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1

Qumer Gill, Asif, and Muhammad Atif Qureshi. "Adaptive Enterprise Architecture Modelling." Journal of Software 10, no. 5 (May 2015): 628–38. http://dx.doi.org/10.17706/jsw.10.5.628-638.

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Wang, Y., Q. Pan, Y. Liang, and L. Zhang. "Adaptive spatiotemporal background modelling." IET Computer Vision 6, no. 5 (September 1, 2012): 451–58. http://dx.doi.org/10.1049/iet-cvi.2010.0229.

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3

Peterson, Donald M., and Kevin J. Riggs. "Adaptive Modelling and Mindreading." Mind and Language 14, no. 1 (March 1999): 80–112. http://dx.doi.org/10.1111/1468-0017.00104.

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4

Oden, J. Tinsley. "Adaptive multiscale predictive modelling." Acta Numerica 27 (May 1, 2018): 353–450. http://dx.doi.org/10.1017/s096249291800003x.

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The use of computational models and simulations to predict events that take place in our physical universe, or to predict the behaviour of engineered systems, has significantly advanced the pace of scientific discovery and the creation of new technologies for the benefit of humankind over recent decades, at least up to a point. That ‘point’ in recent history occurred around the time that the scientific community began to realize that true predictive science must deal with many formidable obstacles, including the determination of the reliability of the models in the presence of many uncertainties. To develop meaningful predictions one needs relevant data, itself possessing uncertainty due to experimental noise; in addition, one must determine model parameters, and concomitantly, there is the overriding need to select and validate models given the data and the goals of the simulation.This article provides a broad overview of predictive computational science within the framework of what is often called the science of uncertainty quantification. The exposition is divided into three major parts. In Part 1, philosophical and statistical foundations of predictive science are developed within a Bayesian framework. There the case is made that the Bayesian framework provides, perhaps, a unique setting for handling all of the uncertainties encountered in scientific prediction. In Part 2, general frameworks and procedures for the calculation and validation of mathematical models of physical realities are given, all in a Bayesian setting. But beyond Bayes, an introduction to information theory, the maximum entropy principle, model sensitivity analysis and sampling methods such as MCMC are presented. In Part 3, the central problem of predictive computational science is addressed: the selection, adaptive control and validation of mathematical and computational models of complex systems. The Occam Plausibility Algorithm, OPAL, is introduced as a framework for model selection, calibration and validation. Applications to complex models of tumour growth are discussed.
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5

Green, D. G., R. E. Reichelt, and R. G. Buck. "Self-adaptive modelling algorithms." Mathematics and Computers in Simulation 30, no. 1-2 (February 1988): 33–38. http://dx.doi.org/10.1016/0378-4754(88)90101-2.

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Popinet, Stéphane. "Quadtree-adaptive tsunami modelling." Ocean Dynamics 61, no. 9 (May 31, 2011): 1261–85. http://dx.doi.org/10.1007/s10236-011-0438-z.

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Guo, Mengmeng, and Wolfgang Karl Härdle. "Adaptive Interest Rate Modelling." Journal of Forecasting 36, no. 3 (July 20, 2016): 241–56. http://dx.doi.org/10.1002/for.2431.

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8

Hill, J., E. E. Popova, D. A. Ham, M. D. Piggott, and M. Srokosz. "Adapting to life: ocean biogeochemical modelling and adaptive remeshing." Ocean Science 10, no. 3 (May 9, 2014): 323–43. http://dx.doi.org/10.5194/os-10-323-2014.

