Relevant bibliographies by topics / Lévy area

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Lévy area'

Author: Grafiati
Published: 23 September 2022
Last updated: 28 September 2022

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Journal articles on the topic "Lévy area"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Lévy area"

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Sauzedde, Isao. "Windings of the planar Brownian motion and Green’s formula." Thesis, Sorbonne université, 2021. http://www.theses.fr/2021SORUS437.

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On s'intéresse dans cette thèse à l'enlacement du mouvement Brownien plan autour des points, dans la succession des travaux de Wendelin Werner en particulier. Dans le premier chapitre, on motive cette étude par celle du cas des courbes plus lisses que le mouvement Brownien. On y démontre notamment une formule de Green pour l'intégrale de Young, sans hypothèse de simplicité de la courbe. Dans le chapitre 2, on étudie l'aire de l'ensemble des points autour desquels l'enlacement du mouvement brownien est plus grand que N. On donne, au sens presque sûr et dans les espaces Lp, une estimation asymptotique au second ordre de cette aire lorsque N tend vers l'infini. Le chapitre 3 est dévoué à la preuve d'un résultat qui montre que les points de grands enlacements se répartissent de manière très équilibrée le long de la trajectoire. Dans le chapitre 4, on utilise les résultats des deux précédents chapitres pour énoncer une formule de Green pour le mouvement brownien. On étudie aussi l'enlacement moyen de points répartis aléatoirement dans le plan. On montre que cet enlacement moyen converge en distribution (presque surement pour la trajectoire), non pas vers une constante (qui serait alors l’aire de Lévy) mais vers une variable de Cauchy centrée en l’aire de Lévy. Dans les deux derniers chapitres, on applique les idées des précédents chapitres pour définir et étudier l’aire de Lévy du mouvement Brownien lorsque la mesure d’aire sous-jacente n’est plus la mesure de Lebesgue mais une mesure aléatoire particulièrement irrégulière. On traite le cas du chaos multiplicatif gaussien en particulier, mais la méthode s’applique dans un cadre plus général
We study the windings of the planar Brownian motion around points, following the previous works of Wendelin Werner in particular. In the first chapter, we motivate this study by the one of smoother curves. We prove in particular a Green formula for Young integration, without simplicity assumption for the curve. In the second chapter, we study the area of the set of points around which the Brownian motion winds at least N times. We give an asymptotic estimation for this area, up to the second order, both in the almost sure sense and in the Lp spaces, when N goes to infinity.The third chapter is devoted to the proof of a result which shows that the points with large winding are distributed in a very balanced way along the trajectory. In the fourth chapter, we use the results from the two previous chapters to give a new Green formula for the Brownian motion. We also study the averaged winding around randomly distributed points in the plan. We show that, almost surely for the trajectory, this averaged winding converges in distribution, not toward a constant (which would be the Lévy area), but toward a Cauchy distribution centered at the Lévy area. In the last two chapters, we apply the ideas from the previous chapters to define and study the Lévy area of the Brownian motion, when the underlying area measure is not the Lebesgue measure anymore, but instead a random and highly irregular measure. We deal with the case of the Gaussian multiplicative chaos in particular, but the tools can be used in a much more general framework
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Lopusanschi, Olga. "Chemins rugueux issus de processus discrets." Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS074/document.

