Why Lévy 
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-stable distributions lack general closed-form expressions for arbitrary 
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Rocha, E.C.; Luz, M. G. E. da; Raposo, Ernesto P.; Viswanathan, G. M.

doi:10.1103/physreve.100.010103

Cited by 7 publications

(5 citation statements)

References 31 publications

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“…We need a quick algorithm to approximate the Lévy distribution and execute the Lévy flight. Mantegna's algorithm generates random noises based on a symmetric Lévy stable distribution 54–56 . A symmetric Lévy stable distribution is best for Lévy flights since its route has to be accidental 52,53 .…”

Section: Proposed Hybrid Methodsmentioning

confidence: 99%

A cloud database route scheduling method using a hybrid optimization algorithm

Baghi

Navimipour

2023

Int J Communication

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Cloud computing has appeared as a technology allowing a company to employ computing resources such as applications, software, and hardware to calculate over the Internet. Scholars have paid great attention to cloud computing because of its cutting-edge availability, cost decrement, and boundless applications. A cloud database is a data storage site on the web where the optimal path is spotted to access the needed database. So, placing the ideal path to a database is crucial. The cloud database defined the scheduling problem to choose the perfect route. Cloud database path scheduling is a multifaceted procedure consisting of congestion control, routing list, and network flow distribution. It has a postponement in searching for the needed source route from the cloud database. Offering numerous infinite resources with the growing database workload is an NP-Hard optimization problem where the query request needs optimal schedules to respond to the required services. So, we have used a hybrid cuckoo search (CS) and genetic algorithm (GA), motivated by a social bird's phenomenon, to solve this problem. Integrating genetic operators has dramatically enhanced the balance between the capability of searching and utilization.

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Section: Proposed Hybrid Methodsmentioning

confidence: 99%

A cloud database route scheduling method using a hybrid optimization algorithm

Baghi

Navimipour

2023

Int J Communication

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“…When the variance is infinite, as is the case when α 0 , α ∞ < 2, then the generalized CLT provides the functional form of the limiting distributions in terms of the Lévy alpha-stable distributions. These distributions are a family of normalized probability density functions that do not generally have closed form expressions [35], except for a few special cases. The Lévy alpha-stable distributions are usually denoted by S(α, β, γ, δ), where the four parameters, namely, α ∈ (0, 2], β ∈ [−1, 1], γ ∈ (0, ∞) and δ ∈ (−∞, ∞) specify the stability, α 0 = 0.5…”

Section: The Zero Energy Statementioning

confidence: 99%

Beyond the universal Dyson singularity for 1-D chains with hopping disorder

Krishna,

Bhatt

2021

Preprint

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We study a simple non-interacting nearest neighbor tight-binding model in one dimension with disorder, where the hopping terms are chosen randomly. This model exhibits a well-known singularity at the band center both in the density of states and localization length. If the probability distribution of the hopping terms is well-behaved, then the singularities exhibit universal behavior, the functional form of which was first discovered by Freeman Dyson in the context of a chain of classical harmonic oscillators. We show here that this universal form can be violated in a tunable manner if the hopping elements are chosen from a divergent probability distribution. We also demonstrate a connection between a breakdown of universality in this quantum problem and an analogous scenario in the classical domain -that of random walks and diffusion with anomalous exponents.

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“…Although Lévy distributions can be cast [9][10][11] in terms of Fox-H functions, whose calculation relies on complex integrals of the Mellin-Barnes type, they generally lack closed-form expressions based on elementary functions [66][67][68]. In this sense, the Cauchy (α = 1) and the limit case of Gaussian (α = 2) distributions constitute notable exceptions when β = 0.…”

Section: The Lévy Flier On a Bounded Domainmentioning

confidence: 99%

Revisiting Lévy flights on bounded domains: a Fock space approach

Araújo¹,

Lukin²,

Luz³

et al. 2020

J. Stat. Mech.

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The statistical description of a one-dimensional superdiffusive Lévy flier restricted to a finite domain is well known to be technically involving. For example, in this type of process the probability distribution P (x, t) and survival probability S(t) cannot be obtained from the method of images. Other methods, such as the fractional derivative approach, also find technical difficulties due to the long jumps combined with the presence of absorbing boundaries. Here we revisit this problem through a different point of view. We map the corresponding master equation to a Schrödinger-like equation and then describe the Lévy flier evolution in a Fock space. The system states are assigned to the available

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Why Lévy α -stable distributions lack general closed-form expressions for arbitrary α

Cited by 7 publications

References 31 publications

A cloud database route scheduling method using a hybrid optimization algorithm

A cloud database route scheduling method using a hybrid optimization algorithm

Beyond the universal Dyson singularity for 1-D chains with hopping disorder

Revisiting Lévy flights on bounded domains: a Fock space approach

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