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Volumn 84, Issue 4, 2011, Pages

Noise can speed convergence in Markov chains

Author keywords

[No Author keywords available]

Indexed keywords

ABSORBING STATE; BIRTH-DEATH PROCESS; BLIND ALGORITHMS; CHEMICAL REACTION NETWORKS; CONVERGENCE RATES; CONVERGENCE TO EQUILIBRIUM; DIFFUSION MODEL; EHRENFEST; FASTER CONVERGENCE; FINITE-STATE; MARKOV CHAIN; MARKOV MODEL; POPULATION GENETICS; STATE DENSITIES; STATE INFORMATION; STATE SPACE; STEADY STATE; SYSTEM STATE; TIME CYCLES; WRIGHT-FISHER MODELS; ZEOLITE CRYSTALLIZATION;

EID: 80054851884     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.041112     Document Type: Article
Times cited : (27)

References (101)
  • 3
    • 51449124184 scopus 로고    scopus 로고
    • Viking, New York
    • B. Kosko, Noise (Viking, New York, 2006).
    • (2006) Noise
    • Kosko, B.1
  • 4
    • 0037066263 scopus 로고    scopus 로고
    • CPCHFT 1439-4235 10.1002/1439-7641(20020315)3:3<285::AID-CPHC285>3. 0.CO;2-A
    • P. Hänggi, Chem. Phys. Chem. CPCHFT 1439-4235 10.1002/1439- 7641(20020315)3:3<285::AID-CPHC285>3.0.CO;2-A 3, 285 (2002).
    • (2002) Chem. Phys. Chem. , vol.3 , pp. 285
    • Hänggi, P.1
  • 6
    • 70649099292 scopus 로고    scopus 로고
    • CPCHFT 1751-8113 10.1088/1751-8113/42/46/465309
    • M. M. Wilde and B. Kosko, J. Phys. A: Math. Theor. CPCHFT 1751-8113 10.1088/1751-8113/42/46/465309 42, 465309 (2009).
    • (2009) J. Phys. A: Math. Theor. , vol.42 , pp. 465309
    • Wilde, M.M.1    Kosko, B.2
  • 7
    • 33751546177 scopus 로고    scopus 로고
    • Noise-enhanced detection of subthreshold signals with carbon nanotubes
    • DOI 10.1109/TNANO.2006.883476
    • I. Lee, X. Liu, C. Zhou, and B. Kosko, IEEE Trans. Nanotechnol. CPCHFT 1536-125X 10.1109/TNANO.2006.883476 5, 613 (2006). (Pubitemid 44837042)
    • (2006) IEEE Transactions on Nanotechnology , vol.5 , Issue.6 , pp. 613-627
    • Lee, I.1    Liu, X.2    Zhou, C.3    Kosko, B.4
  • 8
    • 68149181688 scopus 로고    scopus 로고
    • NNETEB 0893-6080 10.1016/j.neunet.2009.06.044
    • A. Patel and B. Kosko, Neural Netw. NNETEB 0893-6080 10.1016/j.neunet. 2009.06.044 22, 697 (2009).
    • (2009) Neural Netw. , vol.22 , pp. 697
    • Patel, A.1    Kosko, B.2
  • 9
    • 42749099227 scopus 로고    scopus 로고
    • PLEEE8 1539-3755 10.1103/PhysRevE.70.031911
    • B. Kosko and S. Mitaim, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.70.031911 70, 031911 (2004).
    • (2004) Phys. Rev. e , vol.70 , pp. 031911
    • Kosko, B.1    Mitaim, S.2
  • 10
    • 65649144223 scopus 로고    scopus 로고
    • ITPRED 1053-587X 10.1109/TSP.2009.2012893
    • A. Patel and B. Kosko, IEEE Trans. Signal Process. ITPRED 1053-587X 10.1109/TSP.2009.2012893 57, 1655 (2009).
    • (2009) IEEE Trans. Signal Process. , vol.57 , pp. 1655
    • Patel, A.1    Kosko, B.2
  • 11
    • 57749092657 scopus 로고    scopus 로고
    • ITNNEP 1045-9227 10.1109/TNN.2008.2005610
    • A. Patel and B. Kosko, IEEE Trans. Neural Netw. ITNNEP 1045-9227 10.1109/TNN.2008.2005610 19, 1993 (2008).
