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Journal articles on the topic 'Lévy area'

Author: Grafiati

Published: 23 September 2022

Last updated: 19 July 2025

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1

Gottwald, Georg A., and Ian Melbourne. "Time-reversibility and nonvanishing Lévy area." Nonlinearity 37, no. 7 (2024): 075018. http://dx.doi.org/10.1088/1361-6544/ad4947.

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Abstract We give a complete description and clarification of the structure of the Lévy area correction to Itô/Stratonovich stochastic integrals arising as limits of time-reversible deterministic dynamical systems. In particular, we show that time-reversibility forces the Lévy area to vanish only in very specific situations that are easily classified. In the absence of such obstructions, we prove that there are no further restrictions on the Lévy area and that it is typically nonvanishing and far from negligible.

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2

Neuenkirch, A., S. Tindel, and J. Unterberger. "Discretizing the fractional Lévy area." Stochastic Processes and their Applications 120, no. 2 (2010): 223–54. http://dx.doi.org/10.1016/j.spa.2009.10.007.

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3

Li, Juan, Qing An, Hong Lei, Qian Deng, and Gai-Ge Wang. "Survey of Lévy Flight-Based Metaheuristics for Optimization." Mathematics 10, no. 15 (2022): 2785. http://dx.doi.org/10.3390/math10152785.

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Lévy flight is a random walk mechanism which can make large jumps at local locations with a high probability. The probability density distribution of Lévy flight was characterized by sharp peaks, asymmetry, and trailing. Its movement pattern alternated between frequent short-distance jumps and occasional long-distance jumps, which can jump out of local optimal and expand the population search area. The metaheuristic algorithms are inspired by nature and applied to solve NP-hard problems. Lévy flight is used as an operator in the cuckoo algorithm, monarch butterfly optimization, and moth search algorithms. The superiority for the Lévy flight-based metaheuristic algorithms has been demonstrated in many benchmark problems and various application areas. A comprehensive survey of the Lévy flight-based metaheuristic algorithms is conducted in this paper. The research includes the following sections: statistical analysis about Lévy flight, metaheuristic algorithms with a Lévy flight operator, and classification of Lévy flight used in metaheuristic algorithms. The future insights and development direction in the area of Lévy flight are also discussed.

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4

Malham, Simon J. A., and Anke Wiese. "Efficient almost-exact Lévy area sampling." Statistics & Probability Letters 88 (May 2014): 50–55. http://dx.doi.org/10.1016/j.spl.2014.01.022.

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5

Ledoux, M., T. Lyons, and Z. Qian. "Lévy area of Wiener processes in Banach spaces." Annals of Probability 30, no. 2 (2002): 546–78. http://dx.doi.org/10.1214/aop/1023481002.

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6

Capitaine, M., and C. Donati-Martin. "The Lévy Area Process for the Free Brownian Motion." Journal of Functional Analysis 179, no. 1 (2001): 153–69. http://dx.doi.org/10.1006/jfan.2000.3679.

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7

Kilic, Ilker. "A Lévy Flight Based BAT Optimization Algorithm for Block-based Image Compression." Tehnički glasnik 16, no. 4 (2022): 477–83. http://dx.doi.org/10.31803/tg-20220329112403.

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Many metaheuristics have been adopted to solve the codebook generation problem in image processing. In this paper, the Bat algorithm is combined by the Lévy flight distribution to find out the global optimum codebook. The Lévy flight distribution is combined by the local search procedure. Therefore most of the time the bat concentrate on the local area for specific food while it rarely flies to the different parts of the field for better food opportunities. This process strongly guides the bat on the global minimum way and offers better food, then the bat flies to that direction. Consequently, if a bat is captured by a local minimum point accidentally, the Lévy flight step provides a chance to escape from it easily. Numerical results suggest that the proposed Lévy flight based Bat algorithm is better than the classical ones and provides the global optimum codebook for image compression.

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8

Letemplier, Julien, and Thomas Simon. "The area of a spectrally positive stable process stopped at zero." Probability and Mathematical Statistics 38, no. 1 (2018): 27–37. http://dx.doi.org/10.19195/0208-4147.38.1.2.

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A multiplicative identity in law for the area of a spectrally positive Lévy ∝-stable process stopped at zero is established. Extending that of Lefebvre for Brownian motion, it involves an inverse beta random variable and the square of a positive stable random variable. This simple identity makes it possible to study precisely the behaviour of the density at zero, which is Fréchet-like.

