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Journal articles on the topic 'Karhunen-Loéve'

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Published: 4 June 2021

Last updated: 13 February 2022

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1

Tian, Wenbiao, Guosheng Rui, Daoguang Dong, and Jian Kang. "Efficient blind adaptive Karhunen–Loéve transform via parallel search." International Journal of Distributed Sensor Networks 14, no. 6 (June 2018): 155014771878237. http://dx.doi.org/10.1177/1550147718782371.

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This article introduces a new algorithm that constructs an efficient search strategy, called parallel search, for blind adaptive Karhunen–Loéve transform. Unlike anterior Karhunen–Loéve transform, the proposed algorithm converges quickly by searching for solutions in different directions simultaneously. Moreover, the process is “blind,” which means that minimal information about the original data is used. The new algorithm also avoids repeating the Karhunen–Loéve transform basis learning step in data compression applications. Numerical simulation results verify the validity of the theory and illustrate the capability of the proposed algorithm.

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2

Zhou, Xing-Gui, and Wei-Kang Yuan. "Control Vector Parametrization with Karhunen−Loéve Expansion." Industrial & Engineering Chemistry Research 43, no. 1 (January 2004): 127–35. http://dx.doi.org/10.1021/ie0210558.

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3

He, Jun. "Karhunen-Loéve expansion for random earthquake excitations." Earthquake Engineering and Engineering Vibration 14, no. 1 (February 20, 2015): 77–84. http://dx.doi.org/10.1007/s11803-015-0007-4.

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4

TARMAN, I. HAKAN. "A KARHUNEN-LOÉVE ANALYSIS OF TURBULENT THERMAL CONVECTION." International Journal for Numerical Methods in Fluids 22, no. 1 (January 15, 1996): 67–79. http://dx.doi.org/10.1002/(sici)1097-0363(19960115)22:1<67::aid-fld332>3.0.co;2-c.

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5

Chambers, D. H., R. J. Adrian, P. Moin, D. S. Stewart, and H. J. Sung. "Karhunen–Loéve expansion of Burgers’ model of turbulence." Physics of Fluids 31, no. 9 (September 1988): 2573–82. http://dx.doi.org/10.1063/1.866535.

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6

Webber, G. A., R. A. Handler, and L. Sirovich. "The Karhunen–Loéve decomposition of minimal channel flow." Physics of Fluids 9, no. 4 (April 1997): 1054–66. http://dx.doi.org/10.1063/1.869323.

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7

Zhang, Weihua, and Bernd Michaelis. "Shape Control with Karhunen-Loéve-Decomposition: Theory and Experimental Results." Journal of Intelligent Material Systems and Structures 14, no. 7 (July 2003): 415–22. http://dx.doi.org/10.1177/1045389x03034059.

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8

Suvorova, Sofia, and Jim Schroeder. "Automated Target Recognition Using the Karhunen–Loéve Transform with Invariance." Digital Signal Processing 12, no. 2-3 (January 2002): 295–306. http://dx.doi.org/10.1006/dspr.2002.0445.

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9

Sung, H. J., and R. J. Adrian. "Karhunen–Loéve expansion of the derivative of an inhomogeneous process." Physics of Fluids 6, no. 6 (June 1994): 2233–35. http://dx.doi.org/10.1063/1.868173.

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10

Kale, Mehmet Cemil. "A general biorthogonal wavelet based on Karhunen–Loéve transform approximation." Signal, Image and Video Processing 10, no. 4 (January 11, 2016): 791–94. http://dx.doi.org/10.1007/s11760-016-0860-2.

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11

Kale, Mehmet Cemil, Gizem Atac, and Ömer Nezih Gerek. "A biorthogonal wavelet design technique using Karhunen–Loéve transform approximation." Digital Signal Processing 51 (April 2016): 202–22. http://dx.doi.org/10.1016/j.dsp.2015.06.002.

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12

Gharbi, Ridha B., Fuad Qasem, and Nejib Smaoui. "Characterizing Miscible Displacements in Heterogeneous Reservoirs Using the Karhunen–Loéve Decomposition." Petroleum Science and Technology 21, no. 5-6 (January 6, 2003): 747–76. http://dx.doi.org/10.1081/lft-120017448.

