Recursive Genome Function of the Cerebellum: Geometric Unification of Neuroscience and Genomics

  • Andras J. Pellionisz
  • Roy Graham
  • Peter A. Pellionisz
  • Jean-Claude Perez


Recursive Fractal Genome Function in the geometric mind frame of Tensor Network Theory (TNT) leads through FractoGene to a mathematical unification of physiological and pathological development of neural structure and function as governed by the genome. The cerebellum serves as the best platform for unification of neuroscience and genomics. The matrix of massively parallel neural nets of fractal Purkinje brain cells explains the sensorimotor, multidimensional non-Euclidean coordination by the cerebellum acting as a space-time metric tensor. In TNT, the recursion of covariant sensory vectors into contravariant motor executions converges into Eigenstates composing the cerebellar metric as a Moore-Penrose Pseudo-Inverse.

The Principle of Recursion is generalized to genomic systems with the realization that the assembly of proteins from nucleic acids as governed by regulation of coding RNA (cRNA) is a contravariant multicomponent functor, where in turn the quantum states of resulting protein structures both in intergenic and intronic sequences are measured in a covariant manner by noncoding RNA (ncRNA) arising as a result of proteins binding with ncDNA modulated by transcription factors. Thus, cRNA and ncRNA vectors by their interference constitute a genomic metric, the RNA system serving as a Genomic Cerebellum. Recursion through massively parallel neural network and genomic systems raises the question if it obeys the Weyl’s Law of Fractal Quantum Eigenstates, or when derailed, pathologically results in aberrant methylation or chromatin modulation, the root cause of cancerous growth. The growth of fractal Purkinje neurons of the cerebellum is governed by the aperiodical discrete quantum system of sequences of DNA bases, codons, and motifs. The full genome is fractal; the discrete quantum system of pyknon-like elements follows the Zipf-Mandelbrot Parabolic Fractal Distribution curve.

The Fractal Approach to Recursive Iteration has been used to identify fractal defects causing a cerebellar disease, the Friedreich Spinocerebellar Ataxia – in this case as runs disrupting a fractal regulatory sequence. Massive deployment starts by an open domain collaborative definition of a standard for fractal genome dimension in the embedding spaces of the genome-epigenome-methylome to optimally diagnose cancerous hologenome in the nucleotide, codon, or motif-hyperspaces. Recursion is parallelized both by open domain algorithms, and also by proprietary FractoGene algorithms on high performance computing platforms, for genome analytics on accelerated private hybrid clouds with PDA personal interfaces, becoming the mainstay of clinical genomic measures prior and post-cancer intervention in hospitals and serve consumers at large as Personal Genome Assistants.


Fractal Dimension Purkinje Neuron Private Cloud Golden Ratio Mycoplasma Genitalium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Upon presentation, an advice was received from Dr. Hamilton O’ Smith (Venter Institute), to run the Zipf-Mandelbrot Fractal Parabolic Distribution Curve-test, as a control, with an identical number of A, C, T, and G-s, randomly generated. Not only the control-result did not show the Curve, but generated zero repetition for the identical overall length and motif-requirements (there were no points to compose any curve). The creative suggestion is gratefully acknowledged. The authors thank Paul Shapshak Ph.D., Division of Infectious Disease and International Medicine and Dept. of Psychiatry and Behavioral Medicine, University of South Florida College of Medicine, Tampa, Florida, to help prepare the manuscript and to Prof. Sergey Petoukhov, Academician, Moscow, for reference to Gazalé and appreciative comments of the chapter on dual valence, the RNA system serving as a Genomic Cerebellum.

One of us (AJP) also gratefully acknowledges Prof. E.G. Rajan for awarding this work by the “Distinguished Scientist” honor for the presentation of the concepts at the ICSCI 2012 International Conference on Systemics, Cybernetics and Informatics, Hyderabad, India.


  1. Albus JS (1971) Theory of cerebellar function. Math Biosci 10(1/2):25–61CrossRefGoogle Scholar
  2. Amari S (1991) Dualistic geometry of the manifold of higher-order neurons. Neural Netw 4(4):443–451CrossRefGoogle Scholar
  3. Anderson JA (1990) 351–355. In: Anderson JA, Pellionisz A, Rosenfeld E Neurocomputing II. Directions of research. MIT Press.
