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  <div class="maketitle">
  <h2 class="titleHead"><a
id="x1-1doc"></a>
Santa Fe Institute Workshop<br />
Summary Description
  </h2>
  <div class="RRAP">
<span
class="cmr-10">(</span><span class="date" ><span
class="cmr-10">Dated: December 13, 2010</span></span><span
class="cmr-10">)</span>
  </div>
<div class="abstractheading"></div>
        <div class="abstract">
      <!--l. 50--><p class="noindent" ><span
class="cmbx-12">Title</span><span
class="cmr-12">:</span><br
class="newline" /><span
class="cmr-12">&#x00A0;      Randomness, Structure, and Causality:</span><br
class="newline" /><span
class="cmr-12">&#x00A0;</span><span
class="cmr-12">&#x00A0;</span><span
class="cmr-12">&#x00A0;          Measures of complexity from theory to applications</span><br
class="newline" />
      <span
class="cmbx-12">Dates</span><span
class="cmr-12">: 9-13 January 2011</span><br
class="newline" /> <span
class="cmbx-12">Location</span><span
class="cmr-12">: Santa Fe Institute, Santa Fe, New Mexico</span><br
class="newline" /> <span
class="cmbx-12">Organizers</span><span
class="cmr-12">:</span><br
class="newline" /><span
class="cmr-12">&#x00A0;      Jim Crutchfield (SFI and UC Davis, chaos@ucdavis.edu)</span><br
class="newline" /><span
class="cmr-12">&#x00A0;      Jon Machta (SFI and University of Massachusetts, machta@physics.umass.edu)</span>
        </div>
  <div class="frontpagefootnotes">
  </div>
  </div>
<a
id="likesection.1"></a>
  <h3 class="likesectionHead"><a
id="x1-1000"></a>Description</h3>
<!--l. 75--><p class="noindent" >In 1989, SFI hosted a workshop&#8212;<span
class="cmti-10x-x-109">Complexity, Entropy, and the Physics of Information</span>&#8212;on fundamental
                                                                                       
                                                                                       
definitions of complexity. This workshop and the proceedings that resulted [<a
href="#XZure89a">1</a>] stimulated a great deal of
thinking about how to define complexity. In many ways&#8212;some direct, many indirect&#8212;the foundational
theme colored much of SFI&#8217;s research planning and, more generally, the evolution of complex system
science since then. Complex systems science has considerably matured as a field in the intervening
decades and we believe it is now time to revisit fundamental aspects of the field in a workshop format at
SFI. Partly, this is to take stock; but it is also to ask what innovations are needed for the coming
decades, as complex systems continues to extend its influence in the sciences, engineering, and
humanities.
<!--l. 90--><p class="indent" >  The goal of the workshop is to bring together workers from a variety of fields to discuss structural and
dynamical measures of complexity appropriate for their field and the commonality between these
measures. Some of the questions that we will address in the workshop are:
      <ol  class="enumerate1" >
      <li
  class="enumerate" id="x1-1002x1">Are there fundamental measures of complexity that can be applied across disciplines or are
      measures of complexity necessarily tied to particular domains?
      </li>
      <li
  class="enumerate" id="x1-1004x2">How is a system&#8217;s causal organization, reflected in models of its dynamics, related to its
      complexity?
      </li>
      <li
  class="enumerate" id="x1-1006x3">Are  there  universal  mechanisms  at  work  that  lead  to  increases  in  complexity  or  does
      complexity arise for qualitatively different reasons in different settings?
      </li>
      <li
  class="enumerate" id="x1-1008x4">Can we reach agreement on general properties that all measures of complexity must have?
      </li>
      <li
  class="enumerate" id="x1-1010x5">How would the scientific community benefit from a consensus on the properties that measures
      of complexity should possess?</li></ol>
<!--l. 112--><p class="indent" >  It&#8217;s a four-day workshop with about 20 or so participants. We will have a stimulating and highly
interdisciplinary group with representation from physics, biology, computer science, social science, and
mathematics. An important goal is to understand the successes and difficulties in deploying complexity
measures in practice. And so, participants come from both theory and experiment, with a particular
emphasis on those who can constructively bridge the two.
<!--l. 120--><p class="indent" >  Since the 1989 SFI workshop, a number of distinct strands have developed in the effort to measure
complexity. Several of the well-developed strands are based on
                                                                                       
