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La fisica delle parolealla ricerca delle origini del linguaggio
Vittorio LoretoSapienza Università di Roma
Dipartimento di Fisica&
Fondazione ISI, Torino
Language dynamics
Language dynamics is an emerging field that focuses on all processesrelated to the emergence, evolution and extinction of languages.
Language dynamics
How did language emerge in our species?Emergence of conventions on:
names, categories, syntax structures ...
Language dynamics is an emerging field that focuses on all processesrelated to the emergence, evolution and extinction of languages.
Language dynamics
How did language emerge in our species?Emergence of conventions on:
names, categories, syntax structures ...
Language dynamics is an emerging field that focuses on all processesrelated to the emergence, evolution and extinction of languages.
View of language as an evolving and self-organizing system
Time-scales
Time-scales
Time-scales
Cultural time-scale
horizontal transmission
Time-scales
Cultural time-scale
Biological time-scale
horizontal transmission
vertical transmission
Time-scales
KOOTI Farshad & CHA Meeyoung & GUMMADI Khrishna P. & MASON Winter 2012. The Emergence of Conventions in Online Social Networks, Proceedings of the 6th International AAAI Conference on Weblogs and Social Media (ICWSM), Dublin, Ireland.
Emergence of conventions in Twitter
Robotic exps//
Field simulations//
Web gamingTheoretical modeling
//simulations
Field work
new ICT tools
“In silico” linguistics
Traditional linguistics
The “Talking Heads” experiment
L. Steels, The Talking Heads Experiment. Vol.1 - Words and Meanings, Antwerpen, (1999)
Robotic experiments
Grounded Naming Game
Language Games
Let us imagine a language ...The language is meant to serve for communication between a builder A and an assistant B. A is building with building-stones; there are blocks, pillars, slabs and beams. B has to pass the stones, and that in the order in which A needs them. For this purpose they use a language consisting of the words 'block', 'pillar', 'slab', 'beam'. A calls them out; --B brings the stone which he has learnt to bring at such-and-such a call. -- Conceive of this as a complete primitive language.
(L. Wittgenstein)
communication acts of increasing complexitynames, categories, syntax structures ...
Theoretical challenges
• What are the minimal requirements for a shared linguistic feature to emerge?
• What is the asymptotic state (absorbing state, stationary state, slow dynamics)?
• Which features lead to efficiency?
• Which is the role of the system size?
• Which is the role of topology?
Understand how global behaviors emerge out of local interactions
The Naming GameHow a population of individuals bootstrap a shared name?
A. Baronchelli, A. Barrat, E. Caglioti, L. Dall’Asta, M. Felici, V. Servedio, L. Steels, F. Tria
The Naming Game• Population of N agents
• Each agent is characterized by its inventory (or lexicon) i.e. a list of name-object associations
• Agents want to build a shared lexicon
• Homonymy is discarded one single object
• Peer to peer negotiation. At each time step twoagents (speaker and hearer) are selected
The Naming Game• Population of N agents
• Each agent is characterized by its inventory (or lexicon) i.e. a list of name-object associations
• Agents want to build a shared lexicon
• Homonymy is discarded one single object
• Peer to peer negotiation. At each time step twoagents (speaker and hearer) are selected
local (dyadic) interactions
speaker hearer
negotiation + memory + dynamic inventories
The Naming Game
[1] Baronchelli et al. J. Stat. Mech. P06014 (2006)
Basic quantities
N
1
The communication system is efficient
N=1000
N/2
Basic quantities
N
1
The communication system is efficient
N=1000
N/2
Invention
Basic quantities
N
1
The communication system is efficient
N=1000
N/2
Building of correlations
Basic quantities
N
1
The communication system is efficient
N=1000
N/2
Convergence
Scaling relations
The system always converges though with different
modalities (role of the hubs) and time-scales
Interactions among individuals create complex networks: a population can be
represented as a graph.
AgentInteraction
fully connected networksd-dimensional lattices
small-worldrandom graphs
scale-free networks...
The role of topology
Regular lattices
• Fast local consensus• Convergence through coarsening
• Finite memory
With probability p each link is rewired → shortcutsSmall distance among any pairs of nodes.
Finite connectivity (as in lattices) ⇒ small memory
Small-world (as in mean-field) ⇒ fast convergence
Short-time coarsening, then mean-field behavior
Small-world networks
Convergencetime
Maximummemory
small-worldd=1complete graph
Role of topology: summary
Regular lattices Fast local consensuscoarsening
Small-world networksShort-time coarsening, then
mean-field behavior
Is consensus always reached ?
