Skip to main content
SpringerLink
Log in

Universality-Diversity Paradigm: Music, Materiomics, and Category Theory

  • Chapter
Book cover Biomateriomics

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 165))

Abstract

The transition from the material structure to function, or from nanoscale components to the macroscale system, is a challenging proposition. Recognizing how Nature accomplishes such a feat—through universal structural elements, relatively weak building blocks, and self-assembly—is only part of the solution. The complexity bestowed by hierarchical multi-scale structures is not only found in biological materials and systems—it arises naturally within other fields such as music or language, with starkly different functions. If we wish to exploit understanding of the structure of music as it relates to materials, we need to define the relevant properties and functional relations in an abstract sense. One approach may lie in category theory, presented here in the form of ontology logs (ologs), that can transcend the traditional definitions of materials, music, or language, in a consistent and mathematically robust manner.

A sentence should contain no unnecessary words, a paragraph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts…

William Strunk, Jr. and E.B. White, The Elements of Style (1919)

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Systems biology can be considered an umbrella term, encompassing many of the -omic fields previously discussed such as genomics, phenomics, proteomics, interactomics, etc. Indeed, “materiomics” itself is concerned with the material system.

  2. 2.

    http://www.facebook.com.

  3. 3.

    In graphene oxide, for instance, it has been shown both computationally and experimentally that there exists an optimal water content for a fully formed H-bond network between functionalized graphene layers [131]. Additional water and associated H-bonds serve to weaken the system—similar to the cooperativity of H-bonds in β-sheets.

References

  1. R.C. Strohman, The coming kuhnian revolution in biology—commentary. Nat. Biotechnol. 15(3), 194 (1997)

    CAS  Google Scholar 

  2. S. Huang, Complexity—the practical problems of post-genomic biology. Nat. Biotechnol. 18(5), 471–472 (2000)

    CAS  Google Scholar 

  3. A. Lazaris, S. Arcidiacono, Y. Huang, J.F. Zhou, F. Duguay, N. Chretien, E.A. Welsh, J.W. Soares, C.N. Karatzas, Spider silk fibers spun from soluble recombinant silk produced in mammalian cells. Science 295(5554), 472–476 (2002)

    CAS  Google Scholar 

  4. X.X. Xia, Z.G. Qian, C.S. Ki, Y.H. Park, D.L. Kaplan, S.Y. Lee, Native-sized recombinant spider silk protein produced in metabolically engineered escherichia coli results in a strong fiber. Proc. Natl. Acad. Sci. USA 107(32), 14059–14063 (2010)

    CAS  Google Scholar 

  5. S. Eilenberg, S. Maclane, General theory of natural equivalences. Trans. Am. Math. Soc. 58(Sep), 231–294 (1945)

    Google Scholar 

  6. D.I. Spivak, R.E. Kent, Ologs: a categorical framework for knowledge representation. PLoS ONE 7(1), e24274 (2001)

    Google Scholar 

  7. T. Giesa, D.I. Spivak, M.J. Buehler, Reoccurring patterns in hierarchical protein materials and music: the power of analogies. BioNanoScience 1(4), 153–161 (2011)

    Google Scholar 

  8. N. Goldenfeld, L.P. Kadanoff, Simple lessons from complexity. Science 284(5411), 87–89 (1999)

    CAS  Google Scholar 

  9. R.B. Laughlin, D. Pines, The theory of everything. Proc. Natl. Acad. Sci. USA 97(1), 28–31 (2000)

    CAS  Google Scholar 

  10. D. Falk, Universe on a T-shirt: The Quest for the Theory of Everything, 1st edn. (Arcade Publishing, New York, 2004)

    Google Scholar 

  11. U. Alon, Simplicity in biology. Nature 446(7135), 497 (2007)

    CAS  Google Scholar 

  12. J.M. Carlson, J. Doyle, Complexity and robustness. Proc. Natl. Acad. Sci. USA 99, 2538–2545 (2002)

    Google Scholar 

  13. M.E. Csete, J.C. Doyle, Reverse engineering of biological complexity. Science 295(5560), 1664–1669 (2002)

    CAS  Google Scholar 

  14. T. Ackbarow, M.J. Buehler, Hierarchical coexistence of universality and diversity controls robustness and multi-functionality in protein materials. J. Comput. Theor. Nanosci. 5(7), 1193–1204 (2008)