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13

Atanacković, Teodor, Stevan Pilipović, and Dora Seleši. "Wave propagation dynamics in a fractional Zener model with stochastic excitation." Fractional Calculus and Applied Analysis 23, no. 6 (December 1, 2020): 1570–604. http://dx.doi.org/10.1515/fca-2020-0079.

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Abstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loéve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.

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14

Cevenini, G., G. Borzelli, P. Rubegni, M. R. Massai, L. Andreassi, and P. Barbini. "Modified Karhunen-Loéve expansion for evaluating skin-colour-associated melanoma risk factors." Computers in Biology and Medicine 30, no. 4 (July 2000): 171–89. http://dx.doi.org/10.1016/s0010-4825(00)00008-1.

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15

Webber, G. A., R. A. Handler, and L. Sirovich. "Energy dynamics in a turbulent channel flow using the Karhunen-Loéve approach." International Journal for Numerical Methods in Fluids 40, no. 11 (November 20, 2002): 1381–400. http://dx.doi.org/10.1002/fld.414.

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16

Spanos, Pol D., Michael Beer, and John Red-Horse. "Karhunen–Loéve Expansion of Stochastic Processes with a Modified Exponential Covariance Kernel." Journal of Engineering Mechanics 133, no. 7 (July 2007): 773–79. http://dx.doi.org/10.1061/(asce)0733-9399(2007)133:7(773).

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17

Fontanella, Lara, Luigi Ippoliti, and Arcangelo Merla. "Multiresolution Karhunen Loéve analysis of galvanic skin response for psycho-physiological studies." Metrika 75, no. 3 (September 14, 2010): 287–309. http://dx.doi.org/10.1007/s00184-010-0327-3.

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18

CONNELL, R. J., D. KULASIRI, J. LENNON, and D. F. HILL. "COMPUTATIONAL MODELING OF TURBULENT VELOCITY STRUCTURES FOR AN OPEN CHANNEL FLOW USING KARHUNEN–LOÉVE EXPANSION." International Journal of Computational Methods 04, no. 03 (September 2007): 493–519. http://dx.doi.org/10.1142/s0219876207001242.

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This paper develops an analytical two-part covariance kernel from velocity correlations across a two-dimensional (vertical and flow directions) Particle Image Velocimetry (PIV) flow field. This will form the basis of a model of wave action in flood water that includes the underlying turbulence velocity field using Karhunen–Loéve (KL) expansion. The PIV data was from the supercritical flow area immediately upstream of an undular hydraulic jump. This paper derives a one-dimensional solution for the associated integral equations. It also discusses a relationship between the two parts of the kernel and the turbulent production and turbulent dissipation.

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19

GRAUPE, DANIEL, and ZEHUAN LIANG. "Karhunen-Loéve expansions for limb-function discrimination in EMG-controlled stimulation for paraplegics." International Journal of Systems Science 18, no. 1 (January 1987): 131–39. http://dx.doi.org/10.1080/00207728708963954.

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20

Reed, Richard L., and Jeremy A. Roberts. "An energy basis for response matrix methods based on the Karhunen–Loéve Transform." Annals of Nuclear Energy 78 (April 2015): 70–80. http://dx.doi.org/10.1016/j.anucene.2014.12.016.

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21

NOJIMA, Nobuoto, and Masumitsu KUSE. "Mode Decomposition and Synthesis of Temporal Characteristics of Earthquake Motions using Karhunen-Loéve Expansion." Journal of JAEE 17, no. 5 (2017): 5_21–5_37. http://dx.doi.org/10.5610/jaee.17.5_21.

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22

Lin, Jyh-Woei. "Ionospheric Total Electron Content (TEC) Anomalies Associated with Earthquakes through Karhunen-Loéve Transform (KLT)." Terrestrial, Atmospheric and Oceanic Sciences 21, no. 2 (2010): 253. http://dx.doi.org/10.3319/tao.2009.06.11.01(t).

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23

Smaoui, Nejib, and Matar Ibrahim Matar. "Classification Of Human Faces Using Karhunen-LoÉve Decomposition And Radial Basis Function Neural Networks." International Journal of Computer Mathematics 80, no. 3 (March 2003): 325–45. http://dx.doi.org/10.1080/0020716021000014196.

