Quantum QSAR and the eigensystems of stochastic quantum similarity matrices

Journal of Mathematical Chemistry

Volumn 27, Issue 4, 2000, Pages 357-376

  Carbó Dorca, Ramon ^a  

^a UNIVERSITY OF GIRONA   (Spain)

Author keywords

Generalized matrix eigensystems; Quantum objects; Quantum QSAR; Quantum similarity matrices; Quantum similarity measures; Stochastic quantum similarity matrices

Indexed keywords

EID: 0034338032     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1018832008106     Document Type: Article

References (46)

1. J. Klein and D. Babić, J. Chem. Inf. Comput. Sci. 37 (1997) 656.
2. P.G. Mezey, Shape in Chemistry (VCH, New York, 1993).
3. R. Carbó, E. Besalú, L. Amat and X. Fradera, J. Math. Chem. 18 (1995) 237.
4. D. Robert and R. Carbó-Dorca, J. Chem. Inf. Comput. Sci. 38 (1998) 469.
5. L. Amat, D. Robert, E. Besalú and R. Carbó-Dorca, J. Chem. Inf. Comput. Sci. 38 (1998) 624.
6. D. Robert and R. Carbó-Dorca, J. Chem. Inf. Comput. Sci. 38 (1998) 620.
7. D. Robert, L. Amat and R. Carbó-Dorca, J. Chem. Inf. Comput. Sci. 39 (1999) 333.
8. X. Gironés, L. Amat and R. Carbó-Dorca, SAR and QSAR in Environmental Research 10 (1999) 545.
9. R. Carbó-Dorca and E. Besalú, J. Mol. Struct. (Theochem) 451 (1998) 11.
10. R. Carbó-Dorca, Fuzzy sets and Boolean tagged sets, vector semispaces and convex sets, quantum similarity measures and ASA density functions, diagonal vector spaces and quantum chemistry, in: Advances in Molecular Similarity, Vol. 2, eds. R. Carbó-Dorca and P.G. Mezey (JAI Press, London, 1988) p. 43.
11. R. Carbó-Dorca, J. Math. Chem. 23 (1998) 353.
12. R. Carbó-Dorca, L. Amat, E. Besalú, X. Gironés and D. Robert, Quantum molecular similarity: Theory and applications to the evaluation of molecular properties, biological activities and toxicity, Technical report IT-IQC-99-16, Institute of Computational Chemistry, in: Proceedings of the IV Girona Seminar on Molecular Similarity (Kluwer Academic, Dordrecht) (to be published).
13. R. Carbó-Dorca, J. Math. Chem. 22 (1997) 143.
14. R. Carbó-Dorca, E. Besalú, L. Amat and X. Fradera, Quantum molecular similarity measures: Concepts, definitions and applications to QSAR, in: Advances in Molecular Similarity, Vol. 1, eds. R. Carbó-Dorca and P.G. Mezey (JAI Press, London, 1996) p. 1.
15. R. Carbó-Dorca, L. Amat, E. Besalú and M. Lobato, Quantum molecular similarity, in: Advances in Molecular Similarity, Vol. 2, eds. R. Carbó-Dorca and P.G. Mezey (JAI Press, London, 1998) p. 1.
16. R. Carbó and E. Besalú, Theoretical foundations of quantum similarity, in: Molecular Similarity and Reactivity: From Quantum Chemical to Phenomenological Approaches, ed. R. Carbó (Kluwer Academic, Amsterdam, 1995) p. 3.
17. R. Carbó-Dorca, L. Amat, E. Besalú, X. Girones, D. Robert, Quantum mechanical origin of QSAR: Theory and applications, Technical report IT-IQC-99-1, Institute of Computational Chemistry, Computational Medicinal Chemistry, special issue, J. Mol. Struct. (Theochem) (to appear).
18. R. Carbó, B. Calabuig, L. Vera and E. Besalú, Adv. Quantum Chem. 25 (1994) 253.
19. R. Carbó and B. Calabuig, J. Chem. Inf. Comp. Sci. 32 (1992) 600.
