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Journal articles on the topic 'Free Knot Spline'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Gervini, Daniel. "Free-knot spline smoothing for functional data." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68, no. 4 (September 2006): 671–87. http://dx.doi.org/10.1111/j.1467-9868.2006.00561.x.

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2

Wang, Xiao. "Bayesian Free-Knot Monotone Cubic Spline Regression." Journal of Computational and Graphical Statistics 17, no. 2 (June 2008): 373–87. http://dx.doi.org/10.1198/106186008x321077.

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3

Creutzig, Jakob, Thomas Müller-Gronbach, and Klaus Ritter. "Free-knot spline approximation of stochastic processes." Journal of Complexity 23, no. 4-6 (August 2007): 867–89. http://dx.doi.org/10.1016/j.jco.2007.05.003.

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4

Ciarlini, Patrizia, and Daniela Ichim. "Free-knot cubic spline modelling in cryogenic thermometer calibration." Measurement 39, no. 9 (November 2006): 815–20. http://dx.doi.org/10.1016/j.measurement.2006.04.006.

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5

Bittner, Kai, and Hans Georg Brachtendorf. "Fast Algorithms for Adaptive Free Knot Spline Approximation Using Nonuniform Biorthogonal Spline Wavelets." SIAM Journal on Scientific Computing 37, no. 2 (January 2015): B283—B304. http://dx.doi.org/10.1137/14095354x.

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6

MAMIC, G., and M. BENNAMOUN. "AUTOMATED SPLINE SURFACE MODELING AND MATCHING FOR RECOGNITION OF FREE-FORM OBJECTS." International Journal of Image and Graphics 04, no. 01 (January 2004): 51–84. http://dx.doi.org/10.1142/s0219467804001294.

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Surface representations are utilized in a multitude of applications such as computer vision, medical imaging and computer graphics. B-spline surfaces have a number of desirable properties for representing surfaces, however, the complexity of knot placement strategies has prevented their widespread use in high-level vision environments. A solution to this problem is formulated within the reversible jump Markov chain Monte Carlo framework, whereby a derived posterior distribution may be sampled to calculate expected values for the number of knots required, their expected positions and a maximum likelihood estimate for the resulting control net of a given surface. Recognition of individual models may then be achieved using a hash table constructed using the principal components of the model control nets. Results of the fitting procedure, in terms of estimated knot vectors and spline surface errors, and the recognition of objects are provided for a set of free-form objects.

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7

Wang, Xin, Guo Wei, and Jinwei Sun. "Free knot recursive B-spline for compensation of nonlinear smart sensors." Measurement 44, no. 5 (June 2011): 888–94. http://dx.doi.org/10.1016/j.measurement.2011.02.009.

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8

Slassi, Mehdi. "A Milstein-based free knot spline approximation for stochastic differential equations." Journal of Complexity 28, no. 1 (February 2012): 37–47. http://dx.doi.org/10.1016/j.jco.2011.03.005.

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9

Kawasaki, H. "A Second-Order Property of Spline Functions with One Free Knot." Journal of Approximation Theory 78, no. 2 (August 1994): 293–97. http://dx.doi.org/10.1006/jath.1994.1079.

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10

Slassi, Mehdi. "The optimal free knot spline approximation of stochastic differential equations with additive noise." Journal of Computational and Applied Mathematics 261 (May 2014): 62–71. http://dx.doi.org/10.1016/j.cam.2013.09.034.

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11

Lindstrom, Mary J. "Self-modelling with random shift and scale parameters and a free-knot spline shape function." Statistics in Medicine 14, no. 18 (September 30, 1995): 2009–21. http://dx.doi.org/10.1002/sim.4780141807.

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12

Paciorek, Christopher J. "Misinformation in the conjugate prior for the linear model with implications for free-knot spline modelling." Bayesian Analysis 1, no. 2 (June 2006): 375–83. http://dx.doi.org/10.1214/06-ba114.

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13

Yu, Yang, Zhihong Zou, and Shanshan Wang. "Bayesian quantile regression and variable selection for partial linear single-index model: Using free knot spline." Communications in Statistics - Simulation and Computation 48, no. 5 (January 16, 2018): 1429–49. http://dx.doi.org/10.1080/03610918.2017.1414248.