  4. Anderson JA, Pellionisz A, Rosenfeld E (1990) Neurocomputing II. Directions of research. MIT Press, Cambridge, MAGoogle Scholar
  5. Arneth BM (2010) Sequence variability and sequence evolution: An explanation of molecular polymorphisms and why many molecular structures can be preserved although they are not predominant. DNA Cell Biol 29(10):571–576. doi:10.1089/dna.2009.0942PubMedCrossRefGoogle Scholar
  6. Baliga NS, Pan M, Goo YA, Yi EC, Goodlett DR, Dimitrov K, Shannon P, Aebersold R, Ng WV, Hood L (2002) Coordinate regulation of energy transduction modules in Halobacterium sp. analyzed by a global systems approach. Proc Natl Acad Sci USA 99(23):14913–14918PubMedCrossRefGoogle Scholar
  7. Bailey TL, Gribskov M (1998) Methods and statistics for combining match scores (MEME, MAST). J Comput Biol 5:211–221PubMedCrossRefGoogle Scholar
  8. Barnsley MF (2006) Superfractals. Cambridge University Press, CambridgeGoogle Scholar
  9. Barski JJ, Lauth M, Meyer M (2002) Genetic targeting of cerebellar Purkinje cells: history, current status and novel strategies. Cerebellum 1:111–118PubMedCrossRefGoogle Scholar
  10. Battelle Technology Partnership (2011) Economic impact of the human genome project. How a $3.8 Bn investment drove $796 billion in economic impact, created 310,000 jobs and launched the genomic revolution.
  11. Bertalanffy L (1934) Untersuchungen über die Gesetzlichkeit des Wachstums. I. Allgemeine Grundlagen der Theorie; mathematische und physiologische Gesetzlichkeiten des Wachstums bei Wassertieren. Arch Entwicklungsmech 131:613–652CrossRefGoogle Scholar
  12. Berthelsen CL, Glazier JA, Skolnick MH (1992) Global fractal dimension of human DNA sequences treated as pseudorandom walks. Phys Rev 45(12).
  13. Bieberich E (1999) Structure in human consciousness: Fractal approach to the topology of the self perceiving an outer world in an inner space.
  14. Bieberich E (2011) Introduction to the fractality principle of consciousness and the sentyon postulate. Cogn Comput. doi:10.1007/s12559-011-9104-5.
  15. Bloedel JR, Tillery SI, Pellionisz AJ (1988) Experimental–theoretical analysis of the intrinsic geometry of limb movements. Neurosci Abst 14:952Google Scholar
  16. Bonhoeffer S, Herz AV, Boerlijst MC, Nee S, Nowak MA, May RM (1997) No signs of hidden language in noncoding DNA. Phys Rev Lett 76(11):11Google Scholar
  17. Borovik AS, Grosberg AY, Frank-Kamenetskii MD (1994) Fractality of DNA texts. J Biomol Struct Dyn 12(3):655–669PubMedCrossRefGoogle Scholar
  18. Braitenberg V (1967) Is the cerebellar cortex a biological clock in the millisecond range? Prog Brain Res 25:334–346PubMedCrossRefGoogle Scholar
  19. Cartieri FJ (2009) Darwinism and Lamarckism before and after Weisman: a historical, philosophical, and methodological analysis. University of Pittsburg, pp 1–54.
  20. Castaldo I, Pinelli M, Monticelli A, Acquaviva F, Giacchetti M, Filla A et al (2008) DNA methylation in intron 1 of the frataxin gene is related to GAA repeat length and age of onset in Friedreich ataxia patients. J Med Genet 45(12):808–812PubMedCrossRefGoogle Scholar
  21. Chatzidimitriou-Dreismann CA, Steffer RM, Larhammar D (1996) Lack of biological significance in the “linguistic features” of noncoding DNA - a quantitative analysis. Nucleic Acids Res 24(9):1676–1681PubMedCrossRefGoogle Scholar
  22. Chiappelli F, Shapshak P, Commins D, Singer E, Minagar E, Oluwadara O et al (2008) Molecular epigenetics, chromatin, and NeuroAIDS/HIV: immunopathological implications. Bioinformation 3(1):47–52. Google Scholar
