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Journal articles on the topic 'Bilinear optimization'

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Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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1

Berta, Mario, Omar Fawzi, and Volkher B. Scholz. "Quantum Bilinear Optimization." SIAM Journal on Optimization 26, no. 3 (January 2016): 1529–64. http://dx.doi.org/10.1137/15m1037731.

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2

Wang, Cheng. "Optimization of SVM Method with RBF Kernel." Applied Mechanics and Materials 496-500 (January 2014): 2306–10. http://dx.doi.org/10.4028/www.scientific.net/amm.496-500.2306.

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Usually there is no a uniform model to the choice of SVMs kernel function and its parameters for SVM. This paper presents a bilinear grid search method for the purpose of getting the parameter of SVM with RBF kernel, with the approach of combining grid search with bilinear search. Experiment results show that the proposed bilinear grid search has combined both the advantage of moderate training quantity by the bilinear search and of high predict accuracy by the grid search.
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3

Rasina, I. V., and O. V. Baturina. "Control optimization in bilinear systems." Automation and Remote Control 74, no. 5 (May 2013): 802–10. http://dx.doi.org/10.1134/s0005117913050056.

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4

Witsenhausen, H. S. "A simple bilinear optimization problem." Systems & Control Letters 8, no. 1 (October 1986): 1–4. http://dx.doi.org/10.1016/0167-6911(86)90022-8.

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5

Gronski, Jessica, Mohamed-Amin Ben Sassi, Stephen Becker, and Sriram Sankaranarayanan. "Template polyhedra and bilinear optimization." Formal Methods in System Design 54, no. 1 (September 4, 2018): 27–63. http://dx.doi.org/10.1007/s10703-018-0323-1.

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6

Pamarthi, Nagaraju, and N. Nagamalleswara Rao. "Exponential Ant-Lion Rider Optimization for Privacy Preservation in Cloud Computing." Web Intelligence 19, no. 4 (January 20, 2022): 275–93. http://dx.doi.org/10.3233/web-210473.

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The innovative trend of cloud computing is outsourcing data to the cloud servers by individuals or enterprises. Recently, various techniques are devised for facilitating privacy protection on untrusted cloud platforms. However, the classical privacy-preserving techniques failed to prevent leakage and cause huge information loss. This paper devises a novel methodology, namely the Exponential-Ant-lion Rider optimization algorithm based bilinear map coefficient Generation (Exponential-AROA based BMCG) method for privacy preservation in cloud infrastructure. The proposed Exponential-AROA is devised by integrating Exponential weighted moving average (EWMA), Ant Lion optimizer (ALO), and Rider optimization algorithm (ROA). The input data is fed to the privacy preservation process wherein the data matrix, and bilinear map coefficient Generation (BMCG) coefficient are multiplied through Hilbert space-based tensor product. Here, the bilinear map coefficient is obtained by multiplying the original data matrix and with modified elliptical curve cryptography (MECC) encryption to maintain data security. The bilinear map coefficient is used to handle both the utility and the sensitive information. Hence, an optimization-driven algorithm is utilized to evaluate the optimal bilinear map coefficient. Here, the fitness function is newly devised considering privacy and utility. The proposed Exponential-AROA based BMCG provided superior performance with maximal accuracy of 94.024%, maximal fitness of 1, and minimal Information loss of 5.977%.
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7

Konno, Hiroshi, and Michimori Inori. "BOND PORTFOLIO OPTIMIZATION BY BILINEAR FRACTIONAL PROGRAMMING." Journal of the Operations Research Society of Japan 32, no. 2 (1989): 143–58. http://dx.doi.org/10.15807/jorsj.32.143.

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8

Peleg, Dori, and Ron Meir. "A bilinear formulation for vector sparsity optimization." Signal Processing 88, no. 2 (February 2008): 375–89. http://dx.doi.org/10.1016/j.sigpro.2007.08.015.

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9

Shuwaysh Alanazi, Badriah, and Maawiya Ould Sidi. "Optimal Control Problem Governed by an Evolution Equation and Using Bilinear Regular Feedback." Journal of Mathematics 2022 (April 23, 2022): 1–11. http://dx.doi.org/10.1155/2022/3521914.

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We solve an optimal control problem governed by an evolution equation using bilinear regular feedback. Using optimization techniques, we show how to approximate the flow of a reaction-diffusion bilinear system by a desired target. For application, we consider the regional flow problem constrained by a bilinear distributed system. The paper ends by an example illustrating the numerical approach of the proposed method.
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10

Nie, Zelin, Feng Gao, and Chao-Bo Yan. "A Multi-Timescale Bilinear Model for Optimization and Control of HVAC Systems with Consistency." Energies 14, no. 2 (January 12, 2021): 400. http://dx.doi.org/10.3390/en14020400.