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Le présent travail se veut une contribution à l’extension du domaine des applications de la théorie des chemins rugueux à travers l’étude de la convergence des processus discrets, qui permet un nouveau regard sur plusieurs problèmes qui se posent dans le cadre du calcul stochastique classique. Nous étudions la convergence en topologie rugueuse, d’abord des chaînes de Markov sur graphes périodiques, ensuite des marches de Markov cachées, et ce changement de cadre permet d’apporter des informations supplémentaires sur la limite grâce à l’anomalie d’aire, invisible en topologie uniforme. Nous voulons montrer que l’utilité de cet objet dépasse le cadre des équations différentielles. Nous montrons également comment le cadre des chemins rugueux permet d’en- coder la manière dont on plonge un modèle discret dans l’espace des fonctions continues, et que les limites des différents plongements peuvent être différenciées précisément grâce à l’anomalie d’aire. Nous définissons ensuite les temps d’occupation itérés pour une chaîne de Markov et montrons, en utilisant les sommes itérées, qu’ils donnent une structure combinatoire aux marches de Markov cachées. Nous proposons une construction des chemins rugueux en passant par les sommes itérées et la comparons à la construction classique, faite par les intégrales itérées, pour trouver à la limite deux types de chemins rugueux différents, non-géométrique et géométrique respectivement. Pour finir, nous illustrons le calcul et la construction de l’anomalie d’aire et nous donnons quelques résultats supplémentaires sur la convergence des sommes et temps d’occupation itérés
Through the present work, we hope to contribute to extending the domain of applications of rough paths theory by studying the convergence of discrete processes and thus allowing for a new point of view on several issues appearing in the setting of classical stochastic calculus. We study the convergence, first of Markov chains on periodic graphs, then of hidden Markov walks, in rough path topology, and we show that this change of setting allows to bring forward extra information on the limit using the area anomaly, which is invisible in the uniform topology. We want to show that the utility of this object goes beyond the setting of dierential equations. We also show how rough paths can be used to encode the way we embed a discrete process in the space of continuous functions, and that the limits of these embeddings dier precisely by the area anomaly term. We then define the iterated occupation times for a Markov chain and show using iterated sums that they form an underlying combinatorial structure for hidden Markov walks. We then construct rough paths using iterated sums and compare them to the classical construction, which uses iterated integrals, to get two dierent types of rough paths at the limit: the non-geometric and the geometric one respectively. Finally, we illustrate the computation and construction of the area anomaly and we give some extra results on the convergence of iterated sums and occupation times
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Ghaffari, Novin. "Estimation with stable disturbances." Thesis, 2014. http://hdl.handle.net/2152/29165.

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The family of stable distributions represents an important generalization of the Gaussian family; stable random variables obey a generalized central limit theorem where the assumption of finite variance is replaced with one of power law decay in the tails. Possessing heavy tails, asymmetry, and infinite variance, non-Gaussian stable distributions can be suitable for inference in settings featuring impulsive, possibly skewed noise. A general lack of analytical form for the densities and distributions of stable laws has prompted research into computational methods of estimation. This report introduces stable distributions through a discussion of their basic properties and definitions in chapter 1. Chapter 2 surveys applications, and chapter 3 discusses a number of procedures for inference, with particular attention to time series models in the ARMA setting. Further details and an application can be found in the appendices.
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Books on the topic "Lévy area"

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Rydberg, Tina Hviid. Some modelling results in the area of interplay between statistics, mathematical finance, insurance and econometrics. [Aarhus, Denmark]: Dept. of Theoretical Statistics, University of Aarhus, 1998.

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Segal, Robert A. 7. Myth and structure. Oxford University Press, 2015. http://dx.doi.org/10.1093/actrade/9780198724704.003.0008.

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‘Myth and structure’ examines the contributions of Claude Lévi-Strauss to the study of myth. Lévi-Strauss treats myth as a coldly intellectual phenomenon: the oppositions expressed in myth constitute logical puzzles rather than existential predicaments. In calling his approach to myth ‘structuralist’, Lévi-Strauss intends to distinguish it from ‘narrative’ interpretations, or those that adhere to the plot of myth. In his unique brand of myth-ritualism, myths and rituals operate together, but as structural opposites rather than, as for other myth-ritualists, parallels. Other structuralists—Vladimir Propp, Georges Dumézil, Louis Gernet, and Marcel Detienne—are then considered. They have sought to decipher underlying patterns in myth and then to link those patterns to ones in the culture at large.
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Bianconi, Ginestra. Diffusion. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198753919.003.0014.

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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.
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Kistler, S. Ashley. All in the Junkab’al. University of Illinois Press, 2017. http://dx.doi.org/10.5406/illinois/9780252038358.003.0005.

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This chapter explores Q'eqchi' “houses” (junkab'als), as defined by Lévi-Strauss, and analyzes the logic of Q'eqchi' kinship. While consanguinity and marriage play roles in governing Q'eqchi' kin relations, they are not the only, nor the most important, criteria for kinship. Instead, the Q'eqchi' use exchange, among other activities, to create, perform, and maintain relationships of shared substance. Vendors bring new individuals into their families through marketing and use their junkab'alaffiliations to legitimize themselves as marketers. The strong connection between kinship and marketing leads vendors to designate house members as heirs to their positions. It is argues that for Chamelco's marketers and their families, kinship and marketing are mutually encompassing entities.
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Schlieter, Jens. The Integration of Theosophical Narratives on Travels of the “Spiritual Body” (ca. 1860–1905). Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190888848.003.0007.