    CAS  Google Scholar 

  15. M.J. Buehler, Nanomaterials: strength in numbers. Nat. Nanotechnol. 5, 172–174 (2010)

    CAS  Google Scholar 

  16. S.J. Eichhorn, C.A. Baille, N. Zafeiropoulos, L.Y. Mwaikambo, M.P. Ansell, A. Dufresne, K.M. Entwistle, P.J. Herrera-Franco, G.C. Escamilla, L. Groom, M. Hughes, C. Hill, T.G. Rials, P.M. Wild, Current international research into cellulosic fibres and composites. J. Mater. Sci. 36, 2107–2131 (2001)

    CAS  Google Scholar 

  17. W. Hamad, Cellulosic Materials: Fibers, Networks and Composites (Kluwer Academic, Boston, 2002)

    Google Scholar 

  18. K. Abe, H. Yano, Comparison of the characteristics of cellulose microfibril aggregates of wood, rice straw and potato tuber. Cellulose 16(6) (2009)

    CAS  Google Scholar 

  19. Y. Nishiyama, Structure and properties of the cellulose microfibril. J. Wood Sci. 55, 241–249 (2009)

    CAS  Google Scholar 

  20. H. Herrmann, U. Aebi, Intermediate filaments: molecular structure, assembly mechanism, and integration into functionally distinct intracellular scaffolds. Annu. Rev. Biochem. 73, 749–789 (2004)

    CAS  Google Scholar 

  21. N. Mucke, L. Kreplak, R. Kirmse, T. Wedig, H. Herrmann, U. Aebi, J. Langowski, Assessing the flexibility of intermediate filaments by atomic force microscopy. J. Mol. Biol. 335(5), 1241–1250 (2004)

    CAS  Google Scholar 

  22. S. Kim, P. Wong, P.A. Coulombe, A keratin cytoskeletal protein regulates protein synthesis and epithelial cell growth. Nature 441(7091), 362–365 (2006)

    CAS  Google Scholar 

  23. L.H. Gu, P.A. Coulombe, Keratin function in skin epithelia: a broadening palette with surprising shades. Curr. Opin. Cell Biol. 19(1), 13–23 (2007)

    CAS  Google Scholar 

  24. K.N. Dahl, D.E. Discher, K.L. Wilson, The nuclear envelope lamina network has elasticity and a compressibility limit suggestive of a “molecular shock absorber”. Mol. Biol. Cell 15, 119–120 (2004)

    Google Scholar 

  25. A.C. Rowat, J. Lammerding, J.H. Ipsen, Mechanical properties of the cell nucleus and the effect of emerin deficiency. Biophys. J. 91(12), 4649–4664 (2006)

    CAS  Google Scholar 

  26. T. Ackbarow, X. Chen, S. Keten, M.J. Buehler, Hierarchies, multiple energy barriers and robustness govern the fracture mechanics of alpha-helical and beta-sheet protein domains. Proc. Natl. Acad. Sci. USA 104, 16410–16415 (2007)

    CAS  Google Scholar 

  27. S.V. Strelkov, J. Schumacher, P. Burkhard, U. Aebi, H. Herrmann, Crystal structure of the human lamin a coil 2b dimer: implications for the head-to-tail association of nuclear lamins. J. Mol. Biol. 343(4), 1067–1080 (2004)

    CAS  Google Scholar 

  28. M. Arslan, Z. Qin, M.J. Buehler, Coiled-coil intermediate filament stutter instability and molecular unfolding. Comput. Methods Biomech. Biomed. Eng. 14(5), 483–489 (2011)

    Google Scholar 

  29. A. Kaminska, S.V. Strelkov, B. Goudeau, M. Olive, A. Dagvadorj, A. Fidzianska, M. Simon-Casteras, A. Shatunov, M.C. Dalakas, I. Ferrer, H. Kwiecinski, P. Vicart, L.G. Goldfarb, Small deletions disturb desmin architecture leading to breakdown of muscle cells and development of skeletal or cardioskeletal myopathy. Human Genet. 114(3), 306–313 (2004)

    CAS  Google Scholar 

  30. B. Kiss, A. Karsai, M.S.Z. Kellermayer, Nanomechanical properties of desmin intermediate filaments. J. Struct. Biol. 155(2), 327–339 (2006)