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24

Masoudi, Ramin, and John McPhee. "Application of Karhunen–Loéve decomposition and piecewise linearization to a physics-based battery model." Electrochimica Acta 365 (January 2021): 137093. http://dx.doi.org/10.1016/j.electacta.2020.137093.

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25

Kitterrød, Nils-Otto, and Lars Gottschalk. "Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging." Stochastic Hydrology and Hydraulics 11, no. 6 (December 1997): 459–82. http://dx.doi.org/10.1007/bf02428429.

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26

NOJIMA, Nobuoto, and Masumitsu KUSE. "MODAL DECOMPOSITION AND SYNTHESIS OF RESPONSE SPECTRA USING KARHUNEN-LOÉVE TRANSFORM AND DISCRETE COSINE TRANSFORM." Journal of Japan Society of Civil Engineers, Ser. A1 (Structural Engineering & Earthquake Engineering (SE/EE)) 74, no. 4 (2018): I_237—I_248. http://dx.doi.org/10.2208/jscejseee.74.i_237.

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27

Park, S., M. M. R. Williams, A. K. Prinja, and M. D. Eaton. "Modelling non-Gaussian uncertainties and the Karhunen–Loéve expansion within the context of polynomial chaos." Annals of Nuclear Energy 76 (February 2015): 146–65. http://dx.doi.org/10.1016/j.anucene.2014.09.047.

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28

Crevillén-García, D., and H. Power. "Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media." Royal Society Open Science 4, no. 8 (August 2017): 170203. http://dx.doi.org/10.1098/rsos.170203.

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In this study, we apply four Monte Carlo simulation methods, namely, Monte Carlo, quasi-Monte Carlo, multilevel Monte Carlo and multilevel quasi-Monte Carlo to the problem of uncertainty quantification in the estimation of the average travel time during the transport of particles through random heterogeneous porous media. We apply the four methodologies to a model problem where the only input parameter, the hydraulic conductivity, is modelled as a log-Gaussian random field by using direct Karhunen–Loéve decompositions. The random terms in such expansions represent the coefficients in the equations. Numerical calculations demonstrating the effectiveness of each of the methods are presented. A comparison of the computational cost incurred by each of the methods for three different tolerances is provided. The accuracy of the approaches is quantified via the mean square error.

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29

Smaoui, Nejib, and Ridha B. Gharbi. "Using Karhunen–Loéve decomposition and artificial neural network to model miscible fluid displacement in porous media." Applied Mathematical Modelling 24, no. 8-9 (July 2000): 657–75. http://dx.doi.org/10.1016/s0307-904x(00)00008-1.

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30

Liu, Xiang, Ping Xiang, Lizhong Jiang, Zhipeng Lai, Tuo Zhou, and Yuanjun Chen. "Stochastic Analysis of Train–Bridge System Using the Karhunen–Loéve Expansion and the Point Estimate Method." International Journal of Structural Stability and Dynamics 20, no. 02 (January 13, 2020): 2050025. http://dx.doi.org/10.1142/s021945542050025x.

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This paper presents a new method for analyzing the dynamic behavior of train–bridge systems with random rail irregularity aimed at its simplicity, efficiency and accuracy. A vertical train–bridge system is considered, in which the bridge is regarded as a series of simply supported beams, and the train is regarded as a multibody system with suspensions. The Karhunen–Loéve expansion (KLE) is used to simulate the stochastic vertical rail irregularities, and the mean and standard deviation of the system response are calculated by the point estimate method (PEM), based on the Gaussian integration and the dimension reduction method. The proposed KLE–PEM method, which combines the key features of the KLE and PEM, is validated by comparing the results obtained with existing ones. The Monte Carlo simulation (MCS) is used to verify the rationality of the results obtained by the KLE–PEM approach. The results show that the KLE–PEM approach can accurately calculate the response of the vertical train–bridge interaction system with random irregularity. This paper further discusses the responses of the train and bridge system with different speeds for the train.

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31

Mitschang, L., C. Cieslar, T. A. Holak, and H. Oschkinat. "Application of the Karhunen-Loéve transformation to the suppression of undesired resonances in three-dimensional NMR." Journal of Magnetic Resonance (1969) 92, no. 1 (March 1991): 208–17. http://dx.doi.org/10.1016/0022-2364(91)90264-t.

