scholarly journals Optimization-Based Construction of Quadrilateral Table Cartograms

2020 ◽  
Vol 9 (1) ◽  
pp. 43
Author(s):  
Ryo Inoue ◽  
Mao Li
Keyword(s):  
Unique Solution ◽  
Minimization Problem ◽  
Optimization Problem ◽  
Construction Method ◽  
Shape Deformation ◽  
Output Table ◽  
Positive Weights ◽  
Original Table ◽  
New Construction ◽  
Complex Settings

A quadrilateral table cartogram is a rectangle-shaped figure that visualizes table-form data; quadrilateral cells in a table cartogram are transformed to express the magnitude of positive weights by their areas, while maintaining the adjacency of cells in the original table. However, the previous construction method is difficult to implement because it consists of multiple operations that do not have a unique solution and require complex settings to obtain the desired outputs. In this article, we propose a new construction for quadrilateral table cartograms by recasting the construction as an optimization problem. The proposed method is formulated as a simple minimization problem to achieve mathematical clarity. It can generate quadrilateral table cartograms with smaller deformation of rows and columns, thereby aiding readers to recognize the correspondence between table cartograms and original tables. In addition, we also propose a means of sorting rows and/or columns prior to the construction of table cartograms to reduce excess shape deformation. Applications of the proposed method confirm its capability to output table cartograms that clearly visualize the characteristics of datasets.

Numerical Analysis of Metro Station Construction by Large-Diameter Shield and Pile-Beam-Arch Method

2011 ◽  
Vol 368-373 ◽  
pp. 2711-2715 ◽  
Author(s):  
De Yun Ding ◽  
Xiu Ren Yang ◽  
Wei Dong Lu ◽  
Wei Ning Liu ◽  
Mei Yan ◽  
...  
Keyword(s):  
Ground Deformation ◽  
Large Diameter ◽  
Element Model ◽  
Construction Method ◽  
Shield Tunnel ◽  
Outer Diameter ◽  
Shield Tunneling ◽  
Metro Station ◽  
Dimensional Finite Element ◽  
New Construction

In more and more complicated urban building environment, a new construction method that metro engineering is constructed by large-diameter shield and shallow mining method can be regarded as a great attempt in China. By taking the Gaojiayuan station of Beijing metro line 14 as an engineering background, the main construction steps for the platform of the metro station built by a large-size shield with an outer diameter of 10 m and the Pile-Beam-Arch (PBA) method are introduced. Based on the soil-structure interaction theory, a two-dimensional finite element model is used to simulate the shield tunneling and the platform construction by the PBA method to enlarge the shield tunnel. The ground deformation and structural stress of the platform are predicted. The numerical results can be regarded as a valuable reference for the application of the new construction method in Beijing metro line 14.

scholarly journals Table cartogram generation as an optimization problem

2019 ◽  
Vol 1 ◽  
pp. 1-2 ◽  
Author(s):  
Mao Li ◽  
Ryo Inoue
Keyword(s):  
Objective Function ◽  
Least Squares ◽  
Optimization Problem ◽  
Data Representation ◽  
Linear Least Squares ◽  
Original Table ◽  
Outer Border ◽  
Limited Degree ◽  
The Difference ◽  
Operation Results

<p><strong>Abstract.</strong> A table cartogram, visualization of table-form data, is a rectangle-shaped table in which each cell is transformed to express the magnitude of positive weight by its area while maintaining the adjacency relationship of cells in the original table. Winter (2011) applies an area cartogram generation method of Gastner and Newman (2004) for their generation, and Evans et al. (2018) proposes a new geometric procedure. The rows and columns on a table cartogram should be easily recognized by readers, however, no methods have focused to enhance the readability. This study proposes a method that defines table cartogram generation as an optimization problem and attempts to minimize vertical and horizontal deformation. Since the original tables are comprised of regular quadrangles, this study uses quadrangles to express cells in a table cartogram and fixes the outer border to attempt to retain the shape of a standard table.</p><p>This study proposes a two-step approach for table cartogram generation with cells that begin as squares and with fixed outer table borders. The first step only adjusts the vertical and horizontal borders of cells to express weights to the greatest possible degree. All cells maintain their rectangular shape after this step, although the limited degree of freedom of this operation results in low data representation accuracy. The second step adapts the cells of the low-accuracy table cartogram to accurately fit area to weight by relaxing the constraints on the directions of borders of cells. This study utilizes an area cartogram generation method proposed by Inoue and Shimizu (2006), which defines area cartogram generation as an optimization problem. The formulation with vertex coordinate parameters consists of an objective function that minimizes the difference between the given data and size of each cell, and a regularization term that controls the changes of bearing angles. It is formulated as non-linear least squares, and is solved through the iteration of linear least squares by linearizing the problem at the coordinates of vertices and updating the estimated coordinates until the value of the objective function becomes small enough.</p>

A New Constrained Shape Deformation Operator With Applications in Footwear Design

2008 ◽  
Author(s):  
Ying Xu ◽  
Ajay Joneja
Keyword(s):  
Numerical Methods ◽  
Optimization Problem ◽  
Shape Change ◽  
Geometric Approach ◽  
Shape Deformation ◽  
Uzawa Method ◽  
Constrained Optimization Problem ◽  
Integral Property ◽  
Lagrangian Multipliers ◽  
Footwear Design

In this paper, we address a problem that arises in several engineering applications: the deformation of a curve with constraints on its length. Since length is an integral property, typically computed by numerical methods, therefore implementing such shape change operations is non trivial. Recently some researchers have attempted to solve such problems for multi-resolution representations of curves. However, we take a differential geometric approach. The modification problem is formulated as constrained optimization problem, which is subsequently converted to an unconstrained min-max problem using Lagrangian multipliers. This problem is solved using the Uzawa method. The approach is implemented in MATLAB™, and some examples are presented in the paper.

Next Generation CANDU: Conceptual Design for a Short Construction Schedule

2002 ◽  
Author(s):  
Jerry M. Hopwood ◽  
Ian J. W. Love ◽  
Medhat Elgohary ◽  
Neville Fairclough
Keyword(s):  
Conceptual Design ◽  
Critical Path ◽  
Construction Method ◽  
Phase Iii ◽  
Next Generation ◽  
Project Schedule ◽  
Construction Methods ◽  
New Construction ◽  
Construction Strategy ◽  
Construction Schedule

Atomic Energy of Canada Ltd. (AECL) has very successful experience in implementing new construction methods at the Qinshan (Phase III) twin unit CANDU 6 plant in China. This paper examines the construction method that must be implemented during the conceptual design phase of a project if short construction schedules are to be met. A project schedule of 48 months has been developed for the nth unit of NG (Next Generation) CANDU with a 42 month construction period from 1st Concrete to In-Service. An overall construction strategy has been developed involving paralleling project activities that are normally conducted in series. Many parts of the plant will be fabricated as modules and be installed using heavy lift cranes. The Reactor Building (RB), being on the critical path, has been the focus of considerable assessment, looking at alternative ways of applying the construction strategy to this building. A construction method has been chosen which will result in excess of 80% of internal work being completed as modules or as very streamlined traditional construction. This method is being further evaluated as the detailed layout proceeds. Other areas of the plant have been integrated into the schedule and new construction methods are being applied to these so that further modularization and even greater paralleling of activities will be achieved. It is concluded that the optimized construction method is a requirement, which must be implemented through all phases of design to make a 42 month construction schedule a reality. If the construction methods are appropriately chosen, the schedule reductions achieved will make nuclear more competitive.

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