  23. Church GM (2005) The personal genome project. EMBO and Nature Pub. Group, Mol Syst Biol 1:30.
  24. Churchland PS (1986) Neurophilosophy: toward a unified science of the mind-brain. MIT Press.
  25. Collins F (2007) New findings challenge established views on human genome. Nature.
  26. Crick F (1970, seminal notion 1956) Central Dogma of Molecular Biology. Nature 227(8):561–563., 1956: see Google Scholar
  27. D’Angelo E, Mazzarello P, Prestori F, Mapelli J, Solinas S, Lombardo P, Cesana E, Gandolfi D, Congi L (2010) The cerebellar network: from structure to function and dynamics. Brain Res Rev 66:5–15 Published by ElsevierPubMedCrossRefGoogle Scholar
  28. Dahmane N, Ruiz i Altaba A (1999) Sonic hedgehog regulates the growth and patterning of the cerebellum. Development 126:3089–3100. Google Scholar
  29. Daunicht W, Pellionisz A (1987) Spatial arrangement of the vestibular and the oculomotor system in the rat. Brain Res 435:48–56. Google Scholar
  30. Descartes R (1629) Treatise of man. Prometheus Books (in English, 2003)Google Scholar
  31. Dokukin ME, Guz NV, Gaikwad RM, Woodworth CD, Sokolov I (2011) Cell surface as fractal: Normal and cancerous cervical cells demonstrate different fractal behavior of surface adhesion maps at the nanoscale. Phys Rev Lett 107:028101PubMedCrossRefGoogle Scholar
  32. Dow RS, Moruzzi G (1958) The physiology and pathology of the cerebellum. Minnesota University Press, MinneapolisGoogle Scholar
  33. Dupré J, Barnes SB (2008) Genomes and what to make of them. University of Chicago Press, ChicagoGoogle Scholar
  34. Eccles J, Ito M, Szentágothai J (1967) The cerebellum as a neural machine. Springer, New YorkGoogle Scholar
  35. Elnitski L, Piontkivska H, Welch JR (2011) In: Fedorov A, Fedorava L (eds) Advances in genomic sequence analysis and pattern discovery, Chapter 3. Science, engineering and biology informatics, vol 7. World Scientific, Singapore, pp 65–93Google Scholar
  36. Finger S (1994) Origins of neuroscience: a history of explorations into brain function. Oxford University Press, New YorkGoogle Scholar
  37. Fiori S (2008) Lie-group-type neural system learning by manifold retractions. Neural Netw 21(10):1524–1529. Google Scholar
  38. Fire A, Xu S, Montgomery M, Kostas S, Driver S, Mello C (1998) Potent and specific genetic interference by double-stranded RNA in Caenorhabditis elegans. Nature 391(6669):806–811. doi:10.1038/35888 PMID 9486653PubMedCrossRefGoogle Scholar
  39. Flam F (1994) Hints of a language in junk DNA. Science 266:1320PubMedCrossRefGoogle Scholar
  40. Flourens MJP (1824) Recherces expérimentalses fur les propriétés et les sonctions du systéme nerveux dans les anomaux vertébres. Crevot, ParisGoogle Scholar
  41. Foucher I, Montesinos ML, Volovitch M, Prochiantz A, Trembleau A (2003) Joint regulation of the MAP1B promoter by HNF3β/Foxa2 and Engrailed is the result of a highly conserved mechanism for direct interaction of homeoproteins and Fox transcription factors. Development 130:1867–1876. doi:10.1242/dev.00414. Google Scholar
  42. Francis J (2008) Philosophy of mathematics. Global Vision Publishing House, New DelhiGoogle Scholar
  43. Fraser CM, Gocayne JD, White O, Adams MD, Clayton RA, Fleischmann RD et al (1995) The minimal gene complement of Mycoplasma genitalium. Science 270(5235):397–403 NCBI ascension number NCBI L43927PubMedCrossRefGoogle Scholar
  44. Fundenberg G, Getz G, Meyerson M, Mirny L (2011) High-order chromatin architecture determines the landscape of chromosomal alterations in cancer. Nature precedings, hdl:10101/npre.2011.6356.1
  45. Gardner M (1970) Mathematical games. The fantastic combinations of John Conway’s new solitaire game “life”. Scientific American 223:120–123.
  46. Gazalé MJ (1999) Gnomonl: from pharaohs to fractals. Princeton Univ. Press
  47. Gibbs RA, Jeffrey Rogers J, Katze MG, Bumgarner R, Weinstock GM, Mardis ER et al (2007) Evolutionary and biomedical insights from the rhesus macaque genome science 316(5822):222–234.