    CAS  Google Scholar 

  31. M.J. Buehler, Y.C. Yung, Deformation and failure of protein materials in physiologically extreme conditions and disease. Nat. Mater. 8(3), 175–188 (2009)

    CAS  Google Scholar 

  32. M.J. Buehler, Tu(r)ning weakness to strength. Nano Today 5(5), 379–383 (2010)

    CAS  Google Scholar 

  33. J.E. Padilla, C. Colovos, T.O. Yeates, Nanohedra: using symmetry to design self assembling protein cages, layers, crystals, and filaments. Proc. Natl. Acad. Sci. USA 98(5), 2217–2221 (2001)

    CAS  Google Scholar 

  34. M.M.C. Bastings, T.F.A. de Greef, J.L.J. van Dongen, M. Merkx, E.W. Meijer, Macrocyclization of enzyme-based supramolecular polymers. Chem. Sci. 1(1), 79–88 (2010)

    CAS  Google Scholar 

  35. Y. Mori, K. Minamihata, H. Abe, M. Goto, N. Kamiya, Protein assemblies by site-specific avidin-biotin interactions. Organic & Biomolecular Chemistry 9(16), 5641–5644 (2011)

    CAS  Google Scholar 

  36. N. Barkai, S. Leibler, Robustness in simple biochemical networks. Nature 387(6636), 913–917 (1997)

    CAS  Google Scholar 

  37. L.H. Hartwell, J.J. Hopfield, S. Leibler, A.W. Murray, From molecular to modular cell biology. Nature 402(6761), C47–C52 (1999)

    CAS  Google Scholar 

  38. L. Hartwell, Theoretical biology—a robust view of biochemical pathways. Nature 387(6636), 855 (1997)

    CAS  Google Scholar 

  39. K.M. Dipple, J.K. Phelan, E.R.B. McCabe, Consequences of complexity within biological networks: robustness and health, or vulnerability and disease. Mol. Genet. Metab. 74(1–2), 45–50 (2001)

    CAS  Google Scholar 

  40. H. Gao, B. Ji, I.L. Jager, E. Arzt, P. Fratzl, Materials become insensitive to flaws at nanoscale: lessons from nature. Proc. Natl. Acad. Sci. USA 100(10), 5597–5600 (2003)

    CAS  Google Scholar 

  41. F. Vollrath, D. Porter, Spider silk as archetypal protein elastomer. Soft Matter 2(5), 377–385 (2006)

    CAS  Google Scholar 

  42. S. Rammensee, U. Slotta, T. Scheibel, A.R. Bausch, Assembly mechanism of recombinant spider silk proteins. Proc. Natl. Acad. Sci. USA 105(18), 6590–6595 (2008)

    CAS  Google Scholar 

  43. S. Keten, M.J. Buehler, Nanostructure and molecular mechanics of spider dragline silk protein assemblies. J. R. Soc. Interface 7(53), 1709–1721 (2010)

    CAS  Google Scholar 

  44. S. Keten, M.J. Buehler, Geometric confinement governs the rupture strength of h-bond assemblies at a critical length scale. Nano Lett. 8(2), 743–748 (2008)

    CAS  Google Scholar 

  45. S. Keten, M.J. Buehler, Asymptotic strength limit of hydrogen-bond assemblies in proteins at vanishing pulling rates. Phys. Rev. Lett. 100(19), 198301 (2008)

    Google Scholar 

  46. M.J. Buehler, S. Keten, Colloquium: failure of molecules, bones, and the earth itself. Rev. Mod. Phys. 82(2), 1459–1487 (2010)

    Google Scholar 

  47. S. Keten, Z. Xu, B. Ihle, M.J. Buehler, Nanoconfinement controls stiffness, strength and mechanical toughness of beta-sheet crystals in silk. Nat. Mater. 9(4), 359–367 (2010)

    CAS  Google Scholar 

  48. K. Autumn, Y.A. Liang, S.T. Hsieh, W. Zesch, W.P. Chan, T.W. Kenny, R. Fearing, R.J. Full, Adhesive force of a single gecko foot-hair. Nature 405(6787), 681–685 (2000)

    CAS  Google Scholar 

  49. E. Arzt, S. Gorb, R. Spolenak, From micro to nano contacts in biological attachment devices. Proc. Natl. Acad. Sci. USA 100(19), 10603–10606 (2003)

