TY - JOUR

T1 - Functional holography analysis

T2 - Simplifying the complexity of dynamical networks

AU - Baruchi, Itay

AU - Grossman, Danny

AU - Volman, Vladislav

AU - Shein, Mark

AU - Hunter, John

AU - Towle, Vernon L.

AU - Ben-Jacob, Eshel

N1 - Funding Information:
The method presented here has evolved from the joint study with Dr. Ronen Segev, Eyal Hulata, and Yoash Shapira (Ref. ). Much insight has been gained from analyzing the structure of artificial and neural networks in collaboration with Pablo Blinder and Dr. Danny Baranes. One of us (E.B-J.) is most thankful to Professor Steven Schiff for many illuminating conversations, guidance into the foundations and the literature about epilepsy and constructive comments and advices during the development of this research. We thank Professor Robert Benzi, Professor Eytan Domany, Professor Sir Sam Edwards, Professor Herbert Levine, and Professor Itamar Procaccia for constructive comments about the mathematical basis of the method. Preleminary analyses of fMRI measurements are done in collaboration with Dr. Talma Handler and Dr. Yaniv Asaf. This research was partially supported by a grant from the Israel Science Foundation, the Maguy-Glass chair in Physics of Complex Systems, and NSF Grant No. PHY99-07949. One of the authors (E.B-J.) thanks the KITP at University of California Santa Barbara, the Weitzman Institute and the Center for Theoretical and Biological Physics for hospitality during various stages of this research.

PY - 2006

Y1 - 2006

N2 - We present a novel functional holography (FH) analysis devised to study the dynamics of task-performing dynamical networks. The latter term refers to networks composed of dynamical systems or elements, like gene networks or neural networks. The new approach is based on the realization that task-performing networks follow some underlying principles that are reflected in their activity. Therefore, the analysis is designed to decipher the existence of simple causal motives that are expected to be embedded in the observed complex activity of the networks under study. First we evaluate the matrix of similarities (correlations) between the activities of the network's components. We then perform collective normalization of the similarities (or affinity transformation) to construct a matrix of functional correlations. Using dimension reduction algorithms on the affinity matrix, the matrix is projected onto a principal three-dimensional space of the leading eigenvectors computed by the algorithm. To retrieve back information that is lost in the dimension reduction, we connect the nodes by colored lines that represent the level of the similarities to construct a holographic network in the principal space. Next we calculate the activity propagation in the network (temporal ordering) using different methods like temporal center of mass and cross correlations. The causal information is superimposed on the holographic network by coloring the nodes locations according to the temporal ordering of their activities. First, we illustrate the analysis for simple, artificially constructed examples. Then we demonstrate that by applying the FH analysis to modeled and real neural networks as well as recorded brain activity, hidden causal manifolds with simple yet characteristic geometrical and topological features are deciphered in the complex activity. The term "functional holography" is used to indicate that the goal of the analysis is to extract the maximum amount of functional information about the dynamical network as a whole unit.

AB - We present a novel functional holography (FH) analysis devised to study the dynamics of task-performing dynamical networks. The latter term refers to networks composed of dynamical systems or elements, like gene networks or neural networks. The new approach is based on the realization that task-performing networks follow some underlying principles that are reflected in their activity. Therefore, the analysis is designed to decipher the existence of simple causal motives that are expected to be embedded in the observed complex activity of the networks under study. First we evaluate the matrix of similarities (correlations) between the activities of the network's components. We then perform collective normalization of the similarities (or affinity transformation) to construct a matrix of functional correlations. Using dimension reduction algorithms on the affinity matrix, the matrix is projected onto a principal three-dimensional space of the leading eigenvectors computed by the algorithm. To retrieve back information that is lost in the dimension reduction, we connect the nodes by colored lines that represent the level of the similarities to construct a holographic network in the principal space. Next we calculate the activity propagation in the network (temporal ordering) using different methods like temporal center of mass and cross correlations. The causal information is superimposed on the holographic network by coloring the nodes locations according to the temporal ordering of their activities. First, we illustrate the analysis for simple, artificially constructed examples. Then we demonstrate that by applying the FH analysis to modeled and real neural networks as well as recorded brain activity, hidden causal manifolds with simple yet characteristic geometrical and topological features are deciphered in the complex activity. The term "functional holography" is used to indicate that the goal of the analysis is to extract the maximum amount of functional information about the dynamical network as a whole unit.

UR - http://www.scopus.com/inward/record.url?scp=33645678807&partnerID=8YFLogxK

U2 - 10.1063/1.2183408

DO - 10.1063/1.2183408

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C2 - 16599778

AN - SCOPUS:33645678807

SN - 1054-1500

VL - 16

JO - Chaos

JF - Chaos

IS - 1

M1 - 015112

ER -