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Journal articles on the topic 'Lévy area'

Author: Grafiati

Published: 23 September 2022

Last updated: 28 September 2022

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1

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

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2

Li, Juan, Qing An, Hong Lei, Qian Deng, and Gai-Ge Wang. "Survey of Lévy Flight-Based Metaheuristics for Optimization." Mathematics 10, no. 15 (August 5, 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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3

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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4

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

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5

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

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6

Levin, Daniel, and Mark Wildon. "A combinatorial method for calculating the moments of Lévy area." Transactions of the American Mathematical Society 360, no. 12 (July 24, 2008): 6695–709. http://dx.doi.org/10.1090/s0002-9947-08-04526-1.

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7

Hills, Thomas T., Christopher Kalff, and Jan M. Wiener. "Adaptive Lévy Processes and Area-Restricted Search in Human Foraging." PLoS ONE 8, no. 4 (April 5, 2013): e60488. http://dx.doi.org/10.1371/journal.pone.0060488.

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8

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 (August 3, 2010): P08005. http://dx.doi.org/10.1088/1742-5468/2010/08/p08005.

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9

Letemplier, Julien, and Thomas Simon. "The area of a spectrally positive stable process stopped at zero." Probability and Mathematical Statistics 38, no. 1 (July 30, 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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10

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

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11

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

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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 (June 18, 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

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 (July 25, 2018): 467–512. http://dx.doi.org/10.4171/aihpd/60.

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14

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 (March 30, 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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15

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

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16

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 (February 2020): 543–65. http://dx.doi.org/10.1214/19-aihp972.

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17

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 (August 2014): 1585–620. http://dx.doi.org/10.1214/13-aap957.

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18

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 (December 1, 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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19

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 (October 2, 2018): 1283–302. http://dx.doi.org/10.1007/s11009-018-9677-5.

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20

Chen, Pengyu, Hua Yue, Xiaobo Zhai, Zihan Huang, Guang-Hui Ma, Wei Wei, and Li-Tang Yan. "Transport of a graphene nanosheet sandwiched inside cell membranes." Science Advances 5, no. 6 (June 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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21

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 (July 2018): 2404–26. http://dx.doi.org/10.1016/j.spa.2017.09.004.

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22

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 (May 2012): 518–50. http://dx.doi.org/10.1214/10-aihp392.

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23

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 (July 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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24

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 (July 30, 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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25

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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26

Maletz, Jörg. "Arenig biostratigraphy of the Pointe-de-Lévy slice, Quebec Appalachians, Canada." Canadian Journal of Earth Sciences 34, no. 6 (June 1, 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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27

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 (February 14, 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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28

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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29

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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30

Lundy, Mathieu G., Alan Harrison, Daniel J. Buckley, Emma S. Boston, David D. Scott, Emma C. Teeling, W. Ian Montgomery, and Jonathan D. R. Houghton. "Prey field switching based on preferential behaviour can induce Lévy flights." Journal of The Royal Society Interface 10, no. 78 (January 6, 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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31

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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32

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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33

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 (January 29, 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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34

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 (December 1, 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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35

Gehringer, Johann, Xue-Mei Li, and Julian Sieber. "Functional limit theorems for Volterra processes and applications to homogenization*." Nonlinearity 35, no. 4 (March 1, 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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36

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 (January 2015): 161–81. http://dx.doi.org/10.1016/j.spa.2014.08.005.

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37

Donati-Martin, C., and M. Yor. "On some examples of quadratic functionals of Brownian motion." Advances in Applied Probability 25, no. 03 (September 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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38

Li, Desheng. "Design of Two-Dimensional Recursive IIR Filters Using Cooperative Quantum Particle Swarm Optimization with Dynamic Varying Search Area and Lévy Flights." Journal of Computational and Theoretical Nanoscience 12, no. 9 (September 1, 2015): 2678–86. http://dx.doi.org/10.1166/jctn.2015.4162.

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39

Huillet, Thierry. "Energy cascades as branching processes with emphasis on Neveu's approach to Derrida's random energy model." Advances in Applied Probability 35, no. 02 (June 2003): 477–503. http://dx.doi.org/10.1017/s0001867800012349.

