37,757 research outputs found
Rhythmogenic neuronal networks, pacemakers, and k-cores
Neuronal networks are controlled by a combination of the dynamics of
individual neurons and the connectivity of the network that links them
together. We study a minimal model of the preBotzinger complex, a small
neuronal network that controls the breathing rhythm of mammals through periodic
firing bursts. We show that the properties of a such a randomly connected
network of identical excitatory neurons are fundamentally different from those
of uniformly connected neuronal networks as described by mean-field theory. We
show that (i) the connectivity properties of the networks determines the
location of emergent pacemakers that trigger the firing bursts and (ii) that
the collective desensitization that terminates the firing bursts is determined
again by the network connectivity, through k-core clusters of neurons.Comment: 4+ pages, 4 figures, submitted to Phys. Rev. Let
Are randomly grown graphs really random?
We analyze a minimal model of a growing network. At each time step, a new
vertex is added; then, with probability delta, two vertices are chosen
uniformly at random and joined by an undirected edge. This process is repeated
for t time steps. In the limit of large t, the resulting graph displays
surprisingly rich characteristics. In particular, a giant component emerges in
an infinite-order phase transition at delta = 1/8. At the transition, the
average component size jumps discontinuously but remains finite. In contrast, a
static random graph with the same degree distribution exhibits a second-order
phase transition at delta = 1/4, and the average component size diverges there.
These dramatic differences between grown and static random graphs stem from a
positive correlation between the degrees of connected vertices in the grown
graph--older vertices tend to have higher degree, and to link with other
high-degree vertices, merely by virtue of their age. We conclude that grown
graphs, however randomly they are constructed, are fundamentally different from
their static random graph counterparts.Comment: 8 pages, 5 figure
Farsightedly stable networks
We propose a new concept, the pairwise farsightedly stable set, in order to predict which networks may be formed among farsighted players. A set of networks G is pairwise farsightedly stable (i) if all possible pairwise deviations from any network g E G to a network outside G are deterred by the threat of endind worse off or equally well off, (ii) if there exists a farsightedly improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying (i) and (ii). We show that a non-empty pairwise farsightedly stable set always exists and we provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsightedly yields a Pareto dominating betwork, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsightedly stability and other concepts such as the largest consistent set.Networks, Farsighted, Stability, Pairwise, Efficiency
Environmental Regulation Can Arise Under Minimal Assumptions
Models that demonstrate environmental regulation as a consequence of organism and environment coupling all require a number of core assumptions. Many previous models, such as Daisyworld, require that certain environment-altering traits have a selective advantage when those traits also contribute towards global regulation. We present a model that results in the regulation of a global environmental resource through niche construction without employing this and other common assumptions. There is no predetermined environmental optimum towards which regulation should proceed assumed or coded into the model. Nevertheless, polymorphic stable states that resist perturbation emerge from the simulated co-evolution of organisms and environment. In any single simulation a series of different stable states are realised, punctuated by rapid transitions. Regulation is achieved through two main subpopulations that are adapted to slightly different resource values, which force the environmental resource in opposing directions. This maintains the resource within a comparatively narrow band over a wide range of external perturbations. Population driven oscillations in the resource appear to be instrumental in protecting the regulation against mutations that would otherwise destroy it. Sensitivity analysis shows that the regulation is robust to mutation and to a wide range of parameter settings. Given the minimal assumptions employed, the results could reveal a mechanism capable of environmental regulation through the by-products of organisms
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