Sum Method

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Olivier Ladislas De Weck - One of the best experts on this subject based on the ideXlab platform.

  • Adaptive weighted Sum Method for multiobjective optimization: a new Method for Pareto front generation
    Structural and Multidisciplinary Optimization, 2006
    Co-Authors: Olivier Ladislas De Weck
    Abstract:

    This paper presents an adaptive weighted Sum (AWS) Method for multiobjective optimization problems. The Method extends the previously developed biobjective AWS Method to problems with more than two objective functions. In the first phase, the usual weighted Sum Method is performed to approximate the Pareto surface quickly, and a mesh of Pareto front patches is identified. Each Pareto front patch is then refined by imposing additional equality constraints that connect the pseudonadir point and the expected Pareto optimal solutions on a piecewise planar hypersurface in the $$ {m} $$ -dimensional objective space. It is demonstrated that the Method produces a well-distributed Pareto front mesh for effective visualization, and that it finds solutions in nonconvex regions. Two numerical examples and a simple structural optimization problem are solved as case studies.

  • Adaptive weighted-Sum Method for bi-objective optimization: Pareto front generation
    Structural and Multidisciplinary Optimization, 2005
    Co-Authors: I.y. Kim, Olivier Ladislas De Weck
    Abstract:

    This paper presents a new Method that effectively determines a Pareto front for bi-objective optimization with potential application to multiple objectives. A traditional Method for multiobjective optimization is the weighted-Sum Method, which seeks Pareto optimal solutions one by one by systematically changing the weights among the objective functions. Previous research has shown that this Method often produces poorly distributed solutions along a Pareto front, and that it does not find Pareto optimal solutions in non-convex regions. The proposed adaptive weighted Sum Method focuses on unexplored regions by changing the weights adaptively rather than by using a priori weight selections and by specifying additional inequality constraints. It is demonstrated that the adaptive weighted Sum Method produces well-distributed solutions, finds Pareto optimal solutions in non-convex regions, and neglects non-Pareto optimal solutions. This last point can be a potential liability of Normal Boundary Intersection, an otherwise successful multiobjective Method, which is mainly caused by its reliance on equality constraints. The promise of this robust algorithm is demonstrated with two numerical examples and a simple structural optimization problem.

Keita Mori - One of the best experts on this subject based on the ideXlab platform.

  • learning curve for robotic assisted surgery for rectal cancer use of the cumulative Sum Method
    Surgical Endoscopy and Other Interventional Techniques, 2015
    Co-Authors: Tomohiro Yamaguchi, Yusuke Kinugasa, Akio Shiomi, Sumito Sato, Yushi Yamakawa, Hiroyasu Kagawa, Hiroyuki Tomioka, Keita Mori
    Abstract:

    Few data are available to assess the learning curve for robotic-assisted surgery for rectal cancer. The aim of the present study was to evaluate the learning curve for robotic-assisted surgery for rectal cancer by a surgeon at a single institute. From December 2011 to August 2013, a total of 80 consecutive patients who underwent robotic-assisted surgery for rectal cancer performed by the same surgeon were included in this study. The learning curve was analyzed using the cumulative Sum Method. This Method was used for all 80 cases, taking into account operative time. Operative procedures included anterior resections in 6 patients, low anterior resections in 46 patients, intersphincteric resections in 22 patients, and abdominoperineal resections in 6 patients. Lateral lymph node dissection was performed in 28 patients. Median operative time was 280 min (range 135–683 min), and median blood loss was 17 mL (range 0–690 mL). No postoperative complications of Clavien–Dindo classification Grade III or IV were encountered. We arranged operative times and calculated cumulative Sum values, allowing differentiation of three phases: phase I, Cases 1–25; phase II, Cases 26–50; and phase III, Cases 51–80. Our data suggested three phases of the learning curve in robotic-assisted surgery for rectal cancer. The first 25 cases formed the learning phase.