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14

Lu, Wenlong, Luca Pagani, Liping Zhou, Xiaojun Liu, Jian Wang, Richard Leach, and Xiangqian (Jane) Jiang. "Uncertainty-guided intelligent sampling strategy for high-efficiency surface measurement via free-knot B-spline regression modelling." Precision Engineering 56 (March 2019): 38–52. http://dx.doi.org/10.1016/j.precisioneng.2018.09.002.

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15

Chen, Youdong, and Ling Li. "Collision-free trajectory planning for dual-robot systems using B-splines." International Journal of Advanced Robotic Systems 14, no. 4 (July 1, 2017): 172988141772802. http://dx.doi.org/10.1177/1729881417728021.

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This article presents a new approach for planning collision-free trajectories of two robots working in a shared workspace. Based on the B-spline knot refinement and the local modification scheme, the approach only changes the local trajectory around the collision area without changing the shape in the global way. The geometric model of dual-robot is employed by two kinds of geometric elements (sphere and capsule). A collision check method calculates the distance between two robots to determine whether the collisions exist. The collision check is converted to calculate the distance between every two elements. The proposed method has been implemented on a dual-robot system composed of two KUKA manipulators. The numerical and simulation results presented in the article illustrate the efficiency of the proposed technique.

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16

Halida, A., N. Salam, and A. S. Lestia. "Modeling of poverty in Kalimantan with nonparametric spline regression approach." Journal of Physics: Conference Series 2106, no. 1 (November 1, 2021): 012008. http://dx.doi.org/10.1088/1742-6596/2106/1/012008.

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Abstract Poverty is a problem that is always present in any country, including Indonesia. Kalimantan is one of the islands in Indonesia that has not been free from poverty. Therefore, more effective efforts to further reduce poverty are needed. The purpose of the is study was to develop a model that can explain significant factors to poverty in Kalimantan. To achive the objective, first, factors that may have significant influence to the changes in the percentage of poor people should be identified, using regression analysis. In this study, nonparametric regression analysis was used with a spline approach since the relationship between poverty and the explanatory factors did not have a particular pattern. The results of this study showed that, the best was using three knot points, where Open Unemployment Rate (OUR), Human Development Index (HDI), and Economic Growth have a significant effect on poverty in Kalimantan.

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17

Noreen, Iram. "Collision Free Smooth Path for Mobile Robots in Cluttered Environment Using an Economical Clamped Cubic B-Spline." Symmetry 12, no. 9 (September 22, 2020): 1567. http://dx.doi.org/10.3390/sym12091567.

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Mobile robots have various applications in agriculture, autonomous cars, industrial automation, planetary exploration, security, and surveillance. The generation of the optimal smooth path is a significant aspect of mobile robotics. An optimal path for a mobile robot is measured by various factors such as path length, path smoothness, collision-free curve, execution time, and the total number of turns. However, most of the planners generate a non-smooth less optimal and linear piecewise path. Post processing smoothing is applied at the cost of increase in path length. Moreover, current research on post-processing path smoothing techniques does not address the issues of post smoothness collision and performance efficiency. This paper presents a path smoothing approach based on clamped cubic B-Spline to resolve the aforementioned issues. The proposed approach has introduced an economical point insertion scheme with automated knot vector generation while eliminating post smoothness collisions with obstacles. It generates C2 continuous path without any stitching point and passes more closely to the originally planned path. Experiments and comparison with previous approaches have shown that the proposed approach generates better results with reduced path length, and execution time. The test cases used for experiments include a simple structure environment, complex un-structured environment, an environment full of random cluttered narrow obstacles, and a case study of an indoor narrow passage.

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18

Demertzis, Konstantinos, Dimitrios Tsiotas, and Lykourgos Magafas. "Modeling and Forecasting the COVID-19 Temporal Spread in Greece: An Exploratory Approach Based on Complex Network Defined Splines." International Journal of Environmental Research and Public Health 17, no. 13 (June 30, 2020): 4693. http://dx.doi.org/10.3390/ijerph17134693.

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Within the complex framework of anti-COVID-19 health management, where the criteria of diagnostic testing, the availability of public-health resources and services, and the applied anti-COVID-19 policies vary between countries, the reliability and accuracy in the modeling of temporal spread can prove to be effective in the worldwide fight against the disease. This paper applies an exploratory time-series analysis to the evolution of the disease in Greece, which currently suggests a success story of COVID-19 management. The proposed method builds on a recent conceptualization of detecting connective communities in a time-series and develops a novel spline regression model where the knot vector is determined by the community detection in the complex network. Overall, the study contributes to the COVID-19 research by proposing a free of disconnected past-data and reliable framework of forecasting, which can facilitate decision-making and management of the available health resources.