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32

Mathew, Tittu Varghese, Lars Beex, Stéphane PA Bordas, and Sundararajan Natarajan. "A Stochastic Galerkin Cell-based Smoothed Finite Element Method (SGCS–FEM)." International Journal of Computational Methods 17, no. 08 (July 25, 2019): 1950054. http://dx.doi.org/10.1142/s0219876219500543.

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In this paper, the cell-based smoothed finite element method is extended to solve stochastic partial differential equations with uncertain input parameters. The spatial field of Young’s Modulus and the corresponding stochastic results are represented by Karhunen-Loéve expansion and polynomial chaos expansion, respectively. Young’s Modulus of structure is considered to be random for stochastic static as well as free vibration problems. Mathematical expressions and the solution procedure are articulated in detail to evaluate the statistical characteristics of responses in terms of the static displacements and the free vibration frequencies. The feasibility and the effectiveness of the proposed SGCS–FEM method in terms of accuracy and lower demand on the mesh size in the solution domain over that of conventional FEM for stochastic problems are demonstrated by carefully chosen numerical examples. From the numerical study, it is inferred that the proposed framework yields accurate results.

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33

Jiang, Lizhong, Xiang Liu, Tuo Zhou, Ping Xiang, Yuanjun Chen, Yulin Feng, Zhipeng Lai, and Shanshan Cao. "Application of KLE-PEM for Random Dynamic Analysis of Nonlinear Train-Track-Bridge System." Shock and Vibration 2020 (December 28, 2020): 1–10. http://dx.doi.org/10.1155/2020/8886737.

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A nonlinear train-track-bridge system (TTBS) considering the random track irregularity and mass of train is discussed. Based on the Karhunen–Loéve theory, the track irregularity is expressed and input into the TTBS, and the result of random response is calculated using the point estimation method. Two cases are used to compare and validate the applicability of the proposed method, which show that the proposed method has a high precision and efficiency. Then, taking a 7-span bridge and a high-speed train as an example, the calculation results of random response of the nonlinear and linear wheel-rail model are compared, and the results show that for the bridge and rail response, the nonlinear and linear models are almost the same. Finally, comparing the calculated probability distribution results with the test results, it shows that the method can be applied to the prediction of actual response range.

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34

Kumaraian, Mohitrajhu Lingan, Jayamanideep Rebbagondla, Tittu Varghese Mathew, and Sundararajan Natarajan. "Stochastic Vibration Analysis of Functionally Graded Plates with Material Randomness Using Cell-Based Smoothed Discrete Shear Gap Method." International Journal of Structural Stability and Dynamics 19, no. 04 (April 2019): 1950037. http://dx.doi.org/10.1142/s0219455419500378.

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A cell-based smoothed finite element method with discrete shear gap technique is used to study the stochastic free vibration behavior of functionally graded plates with material uncertainty. The plate kinematics is based on the first-order shear deformation theory and the effective material properties are estimated by simple rule of mixtures. The input random field is represented by the Karhunen–Loéve expansion and the polynomial chaos expansion is used to represent the stochastic output response. The accuracy of the proposed approach in terms of the first- and the second-order statistical moments are demonstrated by comparing the results with the Monte Carlo Simulations. A systematic parametric study is carried out to bring out the influence of the material gradient index, the plate aspect ratio and the skewness of the plate on the stochastic global response of functionally graded plates. It is inferred that all the considered parameters significantly influence the statistical moments of the first fundamental mode.

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35

Smaoui, Nejib, and Ali A. Garrouch. "A new approach combining Karhunen-Loéve decomposition and artificial neural network for estimating tight gas sand permeability." Journal of Petroleum Science and Engineering 18, no. 1-2 (July 1997): 101–12. http://dx.doi.org/10.1016/s0920-4105(96)00077-0.

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36

Lin, D. C. "Characterization of low-energy mode vibrations in chaos using entropy balance versus the amplitude-based Karhunen-Loéve expansion." Physical Review E 52, no. 3 (September 1, 1995): 2322–29. http://dx.doi.org/10.1103/physreve.52.2322.