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This chapter demonstrates how Spiritualist and Occultist cultivation practices of “astral travels” began to fuse with the emerging near-death discourse between 1860 and 1905. Of utmost importance are the thoughts and practices of Éliphas Lévi, Helena Blavatsky, Alfred P. Sinnett, and other Theosophists. As intentional and willed temporary excursions of the soul, “astral projection” contributed to the cultural and religious imaginaire of what to experience near death. In addition, ideas and practices of Indian Yoga, or the Buddha’s capability to remember the row of his former existences, gained in his “awakening,” were now read as evidence for the occult spiritual powers of the soul.
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Scully, Stephen, and Alexander C. Loney. Introduction. Edited by Alexander C. Loney and Stephen Scully. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780190209032.013.54.

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The chapter one offers an overview of the structure and themes of the handbook, divided between twelve chapters on Hesiod’s art and the singer/poet’s milieu, and seventeen on matters of reception from archaic art, poetry, and philosophical inquiry to contemporary comic books. The chapter also offers a rationale for its selection of contributors: in the hope of adding fresh insights to the study of Hesiod and his reception, the volume brings together twenty-nine scholars, both junior and senior, many of whom, while experts in their fields, are looking at Hesiodic questions or Hesiodic reception for the first time. When considering the long trajectory of reception studies, the chapter examines the shifting weight of attention from the Works and Days to the Theogony and compares ancient allegory to its very different modern counterpart in theorists like Freud and Lévi-Strauss.
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Colesworthy, Rebecca. Virginia Woolf and the Limits of Feminine Hospitality. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198778585.003.0003.

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Woolf scholars have been at the forefront of bringing economic and especially Keynesian perspectives to bear on modernist literature. This chapter makes the case instead for a sociological approach. Whereas Keynes promoted a separation of egoism and altruism, Marcel Mauss called for a “new morality” that would be a mixture of egoism and altruism. For her part, Woolf, too, conceptualized the modern mind as a mix of contradictory feelings both in her nonfiction and in Mrs. Dalloway, published the same year as Mauss’s The Gift. Drawing historical and conceptual connections between the novel’s representation of feminine consciousness and Claude Lévi-Strauss’s structural re-reading of Mauss, the chapter argues that, in Mrs. Dalloway, everyday metropolitan experience is an experience of gift exchange and, more specifically, of hospitality—of being at once open and closed to the thought of other people in ways that are shaped by gender, class, and nationality.
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Jahanbegloo, Ramin, and Dipankar Gupta. Talking Sociology. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199489374.001.0001.

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A well-known name in contemporary sociology, Dipankar Gupta’s wide range of scholarship and popular columns have justly earned him the reputation of being one of India’s leading public intellectuals. Talking Sociology provides a complete panorama of Gupta’s life and works and his contribution to Indian sociology. In this book of conversations, he shares insights into the key areas of Indian sociology, such as the problem of social stratification, citizenship and democracy, and the caste system and ethnic groups in India. In his view, once we understand the discrete nature of caste identity we begin to appreciate the energy behind caste mobilization and, indeed, of the obduracy of this institution itself. It also discusses the influence of prominent thinkers on Gupta’s works, such as Claude Lévi Strauss, Talcott Parsons, André Beteille, and John Rawls. The ninth in the series of Ramin Jahanbegloo’s conversations with the prominent intellectuals who have made a significant impact in shaping the modern Indian thought, this book discusses Gupta’s array of work and its redefinition and reconstruction of the central concepts of sociology, taking it beyond its disciplinary boundaries.
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Ezra, Elizabeth, and Catherine Wheatley, eds. Shoe Reels. Edinburgh University Press, 2021. http://dx.doi.org/10.3366/edinburgh/9781474451406.001.0001.

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Shoe Reels examines the special relationship between shoes and cinema. The book considers the narrative and aesthetic functions of shoes, asking why they are so memorable, and what their wider cultural resonance might be. Written by experts from a range of disciplines, including film and television studies, philosophy, history, and fashion, this collection covers cinema from its origins to the present day, and spans a global range of films from the United States, Europe, Africa and Asia. Besides protecting the feet, shoes contribute to the performance of gender; they indicate aspects of personality, sexuality, race, ethnicity and social class; and they serve as tools of seduction. As objects designed for the body, shoes also affirm the materiality of individual bodies and the endurance of the human body itself when physical presence has been progressively de-emphasised, first with the advent of technical reproducibility (printing, photography, cinema, radio and the like), and now with the rise of digital technology in the virtual era. The very materiality of shoes—the fact that they are things—is what makes them ripe for analysis. Shoes humanise, setting people apart from non-human animals, but they can also serve to dehumanise. Objects par excellence of hyper-consumption, shoes are situated at the crossroads of sexual fetishism and commodity fetishism. Shoes are clearly more than just good to wear, then: to paraphrase Claude Lévi-Strauss, they are also good to think.
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Payne, Mark. Flowers of Time. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691205946.001.0001.