  48. Gielen CCAM, van Zuylen EJ (1985) Coordination of arm muscles during flexion and supination: application of the tensor analysis approach. Neuroscience 17:527–539. Google Scholar
  49. Glasner ME, Yen CC, Ekland EH, Bartel DP (2000) Recognition of nucleoside triphosphates during RNA-Catalyzed primer extension. Biochemistry 39:15556–15562PubMedCrossRefGoogle Scholar
  50. Grosberg AY, Nechaev SK, Shakhnovich EI (1988) The role of topological constraints in the kinetics of collapse of macromolecules. J Phys France 49:2095–2100. Google Scholar
  51. Grosberg A, Rabin Y, Havlin S, Neer A (1993) Crumpled globule model of the three-dimensional structure of DNA. Europhys Lett 23:373–378. Google Scholar
  52. Hansen KD, Timp W, Bravo HC, Sabunciyan, Langmead B, McDonald OG et al. (2011) Increased methylation variation in epigenetic domains across cancer types. Nat Genet 43(8):768–775PubMedCrossRefGoogle Scholar
  53. Haussler D (1995) A generalized hidden Markov model for DNA parsing. Extended abstract of talk for the workshop on gene-finding and gene structure prediction. University of PennsylvaniaGoogle Scholar
  54. Holmes G (1939) The cerebellum of man. Brain 62:1–30CrossRefGoogle Scholar
  55. Hood LR, Timp W, Bravo HC, Sabunciyan, Langmead B, McDonald OG et al. (2002) My life and adventures integrating biology and technology. Commemorative lecture given when awarded the 2002 Kyoto Prize in Advanced TechnologiesGoogle Scholar
  56. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational properties. Proc Natl Acad Sci (USA) 79:2554–2558CrossRefGoogle Scholar
  57. Izzo JA, Kim N, Elmetwaly S, Schlick T (2011) RAG: an update to the RNA-As-Graphs resource. BMC Bioinformatics 12:219. Google Scholar
  58. Jacob F, Monod JJ (1961) Genetic regulatory mechanisms in the synthesis of proteins. Mol Biol 3:318–356CrossRefGoogle Scholar
  59. Jansen J, Brodal A (1954) Aspects of cerebellar anatomy. The Wistar Institute of Anatomy and BiologyGoogle Scholar
  60. Jensen KL, Styczynsk MPi, Rigoutsos I, Stephanopoulos GN (2006) A generic motif discovery algorithm for sequential data (GEMODA). Bioinformatics 22(1):21–28PubMedCrossRefGoogle Scholar
  61. Jetten AM (2009) Retinoid-related orphan receptors (RORs): critical roles in development, immunity, circadian rhythm, and cellular metabolism. Nuclear Receptor 7:1–32. doi:10.1621/nrs.07003. Google Scholar
  62. Kornberg A, Baker TA (1992) DNA replication. University Science Book, New YorkGoogle Scholar
  63. Kuhn TS (1962) The structure of scientific revolutions, 1st edn. University of Chicago Press, ChicagoGoogle Scholar
  64. Kyle LJ, Styczynski MP, Rigoutsos I, Stephanopoulos GN (2006) A generic motif discovery algorithm for sequential data. Bioinformatics 22(1):21–28. Google Scholar
  65. Laczkó J, Pellionisz AJ, Peterson BW, Buchanan TS (1987) Multidimensional sensorimotor “patterns” arising from a graphics-based tensorial model of the neck-motor system. In: Society of Neuroscience Abstracts 13, vol 1, p 372Google Scholar
  66. Laczkó J, Pellionisz A, Jongen H, Gielen CCCM (1988) Computer modeling of human forelimb muscle activation in multidimensional intrinsic coordinate frames. Soc Neurosci Absts 14–2:955Google Scholar
  67. Lander ES, Linton LM, Birren B, Nusbaum C, Zody MC, Baldwin J et al (2001) Initial sequencing and analysis of the human genome. Nature 409:860–921. Google Scholar
  68. Lestienne F, Liverneaux P, Pellionisz A (1988) Morpho-anatomy of sub-occipital muscles in monkey: a tensor model of the musculo-skeletal head-neck system. Reunion Commune de la Physiological Society et de l’Association des Physiologistes, France 2 July 1988. Proceedings Physiological Society Journal of Physiology (Lond) 2PGoogle Scholar
  69. Lieberman-Aiden E et al (2009) The comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science 326. doi:10.1126/science.1181369Google Scholar
  70. Llinás R, Roy S (2009) The “prediction imperative” as the basis for self-awareness. Phil Trans R Soc B (2009) 364:1301–1307. doi:10.1098/rstb.2008.0309.