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9

Hills, Thomas T., Christopher Kalff, and Jan M. Wiener. "Adaptive Lévy Processes and Area-Restricted Search in Human Foraging." PLoS ONE 8, no. 4 (2013): e60488. http://dx.doi.org/10.1371/journal.pone.0060488.

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10

Schehr, Grégory, and Satya N. Majumdar. "Area distribution and the average shape of a Lévy bridge." Journal of Statistical Mechanics: Theory and Experiment 2010, no. 08 (2010): P08005. http://dx.doi.org/10.1088/1742-5468/2010/08/p08005.

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11

Levin, Daniel, and Mark Wildon. "A combinatorial method for calculating the moments of Lévy area." Transactions of the American Mathematical Society 360, no. 12 (2008): 6695–709. http://dx.doi.org/10.1090/s0002-9947-08-04526-1.

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12

Wang, Shipeng, Xiaoping Yang, Xingqiao Wang, and Zhihong Qian. "A Virtual Force Algorithm-Lévy-Embedded Grey Wolf Optimization Algorithm for Wireless Sensor Network Coverage Optimization." Sensors 19, no. 12 (2019): 2735. http://dx.doi.org/10.3390/s19122735.

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The random placement of a large-scale sensor network in an outdoor environment often causes low coverage. In order to effectively improve the coverage of a wireless sensor network in the monitoring area, a coverage optimization algorithm for wireless sensor networks with a Virtual Force-Lévy-embedded Grey Wolf Optimization (VFLGWO) algorithm is proposed. The simulation results show that the VFLGWO algorithm has a better optimization effect on the coverage rate, uniformity, and average moving distance of sensor nodes than a wireless sensor network coverage optimization algorithm using Lévy-embedded Grey Wolf Optimizer, Cuckoo Search algorithm, and Chaotic Particle Swarm Optimization. The VFLGWO algorithm has good adaptability with respect to changes of the number of sensor nodes and the size of the monitoring area.

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13

Ferreiro-Castilla, Albert, and Frederic Utzet. "Lévy area for Gaussian processes: A double Wiener–Itô integral approach." Statistics & Probability Letters 81, no. 9 (2011): 1380–91. http://dx.doi.org/10.1016/j.spl.2011.04.015.

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14

Kuelbs, James, and Wenbo Li. "A Functional LIL for Stochastic Integrals and the Lévy Area Process." Journal of Theoretical Probability 18, no. 2 (2005): 261–90. http://dx.doi.org/10.1007/s10959-003-2604-9.

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15

Diamantakis, Theo, Darryl D. Holm, and Grigorios A. Pavliotis. "Variational Principles on Geometric Rough Paths and the Lévy Area Correction." SIAM Journal on Applied Dynamical Systems 22, no. 2 (2023): 1182–218. http://dx.doi.org/10.1137/22m1522164.

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16

Li, Juan, Yuan-Hua Yang, Qing An, Hong Lei, Qian Deng, and Gai-Ge Wang. "Moth Search: Variants, Hybrids, and Applications." Mathematics 10, no. 21 (2022): 4162. http://dx.doi.org/10.3390/math10214162.

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Moth search (MS) is a nature-inspired metaheuristic optimization algorithm based on the most representative characteristics of moths, Lévy flights and phototaxis. Phototaxis signifies a movement which organism towards or away from a source of light, which is the representative features for moths. The best moth individual is seen as the light source in Moth search. The moths that have a smaller distance from the best one will fly around the best individual by Lévy flights. For reasons of phototaxis, the moths, far from the fittest one, will fly towards the best one with a big step. These two features, Lévy flights and phototaxis, correspond to the processes of exploitation and exploration for metaheuristic optimization. The superiority of the moth search has been demonstrated in many benchmark problems and various application areas. A comprehensive survey of the moth search was conducted in this paper, which included the three sections: statistical research studies about moth search, different variants of moth search, and engineering optimization/applications. The future insights and development direction in the area of moth search are also discussed.

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17

Duncan, S., G. Estrada-Rodriguez, J. Stocek, M. Dragone, P. A. Vargas, and H. Gimperlein. "Efficient quantitative assessment of robot swarms: coverage and targeting Lévy strategies." Bioinspiration & Biomimetics 17, no. 3 (2022): 036006. http://dx.doi.org/10.1088/1748-3190/ac57f0.