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19

Opschoor, Joost A. A., Philipp C. Petersen, and Christoph Schwab. "Deep ReLU networks and high-order finite element methods." Analysis and Applications 18, no. 05 (February 21, 2020): 715–70. http://dx.doi.org/10.1142/s0219530519410136.

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Approximation rate bounds for emulations of real-valued functions on intervals by deep neural networks (DNNs) are established. The approximation results are given for DNNs based on ReLU activation functions. The approximation error is measured with respect to Sobolev norms. It is shown that ReLU DNNs allow for essentially the same approximation rates as nonlinear, variable-order, free-knot (or so-called “[Formula: see text]-adaptive”) spline approximations and spectral approximations, for a wide range of Sobolev and Besov spaces. In particular, exponential convergence rates in terms of the DNN size for univariate, piecewise Gevrey functions with point singularities are established. Combined with recent results on ReLU DNN approximation of rational, oscillatory, and high-dimensional functions, this corroborates that continuous, piecewise affine ReLU DNNs afford algebraic and exponential convergence rate bounds which are comparable to “best in class” schemes for several important function classes of high and infinite smoothness. Using composition of DNNs, we also prove that radial-like functions obtained as compositions of the above with the Euclidean norm and, possibly, anisotropic affine changes of co-ordinates can be emulated at exponential rate in terms of the DNN size and depth without the curse of dimensionality.

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20

Miyata, Satoshi, and Xiaotong Shen. "Adaptive Free-Knot Splines." Journal of Computational and Graphical Statistics 12, no. 1 (March 2003): 197–213. http://dx.doi.org/10.1198/1061860031284.

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21

Miyata, Satoshi, and Xiaotong Shen. "Free-knot Splines and Adaptive Knot Selection." JOURNAL OF THE JAPAN STATISTICAL SOCIETY 35, no. 2 (2005): 303–24. http://dx.doi.org/10.14490/jjss.35.303.

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22

Lindstrom, Mary J. "Penalized Estimation of Free-Knot Splines." Journal of Computational and Graphical Statistics 8, no. 2 (June 1999): 333. http://dx.doi.org/10.2307/1390640.

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23

Lindstrom, Mary J. "Penalized Estimation of Free-Knot Splines." Journal of Computational and Graphical Statistics 8, no. 2 (June 1999): 333–52. http://dx.doi.org/10.1080/10618600.1999.10474817.

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24

Molinari, Nicolas, Marion Morena, Jean-Paul Cristol, and Jean-Pierre Daurès. "Free knot splines for biochemical data." Computer Methods and Programs in Biomedicine 67, no. 3 (March 2002): 163–67. http://dx.doi.org/10.1016/s0169-2607(01)00123-7.

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25

Molinari, Nicolas. "Free Knot Splines for Supervised Classification." Journal of Classification 24, no. 2 (September 2007): 221–34. http://dx.doi.org/10.1007/s00357-007-0013-y.

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26

Mao, Wenxin, and Linda H. Zhao. "Free-knot polynomial splines with confidence intervals." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 65, no. 4 (October 28, 2003): 901–19. http://dx.doi.org/10.1046/j.1369-7412.2003.00422.x.

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27

Nürnberger, Günther. "The metric projection for free knot splines." Journal of Approximation Theory 71, no. 2 (November 1992): 145–53. http://dx.doi.org/10.1016/0021-9045(92)90113-3.

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28

Dimatteo, I., C. R. Genovese, and R. E. Kass. "Bayesian curve-fitting with free-knot splines." Biometrika 88, no. 4 (December 1, 2001): 1055–71. http://dx.doi.org/10.1093/biomet/88.4.1055.

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29

Stone, Charles J. "Nonparametric M-regression with free knot splines." Journal of Statistical Planning and Inference 130, no. 1-2 (March 2005): 183–206. http://dx.doi.org/10.1016/j.jspi.2003.05.002.

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30

Hu, Yingkang. "Convexity Preserving Approximation by Free Knot Splines." SIAM Journal on Mathematical Analysis 22, no. 4 (July 1991): 1183–91. http://dx.doi.org/10.1137/0522077.

