The Experts below are selected from a list of 539643 Experts worldwide ranked by ideXlab platform
Bjorn Poppe - One of the best experts on this subject based on the ideXlab platform.
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fourier deconvolution reveals the role of the lorentz Function as the convolution Kernel of narrow photon beams
Physics in Medicine and Biology, 2009Co-Authors: Armand Djouguela, D Harder, Wolfgang Kunth, Simon Foschepoth, Andreas Ruhmann, Kay Willborn, Ralf Kollhoff, Bjorn PoppeAbstract:The two-dimensional lateral dose profiles D(x, y) of narrow photon beams, typically used for beamlet-based IMRT, stereotactic radiosurgery and tomotherapy, can be regarded as resulting from the convolution of a two-dimensional rectangular Function R(x, y), which represents the photon fluence profile within the field borders, with a rotation-symmetric convolution Kernel K(r). This Kernel accounts not only for the lateral transport of secondary electrons and small-angle scattered photons in the absorber, but also for the 'geometrical spread' of each pencil beam due to the phase-space distribution of the photon source. The present investigation of the convolution Kernel was based on an experimental study of the associated line-spread Function K(x). Systematic cross-plane scans of rectangular and quadratic fields of variable side lengths were made by utilizing the linear current versus dose rate relationship and small energy dependence of the unshielded Si diode PTW 60012 as well as its narrow spatial resolution Function. By application of the Fourier convolution theorem, it was observed that the values of the Fourier transform of K(x) could be closely fitted by an exponential Function exp(−2πλνx) of the spatial frequency νx. Thereby, the line-spread Function K(x) was identified as the Lorentz Function K(x) = (λ/π)[1/(x2 + λ2)], a single-parameter, bell-shaped but non-Gaussian Function with a narrow core, wide curve tail, full half-width 2λ and convenient convolution properties. The variation of the 'Kernel width parameter' λ with the photon energy, field size and thicKness of a water-equivalent absorber was systematically studied. The convolution of a rectangular fluence profile with K(x) in the local space results in a simple equation accurately reproducing the measured lateral dose profiles. The underlying 2D convolution Kernel (point-spread Function) was identified as K(r) = (λ/2π)[1/(r2 + λ2)]3/2, fitting experimental results as well. These results are discussed in terms of their use for narrow-beam treatment planning.
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the lorentz type convolution Kernel of narrow photon beams
2008Co-Authors: Armand Djouguela, D Harder, Wolfgang Kunth, Kay Willborn, Ralf Kollhoff, Bjorn PoppeAbstract:Transverse dose profiles D(x,y) of narrow photon beams can be regarded as resulting from the convolution of a two-dimensional rectangular Function R(x,y) with a rotation-symmetric convolution Kernel K(r). The Kernel expresses the influences of the geometric penumbra of the accelerator beamhead and of the lateral transport of secondary electrons and small-angle scattered photons in the absorber. Our experimental investigation of the convolution Kernel has shown that the line-spread Function K(x) is closely approximated by the Lorentz Function K(x) = (1/λ) [1/(x2 + λ2)], a single parameter, bell-shaped Function with narrow core, wide socKet, full half-width 2λ and convenient convolution properties [1]. The results of a systematic study of the variation of "Kernel width parameter" λ with photon energy, field side length, and depth in water-equivalent phantom material will now be reported. Furthermore, the associated point-spread Function has been identified as K(r) = (1/2λ) [1/(r2 + λ2)]. For IMRT applications, a simple formula linKing the dose value in the centre of a rectangular photon field with the dose-area product, the field size and parameter λ has been derived from K(r) and has been experimentally confirmed.
Rodney G Downey - One of the best experts on this subject based on the ideXlab platform.
