MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C63AE7.D4D73D90" Questo documento è una pagina Web in file unico, nota anche come archivio Web. La visualizzazione di questo messaggio indica che il browser o l'editor in uso non supporta gli archivi Web. Scaricare un browser che supporti gli archivi Web, come Microsoft Internet Explorer. ------=_NextPart_01C63AE7.D4D73D90 Content-Location: file:///C:/ACB946A1/BerlinWorkshop3A.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 8th Experimental Chaos Conference - ECC, Florence, Italy INFORMATI= ONAL STRUCTURE & COUPLING OF SEMIOTIC SETS

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Fare clic per modificare lo stile= del titolo
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‹intestazione›
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------=_NextPart_01C63AE7.D4D73D90 Content-Location: file:///C:/ACB946A1/BerlinWorkshop3A_file/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C63AE7.D4D73D90 Content-Location: file:///C:/ACB946A1/BerlinWorkshop3A_file/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 8th Experimental Chaos Conference - ECC, Florence, Italy INFORMATI= ONAL STRUCTURE & COUPLING OF SEMIOTIC SETS
Max Planck Institute= for Human Cognitive and Brain Sciences
University of Potsdam
Berlin, 17 March, 2005

STRUCTURE & COUPLING
IN SEMIOTIC SETS <= /span>
Franco F. Orsucci
f.orsucci@ucl.ac.uk =
Institute of Psychiatry,
Catholic University, Rome
&
Department of Psychology,
University College London
With contributions from:
Alessandro Giuliani, Joe Zbilut, Chuck Webber,
Peter Fonagy, Marianna Mazza, Marco Lucciola
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The Voynich mystery
nThe Voynich Manuscript = = has been dubbed “the Most = Mysterious Manuscript in = the World”: ciphered or = hoax?
nit is unknown what a character in the manuscript represents
nsome features suggest that we are in the presence of a natural language
= n
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------=_NextPart_01C63AE7.D4D73D90 Content-Location: file:///C:/ACB946A1/BerlinWorkshop3A_file/slide0025.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 8th Experimental Chaos Conference - ECC, Florence, Italy INFORMATI= ONAL STRUCTURE & COUPLING OF SEMIOTIC SETS
Combinations & Icons
nSecond-Order Entropies of Voynich Text by Dennis J. Stallings nZipf's laws in the Voynich Manuscript by G. Landini.
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C. E. Shannon:
combinatorial of symbols
nInformational structure of texts <= span style=3D'position:absolute;top:39.5%;left:8.23%;width:49.43%;height:5.25%'= >and speech (1949; 1951) nClaude Shannon, 1949, Graphical representation of the constraints = on telegraph (Morse) sym= bols nGraphical representation= of the constraints on symbols of a six letters artificial alphabet nPrediction and entropy of printed English (1951)
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G. K. Zipf:
word distribution
nG. K. Zipf (1949) described two "laws" of word frequencies =
nThe Rank-Frequency Law:
n tokens in a text are sorted by decreasing frequency and a rank number is assigned to each token. <= /span>The plot of  log (frequ= ency) (y axis) versus= log (rank) (x axis) approx= imates a straight line of slope
n -1.
nThe Number-Frequency Law<= /u> :
n Being n the frequency of a token, the plot of log (n) (y axis) versus log (number of tokens with frequency n) (x axis) approximates a straight line of slope -0.5.
= n
Fig. 1 & 2. Plots (showing only the 4000 most co= mmon words) for a number of t= exts in English (original and translated) and the electronic version of Roget's Thesaurus.