    • (2008) IEEE Trans. Neural Netw. , vol.19 , pp. 1993
    • Patel, A.1    Kosko, B.2
  • 12
    • 72149134900 scopus 로고    scopus 로고
    • ITNNEP 1045-9227 10.1109/TNN.2009.2033183
    • D. Applebaum, IEEE Trans. Neural Netw. ITNNEP 1045-9227 10.1109/TNN.2009.2033183 20, 1993 (2009).
    • (2009) IEEE Trans. Neural Netw. , vol.20 , pp. 1993
    • Applebaum, D.1
  • 13
    • 0001016831 scopus 로고    scopus 로고
    • PLEEE8 1539-3755 10.1103/PhysRevE.54.R2185
    • A. R. Bulsara and A. Zador, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.54.R2185 54, R2185 (1996).
    • (1996) Phys. Rev. e , vol.54 , pp. 2185
    • Bulsara, A.R.1    Zador, A.2
  • 15
    • 13444306614 scopus 로고    scopus 로고
    • Constructive role of noise in signal detection from parallel arrays of quantizers
    • DOI 10.1016/j.sigpro.2004.11.002, PII S0165168404003032
    • D. Rousseau and F. Chapeau-Blondeau, Signal Process. SPRODR 0165-1684 10.1016/j.sigpro.2004.11.002 85, 571 (2005). (Pubitemid 40206001)
    • (2005) Signal Processing , vol.85 , Issue.3 , pp. 571-580
    • Rousseau, D.1    Chapeau-Blondeau, F.2
  • 16
    • 78149439930 scopus 로고    scopus 로고
    • IESPEJ 1070-9908 10.1109/LSP.2010.2059376
    • A. Patel and B. Kosko, IEEE Signal Process. Lett. IESPEJ 1070-9908 10.1109/LSP.2010.2059376 17, 1005 (2010).
    • (2010) IEEE Signal Process. Lett. , vol.17 , pp. 1005
    • Patel, A.1    Kosko, B.2
  • 18
    • 0037410108 scopus 로고    scopus 로고
    • SPRODR 0165-1684 10.1016/S0165-1684(03)00039-2
    • A. A. Saha and G. V. Anand, Signal Process. SPRODR 0165-1684 10.1016/S0165-1684(03)00039-2 83, 1193 (2003).
    • (2003) Signal Process. , vol.83 , pp. 1193
    • Saha, A.A.1    Anand, G.V.2
  • 21
    • 9344219973 scopus 로고    scopus 로고
    • ITNNEP 1045-9227 10.1109/TNN.2004.826218
    • S. Mitaim and B. Kosko, IEEE Trans. Neural Netw. ITNNEP 1045-9227 10.1109/TNN.2004.826218 15, 1526 (2004).
    • (2004) IEEE Trans. Neural Netw. , vol.15 , pp. 1526
    • Mitaim, S.1    Kosko, B.2
  • 22
    • 27744437745 scopus 로고    scopus 로고
    • Stochastic resonance in noisy spiking retinal and sensory neuron models
    • DOI 10.1016/j.neunet.2005.06.031, PII S089360800500105X
    • A. Patel and B. Kosko, Neural Netw. NNETEB 0893-6080 10.1016/j.neunet. 2005.06.031 18, 467 (2005). (Pubitemid 43186565)
    • (2005) Neural Networks , vol.18 , Issue.5-6 , pp. 467-478
    • Patel, A.1    Kosko, B.2
  • 25
    • 0033877977 scopus 로고    scopus 로고
    • Can detectability be improved by adding noise?
    • DOI 10.1109/97.809511
    • S. Kay, IEEE Signal Process. Lett. IESPEJ 1070-9908 10.1109/97.809511 7, 8 (2000). (Pubitemid 30547939)
    • (2000) IEEE Signal Processing Letters , vol.7 , Issue.1 , pp. 8-10
    • Kay, S.1
  • 28
    • 0000576595 scopus 로고
    • ASTSC7 0090-5364 10.1214/aos/1176325750
    • L. Tierney, The Annals of Statistics ASTSC7 0090-5364 10.1214/aos/1176325750 22, 1701 (1994).
