Model reduction of structural biological networks by cycle removal

Reducing a graph model is extremely important for the dynamical analysis of large-scale networks. In order to approximate the behavior of such a system it is helpful to be able to simplify the model. In this paper, the graph reduction model is introduced. This method is based on removing edges that close independent cycles in the graph. We apply this novel model reduction paradigm to brain networks, and show the differences between the model approximation error for various brain network graphs ranging from those of healthy controls to those of Alzheimer's patients. The graph simplification for Alzheimer's brain networks yields the smallest approximation error, since the number of independent cycles is smaller than in either the healthy controls or mild cognitive impairment patients.

[1]  Anke Meyer-Bäse,et al.  Stability Analysis of an Unsupervised Competitive Neural Network , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[2]  D. Hu,et al.  Identifying major depression using whole-brain functional connectivity: a multivariate pattern analysis. , 2012, Brain : a journal of neurology.

[3]  Amirhessam Tahmassebi,et al.  iDeepLe: deep learning in a flash , 2018, Defense + Security.

[4]  J. Marsden,et al.  A subspace approach to balanced truncation for model reduction of nonlinear control systems , 2002 .

[5]  Edward T. Bullmore,et al.  Schizophrenia, neuroimaging and connectomics , 2012, NeuroImage.

[6]  A Meyer-Base,et al.  Local and global stability analysis of an unsupervised competitive neural network. , 2008, IEEE transactions on neural networks.

[7]  Huijun Gao,et al.  A Constrained Evolutionary Computation Method for Detecting Controlling Regions of Cortical Networks , 2012, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[8]  Cui Bao-tong Global exponential stability of competitive neural networks with different time-scales , 2008 .

[9]  Anke Meyer-Bäse,et al.  Determining disease evolution driver nodes in dementia networks , 2018, Medical Imaging.

[10]  Anke Meyer-Bäse,et al.  Local exponential stability of competitive neural networks with different time scales , 2004, Eng. Appl. Artif. Intell..

[11]  Anke Meyer-Bäse,et al.  Local uniform stability of competitive neural networks with different time-scales under vanishing perturbations , 2010, Neurocomputing.

[12]  Amir H. Gandomi,et al.  A scalable communication abstraction framework for internet of things applications using Raspberry Pi , 2018, Defense + Security.

[13]  Anke Meyer-Bäse,et al.  Pinning observability of competitive neural networks with different time-constants , 2019, Neurocomputing.

[14]  Joe H. Chow,et al.  Time scale modeling of sparse dynamic networks , 1985 .

[15]  M. Bosworth,et al.  How scattering parameters can benefit the development of all-electric ships , 2015, 2015 IEEE Electric Ship Technologies Symposium (ESTS).

[16]  J. M. A. Scherpen,et al.  Balancing for nonlinear systems , 1993 .

[17]  Anke Meyer-Bäse,et al.  Global Asymptotic Stability of a Class of Dynamical Neural Networks , 2003, Int. J. Neural Syst..

[18]  C. Thiel,et al.  Pro-cognitive drug effects modulate functional brain network organization , 2012, Front. Behav. Neurosci..

[19]  Ludovico Minati,et al.  Connectivity of the amygdala, piriform, and orbitofrontal cortex during olfactory stimulation: a functional MRI study , 2013, Neuroreport.

[20]  M. Kanat Camlibel,et al.  Model reduction of consensus networks by graph simplification , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[21]  J. Rapoport,et al.  The anatomical distance of functional connections predicts brain network topology in health and schizophrenia. , 2013, Cerebral cortex.

[22]  Paul M. Thompson,et al.  Robust identification of partial-correlation based networks with applications to cortical thickness data , 2012, 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI).

[23]  B. Moore Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[24]  A. Meyer-Base,et al.  Flow invariance for competitive multi-modal neural networks , 2003, Proceedings of the International Joint Conference on Neural Networks, 2003..

[25]  Anke Meyer-Bäse,et al.  Gene regulatory networks simplified by nonlinear balanced truncation , 2008, SPIE Defense + Commercial Sensing.

[26]  Anke Meyer-Bäse,et al.  The driving regulators of the connectivity protein network of brain malignancies , 2017, Commercial + Scientific Sensing and Imaging.

[27]  M. Paluš,et al.  The role of nonlinearity in computing graph-theoretical properties of resting-state functional magnetic resonance imaging brain networks. , 2011, Chaos.

[28]  Anke Meyer-Bäse,et al.  Dynamical graph theory networks techniques for the analysis of sparse connectivity networks in dementia , 2017, Commercial + Scientific Sensing and Imaging.

[29]  Anke Meyer-Bäse,et al.  Robust stability analysis of competitive neural networks with different time-scales under perturbations , 2007, Neurocomputing.

[30]  Anke Meyer-Bäse,et al.  Uncertain gene regulatory networks simplified by gramian-based approach , 2012 .

[31]  Behshad Mohebali Characterization of the Common Mode Features of a 3-Phase Full-Bridge Inverter Using Frequency Domain Approaches , 2016 .

[32]  Ignacio A. Illán,et al.  Dynamical Graph Theory Networks Methods for the Analysis of Sparse Functional Connectivity Networks and for Determining Pinning Observability in Brain Networks , 2017, Front. Comput. Neurosci..

[33]  Jorge Munilla,et al.  Exploratory graphical models of functional and structural connectivity patterns for Alzheimer's Disease diagnosis , 2015, Front. Comput. Neurosci..

[34]  Jian-Xin Xu,et al.  Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems , 2004, IEEE Transactions on Automatic Control.