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      Weak pairwise correlations imply strongly correlated network states in a neural population

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          Abstract

          Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher order interactions among large groups of elements play an important role. In the vertebrate retina, we show that weak correlations between pairs of neurons coexist with strongly collective behavior in the responses of ten or more neurons. Surprisingly, we find that this collective behavior is described quantitatively by models that capture the observed pairwise correlations but assume no higher order interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or error-correcting properties, and we provide preliminary evidence for such behavior. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons.

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          Most cited references 21

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          Neural networks and physical systems with emergent collective computational abilities.

           John Hopfield (1982)
          Computational properties of use of biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is given, based on aspects of neurobiology but readily adapted to integrated circuits. The collective properties of this model produce a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. The algorithm for the time evolution of the state of the system is based on asynchronous parallel processing. Additional emergent collective properties include some capacity for generalization, familiarity recognition, categorization, error correction, and time sequence retention. The collective properties are only weakly sensitive to details of the modeling or the failure of individual devices.
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            Singular value decomposition for genome-wide expression data processing and modeling.

            We describe the use of singular value decomposition in transforming genome-wide expression data from genes x arrays space to reduced diagonalized "eigengenes" x "eigenarrays" space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.
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              Correlated neuronal discharge rate and its implications for psychophysical performance.

              Single neurons can signal subtle changes in the sensory environment with surprising fidelity, often matching the perceptual sensitivity of trained psychophysical observers. This similarity poses an intriguing puzzle: why is psychophysical sensitivity not greater than that of single neurons? Pooling responses across neurons should average out noise in the activity of single cells, leading to substantially improved psychophysical performance. If, however, noise is correlated among these neurons, the beneficial effects of pooling would be diminished. To assess correlation within a pool, the responses of pairs of neurons were recorded simultaneously during repeated stimulus presentations. We report here that the observed covariation in spike count was relatively weak, the correlation coefficient averaging 0.12. A theoretical analysis revealed, however, that weak correlation can limit substantially the signalling capacity of the pool. In addition, theory suggests a relationship between neuronal responses and psychophysical decisions which may prove useful for identifying cell populations underlying specific perceptual capacities.
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                Author and article information

                Journal
                2005-12-06
                Article
                10.1038/nature04701
                q-bio/0512013
                Custom metadata
                Full account of work presented at the conference on Computational and Systems Neuroscience (COSYNE), 17-20 March 2005, in Salt Lake City, Utah (http://cosyne.org)
                q-bio.NC q-bio.QM

                Neurosciences

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