As before
New parameter β:inclination to trust
other agents (usual rules: β=1)
Consensus/Fragmentation phase transition
Non-equilibrium phase transition in negotiation dynamics A. Baronchelli, L. Dall'Asta, A. Barrat and V. Loreto Phys. Rev. E 76, 051102 (2007)
β>1/3 stable consensus
β<1/3 stable fragmentation
β<1/3: a hierarchy of transitions (Fully connected graph)
2 words
3 words
4 words
5 words
Consensus/Fragmentation phase transition
Evolutionary time-scales
At each time step one individual is
substituted with a blank slate with
probability r
r = inverse of the average lifetime
Substitute adult individuals with blank-slate
Emergence of creoles languages
with: S. Mufwene, V.D.P. Servedio, F. Tria
Creoles languagesA creole language is a stable natural language developed from the mixing of parent languages.
Salikoko Mufwene
sa ka pèmet - vou konpwann --> ça te permet de comprendreka pèmet klèsi teks-li --> ça lui permet d’éclaircir le texteÇa qui rivé-yo --> ce qui leur est arrivé
The vocabulary of a creole language is largely supplied by the parent languages.
The grammar often has original features that may differ substantially from those of the parent languages.
Europeans (free whites)
Bozals(slaves)
Mulattos (free blacks)
hearer
A E
hearer
A E CNG
interactionhearer
A E C
hearer
A E
hearer
C
hearer
C
NGinteraction
γ
γ
1− γ
1− γ
Emergence of a new language (creole) from the contact of two other languages
E European languageA African languageC Creole language
Census data
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
(N_C
+N_B
) / (N
_E+N
_C+N
_B)
N_C/(N_C+N_B)
Louisiana (1850)Bahamas (1774)
South Carolina (1790)
Georgia (1790)
St Lucia (1776)
St Vincent (1787)
Granada (1785)
Martinique (1776)
Barbados (1786)
Guadalupe (1779)
Jamaica (1787)
St Domingue (1779)
Dominica (1788)
Isle de Bourbon (1776)
Antigua (1774)St Christopher (1774)
Nevis (1774)Cayenne (1780),
Monserrat (1774), Virgin Islands (1774)
Alabama (1820)
Virginia (1790)Mississippi (1800)
Maryland (1790)
North Carolina (1790)
Kentucky (1790)Arkansas (1820)
Tennessee (1790)
New Jersey (1790)
Missouri (1810)
Pennsylvania (1790)
Delaware (1810)
• States with creole • States without creole
(NM
+N
B)/
(NE
u+
NM
+N
B)
NM/(NM + NB)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
(N_C
+N_B
) / (N
_E+N
_C+N
_B)
N_C/(N_C+N_B)
Louisiana (1850)Bahamas (1774)
South Carolina (1790)
Georgia (1790)
St Lucia (1776)
St Vincent (1787)
Granada (1785)
Martinique (1776)
Barbados (1786)
Guadalupe (1779)
Jamaica (1787)
St Domingue (1779)
Dominica (1788)
Isle de Bourbon (1776)
Antigua (1774)St Christopher (1774)
Nevis (1774)Cayenne (1780),
Monserrat (1774), Virgin Islands (1774)
Alabama (1820)
Virginia (1790)Mississippi (1800)
Maryland (1790)
North Carolina (1790)
Kentucky (1790)Arkansas (1820)
Tennessee (1790)
New Jersey (1790)
Missouri (1810)
Pennsylvania (1790)
Delaware (1810)
• States with creole • States without creole(N
M+
NB
)/(N
Eu
+N
M+
NB
)
NM/(NM + NB)
Louisiana; French creale in the sugarcane plantations.
Alabama: cotton plantations smaller ha sugarcane and rice plantations
Caribbean sea
United States
The Category GameHow does a population of agents establish and share an
effective set of categories?
with: A. Baronchelli, A. Puglisi and T. Gong, A. Mukherjee, F. Tria
allow to quickly point out something without giving too many details (lossy compression)
are well calibrated to avoid confusion, i.e. to discriminate something among different things
in brief: must be not too large nor too small
Where do linguistic categories come from?
allow to quickly point out something without giving too many details (lossy compression)
are well calibrated to avoid confusion, i.e. to discriminate something among different things
in brief: must be not too large nor too small
Where do linguistic categories come from?
allow to quickly point out something without giving too many details (lossy compression)
are well calibrated to avoid confusion, i.e. to discriminate something among different things
in brief: must be not too large nor too small
Where do linguistic categories come from?
