# A probabilistic study of neural complexity

@article{Buzzi2009APS, title={A probabilistic study of neural complexity}, author={J{\'e}r{\^o}me Buzzi and Lorenzo Zambotti}, journal={arXiv: Probability}, year={2009} }

G. Edelman, O. Sporns, and G. Tononi have introduced the neural complexity of a family of random variables, defining it as a specific average of mutual information over subfamilies. We show that their choice of weights satisfies two natural properties, namely exchangeability and additivity, and we call any functional satisfying these two properties an intricacy. We classify all intricacies in terms of probability laws on the unit interval and study the growth rate of maximal intricacies when…

## 2 Citations

### Approximate maximizers of intricacy functionals

- Computer Science, Mathematics
- 2009

The main ideas are a random construction of almost maximizers with a high statistical symmetry and the consideration of entropy profiles, i.e., the average entropies of sub-systems of a given size.

### Creative brain and abstract art: A quantitative study on Kandinskij paintings

- ArtThe 2011 International Joint Conference on Neural Networks
- 2011

In this paper, we speculate that abstract art can become an useful paradigm for both studying the relationship between neuroscience and art, and as a benchmark problem for the researches on…

## References

SHOWING 1-10 OF 25 REFERENCES

### Approximate maximizers of intricacy functionals

- Computer Science, Mathematics
- 2009

The main ideas are a random construction of almost maximizers with a high statistical symmetry and the consideration of entropy profiles, i.e., the average entropies of sub-systems of a given size.

### Neural complexity and structural connectivity.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

An approximation of the measure of neural complexity based on mutual information between complementary subsystems of a given neural network is developed, applied to a continuous-time process, which elucidates the relationship between the complexity of a neural system and its structural connectivity.

### Topological approach to neural complexity.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

This work addresses the dependence of this measure on the topological features of a network in the case of a Gaussian stationary process and offers a straightforward and faster algorithm to compute the complexity of a graph than the standard one.

### Measures of degeneracy and redundancy in biological networks.

- Computer ScienceProceedings of the National Academy of Sciences of the United States of America
- 1999

Functional measures of the degeneracy and redundancy of a system with respect to a set of outputs are developed and promise to be useful in characterizing and understanding the functional robustness and adaptability of biological networks.

### Dynamical complexity in small-world networks of spiking neurons.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

The results broadly support the hypothesis that small-world topology promotes dynamical complexity, but reveal a narrow parameter range within which this occurs for the network topology under investigation, and suggest an inverse correlation with phase synchrony inside this range.

### Degeneracy and complexity in biological systems

- BiologyProceedings of the National Academy of Sciences of the United States of America
- 2001

It is argued that degeneracy is a ubiquitous biological property and it is a feature of complexity at genetic, cellular, system, and population levels.

### Analytical description of the evolution of neural networks: learning rules and complexity

- Computer ScienceBiological Cybernetics
- 1999

It is shown that local learning rules are sufficient to model complex dynamical aspects of the evolution of networks, and how far novel statistical formalisms can be employed to evaluate the system's dynamics is demonstrated.

### Inferring statistical complexity.

- Computer SciencePhysical review letters
- 1989

A technique is presented that directly reconstructs minimal equations of motion from the recursive structure of measurement sequences, demonstrating a form of superuniversality that refers only to the entropy and complexity of a data stream.

### A complexity measure for selective matching of signals by the brain.

- Psychology, Computer ScienceProceedings of the National Academy of Sciences of the United States of America
- 1996

A related statistical measure, matching complexity (CM), which reflects the change in CN that occurs after a neural system receives signals from the environment, and is shown to be low when the intrinsic connectivity of a simulated cortical area is randomly organized.

### Complexity, contingency, and criticality.

- GeologyProceedings of the National Academy of Sciences of the United States of America
- 1995

The apparent, historical contingency in many sciences, including geology, biology, and economics, finds a natural interpretation as a self-organized critical phenomenon in simple mathematical models of sandpiles and biological evolution.