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Kolmogorov complexity and solovay Functions
Symposium on Theoretical Aspects of Computer Science, 2009Co-Authors: Laurent Bienvenu, Rodney G DowneyAbstract:Solovay (1975) proved that there exists a computable upper bound~$f$ of the prefix-free Kolmogorov complexity Function~$K$ such that $f(x)=K(x)$ for infinitely many~$x$. In this paper, we consider the class of computable Functions~$f$ such that $K(x) \leq f(x)+O(1)$ for all~$x$ and $f(x) \leq K(x)+O(1)$ for infinitely many~$x$, which we call Solovay Functions. We show that Solovay Functions present interesting connections with randomness notions such as Martin-L\"of randomness and K-triviality.
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Kolmogorov complexity and solovay Functions
arXiv: Computational Complexity, 2009Co-Authors: Laurent Bienvenu, Rodney G DowneyAbstract:Solovay proved that there exists a computable upper bound f of the prefix-free Kolmogorov complexity Function K such that f (x) = K(x) for infinitely many x. In this paper, we consider the class of computable Functions f such that K(x) <= f (x)+O(1) for all x and f (x) <= K(x) + O(1) for infinitely many x, which we call Solovay Functions. We show that Solovay Functions present interesting connections with randomness notions such as Martin-L\"of randomness and K-triviality.
Armand Djouguela - One of the best experts on this subject based on the ideXlab platform.
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fourier deconvolution reveals the role of the lorentz Function as the convolution Kernel of narrow photon beams
Physics in Medicine and Biology, 2009Co-Authors: Armand Djouguela, D Harder, Wolfgang Kunth, Simon Foschepoth, Andreas Ruhmann, Kay Willborn, Ralf Kollhoff, Bjorn PoppeAbstract:The two-dimensional lateral dose profiles D(x, y) of narrow photon beams, typically used for beamlet-based IMRT, stereotactic radiosurgery and tomotherapy, can be regarded as resulting from the convolution of a two-dimensional rectangular Function R(x, y), which represents the photon fluence profile within the field borders, with a rotation-symmetric convolution Kernel K(r). This Kernel accounts not only for the lateral transport of secondary electrons and small-angle scattered photons in the absorber, but also for the 'geometrical spread' of each pencil beam due to the phase-space distribution of the photon source. The present investigation of the convolution Kernel was based on an experimental study of the associated line-spread Function K(x). Systematic cross-plane scans of rectangular and quadratic fields of variable side lengths were made by utilizing the linear current versus dose rate relationship and small energy dependence of the unshielded Si diode PTW 60012 as well as its narrow spatial resolution Function. By application of the Fourier convolution theorem, it was observed that the values of the Fourier transform of K(x) could be closely fitted by an exponential Function exp(−2πλνx) of the spatial frequency νx. Thereby, the line-spread Function K(x) was identified as the Lorentz Function K(x) = (λ/π)[1/(x2 + λ2)], a single-parameter, bell-shaped but non-Gaussian Function with a narrow core, wide curve tail, full half-width 2λ and convenient convolution properties. The variation of the 'Kernel width parameter' λ with the photon energy, field size and thicKness of a water-equivalent absorber was systematically studied. The convolution of a rectangular fluence profile with K(x) in the local space results in a simple equation accurately reproducing the measured lateral dose profiles. The underlying 2D convolution Kernel (point-spread Function) was identified as K(r) = (λ/2π)[1/(r2 + λ2)]3/2, fitting experimental results as well. These results are discussed in terms of their use for narrow-beam treatment planning.
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the lorentz type convolution Kernel of narrow photon beams
2008Co-Authors: Armand Djouguela, D Harder, Wolfgang Kunth, Kay Willborn, Ralf Kollhoff, Bjorn PoppeAbstract:Transverse dose profiles D(x,y) of narrow photon beams can be regarded as resulting from the convolution of a two-dimensional rectangular Function R(x,y) with a rotation-symmetric convolution Kernel K(r). The Kernel expresses the influences of the geometric penumbra of the accelerator beamhead and of the lateral transport of secondary electrons and small-angle scattered photons in the absorber. Our experimental investigation of the convolution Kernel has shown that the line-spread Function K(x) is closely approximated by the Lorentz Function K(x) = (1/λ) [1/(x2 + λ2)], a single parameter, bell-shaped Function with narrow core, wide socKet, full half-width 2λ and convenient convolution properties [1]. The results of a systematic study of the variation of "Kernel width parameter" λ with photon energy, field side length, and depth in water-equivalent phantom material will now be reported. Furthermore, the associated point-spread Function has been identified as K(r) = (1/2λ) [1/(r2 + λ2)]. For IMRT applications, a simple formula linKing the dose value in the centre of a rectangular photon field with the dose-area product, the field size and parameter λ has been derived from K(r) and has been experimentally confirmed.