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The literary lineage of postapocalyptic fiction — stories set after civilization's destruction — is a long one, spanning the biblical tale of Noah and Hesiod's Works and Days to the works of Mary Shelley, Octavia Butler, Cormac McCarthy, and many others. Traveling from antiquity to the present, this book reveals how postapocalyptic fiction differs from other genres — pastoral poetry, science fiction, and the maroon narrative — that also explore human capabilities beyond the constraints of civilization. The book places postapocalyptic fiction into conversation with such theorists as Aristotle, Jean-Jacques Rousseau, Claude Lévi-Strauss, and Carl Schmitt, illustrating how the genre functions as political theory in fictional form. It shows that rather than argue for a particular way of life, postapocalyptic literature reveals what it would be like to inhabit that life. It considers the genre's appeal in our own historical moment, contending that this fiction is the pastoral of our time. Whereas the pastoralist and the maroon could escape to real-world hills and fashion their own versions of freedom, on a fully owned and occupied Earth, only an apocalyptic event can create a space where such freedoms are feasible once again. The book looks at how fictional narratives set after the world's devastation represent new conditions and possibilities for life and humanity.
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Book chapters on the topic "Lévy area"

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Brockwell, Peter J. "Lévy–Driven Continuous–Time ARMA Processes." In Handbook of Financial Time Series, 457–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-71297-8_20.

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Garrido-Atienza, María J., Kening Lu, and Björn Schmalfuß. "Lévy–Areas of Ornstein–Uhlenbeck Processes in Hilbert–Spaces." In Studies in Systems, Decision and Control, 167–88. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19075-4_10.

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HUDSON, ROBIN L. "QUANTUM LÉVY AREA AS QUANTUM MARTINGALE LIMIT." In Quantum Probability and Related Topics, 169–88. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814447546_0010.

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Schürger, Klaus. "Lévy Processes and Benfordʼs Law." In Benford's Law. Princeton University Press, 2015. http://dx.doi.org/10.23943/princeton/9780691147611.003.0006.

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This chapter examines Lévy processes (LPs). These processes can be thought of as random walks in continuous time, having independent and stationary increments, with the assumption that the characteristic function of the state of an LP at time 1 satisfies a certain “Standard Condition” (SC). Exponential Lévy processes (ELPs) in particular are quite attractive for modeling many phenomena. The chapter begins by explaining LPs in more detail, introducing the basic notions as well as providing examples of Lévy processes. It then uses a certain variant of the Poisson Summation Formula to arrive at convergence results for the expectations of certain normalized functionals of the significand of an ELP and obtain, using Azuma's inequality for martingales, large deviation results for these functionals. From here, the chapter calculates the a.s. (almost surely) convergence of normalized functionals and discusses further related conditions and theorems.
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Aïıt-Sahalia, Yacine, and Jean Jacod. "From Diffusions to Semimartingales." In High-Frequency Financial Econometrics. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691161433.003.0001.

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This chapter presents a quick review of the theory of semimartingales, which are processes for which statistical methods are considered in this book. Topics covered include diffusions, Lévy processes, Itô semimartingales, and processes with conditionally independent increments.
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Arı, Yakup. "COGARCH Models." In Emerging Applications of Differential Equations and Game Theory, 79–97. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-0134-4.ch005.

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In this chapter, the features of a continuous time GARCH (COGARCH) process is discussed since the process can be applied as an explicit solution for the stochastic differential equation which is defined for the volatility of unequally spaced time series. COGARCH process driven by a Lévy process is an analogue of discrete time GARCH process and is further generalized to solutions of Lévy driven stochastic differential equations. The Compound Poisson and Variance Gamma processes are defined and used to derive the increments for the COGARCH process. Although there are various parameter estimation methods introduced for COGARCH, this study is focused on two methods which are Pseudo Maximum Likelihood Method and General Methods of Moments. Furthermore, an example is given to illustrate the findings.
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Ari, Yakup. "Continuous Autoregressive Moving Average Models." In Methodologies and Applications of Computational Statistics for Machine Intelligence, 118–41. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-7701-1.ch007.

