A systems identification approach to estimating the connectivity in a neuronal population model.
06 Nov 2014-Vol. 2014, pp 4860-4863
TL;DR: A new approach to estimating the connectivity between neurons in a network model is presented that uses systems identification techniques for nonlinear dynamic models to compute the synaptic connections from other pre-synaptic neurons in the population.
Abstract: Mapping the brain and its complex networked structure has been one of the most researched topics in the last decade and continues to be the path towards understanding brain diseases. In this paper we present a new approach to estimating the connectivity between neurons in a network model. We use systems identification techniques for nonlinear dynamic models to compute the synaptic connections from other pre-synaptic neurons in the population. We are able to show accurate estimation even in the presence of model error and inaccurate assumption of post-synaptic potential dynamics. This allows to compute the connectivity matrix of the network using a very small time window of membrane potential data of the individual neurons. The specificity and sensitivity measures for randomly generated networks are reported.
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TL;DR: It is found that functional controllability characterizes a region's impact on the capacity for the whole system to shift between states, and significantly predicts individual difference in performance on cognitively demanding tasks including those task working memory, language, and emotional intelligence.
Abstract: Network control theory has recently emerged as a promising approach for understanding brain function and dynamics. By operationalizing notions of control theory for brain networks, it offers a fundamental explanation for how brain dynamics may be regulated by structural connectivity. While powerful, the approach does not currently consider other non-structural explanations of brain dynamics. Here we extend the analysis of network controllability by formalizing the evolution of neural signals as a function of effective inter-regional coupling and pairwise signal covariance. We find that functional controllability characterizes a region's impact on the capacity for the whole system to shift between states, and significantly predicts individual difference in performance on cognitively demanding tasks including those task working memory, language, and emotional intelligence. When comparing measurements from functional and structural controllability, we observed consistent relations between average and modal controllability, supporting prior work. In the same comparison, we also observed distinct relations between controllability and synchronizability, reflecting the additional information obtained from functional signals. Our work suggests that network control theory can serve as a systematic analysis tool to understand the energetics of brain state transitions, associated cognitive processes, and subsequent behaviors.
6 citations
Cites methods from "A systems identification approach t..."
...System identification has been successfully applied to both micro- [38] and macro-circuits [39], as well as to human functional magnetic resonance imaging (fMRI) [40, 41]....
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01 Jan 2018
TL;DR: In this paper, the authors extend the analysis of network controllability by formalizing the evolution of neural signals as a function of effective inter-regional coupling and pairwise signal covariance.
Abstract: Network control theory has recently emerged as a promising approach for understanding brain function and dynamics. By operationalizing notions of control theory for brain networks, it offers a fundamental explanation for how brain dynamics may be regulated by structural connectivity. While powerful, the approach does not currently consider other non-structural explanations of brain dynamics. Here we extend the analysis of network controllability by formalizing the evolution of neural signals as a function of effective inter-regional coupling and pairwise signal covariance. We find that functional controllability characterizes a region's impact on the capacity for the whole system to shift between states, and significantly predicts individual difference in performance on cognitively demanding tasks including those task working memory, language, and emotional intelligence. When comparing measurements from functional and structural controllability, we observed consistent relations between average and modal controllability, supporting prior work. In the same comparison, we also observed distinct relations between controllability and synchronizability, reflecting the additional information obtained from functional signals. Our work suggests that network control theory can serve as a systematic analysis tool to understand the energetics of brain state transitions, associated cognitive processes, and subsequent behaviors.
2 citations
References
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01 Jan 2015
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Abstract: Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples.- Local Bifurcations.- Averaging and Perturbation from a Geometric Viewpoint.- Hyperbolic Sets, Sympolic Dynamics, and Strange Attractors.- Global Bifurcations.- Local Codimension Two Bifurcations of Flows.- Appendix: Suggestions for Further Reading. Postscript Added at Second Printing. Glossary. References. Index.
