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1

Nomura, Takanori, Katsunori Matsuoka, Yoshiki Ichioka, and Kazuyoshi Itoh. "Binary Fourier phase-only correlation." Optics Letters 15, no. 14 (July 15, 1990): 810. http://dx.doi.org/10.1364/ol.15.000810.

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2

Farbiash, N., and R. Steinitz. "Spin Correlation in Binary Systems." International Astronomical Union Colloquium 191 (August 2004): 15–19. http://dx.doi.org/10.1017/s0252921100008368.

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AbstractWe examine the correlation of projected rotational velocities in binary systems. It is an extension of previous work (Steinitz and Pyper, 1970; Levato, 1974). An enlarged data basis and new tests enable us to conclude that there is indeed correlation between the projected rotational velocities of components of binaries. In fact we suggest that spins are already correlated.
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3

Harju, Tero, and Dirk Nowotka. "Border correlation of binary words." Journal of Combinatorial Theory, Series A 108, no. 2 (November 2004): 331–41. http://dx.doi.org/10.1016/j.jcta.2004.07.009.

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4

Tsuneda, Akio. "Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences." Entropy 23, no. 10 (September 30, 2021): 1295. http://dx.doi.org/10.3390/e23101295.

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This paper discusses the auto-correlation functions of m-bit random numbers obtained from m chaotic binary sequences generated by one-dimensional nonlinear maps. First, we provide the theoretical auto-correlation function of an m-bit sequence obtained by m binary sequences that are assumed to be uncorrelated to each other. The auto-correlation function is expressed by a simple form using the auto-correlation functions of the binary sequences. This implies that the auto-correlation properties of the m-bit sequences can be easily controlled by the auto-correlation functions of the original binary sequences. In numerical experiments using a computer, we generated m-bit random sequences using some chaotic binary sequences with prescribed auto-correlations generated by one-dimensional chaotic maps. The numerical experiments show that the numerical auto-correlation values are almost equal to the corresponding theoretical ones, and we can generate m-bit sequences with a variety of auto-correlation properties. Furthermore, we also show that the distributions of the generated m-bit sequences are uniform if all of the original binary sequences are balanced (i.e., the probability of 1 (or 0) is equal to 1/2) and independent of one another.
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5

Biondi, Giulio, and Valentina Franzoni. "Discovering Correlation Indices for Link Prediction Using Differential Evolution." Mathematics 8, no. 11 (November 23, 2020): 2097. http://dx.doi.org/10.3390/math8112097.

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Binary correlation indices are crucial for forecasting and modelling tasks in different areas of scientific research. The setting of sound binary correlations and similarity measures is a long and mostly empirical interactive process, in which researchers start from experimental correlations in one domain, which usually prove to be effective in other similar fields, and then progressively evaluate and modify those correlations to adapt their predictive power to the specific characteristics of the domain under examination. In the research of prediction of links on complex networks, it has been found that no single correlation index can always obtain excellent results, even in similar domains. The research of domain-specific correlation indices or the adaptation of known ones is therefore a problem of critical concern. This paper presents a solution to the problem of setting new binary correlation indices that achieve efficient performances on specific network domains. The proposed solution is based on Differential Evolution, evolving the coefficient vectors of meta-correlations, structures that describe classes of binary similarity indices and subsume the most known correlation indices for link prediction. Experiments show that the proposed evolutionary approach always results in improved performances, and in some cases significantly enhanced, compared to the best correlation indices available in the link prediction literature, effectively exploring the correlation space and exploiting its self-adaptability to the given domain to improve over generations.
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6

Gyarmati, Katalin. "On the correlation of binary sequences." Studia Scientiarum Mathematicarum Hungarica 42, no. 1 (January 1, 2005): 79–93. http://dx.doi.org/10.1556/sscmath.42.2005.1.7.

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C. Mauduit conjectured that C2(E)CN3(EN) ?? Nc always holds with some constant 1/2< c = 1. This will be proved for c=2/3, more exactly if for a sequence EN =C {-1,+1}N we have C2 (EN) << N2/3 then C3 (EN) ?? N1/2. Indeed, a more general theorem is proved, involving correlation measures.
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7

Foor, Wesley E. "Binary optical correlation using pyramidal processing." Optical Engineering 33, no. 6 (June 1, 1994): 1838. http://dx.doi.org/10.1117/12.174453.