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Abstract. An outstanding problem in biogeochemical modelling of the ocean is that many of the key processes occur intermittently at small scales, such as the sub-mesoscale, that are not well represented in global ocean models. This is partly due to their failure to resolve sub-mesoscale phenomena, which play a significant role in vertical nutrient supply. Simply increasing the resolution of the models may be an inefficient computational solution to this problem. An approach based on recent advances in adaptive mesh computational techniques may offer an alternative. Here the first steps in such an approach are described, using the example of a simple vertical column (quasi-1-D) ocean biogeochemical model. We present a novel method of simulating ocean biogeochemical behaviour on a vertically adaptive computational mesh, where the mesh changes in response to the biogeochemical and physical state of the system throughout the simulation. We show that the model reproduces the general physical and biological behaviour at three ocean stations (India, Papa and Bermuda) as compared to a high-resolution fixed mesh simulation and to observations. The use of an adaptive mesh does not increase the computational error, but reduces the number of mesh elements by a factor of 2–3. Unlike previous work the adaptivity metric used is flexible and we show that capturing the physical behaviour of the model is paramount to achieving a reasonable solution. Adding biological quantities to the adaptivity metric further refines the solution. We then show the potential of this method in two case studies where we change the adaptivity metric used to determine the varying mesh sizes in order to capture the dynamics of chlorophyll at Bermuda and sinking detritus at Papa. We therefore demonstrate that adaptive meshes may provide a suitable numerical technique for simulating seasonal or transient biogeochemical behaviour at high vertical resolution whilst minimising the number of elements in the mesh. More work is required to move this to fully 3-D simulations.
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Hill, J., E. E. Popova, D. A. Ham, M. D. Piggott, and M. Srokosz. "Adapting to life: ocean biogeochemical modelling and adaptive remeshing." Ocean Science Discussions 10, no. 6 (November 5, 2013): 1997–2051. http://dx.doi.org/10.5194/osd-10-1997-2013.

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Abstract. An outstanding problem in biogeochemical modelling of the ocean is that many of the key processes occur intermittently at small scales, such as the sub-mesoscale, that are not well represented in global ocean models. As an example, state-of-the-art models give values of primary production approximately two orders of magnitude lower than those observed in the ocean's oligotrophic gyres, which cover a third of the Earth's surface. This is partly due to their failure to resolve sub-mesoscale phenomena, which play a significant role in nutrient supply. Simply increasing the resolution of the models may be an inefficient computational solution to this problem. An approach based on recent advances in adaptive mesh computational techniques may offer an alternative. Here the first steps in such an approach are described, using the example of a~simple vertical column (quasi 1-D) ocean biogeochemical model. We present a novel method of simulating ocean biogeochemical behaviour on a vertically adaptive computational mesh, where the mesh changes in response to the biogeochemical and physical state of the system throughout the simulation. We show that the model reproduces the general physical and biological behaviour at three ocean stations (India, Papa and Bermuda) as compared to a high-resolution fixed mesh simulation and to observations. The simulations capture both the seasonal and inter-annual variations. The use of an adaptive mesh does not increase the computational error, but reduces the number of mesh elements by a factor of 2–3, so reducing computational overhead. We then show the potential of this method in two case studies where we change the metric used to determine the varying mesh sizes in order to capture the dynamics of chlorophyll at Bermuda and sinking detritus at Papa. We therefore demonstrate adaptive meshes may provide a~suitable numerical technique for simulating seasonal or transient biogeochemical behaviour at high spatial resolution whilst minimising computational cost.
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10

Xiao, C. M., and P. C. Austin. "Yacht Modelling and Adaptive Control." IFAC Proceedings Volumes 33, no. 21 (August 2000): 405–10. http://dx.doi.org/10.1016/s1474-6670(17)37108-2.

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11

Tan, Shaohua. "NeuroFuzzy adaptive modelling and control." Automatica 32, no. 11 (November 1996): 1618–19. http://dx.doi.org/10.1016/s0005-1098(97)80766-2.

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12

Sander, Ingo, and Axel Jantsch. "Modelling Adaptive Systems in ForSyDe." Electronic Notes in Theoretical Computer Science 200, no. 2 (February 2008): 39–54. http://dx.doi.org/10.1016/j.entcs.2008.02.011.