  71. Lorente De No R (1933) Vestibulo-ocular reflex arc. Arch Neurol Psychiat (Chicago) 30:245–291Google Scholar
  72. Mandelbrot B (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 5(156):3775, pp 636–638. doi:10.1126/science.156.3775.636. Google Scholar
  73. Mandelbrot BB (1983) The fractal geometry of nature, 2nd edn. Freeman, New YorkGoogle Scholar
  74. Manfred R, Roy S (2001) (Quantum) space-time as a statistical geometry of fuzzy lumps and the connection with random metric spaces. Class Quantum Grav 18:3039CrossRefGoogle Scholar
  75. Mantegna RNSV, Buldyrev AL, Goldberger S, Havlin C, Peng K, Simons M, Stanley HE (1994) Linguistic features of noncoding DNA sequences. Phys Rev Lett 73:3169–3172PubMedCrossRefGoogle Scholar
  76. Manto M (2008) The cerebellum, cerebellar disorders, and cerebellar research-two centuries of discoveries. Cerebellum 7(4):505–516PubMedCrossRefGoogle Scholar
  77. Manto M, Marmolino D (2009) Cerebellar ataxias. Curr Opin Neurol 22(4): 419–429. Google Scholar
  78. Marcer PJ (1992) Order and chaos in DNA – the Denis Guichard Prizewinner: Jean-Claude Perez. In: Kibernetes 1992, 21(2):60–61. ISSN 0368-492X.
  79. Mardis ER (2006) Anticipating the $1000 genome. Genome Biol 7(7):12. doi:10.1186/gb-2006-7-7-112Google Scholar
  80. Marmolino D, Acquaviva F (2009) Friedreich’s Ataxia: from the (GAA)n repeat mediated silencing to new promising molecules for therapy. Cerebellum 8(3):245–259PubMedCrossRefGoogle Scholar
  81. Marr D (1969) A theory of cerebellar cortex. J Physiol 202:437–470PubMedGoogle Scholar
  82. Marr D (1982) Vision: a computational Investigation into the human representation and processing of visual information. Freeman, New YorkGoogle Scholar
  83. Mattick JS (2001) Non-coding RNAs: the architects of eukaryotic complexity. EMBO reports 2(11):986–991. doi:10.1093/embo-reports/kve230.
  84. Mattick JS (2004) The hidden genetic code of complex organisms. Sci Am 291(4):60–67PubMedCrossRefGoogle Scholar
  85. Mattick JS (2005) The functional genomics of noncoding RNA. Science 309(5740):1527–1528. Google Scholar
  86. McCulloch WS, Pitts WH (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5:115–133CrossRefGoogle Scholar
  87. Mendel JG (1866) Versuche über PflanzenhybridenVerhandlungen des naturforschenden Vereines. In: Brünn Bd. IV für das Jahr, 1865 Abhandlungen:3–47. For the English translation, see: Druery CT and William Bateson (1901). “Experiments in plant hybridization”. J of the Royal Horticultural Society 26:1–32. Retrieved 2009-10-09Google Scholar
  88. Meyerson M, Gabriel S, Getz G (2011) Advances in understanding cancer genomes through second-generation sequencing. Nature Rev Gen 11:685–696, doi:10.1038/nrg2841CrossRefGoogle Scholar
  89. Minsky M, Papert S (1969) Perceptrons:an introduction to computational geometry. MIT Press, Cambridge, MA. ISBN:0 262 63022 2Google Scholar
  90. Moruzzi G (1950) Problems in cerebellar physiology. C. C Thomas, SpringfieldGoogle Scholar
  91. Neumann J (1958) The computer and the brain (Mrs. Hepsa Ely Silliman Memorial Lectures). Yale University Press, New Haven/London, Second Edition 2000, with Introduction by Patricia Churchland and Paul ChurchlandGoogle Scholar
  92. Oberdick J, Schilling K, Smeyne RJ, Corbin JG, Bocchiaro C, Morgan JI (1993) Control of segment-like patterns of gene expression in the mouse cerebellum. Neuron 10(6):1007–1018. doi:10.1016/0896-6273(93)90050-2. Google Scholar