Glasscommon names
allow to quickly point out something without giving too many details (lossy compression)
are well calibrated to avoid confusion, i.e. to discriminate something among different things
in brief: must be not too large nor too small
Where do linguistic categories come from?
Glasscommon names color names
red
blue
green
green
red
blue
World color survey (WCS)
110 “preindustrialized” languages24 “monolingual” speakers
speakers were asked to:1. name each of the 330 munsell chips2. indicate the best example(s) of each of his basic color terms
Basic Color Terms name all the colors:
English (11 words)
BluePurple
Pinkyellow
Brown
GreenOrange
White
Black
Gray
Red
Courtesy of Lindsey & Brown (2006). PNAS, 102.
Testing universality of color naming
Paul Kay and Terry Regier“Resolving the question of color naming universals”
Proc. Natl. Acad. Sci USA (PNAS) 100, 9085 (2003).
(either real or hypothetical), we found the closest term c* in eachlanguage l* in the BK data set and added up those distances toobtain the sum S.
S ! !l!WCS,l*!BK
!c!l
minc*!l*
distance!c, c*". [2]
Comparing the value for S observed in the WCS data set to thedistribution of values obtained in 1,000 hypothetical randomiza-tions of that data set, Fig. 3b shows that the value of S for theactual WCS data is well below the lower limit of the hypotheticaldistribution. Thus, the WCS data are significantly closer to theBK data than expected by chance, P # 0.001. We then removedfrom the BK data set the only unwritten languages of nonin-dustrialized societies in that data set (Ibibio, Pomo, and Tzeltal),reran this test, and obtained the same qualitative result, P #0.001. This finding indicates a similarity in color naming acrosslanguages of industrialized and nonindustrialized societies.
These universal tendencies are shown in Fig. 4a. The floorplane of this display corresponds to the 320 chromatic (non-neutral) colors in the stimulus array of Fig. 1, and the height ofthe surface at each position represents the number of WCSspeaker centroids falling at that point in color space [MacLaury(23) displays a comparable histogram, restricted to the huedimension]. This distribution of color terms from nonindustri-alized languages is shown from above in the contour plot of Fig.
Fig. 3. Monte Carlo tests. (a) Clustering within the WCS. The distribution ofdispersion values shown in gray was obtained from 1,000 randomized datasets. The arrow indicates the dispersion value obtained from the WCS data. (b)Comparing the WCS with BK. The distribution of separation values shown ingray was obtained from 1,000 randomized data sets. The arrow indicates theseparation value obtained by comparing the WCS data with BK data (1).
Table 2. Languages studied by BK (1)
Index Language Where spoken
1 Arabic (Lebanese colloquial) Lebanon2 Bahasa Indonesia Indonesia3 Bulgarian Bulgaria4 Cantonese China5 Catalan Spain6 (American) English United States7 Hebrew Israel8 Hungarian Hungary9 Ibibio Nigeria
10 Japanese Japan11 Korean Korea12 Mandarin China13 (Mexican) Spanish Mexico14 Pomo United States15 Swahili Tanzania16 Tagalog Philippines17 Thai Thailand18 Tzeltal Mexico19 Urdu Pakistan20 Vietnamese Vietnam
Data reported from one subject per language.
Fig. 4. Distribution of color terms from nonindustrialized languages. (a) Thefloor plane corresponds to the chromatic (non-neutral) portion of the colorstimulus array. The height of the surface at each point in the plane denotes thenumber of speaker centroids in the WCS data set that fall at that position incolor space. (b) The distribution of a is viewed from above by a contour plot.The outermost contour represents a height of 100 centroids, and each subse-quent contour represents an increment in height of 100 centroids. Englishcolor terms fall near the peaks of the WCS distribution.
9088 " www.pnas.org#cgi#doi#10.1073#pnas.1532837100 Kay and Regier
We approach the issue of whether there are universal ten-dencies in color naming by asking two questions:
(i) Do color terms from different languages in the WCS clustertogether in color space to a degree greater than chance?
(ii) Do WCS color terms, all from unwritten languages ofnonindustrialized societies, fall near color terms of writtenlanguages from industrialized societies, as represented by the BKsample?
