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1

van Zijl, Peter C., e Ralph E. Hurd. "Gradient enhanced spectroscopy". Journal of Magnetic Resonance 213, n.º 2 (dezembro de 2011): 474–76. http://dx.doi.org/10.1016/j.jmr.2011.08.018.

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2

Hurd, Ralph E. "Gradient-enhanced spectroscopy". Journal of Magnetic Resonance 213, n.º 2 (dezembro de 2011): 467–73. http://dx.doi.org/10.1016/j.jmr.2011.09.005.

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3

Hurd, Ralph E. "Gradient-enhanced spectroscopy". Journal of Magnetic Resonance (1969) 87, n.º 2 (abril de 1990): 422–28. http://dx.doi.org/10.1016/0022-2364(90)90021-z.

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4

Alfaraj, Mohammed, Yuchun Wang e Yi Luo. "Enhanced isotropic gradient operator". Geophysical Prospecting 62, n.º 3 (4 de março de 2014): 507–17. http://dx.doi.org/10.1111/1365-2478.12106.

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5

Moonen, Chrit T. W., Peter Van Gelderen, Geerten W. Vuister e Peter C. M. Van Zijl. "Gradient-enhanced exchange spectroscopy". Journal of Magnetic Resonance (1969) 97, n.º 2 (abril de 1992): 419–25. http://dx.doi.org/10.1016/0022-2364(92)90327-4.

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6

Gangl, Markus, e Helmut Ritsch. "Cavity-enhanced polarization gradient cooling". Journal of Physics B: Atomic, Molecular and Optical Physics 35, n.º 22 (4 de novembro de 2002): 4565–82. http://dx.doi.org/10.1088/0953-4075/35/22/301.

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7

Marro, Kenneth I., Donghoon Lee e Outi M. Hyyti. "Gradient-enhanced FAWSETS perfusion measurements". Journal of Magnetic Resonance 175, n.º 2 (agosto de 2005): 185–92. http://dx.doi.org/10.1016/j.jmr.2005.04.002.

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8

Poh, L. H., e S. Swaddiwudhipong. "Gradient-enhanced softening material models". International Journal of Plasticity 25, n.º 11 (novembro de 2009): 2094–121. http://dx.doi.org/10.1016/j.ijplas.2009.01.003.

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9

Parella, T., F. Sanchezferrando e A. Virgili. "Selective Gradient-Enhanced Inverse Experiments". Journal of Magnetic Resonance, Series A 112, n.º 1 (janeiro de 1995): 106–8. http://dx.doi.org/10.1006/jmra.1995.1016.

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10

Roumestand, Christian, Pierre Mutzenhardt, Corinne Delay e Daniel Canet. "Gradient-Enhanced Band-Filtering Experiments". Magnetic Resonance in Chemistry 34, n.º 10 (outubro de 1996): 807–14. http://dx.doi.org/10.1002/(sici)1097-458x(199610)34:10<807::aid-omr975>3.0.co;2-9.

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11

SUN, Linjun, Weijun LI, Xin NING, Liping ZHANG, Xiaoli DONG e Wei HE. "Gradient-Enhanced Softmax for Face Recognition". IEICE Transactions on Information and Systems E103.D, n.º 5 (1 de maio de 2020): 1185–89. http://dx.doi.org/10.1587/transinf.2019edl8103.

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12

Vuister, Geerten W., Rolf Boelens, Robert Kaptein, Maurits Burgering e Peter C. M. van Zijl. "Gradient-enhanced 3D NOESY-HMQC spectroscopy". Journal of Biomolecular NMR 2, n.º 3 (maio de 1992): 301–5. http://dx.doi.org/10.1007/bf01875323.

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13

Kövér, Katalin E., Dušan Uhrı́n e Victor J. Hruby. "Gradient- and Sensitivity-Enhanced TOCSY Experiments". Journal of Magnetic Resonance 130, n.º 2 (fevereiro de 1998): 162–68. http://dx.doi.org/10.1006/jmre.1997.1309.

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14

Gerig, J. T. "Gradient-enhanced proton-fluorine NOE experiments". Magnetic Resonance in Chemistry 37, n.º 9 (setembro de 1999): 647–52. http://dx.doi.org/10.1002/(sici)1097-458x(199909)37:9<647::aid-mrc520>3.0.co;2-n.

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15

Ulaganathan, Selvakumar, Ivo Couckuyt, Tom Dhaene, Joris Degroote e Eric Laermans. "Performance study of gradient-enhanced Kriging". Engineering with Computers 32, n.º 1 (19 de fevereiro de 2015): 15–34. http://dx.doi.org/10.1007/s00366-015-0397-y.