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37

Sun, Baichun, Andrej Bóna, Binzhong Zhou, Andrew King, Christian Dupuis, and Anton Kepic. "Drill-rig noise suppression using the Karhunen-Loéve transform for seismic-while-drilling experiment at Brukunga, South Australia." Exploration Geophysics 47, no. 1 (March 2016): 44–57. http://dx.doi.org/10.1071/eg14086.

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38

Smaoui, Nejib, Mohamed Zribi, and Taha Elmokadem. "A novel secure communication scheme based on the Karhunen–Loéve decomposition and the synchronization of hyperchaotic Lü systems." Nonlinear Dynamics 90, no. 1 (July 19, 2017): 271–85. http://dx.doi.org/10.1007/s11071-017-3660-5.

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39

Rajaee, Mojtaba, Sture K. F. Karlsson, and Lawrence Sirovich. "Low-dimensional description of free-shear-flow coherent structures and their dynamical behaviour." Journal of Fluid Mechanics 258 (January 10, 1994): 1–29. http://dx.doi.org/10.1017/s0022112094003228.

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The snapshot form of the Karhunen-Loéve (K–L) expansion has been applied to twodimensional, two-component hot-wire data from the region of a weakly pertubed free shear layer that includes the first pairing process. Low-level external perturbation was provided by a loudspeaker driven by a computer-generated signal composed of two sine waves of equal amplitude at the frequencies of the naturally developing fundamental instability wave and its first subharmonic, separated by a controllable initial phase angle difference. It was found that a large fraction of the fluctuation energy is carried by the first few modes. A low-dimensional empirical eigenfunction space is obtained which describes the shear-flow coherent structures well. Galerkin projection of the Navier-Stokes equations onto this basis set of principal eigenfunction modes results in a low-order system of dynamical equations, and solution of this system of equations describes the dynamics of the coherent structures associated with eigenfunctions. Finally the simulation, as obtained from the system of dynamical equations, is shown to compare reasonably well with the experiments.

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40

Shalimova, I. A., and K. K. Sabelfeld. "Stochastic Analysis of an Elastic 3D Half-Space Respond to Random Boundary Displacements: Exact Results and Karhunen-Loéve Expansion." Journal of Statistical Physics 135, no. 3 (April 17, 2009): 547–69. http://dx.doi.org/10.1007/s10955-009-9737-x.

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41

Rempfer, Dietmar, and Hermann F. Fasel. "Evolution of three-dimensional coherent structures in a flat-plate boundary layer." Journal of Fluid Mechanics 260 (February 10, 1994): 351–75. http://dx.doi.org/10.1017/s0022112094003551.

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Using a data base generated by a numerical simulation, the three-dimensional coherent structures of a transitional, spatially evolving boundary layer are determined and their spatio-temporal behaviour is investigated in detail. The coherent structures are calculated by the proper orthogonal decomposition method (POD), which leads to an expansion of the flow field variables into Karhunen-Loéve eigenfunctions. It is shown that the dynamical coherent structures of the flat-plate boundary layer can be described by pairs of eigenfunctions that contain complete information on the spatial evolution of the structures. It is further demonstrated that first-order coherent structures determined by POD correspond to structures that are observed in experiments. In the region of the boundary layer where the spike signals of transition occur, higher-order coherent structures also play an essential role. By considering these higher-order structures as well as their dynamical behaviour in time, a compact description of the flow phenomena in the boundary layer can be obtained. The description of the events occurring at the spike stages of the transitional boundary layer shows, from a coherent structures point of view, striking similarities to the bursting event of fully turbulent boundary layers.

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42

Smaoui, N., M. Zribi, and T. Elmokadem. "The Secure Transmission of Videos Using the Karhunen-Loéve (K-L) Decomposition and the Synchronization of the Unified Chaotic System with the Hyperchaotic Chen System." Mathematical Problems in Engineering 2018 (October 31, 2018): 1–15. http://dx.doi.org/10.1155/2018/6382532.