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13

Vemaganti, Kumar. "Modelling error estimation and adaptive modelling of perforated materials." International Journal for Numerical Methods in Engineering 59, no. 12 (March 2, 2004): 1587–604. http://dx.doi.org/10.1002/nme.929.

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14

Sulieman Q. Abu-Ein, Sulieman Q. Abu-Ein. "Adaptive Lighting System Modelling and Analysis." International Journal of Mechanical and Production Engineering Research and Development 9, no. 3 (2019): 1483–92. http://dx.doi.org/10.24247/ijmperdjun2019156.

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15

Savvopoulos, Anastasios, and Maria Virvou. "User modelling server for adaptive help." Intelligent Decision Technologies 5, no. 1 (January 5, 2011): 3–16. http://dx.doi.org/10.3233/idt-2011-0094.

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16

Esposito, G., A. Campa, M. Pinto, G. Simone, M. A. Tabocchini, and M. Belli. "Adaptive response: modelling and experimental studies." Radiation Protection Dosimetry 143, no. 2-4 (December 15, 2010): 320–24. http://dx.doi.org/10.1093/rpd/ncq474.

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17

Márton, Lorinc, and Béla Lantos. "FRICTION MODELLING AND ROBUST ADAPTIVE COMPENSATION." IFAC Proceedings Volumes 38, no. 1 (2005): 257–62. http://dx.doi.org/10.3182/20050703-6-cz-1902.01253.

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18

Albakour, M.-Dyaa. "Adaptive domain modelling for information retrieval." ACM SIGIR Forum 47, no. 1 (June 7, 2013): 59. http://dx.doi.org/10.1145/2492189.2492200.

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19

Wang, Fenglin, and Chris K. Mechefske. "Adaptive modelling of transient vibration signals." Mechanical Systems and Signal Processing 20, no. 4 (May 2006): 825–42. http://dx.doi.org/10.1016/j.ymssp.2004.12.004.

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20

Génieys, Stéphane, Vitaly Volpert, and Pierre Auger. "Adaptive dynamics: modelling Darwin's divergence principle." Comptes Rendus Biologies 329, no. 11 (November 2006): 876–79. http://dx.doi.org/10.1016/j.crvi.2006.08.006.

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21

Rakowsky, Uwe K. "Modelling Reliability-Adaptive multi-system operation." International Journal of Automation and Computing 3, no. 2 (April 2006): 192–98. http://dx.doi.org/10.1007/s11633-006-0192-8.

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22

Chan, C. K., and T. Stathaki. "Signal modelling through adaptive Volterra representations." Electronics Letters 33, no. 25 (1997): 2106. http://dx.doi.org/10.1049/el:19971415.

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23

Benjeddou, A., B. H. V. Topping, and C. A. Mota Soares. "Composite Adaptive Structures: Modelling and Simulation." Computers & Structures 84, no. 22-23 (September 2006): 1381–83. http://dx.doi.org/10.1016/j.compstruc.2006.03.003.

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24

Mousavi, S. F., and M. J. Amiri. "Modelling nitrate concentration of groundwater using adaptive neural-based fuzzy inference system." Soil and Water Research 7, No. 2 (May 18, 2012): 73–83. http://dx.doi.org/10.17221/46/2010-swr.

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High nitrate concentration in groundwater is a major problem in agricultural areas in Iran. Nitrate pollution in groundwater of the particular regions in Isfahan province of Iran has been investigated. The objective of this study was to evaluate the performance of Adaptive Neural-Based Fuzzy Inference System (ANFIS) for estimating the nitrate concentration. In this research, 175 observation wells were selected and nitrate, potassium, magnesium, sodium, chloride, bicarbonate, sulphate, calcium and hardness were determined in groundwater samples for five consecutive months. Electrical conductivity (EC) and pH were also measured and the sodium absorption ratio (SAR) was calculated. The five-month average of bicarbonate, hardness, EC, calcium and magnesium are taken as the input data and the nitrate concentration as the output data. Based on the obtained structures, four ANFIS models were tested against the measured nitrate concentrations to assess the accuracy of each model. The results showed that ANFIS1 was the most accurate (RMSE = 1.17 and R<sup>2</sup> = 0.93) and ANFIS4 was the worst (RMSE = 2.94 and R<sup>2</sup> = 0.68) for estimating the nitrate concentration. In ranking the models, ANFIS2 and ANFIS3 ranked the second and third, respectively. The results showed that all ANFIS models underestimated the nitrate concentration. In general, the ANFIS1 model is recommendable for prediction of nitrate level in groundwater of the studied region.
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25