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16

Laurenceau, J., M. Meaux, M. Montagnac e P. Sagaut. "Comparison of Gradient-Based and Gradient-Enhanced Response-Surface-Based Optimizers". AIAA Journal 48, n.º 5 (maio de 2010): 981–94. http://dx.doi.org/10.2514/1.45331.

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17

Yan, Ming, Jianxi Yang, Cen Chen, Joey Tianyi Zhou, Yi Pan e Zeng Zeng. "Enhanced gradient learning for deep neural networks". IET Image Processing 16, n.º 2 (9 de novembro de 2021): 365–77. http://dx.doi.org/10.1049/ipr2.12353.

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18

Lockwood, Brian A., e Mihai Anitescu. "Gradient-Enhanced Universal Kriging for Uncertainty Propagation". Nuclear Science and Engineering 170, n.º 2 (fevereiro de 2012): 168–95. http://dx.doi.org/10.13182/nse10-86.

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19

Simone, Angelo. "Explicit and implicit gradient-enhanced damage models". Revue Européenne de Génie Civil 11, n.º 7-8 (agosto de 2007): 1023–44. http://dx.doi.org/10.1080/17747120.2007.9692975.

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20

de Borst, R., A. Benallal e O. M. Heeres. "A Gradient-Enhanced Damage Approach to Fracture". Le Journal de Physique IV 06, n.º C6 (outubro de 1996): C6–491—C6–502. http://dx.doi.org/10.1051/jp4:1996649.

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21

Manzari, Majid T., e Karma Yonten. "C1finite element analysis in gradient enhanced continua". Mathematical and Computer Modelling 57, n.º 9-10 (maio de 2013): 2519–31. http://dx.doi.org/10.1016/j.mcm.2013.01.003.

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22

Shane, Erica S., John L. Anderson e Michael M. Domach. "Enhanced protein diffusion in a solvent gradient". Industrial & Engineering Chemistry Research 29, n.º 2 (fevereiro de 1990): 309–12. http://dx.doi.org/10.1021/ie00098a024.

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23

Isaksson, P., e R. Hägglund. "Crack-tip fields in gradient enhanced elasticity". Engineering Fracture Mechanics 97 (janeiro de 2013): 186–92. http://dx.doi.org/10.1016/j.engfracmech.2012.11.011.

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24

Martínez-Pañeda, Emilio, Sandra Fuentes-Alonso e Covadonga Betegón. "Gradient-enhanced statistical analysis of cleavage fracture". European Journal of Mechanics - A/Solids 77 (setembro de 2019): 103785. http://dx.doi.org/10.1016/j.euromechsol.2019.05.002.

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25

Floros, Dimosthenis, Fredrik Larsson e Kenneth Runesson. "On configurational forces for gradient-enhanced inelasticity". Computational Mechanics 61, n.º 4 (19 de agosto de 2017): 409–32. http://dx.doi.org/10.1007/s00466-017-1460-x.

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26

Simone, Angelo. "Explicit and implicit gradient-enhanced damage models". Revue européenne de génie civil 11, n.º 7-8 (1 de outubro de 2007): 1023–44. http://dx.doi.org/10.3166/regc.11.1023-1044.

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27

Cho, KyungHyun, Tapani Raiko e Alexander Ilin. "Enhanced Gradient for Training Restricted Boltzmann Machines". Neural Computation 25, n.º 3 (março de 2013): 805–31. http://dx.doi.org/10.1162/neco_a_00397.

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Restricted Boltzmann machines (RBMs) are often used as building blocks in greedy learning of deep networks. However, training this simple model can be laborious. Traditional learning algorithms often converge only with the right choice of metaparameters that specify, for example, learning rate scheduling and the scale of the initial weights. They are also sensitive to specific data representation. An equivalent RBM can be obtained by flipping some bits and changing the weights and biases accordingly, but traditional learning rules are not invariant to such transformations. Without careful tuning of these training settings, traditional algorithms can easily get stuck or even diverge. In this letter, we present an enhanced gradient that is derived to be invariant to bit-flipping transformations. We experimentally show that the enhanced gradient yields more stable training of RBMs both when used with a fixed learning rate and an adaptive one.
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28

Chu, Jun, Jia Luo e Lu Leng. "Non-local Dehazing enhanced by color gradient". Multimedia Tools and Applications 78, n.º 5 (11 de fevereiro de 2018): 5701–13. http://dx.doi.org/10.1007/s11042-018-5673-6.

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29

Peerlings, R. H. J., R. de Borst, W. A. M. Brekelmans e M. G. D. Geers. "Gradient-enhanced damage modelling of concrete fracture". Mechanics of Cohesive-frictional Materials 3, n.º 4 (outubro de 1998): 323–42. http://dx.doi.org/10.1002/(sici)1099-1484(1998100)3:4<323::aid-cfm51>3.0.co;2-z.