  93. Ohno S (1972) So much “Junk DNA” in our genome. Brookhaven Symp Biol (23):366–370.
  94. Oller JW (2010) The antithesis of entropy: Biosemiotic communication from genetics to human language with special emphasis on the Iimmune systems. Entropy 12:631–705. doi:10.3390/e12040631. Google Scholar
  95. Ozery-Flato M, Linhart C, Trakhtenbrot L, Izraeli S, Shamir R (2011) Large-scale analysis of chromosomal aberrations in cancer karyotypes reveals two distinct paths to aneuploidy. Genome Biol 12:R61. doi:10.1186/gb-2011-12-6-r61PubMedCrossRefGoogle Scholar
  96. Pandolfo M (2008) Friedreich ataxia. Arch Neurol 65(10):1296–1303. Google Scholar
  97. Pellionisz AJ (1984a) Coordination: a vector–matrix description of transformations of overcomplete CNS coordinates and a tensorial solution using the Moore-Penrose generalized inverse. J Theor Biol 110:353–375. Google Scholar
  98. Pellionisz A (1985a) Tensorial aspects of the multidimensional approach to the vestibulo-oculomotor reflex and gaze. In: Berthoz A and Melvill-Jones G (eds) Reviews of oculomotor research. I. Adaptive mechanisms in gaze control. Elsevier, Amsterdam, pp 281–296.
  99. Pellionisz AJ (1985b) Tensor network theory of the central nervous system and sensorimotor modeling. In: Palm G, Aertsen A (eds) Brain theory. Springer, Berlin/Heidelberg/New York, pp 121–145Google Scholar
  100. Pellionisz A (1986) David Marr’s theory of the cerebellar cortex: a model in brain theory for the “Galilean Combination of Simplification, Unification and Mathematization”. In: Palm G, Aertsen A (eds) Brain theory. Springer, Berlin/Heidelberg/New York, pp 253–257.
  101. Pellionisz A (1987) Tensor network theory of the central nervous system. In: Adelman G (ed) Encyclopaedia of neuroscience. Birkhäuser, Boston, Basel, Stuttgart, pp 1196–1198.
  102. Pellionisz AJ (1989) Neural geometry: towards a fractal model of neurons. In: Cotterill RMJ (ed) Models of brain function. Cambridge University Press, Cambridge, pp 453–464.
  103. Pellionisz A (2002) FractoGene: utility to use self-similar repetitions in the language-like genetic information as fractal sets. US Patent Application, 1 Aug 2002. In: Simons MJ, Pellionisz AJ (2006a), see also SF-gate, 22 Nov 2002.
  104. Pellionisz A (2003) FractoGene: Design-tool for protein-based self-assembling nanostructures, materials and application. Invited Keynote Lecture at Nano-Bio Technology Session. In: Proceedings of the 204th meeting of the electrochemical society, p 1195Google Scholar
  105. Pellionisz A (2006) PostGenetics: the journey of discovering “junk DNA”; Genetics beyond genes. Invited Keynote Lecture of European inaugural satellite symposium of international postgenetics Society. In: Proceedings of international congress of immunogenomics and immunomics, Akadémiai Kiadó, BudapestGoogle Scholar
  106. Pellionisz A (2008a) The principle of recursive genome function. The Cerebellum 7(3):348–359. doi:10.1007/s12311-008-0035-y. Google Scholar
  107. Pellionisz A (2008b) Is it ready for the dreaded DNA data deluge?
  108. Pellionisz A (2009a) From the principle of recursive genome function to interpretation of hologenome regulation by personal genome computers. Personal Genomes, Cold Spring Harbor Laboratory, 14–17 Sept 2009.
  109. Pellionisz A (2009b) Personal genome computing: breakthroughs, risks and opportunities, Churchill Club Panel.
  110. Pellionisz A (2010) Shop for your life – HolGenTech at PMWC2010.
  111. Pellionisz A, Graf W (1987) Tensor network model of the “three-neuron vestibulo-ocular reflex-arc.” In: Cat J Theoretical Neurobiology 5:127–151.
  112. Pellionisz AJ, Llinás R (1980) Tensorial approach to the geometry of brain function. Cerebellar coordination via a metric tensor. Neuroscience 5:1761–1770. Google Scholar
  113. Pellionisz AJ, Llinás R (1985) Tensor network theory of the metaorganization of functional geometries in the CNS. Neuroscience 16:245–273. Google Scholar
  114. Pellionisz A, Szentágothai J (1973) Dynamic single unit simulation of a realistic cerebellar network model. Brain Res 49:83–99, Elsevier. Google Scholar
  115. Pellionisz AJ, LeGoff B, Laczko J, Berthoz A (1991) Multidimensional geometry intrinsic to head movements around distributed centers of rotation: a neurocomputer paradigm. In: Berthoz A, Graf W, Vidal P (eds) The head-neck sensory-motor system. Oxford University Press, pp 117–125.
