# Saturation Probabilities of Continuous-Time Sigmoidal Networks

@article{Beer2010SaturationPO, title={Saturation Probabilities of Continuous-Time Sigmoidal Networks}, author={R. Beer and B. Daniels}, journal={arXiv: Neurons and Cognition}, year={2010} }

From genetic regulatory networks to nervous systems, the interactions between elements in biological networks often take a sigmoidal or S-shaped form. This paper develops a probabilistic characterization of the parameter space of continuous-time sigmoidal networks (CTSNs), a simple but dynamically-universal model of such interactions. We describe an efficient and accurate method for calculating the probability of observing effectively M-dimensional dynamics in an N-element CTSN, as well as a… Expand

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#### References

SHOWING 1-10 OF 47 REFERENCES

On the Dynamics of Small Continuous-Time Recurrent Neural Networks

- Computer Science
- Adapt. Behav.
- 1995

This article begins a systematic examination of the dynamics of continuous-time recurrent neural networks with a fairly complete description of the possible dynamical behavior and bifurcations of one- and two-neuron circuits. Expand

Analysis of continuous-time switching networks

- Mathematics
- 2000

Abstract Models of a number of biological systems, including gene regulation and neural networks, can be formulated as switching networks, in which the interactions between the variables depend… Expand

Parameter Space Structure of Continuous-Time Recurrent Neural Networks

- Mathematics, Computer Science
- Neural Computation
- 2006

This letter begins a systematic study of the global parameter space structure of continuous-time recurrent neural networks (CTRNNs), a class of neural models that is simple but dynamically universal. Expand

Approximation of dynamical systems by continuous time recurrent neural networks

- Mathematics, Computer Science
- Neural Networks
- 1993

In this paper, we prove that any finite time trajectory of a given n-dimensional dynamical system can be approximately realized by the internal state of the output units of a continuous time… Expand

Dynamic Properties of Network Motifs Contribute to Biological Network Organization

- Computer Science, Medicine
- PLoS biology
- 2005

It is proposed that robust dynamical stability is an influential property that can determine the non-random structure of biological networks. Expand

Modeling and Simulation of Genetic Regulatory Systems: A Literature Review

- Computer Science
- J. Comput. Biol.
- 2002

This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equation, stochastic equations, and so on. Expand

Modeling of continuous time dynamical systems with input by recurrent neural networks

- Computer Science
- 2000

This paper proves that any finite time trajectory of a given n-dimensional dynamical continuous system with input can be approximated by the internal state of the output units of a continuous time… Expand

A Neural Network Model of Chemotaxis Predicts Functions of Synaptic Connections in the Nematode Caenorhabditis elegans

- Biology, Medicine
- Journal of Computational Neuroscience
- 2004

Common patterns of connectivity between the model and biological networks suggest new functions for previously identified connections in the C. elegans nervous system, and it is shown that feedback regulates the latency between sensory input and behavior. Expand

Metabolic stability and epigenesis in randomly constructed genetic nets.

- Biology, Medicine
- Journal of theoretical biology
- 1969

The hypothesis that contemporary organisms are also randomly constructed molecular automata is examined by modeling the gene as a binary (on-off) device and studying the behavior of large, randomly constructed nets of these binary “genes”. Expand

Failure of averaging in the construction of a conductance-based neuron model.

- Physics, Medicine
- Journal of neurophysiology
- 2002

This work randomly varied the maximal conductance of each of the active currents in the model and identified sets of maximal conductances that generate bursting neurons that fire a single action potential at the peak of a slow membrane potential depolarization. Expand