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Abstract Biologically inspired strategies have long been adapted to swarm robotic systems, including biased random walks, reaction to chemotactic cues and long-range coordination. In this paper we apply analysis tools developed for modeling biological systems, such as continuum descriptions, to the efficient quantitative characterization of robot swarms. As an illustration, both Brownian and Lévy strategies with a characteristic long-range movement are discussed. As a result we obtain computationally fast methods for the optimization of robot movement laws to achieve a prescribed collective behavior. We show how to compute performance metrics like coverage and hitting times, and illustrate the accuracy and efficiency of our approach for area coverage and search problems. Comparisons between the continuum model and robotic simulations confirm the quantitative agreement and speed up by a factor of over 100 of our approach. Results confirm and quantify the advantage of Lévy strategies over Brownian motion for search and area coverage problems in swarm robotics.

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18

Hudson, Robin, and Yuchen Pei. "On a causal quantum stochastic double product integral related to Lévy area." Annales de l’Institut Henri Poincaré D 5, no. 4 (2018): 467–512. http://dx.doi.org/10.4171/aihpd/60.

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19

Blanchet, J., and M. Mandjes. "Asymptotics of the area under the graph of a Lévy-driven workload process." Operations Research Letters 41, no. 6 (2013): 730–36. http://dx.doi.org/10.1016/j.orl.2013.10.004.

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20

Bonnefont, Michel, and Nicolas Juillet. "Couplings in $L^{p}$ distance of two Brownian motions and their Lévy area." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 56, no. 1 (2020): 543–65. http://dx.doi.org/10.1214/19-aihp972.

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21

Giles, Michael B., and Lukasz Szpruch. "Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation." Annals of Applied Probability 24, no. 4 (2014): 1585–620. http://dx.doi.org/10.1214/13-aap957.

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22

Yamada, Toshihiro, and Kenta Yamamoto. "A second-order weak approximation of SDEs using a Markov chain without Lévy area simulation." Monte Carlo Methods and Applications 24, no. 4 (2018): 289–308. http://dx.doi.org/10.1515/mcma-2018-2024.

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Abstract This paper proposes a new Markov chain approach to second-order weak approximations of stochastic differential equations (SDEs) driven by d-dimensional Brownian motion. The scheme is explicitly constructed by polynomials of Brownian motions up to second order, and any discrete moment-matched random variables or the Lévy area simulation method are not used. The required number of random variables is still d in one-step simulation of the implementation of the scheme. In the Markov chain, a correction term with Lie bracket of vector fields associated with SDEs appears as the cost of not using moment-matched random variables.

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23

Chen, Pengyu, Hua Yue, Xiaobo Zhai, et al. "Transport of a graphene nanosheet sandwiched inside cell membranes." Science Advances 5, no. 6 (2019): eaaw3192. http://dx.doi.org/10.1126/sciadv.aaw3192.

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The transport of nanoparticles at bio-nano interfaces is essential for many cellular responses and biomedical applications. How two-dimensional nanomaterials, such as graphene and transition-metal dichalcogenides, diffuse along the cell membrane is, however, unknown, posing an urgent and important issue to promote their applications in the biomedical area. Here, we show that the transport of graphene oxides (GOs) sandwiched inside cell membranes varies from Brownian to Lévy and even directional dynamics. Specifically, experiments evidence sandwiched graphene–cell membrane superstructures in different cells. Combined simulations and analysis identify a sandwiched GO–induced pore in cell membrane leaflets, spanning unstable, metastable, and stable states. An analytical model that rationalizes the regimes of these membrane-pore states fits simulations quantitatively, resulting in a mechanistic interpretation of the emergence of Lévy and directional dynamics. We finally demonstrate the applicability of sandwiched GOs in enhanced efficiency of membrane-specific drug delivery. Our findings inform approaches to programming intramembrane transport of two-dimensional nanomaterials toward advantageous biomedical applications.

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24

Abundo, Mario, and Sara Furia. "Joint Distribution of First-Passage Time and First-Passage Area of Certain Lévy Processes." Methodology and Computing in Applied Probability 21, no. 4 (2018): 1283–302. http://dx.doi.org/10.1007/s11009-018-9677-5.

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25

El-Hadidy, Mohamed Abd Allah. "Study of water pollution through a Lévy flight jump diffusion model with stochastic jumps of pollutants." International Journal of Modern Physics B 33, no. 19 (2019): 1950210. http://dx.doi.org/10.1142/s0217979219502102.

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In this paper, we present the multivariate distribution of independent Lévy flight jump diffusion molecules that cause water pollution. We consider that the waiting time of this jump has a Gaussian distribution. Rather than studying the statistical properties of this distribution in water, we estimate the length of the jump distance parameters for each molecule. These estimated jump distances of the molecules are used to predict the proportion of pollution in a large area of the sea.