12,485 citations
TL;DR: A model is presented that reproduces spiking and bursting behavior of known types of cortical neurons and combines the biologically plausibility of Hodgkin-Huxley-type dynamics and the computational efficiency of integrate-and-fire neurons.
Abstract: A model is presented that reproduces spiking and bursting behavior of known types of cortical neurons. The model combines the biologically plausibility of Hodgkin-Huxley-type dynamics and the computational efficiency of integrate-and-fire neurons. Using this model, one can simulate tens of thousands of spiking cortical neurons in real time (1 ms resolution) using a desktop PC.
4,082 citations
"A systems identification approach t..." refers methods in this paper
...We extend the single neuron model, described in [10], to represent the dynamics of a neuronal network....
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...In this paper we use a network of Izhikevich neurons [10] with linear coupling and exponentially decaying postsynaptic potentials to simulate population dynamics....
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Book•
01 Jan 2001
TL;DR: This text introduces the basic mathematical and computational methods of theoretical neuroscience and presents applications in a variety of areas including vision, sensory-motor integration, development, learning, and memory.
Abstract: Theoretical neuroscience provides a quantitative basis for describing what nervous systems do, determining how they function, and uncovering the general principles by which they operate This text introduces the basic mathematical and computational methods of theoretical neuroscience and presents applications in a variety of areas including vision, sensory-motor integration, development, learning, and memory The book is divided into three parts Part I discusses the relationship between sensory stimuli and neural responses, focusing on the representation of information by the spiking activity of neurons Part II discusses the modeling of neurons and neural circuits on the basis of cellular and synaptic biophysics Part III analyzes the role of plasticity in development and learning An appendix covers the mathematical methods used, and exercises are available on the book's Web site
3,441 citations
"A systems identification approach t..." refers background or methods in this paper
...The estimate is updated over every ISI....
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...We therefore implement the recursive storage least squares algorithm by computing the parameters over the time window in between two successive spikes, known as the inter-spike interval (ISI) [12]....
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...As established in [2] and [12], neurons are connected to each other by synapses....
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...The unshaded (white) regions are considered as the ISI data for the recursive storage least squares algorithm, Eq....
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TL;DR: The inception of this journal has been foreshadowed by an ever-increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses.
Abstract: Over the past 20 years, neuroimaging has become a predominant technique in systems neuroscience. One might envisage that over the next 20 years the neuroimaging of distributed processing and connectivity will play a major role in disclosing the brain's functional architecture and operational principles. The inception of this journal has been foreshadowed by an ever-increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. I accepted the invitation to write this review with great pleasure and hope to celebrate and critique the achievements to date, while addressing the challenges ahead.
2,822 citations
"A systems identification approach t..." refers background in this paper
...Understanding the connectivity in a network of neurons is one of the active problems in computational neuroscience [3]....
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TL;DR: This paper contains a further account of the electrical properties of the giant axon of Loligo and deals with the 'inactivation' process which gradually reduces sodium permeability after it has undergone the initial rise associated with depolarization.
Abstract: This paper contains a further account of the electrical properties of the giant axon of Loligo. It deals with the 'inactivation' process which gradually reduces sodium permeability after it has undergone the initial rise associated with depolarization. Experiments described previously (Hodgkin & Huxley, 1952a, b) show that the sodium conductance always declines from its initial maximum, but they leave a number of important points unresolved. Thus they give no information about the rate at which repolarization restores the ability of the membrane to respond with its characteristic increase of sodium conductance. Nor do they provide much quantitative evidence about the influence of membrane potential on the process responsible for inactivation. These are the main problems with which this paper is concerned. The experimental method needs no special description, since it was essentially the same as that used previously (Hodgkin, Huiley & Katz, 1952; Hodgkin & Huxley, 1952b).
1,547 citations
"A systems identification approach t..." refers methods in this paper
...In this section we generate membrane potential data from neuronal population models (20 neurons with 40 % connectivity) based on the Hodgkin Huxley neuron [11]....
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...To validate the ability of the method to produce results in real data we introduce a significant amount of model error by generating data from a population of Hodgkin-Huxley (HH) [11] neurons....
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