Kevlahan, Nicholas K. R. "Adaptive Wavelet Methods for Earth Systems Modelling." Fluids 6, no. 7 (June 29, 2021): 236. http://dx.doi.org/10.3390/fluids6070236.

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This paper reviews how dynamically adaptive wavelet methods can be designed to simulate atmosphere and ocean dynamics in both flat and spherical geometries. We highlight the special features that these models must have in order to be valid for climate modelling applications. These include exact mass conservation and various mimetic properties that ensure the solutions remain physically realistic, even in the under-resolved conditions typical of climate models. Particular attention is paid to the implementation of complex topography in adaptive models. Using wavetrisk as an example, we explain in detail how to build a semi-realistic global atmosphere or ocean model of interest to the geophysical community. We end with a discussion of the challenges that remain to developing a realistic dynamically adaptive atmosphere or ocean climate models. These include scale-aware subgrid scale parameterizations of physical processes, such as clouds. Although we focus on adaptive wavelet methods, many of the topics we discuss are relevant for adaptive mesh refinement (AMR).
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26

Chades, Iadine, Josie Carwardine, Tara Martin, Samuel Nicol, Regis Sabbadin, and Olivier Buffet. "MOMDPs: A Solution for Modelling Adaptive Management Problems." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (September 20, 2021): 267–73. http://dx.doi.org/10.1609/aaai.v26i1.8171.

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In conservation biology and natural resource management, adaptive management is an iterative process of improving management by reducing uncertainty via monitoring. Adaptive management is the principal tool for conserving endangered species under global change, yet adaptive management problems suffer from a poor suite of solution methods. The common approach used to solve an adaptive management problem is to assume the system state is known and the system dynamics can be one of a set of pre-defined models. The solution method used is unsatisfactory, employing value iteration on a discretized belief MDP which restricts the study to very small problems. We show how to overcome this limitation by modelling an adaptive management problem as a restricted Mixed Observability MDP called hidden model MDP (hmMDP). We demonstrate how to simplify the value function, the backup operator and the belief update computation. We show that, although a simplified case of POMDPs, hm-MDPs are PSPACE-complete in the finite-horizon case. We illustrate the use of this model to manage a population of the threatened Gouldian finch, a bird species endemic to Northern Australia. Our simple modelling approach is an important step towards efficient algorithms for solving adaptive management problems.
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Ashby, B., C. Bortolozo, A. Lukyanov, and T. Pryer. "Adaptive modelling of variably saturated seepage problems." Quarterly Journal of Mechanics and Applied Mathematics 74, no. 1 (February 1, 2021): 55–81. http://dx.doi.org/10.1093/qjmam/hbab001.