    CAS  Google Scholar 

  50. M. Varenberg, N.M. Pugno, S.N. Gorb, Spatulate structures in biological fibrillar adhesion. Soft Matter 6(14), 3269–3272 (2010)

    CAS  Google Scholar 

  51. A. Nova, S. Keten, N.M. Pugno, A. Redaelli, M.J. Buehler, Molecular and nanostructural mechanisms of deformation, strength and toughness of spider silk fibrils. Nano Lett. 10(7), 2626–2634 (2010)

    CAS  Google Scholar 

  52. R. Kamien, Music: An Appreciation (McGraw–Hill Humanities/Social Sciences/Languages, New York, 2007)

    Google Scholar 

  53. C. Dodge, T.A. Jerse, Computer Music: Synthesis, Composition, and Performance (Cengage Learning, New York, 1997)

    Google Scholar 

  54. P. Miller, The Smart Swarm: How Understanding Flocks, Schools, and Colonies Can Make Us Better at Communicating, Decision Making, and Getting Things Done (Avery, New York, 2010)

    Google Scholar 

  55. F. Lerdahl, R. Jackendoff, An Overview of Hierarchical Structures in Music (MIT Press, Cambridge, 1983)

    Google Scholar 

  56. F. Lerdahl, R. Jackendoff, An overview of hierarchical structure in music. Music Percept. 1(2), 229–252 (1983)

    Google Scholar 

  57. D.R. Hofstadter, Metamagical Themas: Questing for the Essence of Mind and Pattern (Basic Books, New York, 1985)

    Google Scholar 

  58. J.S. Bamberger, A. Hernndez, Developing Musical Intuitions: A Project-Based Introduction to Making and Understanding Music (Oxford University Press, New York, 2000)

    Google Scholar 

  59. D. Lewin, Generalized Musical Intervals and Transformations (Oxford University Press, New York, 2007)

    Google Scholar 

  60. J. Schmalfeldt, In the Process of Becoming: Analytic and Philosophical Perspectives on Form in Early Nineteenth-Century Music. Oxford Studies in Music Theory (Oxford University Press, New York, 2011)

    Google Scholar 

  61. R. Oppenheimer, Analogy in science. Am. Psychol. 11(3), 127–135 (1956)

    Google Scholar 

  62. S. Vosniadou, A. Ortony, Similarity and Analogical Reasoning (Cambridge University Press, Cambridge, 1989)

    Google Scholar 

  63. J. Bransford, How People Learn: Brain, Mind, Experience, and School, expanded edn. (National Academy Press, Washington, 2000)

    Google Scholar 

  64. D. Gentner, K.J. Holyoak, B.N. Kokinov, The Analogical Mind: Perspectives from Cognitive Science (MIT Press, Cambridge, 2001)

    Google Scholar 

  65. P.C. Taylor, B.J. Fraser, D.L. Fisher, Monitoring constructivist classroom learning environments. Int. J. Educ. Res. 27(4), 293–302 (1997)

    Google Scholar 

  66. R. Stavy, Using analogy to overcome misconceptions about conservation of matter. J. Res. Sci. Teach. 28(4), 305–313 (1991)

    Google Scholar 

  67. C.-C. Tsai, Overcoming junior high school students’ misconceptions about microscopic views of phase change: a study of an analogy activity. J. Sci. Educ. Technol. 8(1), 83–91 (1999)

    Google Scholar 

  68. L.R. Novick, K.J. Holyoak, Mathematical problem-solving by analogy. J. Exp. Psychol. Learn. Mem. Cogn. 17(3), 398–415 (1991)

    CAS  Google Scholar 

  69. S. Kaniel, Y. Harpaz-Itay, E. Ben-Amram, Analogy construction versus analogy solution, and their influence on transfer. Learn. Instr. 16(6), 583–591 (2006)

    Google Scholar 

  70. W. Croft, Typology and Universals, 2nd edn. Cambridge Textbooks in Linguistics (Cambridge University Press, Cambridge, 2003)

    Google Scholar 

  71. G. Sica, What is Category Theory? Advanced Studies in Mathematics and Logic (Polimetrica, Monza, 2006)

    Google Scholar 

  72. N.C. Ellis, D. Larsen-Freeman, R.C. in language learning (Ann Arbor, Mich.), in Language as a Complex Adaptive System. The Best of Language Learning Series (Wiley–Blackwell, Chichester, 2009)

