Fluctuation Scaling of Neuronal Firing and Bursting in Spontaneously Active Brain Circuits

2019 ◽  
Vol 30 (01) ◽  
pp. 1950017
Author(s):  
Xinmeng Guo ◽  
Haitao Yu ◽  
Nathan X. Kodama ◽  
Jiang Wang ◽  
Roberto F. Galán
Keyword(s):  
Power Law ◽  
Power Spectra ◽  
Dominant Frequency ◽  
Neuronal Firing ◽  
Scale Invariant ◽  
Brain Circuits ◽  
Power Law Exponent ◽  
Fluctuation Scaling ◽  
Time Contraction ◽  
Dominant Frequencies

We employed high-density microelectrode arrays to investigate spontaneous firing patterns of neurons in brain circuits of the primary somatosensory cortex (S1) in mice. We recorded from over 150 neurons for 10[Formula: see text]min in each of eight different experiments, identified their location in S1, sorted their action potentials (spikes), and computed their power spectra and inter-spike interval (ISI) statistics. Of all persistently active neurons, 92% fired with a single dominant frequency — regularly firing neurons (RNs) — from 1 to 8[Formula: see text]Hz while 8% fired in burst with two dominant frequencies — bursting neurons (BNs) — corresponding to the inter-burst (2–6[Formula: see text]Hz) and intra-burst intervals (20–160[Formula: see text]Hz). RNs were predominantly located in layers 2/3 and 5/6 while BNs localized to layers 4 and 5. Across neurons, the standard deviation of ISI was a power law of its mean, a property known as fluctuation scaling, with a power law exponent of 1 for RNs and 1.25 for BNs. The power law implies that firing and bursting patterns are scale invariant: the firing pattern of a given RN or BN resembles that of another RN or BN, respectively, after a time contraction or dilation. An explanation for this scale invariance is discussed in the context of previous computational studies as well as its potential role in information processing.

scholarly journals Dynamic changes in rhythmic and arrhythmic neural signatures in the subthalamic nucleus induced by anaesthesia and intubation

2019 ◽  
Author(s):  
Yongzhi Huang ◽  
Kejia Hu ◽  
Alexander L. Green ◽  
Xin Ma ◽  
Martin J. Gillies ◽  
...  
Keyword(s):  
Basal Ganglia ◽  
Subthalamic Nucleus ◽  
Power Law ◽  
High Frequency ◽  
Power Spectra ◽  
Multiple Frequency ◽  
Dynamic Changes ◽  
Frequency Bands ◽  
Power Law Exponent ◽  
Neural Signatures

AbstractBackgroundSubcortical structures including the basal ganglia have been proposed to be crucial for arousal, consciousness, and behavioural responsiveness. However, how basal ganglia contributes to the loss and recovery of consciousness during anaesthesia has not been well characterized.MethodsIn this study, using local field potentials (LFPs) from subthalamic nucleus (STN) and scalp electroencephalogram in 12 Parkinson’s disease patients, we investigate STN neural signatures during propofol general anaesthesia and during intubation as an arousal intervention in anaesthesia.ResultsPropofol-induced anaesthesia resulted in changes in multiple frequency bands in STN LFPs, including increased low-frequency activities (slow-wave oscillation, delta, theta, and alpha bands) and decreased higher-frequency activities. This was also accompanied by increased STN-frontal cortical coherence in alpha frequency band. Beta and high-gamma activities in the STN temporally increased during intubation compared to the status of loss of consciousness. We also show that the dynamic changes in the high frequency activities (80-180 Hz) in STN LFPs induced by propofol and intubation correlated with power-law exponent in the power spectra between 2 and 80 Hz.ConclusionsOur findings suggest that anaesthesia and intubation induced changes in the STN LFPs in multiple frequency bands. They are also consistent with the hypothesis that the power-law exponent in the power spectra between 2 and 80 Hz reflect the excitation/inhibition balance in the STN, which is modulated by anaesthesia and intubation, and further modulate the high frequency activity.

scholarly journals Linearity and time-scale invariance of the creep function in living cells