                                                                                       
      <ul class="itemize1">
      <li class="itemize">Predictive information and excess entropy&#x00A0;[<a
href="#XJunc79">2</a>&#8211;<a
href="#XCrut01a">7</a>],
      </li>
      <li class="itemize">Statistical complexity and causal structure&#x00A0;[<a
href="#XCrut88a">8</a>&#8211;<a
href="#XShal98a">10</a>],
      </li>
      <li class="itemize">Logical depth and computational complexity&#x00A0;[<a
href="#XBenn90">11</a>&#8211;<a
href="#XMach06a">15</a>], and
      </li>
      <li class="itemize">Effective complexity&#x00A0;[<a
href="#XGeLl96">16</a>,&#x00A0;<a
href="#Xay-2008">17</a>].</li></ul>
<!--l. 134--><p class="noindent" >While these measures are broadly based on information theory or the theory of computation, the full set of
connections and contrasts between them is not well developed. Some have sought to clarify
the relationship among these measures [<a
href="#XCrut01a">7</a>,&#x00A0;<a
href="#Xay-2008">17</a>&#8211;<a
href="#XFeld98b">20</a>] and so another goal of the workshop is
to foster this kind of comparative work by bringing together researchers developing various
measures.
<!--l. 141--><p class="indent" >  A second motivation for the workshop is to bring together workers interested in foundational
questions&#8212;who are mainly from the physics, mathematics, and computer science communities&#8212;with
complex systems scientists in experimental, data-driven fields who have developed quantitative
measures of complexity, organization, and emergence that are useful in their fields. The range of
data-driven fields using complexity measures is impressively broad: ranging from molecular
excitation dynamics [<a
href="#XNeru08a">21</a>] and spectroscopic observations of the conformational dynamics of
single molecules [<a
href="#XLi08a">22</a>] through modeling subgrid structure in turbulent fluid flows [<a
href="#XPalm00a">23</a>] and new
visualization methods for emergent flow patterns [<a
href="#XJani07a">24</a>] to monitoring market efficiency [<a
href="#XYang08a">25</a>] and the
organization of animal social structure [<a
href="#XAy07a">26</a>]. The intention is to find relations between the practically
motivated measures and the more general and fundamentally motivated measures. Can the
practically motivated measures be improved by an appreciation of fundamental principles? Can
fundamental definitions be sharpened by consideration of how they interact with real-world
data?
<!--l. 159--><p class="indent" >  Overall, the workshop&#8217;s intention is to re-ignite the efforts that began with <span
class="cmti-10x-x-109">Complexity, Entropy,</span>
<span
class="cmti-10x-x-109">and the Physics of Information </span>workshop. A new level of rigor, in concepts and in analysis,
is now apparent in how statistical mechanics, nonlinear dynamics, information theory, and
computation theory can be applied to complex systems. The meteoric rise of both computer
power and machine learning has led to new algorithms that address many of the original
computational difficulties in managing data from complex systems and in estimating various
complexity measures. Given progress on all these fronts, the time is ripe to develop a much closer
                                                                                       