20. R. Carbó-Dorca, Stochastic transformation of quantum similarity matrices and their use in quantum QSAR (QQSAR) models, Technical report IT-IQC-99-18, Institute of Computational Chemistry, Int. J. Quant. Chem. (1999) (in press).
21. P.H.A. Sneath and R.R. Sokal, Numerical Taxonomy (W.H. Freeman, San Francisco, 1973).
22. W.J. Krzanowski (ed.), Recent Advances in Descriptive Multivariate Analysis, Oxford Science Publications (Clarendon Press, Oxford, 1995).
23. E. Durand, Solutions numériques des équations algébriques, Vol. II (Masson, Paris, 1961).
24. J.H. Wilkinson and C. Reinsch, Linear Algebra (Springer, Berlin, 1971).
25. R. Carbó, M. Arnau and L. Leyda, Int. J. Quant. Chem. 17 (1980) 1185.
26. R. Carbó and B. Calabuig, Int. J. Quant. Chem. 42 (1992) 1681.
27. I.M. Vinogradov (ed.), Encyclopaedia of Mathematics, Vol. 9 (Kluwer Academic, Dordrecht, 1993) p. 9.
28. R. Carbó and L. Domingo, Álgebra Matricial y Lineal, Serie Schaum (McGraw-Hill, Madrid, 1987).
29. K.D. Sen and R. Carbó-Dorca, J. Mol. Struct. (Theochem) 501 (2000) 173.
30. R. Carbó-Dorca, Inward matrix products: Extensions and applications to quantum mechanical foundations of QSAR, Technical report IT-IQC-99-15, Institute of Computational Chemistry, J. Mol. Struct. (Theochem) (submitted).
31. Lahey/Fujitsu Fortran 95, Version 5.5, Lahey Computer Systems, Incline Village (Nevada) (1999).
32. C. Roos, T. Terlaky and J.-P. Vial, Theory and Algorithms for Linear Optimization (Wiley, New York, 1997).
33. R.A. Horn and Ch.A. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1985).
34. I.M. Vinogradov (ed.), Encyclopaedia of Mathematics, Vol. 4 (Kluwer Academic, Dordrecht, 1989).
35. R. Carbó and E. Besalú, J. Math. Chem. 13 (1993) 331-342.
36. R. Carbó and E. Besalú, Computers Chem. 18 (1994) 117-126.
37. R. Carbó and E. Besalú, J. Math. Chem. 18 (1995) 37-72.
38. R. Carbó and E. Besalu, in: Strategies and Applications in Quantum Mechanics, eds. Y. Ellinger and M. Defranceschi (Kluwer Academic, Dordrecht, 1996) pp. 229-248.
39. R. Carbó-Dorca, E. Besalú and X. Gironés, Extended density functions, Technical report IT-IQC-99-2, Institute of Computational Chemistry Adv. Quantum Chem. (in press).
40. R. Carbó, E. Besalú, L. Amat and X. Fradera, J. Math. Chem. 19 (1996) 47.
41. L. Amat, R. Carbó-Dorca and R. Ponec, J. Comp. Chem. 19 (1998) 1575.
42. R. Ponec, L. Amat and R. Carbó-Dorca, J. Comput,-Aided Mol. Design 13 (1999) 259.
43. R. Ponec, L. Amat and R. Carbó-Dorca, J. Phys. Org. Chem. 12 (1999) 447.
44. A. Gallegos, D. Robert and R. Carbó-Dorca, Structure-toxicity relationships of polycyclic aromatic hydrocarbons using molecular quantum similarity, Technical report IT-IQC-00-03, Institute of Computational Chemistry.
45. D. Robert, L. Amat and R. Carbó-Dorca, Quantum similarity QSAR: Study of inhibitors binding to thrombin, trypsin and factor Xa, including a comparison with CoMFA and CoMSIA methods, in: Proceedings of the Third Congress of the Int. Soc. for Theoret. Chem. Phys., Mexico (1999), Int. J. Quant. Chem. (submitted).
46. J.H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon Press, Oxford, 1965).