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8

Luke, H. D., and H. D. Schotten. "Odd-perfect, almost binary correlation sequences." IEEE Transactions on Aerospace and Electronic Systems 31, no. 1 (January 1995): 495–98. http://dx.doi.org/10.1109/7.366335.

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9

Ridout, Martin S., Clarice G. B. Demetrio, and David Firth. "Estimating Intraclass Correlation for Binary Data." Biometrics 55, no. 1 (March 1999): 137–48. http://dx.doi.org/10.1111/j.0006-341x.1999.00137.x.

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10

Luke, H. D. "Binary Alexis sequences with perfect correlation." IEEE Transactions on Communications 49, no. 6 (June 2001): 966–68. http://dx.doi.org/10.1109/26.930625.

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11

Ahlswede, R., J. Cassaigne, and A. Sárközy. "On the correlation of binary sequences." Discrete Applied Mathematics 156, no. 9 (May 2008): 1478–87. http://dx.doi.org/10.1016/j.dam.2006.11.021.

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12

Busboom, Axel, and Hans Dieter Lüke. "Hexagonal binary arrays with perfect correlation." Applied Optics 40, no. 23 (August 10, 2001): 3894. http://dx.doi.org/10.1364/ao.40.003894.

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13

Ahlswede, R., J. Cassaigne, and A. Sárközy. "On the correlation of binary sequences." Electronic Notes in Discrete Mathematics 21 (August 2005): 169–71. http://dx.doi.org/10.1016/j.endm.2005.07.017.

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14

Alam, M. S., and M. A. Karim. "Enhanced correlation discrimination using binary joint transform correlation with feedback." Microwave and Optical Technology Letters 5, no. 14 (December 20, 1992): 752–57. http://dx.doi.org/10.1002/mop.4650051415.

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15

Zucker, Shay. "TODCOR – Two-Dimensional Correlation." Proceedings of the International Astronomical Union 7, S282 (July 2011): 371–78. http://dx.doi.org/10.1017/s1743921311027852.

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AbstractTODCOR is a TwO-Dimensional CORrelation technique to measure radial velocities of the two components of a spectroscopic binary. Assuming the spectra of the two components are known, the technique correlates an observed binary spectrum against a combination of the two spectra with different shifts. TODCOR measures simultaneously the radial velocities of the two stars by finding the maximum correlation. The main use of the technique has been to turn single-lined binaries into double-lined systems. This helps to explore the binary mass-ratio distribution, especially the low-mass regime, where the secondaries are usually very faint and therefore hard to detect. The technique has been generalized to study multi-order spectra, and also triple- and quadruple-lined systems. It has several applications in studying extrasolar planets and in the future may even help to dynamically measure stellar masses of binaries through relativistc effects.
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16

Cavaglià, Marco, and Ashini Modi. "Two-Dimensional Correlation Function of Binary Black Hole Coalescences." Universe 6, no. 7 (July 7, 2020): 93. http://dx.doi.org/10.3390/universe6070093.

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We compute the two-dimensional correlation functions of the binary black hole coalescence detections in LIGO-Virgo’s first and second observation runs. The sky distribution of binary black hole coalescence events is tested for correlations at different angular scales by comparing the observed correlation function to two reference functions that are obtained from mock datasets of localization error regions uniformly distributed in the sky. No excess correlation at any angular scale is found. The power-law slope of the correlation function is estimated to be γ = 2.24 ± 0.33 at the three- σ confidence level, a value consistent with the measured distribution of galaxies.
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17

Knezevic-Stevanovic, Andjela, Goran Babic, Mirjana Kijevcanin, Slobodan Serbanovic, and Dusan Grozdanic. "Liquid mixture viscosities correlation with rational models." Journal of the Serbian Chemical Society 79, no. 3 (2014): 341–44. http://dx.doi.org/10.2298/jsc130610114k.

