Is learning scale-free? Chemistry learning increases EEG fractal power and changes the power law exponent

2020 ◽  
Vol 156 ◽  
pp. 165-177 ◽  
Author(s):  
Amanda Bongers ◽  
Alison B. Flynn ◽  
Georg Northoff
Keyword(s):  
Power Law ◽  
Scale Free ◽  
Chemistry Learning ◽  
Power Law Exponent

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

SELF-ORGANIZED CORONA GRAPHS: A DETERMINISTIC COMPLEX NETWORK MODEL WITH HIERARCHICAL STRUCTURE

2019 ◽  
Vol 22 (06) ◽  
pp. 1950019
Author(s):  
ROHAN SHARMA ◽  
BIBHAS ADHIKARI ◽  
TYLL KRUEGER
Keyword(s):  
Power Law ◽  
Small World ◽  
Self Organization ◽  
Scale Free ◽  
Self Organized ◽  
Power Law Exponent ◽  
Growing Networks ◽  
Growing Network ◽  
Hierarchical Pattern ◽  
Corona Graphs

In this paper, we propose a self-organization mechanism for newly appeared nodes during the formation of corona graphs that define a hierarchical pattern in the resulting corona graphs and we call it self-organized corona graphs (SoCG). We show that the degree distribution of SoCG follows power-law in its tail with power-law exponent approximately 2. We also show that the diameter is less equal to 4 for SoCG defined by any seed graph and for certain seed graphs, the diameter remains constant during its formation. We derive lower bounds of clustering coefficients of SoCG defined by certain seed graphs. Thus, the proposed SoCG can be considered as a growing network generative model which is defined by using the corona graphs and a self-organization process such that the resulting graphs are scale-free small-world highly clustered growing networks. The SoCG defined by a seed graph can also be considered as a network with a desired motif which is the seed graph itself.

scholarly journals Percolation phase transition in weight-dependent random connection models

2021 ◽  
Vol 53 (4) ◽  
pp. 1090-1114
Author(s):  
Peter Gracar ◽  
Lukas Lüchtrath ◽  
Peter Mörters
Keyword(s):  
Phase Transition ◽  
Poisson Process ◽  
Random Graphs ◽  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Dimensional Space ◽  
Geometric Model ◽  
Scale Free ◽  
Power Law Exponent

AbstractWe investigate spatial random graphs defined on the points of a Poisson process in d-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the weight and position of the points, we form an edge between any pair of points independently with a probability depending on the two weights of the points and their distance. Preference is given to short edges and connections to vertices with large weights. We characterize the parameter regime where there is a non-trivial percolation phase transition and show that it depends not only on the power-law exponent of the degree distribution but also on a geometric model parameter. We apply this result to characterize robustness of age-based spatial preferential attachment networks.

THE SCALE-FREE AND SMALL-WORLD PROPERTIES OF COMPLEX NETWORKS ON SIERPINSKI-TYPE HEXAGON

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050054
Author(s):  
KUN CHENG ◽  
DIRONG CHEN ◽  
YUMEI XUE ◽  
QIAN ZHANG
Keyword(s):  
Power Law ◽  
Path Length ◽  
Small World ◽  
The Self ◽  
Renewal Theorem ◽  
Self Similarity ◽  
Scale Free ◽  
Power Law Exponent ◽  
Self Similar ◽  
Encoding Method

In this paper, a network is generated from a Sierpinski-type hexagon by applying the encoding method in fractal. The criterion of neighbor is established to quantify the relationships among the nodes in the network. Based on the self-similar structures, we verify the scale-free and small-world effects. The power-law exponent on degree distribution is derived to be [Formula: see text] and the average clustering coefficients are shown to be larger than [Formula: see text]. Moreover, we give the bounds of the average path length of our proposed network from the renewal theorem and self-similarity.

scholarly journals The contact process on scale-free networks evolving by vertex updating

2017 ◽  
Vol 4 (5) ◽  
pp. 170081 ◽  
Author(s):  
Emmanuel Jacob ◽  
Peter Mörters
Keyword(s):  
Phase Transition ◽  
Power Law ◽  
Mathematical Proof ◽  
Contact Process ◽  
Network Size ◽  
Mean Field Approximation ◽  
Infection Rates ◽  
Scale Free ◽  
Power Law Exponent ◽  
Scale Free Networks

We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all infection rates the infection survives for a long time, at least exponential in the network size, and a phase where for sufficiently small infection rates extinction occurs quickly, at most polynomially in the network size. The phase transition occurs when the power-law exponent crosses the value four. This behaviour is in contrast with that of the contact process on the corresponding static model, where there is no phase transition, as well as that of a classical mean-field approximation, which has a phase transition at power-law exponent three. The new observation behind our result is that temporal variability of networks can simultaneously increase the rate at which the infection spreads in the network, and decrease the time at which the infection spends in metastable states.

scholarly journals Scale-Free Analysis of Intraoperative ECoG During Awake Craniotomy for Glioma

2021 ◽  
Vol 10 ◽  
Author(s):  
Diana Cristina Ghinda ◽  
Ben Lambert ◽  
Junfeng Lu ◽  
Ning Jiang ◽  
Eve Tsai ◽  
...  
Keyword(s):  
Power Law ◽  
Epileptiform Activity ◽  
Tumor Resection ◽  
Structural Mri ◽  
Awake Craniotomy ◽  
Anatomical Location ◽  
Scale Free ◽  
Power Law Exponent ◽  
Peritumoral Tissue ◽  
The Difference

BackgroundElectrocorticography (ECoG) has been utilized in many epilepsy cases however, the use of this technique for evaluating electrophysiological changes within tumoral zones is spare. Nonetheless, epileptic activities seem to arise from the neocortex surrounding the gliomas suggesting a link between epileptogenesis and glioma cell infiltration in the peritumoral area. The purpose of this study was to implement novel scale-free measures to assess how cortical physiology is altered by the presence of an invasive brain tumor.MethodsTwelve patients undergoing an awake craniotomy for resection of a supratentorial glioma were included. ECoG data over the main tumor and the exposed surroundings was acquired intra-operatively just prior to tumor resection. Six of the patients presented with seizures and had data acquired both in the awake and anesthetic state. The corresponding anatomical location of each electrode in relation to the macroscopically-detectable tumor was recorded using the neuronavigation system based on structural anatomical images obtained pre-operatively. The electrodes were classified into tumoral, healthy or peritumoral based on the macroscopically detectable tumoral tissue from the pre-operative structural MRI.ResultsThe electrodes overlying the tumoral tissue revealed higher power law exponent (PLE) values across tumoral area compared to the surrounding tissues. The difference between the awake and anesthetic states was significant in the tumoral and healthy tissue (p < 0.05) but not in the peritumoral tissue. The absence of a significant PLE reduction in the peritumoral tissue from the anesthetic to the awake state could be considered as an index of the presence or absence of infiltration of tumor cells into the peritumoral tissue.ConclusionsThe current study portrays for the first time distinct power law exponent features in the tumoral tissue, which could provide a potential novel electrophysiological marker in the future. The distinct features seen in the peritumoral tissue of gliomas seem to indicate the area where both the onset of epileptiform activity and the tumor infiltration take place.

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.

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