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Table 1. 
Glossary of key terms
TermDefinition
Functional connectivity (FC) Statistical dependencies among neurophysiological time series derived from regions or networks. Most often estimated as a correlation coefficient. 
 
Static functional connectivity An estimate of statistical dependence made under the assumption that the dependence structure does not vary as a function of time. 
 
Statistical stationarity A formal definition of certain statistical properties being invariant to a shift in time. In practice, stationarity can only be assessed given multiple realizations of a time series (rather than for a single dataset). – Strong stationarity: The probability distribution of the time series is invariant under a shift in time. – Weak stationarity (or second-order stationarity): The mean and covariance of the time series are finite and invariant under a shift in time. This is the definition most time series models use in practice. 
 
Time-varying functional connectivity (TVFC) Functional connectivity that varies as a function of time. Also referred to as “dynamic functional connectivity.” 
 
Functional connectivity state A transient pattern of whole-brain functional connectivity. Usually identified by analytic techniques that attempt to model the full repertoire of functional connectivity patterns as being made up of a relatively small number of FC states (often referred to in shorthand simply as “states”). Some of these low-dimensional models constrain the brain to be in a single state at a time, whereas others permit each time point to be a mixture of states. 
 
Activity state A transient pattern of whole-brain activation, analogous to a functional connectivity state. 
 
Windowed functional connectivity Functional connectivity estimated over a defined time window that is shorter than the full time series. Windowing can involve weighting or tapering. “Sliding window” methods can be used to produce time-resolved estimates of functional connectivity (one for each window). 
 
Dynamical system A system composed of interacting components (neurons, brain regions, etc.) whose state evolves forward in time according to a particular rule (such as a difference or differential equation). Such systems yield complex behaviors that can be observed via an (often indirect) measurement process. 
 
Hidden Markov model (HMM) A statistical model wherein observed data are assumed to be generated from a process that moves among unobserved states. Fitting an HMM involves estimating (1) the properties of each state, (2) transition probabilities between the states, and (3) which state is active at each time point. For TVFC applications, each state might correspond to a distinct pattern of brain activity and functional connectivity, the transition probabilities would explain how the brain moves from one state to another, and the estimates of active states would give time-resolved estimates of which state was active at each time point. 
TermDefinition
Functional connectivity (FC) Statistical dependencies among neurophysiological time series derived from regions or networks. Most often estimated as a correlation coefficient. 
 
Static functional connectivity An estimate of statistical dependence made under the assumption that the dependence structure does not vary as a function of time. 
 
Statistical stationarity A formal definition of certain statistical properties being invariant to a shift in time. In practice, stationarity can only be assessed given multiple realizations of a time series (rather than for a single dataset). – Strong stationarity: The probability distribution of the time series is invariant under a shift in time. – Weak stationarity (or second-order stationarity): The mean and covariance of the time series are finite and invariant under a shift in time. This is the definition most time series models use in practice. 
 
Time-varying functional connectivity (TVFC) Functional connectivity that varies as a function of time. Also referred to as “dynamic functional connectivity.” 
 
Functional connectivity state A transient pattern of whole-brain functional connectivity. Usually identified by analytic techniques that attempt to model the full repertoire of functional connectivity patterns as being made up of a relatively small number of FC states (often referred to in shorthand simply as “states”). Some of these low-dimensional models constrain the brain to be in a single state at a time, whereas others permit each time point to be a mixture of states. 
 
Activity state A transient pattern of whole-brain activation, analogous to a functional connectivity state. 
 
Windowed functional connectivity Functional connectivity estimated over a defined time window that is shorter than the full time series. Windowing can involve weighting or tapering. “Sliding window” methods can be used to produce time-resolved estimates of functional connectivity (one for each window). 
 
Dynamical system A system composed of interacting components (neurons, brain regions, etc.) whose state evolves forward in time according to a particular rule (such as a difference or differential equation). Such systems yield complex behaviors that can be observed via an (often indirect) measurement process. 
 
Hidden Markov model (HMM) A statistical model wherein observed data are assumed to be generated from a process that moves among unobserved states. Fitting an HMM involves estimating (1) the properties of each state, (2) transition probabilities between the states, and (3) which state is active at each time point. For TVFC applications, each state might correspond to a distinct pattern of brain activity and functional connectivity, the transition probabilities would explain how the brain moves from one state to another, and the estimates of active states would give time-resolved estimates of which state was active at each time point. 
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