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31

Nürnberger, Günther. "Strongly unique spline approximations with free knots." Constructive Approximation 3, no. 1 (December 1987): 31–42. http://dx.doi.org/10.1007/bf01890551.

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32

Iwasa, Hideaki, Fumiaki Sato, Hiroshi Shimabukuro, Naoshi Yamada, Yoshito Ikada, and S. H. Hyon. "One-knot microvascular anastomosis." Journal of Neurosurgery 66, no. 5 (May 1987): 764–67. http://dx.doi.org/10.3171/jns.1987.66.5.0764.

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✓ Experimental microvascular anastomosis using a glutide copolymer (lactide:glycolide, 80:20) as an external splint was undertaken in 33 rats between the carotid artery and the jugular vein. Both vessels were dissected free over a 1-cm length and cut at the cranial end of the dissected part. The carotid artery was then introduced into a glutide pipe-splint. The arterial wall was turned 180° over the edge of the splint. This reflected artery wall and the glutide were covered by the freed-up jugular vein. One stitch was made around the vein, the artery, and the glutide in a manner similar to binding steel wire over a barrel. Thus, the “one-knot anastomosis” was completed. The patency rate at the anastomosed site was 100%, confirmed by angiography in 30 rats and by direct surgery in three. The time required to produce the anastomosis was between 5 and 7 minutes. Light microscopic observation showed that there was no obstruction by thrombus formation at 1 and 5 weeks after the anastomotic surgery. This technique may be clinically applicable for extracranial-intracranial bypass surgery, reconstruction of venous sinuses, and other vascular procedures.

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33

Stone, Charles J., and Jianhua Z. Huang. "Free knot splines in concave extended linear modeling." Journal of Statistical Planning and Inference 108, no. 1-2 (November 2002): 219–53. http://dx.doi.org/10.1016/s0378-3758(02)00280-x.

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34

Lei, Yunwen, and Lixin Ding. "Approximation and estimation bounds for free knot splines." Computers & Mathematics with Applications 65, no. 7 (April 2013): 1006–24. http://dx.doi.org/10.1016/j.camwa.2013.01.030.

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35

Kopotun, Kirill, and Alexei Shadrin. "On k-Monotone Approximation by Free Knot Splines." SIAM Journal on Mathematical Analysis 34, no. 4 (January 2003): 901–24. http://dx.doi.org/10.1137/s0036141002358514.

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36

Johnson, Matthew S. "Modeling dichotomous item responses with free-knot splines." Computational Statistics & Data Analysis 51, no. 9 (May 2007): 4178–92. http://dx.doi.org/10.1016/j.csda.2006.04.021.

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37

MULANSKY, BERND. "Chebyshev Approximation by Spline Functions with Free Knots." IMA Journal of Numerical Analysis 12, no. 1 (1992): 95–105. http://dx.doi.org/10.1093/imanum/12.1.95.

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38

Fernández‐Rodríguez, Fernando. "Interest Rate Term Structure Modeling Using Free‐Knot Splines*." Journal of Business 79, no. 6 (November 2006): 3083–99. http://dx.doi.org/10.1086/508009.

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39

Holmes, C. C., and B. K. Mallick. "Generalized Nonlinear Modeling With Multivariate Free-Knot Regression Splines." Journal of the American Statistical Association 98, no. 462 (June 2003): 352–68. http://dx.doi.org/10.1198/016214503000143.

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40

Denis, M., and N. Molinari. "Free Knot Splines with RJMCMC in Survival Data Analysis." Communications in Statistics - Theory and Methods 39, no. 14 (July 19, 2010): 2617–29. http://dx.doi.org/10.1080/03610920903072424.

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41

Stone, Charles J., and Jianhua Z. Huang. "Statistical modeling of diffusion processes with free knot splines." Journal of Statistical Planning and Inference 116, no. 2 (October 2003): 451–74. http://dx.doi.org/10.1016/s0378-3758(02)00349-x.

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42

Lindstrom, Mary J. "Bayesian estimation of free-knot splines using reversible jumps." Computational Statistics & Data Analysis 41, no. 2 (December 2002): 255–69. http://dx.doi.org/10.1016/s0167-9473(02)00066-x.

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43

Bessaoud, F., J. P. Daures, and N. Molinari. "Free knot splines for logistic models and threshold selection." Computer Methods and Programs in Biomedicine 77, no. 1 (January 2005): 1–9. http://dx.doi.org/10.1016/j.cmpb.2004.05.009.