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In this paper twenty two selected rational correlation models for liquid mixture viscosities of organic compounds were tested on 219 binary sets of experimental data taken from literature. The binary sets contained 3675 experimental data points for 70 different compounds. The Dimitrov-Kamenski X, Dimitrov-Kamenski XII, and Dimitrov-Kamenski XIII models demonstrated the best correlative characteristics for binary mixtures with overall absolute average deviation less then 2%.
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18

Knezevic-Stevanovic, Andjela, Goran Babic, Mirjana Kijevcanin, Slobodan Serbanovic, and Dusan Grozdanic. "Correlation of the liquid mixture viscosities." Journal of the Serbian Chemical Society 77, no. 8 (2012): 1083–89. http://dx.doi.org/10.2298/jsc120127038k.

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In this paper forty two selected correlation models for liquid mixture viscosities of organic compounds were tested on 219 binary and 41 ternary sets of experimental data taken from literature. The binary sets contained 3675 experimental data points for 70 different compounds. The ternary sets contained 2879 experimental data points for 29 different compounds. The Heric I, Heric-Brewer II, and Krishnan-Laddha models demonstrated the best correlative characteristics for binary mixtures (overall absolute average deviation < 2%). The Heric I, Heric-Brewer II, Krishnan-Laddha and Heric II models demonstrated the best correlative characteristics for ternary mixtures (overall absolute average deviation < 3%).
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19

Rosta, L., O. Blashko, S. Borbély, A. Jákli, and L. Noirez. "Medium range correlation in decomposing binary systems." Acta Physica Hungarica 75, no. 1-4 (December 1994): 239–42. http://dx.doi.org/10.1007/bf03156580.

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20

Tang, X. H., P. Z. Fan, D. B. Li, and N. Suehiro. "Binary array set with zero correlation zone." Electronics Letters 37, no. 13 (2001): 841. http://dx.doi.org/10.1049/el:20010576.

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21

Javidi, Bahram, Chung-Jung Kuo, Ying Feng Chen, and Jacques E. Ludman. "Color object identification by monochromatic binary correlation." Applied Optics 27, no. 5 (March 1, 1988): 949. http://dx.doi.org/10.1364/ao.27.000949.

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22

Verrall, Steven C. "Windowed binary joint transform correlation with feedback." Optical Engineering 38, no. 1 (January 1, 1999): 76. http://dx.doi.org/10.1117/1.602266.

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23

Qunfang, Lei, and Hou Yu-Chun. "Correlation of viscosity of binary liquid mixtures." Fluid Phase Equilibria 154, no. 1 (January 1999): 153–63. http://dx.doi.org/10.1016/s0378-3812(98)00415-4.

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24

Duan, Lian, W. Nick Street, and Yanchi Liu. "Speeding up correlation search for binary data." Pattern Recognition Letters 34, no. 13 (October 2013): 1499–507. http://dx.doi.org/10.1016/j.patrec.2013.05.027.

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25

Turner, Mick, and Jim Austin. "Matching performance of binary correlation matrix memories." Neural Networks 10, no. 9 (December 1997): 1637–48. http://dx.doi.org/10.1016/s0893-6080(97)00059-2.

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26

Karch, Barry K. "Binary joint transform correlation of defocused images." Optical Engineering 32, no. 11 (1993): 2709. http://dx.doi.org/10.1117/12.148111.

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27

Gyarmati, Katalin, and Christian Mauduit. "On the correlation of binary sequences, II." Discrete Mathematics 312, no. 5 (March 2012): 811–18. http://dx.doi.org/10.1016/j.disc.2011.09.013.

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28

OKAMOTO, Yasuharu. "Bayesian estimation of correlation for binary data." Proceedings of the Annual Convention of the Japanese Psychological Association 77 (2013): 1AM—070–1AM—070. http://dx.doi.org/10.4992/pacjpa.77.0_1am-070.

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29

Downie, John D., and Max B. Reid. "Mapping considerations for optimal binary correlation filters." Applied Optics 29, no. 35 (December 10, 1990): 5235. http://dx.doi.org/10.1364/ao.29.005235.