To test for clustering, we represented color terms as pointsin color space, and then tested for clustering of those points.Because the idea of clustering depends essentially on theconcept of distance, we required a color space in whichpsychologically meaningful distances can be calculated. Con-sequently we transformed our 330 color stimuli from Munsellspace, which lacks such a distance metric, to CIEL*a*b* space,which has one (22). CIEL*a*b* is a 3D color space, in whichthe L* dimension represents lightness, and the two remainingdimensions, a* and b*, define a plane orthogonal to L*, suchthat angle in that plane represents hue, and radius representssaturation. We represented each color term T in each languageL by its centroid in this space. This was computed by firstfinding, for each speaker of L who used term T, the centroidin CIEL*a*b* space of the chips named T by that speaker.These speaker centroids were then averaged together to yieldan overall term centroid for T. Finally, that term centroid wascoerced back to the chip most similar to it in the stimulus array,so that our overall representation of the term resided withinthe set of points out of which it was constructed. This coercionwas done by first selecting that row of the array with L* valuenearest that of the centroid [L* values are constant within eachvalue (i.e., lightness) row of the stimulus array]. We thenexamined two chips, the chromatic (colored) chip in that rowwith hue angle in the a*b* plane closest to the centroid, andthe neutral chip in that row, and selected the one that had hueradius in the a*b* plane closest to the average radius of thechips represented by the centroid. This selected chip was ourpoint representation of the color term.
Given such point representations of all color terms, we testedwhether these points were more clustered across languages thanwould be expected by chance, through a Monte Carlo test. Thisrequired first a measure of color-term clustering and then anindication of how clustered one might expect color terms to beby chance.
We defined a measure D of the dispersion of the terms in theWCS data set: for each color term c in each language l, we foundthe closest term c* in each other language l*, and added up those
distances. Distance between terms was defined as CIEL*a*b*distance between their point representations.
D ! !l,l*!WCS
!c!l
minc*!l*
distance!c, c*". [1]
Because D is a measure of dispersion, low values of D indicateclustering.
To determine how much dispersion one would expect bychance, we created a set of randomized hypothetical datasetsthrough computer simulation and measured dispersion inthem. Our randomization method was informed by the obser-vation that general principles of categorization operatingwithin a given language can be expected to produce a certainamount of dispersion in any natural system of categories. Wewanted to be certain that our randomized data sets obeyedsuch within-language principles of categorization. To this end,we started with the actual WCS data set and rotated eachlanguage’s term centroids in the a*b* (hue) plane by a randomamount, the same random amount for all terms within alanguage, but different random amounts for different lan-guages, as shown in Fig. 2. These rotated centroids were thencoerced back to the WCS color array in the manner describedabove. This process produced one hypothetical data set, whichpreserved within-language structure while randomizing cross-language structure, appropriately, as the latter is the centralfocus of this study.
The process creating a randomized data set was repeatedindependently 1,000 times, and the D dispersion measure wascalculated for each hypothetical data set. Fig. 3a shows thedistribution of D in the 1,000 hypothetical data sets comparedwith D in the actual WCS data. The actual WCS D value is wellbelow the lower boundary of the hypothetical distribution.
Fig. 2. Creating a randomized data set.
Fig. 1. Color array from the WCS. For the Munsell notations of the colors in this stimulus array see ref. 1.
9086 " www.pnas.org#cgi#doi#10.1073#pnas.1532837100 Kay and Regier
Human Case
We approach the issue of whether there are universal ten-dencies in color naming by asking two questions:
(i) Do color terms from different languages in the WCS clustertogether in color space to a degree greater than chance?
(ii) Do WCS color terms, all from unwritten languages ofnonindustrialized societies, fall near color terms of writtenlanguages from industrialized societies, as represented by the BKsample?
To test for clustering, we represented color terms as pointsin color space, and then tested for clustering of those points.Because the idea of clustering depends essentially on theconcept of distance, we required a color space in whichpsychologically meaningful distances can be calculated. Con-sequently we transformed our 330 color stimuli from Munsellspace, which lacks such a distance metric, to CIEL*a*b* space,which has one (22). CIEL*a*b* is a 3D color space, in whichthe L* dimension represents lightness, and the two remainingdimensions, a* and b*, define a plane orthogonal to L*, suchthat angle in that plane represents hue, and radius representssaturation. We represented each color term T in each languageL by its centroid in this space. This was computed by firstfinding, for each speaker of L who used term T, the centroidin CIEL*a*b* space of the chips named T by that speaker.These speaker centroids were then averaged together to yieldan overall term centroid for T. Finally, that term centroid wascoerced back to the chip most similar to it in the stimulus array,so that our overall representation of the term resided withinthe set of points out of which it was constructed. This coercionwas done by first selecting that row of the array with L* valuenearest that of the centroid [L* values are constant within eachvalue (i.e., lightness) row of the stimulus array]. We thenexamined two chips, the chromatic (colored) chip in that rowwith hue angle in the a*b* plane closest to the centroid, andthe neutral chip in that row, and selected the one that had hueradius in the a*b* plane closest to the average radius of thechips represented by the centroid. This selected chip was ourpoint representation of the color term.