  • learning curve for robotic assisted surgery for rectal cancer use of the cumulative Sum Method
    Surgical Endoscopy and Other Interventional Techniques, 2015
    Co-Authors: Tomohiro Yamaguchi, Yusuke Kinugasa, Akio Shiomi, Sumito Sato, Yushi Yamakawa, Hiroyasu Kagawa, Hiroyuki Tomioka, Keita Mori
    Abstract:

    Background Few data are available to assess the learning curve for robotic-assisted surgery for rectal cancer. The aim of the present study was to evaluate the learning curve for robotic-assisted surgery for rectal cancer by a surgeon at a single institute.

Tomohiro Yamaguchi - One of the best experts on this subject based on the ideXlab platform.

  • learning curve for robotic assisted surgery for rectal cancer use of the cumulative Sum Method
    Surgical Endoscopy and Other Interventional Techniques, 2015
    Co-Authors: Tomohiro Yamaguchi, Yusuke Kinugasa, Akio Shiomi, Sumito Sato, Yushi Yamakawa, Hiroyasu Kagawa, Hiroyuki Tomioka, Keita Mori
    Abstract:

    Few data are available to assess the learning curve for robotic-assisted surgery for rectal cancer. The aim of the present study was to evaluate the learning curve for robotic-assisted surgery for rectal cancer by a surgeon at a single institute. From December 2011 to August 2013, a total of 80 consecutive patients who underwent robotic-assisted surgery for rectal cancer performed by the same surgeon were included in this study. The learning curve was analyzed using the cumulative Sum Method. This Method was used for all 80 cases, taking into account operative time. Operative procedures included anterior resections in 6 patients, low anterior resections in 46 patients, intersphincteric resections in 22 patients, and abdominoperineal resections in 6 patients. Lateral lymph node dissection was performed in 28 patients. Median operative time was 280 min (range 135–683 min), and median blood loss was 17 mL (range 0–690 mL). No postoperative complications of Clavien–Dindo classification Grade III or IV were encountered. We arranged operative times and calculated cumulative Sum values, allowing differentiation of three phases: phase I, Cases 1–25; phase II, Cases 26–50; and phase III, Cases 51–80. Our data suggested three phases of the learning curve in robotic-assisted surgery for rectal cancer. The first 25 cases formed the learning phase.

  • learning curve for robotic assisted surgery for rectal cancer use of the cumulative Sum Method
    Surgical Endoscopy and Other Interventional Techniques, 2015
    Co-Authors: Tomohiro Yamaguchi, Yusuke Kinugasa, Akio Shiomi, Sumito Sato, Yushi Yamakawa, Hiroyasu Kagawa, Hiroyuki Tomioka, Keita Mori
    Abstract:

    Background Few data are available to assess the learning curve for robotic-assisted surgery for rectal cancer. The aim of the present study was to evaluate the learning curve for robotic-assisted surgery for rectal cancer by a surgeon at a single institute.

Bernard R Brooks - One of the best experts on this subject based on the ideXlab platform.

  • using the isotropic periodic Sum Method to calculate long range interactions of heterogeneous systems
    Journal of Chemical Physics, 2008
    Co-Authors: Bernard R Brooks
    Abstract:

    Isotropic periodic Sum (IPS) is a Method for the calculation of long-range interactions in molecular simulation based on the homogeneity of simulation systems. Three IPS models, 3D IPS, 2D IPS, and 1D IPS have been developed for three common types of homogeneous systems. Based on the fact that 3D IPS can well describe the long-range interactions of a heterogeneous system if a local region larger than the homogeneity scale is used, this work presents a Method based on 3D IPS to calculate long-range interactions for all kinds of simulation systems, including homogeneous, heterogeneous, and finite systems. Unlike the original 3D IPS Method that uses a local region defined by the cutoff distance, this Method uses a local region larger than that defined by the cutoff distance to reach the homogeneity scale. To efficiently calculate interactions within such a large local region, this Method split long-range interactions into two parts, a cutoff part and a long-range part. The cutoff part is calculated by Summing over atom pairs within a cutoff range (about 10 A), and the long-range part is calculated using the discrete fast Fourier transform (DFFT) technique. This Method is applied to electrostatic and van der Waals interactions for both periodic and non-periodic systems. Example simulations demonstrate that this Method can accurately and efficiently calculate long-range interactions for molecular simulation.