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26

Gunavathi, Chellamuthu, and Kandasamy Premalatha. "A Comparative Analysis of Swarm Intelligence Techniques for Feature Selection in Cancer Classification." Scientific World Journal 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/693831.

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Feature selection in cancer classification is a central area of research in the field of bioinformatics and used to select the informative genes from thousands of genes of the microarray. The genes are ranked based onT-statistics, signal-to-noise ratio (SNR), andF-test values. The swarm intelligence (SI) technique finds the informative genes from the top-m ranked genes. These selected genes are used for classification. In this paper the shuffled frog leaping with Lévy flight (SFLLF) is proposed for feature selection. In SFLLF, the Lévy flight is included to avoid premature convergence of shuffled frog leaping (SFL) algorithm. The SI techniques such as particle swarm optimization (PSO), cuckoo search (CS), SFL, and SFLLF are used for feature selection which identifies informative genes for classification. Thek-nearest neighbour (k-NN) technique is used to classify the samples. The proposed work is applied on 10 different benchmark datasets and examined with SI techniques. The experimental results show that the results obtained fromk-NN classifier through SFLLF feature selection method outperform PSO, CS, and SFL.

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27

Liu, Lixing, Hongjie Liu, Jianping Li, Pengfei Wang, and Xin Yang. "Construction of Orchard Agricultural Machinery Dispatching Model Based on Improved Beetle Optimization Algorithm." Agronomy 15, no. 2 (2025): 323. https://doi.org/10.3390/agronomy15020323.

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In order to enhance orchard agricultural efficiency and lower fruit production expenses, we propose a BL-DBO (Beetle Optimization Algorithm introducing Bernoulli mapping and Lévy flights) to solve the agricultural machinery dispatching model within the orchard area. First, we analyze the agricultural machinery dispatching problem in the orchard area and establish its mathematical model with the objective of minimizing dispatching costs as a constraint. To tackle the problems of uneven individual position distribution and the risk of becoming stuck in local optimal solutions in the traditional DBO algorithm, we introduce Bernoulli mapping during the initialization phase of the DBO. This method ensures a uniform distribution of the initialized population. Furthermore, during the iterative process of the algorithm, we incorporated the Lévy flight approach into the positional update equations for beetles involved in breeding, foraging, and theft activities within the DBO. This helps the beetles escape from local optimal solutions. Finally, we conduct experiments based on location information of Shunping Shunnong Orchard and fruit trees in Shijiazhuang. The results indicate that, compared to dispatching using human experience and the traditional DBO algorithm, the dispatching results generated by the BL-DBO not only reduce the number of agricultural machinery purchases but also decrease the energy loss from non-working distances of the machinery, effectively saving fruit production costs.

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28

Qian, Zhongmin, and Xingcheng Xu. "Lévy area analysis and parameter estimation for fOU processes via non-geometric rough path theory." Acta Mathematica Scientia 44, no. 5 (2024): 1609–38. http://dx.doi.org/10.1007/s10473-024-0501-8.

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29

Lopusanschi, Olga, and Damien Simon. "Lévy area with a drift as a renormalization limit of Markov chains on periodic graphs." Stochastic Processes and their Applications 128, no. 7 (2018): 2404–26. http://dx.doi.org/10.1016/j.spa.2017.09.004.

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30

Deya, A., A. Neuenkirch, and S. Tindel. "A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 48, no. 2 (2012): 518–50. http://dx.doi.org/10.1214/10-aihp392.

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31

Bennison, Ashley, John L. Quinn, Alison Debney, and Mark Jessopp. "Tidal drift removes the need for area-restricted search in foraging Atlantic puffins." Biology Letters 15, no. 7 (2019): 20190208. http://dx.doi.org/10.1098/rsbl.2019.0208.

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Understanding how animals forage is a central objective in ecology. Theory suggests that where food is uniformly distributed, Brownian movement ensures the maximum prey encounter rate, but when prey is patchy, the optimal strategy resembles a Lévy walk where area-restricted search (ARS) is interspersed with commuting between prey patches. Such movement appears ubiquitous in high trophic-level marine predators. Here, we report foraging and diving behaviour in a seabird with a high cost of flight, the Atlantic puffin ( Fratercula arctica ), and report a clear lack of Brownian or Levy flight and associated ARS. Instead, puffins foraged using tides to transport them through their feeding grounds. Energetic models suggest the cost of foraging trips using the drift strategy is 28–46% less than flying between patches. We suggest such alternative movement strategies are habitat-specific, but likely to be far more widespread than currently thought.