    Google Scholar 

  73. W. Croft, Pragmatic functions, semantic classes, and lexical categories. Linguistics 48(3), 787–796 (2010)

    Google Scholar 

  74. F.W. Lawvere, S.H. Schanuel, Conceptual Mathematics. A First Introduction to Categories (Cambridge University Press, Cambridge, 2009)

    Google Scholar 

  75. S. Awodey, Category Theory, 2nd edn. Oxford Logic Guides, vol. 52 (Oxford University Press, London, 2010)

    Google Scholar 

  76. R. Brown, T. Porter, Category theory: an abstract setting for analogy and comparison, in What is Category Theory? (Polimetrica, Monza, 2006)

    Google Scholar 

  77. D.I. Spivak, T. Giesa, E. Wood, M.J. Buehler, Category theoretic analysis of hierarchical protein materials and social networks. PLoS ONE 6(9), e23911 (2011)

    CAS  Google Scholar 

  78. P. Csermely, Creative elements: network-based predictions of active centres in proteins and cellular and social networks. Trends Biochem. Sci. 33(12), 569–576 (2008)

    CAS  Google Scholar 

  79. N.M. Pugno, A statistical analogy between collapse of solids and death of living organisms: proposal for a ‘law of life’. Med. Hypotheses 69(2), 441–447 (2007)

    Google Scholar 

  80. M. Gimona, Protein linguistics—a grammar for modular protein assembly? Nat. Rev. Mol. Cell Biol. 7(1), 68–73 (2006)

    CAS  Google Scholar 

  81. S.C. Ji, Isomorphism between cell and human languages: molecular biological, bioinformatic and linguistic implications. Biosystems 44(1), 17–39 (1997)

    CAS  Google Scholar 

  82. H. Peterlik, P. Roschger, K. Klaushofer, P. Fratzl, From brittle to ductile fracture of bone. Nat. Mater. 5(1), 52–55 (2006)

    CAS  Google Scholar 

  83. D. Taylor, J.G. Hazenberg, T.C. Lee, Living with cracks: damage and repair in human bone. Nat. Mater. 6(4), 263–268 (2007)

    CAS  Google Scholar 

  84. D.A. Fletcher, R.D. Mullins, Cell mechanics and the cytoskeleton. Nature 463(7280), 485–492 (2010)

    CAS  Google Scholar 

  85. N. Chomsky, Syntactic Structures, 2nd edn. (de Gruyter, Berlin, 2002)

    Google Scholar 

  86. M. Moortgat, Categorial Investigations: Logical and Linguistic Aspects of the Lambek Calculus (Foris Publications, Providence, 1988)

    Google Scholar 

  87. M.D. Hauser, N. Chomsky, W.T. Fitch, The faculty of language: what is it, who has it, and how did it evolve? Science 298(5598), 1569–1579 (2002)

    CAS  Google Scholar 

  88. D.B. Searls, The language of genes. Nature 420(6912), 211–217 (2002)

    CAS  Google Scholar 

  89. E. Moggi, A Category-Theoretic Account of Program Modules (Springer, London, 1989)

    Google Scholar 

  90. P. Wadler, Monads for functional programming. Math. Struct. Comput. Sci. 2, 461–493 (1992)

    Google Scholar 

  91. M. Barr, C. Wells, Category Theory for Computing Science (Prentice Hall, New York, 1995)

    Google Scholar 

  92. B.C. Pierce, Basic Category Theory for Computer Scientists (MIT Press, Cambridge, 1996)

    Google Scholar 

  93. R. Lakes, Materials with structural hierarchy. Nature 361(6412), 511–515 (1993)

    Google Scholar 

  94. E.M. Marcotte, M. Pellegrini, M.J. Thompson, T.O. Yeates, D. Eisenberg, A combined algorithm for genome-wide prediction of protein function. Nature 402, 83–86 (1999)

    CAS  Google Scholar 

  95. E.M. Marcotte, Detecting protein function and protein-protein interactions from genome sequences. Science 285, 751–753 (1999)