                                                                                       
connection between fundamental theory and applications in many areas of complex systems
science.
<!--l. 1--><p class="indent" >
                                                                                        <a
id="likesection.2"></a><a
id="Q1-1-1"></a>
<!--l. 1--><p class="noindent" >
    <div class="thebibliography">
    <p class="bibitem" ><span class="biblabel">
<a
id="XZure89a"></a><span
class="cmr-10">[1]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">W.</span><span
class="cmr-10">&#x00A0;Zurek, editor. </span><span
class="cmti-10">Entropy, Complexity, and the Physics of Information</span><span
class="cmr-10">, volume VIII of </span><span
class="cmti-10">SFI Studies</span>
    <span
class="cmti-10">in the Sciences of Complexity</span><span
class="cmr-10">. Addison-Wesley, Reading, Massachusetts, 1990.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XJunc79"></a><span
class="cmr-10">[2]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">A.</span><span
class="cmr-10">&#x00A0;del Junco and M.</span><span
class="cmr-10">&#x00A0;Rahe.  Finitary codings and weak bernoulli partitions.  </span><span
class="cmti-10">Proc. AMS</span><span
class="cmr-10">, 75:259,</span>
    <span
class="cmr-10">1979.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XCrut82b"></a><span
class="cmr-10">[3]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">J.</span><span
class="cmr-10">&#x00A0;P. Crutchfield and N.</span><span
class="cmr-10">&#x00A0;H. Packard. Symbolic dynamics of one-dimensional maps: Entropies, finite</span>
    <span
class="cmr-10">precision, and noise. </span><span
class="cmti-10">Intl. J. Theo. Phys.</span><span
class="cmr-10">, 21:433, 1982.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XErik87"></a><span
class="cmr-10">[4]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">K-E. Eriksson and K.</span><span
class="cmr-10">&#x00A0;Lindgren. Structural information in self-organizing systems. </span><span
class="cmti-10">Physica Scripta</span><span
class="cmr-10">,</span>
    <span
class="cmr-10">1987.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XGras86"></a><span
class="cmr-10">[5]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">P.</span><span
class="cmr-10">&#x00A0;Grassberger.  Toward a quantitative theory of self-generated complexity.  </span><span
class="cmti-10">Intl. J. Theo. Phys.</span><span
class="cmr-10">,</span>
    <span
class="cmr-10">25:907, 1986.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XEbel99a"></a><span
class="cmr-10">[6]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">W.</span><span
class="cmr-10">&#x00A0;Ebeling, L.</span><span
class="cmr-10">&#x00A0;Molgedey, J.</span><span
class="cmr-10">&#x00A0;Kurths, and U.</span><span
class="cmr-10">&#x00A0;Schwarz.  Entropy, complexity, predictability and</span>
    <span
class="cmr-10">data analysis of time series and letter sequences. </span><a
href=" http://summa.physik.hu-berlin.de/tsd/" class="url" ><span
class="cmtt-10">http://summa.physik.hu-berlin.de/tsd/</span></a><span
class="cmr-10">, 1999.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XCrut01a"></a><span
class="cmr-10">[7]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">J.</span><span
class="cmr-10">&#x00A0;P. Crutchfield and D.</span><span
class="cmr-10">&#x00A0;P. Feldman. Regularities unseen, randomness observed: Levels of entropy</span>
    <span
class="cmr-10">convergence. </span><span
class="cmti-10">CHAOS</span><span
class="cmr-10">, 13(1):25&#8211;54, 2003.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
                                                                                       
                                                                                       
<a
id="XCrut88a"></a><span
class="cmr-10">[8]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">J.</span><span
class="cmr-10">&#x00A0;P. Crutchfield and K.</span><span
class="cmr-10">&#x00A0;Young. Inferring statistical complexity. </span><span
class="cmti-10">Phys. Rev. Let.</span><span
class="cmr-10">, 63:105&#8211;108, 1989.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XCrut97a"></a><span
class="cmr-10">[9]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">J.</span><span
class="cmr-10">&#x00A0;P. Crutchfield and D.</span><span
class="cmr-10">&#x00A0;P. Feldman. Statistical complexity of simple one-dimensional spin systems.</span>
    <span
class="cmti-10">Phys. Rev. E</span><span
class="cmr-10">, 55(2):1239R&#8211;1243R, 1997.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XShal98a"></a><span
class="cmr-10">[10]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">C.</span><span
class="cmr-10">&#x00A0;R. Shalizi and J.</span><span
class="cmr-10">&#x00A0;P. Crutchfield.  Computational mechanics: Pattern and prediction, structure</span>
    <span
class="cmr-10">and simplicity. </span><span
class="cmti-10">J. Stat. Phys.</span><span
class="cmr-10">, 104:817&#8211;879, 2001.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XBenn90"></a><span
class="cmr-10">[11]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">C.</span><span
class="cmr-10">&#x00A0;H. Bennett. How to define complexity in physics, and why. In W.</span><span
class="cmr-10">&#x00A0;H. Zurek, editor, </span><span
class="cmti-10">Complexity,</span>
    <span
class="cmti-10">Entropy and the Physics of Information</span><span
class="cmr-10">, page 137. SFI Studies in the Sciences of Complexity, Vol.</span><span
class="cmr-10">&#x00A0;7,</span>
    <span
class="cmr-10">Addison-Wesley, 1990.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XVita93a"></a><span
class="cmr-10">[12]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">M.</span><span
class="cmr-10">&#x00A0;Li and P.</span><span
class="cmr-10">&#x00A0;M.</span><span
class="cmr-10">&#x00A0;B. Vitanyi.  </span><span
class="cmti-10">An Introduction to Kolmogorov Complexity and its Applications</span><span
class="cmr-10">.</span>
    <span
class="cmr-10">Springer-Verlag, New York, 1993.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XBenn95"></a><span
class="cmr-10">[13]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">C.</span><span
class="cmr-10">&#x00A0;H. Bennett. Universal computation and physical dynamics. </span><span
class="cmti-10">Physica D</span><span
class="cmr-10">, 86:268, 1995.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XMaGr96"></a><span
class="cmr-10">[14]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">J.</span><span
class="cmr-10">&#x00A0;Machta and R.</span><span
class="cmr-10">&#x00A0;Greenlaw. The computational complexity of generating random fractals. </span><span
class="cmti-10">J. Stat.</span>
    <span
class="cmti-10">Phys.</span><span
class="cmr-10">, 82:1299, 1996.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XMach06a"></a><span
class="cmr-10">[15]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">J.</span><span
class="cmr-10">&#x00A0;Machta.    Complexity,  parallel  computation  and  statistical  physics.    </span><span
class="cmti-10">Complexity  Journal</span><span
class="cmr-10">,</span>
    <span
class="cmr-10">11(5):46&#8211;64, 2006.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XGeLl96"></a><span
class="cmr-10">[16]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">Murray  Gell-Mann  and  Seth  Lloyd.    Information  measures,  effective  complexity,  and  total</span>
    <span
class="cmr-10">information. </span><span
class="cmti-10">Complexity</span><span
class="cmr-10">, 2(1):44&#8211;52, 1996.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="Xay-2008"></a><span
class="cmr-10">[17]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">Nihat Ay, Markus Mueller, and Arleta Szkola. Effective complexity and its relation to logical depth,</span>
    <span
class="cmr-10">2008.</span>
                                                                                       