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32

Pang, Bao, Yong Song, Chengjin Zhang, Hongling Wang, and Runtao Yang. "A Swarm Robotic Exploration Strategy Based on an Improved Random Walk Method." Journal of Robotics 2019 (March 13, 2019): 1–9. http://dx.doi.org/10.1155/2019/6914212.

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An environment can be searched far more efficiently if the appropriate search strategy is used. Because of the limited individual abilities of swarm robots, namely, local sensing and low processing power, random searching is the main search strategy used in swarm robotics. The random walk methods that are used most commonly are Brownian motion and Lévy flight, both of which mimic the self-organized behavior of social insects. However, both methods are somewhat limited when applied to swarm robotics, where having the robots search repeatedly can result in highly inefficient searching. Therefore, by analyzing the characteristics of swarm robotic exploration, this paper proposes an improved random walk method in which each robot adjusts its step size adaptively to reduce the number of repeated searches by estimating the density of robots in the environment. Simulation experiments and experiments with actual robots are conducted to study the effectiveness of the proposed method and evaluate its performance in an exploration mission. The experimental results presented in this paper show that an area is covered more efficiently using the proposed method than it is using either Brownian motion or Lévy flight.

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33

Maletz, Jörg. "Arenig biostratigraphy of the Pointe-de-Lévy slice, Quebec Appalachians, Canada." Canadian Journal of Earth Sciences 34, no. 6 (1997): 733–52. http://dx.doi.org/10.1139/e17-061.

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The Pointe-de-Lévy slice includes a nearly complete Arenig graptolite succession. A conspicuous gap exists in the Yapeenian (Ya) to lower Darriwilian (Da) part (Ya 1 – Da 1). The lithological column is compiled from several sections at Lévis, Quebec, that yield only parts of the complete succession. The graptolite zonation can be compared closely with that from the Cow Head Group of western Newfoundland and the Deep Kill Formation of eastern New York. The Shumardia "Limestone" is differentiated into four graptolite zones and subzones, of which the youngest zone clearly belongs to the Llanvirn. The Araneograptus murrayi and Holmograptus lentus zones are documented for the first time from the Lévis area. The Undulograptus dentatus Zone of the latest Arenig is introduced.

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34

Ekinci, Serdar, Erdal Eker, Davut Izci, Aseel Smerat, and Laith Abualigah. "Enhanced RSA Optimized TID Controller for Frequency Stabilization in a Two-Area Power System." International Journal of Robotics and Control Systems 4, no. 4 (2024): 1886–902. https://doi.org/10.31763/ijrcs.v4i4.1644.

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This study presents an enhanced reptile search algorithm (ImRSA) optimized tilt-integral-derivative (TID) controller for load frequency control (LFC) in a two-area power system consisting of photovoltaic (PV) and thermal power units. The ImRSA integrates Lévy flight and logarithmic spiral search mechanisms to improve the balance between exploration and exploitation, resulting in more efficient optimization performance. The proposed controller is tested against the original reptile search algorithm (RSA) and other state-of-the-art optimization methods, such as modified grey wolf optimization with cuckoo search, black widow optimization, and gorilla troops optimization. Simulation results show that the ImRSA-optimized TID controller outperforms these approaches in terms of undershoot, overshoot, settling time, and the integral of time-weighted absolute error metric. Additionally, the ImRSA demonstrates robustness in managing frequency deviations caused by solar radiation fluctuations in PV systems. The results highlight the superior efficiency and reliability of the proposed method, especially for renewable energy integration in modern power systems.

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35

Li, Desheng. "Cooperative Quantum-Behaved Particle Swarm Optimization with Dynamic Varying Search Areas and Lévy Flight Disturbance." Scientific World Journal 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/370691.

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This paper proposes a novel variant of cooperative quantum-behaved particle swarm optimization (CQPSO) algorithm with two mechanisms to reduce the search space and avoid the stagnation, called CQPSO-DVSA-LFD. One mechanism is called Dynamic Varying Search Area (DVSA), which takes charge of limiting the ranges of particles’ activity into a reduced area. On the other hand, in order to escape the local optima, Lévy flights are used to generate the stochastic disturbance in the movement of particles. To test the performance of CQPSO-DVSA-LFD, numerical experiments are conducted to compare the proposed algorithm with different variants of PSO. According to the experimental results, the proposed method performs better than other variants of PSO on both benchmark test functions and the combinatorial optimization issue, that is, the job-shop scheduling problem.