    • (1994) The Annals of Statistics , vol.22 , pp. 1701
    • Tierney, L.1
  • 30
    • 77956890234 scopus 로고
    • BIOKAX 0006-3444 10.1093/biomet/57.1.97
    • W. K. Hastings, Biometrika BIOKAX 0006-3444 10.1093/biomet/57.1.97 57, 97 (1970).
    • (1970) Biometrika , vol.57 , pp. 97
    • Hastings, W.K.1
  • 33
    • 49749093420 scopus 로고    scopus 로고
    • ASTSC7 0090-5364 10.1214/009053606000001389
    • Y. J. Sung and C. J. Geyer, The Annals of Statistics ASTSC7 0090-5364 10.1214/009053606000001389 35, 990 (2007).
    • (2007) The Annals of Statistics , vol.35 , pp. 990
    • Sung, Y.J.1    Geyer, C.J.2
  • 41
    • 32944457307 scopus 로고
    • PHYSAG 0031-8914 10.1016/S0031-8914(56)90001-5
    • M. J. Klein, Physica PHYSAG 0031-8914 10.1016/S0031-8914(56)90001-5 22, 569 (1956).
    • (1956) Physica , vol.22 , pp. 569
    • Klein, M.J.1
  • 42
    • 33748795802 scopus 로고    scopus 로고
    • Biological applications of the theory of birth-and-death processes
    • DOI 10.1093/bib/bbk006, The Comparative and Functional Genomics (BITS) Workshop
    • A. S. Novozhilov, G. P. Karev, and E. V. Koonin, Briefings in Bioinformatics PHYSAG 1467-5463 10.1093/bib/bbk006 7, 70 (2006). (Pubitemid 44404325)
    • (2006) Briefings in Bioinformatics , vol.7 , Issue.1 , pp. 70-85
    • Novozhilov, A.S.1    Karev, G.P.2    Koonin, E.V.3
  • 43
    • 0041378174 scopus 로고    scopus 로고
    • AAPBBD 0001-8678 10.1239/aap/1059486822
    • S. C. Kou and S. G. Kou, Adv. Appl. Probab. AAPBBD 0001-8678 10.1239/aap/1059486822 35, 641 (2003).
    • (2003) Adv. Appl. Probab. , vol.35 , pp. 641
    • Kou, S.C.1    Kou, S.G.2
  • 45
    • 52949105331 scopus 로고    scopus 로고
    • MCMOEG 0895-7177 10.1016/j.mcm.2008.05.043
    • D. Diermeier and J. A. V. Mieghem, Math. Comput. Modell. MCMOEG 0895-7177 10.1016/j.mcm.2008.05.043 48, 1497 (2008).
    • (2008) Math. Comput. Modell. , vol.48 , pp. 1497
    • Diermeier, D.1    Mieghem, J.A.V.2
  • 47
    • 33644679682 scopus 로고    scopus 로고
    • Distributions in the Ehrenfest process
    • DOI 10.1016/j.spl.2005.09.013, PII S0167715205003676
    • S. Balaji, H. M. Mahmoud, and O. Watanabe, Statistics & Probability Letters PHYADX 0167-7152 10.1016/j.spl.2005.09.013 76, 666 (2006). (Pubitemid 43329365)
    • (2006) Statistics and Probability Letters , vol.76 , Issue.7 , pp. 666-674
    • Balaji, S.1    Mahmoud, H.M.2    Watanabe, O.3
  • 48
    • 3042776908 scopus 로고    scopus 로고
    • PHYADX 0378-4371 10.1016/j.physa.2004.04.029
    • S. Prestipino, Physica A: Stat. Mech. Appl. PHYADX 0378-4371 10.1016/j.physa.2004.04.029 340, 373 (2004).
    • (2004) Physica A: Stat. Mech. Appl. , vol.340 , pp. 373
    • Prestipino, S.1
  • 49
    • 0001135725 scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.38.4794
    • K. Lindgren, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.38.4794 38, 4794 (1988).