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Continuous-space-time branching processes (CSBP) are investigated in order to model random energy cascades. CSBPs are based on spectrally positive Lévy processes and, as such, are characterized by their corresponding Laplace exponents. Special emphasis is put on the CSBPs of Feller, Lamperti and Neveu and on their Poisson point process representations. The Neveu model (either supercritical or subcritical) is of particular interest in physics for its connection with the random energy model of Derrida, as revisited by Ruelle. Exploiting some connections between the partition functions of energy and the Poisson-Dirichlet distributions of Pitman and Yor, some information on the zero-temperature limit is extracted. Finally, for the subcritical versions of the three models, we compute the distribution of some of their interesting features: extinction time and probability, area under the profile (total energy) and width (maximal energy).

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40

Huillet, Thierry. "Energy cascades as branching processes with emphasis on Neveu's approach to Derrida's random energy model." Advances in Applied Probability 35, no. 2 (June 2003): 477–503. http://dx.doi.org/10.1239/aap/1051201657.

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Continuous-space-time branching processes (CSBP) are investigated in order to model random energy cascades. CSBPs are based on spectrally positive Lévy processes and, as such, are characterized by their corresponding Laplace exponents. Special emphasis is put on the CSBPs of Feller, Lamperti and Neveu and on their Poisson point process representations. The Neveu model (either supercritical or subcritical) is of particular interest in physics for its connection with the random energy model of Derrida, as revisited by Ruelle. Exploiting some connections between the partition functions of energy and the Poisson-Dirichlet distributions of Pitman and Yor, some information on the zero-temperature limit is extracted. Finally, for the subcritical versions of the three models, we compute the distribution of some of their interesting features: extinction time and probability, area under the profile (total energy) and width (maximal energy).

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41

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 (May 28, 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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Alkayem, Nizar Faisal, Maosen Cao, and Minvydas Ragulskis. "Damage Diagnosis in 3D Structures Using a Novel Hybrid Multiobjective Optimization and FE Model Updating Framework." Complexity 2018 (September 19, 2018): 1–13. http://dx.doi.org/10.1155/2018/3541676.

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Structural damage detection is a well-known engineering inverse problem in which the extracting of damage information from the dynamic responses of the structure is considered a complex problem. Within that area, the damage tracking in 3D structures is evaluated as a more complex and difficult task. Swarm intelligence and evolutionary algorithms (EAs) can be well adapted for solving the problem. For this purpose, a hybrid elitist-guided search combining a multiobjective particle swarm optimization (MOPSO), Lévy flights (LFs), and the technique for the order of preference by similarity to ideal solution (TOPSIS) is evolved in this work. Modal characteristics are employed to develop the objective function by considering two subobjectives, namely, modal strain energy (MSTE) and mode shape (MS) subobjectives. The proposed framework is tested using a well-known benchmark model. The overall strong performance of the suggested method is maintained even under noisy conditions and in the case of incomplete mode shapes.

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Aschwanden, Markus J. "The Fractality and Size Distributions of Astrophysical Self-Organized Criticality Systems." Astrophysical Journal 934, no. 1 (July 1, 2022): 33. http://dx.doi.org/10.3847/1538-4357/ac6bf2.

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Abstract The statistics of nonlinear processes in avalanching systems, based on the self-organized criticality (SOC) concept of Bak et al. (1988), predicts power-law-like size (or occurrence frequency) distribution functions. Following up on previous work, we define a standard SOC model in terms of six assumptions: (i) area fractality, (ii) volume fractality, (iii) the flux–volume proportionality, (iv) classical diffusion, (v) the Euclidean maximum at the event peak time, and (vi) the spatiotemporal fluence or energy of an avalanche event. We gather data of the fractal dimension and power-law slopes from 162 publications and assemble them in 28 groups (for instance, solar flare energies, or stellar flare energies), from which we find that 75% of the groups are consistent with the standard SOC model. Alternative SOC models (Lévy flight, flat-world, nonfractal) are slightly less correlated with the data. Outliers are attributed to small number statistics, background definition problems, inadequate fitting ranges, and deviations from ideal power laws.

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Mårell, Anders, John P. Ball, and Annika Hofgaard. "Foraging and movement paths of female reindeer: insights from fractal analysis, correlated random walks, and Lévy flights." Canadian Journal of Zoology 80, no. 5 (May 1, 2002): 854–65. http://dx.doi.org/10.1139/z02-061.