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36

Lundy, Mathieu G., Alan Harrison, Daniel J. Buckley, et al. "Prey field switching based on preferential behaviour can induce Lévy flights." Journal of The Royal Society Interface 10, no. 78 (2013): 20120489. http://dx.doi.org/10.1098/rsif.2012.0489.

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Using the foraging movements of an insectivorous bat, Myotis mystacinus , we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response of predators to changes in prey fields can elicit different functional responses, which are considered to be central in the development of stable predator–prey communities. Recognizing how the foraging movements of an animal relate to environmental conditions also elucidates the evolution of optimized search and the prevalence of discrete strategies in natural systems. Applying techniques that use changes in the frequency distribution of movements facilitates exploration of the processes that underpin behavioural changes.

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37

Lundy, Mathieu G., Alan Harrison, Daniel J. Buckley, et al. "Prey field switching based on preferential behaviour can induce Lévy flights." Journal of The Royal Society Interface 10, no. 78 (2013): 20120489. https://doi.org/10.5281/zenodo.13450094.

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(Uploaded by Plazi for the Bat Literature Project) Using the foraging movements of an insectivorous bat, Myotis mystacinus , we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response of predators to changes in prey fields can elicit different functional responses, which are considered to be central in the development of stable predator–prey communities. Recognizing how the foraging movements of an animal relate to environmental conditions also elucidates the evolution of optimized search and the prevalence of discrete strategies in natural systems. Applying techniques that use changes in the frequency distribution of movements facilitates exploration of the processes that underpin behavioural changes.

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38

Lundy, Mathieu G., Alan Harrison, Daniel J. Buckley, et al. "Prey field switching based on preferential behaviour can induce Lévy flights." Journal of The Royal Society Interface 10, no. 78 (2013): 20120489. https://doi.org/10.5281/zenodo.13450094.

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Abstract:

(Uploaded by Plazi for the Bat Literature Project) Using the foraging movements of an insectivorous bat, Myotis mystacinus , we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response of predators to changes in prey fields can elicit different functional responses, which are considered to be central in the development of stable predator–prey communities. Recognizing how the foraging movements of an animal relate to environmental conditions also elucidates the evolution of optimized search and the prevalence of discrete strategies in natural systems. Applying techniques that use changes in the frequency distribution of movements facilitates exploration of the processes that underpin behavioural changes.

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39

Lundy, Mathieu G., Alan Harrison, Daniel J. Buckley, et al. "Prey field switching based on preferential behaviour can induce Lévy flights." Journal of The Royal Society Interface 10, no. 78 (2013): 20120489. https://doi.org/10.5281/zenodo.13450094.

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Abstract:

(Uploaded by Plazi for the Bat Literature Project) Using the foraging movements of an insectivorous bat, Myotis mystacinus , we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response of predators to changes in prey fields can elicit different functional responses, which are considered to be central in the development of stable predator–prey communities. Recognizing how the foraging movements of an animal relate to environmental conditions also elucidates the evolution of optimized search and the prevalence of discrete strategies in natural systems. Applying techniques that use changes in the frequency distribution of movements facilitates exploration of the processes that underpin behavioural changes.

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40

Lundy, Mathieu G., Alan Harrison, Daniel J. Buckley, et al. "Prey field switching based on preferential behaviour can induce Lévy flights." Journal of The Royal Society Interface 10, no. 78 (2013): 20120489. https://doi.org/10.5281/zenodo.13450094.

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(Uploaded by Plazi for the Bat Literature Project) Using the foraging movements of an insectivorous bat, Myotis mystacinus , we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response of predators to changes in prey fields can elicit different functional responses, which are considered to be central in the development of stable predator–prey communities. Recognizing how the foraging movements of an animal relate to environmental conditions also elucidates the evolution of optimized search and the prevalence of discrete strategies in natural systems. Applying techniques that use changes in the frequency distribution of movements facilitates exploration of the processes that underpin behavioural changes.

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Neuenkirch, Andreas, and Taras Shalaiko. "The maximum rate of convergence for the approximation of the fractional Lévy area at a single point." Journal of Complexity 33 (April 2016): 107–17. http://dx.doi.org/10.1016/j.jco.2015.09.008.

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De Bruyne, Benjamin, Satya N. Majumdar, Henri Orland, and Grégory Schehr. "Generating stochastic trajectories with global dynamical constraints." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 12 (2021): 123204. http://dx.doi.org/10.1088/1742-5468/ac3e70.