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A unique secure communication scheme that can be used for the transmission of gray-scale and color videos is presented in this paper. The proposed scheme is developed by using the Karhunen-Loéve (K-L) decomposition and the synchronization of the unified chaotic system with the hyperchaotic Chen system. First, the gray-scale or color video is represented by a set of N frames. In order to reduce the data, the K-L decomposition is used to come up with data coefficients and eigenfunctions that optimally obtain the crux of the N frames. Using only the most energetic eigenfunctions to approximate the original frames results in computational savings. The data coefficients corresponding to the most energetic eigenfunctions are encrypted and transmitted using a master system composed of a combination of the unified chaotic system and the hyperchaotic Chen system. At the receiver end, these coefficients are recovered and a controller of the sliding mode type is utilized forcing the master and slave systems to synchronize. Simulation results illustrate how the proposed control law is able to synchronize the master and the slave systems. In addition, a demonstration of the recovery of the original frames using the decrypted data coefficients along with the eigenfunctions of the frame is provided. The presented simulations indicate that the proposed scheme results in an excellent performance.

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43

Lu, Zhiming, and Dongxiao Zhang. "Accurate, Efficient Quantification of Uncertainty for Flow in Heterogeneous Reservoirs Using the KLME Approach." SPE Journal 11, no. 02 (June 1, 2006): 239–47. http://dx.doi.org/10.2118/93452-pa.

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Summary Accurate modeling of flow in oil/gas reservoirs requires a detailed description of reservoir properties such as permeability and porosity. However, such reservoirs are inherently heterogeneous and exhibit a high degree of spatial variability in medium properties. Significant spatial heterogeneity and a limited number of measurements lead to uncertainty in characterization of reservoir properties and thus to uncertainty in predicting flow in the reservoirs. As a result, the equations that govern flow in such reservoirs are treated as stochastic partial differential equations. The current industrial practice is to tackle the problem of uncertainty quantification by Monte Carlo simulations (MCS). This entails generating a large number of equally likely random realizations of the reservoir fields with parameter statistics derived from sampling, solving deterministic flow equations for each realization, and post-processing the results over all realizations to obtain sample moments of the solution. This approach has the advantages of applying to a broad range of both linear and nonlinear flow problems, but it has a number of potential drawbacks. To properly resolve high-frequency space-time fluctuations in random parameters, it is necessary to employ fine numerical grids in space-time. Therefore, the computational effort for each realization is usually large, especially for large-scale reservoirs. As a result, a detailed assessment of the uncertainty associated with flow-performance predictions is rarely performed. In this work, we develop an accurate yet efficient approach for solving flow problems in heterogeneous reservoirs. We do so by obtaining higher-order solutions of the prediction and the associated uncertainty of reservoir flow quantities using the moment-equation approach based on Karhunen-Loéve decomposition (KLME). The KLME approach is developed on the basis of the Karhunen-Loéve (KL) decomposition, polynomial expansion, and perturbation methods. We conduct MCS and compare these results against different orders of approximations from the KLME method. The 3D computational examples demonstrate that this KLME method is computationally more efficient than both Monte Carlo simulations and the conventional moment-equation method. The KLME approach allows us to evaluate higher-order terms that are needed for highly heterogeneous reservoirs. In addition, like the Monte Carlo method, the KLME approach can be implemented with existing simulators in a straightforward manner, and they are inherently parallel. The efficiency of the KLME method makes it possible to simulate fluid flow in large-scale heterogeneous reservoirs. Introduction Owing to the heterogeneity of geological formations and the incomplete knowledge of medium properties, the medium properties may be treated as random functions, and the equations describing flow and transport in these formations become stochastic. Stochastic approaches to flow and transport in heterogeneous porous media have been extensively studied in the last 2 decades, and many stochastic models have been developed (Dagan 1989; Gelhar 1993; Zhang 2002). Two commonly used approaches for solving stochastic equations are MCS and the moment-equation method. A major disadvantage of the Monte Carlo method, among others, is the requirement for large computational efforts. An alternative to MCS is an approach based on moment equations, the essence of which is to derive a system of deterministic partial differential equations governing the statistical moments [usually the first two moments (i.e., mean and covariance)], and then solve them analytically or numerically.