  • long range lennard jones and electrostatic interactions in interfaces application of the isotropic periodic Sum Method
    Journal of Physical Chemistry B, 2007
    Co-Authors: Jeffery B Klauda, Richard W Pastor, Bernard R Brooks
    Abstract:

    Molecular dynamics (MD) simulations of heptane/vapor, hexadecane/vapor, water/vapor, hexadecane/water, and dipalmitoylphosphatidylcholine (DPPC) bilayers and monolayers are analyzed to determine the accuracy of treating long-range interactions in interfaces with the isotropic periodic Sum (IPS) Method. The Method and cutoff (rc) dependences of surface tensions, density profiles, water dipole orientation, and electrostatic potential profiles are used as metrics. The water/vapor, heptane/vapor, and hexadecane/vapor interfaces are accurately and efficiently calculated with 2D IPS (rc = 10 A). It is demonstrated that 3D IPS is not practical for any of the interfacial systems studied. However, the hybrid Method PME/IPS [Particle Mesh Ewald for electrostatics and 3D IPS for Lennard-Jones (LJ) interactions] provides an efficient way to include both types of long-range forces in simulations of large liquid/vacuum and all liquid/liquid interfaces, including lipid monolayers and bilayers. A previously published pre...

David Y.h. Pui - One of the best experts on this subject based on the ideXlab platform.

  • Real-time Measurements of the Particle Geometric Surface Area by the Weighted-Sum Method on a University Campus
    Aerosol and Air Quality Research, 2020
    Co-Authors: Leo N.y. Cao, David Y.h. Pui
    Abstract:

    ABSTRACT This study conducted field measurements of the particle geometric surface area (GSA) and number concentrations on a university campus via two real-time approaches: applying the weighted-Sum (WS) Method and using a Scanning Mobility Particle Sizer (SMPS). The measurements were conducted on 4 subjects: laser printing, 3D printing, machining (waterjet cutting, sanding, and welding), and environmental aerosols. The highest emissions were found with 3D printing and welding; these concentrations were measured in the printer’s enclosure and when the local exhaust ventilation was on, respectively. In general, the two Methods agreed well with each other, with an overall Pearson correlation coefficient of 0.85, although the concentrations constantly fluctuated over a wide range, from 20 to 4 × 104 μm2 cm–3. Since the GSA concentrations reported in this study are the first measurements for some scenarios, our results can serve as a reference for further research as well as for individuals in the vicinity of these emissions.

  • A novel weighted Sum Method to measure particle geometric surface area in real-time
    Journal of Aerosol Science, 2018
    Co-Authors: Leo N.y. Cao, David Y.h. Pui
    Abstract:

    Abstract This paper reports the development of a novel Method to measure the aerosol geometric surface area (GSA) concentration with a time resolution of a few seconds. In the Method, the commercialized nanoparticle surface area monitor was used and slightly modified. The instrument responses under two different conditions were combined in a weighted Sum (WS) fashion to correlate with the aerosol GSA concentration. We present the GSA concentration results and comparisons with well-known SMPS data in both laboratory testing and field measurement. For the laboratory testing, the two Methods have a good agreement with a Pearson correlation coefficient of 0.9961; for the field measurements including the indoor and outdoor samplings, both Methods agree well with each other. In addition, the new WS Method is more stable in the clean indoor air and suitable for outdoor environmental sampling with a slight overestimation (125% of SMPS).