    CAS  Google Scholar 

  96. D. Eisenberg, E.M. Marcotte, I. Xenarios, T.O. Yeates, Protein function in the post-genomic era. Nature 405(6788), 823–826 (2000)

    CAS  Google Scholar 

  97. F.W. Lawvere, The category of categories as a foundation for mathematics, in Proceedings of the Conference on Categorical Algebra (Springer, New York, 1965)

    Google Scholar 

  98. S.M. Lane, Categories for the Working Mathematician, 2nd edn. (Springer, New York, 1998)

    Google Scholar 

  99. A. Nijholt, From left-regular to Greibach normal form grammars. Inf. Process. Lett. 9(1), 51–55 (1979)

    Google Scholar 

  100. N.C. Maddage, C. Xu, M.S. Kankanhalli, X. Shao, Content-based music structure analysis with applications to music semantics understanding, in Proceedings of the 12th Annual ACM International Conference on Multimedia (2004), pp. 112–119

    Google Scholar 

  101. D. Tymoczko, A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. Oxford Studies in Music Theory (Oxford University Press, New York, 2011)

    Google Scholar 

  102. G. Deline, F. Lin, D. Wen, D. Gagevic, A. Kinshuk, Ontology-driven development of intelligent educational systems, in 2007 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, vols. 1 and 2 (2007), pp. 34–37

    Google Scholar 

  103. M. Halle, From Memory to Speech and Back: Papers on Phonetics and Phonology, 1954–2002. Phonology and Phonetics (de Gruyter, Berlin, 2002)

    Google Scholar 

  104. G.N. Clements, The geometry of phonological features. Phonology 2, 225–252 (1985)

    Google Scholar 

  105. A.S. Abramson, Laryngeal timing in consonant distinctions. Phonetica 34(4), 295–303 (1977)

    CAS  Google Scholar 

  106. M. Jessen, C. Ringen, Laryngeal features in German. Phonology 19, 189–218 (2002)

    Google Scholar 

  107. R. Paparcone, M.J. Buehler, Failure of a beta(1–40) amyloid fibrils under tensile loading. Biomaterials 32(13), 3367–3374 (2011)

    CAS  Google Scholar 

  108. J.E. Cutting, B.S. Rosner, Categories and boundaries in speech and music. Percept. Psychophys. 16(3), 564–570 (1974)

    Google Scholar 

  109. J.A. Moorer, Signal-processing aspects of computer music—survey. Proc. IEEE 65(8), 1108–1137 (1977)

    Google Scholar 

  110. D. Frishman, P. Argos, Knowledge-based protein secondary structure assignment. Protein. Struct. Funct. Genet. 23(4), 566–579 (1995)

    CAS  Google Scholar 

  111. Z.R. Sun, S.J. Hua, A novel method of protein secondary structure prediction with high segment overlap measure: support vector machine approach. J. Mol. Biol. 308(2), 397–407 (2001)

    Google Scholar 

  112. S. Keten, M.J. Buehler, Atomistic model of the spider silk nanostructure. Appl. Phys. Lett. 96(15) (2010)

    Google Scholar 

  113. R. Erickson, Sound Structure in Music (University of California Press, Berkeley, 1975)

    Google Scholar 

  114. D. Deutsch, Music recognition. Psychol. Rev. 76(3), 300 (1969)

    CAS  Google Scholar 

  115. J. Bharucha, C.L. Krumhansl, The representation of harmonic structure in music—hierarchies of stability as a function of context. Cognition 13(1), 63–102 (1983)

    CAS  Google Scholar 

  116. B. Pardo, W.P. Birmingham, Algorithms for chordal analysis. Comput. Music J. 26(2), 27–49 (2002)

    Google Scholar 

  117. D.M. Randel, The Harvard Dictionary of Music, 4th edn. (Belknap Press of Harvard University Press, Cambridge, 2003)

    Google Scholar 

  118. K. Jensen, Multiple scale music segmentation using rhythm, timbre, and harmony. EURASIP J. Adv. Signal Process. (2007)

    Google Scholar 

  119. C.L. Krumhansl, R.N. Shepard, Quantification of the hierarchy of tonal functions within a diatonic context. J. Exp. Psychol. Hum. Percept. Perform. 5(4), 579–594 (1979)

    CAS  Google Scholar 

  120. P. Izar, R.G. Ferreira, T. Sato, Describing the organization of dominance relationships by dominance-directed tree method. Am. J. Primatol. 68(2), 189–207 (2006)

