power law exponent
Recently Published Documents


TOTAL DOCUMENTS

217
(FIVE YEARS 66)

H-INDEX

20
(FIVE YEARS 3)

2022 ◽  
Vol 18 (1) ◽  
pp. e1009739
Author(s):  
Nathan C. L. Kong ◽  
Eshed Margalit ◽  
Justin L. Gardner ◽  
Anthony M. Norcia

Task-optimized convolutional neural networks (CNNs) show striking similarities to the ventral visual stream. However, human-imperceptible image perturbations can cause a CNN to make incorrect predictions. Here we provide insight into this brittleness by investigating the representations of models that are either robust or not robust to image perturbations. Theory suggests that the robustness of a system to these perturbations could be related to the power law exponent of the eigenspectrum of its set of neural responses, where power law exponents closer to and larger than one would indicate a system that is less susceptible to input perturbations. We show that neural responses in mouse and macaque primary visual cortex (V1) obey the predictions of this theory, where their eigenspectra have power law exponents of at least one. We also find that the eigenspectra of model representations decay slowly relative to those observed in neurophysiology and that robust models have eigenspectra that decay slightly faster and have higher power law exponents than those of non-robust models. The slow decay of the eigenspectra suggests that substantial variance in the model responses is related to the encoding of fine stimulus features. We therefore investigated the spatial frequency tuning of artificial neurons and found that a large proportion of them preferred high spatial frequencies and that robust models had preferred spatial frequency distributions more aligned with the measured spatial frequency distribution of macaque V1 cells. Furthermore, robust models were quantitatively better models of V1 than non-robust models. Our results are consistent with other findings that there is a misalignment between human and machine perception. They also suggest that it may be useful to penalize slow-decaying eigenspectra or to bias models to extract features of lower spatial frequencies during task-optimization in order to improve robustness and V1 neural response predictivity.


2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Bing Guan ◽  
Haiyang Yu ◽  
Wei Song ◽  
Jaeho Choi

For the free-space optical (FSO) communication system, the spatial coherence of a laser beam is influenced obviously as it propagates through the atmosphere. This loss of spatial coherence limits the degree to which the laser beam is collimated or focused, resulting in a significant decrease in the power level of optical communication and radar systems. In this work, the analytic expressions of wave structure function for plane and spherical wave propagation through anisotropic non-Kolmogorov turbulence in a horizontal path are derived. Moreover, the new expressions for spatial coherence radius are obtained considering different scales of atmospheric turbulence. Using the newly obtained expressions for the spatial coherent radius, the effects of the inner scales and the outer scales of the turbulence, the power law exponent, and the anisotropic factor are analyzed. The analytical simulation results show that the wave structure functions are greatly influenced by the power law exponent α , the anisotropic factor ζ , the turbulence strength σ ~ R 2 , and the turbulence scales. Moreover, the spatial coherence radiuses are also significantly affected by the anisotropic factor ζ and the turbulence strength σ ~ R 2 , while they are gently influenced by the power law exponent α and the inner scales of the optical waves.


Author(s):  
Christian Minnert ◽  
Karsten Durst

AbstractDifferent loading protocols have been developed in the past to investigate the creep properties of materials using instrumented indentation testing technique. Recently, a new indentation creep method was presented, in which the contact pressure is kept constant during the creep test segment, similar to the constant stress applied in a uniaxial creep experiment. In this study, the results of constant contact pressure creep tests are compared to uniaxial and constant load hold indentation creep experiments on ultrafine grained Cu and CuAl5. The constant contact pressure method yields similar stress exponents as the uniaxial tests, down to indentation strain rates of 10–6 s−1, whereas the constant load hold method results mainly in a relaxation of the material at decreasing applied pressures. Furthermore, a pronounced change in the power law exponent at large stress reductions is found for both uniaxial and constant contact pressure tests, indicating a change in deformation mechanism of ultrafine grained metals. Graphical abstract


2021 ◽  
Author(s):  
Jakob Schreiner ◽  
Kent-Andre Mardal

Abstract Epileptic seizures are due to excessive and synchronous neural activity. Extensive modelling of seizures has been done on the neuronal level, but it remains a challenge to scale these models up to whole brain models. Measurements of the brain’s activity over several spatiotemporal scales follow a power-law distribution in terms of frequency. During normal brain activity, the power-law exponent is often found to be around 2 for frequencies between a few Hz and up to 150 Hz, but is higher during seizures and for higher frequencies. The Bidomain model has been used with success in modelling the electrical activity of the heart, but has been explored far less in the context of the brain. This study extends previous models of epileptic seizures on the neuronal level to the whole brain using the Bidomain model. Our approach is evaluated in terms of power-law distributions. The electric potentials were simulated in 7 idealized 2D models and 3 MRI-derived 3D patient-specific models. Computed electric potentials were found to follow power-law distribtions with slopes ranging from 2 to 5 for frequencies greater than 10-30 Hz.


2021 ◽  
Vol 53 (4) ◽  
pp. 1090-1114
Author(s):  
Peter Gracar ◽  
Lukas Lüchtrath ◽  
Peter Mörters

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.


