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Quantitative languages

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        <b>Quantitative Languages for Complex Systems</b>
      
      
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        <b>Mark A. Smith, Yaneer Bar-Yam and William Gelbart</b>
      
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        We believe that many fields of scientific study are hampered by the lack of precise 
        language to describe the structure, behavior, and dynamics of complex systems. New 
        quantitative languages are needed. The challenge is to develop intuitive, and yet precise 
        and systematic mechanisms for description. Such languages will merge the strength of human 
        language in specifying objects, attributes, relationships and processes with the ability 
        of computer systems to display and manipulate numerical aspects of systematic description. 
        They will also serve as bridges between experimental observations and theoretical 
        treatments.
      
      
        
      
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        The creation of a particular language involves connecting qualitative terms and 
        quantitative representations of the system. We illustrate the development of such 
        languages using the structure of drosophila (fruit fly) wings. In this language, the 
        description of a wing is composed of descriptions of veins (structural support elements of 
        the wing), and the structural constraints on these veins. The veins are described as 
        mathematical curves which capture their shape. The constraints that are satisfied by these 
        curves as parts of the wing are incorporated in the description of the wing. The nature of 
        a "wing" as a class of objects is captured by the set of curves and their constraints. A 
        description of a particular wing is captured by the specific values of parameters which 
        can be captured for individual real wings.
      
      
        
      
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        <u>Graphical illustration of a quantitative wing model <Standard.jpg></u>
      
      
        
      
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        Overlay of default quantitative wing model on real wing <GUI.jpg>
      
      
        <u>After capture of real wing structure-quantitative description of the real wing 
        <Edited.jpg></u>
      
      
        
      
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        <u>Short paper describing the quantitative language <quant_lang_paper.html></u>
      
      
        
      
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        <b>Papers:</b>
      
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        M. A. Smith, Y. Bar-Yam and W. Gelbart: Quntitative languages for complex systems applied 
        to biological structure, 
      
      
        <i>Nonlinear Dynamics in the Life and Social Sciences,</i>
      
      
         W. Sulis and I. Trofimova, eds., NATO Science Series A/320, pp.65-71, 2001, IOS Press. 
      
      
        <u>PDF file <NATOquantitative.pdf></u>
      
      
        
      
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