    • (1988) Phys. Rev. A , vol.38 , pp. 4794
    • Lindgren, K.1
  • 50
    • 0030587992 scopus 로고    scopus 로고
    • A note on expected hitting times for birth and death chains
    • DOI 10.1016/0167-7152(95)00209-X
    • J. Palacios and P. Tetali, Statistics & Probability Letters PLRAAN 0167-7152 10.1016/0167-7152(95)00209-X 30, 119 (1996). (Pubitemid 126167193)
    • (1996) Statistics and Probability Letters , vol.30 , Issue.2 , pp. 119-125
    • Palacios, J.L.1    Tetali, P.2
  • 51
    • 0040867061 scopus 로고
    • JPRBAM 0021-9002 10.2307/3212199
    • S. Karlin and J. McGregor, J. Appl. Probab. JPRBAM 0021-9002 10.2307/3212199 2, 352 (1965).
    • (1965) J. Appl. Probab. , vol.2 , pp. 352
    • Karlin, S.1    McGregor, J.2
  • 52
    • 21344495840 scopus 로고
    • JPRBAM 0021-9002 10.2307/3214525
    • O. Krafft and M. Schaefer, J. Appl. Probab. JPRBAM 0021-9002 10.2307/3214525 30, 964 (1993).
    • (1993) J. Appl. Probab. , vol.30 , pp. 964
    • Krafft, O.1    Schaefer, M.2
  • 53
    • 21844525971 scopus 로고
    • JPRBAM 0021-9002 10.2307/3215318
    • H. Dette, J. Appl. Probab. JPRBAM 0021-9002 10.2307/3215318 31, 930 (1994).
    • (1994) J. Appl. Probab. , vol.31 , pp. 930
    • Dette, H.1
  • 57
    • 34547708461 scopus 로고    scopus 로고
    • Exact solution of the multi-allelic diffusion model
    • DOI 10.1016/j.mbs.2007.01.001, PII S002555640700003X
    • G. Baxter, R. Blythe, and A. McKane, Math. Biosci. MABIAR 0025-5564 10.1016/j.mbs.2007.01.001 209, 124 (2007). (Pubitemid 47238112)
    • (2007) Mathematical Biosciences , vol.209 , Issue.1 , pp. 124-170
    • Baxter, G.J.1    Blythe, R.A.2    McKane, A.J.3
  • 58
    • 60449102221 scopus 로고    scopus 로고
    • JTBIAP 0022-5193 10.1016/j.jtbi.2008.11.025
    • D. Waxman, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2008.11.025 257, 245 (2009).
    • (2009) J. Theor. Biol. , vol.257 , pp. 245
    • Waxman, D.1
  • 60
    • 77958602332 scopus 로고    scopus 로고
    • JTBIAP 0022-5193 10.1016/j.jtbi.2010.10.014
    • D. Waxman, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2010.10.014 269, 79 (2011).
    • (2011) J. Theor. Biol. , vol.269 , pp. 79
    • Waxman, D.1
  • 62
    • 0024856546 scopus 로고
    • CLCMAB 0009-8604 10.1346/CCMN.1989.0370506
    • D. B. Hawkins, Clays and Clay Minerals CLCMAB 0009-8604 10.1346/CCMN.1989.0370506 37, 433 (1989).
    • (1989) Clays and Clay Minerals , vol.37 , pp. 433
    • Hawkins, D.B.1
  • 63
    • 0022239876 scopus 로고
    • GCACAK 0016-7037 10.1016/0016-7037(85)90235-2
    • R. J. Donahoe and J. Liou, Geochim. Cosmochim. Acta GCACAK 0016-7037 10.1016/0016-7037(85)90235-2 49, 2349 (1985).