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30

Shorr, L. M. "A correlation method for binary azeotrope data." Journal of Applied Chemistry 14, no. 9 (May 4, 2007): 376–82. http://dx.doi.org/10.1002/jctb.5010140903.

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31

Jonah, D. A., and S. R. M. Ellis. "Correlation of binary vapour-liquid equilibrium data." Journal of Applied Chemistry 15, no. 3 (May 4, 2007): 151–56. http://dx.doi.org/10.1002/jctb.5010150308.

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32

Vos, J., A. Bobrick, and M. Vučković. "Observed binary populations reflect the Galactic history." Astronomy & Astrophysics 641 (September 2020): A163. http://dx.doi.org/10.1051/0004-6361/201937195.

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Context. Wide hot subdwarf B (sdB) binaries with main-sequence companions are outcomes of stable mass transfer from evolved red giants. The orbits of these binaries show a strong correlation between their orbital periods and mass ratios. The origins of this correlation have, so far, been lacking a conclusive explanation. Aims. We aim to find a binary evolution model which can explain the observed correlation. Methods. Radii of evolved red giants, and hence the resulting orbital periods, strongly depend on their metallicity. We performed a small but statistically significant binary population synthesis study with the binary stellar evolution code MESA. We used a standard model for binary mass loss and a standard metallicity history of the Galaxy. The resulting sdB systems were selected based on the same criteria as was used in observations and then compared with the observed population. Results. We have achieved an excellent match to the observed period-mass ratio correlation without explicitly fine-tuning any parameters. Furthermore, our models produce a very good match to the observed period-metallicity correlation. We predict several new correlations, which link the observed sdB binaries to their progenitors, and a correlation between the orbital period, metallicity, and core mass for subdwarfs and young low-mass helium white dwarfs. We also predict that sdB binaries have distinct orbital properties depending on whether they formed in the Galactic bulge, thin or thick disc, or the halo. Conclusions. We demonstrate, for the first time, how the metallicity history of the Milky Way is imprinted in the properties of the observed post-mass transfer binaries. We show that Galactic chemical evolution is an important factor in binary population studies of interacting systems containing at least one evolved low-mass (Minit < 1.6 M⊙) component. Finally, we provide an observationally supported model of mass transfer from low-mass red giants onto main-sequence stars.
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33

Liao, Yi-Hong, Manzhu Xu, and Song Zhang. "Digital image correlation assisted absolute phase unwrapping." Optics Express 30, no. 18 (August 24, 2022): 33022. http://dx.doi.org/10.1364/oe.470704.

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This paper presents an absolute phase unwrapping method for high-speed three-dimensional (3D) shape measurement. This method uses three phase-shifted patterns and one binary random pattern on a single-camera, single-projector structured light system. We calculate the wrapped phase from phase-shifted images and determine the coarse correspondence through the digital image correlation (DIC) between the captured binary random pattern of the object and the pre-captured binary random pattern of a flat surface. We then developed a computational framework to determine fringe order number pixel by pixel using the coarse correspondence information. Since only one additional pattern is used, the proposed method can be used for high-speed 3D shape measurement. Experimental results successfully demonstrated that the proposed method can achieve high-speed and high-quality measurement of complex scenes.
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34

Pholdee, Nantiwat, and Sujin Bureerat. "Estimation of Distribution Algorithm Using Correlation between Binary Elements: A New Binary-Code Metaheuristic." Mathematical Problems in Engineering 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/6043109.

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A new metaheuristic called estimation of distribution algorithm using correlation between binary elements (EDACE) is proposed. The method searches for optima using a binary string to represent a design solution. A matrix for correlation between binary elements of a design solution is used to represent a binary population. Optimisation search is achieved by iteratively updating such a matrix. The performance assessment is conducted by comparing the new algorithm with existing binary-code metaheuristics including a genetic algorithm, a univariate marginal distribution algorithm, population-based incremental learning, binary particle swarm optimisation, and binary simulated annealing by using the test problems of CEC2015 competition and one real-world application which is an optimal flight control problem. The comparative results show that the new algorithm is competitive with other established binary-code metaheuristics.
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35

Sharma, R. K., K. Tankeshwar, K. N. Pathak, and Srinivasa Ranganathan. "Binary Collision Contribution to Transverse Current Correlation Function." Materials Science Forum 223-224 (July 1996): 23–28. http://dx.doi.org/10.4028/www.scientific.net/msf.223-224.23.