    Google Scholar 

  121. J.A. Sloboda, Music structure and emotional response: some empirical findings. Psychol. Music 19, 110–120 (1991)

    Google Scholar 

  122. T. Schafer, P. Sedlmeier, From the functions of music to music preference. Psychol. Music 37(3), 279–300 (2009)

    Google Scholar 

  123. W.M. Hartmann, Signals, Sound, and Sensation. Modern Acoustics and Signal Processing (American Institute of Physics, Woodbury, 1997)

    Google Scholar 

  124. T. Giesa, M. Arslan, N. Pugno, M.J. Buehler, Nanoconfinement of spider silk fibrils begets superior strength, extensibility and toughness. Nano Lett. 11(11), 5038–5046 (2011)

    CAS  Google Scholar 

  125. E. Bigand, R. Parncutt, F. Lerdahl, Perception of musical tension in short chord sequences: the influence of harmonic function, sensory dissonance, horizontal motion, and musical training. Percept. Psychophys. 58(1), 125–141 (1996)

    Google Scholar 

  126. M. Rohrmeier, Towards a generative syntax of tonal harmony. J. Math. Music 5(1), 35–53 (2011)

    Google Scholar 

  127. S.W. Cranford, A. Tarakanova, N. Pugno, M.J. Buehler, Nonlinear material behaviour of spider silk yields robust webs. Nature (2012)

    Google Scholar 

  128. N.V. Medhekar, A. Ramasubramaniam, R.S. Ruoff, V.B. Shenoy, Hydrogen bond networks in graphene oxide composite paper: structure and mechanical properties. ACS Nano 4(4), 2300–2306 (2010)

    CAS  Google Scholar 

  129. J. Alegre-Cebollada, P. Kosuri, J.A. Rivas-Pardo, J.M. Fernndez, Direct observation of disulfide isomerization in a single protein. Nat. Chem. 3(11), 882–887 (2011)

    CAS  Google Scholar 

  130. S. Keten, C.-C. Chou, A.C.T. van Duin, M.J. Buehler, Tunable nanomechanics of protein disulfide bonds in redox microenvironments. J. Mech. Behav. Biomed. Mat. 5(1), 32–40 (2012)

    CAS  Google Scholar 

  131. O. Compton, S. Cranford, Z. An, K. Putz, C. Brinson, M.J. Buehler, S.B. Ngyen, Tuning the mechanical properties of graphene oxide paper and its associated polymer nanocomposites by controlling cooperative intersheet hydrogen bonding. ACS Nano 6(3), 2008–2019 (2011)

    Google Scholar 

  132. P.K. Zysset, X.E. Guo, C.E. Hoffler, K.E. Moore, S.A. Goldstein, Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J. Biomech. 32(10), 1005–1012 (1999)

    CAS  Google Scholar 

  133. M.D. Lima, S.L. Fang, X. Lepro, C. Lewis, R. Ovalle-Robles, J. Carretero-Gonzalez, E. Castillo-Martinez, M.E. Kozlov, J.Y. Oh, N. Rawat, C.S. Haines, M.H. Haque, V. Aare, S. Stoughton, A.A. Zakhidov, R.H. Baughman, Biscrolling nanotube sheets and functional guests into yarns. Science 331(6013), 51–55 (2011)

    CAS  Google Scholar 

  134. K.T. Nam, D.W. Kim, P.J. Yoo, C.Y. Chiang, N. Meethong, P.T. Hammond, Y.M. Chiang, A.M. Belcher, Virus-enabled synthesis and assembly of nanowires for lithium ion battery electrodes. Science 312(5775), 885–888 (2006)

    CAS  Google Scholar 

  135. N. Huebsch, D.J. Mooney, Inspiration and application in the evolution of biomaterials. Nature 462(7272), 426–432 (2009)

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Steven W. Cranford & Markus J. Buehler

Authors
  1. Steven W. Cranford
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Markus J. Buehler
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Cranford, S.W., Buehler, M.J. (2012). Universality-Diversity Paradigm: Music, Materiomics, and Category Theory. In: Biomateriomics. Springer Series in Materials Science, vol 165. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1611-7_4

Download citation

Publish with us

Policies and ethics

Search

Navigation