4,634 research outputs found
Coupled Maps with Growth and Death: An Approach to Cell Differentiation
An extension of coupled maps is given which allows for the growth of the
number of elements, and is inspired by the cell differentiation problem. The
growth of elements is made possible first by clustering the phases, and then by
differentiating roles. The former leads to the time sharing of resources, while
the latter leads to the separation of roles for the growth. The mechanism of
the differentiation of elements is studied. An extension to a model with
several internal phase variables is given, which shows differentiation of
internal states. The relevance of interacting dynamics with internal states
(``intra-inter" dynamics) to biological problems is discussed with an emphasis
on heterogeneity by clustering, macroscopic robustness by partial
synchronization and recursivity with the selection of initial conditions and
digitalization.Comment: LatexText,figures are not included. submitted to PhysicaD
(1995,revised 1996 May
Dynamical systems with time-dependent coupling: Clustering and critical behaviour
We study the collective behaviour of an ensemble of coupled motile elements
whose interactions depend on time and are alternatively attractive or
repulsive. The evolution of interactions is driven by individual internal
variables with autonomous dynamics. The system exhibits different dynamical
regimes, with various forms of collective organization, controlled by the range
of interactions and the dispersion of time scales in the evolution of the
internal variables. In the limit of large interaction ranges, it reduces to an
ensemble of coupled identical phase oscillators and, to some extent, admits to
be treated analytically. We find and characterize a transition between ordered
and disordered states, mediated by a regime of dynamical clustering.Comment: to appear in Physica
Learning theories reveal loss of pancreatic electrical connectivity in diabetes as an adaptive response
Cells of almost all solid tissues are connected with gap junctions which
permit the direct transfer of ions and small molecules, integral to regulating
coordinated function in the tissue. The pancreatic islets of Langerhans are
responsible for secreting the hormone insulin in response to glucose
stimulation. Gap junctions are the only electrical contacts between the
beta-cells in the tissue of these excitable islets. It is generally believed
that they are responsible for synchrony of the membrane voltage oscillations
among beta-cells, and thereby pulsatility of insulin secretion. Most attempts
to understand connectivity in islets are often interpreted, bottom-up, in terms
of measurements of gap junctional conductance. This does not, however explain
systematic changes, such as a diminished junctional conductance in type 2
diabetes. We attempt to address this deficit via the model presented here,
which is a learning theory of gap junctional adaptation derived with analogy to
neural systems. Here, gap junctions are modelled as bonds in a beta-cell
network, that are altered according to homeostatic rules of plasticity. Our
analysis reveals that it is nearly impossible to view gap junctions as
homogeneous across a tissue. A modified view that accommodates heterogeneity of
junction strengths in the islet can explain why, for example, a loss of gap
junction conductance in diabetes is necessary for an increase in plasma insulin
levels following hyperglycemia.Comment: 15 pages, 5 figures. To appear in PLoS One (2013
Topological Measure Locating the Effective Crossover between Segregation and Integration in a Modular Network
We introduce an easily computable topological measure which locates the
effective crossover between segregation and integration in a modular network.
Segregation corresponds to the degree of network modularity, while integration
is expressed in terms of the algebraic connectivity of an associated
hyper-graph. The rigorous treatment of the simplified case of cliques of equal
size that are gradually rewired until they become completely merged, allows us
to show that this topological crossover can be made to coincide with a
dynamical crossover from cluster to global synchronization of a system of
coupled phase oscillators. The dynamical crossover is signaled by a peak in the
product of the measures of intra-cluster and global synchronization, which we
propose as a dynamical measure of complexity. This quantity is much easier to
compute than the entropy (of the average frequencies of the oscillators), and
displays a behavior which closely mimics that of the dynamical complexity index
based on the latter. The proposed toplogical measure simultaneously provides
information on the dynamical behavior, sheds light on the interplay between
modularity vs total integration and shows how this affects the capability of
the network to perform both local and distributed dynamical tasks
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