Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations

“…fluctuation analysis has been developed for quantifying correlation properties in nonstationary signals, e.g., in physiological time series, because long-range correlations—revealed by an ACF analysis—can arise also as an artifact of the “patchiness” of nonstationary data (Peng et al., 1994, 1995).”

“Unlike deterministic approaches aimed at finding low-dimensional chaos, the SOC framework allows for a highdimensional character of the dynamics and for the presence of stochastic effects.”

“and Marchesi, 1999), heartbeats (Peng et al., 1995), and human”

“…frequencies are a prominent feature of the spontaneous electroencephalogram (EEG) (Berger, 1929; Connors and Amitai, 1997) and are believed to reflect functional states of the brain (Llinás, 1988; Steriade et al., 1993; Arieli et al., 1996; Herculano-Houzel et al., 1999; Tsodyks et al., 1999).”

“…frequencies are a prominent feature of the spontaneous electroencephalogram (EEG) (Berger, 1929; Connors and Amitai, 1997) and are believed to reflect functional states of the brain (Llinás, 1988; Steriade et al., 1993; Arieli et al., 1996; Herculano-Houzel et al., 1999; Tsodyks et al., 1999).”

“…that several complex systems self-organize through local interactions to a critical state with long-range spatiotemporal correlations (Bak et al., 1989; Mantegna and Stanley, 1995; Boettcher and Paczuski, 1996; Paczuski et al., 1996; Bak, 1997; Malamud et al., 1998; Lux and Marchesi, 1999).”

“…frequencies are a prominent feature of the spontaneous electroencephalogram (EEG) (Berger, 1929; Connors and Amitai, 1997) and are believed to reflect functional states of the brain (Llinás, 1988; Steriade et al., 1993; Arieli et al., 1996; Herculano-Houzel et al., 1999; Tsodyks et al., 1999).”

“The scaling exponent a, also termed the “self-similarity parameter” (Lux and Marchesi, 1999), is extracted with linear regression in doublelogarithmic coordinates using a least-squares algorithm.”

“These oscillations arise from correlated activity of a large number of neurons whose interactions are generally nonlinear (Steriade et al., 1990, 1993; Lopez da Silva, 1991).”

“…ERD on the cortical surface has revealed transitions from spatially diffuse to focused and somatotopically specific patterns of alpha suppression (Crone et al., 1998), consistent with the picture of spontaneous cortical states being driven into stimulus specific configurations of correlated…”

“The correlated nature of spontaneous oscillations It has often been noted that spontaneously occurring synchrony in cell populations appears in an irregular manner both temporally and spatiotemporally (Traub et al., 1989; Destexhe et al., 1999; Tsodyks et al., 1999).”

“During event-related desynchronization (ERD), spontaneous 8–13 Hz oscillations are suppressed rapidly (approximately within one cycle) by sensory stimulation (Hari and Salmelin, 1997; Nikouline et al., 2000), memory search (Kaufman et al.”

“…(Bak, 1997), financial markets (Mantegna and Stanley, 1995; Lux and Marchesi, 1999), heartbeats (Peng et al., 1995), and human coordination (Gilden et al., 1995; Chen et al., 1997), exhibit unexpected statistical similarities, most commonly power-law scaling behavior of a particular…”

“, 1987, 1988), ample evidence has indicated that several complex systems self-organize through local interactions to a critical state with long-range spatiotemporal correlations (Bak et al., 1989; Mantegna and Stanley, 1995; Boettcher and Paczuski, 1996; Paczuski et al., 1996; Bak, 1997; Malamud et al., 1998; Lux and…”

“It has often been noted that spontaneously occurring synchrony in cell populations appears in an irregular manner both temporally and spatiotemporally (Traub et al., 1989; Destexhe et al., 1999; Tsodyks et al., 1999).”

“…that several complex systems self-organize through local interactions to a critical state with long-range spatiotemporal correlations (Bak et al., 1989; Mantegna and Stanley, 1995; Boettcher and Paczuski, 1996; Paczuski et al., 1996; Bak, 1997; Malamud et al., 1998; Lux and Marchesi, 1999).”

“3C) is epitomical of fractal objects and is increasingly being acknowledged to hint about the presence of spatial and temporal correlations at many scales (Bassingthwaighte et al., 1994; Barabási and Stanley, 1995; Bak, 1997).”

“For the EEG data, we used so-called surrogate data as control, which are commonly used as a control when probing a signal for a nonrandom temporal structure (Ivanov et al., 1996).”

“The intrinsic neural properties and intricate patterns of connectivity add further complexity to the behavior of neural systems (Llinás, 1988; Connors and Amitai, 1997; Destexhe et al., 1998).”

“…has indicated that several complex systems self-organize through local interactions to a critical state with long-range spatiotemporal correlations (Bak et al., 1989; Mantegna and Stanley, 1995; Boettcher and Paczuski, 1996; Paczuski et al., 1996; Bak, 1997; Malamud et al., 1998; Lux and Marchesi,…”

“…temporal correlations and scaling behavior One of the defining aspects of population oscillations is the ability of neural networks to establish spatiotemporal correlations with millisecond range precision and over large distances mainly through local synaptic connections (Traub et al., 1989).”

“…(Bak, 1997), financial markets (Mantegna and Stanley, 1995; Lux and Marchesi, 1999), heartbeats (Peng et al., 1995), and human coordination (Gilden et al., 1995; Chen et al., 1997), exhibit unexpected statistical similarities, most commonly power-law scaling behavior of a particular observable.”

