scholarly journals Lévy walk dynamics explain gamma burst patterns in primate cerebral cortex

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Yuxi Liu ◽  
Xian Long ◽  
Paul R. Martin ◽  
Samuel G. Solomon ◽  
Pulin Gong
Keyword(s):  
Cerebral Cortex ◽  
Oscillatory Activity ◽  
Motion Processing ◽  
Empirical Observation ◽  
Lévy Walk ◽  
Visual Motion Processing ◽  
Lévy Walks ◽  
Levy Walk ◽  
Primate Cerebral Cortex ◽  
Burst Patterns

AbstractLévy walks describe patterns of intermittent motion with variable step sizes. In complex biological systems, Lévy walks (non-Brownian, superdiffusive random walks) are associated with behaviors such as search patterns of animals foraging for food. Here we show that Lévy walks also describe patterns of oscillatory activity in primate cerebral cortex. We used a combination of empirical observation and modeling to investigate high-frequency (gamma band) local field potential activity in visual motion-processing cortical area MT of marmoset monkeys. We found that gamma activity is organized as localized burst patterns that propagate across the cortical surface with Lévy walk dynamics. Lévy walks are fundamentally different from either global synchronization, or regular propagating waves, because they include large steps that enable activity patterns to move rapidly over cortical modules. The presence of Lévy walk dynamics therefore represents a previously undiscovered mode of brain activity, and implies a novel way for the cortex to compute. We apply a biophysically realistic circuit model to explain that the Lévy walk dynamics arise from critical-state transitions between asynchronous and localized propagating wave states, and that these dynamics yield optimal spatial sampling of the cortical sheet. We hypothesise that Lévy walk dynamics could help the cortex to efficiently process variable inputs, and to find links in patterns of activity among sparsely spiking populations of neurons.

scholarly journals Simulations of Lévy walk

2020 ◽  
Author(s):  
Venkat Abhignan ◽  
Sinduja Rajadurai
Keyword(s):  
Movement Pattern ◽  
Stable Distributions ◽  
Lévy Distribution ◽  
Lévy Walk ◽  
Lévy Walks ◽  
Levy Distribution ◽  
Levy Walk ◽  
The Ideal

AbstractWe simulate stable distributions to study the ideal movement pattern for the spread of a virus using autonomous carrier. We observe Lévy walks to be the most ideal way to spread and further study how the parameters in Lévy distribution affects the spread.

scholarly journals Signatures of active and passive optimized Lévy searching in jellyfish

2014 ◽  
Vol 11 (99) ◽  
pp. 20140665 ◽  
Author(s):  
Andy M. Reynolds
Keyword(s):  
Simulated Annealing ◽  
Water Column ◽  
Movement Patterns ◽  
Search Theory ◽  
Search Pattern ◽  
Global Maximum ◽  
Distributed Resources ◽  
Lévy Walk ◽  
Lévy Walks ◽  
Levy Walk

Some of the strongest empirical support for Lévy search theory has come from telemetry data for the dive patterns of marine predators (sharks, bony fishes, sea turtles and penguins). The dive patterns of the unusually large jellyfish Rhizostoma octopus do, however, sit outside of current Lévy search theory which predicts that a single search strategy is optimal. When searching the water column, the movement patterns of these jellyfish change over time. Movement bouts can be approximated by a variety of Lévy and Brownian (exponential) walks. The adaptive value of this variation is not known. On some occasions movement pattern data are consistent with the jellyfish prospecting away from a preferred depth, not finding an improvement in conditions elsewhere and so returning to their original depth. This ‘bounce’ behaviour also sits outside of current Lévy walk search theory. Here, it is shown that the jellyfish movement patterns are consistent with their using optimized ‘fast simulated annealing’—a novel kind of Lévy walk search pattern—to locate the maximum prey concentration in the water column and/or to locate the strongest of many olfactory trails emanating from more distant prey. Fast simulated annealing is a powerful stochastic search algorithm for locating a global maximum that is hidden among many poorer local maxima in a large search space. This new finding shows that the notion of active optimized Lévy walk searching is not limited to the search for randomly and sparsely distributed resources, as previously thought, but can be extended to embrace other scenarios, including that of the jellyfish R. octopus . In the presence of convective currents, it could become energetically favourable to search the water column by riding the convective currents. Here, it is shown that these passive movements can be represented accurately by Lévy walks of the type occasionally seen in R. octopus . This result vividly illustrates that Lévy walks are not necessarily the result of selection pressures for advantageous searching behaviour but can instead arise freely and naturally from simple processes. It also shows that the family of Lévy walkers is vastly larger than previously thought and includes spores, pollens, seeds and minute wingless arthropods that on warm days disperse passively within the atmospheric boundary layer.

scholarly journals Bridging the gulf between correlated random walks and Lévy walks: autocorrelation as a source of Lévy walk movement patterns