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44

N�rnberger, G. "Strong unicity in nonlinear approximation and free knot splines." Constructive Approximation 10, no. 2 (June 1994): 285–99. http://dx.doi.org/10.1007/bf01263068.

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45

Dikoussar, N. D., and Cs Török. "Data smoothing by splines with free knots." Physics of Particles and Nuclei Letters 5, no. 3 (May 2008): 324–27. http://dx.doi.org/10.1134/s1547477108030394.

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46

Schütze, Torsten, and Hubert Schwetlick. "Constrained approximation by splines with free knots." BIT Numerical Mathematics 37, no. 1 (March 1997): 105–37. http://dx.doi.org/10.1007/bf02510176.

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47

Wang, Ziteng, and Manfei Xie. "Data approximation by L1 spline fits with free knots." Computer Aided Geometric Design 92 (January 2022): 102064. http://dx.doi.org/10.1016/j.cagd.2021.102064.

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48

Battaglin, Francesca, Fang-Shu Ou, Xueping Qu, Monica M. Bertagnolli, Howard S. Hochster, Donna Niedzwiecki, Richard M. Goldberg, et al. "Predictive and prognostic value of HER2 gene expression and HER2 amplification in patients with metastatic colorectal cancer (mCRC) enrolled in CALGB/SWOG 80405 (Alliance)." Journal of Clinical Oncology 38, no. 15_suppl (May 20, 2020): 4086. http://dx.doi.org/10.1200/jco.2020.38.15_suppl.4086.

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4086 Background: The randomized phase III CALGB/SWOG 80405 trial found no difference in overall survival (OS) in first-line mCRC pts treated with either bevacizumab (Bev) or cetuximab (Cet) combined with the same chemotherapy. We investigated the potential prognostic and predictive value of HER2 amplification and HER2 gene expression using NGS and Nanostring data. Methods: Primary tumor DNA from 559 patients (pts) was profiled for HER2 amplification by NGS (Foundation One). Tumor tissue from 925 pts was tested for Nanostring gene expression using an 800 gene panel. OS and progression free survival (PFS) were the endpoints as time-to-event variables. Cox proportional hazard models with gene expression fitted with linear spline (one internal knot at median) were used, adjusting for pts baseline characteristics, treatment assignment, and molecular features (microsatellite instability, BRAF, all RAS). Results: Of 505 tumors with both NGS and Nanostring data, 16 harbored HER2 amplification (copy number variation > 6), limited to microsatellite stable tumors and significantly associated with HER2 expression ( P < 0.001) and wild-type RAS ( P = 0.036). HER2 amplification was neither prognostic nor predictive for OS or PFS. Conversely, HER2 expression higher than median was associated with longer PFS ( P = 0.018) but not OS ( P = 0.13). Among pts with HER2 not amplified, higher HER2 expression was associated with better OS (hazard ratio [HR], 0.83; 95%CI, 0.72-0.97; P = 0.016) and PFS (HR, 0.85; 95%CI, 0.74-0.98; P = 0.027) when the expression was less than median. Additionally, in pts with no HER2 amplification and HER2 expression lower than median, treatment with Cet was associated with worse PFS compared to Bev (HR, 1.46; 95%CI, 1.12-1.90; P = 0.005). This effect was not observed with expression higher than median regardless of HER2 amplification status. Conclusions: To our knowledge, this is the largest analysis of HER2 amplification and gene expression in mCRC pts treated with standard therapy. Our results provide novel insight on the predictive and prognostic value of HER2 gene expression in pts treated with Cet- and Bev-based regimens. Upon validation, these findings could inform pts selection and the design of more effective treatment options for pts with low HER2 expression. Clinical trial information: NCT00265850.

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49

Nürnberger, G., L. Schumaker, M. Sommer, and H. Strauss. "Uniform approximation by generalized splines with free knots." Journal of Approximation Theory 59, no. 2 (November 1989): 150–69. http://dx.doi.org/10.1016/0021-9045(89)90150-0.

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50

Schwetlick, Hubert, and Torsten Schütze. "Least squares approximation by splines with free knots." BIT Numerical Mathematics 35, no. 3 (September 1995): 361–84. http://dx.doi.org/10.1007/bf01732610.

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