  116. Pellionisz AJ, Jorgensen CC, Werbos PJ (1992) Cerebellar neurocontroller project for aerospace applications. In: IJCNN international joint conference on neural networks. IEEE Catalog Number: 92CH3114-6 ISBN: Softbound Edition 0-7803-0559-0.
  117. Perez JC (1988a) De nouvelles voies vers l’Intelligence Artificielle: pluri-disciplinarité, auto-organisation et réseaux neuronaux. Masson, Paris. ISBN 2-225-81815-0Google Scholar
  118. Perez JC (1988b) Fractal chaos: a new neural network holographic model. In: INNS conference, Neural Networks, BostonGoogle Scholar
  119. Perez JC (1990a) Digital holograms computers, concepts and applications. In: Neural networks: biological computers or electronic brains, Les entretiens de Lyon. Springer, ISBN 2-287-00051-8Google Scholar
  120. Perez JC (1990b) Integers neural network systems (INNS) using resonance properties of a Fibonacci’s chaotic golden neuron. Neural Netw 1:859–865. IEEE 90CH2879-5. INSPEC Accession Number: 3926657.−203 Google Scholar
  121. Perez JC (1991) Chaos, DNA, and neuro-computers: a golden link: the hidden language of genes, global language and order in the human genome. Specul Sci Technol 14:336–346Google Scholar
  122. Perez JC (1997) L’ADN décrypté. Résurgence, Liège. ISBN 2-87211-017-8Google Scholar
  123. Perez JC (2008) Scale invariance embedded votes and self-emerging binary logics in the whole human genome. Relating the paper: what is complexity? by Gell-Mann PM. Complexity. 1(1) 1995, Wiley.
  124. Perez JC (2009a) Codex biogenesis. Resurgence, Liege. ISBN 2-87434-044-8.,
  125. Perez JC (2010) Codon population in single-stranded whole human genome DNA are fractal and fine-tuned by the Golden Ration 1.618. Interdiscip Sci: Comput Life Sci 2(3):228–340. doi:10.1007/s12539-010-0022-0.
  126. Perez JC (2011a) Decoding non-coding DNA codes: human genome meta-chromosomes architecture (support from Pr Luc Montagnier FMPRS World AIDS Foundation UNESCO and Jean-rené Fourtou Vivendi Universal chairman), BIT Life Sciences’ third annual world vaccine congress-2011. Beijing March 2011.
  127. Perez JC (2011b) Caminos Interdisciplinaios, Seminario CLAVE_INTER, Espacio Interdisciplinario, Universidad de la Republica Montevideo Uruguay, 27 de Octubre 2011.
  128. Perez JC (2012) Paper in preparation: DNA, waveforms and numbers: Unifying all 1496 HIV1 whole genomesGoogle Scholar
  129. Perez JC, Bertille JM (1990) A spatio temporal novelty detector using Fractal Chaos model. In: IJCNN conference, Neural Networks, WashingtonGoogle Scholar
  130. Peterson BW, Baker JA, Pellionisz AJ (1987) Multidimensional analysis of vestibulo-ocular and vestibulo-colllic reflexes (VOR and VCR). In: Proceedings of the international symposium on basic and applied aspects of vestibular function, Hong KongGoogle Scholar
  131. Peterson BW, Pellionisz AJ, Baker JA, Keshner EA (1989) Functional morphology and neural control of neck muscles in mammals. Am Zoology 29:139–149Google Scholar
  132. Petoukhov S, He M (2010) Symmetrical analysis techniques for genetic systems and bioinformatics: advanced patterns and applications. Medical Information Science Reference. ISBN 978–1605661247.
  133. Rigoutsos I (2006) BM Watson Research Center.
  134. Rigoutsos I, Floratos A (1998) Combinatorial pattern discovery in biological sequences: the TEIRESIAS algorithm. Bioinformatics 14(1):55–67, pmid:9520502PubMedCrossRefGoogle Scholar
  135. Rigoutsos I, Huynh T, Miranda K, Tsirigos A, McHardy A, Platt D (2006) Short blocks from the noncoding parts of the human genome have instances within nearly all known genes and relate to biological processes. Proc Natl Acad Sci 103(17):6605–6610.