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Summary In this article, we present a goal-oriented adaptive finite element method for a class of subsurface flow problems in porous media, which exhibit seepage faces. We focus on a representative case of the steady state flows governed by a nonlinear Darcy–Buckingham law with physical constraints on subsurface-atmosphere boundaries. This leads to the formulation of the problem as a variational inequality. The solutions to this problem are investigated using an adaptive finite element method based on a dual-weighted a posteriori error estimate, derived with the aim of reducing error in a specific target quantity. The quantity of interest is chosen as volumetric water flux across the seepage face, and therefore depends on an a priori unknown free boundary. We apply our method to challenging numerical examples as well as specific case studies, from which this research originates, illustrating the major difficulties that arise in practical situations. We summarise extensive numerical results that clearly demonstrate the designed method produces rapid error reduction measured against the number of degrees of freedom.
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A. DILTS, WILLIAM J. WALSH, AND CON, DAVID. "STATE LABOR-MANAGEMENT RELATIONS LEGISLATION: ADAPTIVE MODELLING." Journal of Collective Negotiations in the Public Sector 22, no. 1 (March 1, 1993): 1. http://dx.doi.org/10.2190/yvgn-n10v-nrkq-u1md.

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Suzuki, Satoshi, Hiroshi Igarashi, Harumi Kobayashi, Tetsuya Yasuda, and Fumio Harashima. "Human Adaptive Mechatronics and Human-System Modelling." International Journal of Advanced Robotic Systems 10, no. 3 (January 2013): 152. http://dx.doi.org/10.5772/55740.

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Stotsky, A. A. "Statistical engine knock modelling and adaptive control." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 222, no. 3 (March 1, 2008): 429–39. http://dx.doi.org/10.1243/09544070jauto707.

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A new statistical concept of the knock control of a spark ignition automotive engine is proposed. The control aim is associated with the statistical hypothesis test which compares the threshold value with the average value of the maximum amplitude of the knock sensor signal at a certain frequency. Achievement of the control aim implies the desired separation between the average value of the maximum amplitude and the target value and hence the desired probability of knock occurrence. This new control concept allows the control algorithm parameters to be connected to the probability of knock occurrence and customer-related data. The regulation error is defined as the difference between the actual and the desired values of the statistic utilized. A control algorithm which is used for minimization of the regulation error realizes a simple count-up—count-down logic. A new adaptation algorithm for the knock detection threshold is developed. The confidence interval method is used as the basis for adaptation. A knock detection threshold is presented using a confidence interval with a certain significance level. The adaptation is performed for an aged engine so that the significance level is the same for the new and the aged engines despite the fact that the detection threshold values are different. This, in turn, guarantees the same knock detection performance for new and aged engines. A simple statistical model which includes generation of the amplitude signals, threshold value determination, and a knock sound model is developed for evaluation of the control concept. The statistical knock audibility concept is associated with the outlier detection method and is used in this paper for knock audibility judgement. A Volvo six-cylinder prototype engine equipped with cylinder pressure and block vibration sensors was used in the experiments. An external microphone was used for the knock sound measurements.
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31

Juuso, Esko K. "Modelling and Simulation in Adaptive Intelligent Control." SNE Simulation Notes Europe 26, no. 2 (June 2016): 109–16. http://dx.doi.org/10.11128/sne.26.on.10338.

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32

Rougier, Nicolas P., and Jérémy Fix. "DANA: Distributed numerical and adaptive modelling framework." Network: Computation in Neural Systems 23, no. 4 (September 20, 2012): 237–53. http://dx.doi.org/10.3109/0954898x.2012.721573.

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33

Ilchmann, Achim, Marie-France Weirig, and Iven M. Y. Mareels. "Modelling and Adaptive Control of Biochemical Processes." IFAC Proceedings Volumes 31, no. 17 (July 1998): 447–52. http://dx.doi.org/10.1016/s1474-6670(17)40377-6.

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34

Franco Correia, Victor M., Maria A. Aguiar Gomes, Afzal Suleman, Cristóvão M. Mota Soares, and Carlos A. Mota Soares. "Modelling and design of adaptive composite structures." Computer Methods in Applied Mechanics and Engineering 185, no. 2-4 (May 2000): 325–46. http://dx.doi.org/10.1016/s0045-7825(99)00265-0.

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35

Romberg, T. M. "Parameter Adaptive Modelling of Mineral Beneficiation Processes." IFAC Proceedings Volumes 18, no. 6 (July 1985): 289–93. http://dx.doi.org/10.1016/s1474-6670(17)60523-8.