                                                                                       
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XLind88b"></a><span
class="cmr-10">[18]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">K.</span><span
class="cmr-10">&#x00A0;Lindgren and M.</span><span
class="cmr-10">&#x00A0;G. Norhdal. Complexity measures and cellular automata. </span><span
class="cmti-10">Complex Systems</span><span
class="cmr-10">,</span>
    <span
class="cmr-10">2(4):409&#8211;440, 1988.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XCrut92c"></a><span
class="cmr-10">[19]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">J.</span><span
class="cmr-10">&#x00A0;P. Crutchfield.  The calculi of emergence: Computation, dynamics, and induction.  </span><span
class="cmti-10">Physica D</span><span
class="cmr-10">,</span>
    <span
class="cmr-10">75:11&#8211;54, 1994.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XFeld98b"></a><span
class="cmr-10">[20]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">D.</span><span
class="cmr-10">&#x00A0;P. Feldman and J.</span><span
class="cmr-10">&#x00A0;P. Crutchfield. Discovering non-critical organization: Statistical mechanical,</span>
    <span
class="cmr-10">information theoretic, and computational views of patterns in simple one-dimensional spin systems.</span>
    <span
class="cmr-10">1998. Santa Fe Institute Working Paper 98-04-026.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XNeru08a"></a><span
class="cmr-10">[21]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">D.</span><span
class="cmr-10">&#x00A0;Nerukh, V.</span><span
class="cmr-10">&#x00A0;Ryabov, and R.C. Glen.  Complex temporal patterns in molecular dynamics: A</span>
    <span
class="cmr-10">direct measure of the phase-space exploration by the trajectory at macroscopic time scales.  </span><span
class="cmti-10">Physical</span>
    <span
class="cmti-10">Review E</span><span
class="cmr-10">, 77(3):036225, 2008.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XLi08a"></a><span
class="cmr-10">[22]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">C.-B. Li, H.</span><span
class="cmr-10">&#x00A0;Yang, and T.</span><span
class="cmr-10">&#x00A0;Komatsuzaki.  Multiscale complex network of protein conformational</span>
    <span
class="cmr-10">fluctuations in single-molecule time series.  </span><span
class="cmti-10">Proceedings of the National Academy of Sciences USA</span><span
class="cmr-10">,</span>
    <span
class="cmr-10">105:536&#8211;541, 2008.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XPalm00a"></a><span
class="cmr-10">[23]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">A.</span><span
class="cmr-10">&#x00A0;J. Palmer, C.</span><span
class="cmr-10">&#x00A0;W. Fairall, and W.</span><span
class="cmr-10">&#x00A0;A. Brewer. Complexity in the atmosphere. </span><span
class="cmti-10">IEEE Transactions</span>
    <span
class="cmti-10">on Geoscience and Remote Sensing</span><span
class="cmr-10">, 38(4):2056&#8211;2063, 2000.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XJani07a"></a><span
class="cmr-10">[24]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">H.</span><span
class="cmr-10">&#x00A0;Janicke,  A.</span><span
class="cmr-10">&#x00A0;Wiebel,  G.</span><span
class="cmr-10">&#x00A0;Scheuermann,  and  W.</span><span
class="cmr-10">&#x00A0;Kollmann.    Multifield  visualization  using</span>
    <span
class="cmr-10">local  statistical  complexity.    </span><span
class="cmti-10">IEEE  Transactions  on  In  Visualization  and  Computer  Graphics</span><span
class="cmr-10">,</span>
    <span
class="cmr-10">13(6):1384&#8211;1391, 2007.</span>
    </p>
    <p class="bibitem" ><span class="biblabel">
<a
id="XYang08a"></a><span
class="cmr-10">[25]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">J.-S. Yang, W.</span><span
class="cmr-10">&#x00A0;Kwak, T.</span><span
class="cmr-10">&#x00A0;Kaizoji, and I.-M. Kim. Increasing market efficiency in the stock markets.</span>
    <span
class="cmti-10">European Physical Journal B</span><span
class="cmr-10">, 61(2):241&#8211;246, 2008.</span>
    </p>
                                                                                       
