The Experts below are selected from a list of 527622 Experts worldwide ranked by ideXlab platform
Cecile Monthus - One of the best experts on this subject based on the ideXlab platform.
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multifractality in the generalized aubry andre quasiperiodic localization model with Power Law hoppings or Power Law fourier coefficients
Fractals, 2019Co-Authors: Cecile MonthusAbstract:The nearest-neighbor Aubry–Andre quasiperiodic localization model is generalized to include Power-Law translation-invariant hoppings Tl ∝ t/la or Power-Law Fourier coefficients Wm ∝ w/mb in the qua...
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multifractality in the generalized aubry andre quasiperiodic localization model with Power Law hoppings or Power Law fourier coefficients
arXiv: Disordered Systems and Neural Networks, 2017Co-Authors: Cecile MonthusAbstract:The nearest-neighbor Aubry-Andre quasiperiodic localization model is generalized to include Power-Law translation-invariant hoppings $T_l\propto t/l^a$ or Power-Law Fourier coefficients $W_m \propto w/m^b$ in the quasi-periodic potential. The Aubry-Andre duality between $T_l$ and $W_m$ is manifest when the Hamiltonian is written in the real-space basis and in the Fourier basis on a finite ring. The perturbative analysis in the amplitude $t$ of the hoppings yields that the eigenstates remain Power-Law localized in real space for $a>1$ and are critical for $a_c=1$ where they follow the Strong Multifractality linear spectrum, as in the equivalent model with random disorder. The perturbative analysis in the amplitude $w$ of the quasi-periodic potential yields that the eigenstates remain delocalized in real space (Power-Law localized in Fourier space) for $b>1$ and are critical for $b_c=1$ where they follow the Weak Multifractality gaussian spectrum in real space (or Strong Multifractality linear spectrum in the Fourier basis). This critical case $b_c=1$ for the Fourier coefficients $W_m$ corresponds to a periodic function with discontinuities, instead of the cosinus of the standard self-dual Aubry-Andre model.
Andreas Klaus - One of the best experts on this subject based on the ideXlab platform.
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statistical analyses support Power Law distributions found in neuronal avalanches
PLOS ONE, 2011Co-Authors: Andreas Klaus, Dietmar PlenzAbstract:The size distribution of neuronal avalanches in cortical networks has been reported to follow a Power Law distribution with exponent close to −1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying Power Law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the Power Law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the Power Law, and (iii) comparison of the Power Law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling (“finite size” effect). This scale-free dynamics suggests the Power Law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to −1.5, which is in line with previous reports. Finally, the Power Law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the Power Law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the Power Law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.
Jonathan Touboul - One of the best experts on this subject based on the ideXlab platform.
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can Power Law scaling and neuronal avalanches arise from stochastic dynamics
PLOS ONE, 2010Co-Authors: Jonathan Touboul, Alain DestexheAbstract:The presence of self-organized criticality in biology is often evidenced by a Power-Law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not necessarily mean that the system exhibits self-organized criticality. We first provide an analysis of multisite local field potential (LFP) recordings of brain activity and show that event size distributions defined as negative LFP peaks can be close to Power-Law distributions. However, this result is not robust to change in detection threshold, or when tested using more rigorous statistical analyses such as the Kolmogorov-Smirnov test. Similar Power-Law scaling is observed for surrogate signals, suggesting that Power-Law scaling may be a generic property of thresholded stochastic processes. We next investigate this problem analytically, and show that, indeed, stochastic processes can produce spurious Power-Law scaling without the presence of underlying self-organized criticality. However, this Power-Law is only apparent in logarithmic representations, and does not survive more rigorous analysis such as the Kolmogorov-Smirnov test. The same analysis was also performed on an artificial network known to display self-organized criticality. In this case, both the graphical representations and the rigorous statistical analysis reveal with no ambiguity that the avalanche size is distributed as a Power-Law. We conclude that logarithmic representations can lead to spurious Power-Law scaling induced by the stochastic nature of the phenomenon. This apparent Power-Law scaling does not constitute a proof of self-organized criticality, which should be demonstrated by more stringent statistical tests.
Bela Suki - One of the best experts on this subject based on the ideXlab platform.
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Power Law creep behavior of a semiflexible chain
Physical Review E, 2008Co-Authors: Arnab Majumdar, Bela Suki, Noah J Rosenblatt, Adriano M Alencar, Dimitrije StamenovicAbstract:Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak Power Law over a wide range of time scales. This Power Law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell's viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the Power-Law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain's creep behavior closely correspond to the behavior observed experimentally in living cells. The Power-Law creep behavior results from a finite-speed propagation of free energy from the chain's end points toward the center of the chain in response to an externally applied stretching force. The property that links the Power Law to the prestress is the chain's stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.
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avalanches and Power Law behaviour in lung inflation
Nature, 1994Co-Authors: Bela Suki, Ferenc Peták, Zoltán Hantos, Albert-lászló Barabási, Eugene H StanleyAbstract:WHEN lungs are emptied during exhalation, peripheral airways close up1. For people with lung disease, they may not reopen for a significant portion of inhalation, impairing gas exchange2,3. A knowledge of the mechanisms that govern reinflation of collapsed regions of lungs is therefore central to the development of ventilation strategies for combating respiratory problems. Here we report measurements of the terminal airway resistance, Rt , during the opening of isolated dog lungs. When inflated by a constant flow, Rt decreases in discrete jumps. We find that the probability distribution of the sizes of the jumps and of the time intervals between them exhibit Power-Law behaviour over two decades. We develop a model of the inflation process in which 'avalanches' of airway openings are seen—with Power-Law distributions of both the size of avalanches and the time intervals between them—which agree quantitatively with those seen experimentally, and are reminiscent of the Power-Law behaviour observed for self-organized critical systems4. Thus Power-Law distributions, arising from avalanches associated with threshold phenomena propagating down a branching tree structure, appear to govern the recruitment of terminal airspaces.
Dietmar Plenz - One of the best experts on this subject based on the ideXlab platform.
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statistical analyses support Power Law distributions found in neuronal avalanches
PLOS ONE, 2011Co-Authors: Andreas Klaus, Dietmar PlenzAbstract:The size distribution of neuronal avalanches in cortical networks has been reported to follow a Power Law distribution with exponent close to −1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying Power Law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the Power Law hypothesis for neuronal avalanches by using more stringent statistical analyses. In particular, we performed the following steps: (i) analysis of finite-size scaling to identify scale-free dynamics in neuronal avalanches, (ii) model parameter estimation to determine the specific exponent of the Power Law, and (iii) comparison of the Power Law to alternative model distributions. Consistent with critical state dynamics, avalanche size distributions exhibited robust scaling behavior in which the maximum avalanche size was limited only by the spatial extent of sampling (“finite size” effect). This scale-free dynamics suggests the Power Law as a model for the distribution of avalanche sizes. Using both the Kolmogorov-Smirnov statistic and a maximum likelihood approach, we found the slope to be close to −1.5, which is in line with previous reports. Finally, the Power Law model for neuronal avalanches was compared to the exponential and to various heavy-tail distributions based on the Kolmogorov-Smirnov distance and by using a log-likelihood ratio test. Both the Power Law distribution without and with exponential cut-off provided significantly better fits to the cluster size distributions in neuronal avalanches than the exponential, the lognormal and the gamma distribution. In summary, our findings strongly support the Power Law scaling in neuronal avalanches, providing further evidence for critical state dynamics in superficial layers of cortex.