The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Yun S Song - One of the best experts on this subject based on the ideXlab platform.
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Padé approximants and exact two-locus sampling distributions
Annals of Applied Probability, 2012Co-Authors: Paul A. Jenkins, Yun S SongAbstract:For population genetics models with recombination, obtaining an exact, analytic sampling distribution has remained a challenging open problem for several decades. Recently, a new perspective based on Asymptotic Series has been introduced to make progress on this problem. Specifically, closed-form expressions have been derived for the first few terms in an Asymptotic expansion of the two-locus sampling distribution when the recombination rate ρ is moderate to large. In this paper, a new computational technique is developed for finding the Asymptotic expansion to an arbitrary order. Computation in this new approach can be automated easily. Furthermore, it is proved here that only a finite number of terms in the Asymptotic expansion is needed to recover (via the method of Pade approximants) the exact two-locus sampling distribution as an analytic function of ρ; this function is exact for all values of ρ ∈ [0, ∞). It is also shown that the new computational framework presented here is flexible enough to incorporate natural selection.
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closed form Asymptotic sampling distributions under the coalescent with recombination for an arbitrary number of loci
arXiv: Probability, 2011Co-Authors: Anand Bhaskar, Yun S SongAbstract:Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case of two loci, a new framework based on Asymptotic Series has recently been developed to derive closed-form results when the recombination rate is moderate to large. In this paper, an arbitrary number of loci is considered and combinatorial approaches are employed to find closed-form expressions for the first couple of terms in an Asymptotic expansion of the multi-locus sampling distribution. These expressions are universal in the sense that their functional form in terms of the marginal one-locus distributions applies to all finite- and infinite-alleles models of mutation.
John P Boyd - One of the best experts on this subject based on the ideXlab platform.
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hyperAsymptotics and the linear boundary layer problem why Asymptotic Series diverge
Siam Review, 2005Co-Authors: John P BoydAbstract:The simplest problem with boundary layers, $\epsilon^{2} u_{xx} - u = - f(x)$, is used to illustrate (i) why the perturbation Series in powers of $\epsilon$ is Asymptotic but divergent, (ii) why the optimally truncated expansion is ``superAsymptotic'' in the sense that that error is proportional to $\exp(- \mbox{[constant]} / \epsilon)$, and (iii) how to obtain an improved "hyperAsymptotic" approximation.
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the devil s invention Asymptotic superAsymptotic and hyperAsymptotic Series
Acta Applicandae Mathematicae, 1999Co-Authors: John P BoydAbstract:Singular perturbation methods, such as the method of multiple scales and the method of matched Asymptotic expansions, give Series in a small parameter e which are Asymptotic but (usually) divergent. In this survey, we use a plethora of examples to illustrate the cause of the divergence, and explain how this knowledge can be exploited to generate a 'hyperAsymptotic' approximation. This adds a second Asymptotic expansion, with different scaling assumptions about the size of various terms in the problem, to achieve a minimum error much smaller than the best possible with the original Asymptotic Series. (This rescale-and-add process can be repeated further.) Weakly nonlocal solitary waves are used as an illustration.
Yannick Meurice - One of the best experts on this subject based on the ideXlab platform.
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simple method to make Asymptotic Series of feynman diagrams converge
Physical Review Letters, 2002Co-Authors: Yannick MeuriceAbstract:We show that, for two nontrivial lambda phi(4) problems (the anharmonic oscillator and the Landau-Ginzburg hierarchical model), improved perturbative Series can be obtained by cutting off the large field contributions. The modified Series converge to values exponentially close to the exact ones. For lambda larger than some critical value, the method outperforms Pade's approximants and Borel summations. The method can also be used for Series which are not Borel summable such as the double-well potential Series. We show that semiclassical methods can be used to calculate the modified Feynman rules, estimate the error, and optimize the field cutoff.
Mengali G. - One of the best experts on this subject based on the ideXlab platform.
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Solar Sail Trajectory Analysis with Asymptotic Expansion Method
Japan Space Forum, 2017Co-Authors: Niccolai L., Quarta A., Mengali G.Abstract:An analytical expression for the trajectory equation of a solar sail-based spacecraft is available in special cases only, such as the well known logarithmic spiral, which however cannot be used when the parking orbit is circular. This paper presents an approximate solution to this problem, obtained by considering the propulsive acceleration as a perturbation effect acting on a Keplerian trajectory. In this context, the spacecraft dynamics are approximated using an Asymptotic Series expansion in terms of non-singular (dimensionless) generalized orbital elements. A first order approximation is shown to be very accurate in predicting the trajectory of the spacecraft and the evolution of the non-singular orbital parameters of the osculating orbit, provided the sail lightness number is sufficiently small. The analytical approximation is validated by simulation
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Solar Sail Trajectory Analysis with Asymptotic Expansion Method
'Elsevier BV', 2017Co-Authors: Niccolai L., Quarta A., Mengali G.Abstract:An analytical expression for the trajectory equation of a solar sail spacecraft is available in special cases only, including the well known logarithmic spiral. The latter, however, cannot be used when the parking orbit is circular. This paper presents an approximate solution to this problem, obtained by considering the propulsive acceleration as a perturbation effect acting on a Keplerian trajectory in a heliocentric (two-dimensional) mission scenario. In this context, the spacecraft dynamics are approximated by an Asymptotic Series expansion in terms of non-singular generalized orbital elements. Under the assumption that the propulsive acceleration is small compared to the local Sun's gravitational attraction, a first order approximation is shown to be very accurate in predicting the trajectory of the spacecraft and the evolution of the non-singular orbital parameters of the osculating orbit. A periodic rectification procedure improves the method accuracy without significantly affecting the computational time, as is confirmed by numerical simulations
Paul A. Jenkins - One of the best experts on this subject based on the ideXlab platform.
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Padé approximants and exact two-locus sampling distributions
Annals of Applied Probability, 2012Co-Authors: Paul A. Jenkins, Yun S SongAbstract:For population genetics models with recombination, obtaining an exact, analytic sampling distribution has remained a challenging open problem for several decades. Recently, a new perspective based on Asymptotic Series has been introduced to make progress on this problem. Specifically, closed-form expressions have been derived for the first few terms in an Asymptotic expansion of the two-locus sampling distribution when the recombination rate ρ is moderate to large. In this paper, a new computational technique is developed for finding the Asymptotic expansion to an arbitrary order. Computation in this new approach can be automated easily. Furthermore, it is proved here that only a finite number of terms in the Asymptotic expansion is needed to recover (via the method of Pade approximants) the exact two-locus sampling distribution as an analytic function of ρ; this function is exact for all values of ρ ∈ [0, ∞). It is also shown that the new computational framework presented here is flexible enough to incorporate natural selection.