  136. Roy S, Llinás R (2007) Dynamic geometry, brain function modeling, and consciousness. Prog Brain Res. 168:133–144. doi:10.1016/S0079-6123(07)68011-X.
  137. Schadt EE, Linderman MD, Sorenson J, Lee L, Nolan GP (2010) Computational solutions to large-scale data management and analysis. Nature Rev Genet (11):647–amp;657.
  138. Schrődinger E (1944) What is life? Dublin Institute for Advanced Studies at Trinity College, Dublin, in Feb 1943.
  139. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423, 623–656Google Scholar
  140. Shapshak P, Chiappelli, F, Commins D, Singer E, Levine AJ, Somboonwit C, Minagar A, Pellionisz, A (2008) Molecular epigenetics, chromatin, and NeuroAIDS/HIV: translational implications. Bioinformation 3(1):53–57. PMCID: PMC2586134 Google Scholar
  141. Shepelyansky DL (2008) Fractal Weyl law for quantum fractal eigenstates. Physical Rev E 77:015202.
  142. Simons M, Pellionisz A (2006a) Genomics, morphogenesis and biophysics: triangulation of purkinje cell development. The Cerebellum 5(1):27–35. Google Scholar
  143. Simons M, Pellionisz A (2006b) Implications of fractal organization of DNA on disease risk genomic mapping and immune function analysis. Australasian and Southeast Asian Tissue Typing Association. In: 30th scientific meeting 22–24 Nov 2006, Chiangmai.
  144. Stagnaro S (2011) Glycocalix quantum-biophysical-semeiotic evaluation plays a central role in demonstration of water memory-information.
  145. Stagnaro S, Caramel S (2011) A new way of therapy based on water memory-information: the Quantum biophysical approach.
  146. Sylvester JJ (1853) On a theory of the syzygetic relations of two rational integral functions, Comprising an application to the theory of Sturm’s functions, and that of the greatest algebraical common measure. Philos Trans R Soc Lond 143:407–548. doi:10.1098/rstl.1853.0018, see also and
  147. Szentágothai J (1949) The elementary vestibulo-ocular reflex arc. J Neurophysiol 13(6):395–407. Google Scholar
  148. Timchenko LT, Caskey CT (1999) Triplet repeat disorders: discussion of molecular mechanisms. Cell Mol Life Sci 55(11):1432–47. Google Scholar
  149. Venter C (2010) Multiple personal genomes await. Nature 464:676–677. doi:10.1038/464676a; Published online 31 March 2010. Google Scholar
  150. Venter JC, Adams MD, Myers EW, Li PW, Mural RJ, Sutton GG et al (2001) Science 291(5507):1304–1351. doi:10.1126/science.1058040.
  151. Wang L, Brown SJ (2006) Bind N: a web-based tool for efficient prediction of DNA and RNA binding sites in amino acid sequences. Nucleic Acids Res 34:W243–W248.
  152. Watson JD (2008) Editorial: the failed war on cancer, People against cancer.
  153. Watson JD (2009) To fight cancer, know the enemy. New York Times August 6, A29
  154. Weyl H (1912) Das asymptotisce lerteihingsgesetz der Eigenwerte linearer partieller Differentialgleichungen. Math Ann 71:441–479. See also in
  155. Wiener N (1948) Cybernetics or control and communication in the cnimal and the machine. Hermann & Cie Editeurs/The Technology Press/Wiley, Paris, Cambridge, MA, New York.
  156. Yamashita S, Tsujino Y, Moriguchi K, Tatematsu M, Ushijima T (2006) Chemical genomic screening for methylation-silenced genes in gastric cancer cell lines using 5-aza-2’-deoxycytidine treatment and oligonucleotide microarray. Cancer Sci 97:64–71. Google Scholar
  157. Zhuangzi (around the 4th century BC) Stanford encyclopedia of philosophy
  158. Zipf GK (1949) Human behaviour and the principle of least-effort. Addison-Wesley, Cambridge, MAGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Andras J. Pellionisz
    • 1
  • Roy Graham
    • 2
  • Peter A. Pellionisz
    • 3
  • Jean-Claude Perez
    • 4
  1. 1.HolGenTechSunnyvaleUSA
  2. 2.DRC ComputerSunnyvaleUSA
  3. 3.UCLAWestwoodUSA
  4. 4.IBM EmeritusMartignasFrance

Personalised recommendations