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30

PEERLINGS, R. H. J., R. DE BORST, W. A. M. BREKELMANS e J. H. P. DE VREE. "GRADIENT ENHANCED DAMAGE FOR QUASI-BRITTLE MATERIALS". International Journal for Numerical Methods in Engineering 39, n.º 19 (15 de outubro de 1996): 3391–403. http://dx.doi.org/10.1002/(sici)1097-0207(19961015)39:19<3391::aid-nme7>3.0.co;2-d.

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31

Wang, Dong, Huan Zhang, Jing Guo, Beichen Cheng, Yuan Cao, Shengjun Lu, Ning Zhao e Jian Xu. "Biomimetic Gradient Polymers with Enhanced Damping Capacities". Macromolecular Rapid Communications 37, n.º 7 (18 de janeiro de 2016): 655–61. http://dx.doi.org/10.1002/marc.201500637.

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32

Bouhlel, Mohamed A., e Joaquim R. R. A. Martins. "Gradient-enhanced kriging for high-dimensional problems". Engineering with Computers 35, n.º 1 (26 de fevereiro de 2018): 157–73. http://dx.doi.org/10.1007/s00366-018-0590-x.

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33

Bouwer, Johann M., Daniel N. Wilke e Schalk Kok. "Spatio-Temporal Gradient Enhanced Surrogate Modeling Strategies". Mathematical and Computational Applications 28, n.º 2 (8 de abril de 2023): 57. http://dx.doi.org/10.3390/mca28020057.

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This research compares the performance of space-time surrogate models (STSMs) and network surrogate models (NSMs). Specifically, when the system response varies over time (or pseudo-time), the surrogates must predict the system response. A surrogate model is used to approximate the response of computationally expensive spatial and temporal fields resulting from some computational mechanics simulations. Within a design context, a surrogate takes a vector of design variables that describe a current design and returns an approximation of the design’s response through a pseudo-time variable. To compare various radial basis function (RBF) surrogate modeling approaches, the prediction of a load displacement path of a snap-through structure is used as an example numerical problem. This work specifically considers the scenario where analytical sensitivities are available directly from the computational mechanics’ solver and therefore gradient enhanced surrogates are constructed. In addition, the gradients are used to perform a domain transformation preprocessing step to construct surrogate models in a more isotropic domain, which is conducive to RBFs. This work demonstrates that although the gradient-based domain transformation scheme offers a significant improvement to the performance of the space-time surrogate models (STSMs), the network surrogate model (NSM) is far more robust. This research offers explanations for the improved performance of NSMs over STSMs and recommends future research to improve the performance of STSMs.
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34

Kang, Shinseong, e Kyunghoon Lee. "Application of Gradient-Enhanced Kriging to Aerodynamic Coefficients Modeling With Physical Gradient Information". Journal of the Korean Society for Aeronautical & Space Sciences 48, n.º 3 (31 de março de 2020): 175–85. http://dx.doi.org/10.5139/jksas.2020.48.3.175.

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35

An, Xinlai, Weikang Bao, Zuhe Zhang, Zhouwen Jiang, Shengyun Yuan, Zesheng You e Yong Zhang. "Gradient Enhanced Strain Hardening and Tensile Deformability in a Gradient-Nanostructured Ni Alloy". Nanomaterials 11, n.º 9 (18 de setembro de 2021): 2437. http://dx.doi.org/10.3390/nano11092437.

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Gradient-nanostructured material is an emerging category of material with spatial gradients in microstructural features. The incompatibility between gradient nanostructures (GNS) in the surface layer and coarse-grained (CG) core and their roles in extra strengthening and strain hardening have been well elucidated. Nevertheless, whether similar mechanisms exist within the GNS is not clear yet. Here, interactions between nanostructured layers constituting the GNS in a Ni alloy processed by surface mechanical rolling treatment were investigated by performing unique microtension tests on the whole GNS and three subdivided nanostructured layers at specific depths, respectively. The isolated nanograined layer at the topmost surface shows the highest strength but a brittle nature. With increasing depths, isolated layers exhibit lower strength but enhanced tensile plasticity. The GNS sample’s behavior complied more with the soft isolated layer at the inner side of GNS. Furthermore, an extra strain hardening was found in the GNS sample, leading to a greater uniform elongation (>3%) as compared to all of three constituent nanostructured layers. This extra strain hardening could be ascribed to the effects of the strain gradients arising from the incompatibility associated with the depth-dependent mechanical performance of various nanostructured layers.
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36

Chen, G., e G. Baker. "Enhanced Approach to Consistency in Gradient-Dependent Plasticity". Advances in Structural Engineering 7, n.º 3 (julho de 2004): 279–83. http://dx.doi.org/10.1260/136943304323213229.