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Abstract We propose a method to exactly generate Brownian paths x c (t) that are constrained to return to the origin at some future time t f , with a given fixed area A f = ∫ 0 t f d t x c ( t ) under their trajectory. We derive an exact effective Langevin equation with an effective force that accounts for the constraint. In addition, we develop the corresponding approach for discrete-time random walks, with arbitrary jump distributions including Lévy flights, for which we obtain an effective jump distribution that encodes the constraint. Finally, we generalise our method to other types of dynamical constraints such as a fixed occupation time on the positive axis T f = ∫ 0 t f d t Θ x c ( t ) or a fixed generalised quadratic area A f = ∫ 0 t f d t x c 2 ( t ) .

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van Steijn, Leonie, Inge M. N. Wortel, Clément Sire, Loïc Dupré, Guy Theraulaz, and Roeland M. H. Merks. "Computational modelling of cell motility modes emerging from cell-matrix adhesion dynamics." PLOS Computational Biology 18, no. 2 (2022): e1009156. http://dx.doi.org/10.1371/journal.pcbi.1009156.

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Lymphocytes have been described to perform different motility patterns such as Brownian random walks, persistent random walks, and Lévy walks. Depending on the conditions, such as confinement or the distribution of target cells, either Brownian or Lévy walks lead to more efficient interaction with the targets. The diversity of these motility patterns may be explained by an adaptive response to the surrounding extracellular matrix (ECM). Indeed, depending on the ECM composition, lymphocytes either display a floating motility without attaching to the ECM, or sliding and stepping motility with respectively continuous or discontinuous attachment to the ECM, or pivoting behaviour with sustained attachment to the ECM. Moreover, on the long term, lymphocytes either perform a persistent random walk or a Brownian-like movement depending on the ECM composition. How the ECM affects cell motility is still incompletely understood. Here, we integrate essential mechanistic details of the lymphocyte-matrix adhesions and lymphocyte intrinsic cytoskeletal induced cell propulsion into a Cellular Potts model (CPM). We show that the combination of de novo cell-matrix adhesion formation, adhesion growth and shrinkage, adhesion rupture, and feedback of adhesions onto cell propulsion recapitulates multiple lymphocyte behaviours, for different lymphocyte subsets and various substrates. With an increasing attachment area and increased adhesion strength, the cells’ speed and persistence decreases. Additionally, the model predicts random walks with short-term persistent but long-term subdiffusive properties resulting in a pivoting type of motility. For small adhesion areas, the spatial distribution of adhesions emerges as a key factor influencing cell motility. Small adhesions at the front allow for more persistent motility than larger clusters at the back, despite a similar total adhesion area. In conclusion, we present an integrated framework to simulate the effects of ECM proteins on cell-matrix adhesion dynamics. The model reveals a sufficient set of principles explaining the plasticity of lymphocyte motility.

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Lian, Zhigang, Dan Luo, Bingrong Dai, and Yangquan Chen. "A Lévy Distribution Based Searching Scheme for the Discrete Targets in Vast Region." Symmetry 14, no. 2 (2022): 272. http://dx.doi.org/10.3390/sym14020272.

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This paper investigates the Discrete Targets Search Problem, (DTSP), which aims to quickly search for discrete objects scattered in a vast symmetry region. Different from continuous function extremal value search, the discrete points search cannot make use of the properties of regular functions, such as function analytic, single/multiple extreme, and monotonicity. Thus, in this paper a new search scheme based on Lévy random distribution is investigated. In comparison with the TraditionalCarpet search or Random search based on other distributions, DTSP can provide much faster search speed which is demonstrated by simulation with different scales problems for the selected scenarios. The simulations experiment proves that DTSP is faster for searching for a discrete single target or multiple targets in a wide area. It provides a new method for solving the discrete target search problem.

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Freitas, C., R. Caldeira, J. Reis, and T. Dellinger. "Foraging behavior of juvenile loggerhead sea turtles in the open ocean: from Lévy exploration to area-restricted search." Marine Ecology Progress Series 595 (May 14, 2018): 203–15. http://dx.doi.org/10.3354/meps12581.

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Kanagasabai, Lenin. "LEVY BASED PHRYNOSOMA DOUGLASSII SWARM, ALASHAN WAPITI OPTIMIZATION, FOREST PONY ALGORITHM AND PANTHERA TIGRIS CORBETTI SEARCH FOR TRUE POWER LOSS REDUCTION IN ELECTRICAL SYSTEM." Suranaree Journal of Science and Technology 31, no. 5 (2024): 010332(1–15). https://doi.org/10.55766/sujst-2024-05-e03917.