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Reducing the energy consumption of the heating, ventilation, and air conditioning (HVAC) systems while ensuring users’ comfort is of both academic and practical significance. However, the-state-of-the-art of the optimization model of the HVAC system is that either the thermal dynamic model is simplified as a linear model, or the optimization model of the HVAC system is single-timescale, which leads to heavy computation burden. To balance the practicality and the overhead of computation, in this paper, a multi-timescale bilinear model of HVAC systems is proposed. To guarantee the consistency of models in different timescales, the fast timescale model is built first with a bilinear form, and then the slow timescale model is induced from the fast one, specifically, with a bilinear-like form. After a simplified replacement made for the bilinear-like part, this problem can be solved by a convexification method. Extensive numerical experiments have been conducted to validate the effectiveness of this model.
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11

Bounit, H. "Regular bilinear systems." IMA Journal of Mathematical Control and Information 22, no. 1 (March 1, 2005): 26–57. http://dx.doi.org/10.1093/imamci/dni003.

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12

Gao, Yuelin, and Siqiao Jin. "A Global Optimization Algorithm for Sum of Linear Ratios Problem." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/276245.

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We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.
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13

Bounit, Hamid, and Abdelali Idrissi. "Time-Varying Regular Bilinear Systems." SIAM Journal on Control and Optimization 47, no. 3 (January 2008): 1097–126. http://dx.doi.org/10.1137/050632245.

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14

Johnson, C. R., and K. J. Burnham. "Use of Bilinear Structures for Modelling a Brewery Fermentation Process." Measurement and Control 29, no. 9 (November 1996): 262–65. http://dx.doi.org/10.1177/002029409602900902.

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This paper presents the results of an investigative study with the aim being to obtain and assess the appropriateness of bilinear model structures for replicating the characteristics of a brewery fermentation process. Based on realtime data taken from a brewery fermentation plant, it is shown that a discrete-time twin-bilinear model, which simultaneously relates temperature to specific gravity and specific gravity to temperature, provides an adequate input/output reconstruction. The ability of the twin-bilinear model structure is discussed and possibilities for its utilization with an adaptive closed loop system are considered.
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15

Bistrickas, V. J., and N. Šimelienė. "Discrete Multistage Optimization and Hierarchical Market." Nonlinear Analysis: Modelling and Control 11, no. 2 (May 18, 2006): 149–56. http://dx.doi.org/10.15388/na.2006.11.2.14755.

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New simple form of mixed solutions is described by bilinear continuous optimization processes. It enables investigate an analytic solutions and the connection between discrete and continuous optimization processes. Connection between discrete and continuous processes is stochastic. Discrete optimization processes are used for the control works in levels and groups of the hierarchical market. Equilibrium between local and global levels of works is investigated in hierarchical market.
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16

Grüne, Lars. "Numerical Stabilization of Bilinear Control Systems." SIAM Journal on Control and Optimization 34, no. 6 (November 1996): 2024–50. http://dx.doi.org/10.1137/s0363012994272290.

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17

Wang, Hualin. "Feedback Stabilization of Bilinear Control Systems." SIAM Journal on Control and Optimization 36, no. 5 (September 1998): 1669–84. http://dx.doi.org/10.1137/s0363012996305498.

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18

KAWANISHI, Michihiro, and Shinichi OMOTO. "Bilinear Matrix Eigenvalue Optimization Using Primal Relaxed Dual Method." Transactions of the Society of Instrument and Control Engineers 41, no. 5 (2005): 419–26. http://dx.doi.org/10.9746/sicetr1965.41.419.

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19

Vinogradskaya, Alla V. "Two-Point Boundary Optimization Problem for Bilinear Control Systems." Journal of Nonlinear Mathematical Physics 4, no. 1-2 (January 1997): 209–13. http://dx.doi.org/10.2991/jnmp.1997.4.1-2.33.

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20

Kobayashi, Takumi. "Low-Rank Bilinear Classification: Efficient Convex Optimization and Extensions." International Journal of Computer Vision 110, no. 3 (March 15, 2014): 308–27. http://dx.doi.org/10.1007/s11263-014-0709-5.

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21

Quesada, I., and I. E. Grossmann. "Global optimization of bilinear process networks with multicomponent flows." Computers & Chemical Engineering 19, no. 12 (December 1995): 1219–42. http://dx.doi.org/10.1016/0098-1354(94)00123-5.

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22

Bloemen, H. H. J., T. J. J. van den Boom, and H. B. Verbruggen. "Optimization algorithms for bilinear model-based predictive control problems." AIChE Journal 50, no. 7 (2004): 1453–61. http://dx.doi.org/10.1002/aic.10122.