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The financial time series have a high frequency and the difference between their observations is not regular. Therefore, continuous models can be used instead of discrete-time series models. The purpose of this chapter is to define Lévy-driven continuous autoregressive moving average (CARMA) models and their applications. The CARMA model is an explicit solution to stochastic differential equations, and also, it is analogue to the discrete ARMA models. In order to form a basis for CARMA processes, the structures of discrete-time processes models are examined. Then stochastic differential equations, Lévy processes, compound Poisson processes, and variance gamma processes are defined. Finally, the parameter estimation of CARMA(2,1) is discussed as an example. The most common method for the parameter estimation of the CARMA process is the pseudo maximum likelihood estimation (PMLE) method by mapping the ARMA coefficients to the corresponding estimates of the CARMA coefficients. Furthermore, a simulation study and a real data application are given as examples.
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Ganesan, T., and Pandian Vasant. "Lévy-Enhanced Swarm Intelligence for Optimizing a Multiobjective Biofuel Supply Chain." In Handbook of Research on Smart Computing for Renewable Energy and Agro-Engineering, 287–309. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-1216-6.ch012.

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Engineering systems are currently plagued by various complexities and uncertainties. Metaheuristics have emerged as an essential tool for effective engineering design and operations. Nevertheless, conventional metaheuristics still struggle to reach optimality in the face of highly complex engineering problems. Aiming to further boost the performance of conventional metaheuristics, strategies such as hybridization and various enhancements have been added into the existing solution methods. In this work, swarm intelligence techniques were employed to solve the real-world, large-scale biofuel supply chain problem. Additionally, the supply chain problem considered in this chapter is multiobjective (MO) in nature. Comparative analysis was then performed on the swarm techniques. To further enhance the search capability of the best solution method (GSA), the Lévy flight component from the Cuckoo Search (CS) algorithm was incorporated into the Gravitational Search Algorithm (GSA) technique; developing the novel Lévy-GSA technique. Measurement metrics were then utilized to analyze the results.
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Davidson, James. "The Classical Central Limit Theorem." In Stochastic Limit Theory, 520–47. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192844507.003.0024.

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In this chapter, the first approach is made to establishing the convergence of scaled random sums, considering independent sequences. The classic Lindeberg–Lévy, Khinchine, Lindeberg–Feller, and Liapunov theorems are proved. The main focus is on the treatment of heterogeneous summands, applying the Lindeberg condition, and extensions are given to allow trending (growing or shrinking) variances. The final sections review cases of the central limit theorem under non-standard conditions and α‎-stable convergence.
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"Biofuel Supply Chain Optimization Using Lévy-Enhanced Swarm Intelligence." In Multi-Objective Optimization of Industrial Power Generation Systems, 169–97. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-1710-9.ch005.

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Supply chain planning/optimization presents various challenges to decision makers globally due to its highly complicated nature as well as its large-scale structure. Over the years various state-of-the-art methods have been employed to model supply chains. Optimization techniques are then applied to such models to help with optimal decision making. However, with highly complex industrial systems such as these, conventional metaheuristics are still plagued by various drawbacks. Strategies such as hybridization and algorithmic modifications have been the focus of previous efforts to improve the performance of conventional metaheuristics. In light of these developments, this chapter presents two solution methods for tackling the biofuel supply chain problem.
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Conference papers on the topic "Lévy area"

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Deshpande, Aditya, Manish Kumar, and Subramanian Ramakrishnan. "Robot Swarm for Efficient Area Coverage Inspired by Ant Foraging: The Case of Adaptive Switching Between Brownian Motion and Lévy Flight." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5229.

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Design of robot swarms inspired by self-organization in social insect groups is currently an active research area with a diverse portfolio of potential applications. In this work, the authors propose a control law for efficient area coverage by a robot swarm in a 2D spatial domain, inspired by the unique dynamical characteristics of ant foraging. The novel idea pursued in the effort is that dynamic, adaptive switching between Brownian motion and Lévy flight in the stochastic component of the search increases the efficiency of the search. Influence of different pheromone (the virtual chemotactic agent that drives the foraging) threshold values for switching between Lévy flights and Brownian motion is studied using two performance metrics — area coverage and visit entropy. The results highlight the advantages of the switching strategy for the control framework, particularly in cases when the object of the search is scarce in quantity or getting depleted in real-time.
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Schroeder, Adam M., Marwan H. Mohamed, and Brian P. Trease. "Emergent Behavior Characterization of an Ant-Inspired, Multiple-Pheromone-Driven Robot Swarm." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67951.