2004 ◽  
Vol 1 (1) ◽  
pp. 91-97 ◽  
Author(s):  
Guillaume Lenormand ◽  
Emil Millet ◽  
Ben Fabry ◽  
James P. Butler ◽  
Jeffrey J. Fredberg
Keyword(s):  
Power Law ◽  
Time Scale ◽  
Relaxation Times ◽  
Cell Types ◽  
Creep Function ◽  
Scale Invariant ◽  
Time Constants ◽  
Frequency Domains ◽  
Power Law Exponent ◽  
The Matrix

We report here the creep function measured in three cell types, after a variety of interventions, and over three time decades (from 3ms to 3.2 s). In each case the response conformed to a power law, implying that no distinct molecular relaxation times or time constants could characterize the response. These results add to a growing body of evidence that stands in contrast to widely used viscoelastic models featuring at most a few time constants. We show instead that the ability of the matrix to deform is time-scale invariant and characterized by only one parameter: the power law exponent that controls the transition between solid-like and liquid-like behaviour. Moreover, we validate linearity by comparison of measurements in the time and frequency domains.

Regional variation of recession flow power-law exponent

2018 ◽  
Vol 32 (7) ◽  
pp. 866-872 ◽  
Author(s):  
Swagat Patnaik ◽  
Basudev Biswal ◽  
Dasika Nagesh Kumar ◽  
Bellie Sivakumar
Keyword(s):  
Power Law ◽  
Regional Variation ◽  
Power Law Exponent ◽  
Flow Power

scholarly journals Growth Rate Exponents of Richtmyer-Meshkov Mixing Layers

2005 ◽  
Vol 73 (3) ◽  
pp. 461-468 ◽  
Author(s):  
Timothy T. Clark ◽  
Ye Zhou
Keyword(s):  
Flow Field ◽  
Power Law ◽  
Mixing Layer ◽  
Power Laws ◽  
Mixing Layers ◽  
Spatial Gradients ◽  
Power Law Exponent ◽  
Virtual Time ◽  
Time Origin ◽  
Density Ratios

The Richtmyer-Meshkov mixing layer is initiated by the passing of a shock over an interface between fluid of differing densities. The energy deposited during the shock passage undergoes a relaxation process during which the fluctuational energy in the flow field decays and the spatial gradients of the flow field decrease in time. This late stage of Richtmyer-Meshkov mixing layers is studied from the viewpoint of self-similarity. Analogies with weakly anisotropic turbulence suggest that both the bubble-side and spike-side widths of the mixing layer should evolve as power-laws in time, with the same power-law exponent and virtual time origin for both sides. The analogy also bounds the power-law exponent between 2∕7 and 1∕2. It is then shown that the assumption of identical power-law exponents for bubbles and spikes yields fits that are in good agreement with experiment at modest density ratios.

scholarly journals Free Convective MHD Flow Past a Vertical Cone with Variable Heat and Mass Flux

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
J. Prakash ◽  
S. Gouse Mohiddin ◽  
S. Vijaya Kumar Varma
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Mass Flux ◽  
Numerical Study ◽  
Convection Boundary Layer ◽  
Vertical Cone ◽  
Local Skin ◽  
Surface Mass ◽  
Flow Past ◽  
Power Law Exponent

A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power law according to qwx=xm and qw*(x)=xm, respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then nondimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature, and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter, and semivertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the published results and are found to be in excellent agreement. The local skin friction, Nusselt number, and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes, and hybrid solar energy systems.

scholarly journals Breakdown coefficients and scaling properties of rain fields

1998 ◽  
Vol 5 (2) ◽  
pp. 93-104 ◽  
Author(s):  
D. Harris ◽  
M. Menabde ◽  
A. Seed ◽  
G. Austin
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Power Law ◽  
Scale Parameter ◽  
Probability Distributions ◽  
Scaling Analysis ◽  
Scaling Properties ◽  
Power Law Exponent ◽  
Scale Similarity ◽  
Parameter Estimation Techniques

Abstract. The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf) of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter  estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width), σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.

scholarly journals A simple conceptual model to interpret the 100 000 years dynamics of paleo-climate records