Rahul Kumar - One of the best experts on this subject based on the ideXlab platform.
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the generalized modified bessel Function and its connection with voigt line profile and humbert Functions
Advances in Applied Mathematics, 2020Co-Authors: Rahul KumarAbstract:Abstract Recently Dixit, Kesarwani, and Moll introduced a generalization K z , w ( x ) of the modified Bessel Function K z ( x ) and showed that it satisfies an elegant theory similar to that of K z ( x ) . In this paper, we show that while K 1 2 ( x ) is an elementary Function, K 1 2 , w ( x ) can be written in the form of an infinite series of Humbert Functions. As an application of this result, we generalize the transformation formula for the logarithm of the DedeKind eta Function η ( z ) . We also establish a connection between K 1 2 , w ( x ) and the cumulative distribution Function corresponding to the Voigt line profile.
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reliability analysis of slope safety factor by using gpr and gp
Geotechnical and Geological Engineering, 2019Co-Authors: Pijush Samui, Rahul Kumar, Uttam Yadav, Sunita Kumari, Dieu Tien BuiAbstract:Reliability analysis of slope is an important aspect of geotechnical engineering practice. However, it is very difficult to assess the estimation of reliability analysis of slope because it include the uncertainty parameters i.e. soil parameters cohesion of soil (c), angle of shearing resistance (φ) and unit weight of soil (γ). In former days, to execute the reliability analysis of slope, several analytical methods were used but at the present days various computer technique (model) are available and among which Gaussian Process Regression (GPR) and Genetic Programming (GP) are part of them. This paper’s primary objective is to survey the fitness of GPR and GP with the help of First Oder Second Moment Method (FOSM) to find out the Reliability analysis of slope. The GP is the non-parametric Kernel probabilistic method. It is adequately assigned by its mean Function m(x) and covariance Function K(x, x′). GP is a standard technique for acquiring computer automatically to resolve a problem from an eminent-level argument of what need to be performed. This study shows that the proposed GPR based FOSM is suitable alternative for reliability analysis of slope.
Laurent Bienvenu - One of the best experts on this subject based on the ideXlab platform.
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Kolmogorov complexity and solovay Functions
Symposium on Theoretical Aspects of Computer Science, 2009Co-Authors: Laurent Bienvenu, Rodney G DowneyAbstract:Solovay (1975) proved that there exists a computable upper bound~$f$ of the prefix-free Kolmogorov complexity Function~$K$ such that $f(x)=K(x)$ for infinitely many~$x$. In this paper, we consider the class of computable Functions~$f$ such that $K(x) \leq f(x)+O(1)$ for all~$x$ and $f(x) \leq K(x)+O(1)$ for infinitely many~$x$, which we call Solovay Functions. We show that Solovay Functions present interesting connections with randomness notions such as Martin-L\"of randomness and K-triviality.
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Kolmogorov complexity and solovay Functions
arXiv: Computational Complexity, 2009Co-Authors: Laurent Bienvenu, Rodney G DowneyAbstract:Solovay proved that there exists a computable upper bound f of the prefix-free Kolmogorov complexity Function K such that f (x) = K(x) for infinitely many x. In this paper, we consider the class of computable Functions f such that K(x) <= f (x)+O(1) for all x and f (x) <= K(x) + O(1) for infinitely many x, which we call Solovay Functions. We show that Solovay Functions present interesting connections with randomness notions such as Martin-L\"of randomness and K-triviality.