Given such point representations of all color terms, we testedwhether these points were more clustered across languages thanwould be expected by chance, through a Monte Carlo test. Thisrequired first a measure of color-term clustering and then anindication of how clustered one might expect color terms to beby chance.
We defined a measure D of the dispersion of the terms in theWCS data set: for each color term c in each language l, we foundthe closest term c* in each other language l*, and added up those
distances. Distance between terms was defined as CIEL*a*b*distance between their point representations.
D ! !l,l*!WCS
!c!l
minc*!l*
distance!c, c*". [1]
Because D is a measure of dispersion, low values of D indicateclustering.
To determine how much dispersion one would expect bychance, we created a set of randomized hypothetical datasetsthrough computer simulation and measured dispersion inthem. Our randomization method was informed by the obser-vation that general principles of categorization operatingwithin a given language can be expected to produce a certainamount of dispersion in any natural system of categories. Wewanted to be certain that our randomized data sets obeyedsuch within-language principles of categorization. To this end,we started with the actual WCS data set and rotated eachlanguage’s term centroids in the a*b* (hue) plane by a randomamount, the same random amount for all terms within alanguage, but different random amounts for different lan-guages, as shown in Fig. 2. These rotated centroids were thencoerced back to the WCS color array in the manner describedabove. This process produced one hypothetical data set, whichpreserved within-language structure while randomizing cross-language structure, appropriately, as the latter is the centralfocus of this study.
The process creating a randomized data set was repeatedindependently 1,000 times, and the D dispersion measure wascalculated for each hypothetical data set. Fig. 3a shows thedistribution of D in the 1,000 hypothetical data sets comparedwith D in the actual WCS data. The actual WCS D value is wellbelow the lower boundary of the hypothetical distribution.
Fig. 2. Creating a randomized data set.
Fig. 1. Color array from the WCS. For the Munsell notations of the colors in this stimulus array see ref. 1.
9086 " www.pnas.org#cgi#doi#10.1073#pnas.1532837100 Kay and Regier
The category gameN individuals performing binary language gamesIndividual task: discriminate stimuli from a continuous [0:1] perceptual space
Real values on the interval [0, 1]
N = 50, dmin = 0.01
N = 50, dmin = 0.02A. Puglisi, A. Baronchelli and VL
“Cultural route to the emergence of linguistic categories”Proc. Natl. Acad. Sci USA (PNAS) 105, 7936 (2008).
Non-uniform across the spectrum
dmin
From Long et al. 2006.
Long PH, Yang ZY, Purves D. 2006. Special statistics in natural scenes predict hue, saturation, and brightness. PNAS, 103(15): 6013-6018.
Human eyes discrimination ability Just Noticeable Difference (JND)
dmin
perceptual space
“In silico” version of the WCS
Individual
“In silico” version of the WCS
Individual
Population
“In silico” version of the WCS
Individual
Population
World
“In silico” version of the WCS
Dhuman Dneutral
Individual
Population
World
“In silico” version of the WCS
1 1.05 1.1 1.15 1.2normalized Dispersion
0
0.1
0.2
0.3
0.4
frequ
ency
0 0.25 0.5 0.75 1stimulus
0
0.02
0.04
JND
human neutral
randomized WCS
simulations
“In silico” version of the WCS
A. Baronchelli, T. Gong, A. Puglisi and VL, Modeling the emergence of universality in color naming patterns PNAS, 107, 2403 (2010).
Hierarchies of colors
with: A. Mukherjee, F. Tria
if a language had a color term with a prototype at any point in the hierarchy, then it would also have color terms with prototypes at all the colors to the left of
that color
Color Implicational hierarchy
Berlin, B., & Kay, P. (1969). Basic color terms. Berkeley: University of California Press.
Evolutionary stages for basic color terms
Kay, P. & McDaniel, K. (1978). The Linguistic Significance of the Meanings of Basic Color Terms. Language, 54 (3): 610-646.
mili cool/dark shades such as blue, green, and blackmola warm/light colours such as red, yellow, and white.