    • (1985) Geochim. Cosmochim. Acta , vol.49 , pp. 2349
    • Donahoe, R.J.1    Liou, J.2
  • 64
    • 20144374437 scopus 로고    scopus 로고
    • The hydrothermal synthesis of zeolites: Precursors, intermediates and reaction mechanism
    • DOI 10.1016/j.micromeso.2005.02.016, PII S1387181105000934
    • C. S. Cundy and P. A. Cox, Microporous Mesoporous Mater. MIMMFJ 1387-1811 10.1016/j.micromeso.2005.02.016 82, 1 (2005). (Pubitemid 40777912)
    • (2005) Microporous and Mesoporous Materials , vol.82 , Issue.1-2 , pp. 1-78
    • Cundy, C.S.1    Cox, P.A.2
  • 66
    • 33746662922 scopus 로고    scopus 로고
    • On imposing detailed balance in complex reaction mechanisms
    • DOI 10.1529/biophysj.105.071852
    • J. Yang, W. J. Bruno, W. S. Hlavacek, and J. E. Pearson, Biophys. J. BIOJAU 0006-3495 10.1529/biophysj.105.071852 91, 1136 (2006). (Pubitemid 44161945)
    • (2006) Biophysical Journal , vol.91 , Issue.3 , pp. 1136-1141
    • Yang, J.1    Bruno, W.J.2    Hlavacek, W.S.3    Pearson, J.E.4
  • 67
    • 34250334739 scopus 로고    scopus 로고
    • Dwell time symmetry in random walks and molecular motors
    • DOI 10.1529/biophysj.106.103044
    • M. Lindén and M. Wallin, Biophys. J. BIOJAU 0006-3495 10.1529/biophysj.106.103044 92, 3804 (2007). (Pubitemid 46910568)
    • (2007) Biophysical Journal , vol.92 , Issue.11 , pp. 3804-3816
    • Linden, M.1    Wallin, M.2
  • 70
    • 16344389735 scopus 로고    scopus 로고
    • Metropolis-Hastings from a stochastic population dynamics perspective
    • DOI 10.1016/S0167-9473(03)00118-X, PII S016794730300118X
    • E. Renshaw, Computational Statistics & Data Analysis CSDADW 0167-9473 10.1016/S0167-9473(03)00118-X 45, 765 (2004). (Pubitemid 38498426)
    • (2004) Computational Statistics and Data Analysis , vol.45 , Issue.4 , pp. 765-786
    • Renshaw, E.1
  • 73
    • 24344485633 scopus 로고    scopus 로고
    • in edited by J. Cejka and H. van Bekkum, Vol. 157 of Studies in Surface Science and Catalysis (Elsevier, New York
    • C. Colella, in Zeolites and Ordered Mesoporous Materials: Progress and Prospects, edited by, J. Cejka, and, H. van Bekkum, Vol. 157 of Studies in Surface Science and Catalysis (Elsevier, New York, 2005), pp. 13-40.
    • (2005) Zeolites and Ordered Mesoporous Materials: Progress and Prospects , pp. 13-40
    • Colella, C.1
  • 74
    • 77957019717 scopus 로고    scopus 로고
    • ACLSER 0169-1317 10.1016/j.clay.2010.07.015
    • Y. Yukselen-Aksoy, Applied Clay Science ACLSER 0169-1317 10.1016/j.clay.2010.07.015 50, 130 (2010).
    • (2010) Applied Clay Science , vol.50 , pp. 130
    • Yukselen-Aksoy, Y.1
  • 78
    • 72049113067 scopus 로고    scopus 로고
    • CMEJAJ 1385-8947 10.1016/j.cej.2009.10.029
    • S. Wang and Y. Peng, Chem. Eng. J. CMEJAJ 1385-8947 10.1016/j.cej.2009. 10.029 156, 11 (2010).
    • (2010) Chem. Eng. J. , vol.156 , pp. 11
    • Wang, S.1    Peng, Y.2
  • 79
    • 0242298223 scopus 로고    scopus 로고
    • Purification of metal electroplating waste waters using zeolites
    • DOI 10.1016/j.watres.2003.08.009
    • E. Álvarez Ayuso, A. García-Sánchez, and X. Querol, Water Res. WATRAG 0043-1354 10.1016/j.watres.2003.08.009 37, 4855 (2003). (Pubitemid 37353021)
    • (2003) Water Research , vol.37 , Issue.20 , pp. 4855-4862
    • Alvarez-Ayuso, E.1    Garcia-Sanchez, A.2    Querol, X.3
  • 82
    • 0033707966 scopus 로고    scopus 로고
    • SSIOD3 0167-2738 10.1016/S0167-2738(00)00632-9
    • J. Weitkamp, Solid State Ionics SSIOD3 0167-2738 10.1016/S0167-2738(00) 00632-9 131, 175 (2000).
