of equilibria. Equilibrium annihilations reduce the number of equilibria and so are associated with catastrophic population collapse. We study the combination of perturbations and parameter drift, using a two-species intraguild predation (IGP) model. For example, we use bifurcation analysis to understand how parameter drift affects equilibrium number, showing that both competition and predation rates in this model are bifurcating parameters. We then introduce a stochastic process to model the effects of population perturbations. We demonstrate how to evaluate the joint effects of perturbations and drift using the common currency of mean first passage time to transitions between stable states. Our methods and results are quite general, and for example, can relate to issues in both pest control and sustainable harvest. Our results show that parameter drift (1) does not importantly change the expected time to reach target points within a basin of attraction, but (2) can dramatically change the expected time to shift between basins of attraction, through its effects on equilibrium resilience. © 2012 Society for Mathematical Biology.
Reilly Ayala H.B.,Bethel College at North Newton |
Reilly Ayala H.B.,University of Notre Dame |
Wacker M.A.,University of Notre Dame |
Siwo G.,University of Notre Dame |
Ferdig M.T.,University of Notre Dame
BMC Genomics | Year: 2010
Background: Elevated parasite biomass in the human red blood cells can lead to increased malaria morbidity. The genes and mechanisms regulating growth and development of Plasmodium falciparum through its erythrocytic cycle are not well understood. We previously showed that strains HB3 and Dd2 diverge in their proliferation rates, and here use quantitative trait loci mapping in 34 progeny from a cross between these parent clones along with integrative bioinformatics to identify genetic loci and candidate genes that control divergences in cell cycle duration.Results: Genetic mapping of cell cycle duration revealed a four-locus genetic model, including a major genetic effect on chromosome 12, which accounts for 75% of the inherited phenotype variation. These QTL span 165 genes, the majority of which have no predicted function based on homology. We present a method to systematically prioritize candidate genes using the extensive sequence and transcriptional information available for the parent lines. Putative functions were assigned to the prioritized genes based on protein interaction networks and expression eQTL from our earlier study. DNA metabolism or antigenic variation functional categories were enriched among our prioritized candidate genes. Genes were then analyzed to determine if they interact with cyclins or other proteins known to be involved in the regulation of cell cycle.Conclusions: We show that the divergent proliferation rate between a drug resistant and drug sensitive parent clone is under genetic regulation and is segregating as a complex trait in 34 progeny. We map a major locus along with additional secondary effects, and use the wealth of genome data to identify key candidate genes. Of particular interest are a nucleosome assembly protein (PFL0185c), a Zinc finger transcription factor (PFL0465c) both on chromosome 12 and a ribosomal protein L7Ae-related on chromosome 4 (PFD0960c). © 2010 Reilly Ayala et al; licensee BioMed Central Ltd.
Engbers J.,Marquette University |
Hammett A.,Bethel College at North Newton
Electronic Journal of Combinatorics | Year: 2014
The lattice of monotone triangles (Mn, ≤) ordered by entry-wise comparisons is studied. Let τmin denote the unique minimal element in this lattice, and τmax the unique maximum. The number of r-tuples of monotone triangles (τ1,..., τr) with minimal infimum τmin (maximal supremum τmax, resp.) is shown to asymptotically approach r|Mn|r-1 as n→∞. Thus, with high probability this event implies that one of theτi is τmin (τmax, resp.). Higher-order error terms are also discussed.
Davis J.M.,Baylor University |
Gravagne I.A.,Baylor University |
Marks II R.J.,Baylor University |
Ramos A.A.,Bethel College at North Newton
Proceedings of the Annual Southeastern Symposium on System Theory | Year: 2010
We revisit the canonical continuous-time and discrete-time matrix algebraic and matrix differential equations that play a central role in Lyapunov-based stability arguments. The goal is to generalize and extend these types of equations and subsequent analysis to dynamical systems on domains other than ℝ or ℤ, called "time scales", e.g. nonuniform discrete domains or domains consisting of a mixture of discrete and continuous components. In particular, we compare and contrast a generalization of the algebraic Lyapunov equation and the dynamic Lyapunov equation in this time scales setting. © IEEE 2010.
Abraham S.,Bethel College at North Newton
Health Care Manager | Year: 2016
Patient falls in the hospital psychiatric inpatient units are more frequent than in the medical-surgical units. The purpose of this study was to explore psychiatric unit directors' perceptions of the factors that contribute to patient falls in the State of Michigan. A quantitative online questionnaire was sent to the directors of psychiatric units in Michigan. Two research questions (RQs) guided the study: (a) What are psychiatric unit directors' perceptions of the possible intrinsic factors that contribute to patient falls in the psychiatric inpatient units, and (b) what are psychiatric unit directors' perceptions of the possible extrinsic factors that contribute to patient falls in the psychiatric inpatient units? In comparing the results, 6 of the 7 factors with the highest mean levels of agreement were intrinsic factors. In the current study, patient gait (mean, 4.65) ranked first, history of falls (mean, 4.52) second, and multiple medications (mean, 4.50) third as fall-risk factors. The need for the involvement of the team members (mean, 4.55) in preventing falls was the most highly rated factor among the extrinsic factors. Educating unit team members in assisting with fall prevention is a critical consideration for leaders. © 2016 Wolters Kluwer Health, Inc.