Mathematical Research Papers and Books from Tian's Evolution algebras and their applications 

(Numbers in brackets refer to References in TIAN) (pdffile)

Mathematical Research Papers, Genetic Algebras, from Section 5.1 History of general genetic algebras,pp.91-93

[30] G. Mendel, Experiments in plant-hybridization, Classic papers in Genetics, pages 1-20, J. A. Peter, editor, Prentice Hall Inc. 1959 (article)

[33] V. A. Kostitzin, Sur les coefficents mendeliens d'heredite, Comptes Rendus de l'Acad des Sci. 1938, 883-885 (in french) (article)

[34] I.M.H. Etherington, Non-associative algebra and the symbolism of genetics, Proc. Royal Soc. Edinburgh, B 61 1941 24-42 (article) (REVIEW)

Other papers by Etherington---Mathematical Reviews (you will need your UCINetID to access any of these papers and/or their reviews) (click here)

[35] H. Gonshor, Contributions to genetic algebras, Proc. Edinburgh Math. Soc. (2) 17 289-298 1970/71 (article) (REVIEW)

[36] R. D. Schafer, Structure of genetic algebras, American Journal of Mathematics 71 121-135 1949 (article) (REVIEW)

[37] P. Holgate, Sequences of powers in genetic algebras, J. Lon. Math. Soc. 42 489-496 1967 (article) (REVIEW)

[38] P. Holgate, Selfing in genetic algebras, J. Math. Biology 6 1978 197-206 (article) (REVIEW)

[39] I. Heuch, Sequences in genetic algebras for overlapping generations, Proc. Edinburgh Math. Soc. (2) 18 1972 19-29 (article) (REVIEW)

[40] O. Reiersol, Genetic algebras studied recursively and by means of differential operators, Math. Scand. 10 1962 25-44 (article) (REVIEW)

[41] V.M. Abraham, Linearising quadratic transformations in genetic algebras, Proc. Lon. Math Soc. 1980 18pp (article) (REVIEW)

[48] M.L. Reed, Algebraic structure of genetic inheritance, Bull. Amer. Math. Soc. (2) 1997 107-130 (article) (REVIEW)

Books

[47] Yuri I. Lyubich, Mathematical Structures in Population Genetics, Springer-Verlag, 1992 (Ayala Science Library) (REVIEW)

[46] Angelika Worz-Busekros, Algebras in Genetics, Springer-Verlag, 1980 (Ayala Science Library) (REVIEW)

[43] N.J.A. Sloane and A.D. Wyner (editors) Claude Elwood Shannon, Collected papers, IEEE Press 1993 (Ayala Science Library)

[44] C.W. Cotterman, A calculus for statistico-genetics, Dissertation, Ohio State University 1940, which is reproduced in

[45] P. Ballonof, Genetics and Social Structure, 1974 (Ayala Science Library)

Thomas Nagylaki, Introduction to Theoretical Population Genetics, Springer-Verlag 1992 (Ayala Science Library) (REVIEW)

Mathematical Research papers, Evolution Algebras, from Sections 5.2 (pp.94-96), 5.3 (pp.96-100), 5.4 (pp.100-107)

[49,50] Rudolph Hagemann, Erwin Baur or Carl Correns: Who Really Created the Theory of Plastid Inheritance, The Journal of Heredity 2000:91(6) (article)

[51] C.W. Birky, Jr., The inheritance of genes in mitochondria and chloroplasts: laws, mechanisms, and models. Annu. Rev. Genet. 35 125-148 2001 (article)

[57] F.M.A. Samen, G.A. Secor,and N.C. Gudmestad,Variability in virulence among asexual progenies of Phytophthora infestans, Phytopathology, 93 293-304 2003 (article)

[54] C.F.Emmerson, G.K.Brown, and J.Poulton, Synthesis of mitrochondrial DNA in permeablised human cultured cells, Nucleic Acids Res. 29 2 2001 (article)

[55] F.Ling and T.Shibata, Mhr1p-dependent concatemeric mitochondrial DNA formation for generating yeast mitochondrial homoplasmic cells, Mol. Biol. Cell, vol. 15 310-322 Jan 2004 (article)

[56] Y.Tang,G.Manfredi,M.Hirano and E.A.Schon, Maintenance of human rearranged mitochondrial DNAs in long term transmitochondrial cell lines, Mol. Biol. Cell, vol 11 2349-2358 Jul 2000 (article)

[58] W.E. Fry and S.B.Goodwin, Reemergence of potato and tomato late blight in the United States, Plant Disease, 1349-1357 dec. 1997 (article)

[59] S.B.Goodwin, B.A.Cohen and W.E. Fry, Panglobal distribution of a single clonal lineage of the Irish potato famine fungus, Proc. Nat. Acad. Sci. USA 91 11591-11595 1994 (article)

[60] S.B.Goodwin, The population genetics of Phytophthora, Phytopathology 87 462-473 1997 (article)

Books

[53] N.W. Gillham, Organelle Genes and Genomes, Oxford University Press 1994 (Ayala Science Library)

[52] C.W.Birky, Jr. Inheritance of mitochondrial mutations, In: Mitochondrial DNA Mutations and Aging, Disease, and Cancer, K.K. Singh editor, Spring 1988 (Ayala Science Library)

From a recent, as yet unpublished paper of TIAN

J.I. Ljubic, Algebraic methods in evolutionary genetics, Biometrical Journal 20:5 1978 511-529 (article) (REVIEW)

P. Fortini and R. Barakat, Genetic algebras for tetraploidy with several loci, Journal of Mathematical Biology 9 1980 297-304 (article) (REVIEW)

T.M. Campos and P. Holgate, Algebraic isotopy in genetics, Mathematical Medicine and Biology, 4:3 1987 215-222 (article) (REVIEW)

I. Heuch, Genetic algebras and time continuous models, Theoretical Population Biology, 4 1973 133-144 (article) (REVIEW)

H. Gradl, Long-time behavior of continuous time models in genetic algebras, Journal of Mathematical Biology, 32 1994 269-274 (article) (REVIEW)