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Information in texts =
n
nSchenkel et al. 1993: Studied long range correlation in various human writings by mapping them into a simple 1d random walk model. This approach allows us to obtain better quality scaling data than the traditional power spectrum methods. Optimally written computer programs seem to have the highest scaling exponent, i.e., close to that of ideal 1/f noise. Literature, on the other hand, leads to smaller exponents. The Bible, however, has the strongest correlation among the Roman letter writings examined.
nAmit et al. 1993: Studied the long-range correlations in various translations of the Bible by mapping them onto a one dimensional random walk model. We show that the exponent α, which characterizes the algebraic decay law of these correlations depends on = both the language and the codification. = Some considerations concerning the origin of these correlations are suggested in terms of which a qualitative explanation of this dependence is presented.
Langua= ge as a dynamical system…see also my book (and cite it!) why the Bible???
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Maturana & Varela
nStructural coupling is a process that occurs when two structurally plastic systems repeatedly perturb one another’s structure in a non-destructive way over a period of tim= e. This leads to the development of structural ‘fit’ between the systems. nThere is an intimate relationship between this process = and the emergence of ‘appropriate’ behaviour from the interplay between interacting systems, because the structure of a system determines its responses to perturbatory environmental events. n“Language is a manner of living together in a flo= w of coordinations of coordinati= ons of consensual behaviours or doings that arises in a history of living in the collaboration of doing things together”. (Maturana 1988)
n&#= 13;
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Control & Sync <= br> in complex systems
nThe history of synchronization goes back to the 17th century when the famous Dutch scientist Christiaan Huygens (1673) reported on his observation of synchronization of two pendulum clocks. = Systematic study of this phenomenon, experimental as well as theoretical, was = started by Edward Appleton (1922) and Balthasar van der Pol (1927). = They showed that the frequency of a triode= generator can be entrained, or synchronized, by a weak external signal with slightly <= span style=3D'position:absolute;top:73.25%;left:8.98%;width:44.75%;height:4.0%'= >different frequency.
nThese studies were of high practical = importance because such generators became = basic elements of radio communication = systems.
nMutual synchronization of two weakly nonlinear oscillators was analytically treated by Mayer (1935) and Gaponov (1936.
nAn important step was done by Stratonovich (1958, 1963) who developed a theory of external synchr= onization of a weakly nonlin= ear oscillator in the presen= ce of random noise.
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This m= ight be skipped!
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Pecora & Carroll
SKIP
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OGY , Ott, Grebogi &= amp; Yorke; Pyragas; Kurths & co.
nLocal geometry of control: saddle dynamics and linearization of stable and unstable manifolds
SKIP
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D/r7m/mK9Qry/wCAP/JLoP8Ar7m/mK9QoAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiig AooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACvP8A42/8kh13/t3/ APSiOvQK8/8Ajb/ySHXf+3f/ANKI6APkCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAK KKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAP//Z ------=_NextPart_01C63AE7.D4D73D90 Content-Location: file:///C:/ACB946A1/BerlinWorkshop3A_file/slide0010.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 8th Experimental Chaos Conference - ECC, Florence, Italy INFORMATI= ONAL STRUCTURE & COUPLING OF SEMIOTIC SETS
Language Dynamics:
order and noise
nThe <= b>lexicon consists of a state-space regions with <= /span>= different regions within that system; the= grammar consists of dynamics (attractors and repellers) which c= onstrain movement in that space. n<= b>Representations, therefore, are highly context-= sensitive, continuously varied and probabilistic. nObjects of mental representation are trajectories through the mental phase-space.
n
<= span style=3D'font-family:"Times New Roman";visibility:hidden'>n
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Order is recurrence
<= span style=3D'font-family:"Times New Roman";font-size:88%;color:#333399;mso-col= or-index: 3'>nRecurrences create patterns, i.e. orde= r.
nAs natural patterns are found in all dynamical systems,= the degree to which those systems exhibit recurrent = patterns bespeaks volumes regarding their underlying dynamics. It should be appreciated that the entire scientific enterprise is based upon the concept of = recurrence.
n Webber & Zbilut, 2004.
