27,391 research outputs found
Implementing vertex dynamics models of cell populations in biology within a consistent computational framework
The dynamic behaviour of epithelial cell sheets plays a central role during development, growth, disease and wound healing. These processes occur as a result of cell adhesion, migration, division, differentiation and death, and involve multiple processes acting at the cellular and molecular level. Computational models offer a useful means by which to investigate and test hypotheses about these processes, and have played a key role in the study of cell–cell interactions. However, the necessarily complex nature of such models means that it is difficult to make accurate comparison between different models, since it is often impossible to distinguish between differences in behaviour that are due to the underlying model assumptions, and those due to differences in the in silico implementation of the model. In this work, an approach is described for the implementation of vertex dynamics models, a discrete approach that represents each cell by a polygon (or polyhedron) whose vertices may move in response to forces. The implementation is undertaken in a consistent manner within a single open source computational framework, Chaste, which comprises fully tested, industrial-grade software that has been developed using an agile approach. This framework allows one to easily change assumptions regarding force generation and cell rearrangement processes within these models. The versatility and generality of this framework is illustrated using a number of biological examples. In each case we provide full details of all technical aspects of our model implementations, and in some cases provide extensions to make the models more generally applicable
On Rearrangement of Items Stored in Stacks
There are stacks, each filled with items, and one empty stack.
Every stack has capacity . A robot arm, in one stack operation (step),
may pop one item from the top of a non-empty stack and subsequently push it
onto a stack not at capacity. In a {\em labeled} problem, all items are
distinguishable and are initially randomly scattered in the stacks. The
items must be rearranged using pop-and-pushs so that in the end, the stack holds items , in that order, from the top to
the bottom for all . In an {\em unlabeled} problem, the
items are of types of each. The goal is to rearrange items so that
items of type are located in the stack for all . In carrying out the rearrangement, a natural question is to find the least
number of required pop-and-pushes.
Our main contributions are: (1) an algorithm for restoring the order of
items stored in an table using only column and row
permutations, and its generalization, and (2) an algorithm with a guaranteed
upper bound of steps for solving both versions of the stack
rearrangement problem when for arbitrary fixed
positive number . In terms of the required number of steps, the labeled and
unlabeled version have lower bounds
and , respectively
The Size of a Polymer of String-Bits: A Numerical Investigation
In string-bit models, string is described as a polymer of point-like
constituents. We attempt to use string-bit ideas to investigate how the size of
string is affected by string interactions in a non-perturbative context.
Lacking adequate methods to deal with the full complications of bit
rearrangement interactions, we study instead a simplified analog model with
only ``direct'' potential interactions among the bits. We use the variational
principle in an approximate calculation of the mean-square size of a polymer as
a function of the number of constituents/bits for various interaction strengths
g in three specific models.Comment: 14 pages, LaTeX, 9 postscript figure
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