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Inspired by chemotactic phenomena observed in ants where individual ants can distinguish their own pheromone from others in their colony, a novel control paradigm for a robot swarm is introduced where each agent deposits an agent-specific, diffusive and evaporative pheromone. Agent’s are repulsed by the pheromone and execute a biased random walk from high-concentration to low-concentration areas. The biased random walk is Lévy flight which causes ‘anomalous diffusion’ by the agents. The ratio of an agent’s sensitivity to its own pheromone compared to other ant’s pheromones, called ‘vanity’, is varied and swarm behavior is characterized using general metrics, e.g. mean squared displacement, and application-specific metrics. It was found that varying the agent vanity resulted in smooth trends in the general behavior metrics, but bifurcations appeared in the application-specific, area coverage metrics. This control scheme is also compared to a scheme that uses a global, common pheromone.
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Wei, Jiamin, YangQuan Chen, Yongguang Yu, and Yuquan Chen. "Improving Cuckoo Search Algorithm With Mittag-Leffler Distribution." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97709.

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Abstract Cuckoo search (CS), as one of the recent nature-inspired metaheuristic algorithms, has proved to be an efficient approach due to the combination of Lévy flights, local search capabilities and guaranteed global convergence. CS uses Lévy flights in global random walk to explore the search space. The Lévy step is taken from the Lévy distribution which is a heavy-tailed probability distribution. In this case, a fraction of large steps are generated, which plays an important role in enhancing search capability of CS. Besides, although many foragers and wandering animals have been shown to follow a Lévy distribution of steps, investigation into the impact of other different heavy-tailed probability distributions on CS is still insufficient up to now. Based on the above considerations, we are motivated to apply the well-known Mittag-Leffler distribution to the standard CS algorithm, and proposed an improved cuckoo search algorithm (CSML) in this paper, where a more efficient search is supposed to take place in the search space thanks to the long jumps. In order to verify the performance of CSML, experiments are carried out on a test suite of 20 benchmark functions. In terms of the observations and results analysis, CSML can be regarded as a new potentially promising algorithm for solving optimization problems.
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Niu, Haoyu, Yuquan Chen, and YangQuan Chen. "Fractional-Order Extreme Learning Machine With Mittag-Leffler Distribution." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97652.

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Abstract Extreme Learning Machine (ELM) has a powerful capability to approximate the regression and classification problems for a lot of data. ELM does not need to learn parameters in hidden neurons, which enables ELM to learn a thousand times faster than conventional popular learning algorithms. Since the parameters in the hidden layers are randomly generated, what is the optimal randomness? Lévy distribution, a heavy-tailed distribution, has been shown to be the optimal randomness in an unknown environment for finding some targets. Thus, Lévy distribution is used to generate the parameters in the hidden layers (more likely to reach the optimal parameters) and better computational results are then derived. Since Lévy distribution is a special case of Mittag-Leffler distribution, in this paper, the Mittag-Leffler distribution is used in order to get better performance. We show the procedure of generating the Mittag-Leffler distribution and then the training algorithm using Mittag-Leffler distribution is given. The experimental result shows that the Mittag-Leffler distribution performs similarly as the Lévy distribution, both can reach better performance than the conventional method. Some detailed discussions are finally presented to explain the experimental results.
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Ramakrishnan, Subramanian, Collin Lambrecht, and Connor Edlund. "Stochastic Dynamics of a Piezoelectric Energy Harvester Subjected to Lévy Flight Excitations." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5404.

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Vibration energy harvesting seeks to exploit the energy of ambient random vibration for power generation, particularly in small scale devices. Piezoelectric transduction is often used as a conversion mechanism in harvesting and the random excitation is typically modeled as a Brownian stochastic process. However, non-Brownian excitations are of potential interest, particularly in the nonequilibrium regime of harvester dynamics. In this work, we investigate the averaged power output of a generic piezoelectric harvester driven by Brownian as well as (non-Brownian) Lévy stable excitations both in the linear and the Duffing regimes. First, a coupled system of stochastic differential equations that model the electromechanical system are presented. Numerical simulation results (based on the Euler-Maruyama scheme) that show the average power output from the system under Brownian and Lévy excitations are presented for the cases where the mechanical degree of freedom behaves as a linear as well as a Duffing oscillator. The results demonstrate that Lévy excitations result in higher expectation values of harvested power. In particular, increasing the noise intensity leads to significant increase in power output in the Levy case when compared with Brownian excitations.
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Ramakrishnan, Subramanian, and Connor Edlund. "Stochastic Stability of a Piezoelectric Vibration Energy Harvester and Stabilization Using Noise." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-9216.