                                                                                       
    <p class="bibitem" ><span class="biblabel">
<a
id="XAy07a"></a><span
class="cmr-10">[26]</span> <span class="bibsp"><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span><span
class="cmr-10">&#x00A0;</span></span></span><span
class="cmr-10">N.</span><span
class="cmr-10">&#x00A0;Ay, J.C. Flack, and D.C. Krakauer.  Robustness and complexity co-constructed in multimodal</span>
    <span
class="cmr-10">signalling networks. </span><span
class="cmti-10">Philos. Trans. Roy. Soc. London B</span><span
class="cmr-10">, 362:441&#8211;447, 2007.</span>
</p>
    </div>
   
</body>

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<a id="x1-1doc"></a> Santa Fe Institute Workshop
Summary Description

(Dated: December 13, 2010)

Title:
  Randomness, Structure, and Causality:
    Measures of complexity from theory to applications
Dates: 9-13 January 2011
Location: Santa Fe Institute, Santa Fe, New Mexico
Organizers:
  Jim Crutchfield (SFI and UC Davis, chaos@ucdavis.edu)
  Jon Machta (SFI and University of Massachusetts, machta@physics.umass.edu)

<a

id="likesection.1"></a>

<a id="x1-1000"></a>Description

In 1989, SFI hosted a workshop—Complexity, Entropy, and the Physics of Information—on fundamental definitions of complexity. This workshop and the proceedings that resulted [<a href="#XZure89a">1</a>] stimulated a great deal of thinking about how to define complexity. In many ways—some direct, many indirect—the foundational theme colored much of SFI’s research planning and, more generally, the evolution of complex system science since then. Complex systems science has considerably matured as a field in the intervening decades and we believe it is now time to revisit fundamental aspects of the field in a workshop format at SFI. Partly, this is to take stock; but it is also to ask what innovations are needed for the coming decades, as complex systems continues to extend its influence in the sciences, engineering, and humanities.

The goal of the workshop is to bring together workers from a variety of fields to discuss structural and dynamical measures of complexity appropriate for their field and the commonality between these measures. Some of the questions that we will address in the workshop are:

  1. Are there fundamental measures of complexity that can be applied across disciplines or are measures of complexity necessarily tied to particular domains?
  2. How is a system’s causal organization, reflected in models of its dynamics, related to its complexity?
  3. Are there universal mechanisms at work that lead to increases in complexity or does complexity arise for qualitatively different reasons in different settings?
  4. Can we reach agreement on general properties that all measures of complexity must have?
  5. How would the scientific community benefit from a consensus on the properties that measures of complexity should possess?