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36

De, Sujit Kumar, Bijay Kumar Swain, Shreerup Goswami, and Madhumita Das. "Adaptive noise risk modelling: fuzzy logic approach." Systems Science & Control Engineering 5, no. 1 (January 2017): 129–41. http://dx.doi.org/10.1080/21642583.2017.1294118.

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37

Jiao, Yue, Yu-Ru Syau, and E. Stanley Lee. "Modelling credit rating by fuzzy adaptive network." Mathematical and Computer Modelling 45, no. 5-6 (March 2007): 717–31. http://dx.doi.org/10.1016/j.mcm.2005.11.016.

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38

Farden, D. C., and J. R. Bellegarda. "Alternate Structures for Adaptive Time Series Modelling." IFAC Proceedings Volumes 20, no. 2 (July 1987): 369–74. http://dx.doi.org/10.1016/s1474-6670(17)55989-3.

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39

Elshafei, Abdel-Latif, Guy A. Dumont, and Ashraf Elnaggar. "Adaptive GPC based on laguerre-filters modelling." Automatica 30, no. 12 (December 1994): 1913–20. http://dx.doi.org/10.1016/0005-1098(94)90051-5.

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Xie, Zhihua, Dimitrios Pavlidis, James R. Percival, Jefferson L. M. A. Gomes, Christopher C. Pain, and Omar K. Matar. "Adaptive unstructured mesh modelling of multiphase flows." International Journal of Multiphase Flow 67 (December 2014): 104–10. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.08.002.

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41

Min, Geyong, and Mohamed Ould-Khaoua. "Modelling adaptive routing in circuit switched networks." Journal of Systems Architecture 47, no. 8 (December 2001): 747–57. http://dx.doi.org/10.1016/s1383-7621(01)00030-3.

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42

Khan, Mohd Javed, and Khurram Mustafa. "Modelling adaptive hypermedia instructional system: a framework." Multimedia Tools and Applications 78, no. 11 (November 6, 2018): 14397–424. http://dx.doi.org/10.1007/s11042-018-6819-2.

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43

Kühnlein, Christian, Piotr K. Smolarkiewicz, and Andreas Dörnbrack. "Modelling atmospheric flows with adaptive moving meshes." Journal of Computational Physics 231, no. 7 (April 2012): 2741–63. http://dx.doi.org/10.1016/j.jcp.2011.12.012.

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Steel, J. A. "Modelling adaptive phytoplankton in a variable environment." Ecological Modelling 78, no. 1-2 (March 1995): 117–27. http://dx.doi.org/10.1016/0304-3800(94)00122-x.

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45

Prave, Rose Sebastianelli, and J. Keith Ord. "An adaptive approach for modelling multiattribute choice." Journal of Multi-Criteria Decision Analysis 4, no. 2 (June 1995): 91–106. http://dx.doi.org/10.1002/mcda.4020040203.

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46

van Moorsel, Aad P. A., and William H. Sanders. "Adaptive uniformization." Communications in Statistics. Stochastic Models 10, no. 3 (January 1994): 619–47. http://dx.doi.org/10.1080/15326349408807313.

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47

Huang, Bin, and Sarat B. Singamneni. "Curved Layer Adaptive Slicing (CLAS) for fused deposition modelling." Rapid Prototyping Journal 21, no. 4 (June 15, 2015): 354–67. http://dx.doi.org/10.1108/rpj-06-2013-0059.