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44

Senseman, David M., and Kay A. Robbins. "High-Speed VSD Imaging of Visually Evoked Cortical Waves: Decomposition Into Intra- and Intercortical Wave Motions." Journal of Neurophysiology 87, no. 3 (March 1, 2002): 1499–514. http://dx.doi.org/10.1152/jn.00475.2001.

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In the pond turtle, Pseudemys scripta elegans, visually evoked cortical waves propagate at different velocities within the primary visual area compared with waves that pass into the secondary visual area. In an effort to separate intra- and intercortical wave motions, movies of visually evoked cortical waves recorded by high-speed voltage-sensitive dye (VSD) imaging were subjected to Karhunen-Loéve (KL) decomposition. This procedure decomposes the VSD movies into a series of basis images that capture different spatial patterns of coherent activity. Most of the energy of the compound wave motion (>95%) was captured by the three largest basis images, M1,1 , M1,2 , and M2,1 . Based on visual comparison with maps of wave front latency, KL basis image M1,2 appears to capture the spread of depolarization within the primary visual area, whereas KL basis image M2,1 appears to capture the spread of depolarization from the primary into the secondary visual area. The contribution of different basis images to the intra- and intercortical wave motions was tested by reconstructing the response using different combinations of KL basis images. Only KL basis images M1,1 and M1,2 were needed to reconstruct intracortical wave motion, while basis images M1,1 and M2,1 were needed to reconstruct intercortical wave motion. It was also found that the direction and speed of wave propagation could be deduced by visual inspection of the basis image projections on to the original data set. The relative advantage of KL decomposition for the analysis of complex wave motions captured by VSD imaging is discussed.

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Vogel, Annika, and Hendrik Elbern. "Efficient ensemble generation for uncertain correlated parameters in atmospheric chemical models: a case study for biogenic emissions from EURAD-IM version 5." Geoscientific Model Development 14, no. 9 (September 10, 2021): 5583–605. http://dx.doi.org/10.5194/gmd-14-5583-2021.

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Abstract:

Abstract. Atmospheric chemical forecasts heavily rely on various model parameters, which are often insufficiently known, such as emission rates and deposition velocities. However, a reliable estimation of resulting uncertainties with an ensemble of forecasts is impaired by the high dimensionality of the system. This study presents a novel approach, which substitutes the problem into a low-dimensional subspace spanned by the leading uncertainties. It is based on the idea that the forecast model acts as a dynamical system inducing multivariate correlations of model uncertainties. This enables an efficient perturbation of high-dimensional model parameters according to their leading coupled uncertainties. The specific algorithm presented in this study is designed for parameters that depend on local environmental conditions and consists of three major steps: (1) an efficient assessment of various sources of model uncertainties spanned by independent sensitivities, (2) an efficient extraction of leading coupled uncertainties using eigenmode decomposition, and (3) an efficient generation of perturbations for high-dimensional parameter fields by the Karhunen–Loéve expansion. Due to their perceived simulation challenge, the method has been applied to biogenic emissions of five trace gases, considering state-dependent sensitivities to local atmospheric and terrestrial conditions. Rapidly decreasing eigenvalues state that highly correlated uncertainties of regional biogenic emissions can be represented by a low number of dominant components. Depending on the required level of detail, leading parameter uncertainties with dimensions of 𝒪(106) can be represented by a low number of about 10 ensemble members. This demonstrates the suitability of the algorithm for efficient ensemble generation for high-dimensional atmospheric chemical parameters.

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Dogan, Muzaffer, and Omer N. Gerek. "A Signal-Specific QMF Bank Design Technique Using Karhunen-Loéve Transform Approximation." EURASIP Journal on Advances in Signal Processing 2011, no. 1 (January 10, 2011). http://dx.doi.org/10.1155/2011/753572.

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Liu, Xiang, Lizhong Jiang, Ping Xiang, Wangbao Zhou, Zhipeng Lai, and Yulin Feng. "Stochastic finite element method based on point estimate and Karhunen–Loéve expansion." Archive of Applied Mechanics, January 4, 2021. http://dx.doi.org/10.1007/s00419-020-01819-8.

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"Karhunen-Loéve expansion of Brownian motion for approximate solutions of linear stochastic differential models using Picard iteration." Journal of Mathematical and Computational Science, 2020. http://dx.doi.org/10.28919/jmcs/4538.

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