The Experts below are selected from a list of 39 Experts worldwide ranked by ideXlab platform
Mohammad Mahmoud Ibrahim - One of the best experts on this subject based on the ideXlab platform.
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bed profile downstream compound sharp crested v notch weir
alexandria engineering journal, 2015Co-Authors: Mohammad Mahmoud IbrahimAbstract:Abstract Triangular weirs are commonly used to measure discharge in open channel flow. They represent an inexpensive, reliable methodology to monitor water allocation. A compound sharp-crested weir consisting of two Triangular Parts with different notch angles was used. The Lower Triangular Part of the weir handles the normal range of discharges while the upper Part measures the higher peak flows. This paper evaluates experimentally the local scour downstream compound sharp crested V-notch weir. Forty-eight (48) experimental runs were conducted. Three models of weirs with different geometries (combination of notch angles), four upstream water levels, three water levels at the tailgate, and two bed materials were used. Multiple regression equations based on energy principal and dimensional analysis theory were deduced to estimate the local scour downstream of the weir models. The developed equations were compared with the experimental data. The comparison between the local scour downstream classical V-notch weir and a compound sharp-crested weir consisting of two Triangular Parts with different notch angles was found to be unnoticed. The study recommended using the compound V-notch weir to pass high discharges instead of the classical V-notch weir.
Veremyev Alexander - One of the best experts on this subject based on the ideXlab platform.
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Bilinear matrix equation characterizes Laplacian and distance matrices of weighted trees
2021Co-Authors: Goubko Mikhail, Veremyev AlexanderAbstract:It is known from the algebraic graph theory that if $L$ is the Laplacian matrix of some tree $G$ with a vertex degree sequence $\mathbf{d}=(d_1, ..., d_n)^\top$ and $D$ is its distance matrix, then $LD+2I=(2\cdot\mathbf{1}-\mathbf{d})\mathbf{1}^\top$, where $\mathbf{1}$ is an all-ones column vector. We prove that if this matrix identity holds for the Laplacian matrix of some graph $G$ with a degree sequence $\mathbf{d}$ and for some matrix $D$, then $G$ is essentially a tree, and $D$ is its distance matrix. This result immediately generalizes to weighted graphs. If the matrix $D$ is symmetric, the Lower Triangular Part of this matrix identity is redundant and can be omitted. Therefore, the above bilinear matrix equation in $L$, $D$, and $\mathbf{d}$ characterizes trees in terms of their Laplacian and distance matrices. Applications to the extremal graph theory (especially, to topological index optimization and to optimal tree problems) and to road topology design are discussed.Comment: 12 page
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Bilinear matrix equation characterizes Laplacian and distance matrices of weighted trees
2020Co-Authors: Goubko Mikhail, Veremyev AlexanderAbstract:It is known from the algebraic graph theory that if $L$ is the Laplacian matrix of some tree $G$ with a vertex degree sequence $\vec{d}=(d_1, ..., d_n)^\top$ and $D$ is its distance matrix, then $LD+2I=(2\cdot\vec{1}-\vec{d})\vec{1}^\top$, where $\vec{1}$ is an all-ones column vector. We prove that if this matrix identity holds for the Laplacian matrix of some graph $G$ with a degree sequence $\vec{d}$ and for some matrix $D$, then $G$ is essentially a tree, and $D$ is its distance matrix. This result immediately generalizes to weighted graphs. If the matrix $D$ is symmetric, the Lower Triangular Part of this matrix identity is redundant and can be omitted. Therefore, the above bilinear matrix equation in $L$, $D$, and $\vec{d}$ characterizes trees in terms of their Laplacian and distance matrices. Applications to the extremal graph theory (especially, to topological index optimization and to optimal tree problems) and to road topology design are discussed.Comment: 12 page
Koko Jonas - One of the best experts on this subject based on the ideXlab platform.
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Parallel Euclidean distance matrix computation on big datasets *
HAL CCSD, 2019Co-Authors: Angeletti Mélodie, Bonny Jean-marie, Koko JonasAbstract:We propose, in this paper, three parallel algorithms to accelerate the Euclidean matrix computation on parallel computers. The first algorithm, designed for shared memory computers and GPU, uses a linear index to fill the block Lower Triangular Part of the distance matrix. The linear index/subscripts conversion is obtained with Triangular number and avoid loops over blocks of columns and rows. The second algorithm (designed for distributed memory computer) in addition to linear index uses circular shift on a 1D periodic topology. The distance matrix is computed iteratively and we show that the number of iterations required is about half the number of processors involved. Numerical experiments are carried-out to demonstrate the performances of the proposed algorithms
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Parallel Euclidean distance matrix computation on big datasets
HAL CCSD, 2019Co-Authors: Angeletti Mélodie, Bonny Jean-marie, Koko JonasAbstract:We propose, in this paper, three parallel algorithms to accelerate the Euclidean matrix computation on parallel computers. The first algorithm, designed for shared memory computers and GPU, uses a linear index to fill the block Lower Triangular Part of the distance matrix. The linear index/subscripts conversion is obtained with Triangular number and avoid loops over blocks of columns and rows. The second algorithm (designed for distributed memory computer) in addition to linear index uses circular shift on a 1D periodic topology. The distance matrix is computed iteratively and we show that the number of iterations required is about half the number of processors involved. Numerical experiments are carried-out to demonstrate the performances of the proposed algorithms
Goubko Mikhail - One of the best experts on this subject based on the ideXlab platform.