<= span style=3D'font-family:"Times New Roman";font-size:88%;color:#333399;mso-col= or-index: 3;visibility:hidden'>n
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Recurrence Quantific= ation Analysi= s
<= span style=3D'font-family:"Times New Roman";font-size:64%;color:#333399;mso-col= or-index: 3'>nRQA was first introduced in physics by Eckmann, Kamphorst & Ruelle (1987).
= nLater, Webber and Zbilut (1994) enhanced the techniq= ue by defining nonlinear variables that were found to be diagnostically useful in the quantitative assessment of time series structure in fields ranging from molecular dynamics, = to physiology and linguistics.
<= span style=3D'font-family:"Times New Roman";font-size:64%;color:#333399;mso-col= or-index: 3'>nThanks to Norbert Marwan also contributed in improvi= ng and diffusing this methodology
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RQA plots
nA recurrence plot is a 2-dimensional N x N pattern of points where N is the number of embedding = vectors obtained from the delay coordinates of the input signal.
nFrom the occurrence of lines parallel to the diagonal in the recurrence plot it can be seen how fast = neighboured trajectories diverge in phase space. Theref= ore, the average length of these lines is a measure of the reciprocal of the largest positive Lyapu= nov exponent.
nREC   =3DPercent recurrence =3D #= RECURS / triangular area.
nDET  =3DPercent determinism =3D #recur= rent points forming upward diagonal lines / #RECURS
nRecurrence plots help revealing phase transitions and instationarities. Visible rectangular block structures with a higher density of points in the recurrence plot indicate phase transitions within the = signal.
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Experiment 1: Structure
nThough orthography actually represents a combination= of conventions we wanted to assess if it might embed a reliable ground for informational measures.
nSee: Nat Neurosci 2000 Jan;3(1):91-96 A cultural eff= ect on brain function. Paulesu et al.
nSuch a technique should recognize: 1) relative invarian= ce with respect to the original language of texts; 2) maximal dependence on dynamical (order dependent) features of texts.
nLinguistic Data Sets:
1.Italian poems of the 20th century (set 1): 9 Italian poems of the last century were chosen with the aim of maximizing the range of variatio= n of the degree of prosodic structuring. The texts include complex poems with a minimum level of redundancy, as well as very structured poe= ms using long repetitive motifs.
2.American (English) poems of the XXth century (set 2<= /b>): this set is composed by 11 American poems chosen with the same criteria adopted for set 1.
3.Swedish contemporary poems and their correspondent Italian translations (set 3).
4.Italian speech samples (set 4)
5.American (English) speech samples (set 5)=
Orsucci F, Giuliani A, Zbilut J in 8 ECC Proceedings, AIP Press
Paper = on phonetics and orthography
------=_NextPart_01C63AE7.D4D73D90 Content-Location: file:///C:/ACB946A1/BerlinWorkshop3A_file/slide0011.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 8th Experimental Chaos Conference - ECC, Florence, Italy INFORMATI= ONAL STRUCTURE & COUPLING OF SEMIOTIC SETS
Results #1
= nFigure shows a combined analysis of American poems (AMP), Italian poems (ITP), American transcriptions (AMS), = and Italian transcriptions (ITS). Scaling of texts along a linear relationship between REC and DET ( r =3D 0.87, p < 0.001). This scaling suggests a possibility of = using the position on the REC-DET = = plane as a simple numerical index of the = = relative complexity of a text.
= nRQA technique provides a reliable = quantitative description of text <= span style=3D'position:absolute;top:73.75%;left:5.24%;width:48.31%;height:4.0%'= >sequences at the orthographic level in terms of structuring, and may be useful <= /span>= for a variety of linguistics-related = studies. =
<= span style=3D'mso-special-format:nobullet;display:none;color:#3333CC;mso-color-= index: 7;font-family:Wingdings;font-size:60%'>n F. Orsucci, K. Walters, A. Giuliani, C. L.Webber, J. P. Zbilut, 42, 80 (1999).
n
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