    • (2000) Solid State Ionics , vol.131 , pp. 175
    • Weitkamp, J.1
  • 83
    • 22144449995 scopus 로고    scopus 로고
    • MIMMFJ 1387-1811 10.1016/j.micromeso.2005.01.039
    • M. Stöcker, Microporous Mesoporous Mater. MIMMFJ 1387-1811 10.1016/j.micromeso.2005.01.039 82, 257 (2005).
    • (2005) Microporous Mesoporous Mater. , vol.82 , pp. 257
    • Stöcker, M.1
  • 84
    • 0035923966 scopus 로고    scopus 로고
    • Early discoveries in zeolite chemistry and catalysis at Union Carbide, and follow-up in industrial catalysis
    • DOI 10.1016/S0926-860X(01)00840-7, PII S0926860X01008407
    • J. A. Rabo and M. W. Schoonover, Appl. Catal., A ACAGE4 0926-860X 10.1016/S0926-860X(01)00840-7 222, 261 (2001). (Pubitemid 34086253)
    • (2001) Applied Catalysis A: General , vol.222 , Issue.1-2 , pp. 261-275
    • Rabo, J.A.1    Schoonover, M.W.2
  • 85
    • 0040005163 scopus 로고
    • ZEOLD3 0144-2449 10.1016/0144-2449(86)90076-X
    • A. Bielanski and A. Malecka, Zeolites ZEOLD3 0144-2449 10.1016/0144-2449(86)90076-X 6, 249 (1986).
    • (1986) Zeolites , vol.6 , pp. 249
    • Bielanski, A.1    Malecka, A.2
  • 86
    • 0021350467 scopus 로고
    • ZEOLD3 0144-2449 10.1016/0144-2449(84)90026-5
    • A. Dyer and D. Keir, Zeolites ZEOLD3 0144-2449 10.1016/0144-2449(84) 90026-5 4, 215 (1984).
    • (1984) Zeolites , vol.4 , pp. 215
    • Dyer, A.1    Keir, D.2
  • 87
  • 91
    • 0345634210 scopus 로고    scopus 로고
    • MRBUAC 0025-5408 10.1016/S0025-5408(99)00052-5
    • H. Ghobarkar and O. Schäf, Mater. Res. Bull. MRBUAC 0025-5408 10.1016/S0025-5408(99)00052-5 34, 517 (1999).
    • (1999) Mater. Res. Bull. , vol.34 , pp. 517
    • Ghobarkar, H.1    Schäf, O.2
  • 94
    • 0042656263 scopus 로고    scopus 로고
    • JCPSA6 0021-9606 10.1063/1.477812
    • M. Falcioni and M. W. Deem, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.477812 110, 1754 (1999).
    • (1999) J. Chem. Phys. , vol.110 , pp. 1754
    • Falcioni, M.1    Deem, M.W.2
  • 96
    • 80054869216 scopus 로고    scopus 로고
    • U.S. Patent no. 6285999: Method for node ranking in a linked database (Sep. 4
    • L. Page, U.S. Patent no. 6285999: Method for node ranking in a linked database (Sep. 4, 2001).
    • (2001)
    • Page, L.1
  • 97
    • 80054869037 scopus 로고    scopus 로고
    • Google, Inc. annual report (Form 10-K) 2010
    • Google, Inc. annual report (Form 10-K) (2010).
  • 98
    • 80054863240 scopus 로고    scopus 로고
    • Google, Inc. annual report (Form 10-K) 2009
    • Google, Inc. annual report (Form 10-K) (2009).
  • 100
    • 58149347777 scopus 로고    scopus 로고
    • JCAMDI 0377-0427 10.1016/j.cam.2008.06.003
    • Y. Lin, X. Shi, and Y. Wei, J. Comput. Appl. Math. JCAMDI 0377-0427 10.1016/j.cam.2008.06.003 224, 702 (2009).
    • (2009) J. Comput. Appl. Math. , vol.224 , pp. 702
    • Lin, Y.1    Shi, X.2    Wei, Y.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.