2010 ◽  
Vol 17 (5) ◽  
pp. 585-592 ◽  
Author(s):  
C. S. Quiroga Lombard ◽  
P. Balenzuela ◽  
H. Braun ◽  
D. R. Chialvo
Keyword(s):  
Large Scale ◽  
Power Spectra ◽  
Greenland Ice Sheet ◽  
Ice Age ◽  
Solar Cycles ◽  
The Holocene ◽  
De Vries ◽  
Last Ice Age ◽  
Paleoclimate Records ◽  
Dominant Frequencies

Abstract. Spectral analyses performed on records of cosmogenic nuclides reveal a group of dominant spectral components during the Holocene period. Only a few of them are related to known solar cycles, i.e., the De Vries/Suess, Gleissberg and Hallstatt cycles. The origin of the others remains uncertain. On the other hand, time series of North Atlantic atmospheric/sea surface temperatures during the last ice age display the existence of repeated large-scale warming events, called Dansgaard-Oeschger (DO) events, spaced around multiples of 1470 years. The De Vries/Suess and Gleissberg cycles with periods close to 1470/7 (~210) and 1470/17 (~86.5) years have been proposed to explain these observations. In this work we found that a conceptual bistable model forced with the De Vries/Suess and Gleissberg cycles plus noise displays a group of dominant frequencies similar to those obtained in the Fourier spectra from paleo-climate during the Holocene. Moreover, we show that simply changing the noise amplitude in the model we obtain similar power spectra to those corresponding to GISP2 δ18O (Greenland Ice Sheet Project 2) during the last ice age. These results give a general dynamical framework which allows us to interpret the main characteristic of paleoclimate records from the last 100 000 years.

Spectral characterization of ciliary beating: variations of frequency with time

1985 ◽  
Vol 249 (1) ◽  
pp. C160-C165 ◽  
Author(s):  
D. Eshel ◽  
Y. Grossman ◽  
Z. Priel
Keyword(s):  
Mathematical Model ◽  
Power Spectra ◽  
Ciliary Beating ◽  
Isolated Lung ◽  
Ciliary Cell ◽  
The Mathematical Model ◽  
Beating Frequency ◽  
Over Time ◽  
Dominant Frequencies

Ciliary beating frequency in tissue culture from frog palate and isolated lung was optically examined using instrumentation that was adjusted to measure a fraction of the surface area of a single ciliary cell. Consecutive 1-s segments of the analogue signal were fast Fourier transformed (FFT) to obtain a power spectrum. At room temperature, these power spectra changed over time from 1 s to the next. Each spectrum contained several dominant frequencies of similar intensities. Cooling the preparation resulted in a single-peak spectrum that was constant over time. A mathematical model is proposed to simulate these findings. The results and the mathematical model support the hypothesis that ciliary beating frequency fluctuates over short periods of time.

scholarly journals Differences in power-law growth over time and indicators of COVID-19 pandemic progression worldwide

2020 ◽  
Author(s):  
Jack Merrin
Keyword(s):  
Error Analysis ◽  
Real Time ◽  
Power Law ◽  
Growth Phase ◽  
Exponential Growth ◽  
Spreading Rate ◽  
Exponential Growth Phase ◽  
Power Law Exponent ◽  
Disease Spreading ◽  
Over Time

1AbstractAn automated statistical and error analysis of 45 countries or regions with more than 1000 cases of COVID-19 as of March 28, 2020, has been performed. This study reveals differences in the rate of disease spreading rate over time in different countries. This survey observes that most countries undergo a beginning exponential growth phase, which transitions into a power-law phase, as recently suggested by Ziff and Ziff. Tracking indicators of growth, such as the power-law exponent, are a good indication of the relative danger different countries are in and show when social measures are effective towards slowing the spread. The data compiled here are usefully synthesizing a global picture, identifying country to country variation in spreading, and identifying countries most at risk. This analysis may factor into how best to track the effectiveness of social distancing policies and quarantines in real-time as data is updated each day.

scholarly journals Scale-free networks with the power-law exponent between 1 and 3

2007 ◽  
Vol 56 (10) ◽  
pp. 5635
Author(s):  
Guo Jin-Li ◽  
Wang Li-Na
Keyword(s):  
Power Law ◽  
Scale Free ◽  
Power Law Exponent ◽  
Scale Free Networks
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