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Vibration energy harvesters convert the energy of ambient, random vibration into electrical power often using piezoelectric transduction. The stochastic dynamics of a piezoelectric harvester with parameteric uncertainties is yet to be fully explored in the nonequilibrium regime. Motivated by mathematical results that establish the counterintuitive phenomenon of stabilization of response in certain nonlinear systems using noise, we investigate the stochastic stability of a generic harvester in the linear and the monostable nonlinear regimes excited by multiplicative noise characterized by both Brownian and the Lévy stable distributions. First, a lower bound on the magnitude of noise intensity that guarantees exponential stability almost surely, is obtained analytically as an inequality in terms of system parameters in the linear case. This result is validated numerically using the Euler-Maruyama scheme. Next, noise-induced stabilization in the harvester dynamics is demonstrated numerically for both the linear and nonlinear cases wherein Lévy noise was found to achieve stabilization at lower noise intensities than Brownian noise. Additionally, the inclusion of a nonlinear stiffness does not have an appreciable affect on the stabilization behavior. The results indicate that stabilization may be achieved using noise and are expected to be useful in harvester design.
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Da Silva, Teofilo Augusto, and Suzete Venturelli. "Computational Image: a review about the image as simulation." In IV Congreso Internacional de Investigación en Artes Visuales. ANIAV 2019. Imagen [N] Visible. Valencia: Universitat Politècnica de València, 2019. http://dx.doi.org/10.4995/aniav.2019.8953.

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This essay it’s a bibliographic review about the issue of the image in the computational art creation environment. With the technological breakthroughs, specially in the computer graphics, the computational images insert themselves in the art field to understand and discuss how they can interfere in sign and meaning matter. WIth the computational technology the images became machine generated and this phenomenon impacts are still under investigation. This work, that have as base the discussions brought by Edmond Couchot, Oliver Grau, Cláudia Gianetti, José Luis Brea, Pierre Lévy, Vilém Flusser, Suzete Venturelli and Cleomar Rocha, aims to show off the consequences, in the artist context, of numerical ambient images uses.
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Piros, Réka Ágnes, Viktória Mozgai, and Bernadett Bajnóczi. "Hun kori lószerszámos leletegyüttesek roncsolásmentes archeometriai vizsgálatának új eredményei." In Hadak útján. A népvándorláskor kutatóinak XXIX. konferenciája. Budapest, 2019. november 15–16. 29th. Bölcsészettudományi Kutatóközpont Magyar Őstörténeti Kutatócsoport, 2022. http://dx.doi.org/10.55722/arpad.kiad.2021.4.1_13.

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A hun kor kései szakaszára keltezhető leletegyüttesek, amelyek közé az általunk vizsgált lévai, nyíregyháza­orosi, valamint pécsüszögi lószerszámzatok sorolhatók, a préselt, aranylemezes tárgyak horizontjának képviselői. A jelen kutatás fő célja az anyagösszetétel és az aranyozás technikájának megállapítása, valamint az egy leletegyüttesen belüli csoportok összetartozásának bizonyítása. Ez lehetőséget teremt arra, hogy nemcsak küllem, hanem anyagösszetétel alapján is igazolást nyerjen a sérült, esetleg elveszett tárgyak garnitúrán belüli pótlása, javítása. A kézi röntgenfluoreszcens spektrométerrel (hXRF) végzett méréseket digitális mikroszkópos képekkel egészítettük ki. A kapott eredmények alapján a tárgyak aranylemezből (Pécsüszög), aranyozott ezüstlemezből (Nyíregyháza­Oros) vagy aranyozott vörösrézből (Léva) készültek. Kémiai összetételük változatos képet mutat, amely alapján jól elkülöníthetők az eltérő ötvözetből készült tárgyak. A tárgyakat tűzi aranyozással (Léva) vagy „füstaranyozással” (leaf gilding) (Nyíregyháza­Oros) díszítették.
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Lúcio, Yan Lieven Souza, Luiza Scapinello Aquino, and Leandro dos Santos Coelho. "Marine Predators Algorithm Approaches on a Multivariable Fractional PID Controller Tuning." In Congresso Brasileiro de Inteligência Computacional. SBIC, 2021. http://dx.doi.org/10.21528/cbic2021-39.