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Lévy based Phrynosoma douglassii inspired optimization (LPD) algorithm, Alashan wapiti optimization (AWO) algorithm, Forest Pony Optimization (FPO) algorithm and Panthera Tigris corbetti optimization (PTC) algorithm are applied to solve the true power loss reduction problem. Camouflage, colour changing, blood spouting and squirt out protection methods of Phrynosoma douglassii are scientifically formulated in the LPD algorithm. Due to Camouflage action, Phrynosoma douglassii alter its body colorant by flattering luminous to evade exposure to the predators. AWO algorithm is formulated based on the natural breeding procedure of Alashan wapiti. There are dual key breeding periods for Alashan wapiti. In the rutting season Alashan wapiti herd alienated into dissimilar folks of numerous proportions. FP algorithm replicates the foraging area nearby Forest Pony with coefficient and scientific execution of foraging. Forest Ponies from upper layer of the organized matrix are designated as Alpha cluster of Forest Ponies. In PTC, during initial period, the location of population associates is rationalized grounded on picking and bout on the prey. This period sources abrupt and widespread vicissitudes in the location of population associates, and as a consequence, it upsurges the aptitude of the global examination and exploration of the procedure in precise glance over of the examination region. Lévy based Phrynosoma douglassii inspired optimization (LPD) algorithm, Alashan wapiti optimization (AWO) algorithm, Forest Pony Optimization (FPO) algorithm and Panthera Tigris corbetti optimization (PTC) algorithm are validated in IEEE 118, 300, 354 systems.

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Gehringer, Johann, Xue-Mei Li, and Julian Sieber. "Functional limit theorems for Volterra processes and applications to homogenization*." Nonlinearity 35, no. 4 (2022): 1521–57. http://dx.doi.org/10.1088/1361-6544/ac4818.

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Abstract We prove an enhanced limit theorem for additive functionals of a multi-dimensional Volterra process ( y t ) t ⩾ 0 in the rough path topology. As an application, we establish weak convergence as ɛ → 0 of the solution of the random ordinary differential equation (ODE) d d t x t ε = 1 ε f ( x t ε , y t ε ) and show that its limit solves a rough differential equation driven by a Gaussian field with a drift coming from the Lévy area correction of the limiting rough driver. Furthermore, we prove that the stochastic flows of the random ODE converge to those of the Kunita type Itô SDE dx t = G(x t , dt), where G(x, t) is a semi-martingale with spatial parameters.

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Donati-Martin, C., and M. Yor. "On some examples of quadratic functionals of Brownian motion." Advances in Applied Probability 25, no. 03 (1993): 570–84. http://dx.doi.org/10.1017/s0001867800025556.

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During the last few years, several variants of P. Lévy's formula for the stochastic area of complex Brownian motion have been obtained. These are of interest in various domains of applied probability, particularly in relation to polymer studies. The method used by most authors is the diagonalization procedure of Paul Lévy. Here we derive one such variant of Lévy's formula, due to Chan, Dean, Jansons and Rogers, via a change of probability method, which reduces the computation of Laplace transforms of Brownian quadratic functionals to the computations of the means and variances of some adequate Gaussian variables. We then show that with the help of linear algebra and invariance properties of the distribution of Brownian motion, we are able to derive simply three other variants of Lévy's formula.

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Diehl, Joscha, Harald Oberhauser, and Sebastian Riedel. "A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations." Stochastic Processes and their Applications 125, no. 1 (2015): 161–81. http://dx.doi.org/10.1016/j.spa.2014.08.005.

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Santos, Flávia Cacho dos, and Nadielli Maria dos Santos Galvão. "Hypertext in language teaching and learning: a bibliometric study." JOURNAL OF RESEARCH AND KNOWLEDGE SPREADING 3, no. 1 (2022): e13619. http://dx.doi.org/10.20952/jrks3113619.

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Powered by digital, hypertext has brought about changes in reading and writing in the information society. With its links, it enables navigation in the "ocean" of ideas, requiring adequate knowledge to navigate. Incomprehension and textual abandonment are consequences that scholars report and that we need to discuss. About them, we highlight Lévy (2011), Marcuschi and Xavier (2010), Castells (2020), Schuab (2016), Schnneider and Carvalho (2018), important authors in the discussion about technology and education. In this paper, we focused on analyzing the need for the debate on hypertext in language teaching-learning with a bibliometric research, whose goal is to provide a broad mapping of a subject, serving as a support for new studies. We obtained, as a result, the idea that hypertext is an area of research evident in developed countries and in need of current research.

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