Stage I
Dani (New Guinea)
Stage VKalam (Papua New Guinea)
mosimb
tund
likañ muk minj-kimemb walin
Hierarchy in the Category Game
[red, (magenta)-red], [violet], [green/yellow], [blue, blue (dark)], [orange] and [cyan]
VL, A. Mukherjee and F. Tria, On the origin of the hierarchy of color namesPNAS 109, 2819 (2012).
Summary
NAMING GAME naming an object
CATEGORY GAMEcategorizing and naming the
color spaceWorld-Color Survey
Hierarchy of basic color names
BLENDING GAME naming related objects
emergence of creoles
combinatoriality & compositionalityemergence of syntax
Ongoing activities
syntax features: combinatoriality, compositionality
grammar: e.g. numeral systems
interplay of cultural and evolutionary time scales
complexity and regularization
...and perspectives
web-based experiments
social computation
field simulations
Field simulationsPut two (or more) humans into a virtual environment that requires them to coordinate their individual actions and… neutralize the use of pre-established communication systems (e.g., speech, writing, body language…)
B. Galantucci e S. Garrod (eds.)Social Behaviour and Communication in Biological and Artificial SystemsInteraction Studiesvolume 115 issue 12 (2010)
Galantucci, B. (2005). An experimental study of the emergence of human communication systems.Cognitive Science, 29 (5), 737–67.
Social computation
Populations of users facing collectivelydifficult problems using a small cognitive
overhead
Social computation
Populations of users facing collectivelydifficult problems using a small cognitive
overhead
http://www.espgame.org/
! !
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A new platform for web-based experiments
http://www.xtribe.eu/
with: S. Caminiti, C. Cicali, P. Gravino, V.D.P. Servedio, A. Sirbu, F. Tria
VL and L. Steels, Emergence of Language, Nature Phys., Vol. 3, 758-760 (2007).
A. Puglisi, A. Baronchelli and VL, Cultural route to the emergence of linguistics categories Proc. Natl. Acad. Sci. USA, 105, 7936 (2008).
C. Castellano, S. Fortunato and VL,Statistical physics of social dynamicsRev. Mod. Phys., 81, 591-645 (2009).
A. Baronchelli, T. Gong, A. Puglisi and VL, Modeling the emergence of universality in color naming patternsProc. Natl. Acad. Sci. USA, 107, 2403 (2010).
A. Mukherjee, F. Tria, A. Baronchelli, A. Puglisi and VL, Aging in language dynamicsPLoS ONE, 6, e16677 (2011).
VL, A. Mukherjee and F. Tria, On the origin of the hierarchy of color namesProc. Natl. Acad. Sci. USA, 109, 2819 (2012).
F. . Tria, B. Galantucci and VLNaming a structured world: a cultural route to duality of patterningPLoS ONE, 7(6), e37744 (2012).
Recent publications
http://samarcanda.phys.uniroma1.it/vittorioloreto/
Thankyou
VL and L. Steels, Emergence of Language, Nature Phys., Vol. 3, 758-760 (2007).
A. Puglisi, A. Baronchelli and VL, Cultural route to the emergence of linguistics categories Proc. Natl. Acad. Sci. USA, 105, 7936 (2008).
C. Castellano, S. Fortunato and VL,Statistical physics of social dynamicsRev. Mod. Phys., 81, 591-645 (2009).
A. Baronchelli, T. Gong, A. Puglisi and VL, Modeling the emergence of universality in color naming patternsProc. Natl. Acad. Sci. USA, 107, 2403 (2010).
A. Mukherjee, F. Tria, A. Baronchelli, A. Puglisi and VL, Aging in language dynamicsPLoS ONE, 6, e16677 (2011).
VL, A. Mukherjee and F. Tria, On the origin of the hierarchy of color namesProc. Natl. Acad. Sci. USA, 109, 2819 (2012).
F. . Tria, B. Galantucci and VLNaming a structured world: a cultural route to duality of patterningPLoS ONE, 7(6), e37744 (2012).
Recent publications
http://samarcanda.phys.uniroma1.it/vittorioloreto/
Andrea Baronchelli
Tao Gong
Animesh Mukherjee
Andrea Puglisi
Francesca Tria
Category Game
Thankyou
Andrea Baronchelli
Alain Barrat
Emanuele Caglioti
Luca Dall’Asta
Maddalena Felici
Salikoko Mufwene
Martina Pugliese
Vito D.P. Servedio
Luc Steels
Francesca Tria
Naming Game