63,459 research outputs found
Complex Aggregates over Clusters of Elements
Complex aggregates have been proposed as a way to bridge the gap between approaches that handle sets by imposing conditions on specific elements, and approaches that handle them by imposing conditions on aggregated values. A complex aggregate summarises a subset of the elements in a set, where this subset is defined by conditions on the attribute values. In this paper, we present a new type of complex aggregate, where this subset is defined to be a cluster of the set. This is useful if subsets that are relevant for the task at hand are difficult to describe in terms of attribute conditions. This work is motivated from the analysis of flow cytometry data, where the sets are cells, and the subsets are cell populations. We describe two approaches to aggregate over clusters on an abstract level, and validate one of them empirically, motivating future research in this direction
In silico transitions to multicellularity
The emergence of multicellularity and developmental programs are among the
major problems of evolutionary biology. Traditionally, research in this area
has been based on the combination of data analysis and experimental work on one
hand and theoretical approximations on the other. A third possibility is
provided by computer simulation models, which allow to both simulate reality
and explore alternative possibilities. These in silico models offer a powerful
window to the possible and the actual by means of modeling how virtual cells
and groups of cells can evolve complex interactions beyond a set of isolated
entities. Here we present several examples of such models, each one
illustrating the potential for artificial modeling of the transition to
multicellularity.Comment: 21 pages, 10 figures. Book chapter of Evolutionary transitions to
multicellular life (Springer
Exact results and mean field approximation for a model of molecular aggregation
We present a simple one-dimensional model with molecular interactions
favouring the formation of clusters with a defined optimal size. Increasing the
density, at low temperature, the system goes from a nearly-ideal gas of
independent molecules to a system with most of the molecules in optimal
clusters, in a way that resembles the formation of micelles in a dilution of
amphiphilic molecules, at the critical micellar concentration. Our model is
simple enough to have an exact solution, but it contains some basic features of
more realistic descriptions of amphiphilic systems: molecular excluded volume
and molecular attractions which are saturated at the optimal cluster. The
comparison between the exact results and the mean field density functional
approximation suggests new approaches to study the more complex and realistic
models of micelle formation; in particular it addresses the long-standing
controversy surrounding separation of internal degrees of freedom in the
formulation of cluster association phenomena.Comment: 7 pages, 5 figures, some minor correction
Restructuring of colloidal aggregates in shear flow: Coupling interparticle contact models with Stokesian dynamics
A method to couple interparticle contact models with Stokesian dynamics (SD)
is introduced to simulate colloidal aggregates under flow conditions. The
contact model mimics both the elastic and plastic behavior of the cohesive
connections between particles within clusters. Owing to this, clusters can
maintain their structures under low stress while restructuring or even breakage
may occur under sufficiently high stress conditions. SD is an efficient method
to deal with the long-ranged and many-body nature of hydrodynamic interactions
for low Reynolds number flows. By using such a coupled model, the restructuring
of colloidal aggregates under stepwise increasing shear flows was studied.
Irreversible compaction occurs due to the increase of hydrodynamic stress on
clusters. Results show that the greater part of the fractal clusters are
compacted to rod-shaped packed structures, while the others show isotropic
compaction.Comment: A simulation movie be found at
http://www-levich.engr.ccny.cuny.edu/~seto/sites/colloidal_aggregates_shearflow.htm
A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains
A spectral method for identifying lumping in large Markov chains is
presented. Identification of meta stable states is treated as a special case.
The method is based on spectral analysis of a self-adjoint matrix that is a
function of the original transition matrix. It is demonstrated that the
technique is more robust than existing methods when applied to noisy
non-reversible Markov chains.Comment: 10 pages, 7 figure
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