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36

Sang-Hyo Kim and Jong-Seon No. "New families of binary sequences with low correlation." IEEE Transactions on Information Theory 49, no. 11 (November 2003): 3059–65. http://dx.doi.org/10.1109/tit.2003.818399.

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37

Bowman, Dale. "Effects of correlation in modeling clustered binary data." Journal of Statistical Computation and Simulation 69, no. 4 (July 2001): 369–89. http://dx.doi.org/10.1080/00949650108812101.

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38

Bandyopadhyay, Uttam, and Parthasarathi Chakrabarti. "Correlation Tests Detecting Order Restrictions in Binary Response." Calcutta Statistical Association Bulletin 68, no. 1-2 (May 2016): 38–51. http://dx.doi.org/10.1177/0008068316634948.

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39

Savvin, M. V., and A. V. Nazarov. "Simulation of Correlation Effects in Ordering Binary Alloys." KnE Materials Science 4, no. 1 (May 6, 2018): 378. http://dx.doi.org/10.18502/kms.v4i1.2188.

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40

Flannery, David L., John S. Loomis, and Mary E. Milkovich. "Design elements of binary phase-only correlation filters." Applied Optics 27, no. 20 (October 15, 1988): 4231. http://dx.doi.org/10.1364/ao.27.004231.

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41

Duan, Lian, W. Nick Street, Yanchi Liu, Songhua Xu, and Brook Wu. "Selecting the Right Correlation Measure for Binary Data." ACM Transactions on Knowledge Discovery from Data 9, no. 2 (November 17, 2014): 1–28. http://dx.doi.org/10.1145/2637484.

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42

MacGowan, David. "Time correlation functions in a binary liquid mixture." Physical Review A 36, no. 3 (August 1, 1987): 1367–73. http://dx.doi.org/10.1103/physreva.36.1367.

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43

Fielding, Kenneth H. "Optical fingerprint identification by binary joint transform correlation." Optical Engineering 30, no. 12 (1991): 1958. http://dx.doi.org/10.1117/12.56030.

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44

Musharaf Ali, Sk, Alok Samanta, and Swapan K. Ghosh. "Transverse current correlation in a binary fluid mixture." Chemical Physics Letters 369, no. 1-2 (February 2003): 101–6. http://dx.doi.org/10.1016/s0009-2614(02)02000-6.

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45

Sim, Songyong. "A test for spatial correlation for binary data." Statistics & Probability Letters 47, no. 2 (April 2000): 129–34. http://dx.doi.org/10.1016/s0167-7152(99)00148-0.

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46

Speidel, Joachim. "A simplified motion estimator based on binary correlation." Signal Processing: Image Communication 2, no. 1 (May 1990): 29–37. http://dx.doi.org/10.1016/0923-5965(90)90044-i.

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47

Gates, John. "The feasibility of correlation specifications for binary variables." Applied Mathematical Modelling 19, no. 9 (September 1995): 560–65. http://dx.doi.org/10.1016/0307-904x(95)00081-t.

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48

Chizhov, V. E. "An integral equation for the binary correlation function." USSR Computational Mathematics and Mathematical Physics 29, no. 4 (January 1989): 143–48. http://dx.doi.org/10.1016/0041-5553(89)90130-4.

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49

Johnson, Charles R., and Pablo Tarazaga. "Binary Representation of Normalized Symmetric and Correlation Matrices." Linear and Multilinear Algebra 52, no. 5 (September 2004): 359–66. http://dx.doi.org/10.1080/03081080310001625219.

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50

Bartelt, Hartmut, and Joseph Horner. "Improving binary phase correlation filters using iterative techniques." Applied Optics 24, no. 18 (September 15, 1985): 2894. http://dx.doi.org/10.1364/ao.24.002894.

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