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Food-plant and foraging-site selection by semidomesticated female reindeer (Rangifer tarandus tarandus L.) was studied to shed light on the searching and foraging behaviour of this herbivore. The aims of the study were (i) to determine the role of food biomass and (or) plant nitrogen content in feeding-site selection and (ii) to analyse the extent to which movement patterns of reindeer are related to availability of food resources using several models of searching behaviour (fractal analysis, correlated random walks, and Lévy flights). The study was conducted in summer 1999 in a mountainous area of northern Sweden. Reindeer selected different plant communities during this period and changed search pattern in late summer. We found that reindeer selected feeding sites with higher green biomass of Betula spp. and Salix spp. However, there was no sharp threshold for foraging as suggested by some models. Contrary to qualitative predictions of optimal-foraging theory, we found no selection of feeding sites on the basis of the nitrogen content of food. The changed search pattern in late summer and the discrepancy between reindeer foraging paths and a correlated random walk model suggests that reindeer were responding to their environment by changing their searching behaviour.

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Hills, Thomas T., and Stephen Butterfill. "From foraging to autonoetic consciousness: The primal self as a consequence of embodied prospective foraging." Current Zoology 61, no. 2 (April 1, 2015): 368–81. http://dx.doi.org/10.1093/czoolo/61.2.368.

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Abstract The capacity to adapt to resource distributions by modulating the frequency of exploratory and exploitative behaviors is common across metazoans and is arguably a principal selective force in the evolution of cognition. Here we (1) review recent work investigating behavioral and biological commonalities between external foraging in space and internal foraging over environments specified by cognitive representations, and (2) explore the implications of these commonalities for understanding the origins of the self. Behavioural commonalities include the capacity for what is known as area-restricted search in the ecological literature: this is search focussed around locations where resources have been found in the past, but moving away from locations where few resources are found, and capable of producing movement patterns mimicking Lévy flights. Area-restricted search shares a neural basis across metazoans, and these biological commonalities in vertebrates suggest an evolutionary homology between external and internal foraging. Internal foraging, and in particular a form we call embodied prospective foraging, makes available additional capacities for prediction based on search through a cognitive representation of the external environment, and allows predictions about outcomes of possible future actions. We demonstrate that cognitive systems that use embodied prospective foraging require a primitive sense of self, needed to distinguish actual from simulated action. This relationship has implications for understanding the evolution of autonoetic consciousness and self-awareness.

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Magnen, Jacques, and Jérémie Unterberger. "From Constructive Field Theory to Fractional Stochastic Calculus. (II) Constructive Proof of Convergence for the Lévy Area of Fractional Brownian Motion with Hurst Index $${{\alpha}\,{\in}\,(\frac{1}{8},\frac{1}{4})}$$." Annales Henri Poincaré 13, no. 2 (July 19, 2011): 209–70. http://dx.doi.org/10.1007/s00023-011-0119-y.

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Jurek, Zbigniew J. "Generalized Lévy stochastic areas and selfdecomposability." Statistics & Probability Letters 64, no. 2 (August 2003): 213–22. http://dx.doi.org/10.1016/s0167-7152(03)00153-6.

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Nourdin, Ivan, and Thomas Simon. "Correcting Newton–Côtes integrals by Lévy areas." Bernoulli 13, no. 3 (August 2007): 695–711. http://dx.doi.org/10.3150/07-bej6015.

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Avanzi, Benjamin, Jamie Tao, Bernard Wong, and Xinda Yang. "Capturing non-exchangeable dependence in multivariate loss processes with nested Archimedean Lévy copulas." Annals of Actuarial Science 10, no. 1 (December 11, 2015): 87–117. http://dx.doi.org/10.1017/s1748499515000135.

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AbstractThe class of spectrally positive Lévy processes is a frequent choice for modelling loss processes in areas such as insurance or operational risk. Dependence between such processes (e.g. between different lines of business) can be modelled with Lévy copulas. This approach is a parsimonious, efficient and flexible method which provides many of the advantages akin to distributional copulas for random variables. Literature on Lévy copulas seems to have primarily focussed on bivariate processes. When multivariate settings are considered, these usually exhibit an exchangeable dependence structure (whereby all subset of the processes have an identical marginal Lévy copula). In reality, losses are not always associated in an identical way, and models allowing for non-exchangeable dependence patterns are needed. In this paper, we present an approach which enables the development of such models. Inspired by ideas and techniques from the distributional copula literature we investigate the procedure of nesting Archimedean Lévy copulas. We provide a detailed analysis of this construction, and derive conditions under which valid multivariate (nested) Lévy copulas are obtained. Our results are discussed and illustrated, notably with an example of model fitting to data.

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Scheicher, Klaus. "Complexity and effective dimension of discrete Lévy areas." Journal of Complexity 23, no. 2 (April 2007): 152–68. http://dx.doi.org/10.1016/j.jco.2006.12.006.

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