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23

Paramarthi, Nagaraju, Nagaraju Pamarthi, and Nagamalleswara Rao N. "A Data Obfuscation Method Using Ant-Lion-Rider Optimization for Privacy Preservation in the Cloud." International Journal of Distributed Systems and Technologies 13, no. 5 (January 1, 2022): 1–21. http://dx.doi.org/10.4018/ijdst.300353.

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In this paper, a obfuscation-based technique namely, AROA based BMCG method is developed for secure data transmission in cloud. Initially, the input data with the mixed attributes is provided to the privacy preservation process directly, where the data matrix and bilinear map coefficient generation co-efficient is multiplied through Hilbert space-based tensor product. Here, bilinear map co-efficient is the new co-efficient proposed to multiply with original data matrix and the OB-MECC Encryption is utilized in the privacy preservation phase to maintain the security of the data. The derivation of bilinear map co-efficient is used to handle both the utility and the sensitive information. The new algorithm called, AROA is developed by integrating the ALO with ROA. The performance and the comparative analysis of the proposed AROA based BMCG method is done using the metrics, such as accuracy and information loss. The proposed AROA based BMCG method obtained a maximal accuracy of 94% and minimal information loss of 6% respectively.
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24

Rapisarda, P., and H. L. Trentelman. "Linear Hamiltonian Behaviors and Bilinear Differential Forms." SIAM Journal on Control and Optimization 43, no. 3 (January 2004): 769–91. http://dx.doi.org/10.1137/s0363012902414664.

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25

Hintermüller, Michael, Daniel Marahrens, Peter A. Markowich, and Christof Sparber. "Optimal Bilinear Control of Gross--Pitaevskii Equations." SIAM Journal on Control and Optimization 51, no. 3 (January 2013): 2509–43. http://dx.doi.org/10.1137/120866233.

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26

Georgiev, Pando, Panos Pardalos, and Fabian Theis. "A bilinear algorithm for sparse representations." Computational Optimization and Applications 38, no. 2 (July 20, 2007): 249–59. http://dx.doi.org/10.1007/s10589-007-9043-y.

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27

Agrawal, S. K., X. Xu, and N. Faiz. "Optimization of Bilinear Systems Using a Higher-Order Variational Method." Journal of Optimization Theory and Applications 105, no. 1 (April 2000): 55–72. http://dx.doi.org/10.1023/a:1004609911204.

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28

Quesada, Ignacio, and Ignacio E. Grossmann. "A global optimization algorithm for linear fractional and bilinear programs." Journal of Global Optimization 6, no. 1 (January 1995): 39–76. http://dx.doi.org/10.1007/bf01106605.

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29

Chellapilla, K., and S. S. Rao. "Optimization of bilinear time series models using fast evolutionary programming." IEEE Signal Processing Letters 5, no. 2 (February 1998): 39–42. http://dx.doi.org/10.1109/97.659546.

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30

Kolodziej, Scott, Pedro M. Castro, and Ignacio E. Grossmann. "Global optimization of bilinear programs with a multiparametric disaggregation technique." Journal of Global Optimization 57, no. 4 (January 3, 2013): 1039–63. http://dx.doi.org/10.1007/s10898-012-0022-1.

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31

Clason, Christian, and Gregory von Winckel. "On a bilinear optimization problem in parallel magnetic resonance imaging." Applied Mathematics and Computation 216, no. 5 (May 2010): 1443–52. http://dx.doi.org/10.1016/j.amc.2010.02.047.

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32

Würker, U. "On decomposition in bilinear programming." Optimization 20, no. 1 (January 1989): 45–60. http://dx.doi.org/10.1080/02331938908843413.

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33

Ying, Y. Q., M. Rao, and Y. X. Sun. "Suboptimal control for bilinear systems." Optimal Control Applications and Methods 14, no. 3 (July 1993): 195–201. http://dx.doi.org/10.1002/oca.4660140305.

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34

Bichiou, Salim, Mohamed Karim Bouafoura, and Naceur Benhadj Braiek. "Time Optimal Control Laws for Bilinear Systems." Mathematical Problems in Engineering 2018 (2018): 1–10. http://dx.doi.org/10.1155/2018/5217427.

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The aim of this paper is to determine the feedforward and state feedback suboptimal time control for a subset of bilinear systems, namely, the control sequence and reaching time. This paper proposes a method that uses Block pulse functions as an orthogonal base. The bilinear system is projected along that base. The mathematical integration is transformed into a product of matrices. An algebraic system of equations is obtained. This system together with specified constraints is treated as an optimization problem. The parameters to determine are the final time, the control sequence, and the states trajectories. The obtained results via the newly proposed method are compared to known analytical solutions.
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35

Rebennack, Steffen, Artyom Nahapetyan, and Panos M. Pardalos. "Bilinear modeling solution approach for fixed charge network flow problems." Optimization Letters 3, no. 3 (February 13, 2009): 347–55. http://dx.doi.org/10.1007/s11590-009-0114-0.