It’s a four-day workshop with about 20 or so participants. We will have a stimulating and highly interdisciplinary group with representation from physics, biology, computer science, social science, and mathematics. An important goal is to understand the successes and difficulties in deploying complexity measures in practice. And so, participants come from both theory and experiment, with a particular emphasis on those who can constructively bridge the two.

Since the 1989 SFI workshop, a number of distinct strands have developed in the effort to measure complexity. Several of the well-developed strands are based on

  • Predictive information and excess entropy [<a href="#XJunc79">2</a>–<a href="#XCrut01a">7</a>],
  • Statistical complexity and causal structure [<a href="#XCrut88a">8</a>–<a href="#XShal98a">10</a>],
  • Logical depth and computational complexity [<a href="#XBenn90">11</a>–<a href="#XMach06a">15</a>], and
  • Effective complexity [<a href="#XGeLl96">16</a>, <a href="#Xay-2008">17</a>].

While these measures are broadly based on information theory or the theory of computation, the full set of connections and contrasts between them is not well developed. Some have sought to clarify the relationship among these measures [<a href="#XCrut01a">7</a>, <a href="#Xay-2008">17</a>–<a href="#XFeld98b">20</a>] and so another goal of the workshop is to foster this kind of comparative work by bringing together researchers developing various measures.

A second motivation for the workshop is to bring together workers interested in foundational questions—who are mainly from the physics, mathematics, and computer science communities—with complex systems scientists in experimental, data-driven fields who have developed quantitative measures of complexity, organization, and emergence that are useful in their fields. The range of data-driven fields using complexity measures is impressively broad: ranging from molecular excitation dynamics [<a href="#XNeru08a">21</a>] and spectroscopic observations of the conformational dynamics of single molecules [<a href="#XLi08a">22</a>] through modeling subgrid structure in turbulent fluid flows [<a href="#XPalm00a">23</a>] and new visualization methods for emergent flow patterns [<a href="#XJani07a">24</a>] to monitoring market efficiency [<a href="#XYang08a">25</a>] and the organization of animal social structure [<a href="#XAy07a">26</a>]. The intention is to find relations between the practically motivated measures and the more general and fundamentally motivated measures. Can the practically motivated measures be improved by an appreciation of fundamental principles? Can fundamental definitions be sharpened by consideration of how they interact with real-world data?

Overall, the workshop’s intention is to re-ignite the efforts that began with Complexity, Entropy, and the Physics of Information workshop. A new level of rigor, in concepts and in analysis, is now apparent in how statistical mechanics, nonlinear dynamics, information theory, and computation theory can be applied to complex systems. The meteoric rise of both computer power and machine learning has led to new algorithms that address many of the original computational difficulties in managing data from complex systems and in estimating various complexity measures. Given progress on all these fronts, the time is ripe to develop a much closer connection between fundamental theory and applications in many areas of complex systems science.

<a id="likesection.2"></a><a id="Q1-1-1"></a>

<a id="XZure89a"></a>[1]    W. Zurek, editor. Entropy, Complexity, and the Physics of Information, volume VIII of SFI Studies in the Sciences of Complexity. Addison-Wesley, Reading, Massachusetts, 1990.

<a id="XJunc79"></a>[2]    A. del Junco and M. Rahe. Finitary codings and weak bernoulli partitions. Proc. AMS, 75:259, 1979.

<a id="XCrut82b"></a>[3]    J. P. Crutchfield and N. H. Packard. Symbolic dynamics of one-dimensional maps: Entropies, finite precision, and noise. Intl. J. Theo. Phys., 21:433, 1982.

<a id="XErik87"></a>[4]    K-E. Eriksson and K. Lindgren. Structural information in self-organizing systems. Physica Scripta, 1987.

<a id="XGras86"></a>[5]    P. Grassberger. Toward a quantitative theory of self-generated complexity. Intl. J. Theo. Phys., 25:907, 1986.

<a id="XEbel99a"></a>[6]    W. Ebeling, L. Molgedey, J. Kurths, and U. Schwarz. Entropy, complexity, predictability and data analysis of time series and letter sequences. <a href=" http://summa.physik.hu-berlin.de/tsd/" class="url" >http://summa.physik.hu-berlin.de/tsd/</a>, 1999.

