188 research outputs found
Inhibition causes ceaseless dynamics in networks of excitable nodes
The collective dynamics of a network of excitable nodes changes dramatically
when inhibitory nodes are introduced. We consider inhibitory nodes which may be
activated just like excitatory nodes but, upon activating, decrease the
probability of activation of network neighbors. We show that, although the
direct effect of inhibitory nodes is to decrease activity, the collective
dynamics becomes self-sustaining. We explain this counterintuitive result by
defining and analyzing a "branching function" which may be thought of as an
activity-dependent branching ratio. The shape of the branching function implies
that for a range of global coupling parameters dynamics are self-sustaining.
Within the self-sustaining region of parameter space lies a critical line along
which dynamics take the form of avalanches with universal scaling of size and
duration, embedded in ceaseless timeseries of activity. Our analyses, confirmed
by numerical simulation, suggest that inhibition may play a counterintuitive
role in excitable networks.Comment: 11 pages, 6 figure
Predicting criticality and dynamic range in complex networks: effects of topology
The collective dynamics of a network of coupled excitable systems in response
to an external stimulus depends on the topology of the connections in the
network. Here we develop a general theoretical approach to study the effects of
network topology on dynamic range, which quantifies the range of stimulus
intensities resulting in distinguishable network responses. We find that the
largest eigenvalue of the weighted network adjacency matrix governs the network
dynamic range. Specifically, a largest eigenvalue equal to one corresponds to a
critical regime with maximum dynamic range. We gain deeper insight on the
effects of network topology using a nonlinear analysis in terms of additional
spectral properties of the adjacency matrix. We find that homogeneous networks
can reach a higher dynamic range than those with heterogeneous topology. Our
analysis, confirmed by numerical simulations, generalizes previous studies in
terms of the largest eigenvalue of the adjacency matrix.Comment: 4 pages, 3 figure
Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus
We study the effects of network topology on the response of networks of
coupled discrete excitable systems to an external stochastic stimulus. We
extend recent results that characterize the response in terms of spectral
properties of the adjacency matrix by allowing distributions in the
transmission delays and in the number of refractory states, and by developing a
nonperturbative approximation to the steady state network response. We confirm
our theoretical results with numerical simulations. We find that the steady
state response amplitude is inversely proportional to the duration of
refractoriness, which reduces the maximum attainable dynamic range. We also
find that transmission delays alter the time required to reach steady state.
Importantly, neither delays nor refractoriness impact the general prediction
that criticality and maximum dynamic range occur when the largest eigenvalue of
the adjacency matrix is unity
A Network Approach to Analyzing Highly Recombinant Malaria Parasite Genes
The var genes of the human malaria parasite Plasmodium falciparum present a challenge to population geneticists due to their extreme diversity, which is generated by high rates of recombination. These genes encode a primary antigen protein called PfEMP1, which is expressed on the surface of infected red blood cells and elicits protective immune responses. Var gene sequences are characterized by pronounced mosaicism, precluding the use of traditional phylogenetic tools that require bifurcating tree-like evolutionary relationships. We present a new method that identifies highly variable regions (HVRs), and then maps each HVR to a complex network in which each sequence is a node and two nodes are linked if they share an exact match of significant length. Here, networks of var genes that recombine freely are expected to have a uniformly random structure, but constraints on recombination will produce network communities that we identify using a stochastic block model. We validate this method on synthetic data, showing that it correctly recovers populations of constrained recombination, before applying it to the Duffy Binding Like-α (DBLα) domain of var genes. We find nine HVRs whose network communities map in distinctive ways to known DBLα classifications and clinical phenotypes. We show that the recombinational constraints of some HVRs are correlated, while others are independent. These findings suggest that this micromodular structuring facilitates independent evolutionary trajectories of neighboring mosaic regions, allowing the parasite to retain protein function while generating enormous sequence diversity. Our approach therefore offers a rigorous method for analyzing evolutionary constraints in var genes, and is also flexible enough to be easily applied more generally to any highly recombinant sequences
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Critical Dynamics in Complex Excitable Networks
We study the effect of network structure on the dynamical response of networks of coupled discrete-state excitable elements to two distinct types of stimulus. First, we consider networks which are stochastically stimulated by an external source. Such systems have been used as toy models for the dynamics of some human sensory neuronal networks and neuron cultures. The collective dynamics of such systems depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenvalue of the weighted network adjacency matrix governs the network dynamic range. Specifically, a largest eigenvalue equal to one corresponds to a critical regime with maximum dynamic range. This result appears to hold for random, all-to-all, and scale free topologies, and is robust to the inclusion of time delays and refractory states. We gain deeper insight into the effects of network topology using a nonlinear analysis in terms of additional spectral properties of the adjacency matrix. We find that homogeneous networks can reach a higher dynamic range than those with heterogeneous topology. Second, we consider networks stimulated only once at a single node, with dynamics allowed to evolve without additional stimulus. Each realization of such a process will create a cascade of activity of varying duration and size. We analyze the distributions of cascade size and duration in complex networks resulting from a single nodal excitation, finding that when the largest eigenvalue is equal to one, so-called ``critical avalanches\u27\u27 are power-law distributed in size, with exponent -3/2, and power-law distributed in duration, with exponent -2. We employ techniques from dynamical systems to recover the differences among avalanches started at different network nodes, also deriving distributions for avalanches in subcritical and supercritical regimes
A physical model for efficient ranking in networks
We present a physically inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that interactions are more likely to occur between individuals with similar ranks. It provides a natural statistical significance test for the inferred hierarchy, and it can be used to perform inference tasks such as predicting the existence or direction of edges. The ranking is obtained by solving a linear system of equations, which is sparse if the network is; thus, the resulting algorithm is extremely efficient and scalable. We illustrate these findings by analyzing real and synthetic data, including data sets from animal behavior, faculty hiring, social support networks, and sports tournaments. We show that our method often outperforms a variety of others, in both speed and accuracy, in recovering the underlying ranks and predicting edge directions
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