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36

Mangasarian, Olvi L. "Primal-dual bilinear programming solution of the absolute value equation." Optimization Letters 6, no. 7 (June 4, 2011): 1527–33. http://dx.doi.org/10.1007/s11590-011-0347-6.

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37

Zhang, Ji-hong, Xi Chen, and Xiao-song Ding. "Degeneracy removal in cutting plane methods for disjoint bilinear programming." Optimization Letters 11, no. 3 (February 15, 2016): 483–95. http://dx.doi.org/10.1007/s11590-016-1016-6.

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38

Brivadis, Lucas, Jean-Paul A. Gauthier, Ludovic Sacchelli, and Ulysse Serres. "Avoiding Observability Singularities in Output Feedback Bilinear Systems." SIAM Journal on Control and Optimization 59, no. 3 (January 2021): 1759–80. http://dx.doi.org/10.1137/19m1272925.

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39

Ito, Kazufumi, and Karl Kunisch. "Optimal Bilinear Control of an Abstract Schrödinger Equation." SIAM Journal on Control and Optimization 46, no. 1 (January 2007): 274–87. http://dx.doi.org/10.1137/05064254x.

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40

Ouzahra, Mohamed. "Exponential and Weak Stabilization of Constrained Bilinear Systems." SIAM Journal on Control and Optimization 48, no. 6 (January 2010): 3962–74. http://dx.doi.org/10.1137/080739161.

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41

Du, Yi Xian, Shuang Qiao Yan, Huang Hai Xie, Yan Zhang, and Qi Hua Tian. "Research of Topology Optimization of Nodal Density Based on Bilinear Interpolation." Applied Mechanics and Materials 713-715 (January 2015): 1825–29. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.1825.

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With the purpose to overcome the numerical instabilities and to generate more distinct structural layouts in the topology optimization, by using bilinear interpolation function, a topology optimization model of density interpolation based on nodal density is established, smooth density field is constructed. This method can ensure that the density field in the fixed design domain owns C0 continuity, and checkerboard patterns are naturally avoided in the nature of mathematics. After adding the sensitivity filtering, the optimal structures are smoother and have lesser details, which is helpful for manufacturing. Two numerical examples show that not only checkerboard pattern can be solved by the proposed method, but also the middle density nodal can be suppressed effectively.
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42

COSTA, O. L. V., GISELLE M. S. FERREIRA, and C. S. KUBRUSLY. "On mean-square-stable bilinear systems." IMA Journal of Mathematical Control and Information 12, no. 4 (1995): 325–29. http://dx.doi.org/10.1093/imamci/12.4.325.

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43

Guojun, J. "Stability of bilinear time-delay systems." IMA Journal of Mathematical Control and Information 18, no. 1 (March 1, 2001): 53–60. http://dx.doi.org/10.1093/imamci/18.1.53.

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44

Yuan, Zhenyi, and Jorge Cortes. "Data-Driven Optimal Control of Bilinear Systems." IEEE Control Systems Letters 6 (2022): 2479–84. http://dx.doi.org/10.1109/lcsys.2022.3164983.

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45

Bennett, Kristin P., and O. L. Mangasarian. "Bilinear separation of two sets inn-space." Computational Optimization and Applications 2, no. 3 (November 1993): 207–27. http://dx.doi.org/10.1007/bf01299449.

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46

Zhang, Wenjuan, Xiangchu Feng, Feng Xiao, and Xudong Wang. "A class of bilinear matrix constraint optimization problem and its applications." Knowledge-Based Systems 231 (November 2021): 107429. http://dx.doi.org/10.1016/j.knosys.2021.107429.

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47

Khlebnikov, M. V. "Optimization of Bilinear Control Systems Subjected to Exogenous Disturbances. I. Analysis." Automation and Remote Control 80, no. 2 (February 2019): 234–49. http://dx.doi.org/10.1134/s0005117919020036.

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48

Khlebnikov, M. V. "Optimization of Bilinear Control Systems Subjected to Exogenous Disturbances. II. Design." Automation and Remote Control 80, no. 8 (August 2019): 1390–402. http://dx.doi.org/10.1134/s0005117919080022.

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49

Rashid, Kashif. "A Bilinear Interpolation Procedure for Dual Gas-lift and Choke Optimization." Industrial & Engineering Chemistry Research 52, no. 46 (November 5, 2013): 16284–93. http://dx.doi.org/10.1021/ie4011589.

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50

Zorn, Keith, and Nikolaos V. Sahinidis. "Global optimization of general non-convex problems with intermediate bilinear substructures." Optimization Methods and Software 29, no. 3 (April 23, 2013): 442–62. http://dx.doi.org/10.1080/10556788.2013.783032.

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