2010 ◽  
Vol 7 (53) ◽  
pp. 1753-1758 ◽  
Author(s):  
Andy M. Reynolds
Keyword(s):  
Animal Movement ◽  
Probability Distributions ◽  
Movement Patterns ◽  
Lévy Walk ◽  
Lévy Walks ◽  
Correlated Random Walks ◽  
Levy Walk ◽  
Simple Scaling ◽  
Experimental And Theoretical Studies ◽  
Intense Debate

For many years, the dominant conceptual framework for describing non-oriented animal movement patterns has been the correlated random walk (CRW) model in which an individual's trajectory through space is represented by a sequence of distinct, independent randomly oriented ‘moves’. It has long been recognized that the transformation of an animal's continuous movement path into a broken line is necessarily arbitrary and that probability distributions of move lengths and turning angles are model artefacts. Continuous-time analogues of CRWs that overcome this inherent shortcoming have appeared in the literature and are gaining prominence. In these models, velocities evolve as a Markovian process and have exponential autocorrelation. Integration of the velocity process gives the position process. Here, through a simple scaling argument and through an exact analytical analysis, it is shown that autocorrelation inevitably leads to Lévy walk (LW) movement patterns on timescales less than the autocorrelation timescale. This is significant because over recent years there has been an accumulation of evidence from a variety of experimental and theoretical studies that many organisms have movement patterns that can be approximated by LWs, and there is now intense debate about the relative merits of CRWs and LWs as representations of non-orientated animal movement patterns.

scholarly journals Intermittent inverse-square Lévy walks are optimal for finding targets of all sizes

2021 ◽  
Vol 7 (15) ◽  
pp. eabe8211
Author(s):  
Brieuc Guinard ◽  
Amos Korman
Keyword(s):  
Random Walk ◽  
Mathematical Proof ◽  
Higher Dimensions ◽  
Two Dimensional ◽  
Power Law Distribution ◽  
Arbitrary Size ◽  
Lévy Walk ◽  
Lévy Walks ◽  
Levy Walk ◽  
Biological Organisms

Lévy walks are random walk processes whose step lengths follow a long-tailed power-law distribution. Because of their abundance as movement patterns of biological organisms, substantial theoretical efforts have been devoted to identifying the foraging circumstances that would make such patterns advantageous. However, despite extensive research, there is currently no mathematical proof indicating that Lévy walks are, in any manner, preferable strategies in higher dimensions than one. Here, we prove that in finite two-dimensional terrains, the inverse-square Lévy walk strategy is extremely efficient at finding sparse targets of arbitrary size and shape. Moreover, this holds even under the weak model of intermittent detection. Conversely, any other intermittent Lévy walk fails to efficiently find either large targets or small ones. Our results shed new light on the Lévy foraging hypothesis and are thus expected to affect future experiments on animals performing Lévy walks.

Diffusion

2018 ◽  
Author(s):  
Ginestra Bianconi
Keyword(s):  
Random Walks ◽  
Spectral Properties ◽  
Diffusion Constant ◽  
Network Structures ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Lévy Walk ◽  
Number Of Layers ◽  
Levy Walk ◽  
Speed Up

This chapter addresses diffusion, random walks and congestion in multilayer networks. Here it is revealed that diffusion on a multilayer network can be significantly speed up with respect to diffusion taking place on its single layers taken in isolation, and that sometimes it is possible also to observe super-diffusion. Diffusion is here characterized on multilayer network structures by studying the spectral properties of the supra-Laplacian and the dependence on the diffusion constant among different layers. Random walks and its variations including the Lévy Walk are shown to reflect the improved navigability of multilayer networks with more layers. These results are here compared with the results of traffic on multilayer networks that, on the contrary, point out that increasing the number of layers could be detrimental and could lead to congestion.

scholarly journals Amoebic Foraging Model of Metastatic Cancer Cells

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1140
Author(s):  
Daiki Andoh ◽  
Yukio-Pegio Gunji
Keyword(s):  
Bayesian Inference ◽  
Cancer Cells ◽  
Metastatic Cancer ◽  
Gait Patterns ◽  
Lévy Walk ◽  
Levy Walk ◽  
Unicellular Organisms ◽  
Living Organisms ◽  
Walk Algorithm ◽  
Metastatic Cancer Cells

The Lévy walk is a pattern that is often seen in the movement of living organisms; it has both ballistic and random features and is a behavior that has been recognized in various animals and unicellular organisms, such as amoebae, in recent years. We proposed an amoeba locomotion model that implements Bayesian and inverse Bayesian inference as a Lévy walk algorithm that balances exploration and exploitation, and through a comparison with general random walks, we confirmed its effectiveness. While Bayesian inference is expressed only by P(h) = P(h|d), we introduce inverse Bayesian inference expressed as P(d|h) = P(d) in a symmetry fashion. That symmetry contributes to balancing contracting and expanding the probability space. Additionally, the conditions of various environments were set, and experimental results were obtained that corresponded to changes in gait patterns with respect to changes in the conditions of actual metastatic cancer cells.

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