“However, the complexity of the EEG has rendered it impossible to reliably distinguish the waxing and waning of oscillations over epochs longer than 2–15 sec from that of filtered white noise (Paluš, 1996; Cerf et al., 1997; Stam et al., 1999).”

“It can be used to test a model for its ability to generate scale-free behavior (Ivanov et al., 1998).”

“…frequencies are a prominent feature of the spontaneous electroencephalogram (EEG) (Berger, 1929; Connors and Amitai, 1997) and are believed to reflect functional states of the brain (Llinás, 1988; Steriade et al., 1993; Arieli et al., 1996; Herculano-Houzel et al., 1999; Tsodyks et al., 1999).”

“b)/2 (Rangarajan and Ding 2000).”

“However, the complexity of the EEG has rendered it impossible to reliably distinguish the waxing and waning of oscillations over epochs longer than 2–15 sec from that of filtered white noise (Paluš, 1996; Cerf et al., 1997; Stam et al., 1999).”

“From a theoretical point of view and based on simulations, it has been argued that a state of criticality would be optimal for a network to swiftly adapt to new situations (Alstrøm and Stassinopoulos 1995; Stassinopoulos and Bak, 1995; Bonabeau, 1997; Chialvo and Bak, 1999).”

“, 1991), or motor activity (Pfurtscheller, 1989; Crone et al., 1998).”

“…desynchronization (ERD), spontaneous 8–13 Hz oscillations are suppressed rapidly (approximately within one cycle) by sensory stimulation (Hari and Salmelin, 1997; Nikouline et al., 2000), memory search (Kaufman et al., 1991), or motor activity (Pfurtscheller, 1989; Crone et al., 1998).”

“Spontaneous brain activity from 10 normal subjects (aged 20–30 years, one female) was recorded simultaneously with magnetoencephalography (MEG) and EEG using a whole-scalp magnetometer array containing 122 planar gradiometers (Knuutila et al., 1993) and a 64-channel EEG cap (Virtanen et al., 1996).”

“During event-related desynchronization (ERD), spontaneous 8–13 Hz oscillations are suppressed rapidly (approximately within one cycle) by sensory stimulation (Hari and Salmelin, 1997; Nikouline et al., 2000), memory search (Kaufman et al.”

“Spontaneous brain activity from 10 normal subjects (aged 20–30 years, one female) was recorded simultaneously with magnetoencephalography (MEG) and EEG using a whole-scalp magnetometer array containing 122 planar gradiometers (Knuutila et al., 1993) and a 64-channel EEG cap (Virtanen et al., 1996).”

“From a theoretical point of view and based on simulations, it has been argued that a state of criticality would be optimal for a network to swiftly adapt to new situations (Alstrøm and Stassinopoulos 1995; Stassinopoulos and Bak, 1995; Bonabeau, 1997; Chialvo and Bak, 1999).”

“…criticality; complexity Oscillations at various frequencies are a prominent feature of the spontaneous electroencephalogram (EEG) (Berger, 1929; Connors and Amitai, 1997) and are believed to reflect functional states of the brain (Llinás, 1988; Steriade et al., 1993; Arieli et al., 1996;…”

“From a theoretical point of view and based on simulations, it has been argued that a state of criticality would be optimal for a network to swiftly adapt to new situations (Alstrøm and Stassinopoulos 1995; Stassinopoulos and Bak, 1995; Bonabeau, 1997; Chialvo and Bak, 1999).”

“…that several complex systems self-organize through local interactions to a critical state with long-range spatiotemporal correlations (Bak et al., 1989; Mantegna and Stanley, 1995; Boettcher and Paczuski, 1996; Paczuski et al., 1996; Bak, 1997; Malamud et al., 1998; Lux and Marchesi, 1999).”

“From a theoretical point of view and based on simulations, it has been argued that a state of criticality would be optimal for a network to swiftly adapt to new situations (Alstrøm and Stassinopoulos 1995; Stassinopoulos and Bak, 1995; Bonabeau, 1997; Chialvo and Bak, 1999).”

“However, the complexity of the EEG has rendered it impossible to reliably distinguish the waxing and waning of oscillations over epochs longer than 2–15 sec from that of filtered white noise (Paluš, 1996; Cerf et al., 1997; Stam et al., 1999).”

“Parts of this work have been published previously in abstract form (Linkenkaer-Hansen et al., 2000).”

“This timescale invariance of wavelet correlations and the brain functional network parameters derived from them is a theoretically predictable corollary of the long-range autocorrelations of neurophysiological time series 82–84 .”

“This 1/f distribution has also been observed in studies of spontaneous electroencephalography (EEG”

“…many people argue for criticality and power law effects in large-scale cortical activity (e.g., Freyer et al., 2009; Kitzbichler et al., 2009; Linkenkaer-Hansen et al., 2001; Stam and de Bruin, 2004), other people do not (Bedard et al., 2006; Miller et al., 2007; Touboul and Des-texhe, 2009).”

“On the other hand, multisecond periodicities or infraslow oscillations have been reported in both local field potential recordings from rat basal ganglia and monkey cortex [31,41,42] and the surface EEG in humans [ 43 ].”

“, 2002), and EEG time series in humans (Linkenkaer-Hansen et al., 2001; Worrell et al., 2002)] our results go beyond the phenomenological description of a power law only.”