# When are correlations strong

@article{Azhar2010WhenAC, title={When are correlations strong}, author={Feraz Azhar and William Bialek}, journal={arXiv: Neurons and Cognition}, year={2010} }

The inverse problem of statistical mechanics involves finding the minimal Hamiltonian that is consistent with some observed set of correlation functions. This problem has received renewed interest in the analysis of biological networks; in particular, several such networks have been described successfully by maximum entropy models consistent with pairwise correlations. These correlations are usually weak in an absolute sense (e.g., correlation coefficients ~ 0.1 or less), and this is sometimes…

## 8 Citations

### Searching for Collective Behavior in a Large Network of Sensory Neurons

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The properties of the neural vocabulary are explored by estimating its entropy, which constrains the population's capacity to represent visual information, and classifying activity patterns into a small set of metastable collective modes, showing that the neural codeword ensembles are extremely inhomogenous.

### A dynamical state underlying the second order maximum entropy principle in neuronal networks

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This work addresses the issue of why the second order maximum entropy model, by using only firing rates and second order correlations of neurons as constraints, can well capture the observed distribution of neuronal firing patterns in many neuronal networks, and explores a possible dynamical state in which this recursive relation gives rise to the strengths of higher order interactions always smaller than the lower orders.

### Inferring structural connectivity using Ising couplings in models of neuronal networks

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This paper studies the performance of the Ising model couplings to infer the synaptic connectivity in in silico networks of neurons and compares its performance against partial and cross-correlations for different correlation levels, firing rates, network sizes, network densities, and topologies.

### Chaotic Dynamics in Networks of Spiking Neurons in the Balanced State

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- 2011

It is demonstrated that neural networks in the balanced state appear to generally exhibit chaotic dynamics, and a novel approach was introduced to thoroughly characterize neural network dynamics and quantify information preservation and erasure.

### Bounds on the Entropy of a Binary System with Known Mean and Pairwise Constraints

- Computer Science
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Author(s): Albanna, Badr Faisal | Advisor(s): DeWeese, Michael R | Abstract: Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured…

### The role of fluctuations in determining cellular network thermodynamics

- PhysicsPloS one
- 2020

This work develops a thermodynamic description of biological networks at the level of microscopic interactions between network variables, and conjecture that there is an upper limit to the rate of dissipative heat produced by a biological system that is associated with system size or modularity.

### Properties of a Multidimensional Landscape Model for Determining Cellular Network Thermodynamics

- PhysicsbioRxiv
- 2019

The magnitudes of the landscape gradients and the dynamic correlated fluctuations of network variables are experimentally accessible and provide insight into the composition of the network and the relative thermodynamic contributions from network components.

### Collective behaviour of social bots is encoded in their temporal Twitter activity

- Computer ScienceBig Data
- 2018

It is shown that, while pairwise correlations between users are weak, they co-exist with collective correlated states; however the statistics of correlations and co-spiking probability differ in both populations.

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