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In this paper, a performance comparison between the Marine Predators Algorithm (MPA), a metaheuristic paradigm, and two other designed variants for the tuning of a fractional proportional-integrative-derivative (PID) controller in a multiple-input multiple-output (MIMO) application is presented. The practical system plant corresponds to a ball mill pulverizing system, whose structure presents two inputs and two outputs. To encounter the optimal response on the MIMO control of this system a MPA approach applied to PID tuning is suitable, as it presents both the capability to diversify the search space (exploration) and to improve the quality of current solutions (exploitation) in search space. The MPA is a metaheuristic inspired by the extensive hunting strategy of ocean predators called Lévy and Brownian movements, it focuses on an optimal confront rate procedure in natural interaction between predator and prey in the marine ecosystem. The original MPA itself presents a satisfactory performance, in terms of statistical metrics. Nevertheless, it can be improved through the modification and addition of distinct techniques. In order to achieve those modifications, three variants are implemented exploring different procedures namely the oppositional-based learning and application of quantum mechanics. The optimal parameter values for the PID controller are analyzed by minimizing the integral time squared error (ITSE) index of the system’s response. The simulations are performed using the SIMULINK/MATLAB computational environment. Statistical measures including best, mean, median and standard deviation of the system response error for the tuned controllers are evaluated and compared over fifty runs. The obtained results suggest that the use of the mentioned proposals has an advantage in enhancing the tuning efficiency of the MPA in this application.
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Uya, Yifan. "Collaborative Vibration: The Mythic Journey of A Coal Boy." In LINK 2021. Tuwhera Open Access, 2021. http://dx.doi.org/10.24135/link2021.v2i1.119.

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Acknowledging the Anthropocene crisis, my research examines myth and myth-making to reimagine the role of Claude Lévi-Strauss’ bricoleur concept. Following Joseph M. Coll’s Taoist and Buddhist systemic thinking inspired theory of sustainable transformation, the practice-led project evolves into the making of an essayist film that conveys a specific personal myth.My research reckons that a bricoleur should perceive myth-making as an organic growing organisation that acquires intuition and posteriori knowledge. And focus on a narrative that evolves into the mythic identity of a piece of coal and a bar-tailed godwit corresponding to designated oppositional values and semiotic assets. Apart from the practitioner works of Stan Brakhage, Chris Marker and Adam Curtis, my research also dives into Elysia Crampton Chuquimia, Howie Lee and Yaksha‘s musical languages to explore the other narrative possibilities when re-examining history in a socially conscious manner. As the film soundtrack is also part of the myth-making production. My practice-led project inevitably evolves into the subject of the self as the production presents a negotiation through metaphors and signifiers concerning memory, history and experience. The filmmaking echoes a search for the wisdom of self-acceptance. It adopts Stephen Yablo’s understanding of conceivability to generate and regenerate meaningful assets. Concepts are planted to grow into newer representations compromising posteriori knowledge and self-realisations, with informal syllogistic reasoning concerning the epistemological nature of imagination and the transformative structure of myth. The contextual knowledge of my research examines the subject of myth and myth-making through Jacques Lacan's theory of fantasy, Jungian analytical psychology and Claude Lévi-Strauss knowledge of structural linguistics. It adopts Lévi-Strauss’ canonical myth formula concerning the missing discussion of experience, community, and the wilder contexts of shamanology. Maurice Merleau-Ponty's phenomenological body and Martin Heidegger's thoughts on the philosophy of technology concerning the body-to-technology relation and the notion of symbolic light and darkness. With critics on the instrumentalist stance of technology and Rene Descartes's modal metaphysics concerning Arnold Gehlen’s conservative alert of mankind’s debased condition of modern existence, my research proposes that myth-making is a necessary altruistic form of social technology that can transform experience into wisdom. Acknowledging that will is the priority for behaviour change. The production examines the Dao of myth and myth-making as a specific technological answer to resolve David Attenborough's calling for a global transformation and collaboration in his book A Life of Our Planet. To further develop such a technology, my research seeks a systemic understanding of myth and myth-making. Therefore, my research hypothesis a wholistic and heuristic methodology, namely Daoist bricoleur. By experiencing a personal myth, I celebrate my Manchu and Chinese culture origin and the complexity of my upbringing. My research visits the endangered Manchu Ulabun storytelling tradition and reckons the film production rely on the structural establishment of critical mythic fragments founded on autobiography and social conventions. As a permanent resident of New Zealand born in a coal-mining town in eastern Inner Mongolia, China, with an unverifiable ancestral clan name related to Kangxi, Yongzheng and Qianlong Emperor of the Qing Dynasty and much more.
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