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Purpose – This paper aims to develop a new slicing method for fused deposition modelling (FDM), the curved layer adaptive slicing (CLAS), combining adaptive flat layer and curved layer slicing together. Design/methodology/approach – This research begins with a review of current curved layer and adaptive slicing algorithms employed in the FDM and further improvement of the same, where possible. The two approaches are then integrated to develop the adaptive curved layer slicing based on the three-plane intersection method for curved layer offsetting and consideration of facet angles together with the residual heights for adaptive slicing. A practical implementation showed that curved layer adaptive layers respond in similar lines to the flat layer counterparts in terms of the mechanical behaviour of FDM parts. Findings – CLAS is effective in capturing sharply varying surface profiles and other finer part details, apart from imparting fibre continuity. Three-point bending tests on light curved parts made of curved layers of varying thicknesses prove thicker curved layers to result in better mechanical properties. Research limitations/implications – The algorithms developed in this research can handle relatively simple shapes to develop adaptive curved slices, but further developments are necessary for more complex shapes. The test facilities also need further improvements, to be able to programmatically implement adaptive curved layer slicing over a wide range of thicknesses. Practical implications – When fully developed and implemented, CLAS will allow for better FDM part construction with lesser build times. Originality/value – This research fills a gap in terms of integrating both curved layer and adaptive slicing techniques to better slice and build a part of given geometry using FDM.
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Kamaruddin, Mohd Nazeri, Tan Kim Geok, Omar Abdul Aziz, Tharek Abd Rahman, Ferdous Hossain, and Azlan Abdul Aziz. "Adaptive 3D ray tracing approach for indoor radio signal prediction at 3.5 GHz." International Journal of Electrical and Computer Engineering (IJECE) 12, no. 2 (April 1, 2022): 1617. http://dx.doi.org/10.11591/ijece.v12i2.pp1617-1625.

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This paper explained an adaptive ray tracing technique in modelling indoor radio wave propagation. As compared with conventional ray tracing approach, the presented ray tracing approach offers an optimized method to trace the travelling radio signal by introducing flexibility and adaptive features in ray launching algorithm in modelling the radio wave for indoor scenarios. The simulation result was compared with measurements data for verification. By analyzing the results, the proposed adaptive technique showed a better improvement in simulation time, power level and coverage in modelling the radio wave propagation for indoor scenario and may benefit in the development of signal propagation simulators for future technologies.
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49

Listopadskis, Narimantas. "Modelling of vehicle motion." Lietuvos matematikos rinkinys 40 (December 18, 2000): 415–22. http://dx.doi.org/10.15388/lmr.2000.35203.

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The problem is to calculate the path trajectory for a vehicle following a wire in the floor. Motion of the vehicle is determined by system of differential equations. Fourth-order Runge-Kutta adaptive method was used for solving of the obtained systems of the differential equations.
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BONTCHEVA, KALINA, and VANIA DIMITROVA. "EXAMINING THE USE OF CONCEPTUAL GRAPHS IN ADAPTIVE WEB-BASED SYSTEMS THAT AID TERMINOLOGY LEARNING." International Journal on Artificial Intelligence Tools 13, no. 02 (June 2004): 299–331. http://dx.doi.org/10.1142/s0218213004001569.

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Abstract:
This paper discussed the use of Conceptual Graphs (CGs) for implementing tasks employed in web-based educational systems that aid terminology learning. Specifically, we focus on two critical issues in intelligent tutoring - student diagnosis and generation of adaptive explanations. Both tasks are demonstrated in terminological domains where learners have to familiarize themselves with concepts in a specific subject area (e.g. computing, finance, chemistry). Based on CG reasoning, robust and computationally tractable algorithms for student modelling and adaptive explanation generation are defined. Two intelligent systems are presented — STyLE-OLM and HYLITE+. STyLE-OLM is an interactive learner modelling system that extracts extended models of the learners' cognition. HYLITE+ is a natural language generation system that generates adaptive Web pages based on a learner model(LM). The two systems are complementary and have been implemented separately. However, considered together they cover most of the key tasks in adaptive web-based educational hypermedia that aid learning technical terminology. Based on evaluative studies of STyLE-OLM and HYLITE+, the use of CGs for interactive open student modelling and adaptive concept explanations is examined. The applicability of CGs in adaptive web-based systems that aid learning technical terminology is discussed.
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