The Gauss center research in multiscale scientific computation.
The generalized Turner-Bradley-Kirk-Pruitt equation.
The Geometric and Dynamic Essence of Phyllotaxis
We present a dynamic geometric model of phyllotaxis based on two postulates, primordia formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate are all variations of the same unifying phenomenon and that the difference lies in the changes in position of initial primordia. We explore the set of all initial positions and color-code its points depending on the phyllotactic pattern that arises.
The HPV vaccination strategy: could male vaccination have a significant impact?
The Immune System – Complexity Exemplified
The Importance of Spatial Distribution of Stemness and Proliferation State in Determining Tumor Radioresponse
Tumor growth and progression is a complex phenomenon dependent on the interaction of multiple intrinsic and extrinsic factors. Necessary for tumor development is a small subpopulation of potent cells, so-called cancer stem cells, that can undergo an unlimited number of cell divisions and which are proposed to divide symmetrically with a small probability to produce more cancer stem cells. We show that the majority of cells in a tumor must indeed be non-stem cancer cells with limited life span and...
The Influence of Look-Ahead on the Error Rate of Transcription
In this paper we study the error rate of RNA synthesis in the look-ahead model for the random walk of RNA polymerase along DNA during transcription. The model’s central assumption is the existence of a window of activity in which ribonucleoside triphosphates (rNTPs) bind reversibly to the template DNA strand before being hydrolyzed and linked covalently to the nascent RNA chain. An unknown, but important, integer parameter of this model is the window...
The influence of symmetry on the probability of assembly pathways for icosahedral viral shells.
The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology
We discuss theoretical and experimental approaches to three distinct developmental systems that illustrate how theory can influence experimental work and vice-versa. The chosen systems – Drosophila melanogaster, bacterial pattern formation, and pigmentation patterns – illustrate the fundamental physical processes of signaling, growth and cell division, and cell movement involved in pattern formation and development. These systems exemplify the current state of theoretical and experimental understanding...
The Kneser property for abstract retarded functional differential equations with infinite delay.
The Language of Caring: Quantitating Medical Practice Patterns using Symbolic Dynamics
Real-world medical decisions rarely involve binary Ðsole condition present or absent- patterns of patient pathophysiology. Similarly, provider interventions are rarely unitary in nature: the clinician often undertakes multiple interventions simultaneously. Conventional approaches towards complex physiologic derangements and their associated management focus on the frequencies of joint appearances, treating the individual derangements of physiology...
The non-uniform spatial development of a micrometastasis.
The number of -matchings in almost every tree is a zero residue.
The onset of necrosis in a 3D cellular automaton model of EMT6 multi-cellular spheroids
A 3-dimensional (3D) extension to a previously reported scaled 2-dimensional Cellular Automaton (CA) model of avascular multi-cellular spheroid growth is presented and analysed for the EMT6/Ro cell line. The model outputs are found to compare favourably with reported experimentally obtained data for in vitro spheroids of the same cell line. Necrosis (unprogrammed central cell death) is observed to be delayed when compared with the experimental data. Furthermore, it is found that necrosis arises...
The optimal shape of a dendrite sealed at both ends
The p and the Peas: An Intuitive Modeling Approach to Hypothesis Testing
We propose a novel approach to introducing hypothesis testing into the biology curriculum. Instead of telling students the hypothesis and what kind of data to collect followed by a rigid recipe of testing the hypothesis with a given test statistic, we ask students to develop a hypothesis and a mathematical model that describes the null hypothesis. Simulation of the model under the null hypothesis allows students to compare their experimental data...
The pattern of genetic hitchhiking under recurrent mutation.
The periods of the Volterra-Lotka system.
The permanence and extinction of a discrete predator-prey system with time delay and feedback controls.
The permanence in a single species nonautonomous system with delays and feedback control.