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Bilinear matrix equation characterizes Laplacian and distance matrices of weighted trees
2021Co-Authors: Goubko Mikhail, Veremyev AlexanderAbstract:It is known from the algebraic graph theory that if $L$ is the Laplacian matrix of some tree $G$ with a vertex degree sequence $\mathbf{d}=(d_1, ..., d_n)^\top$ and $D$ is its distance matrix, then $LD+2I=(2\cdot\mathbf{1}-\mathbf{d})\mathbf{1}^\top$, where $\mathbf{1}$ is an all-ones column vector. We prove that if this matrix identity holds for the Laplacian matrix of some graph $G$ with a degree sequence $\mathbf{d}$ and for some matrix $D$, then $G$ is essentially a tree, and $D$ is its distance matrix. This result immediately generalizes to weighted graphs. If the matrix $D$ is symmetric, the Lower Triangular Part of this matrix identity is redundant and can be omitted. Therefore, the above bilinear matrix equation in $L$, $D$, and $\mathbf{d}$ characterizes trees in terms of their Laplacian and distance matrices. Applications to the extremal graph theory (especially, to topological index optimization and to optimal tree problems) and to road topology design are discussed.Comment: 12 page
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Bilinear matrix equation characterizes Laplacian and distance matrices of weighted trees
2020Co-Authors: Goubko Mikhail, Veremyev AlexanderAbstract:It is known from the algebraic graph theory that if $L$ is the Laplacian matrix of some tree $G$ with a vertex degree sequence $\vec{d}=(d_1, ..., d_n)^\top$ and $D$ is its distance matrix, then $LD+2I=(2\cdot\vec{1}-\vec{d})\vec{1}^\top$, where $\vec{1}$ is an all-ones column vector. We prove that if this matrix identity holds for the Laplacian matrix of some graph $G$ with a degree sequence $\vec{d}$ and for some matrix $D$, then $G$ is essentially a tree, and $D$ is its distance matrix. This result immediately generalizes to weighted graphs. If the matrix $D$ is symmetric, the Lower Triangular Part of this matrix identity is redundant and can be omitted. Therefore, the above bilinear matrix equation in $L$, $D$, and $\vec{d}$ characterizes trees in terms of their Laplacian and distance matrices. Applications to the extremal graph theory (especially, to topological index optimization and to optimal tree problems) and to road topology design are discussed.Comment: 12 page
Angeletti Mélodie - One of the best experts on this subject based on the ideXlab platform.
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Parallel Euclidean distance matrix computation on big datasets *
HAL CCSD, 2019Co-Authors: Angeletti Mélodie, Bonny Jean-marie, Koko JonasAbstract:We propose, in this paper, three parallel algorithms to accelerate the Euclidean matrix computation on parallel computers. The first algorithm, designed for shared memory computers and GPU, uses a linear index to fill the block Lower Triangular Part of the distance matrix. The linear index/subscripts conversion is obtained with Triangular number and avoid loops over blocks of columns and rows. The second algorithm (designed for distributed memory computer) in addition to linear index uses circular shift on a 1D periodic topology. The distance matrix is computed iteratively and we show that the number of iterations required is about half the number of processors involved. Numerical experiments are carried-out to demonstrate the performances of the proposed algorithms
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Parallel Euclidean distance matrix computation on big datasets
HAL CCSD, 2019Co-Authors: Angeletti Mélodie, Bonny Jean-marie, Koko JonasAbstract:We propose, in this paper, three parallel algorithms to accelerate the Euclidean matrix computation on parallel computers. The first algorithm, designed for shared memory computers and GPU, uses a linear index to fill the block Lower Triangular Part of the distance matrix. The linear index/subscripts conversion is obtained with Triangular number and avoid loops over blocks of columns and rows. The second algorithm (designed for distributed memory computer) in addition to linear index uses circular shift on a 1D periodic topology. The distance matrix is computed iteratively and we show that the number of iterations required is about half the number of processors involved. Numerical experiments are carried-out to demonstrate the performances of the proposed algorithms