<a id="XCrut01a"></a>[7]    J. P. Crutchfield and D. P. Feldman. Regularities unseen, randomness observed: Levels of entropy convergence. CHAOS, 13(1):25–54, 2003.

<a id="XCrut88a"></a>[8]    J. P. Crutchfield and K. Young. Inferring statistical complexity. Phys. Rev. Let., 63:105–108, 1989.

<a id="XCrut97a"></a>[9]    J. P. Crutchfield and D. P. Feldman. Statistical complexity of simple one-dimensional spin systems. Phys. Rev. E, 55(2):1239R–1243R, 1997.

<a id="XShal98a"></a>[10]    C. R. Shalizi and J. P. Crutchfield. Computational mechanics: Pattern and prediction, structure and simplicity. J. Stat. Phys., 104:817–879, 2001.

<a id="XBenn90"></a>[11]    C. H. Bennett. How to define complexity in physics, and why. In W. H. Zurek, editor, Complexity, Entropy and the Physics of Information, page 137. SFI Studies in the Sciences of Complexity, Vol. 7, Addison-Wesley, 1990.

<a id="XVita93a"></a>[12]    M. Li and P. M. B. Vitanyi. An Introduction to Kolmogorov Complexity and its Applications. Springer-Verlag, New York, 1993.

<a id="XBenn95"></a>[13]    C. H. Bennett. Universal computation and physical dynamics. Physica D, 86:268, 1995.

<a id="XMaGr96"></a>[14]    J. Machta and R. Greenlaw. The computational complexity of generating random fractals. J. Stat. Phys., 82:1299, 1996.

<a id="XMach06a"></a>[15]    J. Machta. Complexity, parallel computation and statistical physics. Complexity Journal, 11(5):46–64, 2006.

<a id="XGeLl96"></a>[16]    Murray Gell-Mann and Seth Lloyd. Information measures, effective complexity, and total information. Complexity, 2(1):44–52, 1996.

<a id="Xay-2008"></a>[17]    Nihat Ay, Markus Mueller, and Arleta Szkola. Effective complexity and its relation to logical depth, 2008.

<a id="XLind88b"></a>[18]    K. Lindgren and M. G. Norhdal. Complexity measures and cellular automata. Complex Systems, 2(4):409–440, 1988.

<a id="XCrut92c"></a>[19]    J. P. Crutchfield. The calculi of emergence: Computation, dynamics, and induction. Physica D, 75:11–54, 1994.

<a id="XFeld98b"></a>[20]    D. P. Feldman and J. P. Crutchfield. Discovering non-critical organization: Statistical mechanical, information theoretic, and computational views of patterns in simple one-dimensional spin systems. 1998. Santa Fe Institute Working Paper 98-04-026.

<a id="XNeru08a"></a>[21]    D. Nerukh, V. Ryabov, and R.C. Glen. Complex temporal patterns in molecular dynamics: A direct measure of the phase-space exploration by the trajectory at macroscopic time scales. Physical Review E, 77(3):036225, 2008.

<a id="XLi08a"></a>[22]    C.-B. Li, H. Yang, and T. Komatsuzaki. Multiscale complex network of protein conformational fluctuations in single-molecule time series. Proceedings of the National Academy of Sciences USA, 105:536–541, 2008.

<a id="XPalm00a"></a>[23]    A. J. Palmer, C. W. Fairall, and W. A. Brewer. Complexity in the atmosphere. IEEE Transactions on Geoscience and Remote Sensing, 38(4):2056–2063, 2000.

<a id="XJani07a"></a>[24]    H. Janicke, A. Wiebel, G. Scheuermann, and W. Kollmann. Multifield visualization using local statistical complexity. IEEE Transactions on In Visualization and Computer Graphics, 13(6):1384–1391, 2007.

<a id="XYang08a"></a>[25]    J.-S. Yang, W. Kwak, T. Kaizoji, and I.-M. Kim. Increasing market efficiency in the stock markets. European Physical Journal B, 61(2):241–246, 2008.


<a id="XAy07a"></a>[26]    N. Ay, J.C. Flack, and D.C. Krakauer. Robustness and complexity co-constructed in multimodal signalling networks. Philos. Trans. Roy. Soc. London B, 362:441–447, 2007.

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