2021 ◽  
Author(s):  
Ketika Garg ◽  
Christopher T. Kello ◽  
Paul E Smaldino

Search requires balancing exploring for more options and exploiting the ones previously found. Individuals foraging in a group face another trade-off: whether to engage in social learning to exploit the solutions found by others or to solitarily search for unexplored solutions. Social learning can decrease the costs of finding new resources, but excessive social learning can decrease the exploration for new solutions. We study how these two trade-offs interact to influence search efficiency in a model of collective foraging under conditions of varying resource abundance, resource density, and group size. We modeled individual search strategies as Lévy walks, where a power-law exponent (μ) controlled the trade-off between exploitative and explorative movements in individual search. We modulated the trade-off between individual search and social learning using a selectivity parameter that determined how agents responded to social cues in terms of distance and likely opportunity costs. Our results show that social learning is favored in rich and clustered environments, but also that the benefits of exploiting social information are maximized by engaging in high levels of individual exploration. We show that selective use of social information can modulate the disadvantages of excessive social learning, especially in larger groups and with limited individual exploration. Finally, we found that the optimal combination of individual exploration and social learning gave rise to trajectories with μ ≈ 2 and provide support for the general optimality such patterns in search. Our work sheds light on the interplay between individual search and social learning, and has broader implications for collective search and problem-solving.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jiu-Tao Hang ◽  
Yu Kang ◽  
Guang-Kui Xu ◽  
Huajian Gao

AbstractLiving cells are a complex soft material with fascinating mechanical properties. A striking feature is that, regardless of their types or states, cells exhibit a universal power-law rheological behavior which to this date still has not been captured by a single theoretical model. Here, we propose a cellular structural model that accounts for the essential mechanical responses of cell membrane, cytoplasm and cytoskeleton. We demonstrate that this model can naturally reproduce the universal power-law characteristics of cell rheology, as well as how its power-law exponent is related to cellular stiffness. More importantly, the power-law exponent can be quantitatively tuned in the range of 0.1 ~ 0.5, as found in most types of cells, by varying the stiffness or architecture of the cytoskeleton. Based on the structural characteristics, we further develop a self-similar hierarchical model that can spontaneously capture the power-law characteristics of creep compliance over time and complex modulus over frequency. The present model suggests that mechanical responses of cells may depend primarily on their generic architectural mechanism, rather than specific molecular properties.


2021 ◽  
Vol 8 ◽  
Author(s):  
Lauren Smith ◽  
William Richard Turrell

Eighty surveys of ten Scottish beaches recorded litter sizes and weights. A simple model of fragmentation explains the distribution of plastic beach litter weights, producing a logarithmic cascade in weight-frequencies having a power law exponent of 1.6. Implications of fragmentation are numerous. Heavy litter is rare, light fragments are common. Monitoring by number is sensitive to minimum observable fragment size, age of the litter, and energy of the foreshore. Mean litter item weights should be used to calculate beach plastic loadings. Presence/absence of mega litter can distort monitoring by weight. Multiple surveys are needed to estimate mega litter statistics. Monitoring by weight can change the perception of the importance of litter sources (e.g., in our surveys, contribution from fishing was 6% by number, 41% by weight). In order to introduce consistency between beach surveys using visual methods by number, a standard minimum plastic fragment size should be introduced.


Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Albert Kwame Kwaw ◽  
Zhi Dou ◽  
Jinguo Wang ◽  
Yuting Zhang ◽  
Xueyi Zhang ◽  
...  

In this study, four homogeneous porous media (HPM1-HPM4), consisting of distinct proportions of sand-sized and clay-sized solid beads, were prepared and used as single fracture infills. Flow and nonreactive solute transport experiments in HPM1-HPM4 under three flow rates were conducted, and the measured breakthrough curves (BTCs) were quantified using conventional advection-dispersion equation (ADE), mobile-immobile model (MIM), and continuous time random walk (CTRW) model with truncated power law transition time distribution. The measured BTCs showed stronger non-Fickian behaviour in HPM2-HPM4 (which had clay) than in HPM1 (which had no clay), implying that clay enhanced the non-Fickian transport. As the fraction of clay increased, the global error of ADE fits also increased, affirming the inefficiency of ADE in capturing the clay-induced non-Fickian behaviour. MIM and CTRW performed better in capturing the non-Fickian behaviour. Nonetheless, CTRW’s performance was robust. 12.5% and 25% of clay in HPM2 and HPM3, respectively, decreased the flowing fluid region and increased the solute exchange rate between the flowing and stagnant fluid regions in MIM. For CTRW, the power law exponent ( β CTRW ) values were 1.96, 1.75, and 1.63 in HPM1-HPM3, respectively, implying enhanced non-Fickian behaviour. However, for HPM4, whose clay fraction was 50%, the β CTRW value was 1.87, implying a deviation in the trend of non-Fickian enhancement with increasing clay fraction. This deviation indicated that non-Fickian behaviour enhancement depended on the fraction of clay present. Moreover, increasing flow rate enhanced the non-Fickian transport based on β CTRW .


Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1871
Author(s):  
Matt G. Hall ◽  
Carson Ingo

In this article, we consider how differing approaches that characterize biological microstructure with diffusion weighted magnetic resonance imaging intersect. Without geometrical boundary assumptions, there are techniques that make use of power law behavior which can be derived from a generalized diffusion equation or intuited heuristically as a time dependent diffusion process. Alternatively, by treating biological microstructure (e.g., myelinated axons) as an amalgam of stick-like geometrical entities, there are approaches that can be derived utilizing convolution-based methods, such as the spherical means technique. Since data acquisition requires that multiple diffusion weighting sensitization conditions or b-values are sampled, this suggests that implicit mutual information may be contained within each technique. The information intersection becomes most apparent when the power law exponent approaches a value of 12, whereby the functional form of the power law converges with the explicit stick-like geometric structure by way of confluent hypergeometric functions. While a value of 12 is useful for the case of solely impermeable fibers, values that diverge from 12 may also reveal deep connections between approaches, and potentially provide insight into the presence of compartmentation, exchange, and permeability within heterogeneous biological microstructures. All together, these disparate approaches provide a unique opportunity to more completely characterize the biological origins of observed changes to the diffusion attenuated signal.


Sign in / Sign up

Export Citation Format

Share Document