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37

Titscher, Thomas, Javier Oliver e Jörg F. Unger. "Implicit–Explicit Integration of Gradient-Enhanced Damage Models". Journal of Engineering Mechanics 145, n.º 7 (julho de 2019): 04019040. http://dx.doi.org/10.1061/(asce)em.1943-7889.0001608.

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38

Laurent, Luc, Rodolphe Le Riche, Bruno Soulier e Pierre-Alain Boucard. "An Overview of Gradient-Enhanced Metamodels with Applications". Archives of Computational Methods in Engineering 26, n.º 1 (17 de julho de 2017): 61–106. http://dx.doi.org/10.1007/s11831-017-9226-3.

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39

Li, Xikui, Junbo Zhang e Xue Zhang. "Micro-macro homogenization of gradient-enhanced Cosserat media". European Journal of Mechanics - A/Solids 30, n.º 3 (maio de 2011): 362–72. http://dx.doi.org/10.1016/j.euromechsol.2010.10.008.

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40

Ulaganathan, Selvakumar, Ivo Couckuyt, Francesco Ferranti, Eric Laermans e Tom Dhaene. "Performance study of multi-fidelity gradient enhanced kriging". Structural and Multidisciplinary Optimization 51, n.º 5 (26 de novembro de 2014): 1017–33. http://dx.doi.org/10.1007/s00158-014-1192-x.

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41

Jiang, Ting, e XiaoJian Zhou. "Gradient/Hessian-enhanced least square support vector regression". Information Processing Letters 134 (junho de 2018): 1–8. http://dx.doi.org/10.1016/j.ipl.2018.01.014.

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42

Tyburn, Jean-Max, Ian M. Brereton e David M. Doddrell. "Coherence selection in gradient-enhanced, heteronuclear correlation spectroscopy". Journal of Magnetic Resonance (1969) 97, n.º 2 (abril de 1992): 305–12. http://dx.doi.org/10.1016/0022-2364(92)90315-x.

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43

Li, Gang, e Fuh-Gwo Yuan. "Gradient enhanced damage sizing for structural health management". Smart Materials and Structures 24, n.º 2 (23 de janeiro de 2015): 025036. http://dx.doi.org/10.1088/0964-1726/24/2/025036.

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44

Chen, Tinggui, Junrui Jiao e Dejie Yu. "Enhanced broadband acoustic sensing in gradient coiled metamaterials". Journal of Physics D: Applied Physics 54, n.º 8 (8 de dezembro de 2020): 085501. http://dx.doi.org/10.1088/1361-6463/abc6d7.

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45

Zhang, Chun-Lei, Hui-Jing Du, Jian-Zhuo Zhu, Tian-Fu Xu e Xiao-Yong Fang. "Enhanced Photovoltaic Properties of Gradient Doping Solar Cells". Chinese Physics Letters 29, n.º 12 (dezembro de 2012): 127305. http://dx.doi.org/10.1088/0256-307x/29/12/127305.

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46

Zuiderweg, Erik R. P., e Aikaterini Rousaki. "Gradient-enhanced TROSY described with Cartesian product operators". Concepts in Magnetic Resonance Part A 38A, n.º 6 (novembro de 2011): 280–88. http://dx.doi.org/10.1002/cmr.a.20228.

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47

Xu, Yanjie, e Leong Hien Poh. "Localizing gradient‐enhanced Rousselier model for ductile fracture". International Journal for Numerical Methods in Engineering 119, n.º 9 (15 de abril de 2019): 826–51. http://dx.doi.org/10.1002/nme.6074.

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48

Geers, M. G. D., R. L. J. M. Ubachs e R. A. B. Engelen. "Strongly non-local gradient-enhanced finite strain elastoplasticity". International Journal for Numerical Methods in Engineering 56, n.º 14 (2003): 2039–68. http://dx.doi.org/10.1002/nme.654.

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49

Peerlings, R. H. J., W. A. M. Brekelmans, R. de Borst e M. G. D. Geers. "Gradient-enhanced damage modelling of high-cycle fatigue". International Journal for Numerical Methods in Engineering 49, n.º 12 (2000): 1547–69. http://dx.doi.org/10.1002/1097-0207(20001230)49:12<1547::aid-nme16>3.0.co;2-d.

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50

Hurd, R. E., A. Deese, M. O'Neil Johnson, S. Sukumar e P. C. M. van Zijl. "Impact of Differential Linearity in Gradient-Enhanced NMR". Journal of Magnetic Resonance, Series A 119, n.º 2 (abril de 1996): 285–88. http://dx.doi.org/10.1006/jmra.1996.0089.

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